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  • Springer  (123)
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Year
  • 1
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    Stochastic environmental research and risk assessment 11 (1997), S. 397-422 
    ISSN: 1436-3259
    Keywords: Random flow field ; diffusion ; concentration ; fluctuations ; covariance ; variance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The concentration c(x,t) of a nonreactive solute undergoing advection and diffusion in a spatially random divergence-free flow field is analyzed. A leading order formulation for the spatial covariance of the concentration field, $$\overline {c'\left( {x,t} \right)c'\left( {x,t} \right)} $$ , is made. That formulation includes the velocity variability induced macrodispersive flux of the covariance field, and the smoothing effects of diffusion. Previous formulations of the concentration covariance had dropped at least one of these effects. It is shown that both these effects need to be included to obtain a qualitatively correct description of the concentration fluctuations.
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  • 2
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    Adsorption 2 (1996), S. 77-87 
    ISSN: 1572-8757
    Keywords: diffusion ; molecular-dynamics simulation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract In this paper, we review our recent theoretical and simulation studies of the surface diffusion of n-alkanes, ranging in size from ethane to hexadecane, physically adsorbed on Pt(111). The model system exhibits many features seen experimentally. Through both animation of the molecular trajectories and determination of the minimum-energy path for nearest-neighbor hopping, we find that the shorter molecules (ethane through octane) all have similar diffusion mechanisms, involving coupled translation and rigid rod-like rotation in the surface plane. In addition, the diffusion energy barriers for these molecules increase nearly linearly with chain length in both the static and dynamic calculations. The diffusion of decane and hexadecane does not adhere to the trends for the shorter molecules and a decrease can be observed in the dynamical diffusion energies for these molecules. The diffusion of the longer molecules involves hops, with unique mechanisms, to second and third neighbor sites. Our static analysis has indicated, for decane, that the diffusion-energy barrier for third-neighbor hopping is lower than that for nearest-neighbor hopping and is in agreement with the trend seen in the dynamical diffusion barriers. Even though there is agreement between theoretical and simulated diffusion energy barriers for many of the molecules, the motion observed in the MD simulations does not agree with the assumptions of the hopping model. A model that can incorporate the influence of long flights would provide a more realistic description of the motion.
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  • 3
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    Adsorption 2 (1996), S. 95-101 
    ISSN: 1572-8757
    Keywords: osmosis ; reverse osmosis ; adsorption ; diffusion ; molecular dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract Computer simulation studies using the method of molecular dynamics have been carried out to investigate osmosis and reverse osmosis in solutions separated by semi-permeable membranes. The method has been used to study the dynamic approach to equilibrium in such systems from their initial nonequilibrium state. In addition density profiles of both the solute and solvent molecules have been investigated, especially near the walls for adsorption effects. Finally the diffusion coefficients and osmotic pressure have also been measured. Our results show both osmosis and reverse osmosis, as well as a smooth transition between the two when either the solution concentration is changed, or the density (pressure) difference between the solvent and solution compartments is varied. We believe this new method can be used to improve our understanding of these two important phenomena at the molecular level.
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  • 4
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    Adsorption 2 (1996), S. 133-143 
    ISSN: 1572-8757
    Keywords: diffusion ; sorption kinetics ; ZLC
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The theoretical model and underlying assumptions used in the analysis of ZLC (zero length column) desorption curves are examined in detail. It is shown that the long time analysis generally yields reliable diffusivity values although, if the initial equilibrium condition is not properly established there will be significant error in the apparent equilibrium constant. The short time analysis is much more sensitive to such errors and a modified way of data analysis is suggested to overcome this problem. Varying the initial equilibration time provides an alternative ZLC experiment that can be used to establish the nature of the rate controlling mass transfer resistance. The utility of this approach is illustrated experimentally for the system C3H8-13X zeolite.
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  • 5
    ISSN: 1572-8757
    Keywords: diffusion ; kinetic measurements ; NaX zeolite ; water
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The thermal frequency response and pulsed field gradient NMR methods are applied in a comparative study of water diffusion in zeolite NaX under non-equilibrium and equilibrium conditions. The obtained results are found to be in satisfactory agreement with each other, indicating that by applying the thermal frequency response method, complications due to uncontrolled water adsorption at the chamber walls inherent in conventional frequency response measurements may be circumvented.
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  • 6
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    Adsorption 2 (1996), S. 265-277 
    ISSN: 1572-8757
    Keywords: frequency response ; diffusion cell ; kinetics ; diffusion ; heat effects
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract This paper deals with frequency response (FR) analysis of a closed diffusion cell system with two resonators, that is both the LHS and RHS volumes are modulated. The analysis is made for a homogeneous particle described by a single effective diffusivity as well as a biporous pellet described by macropore and micropore diffusions. It is shown that if the perturbation of the volume of the reservoir #2 is lagged behind that of the reservoir #1 by 3π/2, the pressure response in reservoir #1 is significantly enhanced with larger amplitude as well as phase angle. When the perturbations of the two reservoirs are out of phase, the heat effect is reduced and can become insignificant when the two perturbations are completely out of phase (ψ = π). Under such a condition, the pressure difference between the two reservoirs could be doubled. In the case of biporous pellets, it is shown that the FR behaviours obtained for micropore diffusion control and macropore diffusion control are well distinguished. In the former case, the FR system reduces to a traditional batch adsorber one while in the latter case, the FR behaviour is the same as for a two resonator system with homogeneous particles. This difference can be used for the discrimination of micropore and macropore diffusion processes.
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  • 7
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    Adsorption 6 (2000), S. 125-136 
    ISSN: 1572-8757
    Keywords: diffusion ; mathematical model ; analytical solution ; hollow material ; composite material ; mass transfer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The diffusion in hollow particles of solid adsorbent materials was analyzed based on analytical solutions to the basic diffusion equation. Three geometric shapes (plane sheet, cylinder, and sphere) of sorbent material were considered for two kinds of boundary conditions. The equations for determining the equivalent sizes compared to their corresponding solid particles were obtained directly from the theoretical expressions of sorption uptake curves. Among the three hollow particles of impermeable inner surface, the sphere gives the highest gain in effective diffusion rate compared to the corresponding solid particle. For permeable inner surface, at lower hollow volume fractions, the plane sheet shows the highest gain, while at higher hollow volume fractions, the sphere shows the highest gain in effective diffusion rate.
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  • 8
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    Celestial mechanics and dynamical astronomy 73 (1999), S. 65-76 
    ISSN: 1572-9478
    Keywords: resonance ; chaotic motion ; diffusion ; secondary resonances
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a 3-D symplectic mapping model that is valid at the 2:1 mean motion resonance in the asteroid motion, in the Sun-Jupiter-asteroid model. This model is used to study the dynamics inside this resonance and several features of the system have been made clear. The introduction of the third dimension, through the inclination of the asteroid orbit, plays an important role in the evolution of the asteroid and the appearance of chaotic motion. Also, the existence of the secondary resonances is clearly shown and their role in the appearance of chaotic motion and the slow diffusion of the elements of the orbit is demonstrated.
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  • 9
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    Celestial mechanics and dynamical astronomy 64 (1996), S. 21-31 
    ISSN: 1572-9478
    Keywords: KAM tori ; diffusion ; symplectic maps ; standard map
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Using mappings as model problem we study the structure around the last invariant KAM torus for different values of the perturbing parameter. We used the standard map for the analysis of the hierarchical structure existing around invariant KAM tori applying two complementary methods: the Laskar's frequency map analysis and the sup-map analysis. We recover and extend the theoretical prediction recently given by Morbidelli and Giorgilli about the existence of a neighborhood almost completely full of slave tori around a chief torus. We then make tests about the diffusion in order to measure the barrier to diffusion which still remains after the break-up of the last KAM torus.
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  • 10
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    Celestial mechanics and dynamical astronomy 54 (1992), S. 91-110 
    ISSN: 1572-9478
    Keywords: Resonance ; libration ; chaos ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The methods for an investigation of the evolution of orbits with large eccentricities are presented. The role of resonances in the motion of comets is considered. The expansion of the disturbing function in the restricted three-body problem is obtained for cometary orbits. The method is based on the proximity of cometary eccentricities to 1. The Hamiltonian describing the basic perturbations in the motion of long-period comets is constructed. It leads to mappings for the description of cometary dynamics. The long-term evolution of short-period comets is considered. The importance of temporary librations near commensurabilities with Jupiter is emphasized. The analytical dependence of the diffusion rate upon the orbital elements of nearly-parabolic comets is found. The results of calculations of the diffusion rate taking into account perturbations from the outer planets are presented. A numerical study of cometary dynamics using mappings is carried out. A distribution like the Oort cloud is a typical stage of the evolution of comets in nearly-parabolic orbits under planetary perturbations. A change of the partial density of meteor streams is studied. For the case of librations the dispersion speed of meteor streams under the action of planetary perturbations is substantially less than that for the case of typical chaos. A similarity between the observed structure of the meteor streams and resonant properties of the motion is discussed.
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  • 11
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    Celestial mechanics and dynamical astronomy 70 (1998), S. 23-39 
    ISSN: 1572-9478
    Keywords: resonant orbit ; transversal intersection ; resonant jump ; diffusion ; instability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The importance of the stability characteristics of the planar elliptic restricted three-body problem is that they offer insight about the general dynamical mechanisms causing instability in celestial mechanics. To analyze these concerns, elliptic–elliptic and hyperbolic–elliptic resonance orbits (periodic solutions with lower period) are numerically discovered by use of Newton's differential correction method. We find indications of stability for the elliptic–elliptic resonance orbits because slightly perturbed orbits define a corresponding two-dimensional invariant manifold on the Poincaré surface-section. For the resonance orbit of the hyperbolic–elliptic type, we show numerically that its stable and unstable manifolds intersect transversally in phase-space to induce instability. Then, we find indications that there are orbits which jump from one resonance zone to the next before escaping to infinity. This phenomenon is related to the so-called Arnold diffusion.
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  • 12
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    Optical review 7 (2000), S. 383-388 
    ISSN: 1349-9432
    Keywords: near-axis scattered light ; optical computed tomography ; time-resolved measurement ; scattering ; diffusion ; random media ; visibility ; photon migration ; computed tomography ; biomedical optics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract To find a basic principle of optical computed tomography (optical CT), a fundamental study was conducted on the use of scattered light in diffuse random media. We call the scattered light that propagates along the optical axis of the incident light beam near-axis scattered light (NASL). The use of NASL for the imaging through a diffuse medium was proposed and its basic characteristics were analyzed. The existence and measurability of NASL were confirmed in the simulation and measurement. To detect NASL efficiently, a technique called the scattering angle differential technique was developed. In CT imaging with a model phantom, the feasibility and effectiveness of the proposed technique were verified. We found that this technique alone was not sufficient to obtain the cross sectional image of an animal body, therefore a technique called the contact technique was devised to overcome the problems of reflection and refraction at the air-tissue interface. Finally, a prototype system was developed which integrated all the proposed techniques. With this system, we could obtain the CT images of a living mouse, in which the blood-rich organs such as liver and kidneys were clearly recognizable.
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  • 13
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    Adsorption 6 (2000), S. 287-291 
    ISSN: 1572-8757
    Keywords: diffusion ; shrinking core ; rectangular isotherm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract The transient uptake response of an adsorbent particle, subjected to a step change in surface concentration, is considered. It is shown that, when the isotherm is highly favorable, the theoretical curves derived for a Langmuirian system reduce asymptotically to the much simpler form for a rectangular isotherm. The simple rectangular model provides a useful approximation even when the form of the actual isotherm is quite far from the rectangular limit.
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  • 14
    ISSN: 1572-8757
    Keywords: wool ; water vapour ; adsorption ; diffusion ; column dynamics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract Adsorption of water vapour on wool provides not only textile comfort, but also convenience in transportation due to increase in its bulk density. The adsorption and desorption isotherms of water vapour for wool were determined by both volumetric technique using a Coulter Omnisorp 100CX instrument and gravimetric method employing a Cahn 2000 electronic microbalance. Adsorption isotherm fitting to B.E.T. model and hysteresis on desorption was observed. The average effective diffusion coefficient of water in wool was found to be 8.4 × 10-14 m2s-1 at 25°C from gravimetric data. The effects of packing height and air velocity on the breakthrough curves were also investigated in the wool packed columns. For pseudo first order model, k values changing between 0.33 × 10-6 − 69 × 10-6 s-1 was obtained for 2.2–6.4 cm s-1 air velocity and 0.05–0.20 m packing height ranges.
