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  • Articles  (105)
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  • diffusion  (64)
  • optimal control
  • Springer  (78)
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  • Articles  (105)
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  • Springer  (78)
  • Wiley-Blackwell  (27)
  • American Geophysical Union
  • American Institute of Physics (AIP)
  • American Physical Society
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  • 2005-2009
  • 2000-2004  (36)
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  • 1
    Electronic Resource
    Electronic Resource
    Advection-diffusion in spatially random flows: Formulation of concentration covariance (1997)
    Springer
    Stochastic environmental research and risk assessment 11 (1997), S. 397-422 
    Details
    ISSN: 1436-3259
    Keywords: Random flow field ; diffusion ; concentration ; fluctuations ; covariance ; variance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The concentration c(x,t) of a nonreactive solute undergoing advection and diffusion in a spatially random divergence-free flow field is analyzed. A leading order formulation for the spatial covariance of the concentration field, $$\overline {c'\left( {x,t} \right)c'\left( {x,t} \right)} $$ , is made. That formulation includes the velocity variability induced macrodispersive flux of the covariance field, and the smoothing effects of diffusion. Previous formulations of the concentration covariance had dropped at least one of these effects. It is shown that both these effects need to be included to obtain a qualitatively correct description of the concentration fluctuations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02427926
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  • 2
    Electronic Resource
    Electronic Resource
    Analysis of Diffusion in Hollow Geometries (2000)
    Springer
    Adsorption 6 (2000), S. 125-136 
    Details
    ISSN: 1572-8757
    Keywords: diffusion ; mathematical model ; analytical solution ; hollow material ; composite material ; mass transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The diffusion in hollow particles of solid adsorbent materials was analyzed based on analytical solutions to the basic diffusion equation. Three geometric shapes (plane sheet, cylinder, and sphere) of sorbent material were considered for two kinds of boundary conditions. The equations for determining the equivalent sizes compared to their corresponding solid particles were obtained directly from the theoretical expressions of sorption uptake curves. Among the three hollow particles of impermeable inner surface, the sphere gives the highest gain in effective diffusion rate compared to the corresponding solid particle. For permeable inner surface, at lower hollow volume fractions, the plane sheet shows the highest gain, while at higher hollow volume fractions, the sphere shows the highest gain in effective diffusion rate.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008913301145
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal Control of One-Dimensional Partial Differential Algebraic Equations with Applications (2000)
    Springer
    Annals of operations research 98 (2000), S. 45-64 
    Details
    ISSN: 1572-9338
    Keywords: optimal control ; partial differential equations ; numerical methods ; transdermal systems ; acetylene reactors
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We present an approach to compute optimal control functions in dynamic models based on one-dimensional partial differential algebraic equations (PDAE). By using the method of lines, the PDAE is transformed into a large system of usually stiff ordinary differential algebraic equations and integrated by standard methods. The resulting nonlinear programming problem is solved by the sequential quadratic programming code NLPQL. Optimal control functions are approximated by piecewise constant, piecewise linear or bang-bang functions. Three different types of cost functions can be formulated. The underlying model structure is quite flexible. We allow break points for model changes, disjoint integration areas with respect to spatial variable, arbitrary boundary and transition conditions, coupled ordinary and algebraic differential equations, algebraic equations in time and space variables, and dynamic constraints for control and state variables. The PDAE is discretized by difference formulae, polynomial approximations with arbitrary degrees, and by special update formulae in case of hyperbolic equations. Two application problems are outlined in detail. We present a model for optimal control of transdermal diffusion of drugs, where the diffusion speed is controlled by an electric field, and a model for the optimal control of the input feed of an acetylene reactor given in form of a distributed parameter system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019231718807
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  • 4
    Electronic Resource
    Electronic Resource
    The Optimal Control of a Train (2000)
    Springer
    Annals of operations research 98 (2000), S. 65-87 
    Details
    ISSN: 1572-9338
    Keywords: train control ; optimal control ; discrete control ; optimal switching times
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider the problem of determining an optimal driving strategy in a train control problem with a generalised equation of motion. We assume that the journey must be completed within a given time and seek a strategy that minimises fuel consumption. On the one hand we consider the case where continuous control can be used and on the other hand we consider the case where only discrete control is available. We pay particular attention to a unified development of the two cases. For the continuous control problem we use the Pontryagin principle to find necessary conditions on an optimal strategy and show that these conditions yield key equations that determine the optimal switching points. In the discrete control problem, which is the typical situation with diesel-electric locomotives, we show that for each fixed control sequence the cost of fuel can be minimised by finding the optimal switching times. The corresponding strategies are called strategies of optimal type and in this case we use the Kuhn–Tucker equations to find key equations that determine the optimal switching times. We note that the strategies of optimal type can be used to approximate as closely as we please the optimal strategy obtained using continuous control and we present two new derivations of the key equations. We illustrate our general remarks by reference to a typical train control problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019235819716
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  • 5
    Electronic Resource
    Electronic Resource
    Average Cost Optimality for an Unreliable Two-Machine Flowshop with Limited Internal Buffer (2000)
    Springer
    Annals of operations research 98 (2000), S. 333-351 
    Details
    ISSN: 1572-9338
    Keywords: production planning ; stochastic dynamic programming ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to nonnegativity and upper bound constraints on work-in-process. The objective is to choose machine production rates over time to minimize the long-run average inventory/backlog and production costs. For sufficiently large upper bound on the work-in-process, the problem is formulated as a stochastic dynamic program. We then establish a verification theorem and a partial characterization of the optimal control policy if it exists.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019272811055
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  • 6
    Electronic Resource
    Electronic Resource
    On Quantitative Stability in Optimization and Optimal Control (2000)
    Springer
    Set-valued analysis 8 (2000), S. 31-50 
    Details
    ISSN: 1572-932X
    Keywords: stability in optimization ; generalized equations ; Lipschitz continuity ; mathematical programming ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study two continuity concepts for set-valued maps that play central roles in quantitative stability analysis of optimization problems: Aubin continuity and Lipschitzian localization. We show that various inverse function theorems involving these concepts can be deduced from a single general result on existence of solutions to an inclusion in metric spaces. As applications, we analyze the stability with respect to canonical perturbations of a mathematical program in a Hilbert space and an optimal control problem with inequality control constraints. For stationary points of these problems, Aubin continuity and Lipschitzian localization coincide; moreover, both properties are equivalent to surjectivity of the map of the gradients of the active constraints combined with a strong second-order sufficient optimality condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008714222851
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  • 7
    Electronic Resource
    Electronic Resource
    Numerical Schemes for Discontinuous Value Functions of Optimal Control (2000)
    Springer
    Set-valued analysis 8 (2000), S. 111-126 
    Details
    ISSN: 1572-932X
    Keywords: viability ; optimal control ; value function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we explain that various (possibly discontinuous) value functions for optimal control problem under state-constraints can be approached by a sequence of value functions for suitable discretized systems. The key-point of this approach is the characterization of epigraphs of the value functions as suitable viability kernels. We provide new results for estimation of the convergence rate of numerical schemes and discuss conditions for the convergence of discrete optimal controls to the optimal control for the initial problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008774508738
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  • 8
    Electronic Resource
    Electronic Resource
    Approximate Optimal Control and Stability of Nonlinear Finite- and Infinite-Dimensional Systems (2000)
    Springer
    Annals of operations research 98 (2000), S. 19-44 
    Details
    ISSN: 1572-9338
    Keywords: optimal control ; nonlinear systems ; parabolic systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider first nonlinear systems of the form x=A(x)x+B(x)u together with a standard quadratic cost functional and replace the system by a sequence of time-varying approximations for which the optimal control problem can be solved explicitly. We then show that the sequence converges. Although it may not converge to a global optimal control of the nonlinear system, we also consider a similar approximation sequence for the equation given by the necessary conditions of the maximum principle and we shall see that the first method gives solutions very close to the optimal solution in many cases. We shall also extend the results to parabolic PDEs which can be written in the above form on some Hilbert space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019279617898
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  • 9
    Electronic Resource
    Electronic Resource
    Instability and Diffusion in the Elliptic Restricted Three-body Problem (1998)
    Springer
    Celestial mechanics and dynamical astronomy 70 (1998), S. 23-39 
    Details
    ISSN: 1572-9478
    Keywords: resonant orbit ; transversal intersection ; resonant jump ; diffusion ; instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The importance of the stability characteristics of the planar elliptic restricted three-body problem is that they offer insight about the general dynamical mechanisms causing instability in celestial mechanics. To analyze these concerns, elliptic–elliptic and hyperbolic–elliptic resonance orbits (periodic solutions with lower period) are numerically discovered by use of Newton's differential correction method. We find indications of stability for the elliptic–elliptic resonance orbits because slightly perturbed orbits define a corresponding two-dimensional invariant manifold on the Poincaré surface-section. For the resonance orbit of the hyperbolic–elliptic type, we show numerically that its stable and unstable manifolds intersect transversally in phase-space to induce instability. Then, we find indications that there are orbits which jump from one resonance zone to the next before escaping to infinity. This phenomenon is related to the so-called Arnold diffusion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008200806138
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  • 10
    Electronic Resource
    Electronic Resource
    Nonlinear Potentials for Hamilton–Jacobi–Bellman Equations. II (1997)
    Springer
    Acta applicandae mathematicae 46 (1997), S. 29-48 
    Details
    ISSN: 1572-9036
    Keywords: Hamilton–Jacobi–Bellman equations ; nonlinear potentials ; nonlinear PDE ; viscosity solutions ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A formal method of constructing the viscosity solutions for abstract nonlinear equations of Hamilton–Jacobi–Bellman (HJB) type was developed in the previous work of the author. A new advantage of this method (which was called an ‘nonlinear potentials’ method) is that it gives a possibility to choose at the first step an expected regularity of the solution and then – to construct this solution. This makes the whole procedure more simple because an analysis of regularity of viscosity solutions is usually the most complicated step. Nonlinear potentials method is a generalization of Krylov's approach to study HJB equations. In this article nonlinear potentials method is applied to elliptic degenerate HJB equations in Rd with variable coefficients.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005786132384
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  • 11
    Electronic Resource
    Electronic Resource
    Topological properties of the solution set of a class of nonlinear evolutions inclusions (1997)
    Springer
    Czechoslovak mathematical journal 47 (1997), S. 409-424 
    Details
    ISSN: 1572-9141
    Keywords: R δ-set ; homotopic ; contractible ; evolution triple ; evolution inclusion ; compact embedding ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field F(t, x), we are able to show that the solution set is in fact an R δ-set. Finally some applications to infinite dimensional control systems are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022451115373
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  • 12
    Electronic Resource
    Electronic Resource
    On the existence of optimal controls for nonlinear infinite dimensional systems (1998)
    Springer
    Czechoslovak mathematical journal 48 (1998), S. 291-312 
    Details
    ISSN: 1572-9141
    Keywords: evolution triple ; optimal control ; monotone operator ; hemicontinuous operator ; parabolic system ; property (Q)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022889404413
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  • 13
    Electronic Resource
    Electronic Resource
    Fundamental Study on Near-Axis Scattered Light and Its Application to Optical Computed Tomography (2000)
    Springer
    Optical review 7 (2000), S. 383-388 
    Details
    ISSN: 1349-9432
    Keywords: near-axis scattered light ; optical computed tomography ; time-resolved measurement ; scattering ; diffusion ; random media ; visibility ; photon migration ; computed tomography ; biomedical optics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract To find a basic principle of optical computed tomography (optical CT), a fundamental study was conducted on the use of scattered light in diffuse random media. We call the scattered light that propagates along the optical axis of the incident light beam near-axis scattered light (NASL). The use of NASL for the imaging through a diffuse medium was proposed and its basic characteristics were analyzed. The existence and measurability of NASL were confirmed in the simulation and measurement. To detect NASL efficiently, a technique called the scattering angle differential technique was developed. In CT imaging with a model phantom, the feasibility and effectiveness of the proposed technique were verified. We found that this technique alone was not sufficient to obtain the cross sectional image of an animal body, therefore a technique called the contact technique was devised to overcome the problems of reflection and refraction at the air-tissue interface. Finally, a prototype system was developed which integrated all the proposed techniques. With this system, we could obtain the CT images of a living mouse, in which the blood-rich organs such as liver and kidneys were clearly recognizable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s10043-000-0383-4
