Related papers: Anosov C-systems and random number generators
Artificial ice systems have been designed to replicate paradigmatic phenomena observed in frustrated spin systems. Here we present a detailed theoretical analysis based on Monte-Carlo simulations of the low energy phases in an artificial…
In the 1960s and 1970s a large part of the theory of dynamical systems concerned the case of uniformly hyperbolic or Axiom A dynamical system and abstract ergodic theory of smooth dynamical systems. However since around 1980 an emphasize…
We complete previous investigations on the dynamical stability of barotropic stars and collisionless stellar systems. A barotropic star that minimizes the energy functional at fixed mass is a nonlinearly dynamically stable stationary…
This chapter is devoted to the computation of equilibrium (thermodynamic) properties of quantum systems. In particular, we will be interested in the situation where the interaction between particles is so strong that it cannot be treated as…
Monte Carlo simulations are methods for simulating statistical systems. The aim is to generate a representative ensemble of configurations to access thermodynamical quantities without the need to solve the system analytically or to perform…
We show several results on convergence of the Monte Carlo method applied to consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Our method is based on combination of several new concepts. We…
The wave-function Monte-Carlo method, also referred to as the use of "quantum-jump trajectories", allows efficient simulation of open systems by independently tracking the evolution of many pure-state "trajectories". This method is ideally…
We study the asymptotic properties of the trajectories of a discrete-time random dynamical system in an infinite-dimensional Hilbert space. Under some natural assumptions on the model, we establish a multiplica-tive ergodic theorem with an…
The authors consider a mathematical model for the coupled atmosphere-ocean system, namely, the coupled quasigeostrophic flow-energy balance model. This model consists of the large scale quasigeostrophic oceanic flow model and the transport…
We consider dynamically constrained Monte-Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever…
We show that the time-1 map of an Anosov flow, whose strong-unstable foliation is $C^2$ smooth and minimal, is $C^2$ close to a diffeomorphism having positive central Lyapunov exponent Lebesgue almost everywhere and a unique physical…
In this paper we show that many projective Anosov representations act convex cocompactly on some properly convex domain in real projective space. In particular, if a non-elementary word hyperbolic group is not commensurable to a non-trivial…
In this paper the author considers the motion of a relativistic perfect fluid with self-interaction mediated by Nordstrom's scalar theory of gravity. The evolution of the fluid is determined by a quasilinear hyperbolic system of PDEs, and a…
Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical $\delta-$ shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the…
We present computer simulations of a dynamic Monte Carlo algorithm for polymer chains on the FCC lattice which takes explicitly into account the possibility to overcome topological constraints by controlling the rate at which nearby polymer…
The superconducting transition temperature $T_c$ of the two-dimensional attractive Hubbard model is computed in the vicinity of both ordinary (logarithmic) and higher-order (power-law) Van Hove singularities using determinant quantum Monte…
The dynamical justifications which lie at the basis of an effective Statistical Mechanics for self gravitating systems are formulated, analyzing some among the well known obstacles thought to prevent a rigorous Statistical treatment. It is…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
One of the most demanding calculations is to generate random samples from a specified probability distribution (usually with an unknown normalizing prefactor) in a high-dimensional configuration space. One often has to resort to using a…
The configurational density of states (CDOS) encodes all the relevant thermodynamic information contained in the interaction potentials for statistical mechanical systems. However, its explicit computation is usually a challenge for…