arXiv subjects

Adrian Baule

Publications and source records attributed to Adrian Baule.

At least 19 recordsLinked to original sources

arXiv2025

An effective potential for generative modelling with active matter

Score-based diffusion models generate samples from a complex underlying data distribution by time-reversal of a diffusion process and represent the state-of-the-art in many generative AI applications. Here, I show how a generative diffusion model can be implemented based on an underlying active particle process with finite correlation time. Time reversal is achieved by imposing an effective time-dependent potential on the position coordinate, which can be readily implemented in simulations and experiments to generate new synthetic data samples driven by active fluctuations. The effective potential is valid to first order in the persistence time and leads to a force field that is fully determined by the standard score function and its derivatives up to 2nd order. Numerical experiments for artificial data distributions confirm the validity of the effective potential, which opens up new avenues to exploit fluctuations in active and living systems for generative AI purposes.

cond-mat.stat-mech↗

arXiv2025

Generative modelling with jump-diffusions

Score-based diffusion models generate samples from an unknown target distribution using a time-reversed diffusion process. While such models represent state-of-the-art approaches in industrial applications such as artificial image generation, it has recently been noted that their performance can be further improved by considering injection noise with heavy tailed characteristics. Here, I present a generalization of generative diffusion processes to a wide class of non-Gaussian noise processes. I consider forward processes driven by standard Gaussian noise with super-imposed Poisson jumps representing a finite activity Levy process. The generative process is shown to be governed by a generalized score function that depends on the jump amplitude distribution and can be estimated by minimizing a simple MSE loss as in conventional Gaussian models. Both probability flow ODE and SDE formulations are derived using basic technical effort. A detailed implementation for a pure jump process with Laplace distributed amplitudes yields a generalized score function in closed analytical form and is shown to outperform the equivalent Gaussian model in specific parameter regimes.

cs.LG↗

arXiv2022

Exponential increase of transition rates in metastable systems driven by non-Gaussian noise

Non-Gaussian noise influences many complex out-of-equilibrium systems on a wide range of scales such as quantum devices, active and living matter, and financial markets. Despite the ubiquitous nature of non-Gaussian noise, its effect on activated transitions between metastable states has so far not been understood in generality, notwithstanding prior work focusing on specific noise types and scaling regimes. Here, we present a unified framework for a general class of non-Gaussian noise, which we take as any finite-intensity noise with independent and stationary increments. Our framework identifies optimal escape paths as minima of a stochastic action, which enables us to derive analytical results for the dominant scaling of the escape rates in the weak-noise regime generalizing the conventional Arrhenius law. We show that non-Gaussian noise always induces a more efficient escape, by reducing the effective potential barrier compared to the Gaussian case with the same noise intensity. Surprisingly, for a broad class of amplitude distributions even noise of infinitesimally small intensity can induce an exponentially larger escape rate. As the underlying reason we identify the appearance of discontinuous minimal action paths, for which escape from the metastable state involves a finite jump. We confirm the existence of such paths by calculating the prefactor of the escape rate, as well as by numerical simulations. Our results highlight fundamental differences in the escape behaviour of systems subject to thermal and non-thermal fluctuations, which can be tuned to optimize switching behaviour in metastable systems.

cond-mat.stat-mech↗

arXiv2022

Universal Poisson statistics of a passive tracer diffusing in dilute active suspensions

The statistics of a passive tracer immersed in a suspension of active self-propelled particles (swimmers) is derived from first principles by considering a perturbative expansion of the tracer interaction with the microscopic swimmer field. To first order in the swimmer density, the tracer statistics is exactly represented as a spatial Poisson process combined with independent swimmer-tracer scattering events, rigorously reducing the multi-particle dynamics to two-body interactions. The Poisson representation is valid in any dimensions and for arbitrary interaction forces and swimmer dynamics. It provides in particular an analytical derivation of the coloured Poisson process introduced in [K. Kanazawa et al.; Nature 579, 364 (2020)] highlighting that such a non-Markovian process can be obtained from Markovian dynamics by a variable transformation.