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  • 14
    Electronic Resource
    Electronic Resource
    The Rectangular Isotherm Model for Adsorption Kinetics (2000)
    Springer
    Adsorption 6 (2000), S. 287-291 
    Details
    ISSN: 1572-8757
    Keywords: diffusion ; shrinking core ; rectangular isotherm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The transient uptake response of an adsorbent particle, subjected to a step change in surface concentration, is considered. It is shown that, when the isotherm is highly favorable, the theoretical curves derived for a Langmuirian system reduce asymptotically to the much simpler form for a rectangular isotherm. The simple rectangular model provides a useful approximation even when the form of the actual isotherm is quite far from the rectangular limit.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026504730443
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  • 15
    Electronic Resource
    Electronic Resource
    A Study of Adsorption of Water Vapour on Wool under Static and Dynamic Conditions (1998)
    Springer
    Adsorption 4 (1998), S. 63-73 
    Details
    ISSN: 1572-8757
    Keywords: wool ; water vapour ; adsorption ; diffusion ; column dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract Adsorption of water vapour on wool provides not only textile comfort, but also convenience in transportation due to increase in its bulk density. The adsorption and desorption isotherms of water vapour for wool were determined by both volumetric technique using a Coulter Omnisorp 100CX instrument and gravimetric method employing a Cahn 2000 electronic microbalance. Adsorption isotherm fitting to B.E.T. model and hysteresis on desorption was observed. The average effective diffusion coefficient of water in wool was found to be 8.4 × 10-14 m2s-1 at 25°C from gravimetric data. The effects of packing height and air velocity on the breakthrough curves were also investigated in the wool packed columns. For pseudo first order model, k values changing between 0.33 × 10-6 − 69 × 10-6 s-1 was obtained for 2.2–6.4 cm s-1 air velocity and 0.05–0.20 m packing height ranges.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008839404382
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  • 16
    Electronic Resource
    Electronic Resource
    Film Model Approximation for Multicomponent Adsorption (2000)
    Springer
    Adsorption 6 (2000), S. 5-13 
    Details
    ISSN: 1572-8757
    Keywords: multicomponent adsorption ; diffusion ; Maxwell-Stefan model ; linear driving force approximation ; Langmuir isotherm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract An approximate rate equation based on a film-model representation of diffusional mass transfer is developed to describe the kinetics of multicomponent adsorption. The model describes mass transfer as a pseudo-steady state diffusion process through a flat film of thickness equal to one fifth of the particle radius. Starting with an irreversible thermodynamics description of multicomponent diffusion, the flux relationships are integrated across the film yielding analytical expressions for the rate of mass transfer in a multicomponent adsorption system, when adsorption equilibria are described by the extended Langmuir isotherm. The new approximate rate equation can be conveniently used in the numerical simulation of adsorption systems with concentration-dependent micropore or surface diffusivity, and describes the effects of diffusional flux coupling. Results of accuracy comparable with that obtained when using the classical linear-driving-force approximation for systems with constant diffusivities are obtained with this new rate equation for both batch and fixed-bed adsorption calculations. A generalization of the approach based on the Gibbs adsorption isotherm describes mass transfer rates in terms of the spreading-pressure gradient and provides an extension to other multicomponent isotherm forms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008927713530
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  • 17
    Electronic Resource
    Electronic Resource
    Periodic one-dimensional hopping model with one mobile directional impurity (1997)
    Springer
    Journal of statistical physics 87 (1997), S. 545-575 
    Details
    ISSN: 1572-9613
    Keywords: Random hopping model ; bond impurity ; diffusion ; asymmetric exclusion process ; electrophoresis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Analytic solution is given in the steady-state limitt→∞ for the system of master equations describing a random walk on one-dimensional periodic lattices with arbitrary hopping rates containing one mobile directional impurity (defect bond). Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of master equations leads naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasiwalker. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasiparticle through physically meaningful equations. Applications in driven diffusive systems are shown, and connections with the Duke-Rubinstein reptation models for gel electrophoresis are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02181236
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  • 18
    Electronic Resource
    Electronic Resource
    A Diffusion Equation from the Relativistic Ornstein–Uhlenbeck Process (1998)
    Springer
    Journal of statistical physics 90 (1998), S. 1179-1199 
    Details
    ISSN: 1572-9613
    Keywords: Irreversibility ; relativistic Ornstein–Uhlenbeck process ; relativistic statistical physics ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We derive, in the “hydrodynamic” limit (large space and time scales), an evolution equation for the particle density in physical space from the (special) relativistic Ornstein–Uhlenbeck process introduced by Debbasch, Mallick, and Rivet. This equation turns out to be identical with the classical diffusion equation, without any relativistic correction. We prove that, in the “hydrodynamic” limit, this result is indeed compatible with special relativity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1023275210656
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  • 19
    Electronic Resource
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    Effective Potential for the Reaction-Diffusion-Decay System (2000)
    Springer
    Journal of statistical physics 99 (2000), S. 903-941 
    Details
    ISSN: 1572-9613
    Keywords: effective potential ; reaction ; diffusion ; decay
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In previous work we have developed a general method for casting stochastic partial differential equations (SPDEs) into a functional integral formalism, and have derived the one-loop effective potential for these systems. In this paper we apply the same formalism to a specific field theory of considerable interest, the reaction-diffusion-decay system. When this field theory is subject to white noise we can calculate the one-loop effective potential (for arbitrary polynomial reaction kinetics) and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions. For specific choices of interaction terms the one-loop renormalizability can be extended to higher dimensions. We also show how to include the effects of fluctuations in the study of pattern formation away from equilibrium, and conclude that noise affects the stability of the system in a way which is calculable.
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    URL: http://dx.doi.org/10.1023/A:1018699630306
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  • 20
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    Dynamic Light Scattering Measurement of Nanometer Particles in Liquids (2000)
    Springer
    Journal of nanoparticle research 2 (2000), S. 123-131 
    Details
    ISSN: 1572-896X
    Keywords: nanoparticle ; characterization ; light scattering ; PCS ; interferometry ; diffusion ; polydispersivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics , Technology
    Notes: Abstract Dynamic light scattering (DLS) techniques for studying sizes and shapes of nanoparticles in liquids are reviewed. In photon correlation spectroscopy (PCS), the time fluctuations in the intensity of light scattered by the particle dispersion are monitored. For dilute dispersions of spherical nanoparticles, the decay rate of the time autocorrelation function of these intensity fluctuations is used to directly measure the particle translational diffusion coefficient, which is in turn related to the particle hydrodynamic radius. For a spherical particle, the hydrodynamic radius is essentially the same as the geometric particle radius (including any possible solvation layers). PCS is one of the most commonly used methods for measuring radii of submicron size particles in liquid dispersions. Depolarized Fabry-Perot interferometry (FPI) is a less common dynamic light scattering technique that is applicable to optically anisotropic nanoparticles. In FPI the frequency broadening of laser light scattered by the particles is analyzed. This broadening is proportional to the particle rotational diffusion coefficient, which is in turn related to the particle dimensions. The translational diffusion coefficient measured by PCS and the rotational diffusion coefficient measured by depolarized FPI may be combined to obtain the dimensions of non-spherical particles. DLS studies of liquid dispersions of nanometer-sized oligonucleotides in a water-based buffer are used as examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1010067107182
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  • 21
    Electronic Resource
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    Diffusion of Randon in Porous Media Saturated with Gels and Emulsions (1997)
    Springer
    Transport in porous media 27 (1997), S. 171-184 
    Details
    ISSN: 1573-1634
    Keywords: diffusion ; randon ; gel ; emulsion ; environmental protection.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract The effective diffusion coefficient of radon was determined in polymer/silicate gels and clay suspension used as sealing materials in environmental protection. On the basis of the experimental findings, it was concluded that both materials drastically decrease the convective mass transport in porous media. Simultaneously, the effective diffusion coefficient was reduced significantly. Thus, the radon flux might be decreased by 5 to 6 orders of magnitude in porous systems originally having gas or low water saturation by injection of gel-forming materials or placement of clay suspensions. At high water saturation, however, the diffusion transport of radon can be slightly restricted in consolidated and unconsolidated porous media. The laboratory studies may firmly allow us to conclude that hydrogels and clay suspensions are prospective candidates in an integrated environmental technology to be used for restriction of radon migration in subsurface regions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006564200829
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  • 22
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    Competitive reversals inside ecological reserves: the role of external habitat degradation (1998)
    Springer
    Journal of mathematical biology 37 (1998), S. 491-533 
    Details
    ISSN: 1432-1416
    Keywords: Key words: Competition ; Edge effects ; Reaction ; diffusion ; Lotka ; Volterra ; Ecological reserves
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  Habitat degradation is the slow – and often subtle – deterioration in habitat quality that accompanies human activities through increases in road density, pesticide use, hunting pressure, etc. Such degradation is of particular concern in fragmented habitats where economic or jurisdictional boundaries rather than ecological ones determine the level of exploitation adjoining habitat patches endure. To examine the consequences habitat degradation might have on species interactions, we posited a patch of pristine habitat surrounded by “matrix” habitat whose degradation level was variable. Using a coupled pair of diffusive Lotka–Volterra competition equations with Robin (mixed) boundary conditions, we modeled the dynamics of two competing species inhabiting the pristine patch and incorporated matrix degradation through a tunable “hostility” parameter representing species’ mortality rates in the matrix. We found that the numerical range of competition coefficients over which one species is the competitive dominant and the other inferior may grow or shrink as matrix quality deteriorates. In some cases, degradation of the exterior habitat would bring about a complete competitive reversal inside the preserve. This result, wherein a formerly inferior species supplants a formerly dominant one – even inside the “protected” remnant patch itself – has policy implications for both nature reserve design and management of human activities outside park boundaries.
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    URL: http://dx.doi.org/10.1007/s002850050139
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    The evolution of slow dispersal rates: a reaction diffusion model (1998)
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    Journal of mathematical biology 37 (1998), S. 61-83 
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    ISSN: 1432-1416
    Keywords: Key words: Evolution of dispersal ; Migration modification ; Reaction ; diffusion ; Montone systems ; Perturbation of Morse decomposition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  We consider n phenotypes of a species in a continuous but heterogeneous environment. It is assumed that the phenotypes differ only in their diffusion rates. With haploid genetics and a small rate of mutation, it is shown that the only nontrivial equilibrium is a population dominated by the slowest diffusing phenotype. We also prove that if there are only two possible phenotypes, then this equilibrium is a global attractor and conjecture that this is true in general. Numerical simulations supporting this conjecture and suggesting that this is a robust phenomenon are also discussed.
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    URL: http://dx.doi.org/10.1007/s002850050120
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    Simulation of electrochemical behavior of partially blocked electrodes under linear potential sweep conditions (2000)
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    Journal of mathematical chemistry 27 (2000), S. 267-278 
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    ISSN: 1572-8897
    Keywords: partially blocked electrodes ; modelling ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract The paper presents nonlinear model which stands for effective digital simulation of electrochemical behavior of partially blocked electrodes under linear potential sweep and cyclic voltammetry conditions. The model is based on a system of diffusion equations, also involving the Nernst diffusion layer. The mass transport is assumed to be regular in the entire diffusion space. The influence of the thickness of the resist layer on the behavior of the partially blocked electrodes is investigated. The agreement between the theoretical results and experimental ones is obtained to be admirable for several model electrodes with different blocking degree.
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    URL: http://dx.doi.org/10.1023/A:1018867621310
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    The optimal control variational principle and finite elements analysis for viscoplastic dynamics (1997)
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    Applied mathematics and mechanics 18 (1997), S. 61-68 
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    ISSN: 1573-2754
    Keywords: viscoplastic dynamics ; optimal control ; variational principle ; finite element method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract This paper presents the optimal control variational principle for Perzyna model which is one of the main constitutive relation of viscoplasticity in dynamics. And it could also be transformed to solve the parametric quadratic programming problem. The FEM form of this problem and its implementation have also been discussed in the paper.
