10,683 research outputs found
Statistical switching kinetics in ferroelectrics
By assuming a more realistic nucleation and polarization reversal scenario we
build a new statistical switching model for ferroelectrics, which is different
from either the Kolmogorov-Avrami-Ishibashi (KAI) model or the
Nucleation-Limited-Switching (NLS) model. After incorporating a time-dependent
depolarization field this model gives a good description about the retardation
behavior in polycrystalline thin films at medium or low fields, which can not
be described by the traditional KAI model. This model predicts correctly n=1
for polycrystalline thin films at high Eappl or ceramic bulks in the ideal
case
New variable separation approach: application to nonlinear diffusion equations
The concept of the derivative-dependent functional separable solution, as a
generalization to the functional separable solution, is proposed. As an
application, it is used to discuss the generalized nonlinear diffusion
equations based on the generalized conditional symmetry approach. As a
consequence, a complete list of canonical forms for such equations which admit
the derivative-dependent functional separable solutions is obtained and some
exact solutions to the resulting equations are described.Comment: 19 pages, 2 fig
Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations
An approximate perturbed direct homotopy reduction method is proposed and
applied to two perturbed modified Korteweg-de Vries (mKdV) equations with
fourth order dispersion and second order dissipation. The similarity reduction
equations are derived to arbitrary orders. The method is valid not only for
single soliton solution but also for the Painlev\'e II waves and periodic waves
expressed by Jacobi elliptic functions for both fourth order dispersion and
second order dissipation. The method is valid also for strong perturbations.Comment: 8 pages, 1 figur
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