cond-mat.soft↗

arXiv2021

Structural analysis of disordered dimer packings

Jammed disordered packings of non-spherical particles show significant variation in the packing density as a function of particle shape for a given packing protocol. Rotationally symmetric elongated shapes such as ellipsoids, spherocylinders, and dimers, e.g., pack significantly denser than spheres over a narrow range of aspect ratios, exhibiting a characteristic peak at aspect ratios of $α_{\rm max}\approx 1.4-1.5$. However, the structural features that underlie this non-monotonic behaviour in the packing density are unknown. Here, we study disordered packings of frictionless dimers in three dimensions generated by a gravitational pouring protocol in LAMMPS. Focusing on the characteristics of contacts as well as orientational and translational order metrics, we identify a number of structural features that accompany the formation of maximally dense packings as the dimer aspect ratio $α$ is varied from the spherical limit. Our results highlight that dimer packings undergo significant structural changes as $α$ increases up to $α_{\rm max}$ manifest in the reorganisation of the contact configurations between neighbouring dimers, increasing nematic order, and decreasing local translational order. Remarkably, for $α>α_{\rm max}$ our metrics remain largely unchanged, indicating that the peak in the packing density is related to the interplay of structural rearrangements for $α<α_{\rm max}$ and subsequent excluded volume effects with unchanged structure for $α>α_{\rm max}$.

cond-mat.soft↗

arXiv2020

Kinetics of random sequential adsorption of two-dimensional shapes on a one-dimensional line

Saturated random sequential adsorption packings built of two-dimensional ellipses, spherocylinders, rectangles, and dimers placed on a one-dimensional line are studied to check analytical prediction concerning packing growth kinetics [A. Baule, Phys. Rev. Let. 119, 028003 (2017)]. The results show that the kinetics is governed by the power-law with the exponent $d=1.5$ and $2.0$ for packings built of ellipses and rectangles, respectively, which is consistent with analytical predictions. However, for spherocylinders and dimers of moderate width-to-height ratio, a transition between these two values is observed. We argue that this transition is a finite size effect that arises for spherocylinders due to the properties of the contact function. In general, it appears that the kinetics of packing growth can depend on packing size even for very large packings.

cond-mat.stat-mech↗

arXiv2019

Loopy Lévy flights enhance tracer diffusion in active suspensions

Brownian motion is widely used as a paradigmatic model of diffusion in equilibrium media throughout the physical, chemical, and biological sciences. However, many real world systems, particularly biological ones, are intrinsically out-of-equilibrium due to the energy-dissipating active processes underlying their mechanical and dynamical features. The diffusion process followed by a passive tracer in prototypical active media such as suspensions of active colloids or swimming microorganisms indeed differs significantly from Brownian motion, manifest in a greatly enhanced diffusion coefficient, non-Gaussian tails of the displacement statistics, and crossover phenomena from non-Gaussian to Gaussian scaling. While such characteristic features have been extensively observed in experiments, there is so far no comprehensive theory explaining how they emerge from the microscopic active dynamics. Here we present a theoretical framework of the enhanced tracer diffusion in an active medium from its microscopic dynamics by coarse-graining the hydrodynamic interactions between the tracer and the active particles as a stochastic process. The tracer is shown to follow a non-Markovian coloured Poisson process that accounts quantitatively for all empirical observations. The theory predicts in particular a long-lived Lévy flight regime of the tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, thus suggesting that the optimal foraging strategy of swimming microorganisms might crucially depend on the density in order to exploit the Lévy flights of nutrients. Our framework provides the first validation of the celebrated Lévy flight model from a physical microscopic dynamics.

