4,160 research outputs found
Towards a nonequilibrium thermodynamics: a self-contained macroscopic description of driven diffusive systems
In this paper we present a self-contained macroscopic description of
diffusive systems interacting with boundary reservoirs and under the action of
external fields. The approach is based on simple postulates which are suggested
by a wide class of microscopic stochastic models where they are satisfied. The
description however does not refer in any way to an underlying microscopic
dynamics: the only input required are transport coefficients as functions of
thermodynamic variables, which are experimentally accessible. The basic
postulates are local equilibrium which allows a hydrodynamic description of the
evolution, the Einstein relation among the transport coefficients, and a
variational principle defining the out of equilibrium free energy. Associated
to the variational principle there is a Hamilton-Jacobi equation satisfied by
the free energy, very useful for concrete calculations. Correlations over a
macroscopic scale are, in our scheme, a generic property of nonequilibrium
states. Correlation functions of any order can be calculated from the free
energy functional which is generically a non local functional of thermodynamic
variables. Special attention is given to the notion of equilibrium state from
the standpoint of nonequilibrium.Comment: 21 page
A combinatorial proof of tree decay of semi-invariants
We consider finite range Gibbs fields and provide a purely combinatorial
proof of the exponential tree decay of semi--invariants, supposing that the
logarithm of the partition function can be expressed as a sum of suitable local
functions of the boundary conditions. This hypothesis holds for completely
analytical Gibbs fields; in this context the tree decay of semi--invariants has
been proven via analyticity arguments. However the combinatorial proof given
here can be applied also to the more complicated case of disordered systems in
the so called Griffiths' phase when analyticity arguments fail
Renormalization Group in the uniqueness region: weak Gibbsianity and convergence
We analyze the block averaging transformation applied to lattice gas models
with short range interaction in the uniqueness region below the critical
temperature. We prove weak Gibbsianity of the renormalized measure and
convergence of the renormalized potential in a weak sense. Since we are
arbitrarily close to the coexistence region we have a diverging characteristic
length of the system: the correlation length or the critical length for
metastability, or both. Thus, to perturbatively treat the problem we have to
use a scale-adapted expansion. Moreover, such a model below the critical
temperature resembles a disordered system in presence of Griffiths'
singularity. Then the cluster expansion that we use must be graded with its
minimal scale length diverging when the coexistence line is approached
The Pomeron in Elastic and Deep Inelastic Scattering
We discuss some properties of the Pomeron in high energy elastic
hadron-hadron and deep inelastic lepton-hadron scattering. A number of issues
concerning the nature and the origin of the Pomeron are briefly recalled here.
The novelty in this paper resides essentially in its presentation; we strive at
discussing all these various issues in the following unifying perspective : it
is our contention that the Pomeron is one and the same in all reactions.
Various examples will be provided illustrating why we do not believe that one
should invoke additional tools to describe the data. For pedagogical
convenience, we list below the topics to be covered in the following.
-- 1. Introduction. How many Pomerons?
-- 2. The Pomeron in the -matrix theory
-- 3. The Pomeron in QCD
-- 4. The Pomeron in deep inelastic scattering
-- 5. The Pomeron structure
-- 6. (Temporary?) ConclusionsComment: 32 pages in TeX; 27 figures (available on request from
[email protected]
Long range correlations and phase transition in non-equilibrium diffusive systems
We obtain explicit expressions for the long range correlations in the ABC
model and in diffusive models conditioned to produce an atypical current of
particles.In both cases, the two-point correlation functions allow to detect
the occurrence of a phase transition as they become singular when the system
approaches the transition
Perturbative analysis of disordered Ising models close to criticality
We consider a two-dimensional Ising model with random i.i.d. nearest-neighbor
ferromagnetic couplings and no external magnetic field. We show that, if the
probability of supercritical couplings is small enough, the system admits a
convergent cluster expansion with probability one. The associated polymers are
defined on a sequence of increasing scales; in particular the convergence of
the above expansion implies the infinite differentiability of the free energy
but not its analyticity. The basic tools in the proof are a general theory of
graded cluster expansions and a stochastic domination of the disorder
Crossover to the KPZ equation
We characterize the crossover regime to the KPZ equation for a class of
one-dimensional weakly asymmetric exclusion processes. The crossover depends on
the strength asymmetry () and it occurs at
. We show that the density field is a solution of an
Ornstein-Uhlenbeck equation if , while for it is
an energy solution of the KPZ equation. The corresponding crossover for the
current of particles is readily obtained.Comment: Published by Annales Henri Poincare Volume 13, Number 4 (2012),
813-82
Lagrangian phase transitions in nonequilibrium thermodynamic systems
In previous papers we have introduced a natural nonequilibrium free energy by
considering the functional describing the large fluctuations of stationary
nonequilibrium states. While in equilibrium this functional is always convex,
in nonequilibrium this is not necessarily the case. We show that in
nonequilibrium a new type of singularities can appear that are interpreted as
phase transitions. In particular, this phenomenon occurs for the
one-dimensional boundary driven weakly asymmetric exclusion process when the
drift due to the external field is opposite to the one due to the external
reservoirs, and strong enough.Comment: 10 pages, 2 figure
Evaluation of the stress–strain curve of metallic materials by spherical indentation
AbstractA method for deducing the stress–strain uniaxial properties of metallic materials from instrumented spherical indentation is presented along with an experimental verification.An extensive finite element parametric analysis of the spherical indentation was performed in order to generate a database of load vs. depth of penetration curves for classes of materials selected in order to represent the metals commonly employed in structural applications. The stress–strain curves of the materials were represented with three parameters: the Young modulus for the elastic regime, the stress of proportionality limit and the strain-hardening coefficient for the elastic–plastic regime.The indentation curves simulated by the finite element analyses were fitted in order to obtain a continuous function which can produce accurate load vs. depth curves for any combination of the constitutive elastic–plastic parameters. On the basis of this continuous function, an optimization algorithm was then employed to deduce the material elastic–plastic parameters and the related stress–strain curve when the measured load vs. depth curve is available by an instrumented spherical indentation test.The proposed method was verified by comparing the predicted stress–strain curves with those directly measured for several metallic alloys having different mechanical properties.This result confirms the possibility to deduce the complete stress–strain curve of a metal alloy with good accuracy by a properly conducted instrumented spherical indentation test and a suitable interpretation technique of the measured quantities
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