460 research outputs found
Reversible viscosity and Navier--Stokes fluids
Exploring the possibility of describing a fluid flow via a time-reversible
equation and its relevance for the fluctuations statistics in stationary
turbulent (or laminar) incompressible Navier-Stokes flows.Comment: 7 pages 6 figures, v2: replaced Fig.6 and few changes. Last version:
appendix cut shorter, because of a computational erro
The renormalized -trajectory by perturbation theory in a running coupling II: the continuous renormalization group
The renormalized trajectory of massless -theory on four dimensional
Euclidean space-time is investigated as a renormalization group invariant curve
in the center manifold of the trivial fixed point, tangent to the
-interaction. We use an exact functional differential equation for its
dependence on the running -coupling. It is solved by means of
perturbation theory. The expansion is proved to be finite to all orders. The
proof includes a large momentum bound on amputated connected momentum space
Green's functions.Comment: 26 pages LaTeX2
Chaotic Hypothesis, Fluctuation Theorem and singularities
The chaotic hypothesis has several implications which have generated interest
in the literature because of their generality and because a few exact
predictions are among them. However its application to Physics problems
requires attention and can lead to apparent inconsistencies. In particular
there are several cases that have been considered in the literature in which
singularities are built in the models: for instance when among the forces there
are Lennard-Jones potentials (which are infinite in the origin) and the
constraints imposed on the system do not forbid arbitrarily close approach to
the singularity even though the average kinetic energy is bounded. The
situation is well understood in certain special cases in which the system is
subject to Gaussian noise; here the treatment of rather general singular
systems is considered and the predictions of the chaotic hypothesis for such
situations are derived. The main conclusion is that the chaotic hypothesis is
perfectly adequate to describe the singular physical systems we consider, i.e.
deterministic systems with thermostat forces acting according to Gauss'
principle for the constraint of constant total kinetic energy (``isokinetic
Gaussian thermostats''), close and far from equilibrium. Near equilibrium it
even predicts a fluctuation relation which, in deterministic cases with more
general thermostat forces (i.e. not necessarily of Gaussian isokinetic nature),
extends recent relations obtained in situations in which the thermostatting
forces satisfy Gauss' principle. This relation agrees, where expected, with the
fluctuation theorem for perfectly chaotic systems. The results are compared
with some recent works in the literature.Comment: 7 pages, 1 figure; updated to take into account comments received on
the first versio
The renormalized -trajectory by perturbation theory in the running coupling
We compute the renormalized trajectory of -theory by perturbation
theory in a running coupling. We introduce an iterative scheme without
reference to a bare action. The expansion is proved to be finite to every order
of perturbation theory.Comment: 23 pages LaTeX, Large momentum bound correcte
Experimental test of the Gallavotti-Cohen fluctuation theorem in turbulent flows
We test the fluctuation theorem from measurements in turbulent flows. We
study the time fluctuations of the force acting on an obstacle, and we consider
two experimental situations: the case of a von K\'arm\'an swirling flow between
counter-rotating disks (VK) and the case of a wind tunnel jet. We first study
the symmetries implied by the Gallavotti-Cohen fluctuation theorem (FT) on the
probability density distributions of the force fluctuations; we then test the
Sinai scaling. We observe that in both experiments the symmetries implied by
the FT are well verified, whereas the Sinai scaling is established, as
expected, only for long times
A Quantum Analogue of the Jarzynski Equality
A quantum analogue of the Jarzynski equality is constructed. This equality
connects an ensemble average of exponentiated work with the Helmholtz
free-energy difference in a nonequilibrium switching process subject to a
thermal heat bath. To confirm its validity in a practical situation, we also
investigate an open quantum system that is a spin 1/2 system with a scanning
magnetic field interacting with a thermal heat bath. As a result, we find that
the quantum analogue functions well.Comment: 7 pages, 1 figure; to appear in J. Phys. Soc. Jpn. 69 (2000
Running coupling expansion for the renormalized -trajectory from renormalization invariance
We formulate a renormalized running coupling expansion for the
--function and the potential of the renormalized --trajectory on
four dimensional Euclidean space-time. Renormalization invariance is used as a
first principle. No reference is made to bare quantities. The expansion is
proved to be finite to all orders of perturbation theory. The proof includes a
large momentum bound on the connected free propagator amputated vertices.Comment: 14 pages LaTeX2e, typos and references correcte
Jarzynski equality for the transitions between nonequilibrium steady states
Jarzynski equality [Phys. Rev. E {\bf 56}, 5018 (1997)] is found to be valid
with slight modefication for the transitions between nonequilibrium stationary
states, as well as the one between equilibrium states. Also numerical results
confirm its validity. Its relevance for nonequilibrium thermodynamics of the
operational formalism is discussed.Comment: 5 pages, 2 figures, revte
The scaling limit of the energy correlations in non integrable Ising models
We obtain an explicit expression for the multipoint energy correlations of a
non solvable two-dimensional Ising models with nearest neighbor ferromagnetic
interactions plus a weak finite range interaction of strength , in a
scaling limit in which we send the lattice spacing to zero and the temperature
to the critical one. Our analysis is based on an exact mapping of the model
into an interacting lattice fermionic theory, which generalizes the one
originally used by Schultz, Mattis and Lieb for the nearest neighbor Ising
model. The interacting model is then analyzed by a multiscale method first
proposed by Pinson and Spencer. If the lattice spacing is finite, then the
correlations cannot be computed in closed form: rather, they are expressed in
terms of infinite, convergent, power series in . In the scaling limit,
these infinite expansions radically simplify and reduce to the limiting energy
correlations of the integrable Ising model, up to a finite renormalization of
the parameters. Explicit bounds on the speed of convergence to the scaling
limit are derived.Comment: 75 pages, 11 figure
Thermodynamic entropy production fluctuation in a two dimensional shear flow model
We investigate fluctuations in the momentum flux across a surface
perpendicular to the velocity gradient in a stationary shear flow maintained by
either thermostated deterministic or by stochastic boundary conditions. In the
deterministic system the Gallavotti-Cohen (GC)relation for the probability of
large deviations, which holds for the phase space volume contraction giving the
Gibbs ensemble entropy production, never seems to hold for the flux which gives
the hydrodynamic entropy production. In the stochastic case the GC relation is
found to hold for the total flux, as predicted by extensions of the GC theorem
but not for the flux across part of the surface. The latter appear to satisfy a
modified GC relation. Similar results are obtained for the heat flux in a
steady state produced by stochastic boundaries at different temperatures.Comment: 9 postscript figure
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