arXiv subjects

Peter Sollich

Publications and source records attributed to Peter Sollich.

At least 37 records · Page 2Linked to original sources

arXiv2024

Mobility-induced kinetic effects in multicomponent mixtures

We give an overview exploring the role of kinetics in multicomponent mixtures. Compared to the most commonly studied binary (single species plus solvent) case, multicomponent fluids show a rich interplay between kinetics and thermodynamics due to the possibility of fractionation, interdiffusion of mixture components and collective motion. This leads to a competition between multiple timescales that change depending on the underlying kinetics. At high densities, crowding effects are relevant and non-equilibrium structures can become long-lived. We present the main approaches for the study of kinetic effects in multicomponents mixtures, including the role of crowding, and explore their consequences for equilibrium and non-equilibrium scenarios. We conclude by identifying the main challenges in the field.

cond-mat.soft↗

arXiv2024

Challenges in the rheology of glasses

In this contribution to the proceedings of the 29th Solvay Conference on Physics I will give an overview of some key challenges in our theoretical understanding of the rheology of glasses, focussing on (i) steady shear flow curves and their relation to the glass and jamming transitions, (ii) ductile versus brittle yielding in shear startup and (iii) yielding under oscillatory shear. I will also briefly discuss connections to the reversible-irreversible and random organization transitions as well as to the broad field of memory formation in materials.

cond-mat.soft↗

arXiv2023

Multifractality and statistical localization in highly heterogeneous random networks

We consider highly heterogeneous random networks with symmetric interactions in the limit of high connectivity. A key feature of this system is that the spectral density of the corresponding ensemble exhibits a divergence within the bulk. We study the structure of the eigenvectors associated with this divergence and find that they are multifractal with the statistics of eigenvector elements matching those of the resolvent entries. The corresponding localization mechanism relies on the statistical properties of the nodes rather than on any spatial structure around a localization centre. This "statistical localization" mechanism is potentially relevant for explaining localization in different models that display singularities in the bulk of the spectrum of eigenvalues

cond-mat.dis-nn↗

arXiv2023

Exploiting memory effects to detect the boundaries of biochemical subnetworks

Partial measurements of biochemical reaction networks are ubiquitous and limit our ability to reconstruct the topology of the reaction network and the strength of the interactions amongst both the observed and the unobserved molecular species. Here, we show how we can utilize noisy time series of such partially observed networks to determine which species of the observed part form its boundary, i.e. have significant interactions with the unobserved part. This opens a route to reliable network reconstruction. The method exploits the memory terms arising from projecting the dynamics of the entire network onto the observed subnetwork. We apply it to the dynamics of the Epidermal Growth Factor Receptor (EGFR) network and show that it works even for substantial noise levels.

physics.bio-ph↗

arXiv2023

Thawed Matrix method for computing Local Mechanical Properties of Amorphous Solids

We present a method for computing locally varying nonlinear mechanical properties in particle simulations of amorphous solids. Plastic rearrangements outside a probed region are suppressed by introducing an external field that directly penalizes large nonaffine displacements. With increasing strength of the field, plastic deformation can be localized. We characterize the distribution of local plastic yield stresses (residual local stresses to instability) with our approach, and assess the correlation of their spatial maps with plastic activity in a model two-dimensional amorphous solid. Our approach reduces artefacts inherent in a previous method known as the "frozen matrix" approach that enforces fully affine deformation, and improves the prediction of plastic rearrangements from structural information.

cond-mat.soft↗

arXiv2023

Intermittent relaxation and avalanches in extremely persistent active matter

We use numerical simulations to study the dynamics of dense assemblies of self-propelled particles in the limit of extremely large, but finite, persistence times. In this limit, the system evolves intermittently between mechanical equilibria where active forces balance interparticle interactions. We develop an efficient numerical strategy allowing us to resolve the statistical properties of elastic and plastic relaxation events caused by activity-driven fluctuations. The system relaxes via a succession of scale-free elastic events and broadly distributed plastic events that both depend on the system size. Correlations between plastic events lead to emergent dynamic facilitation and heterogeneous relaxation dynamics. Our results show that dynamical behaviour in extremely persistent active systems is qualitatively similar to that of sheared amorphous solids, yet with some important differences.

cond-mat.soft↗

arXiv2023

Accurate dynamics from self-consistent memory in stochastic chemical reactions with small copy numbers

We present a method that captures the fluctuations beyond mean field in chemical reactions in the regime of small copy numbers and hence large fluctuations, using self-consistently determined memory: by integrating information from the past we can systematically improve our approximation for the dynamics of chemical reactions. This memory emerges from a perturbative treatment of the effective action of the Doi-Peliti field theory for chemical reactions. By dressing only the response functions and by the self-consistent replacement of bare responses by the dressed ones, we show how a very small class of diagrams contributes to this expansion, with clear physical interpretations. From these diagrams, a large sub-class can be further resummed to infinite order, resulting in a method that is stable even for large values of the expansion parameter or equivalently large reaction rates. We demonstrate this method and its accuracy on single and multi-species binary reactions across a range of reaction constant values.