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    URL: http://dx.doi.org/10.1007/BF02457502
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    Application of convection-diffusion equation to the analyses of contamination between batches in multi-products pipeline transport (1998)
    Springer
    Applied mathematics and mechanics 19 (1998), S. 757-764 
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    ISSN: 1573-2754
    Keywords: products pipeline ; batching transport ; contamination ; convection ; diffusion ; numerical computation ; turbulent flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract Contamination between batches in multi-products pipeline transport is studied. The influences of convection and diffusion on the contamination are studied in detail. Diffusion equations, which are mainly controlled by convection, are developed under turbulent pipe flow. The diffusion equation, is separated into a pure convection equation and a pure diffusion equation which are solved by characteristics method and finite difference method respectively to obtain numerical solutions. The results of numerical computation explain the forming and developing of contamination very well.
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    URL: http://dx.doi.org/10.1007/BF02457750
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    Scheduling Under Common Due Date, A Single Resource and Precedence Constraints—A Dynamic Approach (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 353-364 
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    ISSN: 1573-7594
    Keywords: scheduling ; optimal control ; time-decomposition methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper discusses dynamic methods for solving a class of multi-project scheduling problems in which rates of job performances are controllable and resources such as money, energy or manpower per time unit, are renewable and continuously divisible. The objective is to complete the projects as close to the common due date as possible. Two different ways of imposing sequential precedence relations between project jobs are explored by formulating two dynamic models and studying their relationships on the optimal solution. Efficient time-decomposition algorithms for finding either globally optimal schedules or lower bound guided near-optimal solutions are suggested and computationally tested.
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    URL: http://dx.doi.org/10.1023/A:1008345132480
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    Modeling, Analysis, and Optimal Control of a Class of Hybrid Systems (1998)
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    Discrete event dynamic systems 8 (1998), S. 175-201 
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    ISSN: 1573-7594
    Keywords: hybrid systems ; optimal control ; calculus of variations ; manufacturing systems ; queueing systems ; nonsmooth optimization ; two point boundary value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We propose a modeling framework for a class of hybrid systems which arise in many manufacturing environments and study related optimal control problems. In this framework, discrete entities have a state characterized by a temporal component whose evolution is described by event-driven dynamics, and a physical component whose evolution is described by time-driven dynamics. As a first step towards developing an optimal control theory for such hybrid systems, we formulate a problem consisting of a single-stage manufacturing process and use calculus of variations techniques to obtain structural properties and an explicit algorithm for deriving optimal policies.
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    URL: http://dx.doi.org/10.1023/A:1008237701804
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    Optimal Production Planning in a Multi-Product Stochastic Manufacturing System with Long-Run Average Cost (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 37-54 
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    ISSN: 1573-7594
    Keywords: Production planning ; stochastic dynamic programming ; vanishing discount approach ; optimal control ; long-run average cost
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    Topics: Mathematics
    Notes: Abstract This paper is concerned with the problem of production planning in a flexible manufacturing system consisting of a single or parallel failure-prone machines producing a number of different products. The objective is to choose the rates of production of the various products over time in order to meet their demands at the minimum long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach for the average cost problem that the Hamilton-Jacobi-Bellman equation in terms of directional derivatives has a solution consisting of the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem, and in specifying an optimal control policy in terms of the potential function. The results settle a hitherto open problem as well as generalize known results.
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    URL: http://dx.doi.org/10.1023/A:1008256409920
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    Diffusive Transport of Volatile Pollutants in Nonaqueous-Phase Liquid Contaminated Soil: A Fractal Model (1998)
    Springer
    Transport in porous media 30 (1998), S. 125-154 
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    ISSN: 1573-1634
    Keywords: NAPL ; multiphase ; fractal ; soil ; diffusion ; transport ; heterogeneous porous medium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Volatile organic chemicals from nonaqueous phase liquids trapped in soil spread quickly both into the atmosphere and the groundwater system, resulting in long-lasting pollution of the environment. The extent and speed of spread is strongly influenced by the heterogeneities present in the soil, which interact with the various mechanisms of transport in a complex manner. A semi-analytical model is presented to investigate the effect of soil-heterogeneities on the spreading of pollutants from a nonaqueous phase liquid trapped in a soil. Based on field evidence, soil heterogeneities are modeled as a self-similar fractal process, and diffusive transport of organic chemicals in such a substrate is studied. Various mechanisms of, and resistance to, transport of these contaminants are considered, and it is illustrated how each of these are altered by the presence of heterogeneities. More specifically, it is shown that, while the transport processes at early time are governed by volatilization and dissolution and are quite unaffected by the heterogeneities, the transport processes at late time are strongly dependent on the heterogeneities of the soil and its sorption characteristics. In addition, how failure to recognize these heterogeneities in the soil may result in unsuccessful design of appropriate remediation techniques is discussed.
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    Fluxes of methane and carbon dioxide from a small productive lake to the atmosphere (2000)
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    Biogeochemistry 49 (2000), S. 1-19 
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    ISSN: 1573-515X
    Keywords: carbon dioxide ; diffusion ; ebullition ; emission ; freshwater ; hypertrophic lakes ; methane
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract The fluxes of CH4 and CO2 to the atmosphere, and the relative contributions of ebullition and molecular diffusion, were determined for a small hypertrophic freshwater lake (Priest Pot, UK) over the period May to October 1997. The average total flux of CH4 and CO2 (estimated from 7 sites on the lake) was approximately 52 mmol m−2 d−1 and was apportioned 12 and 40 mmol m−2 d−1 toCH4 and CO2 respectively. Diffusion across the air-water interface accounted for the loss of 0.4and 40 mmol m−2 d−1 of CH4 and CO2 respectively whilst the corresponding figures for ebullition losses were 12.0 (CH4) and 0.23 (CO2) mmol m−2 d−1. Most CH4 (96%) was lost by ebullition, and most CO2 (99%) by diffusive processes. The ebullition of gas, measured at weekly intervals along a transect of the lake, showed high spatial and temporal variation. The CH4 content of the trapped gas varied between 44 and 88% (by volume) and was highest at the deepest points. Pulses of gas ebullition were detected during periods of rapidly falling barometric pressure. Therelevance of the measurements to global estimates ofcarbon emission from freshwaters are discussed.
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    URL: http://dx.doi.org/10.1023/A:1006269900174
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    Onset of Mobilization and the Fraction of Trapped Foam in Porous Media (1997)
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    Transport in porous media 28 (1997), S. 253-284 
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    ISSN: 1573-1634
    Keywords: foam ; mobilization ; network simulation ; pressure gradient ; trapping ; diffusion
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    Topics: Geosciences , Technology
    Notes: Abstract Usually, foam in a porous medium flows through a small and spatially varying fraction of available pores, while the bulk of it remains trapped. The trapped foam is under a pressure gradient corresponding to the pressure gradient imposed by the flowing foam and continuous wetting liquid. The imposed pressure gradient and coalescence of the stationary foam lamellae periodically open flow channels in the trapped foam region. Foam lamellae in each of these channels flow briefly, but channels are eventually plugged by smaller bubbles entering into the trapped region. The result is a cycling of flow channels that open and close throughout the trapped foam, leading to intermittent pulsing of foam flow in that region. The dynamic behavior of foam trapped in porous media is modeled here with a pore network simulator. We predict the magnitude of the pressure drop leading to the onset of flow of foam lamellae in the region containing trapped foam. This mobilization pressure drop depends only on the number of lamellae in the flow path and on the geometry of the pores that make up this path. The principles learned in this study allow us to predict the fraction of foam that is trapped in a porous medium under given flow conditions. We present here the first analytic expression for the trapped foam fraction as a function of the pressure gradient, and of the mean and standard deviation of the pore size distribution. This expression provides a missing piece for the continuum foam flow models based on the moments of the volume-averaged population balance of foam bubbles.
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    Experiments on Solute Transport in Aggregated Porous Media: Are Diffusions Within Aggregates and Hydrodynamic Dispersion Independent? (1997)
    Springer
    Transport in porous media 29 (1997), S. 281-307 
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    ISSN: 1573-1634
    Keywords: solute transport ; nonequilibrium ; heterogeneous porous media ; dispersion ; diffusion ; experiments ; modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Technology
    Notes: Abstract Two region models for solute transport in porous media assume that hydrodynamic dispersion in mobile water and solute diffusion within immobile water regions are independent. Experimental and theoretical results for transport through a macropore indicate that hydrodynamic dispersion and solute exchange are interdependent. Experiments were carried out to investigate this problem for a column packed with spherical porous aggregates. The effective diffusion coefficient of a tracer within the agreggates was determined from specific experiments. The dispersivity of the bed was determined from experiments carried out with a column filled with nonporous beads. We took advantage of the dependence of hydrodynamic dispersion on density ratios between the invading and displaced solutions to obtain a set of breakthrough curves corresponding to situations where the diffusion coefficient remains constant, whereas the dispersivity varies. Simulations reproduce correctly the experiments. Small discrepancies are noted that can be corrected either by increasing the dispersion coefficient or by fitting the external mass transfer coefficient. Increased dispersion coefficients probably reveal a modification of Taylor dispersion due to solute exchange. The fitted external mass transfer coefficients are close to the values obtained with classical correlations of the chemical engineering literature.
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    Automaton Simulations of Dispersion in Porous Media (1998)
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    Transport in porous media 32 (1998), S. 187-198 
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    ISSN: 1573-1634
    Keywords: diffusion ; dispersion ; miscible ; automaton
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    Topics: Geosciences , Technology
    Notes: Abstract A thermodynamic lattice gas (automaton) model is used to simulate dispersion in porous media. Simulations are constructed at two distinctly different scales, the pore scale at which capillary models are constructed and large scale or Darcy scale at which probabilistic collision rules are introduced. Both models allow for macroscopic (pore scale) phase separation. The pore scale models clearly show the effect of pore structure on dispersion. The large scale (mega scale) simulations indicate that when the pressure difference between the displacing phase and displaced phase is properly chosen (representing the average pressure gradient between the phases). The simulation results are consistent with both theoretical predictions and experimental observations.
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    Cosmic-Ray Transport Coefficients (1998)
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    Space science reviews 83 (1998), S. 351-363 
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    ISSN: 1572-9672
    Keywords: cosmic rays ; charged-particle transport ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A review of cosmic-ray transport coefficients, based on historic and recent observations and theoretical insights, is presented. Particular emphasis is on the transport of cosmic rays across the magnetic field, which is of foremost importance, and is presently poorly understood and widely debated.
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    URL: http://dx.doi.org/10.1023/A:1005087326666
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    Microscopic Chaos and Diffusion (2000)
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    Journal of statistical physics 101 (2000), S. 775-817 
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    ISSN: 1572-9613
    Keywords: chaos ; diffusion ; Ehrenfest wind-tree model ; Lorentz gas ; statistical mechanics ; periodic orbits ; Brownian motion ; billiards ; time series analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of models involving a single particle moving in two dimensions and colliding with fixed scatterers. We find that a number of microscopically nonchaotic models exhibit diffusion, and that the standard methods of chaotic time series analysis are ill suited to the problem of distinguishing between chaotic and nonchaotic microscopic dynamics. However, we show that periodic orbits play an important role in our models, in that their different properties in our chaotic and nonchaotic models can be used to distinguish them at the level of time series analysis, and in systems with absorbing boundaries. Our findings are relevant to experiments aimed at verifying the existence of chaoticity and related dynamical properties on a microscopic level in diffusive systems.
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    Coverage and Structure of Films of Spherical Particles Deposited after Diffusing in a Gravitational Field (1998)
    Springer
    Journal of statistical physics 92 (1998), S. 891-908 
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    ISSN: 1572-9613
    Keywords: Random sequential adsorption ; hard-sphere particles ; gravity ; diffusion ; coverage ; structure
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    Topics: Physics
    Notes: Abstract We investigate the coverage and structure of a layer of particles deposited on a line after diffusion in a gravitational field. The dynamics of the depositing particles is controlled by the gravity number N G(=πd 4 Δρg/6k B T), where d is the diameter of the particles, Δρ is the density difference between the particles and the solution, g is the acceleration due to gravity, k B is Boltzmann's constant, and T is the temperature. The position-dependent flux of particles in a gap formed by two preadsorbed particles is estimated by superposition of solutions of a steady-state convective diffusion equation for the flux in the presence of a single preadsorbed particle. The saturation coverages are found with a recursion relation and are in good agreement with those obtained from Brownian dynamics simulation. The jamming coverage increases rapidly with increasing particle size, particularly for large values of Δρ. An algorithm is presented to generate adsorbed configurations from which the structure of the deposit is determined.
