Publications

Alexis Poncet's articles on arXiv

[1]  http://arxiv.org/abs/2502.21007v1 [ html pdf ]

Melting of non reciprocal solids: how dislocations propel and fission in flowing crystals

Stéphane Guillet, Alexis Poncet, Marine Le Blay, William. T. M Irvine, Vincenzo Vitelli, Denis Bartolo

Subjects: Soft Condensed Matter (cond-mat.soft)

When soft matter is driven out of equilibrium its constituents interact via effective interactions that escape Newton's action-reaction principle. Prominent examples include the hydrodynamic interactions between colloidal particles driven in viscous fluids, phoretic interactions between chemically active colloids, and quorum sensing interactions in bacterial colonies. Despite a recent surge of interest in non-reciprocal physics a fundamental question remains : do non-reciprocal interactions alter or strengthen the ordered phases of matter driven out of equilibrium? Here, through a combination of experiments and simulations, we show how nonreciprocal forces propel and fission dislocations formed in hydrodynamically driven Wigner crystals. We explain how dislocation motility results in the continuous reshaping of grain-boundary networks, and how their fission reaction melts driven crystals from their interfaces. Beyond the specifics of hydrodynamics, we argue theoretically that topological defects and nonreciprocal interactions should invariably conspire to deform and ultimately destroy crystals whose the elementary units defy Newton's third law

[2]  http://arxiv.org/abs/2404.12918v1 [ html pdf ]

Interpreting neural operators: how nonlinear waves propagate in non-reciprocal solids

Jonathan Colen, Alexis Poncet, Denis Bartolo, Vincenzo Vitelli

Subjects: Soft Condensed Matter (cond-mat.soft); Soft Condensed Matter (cond-mat.soft),Fluid Dynamics (physics.flu-dyn)

We present a data-driven pipeline for model building that combines interpretable machine learning, hydrodynamic theories, and microscopic models. The goal is to uncover the underlying processes governing nonlinear dynamics experiments. We exemplify our method with data from microfluidic experiments where crystals of streaming droplets support the propagation of nonlinear waves absent in passive crystals. By combining physics-inspired neural networks, known as neural operators, with symbolic regression tools, we generate the solution, as well as the mathematical form, of a nonlinear dynamical system that accurately models the experimental data. Finally, we interpret this continuum model from fundamental physics principles. Informed by machine learning, we coarse grain a microscopic model of interacting droplets and discover that non-reciprocal hydrodynamic interactions stabilise and promote nonlinear wave propagation.

[3]  http://arxiv.org/abs/2305.06078v1 [ html pdf ]

Active hydraulics laws from frustration principles

Camille Jorge, Amélie Chardac, Alexis Poncet, Denis Bartolo

Subjects: Soft Condensed Matter (cond-mat.soft)

Viscous flows are laminar and deterministic. Robust linear laws accurately predict their streamlines in structures as complex as blood vessels, porous media and pipe networks. However, biological and synthetic active fluids defy these fundamental laws. Irrespective of their microscopic origin, confined active flows are intrinsically bistable, and therefore non-linear. As a consequence, their emergent patterns in channel networks are out of reach of available theories, and lack quantitative experiments. Here, we lay out the basic laws of active hydraulics. We show that active hydraulic flows are non-deterministic and yield degenerate streamline patterns ruled by frustration at nodes with an odd coordination number. More precisely, colloidal-roller experiments in trivalent networks reveal how active-hydraulic flows realize dynamical spin ices. The resulting streamline patterns split into two distinct classes of self-similar loops, which reflect the fractionalization of topological defects at the subchannel scales. Informed by our measurements, we formulate the laws of active hydraulics as a double spin model. A series of mappings on loop O(n) models then allow us to exactly predict the geometry of the degenerate streamlines. We expect our fundamental understanding to provide robust design rules for active microfluidic devices, and to offer unanticipated avenues to understand the motion of living cells and organisms in complex habitats.

[4]  http://arxiv.org/abs/2302.02929v2 [ html pdf ]

Exact spatial correlations in single-file diffusion

Aurélien Grabsch, Pierre Rizkallah, Alexis Poncet, Pierre Illien, Olivier Bénichou

Subjects: Statistical Mechanics (cond-mat.stat-mech)

Journal ref: Phys. Rev. E 107, 044131 (2023)

Single-file diffusion refers to the motion of diffusive particles in narrow channels, so that they cannot bypass each other. This constraint leads to the subdiffusion of a tagged particle, called the tracer. This anomalous behaviour results from the strong correlations that arise in this geometry between the tracer and the surrounding bath particles. Despite their importance, these bath-tracer correlations have long remained elusive, because their determination is a complex many-body problem. Recently, we have shown that, for several paradigmatic models of single-file diffusion such as the Simple Exclusion Process, these bath-tracer correlations obey a simple exact closed equation. In this paper, we provide the full derivation of this equation, as well as an extension to another model of single-file transport: the double exclusion process. We also make the connection between our results and the ones obtained very recently by several other groups, and which rely on the exact solution of different models obtained by the inverse scattering method.

