scholarly journals Solution of a Diffusion Problem in a Non-Homogeneous Flow and Diffusion Field by the Integral Representation Method (IRM)

2014 ◽  
Vol 3 (1) ◽  
pp. 15
Author(s):  
Hiroshi Isshiki
Keyword(s):  
Integral Representation ◽  
Diffusion Problem ◽  
Diffusion Field ◽  
Homogeneous Flow ◽  
Representation Method ◽  
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.

Laplace- and diffusion-field-controlled growth in electrochemical deposition

1989 ◽  
Vol 62 (23) ◽  
pp. 2703-2706 ◽  
Author(s):  
P. Garik ◽  
D. Barkey ◽  
E. Ben-Jacob ◽  
E. Bochner ◽  
N. Broxholm ◽  
...  
Keyword(s):  
Electrochemical Deposition ◽  
Diffusion Field ◽  
Controlled Growth ◽  
And Diffusion

Diffusion in Potential Fields: Time-Dependent Capture on Radial and Rectangular Substrates

2004 ◽  
Vol 859 ◽  
Author(s):  
J. A. Venables ◽  
P. Yang
Keyword(s):  
Periodic Boundary ◽  
Energy Surface ◽  
Periodic Boundary Conditions ◽  
Nucleation And Growth ◽  
Time Dependent ◽  
Potential Fields ◽  
Diffusion Field ◽  
Rectangular Array ◽  
Diffusion Controlled ◽  
And Diffusion

ABSTRACTIn models of nucleation and growth on surfaces, it is usually assumed that the energy surface of the substrate is flat, that diffusion is isotropic, and that capture numbers can be calculated in the diffusion-controlled limit. We lift these restrictions analytically, and introduce a hybrid discrete FFT method of solving for the 2D time-dependent diffusion field of adparticles on general non-uniform substrates. The method, with periodic boundary conditions, is appropriate, for example, following nucleation on a regular (rectangular) array of defects. The programs, which have been realized in Matlab®6.5, are instructive for visualizing potential and diffusion fields, and for producing illustrative movies of crystal growth under various conditions. Here we demonstrate the time-dependence of capture numbers in the initial stages of annealing at high adparticle concentration in the presence of repulsive adparticle-cluster interactions; however it is clear that the method works in general for deposition, growth and annealing at all times.

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.

Numerical simulation of velocity field and diffusion field in an urban area

1990 ◽  
Vol 15 (3-4) ◽  
pp. 345-356 ◽  
Author(s):  
Shuzo Murakami ◽  
Akashi Mochida ◽  
Yoshihiko Hayashi ◽  
Kazuki Hibi
Keyword(s):  
Numerical Simulation ◽  
Velocity Field ◽  
Urban Area ◽  
Diffusion Field ◽  
And Diffusion

Numerical Solution of Two-Dimensional Advection–Diffusion Equation Using Generalized Integral Representation Method

2017 ◽  
Vol 14 (01) ◽  
pp. 1750028 ◽  
Author(s):  
Gantulga Tsedendorj ◽  
Hiroshi Isshiki
Keyword(s):  
Diffusion Equation ◽  
Integral Representation ◽  
Approximate Solutions ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Infinite Domain ◽  
Advection Diffusion Equation ◽  
Advection Diffusion ◽  
Representation Method ◽  
Advective Diffusion

Generalized integral representation method (GIRM) is designed to numerically solve initial and boundary value problems for differential equations. In this work, we develop numerical schemes based on 1- and 2-step GIRMs for evaluation of the two-dimensional problem of advective diffusion in an infinite domain. Accurate approximate solutions are obtained in both cases of GIRM and compared to the exact ones. The derivation of GIRM is straightforward and implementation is simple.

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