2,248 research outputs found
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 , where
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 symbols, within a given realization, the density of the initial
-block within larger -blocks approaches , uniformly in ,
as tends to infinity. Again, similar results hold for processes with other
indexing groups.Comment: To appear in Journal d'Analyse Mathematiqu
Rigorous Non-Perturbative Ornstein-Zernike Theory for Ising Ferromagnets
We rigorously derive the Ornstein-Zernike asymptotics of the pair-correlation
functions for finite-range Ising ferromagnets in any dimensions and at any
temperature above critical
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
On dominant contractions and a generalization of the zero-two law
Zaharopol proved the following result: let T,S:L^1(X,{\cf},\m)\to
L^1(X,{\cf},\m) be two positive contractions such that . If
then for all n\in\bn. In the present paper we
generalize this result to multi-parameter contractions acting on . As an
application of that result we prove a generalization of the "zero-two" law.Comment: 10 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
The Case for Enlarging the House of Representatives
This report makes the case for expanding the House of Representatives to bring the American people a little closer to their government, and their government closer to them. The Case for Enlarging the House of Representatives is an independent byproduct of Our Common Purpose: Reinventing American Democracy for the 21st Century, the final report of the American Academy of Arts and Sciences' Commission on the Practice of Democratic Citizenship. The Commission represents a cross-partisan cohort of leaders from academia, civil society, philanthropy, and the policy sphere who reached unanimous agreement on thirty-one recommendations to improve American democracy. The report takes as a premise that political institutions, civic culture, and civil society reinforce one another. A nation may have impeccably designed bodies of government, but it also needs an engaged citizenry to ensure these institutions function as intended. As a result, Our Common Purpose argues that reforming only one of these areas is insufficient. Progress must be made across all three. To build a better democracy, the United States needs better-functioning institutions as well as a healthier political culture and a more resilient civil society
Liquid Transport Due to Light Scattering
Using experiments and theory, we show that light scattering by
inhomogeneities in the index of refraction of a fluid can drive a large-scale
flow. The experiment uses a near-critical, phase-separated liquid, which
experiences large fluctuations in its index of refraction. A laser beam
traversing the liquid produces a large-scale deformation of the interface and
can cause a liquid jet to form. We demonstrate that the deformation is produced
by a scattering-induced flow by obtaining good agreements between the measured
deformations and those calculated assuming this mechanism.Comment: 4 pages, 5 figures, submitted to Physical Review Letters v2: Edited
based on comments from referee
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