Hydrodynamic Limit for an Hamiltonian System with Boundary Conditions and Conservative Noise

We study the hyperbolic scaling limit for a chain of N coupled anharmonic oscillators. The chain is attached to a point on the left and there is a force (tension) $\tau$ acting on the right. In order to provide good ergodic properties to the system, we perturb the Hamiltonian dynamics with random local exchanges of velocities between the particles, so that momentum and energy are locally conserved. We prove that in the macroscopic limit the distributions of the elongation, momentum and energy, converge to the solution of the Euler system of equations, in the smooth regime.Comment: New deeply revised version. 1 figure adde

Driven Tracer Particle and Einstein Relation in One Dimensional Symmetric Simple Exclusion Process

We investigate the behavior of a tagged particle under the action of an external constant driving force in an infinite system of particles evolving in a one dimensional lattice according to symmetric random walks with hard core interaction

Exploring the Issues of Security, Privacy and Trust in eGovernment: UK Citizens\u27 Perspective

Recognising the potential that Information and Communications Technologies (ICTs)2 offer for competitiveness and the effectiveness of communities, Governments across the globe are striving to provide online products and services3 to all user groups. There are various definitions of e-government within the literature, and the one being applied in this research is: Egovernment is the application of technology to enable, enhance and improve access to the delivery of government services for the benefit of citizens, employees and enterprise (Silcock, 2001) Whilst there are diverse definitions of e-government, there are also variations in the classification of e-government, each dependent upon the relation between the various stakeholders. Bélanger and Hiller (2005) classified e-government into six categories: Government Delivering Services to Individuals (G2IS), Government to Individuals as a Part of the Political Process (G2IP), Government to Business as a Citizen (G2BC), Government to Business in the Marketplace (G2BMKT), Government to Employees (G2E) and Government to Government (G2G). G2IS involves communication and services between government and citizens (G2C); G2IP involves the relationship that the government has with citizens as a part of the democratic process, such as e-voting. G2BC involves organizations paying taxes or filing reports, and G2BMKT focuses on business transactions between government and businesses, such as e-procurement. Electronic interactions between Government and Citizen can also be classified as a ‘Government to Citizen’ (G2C) model of eGovernment (Beynon-Davies: 2007). This is also referred to as the ‘Transactional’ stage of eGovernment, where the interaction can occur with an agency (NAO, 2007). This interaction involves the receipt or dissemination of information, the completion or submission of a form, the sending of payments, the inspection of an account, or more complicated sets of dealings. It is such transactions that can be perceived to be of sensitive nature for citizens and users are reluctant to conduct transactions, with concerns ranging from: payment security, not understanding how to integrate information and customization impacting their privacy (Belanger & Hiller; 2005). This leads onto security and privacy and their possible effects on transactional stage adoption. In this research paper the aim is to explore how UK is dealing with the issues of security, privacy and trust when adopting and using online government products or services. This is pertinent at this time as the government is taking large steps to increase adoption and usage amongst citizens. By undertaking this research, several contributions are made: Governments around the globe, including, UK are increasingly seeking success at e-Government adoption and usage and such research assists policymakers in obtaining a better understanding. For industry, private sector organizations are partners in the provision of the infrastructure and involved in many other implementation and adoption e-Government projects and research such as this allows them to consider these factors in more depth. For academics, security, privacy and trust are issues of immense importance and research such as this allows academics to become more aware of these topics

From a kinetic equation to a diffusion under an anomalous scaling

A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (K(t), i(t), Y(t)), where (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance, and Y(t) is an additive functional of K(t). We prove that under an anomalous rescaling Y converges in distribution to a two-dimensional Brownian motion. As a consequence, the appropriately rescaled solution of the Boltzmann equation converges to a diffusion equation

Fluctuations in the weakly asymmetric exclusion process with open boundary conditions

accepted in Journal of Statistical PhysicsWe investigate the fluctuations around the average density profile in the weakly asymmetric exclusion process with open boundaries in the steady state. We show that these fluctuations are given, in the macroscopic limit, by a centered Gaussian field and we compute explicitly its covariance function. We use two approaches. The first method is dynamical and based on fluctuations around the hydrodynamic limit. We prove that the density fluctuations evolve macroscopically according to an autonomous stochastic equation, and we search for the stationary distribution of this evolution. The second approach, which is based on a representation of the steady state as a sum over paths, allows one to write the density fluctuations in the steady state as a sum over two independent processes, one of which is the derivative of a Brownian motion, the other one being related to a random path in a potential

Nonequilibrium dynamics of a stochastic model of anomalous heat transport

We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math. Theor. 42 (2009) 025001], we have studied the stationary state of this system with fixed boundary conditions, finding analytical exact expressions for the temperature profile and the heat current in the thermodynamic (continuum) limit. In this paper we extend the analysis to the evolution of the covariance matrix and to generic boundary conditions. Our main purpose is to construct a hydrodynamic description of the relaxation to the stationary state, starting from the exact equations governing the evolution of the correlation matrix. We identify and adiabatically eliminate the fast variables, arriving at a continuity equation for the temperature profile T(y,t), complemented by an ordinary equation that accounts for the evolution in the bulk. Altogether, we find that the evolution of T(y,t) is the result of fractional diffusion.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica

Orientation dynamics of weakly Brownian particles in periodic viscous flows

Evolution equations for the orientation distribution of axisymmetric particles in periodic flows are derived in the regime of small but non-zero Brownian rotations. The equations are based on a multiple time scale approach that allows fast computation of the relaxation processes leading to statistical equilibrium. The approach has been applied to the calculation of the effective viscosity of a thin disk suspension in gravity waves.Comment: 16 pages, 7 eps figures include

Anomalous transport and relaxation in classical one-dimensional models

After reviewing the main features of anomalous energy transport in 1D systems, we report simulations performed with chains of noisy anharmonic oscillators. The stochastic terms are added in such a way to conserve total energy and momentum, thus keeping the basic hydrodynamic features of these models. The addition of this "conservative noise" allows to obtain a more efficient estimate of the power-law divergence of heat conductivity kappa(L) ~ L^alpha in the limit of small noise and large system size L. By comparing the numerical results with rigorous predictions obtained for the harmonic chain, we show how finite--size and --time effects can be effectively controlled. For low noise amplitudes, the alpha values are close to 1/3 for asymmetric potentials and to 0.4 for symmetric ones. These results support the previously conjectured two-universality-classes scenario

Hydrodynamic limit for the velocity flip model

We study the diffusive scaling limit for a chain of $N$ coupled oscillators. In order to provide the system with good ergodic properties, we perturb the Hamiltonian dynamics with random flips of velocities, so that the energy is locally conserved. We derive the hydrodynamic equations by estimating the relative entropy with respect to the local equilibrium state modified by a correction term