Kramers' diffusion problem and diffusion across characteristic boundaries

1982 ◽  
pp. 318-345 ◽  
Author(s):  
B. Matkowsky ◽  
Z. Schuss
Keyword(s):  
Diffusion Problem ◽  
And Diffusion

Role of facilitated diffusion of calcium by calbindin in intestinal calcium absorption

1992 ◽  
Vol 262 (2) ◽  
pp. C517-C526 ◽  
Author(s):  
J. J. Feher ◽  
C. S. Fullmer ◽  
R. H. Wasserman
Keyword(s):  
Negative Feedback ◽  
Calcium Absorption ◽  
Feedback Inhibition ◽  
Basolateral Membrane ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Facilitated Diffusion ◽  
Calbindin D9k ◽  
And Diffusion

Computer simulations of transcellular Ca2+ transport in enterocytes were carried out using the simulation program SPICE. The program incorporated a negative-feedback entry of Ca2+ at the brush-border membrane that was characterized by an inhibitor constant of 0.5 microM cytosolic Ca2+ concentration ([Ca2+]). The basolateral Ca(2+)-ATPase was simulated by a four-step mechanism that resulted in Michaelis-Menten kinetics with a Michaelis constant of 0.24 microM [Ca2+]. The cytosolic diffusion of Ca2+ was simulated by dividing the cytosol into 10 slabs of equal width. Ca2+ binding to calbindin-D9K was simulated in each slab, and diffusion of free Ca2+, free calbindin, and Ca(2+)-laden calbindin was simulated between each slab. The cytosolic [Ca2+] of the simulated cells was regulated within the physiological range. Calbindin-D9K reduced the cytosolic [Ca2+] gradient, increased Ca2+ entry into the cell by removing the negative-feedback inhibition of Ca2+ entry, increased cytosolic Ca2+ flow, and increased the efflux of Ca2+ across the basolateral membrane by increasing the free [Ca2+] immediately adjacent to the pump. The enhancement of transcellular Ca2+ transport was nearly linearly dependent on calbindin-D9K concentration. The values of the dissociation constant (Kd) for calbindin-D9K were previously obtained experimentally in the presence and absence of KCl. Calbindin with the Kd obtained in the presence of KCl enhanced the simulated Ca2+ transport more than with the Kd obtained in the absence of KCl. This result suggests that the physiological Kd of calbindin is optimal for the enhancement of transcellular Ca2+ transport. The simulated Ca2+ flow was less than that predicted from the "near-equilibrium" analytic solution of the reaction-diffusion problem.

ON ONE EFFECTIVE DIFFERENCE SCHEME FOR THE CONVECTION‐DIFFUSION PROBLEM

2001 ◽  
Vol 6 (2) ◽  
pp. 231-240
Author(s):  
G. Gromyko
Keyword(s):  
Difference Scheme ◽  
Iterative Algorithm ◽  
Diffusion Problem ◽  
Point Of View ◽  
Numerical Calculations ◽  
Test Problems ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
The Given ◽  
And Diffusion

The given paper is devoted to build‐up of the special economic difference schemes for non‐stationary one and two‐dimensional problems of a convection ‐ diffusion permitting to take into account convective and diffusion terms from the uniform point of view. On the basis of a multicomponent schemes build‐up procedure, bound up with region decomposition of the cells of mesh, the economic multicomponent iterative algorithm is constructed. A series of numerical calculations on some test problems solution including Burgers problem is reduced, and the comparison with known, most spread schemes is proceeded.

scholarly journals ECONOMIC ALGORITHM FOR EVALUATING THE PARAMETER FOR THE GLOBAL MODEL OF TRANSFER AND DIFFUSION

2020 ◽  
Vol 4 (1) ◽  
pp. 123-128
Author(s):  
Marina V. Platonova ◽  
Ekaterina G. Klimova
Keyword(s):  
Data Assimilation ◽  
Diffusion Problem ◽  
Global Model ◽  
Model Data ◽  
Unknown Parameters ◽  
Concentration Data ◽  
Passive Impurity ◽  
Transport And Diffusion ◽  
And Diffusion ◽  
Joint Assessment

The paper considers the data assimilation algorithm for the global model of transport and diffusion. An algorithm is proposed for finding an estimate of an unknown parameter for the transport and diffusion problem of a passive impurity. Various options for data assimilation algorithms with unknown parameters are described: searching for a joint assessment of a system and a parameter and evaluating only a parameter. The problems of implementing data assimilation algorithms and methods for solving them are shown. The ensemble algorithm of the Kalman filter is given, the economical use of it is argued. An important property of the proposed algorithm is its locality - the algorithm can be applied locally in subdomains. The results of numerical experiments with model data for estimating the unknown emission of a passive impurity from concentration data are presented. A comparative analysis of the results is carried out

scholarly journals Numerical Analysis of Convection–Diffusion Using a Modified Upwind Approach in the Finite Volume Method

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1869
Author(s):  
Arafat Hussain ◽  
Zhoushun Zheng ◽  
Eyaya Fekadie Anley
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Scheme ◽  
Diffusion Problem ◽  
Second Order ◽  
Order Accuracy ◽  
Central Difference ◽  
Convection Diffusion ◽  
Volume Method ◽  
And Diffusion

The main focus of this study was to develop a numerical scheme with new expressions for interface flux approximations based on the upwind approach in the finite volume method. Our new proposed numerical scheme is unconditionally stable with second-order accuracy in both space and time. The method is based on the second-order formulation for the temporal approximation, and an upwind approach of the finite volume method is used for spatial interface approximation. Some numerical experiments have been conducted to illustrate the performance of the new numerical scheme for a convection–diffusion problem. For the phenomena of convection dominance and diffusion dominance, we developed a comparative study of this new upwind finite volume method with an existing upwind form and central difference scheme of the finite volume method. The modified numerical scheme shows highly accurate results as compared to both numerical schemes.

scholarly journals Exponential Stability in Hyperbolic Thermoelastic Diffusion Problem with Second Sound

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Moncef Aouadi
Keyword(s):  
Exponential Stability ◽  
Classical Theory ◽  
Hyperbolic Equations ◽  
Propagation Speed ◽  
Diffusion Problem ◽  
Second Sound ◽  
Thermoelastic Diffusion ◽  
Infinite Propagation Speed ◽  
And Diffusion ◽  
Cattaneo’S Law

We consider a thermoelastic diffusion problem in one space dimension with second sound. The thermal and diffusion disturbances are modeled by Cattaneo's law for heat and diffusion equations to remove the physical paradox of infinite propagation speed in the classical theory within Fourier's law. The system of equations in this case is a coupling of three hyperbolic equations. It poses some new analytical and mathematical difficulties. The exponential stability of the slightly damped and totally hyperbolic system is proved. Comparison with classical theory is given.

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