The Recent Generalizations of Colored Symmetry
The relativistic Enskog equation near the vacuum.
The representation theory of the Temperley-Lieb algebras.
The role of the patch test in 2D atomistic-to-continuum coupling methods∗
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∗
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
In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the -stable regenerative set. We then apply these results to the strip wetting model which is a random walk constrained above a wall and rewarded or penalized when it hits the strip where is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.
The shape of a typical boxed plane partition.
The short-range expansion in solid state physics
The size of a pond in 2D invasion percolation.
The spectral gap for a Glauber-type dynamics in a continuous gas
The spectrum of Schrödinger operators with random magnetic fields
We shall consider the Schrödinger operators on with the magnetic field given by a nonnegative constant field plus random 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 stationary Boltzmann equation in the slab with given weighted mass for hard and soft forces
The stochastic Ising model with the mixed boundary conditions.
The stochastic limit in the analysis of some modified open BCS models
The structural influence of the forces of the stability of dynamical systems.
The three dimensional polyominoes of minimal area.
The time constant and critical probabilities in percolation models.
The time for a critical nearest particle system to reach equilibrium starting with a large gap.
The triangle and the open triangle
We show that for percolation on any transitive graph, the triangle condition implies the open triangle condition.
The umbral transfer-matrix method. III: Counting animals.