Coupling of adsorption and diffusion in porous and granular materials. A 1-D example of the boundary value problem

2000 ◽  
Vol 70 (7) ◽  
pp. 519-531 ◽  
Author(s):  
B. Albers
Keyword(s):  
Boundary Value Problem ◽  
Granular Materials ◽  
Boundary Value ◽  
And Diffusion

scholarly journals Local Dynamics of Logistic Equation with Delay and Diffusion

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1566
Author(s):  
Sergey Kashchenko
Keyword(s):  
Boundary Value Problem ◽  
Equilibrium State ◽  
Boundary Value ◽  
Small Neighborhood ◽  
Logistic Equation ◽  
Asymptotic Formulas ◽  
Parametric Perturbation ◽  
Original Boundary ◽  
And Diffusion ◽  
Equation With Delay

The behavior of all the solutions of the logistic equation with delay and diffusion in a sufficiently small positive neighborhood of the equilibrium state is studied. It is assumed that the Andronov–Hopf bifurcation conditions are met for the coefficients of the problem. Small perturbations of all coefficients are considered, including the delay coefficient and the coefficients of the boundary conditions. The conditions are studied when these perturbations depend on the spatial variable and when they are time-periodic functions. Equations on the central manifold are constructed as the main results. Their nonlocal dynamics determines the behavior of all the solutions of the original boundary value problem in a sufficiently small neighborhood of the equilibrium state. The ability to control the dynamics of the original problem using the phase change in the perturbing force is set. The numerical and analytical results regarding the dynamics of the system with parametric perturbation are obtained. The asymptotic formulas for the solutions of the original boundary value problem are given.

scholarly journals Analysis of the Fully Developed Chute Flow of Granular Materials

1992 ◽  
Vol 59 (1) ◽  
pp. 109-119 ◽  
Author(s):  
Hojin Ahn ◽  
Christopher E. Brennen ◽  
Rolf H. Sabersky
Keyword(s):  
Boundary Value Problem ◽  
Granular Materials ◽  
Solid Fraction ◽  
Shooting Method ◽  
Constitutive Relations ◽  
Boundary Value ◽  
Granular Temperature ◽  
Mean Velocity ◽  
Chute Flow ◽  
Two Parameters

Existing constitutive relations and governing equations have been used to solve for fully developed chute flows of granular materials. In particular, the results of Lun et al. (1984) have been employed and the boundary value problem has been formulated with two parameters (the coefficient of restitution between particles, and the chute inclination), and three boundary values at the chute base wall, namely the values of solid fraction, granular temperature, and mean velocity at the wall. The boundary value problem has been numerically solved by the “shooting method.” The results show the significant role played by granular conduction in determining the profiles of granular temperature, solid fraction, and mean velocity in chute flows. These analytical results are also compared with experimental measurements of velocity fluctuation, solid fraction, and mean velocity made by Ahn et al. (1989), and with the computer simulations by Campbell and Brennen (1985b).

Sign in / Sign up

Export Citation Format

Share Document