Analytic solutions for the temperature-field behaviour of the Ginzburg-Landau Ising type mean-field model with Dirichlet boundary conditions

2019 ◽  
Author(s):  
Peter A. Djondjorov ◽  
Vassil M. Vassilev ◽  
Daniel M. Danchev
Keyword(s):  
Temperature Field ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Field Model ◽  
Mean Field ◽  
Analytic Solutions ◽  
Dirichlet Boundary Conditions ◽  
Mean Field Model ◽  
Ginzburg Landau ◽  
Field Behaviour

scholarly journals The nonlocal mean-field equation on an interval

2019 ◽  
Vol 22 (05) ◽  
pp. 1950028
Author(s):  
Azahara DelaTorre ◽  
Ali Hyder ◽  
Luca Martinazzi ◽  
Yannick Sire
Keyword(s):  
Field Equation ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mean Field ◽  
Higher Order ◽  
Dirichlet Boundary Conditions ◽  
Field Equations ◽  
Mean Field Equations ◽  
Blowing Up ◽  
Mean Field Equation

We consider the fractional mean-field equation on the interval [Formula: see text] [Formula: see text] subject to Dirichlet boundary conditions, and prove that existence holds if and only if [Formula: see text]. This requires the study of blowing-up sequences of solutions. We provide a series of tools in particular which can be used (and extended) to higher-order mean field equations of nonlocal type.

BOUNDARY EFFECTS IN THE COMPLEX GINZBURGàLANDAU EQUATION

1999 ◽  
Vol 09 (11) ◽  
pp. 2209-2214 ◽  
Author(s):  
VÍCTOR M. EGUÍLUZ ◽  
EMILIO HERNÁNDEZ-GARCÍA ◽  
ORESTE PIRO
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Landau Equation ◽  
Plane Waves ◽  
Finite Geometry ◽  
Dirichlet Boundary Conditions ◽  
Boundary Effects ◽  
Two Dimensional ◽  
Ginzburg Landau ◽  
Robust Solutions

The effect of a finite geometry on the two-dimensional complex Ginzburg–Landau equation is addressed. Boundary effects induce the formation of novel states. For example, target-like solutions appear as robust solutions under Dirichlet boundary conditions. Synchronization of plane waves emitted by boundaries, entrainment by corner emission, and anchoring of defects by shock lines are also reported.

An exact analysis for heat conduction in laminated infinite cylindrical arches subjected to Dirichlet boundary conditions

2020 ◽  
Vol 64 (1-4) ◽  
pp. 509-516
Author(s):  
Hai Qian ◽  
Yuexiang Qiu ◽  
Yang Yang ◽  
Fuzhe Xie
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Superposition Principle ◽  
Dirichlet Boundary Conditions ◽  
Linear Superposition ◽  
Temperature Boundary ◽  
Temperature Filed ◽  
Temperature Solution

The temperature field within a layered arch subjected to Dirichlet Boundary Conditions is investigated based on the exact heat conduction theory. An analytical method is shown to obtain the temperature field in the arch. Because of the complex of the temperature boundary conditions, the temperature field is divided into two parts with the linear superposition principle. The first part is a temperature filed from the temperature boundary conditions on the lateral surfaces. The second part is from the temperature conditions on the outside surfaces expect the influence from the two edges. The temperature solution of the first part is constructed directly according to the temperature boundary conditions on the lateral surfaces. The temperature solution of the second part is studied with transfer matrix method. The convergence of the solutions is checked with respect to the number of the terms of series. Comparing the results with those obtained from the finite element method, the correctness of the present method is verified. Finally, the influences of surface temperature and the thickness-radius ratio h∕r0 on the distribution of temperature in the arch are discussed in detail.

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