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Clusters in middle-phase percolation on hyperbolic plane

Jan Czajkowski (2011)

Banach Center Publications

I consider p-Bernoulli bond percolation on transitive, nonamenable, planar graphs with one end and on their duals. It is known from [BS01] that in such a graph G we have three essential phases of percolation, i.e. 0 < p c ( G ) < p u ( G ) < 1 , where p c is the critical probability and p u -the unification probability. I prove that in the middle phase a.s. all the ends of all the infinite clusters have one-point boundaries in ∂ℍ². This result is similar to some results in [Lal].

Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems

Markos A. Katsoulakis, Petr Plecháč, Luc Rey-Bellet, Dimitrios K. Tsagkarogiannis (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic lattice systems of interacting particles at equilibrium. The proposed algorithms are derived from an initial coarse-grained approximation that is directly computable by Monte Carlo simulations, and the corresponding numerical error is calculated using the...

Coexistence probability in the last passage percolation model is 6 - 8 log 2

David Coupier, Philippe Heinrich (2012)

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

A competition model on ℕ 2 between three clusters and governed by directed last passage percolation is considered. We prove that coexistence, i.e. the three clusters are simultaneously unbounded, occurs with probability 6 - 8 log 2 . When this happens, we also prove that the central cluster almost surely has a positive density on ℕ 2 . Our results rely on three couplings, allowing to link the competition interfaces (which represent the borderlines between the clusters) to some particles in the multi-TASEP, and...

Combining stochastic and deterministic approaches within high efficiency molecular simulations

Bruno Escribano, Elena Akhmatskaya, Jon Mujika (2013)

Open Mathematics

Generalized Shadow Hybrid Monte Carlo (GSHMC) is a method for molecular simulations that rigorously alternates Monte Carlo sampling from a canonical ensemble with integration of trajectories using Molecular Dynamics (MD). While conventional hybrid Monte Carlo methods completely re-sample particle’s velocities between MD trajectories, our method suggests a partial velocity update procedure which keeps a part of the dynamic information throughout the simulation. We use shadow (modified) Hamiltonians,...

Comparison of Vlasov solvers for spacecraft charging simulation

Nicolas Vauchelet, Jean-Paul Dudon, Christophe Besse, Thierry Goudon (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The modelling and the numerical resolution of the electrical charging of a spacecraft in interaction with the Earth magnetosphere is considered. It involves the Vlasov-Poisson system, endowed with non standard boundary conditions. We discuss the pros and cons of several numerical methods for solving this system, using as benchmark a simple 1D model which exhibits the main difficulties of the original models.

Complete positivity and the neutral kaon system

Fabio Benatti, roberto Floreanini (1998)

Banach Center Publications

New experiments on neutral K-mesons might turn out to be promising tests of the hypothesis of Complete Positivity in the physics of open quantum systems. In particular, a consistent dynamical description of correlated neutral kaons seems to ask for Complete Positivity.

Computational fluctuating fluid dynamics

John B. Bell, Alejandro L. Garcia, Sarah A. Williams (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper describes the extension of a recently developed numerical solver for the Landau-Lifshitz Navier-Stokes (LLNS) equations to binary mixtures in three dimensions. The LLNS equations incorporate thermal fluctuations into macroscopic hydrodynamics by using white-noise fluxes. These stochastic PDEs are more complicated in three dimensions due to the tensorial form of the correlations for the stochastic fluxes and in mixtures due to couplings of energy and concentration fluxes (e.g., Soret...

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