Translating patterns in a generalized Ginzburg-Landau amplitude equation

1995 ◽  
pp. 165-180
Author(s):  
Jinqiao Duan
Keyword(s):  
Amplitude Equation ◽  
Ginzburg Landau

The Effect of Throughflow on Weakly Nonlinear Convection in a Viscoelastic Saturated Porous Medium

2020 ◽  
Vol 9 (1) ◽  
pp. 36-46
Author(s):  
Palle Kiran ◽  
B. S. Bhadauria ◽  
R. Roslan
Keyword(s):  
Heat Transport ◽  
Viscoelastic Fluid ◽  
Flow Direction ◽  
Saturated Porous Medium ◽  
Finite Amplitude ◽  
Amplitude Equation ◽  
Bottom Plate ◽  
Amplitude Analysis ◽  
Ginzburg Landau ◽  
Weakly Nonlinear

In this paper we have investigated the effect of throughflow on thermal convection in a viscoelastic fluid saturated porous media. The governing equations are modelled in the presence of throughflow. These equations are made dimensionless and the obtained nonlinear problem solved numerically. There are two types of throughflow effects on thermal instability inflow and outflow investigated by finite amplitude analysis. This finite amplitude equation is obtained using the complex Ginzburg-Landau amplitude equation (CGLE) for a weak nonlinear oscillatory convection. The heat transport analysis is given by complex Ginzburg-Landau amplitude equation (CGLE). The numerical results indicate that due to the non-uniform throughflow there is instability at the bottom plate and influence the heat transfer in the system. The vertical throughflow is having both stable and unstable modes depending on flow direction. The nature of viscoelastic fluid is having both effects either stabilize or destabilize. Further, it is found that the nonlinear throughflow effects have dual role on heat transport. The solutions of the present problem are obtained numerically by using Runge-Kutta fourth order method.

Transition from pulses to fronts in the cubic–quintic complex Ginzburg–Landau equation

2009 ◽  
Vol 367 (1901) ◽  
pp. 3227-3238 ◽  
Author(s):  
Pablo Gutiérrez ◽  
Daniel Escaff ◽  
Orazio Descalzi
Keyword(s):  
Numerical Simulations ◽  
Control Parameter ◽  
Approximation Scheme ◽  
Landau Equation ◽  
Amplitude Equation ◽  
Ginzburg Landau ◽  
Analytical Expression ◽  
Localized Structures ◽  
Upper Limit ◽  
Pulse Type

The cubic–quintic complex Ginzburg–Landau is the amplitude equation for systems in the vicinity of an oscillatory sub-critical bifurcation (Andronov–Hopf), and it shows different localized structures. For pulse-type localized structures, we review an approximation scheme that enables us to compute some properties of the structures, like their existence range. From that scheme, we obtain conditions for the existence of pulses in the upper limit of a control parameter. When we study the width of pulses in that limit, the analytical expression shows that it is related to the transition between pulses and fronts. This fact is consistent with numerical simulations.

scholarly journals Ginzburg-Landau amplitude equation for nonlinear nonlocal models

2021 ◽  
Vol 103 (2) ◽  
Author(s):  
Stefano Garlaschi ◽  
Deepak Gupta ◽  
Amos Maritan ◽  
Sandro Azaele
Keyword(s):  
Amplitude Equation ◽  
Ginzburg Landau ◽  
Nonlocal Models

scholarly journals Superconducting Order Parameter Nucleation and Critical Currents in the Presence of Weak Stray Fields in Superconductor/Insulator/Ferromagnet Hybrids

Coatings ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 507
Author(s):  
Vasiliy N. Kushnir ◽  
Serghej L. Prischepa ◽  
Michela Trezza ◽  
Carla Cirillo ◽  
Carmine Attanasio
Keyword(s):  
Phenomenological Theory ◽  
Critical Currents ◽  
Superconducting Phase ◽  
Stray Field ◽  
Superconducting Properties ◽  
Ginzburg Landau ◽  
Ferromagnetic Layers ◽  
Linearized System ◽  
Critical Current Density Jc ◽  
Usadel Equations

The stray fields produced by ferromagnetic layers in Superconductor/Insulator/Ferromagnet (S/I/F) heterostructures may strongly influence their superconducting properties. Suitable magnetic configurations can be exploited to manipulate the main parameters of the hybrids. Here, the nucleation of the superconducting phase in an external magnetic field that periodically oscillates along the film width is studied on the base of the numerical solution of the linearized system of Usadel equations. In addition, the effect of the magnetic configuration of the F-layer on the temperature dependence of the critical current density, Jc(T), is investigated in the framework of the Ginzburg–Landau phenomenological theory on the base of the oscillating model of a stray field. By following this approach, the Jc(T) dependence of a Nb/SiO2/PdNi trilayer is reproduced for different magnetic configurations of the PdNi layer.

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