arXiv subjects

Cesare Nardini

Publications and source records attributed to Cesare Nardini.

At least 19 recordsLinked to original sources

arXiv2026

Bulk and microphase separation in chiral active systems

Many active particles phase-separate due to quorum-sensing interactions, and their self-propulsion mechanisms often break chiral symmetry. Using particle and continuum models, we uncover the role of chirality in inducing bulk or microphase separation, including a chiral phase formed of vapor bubbles. Analytical predictions for the emergence of these phases require a coarse-graining technique based on multiple-scale analysis. Further, introducing a minimal active field theory, we show that, in the bulk phase separation regime, chirality does not alter the diffusive $t^{1/3}$ coarsening law nor the dynamical exponent associated with capillary waves, but induces traveling waves at the interface. We finally demonstrate that, even in the absence of fluid flows, chirality can cause the breakup of elongated droplets, resembling phenomena previously observed experimentally.

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arXiv2026

Nucleation and time-reversal symmetry breaking in nonconserved scalar field theories

Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one in terms of a single reaction coordinate that corresponds to the radius of a nucleating droplet. In this work, we provide a full account of nonequilibrium nucleation theory (NNT), which generalizes CNT to non-equilibrium field theories with non-conserved order parameter. We present two equivalent derivations of the dynamics of the droplet radius: a stochastic route, based on a direct projection of the stochastic field equation onto the radial reaction coordinate, and a route based on the minimization of the Freidlin-Wentzell action. Crucially, the quasipotential barrier predicted by NNT differs from the one found when assuming the instanton to be the time-reversal of the relaxation dynamics. Whereas the interfacial density profile differs from that on the relaxation path, an analytical derivation of NNT remains possible using a careful definition of the reaction coordinate. This leverages the perturbative structure that (in common with CNT) emerges in the limit of large critical radius. We further derive with similar techniques the dynamics of capillary waves, whose stability is required for the CNT/NNT precept of a near-spherical droplet to prevail. After deriving our theory for generic non-conserved field-theories, we address two explicit examples: a non-equilibrium generalization of Model A (Active Model A), and a population dynamics model (with two choices of noise that each break time-reversal symmetry). In both cases, we validate our analytical NNT against numerical results obtained by action minimization, with excellent agreement. NNT provide a systematic framework for constructing nucleation theories in a broad class of non-equilibrium systems from active matter, reaction-diffusion systems and population dynamics.

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arXiv2026

Nonequilibrium nucleation theory for nonconserved fields: from active matter to population dynamics

Classical nucleation theory (CNT) describes the formation of a stable phase from a metastable one. In equilibrium systems, it quantifies the free-energy competition between a favorable bulk gain and an unfavorable interfacial cost. For systems without detailed balance, the corresponding nonequilibrium nucleation theory (NNT) was so far developed only for cases with a conserved order parameter, such as active fluid-fluid phase separation. Here we construct the NNT for systems with a (single, scalar) nonconserved order parameter. Unlike in the conserved case, the nucleation barrier controlling (noise-driven) droplet growth is profoundly altered by deviations in the interfacial density profile from the one arising during (deterministic) droplet relaxation. The barrier can nonetheless be analysed by carefully defining the reaction coordinate (droplet radius) to project out those deviations. We give explicit NNT predictions for models drawn from population dynamics and active matter, finding excellent agreement with numerical studies.

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arXiv2026

Generic nonlocal statistics of the stationary measure in conserved active systems

The stationary measure of equilibrium systems with detailed balance follows a Boltzmann distribution, so that for short-ranged interactions the measure is local, meaning that distant spatial domains are statistically independent. In contrast, active systems break detailed balance, and can have nonlocal stationary measure even for fully local dynamics. Here, by expanding in nonlinearity about a Gaussian-model limit, we construct the measure perturbatively deep in the disordered phase for a class of models that includes Active Model A, Active Model B+, Model AB, the Nonreciprocal Cahn--Hilliard model, and the Toner--Tu model. In this regime, nonlocality is linked to a dynamical conservation law. Our results generically preclude construction of a Landau--Ginzburg expansion of the stationary measure (as opposed to the dynamical equations) for conserved active field theories.

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arXiv2026

Eppur si muove: Shape of topological defects -- and consequent motion -- in active nematics

Topological defects in systems with liquid-crystalline order are crucial in determining their large-scale properties. In active systems, they are known to have properties impossible at equilibrium: for example, $+1/2$ defects in nematically-ordered systems self-propel. While some previous theoretical descriptions relied on assuming that the defect shape remains unperturbed by activity, we show that this assumption can lead to inconsistent predictions. We compute the shape of $-1/2$ defects and show that the one of $+1/2$ is intimately related to their self-propulsion speed. Our analytical predictions are corroborated via numerical simulations of a generic active nematic theory.

