For the backward diffusion equation, a stable discrete energy regularization algorithm is proposed. Existence and uniqueness of the numerical solution are given. Moreover, the error between the solution of the given backward diffusion equation and the numerical solution via the regularization method can be estimated. Some numerical experiments illustrate the efficiency of the method, and its ap...

The present paper is aimed to study an exact analysis of the free vibrations of a simply supported, homogeneous, transversely isotropic, cylindrical panel based on three-dimensional generalized theories of thermoelastic diffusion. After applying the displacement potential functions in the basic governing equations of generalized thermoelastic diffusion, it is noticed that a purely transverse mo...

In this paper, the one-dimensional α-fractional diffusion equation is revisited. This equation is a particular case of the timeand space-fractional diffusion equation with the quotient of the orders of the timeand space-fractional derivatives equal to one-half. First, some integral representations of its fundamental solution including the Mellin-Barnes integral representation are derived. Then ...

Infinitely extended two-dimensional reaction–diffusion lattices composed of bistable cells are considered. A class of particular stable stationary solutions, called pattern solutions, is introduced and examples are given. Pattern solutions persist at high diffusion coefficients whereas all other stable stationary solutions, with the exception of the constant solutions, disappear one after the o...

The study of solution dynamics is a very fundamental area of research with wide ranging importance from physical chemistry through to the life sciences. A common theme is that the interactions which control the dynamics and organization of solutions are generally very weak. Translational diffusion provides a non-invasive, direct and natural probe of the dynamics and pulsed gradient spin-echo (P...

Material transports in hyaluronan (HA) aqueous solution were investigated applying two different techniques, i.e., pulsed field gradient NMR (PFG-NMR) and photochemical quenching, to the measurement of diffusion constants to show a sharp contrast resulting from the difference of the spectroscopic observation time while the same probe molecules were commonly used in two experiments. The value fr...

1. It is shown that NaCl acts like CaCl(2) or LaCl(3) in preventing the diffusion of strong acids through the membrane of the egg of Fundulus with this difference only that a M/8 solution of NaCl acts like a M/1,000 solution of CaCl(2) and like a M/30,000 solution of LaCl(3). 2. It is shown that these salts inhibit the diffusion of non-dissociated weak acid through the membrane of the Fundulus ...

In this paper, we embark on a new strategy for computing the steady state solution of the diffusion equation. The new strategy is to solve an equivalent first-order hyperbolic system instead of the second-order diffusion equation, introducing solution gradients as additional unknowns. We show that schemes developed for the first-order system allow O(h) time step instead of O(h) and converge ver...

BACKGROUND The diffusion and reaction of the transmitter acetylcholine in neuromuscular junctions and the diffusion and binding of Ca2+ in the dyadic clefts of ventricular myocytes have been extensively modeled by Monte Carlo simulations and by finite-difference and finite-element solutions. However, an analytical solution that can serve as a benchmark for testing these numerical methods has be...

In this paper, we discuss the numerical solution of space fractional diffusion equations. The method of solution is based on using Chebyshev polynomials and finite difference with Gauss-Lobatto points. The validity and reliability of this scheme is tested by its application in various space fractional diffusion equations. The obtained results reveal that the proposed method is more accurate and...