Deterministic and stochastic perturbations of area preserving flows on a two-dimensional torus

2011 ◽  
Vol 32 (3) ◽  
pp. 899-918 ◽  
Author(s):  
DMITRY DOLGOPYAT ◽  
MARK FREIDLIN ◽  
LEONID KORALOV
Keyword(s):  
Incompressible Flows ◽  
Saddle Points ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Dimensional Torus ◽  
Ergodic Component ◽  
Stochastic Perturbations ◽  
Long Time ◽  
Area Preserving

AbstractWe study deterministic and stochastic perturbations of incompressible flows on a two-dimensional torus. Even in the case of purely deterministic perturbations, the long-time behavior of such flows can be stochastic. The stochasticity is caused by instabilities near the saddle points as well as by the ergodic component of the locally Hamiltonian system on the torus.

scholarly journals Long Time Behavior of the Solution of the Two-Dimensional Dissipative QGE in Lei–Lin Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Moez Benhamed ◽  
Sahar Mohammad Abusalim
Keyword(s):  
Asymptotic Behavior ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Long Time

In this paper, we study the asymptotic behavior of the two-dimensional quasi-geostrophic equations with subcritical dissipation. More precisely, we establish that θtX1−2α vanishes at infinity.

Two-Dimensional Phase Transitions of Chemisorbed Uracil on Ag(111):  Modeling of Short- and Long-Time Behavior

1996 ◽  
Vol 100 (47) ◽  
pp. 18491-18501 ◽  
Author(s):  
Rolando Guidelli ◽  
Maria Luisa Foresti ◽  
Massimo Innocenti
Keyword(s):  
Phase Transitions ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Long Time

TIP INSTABILITY DURING CONFINED DIFFUSION-LIMITED GROWTH

1988 ◽  
Vol 02 (08) ◽  
pp. 945-951 ◽  
Author(s):  
DAVID A. KESSLER ◽  
HERBERT LEVINE
Keyword(s):  
Evolution Equations ◽  
Dynamical Behavior ◽  
Stable Steady State ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Limited Growth ◽  
Channel Geometry ◽  
Diffusion Limited ◽  
Long Time

We study diffusion-limited crystal growth in a two dimensional channel geometry. We demonstrate that although there exists a linearly stable steady-state finger solution of the pattern evolution equations, the true dynamical behavior can be controlled by a tip-widening instability. Possible scenarios for the long-time behavior of the system are presented.

The asymptotic behavior of a stochastic multigroup SIS model

2018 ◽  
Vol 11 (03) ◽  
pp. 1850037 ◽  
Author(s):  
Chunyan Ji ◽  
Daqing Jiang
Keyword(s):  
Asymptotic Behavior ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Endemic Equilibrium ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Sis Model ◽  
Stochastic Perturbations ◽  
Long Time ◽  
Theoretical Results

In this paper, we explore the long time behavior of a multigroup Susceptible–Infected–Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.

Phase Transition in Two-Dimensional Biased Diffusion

1998 ◽  
Vol 09 (07) ◽  
pp. 1021-1024 ◽  
Author(s):  
Alexander Kirsch
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Drift Velocity ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Long Time ◽  
Biased Diffusion

We investigate the long-time behavior of the drift velocity of two-dimensional biased diffusion with varying bias B and percentage p of allowed sites. A phase diagram for the drift/no-drift transition depending on B and p is presented.

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