Displaying similar documents to “Discrete Spectrum of the Periodic Schrödinger Operator with a Variable Metric Perturbed by a Nonnegative Potential”

A non elliptic spectral problem related to the analysis of superconducting micro-strip lines

Anne-Sophie Bonnet-Bendhia, Karim Ramdani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is devoted to the spectral analysis of a non elliptic operator , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator has been derived, we determine its continuous spectrum. Then, we show that is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization,...

The continuous Coupled Cluster formulation for the electronic Schrödinger equation

Thorsten Rohwedder (2013)

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

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Nowadays, the Coupled Cluster (CC) method is the probably most widely used high precision method for the solution of the main equation of electronic structure calculation, the . Traditionally, the equations of CC are formulated as a nonlinear approximation of a Galerkin solution of the electronic Schrödinger equation, within a given discrete subspace. Unfortunately, this concept prohibits the direct application of concepts of nonlinear numerical analysis to obtain existence and uniqueness...

Bound states of a converging quantum waveguide

Giuseppe Cardone, Sergei A. Nazarov, Keijo Ruotsalainen (2013)

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

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We consider a two-dimensional quantum waveguide composed of two semi-strips of width 1 and 1 −  where  > 0 is a small real parameter, the waveguide is gently converging. The width of the junction zone for the semi-strips is 1 + (√ε). We will present a sufficient condition for the existence of a weakly coupled bound state below , the lower bound of the continuous spectrum. This eigenvalue in the discrete spectrum is unique and its asymptotics is constructed and...

The periodic unfolding method for a class of parabolic problems with imperfect interfaces

Zhanying Yang (2014)

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

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In this paper, we use the adapted periodic unfolding method to study the homogenization and corrector problems for the parabolic problem in a two-component composite with -periodic connected inclusions. The condition imposed on the interface is that the jump of the solution is proportional to the conormal derivative a function of order with ≤ −1. We give the homogenization results which include those obtained by Jose in [54 (2009) 189–222]. We also get the corrector...

On multiplicatively dependent linear numeration systems, and periodic points

Christiane Frougny (2010)

RAIRO - Theoretical Informatics and Applications

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Two linear numeration systems, with characteristic polynomial equal to the minimal polynomial of two Pisot numbers and respectively, such that and are multiplicatively dependent, are considered. It is shown that the conversion between one system and the other one is computable by a finite automaton. We also define a sequence of integers which is equal to the number of periodic points of a sofic dynamical system associated with some Parry number.

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...

Spectral Galerkin approximation of Fokker-Planck equations with unbounded drift

David J. Knezevic, Endre Süli (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is concerned with the analysis and implementation of spectral Galerkin methods for a class of Fokker-Planck equations that arises from the kinetic theory of dilute polymers. A relevant feature of the class of equations under consideration from the viewpoint of mathematical analysis and numerical approximation is the presence of an unbounded drift coefficient, involving a smooth convex potential that is equal to +∞ along the boundary ∂ of the computational domain . Using...

Spectral analysis in a thin domain with periodically oscillating characteristics

Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper deals with a Dirichlet spectral problem for an elliptic operator with -periodic coefficients in a 3D bounded domain of small thickness . We study the asymptotic behavior of the spectrum as and tend to zero. This asymptotic behavior depends crucially on whether and are of the same order ( ≈ ), or is much less than ( =   < 1), or is much greater than ...

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 () &gt; 0 such that, for 0 &lt;  &lt; (), the problem has an -bump complex-valued solution. As a result, when  → 0, the equation has more and more multi-bump complex-valued solutions.

Spectral analysis in a thin domain with periodically oscillating characteristics

Rita Ferreira, Luísa M. Mascarenhas, Andrey Piatnitski (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The paper deals with a Dirichlet spectral problem for an elliptic operator with -periodic coefficients in a 3D bounded domain of small thickness . We study the asymptotic behavior of the spectrum as and tend to zero. This asymptotic behavior depends crucially on whether and are of the same order ( ≈ ), or is much less than ( =   &lt; 1), or is much greater than ( =   &gt; 1). We consider all three cases. ...