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  • 15
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    Adsorption 5 (1999), S. 135-143 
    ISSN: 1572-8757
    Keywords: diffusion ; kinetics measurements ; frequency response ; NaX zeolite ; silicalite
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract A Frequency Response Method based on the infrared measurement of the sample temperature has been developed for adsorption kinetics measurements. It consists in modulating the experimental chamber volume at constant frequency. The complex ratio of the temperature response over the pressure response is independent of time but is a function of the frequency depending on all the kinetics parameters of the system. This method is accurate and allows to measure very fast kinetics. Its major drawback is that a spurious signal is observed at high pressure in absence of adsorption. The results obtained with silicalite-propane and NaX-carbon dioxide are compared with results obtained from other techniques (NMR, permeation, etc.).
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  • 16
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    Adsorption 6 (2000), S. 5-13 
    ISSN: 1572-8757
    Keywords: multicomponent adsorption ; diffusion ; Maxwell-Stefan model ; linear driving force approximation ; Langmuir isotherm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Abstract An approximate rate equation based on a film-model representation of diffusional mass transfer is developed to describe the kinetics of multicomponent adsorption. The model describes mass transfer as a pseudo-steady state diffusion process through a flat film of thickness equal to one fifth of the particle radius. Starting with an irreversible thermodynamics description of multicomponent diffusion, the flux relationships are integrated across the film yielding analytical expressions for the rate of mass transfer in a multicomponent adsorption system, when adsorption equilibria are described by the extended Langmuir isotherm. The new approximate rate equation can be conveniently used in the numerical simulation of adsorption systems with concentration-dependent micropore or surface diffusivity, and describes the effects of diffusional flux coupling. Results of accuracy comparable with that obtained when using the classical linear-driving-force approximation for systems with constant diffusivities are obtained with this new rate equation for both batch and fixed-bed adsorption calculations. A generalization of the approach based on the Gibbs adsorption isotherm describes mass transfer rates in terms of the spreading-pressure gradient and provides an extension to other multicomponent isotherm forms.
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  • 17
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    The journal of supercomputing 12 (1998), S. 57-68 
    ISSN: 1573-0484
    Keywords: load balancing ; ray tracing ; rendering ; graphics ; image processing ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper examines the effectiveness of load balancing strategies for ray tracing on large parallel computer systems and cluster computers. Popular static load balancing strategies are shown to be inadequate for rendering complex images with contemporary ray tracing algorithms, and for rendering NTSC resolution images on 128 or more computers. Strategies based on image tiling are shown to be ineffective except on very small numbers of computers. A dynamic load balancing strategy, based on a diffusion model, is applied to a parallel Monte Carlo rendering system. The diffusive strategy is shown to remedy the defects of the static strategies. A hybrid strategy that combines static and dynamic approaches produces nearly optimal performance on a variety of images and computer systems. The theoretical results should be relevant to other rendering and image processing applications.
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  • 18
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    Journal of paleolimnology 22 (1999), S. 227-251 
    ISSN: 1573-0417
    Keywords: diagenesis ; models ; metals ; porewater ; diffusion ; bioturbation ; irrigation ; remobilization ; iron ; manganese ; concretions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Geosciences
    Notes: Abstract This review aims to distill and synthesize the existing information on the use of models to describe and predict the distribution and movement of metals in lacustrine sediments. As such it examines the causes of metal diagenesis, the origin and form of the equations that govern these phenomena, and the predictability or measurability of the parameters that appear in the models. The paper concludes by highlighting some seminal results from modelling studies, including the determination of the factors controlling the formation of surficial Mn-Fe-enriched zone or layers, the substantial contribution possible from metal reduction to organic matter regeneration, the calculation of mixing-corrected metal input histories to lakes, and the prediction of growth rates and morphologies for both deep-sea and lacustrine ferromanganese nodules.
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  • 19
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    Surveys in geophysics 16 (1995), S. 695-710 
    ISSN: 1573-0956
    Keywords: Blowing snow ; airborne particles ; saltation ; diffusion ; image processing ; concentration profile ; fall velocity ; threshold friction velocity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Snow drift transport may cause avalanches on the roads during the periods of snowfall and strong wind. To better understand the factors influencing transport we have developed a theoretical model. This model is based on the boundary layer theory, where the particle mass conservation is considered. Assuming that the saturation is reached, the concentration profile can be represented by a negative exponential law. By means of this analysis, the influence of particle characteristics is explored through the roles of threshold friction velocity and fall velocity. Using fluid mechanics laws, an analysis of the concentration profile resulting from the effect of the wind on a particle bed was also developed. For several velocities of flow and for different kinds of particles an experimental determination of the concentration profile was achieved. We used a laser visualisation and image processing technique to carry out these experiments. The obtained results fit with the values predicted by the theoretical model.
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  • 20
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    Surveys in geophysics 20 (1999), S. 1-31 
    ISSN: 1573-0956
    Keywords: heterogeneous atmospheric chemistry ; chemistry ; Henry′s law ; accommodation coefficient ; cloud droplet ; aerosol particle ; solubility ; volatility ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract For detailed modeling of atmospheric chemistry it is necessary to consider aqueous-phase reactions in cloud droplets and deliquesced aerosol particles. Often, the gas-phase concentration is in equilibrium with the aqueous phase. Then Henry′s law can be used to describe the distribution between the phases provided that the Henry′s law coefficient is known. In some cases, thermodynamic equilibrium will not be reached and it is necessary to use kinetic expressions of the rates involved. These rates depend on diffusion constants, accommodation coefficients, Henry′s law coefficients, particle size distributions, and several other parameters. This review describes how these processes can be treated in computer modeling and how the necessary data can be obtained. Even though it is written primarily for use in modeling atmospheric chemistry, some parts will also be useful for waste water and pesticide control and in other areas where the distribution of chemicals between the aqueous and the gas phase is important.
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  • 21
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    Marketing letters 8 (1997), S. 205-216 
    ISSN: 1573-059X
    Keywords: diffusion ; pricing ; elasticities ; innovations ; stochastic models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract Extending the work of Parker (1992), which considers only firstpurchases, and Simon (1989), which considers brand-level sales, weempirically provide support for the hypothesis that total categorysales price elasticities first decease in absolute value but thenultimately increase if the product in question faces the decline phaseof the product life cycle (due to competitive substitutes, changes intastes, and so on). As an interesting artifact of the methodology, thearticle also shows how the Bass model can be easily modified to accountfor total category sales (first plus repeat purchases) and that, in thelimit, the Bass model converges to stochastic repeat purchase models(bridging two radically different modeling traditions). If unadjusted,the Bass model applied to sales data is grossly misspecified when thetime series studied exceeds five to ten years for consumer durables.
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  • 22
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    Journal of statistical physics 81 (1995), S. 761-775 
    ISSN: 1572-9613
    Keywords: Logistic map ; diffusion ; Fisher equation ; chaos ; oscillations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The dynamics of a biological population governed by a modified Fisher equation is studied by means of Monte Carlo simulations. Reproduction of the population occurs at discrete times, while transport caused by diffusion and conduction takes place on shorter time scales. The discrete reproduction, modeled with a set of coupled logistic maps, exhibits phenomena which are not evident in the usual continuum version of the Fisher equation. Several mechanisms for biennial oscillations of the total population are investigated. One of these shows an ordered coupling between random diffusive motion and the chaotic attractor of the logistic map.
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    Journal of statistical physics 85 (1996), S. 179-191 
    ISSN: 1572-9613
    Keywords: Reaction kinetics ; diffusion ; segregation ; partial differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We examine the long-time behavior of A+B→0 reaction-diffusion systems with initially segregated species A and B. All of our analysis is carried out for arbitrary (positive) values of the diffusion constantsD A andD B and initial concentrationsa 0 andb 0 of A's and B's. We divide the domain of the partial differential equations describing the problem into several regions in which they can be reduced to simpler, solvable equations, and we merge the solutions. Thus we derive general formulas for the concentration profiles outside the reaction zone, the location of the reaction zone center, and the total reaction rate. An asymptotic condition for the reaction front to be stationary is also derived. The properties of the reaction layer are studied in the mean-field approximation, and we show that not only the scaling exponents, but also the scaling functions are independent ofD A,D B,a 0 andb 0.
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    Journal of statistical physics 58 (1990), S. 57-86 
    ISSN: 1572-9613
    Keywords: Cellular automata ; lattice gases ; mode coupling theory ; staggered modes ; Green-Kubo relations ; viscosity ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Hydrodynamic excitations in lattice gas cellular automata are described in terms of equilibrium time correlation functions for the local conserved variables. For large space and time scales the linearized hydrodynamic equations are obtained to Navier-Stokes order. Exact expressions for the associated susceptibilities and transport coefficients are identified in terms of correlation functions. The general form of the time correlation functions for conserved densities in the hydrodynamic limit is given and illustrated by some examples suitable for comparison with computer simulation. The transport coefficients are related to time correlation functions for the conserved fluxes in a way analogous to the Green-Kubo expressions for continuous fluids. The general results are applied for a one-component fluid and several types of binary diffusion. Also discussed are the effects of unphysical slow modes such as staggered particle or momentum densities.
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    Journal of statistical physics 62 (1991), S. 1153-1171 
    ISSN: 1572-9613
    Keywords: Lorentz model ; Ehrenfest wind-tree model ; lattice gas ; diffusion ; abnormal diffusion ; bond percolation ; polymer chain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Diffusive behavior in various Lorentz lattice gases, especially wind-tree-like models, is discussed. Comparisons between lattice and continuum models as well as deterministic and probabilistic models are made. In one deterministic model, where the scatterers behave like double-sided mirrors, a new kind of abnormal diffusion is found, viz., the mean square displacement is proportional to the time, but the probability density distribution function is non-Gaussian. The connections of this mirror model with the percolation problem and the statistics of polymer chains on a lattice are also discussed.
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    Journal of statistical physics 63 (1991), S. 399-404 
    ISSN: 1572-9613
    Keywords: Percolation ; diffusion ; fractals ; correlated random walks ; number of visited sites
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Correlated random walk of particles in the infinite cluster of percolating lattices in two dimensions is investigated. For infinitely strong forward correlations (no change of direction except at the boundaries) trapping of the particles in small regions of the infinite cluster is observed.
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  • 27
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    Journal of statistical physics 63 (1991), S. 305-313 
    ISSN: 1572-9613
    Keywords: Turbulence ; diffusion ; helicity ; convection ; incompressible fluids
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Through the use of the Novikov-Furutsu formula for Gaussian processes an equation is obtained for the diffusion of the ensemble average of a passive scalar in an incompressible turbulent velocity field in terms of the two-point, two-time correlator of this field. The equation is valid for turbulence which is not necessarily homogeneous or stationary and thus generalizes previous work.
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    Journal of statistical physics 74 (1994), S. 1227-1232 
    ISSN: 1572-9613
    Keywords: Schrödinger's operator ; spectrum ; diffusion
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    Topics: Physics
    Notes: Abstract It is proved that the ground state Λ(L) of (−1)x the Schrödinger operator with white noise potential, on an interval of lengthL, subject to Neumann, periodic, or Dirichlet conditions, satisfies the law $$\mathop {\lim }\limits_{L \uparrow \infty } P[(L/\pi )\Lambda ^{1/2} \exp ( - \tfrac{8}{3}\Lambda ^{3/2} ) 〉 x] = \left\{ {\begin{array}{*{20}c} {1forx〈 0} \\ {e^{ - x} forx \geqslant 0} \\ \end{array} } \right.$$
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    Journal of statistical physics 75 (1994), S. 189-213 
    ISSN: 1572-9613
    Keywords: Multidimensional piecewise expanding mappings ; deterministic chaos ; diffusion ; central limit theorem ; local limit theorem ; Markov processes
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    Topics: Physics
    Notes: Abstract Strongly chaotic systems (e.g., piecewise expanding mappings) exhibit diffusion-like behavior in the sense of central limit theorems. To find more precise statements about the similarity to probabilistic diffusion, we study how the evolution of probability densities underd-dimensional piecewise expanding mappings can be modeled by Markov processes with smooth transition probabilities (such as diffusion processes). Our results can be viewed as a special type of local limit theorem.