cond-mat.stat-mech↗

arXiv2019

Optimal random deposition of interacting particles

Irreversible random sequential deposition of interacting particles is widely used to model aggregation phenomena in physical, chemical, and biophysical systems. We show that in one dimension the exact time dependent solution of such processes can be found for arbitrary interaction potentials with finite range. The exact solution allows to rigorously prove characteristic features of the deposition kinetics, which have previously only been accessible by simulations. We show in particular that a unique interaction potential exists that leads to a maximally dense line coverage for a given interaction range. Remarkably, this distribution is singular and can only be expressed as a mathematical limit. The relevance of these results for models of nucleosome packing on DNA is discussed. The results highlight how the generation of an optimally dense packing requires a highly coordinated packing dynamics, which can be effectively tuned by the interaction potential even in the presence of intrinsic randomness.

cond-mat.stat-mech↗

arXiv2018

Weak Galilean invariance as a selection principle for coarse-grained diffusive models

Galilean invariance is a cornerstone of classical mechanics. It states that for closed systems the equations of motion of the microscopic degrees of freedom do not change under Galilean transformations to different inertial frames. However, the description of real world systems usually requires coarse-grained models integrating complex microscopic interactions indistinguishably as friction and stochastic forces, which intrinsically violate Galilean invariance. By studying the coarse-graining procedure in different frames, we show that alternative rules -- denoted as "weak Galilean invariance" -- need to be satisfied by these stochastic models. Our results highlight that diffusive models in general can not be chosen arbitrarily based on the agreement with data alone but have to satisfy weak Galilean invariance for physical consistency.

cond-mat.stat-mech↗

arXiv2017

Edwards Statistical Mechanics for Jammed Granular Matter

In 1989, Sir Sam Edwards made the visionary proposition to treat jammed granular materials using a volume ensemble of equiprobable jammed states in analogy to thermal equilibrium statistical mechanics, despite their inherent athermal features. Since then, the statistical mechanics approach for jammed matter has garnered an extraordinary amount of attention by both theorists and experimentalists. Here, we review a systematic approach to jammed matter based on the Edwards statistical mechanical ensemble. We discuss the construction of microcanonical and canonical ensembles based on the volume function, which replaces the Hamiltonian in jammed systems. The importance of approximation schemes at various levels is emphasized leading to quantitative predictions for ensemble averaged quantities such as packing fractions and contact force distributions. An overview of the phenomenology of jammed states and experiments, simulations, and theoretical models scrutinizing the strong assumptions underlying Edwards' approach is given including recent results suggesting the validity of Edwards ergodic hypothesis for jammed states. A theoretical framework for packings whose constitutive particles range from spherical to non-spherical shapes like dimers, polymers, ellipsoids, spherocylinders or tetrahedra, hard and soft, frictional, frictionless and adhesive, monodisperse and polydisperse particles in any dimensions is discussed providing insight into an unifying phase diagram for all jammed matter. Furthermore, the connection between the Edwards' ensemble of metastable jammed states and metastability in spin-glasses is established. This highlights that the packing problem can be understood as a constraint satisfaction problem for excluded volume and force and torque balance leading to a unifying framework between the Edwards ensemble of equiprobable jammed states and out-of-equilibrium spin-glasses.

cond-mat.soft↗

arXiv2017

Shape universality classes in the random sequential addition of non-spherical particles

Random sequential addition (RSA) models are used in a large variety of contexts to model particle aggregation and jamming. A key feature of these models is the algebraic time dependence of the asymptotic jamming coverage as $t\to\infty$. For the RSA of monodisperse non-spherical particles the scaling is generally believed to be $~t^{-ν}$, where $ν=1/d_{\rm f}$ for a particle with $d_{\rm f}$ degrees of freedom. While the $d_{\rm f}=1$ result of spheres (Renyi's classical car parking problem) can be derived analytically, evidence for the $1/d_{\rm f}$ scaling for arbitrary particle shapes has so far only been provided from empirical studies on a case-by-case basis. Here, we show that the RSA of arbitrary non-spherical particles, whose centres of mass are constrained to fall on a line, can be solved analytically for moderate aspect ratios. The asymptotic jamming coverage is determined by a Laplace-type integral, whose asymptotics is fully specified by the contact distance between two particles of given orientations. The analysis of the contact function $r$ shows that the scaling exponent depends on particle shape and falls into two universality classes for generic shapes with $\tilde{d}$ orientational degrees of freedom: (i) $ν=1/(1+\tilde{d}/2)$ when $r$ is a smooth function of the orientations as for smooth convex shapes, e.g., ellipsoids; (ii) $ν=1/(1+\tilde{d})$ when $r$ contains singularities due to flat sides as for, e.g., spherocylinders and polyhedra. The exact solution explains in particular why many empirically observed scalings in $2d$ and $3d$ fall in between these two limiting values.

