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  • 1
    Digitale Medien
    Digitale Medien
    Analysis of Diffusion in Hollow Geometries (2000)
    Springer
    Adsorption 6 (2000), S. 125-136 
    Details
    ISSN: 1572-8757
    Schlagwort(e): diffusion ; mathematical model ; analytical solution ; hollow material ; composite material ; mass transfer
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Physik , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008913301145
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  • 2
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): optimal control ; partial differential equations ; numerical methods ; transdermal systems ; acetylene reactors
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1019231718807
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  • 3
    Digitale Medien
    Digitale Medien
    The Optimal Control of a Train (2000)
    Springer
    Annals of operations research 98 (2000), S. 65-87 
    Details
    ISSN: 1572-9338
    Schlagwort(e): train control ; optimal control ; discrete control ; optimal switching times
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1019235819716
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  • 4
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): production planning ; stochastic dynamic programming ; optimal control ; long-run average cost
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1019272811055
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  • 5
    Digitale Medien
    Digitale Medien
    On Quantitative Stability in Optimization and Optimal Control (2000)
    Springer
    Set-valued analysis 8 (2000), S. 31-50 
    Details
    ISSN: 1572-932X
    Schlagwort(e): stability in optimization ; generalized equations ; Lipschitz continuity ; mathematical programming ; optimal control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008714222851
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  • 6
    Digitale Medien
    Digitale Medien
    Numerical Schemes for Discontinuous Value Functions of Optimal Control (2000)
    Springer
    Set-valued analysis 8 (2000), S. 111-126 
    Details
    ISSN: 1572-932X
    Schlagwort(e): viability ; optimal control ; value function
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008774508738
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  • 7
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): optimal control ; nonlinear systems ; parabolic systems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1019279617898
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  • 8
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): resonant orbit ; transversal intersection ; resonant jump ; diffusion ; instability
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008200806138
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  • 9
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): evolution triple ; optimal control ; monotone operator ; hemicontinuous operator ; parabolic system ; property (Q)
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022889404413
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  • 10
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): near-axis scattered light ; optical computed tomography ; time-resolved measurement ; scattering ; diffusion ; random media ; visibility ; photon migration ; computed tomography ; biomedical optics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s10043-000-0383-4
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  • 11
    Digitale Medien
    Digitale Medien
    The Rectangular Isotherm Model for Adsorption Kinetics (2000)
    Springer
    Adsorption 6 (2000), S. 287-291 
    Details
    ISSN: 1572-8757
    Schlagwort(e): diffusion ; shrinking core ; rectangular isotherm
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Physik , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1026504730443
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  • 12
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): wool ; water vapour ; adsorption ; diffusion ; column dynamics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Physik , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008839404382
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  • 13
    Digitale Medien
    Digitale Medien
    Film Model Approximation for Multicomponent Adsorption (2000)
    Springer
    Adsorption 6 (2000), S. 5-13 
    Details
    ISSN: 1572-8757
    Schlagwort(e): multicomponent adsorption ; diffusion ; Maxwell-Stefan model ; linear driving force approximation ; Langmuir isotherm
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Physik , Werkstoffwissenschaften, Fertigungsverfahren, Fertigung
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008927713530
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  • 14
    Digitale Medien
    Digitale Medien
    A Diffusion Equation from the Relativistic Ornstein–Uhlenbeck Process (1998)
    Springer
    Journal of statistical physics 90 (1998), S. 1179-1199 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Irreversibility ; relativistic Ornstein–Uhlenbeck process ; relativistic statistical physics ; diffusion
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1023275210656
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  • 15
    Digitale Medien
    Digitale Medien
    Effective Potential for the Reaction-Diffusion-Decay System (2000)
    Springer
    Journal of statistical physics 99 (2000), S. 903-941 
    Details
    ISSN: 1572-9613
    Schlagwort(e): effective potential ; reaction ; diffusion ; decay
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1018699630306
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  • 16
    Digitale Medien
    Digitale Medien
    Dynamic Light Scattering Measurement of Nanometer Particles in Liquids (2000)
    Springer
    Journal of nanoparticle research 2 (2000), S. 123-131 
    Details
    ISSN: 1572-896X
    Schlagwort(e): nanoparticle ; characterization ; light scattering ; PCS ; interferometry ; diffusion ; polydispersivity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik , Technik allgemein