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    Journal of statistical physics 87 (1997), S. 545-575 
    ISSN: 1572-9613
    Keywords: Random hopping model ; bond impurity ; diffusion ; asymmetric exclusion process ; electrophoresis
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    Topics: Physics
    Notes: Abstract Analytic solution is given in the steady-state limitt→∞ for the system of master equations describing a random walk on one-dimensional periodic lattices with arbitrary hopping rates containing one mobile directional impurity (defect bond). Due to the defect, translational invariance is broken, even if all other rates are identical. The structure of master equations leads naturally to the introduction of a new entity, associated with the walker-impurity pair which we call the quasiwalker. The velocities and diffusion constants for both the random walker and impurity are given, being simply related to that of the quasiparticle through physically meaningful equations. Applications in driven diffusive systems are shown, and connections with the Duke-Rubinstein reptation models for gel electrophoresis are discussed.
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    Journal of statistical physics 90 (1998), S. 1179-1199 
    ISSN: 1572-9613
    Keywords: Irreversibility ; relativistic Ornstein–Uhlenbeck process ; relativistic statistical physics ; diffusion
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    Topics: Physics
    Notes: Abstract We derive, in the “hydrodynamic” limit (large space and time scales), an evolution equation for the particle density in physical space from the (special) relativistic Ornstein–Uhlenbeck process introduced by Debbasch, Mallick, and Rivet. This equation turns out to be identical with the classical diffusion equation, without any relativistic correction. We prove that, in the “hydrodynamic” limit, this result is indeed compatible with special relativity.
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    Journal of statistical physics 94 (1999), S. 203-217 
    ISSN: 1572-9613
    Keywords: lattice Boltzmann ; diffusion ; eigenmode analysis
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    Topics: Physics
    Notes: Abstract We present a diffusion lattice Boltzmann (DLB) scheme which is derived from first principles. As opposed to the traditional lattice BGK schemes the DLB is valid for orthorhombic lattices and it has two eigenvalues of the collision operator. It is shown that the diffusion coefficient depends only on one eigenvalue of the collision operator. Hence, the DLB scheme can be optimized with means of the additional eigenvalue of the collision operator and with different lattice spacing along the principal axes. The properties of the DLB scheme concerning consistency, stability, and accuracy are studied with eigenmode analysis. This analysis shows that the DLB scheme is consistent with diffusion for a wide range of diffusion coefficients, it has unconditional stability, and that it has third-order accuracy. Furthermore, it is shown that accuracy is improved by setting the additional eigenvalue to zero and by densifying the lattice spacing along the direction of the density gradient.
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    Journal of statistical physics 99 (2000), S. 903-941 
    ISSN: 1572-9613
    Keywords: effective potential ; reaction ; diffusion ; decay
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    Topics: Physics
    Notes: Abstract In previous work we have developed a general method for casting stochastic partial differential equations (SPDEs) into a functional integral formalism, and have derived the one-loop effective potential for these systems. In this paper we apply the same formalism to a specific field theory of considerable interest, the reaction-diffusion-decay system. When this field theory is subject to white noise we can calculate the one-loop effective potential (for arbitrary polynomial reaction kinetics) and show that it is one-loop ultraviolet renormalizable in 1, 2, and 3 space dimensions. For specific choices of interaction terms the one-loop renormalizability can be extended to higher dimensions. We also show how to include the effects of fluctuations in the study of pattern formation away from equilibrium, and conclude that noise affects the stability of the system in a way which is calculable.
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    Journal of intelligent and robotic systems 17 (1996), S. 309-325 
    ISSN: 1573-0409
    Keywords: modeling ; camera ; CCD ; subpixel ; simulation ; vision ; image ; diffusion ; CAD ; CIM ; bias
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract In this paper we propose a modeling of an acquisition line made up of a CCD camera, a lens and a frame grabber card. The purpose of this modeling is to simulate the acquisition process in order to obtain images of virtual objects. The response time has to be short enough to permit interactive simulation. All the stages are modelised: in the first phase, we present a geometric model which supplies a point to point transformation that provides, for a space point in the camera field, the corresponding point on the plane of the CCD sensor. The second phase consists of modeling the discrete space which implies passing from the continous known object view to a discrete image, in accordance with the different orgin of the contrast loss. In the third phase, the video signal is reconstituted in order to be sampled by the frame grabber card. The practical results are close to reality when compared to image processing. This tool makes it possible to obtain a short computation time simulation of a vision sensor. This enables interactivity either with the user or with software for the design/simulation of an industrial workshop equipped with a vision system. It makes testing possible and validates the choice of sensor placement and image processing and analysis. Thanks to this simulation tool, we can control perfectly the position of the object image placed under the camera and in this way, we can characterise the performance of subpixel accuracy determining methods for object positioning.
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    Journal of nanoparticle research 2 (2000), S. 123-131 
    ISSN: 1572-896X
    Keywords: nanoparticle ; characterization ; light scattering ; PCS ; interferometry ; diffusion ; polydispersivity
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    Topics: Physics , Technology
    Notes: Abstract Dynamic light scattering (DLS) techniques for studying sizes and shapes of nanoparticles in liquids are reviewed. In photon correlation spectroscopy (PCS), the time fluctuations in the intensity of light scattered by the particle dispersion are monitored. For dilute dispersions of spherical nanoparticles, the decay rate of the time autocorrelation function of these intensity fluctuations is used to directly measure the particle translational diffusion coefficient, which is in turn related to the particle hydrodynamic radius. For a spherical particle, the hydrodynamic radius is essentially the same as the geometric particle radius (including any possible solvation layers). PCS is one of the most commonly used methods for measuring radii of submicron size particles in liquid dispersions. Depolarized Fabry-Perot interferometry (FPI) is a less common dynamic light scattering technique that is applicable to optically anisotropic nanoparticles. In FPI the frequency broadening of laser light scattered by the particles is analyzed. This broadening is proportional to the particle rotational diffusion coefficient, which is in turn related to the particle dimensions. The translational diffusion coefficient measured by PCS and the rotational diffusion coefficient measured by depolarized FPI may be combined to obtain the dimensions of non-spherical particles. DLS studies of liquid dispersions of nanometer-sized oligonucleotides in a water-based buffer are used as examples.
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    Environmental and resource economics 2 (1992), S. 615-634 
    ISSN: 1573-1502
    Keywords: Cleaner technologies ; environmental policy ; economic instruments ; efficiency ; innovation ; diffusion
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    Topics: Energy, Environment Protection, Nuclear Power Engineering , Economics
    Notes: Abstract This article identifies and analyzes factors that affect the willingness of firms and consumers to develop and adopt cleaner technologies. “Cleaner technologies” is used as a general term for pollution abatement technologies, re-use systems, and environmentally sound consumer products and materials. The article also contains the findings of three case studies on cleaner technologies (CFC substitutes, low-solvent paints and coatings, and membrane technology), in which the importance of the identified factors is investigated. From the case studies some general conclusions are drawn about these factors, and the way in which policy instruments can be used to stimulate innovation in and diffusion of cleaner technologies. No single policy instrument is considered to be optimal. Instead a policy mix is needed, involving a much wider use of economic instruments.
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    Transport in porous media 27 (1997), S. 171-184 
    ISSN: 1573-1634
    Keywords: diffusion ; randon ; gel ; emulsion ; environmental protection.
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    Topics: Geosciences , Technology
    Notes: Abstract The effective diffusion coefficient of radon was determined in polymer/silicate gels and clay suspension used as sealing materials in environmental protection. On the basis of the experimental findings, it was concluded that both materials drastically decrease the convective mass transport in porous media. Simultaneously, the effective diffusion coefficient was reduced significantly. Thus, the radon flux might be decreased by 5 to 6 orders of magnitude in porous systems originally having gas or low water saturation by injection of gel-forming materials or placement of clay suspensions. At high water saturation, however, the diffusion transport of radon can be slightly restricted in consolidated and unconsolidated porous media. The laboratory studies may firmly allow us to conclude that hydrogels and clay suspensions are prospective candidates in an integrated environmental technology to be used for restriction of radon migration in subsurface regions.
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    Transport in porous media 8 (1992), S. 99-131 
    ISSN: 1573-1634
    Keywords: Characteristic ; wavespeed ; shock ; expansion fan ; Rankine-Hugoniot equations ; entropy inequality ; two-phase flow ; counterflow ; saturation ; pressure ; convection ; diffusion
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    Topics: Geosciences , Technology
    Notes: abstract New concepts are introduced to describe single-component two-phase flow under gravity. The phases can flow simultaneously in opposite directions (counterflow), but information travels either up or down, depending on the sign of the wavespeedC. Wavespeed, saturation and other quantities are defined on a two-sheeted surface over the mass-energy flow plane, the sheets overlapping in the counterflow region. A saturation shock is represented as an instantaneous displacement along a line of constant volume fluxJ Q in the flow plane. Most shocks are of the wetting type, that is, they leave the environment more saturated after their passage. When flow is horizontal all shocks are wetting, but it is a feature of vertical two-phase flow that for sufficiently small mass and energy flows there also exist drying shocks associated with lower final saturations.
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    Journal of fluorescence 2 (1992), S. 7-21 
    ISSN: 1573-4994
    Keywords: Fluorescence ; quenching ; diffusion ; dimensionality
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    Topics: Physics
    Notes: Abstract The fluorescence decay curves obtained from diffusion-influenced quenching in various spatial dimensions are discussed. The two-dimensional quenching has, because of intractable fitting functions, previously been dealt with only in the completely diffusion-controlled case (corresponding to the Smoluchowski boundary condition). In this paper, an approximation for the two-dimensional (2D)-quenching behavior with the Collins-Kimball boundary condition is presented. The nonlinear least-squares method has been used to analyze simulated decay data. The consequences the choice of an incorrect model has on the final results as well as the possibility to discriminate between different dimensionalities are investigated. Also, some inherent properties of the fitting functions are studied.
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    Acta mechanica Sinica 10 (1994), S. 16-26 
    ISSN: 1614-3116
    Keywords: elastic material ; surface energy ; diffusion
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The free energy of a stressed crystal is assumed to consist of elastic strain energy and surface energy, and the chemical potential for surface diffusion at constant temperature is obtained under this assumption. A gradient in chemical potential results in diffusive mass transport along the surface. The result is applied in considering the phenomena of instability of a flat surface in a stressed material under fluctuations in surface shape, and the transient evolution of surface roughness due to an initial perturbation in the nearly flat free surface of the material, both under plane strain conditions.
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    Applied mathematics and mechanics 19 (1998), S. 757-764 
    ISSN: 1573-2754
    Keywords: products pipeline ; batching transport ; contamination ; convection ; diffusion ; numerical computation ; turbulent flow
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract Contamination between batches in multi-products pipeline transport is studied. The influences of convection and diffusion on the contamination are studied in detail. Diffusion equations, which are mainly controlled by convection, are developed under turbulent pipe flow. The diffusion equation, is separated into a pure convection equation and a pure diffusion equation which are solved by characteristics method and finite difference method respectively to obtain numerical solutions. The results of numerical computation explain the forming and developing of contamination very well.
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    Applied mathematics and mechanics 20 (1999), S. 457-464 
    ISSN: 1573-2754
    Keywords: nonlinear ; competitive system ; diffusion ; equilibrium ; persistence
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract In this paper, the stabilities of boundary equilibrium and positive equilibrium of two-species Ayala competitive systems with two different diffusions are discussed, and dynamic behaviors of species are obtained. At the same time, the dynamic behaviors between systems with diffusion and those without diffusion are compared. This shows the influence of diffusions on the persistence of species.
