69 research outputs found
Phase transition in protocols minimizing work fluctuations
For two canonical examples of driven mesoscopic systems - a
harmonically-trapped Brownian particle and a quantum dot - we numerically
determine the finite-time protocols that optimize the compromise between the
standard deviation and the mean of the dissipated work. In the case of the
oscillator, we observe a collection of protocols that smoothly trade-off
between average work and its fluctuations. However, for the quantum dot, we
find that as we shift the weight of our optimization objective from average
work to work standard deviation, there is an analog of a first-order phase
transition in protocol space: two distinct protocols exchange global optimality
with mixed protocols akin to phase coexistence. As a result, the two types of
protocols possess qualitatively different properties and remain distinct even
in the infinite duration limit: optimal-work-fluctuation protocols never
coalesce with the minimal work protocols, which therefore never become
quasistatic.Comment: 6 pages, 6 figures + SI as ancillary fil
From Phase to Micro-Phase Separation in Flocking Models: The Essential Role of Non-Equilibrium Fluctuations
We show that the flocking transition in the Vicsek model is best understood
as a liquid-gas transition, rather than an order-disorder one. The full phase
separation observed in flocking models with Z2 rotational symmetry is, however,
replaced by a microphase separation leading to a smectic arrangement of
traveling ordered bands. Remarkably, continuous deterministic descriptions do
not account for this difference, which is only recovered at the fluctuating
hydrodynamics level. Scalar and vectorial order parameters indeed produce
different types of number fluctuations, which we show to be essential in
selecting the inhomogeneous patterns. This highlights an unexpected role of
fluctuations in the selection of flock shapes.Comment: 5 p., 5 fig.. Supplementary material: 7 movie
Non-equilibrium forces following quenches in active and thermal matter
Non-equilibrium systems are known to exhibit long-ranged correlations due to
conservation of quantities like density or momentum. This, in turn, leads to
long-ranged fluctuation-induced (Casimir) forces, predicted to arise in a
variety of non-equilibrium settings. Here, we study such forces, which arise
transiently between parallel plates or compact inclusions in a gas of
particles, following a change ("quench") in temperature or activity of the
medium. Analytical calculations, as well as numerical simulations of passive or
active Brownian particles, indicate two distinct forces: (i) The immediate
effect of the quench is adsorption or desorption of particles of the medium to
the immersed objects, which in turn initiates a front of relaxing (mean)
density. This leads to time-dependent {\it density-induced forces}. (ii) A
long-term effect of the quench is that density fluctuations are modified,
manifested as transient (long-ranged) (pair-)correlations that relax
diffusively to their (short-ranged) steady-state limit. As a result, transient
{\it fluctuation-induced forces} emerge. We discuss the properties of
fluctuation-induced and density-induced forces as regards universality,
relaxation as a function of time, and scaling with distance between objects.
Their distinct signatures allow us to distinguish the two types of forces in
simulation data. Finally, we propose several scenarios for their experimental
observation.Comment: - Added Journal reference and DOI - Modified title - Fixed minor
typos - Added plot of Eq. (32) [16 pages, 11 figures
Response of active Brownian particles to shear flow
We study the linear response of interacting active Brownian particles in an
external potential to simple shear flow. Using a path integral approach, we
derive the linear response of any state observable to initiating shear in terms
of correlation functions evaluated in the unperturbed system. For systems and
observables which are symmetric under exchange of the and coordinates,
the response formula can be drastically simplified to a form containing only
state variables in the corresponding correlation functions (compared to the
generic formula containing also time derivatives). In general, the shear
couples to the particles by translational as well as rotational advection, but
in the aforementioned case of symmetry only translational advection is
relevant in the linear regime. We apply the response formulas analytically in
solvable cases and numerically in a specific setup. In particular, we
investigate the effect of a shear flow on the morphology and the stress of
confined active particles in interaction, where we find that the activity as
well as additional alignment interactions generally increase the response.Comment: 13 pages, 4 figure
Mechanical pressure and momentum conservation in dry active matter
We relate the breakdown of equations of states for the mechanical pressure of
generic dry active systems to the lack of momentum conservation in such
systems. We show how sources and sinks of momentum arise generically close to
confining walls. These typically depend on the interactions of the container
with the particles, which makes the mechanical pressure a container-dependent
quantity. We show that an equation of state is recovered if the dynamics of the
orientation of active particles are decoupled from other degrees of freedom and
lead to an apolar bulk steady-state. This is related to the fact that the mean
steady-state active force density is the divergence of the flux of "active
impulse", an observable which measures the mean momentum particles will receive
from the substrate in the future
Generic long-range interactions between passive bodies in an active fluid
Because active particles break time-reversal symmetry, a single non-spherical
body placed in an active fluid generates currents. We show that when two or
more passive bodies are placed in an active fluid these currents lead to
long-range interactions. Using a multipole expansion we characterize their