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1010067107182
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  • 17
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Key words: Competition ; Edge effects ; Reaction ; diffusion ; Lotka ; Volterra ; Ecological reserves
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002850050139
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  • 18
    Digitale Medien
    Digitale Medien
    The evolution of slow dispersal rates: a reaction diffusion model (1998)
    Springer
    Journal of mathematical biology 37 (1998), S. 61-83 
    Details
    ISSN: 1432-1416
    Schlagwort(e): Key words: Evolution of dispersal ; Migration modification ; Reaction ; diffusion ; Montone systems ; Perturbation of Morse decomposition
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/s002850050120
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  • 19
    Digitale Medien
    Digitale Medien
    Simulation of electrochemical behavior of partially blocked electrodes under linear potential sweep conditions (2000)
    Springer
    Journal of mathematical chemistry 27 (2000), S. 267-278 
    Details
    ISSN: 1572-8897
    Schlagwort(e): partially blocked electrodes ; modelling ; diffusion
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1018867621310
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  • 20
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1573-2754
    Schlagwort(e): products pipeline ; batching transport ; contamination ; convection ; diffusion ; numerical computation ; turbulent flow
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Mathematik , Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02457750
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  • 21
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1573-7594
    Schlagwort(e): scheduling ; optimal control ; time-decomposition methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008345132480
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  • 22
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    Digitale Medien
    Modeling, Analysis, and Optimal Control of a Class of Hybrid Systems (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 175-201 
    Details
    ISSN: 1573-7594
    Schlagwort(e): hybrid systems ; optimal control ; calculus of variations ; manufacturing systems ; queueing systems ; nonsmooth optimization ; two point boundary value problems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008237701804
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  • 23
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    Digitale Medien
    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 
    Details
    ISSN: 1573-7594
    Schlagwort(e): Production planning ; stochastic dynamic programming ; vanishing discount approach ; optimal control ; long-run average cost
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008256409920
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  • 24
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    Digitale Medien
    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 
    Details
    ISSN: 1573-1634
    Schlagwort(e): NAPL ; multiphase ; fractal ; soil ; diffusion ; transport ; heterogeneous porous medium
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Technik allgemein
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1006554303400
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  • 25
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    Digitale Medien
    Fluxes of methane and carbon dioxide from a small productive lake to the atmosphere (2000)
    Springer
    Biogeochemistry 49 (2000), S. 1-19 
    Details
    ISSN: 1573-515X
    Schlagwort(e): carbon dioxide ; diffusion ; ebullition ; emission ; freshwater ; hypertrophic lakes ; methane
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Geologie und Paläontologie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1006269900174
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  • 26
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    Digitale Medien
    Automaton Simulations of Dispersion in Porous Media (1998)
    Springer
    Transport in porous media 32 (1998), S. 187-198 
    Details
    ISSN: 1573-1634
    Schlagwort(e): diffusion ; dispersion ; miscible ; automaton
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Technik allgemein
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1006566117582
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  • 27
    Digitale Medien
    Digitale Medien
    Cosmic-Ray Transport Coefficients (1998)
    Springer
    Space science reviews 83 (1998), S. 351-363 
    Details
    ISSN: 1572-9672
    Schlagwort(e): cosmic rays ; charged-particle transport ; diffusion
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1005087326666
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  • 28
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    Digitale Medien
    Microscopic Chaos and Diffusion (2000)
    Springer
    Journal of statistical physics 101 (2000), S. 775-817 
    Details
    ISSN: 1572-9613
    Schlagwort(e): chaos ; diffusion ; Ehrenfest wind-tree model ; Lorentz gas ; statistical mechanics ; periodic orbits ; Brownian motion ; billiards ; time series analysis
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1026477605331
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  • 29
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    Digitale Medien
    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 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Random sequential adsorption ; hard-sphere particles ; gravity ; diffusion ; coverage ; structure
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1023040509781
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  • 30
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    Digitale Medien
    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 
    Details
    ISSN: 1572-9613
    Schlagwort(e): Boltzmann equation ; semiconductor ; diffusion ; energy transport model ; entropy dissipation rate