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  • 43
    ISSN: 1573-7691
    Keywords: Hyperviscous ; shocks ; diffusion ; shock capturing
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    Topics: Computer Science
    Notes: Abstract We solve two problems ofx∈[−∞, ∞] for arbitrary orderj. The first is to compute shock-like solutions to the hyperdiffusion equation,u1=(−1) j+1 u 2j,x. The second is to compute similar solutions to the stationary form of the hyper-Burgers equation, (−1) j u 2j.x+uu x=0; these tanh-like solutions are asymptotic approximations to the shocks of the corresponding time dependent equation. We solve the hyperdiffusion equation with a Fourier integral and the method of steepest descents. The hyper Burgers equation is solved by a Fourier pseudospectral method with a polynomial subtraction. Except for the special case of ordinary diffusion (j=1), the jump across the shock zone is described bynonmonotonic, oscillatory functions. By smearing the front over the width of a grid spacing, it is possible to numerically resolve the shock with a weaker and weaker viscosity coefficient asj, the order of the damping, increases. This makes such “hyperviscous” dampings very attractive for coping with fronts since, outside the frontal zone, the impact of the artificial hyperviscosity is much smaller than with ordinary viscosity. Unfortunately, both the intensity of the oscillations and the slowness of their exponential decay from the center of the shock zone decrease asj increases so that the shock zone is muchwider than for ordinary diffusion. We also examined generalizations of Burgers equation with “spectral viscosity”, that is, damping which is tailored to yield exponentially small errors outside the frontal zone when combined with spectral methods. We find behavior similar to high order hyperviscosity. We conclude that high order damping, as a tool for shock-capturing, offers both advantages and drawbacks. Monotonicity, which has been the holy grail of so much recent algorithm development, is a reasonable goal only for ordinary viscosity. Hyperviscous fronts and shock zones in flows with “spectral viscosity” aresupposed to oscillate.
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    Transport in porous media 37 (1999), S. 93-128 
    ISSN: 1573-1634
    Keywords: diffusion ; partitioning ; homogeneous ; nonhomogeneous ; laminate ; analytical ; algebraic ; eigenfunction ; composite.
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    Topics: Geosciences , Technology
    Notes: Abstract Studies of the transport of contaminants and nutrients in industrial and environmental systems are complicated by the heterogeneous nature of the supporting porous or permeable media, and by the numerical problems associated with high Peclet number advection and sharp interface models. In order to provide independent theoretical checks of numerical transport theories, this set of papers presents analytical solutions to diffusive transport equations in simplified (one-dimensional) laminate systems subject to partitioning interactions. Here, in Part I, a standard separation of variables technique is used to develop analytical eigenfunction expansions of the concentration solution in an N-laminate system subject to steady Cauchy (third-type) nonhomogeneous boundary conditions. Both Cartesian and radial (axisymmetric) coordinate systems are considered. The solutions are developed for two different interface partitioning formulations, allowing the partitioning processes to be described by instantaneous equilibration mechanisms, or in terms of gradual equilibration mediated by mass transfer coefficients. Worked examples are presented and limitations of the approach discussed.
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    Water resources management 12 (1998), S. 409-432 
    ISSN: 1573-1650
    Keywords: diffusion ; dispersion ; fracture network ; percolation theory
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    Topics: Architecture, Civil Engineering, Surveying , Geography
    Notes: Abstract Dispersion and transport of mass in a fracture network is a percolation process. Macro-scale dispersion is related to travel time, distance, mass distribution and fracture geometry. This article presents a stochastic, discrete fracture model in conjunction with percolation theory to investigate the dispersion phenomenon and the power law relationship between mean square travel paths displacement 〈 r2 〉 and particle travel time t. For imposed boundary conditions, particle dispersion is simulated to observe percolation thresholds and dispersion trends in different network structures. Simulation results demonstrate that the critical exponent values of t in the percolated networks are extremely close to the theoretical value of 1.27 and occur at certain percolation factors. Below these percolation factors, the exponents of t increase with decreasing percolation factors, above these percolation factors, exponents decrease with increasing percolation factors. In our simulated cases, the proportionality between 〈 r2 〉 and time t is given by t raised to a power between 1.27 and 1.66, depending on the fracture pattern. The coefficient of anisotropic dispersion tensor increases with increasing distance. The percolation process is related to travel time and distance, and cannot be interpreted as a Fickian diffusive process.
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    Transport in porous media 21 (1995), S. 47-70 
    ISSN: 1573-1634
    Keywords: ‘Long-tail’ effect ; pollutant ; diffusion ; double porosity ; homogenization ; modelization
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    Topics: Geosciences , Technology
    Notes: Abstract In the paper anomalous diffusion appearing in a porous medium composed of two porous components of considerably different diffusion characteristics is examined. The differences in diffusivities are supposed to result either from two medium types being present or from variations in pore size (double porosity media). The ‘long-tail’ effect is predicted using the homogenization approach based on the application of multiple scale asymptotic developments. It is shown that, if the ratio of effective diffusion coefficients of two porous media is of the order of magnitude smaller or equal O(ε 2), whereε is a homogenization parameter, then the macroscopic behaviour of the composite may be affected by the presence of ‘tail-effect’. The results of the theoretical analysis were applied to a problem of diffusion in a bilaminate composite. Analytical calculations were performed to show the presence of the ‘long-tail’ effect in two particular cases.
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    Transport in porous media 30 (1998), S. 125-154 
    ISSN: 1573-1634
    Keywords: NAPL ; multiphase ; fractal ; soil ; diffusion ; transport ; heterogeneous porous medium
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    Topics: Geosciences , Technology
    Notes: Abstract Volatile organic chemicals from nonaqueous phase liquids trapped in soil spread quickly both into the atmosphere and the groundwater system, resulting in long-lasting pollution of the environment. The extent and speed of spread is strongly influenced by the heterogeneities present in the soil, which interact with the various mechanisms of transport in a complex manner. A semi-analytical model is presented to investigate the effect of soil-heterogeneities on the spreading of pollutants from a nonaqueous phase liquid trapped in a soil. Based on field evidence, soil heterogeneities are modeled as a self-similar fractal process, and diffusive transport of organic chemicals in such a substrate is studied. Various mechanisms of, and resistance to, transport of these contaminants are considered, and it is illustrated how each of these are altered by the presence of heterogeneities. More specifically, it is shown that, while the transport processes at early time are governed by volatilization and dissolution and are quite unaffected by the heterogeneities, the transport processes at late time are strongly dependent on the heterogeneities of the soil and its sorption characteristics. In addition, how failure to recognize these heterogeneities in the soil may result in unsuccessful design of appropriate remediation techniques is discussed.
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    Transport in porous media 19 (1995), S. 139-156 
    ISSN: 1573-1634
    Keywords: Porous media ; heat ; nonisothermal transport ; unsaturated zone ; evaporation ; precipitation ; diffusion ; salinity
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    Topics: Geosciences , Technology
    Notes: Abstract Heat-transfer phenomena as well as moisture movement in unsaturated soils due to thermal gradients, have been extensively studied during the last four decades. Less attention has been devoted to the transport and redistribution of solutes caused by heating. Solar radiation, radioactive waste repositories, underground energy storage, buried electric cables and steam pipes, disposal of waste heat from power plants are examples of heat sources in the soil. Soil-water properties, such as surface tension, viscosity, density, as well as the equilibrium composition of phases, depend on temperature. Hence, nonuniform heating of a soil partially saturated by saline water has an effect on such processes as water flow under capillary and gravitational forces, evaporation, condensation and diffusion of vapor and transport and precipitation of salts. A mathematical model is presented for the migration of salts in the vadoze zone in the soil under nonisothermal conditions, taking into account the above-mentioned phenomena. The physical assumptions underlying the model are briefly discussed. The study of a particular case shows that under certain conditions, a heat source may attract dissolved salts, and cause their precipitation in the hot area.
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    Transport in porous media 21 (1995), S. 175-188 
    ISSN: 1573-1634
    Keywords: diffusion ; dispersion ; percolation ; fractals ; scaling
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    Topics: Geosciences , Technology
    Notes: Abstract Two fundamental questions regarding the application of percolation theory to transport in porous media are addressed. First, when ‘critical path’ arguments (based on a sufficiently wide spread of microscopic transition rates) are invoked (in analogy to the case of transport in disordered semiconductors) to justify the application of percolation theory to the determination of relevant transport properties, then for long time scales (compared to the inverse of the ‘critical’ percolation rate), the fractal structure of the ‘critical’ path is relevant to transport, but not at short time scales. These results have been demonstrated concretely in the case of disordered semiconductors, and are in direct contradiction to the claims of the review. Second, the relevance of deterministic or stochastic methods to transport has been treated heretofore by most authors as a question of practicality. But, at least under some conditions, concrete criteria distinguish between the two types of transport. Percolative (deterministic) transport is temporally reproducible and spatially inhomogeneous while diffusive (stochastic) transport is temporally irreproducible, but homogeneous, and a cross-over from stochastic to percolative transport occurs when the spread of microscopic transition rates exceeds 4–5 orders of magnitude. It is likely that such conditions are frequently encountered in soil transport. Moreover, clear evidence for deterministic transport (although not necessarily percolative) exists in such phenomena as preferential flow. On the other hand, the physical limitation of transport to (fractally connected) pore spaces within soils (analogously to transport in metal-insulator composites) can make transport diffusive on a fractal structure, rather than percolative.
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    Asia Pacific financial markets 1 (1994), S. 101-109 
    ISSN: 1573-6946
    Keywords: Memory ; heteroscedasticity ; diffusion ; rescaled range ; fractal ; martingale
    Source: Springer Online Journal Archives 1860-2000
    Topics: Economics
    Notes: Abstract This paper examines evidence of long-term memory in the yen/dollar price change as well as in the daily estimate of volatility of the exchange rate series. The methodology used is due to Lo (1989) which is robust to the presence of heteroscedasticity and is applied to a ten year data set. The result shows no evidence of long-term memory in the price change series indicating efficient pricing by the market participants. The volatility series, however, shows evidence of long-term memory which may have implications for traders dealing with long lived assets.
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    Biogeochemistry 9 (1990), S. 53-74 
    ISSN: 1573-515X
    Keywords: sulfate reduction ; sulfide accumulation ; diffusion ; modelling ; pyrite
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    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract Sulfate reduction and sulfide accumulation were examined in fine-grained sediments from rapidly accreting abandoned channels and mussel culture areas in the Eastern Scheldt, which covered 4 and 5% of the total surface area, respectively. Reduction rates were measured in batch experiments in which the SO4 2− depletion was measured during anoxic incubation. The reduction rates in summer varied between 14–68 mmol SO4 2− m−2 day−1 and were related to the sedimentation rate. In the most rapidly accreting channels, SO4 2− was exhausted below 15–50 cm and methanogenesis became the terminal process of organic carbon oxidation One-dimensional modelling of sulfate profiles in mussel banks indicated that the subsurface influx of SO4 2− was almost of the same order as the diffusive flux at the sediment-seawater interface, during the initial stages of the mussel bank accretion. The energy dissipation of waves and tidal currents on the mussel bank surface increased the apparent sediment diffusivity up to 3-fold, especially in the winter The results indicate that acid volatile sulfide (AVS) was the major, in-situ reduced, sulfur compound in the sediment. The sulfidation of easily extractable iron was nearly complete. Pyrite concentrations (40–80 μM S cm−3) were as high as the AVS concentrations, but there was apparently no in-situ transformation of AVS into pyrite. The detrital pyrite originated from eroding marine sediments elsewhere
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    ISSN: 1573-515X
    Keywords: carbon dioxide ; diffusion ; ebullition ; emission ; freshwater ; hypertrophic lakes ; methane
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    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract The fluxes of CH4 and CO2 to the atmosphere, and the relative contributions of ebullition and molecular diffusion, were determined for a small hypertrophic freshwater lake (Priest Pot, UK) over the period May to October 1997. The average total flux of CH4 and CO2 (estimated from 7 sites on the lake) was approximately 52 mmol m−2 d−1 and was apportioned 12 and 40 mmol m−2 d−1 toCH4 and CO2 respectively. Diffusion across the air-water interface accounted for the loss of 0.4and 40 mmol m−2 d−1 of CH4 and CO2 respectively whilst the corresponding figures for ebullition losses were 12.0 (CH4) and 0.23 (CO2) mmol m−2 d−1. Most CH4 (96%) was lost by ebullition, and most CO2 (99%) by diffusive processes. The ebullition of gas, measured at weekly intervals along a transect of the lake, showed high spatial and temporal variation. The CH4 content of the trapped gas varied between 44 and 88% (by volume) and was highest at the deepest points. Pulses of gas ebullition were detected during periods of rapidly falling barometric pressure. Therelevance of the measurements to global estimates ofcarbon emission from freshwaters are discussed.
