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Div-curl lemma revisited: Applications in electromagnetism

Marián Slodička, Ján Jr. Buša (2010)

Kybernetika

Two new time-dependent versions of div-curl results in a bounded domain Ω 3 are presented. We study a limit of the product v k w k , where the sequences v k and w k belong to Ł 2 ( Ω ) . In Theorem 2.1 we assume that × v k is bounded in the L p -norm and · w k is controlled in the L r -norm. In Theorem 2.2 we suppose that × w k is bounded in the L p -norm and · w k is controlled in the L r -norm. The time derivative of w k is bounded in both cases in the norm of - 1 ( Ω ) . The convergence (in the sense of distributions) of v k w k to the product v w of weak limits...

Duality of Schramm-Loewner evolutions

Julien Dubédat (2009)

Annales scientifiques de l'École Normale Supérieure

In this note, we prove a version of the conjectured duality for Schramm-Loewner Evolutions, by establishing exact identities in distribution between some boundary arcs of chordal SLE κ , κ > 4 , and appropriate versions of SLE κ ^ , κ ^ = 16 / κ .

Dynamic stability and spatial heterogeneityin the individualbased modelling of a lotkavolterra gas

Jacek Waniewski, Wojciech Jędruch, Norbert Żołek (2004)

International Journal of Applied Mathematics and Computer Science

Computer simulation of a few thousands of particles moving (approximately) according to the energy and momentum conservation laws on a tessellation of squares in discrete time steps and interacting according to the predator-prey scheme is analyzed. The population dynamics are described by the basic Lotka-Volterra interactions (multiplication of preys, predation and multiplication of predators, death of predators), but the spatial effects result in differences between the system evolution and the...

Dynamical instability of symmetric vortices.

Luis Almeida, Yan Guo (2001)

Revista Matemática Iberoamericana

Using the Maxwell-Higgs model, we prove that linearly unstable symmetric vortices in the Ginzburg-Landau theory are dynamically unstable in the H1 norm (which is the natural norm for the problem).In this work we study the dynamic instability of the radial solutions of the Ginzburg-Landau equations in R2 (...)

Dynamical Percolation

Olle Häggström, Yuval Peres, Jeffrey E. Steif (1997)

Annales de l'I.H.P. Probabilités et statistiques

Dynamical sensitivity of the infinite cluster in critical percolation

Yuval Peres, Oded Schramm, Jeffrey E. Steif (2009)

Annales de l'I.H.P. Probabilités et statistiques

In dynamical percolation, the status of every bond is refreshed according to an independent Poisson clock. For graphs which do not percolate at criticality, the dynamical sensitivity of this property was analyzed extensively in the last decade. Here we focus on graphs which percolate at criticality, and investigate the dynamical sensitivity of the infinite cluster. We first give two examples of bounded degree graphs, one which percolates for all times at criticality and one which has exceptional...

Dynamics of Stochastic Neuronal Networks and the Connections to Random Graph Theory

R. E. Lee DeVille, C. S. Peskin, J. H. Spencer (2010)

Mathematical Modelling of Natural Phenomena

We analyze a stochastic neuronal network model which corresponds to an all-to-all network of discretized integrate-and-fire neurons where the synapses are failure-prone. This network exhibits different phases of behavior corresponding to synchrony and asynchrony, and we show that this is due to the limiting mean-field system possessing multiple attractors. We also show that this mean-field limit exhibits a first-order phase transition as a function...

Dynamics of systems with Preisach memory near equilibria

Stephen McCarthy, Dmitrii Rachinskii (2014)

Mathematica Bohemica

We consider autonomous systems where two scalar differential equations are coupled with the input-output relationship of the Preisach hysteresis operator, which has an infinite-dimensional memory. A prototype system of this type is an LCR electric circuit where the inductive element has a ferromagnetic core with a hysteretic relationship between the magnetic field and the magnetization. Further examples of such systems include lumped hydrological models with two soil layers; they can also appear...

Dynamique des nombres et physique des oscillateurs

Jacky Cresson (2008)

Journal de Théorie des Nombres de Bordeaux

Nous présentons un modèle mathématique permettant de reproduire le spectre expérimental des fréquences dans un composant électronique appelé boucle ouverte. Le spectre semble s’organiser suivant une contrainte de nature diophantienne sur les fréquences. Sa structure peut donc se comprendre via une étude de l’ensemble des fractions continues en fonction de leur longueur et de la taille des quotients partiels.

Dynamique des points vortex dans une équation de Ginzburg-Landau complexe

Evelyne Miot (2009/2010)

Séminaire Équations aux dérivées partielles

On considère une équation de Ginzburg-Landau complexe dans le plan. On étudie un régime asymptotique à petit paramètre dans lequel les solutions comportent des singularités ponctuelles, appelées points vortex, et on détermine un système d’équations différentielles ordinaires du premier ordre décrivant la dynamique de ces points jusqu’au premier temps de collision.

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