Ergodicity Breaking in a Deterministic Dynamical System

The concept of weak ergodicity breaking is defined and studied in the context of deterministic dynamics. We show that weak ergodicity breaking describes a weakly chaotic dynamical system: a nonlinear map which generates subdiffusion deterministically. In the non-ergodic phase non-trivial distribution of the fraction of occupation times is obtained. The visitation fraction remains uniform even in the non-ergodic phase. In this sense the non-ergodicity is quantified, leading to a statistical mechanical description of the system even though it is not ergodic.Comment: 11 pages, 4 figure

VALUING RISK-REDUCING INTERVENTIONS WITH HEDONIC MODELS: THE CASE OF EROSION PROTECTION

This article extends the literature on economic valuation of public interventions that reduce environmental risk. We consider the case where risk-reducing interventions have different characteristics than the risk proxies used in hedonic regressions. We then demonstrate the importance of these considerations by reexamining an existing analysis of shoreline protection where we estimate risk using a latent variables model. The results show substantially different and arguably more plausible results.Environmental Economics and Policy, Risk and Uncertainty,

One-parameter scaling theory for DNA extension in a nanochannel

Experiments measuring DNA extension in nanochannels are at odds with even the most basic predictions of current scaling arguments for the conformations of confined semiflexible polymers such as DNA. We show that a theory based on a weakly self-avoiding, one-dimensional "telegraph" process collapses experimental data and simulation results onto a single master curve throughout the experimentally relevant region of parameter space and explains the mechanisms at play.Comment: Revised version. 5 pages, 4 figures, revised version, supplementary informatio

Chaotic properties of systems with Markov dynamics

We present a general approach for computing the dynamic partition function of a continuous-time Markov process. The Ruelle topological pressure is identified with the large deviation function of a physical observable. We construct for the first time a corresponding finite Kolmogorov-Sinai entropy for these processes. Then, as an example, the latter is computed for a symmetric exclusion process. We further present the first exact calculation of the topological pressure for an N-body stochastic interacting system, namely an infinite-range Ising model endowed with spin-flip dynamics. Expressions for the Kolmogorov-Sinai and the topological entropies follow.Comment: 4 pages, to appear in the Physical Review Letter

Shuttle/spacelab MMAP/electromagnetic environment experiment phase B definition study

Progress made during the first five months of the Phase B definition study for the MMAP/Electromagnetic Environment Experiment (EEE) was described. An antenna/receiver assembly has been defined and sized for stowing in a three pallet bay area in the shuttle. Six scanning modes for the assembly are analyzed and footprints for various antenna sizes are plotted. Mission profiles have been outlined for a 400 km height, 57 deg inclination angle, circular orbit. Viewing time over 7 geographical areas are listed. Shuttle interfaces have been studied to determine what configuration the antenna assembly must have to be shared with other experiments of the Microwave Multi-Applications Payload (MMAP) and to be stowed in the shuttle bay. Other results reported include a frequency plan, a proposed antenna subsystem design, a proposed receiver design, preliminary outlines of the experiment controls and an analysis of on-board and ground data processing schemes

First principles simulations of 2D Cu superlattices on the MgO(001) surface

First principles slab simulations of copper 2D superlattices of different densities on the perfect MgO(0 0 1) surface are performed using the DFT method as implemented into the CRYSTAL98 computer code. In order to clarify the nature of interfacial bonding, we consider regular 1/4, 1/2 and I monolayer (ML) coverages and compare results of our calculations with various experimental and theoretical data. Our general conclusion is that the physical adhesion associated with a Cu polarization and charge redistribution gives the predominant contribution to the bonding of the regular Cu 2D layer on the MgO(0 0 1) surface. (C) 2003 Elsevier B.V. All rights reserved

The kinetic MC modelling of reversible pattern formation in initial stages of thin metallic film growth on crystalline substrates

The results of kinetic MC simulations of the reversible pattern formation during the adsorption of mobile metal atoms on crystalline substrates are discussed. Pattern formation, simulated for submonolayer metal coverage, is characterized in terms of the joint correlation functions for a spatial distribution of adsorbed atoms. A wide range of situations, from the almost irreversible to strongly reversible regimes, is simulated. We demonstrate that the patterns obtained are defined by a key dimensionless parameter: the ratio of the mutual attraction energy between atoms to the substrate temperature. Our ab initio calculations for the nearest Ag-Ag adsorbate atom interaction on an MgO substrate give an attraction energy as large as 1.6 eV, close to that in a free molecule. This is in contrast to the small Ag adhesion and migration energies (0.23 and 0.05 eV, respectively) on a defect-free MgO substrate. (C) 2003 Elsevier Science Ltd. All rights reserved

Emission from dielectric cavities in terms of invariant sets of the chaotic ray dynamics

In this paper, the chaotic ray dynamics inside dielectric cavities is described by the properties of an invariant chaotic saddle. I show that the localization of the far field emission in specific directions is related to the filamentary pattern of the saddle's unstable manifold, along which the energy inside the cavity is distributed. For cavities with mixed phase space, the chaotic saddle is divided in hyperbolic and non-hyperbolic components, related, respectively, to the intermediate exponential (t<t_c) and the asymptotic power-law (t>t_c) decay of the energy inside the cavity. The alignment of the manifolds of the two components of the saddle explains why even if the energy concentration inside the cavity dramatically changes from tt_c, the far field emission changes only slightly. Simulations in the annular billiard confirm and illustrate the predictions.Comment: Corrected version, as published. 9 pages, 6 figure

Capturing correlations in chaotic diffusion by approximation methods

We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing these correlations by incorporating higher order terms, all schemes converge to the analytically exact result. Two of these methods are based on expanding the Taylor-Green-Kubo formula for diffusion, whilst the third method approximates Markov partitions and transition matrices by using the escape rate theory of chaotic diffusion. We check the practicability of the different methods by working them out analytically and numerically for a simple one-dimensional map, study their convergence and critically discuss their usefulness in identifying a possible fractal instability of parameter-dependent diffusion, in case of dynamics where exact results for the diffusion coefficient are not available.Comment: 11 pages, 5 figure

Steady-state conduction in self-similar billiards

The self-similar Lorentz billiard channel is a spatially extended deterministic dynamical system which consists of an infinite one-dimensional sequence of cells whose sizes increase monotonically according to their indices. This special geometry induces a nonequilibrium stationary state with particles flowing steadily from the small to the large scales. The corresponding invariant measure has fractal properties reflected by the phase-space contraction rate of the dynamics restricted to a single cell with appropriate boundary conditions. In the near-equilibrium limit, we find numerical agreement between this quantity and the entropy production rate as specified by thermodynamics