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    Journal of bioenergetics and biomembranes 27 (1995), S. 513-525 
    ISSN: 1573-6881
    Keywords: Trypanosoma brucei ; glycolysis ; glycosome ; flux control ; Metabolic Control Analysis ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Physics
    Notes: Abstract Unlike other eukaryotic cells, trypanosomes possess a compartmentalized glycolytic pathway. The conversion of glucose into 3-phosphoglycerate takes place in specialized peroxisomes, called glycosomes. Further conversion of this intermediate into pyruvate occurs in the cytosol. Due to this compartmentation, many regulatory mechanisms operating in other cell types cannot work in trypanosomes. This is reflected by the insensitivity of the glycosomal enzymes to compounds that act as activity regulators in other cell types. Several speculations have been raised about the function of compartmentation of glycolysis in trypanosomes. We calculate that even in a noncompartmentalized trypanosome the flux through glycolysis should not be limited by diffusion. Therefore, the sequestration of glycolytic enzymes in an organelle may not serve to overcome a diffusion limitation. We also search the available data for a possible relation between compartmentation and the distribution of control of the glycolytic flux among the glycolytic enzymes. Under physiological conditions, the rate of glycolytic ATP production in the bloodstream form of the parasite is possibly controlled by the oxygen tension, but not by the glucose concentration. Within the framework of Metabolic Control Analysis, we discuss evidence that glucose transport, although it does not qualify as the sole rate-limiting step, does have a high flux control coefficient. This, however, does not distinguish trypanosomes from other eukaryotic cell types without glycosomes.
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    Journal of economic growth 2 (1997), S. 1-26 
    ISSN: 1573-7020
    Keywords: growth ; technology ; diffusion ; convergence ; adaptation
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    Topics: Economics
    Notes: Abstract We construct a model that combines elements of endogenousgrowth with the convergence implications of the neoclassicalgrowth model. In the long run, the world growth rate is drivenby discoveries in the technologically leading economies. Followersconverge toward the leaders because copying is cheaper than innovationover some range. A tendency for copying costs to increase reducesfollowers‘ growth rates and thereby generates a pattern of conditionalconvergence. We discuss how countries are selected to be technologicalleaders, and we assess welfare implications. Poorly defined intellectualproperty rights imply that leaders have insufficient incentiveto invent and followers have excessive incentive to copy.
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    International journal of computer vision 34 (1999), S. 97-122 
    ISSN: 1573-1405
    Keywords: edge detection ; image reconstruction ; scale space ; diffusion ; blur ; deblurring ; denoising ; diffusion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We address the problem of computing a general-purpose early visual representation that satisfies two criteria. 1) Explicitness: To be more useful than the original pixel array, the representation must take a significant step toward making important image structure explicit. 2) Completeness: To support a diverse set of high-level tasks, the representation must not discard information of potential perceptual relevance. The most prevalent representation in image processing and computer vision that satisfies the completeness criterion is the wavelet code. In this paper, we propose a very different code which represents the location of each edge and the magnitude and blur scale of the underlying intensity change. By making edge structure explicit, we argue that this representation better satisfies the first criterion than do wavelet codes. To address the second criterion, we study the question of how much visual information is lost in the representation. We report a novel method for inverting the edge code to reconstruct a perceptually accurate estimate of the original image, and thus demonstrate that the proposed representation embodies virtually all of the perceptually relevant information contained in a natural image. This result bears on recent claims that edge representations do not contain all of the information needed for higher level tasks.
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    Transport in porous media 14 (1994), S. 73-84 
    ISSN: 1573-1634
    Keywords: Clay barriers ; carbonate ; diffusion ; sorption ; mass transport ; nuclear fuel waste management
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    Topics: Geosciences , Technology
    Notes: Abstract Diffusion coefficients are critical parameters for predicting migration rates and fluxes of contaminants through clay-based barrier materials used in many waste containment strategies. Cabon-14 is present in high-level nuclear fuel waste and also in many low-level wastes such as those generated from some medical research activities. Diffusion coefficients were measured for14C (in the form of carbonate) in bentonite compacted to a series of dry bulk densities,ρ b, ranging from about 0.9 to 1.6 Mg/m3. The clay was saturated with a Na-Ca-Cl-dominated groundwater solution typical of those found deep in plutonic rock on the Canadian Shield. Both effective,D e, and apparent,D a, diffusion coefficients were determined.D e is defined asD 0 Τ a n e, where D0 is the diffusion coefficient in pure bulk water,Τ a the apparent tortuosity factor, andn e the effective porosity available for diffusion; andD a is defined asD 0 Τ a n e/(n e +ρ b K d ), where Kd is the solid/liquid distribution coefficient. BothD e andD a decrease with increasingρ b:D e values range from about 10×10−12 m2/s atρ b≃0.9 Mg/m3 to 0.6×10−12 m2/s at 1.6 Mg/m3, andD a values vary from approximately 40×10−12 to 4×10−12 m2/s over the same density range. The decrease inD e andD a is attributed to a decrease in bothΤ a andn e asρ b increases. The data indicate thatn e is 〈10% of the total solution-filled porosity of the clay at all densities.K d values for14C with the clay range from about 0.3 to 〈0.1 m3/Mg; this indicates there is a small amount of14C sorbed on the clay and/or some14C is isotopically exchanged with12C in carbonate phases present in the clay. Finally, theD e values for14C are lower than those of other diffusants — I−, Cl−, TcO4 −, and Cs+ — that have been measured in this clay and pore-water solution. This is attributed to lower values for bothn e andD 0 for14C species relative to those of the other diffusants.
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    Transport in porous media 6 (1991), S. 651-666 
    ISSN: 1573-1634
    Keywords: Mathematical analysis ; partial differential equation ; nonlinear ; diffusion ; advection ; Fokker-Planck ; qualitative behaviour ; unsaturated soils ; wetting-fronts
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    Topics: Geosciences , Technology
    Notes: Abstract The Richards equation is widely used as a model for the flow of water in unsaturated soils. For modelling one-dimensional flow in a homogeneous soil, this equation can be cast in the form of a specific nonlinear partial differential equation with a time derivative and one spatial derivative. This paper is a survey of recent progress in the pure mathematical analysis of this last equation. The emphasis is on the interpretation of the results of the analysis. These are explained in terms of the qualitative behaviour of the flow of water in an unsaturated soil which is described by the Richards equation.
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    Transport in porous media 12 (1993), S. 107-123 
    ISSN: 1573-1634
    Keywords: Nuclear magnetic resonance imaging (MRI) ; miscible displacement ; buoyancy ; three-dimensional ; diffusion ; permeability
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    Topics: Geosciences , Technology
    Notes: Abstract Nuclear Magnetic Resonance Imaging (MRI) can noninvasively map the spatial distribution of Nuclear Magnetic Resonance (NMR)-sensitive nuclei. This can be utilized to investigate the transport of fluids (and solute molecules) in three-dimensional model systems. In this study, MRI was applied to the buoyancy-driven transport of aqueous solutions, across an unstable interface in a three-dimensional box model in the limit of a small Péclet number (Pe〈0.4). It is demonstrated that MRI is capable of distinguishing between convective transport (‘fingering’) and molecular diffusion and is able to quantify these processes. The results indicate that for homogeneous porous media, the total fluid volume displaced through the interface and the amplitude of the fastest growing finger are linearly correlated with time. These linear relations yielded mean and maximal displacement velocities which are related by a constant dimensionless value (2.4±0.1). The mean displacement velocity (U) allows us to calculate the media permeability which was consistent between experiments (1.4±0.1×10−7cm2).U is linearly correlated with the initial density gradient, as predicted by theory. An extrapolation of the density gradient to zero velocity enables an approximate determination of the critical density gradient for the onset of instability in our system (0.9±0.3×10−3 g/cm3), a value consistent with the value predicted by a calculation based upon the modified Rayleigh number. These results suggest that MRI can be used to study complex fluid patterns in three-dimensional box models, offering a greater flexibility for the simulation of natural conditions than conventional experimental modelling methods.
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    Transport in porous media 19 (1995), S. 1-13 
    ISSN: 1573-1634
    Keywords: Contaminant ; ground water ; aquifer ; aquitard ; aquifuge ; multi-layered aquifer ; convection ; diffusion ; sorption ; numerical method ; approximation
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    Topics: Geosciences , Technology
    Notes: Abstract A model of the process of the contaminant convective diffusion with nonlinear sorption in one-layered aquifer and multi-layered, consisting of basic aquifers with an aquifer dividing them by, is considered here. A three-dimensional formulation of the problem with a special averaging is reduced to a two-dimensional one, allowing to investigate the interaction of aquifers taking into account the aquitard of arbitrary thickness, and its absence as well.
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    Transport in porous media 7 (1992), S. 223-253 
    ISSN: 1573-1634
    Keywords: Characteristic ; wavespeed ; shock ; expansion fan ; Rankine-Hugoniot equations ; entropy inequality ; two-phase flow ; saturation ; pressure ; geothermal ; convection ; diffusion
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    Topics: Geosciences , Technology
    Notes: Abstract In the absence of capillarity the single-component two-phase porous medium equations have the structure of a nonlinear parabolic pressure (equivalently, temperature) diffusion equation, with derivative coupling to a nonlinear hyperbolic saturation wave equation. The mixed parabolic-hyperbolic system is capable of substaining saturation shock waves. The Rankine-Hugoniot equations show that the volume flux is continuous across such a shock. In this paper we focus on the horizontal one-dimensional flow of water and steam through a block of porous material within a geothermal reservoir. Starting from a state of steady flow we study the reaction of the system to simple changes in boundary conditions. Exact results are obtainable only numerically, but in some cases analytic approximations can be derived. When pressure diffusion occurs much faster than saturation convection, the numerical results can be described satisfactorily in terms of either saturation expansion fans, or isolated saturation shocks. At early times, pressure and saturation profiles are functionally related. At intermediate times, boundary effects become apparent. At late times, saturation convection dominates and eventually a steady-state is established. When both pressure diffusion and saturation convection occur on the same timescale, initial simple shock profiles evolve into multiple shocks, for which no theory is currently available. Finally, a parameter-free system of equations is obtained which satisfactorily represents a particular case of the exact equations.
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    Transport in porous media 28 (1997), S. 253-284 
    ISSN: 1573-1634
    Keywords: foam ; mobilization ; network simulation ; pressure gradient ; trapping ; diffusion
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    Topics: Geosciences , Technology
    Notes: Abstract Usually, foam in a porous medium flows through a small and spatially varying fraction of available pores, while the bulk of it remains trapped. The trapped foam is under a pressure gradient corresponding to the pressure gradient imposed by the flowing foam and continuous wetting liquid. The imposed pressure gradient and coalescence of the stationary foam lamellae periodically open flow channels in the trapped foam region. Foam lamellae in each of these channels flow briefly, but channels are eventually plugged by smaller bubbles entering into the trapped region. The result is a cycling of flow channels that open and close throughout the trapped foam, leading to intermittent pulsing of foam flow in that region. The dynamic behavior of foam trapped in porous media is modeled here with a pore network simulator. We predict the magnitude of the pressure drop leading to the onset of flow of foam lamellae in the region containing trapped foam. This mobilization pressure drop depends only on the number of lamellae in the flow path and on the geometry of the pores that make up this path. The principles learned in this study allow us to predict the fraction of foam that is trapped in a porous medium under given flow conditions. We present here the first analytic expression for the trapped foam fraction as a function of the pressure gradient, and of the mean and standard deviation of the pore size distribution. This expression provides a missing piece for the continuum foam flow models based on the moments of the volume-averaged population balance of foam bubbles.
