9,471 research outputs found
Macroscopic limit of a one-dimensional model for aging fluids
We study a one-dimensional equation arising in the multiscale modeling of
some non-Newtonian fluids. At a given shear rate, the equation provides the
instantaneous mesoscopic response of the fluid, allowing to compute the
corresponding stress. In a simple setting, we study the well-posedness of the
equation and next the long-time behavior of its solution. In the limit of a
response of the fluid much faster than the time variations of the ambient shear
rate, we derive some equivalent macroscopic differential equations that relate
the shear rate and the stress. Our analytical conclusions are confronted to
some numerical experiments. The latter quantitatively confirm our derivations
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
A simple model for heterogeneous flows of yield stress fluids
Various experiments evidence spatial heterogeneities in sheared yield stress
fluids. To account for heterogeneities in the velocity gradient direction, we
use a simple model corresponding to a non-monotonous local constitutive curve
and study a simple shear geometry. Different types of boundary conditions are
considered. Under controlled macroscopic shear stress , we find
homogeneous flow in the bulk and a hysteretic macroscopic stress - shear rate
curve. Under controlled macroscopic shear rate , shear banding is
predicted within a range of values of . For small shear rates,
stick slip can also be observed. These qualitative behaviours are robust when
changing the boundary conditions.Comment: 13 pages, 13 figure
Thermal properties of slow dynamics
The limit of small entropy production is reached in relaxing systems long
after preparation, and in stationary driven systems in the limit of small
driving power. Surprisingly, for extended systems this limit is not in general
the Gibbs-Boltzmann distribution, or a small departure from it. Interesting
cases in which it is not are glasses, phase-separation, and certain driven
complex fluids.
We describe a scenario with several coexisting temperatures acting on
different timescales, and partial equilibrations at each time scale. This
scenario entails strong modifications of the fluctuation-dissipation equalities
and the existence of some unexpected reciprocity relations. Both predictions
are open to experimental verification, particularly the latter.
The construction is consistent in general, since it can be viewed as the
breaking of a symmetry down to a residual group. It does not assume the
presence of quenched disorder. It can be -- and to a certain extent has been --
tested numerically, while some experiments are on their way. There is
furthermore the perspective that analytic arguments may be constructed to prove
or disprove its generality.Comment: 11 pages, invited talk to be presented at STATPHYS 20, Pari
Modeling the mechanics of amorphous solids at different length and time scales
We review the recent literature on the simulation of the structure and
deformation of amorphous glasses, including oxide and metallic glasses. We
consider simulations at different length and time scales. At the nanometer
scale, we review studies based on atomistic simulations, with a particular
emphasis on the role of the potential energy landscape and of the temperature.
At the micrometer scale, we present the different mesoscopic models of
amorphous plasticity and show the relation between shear banding and the type
of disorder and correlations (e.g. elastic) included in the models. At the
macroscopic range, we review the different constitutive laws used in finite
element simulations. We end the review by a critical discussion on the
opportunities and challenges offered by multiscale modeling and transfer of
information between scales to study amorphous plasticity.Comment: 58 pages, 14 figure
Scaling and aging in the homogeneous cooling state of a granular fluid of hard particles
The presence of the aging phenomenon in the homogeneous cooling state (HCS)
of a granular fluid composed of inelastic hard spheres or disks is
investigated. As a consequence of the scaling property of the -particle
distribution function, it is obtained that the decay of the normalized two-time
correlation functions slows down as the time elapsed since the beginning of the
measurement increases. This result is confirmed by molecular dynamics
simulations for the particular case of the total energy of the system. The
agreement is also quantitative in the low density limit, for which an explicit
analytical form of the time correlation function has been derived. The reported
results also provide support for the existence of the HCS as a solution of the
N-particle Liouville equation.Comment: 17 pages, 3 figures; v3 revised version (minor changes, corrected
typos, v2=v1 due to a submission error)accepted for publication in J. Phys.
A: Math. Theo
Mesoscopic model for soft flowing systems with tunable viscosity ratio
We propose a mesoscopic model of binary fluid mixtures with tunable viscosity
ratio based on the two-range pseudo-potential lattice Boltzmann method, for the
simulation of soft flowing systems. In addition to the short range repulsive
interaction between species in the classical single-range model, a competing
mechanism between the short range attractive and mid-range repulsive
interactions is imposed within each species. Besides extending the range of
attainable surface tension as compared with the single-range model, the
proposed scheme is also shown to achieve a positive disjoining pressure,
independently of the viscosity ratio. The latter property is crucial for many
microfluidic applications involving a collection of disperse droplets with a
different viscosity from the continuum phase. As a preliminary application, the
relative effective viscosity of a pressure-driven emulsion in a planar channel
is computed.Comment: 14page
The effective temperature
This review presents the effective temperature notion as defined from the
deviations from the equilibrium fluctuation-dissipation theorem in out of
equilibrium systems with slow dynamics. The thermodynamic meaning of this
quantity is discussed in detail. Analytic, numeric and experimental
measurements are surveyed. Open issues are mentioned.Comment: 58 page
- …