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arXiv2026

Active Cahn-Hilliard theory for nonequilibrium phase separation: quantitative macroscopic predictions and a microscopic derivation

Phase-separating active systems can display phenomenology that is impossible in equilibrium. The binodal densities are not solely determined by a bulk (effective) free energy, but also affected by gradient terms, while capillary waves and Ostwald processes are determined by three distinct interfacial tensions. These and related phenomena were so far explained at continuum level using a top-down minimal theory (Active Model B+). This theory, by Taylor-expanding in the scalar order parameter (or density), effectively assumes that phase separation is weak, which is not true across most of the phase diagram. Here, we develop a quantitative account of active phase separation, by introducing an active counterpart of Cahn-Hilliard theory, constructing the density current from all possible terms with up to four spatial derivatives without Taylor-expanding in the density. From this O(grad^4) theory, we show how to compute binodals and interfacial tensions for arbitrary choices of the five density-dependent 'coefficient functions' that specify the theory (replacing the four constant coefficients of Active Model B+). We further consider a particle model composed of thermal quorum-sensing active particles (tQSAPs) yielding a fully specified example of the O(grad^4) theory upon coarse-graining. We find that to coarse-grain consistently at O(grad^4) requires a systematic procedure, based on multiple-scale analysis, to eliminate fast-evolving orientational moments. Using this, we calculate from microscopic physics all five coefficient functions of the active Cahn-Hilliard theory for tQSAPs. We identify contributions that were missed in previous continuum theories, and show how neglecting them becomes justified only in the limit of large quorum-sensing range parameter. Comparison with particle simulations of tQSAPs shows that our O(grad^4) theory improves on previous continuum models [...]

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arXiv2025

Pseudo-giant number fluctuations and nematic order in microswimmer suspensions

Giant number fluctuations (GNFs), whereby the standard deviation $ΔN$ in the local number of particles $\langle N \rangle$ grows faster than $\sqrt{\langle N \rangle}$, are a hallmark property of dry active matter systems with orientational order, such as a collection of granular particles on a vibrated plate. This contrasts with momentum-conserving ("wet") active matter systems, such as suspensions of swimming bacteria, where no theoretical prediction of GNFs exist, although numerous experimental observations of such enhanced fluctuations have been reported. In this Letter, we numerically confirm the emergence of super-Gaussian number fluctuations in a 3-dimensional suspension of pusher microswimmers undergoing a transition to collective motion. These fluctuations emerge sharply above the transition, but only for sufficiently large values of the bacterial persistence length $\ell_p = v_s / λ$, where $v_s$ is the bacterial swimming speed and $λ$ the tumbling rate. Crucially, these "pseudo-GNFs" differ from true GNFs, as they only occur on length scales shorter than the typical size $ξ$ of nematic patches in the collective motion state, which is in turn proportional to the single-swimmer persistence length $\ell_p$. Our results thus suggest that observations of enhanced density fluctuations in biological active matter systems actually represent transient effects that decay away beyond mesoscopic length scales, and raises the question to what extent "true" GNFs with universal properties can exist in the presence of fluid flows.

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arXiv2025

Random organization criticality with long-range hydrodynamic interactions

Driven soft athermal systems may display a reversible-irreversible transition between an absorbing, arrested state and an active phase where a steady-state dynamics sets in. A paradigmatic example consists in cyclically sheared suspensions under stroboscopic observation, for which in absence of contacts during a shear cycle particle trajectories are reversible and the stroboscopic dynamics is frozen, while contacts lead to diffusive stroboscopic motion. The Random Organization Model (ROM), which is a minimal model of the transition, shows a transition which falls into the Conserved Directed Percolation (CDP) universality class. However, the ROM ignores hydrodynamic interactions between suspended particles, which make contacts a source of long-range mechanical noise that in turn can create new contacts. Here, we generalize the ROM to include long-range interactions decaying like inverse power laws of the distance. Critical properties continuously depend on the decay exponent when it is smaller than the space dimension. Upon increasing the interaction range, the transition turns convex (that is, with an order parameter exponent $β> 1$), fluctuations turn from diverging to vanishing, and hyperuniformity at the transition disappears. We rationalize this critical behavior using a local mean-field model describing how particle contacts are created via mechanical noise, showing that diffusive motion induced by long-range interactions becomes dominant for slowly-decaying interactions.

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arXiv2025

Interface dynamics of wet active systems

We study the roughening of interfaces in phase-separated active suspensions on substrates. At both large length and timescales, we show that the interfacial dynamics belongs to the |q|KPZ universality class discussed in Besse et al. Phys. Rev. Lett. 130, 187102 (2023). This holds despite the presence of long-ranged fluid flows. At early times, however, or for sufficiently small systems, the roughening exponents are the same as those in the presence of a momentum-conserving fluid. Surprisingly, when the effect of substrate friction can be ignored, the interface becomes random beyond a de Gennes-Taupin lengthscale which depends on the interfacial tension.

