arXiv subjects

Cesare Nardini

Publications and source records attributed to Cesare Nardini.

At least 37 records · Page 2Linked to original sources

arXiv2021

Capillary interfacial tension in active phase separation

In passive fluid-fluid phase separation, a single interfacial tension sets both the capillary fluctuations of the interface and the rate of Ostwald ripening. We show that these phenomena are governed by two different tensions in active systems, and compute the capillary tension $σ_{cw}$ which sets the relaxation rate of interfacial fluctuations in accordance with capillary wave theory. We discover that strong enough activity can cause negative $σ_{cw}$. In this regime, depending on the global composition, the system self-organizes, either into a microphase-separated state in which coalescence is highly inhibited, or into an `active foam' state. Our results are obtained for Active Model B+, a minimal continuum model which, although generic, admits significant analytical progress.

cond-mat.soft↗

arXiv2021

Absorbing phase transitions in systems with mediated interactions

Experiments of periodically sheared colloidal suspensions or soft amorphous solids display a transition from reversible to irreversible particle motion that, when analysed stroboscopically in time, is interpreted as an absorbing phase transition with infinitely many absorbing states. In these systems interactions mediated by hydrodynamics or elasticity are present, causing passive regions to be affected by nearby active ones. We show that mediated interactions induce a new universality class of absorbing phase transitions, distinct from Conserved Directed Percolation, and we obtain the corresponding critical exponents. We do so with large-scale numerical simulations of a minimal model for the stroboscopic dynamics of sheared soft materials and derive the minimal field theoretical description.

cond-mat.soft↗

arXiv2021

Self-Organized Critical Coexistence Phase in Repulsive Active Particles

We revisit motility-induced phase separation in two models of active particles interacting by pairwise repulsion. We show that the resulting dense phase contains gas bubbles distributed algebraically up to a typically large cutoff scale. At large enough system size and/or global density, all the gas may be contained inside the bubbles, at which point the system is microphase-separated with a finite cut-off bubble scale. We observe that the ordering is anomalous, with different dynamics for the coarsening of the dense phase and of the gas bubbles. This phenomenology is reproduced by a "reduced bubble model" that implements the basic idea of reverse Ostwald ripening put forward in Tjhung et al. [Phys. Rev. X 8, 031080 (2018)].

cond-mat.stat-mech↗

arXiv2020

Swimming suppresses correlations in dilute suspensions of pusher microorganisms

Active matter exhibits various forms of non-equilibrium states in the absence of external forcing, including macroscopic steady-state currents. Such states are often too complex to be modelled from first principles and our understanding of their physics relies heavily on minimal models. These have mostly been studied in the case of "dry" active matter, where particle dynamics are dominated by friction with their surroundings. Significantly less is known about systems with long-range hydrodynamic interactions that belong to "wet" active matter. Dilute suspensions of motile bacteria, modelled as self-propelled dipolar particles interacting solely through long-ranged hydrodynamic fields, are arguably the most studied example from this class of active systems. Their phenomenology is well-established: at sufficiently high density of bacteria, there appear large-scale vortices and jets comprising many individual organisms, forming a chaotic state commonly known as bacterial turbulence. As revealed by computer simulations, below the onset of collective motion, the suspension exhibits very strong correlations between individual microswimmers stemming from the long-ranged nature of dipolar fields. Here we demonstrate that this phenomenology is captured by the minimal model of microswimmers. We develop a kinetic theory that goes beyond the commonly used mean-field assumption, and explicitly takes into account such correlations. Notably, these can be computed exactly within our theory. We calculate the fluid velocity variance, spatial and temporal correlation functions, the fluid velocity spectrum, and the enhanced diffusivity of tracer particles. We find that correlations are suppressed by particle self-propulsion, although the mean-field behaviour is not restored even in the limit of very fast swimming.

cond-mat.soft↗

arXiv2020

Fluctuation-induced phase separation in metric and topological models of collective motion

We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a density-dependent shift of the onset of order, which in turns changes the nature of the transition into a phase-separation scenario. Our results apply to a range of systems, including the topological models in which particles interact with a fixed number of nearest neighbors, which were believed so far to exhibit a continuous onset of order. Our analytical predictions are confirmed by numerical simulations of fluctuating hydrodynamics and microscopic models.