[5]  http://arxiv.org/abs/2202.09278v1 [ html pdf ]

Exact time dependence of the cumulants of a tracer position in a dense lattice gas

Alexis Poncet, Aurélien Grabsch, Olivier Bénichou, Pierre Illien

Subjects: Statistical Mechanics (cond-mat.stat-mech); Statistical Mechanics (cond-mat.stat-mech),Soft Condensed Matter (cond-mat.soft)

We develop a general method to calculate the exact time dependence of the cumulants of the position of a tracer particle in a dense lattice gas of hardcore particles. More precisely, we calculate the cumulant generating function associated with the position of a tagged particle at arbitrary time, and at leading order in the density of vacancies on the lattice. In particular, our approach gives access to the short-time dynamics of the cumulants of the tracer position -- a regime in which few results are known. The generality of our approach is demonstrated by showing that it goes beyond the case of a symmetric 1D random walk, and covers the important situations of (i) a biased tracer; (ii) comb-like structures; and (iii) $d$-dimensional situations.

[6]  http://arxiv.org/abs/2110.09269v2 [ html pdf ]

Exact closure and solution for spatial correlations in single-file diffusion

Aurélien Grabsch, Alexis Poncet, Pierre Rizkallah, Pierre Illien, Olivier Bénichou

Subjects: Statistical Mechanics (cond-mat.stat-mech)

Single-file transport, where particles diffuse in narrow channels while not overtaking each other, is a fundamental model for the tracer subdiffusion observed in confined systems, such as zeolites or carbon nanotubes. This anomalous behavior originates from strong bath-tracer correlations in 1D, which, despite extensive effort, have however remained elusive, because they involve an infinite hierarchy of equations. Here, for the Symmetric Exclusion Process, a paradigmatic model of single-file diffusion, we break the hierarchy and unveil a closed exact equation satisfied by these correlations, which we solve. Beyond quantifying the correlations, the central role of this key equation as a novel tool for interacting particle systems is further demonstrated by showing that it applies to out-of equilibrium situations, other observables and other representative single-file systems.

[7]  http://arxiv.org/abs/2102.03263v2 [ html pdf ]

Motile dislocations knead odd crystals into whorls

Ephraim S. Bililign, Florencio Balboa Usabiaga, Yehuda A. Ganan, Alexis Poncet, Vishal Soni, Sofia Magkiriadou, Michael J. Shelley, Denis Bartolo, William T. M. Irvine

Subjects: Soft Condensed Matter (cond-mat.soft)

The competition between thermal fluctuations and potential forces is the foundation of our understanding of phase transitions and matter in equilibrium. Driving matter out of equilibrium allows for a new class of interactions which are neither attractive nor repulsive but transverse. The existence of such transverse forces immediately raises the question of how they interfere with basic principles of material self-organization. Despite a recent surge of interest, this question remains open. Here, we show that activating transverse forces by homogeneous rotation of colloidal units generically turns otherwise quiescent solids into a crystal whorl state dynamically shaped by self-propelled dislocations. Simulations of both a minimal model and a full hydrodynamics model establish the generic nature of the chaotic dynamics of these self-kneading polycrystals. Using a continuum theory, we explain how odd and Hall stresses conspire to destabilize chiral crystals from within. This chiral instability produces dislocations that are unbound by their self-propulsion. Their proliferation eventually leads to a crystalline whorl state out of reach of equilibrium matter.

[8]  http://arxiv.org/abs/2110.02897v2 [ html pdf ]

When soft crystals defy Newton's third law: Non-reciprocal mechanics and dislocation motility

Alexis Poncet, Denis Bartolo

Subjects: Soft Condensed Matter (cond-mat.soft)

The effective interactions between the constituents of driven soft matter generically defy Newton's third law. Combining theory and numerical simulations, we establish that six classes of mechanics with no counterparts in equilibrium systems emerge in elastic crystals challenged by nonreciprocal interactions. Going beyond linear deformations, we reveal that interactions violating Newton's third law generically turn otherwise quiescent dislocations into motile singularities which steadily glide though periodic lattices.

