Spatial Structure of Stationary Nonequilibrium States in the Thermostatted Periodic Lorentz Gas

We investigate analytically and numerically the spatial structure of the non-equilibrium stationary states (NESS) of a point particle moving in a two dimensional periodic Lorentz gas (Sinai Billiard). The particle is subject to a constant external electric field E as well as a Gaussian thermostat which keeps the speed |v| constant. We show that despite the singular nature of the SRB measure its projections on the space coordinates are absolutely continuous. We further show that these projections satisfy linear response laws for small E. Some of them are computed numerically. We compare these results with those obtained from simple models in which the collisions with the obstacles are replaced by random collisions.Similarities and differences are noted.Comment: 24 pages with 9 figure

Heat Conduction in two-dimensional harmonic crystal with disorder

We study the problem of heat conduction in a mass-disordered two-dimensional harmonic crystal. Using two different stochastic heat baths, we perform simulations to determine the system size (L) dependence of the heat current (J). For white noise heat baths we find that J ~ 1/L^a with $a \approx 0.59$ while correlated noise heat baths gives $a \approx 0.51$. A special case with correlated disorder is studied analytically and gives a=3/2 which agrees also with results from exact numerics.Comment: Revised version. 4 pages, 3 figure

Local Temperature and Universal Heat Conduction in FPU chains

It is shown numerically that for Fermi Pasta Ulam (FPU) chains with alternating masses and heat baths at slightly different temperatures at the ends, the local temperature (LT) on small scales behaves paradoxically in steady state. This expands the long established problem of equilibration of FPU chains. A well-behaved LT appears to be achieved for equal mass chains; the thermal conductivity is shown to diverge with chain length N as N^(1/3), relevant for the much debated question of the universality of one dimensional heat conduction. The reason why earlier simulations have obtained systematically higher exponents is explained.Comment: 4 pages, 3 figures, revised published versio

Universality of One-Dimensional Heat Conductivity

We show analytically that the heat conductivity of oscillator chains diverges with system size N as N^{1/3}, which is the same as for one-dimensional fluids. For long cylinders, we use the hydrodynamic equations for a crystal in one dimension. This is appropriate for stiff systems such as nanotubes, where the eventual crossover to a fluid only sets in at unrealistically large N. Despite the extra equation compared to a fluid, the scaling of the heat conductivity is unchanged. For strictly one-dimensional chains, we show that the dynamic equations are those of a fluid at all length scales even if the static order extends to very large N. The discrepancy between our results and numerical simulations on Fermi-Pasta-Ulam chains is discussed.Comment: 7 pages, 2 figure

Intriguing Heat Conduction of a Polymer Chain

We study heat conduction in a one-dimensional chain of particles with longitudinal as well as transverse motions. The particles are connected by two-dimensional harmonic springs together with bending angle interactions. Using equilibrium and nonequilibrium molecular dynamics, three types of thermal conducting behaviors are found: a logarithmic divergence with system sizes for large transverse coupling, 1/3 power-law at intermediate coupling, and 2/5 power-law at low temperatures and weak coupling. The results are consistent with a simple mode-coupling analysis of the same model. The 1/3 power-law divergence should be a generic feature for models with transverse motions.Comment: 4 page

Analyticity of the SRB measure for a class of simple Anosov flows

We consider perturbations of the Hamiltonian flow associated with the geodesic flow on a surface of constant negative curvature. We prove that, under a small perturbation, not necessarely of Hamiltonian character, the SRB measure associated to the flow exists and is analytic in the strength of the perturbation. An explicit example of "thermostatted" dissipative dynamics is constructed.Comment: 23 pages, corrected typo

Fluctuation relation for a L\'evy particle

We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the L\'evy type. In the stationary regime, the probability density of the work is found to have ``fat'' power-law tails which assign a relatively high probability to large fluctuations compared with the case where the random forcing is Gaussian. These tails lead to a strong violation of existing fluctuation theorems, as the ratio of the probabilities of positive and negative work fluctuations of equal magnitude behaves in a non-monotonic way. Possible experiments that could probe these features are proposed.Comment: 5 pages, 2 figures, RevTeX4; v2: minor corrections and references added; v3: typos corrected, new conclusion, close to published versio

New application of open source data and Rock Engineering System for debris flow susceptibility analysis

This research describes a quantitative, rapid, and low-cost methodology for debris flow susceptibility evaluation at the basin scale using open-access data and geodatabases. The proposed approach can aid decision makers in land management and territorial planning, by first screening for areas with a higher debris flow susceptibility. Five environmental predisposing factors, namely, bedrock lithology, fracture network, quaternary deposits, slope inclination, and hydrographic network, were selected as independent parameters and their mutual interactions were described and quantified using the Rock Engineering System (RES) methodology. For each parameter, specific indexes were proposed, aiming to provide a final synthetic and representative index of debris flow susceptibility at the basin scale. The methodology was tested in four basins located in the Upper Susa Valley (NW Italian Alps) where debris flow events are the predominant natural hazard. The proposed matrix can represent a useful standardized tool, universally applicable, since it is independent of type and characteristic of the basin

Temperature Profiles in Hamiltonian Heat Conduction

We study heat transport in the context of Hamiltonian and related stochastic models with nearest-neighbor coupling, and derive a universal law for the temperature profiles of a large class of such models. This law contains a parameter $\alpha$, and is linear only when $\alpha=1$. The value of $\alpha$ depends on energy-exchange mechanisms, including the range of motion of tracer particles and their times of flight.Comment: Revised text, same results Second revisio