2,429 research outputs found
Irreducible Hamiltonian BRST-anti-BRST symmetry for reducible systems
An irreducible Hamiltonian BRST-anti-BRST treatment of reducible first-class
systems based on homological arguments is proposed. The general formalism is
exemplified on the Freedman-Townsend model.Comment: LaTeX 2.09, 35 page
Onset of collective and cohesive motion
We study the onset of collective motion, with and without cohesion, of groups
of noisy self-propelled particles interacting locally. We find that this phase
transition, in two space dimensions, is always discontinuous, including for the
minimal model of Vicsek et al. [Phys. Rev. Lett. {\bf 75},1226 (1995)] for
which a non-trivial critical point was previously advocated. We also show that
cohesion is always lost near onset, as a result of the interplay of density,
velocity, and shape fluctuations.Comment: accepted for publication in Phys. Rev. Let
Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
Considering a gas of self-propelled particles with binary interactions, we
derive the hydrodynamic equations governing the density and velocity fields
from the microscopic dynamics, in the framework of the associated Boltzmann
equation. Explicit expressions for the transport coefficients are given, as a
function of the microscopic parameters of the model. We show that the
homogeneous state with zero hydrodynamic velocity is unstable above a critical
density (which depends on the microscopic parameters), signaling the onset of a
collective motion. Comparison with numerical simulations on a standard model of
self-propelled particles shows that the phase diagram we obtain is robust, in
the sense that it depends only slightly on the precise definition of the model.
While the homogeneous flow is found to be stable far from the transition line,
it becomes unstable with respect to finite-wavelength perturbations close to
the transition, implying a non trivial spatio-temporal structure for the
resulting flow. We find solitary wave solutions of the hydrodynamic equations,
quite similar to the stripes reported in direct numerical simulations of
self-propelled particles.Comment: 33 pages, 11 figures, submitted to J. Phys.
Experimental scaling law for the sub-critical transition to turbulence in plane Poiseuille flow
We present an experimental study of transition to turbulence in a plane
Poiseuille flow. Using a well-controlled perturbation, we analyse the flow
using extensive Particule Image Velocimetry and flow visualisation (using Laser
Induced Fluorescence) measurements and use the deformation of the mean velocity
profile as a criterion to characterize the state of the flow. From a large
parametric study, four different states are defined depending on the values of
the Reynolds number and the amplitude of the perturbation. We discuss the role
of coherent structures, like hairpin vortices, in the transition. We find that
the minimal amplitude of the perturbation triggering transition scales like
Re^-1
Permutation-invariant distance between atomic configurations
We present a permutation-invariant distance between atomic configurations,
defined through a functional representation of atomic positions. This distance
enables to directly compare different atomic environments with an arbitrary
number of particles, without going through a space of reduced dimensionality
(i.e. fingerprints) as an intermediate step. Moreover, this distance is
naturally invariant through permutations of atoms, avoiding the time consuming
associated minimization required by other common criteria (like the Root Mean
Square Distance). Finally, the invariance through global rotations is accounted
for by a minimization procedure in the space of rotations solved by Monte Carlo
simulated annealing. A formal framework is also introduced, showing that the
distance we propose verifies the property of a metric on the space of atomic
configurations. Two examples of applications are proposed. The first one
consists in evaluating faithfulness of some fingerprints (or descriptors), i.e.
their capacity to represent the structural information of a configuration. The
second application concerns structural analysis, where our distance proves to
be efficient in discriminating different local structures and even classifying
their degree of similarity
Criterion for purely elastic Taylor-Couette instability in the flows of shear-banding fluids
In the past twenty years, shear-banding flows have been probed by various
techniques, such as rheometry, velocimetry and flow birefringence. In micellar
solutions, many of the data collected exhibit unexplained spatio-temporal
fluctuations. Recently, it has been suggested that those fluctuations originate
from a purely elastic instability of the flow. In cylindrical Couette geometry,
the instability is reminiscent of the Taylor-like instability observed in
viscoelastic polymer solutions. In this letter, we describe how the criterion
for purely elastic Taylor-Couette instability should be adapted to
shear-banding flows. We derive three categories of shear-banding flows with
curved streamlines, depending on their stability.Comment: 6 pages, 3 figure
Potential "ways of thinking" about the shear-banding phenomenon
Shear-banding is a curious but ubiquitous phenomenon occurring in soft
matter. The phenomenological similarities between the shear-banding transition
and phase transitions has pushed some researchers to adopt a 'thermodynamical'
approach, in opposition to the more classical 'mechanical' approach to fluid
flows. In this heuristic review, we describe why the apparent dichotomy between
those approaches has slowly faded away over the years. To support our
discussion, we give an overview of different interpretations of a single
equation, the diffusive Johnson-Segalman (dJS) equation, in the context of
shear-banding. We restrict ourselves to dJS, but we show that the equation can
be written in various equivalent forms usually associated with opposite
approaches. We first review briefly the origin of the dJS model and its initial
rheological interpretation in the context of shear-banding. Then we describe
the analogy between dJS and reaction-diffusion equations. In the case of
anisotropic diffusion, we show how the dJS governing equations for steady shear
flow are analogous to the equations of the dynamics of a particle in a quartic
potential. Going beyond the existing literature, we then draw on the Lagrangian
formalism to describe how the boundary conditions can have a key impact on the
banding state. Finally, we reinterpret the dJS equation again and we show that
a rigorous effective free energy can be constructed, in the spirit of early
thermodynamic interpretations or in terms of more recent approaches exploiting
the language of irreversible thermodynamics.Comment: 14 pages, 6 figures, tutorial revie
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