Multichannel Quantum-Classical Diffusion Equations

2003 ◽  
pp. 855-883
Author(s):  
M. V. Basilevsky ◽  
A. I. Voronin
Keyword(s):  
Diffusion Equations ◽  
Classical Diffusion

scholarly journals Non-classical diffusion equations related to birth-death processes with two boundaries

1996 ◽  
Vol 54 (3) ◽  
pp. 423-443 ◽  
Author(s):  
Z. G. Mansourati ◽  
L. L. Campbell
Keyword(s):  
Diffusion Equations ◽  
Classical Diffusion ◽  
Birth Death

scholarly journals Classical and Quantum Models of Diffusion

2021 ◽  
Vol 03 (02) ◽  
pp. 1-1
Author(s):  
Angelo Morro ◽  
Keyword(s):  
Diffusion Models ◽  
Diffusion Equations ◽  
Classical Diffusion ◽  
Quantum Models ◽  
Classical Models ◽  
Quantum And Classical Models

The objective of the paper is twofold: first, to review the classical diffusion models and show the approximations at the origin of the parabolic character of the classical equations; second, to demonstrate a connection between the quantum and classical models of diffusion. As diffusion is inherently related to the motion of constituents, the consistent models are framed within the dynamics of mixtures. The derivation of diffusion equations is then determined based on the related, pertinent approximations.

Computer Simulation of Amperometric Biosensor Response to Mixtures of Compounds

2002 ◽  
Vol 7 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
J. Christensen ◽  
F. Ivanauskas ◽  
J. Kulys
Keyword(s):  
Computer Simulation ◽  
Enzymatic Reaction ◽  
Diffusion Equations ◽  
Response Data ◽  
Finite Difference Technique ◽  
Stationary Diffusion ◽  
Biosensor Array ◽  
Menten Kinetic ◽  
Biosensor Response

A mathematical model of amperometric biosensors has been developed. The model bases on non-stationary diffusion equations containing a non-linear term related to Michaelis-Menten kinetic of the enzymatic reaction. The model describes the biosensor response to mixtures of multiple compounds in two regimes of analysis: batch and flow injection. Using computer simulation, large amount of biosensor response data were synthesised for calibration of a biosensor array to be used for characterization of wastewater. The computer simulation was carried out using the finite difference technique.

Certain problems with the application of stochastic diffusion processes for description of chemical engineering phenomena; Kolmogorov and classic diffusion equations

1988 ◽  
Vol 53 (6) ◽  
pp. 1181-1197
Author(s):  
Vladimír Kudrna
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Parabolic Type ◽  
Diffusion Equations ◽  
Stochastic Motion ◽  
Energy Component ◽  
Classic Form

The paper presents alternative forms of partial differential equations of the parabolic type used in chemical engineering for description of heat and mass transfer. It points at the substantial difference between the classic form of the equations, following from the differential balances of mass and enthalpy, and the form following from the concept of stochastic motion of particles of mass or energy component. Examples are presented of the processes that may be described by the latter method. The paper also reviews the cases when the two approaches become identical.

QELSS diffusion data for moderately broad molar mass distribution polymer samples compared with data from classical gradient techniques

1989 ◽  
Vol 54 (7) ◽  
pp. 1821-1829
Author(s):  
Bedřich Porsch ◽  
Simon King ◽  
Lars-Olof Sundelöf
Keyword(s):  
Diffusion Coefficient ◽  
Mass Distribution ◽  
Molar Mass ◽  
Molar Mass Distribution ◽  
Diffusion Data ◽  
Mass Distributions ◽  
Classical Diffusion ◽  
Polydisperse Polymer

The differences between the QELSS and classical diffusion coefficient of a polydisperse polymer resulting from distinct definitions of experimentally accessible average values are calculated for two assumed specific forms of molar mass distributions. Predicted deviations are compared with the experiment using NBS 706 standard polystyrene. QELSS Dz of this sample relates within 2-4% to the classical diffusion coefficient, if the Schulz-Zimm molar mass distribution is assumed to be valid. In general, differences between the height-area and QELSS diffusion coefficient of about 20% may be found for Mw/Mn ~ 2, and this value may increase above 35%, if strongly tailing molar mass distribution pertains to the sample.

Certain problems with the application of stochastic diffusion processes for description of chemical engineering phenomena; Diffusion equations in curvilinear coordinates

1991 ◽  
Vol 56 (3) ◽  
pp. 602-618
Author(s):  
Vladimír Kudrna
Keyword(s):  
Heat Transfer ◽  
Mass Transport ◽  
Probability Density ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Curvilinear Coordinates ◽  
Diffusion Equations ◽  
Parabolic Partial Differential Equations ◽  
Spherical Coordinates ◽  
Transformation Procedure

Parabolic partial differential equations used in chemical engineering for the description of mass transport and heat transfer and analogous relationship derived in stochastic processes theory are given. A standard transformation procedure is applied, allowing these relations to be generally written in curvilinear coordinates and particular expressions for cylindrical and spherical coordinates to be derived. The relation between the probability density for the position of a discernible particle and the concentration of a set of such particles is discussed.

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