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1018635827617
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  • 31
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    Digitale Medien
    Transient Chaos and Critical States in Generalized Baker Maps (2000)
    Springer
    Journal of statistical physics 101 (2000), S. 107-124 
    Details
    ISSN: 1572-9613
    Schlagwort(e): transient chaos ; conditionally invariant measures ; natural measures ; critical state ; diffusion
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1026459432086
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  • 32
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    Digitale Medien
    Nonequilibrium Phase Transition in a Model of Diffusion, Aggregation, and Fragmentation (2000)
    Springer
    Journal of statistical physics 99 (2000), S. 1-29 
    Details
    ISSN: 1572-9613
    Schlagwort(e): diffusion ; aggregation ; phase transition ; nonequilibrium
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1018632005018
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  • 33
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    Digitale Medien
    Prediction of Fluid Mixture Transport Properties by Molecular Dynamics (1998)
    Springer
    International journal of thermophysics 19 (1998), S. 437-448 
    Details
    ISSN: 1572-9567
    Schlagwort(e): alkanes ; carbon dioxide ; diffusion ; mixtures ; molecular dynamics ; thermal conductivity ; viscosity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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%.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022513411043
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  • 34
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1572-9567
    Schlagwort(e): acoustic waves ; convection ; diffusion ; heat transfer ; near-critical fluid ; piston effect
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022602128559
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  • 35
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1572-9567
    Schlagwort(e): diffusion ; intermolecular potentials ; Raman and Rayleigh spectra ; second virial coefficients ; tetramethylmethane ; tetramethylsilane ; transport properties ; viscosity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1006706510540
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  • 36
    Digitale Medien
    Digitale Medien
    Maximum Principle for a Control Problem Governed by an Evolution Equation (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 263-276 
    Details
    ISSN: 1573-2878
    Schlagwort(e): optimal control ; distributed-parameter systems ; Pontryagin maximum principle ; Ekeland variational principle ; unbounded controls
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004654800011
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  • 37
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1573-2878
    Schlagwort(e): hierarchical control ; manufacturing systems ; stochastic dynamic programming ; optimal control ; long-run average cost
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004667028547
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  • 38
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 1573-2878
    Schlagwort(e): variational inequalities ; optimal control ; state constraint ; maximum principle
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004613630675
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  • 39
    Digitale Medien
    Digitale Medien
    Instabilities in Concave, Dynamic, Economic Optimization (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 275-286 
    Details
    ISSN: 1573-2878
    Schlagwort(e): optimal control ; thresholds ; multiple equilibria ; instability ; concavity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1026408814862
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  • 40
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    Digitale Medien
    Approximate Solutions to the Time-Invariant Hamilton–Jacobi–Bellman Equation (1998)
    Springer
    Journal of optimization theory and applications 96 (1998), S. 589-626 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Nonlinear control ; optimal control ; Hamilton–Jacobi–Bellman equation ; feedback synthesis ; successive approximation ; Galerkin approximation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022664528457
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  • 41
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    Digitale Medien
    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 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Robust stabilization ; optimal control ; time-delay systems ; Razumikhin-type approach
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022645116123
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  • 42
    Digitale Medien
    Digitale Medien
    Based on wavelet analysis to optimal control of motion planning of space manipulator (2000)
    Springer
    Applied mathematics and mechanics 21 (2000), S. 1161-1168 
    Details
    ISSN: 1573-2754
    Schlagwort(e): space manipulator ; motion planning ; optimal control ; wavelet analysis ; TP241
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Maschinenbau , Mathematik , Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02458994
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  • 43
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    Digitale Medien
    Investigations of grain boundaries in copper using emission Mössbauer spectroscopy (2000)
    Springer
    Hyperfine interactions 126 (2000), S. 215-218 
    Details
    ISSN: 1572-9540
    Schlagwort(e): emission Mössbauer spectroscopy ; grain boundary ; diffusion ; copper ; 57Co
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1012611006412
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  • 44
    Digitale Medien
    Digitale Medien
    Implantation and diffusion of 73As in GaAs and GaP (2000)
    Springer
    Hyperfine interactions 129 (2000), S. 337-347 
    Details
    ISSN: 1572-9540