cond-mat.stat-mech↗

arXiv2017

Feynman-Kac equation for anomalous processes with space- and time-dependent forces

Functionals of a stochastic process Y(t) model many physical time-extensive observables, e.g. particle positions, local and occupation times or accumulated mechanical work. When Y(t) is a normal diffusive process, their statistics are obtained as the solution of the Feynman-Kac equation. This equation provides the crucial link between the expected values of diffusion processes and the solutions of deterministic second-order partial differential equations. When Y(t) is an anomalous diffusive process, generalizations of the Feynman-Kac equation that incorporate power-law or more general waiting time distributions of the underlying random walk have recently been derived. A general representation of such waiting times is provided in terms of a Lévy process whose Laplace exponent is related to the memory kernel appearing in the generalized Feynman-Kac equation. The corresponding anomalous processes have been shown to capture nonlinear mean square displacements exhibiting crossovers between different scaling regimes, which have been observed in biological systems like migrating cells or diffusing macromolecules in intracellular environments. However, the case where both space- and time-dependent forces drive the dynamics of the generalized anomalous process has not been solved yet. Here, we present the missing derivation of the Feynman-Kac equation in such general case by using the subordination technique. Furthermore, we discuss its extension to functionals explicitly depending on time, which are relevant for the stochastic thermodynamics of anomalous diffusive systems. Exact results on the work fluctuations of a simple non-equilibrium model are obtained. In this paper we also provide a pedagogical introduction to Lévy processes, semimartingales and their associated stochastic calculus, which underlie the mathematical formulation of anomalous diffusion as a subordinated process.

cond-mat.stat-mech↗

arXiv2016

Gaussian white noise as a resource for microscopic engines

We show that uncorrelated Gaussian noise, despite its paradigmatic association with thermal equilibrium, can drive a system out of equilibrium and can serve as a resource from which work can be extracted. We consider an overdamped particle in a periodic potential with an internal degree of freedom and a state-dependent friction, coupled to an equilibrium bath. Applying additional Gaussian white noise drives the system into a non-equilibrium steady state and causes a finite current if the potential is spatially asymmetric. We calculate the current explicitly in the three complementary limits. Since the particle current is driven solely by additive Gaussian white noise, this shows that the latter can potentially be exploited as a work resource to power small engines. By comparing the extracted power to the energy injection due to the noise, we find an expression for the efficiency of such an engine.

cond-mat.stat-mech↗

arXiv2015

Interplay between consensus and coherence in a model of interacting opinions

The formation of agents' opinions in a social system is the result of an intricate equilibrium among several driving forces. On the one hand, the social pressure exerted by peers favours the emergence of local consensus. On the other hand, the concurrent participation of agents to discussions on different topics induces each agent to develop a coherent set of opinions across all the topics in which he is active. Moreover, the pervasive action of external stimuli, such as mass media, pulls the entire population towards a specific configuration of opinions on different topics. Here we propose a model in which agents with interrelated opinions, interacting on several layers representing different topics, tend to spread their own ideas to their neighbourhood, strive to maintain internal coherence, due to the fact that each agent identifies meaningful relationships among its opinions on the different topics, and are at the same time subject to external fields, resembling the pressure of mass media. We show that the presence of heterogeneity in the internal coupling assigned by agents to their different opinions allows to obtain states with mixed levels of consensus, still ensuring that all the agents attain a coherent set of opinions. Furthermore, we show that all the observed features of the model are preserved in the presence of thermal noise up to a critical temperature, after which global consensus is no longer attainable. This suggests the relevance of our results for real social systems, where noise is inevitably present in the form of information uncertainty and misunderstandings. The model also demonstrates how mass media can be effectively used to favour the propagation of a chosen set of opinions, thus polarising the consensus of an entire population.