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arXiv2025

Fluctuation-Induced First Order Transition to Collective Motion

The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a `discontinuous' coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in `topological' ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k-nearest neighbors or Voronoi alignment.

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arXiv2024

Statistical properties of microphase and bubbly phase-separated active fluids

In phase-separated active fluids, the Ostwald process can go into reverse leading to either microphase separation or bubbly phase separation. We show that the latter is formed of two macroscopic regions that are occupied by the homogeneous fluid and by the microphase separated one. Within the microphase separated fluid, the relative rate of the Ostwald process, coalescence, and nucleation determines whether the size distribution of mesoscopic domains is narrowly peaked or displays a broad range of sizes before attaining a cutoff independent of system-size. Our results are obtained via large-scale simulations of a minimal field theory for active phase separation and reproduced by an effective model in which the degrees of freedom are the locations and sizes of the microphase-separated domains.

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arXiv2024

Hyperuniformity in phase ordering: the roles of activity, noise, and non-constant mobility

Hyperuniformity emerges generically in the coarsening regime of phase-separating fluids. Numerical studies of active and passive systems have shown that the structure factor $S(q)$ behaves as $q^ς$ for $q\to 0$, with hyperuniformity exponent $ς= 4$. For passive systems, this result was explained in 1991 by a qualitative scaling analysis of Tomita, exploiting isotropy at scales much larger than the coarsening length $\ell$. Here we reconsider and extend Tomita's argument to address cases of active phase separation and of non-constant mobility, again finding $ς=4$. We further show that dynamical noise of variance $D$ creates a transient $ς= 2$ regime for $\hat q\ll \hat{q}_\ast \sim \sqrt{D} t^{[1-(d+2)ν]/2}$, crossing over to $ς= 4$ at larger $\hat{q}$. Here, $ν$ is the coarsening exponent, with $\ell\sim t^ν$, and $\hat{q} \propto q \ell$ is the rescaled wavenumber. In diffusive coarsening, $ν=1/3$, so the rescaled crossover wavevector $\hat{q}_\ast$ vanishes at large times when $d\geq 2$. The slowness of this decay suggests a natural explanation for experiments that observe a long-lived $ς= 2$ scaling in phase-separating active fluids (where noise is typically large). Conversely, in $d=1$, we demonstrate that with noise the $ς= 2$ regime survives as $t\to\infty$, with $\hat{q}_\ast\sim D^{5/6}$. (The structure factor is not then determined by the zero-temperature fixed point.) We confirm our analytical predictions by numerical simulations of active and passive continuum theories in the deterministic case and of Model B for the stochastic case. We also compare them with related findings for a system near an absorbing-state transition rather than undergoing phase separation. A central role is played throughout by the presence or absence of a conservation law for the centre of mass position of the order parameter field.

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arXiv2024

Collective motion in a sheet of microswimmers

Self-propelled micron-size particles suspended in a fluid, like bacteria or synthetic microswimmers, are strongly non-equilibrium systems where particle motility breaks the microscopic detailed balance, often resulting in large-scale collective motion. Previous theoretical work has identified long-range hydrodynamic interactions as the main driver of collective motion in unbounded dilute suspension of rear-actuated ("pusher") microswimmers. In contrast, most experimental studies of collective motion in microswimmer suspensions have been carried out in quasi-2-dimensional geometries such as in thin films or near solid or fluid interfaces, where both the swimmers' motion and their long-range flow fields become altered due to the proximity of a boundary. Here, we study numerically a minimal model of microswimmers in such a restricted geometry, where the particles move in the midplane between two no-slip walls. For pushers, we demonstrate collective motion with only short-ranged order, in contrast with the long-ranged flows observed in unbounded systems. For front-actuated ("puller") microswimmers, we discover a long-wavelength density instability resulting in the formation of dense microswimmer clusters. Both types of collective motion are fundamentally different from their previously studied counterparts in unbounded domains. Our results illustrate that hydrodynamic screening due to the presence of a wall is subdominant in determining the collective state of the suspension, which is instead dictated by the geometrical restriction of the swimmers' motion.

