Solutions to Space-Time Fractional Complex Ginzburg-Landau Equations With the Complete Discrimination System for Polynomial Method

2021 ◽  
Vol 42 (8) ◽  
pp. 874-880
Author(s):  
HU Yan ◽  
◽  
◽  
SUN Yuhuai
Keyword(s):  
Space Time ◽  
Polynomial Method ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations ◽  
Complete Discrimination System

CHARACTERIZATION OF SYNCHRONIZED SPATIOTEMPORAL STATES IN COUPLED NONIDENTICAL COMPLEX GINZBURG–LANDAU EQUATIONS

2000 ◽  
Vol 10 (10) ◽  
pp. 2381-2389 ◽  
Author(s):  
J. BRAGARD ◽  
F. T. ARECCHI ◽  
S. BOCCALETTI
Keyword(s):  
Space Time ◽  
Dynamical Regime ◽  
Complete Synchronization ◽  
Ginzburg Landau ◽  
Synchronization Process ◽  
One Dimensional ◽  
Spatially Extended ◽  
Dynamical Regimes ◽  
Ginzburg Landau Equations

We characterize the synchronization of two nonidentical spatially extended fields ruled by one-dimensional Complex Ginzburg–Landau equations, in the two regimes of phase and amplitude turbulence. If two fields display the same dynamical regime, the coupling induces a transition to a completely synchronized state. When, instead, the two fields are in different dynamical regimes, the transition to complete synchronization is mediated by defect synchronization. In the former case, the synchronized manifold is dynamically equivalent to that of the unsynchronized systems, while in the latter case the synchronized state substantially differs from the unsynchronized one, and it is mainly dictated by the synchronization process of the space-time defects.

PATTERNS, DEFECTS, AND EVOLUTION OF BÉNARD–MARANGONI CELLS

1996 ◽  
Vol 06 (09) ◽  
pp. 1665-1671 ◽  
Author(s):  
J. BRAGARD ◽  
J. PONTES ◽  
M.G. VELARDE
Keyword(s):  
Fluid Layer ◽  
Ambient Air ◽  
Finite Geometry ◽  
Amplitude Equations ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Numerical Exploration ◽  
Ginzburg Landau Equations ◽  
Rigid Plane ◽  
Selection Of

We consider a thin fluid layer of infinite horizontal extent, confined below by a rigid plane and open above to the ambient air, with surface tension linearly depending on the temperature. The fluid is heated from below. First we obtain the weakly nonlinear amplitude equations in specific spatial directions. The procedure yields a set of generalized Ginzburg–Landau equations. Then we proceed to the numerical exploration of the solutions of these equations in finite geometry, hence to the selection of cells as a result of competition between the possible different modes of convection.

Geometric effect on the vortex configuration and motion in mesoscopic superconducting cylinders

2015 ◽  
Vol 29 (03) ◽  
pp. 1550009 ◽  
Author(s):  
Shan-Shan Wang ◽  
Guo-Qiao Zha
Keyword(s):  
Phase Transitions ◽  
Vortex Dynamics ◽  
Axial Symmetry ◽  
Time Dependent ◽  
Vortex Matter ◽  
Ginzburg Landau ◽  
Geometric Effect ◽  
Multiply Connected ◽  
Vortex States ◽  
Ginzburg Landau Equations

Based on the time-dependent Ginzburg–Landau equations, we study numerically the vortex configuration and motion in mesoscopic superconducting cylinders. We find that the effects of the geometric symmetry of the system and the noncircular multiply-connected boundaries can significantly influence the steady vortex states and the vortex matter moving. For the square cylindrical loops, the vortices can enter the superconducting region in multiples of 2 and the vortex configuration exhibits the axial symmetry along the square diagonal. Moreover, the vortex dynamics behavior exhibits more complications due to the existed centered hole, which can lead to the vortex entering from different edges and exiting into the hole at the phase transitions.

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