A mean-field model of superconducting vortices

1996 ◽  
Vol 7 (2) ◽  
pp. 97-111 ◽  
Author(s):  
S. J. Chapman ◽  
J. Rubinstein ◽  
M. Schatzman
Keyword(s):  
Steady State ◽  
Field Model ◽  
Local Existence ◽  
Mean Field ◽  
State Problem ◽  
Mean Field Model ◽  
Type Ii Superconductor ◽  
Superconducting Vortices ◽  
Steady State Problem ◽  
Steady State Solutions

A mean-field model for the motion of rectilinear vortices in the mixed state of a type-II superconductor is formulated. Steady-state solutions for some simple geometries are examined, and a local existence result is proved for an arbitrary smooth geometry. Finally, a variational formulation of the steady-state problem is given which shows the solution to be unique.

Analysis of a mean field model of superconducting vortices

1999 ◽  
Vol 10 (4) ◽  
pp. 319-352 ◽  
Author(s):  
R. SCHÄTZLE ◽  
V. STYLES
Keyword(s):  
Weak Solution ◽  
Steady State ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Field Model ◽  
Mean Field ◽  
Two Dimensions ◽  
Mean Field Model ◽  
Superconducting Vortices

We study a mean-field model of superconducting vortices in one and two dimensions. The existence of a weak solution and a steady-state solution of the model are proved. A special case of the steady-state problem is shown to be of the form of a free boundary problem. The solutions of this free boundary problem are investigated. It is also shown that the weak solution of the one-dimensional model is unique and satisfies an entropy inequality.

Steady-state properties of a mean-field model of driven inelastic mixtures

2002 ◽  
Vol 66 (1) ◽  
Author(s):  
Umberto Marini Bettolo Marconi ◽  
Andrea Puglisi
Keyword(s):  
Steady State ◽  
Field Model ◽  
Mean Field ◽  
Mean Field Model

Convergence of a homotopy finite element method for computing steady states of Burgers’ equation

2019 ◽  
Vol 53 (5) ◽  
pp. 1629-1644 ◽  
Author(s):  
Wenrui Hao ◽  
Yong Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Steady State ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Steady State Solution ◽  
State Problem ◽  
Steady State Problem ◽  
Steady State Solutions ◽  
Element Method

In this paper, the convergence of a homotopy method (1.1) for solving the steady state problem of Burgers’ equation is considered. When ν is fixed, we prove that the solution of (1.1) converges to the unique steady state solution as ε → 0, which is independent of the initial conditions. Numerical examples are presented to confirm this conclusion by using the continuous finite element method. In contrast, when ν = ε →, numerically we show that steady state solutions obtained by (1.1) indeed depend on initial conditions.

scholarly journals A Mean-Field Description of Bursting Dynamics in Spiking Neural Networks with Short-Term Adaptation

2020 ◽  
Vol 32 (9) ◽  
pp. 1615-1634 ◽  
Author(s):  
Richard Gast ◽  
Helmut Schmidt ◽  
Thomas R. Knösche
Keyword(s):  
Population Dynamics ◽  
Phase Transitions ◽  
Steady State ◽  
Field Model ◽  
Mean Field ◽  
Short Term ◽  
Mean Field Model ◽  
Neural Communication ◽  
Short Term Adaptation ◽  
The Mean

Bursting plays an important role in neural communication. At the population level, macroscopic bursting has been identified in populations of neurons that do not express intrinsic bursting mechanisms. For the analysis of phase transitions between bursting and non-bursting states, mean-field descriptions of macroscopic bursting behavior are a valuable tool. In this article, we derive mean-field descriptions of populations of spiking neurons and examine whether states of collective bursting behavior can arise from short-term adaptation mechanisms. Specifically, we consider synaptic depression and spike-frequency adaptation in networks of quadratic integrate-and-fire neurons. Analyzing the mean-field model via bifurcation analysis, we find that bursting behavior emerges for both types of short-term adaptation. This bursting behavior can coexist with steady-state behavior, providing a bistable regime that allows for transient switches between synchronized and nonsynchronized states of population dynamics. For all of these findings, we demonstrate a close correspondence between the spiking neural network and the mean-field model. Although the mean-field model has been derived under the assumptions of an infinite population size and all-to-all coupling inside the population, we show that this correspondence holds even for small, sparsely coupled networks. In summary, we provide mechanistic descriptions of phase transitions between bursting and steady-state population dynamics, which play important roles in both healthy neural communication and neurological disorders.

Steady-State Problem of an S-K-T Competition Model with Spatially Degenerate Coefficients

2021 ◽  
Vol 31 (11) ◽  
pp. 2150165
Author(s):  
Hao Zhou ◽  
Yu-Xia Wang
Keyword(s):  
Steady State ◽  
Global Bifurcation ◽  
Steady State Solution ◽  
Competition Model ◽  
State Solution ◽  
State Problem ◽  
Cross Diffusion ◽  
Positive Steady State ◽  
Steady State Problem ◽  
Steady State Solutions

In this paper, we study the steady-state problem of an S-K-T competition model with a spatially degenerate intraspecific competition coefficient. First, the global bifurcation continuum of positive steady-state solutions from its semitrivial steady-state solution is given, which depends on the spatial heterogeneity and cross-diffusion. Second, two limiting systems are derived as the cross-diffusion coefficient tends to infinity. Moreover, we demonstrate the existence of positive steady-state solutions near the two limiting systems, and show which one of the limiting systems characterizes the positive steady-state solution.

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