    Schlagwort(e): diffusion ; 73As ; GaAs ; GaP ; computer simulation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1012641212173
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  • 45
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    Digitale Medien
    Optimization of Bilinear Systems Using a Higher-Order Variational Method (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 55-72 
    Details
    ISSN: 1573-2878
    Schlagwort(e): optimal control ; bilinear systems ; nilpotent Lie algebra ; products of exponentials
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004609911204
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  • 46
    Digitale Medien
    Digitale Medien
    Optimal Expenditure Patterns of a Double-Path Engineering Project (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 441-455 
    Details
    ISSN: 1573-2878
    Schlagwort(e): expenditure patterns ; research and development ; optimal control ; calculus of variations
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004670120484
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  • 47
    Digitale Medien
    Digitale Medien
    Universal Near-Optimal Feedbacks (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 89-122 
    Details
    ISSN: 1573-2878
    Schlagwort(e): optimal control ; differential games ; Euler polygonal arcs ; nonsmooth analysis ; proximal aiming ; infinitesimal decrease ; discontinuous universal near-optimal feedback
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004608800846
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  • 48
    Digitale Medien
    Digitale Medien
    Optimal Control of Rigid Body Angular Velocity with Quadratic Cost (1998)
    Springer
    Journal of optimization theory and applications 96 (1998), S. 507-532 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Rigid bodies ; Hamilton–Jacobi equation ; Riccati equation ; optimal control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022656326640
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  • 49
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    Digitale Medien
    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 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; nonlinear dynamic systems ; transformations ; optimal control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022666831628
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  • 50
    Digitale Medien
    Digitale Medien
    Optimal Control of a Stochastic Assembly Production Line (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 681-700 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Manufacturing systems ; bang–bang control ; dynamic programming ; optimal control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022632231356
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  • 51
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    Digitale Medien
    Finite-Time Optimal Control of Polynomial Systems Using Successive Suboptimal Approximations (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 477-489 
    Details
    ISSN: 1573-2878
    Schlagwort(e): optimal control ; polynomial systems ; quasilinearization ; successive approximation ; convergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004674221393
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  • 52
    Digitale Medien
    Digitale Medien
    Stochastic Games for N Players (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 543-565 
    Details
    ISSN: 1573-2878
    Schlagwort(e): stochastic games ; dynamic programming ; optimal control ; regularity theory ; Nash point
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004637022496
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  • 53
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    Digitale Medien
    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 
    Details
    ISSN: 1573-2878
    Schlagwort(e): optimal control ; state constraints ; dynamic programming ; Hamilton-Jacobi equation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004668504089
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  • 54
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    Digitale Medien
    Optimal Control Problem for the Lyapunov Exponents of Random Matrix Products (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 347-369 
    Details
    ISSN: 1573-2878
    Schlagwort(e): random matrix products ; Lyapunov exponents ; Markov processes ; decision models ; optimal policy ; optimal control ; system spectrum
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004661918667
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  • 55
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    Digitale Medien
    Bilinear Control and Application to Flexible a.c. Transmission Systems (2000)
    Springer
    Journal of optimization theory and applications 105 (2000), S. 621-637 
    Details
    ISSN: 1573-2878
    Schlagwort(e): bilinear systems ; optimal control ; controllability ; stabilization ; electric power
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1004645224313
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  • 56
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): Nonlinear ship steering dynamics ; optimal control ; saturation ; slew rate limitation ; sequential gradient-restoration algorithm
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1022674516570
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  • 57
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    Digitale Medien
    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
    Schlagwort(e): optimal control ; cell mapping method ; dynamic programing ; parametric control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008375230648
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  • 58
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    Digitale Medien
    Grain Boundary Migration in Solid State Discontinuous Reactions (1998)
    Springer
    Interface science 6 (1998), S. 113-131 
    Details
    ISSN: 1573-2746