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arXiv2023

Hydrodynamic instabilities in a 2-D sheet of microswimmers embedded in a 3-D fluid

A collection of microswimmers immersed in an incompressible fluid is characterised by strong interactions due to the long-range nature of the hydrodynamic fields generated by individual organisms. As a result, suspensions of rear-actuated `pusher' swimmers such as bacteria exhibit a collective motion state often referred to as `bacterial turbulence', characterised by large-scale chaotic flows. The onset of collective motion in pusher suspensions is classically understood within the framework of mean-field kinetic theories for dipolar swimmers. In bulk 2-D and 3-D, the theory predicts that the instability leading to bacterial turbulence is due to mutual swimmer reorientation and sets in at the largest length scale available to the suspension. Here, we construct a similar kinetic theory for the case of a dipolar microswimmer suspension restricted to a two-dimensional plane embedded in a three-dimensional incompressible fluid. This setting qualitatively mimics the effect of swimming close to a two-dimensional interface. We show that the in-plane flow fields are effectively compressible in spite of the incompressibility of the 3-D bulk fluid, and that microswimmers on average act as sources (pushers) or sinks (pullers). We analyse stability of the homogeneous and isotropic state, and find two types of instability that are qualitatively different from the bulk, three-dimensional case: First, we show that the analogue of the orientational pusher instability leading to bacterial turbulence in bulk systems instead occurs at the smallest length-scale available to the system. Second, an instability associated with density variations arises in puller suspensions as a generic consequence of the effective in-plane compressibility. We conclude that confinement can have a crucial role in determining the collective behaviour of microswimmer suspensions.

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arXiv2023

Interface roughening in nonequilibrium phase-separated systems

Interfaces of phase-separated systems roughen in time due to capillary waves. Because of fluxes in the bulk, their dynamics is nonlocal in real space and is not described by the Edwards-Wilkinson or Kardar-Parisi-Zhang (KPZ) equations, nor their conserved counterparts. We show that in the absence of detailed balance, the phase-separated interface is described by a new universality class that we term |q|KPZ. We compute the associated critical exponents via one-loop renormalization group, and corroborate the results by numerical integration of the |q|KPZ equation. Deriving the effective interface dynamics from a minimal field theory of active phase separation, we finally argue that the |q|KPZ universality class generically describes liquid-vapor interfaces in active systems.

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arXiv2022

Fluctuating kinetic theory and fluctuating hydrodynamics of aligning active particles: the dilute limit

Kinetic and hydrodynamic theories are widely employed for describing the collective behaviour of active matter systems. At the fluctuating level, these have been obtained from explicit coarse-graining procedures in the limit where each particle interacts weakly with many others, so that the total forces and torques exerted on each of them is of order unity at all times. Such limit is however not relevant for dilute systems that mostly interact via alignment; there, collisions are rare and make the self-propulsion direction to change abruptly. We derive a fluctuating kinetic theory, and the corresponding fluctuating hydrodynamics, for aligning self-propelled particles in the limit of dilute systems. We discover that fluctuations at kinetic level are not Gaussian and depend on the interactions among particles, but that only their Gaussian part survives in the hydrodynamic limit. At variance with fluctuating hydrodynamics for weakly interacting particles, we find that the noise variance at hydrodynamic level depends on the interaction rules among particles and is proportional to the square of the density, reflecting the binary nature of the aligning process. The results of this paper, which are derived for polar self-propelled particles with polar alignment, could be straightforwardly extended to polar particles with nematic alignment or to fully nematic systems.

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arXiv2022

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff -- which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing for simplicity on models with a purely diffusive scalar field, such as `Model B' which describes phase separation in binary fluid mixtures. We address the requirement that the steady state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for `active field theories' in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR) we must make a careful treatment of so-called `spurious drift' and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative, via off-diagonal couplings to additional fields that encode thermodynamically the underlying chemical processes responsible for activity. In this case the spurious drift terms need careful accounting, not just to evaluate correctly the EPR, but also to numerically implement the Langevin dynamics itself.

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arXiv2021

Statistical Mechanics of Active Ornstein Uhlenbeck Particles

We review and extend recent developments on the statistical properties of Active Ornstein Uhlenbeck particles (AOUPs). In this simplest of models, the Gaussian white noise of overdamped Brownian colloids is replaced by a Gaussian colored noise. This suffice to grant this system the hallmark properties of active matter, while still allowing for analytical progress. We first detail the perturbative derivation of the steady state of AOUPs in the small persistence time limit. We show the existence of an effective equilibrium regime in which detailed-balance is obeyed with respect to a non-Boltzmann distribution and detail the corresponding fluctuation-dissipation theorem. We then characterize the departure from equilibrium by computing several relevant observables (entropy production, ratchet current). At the collective level, we show AOUPs to experience motility-induced phase separation both in the presence of pairwise forces or due to quorum-sensing interactions. The latter can be accounted for by considering the steady-state of AOUPs with spatially varying propulsion speed or persistence time. Finally, we discuss how the emerging properties of AOUPs can be characterized from the dynamics of their collective modes, which we construct explicitly.

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