1,739 research outputs found
Boltzmann and hydrodynamic description for self-propelled particles
We study analytically the emergence of spontaneous collective motion within
large bidimensional groups of self-propelled particles with noisy local
interactions, a schematic model for assemblies of biological organisms. As a
central result, we derive from the individual dynamics the hydrodynamic
equations for the density and velocity fields, thus giving a microscopic
foundation to the phenomenological equations used in previous approaches. A
homogeneous spontaneous motion emerges below a transition line in the
noise-density plane. Yet, this state is shown to be unstable against spatial
perturbations, suggesting that more complicated structures should eventually
appear.Comment: 4 pages, 3 figures, final versio
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
Optimization of dispersive coefficients in the homogenization of the wave equation in periodic structures
International audienceWe study dispersive effects of wave propagation in periodic media, which can be modelled by adding a fourth-order term in the homogenized equation. The corresponding fourth-order dispersive tensor is called Burnett tensor and we numerically optimize its values in order to minimize or maximize dispersion. More precisely, we consider the case of a two-phase composite medium with an 8-fold symmetry assumption of the periodicity cell in two space dimensions. We obtain upper and lower bound for the dispersive properties, along with optimal microgeometries
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.
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
Magnetization process from Chern-Simons theory and its application to SrCu(BO)
URL: http://www-spht.cea.fr/articles/T02/081 16th Nishinomiya-Yukawa Memorial Symposium, Nishinomiya, Japan, November 2001 http://fr.arxiv.org/abs/cond-mat/0204161In two-dimensional systems, it is possible transmute bosons into fermions by use of a Chern-Simons gauge field. Such a mapping is used to compute magnetization processes of two-dimensional magnets. The calculation of the magnetization curve then involves the structure of the Hofstadter problem for the lattice under consideration. Certain features of the Hofstadter butterfly are shown to imply the appearance of magnetization plateaus. While not always successfull, this approach leads to interesting results when applied to the 2D AF magnet \SrCu
Local spin spirals in the Neel phase of La_{2-x}Sr_xCuO_4
Experimental observations of lightly doped La_{2-x}Sr_xCuO_4, x < 0.02,
revealed remarkable magnetic properties such as the incommensurate noncollinear
ordering (additional to the Neel ordering) and a tremendous doping dependence
of the uniform longitudinal susceptibility. We show that the spiral solution of
the t-t'-t''-J model obtained by taking into account the Coulomb trapping of
holes by Sr ions describes these puzzling data perfectly well. Our solution
firstly explains why the incommensurate structure is directed along the
orthorhombic b-axis, and secondly allows a numerical calculation of the
positions and shapes of the incommensurate neutron scattering peaks. Thirdly,
we calculate the doping dependence of the spin-wave gap, and lastly, we study
the longitudinal magnetic susceptibility and show that its doping dependence is
due to the noncollinearity of the spin spiral.Comment: 13 pages, 8 figure
On the Stress Tensor Light-ray Operator Algebra
We study correlation functions involving generalized ANEC operators of the
form in four dimensions. We
compute two, three, and four-point functions involving external scalar states
in both free and holographic Conformal Field Theories. From this information,
we extract the algebra of these light-ray operators. We find a global
subalgebra spanned by which annihilate the conformally
invariant vacuum and transform among themselves under the action of the
collinear conformal group that preserves the light-ray. Operators outside this
range give rise to an infinite central term, in agreement with previous
suggestions in the literature. In free theories, even some of the operators
inside the global subalgebra fail to commute when placed at spacelike
separation on the same null-plane. This lack of commutativity is not
integrable, presenting an obstruction to the construction of a well defined
light-ray algebra at coincident coordinates. For holographic CFTs the
behavior worsens and operators with fail to commute at spacelike
separation. We reproduce this result in the bulk of AdS where we present new
exact shockwave solutions dual to the insertions of these (exponentiated)
operators on the boundary.Comment: 56 pages + appendices, 9 figures; references and minor clarifications
adde
- …