[9]  http://arxiv.org/abs/2103.13083v2 [ html pdf ]

Generalised density profiles in single-file systems

Alexis Poncet, Aurélien Grabsch, Pierre Illien, Olivier Bénichou

Subjects: Statistical Mechanics (cond-mat.stat-mech); Statistical Mechanics (cond-mat.stat-mech),Soft Condensed Matter (cond-mat.soft)

Single-file diffusion refers to the motion in narrow channels of particles which cannot bypass each other. These strong correlations between particles lead to tracer subdiffusion, which has been observed in contexts as varied as transport in porous media, zeolites or confined colloidal suspensions, and theoretically studied in numerous works. Most approaches to this celebrated many-body problem were restricted to the description of the tracer only, whose essential properties, such as large deviation functions or two-time correlation functions, were determined only recently. Here, we go beyond this standard description by introducing and determining analytically generalised density profiles (GDPs) in the frame of the tracer. In addition to controlling the statistical properties of the tracer, these quantities fully characterise the correlations between the tracer position and the bath particles density. Considering the hydrodynamic limit of the problem, we unveil universal scaling properties of the GDPs with space and time, and a non-monotonic dependence with the distance to the tracer despite the absence of any asymmetry. Our analytical approach provides exact results for the GDPs of paradigmatic models of single-file diffusion, such as Brownian particles with hardcore repulsion, the Symmetric Exclusion Process and the Random Average Process. The range of applicability of our approach is further illustrated by considering extensions to general interactions between particles and out-of-equilibrium situations.

[10]  http://arxiv.org/abs/2006.08202v4 [ html pdf ]

Pair correlation of dilute Active Brownian Particles: from low activity dipolar correction to high activity algebraic depletion wings

Alexis Poncet, Olivier Bénichou, Vincent Démery, Daiki Nishiguchi

Subjects: Statistical Mechanics (cond-mat.stat-mech); Statistical Mechanics (cond-mat.stat-mech),Soft Condensed Matter (cond-mat.soft)

Journal ref: Phys. Rev. E 103, 012605 (2021)

We study the pair correlation of Active Brownian Particles at low density using numerical simulations and analytical calculations. We observe a winged pair correlation: while particles accumulate in front of an active particle as expected, the depletion wake consists of two depletion wings. In the limit of soft particles, we obtain a closed equation for the pair correlation, allowing us to characterize the depletion wings. In particular, we unveil two regimes at high activity where the wings adopt a self-similar profile and decay algebraically. We also perform experiments of self-propelled Janus particles and indeed observe the depletion wings.

[11]  http://arxiv.org/abs/2012.06490v1 [ html pdf ]

Cumulant generating functions of a tracer in quenched dense symmetric exclusion processes

Alexis Poncet, Olivier Bénichou, Pierre Illien

Subjects: Statistical Mechanics (cond-mat.stat-mech)

Journal ref: Phys. Rev. E 103, 040103 (2021)

The Symmetric Exclusion Process (SEP), where particles hop on a 1D lattice with the restriction that there can only be one particle per site, is a paradigmatic model of interacting particle systems. Recently, it has been shown that the nature of the initial conditions - annealed or quenched - has a quantitative impact on the long-time properties of tracer diffusion. However, so far, all the studies in the quenched case focused on the low-density limit of the SEP. Here, we derive the cumulant generating function of the tracer position in the dense limit with quenched initial conditions. Importantly, our approach also allows us to consider the nonequilibrium situations of (i) a biased tracer in the SEP and (ii) a symmetric tracer in a step of density. In the former situation, we show that the initial conditions have a striking impact, and change the very dependence of the cumulants on the bias.

[12]  http://arxiv.org/abs/1909.06184v1 [ html pdf ]

Bath-Mediated Interactions between Driven Tracers in Dense Single-Files

Alexis Poncet, Olivier Bénichou, Vincent Démery, Gleb Oshanin

Subjects: Statistical Mechanics (cond-mat.stat-mech)

Journal ref: Phys. Rev. Research 1, 033089 (2019)

Single-file transport, where particles cannot bypass each other, has been observed in various experimental setups. In such systems, the behaviour of a tracer particle (TP) is subdiffusive, which originates from strong correlations between particles. These correlations are especially marked when the TP is driven and leads to inhomogeneous density profiles. Determining the impact of this inhomogeneity when several TPs are driven in the system is a key question, related to the general issue of bath-mediated interactions, which are known to induce collective motion and lead to the formation of clusters or lanes in a variety of systems. Quantifying this collective behaviour, the emerging interactions and their dependence on the amplitude of forces driving the TPs, remains a challenging but largely unresolved issue. Here, considering dense single-file systems, we analytically determine the entire dynamics of the correlations and reveal out of equilibrium cooperativity and competition effects between driven TPs.