cond-mat.soft↗

arXiv2020

Symmetric mixtures of pusher and puller microswimmers behave as noninteracting suspensions

Suspensions of rear- and front-actuated microswimmers immersed in a fluid, known respectively as ``pushers'' and ``pullers'', display qualitatively different collective behaviours: beyond a characteristic density, pusher suspensions exhibit a hydrodynamic instability leading to collective motion known as active turbulence, a phenomenon which is absent for pullers. In this Letter, we describe the collective dynamics of a binary pusher--puller mixture using kinetic theory and large-scale particle-resolved simulations. We derive and verify an instability criterion, showing that the critical density for active turbulence moves to higher values as the fraction $χ$ of pullers is increased and disappears for $χ\geq 0.5$. We then show analytically and numerically that the two-point hydrodynamic correlations of the 1:1 mixture are equal to those of a suspension of noninteracting swimmers. Strikingly, our numerical analysis furthermore shows that the full probability distribution of the fluid velocity fluctuations collapses onto the one of a noninteracting system at the same density, where swimmer--swimmer correlations are strictly absent. Our results thus indicate that the fluid velocity fluctuations in 1:1 pusher--puller mixtures are exactly equal to those of the corresponding noninteracting suspension at any density, a surprising cancellation with no counterpart in equilibrium long-range interacting systems.

cond-mat.soft↗

arXiv2019

The 2019 Motile Active Matter Roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of active matter in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines.

cond-mat.soft↗

arXiv2019

Particle-resolved lattice Boltzmann simulations of 3-dimensional active turbulence

Collective behaviour in suspensions of microswimmers is often dominated by the impact of long-ranged hydrodynamic interactions. These phenomena include active turbulence, where suspensions of pusher bacteria at sufficient densities exhibit large-scale, chaotic flows. To study this collective phenomenon, we use large-scale (up to $N=3\times 10^6$) particle-resolved lattice Boltzmann simulations of model microswimmers described by extended stresslets. Such system sizes enable us to obtain quantitative information about both the transition to active turbulence and characteristic features of the turbulent state itself. In the dilute limit, we test analytical predictions for a number of static and dynamic properties against our simulation results. For higher swimmer densities, where swimmer-swimmer interactions become significant, we numerically show that the length- and timescales of the turbulent flows increase steeply near the predicted finite-system transition density.

cond-mat.soft↗

arXiv2018

From bulk to microphase separation in scalar active matter: A perturbative renormalization group analysis

We consider a dynamical field theory (Active Model B+) that minimally extends the equilibrium Model B for diffusive phase separation of a scalar field, by adding leading-order terms that break time-reversal symmetry. It was recently shown that such active terms can cause the bulk phase separation of Model B to be replaced by a steady state of microphase separation at a finite length scale. This phenomenon was understood at mean-field level as due to the activity-induced reversal of the Ostwald ripening mechanism, which provides the kinetic pathway to bulk phase separation in passive fluids. This reversal occurs only in certain ranges for the activity parameters. In this paper we go beyond such a mean-field analysis and develop a $1$-loop Renormalisation Group (RG) approach. We first show that, in the parameter range where bulk phase separation is still present, the critical point belongs formally to the same (Wilson-Fisher) universality class as the passive Model B. In contrast, in a parameter range associated with microphase separation, we find that an unstable non-equilibrium fixed point of the RG flow arises for $d\geq 2$, colliding with the Wilson-Fisher point in $d\to 2^+$ and making it unstable in $d=2$. At large activity, the flow in this region is towards strong coupling. We argue that the phase transition to microphase separation in active systems, in the physically relevant dimensions $d=2$ and $3$, very probably belongs to a new non-equilibrium universality class. Because it is governed by the strong-coupling regime of the RG flow, our perturbative analysis leaves open the quantitative characterization of this new class.

cond-mat.stat-mech↗

arXiv2018

Cluster phases and bubbly phase separation in active fluids: Reversal of the Ostwald process