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    On the Convergence of the Boltzmann Equation for Semiconductors Toward the Energy Transport Model (2000)
    Springer
    Journal of statistical physics 98 (2000), S. 835-870 
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    ISSN: 1572-9613
    Keywords: Boltzmann equation ; semiconductor ; diffusion ; energy transport model ; entropy dissipation rate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The diffusion limit of the Boltzmann equation of semiconductors is analyzed. The dominant collisions are the elastic collisions on one hand and the electron–electron collisions with the Pauli exclusion terms on the other hand. Under a nondegeneracy hypothesis on the distribution function, a lower bound of the entropy dissipation rate of the leading term of the Boltzmann kernel for semiconductors in terms of a distance to the space of Fermi–Dirac functions is proved. This estimate and a mean compactness lemma are used to prove the convergence of the solution of the Boltzmann equation to a solution of the energy transport model.
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    Transient Chaos and Critical States in Generalized Baker Maps (2000)
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    Journal of statistical physics 101 (2000), S. 107-124 
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    ISSN: 1572-9613
    Keywords: transient chaos ; conditionally invariant measures ; natural measures ; critical state ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Generalized multibaker maps are introduced to model dissipative systems which are spatially extended only in certain directions and escape of particles is allowed in other ones. Effects of nonlinearity are investigated by varying a control parameter. Emphasis is put on the appearance of the critical state representing the borderline of transient chaos, where anomalous behavior sets in. The investigations extend to the conditionally invariant and the related natural measures and to transient diffusion in normal and critical states as well. Permanent chaos is also considered as a special case.
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    Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation, and Fragmentation (2000)
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    Journal of statistical physics 99 (2000), S. 1-29 
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    ISSN: 1572-9613
    Keywords: diffusion ; aggregation ; phase transition ; nonequilibrium
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    Topics: Physics
    Notes: Abstract We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact, and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady-state mass distribution decays exponentially for large mass in one phase. In the other phase, the mass distribution decays as a power law accompanied, in addition, by the formation of an infinite aggregate. The model is solved exactly within a mean-field approximation which keeps track of the distribution of masses. In one dimension, by mapping to an equivalent lattice gas model, exact steady states are obtained in two extreme limits of the parameter space. Critical exponents and the phase diagram are obtained numerically in one dimension. We also study the time-dependent fluctuations in an equivalent interface model in (1+1) dimension and compute the roughness exponent χ and the dynamical exponent z analytically in some limits and numerically otherwise. Two new fixed points of interface fluctuations in (1+1) dimension are identified. We also generalize our model to include arbitrary fragmentation kernels and solve the steady states exactly for some special choices of these kernels via mappings to other solvable models of statistical mechanics.
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    Prediction of Fluid Mixture Transport Properties by Molecular Dynamics (1998)
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    International journal of thermophysics 19 (1998), S. 437-448 
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    ISSN: 1572-9567
    Keywords: alkanes ; carbon dioxide ; diffusion ; mixtures ; molecular dynamics ; thermal conductivity ; viscosity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Equilibrium molecular dynamics simulations of mixtures of n-decane with methane, ethane, and carbon dioxide and of the mixture carbon dioxide–ethane were performed using the anisotropic united atoms model for n-decane and one-and two-center Lennard–Jones models for the light components. The Green–Kubo relations were used to calculate the viscosity, thermal conductivity, and inter- and intradiffusion. Viscosities are predicted with a maximum deviation of 30% at low gas concentrations and less than 10% deviation at high gas concentrations. The viscosity and thermal conductivity are less sensitive to the cross interactions than the diffusion coefficients, which exhibit deviations between models and with experiments of up to 60%.
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    Cancellation of the Heating Piston Effect by Convective Enhancement of a Cooling Piston Effect (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 1185-1195 
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    ISSN: 1572-9567
    Keywords: acoustic waves ; convection ; diffusion ; heat transfer ; near-critical fluid ; piston effect
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract This work brings new insight to the question of the piston effect, which has been found to be the main cause of temperature equilibration in the vicinity of the liquid–vapor critical point under weightlessness conditions. The thermalization process of a near-critical fluid confined in a cavity and submitted to local heating is modeled with special emphasis on the role of gravity and boundary conditions. The solution of the unsteady Navier–Stokes equations written for a hypercom-pressible low-heat-diffusing van der Waals gas is obtained in a 2-D configuration by means of a finite-volume numerical code. Under Earth gravity conditions, the results show that the thermal plume rising from a heat source strongly decreases and rapidly cancels bulk fluid heating when it strikes the top thermo-stated wall. It is proved that convection does not prevent heat transfer by the piston effect but that it causes a sudden enhancement of the cooling piston effect generated at the thermostated top boundary, which leads to an early equilibrium between the cooling and heating piston effects.
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    Thermophysical Properties of Tetramethylmethane and Tetramethylsilane Gas Calculated by Means of an Isotropic Temperature-Dependent Potential (2000)
    Springer
    International journal of thermophysics 21 (2000), S. 1439-1461 
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    ISSN: 1572-9567
    Keywords: diffusion ; intermolecular potentials ; Raman and Rayleigh spectra ; second virial coefficients ; tetramethylmethane ; tetramethylsilane ; transport properties ; viscosity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract An isotropic temperature-dependent potential (ITDP) is calculated for the description of binary interactions in gaseous tetramethylmethane, C(CH3)4, and tetramethylsilane, Si(CH3)4. The potential parameters of C(CH3)4 and Si(CH3)4 are determined by solving an inverse problem of minimization of the sum of weighted squared relative deviations between experimental and calculated pure gas viscosity (η), second (pVT)-virial coefficient (B), and second acoustic virial coefficient (β) data. At T=0 K they are obtained for C(CH3)4 and Si(CH3)4, respectively, as repulsive parameter n=28.02(12) and 20.79(11), equilibrium distance r m=5.7790(30)×10−10 and 5.9051(36)×10−10 m, potential well depth ε/k B=586.32(42) and 674.75(91) K, and the first excited-level enlargement δ=0.0141(3)×10−10 and 0.0188(3)×10−10 m. The influence of the temperature on the potential parameters r m(T) and ε(T) is implied in the temperature dependence of the effective excited-state enlargement, calculated via the vibrational partition function. The calculated complete sets of normal vibrational frequencies for C(CH3)4 and Si(CH3)4 are consistent with the available experimental data. In addition, good agreement is observed between the calculations and new Raman spectroscopic measurements on C(CH3)4. Tables for recommended thermophysical properties (B, η, and self-diffusion ρD) and effective potential parameters (r m and ε) of the two globular gases are given for the temperature range between 250 and 800 K.
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    Maximum Principle for a Control Problem Governed by an Evolution Equation (2000)
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    Journal of optimization theory and applications 105 (2000), S. 263-276 
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    ISSN: 1573-2878
    Keywords: optimal control ; distributed-parameter systems ; Pontryagin maximum principle ; Ekeland variational principle ; unbounded controls
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove the maximum principle for an optimal control problem governed by the system $$y'(t) + A(t)y(t) = f(t,y(t),u(t)),{\text{ }}u(t) \in U(t), $$ with state constraint $$(y(0),y(T)) \in C \subset H \times H $$ , under three different hypotheses: (H1) C is a convex set with nonempty interior; (H2) $$C = \{ y_0 \} \times C_{0,} {\text{ with }}C_0 $$ a convex set with nonempty interior in H and the evolution system satisfying compactness hypotheses; (H3) the periodic case $$y(0) = y(T)$$ , with the evolution system satisfying compactness hypotheses. We do not assume the controls to be bounded. We give some examples for distributed control problems.
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    Hierarchical Production Control in Dynamic Stochastic Jobshops with Long-Run Average Cost (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 231-264 
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    ISSN: 1573-2878
    Keywords: hierarchical control ; manufacturing systems ; stochastic dynamic programming ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a production planning problem for a dynamic jobshop producing a number of products and subject to breakdown and repair of machines. The machine capacities are assumed to be finite-state Markov chains. As the rates of change of the machine states approach infinity, an asymptotic analysis of this stochastic manufacturing systems is given. The analysis results in a limiting problem in which the stochastic machine availability is replaced by its equilibrium mean availability. The long-run average cost for the original problem is shown to converge to the long-run average cost of the limiting problem. The convergence rate of the long-run average cost for the original problem to that of the limiting problem together with an error estimate for the constructed asymptotic optimal control is established.
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    Some Optimal Control Problems Governed by Elliptic Variational Inequalities with Control and State Constraint on the Boundary (2000)
    Springer
    Journal of optimization theory and applications 106 (2000), S. 627-655 
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    ISSN: 1573-2878
    Keywords: variational inequalities ; optimal control ; state constraint ; maximum principle
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    Topics: Mathematics
    Notes: Abstract This work deals with the necessary conditions of optimality for some optimal control problems governed by elliptic variational inequalities. Boundary control and state constrained problems are considered. The techniques used are based on those in Ref. 1 and a new penalty functional is defined in this paper.
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    Instabilities in Concave, Dynamic, Economic Optimization (2000)
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    Journal of optimization theory and applications 107 (2000), S. 275-286 
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    ISSN: 1573-2878
    Keywords: optimal control ; thresholds ; multiple equilibria ; instability ; concavity
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    Topics: Mathematics
    Notes: Abstract An important and numerous literature argues that nonconcavity (often convexity with respect to the state) of the Hamiltonian leads to multiple steady states, instability, and a threshold. This threshold property provides a powerful paradigm to explain history dependency and hysteresis. This paper shows that economically relevant properties (in particular, multiple steady states and thresholds) are possible in strict concave models too. Two corresponding necessary conditions with intuitive economic interpretation are derived.
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    Convergence of Solutions to Equations Arising in Neural Networks (1997)
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    Journal of optimization theory and applications 94 (1997), S. 533-560 
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    ISSN: 1573-2878
    Keywords: Polynomial differential equations ; convergence of solutions ; neural network systems ; optimal control
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    Notes: Abstract We study polynomial ordinary differential systems $$\dot M(t) = QM - M(M'QM){\text{, }}M(0) = M_0 ,t \geqslant 0,$$ whereQ≥0 is an n×n matrix and M(t) is an n×k matrix. It is proven that, as t grows to infinity, the solution M(t) tends to a limit BU, where U is a k×k orthogonal matrix and B is an n×k matrix whose columns are k pairwise orthogonal, normalized eigenvectors of Q. Moreover, for almost every M 0, these eigenvectors correspond to the k maximal eigenvalues of Q; for an arbitrary Q with independent columns, we provide a procedure of computing B by employing elementary matrix operations on M 0. This result is significant for the study of certain neural network systems, and in this context it shows that M(∞) provides a principal component analyzer.
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    Mixed Frank–Wolfe Penalty Method with Applications to Nonconvex Optimal Control Problems (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 311-334 
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    ISSN: 1573-2878
    Keywords: Mixed penalty method ; Frank–Wolfe method ; optimal control ; relaxed control ; lumped systems ; distributed systems
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    Topics: Mathematics
    Notes: Abstract We consider a general optimization problem which is an abstract formulation of a broad class of state-constrained optimal control problems in relaxed form. We describe a generalized mixed Frank–Wolfe penalty method for solving the problem and prove that, under appropriate assumptions, accumulation points of sequences constructed by this method satisfy the necessary conditions for optimality. The method is then applied to relaxed optimal control problems involving lumped as well as distributed parameter systems. Numerical examples are given.
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    In Optimal Control Problem in Economics with Four Linear Controls (1997)
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    Journal of optimization theory and applications 94 (1997), S. 619-634 
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    ISSN: 1573-2878
    Keywords: Microeconomic models ; optimal control ; linear controls ; singular subarcs ; necessary conditions ; minimum principle as LP ; direct collocation method ; indirect multiple shooting method
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    Topics: Mathematics
    Notes: Abstract An optimal control problem with four linear controls describing a sophisticated concern model is investigated. The numerical solution of this problem by combination of a direct collocation and an indirect multiple shooting method is presented and discussed. The approximation provided by the direct method is used to estimate the switching structure caused by the four controls occurring linearly. The optimal controls have bang-bang subarcs as well as constrained and singular subarcs. The derivation of necessary conditions from optimal control theory is aimed at the subsequent application of an indirect multiple shooting method but is also interesting from a mathematical point of view. Due to the linear occurrence of the controls, the minimum principle leads to a linear programming problem. Therefore, the Karush–Kuhn–Tucker conditions can be used for an optimality check of the solution obtained by the indirect method.
