Dynamic transition and pattern formation in Taylor problem

Abstract

The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, by using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In particular, it is shown that as the Taylor number crosses the critical number, the system undergoes either a continuous or a jump dynamic transition, dictated by the sign of a computable, nondimensional parameter R. In addition, it is also shown that the new transition states have the Taylor vortex type of flow structure, which is structurally stable.

The dynamic bifurcation of the Brusselator model in two-dimensional region

“…The technical method for the analysis is the dynamical transition theory in [4], which has been developed by Ma and Wang [3,4,5,6,7]. With this method in our disposal, we study the dynamic bifurcation of the Brusselator Model in this work.…”

Bifurcation solutions of Gross-Pitaevskii equations for spin-1 Bose-Einstein condensates

“…In nature, it is well-known that there are two different kinds of phase transitions including the dynamical phase transitions, and topological phase transitions (TPTs), also called the pattern formation transitions, for the details we refer to [22,30]. The rigorous theory of dynamical phase transitions in the dissipative system goes back to the pioneering work established by Ma and Wang in [28], many interesting results related to dynamical phase transitions refer to [12,18,22,23,24,25,26,27,28,36,37]. For the rigorous mathematical theory associated with topological phase transitions, we refer to [22] and the series works for TPTs in [30].…”

S1 attractor bifurcation analysis for a three-species cooperating model

“…The authors apply the attractor bifurcation theory [1,2] to provide a strict mathematical interpretation of the magnetohydrodynamic convection [3] and Taylor problem [4]. Here we will apply the theory to consider the three-species cooperating model [5][6][7][8][9][10] in one-dimensional…”