It is known that purely repulsive self-propelled colloids can undergo bulk liquid-vapor phase separation. In experiments and large scale simulations, however, more complex steady states are also seen, comprising a dynamic population of dense clusters in a sea of vapor, or dilute bubbles in a liquid. Here we show that these microphase-separated states should emerge generically in active matter, without any need to invoke system-specific details. We give a coarse-grained description of them, and predict transitions between regimes of bulk phase separation and microphase separation. We achieve these results by extending the $ϕ^4$ field theory of passive phase separation to allow for all local currents that break detailed balance at leading order in the gradient expansion. These local active currents, whose form we show to emerge from coarse-graining of microscopic models, include a mixture of irrotational and rotational contributions, and can be viewed as arising from an effective nonlocal chemical potential. Such contributions influence, and in some parameter ranges reverse, the classical Ostwald process that would normally drive bulk phase separation to completion.

cond-mat.soft↗

arXiv2018

Strong coupling in conserved surface roughening: A new universality class?

The Kardar-Parisi-Zhang (KPZ) equation defines the main universality class for nonlinear growth and roughening of surfaces. But under certain conditions, a conserved KPZ equation (cKPZ) is thought to set the universality class instead. This has non-mean-field behavior only in spatial dimension $d<2$. We point out here that cKPZ is incomplete: it omits a symmetry-allowed nonlinear gradient term of the same order as the one retained. Adding this term, we find a parameter regime where the $1$-loop renormalization group flow diverges. This suggests a phase transition to a new growth phase, possibly ruled by a strong coupling fixed point and thus described by a new universality class, for any $d>1$. In this phase, numerical integration of the model in $d=2$ gives clear evidence of non mean-field behavior.

cond-mat.stat-mech↗

arXiv2017

Process interpretation of current entropic bounds

We show for Markov diffusion processes that the quadratic entropic bound, recently derived for the rate functions of nonequilibrium currents, can be seen as being produced by an effective process that creates current fluctuations in a sub-optimal way by modifying only the non-reversible part of the drift or force of the process considered while keeping its reversible part constant. This provides a clear interpretation of the bound in terms of a physical process, which explains, among other things, its relation to the fluctuation relation, linear response, and reversible limits. The existence of more general quadratic bounds, and related uncertainty relations, for physical quantities other than currents is also discussed.

cond-mat.stat-mech↗

arXiv2017

The role of correlations in the collective behaviour of microswimmer suspensions

In this Letter, we study the collective behaviour of a large number of self-propelled microswimmers immersed in a fluid. Using unprecedently large-scale lattice Boltzmann simulations, we reproduce the transition to bacterial turbulence. We show that, even well below the transition, swimmers move in a correlated fashion that cannot be described by a mean-field approach. We develop a novel kinetic theory that captures these correlations and is non-perturbative in the swimmer density. To provide an experimentally accessible measure of correlations, we calculate the diffusivity of passive tracers and reveal its non-trivial density dependence. The theory is in quantitative agreement with the lattice Boltzmann simulations and captures the asymmetry between pusher and puller swimmers below the transition to turbulence.

cond-mat.soft↗

arXiv2017

Entropy production in field theories without time reversal symmetry: Quantifying the non-equilibrium character of active matter

Active matter systems operate far from equilibrium due to the continuous energy injection at the scale of constituent particles. At larger scales, described by coarse-grained models, the global entropy production rate S quantifies the probability ratio of forward and reversed dynamics and hence the importance of irreversibility at such scales: it vanishes whenever the coarse-grained dynamics of the active system reduces to that of an effective equilibrium model. We evaluate S for a class of scalar stochastic field theories describing the coarse-grained density of self-propelled particles without alignment interactions, capturing such key phenomena as motility-induced phase separation. We show how the entropy production can be decomposed locally (in real space) or spectrally (in Fourier space), allowing detailed examination of the spatial structure and correlations that underly departures from equilibrium. For phase-separated systems, the local entropy production is concentrated mainly on interfaces with a bulk contribution that tends to zero in the weak-noise limit. In homogeneous states, we find a generalized Harada-Sasa relation that directly expresses the entropy production in terms of the wavevector-dependent deviation from the fluctuation-dissipation relation between response functions and correlators. We discuss extensions to the case where the particle density is coupled to a momentum-conserving solvent, and to situations where the particle current, rather than the density, should be chosen as the dynamical field. We expect the new conceptual tools developed here to be broadly useful in the context of active matter, allowing one to distinguish when and where activity plays an essential role in the dynamics.

