29 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
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
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
Pattern formation in flocking models: A hydrodynamic description
International audienceWe study in detail the hydrodynamic theories describing the transition to collective motion in polar active matter, exemplified by the Vicsek and active Ising models. Using a simple phenomenological theory, we show the existence of an infinity of propagative solutions, describing both phase and microphase separation, that we fully characterize. We also show that the same results hold specifically in the hydrodynamic equations derived in the literature for the active Ising model and for a simplified version of the Vicsek model. We then study numerically the linear stability of these solutions. We show that stable ones constitute only a small fraction of them, which, however, includes all existing types. We further argue that, in practice, a coarsening mechanism leads towards phase-separated solutions. Finally, we construct the phase diagrams of the hydrodynamic equations proposed to qualitatively describe the Vicsek and active Ising models and connect our results to the phenomenology of the corresponding microscopic models
Generalized thermodynamics of phase equilibria in scalar active matter.
Motility-induced phase separation (MIPS) arises generically in fluids of self-propelled particles when interactions lead to a kinetic slowdown at high densities. Starting from a continuum description of scalar active matter akin to a generalized Cahn-Hilliard equation, we give a general prescription for the mean densities of coexisting phases in flux-free steady states that amounts, at a hydrodynamics scale, to extremizing an effective free energy. We illustrate our approach on two well-known models: self-propelled particles interacting either through a density-dependent propulsion speed or via direct pairwise forces. Our theory accounts quantitatively for their phase diagrams, providing a unified description of MIPS