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    Approximate Solutions to the Time-Invariant Hamilton–Jacobi–Bellman Equation (1998)
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    Journal of optimization theory and applications 96 (1998), S. 589-626 
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    ISSN: 1573-2878
    Keywords: Nonlinear control ; optimal control ; Hamilton–Jacobi–Bellman equation ; feedback synthesis ; successive approximation ; Galerkin approximation
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    Topics: Mathematics
    Notes: Abstract In this paper, we develop a new method to approximate the solution to the Hamilton–Jacobi–Bellman (HJB) equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB equation to a sequence of linear partial differential equations. These equations are then approximated via the Galerkin spectral method. The resulting algorithm has several important advantages over previously reported methods. Namely, the resulting control is in feedback form and its associated region of attraction is well defined. In addition, all computations are performed off-line and the control can be made arbitrarily close to optimal. Accordingly, this paper presents a new tool for designing nonlinear control systems that adhere to a prescribed integral performance criterion.
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    Robust Stabilization for a Class of Uncertain Nonlinear Systems with Time-Varying Delay: Razumikhin-Type Approach (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 161-173 
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    Keywords: Robust stabilization ; optimal control ; time-delay systems ; Razumikhin-type approach
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    Notes: Abstract In this paper, using a Razumikhin-type approach, the stabilization of a class of uncertain nonlinear systems with time-varying delay is considered. The proposed controller is based on a specific optimal control problem. Global asymptotic stability is guaranteed for the proposed control if some algebraic condition is met. An example illustrates the use of the main result.
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    Based on wavelet analysis to optimal control of motion planning of space manipulator (2000)
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    Applied mathematics and mechanics 21 (2000), S. 1161-1168 
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    ISSN: 1573-2754
    Keywords: space manipulator ; motion planning ; optimal control ; wavelet analysis ; TP241
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract The optimal control problem of nonholonomic motion planning of space manipulator was discussed. Utilizing the method of wavelet analysis, the discrete orthogonal wavelets were introduced to solve the optimal control problem, the classical Fourier basic functions were replaced by the wavelet expansion approximation. A numerical algorithm of optimal control was proposed based on wavelet analysis. The numerical simulation shows, the method is effective for nonholonomic motion planning of space manitulator.
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    Investigations of grain boundaries in copper using emission Mössbauer spectroscopy (2000)
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    Hyperfine interactions 126 (2000), S. 215-218 
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    ISSN: 1572-9540
    Keywords: emission Mössbauer spectroscopy ; grain boundary ; diffusion ; copper ; 57Co
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    Topics: Physics
    Notes: Abstract Grain boundaries (GBs) in pure Cu specimens were studied by means of 57Fe emission Mössbauer spectroscopy. A spectrum component which can be ascribed to iron atoms at GBs is represented by the single line with isomer shift 0.67 ± 0.05 mm/s. It is interpreted as iron atoms at GB sites with expanded atomic volumes and highly symmetric distribution of surrounding atoms.
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    Implantation and diffusion of 73As in GaAs and GaP (2000)
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    Hyperfine interactions 129 (2000), S. 337-347 
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    Keywords: diffusion ; 73As ; GaAs ; GaP ; computer simulation
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    Topics: Physics
    Notes: Abstract Self-diffusion on the As sublattice in intrinsic GaAs and foreign-atom diffusion on the P sublattice in intrinsic GaP were investigated in a direct way by As tracer diffusion measurements using the radioisotope 73As. For this purpose 73As was implanted in both materials at the ISOLDE facility of CERN. Then diffusion annealings were performed followed by serial sectioning and counting of the radioactivity in each section. The resulting profiles were simulated within a computer model which accounts for the observed loss of tracer to the diffusion ambient. The so-obtained diffusion coefficients for As in GaAs and GaP are compared with existing diffusivities in these compounds.
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    Optimization of Bilinear Systems Using a Higher-Order Variational Method (2000)
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    Journal of optimization theory and applications 105 (2000), S. 55-72 
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    ISSN: 1573-2878
    Keywords: optimal control ; bilinear systems ; nilpotent Lie algebra ; products of exponentials
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    Topics: Mathematics
    Notes: Abstract This paper derives some optimization results for bilinear systems using a higher-order method by characterizing them over matrix Lie groups. In the derivation of the results, first a bilinear system is transformed to a left-invariant system on matrix Lie groups. Then, the product of exponential representation is used to express this system in canonical form. Next, the conditions for optimality are obtained by the principles of variational calculus. It is demonstrated that closed-form analytical solutions exist for classes of bilinear systems whose Lie algebra are nilpotent.
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    Optimal Expenditure Patterns of a Double-Path Engineering Project (2000)
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    Journal of optimization theory and applications 105 (2000), S. 441-455 
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    ISSN: 1573-2878
    Keywords: expenditure patterns ; research and development ; optimal control ; calculus of variations
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract The optimal expenditure pattern for a double-path engineering project, i.e., a project composed of a nonroutine risky R&D path and a routine nonrisky preparatory path, manufacturing related or marketing related, is studied via the calculus of variations to derive a set of twin second-order nonlinear differential equations whose solution yields the optimal joint expenditure. Assuming independence between the risky and nonrisky paths, a constant return per unit time, a gamma-type unimodal conditional-completion density function for the R&D activity, and the principle of diminishing returns on the effort, we find an interesting interplay between the two paths for the peak position and termination of the expenditures. Counterintuitively, we find that the peak expenditure of the R&D path does not necessarily precede that of the preparatory path, although both path expenditure peaks obey the well-known Kamien–Schwartz theorem. That is, for both paths, the expenditure peak positions precede always the peak of the conditional-completion density function of the R&D path.
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    Universal Near-Optimal Feedbacks (2000)
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    Journal of optimization theory and applications 107 (2000), S. 89-122 
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    Keywords: optimal control ; differential games ; Euler polygonal arcs ; nonsmooth analysis ; proximal aiming ; infinitesimal decrease ; discontinuous universal near-optimal feedback
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a general fixed-duration optimal control problem, the proximal aiming technique of nonsmooth analysis is employed in order to construct a discontinuous feedback law, whose Euler solutions are all optimal to within a prescribed tolerance, universally for all initial data in a prescribed bounded set. The technique is adapted in order to construct universal near-saddle points for two-player fixed-duration differential games of the Krasovskii–Subbotin type.
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    Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost (1997)
    Springer
    Journal of optimization theory and applications 92 (1997), S. 161-188 
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    ISSN: 1573-2878
    Keywords: Production planning ; stochastic dynamic programming ; vanishing discount approach ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the optimal production planning in a dynamic stochastic manufacturing system consisting of a single machine that is failure prone and facing a constant demand. The objective is to choose the rate of production over time in order to minimize the long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach that the Hamilton–Jacobi–Bellman equation for the average cost problem has a solution giving rise to the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem. Finally, the optimal control policy is specified in terms of the potential function.
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    ℓ1-Minimization with Magnitude Constraints in the Frequency Domain (1997)
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    Journal of optimization theory and applications 93 (1997), S. 27-51 
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    ISSN: 1573-2878
    Keywords: Robust control ; multiobjective control ; optimal control ; $$\ell _1 $$ –control ; computational methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we study the $$\ell _1 $$ -optimal control problem with additional constraints on the magnitude of the closed-loop frequency response. In particular, we study the case of magnitude constraints at fixed frequency points (a finite number of such constraints can be used to approximate an $$H_\infty $$ -norm constraint). In previous work, we have shown that the primal-dual formulation for this problem has no duality gap and both primal and dual problems are equivalent to convex, possibly infinite-dimensional, optimization problems with LMI constraints. Here, we study the effect of approximating the convex magnitude constraints with a finite number of linear constraints and provide a bound on the accuracy of the approximation. The resulting problems are linear programs. In the one-block case, both primal and dual programs are semi-infinite dimensional. The optimal cost can be approximated, arbitrarily well from above and within any predefined accuracy from below, by the solutions of finite-dimensional linear programs. In the multiblock case, the approximate LP problem (as well as the exact LMI problem) is infinite-dimensional in both the variables and the constraints. We show that the standard finite-dimensional approximation method, based on approximating the dual linear programming problem by sequences of finite-support problems, may fail to converge to the optimal cost of the infinite-dimensional problem.
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    Dynamic Sampling Applied to Problems in Optimal Control (1997)
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    Journal of optimization theory and applications 95 (1997), S. 565-580 
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    Keywords: Brownian motion ; diffusion processes ; observers ; dynamic sampling ; optimal control
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    Topics: Mathematics
    Notes: Abstract Dynamic sampling utilizes the option of varying the sampling rates according to the situation of the systems, thus obtaining procedures with improved efficiencies. In this paper, the technique is applied to a typical problem in optimal control theory, that of tracking and controlling the position of an object. It is shown that the dynamic sampling results in a significantly improved procedure for this case, even when applying a suboptimal policy which can be analyzed in closed form.
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    Optimal Control of Rigid Body Angular Velocity with Quadratic Cost (1998)
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    Journal of optimization theory and applications 96 (1998), S. 507-532 
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    Keywords: Rigid bodies ; Hamilton–Jacobi equation ; Riccati equation ; optimal control
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    Topics: Mathematics
    Notes: Abstract In this paper, we consider the problem of obtaining optimal controllers which minimize a quadratic cost function for the rotational motion of a rigid body. We are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by the Euler equations. We obtain conditions which guarantee the existence of linear stabilizing optimal and suboptimal controllers. These controllers have a very simple structure.
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    Optimization of a Class of Nonlinear Dynamic Systems: New Efficient Method without Lagrange Multipliers (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 11-28 
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    Keywords: Optimization ; nonlinear dynamic systems ; transformations ; optimal control
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    Topics: Mathematics
    Notes: Abstract This paper deals with optimization of a class of nonlinear dynamic systems with n states and m control inputs commanded to move between two fixed states in a prescribed time. Using conventional procedures with Lagrange multipliers, it is well known that the optimal trajectory is the solution of a two-point boundary-value problem. In this paper, a new procedure for dynamic optimization is presented which relies on tools of feedback linearization to transform nonlinear dynamic systems into linear systems. In this new form, the states and controls can be written as higher derivatives of a subset of the states. Using this new form, it is possible to change constrained dynamic optimization problems into unconstrained problems. The necessary conditions for optimality are then solved efficiently using weighted residual methods.
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    Optimal Control of a Stochastic Assembly Production Line (1998)
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    Journal of optimization theory and applications 98 (1998), S. 681-700 
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    Keywords: Manufacturing systems ; bang–bang control ; dynamic programming ; optimal control
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract The system under consideration comprises n workstations in parallel and one assembly workstation. The workstations are either reliable or unreliable and the product demand is random. The n different type parts are processed first in the parallel workstations and then are joined in the assembly workstation. By minimizing the expected discounted cost, it is shown that the optimal control policy is of the bang–bang type and can be described by a set of switching manifolds. The structural properties of the optimal policy, such as monotonicity and asymptotic behavior, are investigated. These structural properties are very useful to find the optimal policy in large-size systems. Three numerical examples are given to demonstrate the results.
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    Finite-Time Optimal Control of Polynomial Systems Using Successive Suboptimal Approximations (2000)
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    Journal of optimization theory and applications 105 (2000), S. 477-489 
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    Keywords: optimal control ; polynomial systems ; quasilinearization ; successive approximation ; convergence
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    Notes: Abstract It is shown in this paper that the finite-time optimal control of polynomial systems can be obtained by solving a sequence of optimal control problems for the linearized problem. The paper provides proof of convergence as well as illustration of the procedure by two examples.
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    Stochastic Games for N Players (2000)
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    Journal of optimization theory and applications 105 (2000), S. 543-565 
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    Keywords: stochastic games ; dynamic programming ; optimal control ; regularity theory ; Nash point
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    Notes: Abstract The objective of this paper is to present a useful application of the theory of regularity of systems of nonlinear partial differential equations to the solution of stochastic differential games with N players. It is particularly interesting to notice that the structure of games fits perfectly with what is requested to prove the regularity property which is needed.