cond-mat.stat-mech↗

arXiv2023

Long-range Velocity Correlations from Active Dopants

One of the most remarkable observations in dense active matter systems is the appearance of long-range velocity correlations without any explicit aligning interaction (of e.g.\ Vicsek type). Here we show that this kind of long range velocity correlation can also be generated in a dense athermal passive system by the inclusion of a very small fraction of active Brownian particles. We develop a continuum theory to explain the emergence of velocity correlations generated via such active dopants. We validate the predictions for the effects of magnitude and persistence time of the active force and the area fractions of active or passive particles using extensive Brownian dynamics simulation of a canonical active-passive mixture. Our work decouples the roles that density and activity play in generating long range velocity correlations in such exotic non-equilibrium steady states.

cond-mat.soft↗

arXiv2023

Nonequilibrium mixture dynamics: A model for mobilities and its consequences

Extending the famous Model B for the time evolution of a liquid mixture, we derive an approximate expression for the mobility matrix that couples the different mixture components. This approach is based on a single component fluid with particles that are artificially grouped into separate species labelled by ``colors''. The resulting mobility matrix depends on a single dimensionless parameter, which can be determined efficiently from experimental data or numerical simulations, and includes existing standard forms as special cases. We identify two distinct mobility regimes, corresponding to collective motion and interdiffusion, respectively, and show how they emerge from the microscopic properties of the fluid. As a test scenario, we study the dynamics after a thermal quench, providing a number of general relations and analytical insights from a Gaussian theory. Specifically, for systems with two or three components, analytical results for the time evolution of the equal time correlation function compare well to results of Monte Carlo simulations of a lattice gas. A rich behavior is observed, including the possibility of transient fractionation.

cond-mat.stat-mech↗

arXiv2022

Non-reciprocity across scales in active mixtures

In active matter, the lack of momentum conservation makes non-reciprocal interactions the rule rather than the exception. They lead to a rich set of emerging behaviors that are hard to account for and to predict starting from the microscopic scale, due to the absence of a generic theoretical framework out of equilibrium. Here we consider bacterial mixtures that interact via mediated, non-reciprocal interactions like quorum-sensing and chemotaxis. By explicity relating microscopic and macroscopic dynamics, we show that non-reciprocity may fade as coarse-graining proceeds, leading to large-scale bona fide equilibrium descriptions. In turns, this allows us to account quantitatively, and without fitting parameters, for the rich behaviors observed in microscopic simulations including phase separation, demixing or multi-phase coexistence. We also derive the condition under which non-reciprocity is strong enough to survive coarse-graining, leading to a wealth of dynamical patterns. Again, the explicit coarse-graining of the dynamics allows us to predict the phase diagram of the system starting from its microscopic description. All in all, our work demonstrates that the fate of non-reciprocity across scales is a subtle and important question.

cond-mat.stat-mech↗

arXiv2022

Composition Dependent Instabilities in Mixtures With Many Components

Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study the instabilities of a mixture model where the second virial coefficients are taken as random Gaussian variables. Using tools from free probability theory we obtain the exact spinodal curve and the nature of instabilities for a mixture with an arbitrary composition, thus lifting the assumption of uniform mixture component densities pervading previous studies. We show that, by controlling the volume fraction of only a few components, one can systematically change the nature of the spinodal instability and achieve demixing for realistic scenarios by a strong {\em composition imbalance amplification}. This results from a non-trivial interplay of entropic effects due to non-uniform composition and complexity in the interactions. Our approach allows for the inclusion of any finite number of structured interactions, leading to a competition between different forms of demixing as density is varied.

cond-mat.stat-mech↗

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

Towards Robust Waveform-Based Acoustic Models

We study the problem of learning robust acoustic models in adverse environments, characterized by a significant mismatch between training and test conditions. This problem is of paramount importance for the deployment of speech recognition systems that need to perform well in unseen environments. First, we characterize data augmentation theoretically as an instance of vicinal risk minimization, which aims at improving risk estimates during training by replacing the delta functions that define the empirical density over the input space with an approximation of the marginal population density in the vicinity of the training samples. More specifically, we assume that local neighborhoods centered at training samples can be approximated using a mixture of Gaussians, and demonstrate theoretically that this can incorporate robust inductive bias into the learning process. We then specify the individual mixture components implicitly via data augmentation schemes, designed to address common sources of spurious correlations in acoustic models. To avoid potential confounding effects on robustness due to information loss, which has been associated with standard feature extraction techniques (e.g., FBANK and MFCC features), we focus on the waveform-based setting. Our empirical results show that the approach can generalize to unseen noise conditions, with 150% relative improvement in out-of-distribution generalization compared to training using the standard risk minimization principle. Moreover, the results demonstrate competitive performance relative to models learned using a training sample designed to match the acoustic conditions characteristic of test utterances.

