Displaying similar documents to “Equidistribution of preimages over nonarchimedean fields for maps of good reduction”

Which electric fields are realizable in conducting materials?

Marc Briane, Graeme W. Milton, Andrejs Treibergs (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper we study the realizability of a given smooth periodic gradient field ∇ defined in R, in the sense of finding when one can obtain a matrix conductivity such that ∇ is a divergence free current field. The construction is shown to be always possible locally in R provided that ∇ is non-vanishing. This condition is also necessary in dimension two but not in dimension three. In fact the realizability may fail for non-regular gradient fields, and in general the conductivity cannot...

Hexahedral H(div) and H(curl) finite elements

Richard S. Falk, Paolo Gatto, Peter Monk (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We study the approximation properties of some finite element subspaces of H(div;Ω) and H(curl;Ω) defined on hexahedral meshes in three dimensions. This work extends results previously obtained for quadrilateral H(div;Ω) finite elements and for quadrilateral scalar finite element spaces. The finite element spaces we consider are constructed starting from a given finite dimensional space of vector fields on the reference cube, which is then transformed to a space of vector fields on a...

Dimension reduction for functionals on solenoidal vector fields

Stefan Krömer (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We study integral functionals constrained to divergence-free vector fields in on a thin domain, under standard -growth and coercivity assumptions, 1    ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject...

Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields

Huirong Pi, Chunhua Wang (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we are concerned with the existence of multi-bump solutions for a nonlinear Schrödinger equations with electromagnetic fields. We prove under some suitable conditions that for any positive integer , there exists () > 0 such that, for 0 <  < (), the problem has an -bump complex-valued solution. As a result, when  → 0, the equation has more and more multi-bump complex-valued solutions.

Dimension reduction for functionals on solenoidal vector fields

Stefan Krömer (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We study integral functionals constrained to divergence-free vector fields in on a thin domain, under standard -growth and coercivity assumptions, 1    ∞. We prove that as the thickness of the domain goes to zero, the Gamma-limit with respect to weak convergence in is always given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject...

Coexisting cycles in a class of 3-D discrete maps

Anna Agliari (2012)

ESAIM: Proceedings

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In this paper we consider the class of three-dimensional discrete maps () = [(), (), ()], where : ℝ → ℝ is an endomorphism. We show that all the cycles of the 3-D map can be obtained by those of (), as well as their local bifurcations. In particular we obtain that any local bifurcation is of co-dimension 3, that is three eigenvalues cross simultaneously the unit circle. As the map exhibits coexistence of...

A note on univoque self-Sturmian numbers

Jean-Paul Allouche (2010)

RAIRO - Theoretical Informatics and Applications

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We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic Sturmian sequences. As a corollary to our study we obtain that a real number in is univoque and self-Sturmian if and only if the -expansion of is of the form , where is a characteristic...

Weak notions of jacobian determinant and relaxation

Guido De Philippis (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the and the , which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.

Weak notions of Jacobian determinant and relaxation

Guido De Philippis (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper we study two weak notions of Jacobian determinant for Sobolev maps, namely the and the , which in general could be different. We show some cases of equality and use them to give an explicit expression for the relaxation of some polyconvex functionals.

Basic principles of mixed Virtual Element Methods

F. Brezzi, Richard S. Falk, L. Donatella Marini (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The aim of this paper is to give a simple, introductory presentation of the extension of the Virtual Element Method to the discretization of (div)-conforming vector fields (or, more generally, of ( − 1) − ). As we shall see, the methods presented here can be seen as extensions of the so-called BDM family to deal with more general element geometries (such as polygons with an almost arbitrary geometry). For the sake of simplicity, we limit ourselves to the 2-dimensional case, with the...

Encoding FIX in Object Calculi

Roy L. Crole (2010)

RAIRO - Theoretical Informatics and Applications

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We show that the type theory introduced by Crole and Pitts [3] can be encoded in variants of Abadi and Cardelli's object calculi. More precisely, we show that the type theory presented with judgements of both equality and operational reduction can be translated into object calculi, and the translation proved sound. The translations we give can be seen as using object calculi as a metalanguge within which can be represented; an analogy can be drawn with Martin Löf's Theory of Arities...

Some special solutions of self similar type in MHD, obtained by a separation method of variables

Michel Cessenat, Philippe Genta (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We use a method based on a separation of variables for solving a first order partial differential equations system, using a very simple modelling of MHD. The method consists in introducing three unknown variables , , in addition to the time variable and then in searching a solution which is separated with respect to and only. This is allowed by a very simple relation, called a “metric separation equation”, which...

Corrigendum: Complexity of infinite words associated with beta-expansions

Christiane Frougny, Zuzana Masáková, Edita Pelantová (2010)

RAIRO - Theoretical Informatics and Applications

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We add a sufficient condition for validity of Propo- sition 4.10 in the paper Frougny (2004). This condition is not a necessary one, it is nevertheless convenient, since anyway most of the statements in the paper Frougny (2004) use it.


Substitution systems associated with the dynamical system (𝒜, )

Maria de Fátima Correia, Carlos Ramos, Sandra Vinagre (2012)

ESAIM: Proceedings

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We consider the dynamical system (𝒜, ), where 𝒜 is a class of differential real functions defined on some interval and : 𝒜 → 𝒜 is an operator := , where is a differentiable -modal map. If we consider functions in 𝒜 whose critical values are periodic points for then, we show how to define and characterize a substitution system associated with (𝒜, ...

Variational approximation of a functional of Mumford–Shah type in codimension higher than one

Francesco Ghiraldin (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we consider a new kind of Mumford–Shah functional () for maps : ℝ → ℝ with  ≥ . The most important novelty is that the energy features a singular set of codimension greater than one, defined through the theory of distributional jacobians. After recalling the basic definitions and some well established results, we prove an approximation property for the energy ()  −convergence, in the same spirit of the work by Ambrosio and Tortorelli [L....