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    Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems (2000)
    Springer
    Journal of optimization theory and applications 104 (2000), S. 20-40 
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    ISSN: 1573-2878
    Keywords: optimal control ; state constraints ; dynamic programming ; Hamilton-Jacobi equation
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    Notes: Abstract In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semicontinuous generalized solution of the Hamilton-Jacobi equation. This is achieved under a constraint qualification (CQ) concerning the interaction of the state and dynamic constraints. The novelty of the results reported here is partly the nature of (CQ) and partly the proof techniques employed, which are based on new estimates of the distance of the set of state trajectories satisfying a state constraint from a given trajectory which violates the constraint.
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    Optimal Control Problem for the Lyapunov Exponents of Random Matrix Products (2000)
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    Journal of optimization theory and applications 105 (2000), S. 347-369 
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    Keywords: random matrix products ; Lyapunov exponents ; Markov processes ; decision models ; optimal policy ; optimal control ; system spectrum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with the optimal control problem for the Lyapunov exponents of stochastic matrix products when these matrices depend on a controlled Markov process with values in a finite or countable set. Under some hypotheses, the reduced process satisfies the Doeblin condition and the existence of an optimal control is proved. Furthermore, with this optimal control, the spectrum of the system consists of only one element.
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    Bilinear Control and Application to Flexible a.c. Transmission Systems (2000)
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    Journal of optimization theory and applications 105 (2000), S. 621-637 
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    Keywords: bilinear systems ; optimal control ; controllability ; stabilization ; electric power
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is an integrated overview of bilinear systems (BLS) research which has evolved over the past few decades, and a new result on control of flexible a.c. transmission systems (FACTS) is presented. BLS may be derived in many cases from principles of physics, chemistry, biology, socioeconomics, and engineering. In other cases, BLS are more accurate approximations to nonlinear systems than are traditional linear systems, as shown for example by the added bilinear terms (in state and control) for the Taylor series. While an appropriately designed linear control system may be optimum relative to some quadratic performance index without added constraints, bilinear or parametric control can be designed to improve more global performance and indeed to increase the region of attainable states. Such controllability and stabilization of BLS and of a series line-capacitor controlled FACTS is presented.
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    Application of Stochastic Global Optimization Algorithms to Practical Problems (1997)
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    Journal of optimization theory and applications 95 (1997), S. 545-563 
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    ISSN: 1573-2878
    Keywords: Global optimization ; real life problems ; pig liver likelihood function ; many-body potential function ; tank reactor ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We describe global optimization problems from three different fields representing many-body potentials in physical chemistry, optimal control of a chemical reactor, and fitting a statistical model to empirical data. Historical background for each of the problems as well as the practical significance of the first two are given. The problems are solved by using eight recently developed stochastic global optimization algorithms representing controlled random search (4 algorithms), simulated annealing (2 algorithms), and clustering (2 algorithms). The results are discussed, and the importance of global optimization in each respective field is focused.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022617804737
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    Optimal Control of a Ship for a Course-Changing Maneuver (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 281-297 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear ship steering dynamics ; optimal control ; saturation ; slew rate limitation ; sequential gradient-restoration algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The steering control of a ship during a course-changing maneuver is formulated as a Bolza optimal control problem, which is solved via the sequential gradient-restoration algorithm (SGRA). Nonlinear differential equations describing the yaw dynamics of a steering ship are employed as the differential constraints, and both amplitude and slew rate limits on the rudder are imposed. Two performance indices are minimized: one measures the time integral of the squared course deviation between the actual ship course and a target course; the other measures the time integral of the absolute course deviation. Numerical results indicate that a smooth transition from the initial set course to the target course is achievable, with a trade-off between the speed of response and the amount of course angle overshoot.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022674516570
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    Solution of Fixed Final State Optimal Control Problems via Simple Cell Mapping (2000)
    Springer
    Nonlinear dynamics 23 (2000), S. 391-403 
    Details
    ISSN: 1573-269X
    Keywords: optimal control ; cell mapping method ; dynamic programing ; parametric control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A strategy is proposed to solve the fixed final state optimalcontrol problem using the simple cell mapping method. A non-uniform timestep simple cell mapping is developed to create a general database fromwhich solutions of various optimal control problems can be obtained. Atwo-stage backward search algorithm is proposed to eliminate degeneratedpaths often associated with the simple cell mapping. The proposed methodcan accurately delineate the switching curves and eliminate false limitcycles in the solution. The method is applied to two optimal controlproblems with bang-bang control. The well-known minimum time controlproblem of moving a point mass from any initial condition to the originof the phase plane is studied first. This example has exact solutionsavailable which provide a yardstick to examine the accuracy of themethod. The cell size dependence of the solution accuracy is studiednumerically. The second example is a variable stiffness feedback controlproblem with tuning range saturation. The strategy proposed is able toprovide the switching curves in the phase plane. This result has notbeen obtained before.
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    Diffusive fluxes associated with interfacial defeet motion and interaction (1997)
    Springer
    Interface science 4 (1997), S. 99-118 
    Details
    ISSN: 1573-2746
    Keywords: diffusion ; interfacial defects ; glide ; climb ; defect interaction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The diffusional flux associated with the motion of interfacial defects is described by an equation expressed in terms of the topological parameters which characterise defects, namely their Burgers vectors and step heights, the defect velocity and the concentration of each atomic species in the two adjacent crystals. This expression demonstrates that glide/climb behaviour of grain boundary defects is analogous to motion of dislocations in single crystals; climb motion results if a component of b is perpendicular to the interface plane. However, the situation is more complex in the case of interphase interface defects, but the present approach, which considers the step and dislocation portions of defects separately, enables a straightforward analysis. Several examples are illustrated to show the various possibilities, such as climb motion even when b is parallel to the interface, and glide motion when b is not. The latter case arises in martensitic transformation where the existence of an invariant-plane-strain relation at the interface leads to equal and opposite fluxes to the step and dislocation portions of transformation defects so that overall the motion is diffusionless. Interfacial processes involve the motion and interaction of defects. The present analysis facilitates the consideration of diffusive fluxes associated with defect interaction since the step and dislocation portions can be treated independently. A general expression is derived for the total flux arising, and a particular case, the interaction of transformation dislocations with crystal dislocations which have reached the interface during lattice-invariant deformation in martensite formation, is considered.
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    Grain Boundary Diffusion in Metallic Nano and Polycrystals (1997)
    Springer
    Interface science 5 (1997), S. 54-62 
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    ISSN: 1573-2746
    Keywords: grain boundaries ; diffusion ; segregation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract An outline is given of the recent theoretical and experimentalknowledge of grain boundary diffusion in metals. First what is knownabout the classification of the diffusion regimes encountered inpresence of stationary or moving grain boundaries and the non linearsegregation effects on the shape of the depth penetration profiles isbriefly described. Then a summarizing description of some importantrecent experimental results is presented.
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    Grain Boundary Migration in Solid State Discontinuous Reactions (1998)
    Springer
    Interface science 6 (1998), S. 113-131 
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    ISSN: 1573-2746
    Keywords: discontinuous reactions ; discontinuous precipitation ; discontinuous coarsening ; discontinuous dissolution ; grain boundary ; migration ; diffusion ; kinetics ; mechanism
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Discontinuous reactions are a special class of solid state moving boundary reactions characterized by a discontinuous change in orientation and composition across the migrating reaction front that provides a short circuit path of solute transport. Grain boundary migration in discontinuous reactions is both of technological as well as fundamental interest. In this paper, the initiation/growth mechanism, product morphology, driving force, reaction kinetics, and effect of external parameters on the major discontinuous reactions, namely, discontinuous precipitation, coarsening, dissolution, and diffusion induced grain boundary migration have been discussed. In addition, a number of interesting features about boundary migration in discontinuous reactions has been analyzed. Finally, the scope and necessity of continued research attention in this area have been highlighted.
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    Excess Volume of the Solid/Liquid Interface in Fe-6 at.%Si Bicrystals Wetted by Liquid Zinc (1998)
    Springer
    Interface science 6 (1998), S. 179-186 
    Details
    ISSN: 1573-2746
    Keywords: grain boundary energy ; diffusion ; segregation ; solid/liquid interface ; wetting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The pressure effect on grain boundary wetting in Fe-6 at.%Si bicrystals of different misorientation angles but constant misorientation axis has been studied. The wetting agent was liquid zinc. It was found that the pressure for the dewetting transition is higher for the near Σ5 boundary than for the other general boundaries, where Σ is the inverse density of the coincidence sites in the two misoriented crystal lattices. This result was explained assuming a thinner liquid film wetting the near Σ5 boundary than in the case of nonperiodic grain boundaries. Furthermore, the wetting angle increased with increasing pressure. The wetting angle dependence on pressure could be understood assuming a excess surface volume of the solid/liquid (S/L) interface higher than 0.2 nm. This is considerably higher than the estimated excess volumes of grain boundaries based on computer simulations. To explain this result, it was postulated that in the system studied, where diffusion of Zn, Fe and Si perpendicular to the S/L interface takes place, the S/L interface is relatively thick and the interaction between the two crystals separated by the melt extends over more than 2 nm distance. This long-range interaction was rationalized in terms of clusters of several atoms, detaching from the solid and dissolving in the melt at some distance from the bulk.
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    Some moving-boundary problems arising from a model for solid-state diffusion (1997)
    Springer
    Journal of engineering mathematics 31 (1997), S. 1-27 
    Details
    ISSN: 1573-2703
    Keywords: moving boundary ; diffusion ; semiconductor ; impurity ; mask edge
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract In this paper we formulate and analyse moving-boundary problems arising from the dissociative model for impurity diffusion in a semiconductor. We consider one-dimensional surface-source and implant problems and two-dimensional diffusion under a mask edge. The diffused profiles which result exhibit a number of novel features.
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    The Kinetics of the Cd21Ni5 Intermetallic Growth under High Hydrostatic Pressure (2000)
    Springer
    Interface science 8 (2000), S. 77-84 
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    ISSN: 1573-2746
    Keywords: intermetallic growth ; interfacial reaction ; diffusion ; high hydrostatic pressure ; activation volume
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The kinetics of growth of the Cd21Ni5 intermetallic phase in two-layer Cd-Ni samples has been studied at hydrostatic pressures 0.05–0.9 GPa and at temperatures 200–280°C. Arrhenius equations for both interdiffusion through the growing phase layer and the interfacial reaction have been obtained for different pressures. The activation volumes have been found to be 0.9V0 for interdiffusion and 1.6V0 for interfacial reaction, where V_0 ≈ 1.8 × 10-29m3 is the average volume per atom in the Cd21Ni5 lattice. Atomistic mechanisms of intermetallic growth are discussed.
