425 research outputs found
Temperature in and out of equilibrium: a review of concepts, tools and attempts
We review the general aspects of the concept of temperature in equilibrium
and non-equilibrium statistical mechanics. Although temperature is an old and
well-established notion, it still presents controversial facets. After a short
historical survey of the key role of temperature in thermodynamics and
statistical mechanics, we tackle a series of issues which have been recently
reconsidered. In particular, we discuss different definitions and their
relevance for energy fluctuations. The interest in such a topic has been
triggered by the recent observation of negative temperatures in condensed
matter experiments. Moreover, the ability to manipulate systems at the micro
and nano-scale urges to understand and clarify some aspects related to the
statistical properties of small systems (as the issue of temperature's
"fluctuations"). We also discuss the notion of temperature in a dynamical
context, within the theory of linear response for Hamiltonian systems at
equilibrium and stochastic models with detailed balance, and the generalised
fluctuation-response relations, which provide a hint for an extension of the
definition of temperature in far-from-equilibrium systems. To conclude we
consider non-Hamiltonian systems, such as granular materials, turbulence and
active matter, where a general theoretical framework is still lacking.Comment: Review article, 137 pages, 12 figure
Multiple-scale analysis and renormalization for pre-asymptotic scalar transport
Pre-asymptotic transport of a scalar quantity passively advected by a
velocity field formed by a large-scale component superimposed to a small-scale
fluctuation is investigated both analytically and by means of numerical
simulations. Exploiting the multiple-scale expansion one arrives at a
Fokker--Planck equation which describes the pre-asymptotic scalar dynamics.
Such equation is associated to a Langevin equation involving a multiplicative
noise and an effective (compressible) drift. For the general case, no explicit
expression for both the effective drift and the effective diffusivity (actually
a tensorial field) can be obtained. We discuss an approximation under which an
explicit expression for the diffusivity (and thus for the drift) can be
obtained. Its expression permits to highlight the important fact that the
diffusivity explicitly depends on the large-scale advecting velocity. Finally,
the robustness of the aforementioned approximation is checked numerically by
means of direct numerical simulations.Comment: revtex4, 12 twocolumn pages, 3 eps figure
Broken ergodicity and glassy behavior in a deterministic chaotic map
A network of elements is studied in terms of a deterministic globally
coupled map which can be chaotic. There exists a range of values for the
parameters of the map where the number of different macroscopic configurations
is very large, and there is violation of selfaveraging. The time averages of
functions, which depend on a single element, computed over a time , have
probability distributions that do not collapse to a delta function, for
increasing and . This happens for both chaotic and regular motion, i.e.
positive or negative Lyapunov exponent.Comment: 3 pages RevTeX 3.0, 4 figures included (postscript), files packed
with uufile
Introduction to chaos and diffusion
This contribution is relative to the opening lectures of the ISSAOS 2001
summer school and it has the aim to provide the reader with some concepts and
techniques concerning chaotic dynamics and transport processes in fluids. Our
intention is twofold: to give a self-consistent introduction to chaos and
diffusion, and to offer a guide for the reading of the rest of this volume.Comment: 39 page
Relative dispersion in fully developed turbulence: from Eulerian to Lagrangian statistics in synthetic flows
The effect of Eulerian intermittency on the Lagrangian statistics of relative
dispersion in fully developed turbulence is investigated. A scaling range
spanning many decades is achieved by generating a multi-affine synthetic
velocity field with prescribed intermittency features. The scaling laws for the
Lagrangian statistics are found to depend on Eulerian intermittency in
agreement with a multifractal description. As a consequence of the Kolmogorov's
law, the Richardson's law for the variance of pair separation is not affected
by intermittency corrections.Comment: 4 pages RevTeX, 4 PostScript figure
Anomalous mobility of a driven active particle in a steady laminar flow
We study, via extensive numerical simulations, the force-velocity curve of an
active particle advected by a steady laminar flow, in the nonlinear response
regime. Our model for an active particle relies on a colored noise term that
mimics its persistent motion over a time scale . We find that the
active particle dynamics shows non-trivial effects, such as negative
differential and absolute mobility (NDM and ANM, respectively). We explore the
space of the model parameters and compare the observed behaviors with those
obtained for a passive particle () advected by the same laminar flow.
Our results show that the phenomena of NDM and ANM are quite robust with
respect to the details of the considered noise: in particular for finite
a more complex force-velocity relation can be observed.Comment: 12 pages, 9 figures, paper submitted for the Special Issue of Journal
of Physics: Condensed Matter, "Transport in Narrow Channels", Guest Editors
P. Malgaretti, G. Oshanin, J. Talbo
Anomalous force-velocity relation of driven inertial tracers in steady laminar flows
We study the nonlinear response to an external force of an inertial tracer
advected by a two-dimensional incompressible laminar flow and subject to
thermal noise. In addition to the driving external field , the main
parameters in the system are the noise amplitude and the characteristic
Stokes time of the tracer. The relation velocity vs force shows
interesting effects, such as negative differential mobility (NDM), namely a
non-monotonic behavior of the tracer velocity as a function of the applied
force, and absolute negative mobility (ANM), i.e. a net motion against the
bias. By extensive numerical simulations, we investigate the phase chart in the
parameter space of the model, , identifying the regions where NDM,
ANM and more common monotonic behaviors of the force-velocity curve are
observed.Comment: 5 pages, 13 figures. Contribution to the Topical Issue "Fluids and
Structures: Multi-scale coupling and modeling", edited by Luca Biferale,
Stefano Guido, Andrea Scagliarini, Federico Toschi. The final publication is
available at Springer via http://dx.doi.org/10.1140/epje/i2017-11571-
On the concept of complexity in random dynamical systems
We introduce a measure of complexity in terms of the average number of bits
per time unit necessary to specify the sequence generated by the system. In
random dynamical system, this indicator coincides with the rate K of divergence
of nearby trajectories evolving under two different noise realizations.
The meaning of K is discussed in the context of the information theory, and
it is shown that it can be determined from real experimental data. In presence
of strong dynamical intermittency, the value of K is very different from the
standard Lyapunov exponent computed considering two nearby trajectories
evolving under the same randomness. However, the former is much more relevant
than the latter from a physical point of view as illustrated by some numerical
computations for noisy maps and sandpile models.Comment: 35 pages, LaTe
Front propagation in laminar flows
The problem of front propagation in flowing media is addressed for laminar
velocity fields in two dimensions. Three representative cases are discussed:
stationary cellular flow, stationary shear flow, and percolating flow.
Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius
type are considered under the assumption of no feedback of the concentration on
the velocity. Numerical simulations of advection-reaction-diffusion equations
have been performed by an algorithm based on discrete-time maps. The results
show a generic enhancement of the speed of front propagation by the underlying
flow. For small molecular diffusivity, the front speed depends on the
typical flow velocity as a power law with an exponent depending on the
topological properties of the flow, and on the ratio of reactive and advective
time-scales. For open-streamline flows we find always , whereas for
cellular flows we observe for fast advection, and for slow advection.Comment: Enlarged, revised version, 37 pages, 14 figure
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