cond-mat.stat-mech↗

arXiv2016

Absence of thermalization for systems with long-range interactions coupled to a thermal bath

We investigate the dynamics of a small long-range interacting system, in contact with a large long-range thermal bath. Our analysis reveals the existence of striking anomalies in the energy flux between the bath and the system. In particular, we find that the evolution of the system is not influenced by the kinetic temperature of the bath, as opposed to what happens for short-range collisional systems. As a consequence, the system may get hotter also when its initial temperature is larger than the bath temperature. This observation is explained quantitatively in the framework of the collisionless Vlasov description of toy models with long-range interactions and shown to be valid whenever the Vlasov picture applies, from cosmology to plasma physics.

cond-mat.stat-mech↗

arXiv2016

How far from equilibrium is active matter?

Active matter systems are driven out of thermal equilibrium by a lack of generalized Stokes-Einstein relation between injection and dissipation of energy at the microscopic scale. We consider such a system of interacting particles, propelled by persistent noises, and show that, at small but finite persistence time, their dynamics still satisfy a time-reversal symmetry. To do so, we compute perturbatively their steady-state measure and show that, for short persistent times, the entropy production rate vanishes. This endows such systems with an effective Fluctuation-Dissipation theorem akin to that of thermal equilibrium systems. Last we show how interacting particle systems with viscous drags and correlated noises can be seen as in equilibrium with a visco-elastic bath but driven out of equilibrium by non-conservative forces, hence providing an energetic insight on the departure of active systems from equilibrium.

cond-mat.stat-mech↗

arXiv2016

Perturbative calculation of quasi-potential in non-equilibrium diffusions: a mean-field example

In stochastic systems with weak noise, the logarithm of the stationary distribution becomes proportional to a large deviation rate function called the quasi-potential. The quasi-potential, and its characterization through a variational problem, lies at the core of the Freidlin-Wentzell large deviations theory%.~\cite{freidlin1984}.In many interacting particle systems, the particle density is described by fluctuating hydrodynamics governed by Macroscopic Fluctuation Theory%, ~\cite{bertini2014},which formally fits within Freidlin-Wentzell's framework with a weak noise proportional to $1/\sqrt{N}$, where $N$ is the number of particles. The quasi-potential then appears as a natural generalization of the equilibrium free energy to non-equilibrium particle systems. A key physical and practical issue is to actually compute quasi-potentials from their variational characterization for non-equilibrium systems for which detailed balance does not hold. We discuss how to perform such a computation perturbatively in an external parameter $λ$, starting from a known quasi-potential for $λ=0$. In a general setup, explicit iterative formulae for all terms of the power-series expansion of the quasi-potential are given for the first time. The key point is a proof of solvability conditions that assure the existence of the perturbation expansion to all orders. We apply the perturbative approach to diffusive particles interacting through a mean-field potential. For such systems, the variational characterization of the quasi-potential was proven by Dawson and Gartner%. ~\cite{dawson1987,dawson1987b}. Our perturbative analysis provides new explicit results about the quasi-potential and about fluctuations of one-particle observables in a simple example of mean field diffusions: the Shinomoto-Kuramoto model of coupled rotators%. ~\cite{shinomoto1986}. This is one of few systems for which non-equilibrium free energies can be computed and analyzed in an effective way, at least perturbatively.

cond-mat.stat-mech↗

arXiv2016

Fluctuations of large-scale jets in the stochastic 2D Euler equation

Two-dimensional turbulence in a rectangular domain self-organises into large-scale unidirectional jets. While several results are present to characterize the mean jets velocity profile, much less is known about the fluctuations. We study jets dynamics in the stochastically forced two-dimensional Euler equations. In the limit where the average jets velocity profile evolves slowly with respect to turbulent fluctuations, we employ a multi-scale (kinetic theory) approach, which relates jet dynamics to the statistics of Reynolds stresses. We study analytically the Gaussian fluctuations of Reynolds stresses and predict the spatial structure of the jets velocity covariance. Our results agree qualitatively well with direct numerical simulations, clearly showing that the jets velocity profile are enhanced away from the stationary points of the average velocity profile. A numerical test of our predictions at quantitative level seems out of reach at the present day.

physics.flu-dyn↗