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    Dual-mode free volume model for diffusion of gas molecules in glassy polymers (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1737-1746 
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    ISSN: 0887-6266
    Keywords: free volume ; dual mode ; diffusion ; glassy polymer ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The development of a new model for the diffusion of gas molecules in glassy polymers is presented which utilizes concepts from free volume theory and relies on a dual-mode interpretation of sorptive dilation in glassy polymers. Three assumptions are made in the development of the model. First, the free volume available for molecular transport processes is taken as constant below the glass transition temperature. Second, two populations of gas molecules are assumed to exist - one which contributes to the maintenance of an iso-free volume state upon sorptive dilation and one which does not contribute owing to sorption into regions of unrelaxed volume. Third, the former population is assumed to be mobile while the latter is not. The resulting model predicts, at constant temperature, a diffusion coefficient that is independent of solute volume fraction. This is in contrast to the widely used dual-mode sorption model with partial immobilization for gas transport in glassy polymers which leads to a diffusion coefficient that is dependent on solute mole fraction through the molar gas concentration. The new model is used to interpret gas transport data from permeation experiments for carbon dioxide, methane, and ethylene in three polycarbonates. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1737-1746, 1997
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    Diffusion of methyl ethyl ketone in polyisobutylene: Comparison of spectroscopic and gravimetric techniques (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1261-1267 
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    ISSN: 0887-6266
    Keywords: FTIR-ATR spectroscopy ; gravimetric sorption ; diffusion ; polymer ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: In this study, vapor sorption FTIR-ATR (Fourier Transform Infrared Attenuated Total Reflectance) spectroscopy was combined with a conventional gravimetric sorption balance to examine diffusion in polymers. Mutual diffusion coefficients of methyl ethyl ketone in polyisobutylene were measured using both methods at various penetrant activities and temperatures in the range 40-60°C. Actual penetrant concentrations were determined from the sorption balance. The diffusion coefficients from the two techniques agree very well with each other. In addition, the diffusivity data from both techniques could be correlated successfully as a function of temperature and concentration with the Vrentas and Duda free-volume model. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1261-1267, 1997
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    Development of a simple experimental method to measure interphase composition profiles generated by diffusion in polymers (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 2435-2445 
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    ISSN: 0887-6266
    Keywords: diffusion ; interphase ; composition profiles ; interdiffusion ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: An experimental method to determine interphase composition profiles in amorphous polymers pairs and polymer-solvent pairs is presented. The method is based on the measurement of dynamic mechanical properties of slender composite beams, and well-established properties of amorphous polymer homogeneous blends and solutions. The method does not require tracers. A simple calibration procedure is included in the description, and some results for a polystyrene-polystyrene pair are used to illustrate the method application. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2435-2445, 1997
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    Terminal relaxation and diffusion of entangled three-arm star polymers: Temperature and molecular weight dependencies (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 2503-2510 
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    ISSN: 0887-6266
    Keywords: rheology ; diffusion ; star-branched polymers ; polyisoprene ; terminal viscosity ; molecular weight dependence ; temperature dependence ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Recent experimental investigation of the terminal relaxation in high molecular weight polyisoprenes by dynamic mechanical measurements (C. A. Bero and C.M. Roland, Macromolecules, 29, 1562 (1996)) has found the terminal relaxation times to be more sensitive to changes in temperature for three-arm stars than for the linear polyisoprenes. Moreover, these measurements, carried out with significantly higher molecular weight samples than heretofore, show that the molecular weight dependence of the terminal relaxation times for three-arm star polyisoprenes is much weaker than the exponential dependence previously proposed (L. J. Fetters, et al., Macromolecules, 26, 647 (1993)). Tracer diffusion of labeled linear and three-arm star polyethylene-like diffusant molecules in a highly entangled linear polyethylene matrix exhibit temperature and molecular weight dependencies similar to those observed spectroscopically from bulk polymers. Both the temperature and molecular weight dependencies for the star-branched polymers are at variance with the predictions of the reptation model. It is shown here, however, that these observations can be reconciled through application of the coupling model of relaxation. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2503-2510, 1997
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    Synthesis, physical characterization, and acetone sorption kinetics in random copolymers of poly(ethylene terephthalate) and poly(ethylene 2,6-naphthalate) (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 2981-3000 
    Details
    ISSN: 0887-6266
    Keywords: sorption ; diffusion ; acetone ; poly(ethylene terephthalate) ; poly(ethylene 2,6-naphthalate) ; copolymers ; positron annihilation lifetime spectroscopy ; infrared spectroscopy ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Random copolymers of poly(ethylene terephthalate) (PET) and poly(ethylene 2,6-naphthalate) (PEN) were synthesized by melt condensation. In a series of thin, solvent cast films of varying PEN content, acetone diffusivity and solubility were determined at 35°C and an acetone pressure of 5.4 cm Hg. The kinetics of acetone sorption in the copolymer films are well described by a Fickian model. Both solubility and diffusivity decrease with increasing PEN content. The acetone diffusion coefficient decreases 93% from PET to PET/85PEN, a copolymer in which 85 weight percent of the dimethyl terephthalate in PET has been replace by dimethyl naphthalate 2,6-dicarboxylate. The acetone solubility coefficient in the amorphous regions of the polymer decreases by approximately a factor of two over the same composition range. The glass/rubber transition temperatures of these materials rise monotonically with increasing PEN content. Copolymers containing 20 to 80 wt % PEN are amorphous. Samples with 〈20% or 〉80% PEN contain measurable levels of crystallinity. Estimated fractional free volume in the amorphous regions of these samples is lower in the copolymers than in either of the homopolymers. Relative free volume as probed by positron annihilation lifetime spectroscopy (PALS) decreases systematically with increasing PEN content. Acetone diffusion coefficients correlate well with PALS results. Infrared spectroscopy suggests an increase in the fraction of ethylene glycol units in the trans conformation in the amorphous phase as the concentration of PEN in the copolymer increases. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2981-3000, 1998
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    Styrene and isoprene friction factors in styrene-isoprene matrices (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 3079-3086 
    Details
    ISSN: 0887-6266
    Keywords: diffusion ; block copolymer ; monomeric friction factor ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Monomeric friction factors, Ξ, for polystyrene (PS), polyisoprene (PI), and a polystyrene-polyisoprene (SI) diblock copolymer have been determined as a function of temperature in four poly(styrene-b-isoprene-b-styrene-b-isoprene) tetrablock copolymer matrices. The Rouse model has been used to calculate the friction factors from tracer diffusion coefficients measured by forced Rayleigh scattering. Within the experimental temperature range the tetrablock copolymers are disordered, allowing for measurement of the diffusion coefficient in matrices with average compositions determined by the tetrablock copolymers (23, 42, 60, and 80% styrene by volume). Remarkably, for a given matrix composition the styrene and isoprene friction factors are essentially equivalent. Furthermore, at a constant interval from the system glass transition temperature, Tg, all of the friction factors (obtained from homopolymer, diblock copolymer, and tetrablock copolymer dynamics) agree to within an order of magnitude. This is in marked contrast to results for miscible polymer blends, where the individual components generally have distinct composition dependences and magnitudes at constant T - Tg. The homopolymer friction factors in the tetrablock matrices were systematically slightly higher than those of the diblock, which in turn were slightly higher than those of the homopolymers in their respective melts, when all compared at constant T - Tg. This is attributed to the local spatial distribution of styrene and isoprene segments in the tetrablocks, which presents a nonuniform free energy surface to the tracer molecules. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 3079-3086, 1998
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    Steric hindrance effects on dielectric relaxation and polymerization kinetics of a monoamine-triepoxide mixture, thermochemistry, and diffusion control (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 2703-2716 
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    ISSN: 0887-6266
    Keywords: calorimetry ; dielectrics ; diffusion ; monoamine-triepoxide ; thermoset ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Calorimetry and dielectric relaxation spectroscopy during the growth of a polymer network in the stoichiometric mixture of a triepoxide with 4-chloroaniline have been performed in separate experiments to investigate the increase in the relaxation time with the number of covalent bonds. A comparison with the corresponding study of triepoxide-aniline and triepoxide-3-chloroaniline mixtures shows that steric hindrance of the amine group by chlorine slows the molecular dynamics and the relaxation time of the state containing a fixed number of bonds. The polymerization kinetics measured during ramp heating does not yield a reliable activation energy. A recent empirical relation between the relaxation time and the extent of polymerization, and the condition for the onset of diffusion-control kinetics have been examined using the data for these three polymerizing mixtures. The results show substantial deviations from the empirical relation and appear to conflict with our basic understanding of the polymerization process. It is shown mathematically that features attributed to the onset of diffusion-controlled kinetics can arise from thermochemical behavior alone, without reference to the molecular dynamics. An earlier theory for the change in the kinetics of an addition reaction from mass control to diffusion control has been considered, and is seen as relevant to the polymerization reactions. It is argued that the dielectric relaxation rate does not directly indicate the chemical reaction rate because the reorientational motion of the dipolar entities may not be coupled to the rotational and translational diffusion that brings the sterically hindered chemically reacting sites together. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2703-2716, 1998
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    A new finite volume method for the solution of convection-diffusion equations: analysis of stability and convergence (1997)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 13 (1997), S. 923-940 
    Details
    ISSN: 1069-8299
    Keywords: finite volume ; convection ; diffusion ; convergence ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new high order FV method is presented for the solution of convection-diffusion equations, based on a 4-point approximation of the diffusive term and on the definition of a quadratic profile for the approximation of the convective term, in which coefficients are obtained by imposing conditions on the truncation error. The method works on unequal volumes (ratios of consecutive volume sizes in the interval [1/3,3]). The properties of this method are analysed formally. Numerical examples are given. © 1997 John Wiley & Sons, Ltd.
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    Sorption and diffusion of aliphatic hydrocarbons into crosslinked natural rubber (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 725-734 
    Details
    ISSN: 0887-6266
    Keywords: swelling ; sorption ; diffusion ; natural rubber ; interaction parameter ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The sorption and transport of four aliphatic hydrocarbons into natural rubber crosslinked by different vulcanization systems [conventional (CV), efficient (EV), peroxide (DCP) and a mixed system consisting of sulfur and peroxide (mixed)] were investigated in the temperature interval of 28-60°C. Of the four systems, natural rubber vulcanized by DCP exhibited lowest penetrant uptake. It was observed that the kinetics of liquid sorption in every case deviates from the regular Fickian trend, characteristic of sorption of liquids by rubbers. The diffusion coefficient, activation energy of sorption, enthalpy, entropy, and the rubber-solvent interaction parameter were evaluated for the four systems from the swelling data. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 725-734, 1997
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    Diffusion of gold and silver in bisphenol trimethylcyclohexanen polycarbonate (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1043-1048 
    Details
    ISSN: 0887-6266
    Keywords: diffusion ; gold, silver ; polycarbonate ; glassy state ; free-volume theory ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Diffusion coefficients between 5 × 10-14 and 1 × 10-16 cm2 s-1 have been measured for diffusion of gold and silver in the glassy state of bisphenol trimethylcyclohexanen polycarbonate in the temperature range between Tg = 507 K and 420 K using the radiotracer technique in combination with ion-beam sputtering for serial sectioning. The Arrhenius plot exhibits a downward curvature, which is interpreted within an extension of the free-volume theory to the glassy state by Vrentas and Duda. The very small metal diffusivities in comparison to values for gas molecules of comparable size suggest substantial interaction energies. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35:1043-1048, 1997
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    Surface mobility and diffusion at interfaces of polystyrene in the vicinity of the glass transition (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 567-572 
    Details
    ISSN: 0887-6266
    Keywords: surface ; interfaces ; diffusion ; polystyrene ; polyphenylene oxide ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Symmetric polydisperse (Mw = 23 × 104, Mw/Mn = 2.84) and monodisperse (Mw = 21 × 104, Mw/Mn 〈 1.05) polystyrene (PS), and asymmetric polydisperse PS/poly(2,6-dimethyl 1,4-phenylene oxide) (PPO) interfaces have been bonded in the vicinity of the glass transition temperature (Tg) of PS. In a lap-shear joint geometry, strength develops in all cases with time to the fourth power, which indicates that it is diffusion controlled. Strength developing at short times at the polydisperse PS/PS interface, at 90°C, is higher than that at the monodisperse interface, at 92°C (at Tg - 13°C in both cases), presumably due to the contribution of the low molecular weight species. The decrease of strength at the PS/PPO interface when the bonding temperature decreases from 113 to 70°C, i.e., from Tg + 10°C to Tg - 33°C of the bulk PS, indicates a high molecular mobility at the surface as compared to that in the bulk, and can be expressed by a classical diffusion equation, which is valid above Tg (of the surface layer). © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 567-572, 1998
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    Mobility of a tackifying resin in a pressure-sensitive adhesive (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 373-381 
    Details
    ISSN: 0887-6266