[13]  http://arxiv.org/abs/1707.06085v2 [ html pdf ]

Unbinding transition of probes in single-file systems

Olivier Bénichou, Vincent Démery, Alexis Poncet

Subjects: Statistical Mechanics (cond-mat.stat-mech)

Journal ref: Phys. Rev. Lett. 120, 070601 (2018)

Single-file transport, arising in quasi one-dimensional geometries where particles cannot pass each other, is characterized by the anomalous dynamics of a probe, notably its response to an external force. In these systems, the motion of several probes submitted to different external forces, although relevant to mixtures of charged and neutral or active and passive objects, remains unexplored. Here, we determine how several probes respond to external forces. We rely on a hydrodynamic description of the symmetric exclusion process to obtain exact analytical results at long times. We show that the probes can either move as a whole, or separate into two groups moving away from each other. In between the two regimes, they separate with a different dynamical exponent, as $t^{1/4}$. This unbinding transition also occurs in several continuous single-file systems and is expected to be observable.

[14]  http://arxiv.org/abs/1801.08067v1 [ html pdf ]

$N$-tag Probability Law of the Symmetric Exclusion Process

Alexis Poncet, Olivier Bénichou, Vincent Démery, Gleb Oshanin

Subjects: Statistical Mechanics (cond-mat.stat-mech)

Journal ref: Phys. Rev. E 97, 062119 (2018)

The Symmetric Exclusion Process (SEP), in which particles hop symmetrically on a discrete line with hard-core constraints, is a paradigmatic model of subdiffusion in confined systems. This anomalous behavior is a direct consequence of strong spatial correlations induced by the requirement that the particles cannot overtake each other. Even if this fact has been recognised qualitatively for a long time, up to now there is no full quantitative determination of these correlations. Here we study the joint probability distribution of an arbitrary number of tagged particles in the SEP. We determine analytically the large time limit of all cumulants for an arbitrary density of particles, and their full dynamics in the high density limit. In this limit, we unveil a universal scaling form shared by the cumulants and obtain the time-dependent large deviation function of the problem.

[15]  http://arxiv.org/abs/1608.00094v2 [ html pdf ]

Universal Long Ranged Correlations in Driven Binary Mixtures

Alexis Poncet, Olivier Bénichou, Vincent Démery, Gleb Oshanin

Subjects: Statistical Mechanics (cond-mat.stat-mech); Statistical Mechanics (cond-mat.stat-mech),Soft Condensed Matter (cond-mat.soft)

Journal ref: Phys. Rev. Lett. 118, 118002 (2017)

When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The nature of this "laning transition" is still being debated and, in particular, the pair correlation functions, which are the key observables to quantify this phenomenon, have not been characterized yet. Here, we determine the correlations using an analytical approach based on a linearization of the stochastic equations for the density fields, which is valid for dense systems of soft particles. We find that the correlations decay algebraically along the direction of motion, and have a self-similar exponential profile in the transverse direction. Brownian dynamics simulations confirm our theoretical predictions and show that they also hold beyond the validity range of our analytical approach, pointing to a universal behavior.

[16]  http://arxiv.org/abs/1512.09100v1 [ html pdf ]

Universal non-Debye scaling in the density of states of amorphous solids

Patrick Charbonneau, Eric I. Corwin, Giorgio Parisi, Alexis Poncet, Francesco Zamponi

Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn); Disordered Systems and Neural Networks (cond-mat.dis-nn),Soft Condensed Matter (cond-mat.soft)

Journal ref: Phys. Rev. Lett. 117, 045503 (2016)

At the jamming transition, amorphous packings are known to display anomalous vibrational modes with a density of states (DOS) that remains constant at low frequency. The scaling of the DOS at higher densities remains, however, unclear. One might expect to find simple Debye scaling, but recent results from effective medium theory and the exact solution of mean-field models both predict an anomalous, non-Debye scaling. Being mean-field solutions, however, these solutions are only strictly applicable to the limit of infinite spatial dimension, and it is unclear what value they have for finite-dimensional systems. Here, we study packings of soft spheres in dimensions 3 through 7 and find, far from jamming, a universal non-Debye scaling of the DOS that is consistent with the mean-field predictions. We also consider how the soft mode participation ratio converges to the mean-field prediction as dimension increases.

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