Return times, recurrence densities and entropy for actions of some discrete amenable groups

Results of Wyner and Ziv and of Ornstein and Weiss show that if one observes the first k outputs of a finite-valued ergodic process, then the waiting time until this block appears again is almost surely asymptotic to $2^{hk}$, where $h$ is the entropy of the process. We examine this phenomenon when the allowed return times are restricted to some subset of times, and generalize the results to processes parameterized by other discrete amenable groups. We also obtain a uniform density version of the waiting time results: For a process on $s$ symbols, within a given realization, the density of the initial $k$-block within larger $n$-blocks approaches $2^{-hk}$, uniformly in $n>s^k$, as $k$ tends to infinity. Again, similar results hold for processes with other indexing groups.Comment: To appear in Journal d'Analyse Mathematiqu

Design of a geodetic database and associated tools for monitoring rock-slope movements: the example of the top of Randa rockfall scar

International audienceThe need for monitoring slope movements increases with the increasing need for new areas to inhabit and new land management requirements. Rock-slope monitoring implies the use of a database, but also the use of other tools to facilitate the analysis of movements. The experience and the philosophy of monitoring the top of the Randa rockfall scar which is sliding down into the valley near Randa village in Switzerland are presented. The database includes data correction tools, display facilities and information about benchmarks. Tools for analysing the movement acceleration and spatial changes and forecasting movement are also presented. Using the database and its tools it was possible to discriminate errors from critical slope movement. This demonstrates the efficiency of these tools in monitoring the Randa scar

Ion structure in warm dense matter: benchmarking solutions of hypernetted-chain equations by first-principle simulations

We investigate the microscopic structure of strongly coupled ions in warm dense matter using ab initio simulations and hypernetted chain (HNC) equations. We demonstrate that an approximate treatment of quantum effects by weak pseudopotentials fails to describe the highly degenerate electrons in warm dense matter correctly. However, one-component HNC calculations for the ions agree well with first-principles simulations if a linearly screened Coulomb potential is used. These HNC results can be further improved by adding a short-range repulsion that accounts for bound electrons. Examples are given for recently studied light elements, lithium and beryllium, and for aluminum where the extra short-range repulsion is essential

Mapping a Homopolymer onto a Model Fluid

We describe a linear homopolymer using a Grand Canonical ensemble formalism, a statistical representation that is very convenient for formal manipulations. We investigate the properties of a system where only next neighbor interactions and an external, confining, field are present, and then show how a general pair interaction can be introduced perturbatively, making use of a Mayer expansion. Through a diagrammatic analysis, we shall show how constitutive equations derived for the polymeric system are equivalent to the Ornstein-Zernike and P.Y. equations for a simple fluid, and find the implications of such a mapping for the simple situation of Van der Waals mean field model for the fluid.Comment: 12 pages, 3 figure

Solution of the Percus-Yevick equation for hard discs

We solve the Percus-Yevick equation in two dimensions by reducing it to a set of simple integral equations. We numerically obtain both the pair correlation function and the equation of state for a hard disc fluid and find good agreement with available Monte-Carlo calculations. The present method of resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure

Thermodynamic and dynamic anomalies for a three dimensional isotropic core-softened potential

Using molecular dynamics simulations and integral equations (Rogers-Young, Percus-Yevick and hypernetted chain closures) we investigate the thermodynamic of particles interacting with continuous core-softened intermolecular potential. Dynamic properties are also analyzed by the simulations. We show that, for a chosen shape of the potential, the density, at constant pressure, has a maximum for a certain temperature. The line of temperatures of maximum density (TMD) was determined in the pressure-temperature phase diagram. Similarly the diffusion constant at a constant temperature, $D$, has a maximum at a density $\rho_{max}$ and a minimum at a density $\rho_{min}<\rho_{max}$. In the pressure-temperature phase-diagram the line of extrema in diffusivity is outside of TMD line. Although in this interparticle potential lacks directionality, this is the same behavior observed in SPC/E water.Comment: 16 page

Evolution of collision numbers for a chaotic gas dynamics

We put forward a conjecture of recurrence for a gas of hard spheres that collide elastically in a finite volume. The dynamics consists of a sequence of instantaneous binary collisions. We study how the numbers of collisions of different pairs of particles grow as functions of time. We observe that these numbers can be represented as a time-integral of a function on the phase space. Assuming the results of the ergodic theory apply, we describe the evolution of the numbers by an effective Langevin dynamics. We use the facts that hold for these dynamics with probability one, in order to establish properties of a single trajectory of the system. We find that for any triplet of particles there will be an infinite sequence of moments of time, when the numbers of collisions of all three different pairs of the triplet will be equal. Moreover, any value of difference of collision numbers of pairs in the triplet will repeat indefinitely. On the other hand, for larger number of pairs there is but a finite number of repetitions. Thus the ergodic theory produces a limitation on the dynamics.Comment: 4 pages, published versio

Structure of strongly coupled, multi-component plasmas

We investigate the short-range structure in strongly coupled fluidlike plasmas using the hypernetted chain approach generalized to multicomponent systems. Good agreement with numerical simulations validates this method for the parameters considered. We found a strong mutual impact on the spatial arrangement for systems with multiple ion species which is most clearly pronounced in the static structure factor. Quantum pseudopotentials were used to mimic diffraction and exchange effects in dense electron-ion systems. We demonstrate that the different kinds of pseudopotentials proposed lead to large differences in both the pair distributions and structure factors. Large discrepancies were also found in the predicted ion feature of the x-ray scattering signal, illustrating the need for comparison with full quantum calculations or experimental verification

Longitudinal Relationships between Alzheimer Disease Progression and Psychosis, Depressed Mood, and Agitation/Aggression

OBJECTIVES: Behavioral and psychological symptoms of dementia (BPSD) are prevalent in Alzheimer disease (AD) and are related to poor outcomes such as nursing home placement. No study has examined the impact of individual BPSD on dependence, a clinically important feature that reflects changing patient needs and their effect on caregivers. The current study characterized independent cross-sectional and longitudinal relationships between three BPSD (psychosis, depressed mood, and agitation/aggression), cognition, and dependence to better understand the interplay between these symptoms over time. DESIGN: The Predictors Study measured changes in BPSD, cognition, and dependence every 6 months in patients with AD. Cross-sectional and longitudinal relationships between individual BPSD, cognition, and dependence over 6 years were characterized by using multivariate latent growth curve modeling. This approach characterizes independent changes in multiple outcome measures over time. SETTING: Four memory clinics in the United States and Europe. PARTICIPANTS: A total of 517 patients with probable AD. MEASUREMENTS: Columbia University Scale for Psychopathology, modified Mini-Mental State Examination, and Dependence Scale. RESULTS: Both psychosis and depressed mood at study entry were associated with worse subsequent cognitive decline. Independent of cognitive decline, initial psychosis was associated with worse subsequent increases in dependence. Rates of increase in agitation/aggression separately correlated with rates of declines in both cognition and independence. CONCLUSIONS: Although purely observational, our findings support the poor prognosis associated with psychosis and depression in AD. Results also show that agitation/aggression tracks declines in cognition and independence independently over time. Targeted intervention for individual BPSD, particularly psychosis, could have broad effects not only on patient well-being but also on care costs and family burden