    Keywords: pressure-sensitive adhesive ; PSA ; tackifier ; tack adhesion ; polyisoprene ; poly(ethylene-propylene) ; pulsed gradient spin echo-nuclear magnetic resonance ; PGSE-NMR ; diffusion ; n-butyl ester of abietic acid ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A detailed study of the mobility of a tackifying resin in a pressure-sensitive adhesive (PSA) has been done for the first time. The objective of this work is to relate changes in adhesive performance with tackifier loading to tackifier mobility. Tackifiers are low-molecular weight resins that improve the overall performance of PSAs. They increase the adhesive tack or the ability to form a bond of measurable strength after brief contact under slight applied pressure. In this study the diffusion of n-butyl ester of abietic acid (n-BEAA) in either polyisoprene (PI) (Mw = 195,000 Mw/Mn ∼ 1.05) or poly(ethylene-propylene) (PEP) (Mw = 40,000 Mw/Mn ∼ 2.30) was measured by Pulsed Gradient Spin Echo-Nuclear Magnetic Resonance (PGSE-NMR) as a function of both tackifier concentration and temperature. The concentration dependence of the tackifier's diffusion coefficient was weak for both systems. The weak variation in mobility with composition for the PI/n-BEAA system was consistent with that system's weak variation in tack with composition. On the other hand, blends of PEP/n-BEAA showed only modest variation in mobility, even though these adhesive systems showed appreciable enhancement of tack at intermediate compositions. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 373-381, 1998
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    Understanding isothermal semicrystalline polymer drying: Mathematical models and experimental characterization (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 2771-2780 
    Details
    ISSN: 0887-6266
    Keywords: drying ; semicrystalline polymers ; poly(vinyl alcohol) ; solvent removal ; modeling ; diffusion ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The drying mechanism of semicrystalline poly(vinyl alcohol) (PVA) was investigated. PVA samples of various molecular weights were crystallized by annealing at temperatures slightly above the glass transition temperature of PVA, and swollen in water for different time periods. The water volume fraction in the sample was measured using a buoyancy technique. The samples were dried in air at constant temperatures, and the drying kinetics were investigated using thermogravimetric analysis. The change in degree of crystallinity of the swollen polymer during drying was measured by differential scanning calorimetry (DSC) as well as by Fourier transform infrared spectroscopy (FTIR). The degree of crystallinity of the samples increased during drying, which in turn was found to alter the drying rate. The drying kinetics were faster at higher temperatures, for lower molecular weights, and for lower degrees of crystallinity. A mathematical model was developed to predict drying rates of semicrystalline polymers by considering the crystallization kinetics during drying. The model predictions included the thickness of the polymer sample, the degree of crystallinity of the polymer, and the water weight loss as functions of drying time. Model predictions were found to agree reasonably well with the experimental results. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2771-2780, 1998
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    Interdiffusion measurements of modified poly(arylether sulfone)s using nuclear reaction analysis (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 2083-2091 
    Details
    ISSN: 0887-6266
    Keywords: nuclear reaction analysis ; copolymer blends ; diffusion ; poly(arylether sulfone)s ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The interdiffusion and miscibility behavior of three different types of modified poly(arylether sulfone)s with deuterated poly(arylether sulfone) is studied by depth profiling using the nuclear reaction D(3He, α)p. The diffusion coefficients are found to be in the range of 10-15 and 10-14 cm2/s at 195°C. A random copolymer of poly(arylether sulfone) containing 4,4-bis-(4′-hydroxyphenyl)valeric acid units is only partially miscible with deuterated poly(arylether sulfone) when the comonomer content is 8.8 mol %, whereas blends with comonomer contents of 1.7 and 4.5 mol % are miscible as indicated by complete interdiffusion. The transition from miscibility to immiscibility is caused by repulsive interactions of copolymer segments and can be explained in terms of a mean-field theory of random copolymer blends. Also, poly(arylether sulfone)s grafted with 0.4 wt % maleic anhydride or having pyromellitic anhydride endgroups are miscible with deuterated poly(arylether sulfone)s. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2083-2091, 1997
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    Diffusion of small molecules in glassy polymers (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 2397-2408 
    Details
    ISSN: 0887-6266
    Keywords: diffusion ; glassy polymers ; small molecules ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Small molecules in glassy polymers are considered to occupy sites with a distribution of free energies of dissolution. Then their diffusivity depends on concentration and temperature in the same way as it has been derived for hydrogen atoms in metallic glasses. For hydrogen it was shown that the tracer diffusion coefficient is proportional to the activity coefficient of the solute atoms. The latter can be evaluated from measured data of sorption of the small molecules in the polymer. Knowing this quantity, the thermodynamic factor can be calculated and the concentration dependence of the mutual diffusion coefficient is obtained in excellent agreement with published experimental results. New experimental results are presented for the diffusion coefficient of CO2 in Kapton and four polycarbonates (BPA-PC, BPZ-PC, TMBPA-PC, and TMC-PC) in the low CO2 pressure range of a few mbar up to 1 bar. The results are in agreement with the model developed for hydrogen. The reference diffusion coefficient, which is a fitting parameter of the model that is independent of the distribution of free energies is smallest for the polycarbonate BPZ-PC having a high γ-relaxation temperature. This correlation between the diffusion coefficient and the dynamics of the polymer can be found for other substituted polycarbonates as well. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2397-2408, 1997
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    Clustering and percolation effects in microcrystalline starch-reinforced thermoplastic (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 2211-2224 
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    ISSN: 0887-6266
    Keywords: starch ; mechanical properties ; percolation ; clustering ; diffusion ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The use of starch microcrystals as biodegradable particulate filler is evaluated by processing composite materials with a weight fraction of starch ranging from 0 to 60%. In a previous work [Macromolecules, 29, 7624] the preparation technique of a colloidal suspension of hydrolyzed starch and the processing of composite materials by freeze drying and molding a mixture of aqueous suspensions of starch microcrystals and synthetic polymer matrix were presented. Starch microcrystals with dimensions of a few nanometers were obtained from potatoes' starch granules, and it was found that this filler produces a great reinforcing effect, especially at a temperature higher than Tg of the synthetic matrix. Classical models for polymers containing nearly spherical particles based on a mean field approach could not explain this reinforcing effect. The morphology of these nanocomposite systems is discussed in light of aggregate formation and percolation concepts. The sorption behavior of these materials is also performed. Starch is a hygroscopic material, and it is found that the composites absorb more water, as the starch content is higher. The diffusion coefficient of the penetrant is predicted from modified mechanical three branch series-parallel model based on a percolation approach. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2211-2224, 1998
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    Effects of CO2 conditioning on sorption, dilation, and transport properties of polysulfone (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 1695-1702 
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    ISSN: 0887-6266
    Keywords: sorption ; dilation ; diffusion ; conditioning effect ; glassy polymer ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Sorption, dilation, and diffusion behaviors were studied for the system of polysulfone/CO2 with regard to the effects of CO2 conditioning, i.e., exposure to high-pressure CO2. Concurrent measurements of solubility, dilation, and diffusivity were performed for polysulfone films before and after the conditioning at 25 and 50 atm. While the solubility and dilation were enhanced by the conditioning, the diffusivity appeared to be depressed. Results were analyzed on the basis of the dual-mode sorption model, with the assumption that the Henry's law dissolution was not affected by the conditioning. Consistent description was achieved then by attributing the changes to increased amount of Langmuir adsorption. The conditioning effect on the diffusivity, which had not been reported before based on CO2 sorption kinetics, suggests that the permeability of glassy polymers would not always be enhanced by the conditioning, but may also be decreased. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1695-1702, 1998
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    Temperature and concentration dependence of diffusion coefficients in ethylene-propylene-diene copolymers (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 1713-1719 
    Details
    ISSN: 0887-6266
    Keywords: polymer ; diffusion ; free-volume theory ; inverse gas chromatography ; gravimetric sorption ; ethylene-propylene-diene ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Self-diffusion and partition coefficients were measured for two commercial ethylene-propylene-diene copolymers (EPDM) and five solvents at infinite dilution using inverse gas chromatography. Mutual diffusion coefficients for solvents in EPDM also were measured for finite concentration using gravimetric sorption for three of the solvents. From the inverse gas chromatography experimental values for self-diffusion coefficients were obtained. Free-volume parameters were obtained through regression of the self-diffusion coefficient as a function of temperature. Mutual diffusion coefficients as a function of concentration were predicted using free volume theory and compared with experimental data obtained using gravimetric sorption. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1713-1719, 1998
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    Carbon dioxide-poly(vinylidene fluoride) interactions at high pressure (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 2435-2447 
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    ISSN: 0887-6266
    Keywords: poly(vinylidene fluoride) ; carbon dioxide ; supercritical fluid ; diffusion ; partial molar volume ; solubility parameter ; mass sorption ; high pressure ; dilation ; Sanchez-Lacombe model ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The article reports on the behaviour of poly(vinylidene fluoride) in carbon dioxide at 42°C and 80°C and in a pressure range of 0.1-30 MPa. Experimental techniques for the measurement of gas mass uptake and polymer dilatation are described and the corresponding data are reported as mass sorption and dilatation isotherms, respectively. The mass uptake experiment was also used to follow the evolution of the coefficient of diffusion of carbon dioxide into the polymer as a function of pressure or concentration. An analysis for the calculation of the partial molar volume of carbon dioxide as a function of pressure is also given, which shows that the ‘apparent’ partial molar volume of the carbon dioxide decreases with pressure to very low values, at high pressure. The computed values are significantly less than those for either the liquid or the solid phases of pure carbon dioxide, and also lower than some data previously reported for silicone elastomers. A consideration of the origins of this apparent anomaly is given in the conclusions. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2435-2447, 1998
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    Observations on the dynamics of nonsolvent-induced phase inversion (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 569-585 
    Details
    ISSN: 0887-6266
    Keywords: phase inversion ; diffusion ; in situ dynamics ; membrane morphology ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The diffusion and gelation dynamics of nonsolvent-induced phase inversion in several polyethersulfone (PES)/solvent/nonsolvent systems are observed using a dark-ground optical technique. The observed dynamics are correlated with the resultant morphologies of the solidified gels obtained via scanning electron microscopy. In situ dynamic measurements show that rapid precipitations result in finger formation and delayed precipitations result in sponge formation. Rapid precipitations for some systems also exhibit an initial region of high, anomalous diffusion front motion which correlates well with the appearance of finger-like macrovoids in the film sublayer. Micrographs of both thin (200-300 μm) and thick (3 mm) films formed by liquid-liquid demixing clearly show that the overall morphologies scale with initial film thickness. However, as observed for the cellulose acetate (CA)/dimethylsulfoxide (DMSO)/H2O system, the possibility of crystallization can complicate the scaling analysis. A ternary diffusion model is also employed to describe the isothermal diffusion encountered during the formation of PES membranes. Binary thermodynamic and kinetic parameters needed for computations are determined from experimental data. Model results agree well with experimental observations. The model accurately predicts the transition from finger-to-sponge formation, as well as other observed trends in dynamics and morphology. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 569-585, 1997
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    Multicomponent diffusion of methyl ethyl ketone and toluene in polyisobutylene from vapor sorption FTIR-ATR spectroscopy (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 337-344 
    Details
    ISSN: 0887-6266
    Keywords: infrared spectroscopy ; multicomponent ; diffusion ; polymer ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: In this study, diffusion coefficients of toluene/methyl ethyl ketone (MEK) mixtures in polyisobutylene were measured at 50°C using vapor sorption FTIR-ATR (Fourier Transform Infrared Attenuated Total Reflectance) spectroscopy. For three mixture compositions, the diffusion coefficients were determined using a diffusion framework for ternary systems. The “crossterm” diffusion coefficient for MEK was found to be very small under the experimental conditions studied here, while that for toluene was found to increase with increasing MEK concentration. On the basis of this finding, a binary diffusion model was used to determine diffusion coefficients for MEK over a wide range of mixture compositions and the results compared well with those determined from pure MEK transport data. Relative transport rates during integral sorption experiments with mixtures were used to explain the results. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 337-344, 1998
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    Role and effect of dopant ion on sorption-induced motion of polypyrrole films (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 2635-2642 
    Details
    ISSN: 0887-6266
    Keywords: polypyrrole film ; bending ; strain ; sorption isotherm ; diffusion ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The sorption-induced bending and recovery motion of PPy films containing different dopant ions have been investigated, and the interaction between water vapor and PPy was studied from sorption isotherms and kinetics. It was found that the PPy/BF4 film exhibited the most rapid motion, and the initial speeds of bending and recovery motion were 7.9 and 5.9 mm s-1, respectively. The linear expansion coefficient of the film increased in order of PPy/DBS, PPy/TsO, PPy/ClO4, and PPy/BF4, which is consistent with the packing density of the PPy chains (φPPy). The dual-mode sorption model applied to the isothermal sorption of water vapor to the PPy demonstrated that the Langmuir's capacity constant increased in the same order with the φPPy, while the Henry's law constant was nearly constant. The sorption kinetics obeyed Fickian despite the dimensional change of the films, and the PPy/BF4 film had the largest diffusion coefficient of 3.13 × 10-8 cm2 s-1. The experimental results indicated that the kind of dopant ion was crucial to the thermodynamics and kinetics of sorption, and the quick and intensive bending motion of PPy/BF4 films was attributed to the fast diffusion of water vapor, which caused the large dimensional change of the film.© 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2635-2642, 1998
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