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    Marketing letters 7 (1996), S. 95-109 
    ISSN: 1573-059X
    Keywords: trials ; diffusion ; order-of-entry ; price ; advertising ; elasticities
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    Topics: Economics
    Notes: Abstract This paper considers the diffusion process of new brands in order to estimate marketing mix elasticities and order-of-entry effects. Using an empirical case, we test hypotheses regarding the role of order of entry on brand trial processes within a new category. Consistent with research hypotheses, the results demonstrate that the diffusion rate of a brand's trials and its pricing and advertising elasticities vary systematically as a function of competitive entry. Competitive influences (which are negative) increase as order of entry is delayed. Short-term price elasticities are found to be an inverted U relationship with the order of entry, whereby early followers have the highest elasticities, as compared to the pioneer and to later followers. Advertising elasticities decline as the number of competitors increases.
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    Keywords: solute transport ; nonequilibrium ; heterogeneous porous media ; dispersion ; diffusion ; experiments ; modelling
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    Notes: Abstract Two region models for solute transport in porous media assume that hydrodynamic dispersion in mobile water and solute diffusion within immobile water regions are independent. Experimental and theoretical results for transport through a macropore indicate that hydrodynamic dispersion and solute exchange are interdependent. Experiments were carried out to investigate this problem for a column packed with spherical porous aggregates. The effective diffusion coefficient of a tracer within the agreggates was determined from specific experiments. The dispersivity of the bed was determined from experiments carried out with a column filled with nonporous beads. We took advantage of the dependence of hydrodynamic dispersion on density ratios between the invading and displaced solutions to obtain a set of breakthrough curves corresponding to situations where the diffusion coefficient remains constant, whereas the dispersivity varies. Simulations reproduce correctly the experiments. Small discrepancies are noted that can be corrected either by increasing the dispersion coefficient or by fitting the external mass transfer coefficient. Increased dispersion coefficients probably reveal a modification of Taylor dispersion due to solute exchange. The fitted external mass transfer coefficients are close to the values obtained with classical correlations of the chemical engineering literature.
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    Transport in porous media 32 (1998), S. 187-198 
    ISSN: 1573-1634
    Keywords: diffusion ; dispersion ; miscible ; automaton
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    Topics: Geosciences , Technology
    Notes: Abstract A thermodynamic lattice gas (automaton) model is used to simulate dispersion in porous media. Simulations are constructed at two distinctly different scales, the pore scale at which capillary models are constructed and large scale or Darcy scale at which probabilistic collision rules are introduced. Both models allow for macroscopic (pore scale) phase separation. The pore scale models clearly show the effect of pore structure on dispersion. The large scale (mega scale) simulations indicate that when the pressure difference between the displacing phase and displaced phase is properly chosen (representing the average pressure gradient between the phases). The simulation results are consistent with both theoretical predictions and experimental observations.
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    Transport in porous media 37 (1999), S. 183-212 
    ISSN: 1573-1634
    Keywords: diffusion ; partitioning ; harmonic ; laminate ; interface ; lag ; attenuation ; dispersion.
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    Notes: Abstract The migration of organic compounds in stratified media is of fundamental concern in environmental and chemical engineering research. The diffusive transport of volatile organic compounds through laminate systems is characterized by partitioning, i.e., the development of concentration discontinuities at the interfaces between the individual laminae. If the transport is governed by cyclic transients, the relevant equations can be written in terms of coupled systems of diffusion equations subject to sinusoidal boundary conditions. This paper solves these systems of equations to present new algebraic solutions for propagation of the sinusoidal modes through arbitrary (finite) numbers of contiguous one-dimensional laminae. Both Cartesian and radial coordinate systems are considered. Two independent formulations of the lamina interface matching conditions are considered, corresponding to (1) an instantaneous partitioning model and to (2) a mass-limited partitioning model. It is shown that sinusoidal components of the concentration solutions propagate dispersively throughout the laminates. This is manifested, for example, in changes in shape of concentration pulses as measured at different points in the laminate system. Algorithms for generating exact dispersion relations for partitioning laminates are given, and an experimental technique for studying interfacial dynamics via frequency domain measurements is proposed.
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    Hydrogeology journal 7 (1999), S. 209-218 
    ISSN: 1435-0157
    Keywords: Key words tracer tests ; fractured rocks ; Germany ; diffusion ; analytical solutions
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    Topics: Geosciences
    Description / Table of Contents: Résumé Deux multitraçages ont été réalisés dans l'une des zones principales de failles du bassin de Lange Bramke (massif du Harz, Allemagne); les résultats confirment le rôle prédominant de la zone de failles pour l'écoulement souterrain et le transport de soluté. Les traceurs, possédant des coefficients de diffusion différents (deutérium, bromure, uranine et éosine), ont fourni des courbes de restitution qui ne peuvent être expliquées que par un modèle qui associe un transport advectif-dispersif dans les fractures à un échange par diffusion moléculaire dans la matrice. A l'échelle des expériences (distance maximale de 225 m), l'influence des fractures adjacentes a été négligée. Ce modèle a fourni pour chaque traceur pratiquement les mêmes paramètres pour la roche et le transport, ce qui signifie que l'approximation de la fracture unique est acceptable et que la diffusion dans la matrice joue un rôle important. La conductivité hydraulique de la zone de faille fournie par les traçages est d'environ 1,5×10–2 m/s, alors que la conductivité hydraulique régionale de la roche fracturée dans son ensemble est de l'ordre de 3×10–7 m/s, selon l'estimation tirée des âges tritium et de la porosité de la matrice d'environ 2%. Ces valeurs montrent que la conductivité hydraulique le long de la faille est supérieure de plusieurs ordres de grandeur à celle de la partie fracturée restante de l'aquifère, ce qui confirme le rôle prédominant joué par les zones de failles comme drains de l'eau et comme axes d'écoulement rapide.
    Abstract: Resumen Dos ensayos con múltiples trazadores realizados en una de las zonas más fracturadas de la cuenca de Lange Bramke (Montes Harz, Alemania) confirman el papel dominante de la zona de fractura en el flujo de agua subterránea y el transporte de solutos. Trazadores con distintos coeficientes de difusión molecular (deuterio, bromuro, uranina y eosina) dieron curvas de llegada que sólo pueden ser explicadas mediante un modelo que acople el transporte advectivo-dispersivo en las fracturas con la difusión en la matriz. Para la escala de los ensayos (distancia máxima de 225 m), se usó como aproximación que la influencia de las fracturas adyacentes podía despreciarse. Este modelo dio lugar para cada trazador a valores muy similares de los parámetros de transporte, lo que supone que la aproximación de fractura única es aceptable y que la difusión en la matriz es un mecanismo importante. La conductividad hidráulica de la zona fracturada obtenida de los ensayos es de unos 1.5×10–2 m/s, mientras que la conductividad hidráulica regional para la matriz rocosa es de unos 3×10–7 m/s, valor estimado de la edad del tritio y la porosidad de la matriz es del 2%. Estos resultados indican que la conductividad hidráulica a lo largo de la fractura es varios órdenes de magnitud mayor que la correspondiente al resto de la parte fracturada del acuífero, lo que confirma el papel dominante de las fracturas como zonas conductoras preferentes de agua.
    Notes: Abstract  Two multitracer tests performed in one of the major cross-fault zones of the Lange Bramke basin (Harz Mountains, Germany) confirm the dominant role of the fault zone in groundwater flow and solute transport. Tracers having different coefficients of molecular diffusion (deuterium, bromide, uranine, and eosine) yielded breakthrough curves that can only be explained by a model that couples the advective–dispersive transport in the fractures with the molecular diffusion exchange in the matrix. For the scale of the tests (maximum distance of 225 m), an approximation was used in which the influence of adjacent fractures is neglected. That model yielded nearly the same rock and transport parameters for each tracer, which means that the single-fracture approximation is acceptable and that matrix diffusion plays an important role. The hydraulic conductivity of the fault zone obtained from the tracer tests is about 1.5×10–2 m/s, whereas the regional hydraulic conductivity of the fractured rock mass is about 3×10–7 m/s, as estimated from the tritium age and the matrix porosity of about 2%. These values show that the hydraulic conductivity along the fault is several orders of magnitude larger than that of the remaining fractured part of the aquifer, which confirms the dominant role of the fault zones as collectors of water and conductors of fast flow.
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    Rheologica acta 29 (1990), S. 215-222 
    ISSN: 1435-1528
    Keywords: Polymermigration ; diffusion ; mixture ; thermodynamics ; velocitygradient flow
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    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract Molecular migration in nonhomogeneous flows of a polyelectrolyte solution is considered. The solution is modelled as a binary mixture whose electrically-charged constituents are regarded as compressible fluids. Upon deriving a set of thermodynamic restrictions for the mixture, non-equilibrium quantities are examined in detail. As a result, two schemes are elaborated for the description of cross streamline migration, induced by the second gradient of the velocity, where also occur coupling effects. In the first scheme the migration effect is described through a stress term which involves a coupling with the conformation of the macromolecule; in the second scheme it is described through a term in the diffusion velocity where coupling occurs with the velocity gradient. In both cases the thermodynamic approach leads to a systematic framework with a minimal number of constitutive coefficients, which is an essential aspect for any comparison with experimental data.
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    Rheologica acta 30 (1991), S. 263-269 
    ISSN: 1435-1528
    Keywords: Relaxation ; diffusion ; stretched exponential
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    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract In this contribution, we model the “long-time” behaviour of the desorption from an LDPE sheet, using non-Markovian random walks. It is shown that the mass of penetrant in the final stage of desorption decays as t −m , where m is proportional to the exponent of the probability distribution ψ(t) ∼ t −(1+u), 0 〈 v 〈 1. Furthermore, it is shown that this model may lead to the so-called mechanical stretched exponential relaxation, and that Wagner's memory function can be obtained as a special case.
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    Journal of atmospheric chemistry 15 (1992), S. 1-37 
    ISSN: 1573-0662
    Keywords: Air pollution models ; advection ; diffusion ; deposition ; chemical reactions ; photo-oxidants ; emissions ; ozone ; episodes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences
    Notes: Abstract A long-range transport model with nonlinear chemical reactions is described. The model contains 35 pollutants and 70 chemical reactions. This is a Eulerian model defined on a space domain containing the whole of Europe. The spherical space domain (corresponding to the Earth's surface covered by the model) is mapped into a square plane domain and discretized by using a 32×32 grid. The grid increments are equidistant (both along the Ox axis and along the Oy axis). The choice of values of the physical parameters involved in the model and the numerical treatment of the model are shortly discussed. The model is tested with meteorological data for 1985 and 1989. The numerical results are compared with measurements at stations located in different European countries. Extensive comparisons of ozone concentrations for July 1985 with measurements taken at 24 European stations are also carried out. Results concerning three episodes in July 1985 as well as results obtained in the study of the sensitivity of the ozone concentrations to variations of NO x and/or anthropogenic VOC emissions are presented. The advantages and the limitations of such a model are discussed. The model is continuously improved by adding new modules to it. The plans for improvements in the near future are outlined.
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    Journal of biological physics 21 (1995), S. 37-49 
    ISSN: 1573-0689
    Keywords: Membranes ; solutions ; diffusion ; gravitation force ; near-membrane layers
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    Topics: Biology , Physics
    Notes: Abstract This paper presents an interferometric method of the investigation of near-membrane diffusion layers. With the aid of this method a concrete investigation was made of such layers formed in the neighbourhood of a horizontally situated membrane which separates solutions of different concentrations. On the basis of interferograms obtained, a computer analysis of these interferograms is made. This permitted to obtain, among others, curves of the distribution of solution concentrations within these layers. These curves are next compared with curves made on the basis of equations given in the paper [16]. A satisfactory compatibility between the results of the experimental and theoretical investigations are obtained.
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    Space science reviews 83 (1998), S. 351-363 
    ISSN: 1572-9672
    Keywords: cosmic rays ; charged-particle transport ; diffusion
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    Topics: Physics
    Notes: Abstract A review of cosmic-ray transport coefficients, based on historic and recent observations and theoretical insights, is presented. Particular emphasis is on the transport of cosmic rays across the magnetic field, which is of foremost importance, and is presently poorly understood and widely debated.
