Several algorithms in optimization, computer science and statistical mechanics are closely related to the problem of sampling from a Boltzmann distribution parameterized by the so-called temperature over a finite set. These include (i) Simulated Annealing (SA) [6], (ii) calculating the permanent of a nonnegative matrix [1], (iii) estimating the volume of a convex body [7], and (iv) computing pa...

We consider the flow of a dilute gas around a macroscopic heavy object. The state of the gas is described by an extended Boltzmann equation where the interactions between the gas molecules and the object are taken into account in computing the rate of change of the distribution function of the gas. We then show that the extended Boltzmann is equivalent to the usual Boltzmann equation, supplemen...

A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson–Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson–Boltzmann equation is introduced as an auxiliary problem, making it possible to study the original nonlinear equation with delta distribution sources. A priori error estimates for the f...

Nuclear reactions in stars occur between nuclei in the high-energy tail of the energy distribution and are sensitive to possible deviations from the standard equilibrium thermal-energy distribution. We are able to derive strong constraints on such deviations by using the detailed helioseismic information of the solar structure. If a small deviation is parameterized with a factor exp{−δ(E/kT) 2 ...