leading-order behaviors in terms of single-body properties and show that they
decay as a power law with the distance between the bodies, are anisotropic, and
do not obey an action--reaction principle. The interactions lead to rich
dynamics of the bodies, illustrated by the spontaneous synchronized rotation of
pinned non-chiral bodies and the formation of traveling bound pairs. The
occurrence of these phenomena depends on tunable properties of the bodies, thus
opening new possibilities for self-assembly mediated by active fluids.Comment: 21 pages, 6 figure
Generalized thermodynamics of Motility-Induced Phase Separation: Phase equilibria, Laplace pressure, and change of ensembles
Motility-induced phase separation (MIPS) leads to cohesive active matter in
the absence of cohesive forces. We present, extend and illustrate a recent
generalized thermodynamic formalism which accounts for its binodal curve. Using
this formalism, we identify both a generalized surface tension, that controls
finite-size corrections to coexisting densities, and generalized forces, that
can be used to construct new thermodynamic ensembles. Our framework is based on
a nonequilibrium generalization of the Cahn-Hilliard equation and we discuss
its application to active particles interacting either via quorum-sensing
interactions or directly through pairwise forces.Comment: 33 pages, 14 figure
Physique statistique de la matière active
Active systems, composed of particles capable of using the energy stored in theirmedium to self-propel, are ubiquitous in nature. They are found at all scales :from molecular motors to cellular tissues, bacterial colonies and animal groups.These out-of-equilibrium systems have attracted a lot of attention from the physicscommunity because they show a richer phenomenology than passive systems thatwe can still understand using simple models.In this thesis, we study analytically and numerically minimal models of activeparticles. They allow us to understand different phenomena that are characteristicof active matter and to study the large-scale behavior of several classes of systems.The thermodynamics of active systems is fundamentally different from thatof equilibrium systems. In particular, we show that the mechanical pressure ofan active particle fluid is not given by an equation of state. The pressure isnot a property of the fluid and depends on the details of the interaction with thecontaining vessel.We also study two phase transitions that specific to active matter : The motility-induced phase separation and the transition to collective motion. In both cases, weobserve a phase separation between a liquid and a gas and study their coexistence.For the transition to collective motion, we exhibit two universality classes, basedon the particles’ symmetry, which have different types of coexistence phases.Les systèmes actifs, composés de particules capables de transformer l’énergiestockée dans leur environnement pour s’autopropulser, sont omniprésents dans lanature. On les trouve à toutes les échelles : des moteurs moléculaires aux groupesd’animaux, en passant par les tissus cellulaires et les colonies de bactéries. Cessystèmes hors d’équilibre ont attiré l’attention des physiciens car ils présententune phénoménologie plus riche que les systèmes passifs, que l’on peut cependantcomprendre à partir de modèles simples.Dans cette thèse, nous avons étudié analytiquement et numériquement desmodèles minimaux de particules actives. Ceux-ci nous ont permis de comprendredifférents phénomènes spécifiques à la matière active et d’étudier le comportementà grand échelle de plusieurs classes de systèmes.La thermodynamique des systèmes actifs est fondamentalement différente decelle des systèmes d’équilibre. Nous montrons en particulier que la pression méca-nique d’un fluide de particules actives n’est pas donnée par une équation d’état.La pression n’est donc pas seulement une propriété du fluide et dépend du détaildes interactions avec les parois du récipient dans lequel il est confiné.Nous étudions également deux transitions de phase propres à la matière active :la séparation de phase induite par la motilité et la transition vers le mouvementcollectif. Dans les deux cas, on observe une séparation de phase entre un liquideet un gaz dont nous étudions la coexistence. Pour la transition vers le mouvementcollectif on distingue deux classes d’universalité, en fonction de la symétrie desparticules, qui ont des coexistences de phase différentes
Sedimentation of self-propelled Janus colloids: polarization and pressure
We study experimentally-using Janus colloids-and theoretically-using Active
Brownian Particles- the sedimentation of dilute active colloids. We first
confirm the existence of an exponential density profile. We show experimentally
the emergence of a polarized steady state outside the effective equilibrium
regime, i.e. when v_s is not much smaller than the propulsion speed. The
experimental distribution of polarization is very well described by the
theoretical prediction with no fitting parameter. We then discuss and compare
three different definitions of pressure for sedimenting particles: the weight
of particles above a given height, the flux of momentum and active impulse, and
the force density measured by pressure gauges
Towards Distance-Based Phylogenetic Inference in Average-Case Linear-Time
Computing genetic evolution distances among a set of taxa dominates the running time of many phylogenetic inference methods. Most of genetic evolution distance definitions rely, even if indirectly, on computing the pairwise Hamming distance among sequences or profiles. We propose here an average-case linear-time algorithm to compute pairwise Hamming distances among a set of taxa under a given Hamming distance threshold. This article includes both a theoretical analysis and extensive experimental results concerning the proposed algorithm. We further show how this algorithm can be successfully integrated into a well known phylogenetic inference method
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