physics.soc-ph↗

arXiv2015

Anomalous processes with general waiting times: functionals and multi-point structure

Many transport processes in nature exhibit anomalous diffusive properties with non-trivial scaling of the mean square displacement, e.g., diffusion of cells or of biomolecules inside the cell nucleus, where typically a crossover between different scaling regimes appears over time. Here, we investigate a class of anomalous diffusion processes that is able to capture such complex dynamics by virtue of a general waiting time distribution. We obtain a complete characterization of such generalized anomalous processes, including their functionals and multi-point structure, using a representation in terms of a normal diffusive process plus a stochastic time change. In particular, we derive analytical closed form expressions for the two-point correlation functions, which can be readily compared with experimental data.

cond-mat.stat-mech↗

arXiv2015

Langevin formulation of a subdiffusive continuous time random walk in physical time

Systems living in complex non equilibrated environments often exhibit subdiffusion characterized by a sublinear power-law scaling of the mean square displacement. One of the most common models to describe such subdiffusive dynamics is the continuous time random walk (CTRW). Stochastic trajectories of a CTRW can be described mathematically in terms of a subordination of a normal diffusive process by an inverse Levy-stable process. Here, we propose a simpler Langevin formulation of CTRWs without subordination. By introducing a new type of non-Gaussian noise, we are able to express the CTRW dynamics in terms of a single Langevin equation in physical time with additive noise. We derive the full multi-point statistics of this noise and compare it with the noise driving scaled Brownian motion (SBM), an alternative stochastic model describing subdiffusive behaviour. Interestingly, these two noises are identical up to the level of the 2nd order correlation functions, but different in the higher order statistics. We extend our formalism to general waiting time distributions and force fields, and compare our results with those of SBM.

cond-mat.stat-mech↗

arXiv2014

Adhesive Loose Packings of Small Particles

We explore adhesive loose packings of dry small spherical particles of micrometer size using 3D discrete-element simulations with adhesive contact mechanics. A dimensionless adhesion parameter ($Ad$) successfully combines the effects of particle velocities, sizes and the work of adhesion, identifying a universal regime of adhesive packings for $Ad>1$. The structural properties of the packings in this regime are well described by an ensemble approach based on a coarse-grained volume function that includes correlations between bulk and contact spheres. Our theoretical and numerical results predict: (i) An equation of state for adhesive loose packings that appears as a continuation from the frictionless random close packing (RCP) point in the jamming phase diagram; (ii) The existence of a maximal loose packing point at the coordination number $Z=2$ and packing fraction $ϕ=1/2^{3}$. Our results highlight that adhesion leads to a universal packing regime at packing fractions much smaller than the random loose packing, which can be described within a statistical mechanical framework. We present a general phase diagram of jammed matter comprising frictionless, frictional, adhesive as well as non-spherical particles, providing a classification of packings in terms of their continuation from the spherical frictionless RCP.

cond-mat.soft↗

arXiv2014

Fundamental challenges in packing problems: from spherical to non-spherical particles

Random packings of objects of a particular shape are ubiquitous in science and engineering. However, such jammed matter states have eluded any systematic theoretical treatment due to the strong positional and orientational correlations involved. In recent years progress on a fundamental description of jammed matter could be made by starting from a constant volume ensemble in the spirit of conventional statistical mechanics. Recent work has shown that this approach, first introduced by S. F. Edwards more than two decades ago, can be cast into a predictive framework to calculate the packing fractions of both spherical and non-spherical particles.

cond-mat.soft↗