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    Journal of biological physics 18 (1992), S. 297-306 
    ISSN: 1573-0689
    Keywords: biological fluid dynamics ; diffusion ; turbulence
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    Topics: Biology , Physics
    Notes: Abstract The effect of turbulent fluid motion on the diffusion of simple organisms is discussed. The net reproduction rate and the turbulent flow are assumed to be Gaussian-correlated random variables. For homogeneous istropic turbulence, simple equations for the average concentration of the organisms are derived in terms of the energy density of the fluid. It is shown that the effective diffusivity generated by the motion is positive-definite, and is independent of the helicity of the flow.
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    Foundations of physics 5 (1992), S. 63-69 
    ISSN: 1572-9524
    Keywords: mechanics ; probability ; stochastic ; quantum ; diffusion
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    Topics: Physics
    Notes: Abstract A direct construction is provided showing that the classical expectation value for the energy of a particle executing a classical diffusion process is equivalent to the quantum mechanical form with a Hamiltonian structured like that for a charged particle in an electromagnetic field.
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    Journal of statistical physics 101 (2000), S. 775-817 
    ISSN: 1572-9613
    Keywords: chaos ; diffusion ; Ehrenfest wind-tree model ; Lorentz gas ; statistical mechanics ; periodic orbits ; Brownian motion ; billiards ; time series analysis
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    Topics: Physics
    Notes: Abstract We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of models involving a single particle moving in two dimensions and colliding with fixed scatterers. We find that a number of microscopically nonchaotic models exhibit diffusion, and that the standard methods of chaotic time series analysis are ill suited to the problem of distinguishing between chaotic and nonchaotic microscopic dynamics. However, we show that periodic orbits play an important role in our models, in that their different properties in our chaotic and nonchaotic models can be used to distinguish them at the level of time series analysis, and in systems with absorbing boundaries. Our findings are relevant to experiments aimed at verifying the existence of chaoticity and related dynamical properties on a microscopic level in diffusive systems.
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    Journal of statistical physics 63 (1991), S. 291-303 
    ISSN: 1572-9613
    Keywords: Stochastic process ; diffusion ; gravity ; Vlasov equation
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    Topics: Physics
    Notes: Abstract The one-dimensional gravitational system consists ofN parallel sheets of constant mass density. The sheets move perpendicular to their surface solely under their mutual gravitational attraction. When a pair has an encounter, they simply pass through each other. In this paper I consider the motion of a single sheet in an equilibrium ensemble. Under the assumption that the times separating encounters are random, I show that the acceleration and velocity(A, V) of a labeled sheet form a Markovian pair. Further, I prove that, in the limit of largeN, (1)the(A, V) process is deterministic, (2) the(A, V) process obeys Vlasov dynamics, and (3) that scaled fluctuations in(A, V) comprise a diffusion which obeys a generalized Ornstein-Uhlenbeck process with time-dependent drift and diffusion tensors.
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  • 76
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    Journal of statistical physics 65 (1991), S. 1057-1083 
    ISSN: 1572-9613
    Keywords: Chemical kinetics ; reversible reactions ; diffusion ; bimolecular ; master equation ; simulation
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    Notes: Abstract Computer simulations of a simple model of a reversible diffusion-influenced reaction are used to test various approximate theoretical treatments. The model is a random walk in continuous time ofN particles on a one-dimensional lattice. The particles can be trapped reversibly at the origin. They move independently, except that only one particle at a time can occupy the origin. The theory is formulated in general terms using master equations for the probability distribution of occupancy numbers of different lattice sites. The general theoretical problem is not solved, although some exact consequences are presented. Several approximation schemes are described and tested by comparison with the simulations.
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  • 77
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    Journal of statistical physics 65 (1991), S. 1109-1122 
    ISSN: 1572-9613
    Keywords: Trapping reaction ; fluctuation phenomena ; diffusion
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    Notes: Abstract We present both mean-field and many-particle descriptions of trapping reaction kinetics in systems in which traps are not randomly distributed in space, but are attached to the segments of polymer coils.
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  • 78
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    Journal of statistical physics 66 (1992), S. 1415-1462 
    ISSN: 1572-9613
    Keywords: Spatially extended dynamical system ; cellular automata ; attractor ; basin ; separatrix ; diffusion ; dislocation ; domain ; invariant set ; finite automata ; transducer
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    Notes: Abstract Local space-time structures, such as domains and the intervening dislocations, dominate a wide class of cellular automaton (CA) behavior. For such spatially-extended dynamics regular domains, vicinities, and attractors are introduced as organizing principles to identify the discretized analogs of attractors, basins, and separatrices: structures used in classifying dissipative continuous-state dynamical systems. We describe the attractor-basin portrait of nonlinear elementary CA rule 18, whose global dynamics is largely determined by a single regular attracting domain. The latter's basin is analyzed in terms of subbasin and portal structures associated with particle annihilation. The conclusion is that the computational complexity of such CA is more apparent than real. Transducer machines are constructed that automatically identify domain and dislocation structures in space-time, count the number of dislocations in a spatial pattern, and implement an isomorphism between rule 18 and rule 90. We use a transducer to trace dislocation trajectories, and confirm that in rule 18, isolated dislocation trajectories, as well as a dislocation gas, agree extremely well with the classical model of annihilating diffusive particles. The CA efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space-time.
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  • 79
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    Journal of statistical physics 70 (1993), S. 1085-1098 
    ISSN: 1572-9613
    Keywords: Conductivity ; diffusion ; field-dependence ; Lorentz gas ; Lyapunov exponents
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    Notes: Abstract The conductivity and diffusion of a color-charged two-dimensional thermostatted Lorentz gas in a color field is studied by a variety of methods. In this gas, point particles move through a regular triangular array of soft scatterers, where, in the presence of a field, a nonequilibrium stationary state is reached by coupling to a Gaussian thermostat. The zero-field conductivity and diffusion coefficient are computed with equilibrium molecular dynamics dynamics from the Green-Kubo formula and the Einstein relation. Their values are consistent and approach those obtained by Machta and Zwanzig in the limit of hard (disk) scatterers. The field-dependent conductivity is obtained from its constitutive relation, from the coupling constant to the thermostat, and by using the recently derived conjugate pairing rule of Evans, Cohen, and Morriss, from the two maximal Lyapunov exponents of the Lorentz gas in the stationary state. All these methods give consistent results. Finally, elements of the field-dependent diffusion tensor have been computed. At zero field, they are consistent with the zero-field conductivity, but they vanish beyond a critical field strength, suggesting a dynamical phase transition at the critical field; the conductivity appears to remain finite, approaching a constant value for large field strengths.
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  • 80
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    Journal of statistical physics 81 (1995), S. 497-513 
    ISSN: 1572-9613
    Keywords: Lorentz lattice gas ; Lyapunov exponents ; dynamical chaos ; KS entropy ; diffusion ; kinetic theory of gases ; random walks
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    Notes: Abstract This paper provides an introduction to the applications of dynamical systems theory to nonequilibrium statistical mechanics, in particular to a study of nonequilibrium phenomena in Lorentz lattice gases with stochastic collision rules. Using simple arguments, based upon discussions in the mathematical literature, we show that such lattice gases belong to the category of dynamical systems with positive Lyapunov exponents. This is accomplished by showing how such systems can be expressed in terms of continuous phase space variables. Expressions for the Lyapunov exponent of a one-dimensional Lorentz lattice gas with periodic boundaries are derived. Other quantities of interest for the theory of irreversible processes are discussed.
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    Journal of statistical physics 84 (1996), S. 233-261 
    ISSN: 1572-9613
    Keywords: Random lattice ; diffusion ; critical behavior ; hyperscaling ; propagation ; cellular boundaries
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    Notes: Abstract We study the motion of a point particle along the bonds of a two-dimensional random lattice, whose sites are randomly occupied with right and left rotators, which scatter the particle according to deterministic scattering rules. We consider both a Poisson (PRL) and a vectorized random lattice (VRL) and fixed as well as flipping scatterers. On both lattices, for fixed scatterers and equal concentrations of right and left rotators the same anomalous diffusion of the particle is obtained as before for the triangular lattice, where the mean square displacement is ∼t, the diffusion process non-Gaussian, and the particle trajectories exhibit scaling behavior as at a percolation threshold. For unequal concentrations the particle is trapped exponentially rapidly. This system can be considered as an extreme case of the Lorentz lattice gases on regular lattices discussed before or as an example of the motion of a particle along cracks or (grain or cellular) boundaries on a two-dimensional surface.
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  • 82
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    Journal of statistical physics 92 (1998), S. 891-908 
    ISSN: 1572-9613
    Keywords: Random sequential adsorption ; hard-sphere particles ; gravity ; diffusion ; coverage ; structure
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    Notes: Abstract We investigate the coverage and structure of a layer of particles deposited on a line after diffusion in a gravitational field. The dynamics of the depositing particles is controlled by the gravity number N G(=πd 4 Δρg/6k B T), where d is the diameter of the particles, Δρ is the density difference between the particles and the solution, g is the acceleration due to gravity, k B is Boltzmann's constant, and T is the temperature. The position-dependent flux of particles in a gap formed by two preadsorbed particles is estimated by superposition of solutions of a steady-state convective diffusion equation for the flux in the presence of a single preadsorbed particle. The saturation coverages are found with a recursion relation and are in good agreement with those obtained from Brownian dynamics simulation. The jamming coverage increases rapidly with increasing particle size, particularly for large values of Δρ. An algorithm is presented to generate adsorbed configurations from which the structure of the deposit is determined.
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  • 83
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    Journal of statistical physics 98 (2000), S. 835-870 
    ISSN: 1572-9613
    Keywords: Boltzmann equation ; semiconductor ; diffusion ; energy transport model ; entropy dissipation rate
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    Notes: Abstract The diffusion limit of the Boltzmann equation of semiconductors is analyzed. The dominant collisions are the elastic collisions on one hand and the electron–electron collisions with the Pauli exclusion terms on the other hand. Under a nondegeneracy hypothesis on the distribution function, a lower bound of the entropy dissipation rate of the leading term of the Boltzmann kernel for semiconductors in terms of a distance to the space of Fermi–Dirac functions is proved. This estimate and a mean compactness lemma are used to prove the convergence of the solution of the Boltzmann equation to a solution of the energy transport model.
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  • 84
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    Journal of statistical physics 101 (2000), S. 107-124 
    ISSN: 1572-9613
    Keywords: transient chaos ; conditionally invariant measures ; natural measures ; critical state ; diffusion
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    Notes: Abstract Generalized multibaker maps are introduced to model dissipative systems which are spatially extended only in certain directions and escape of particles is allowed in other ones. Effects of nonlinearity are investigated by varying a control parameter. Emphasis is put on the appearance of the critical state representing the borderline of transient chaos, where anomalous behavior sets in. The investigations extend to the conditionally invariant and the related natural measures and to transient diffusion in normal and critical states as well. Permanent chaos is also considered as a special case.
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  • 85
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    Journal of statistical physics 62 (1991), S. 1059-1071 
    ISSN: 1572-9613
    Keywords: Dynamic properties ; Brownian motion ; diffusion ; superstrong polymers ; polymers ; nonpolymeric molecules ; liquid crystalline phases
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    Notes: Abstract This paper presents a summary of unique highly nonlinear static and dynamic theories for chain molecules (actually, for almost any kind of organic molecule), including the first superstrong polymers. These theories have been used to predict and explain (1) the physical self-assembly (self-ordering) of specific kinds of molecules into liquid crystalline (LC) phases (i.e., partially ordered phases) and (2) the diffusion of these molecules in various LC phases and the isotropic (I) liquid phase.
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    Journal of statistical physics 63 (1991), S. 897-914 
    ISSN: 1572-9613
    Keywords: Transport ; diffusion
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    Notes: Abstract This paper considers the one-dimensional advection and diffusion of a passive scalar in the context of baker's maps of the unit interval. Our main interest is the thermal transport between two points held at fixed temperatures, when a deterministic sequence of maps of various scales are involved. Molecular diffusion occurs during the periods of rest between maps. We focus on the behavior of the transport in the limit of infinite Péclet number (or small molecular diffusion). Various asymptotic results are presented and compared with numerical calculations. Convergence to turbulent transport independent of molecular diffusion is observed as the number of scales is increased.