    Schlagwort(e): discontinuous reactions ; discontinuous precipitation ; discontinuous coarsening ; discontinuous dissolution ; grain boundary ; migration ; diffusion ; kinetics ; mechanism
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008672705642
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  • 59
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    Digitale Medien
    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
    Schlagwort(e): grain boundary energy ; diffusion ; segregation ; solid/liquid interface ; wetting
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008636600201
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  • 60
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    Digitale Medien
    The Kinetics of the Cd21Ni5 Intermetallic Growth under High Hydrostatic Pressure (2000)
    Springer
    Interface science 8 (2000), S. 77-84 
    Details
    ISSN: 1573-2746
    Schlagwort(e): intermetallic growth ; interfacial reaction ; diffusion ; high hydrostatic pressure ; activation volume
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie , Maschinenbau , Physik
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1023/A:1008739521785
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  • 61
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    Digitale Medien
    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
    Schlagwort(e): sorption ; diffusion ; acetone ; poly(ethylene terephthalate) ; poly(ethylene 2,6-naphthalate) ; copolymers ; positron annihilation lifetime spectroscopy ; infrared spectroscopy ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 14 Ill.
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  • 62
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): diffusion ; block copolymer ; monomeric friction factor ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
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  • 63
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 0887-6266
    Schlagwort(e): calorimetry ; dielectrics ; diffusion ; monoamine-triepoxide ; thermoset ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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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  • 64
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): surface ; interfaces ; diffusion ; polystyrene ; polyphenylene oxide ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 4 Ill.
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  • 65
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): 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
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 6 Ill.
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  • 66
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): drying ; semicrystalline polymers ; poly(vinyl alcohol) ; solvent removal ; modeling ; diffusion ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 13 Ill.
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  • 67
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 0887-6266
    Schlagwort(e): starch ; mechanical properties ; percolation ; clustering ; diffusion ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 15 Ill.
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  • 68
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 0887-6266
    Schlagwort(e): sorption ; dilation ; diffusion ; conditioning effect ; glassy polymer ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 8 Ill.
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  • 69
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): polymer ; diffusion ; free-volume theory ; inverse gas chromatography ; gravimetric sorption ; ethylene-propylene-diene ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 7 Ill.
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  • 70
    Digitale Medien
    Digitale Medien
    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 
    Details
    ISSN: 0887-6266
    Schlagwort(e): 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
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 10 Ill.
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  • 71
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): infrared spectroscopy ; multicomponent ; diffusion ; polymer ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 5 Ill.
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  • 72
    Digitale Medien
    Digitale Medien
    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
    Schlagwort(e): polypyrrole film ; bending ; strain ; sorption isotherm ; diffusion ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: 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
    Zusätzliches Material: 7 Ill.
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  • 73
    Digitale Medien
    Digitale Medien
    Theoretical study of sorption-induced bending of polypyrrole films (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 2237-2246 
    Details
    ISSN: 0887-6266
    Schlagwort(e): polypyrrole film ; bending ; water vapor sorption ; diffusion ; anisotropic expansion ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: Polypyrrole films containing perchlorate were electrochemically synthesized and the bending and recovery motion of the films obtained has been investigated. It was found that the thickness of the film and ambient relative humidity (RH) were crucial to the motion of film: An increase of the film thickness decreased the displacement of the bending but increased the bending stress. On the other hand, an increase of the ambient RH decreased both functions. The motion of film was caused by the difference of expansion on both sides of the film owing to anisotropic sorption of water vapor, which could be expressed by the diffusion-limited bending model. The diffusion coefficients calculated from the bending and recovery motion at 25°C, RH 50% were 12.2 × 10-8 cm2 s-1 and 3.5 × 10-8 cm2 s-1, respectively. The maximum expansion of the film surface calculated from the bending curve was about 0.36%. © 1998 John Wiley & Sons, Inc. J. Polym. Sci. B Polym. Phys. 36: 2237-2246, 1998
    Zusätzliches Material: 10 Ill.
