8,201 research outputs found
A local fluctuation theorem for large systems
The fluctuation theorem characterizes the distribution of the dissipation in
nonequilibrium systems and proves that the average dissipation will be
positive. For a large system with no external source of fluctuation,
fluctuations in properties will become unobservable and details of the
fluctuation theorem are unable to be explored. In this letter, we consider such
a situation and show how a fluctuation theorem can be obtained for a small open
subsystem within the large system. We find that a correction term has to be
added to the large system fluctuation theorem due to correlation of the
subsystem with the surroundings. Its analytic expression can be derived
provided some general assumptions are fulfilled, and its relevance it checked
using numerical simulations.Comment: 5 pages, 5 figures; revised and supplementary material include
Global well-posedness of a conservative relaxed cross diffusion system
We prove global existence in time of solutions to relaxed conservative cross
diffusion systems governed by nonlinear operators of the form where the represent
density-functions, is a spatially regularized form of
and the nonlinearities are merely assumed to be
continuous and bounded from below. Existence of global weak solutions is
obtained in any space dimension. Solutions are proved to be regular and unique
when the are locally Lipschitz continuous
Variations of Hausdorff Dimension in the Exponential Family
In this paper we deal with the following family of exponential maps
. Denoting
the hyperbolic dimension of . It is known that the
function is real analytic in , and
that it is continuous in . In this paper we prove that this map is
C on , with . Moreover, depending on the value of
, we give estimates of the speed of convergence towards 0.Comment: 32 pages. A para\^itre dans Annales Academi{\ae} Scientiarum
Fennic{\ae} Mathematic
Stabilization and controllability of first-order integro-differential hyperbolic equations
In the present article we study the stabilization of first-order linear
integro-differential hyperbolic equations. For such equations we prove that the
stabilization in finite time is equivalent to the exact controllability
property. The proof relies on a Fredholm transformation that maps the original
system into a finite-time stable target system. The controllability assumption
is used to prove the invertibility of such a transformation. Finally, using the
method of moments, we show in a particular case that the controllability is
reduced to the criterion of Fattorini
Bifurcations of a large scale circulation in a quasi-bidimensional turbulent flow
We report the experimental study of the bifurcations of a large-scale
circulation that is formed over a turbulent flow generated by a spatially
periodic forcing. After shortly describing how the flow becomes turbulent
through a sequence of symmetry breaking bifurcations, we focus our study on the
transitions that occur within the turbulent regime. They are related to changes
in the shape of the probability density function (PDF) of the amplitude of the
large scale flow. We discuss the nature of these bifurcations and how to model
the shape of the PDF.Comment: 6 pages, 9 figure
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