16,115 research outputs found
Action functional and quasi-potential for the Burgers equation in a bounded interval
Consider the viscous Burgers equation on
the interval with the inhomogeneous Dirichlet boundary conditions
, . The flux is the function , is the viscosity, and the boundary data satisfy
. We examine the quasi-potential corresponding to an action
functional, arising from non-equilibrium statistical mechanical models,
associated to the above equation. We provide a static variational formula for
the quasi-potential and characterize the optimal paths for the dynamical
problem. In contrast with previous cases, for small enough viscosity, the
variational problem defining the quasi potential admits more than one
minimizer. This phenomenon is interpreted as a non-equilibrium phase transition
and corresponds to points where the super-differential of the quasi-potential
is not a singleton
The Conflict of Rigidity and Precision in Designation
My paper provides reasons in support of the view that vague identity claims originate from a conflict between rigidity and precision in designation. To put this stricly, let x be the referent of the referential terms P and Q. Then, that the proposition “that any x being both a P and a Q” is vague involves that the semantic intuitions at work in P and Q reveal a conflict between P and Q being simultaneously rigid and precise designators. After having shortly commented on an example of vague identity claim, I make the case for my proposal, by discussing how reference by baptism conflicts with descriptive attitudes towards understanding conceptual contents
Donsker-Varadhan asymptotics for degenerate jump Markov processes
We consider a class of continuous time Markov chains on a compact metric
space that admit an invariant measure strictly positive on open sets together
with absorbing states. We prove the joint large deviation principle for the
empirical measure and flow. Due to the lack of uniform ergodicity, the zero
level set of the rate function is not a singleton. As corollaries, we obtain
the Donsker-Varadhan rate function for the empirical measure and a variational
expression of the rate function for the empirical flow
Pre-relaxation in weakly interacting models
We consider time evolution in models close to integrable points with hidden
symmetries that generate infinitely many local conservation laws that do not
commute with one another. The system is expected to (locally) relax to a
thermal ensemble if integrability is broken, or to a so-called generalised
Gibbs ensemble if unbroken. In some circumstances expectation values exhibit
quasi-stationary behaviour long before their typical relaxation time. For
integrability-breaking perturbations, these are also called pre-thermalisation
plateaux, and emerge e.g. in the strong coupling limit of the Bose-Hubbard
model. As a result of the hidden symmetries, quasi-stationarity appears also in
integrable models, for example in the Ising limit of the XXZ model. We
investigate a weak coupling limit, identify a time window in which the effects
of the perturbations become significant and solve the time evolution through a
mean-field mapping. As an explicit example we study the XYZ spin-
chain with additional perturbations that break integrability. One of the most
intriguing results of the analysis is the appearance of persistent oscillatory
behaviour. To unravel its origin, we study in detail a toy model: the
transverse-field Ising chain with an additional nonlocal interaction
proportional to the square of the transverse spin per unit length [Phys. Rev.
Lett. 111, 197203 (2013)]. Despite being nonlocal, this belongs to a class of
models that emerge as intermediate steps of the mean-field mapping and shares
many dynamical properties with the weakly interacting models under
consideration.Comment: 69 pages, 17 figures, improved exposition, figures 1 and 13 added,
some typos correcte
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
Comparison of calculated radiochemical cross sections with experimental results for incident protons and negative pions in the 50 to 400 MeV region - Effect of varying a few nuclear parameters in the calculations
Effect of varying nuclear parameters in calculating radiochemical cross sections for incident proton and negative pion reactions in 50 to 400 MeV regio
Some Effects of a Modified Evaporation Program on Calculations of Radiochemical Cross Sections and Particle Multiplicities for Protons on Carbon and Aluminum Targets
Modified Fortran evaporation program used for calculating radiochemical cross sections and particle multiplicities for protons on carbon and aluminum target
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