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R. Esposito

Publications and source records attributed to R. Esposito.

18 recordsLinked to original sources
arXiv2013

Propagation of Chaos for a Thermostated Kinetic Model

We consider a system of N point particles moving on a d-dimensional torus. Each particle is subject to a uniform field E and random speed conserving collisions. This model is a variant of the Drude-Lorentz model of electrical conduction. In order to avoid heating by the external field, the particles also interact with a Gaussian thermostat which keeps the total kinetic energy of the system constant. The thermostat induces a mean-field type of interaction between the particles. Here we prove that, starting from a product measure, in the large N limit, the one particle velocity distribution satisfies a self consistent Vlasov-Boltzmann equation.. This is a consequence of "propagation of chaos", which we also prove for this model.

math-ph↗
arXiv2011

Analysis of Droplets in Lattice Systems with Long-range Kac Potentials

We investigate the geometry of typical equilibrium configurations for a lattice gas in a finite macroscopic domain with attractive, long range Kac potentials. We focus on the case when the system is below the critical temperature and has a fixed number of occupied sites.We connect the properties of typical configurations to the analysis of the constrained minimizers of a mesoscopic non-local free energy functional, which we prove to be the large deviation functional for a density profile in the canonical Gibbs measure with prescribed global density. In the case in which the global density of occupied sites lies between the two equilibrium densities that one would have without a constraint on the particle number, a "droplet" of the high (low) density phase may or may not form in a background of the low (high) density phase. We determine the critical density for droplet formation, and the nature of the droplet, as a function of the temperature and the size of the system, by combining the present large deviation principle with the analysis of the mesoscopic functional given in CCELM

cond-mat.stat-mech↗
arXiv2009

Droplet minimizers for the Gates-Lebowitz-Penrose free energy functional

We study the structure of the constrained minimizers of the Gates-Lebowitz-Penrose free-energy functional ${\mathcal F}_{\rm GLP}(m)$, non-local functional of a density field $m(x)$, $x\in {\mathcal T}_L$, a $d$-dimensional torus of side length $L$. At low temperatures, ${\mathcal F}_{\rm GLP}$ is not convex, and has two distinct global minimizers, corresponding to two equilibrium states. Here we constrain the average density $L^{-d}\int_{{\cal T}_L}m(x)\dd x$ to be a fixed value $n$ between the densities in the two equilibrium states, but close to the low density equilibrium value. In this case, a "droplet" of the high density phase may or may not form in a background of the low density phase, depending on the values $n$ and $L$. We determine the critical density for droplet formation, and the nature of the droplet, as a function of $n$ and $L$. The relation between the free energy and the large deviations functional for a particle model with long-range Kac potentials, proven in some cases, and expected to be true in general, then provides information on the structure of typical microscopic configurations of the Gibbs measure when the range of the Kac potential is large enough.

math-ph↗
arXiv2009

Phase Transition in a Vlasov-Boltzmann Binary Mixture

There are not many kinetic models where it is possible to prove bifurcation phenomena for any value of the Knudsen number. Here we consider a binary mixture over a line with collisions and long range repulsive interaction between different species. It undergoes a segregation phase transition at sufficiently low temperature. The spatially homogeneous Maxwellian equilibrium corresponding to the mixed phase, minimizing the free energy at high temperature, changes into a maximizer when the temperature goes below a critical value, while non homogeneous minimizers, corresponding to coexisting segregated phases, arise. We prove that they are dynamically stable with respect to the Vlasov-Boltzmann evolution, while the homogeneous equilibrium becomes dynamically unstable.

math-ph↗
arXiv2008

Stability for Rayleigh-Benard convective solutions of the Boltzmann equation

We consider the Boltzmann equation for a gas in a horizontal slab, subject to a gravitational force. The boundary conditions are of diffusive type, specifying the wall temperatures, so that the top temperature is lower than the bottom one (Benard setup). We consider a 2-dimensional convective stationary solution, which is close for small Knudsen number to the convective stationary solution of the Oberbeck-Boussinesq equations, near above the bifurcation point, and prove its stability under 2-d small perturbations, for Rayleigh number above and close to the bifurcation point and for small Knudsen number.