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  • 87
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    Keywords: Reaction kinetics ; diffusion ; capillary ; segregation
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    Notes: Abstract An experimental investigation of one-dimensional, diffusion-limited A+B→C chemical reactions is reported. The persistence of reactant segregation and the formation of a depletion zone is observed and expressed in terms of the universal time exponents:α (motion of the boundary zone),β (width of instantaneous product formation zone),γ (rate of instantaneous local formation of product),δ (rate of instantaneous global formation of product), etc. There is good agreement with the recently predicted and/or simulated values:α=1/2,β=1/6,γ=2/3,δ=1/2, in contrast to classical predictions (α=0,β=1/2,γ=0,δ=−1/2). Furthermore, classically the segregation would not be preserved and there would be no formation of a depletion zone and no motion (just dissipation) of the reaction zone. We also discuss the relations to electrode oxidation-reduction reactions, i.e., A+C→C where C is a catalyst, electrode, or “trap.”
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    Journal of statistical physics 65 (1991), S. 1085-1093 
    ISSN: 1572-9613
    Keywords: Reversible reactions ; saturable traps ; bimolecular ; diffusion ; superposition approximation ; cubic lattice
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    Notes: Abstract Simulations of the kinetics of the reversible diffusion-influenced reaction A+B⇄AB on a cubic lattice, with initial conditions [A] = [B], [AB]=0, are compared with the predictions of two approximate theoretical formalisms. The first involves a simple rate equation with rate coefficients that are proportional to the time-dependent rate coefficient for an irreversible reaction. The second, which is based on a superposition approximation, contains a rate coefficient that explicitly depends on the bulk concentrations. Both reduce to the Smoluchowski approach in the irreversible limit. The results obtained using the modified rate equation formalism are exact at short times, but tend to approach equilibrium too rapidly. The predictions of the computationally more demanding superposition formalism agree remarkably well with the simulations for all times for the range of parameters examined.
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    Journal of statistical physics 68 (1992), S. 563-573 
    ISSN: 1572-9613
    Keywords: Lattice gas ; cellular automata ; diffusion
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    Notes: Abstract A one-dimensional lattice-gas model is proposed and used to simulate diffusion processes in one dimension. Explicit forms of transport coefficients are given as a function of density and kinetic energy within the Boltzmann approximation. Without definitions of temperature and pressure, a steady nontrivial solution is given analytically in the nonconvective case when the kinetic energy is kept constant.
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    Journal of statistical physics 70 (1993), S. 197-211 
    ISSN: 1572-9613
    Keywords: Langevin equation ; diffusion ; superdiffusive transport
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    Notes: Abstract We discuss some aspects of the intriguing problem of interplay between molecular diffusion and the geometry of the velocity field in the diffusion of test particles. By simple arguments one can understand how the diffusion coefficient can have a large enhancement from the combined effects of the noise and the drift terms in the Langevin equation ruling the motion of test particles. The same effects give rise to the superdiffusive transport observed in media with correlated random velocity fields.
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  • 91
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    Journal of statistical physics 81 (1995), S. 379-393 
    ISSN: 1572-9613
    Keywords: Lattice-Boltzmann ; multiphase flow ; diffusion
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    Notes: Abstract A lattice Boltzmann model for simulating fluids with multiple components and interparticle forces proposed by Shan and Chen is described in detail. Macroscopic equations governing the motion of each component are derived by using the Chapman-Enskog method. The mutual diffusivity in a binary mixture is calculated analytically and confirment by numerical simulation. The diffusivity is generally a function of the concentrations of the two components but independent of the fluid velocity, so that the diffusion is Galilean invariant. The analytically calculated shear kinematic viscosity of this model is also confiremoed numerically.
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    Journal of statistical physics 99 (2000), S. 1-29 
    ISSN: 1572-9613
    Keywords: diffusion ; aggregation ; phase transition ; nonequilibrium
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    Notes: Abstract We study the nonequilibrium phase transition in a model of aggregation of masses allowing for diffusion, aggregation on contact, and fragmentation. The model undergoes a dynamical phase transition in all dimensions. The steady-state mass distribution decays exponentially for large mass in one phase. In the other phase, the mass distribution decays as a power law accompanied, in addition, by the formation of an infinite aggregate. The model is solved exactly within a mean-field approximation which keeps track of the distribution of masses. In one dimension, by mapping to an equivalent lattice gas model, exact steady states are obtained in two extreme limits of the parameter space. Critical exponents and the phase diagram are obtained numerically in one dimension. We also study the time-dependent fluctuations in an equivalent interface model in (1+1) dimension and compute the roughness exponent χ and the dynamical exponent z analytically in some limits and numerically otherwise. Two new fixed points of interface fluctuations in (1+1) dimension are identified. We also generalize our model to include arbitrary fragmentation kernels and solve the steady states exactly for some special choices of these kernels via mappings to other solvable models of statistical mechanics.
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  • 93
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    International journal of thermophysics 11 (1990), S. 835-861 
    ISSN: 1572-9567
    Keywords: compressibility ; dichloroethane ; diffusion ; high pressure ; p, V, T, data ; rough hard sphere ; viscosity
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    Notes: Abstract (p, V, T) data for dichloroethane (DCE) have been obtained at 278.15, 288.15, 298.15, 313.15, 323.15, and 338.15 K for pressures either slightly below the freezing pressure or up to a maximum of 280 M Pa, together with densities at 0.1 MPa. A high-pressure self-centering falling-body viscometer method has been used to measure shear viscosities at 278.15, 288.15, 298.15, 313.15, and 323.15 K for pressures either slightly below the freezing pressure or up to a maximum of 330 MPa. Self-diffusion coefficients for DCE are reported at 278.15, 288.15, 298.15, and 313.15 K for maximum pressures up to 300 MPa. Isothermal compressibilities, isobaric expansivities, and internal pressures have been evaluated from the volumetric data. The shear viscosities and self-diffusion coefficients have been interpreted in terms of a modified rough hard-spheres theory. The anomalous behavior observed for p-V-T, shear viscosities, and self diffusion at higher temperatures and pressures is suspected to be the result of temperature and pressure altering the population ratio of the two molecular conformers, trans and gauche.
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    International journal of thermophysics 11 (1990), S. 863-873 
    ISSN: 1572-9567
    Keywords: diffusion ; hard-sphere theory ; n-alkanes ; thermal conductivity ; viscosity
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    Notes: Abstract Thermal conductivity, viscosity, and self-diffusion coefficient data for liquid n-alkanes are satisfactorily correlated simultaneously by a method based on the hard-sphere theory of transport properties. Universal curves are developed for the reduced transport properties λ *, η *, and D * as a function of the reduced volume. A consistent set of equations is derived for the characteristic volume and for the parameters R λ, R η, and R D, introduced to account for the nonsphericity and roughness of the molecules. The temperature range of the above scheme extends from 110 to 370 K, and the pressure range up to 650 MPa.
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  • 95
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    International journal of thermophysics 12 (1991), S. 837-854 
    ISSN: 1572-9567
    Keywords: diffusion ; helium ; thermal conductivity ; thermal diffusion ; transport properties ; virials ; viscosity
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    Notes: Abstract Second virial coefficients and transport properties of helium are presented based on a state-of-the-art interatomic potential which was constructed with the use of a multiproperty fit. The experimental potential employed to produce these properties accurately reproduces a wide range of bulk and microscopic data and agrees well with ab initio calculations which were not available at the time of its construction. Virial coefficients of 3He and 4He are presented from 2 to 600 K, and transport properties of pure 3He and 4He gases and 3He-4He mixtures are presented from 5 to 6000 K.
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  • 96
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    International journal of thermophysics 13 (1992), S. 895-905 
    ISSN: 1572-9567
    Keywords: benzene ; diffusion ; ethylbenzene ; hard-sphere theory ; mesitylene ; thermal conductivity ; toluene ; viscosity ; xylene
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    Topics: Physics
    Notes: Abstract A previously described method, based on consideration of hard-sphere theory, is used for the simultaneous correlation of the coefficients of self-diffusion, viscosity, and thermal conductivity for benzene, toluene, o-, m-, and p-xylene, mesitylene, and ethylbenzene in excellent agreement with experiment, over extended temperature and pressure ranges. Values are given for the roughness factors R D , R η, and R λ, and the characteristic volume, V 0, is expressed as a function of both carbon number and temperature.
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    International journal of thermophysics 13 (1992), S. 729-733 
    ISSN: 1572-9567
    Keywords: diffusion ; hard-sphere theory ; molecular dynamics
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    Notes: Abstract Recent accurate calculations of the corrections to Enskog theory for hard-sphere diffusion have resulted in a revision of the hard-sphere based correlation for dense fluid transport coefficients. The expression previously given for. the reduced diffusion coefficient in terms of reduced volume is adjusted in line with these values. No changes are required to the characteristic volumes but the roughness factors are reduced. Of particular note is the fact that methane now corresponds to a rough hard-sphere system.
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  • 98
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    International journal of thermophysics 19 (1998), S. 437-448 
    ISSN: 1572-9567
    Keywords: alkanes ; carbon dioxide ; diffusion ; mixtures ; molecular dynamics ; thermal conductivity ; viscosity
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    Notes: Abstract Equilibrium molecular dynamics simulations of mixtures of n-decane with methane, ethane, and carbon dioxide and of the mixture carbon dioxide–ethane were performed using the anisotropic united atoms model for n-decane and one-and two-center Lennard–Jones models for the light components. The Green–Kubo relations were used to calculate the viscosity, thermal conductivity, and inter- and intradiffusion. Viscosities are predicted with a maximum deviation of 30% at low gas concentrations and less than 10% deviation at high gas concentrations. The viscosity and thermal conductivity are less sensitive to the cross interactions than the diffusion coefficients, which exhibit deviations between models and with experiments of up to 60%.
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    International journal of thermophysics 20 (1999), S. 267-277 
    ISSN: 1572-9567
    Keywords: diffusion ; liquid metals ; shear viscosity ; simple liquids ; thermal conductivity
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    Notes: Abstract Several simple approximate hard-sphere relations for transport coefficients are compared with the results of molecular dynamics (MD) simulations performed on Lennard–Jones (LJ) fluids. Typically the individual transport coefficients: self-diffusion coefficients, D, shear viscosity, ηs, bulk viscosity, ηB, and thermal conductivity, λ, agree within a factor of two of the exact results over the fluid and liquid parts of the phase diagram, which seems reasonable in view of the approximations involved in the models. We have also considered the ratio, λ/ηs, and the product, Dηs, for which simple analytic expressions exist in the hardsphere models. These two quantities also agree within a factor of two of the simulation values and hard sphere analytic expressions. Using time correlation functions, Tankeshwar has recently related the ratio λ/D to thermodynamic quantities, in particular, to the differences in specific heats, C p − C V, and to the isothermal compressibility, κT. Using D and thermodynamic values taken solely from LJ MD simulations, his relation was tested and found to give typically better than ~20% agreement at liquid densities, deteriorating somewhat as density decreases into the gas phase. Finally liquid metals are considered. In this case, λ is dominated by its electronic contribution, which is related approximately to the electrical conductivity by the Wiedemann–Franz Law. Some theoretical results for the electrical conductivity of Na are referenced, which allow a semiquantitative understanding of the measured thermal conductivity of the liquid metal. Shear viscosity is also discussed and, following the work of Tosi, is found to be dominated by ionic contributions; Nevertheless, at the melting temperature of Na, a relation emerges between thermal conductivity, electrical resistivity and shear viscosity.
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    International journal of thermophysics 13 (1992), S. 269-281 
    ISSN: 1572-9567
    Keywords: diffusion ; hard-sphere theory ; n-alkanes ; thermal conductivity ; viscosity
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    Notes: Abstract Recent accurate measurements of the self-diffusion coefficient for n-hexadecane and n-octane and of the viscosity coefficient for n-heptane, n-nonane, and n-undecane over wide pressure ranges have been used to provide a critical test of a previously described method, based on consideration of hard-sphere theory, for the correlation of transport coefficient data. It is found that changes are required to the universal curve for the reduced viscosity coefficient as a function of reduced volume and, also, to the parameters R D, R η , and R λ which were introduced to account for effects of nonspherical molecular shape. The scheme now accounts most satisfactorily for the self-diffusion, viscosity, and thermal conductivity coefficient data for all n-alkanes from methane to hexadecane at densities greater than the critical density.
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