scholarly journals Stationary solutions of two-dimensional heterogeneous energy models with multiple species

2004 ◽  
Author(s):  
Annegret Glitzky ◽  
Rolf Hünlich
Keyword(s):  
Stationary Solutions ◽  
Two Dimensional ◽  
Energy Models ◽  
Multiple Species

scholarly journals Complex magnetism of the two-dimensional antiferromagnetic Ge2F: from a Néel spin-texture to a potential antiferromagnetic skyrmion

RSC Advances ◽  
2021 ◽  
Vol 11 (15) ◽  
pp. 8654-8663
Author(s):  
Fatima Zahra Ramadan ◽  
Flaviano José dos Santos ◽  
Lalla Btissam Drissi ◽  
Samir Lounis
Keyword(s):  
Density Functional Theory ◽  
Magnetic Properties ◽  
Density Functional ◽  
Low Energy ◽  
Two Dimensional ◽  
Functional Theory ◽  
2D Material ◽  
Energy Models ◽  
Spin Texture

Based on density functional theory combined with low-energy models, we explore the magnetic properties of a hybrid atomic-thick two-dimensional (2D) material made of germanene doped with fluorine atoms in a half-fluorinated configuration (Ge2F).

ON STABILITY OF PHYSICALLY REASONABLE SOLUTIONS TO THE TWO-DIMENSIONAL NAVIER–STOKES EQUATIONS

2019 ◽  
pp. 1-52
Author(s):  
Yasunori Maekawa
Keyword(s):  
Stokes Equations ◽  
Stationary Solutions ◽  
Navier Stokes ◽  
Domain Modeling ◽  
Asymptotically Stable ◽  
Two Dimensional ◽  
Spatial Infinity ◽  
Navier Stokes Equations ◽  
Unique Existence ◽  
Fundamental Object

The flow past an obstacle is a fundamental object in fluid mechanics. In 1967 Finn and Smith proved the unique existence of stationary solutions, called the physically reasonable solutions, to the Navier–Stokes equations in a two-dimensional exterior domain modeling this type of flows when the Reynolds number is sufficiently small. The asymptotic behavior of their solution at spatial infinity has been studied in detail and well understood by now, while its stability has remained open due to the difficulty specific to the two-dimensionality. In this paper, we prove that the physically reasonable solutions constructed by Finn and Smith are asymptotically stable with respect to small and well-localized initial perturbations.

scholarly journals Finding analytic stationary solutions to the chemical master equation by gluing state spaces at one or two states recursively

2017 ◽  
Author(s):  
X. Flora Meng ◽  
Ania-Ariadna Baetica ◽  
Vipul Singhad ◽  
Richard M. Murray
Keyword(s):  
Master Equation ◽  
Analytic Solutions ◽  
Stationary Solutions ◽  
Chemical Master Equation ◽  
Biochemical Reaction ◽  
Reaction Networks ◽  
Two Dimensional ◽  
Biochemical Reaction Networks ◽  
State Spaces ◽  
Elementary Reactions

AbstractNoise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model that describes how the probability distribution of a chemically reacting system varies with time. Knowing analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterise state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing stationary distributions that satisfy user-specified constraints. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and chemical reactions with two-dimensional state spaces.Subject AreasSystems biology, synthetic biology, biomathematics, bioengineering

CHAOTIC STATIONARY SOLUTIONS OF CELLULAR NEURAL NETWORKS

2003 ◽  
Vol 13 (11) ◽  
pp. 3499-3504 ◽  
Author(s):  
FANG-YUE CHEN ◽  
ZENG-RONG LIU
Keyword(s):  
Neural Networks ◽  
Stationary Solution ◽  
Main Tool ◽  
Stationary Solutions ◽  
Cellular Neural Networks ◽  
Cantor Set ◽  
Two Dimensional ◽  
One Dimensional ◽  
Specific Term

This study describes the chaotic stationary solutions of one-dimensional Cellular Neural Networks (CNN) without inputs with a specific term by applying the iteration map method. Under perfectly determined specific parameters, the map which corresponds to the stationary solution of CNN is two-dimensional and has a hyperbolic invariant Cantor set on which it is topologically conjugate to a two-sided shift of symbols space. The used main tool is the Conley–Moser conditions.

Circular stationary solutions in two-dimensional neural fields

2001 ◽  
Vol 85 (3) ◽  
pp. 211-217 ◽  
Author(s):  
Herrad Werner ◽  
Tim Richter
Keyword(s):  
Stationary Solutions ◽  
Two Dimensional ◽  
Neural Fields
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