cs.SD↗

arXiv2022

Delayed elastic contributions to the viscoelastic response of foams

We show that the slow viscoelastic response of a foam is that of a power-law fluid with a terminal relaxation. Investigations of the foam mechanics in creep and recovery tests reveal that the power-law contribution is fully reversible, indicative of a delayed elastic response. We demonstrate how this contribution fully accounts for the non-Maxwellian features observed in all tests, probing the linear mechanical response function. The associated power-law spectrum is consistent with soft glassy rheology of systems with mechanical noise temperatures just above the glass transition [Fielding et al., J.Rheol. 44, 323(2000)] and originates from a combination of superdiffusive bubble dynamics and stress diffusion, as recently evidenced in simulations of coarsening foam [Hwang et al., Nat.Mater. 15, 1031 (2016)].

cond-mat.soft↗

arXiv2022

Mean field description of aging linear response in athermal amorphous solids

We study the linear response to strain in a mean field elastoplastic model for athermal amorphous solids, incorporating the power-law mechanical noise spectrum arising from plastic events. In the "jammed" regime of the model, where the plastic activity exhibits a non-trivial slow relaxation referred to as aging, we find that the stress relaxes incompletely to an age-dependent plateau, on a timescale which grows with material age. We determine the scaling behaviour of this aging linear response analytically, finding that key scaling exponents are universal and independent of the noise exponent $μ$. For $μ>1$, we find simple aging, where the stress relaxation timescale scales linearly with the age $t_{\rm w}$ of the material. At $μ=1$, which corresponds to interactions mediated by the physical elastic propagator, we find instead a $t_{\rm w}^{1/2}$ scaling arising from the stretched exponential decay of the plastic activity. We compare these predictions with measurements of the linear response in computer simulations of a model jammed system of repulsive soft athermal particles, during its slow dissipative relaxation towards mechanical equilibrium, and find good agreement with the theory.

cond-mat.soft↗

arXiv2022

Localization properties of the sparse Barrat-Mézard trap model

Inspired by works on the Anderson model on sparse graphs, we devise a method to analyze the localization properties of sparse systems that may be solved using cavity theory. We apply this method to study the properties of the eigenvectors of the master operator of the sparse Barrat-Mézard trap model, with an emphasis on the extended phase. As probes for localization, we consider the inverse participation ratio and the correlation volume, both dependent on the distribution of the diagonal elements of the resolvent. Our results reveal a rich and non-trivial behavior of the estimators across the spectrum of relaxation rates and an interplay between entropic and activation mechanisms of relaxation that give rise to localized modes embedded in the bulk of extended states. We characterize this route to localization and find it to be distinct from the paradigmatic Anderson model or standard random matrix systems.

cond-mat.dis-nn↗

arXiv2022

Mean field theory of yielding under oscillatory shear

We study a mean field elastoplastic model, embedded within a disordered landscape of local yield barriers, to shed light on the behaviour of athermal amorphous solids subject to oscillatory shear. We show that the model presents a genuine dynamical transition between an elastic and a yielded state, and qualitatively reproduces the dependence on the initial degree of annealing found in particle simulations. For initial conditions prepared below the analytically derived threshold energy, we observe a non-trivial, non-monotonic approach to the yielded state. The timescale diverges as one approaches the yielding point from above, which we identify with the fatigue limit. We finally discuss the connections to brittle yielding under uniform shear.

cond-mat.soft↗

arXiv2021

Memory in Non-Monotonic Stress Response of an Athermal Disordered Solid

Athermal systems across a large range of length scales, ranging from foams and granular bead packings to crumpled metallic sheets, exhibit slow stress relaxation when compressed. Experimentally they show a non-monotonic stress response when decompressed somewhat after an initial compression, i.e. under a two-step, Kovacs-like protocol. It turns out that from this response one can tell for how long the system was in a compressed state, suggesting an interpretation as a memory effect. In this work we use a model of an athermal jammed solid, specifically a binary mixture of soft harmonic particles, to explore this phenomenon through in-silico experiments. Using extensive simulations under conditions analogous to those in experiment, we observe identical phenomenology in the stress response under a two-step protocol. Our model system also recovers the behaviour under a more recently studied three-step protocol, which consists of a compression followed by a decompression and then a final compression. We show that the observed response in both two-step and three-step protocols can be understood using Linear Response Theory. In particular, a linear scaling with age for the two-step protocol arises generically for slow linear responses with power law or logarithmic decay and does not in itself point to any underlying aging dynamics.

cond-mat.soft↗