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The role of the patch test in 2D atomistic-to-continuum coupling methods∗

Christoph Ortner (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction,...

The role of the patch test in 2D atomistic-to-continuum coupling methods∗

Christoph Ortner (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction,...

The scaling limits of a heavy tailed Markov renewal process

Julien Sohier (2013)

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

In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the α -stable regenerative set. We then apply these results to the strip wetting model which is a random walk S constrained above a wall and rewarded or penalized when it hits the strip [ 0 , ∞ ) × [ 0 , a ] where a is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.

The spectrum of Schrödinger operators with random δ magnetic fields

Takuya Mine, Yuji Nomura (2009)

Annales de l’institut Fourier

We shall consider the Schrödinger operators on ℝ 2 with the magnetic field given by a nonnegative constant field plus random δ magnetic fields of the Anderson type or of the Poisson-Anderson type. We shall investigate the spectrum of these operators by the method of the admissible potentials by Kirsch-Martinelli. Moreover, we shall prove the lower Landau levels are infinitely degenerated eigenvalues when the constant field is sufficiently large, by estimating the growth order of the eigenfunctions...

The triangle and the open triangle

Gady Kozma (2011)

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

We show that for percolation on any transitive graph, the triangle condition implies the open triangle condition.

Theoretical and numerical comparison of some sampling methods for molecular dynamics

Eric Cancès, Frédéric Legoll, Gabriel Stoltz (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The purpose of the present article is to compare different phase-space sampling methods, such as purely stochastic methods (Rejection method, Metropolized independence sampler, Importance Sampling), stochastically perturbed Molecular Dynamics methods (Hybrid Monte Carlo, Langevin Dynamics, Biased Random Walk), and purely deterministic methods (Nosé-Hoover chains, Nosé-Poincaré and Recursive Multiple Thermostats (RMT) methods). After recalling some theoretical convergence properties for the...

Theory of Dilute Binary Granular Gas Mixtures

D. Serero, S. H. Noskowicz, I. Goldhirsch (2010)

Mathematical Modelling of Natural Phenomena

A computer-aided method for accurately carrying out the Chapman-Enskog expansion of the Boltzmann equation, including its inelastic variant, is presented and employed to derive a hydrodynamic description of a dilute binary mixture of smooth inelastic spheres. Constitutive relations, formally valid for all physical values of the coefficients of restitution, are calculated by carrying out the pertinent Chapman-Enskog expansion to sufficient high orders in the Sonine polynomials to ensure numerical...

Topics in statistical physics involving braids

J. McCabe, T. Wydro (1998)

Banach Center Publications

We review the appearance of the braid group in statistical physics. In particular, we explain its relevance to the anyon model of fractional statistics and conformal field theory.

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