Abstract: In this paper, one dimensional advection diffusion
model is analyzed using finite difference method based on
Crank-Nicolson scheme. A practical problem of filter cake washing
of chemical engineering is analyzed. The model is converted into
dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the
Crank-Nicolson spatial derivative scheme is used in space domain
and forward difference scheme is used in time domain. The scheme is
found to be unconditionally convergent, stable, first order accurate in
time and second order accurate in space domain. For a test problem,
numerical results are compared with the analytical ones for different
values of parameter.
Abstract: Calcium [Ca2+] is an important second messenger
which plays an important role in signal transduction. There are
several parameters that affect its concentration profile like buffer
source etc. The effect of stationary immobile buffer on Ca2+
concentration has been incorporated which is a very important
parameter needed to be taken into account in order to make the
model more realistic. Interdependence of all the important parameters
like diffusion coefficient and influx over [Ca2+] profile has been
studied. Model is developed in the form of advection diffusion
equation together with buffer concentration. A program has been
developed using finite volume method for the entire problem and
simulated on an AMD-Turion 32-bit machine to compute the
numerical results.
Abstract: Mathematical and computational modeling of calcium
signalling in nerve cells has produced considerable insights into how
the cells contracts with other cells under the variation of biophysical
and physiological parameters. The modeling of calcium signaling in
astrocytes has become more sophisticated. The modeling effort has
provided insight to understand the cell contraction. Main objective
of this work is to study the effect of voltage gated (Operated)
calcium channel (VOC) on calcium profile in the form of advection
diffusion equation. A mathematical model is developed in the form
of advection diffusion equation for the calcium profile. The model
incorporates the important physiological parameter like diffusion
coefficient etc. Appropriate boundary conditions have been framed.
Finite volume method is employed to solve the problem. A program
has been developed using in MATLAB 7.5 for the entire problem
and simulated on an AMD-Turion 32-bite machine to compute the
numerical results.