math-ph↗
arXiv2003

Real-time Control System Prototype for Mechanical and Optical Systems based on Parallel Computing Techniques

Real-time control systems often require dedicated hardware and software, including real-time operating systems, while many systems are available for off-line computing, mainly based on standard system units (PCs), standard network connections (Ethernet), standard operating systems (Linux) and software independent from the particular architecture of the single unit. In order to try to get the advantages of both the technologies, we built an hybrid control system prototype using network based parallel computing architecture within real-time control system. In this paper we describe the architecture of the implemented system, the preliminary tests we performed for its characterization and the architecture of the control system we used for the real-time control tests.

physics.ins-det↗
arXiv2003

A GRID solution for Gravitational Waves Signal Analysis from Coalescing Binaries: preliminary algorithms and tests

The analysis of data coming from interferometric antennas for gravitational waves detection may require a huge amount of computing power. The usual approach to the detection strategy is to set-up computer farms able to perform several tasks in parallel, exchanging data through network links. In this paper a new computation strategy is presented. This strategy is based on the GRID environment that allows several geographically distributed computing resources to exchange data and programs in secure way, using standard infrastructures. The computing resources can be geographically distributed also on a large scale. Some preliminary tests were performed using a subnetwork of the GRID infrastructure, producing good results in terms of distribution efficiency and time duration.

hep-ex↗
arXiv2003

Standard FTP and GridFTP protocols for international data transfer in Pamela Satellite Space Experiment

Physics applications often involve large amounts of data and/or computing and often require secure resource sharing across organizational boundaries, and are thus not easily handled by today's Internet and Web infrastructures. Pamela (a Payload Antimatter Matter Exploration and Light-nuclei Astrophysics), is a permanent magnet core facility with a variety of specialized detectors. It allows the investigation of the cosmic radiation: origin and evolution of matter in the galaxy, search for antimatter and dark matter of cosmological significance, understanding of origin and acceleration of relativistic particles in the galaxy. Pamela will be put in an elliptical orbit at an altitude between 300 and 600 Km, on board of the Resurs DK1 Russian satellite in the fall of the year 2003. The Napoli INFN Computing Center and the Pamela Teams of the Universities of Rome, Trieste and Stockholm have performed several network tests in order to make a comparison between Standard FTP and GridFTP protocols.

hep-ex↗
arXiv2003

OpenMosix approach to build scalable HPC farms with an easy management infrastructure

The OpenMosix approach is a good solution to build powerful and scalable computing farms. Furthermore an easy management infrastructure is implemented using diskless nodes and network boot procedures. In HENP environment, the choice of OpenMosix has been proven to be an optimal solution to give a general performance boost on implemented systems thanks to its load balancing and process migration features. In this poster we give an overview of the activities, carried out by our computing center, concerning the installation, management, monitoring, and usage of HPC Linux clusters running OpenMosix.

hep-ex↗
arXiv2003

Evaluating current processors performance and machines stability

Accurately estimate performance of currently available processors is becoming a key activity, particularly in HENP environment, where high computing power is crucial. This document describes the methods and programs, opensource or freeware, used to benchmark processors, memory and disk subsystems and network connection architectures. These tools are also useful to stress test new machines, before their acquisition or before their introduction in a production environment, where high uptimes are requested.

hep-ex↗
arXiv2003

Web portals, instant messaging and web communities: new tools for online collaboration

Web portals are nowadays very popular. This type of web sites let users to share information, request advice or help in a particular field, and furthermore allow them to create and extend sites content. Combined with instant messaging systems, used to send messages or files instantaneously to a user or a group of users, and with various kinds of chat programs, which connect two or more individuals simulating a conversation, it is now possible to create "web communities". In this paper we present the opensource tools used to create the "Grid Support Community" of the National Institute for Nuclear Physics in Italy.

hep-ex↗
arXiv2003

Some Considerations on the derivation of the nonlinear Quantum Boltzmann Equation