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  • 74
    Digitale Medien
    Digitale Medien
    Crystallization-induced composition inhomogeneities in PVDF/PMMA blends (1998)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 36 (1998), S. 2923-2930 
    Details
    ISSN: 0887-6266
    Schlagwort(e): polymer blends ; crystallization ; diffusion ; composition inhomogeneities ; internal spherulite structure ; Physics ; Polymer and Materials Science
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Physik
    Notizen: Composition profiles develop around growing PVDF spherulites in a blend with PMMA. These profiles assume stationary courses after a certain crystallization time provided that the overall degree of crystallinity is not too high. The composition-dependent growth rate and the diffusion-controlled remove of the surplus PMMA from the spherulite surface are then in a stationary equilibrium. The internal structure of the spherulites will then be homogeneous, too. Upon isothermal crystallization of a PVDF/PMMA = 60/40 (wt %) blend at 160°C for at least 4 h, the spherulites internal degree of crystallinity xc as related to the PVDF fraction obeys the inequality 55 wt % ≤ xc ≤ 84 wt %. The overall PMMA content within the spherulites as averaged over its whole inside has been determined by IR microscopy. It amounts to about 15 wt %. In contrast, the PMMA content of the amorphous phase within the spherulites (averaged again over its whole inside) ranges between 28 and 52 wt %. This composition jumps at the spherulite surface to 52 wt %. From the slope of the composition profiles outside the spherulites that have a width of more than 50 μm, the effective chain diffusion coefficient in blends as averaged over both components can be calculated to amount to (250 ± 100) μm2h-1. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2923-2930, 1998
    Zusätzliches Material: 6 Ill.
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  • 75
    Digitale Medien
    Digitale Medien
    Solving boundary-value problems using hp-version finite elements in time (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 425-440 
    Details
    ISSN: 0029-5981
    Schlagwort(e): numerical methods ; time-marching ; dynamics ; optimal control ; boundary-value problems ; Engineering ; Numerical Methods and Modeling
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: An hp-version finite element method for one-dimensional boundary value problems is presented. The method is based on a similar approach developed by the authors for solution of optimal control problems. The primary applications for the methodology include two-point- and multi-point-boundary-value problems, for example, in the time domain. Results presented for a 7-state/3-phase missile problem show that the method is very efficient for time-marching applications. Furthermore, it easily solves time-domain problems with discontinuities in the system equations and/or in the states, where the time at which these jumps (i.e. ‘events’) take place is determined by equations that govern the states. An example involving friction with intermittent sticking is presented to illustrate the power of the method. © 1998 John Wiley & Sons, Ltd.
    Zusätzliches Material: 9 Ill.
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  • 76
    Digitale Medien
    Digitale Medien
    Contaminant transport under variable density flow in fractured porous media (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    International Journal for Numerical and Analytical Methods in Geomechanics 22 (1998), S. 575-595 
    Details
    ISSN: 0363-9061
    Schlagwort(e): contaminant transport ; variable density flow ; fractures ; leakage ; dispersion ; diffusion ; Engineering ; Civil and Mechanical Engineering
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Geologie und Paläontologie
    Notizen: A numerical model for simulating flow and transport of contaminants with variable density in fractured porous media is presented. The non-linearities arising from the density variation and the velocty-dependent dispersion terms have been handled by Picard method. It is shown that the contaminant transport in a fractured porous medium is initially dominated by fractures. However, with time increasing, the contaminant concentration in porous blocks increases, due to the leakage of contaminant from the fracture network to the porous blocks. It is also shown that the high density of contaminant has a greater effect on its transport in the fracture network than in the porous blocks. © 1998 John Wiley & Sons, Ltd.
    Zusätzliches Material: 12 Ill.
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