Biomedical subjects
Publications and source records attributed to Kwok Sau Fa.
We investigate the motion of a particle governed by a generalized Langevin equation with fractional derivative, nonlocal dissipative force, and long-time correlation function. We derive general expressions for the variances with a linear external force. We also analyze their asymptotic behaviors for the power-law correlation function without external force.
We consider the Langevin equation with a multiplicative noise term that depends on time and space. The corresponding Fokker-Planck equation in the Stratonovich approach is investigated. Its exact solution is obtained for an arbitrary multiplicative noise term given by g (x,t) =D (x) T (t) , and the behaviors of probability distributions, for some specific functions of D (x) , are analyzed. We show that the asymptotic shape of the random-walk model and power-law decay obtained from other approaches can be reproduced from our solutions, by employing two simple functions for g (x,t) . In particular, for D(x) approximately /x/(-theta/2) , the physical solutions for the probability distribution in the Ito, Stratonovich, and postpoint discretization approaches can be obtained and analyzed.
We consider the time-fractional diffusion equation with time dependent diffusion coefficient given by (O)O(alpha)(C)(t) W (x,t) = D(alpha,gamma)(t)(gamma) [theta(2) W (x,t) /theta x(2)], where O is the Caputo operator. We investigate its solutions in the infinite and the finite domains. The mean squared displacement and the mean first passage time are also considered. In particular, for alpha = 0 , the mean squared displacement is given by approximately t(gamma) and we verify that the mean first passage time is finite for superdiffusive regimes.
We investigate the solutions and the first passage time for anomalous diffusion processes governed by the usual diffusion equation. We consider a space- and time-dependent diffusion coefficient and the presence of absorbing boundaries. We obtain analytical results for the probability distribution and the first passage time distribution for finite and semi-infinite intervals. In addition, we compare our results for the first passage time distribution with the one obtained by the usual diffusion equation with constant diffusion coefficient.
We investigate one-dimensional equations for the diffusion with a nonconstant diffusion coefficient inside the second derivative and between the derivatives. In particular, we employ the diffusion coefficient D(x) proportional to /x/(-theta)(theta in R) and a quartic potential. These diffusion equations present a rich variety of behaviors associated with different regimes. Results of two approaches are analyzed and compared. We also investigate the mean first passage time of these systems. We show that the system with the coefficient D(x) between the derivatives can produce different behaviors for the mean first passage time in comparison with those obtained by the system with the coefficient inside the derivatives.