We identify the limit of the internal DLA cluster generated by Sinai’s walk as the law of a functional of a brownian motion which turns out to be a new interpretation of the Arcsine law.
The purpose of this article is to show that electrons and protons, interacting by Coulomb forces and governed by quantum statistical mechanics at suitable temperature and density, form a gas of Hydrogen atoms or molecules.
The existence of solutions to the Cauchy problem for a nonlinear parabolic equation describing the gravitational interaction of particles is studied under minimal regularity assumptions on the initial conditions. Self-similar solutions are constructed for some homogeneous initial data.
The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical comparisons...
The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical...
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 stationary electronic Schrödinger equation. Traditionally, the equations of CC are formulated as a nonlinear approximation of a Galerkin solution of the electronic Schrödinger equation, i.e. within a given discrete subspace. Unfortunately, this concept prohibits the direct application of concepts of nonlinear numerical analysis...
We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed -dimensional polymer interacting with a random potential, which is constant in the deterministic direction and i.i.d. in the orthogonal directions. The potential at each site is a positive random variable with a polynomial tail at infinity. We show that, as the size of the system diverges, the polymer extremity is localized almost surely at one single point which grows ballistically....
When a permanent magnet is released above a superconductor, it is levitated. This is due to the Meissner-effect, i.e. the repulsion of external magnetic fields within the superconductor. In experiments, an interesting behavior of the levitated magnet can be observed: it might start to oscillate with increasing amplitude and some magnets even reach a continuous rotation. In this paper we develop a mathematical model for this effect and identify by analytical methods as well with finite element simulations...
We discuss the different roles of the entropy principle in modern thermodynamics. We start with the approach of rational thermodynamics in which the entropy principle becomes a selection rule for physical constitutive equations. Then we discuss the entropy principle for selecting admissible discontinuous weak solutions and to symmetrize general systems of hyperbolic balance laws. A particular attention is given on the local and global well-posedness of the relative Cauchy problem for smooth solutions....