Hydrodynamic scaling limit of continuum solid-on-solid model.
Marking (1, 2) points of the brownian web and applications
The brownian web (BW), which developed from the work of Arratia and then Tóth and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional space–time that arises as the scaling limit of the discrete web (DW) of coalescing simple random walks. Two recently introduced extensions of the BW, the brownian net (BN) constructed by Sun and Swart, and the dynamical brownian web (DyBW) proposed by Howitt and Warren, are (or should be) scaling limits of corresponding...
Molecular Simulation in the Canonical Ensemble and Beyond
In this paper, we discuss advanced thermostatting techniques for sampling molecular systems in the canonical ensemble. We first survey work on dynamical thermostatting methods, including the Nosé-Poincaré method, and generalized bath methods which introduce a more complicated extended model to obtain better ergodicity. We describe a general controlled temperature model, projective thermostatting molecular dynamics (PTMD) and demonstrate that it flexibly accommodates existing alternative thermostatting...
Nonisothermal systems of self-attracting Fermi-Dirac particles
The existence of stationary solutions and blow up of solutions for a system describing the interaction of gravitationally attracting particles that obey the Fermi-Dirac statistics are studied.
Nonlocal quadratic evolution problems
Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data. Monte Carlo approximation schemes by interacting...
Nonuniqueness of steady states in annular domains for Streater equations
Models introduced by R. F. Streater describe the evolution of the density and temperature of a cloud of self-gravitating particles. We study nonuniqueness of steady states in annular domains in , d ≥ 2.
On some parabolic-elliptic system with self-similar pressure term
A priori estimates for solutions of a system describing the interaction of gravitationally attracting particles with a self-similar pressure term are proved. The presented theory covers the case of the model with diffusions that obey either Fermi-Dirac statistics or a polytropic one.
Special points of the Brownian net.
Stationary solutions of the generalized Smoluchowski-Poisson equation
The existence of steady states in the microcanonical case for a system describing the interaction of gravitationally attracting particles with a self-similar pressure term is proved. The system generalizes the Smoluchowski-Poisson equation. The presented theory covers the case of the model with diffusion that obeys the Fermi-Dirac statistic.
The spectral gap for a Glauber-type dynamics in a continuous gas
Theoretical and numerical comparison of some sampling methods for molecular dynamics
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...
Weak- solutions for a model of self-gravitating particles with an external potential
The existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential is studied in weak- spaces (i.e. Markiewicz spaces). The main goal is to prove the existence of global solutions and to study their large time behaviour.