In this paper we analyze a system of N identical quantum particles in a weak-coupling regime. The time evolution of the Wigner transform of the one-particle reduced density matrix is represented by means of a perturbative series. The expansion is obtained upon iterating the Duhamel formula. For short times, we rigorously prove that a subseries of the latter, converges to the solution of the Boltzmann equation which is physically relevant in the context. In particular, we recover the transition rate as it is predicted by Fermi's Golden Rule. However, we are not able to prove that the quantity neglected while retaining a subseries of the complete original perturbative expansion, indeed vanishes in the limit: we only give plausibility arguments in this direction. The present study holds in any space dimension greater than 2.

math-ph↗
arXiv2002

Hydrodynamics of a driven lattice gas with open boundaries: the asymmetric simple exclusion

We consider the asymmetric simple exclusion process in $d\ge 3$ with open boundaries. The particle reservoirs of constant densities are modeled by birth and death processes at the boundary. We prove that, if the initial density and the densities of the boundary reservoirs differ for order of $ε$ from 1/2, the density empirical field, rescaled as $ε^{-1}$, converges to the solution of the initial-boundary value problem for the viscous Burgers equation in a finite domain with given density on the boundary.

math-ph↗
arXiv2001

Binary Fluids with Long Range Segregating Interaction I: Derivation of Kinetic and Hydrodynamic Equations

We study the evolution of a two component fluid consisting of ``blue'' and ``red'' particles which interact via strong short range (hard core) and weak long range pair potentials. At low temperatures the equilibrium state of the system is one in which there are two coexisting phases. Under suitable choices of space-time scalings and system parameters we first obtain (formally) a mesoscopic kinetic Vlasov-Boltzmann equation for the one particle position and velocity distribution functions, appropriate for a description of the phase segregation kinetics in this system. Further scalings then yield Vlasov-Euler and incompressible Vlasov-Navier-Stokes equations. We also obtain, via the usual truncation of the Chapman-Enskog expansion, compressible Vlasov-Navier-Stokes equations.

math-ph↗
arXiv2000

Equilibrium Fluctuations for Lattice Gases

The authors in a previous paper proved the hydrodynamic incompressible limit in $d\ge 3$ for a thermal lattice gas, namely a law of large numbers for the density, velocity field and energy. In this paper the equilibrium fluctuations for this model are studied and a central limit theorem is proved for a suitable modification of the vector fluctuation field $\z(t)$, whose components are the density, velocity and energy fluctuations fields. We consider a modified fluctuation field $ξ^\e(t)=\exp \{-\ve^{-1}t E\}\z^\ve$, where $E$ is the linearized Euler operator around the equilibrium and prove that $ξ^\e(t)$ converges to a vector generalized Ornstein-Uhlenbeck process $ξ(t)$, which is formally solution of the stochastic differential equation $d ξ(t)=Nξ(t)dt+ B dW_t$, with $ BB^*=-2 NC$, where $C$ is the compressibility matrix, $N$ is a matrix whose entries are second order differential operators and $B$ is a mean zero Gaussian field. The relation $-2NC=BB^*$ is the fluctuation-dissipation relation.

math-ph↗
arXiv1997

Kinetics of a Model Weakly Ionized Plasma in the Presence of Multiple Equilibria

We study, globaly in time, the velocity distribution $f(v,t)$ of a spatially homogeneous system that models a system of electrons in a weakly ionized plasma, subjected to a constant external electric field $E$. The density $f$ satisfies a Boltzmann type kinetic equation containing a full nonlinear electron-electron collision term as well as linear terms representing collisions with reservoir particles having a specified Maxwellian distribution. We show that when the constant in front of the nonlinear collision kernel, thought of as a scaling parameter, is sufficiently strong, then the $L^1$ distance between $f$ and a certain time dependent Maxwellian stays small uniformly in $t$. Moreover, the mean and variance of this time dependent Maxwellian satisfy a coupled set of nonlinear ODE's that constitute the ``hydrodynamical'' equations for this kinetic system. This remain true even when these ODE's have non-unique equilibria, thus proving the existence of multiple stabe stationary solutions for the full kinetic model. Our approach relies on scale independent estimates for the kinetic equation, and entropy production estimates. The novel aspects of this approach may be useful in other problems concerning the relation between the kinetic and hydrodynamic scales globably in time.

physics.plasm-ph↗