Seminars
Elisabeth Agoritsas: Mean-field dynamics of many-body systems: global shear versus random local forcing
In infinite dimension, many-body systems of pairwise interacting particles provide exact analytical benchmarks for features of amorphous materials, such as the stress-strain curve of glasses under quasistatic shear. Here, instead of a global shear, we consider an alternative driving protocol which consists of randomly assigning a constant local displacement field on each particle, with a finite spatial correlation length and a given spatial structure. We are then able to establish a direct equivalence between a global forcing (external shear) and a random local forcing (reminiscent of active matter), upon a simple rescaling of the control parameter (the accumulated strain). In this framework, global shear is thus simply a special case of a much broader family of local forcing, that can be explored by tuning its spatial correlations. Our predictions are moreover found to be in remarkably good agreement with two-dimensional numerical simulations. These results hint at a unifying framework for establishing rigorous analogies, at the mean-field level, between different families driven disordered systems, such as sheared granular materials and active matter.
Ada Altieri: Evidence of glassy phases in large well-mixed ecosystems both in the competitive and cooperative case
Many complex systems in Nature, from metabolic networks to ecosystems, appear to be poised at the edge of stability, hence displaying enormous responses to external perturbations. This feature, also known in physics as marginal stability, is often the consequence of the complex underlying interaction network, which can induce large-scale collective dynamics and therefore critical behaviors. In this seminar, I will present the problem of ecological complexity by focusing on a reference model in theoretical ecology, the disordered Lotka-Volterra model with random symmetric interactions and finite demographic noise. By using techniques rooted in mean-field spin-glass theory, I will show how to obtain a full characterization of the number of locally stable equilibria and the resulting phase diagram. Notably, I will relate emerging collective behaviors and slow relaxation dynamics to the appearance of different disordered phases akin to those occurring in glassy systems, with a special emphasis on an amorphous “Gardner phase”.
Finally, I will discuss the extension of these results: i) to the case of strong competitive interactions; ii) to non-logistic growth functions in the dynamics of the species abundances in order to model intra-specific cooperative effects in ecological and biological communities.
Gerard Ben Arous: The complexity of the Elastic Manifold
This is joint work with Paul Bourgade and Benjamin McKenna (Courant Institute, NYU). The elastic manifold is a paradigmatic representative of the class of disordered elastic systems. These models describe random surfaces with rugged shapes resulting from a competition between random spatial impurities (preferring disordered configurations), on the one hand, and elastic self-interactions (preferring ordered configurations), on the other. The elastic manifold model is interesting because it displays a depinning phase transition and has a long history as a testing ground for new approaches in statistical physics of disordered media, for example for fixed dimension by Fisher (1986) using functional renormalization group methods, and in the high-dimensional limit by Mézard and Parisi (1992) using the replica method.
We study the topology of the energy landscape of this model in the Mézard-Parisi setting, and compute the (annealed) topological complexity both of total critical points and of local minima. Our main result confirms the recent formulas by Fyodorov and Le Doussal (2020) and allows to identify the boundary between simple and glassy phases. The core argument relies on the analysis of the asymptotic behavior of large random determinants in the exponential scale.
Jasna Brujic: Making and Folding Colloidomers by Non-equilibrium Design Strategies
In self-assembly, building blocks rearrange, stick to each other in programmed ways, and finally assemble themselves into a material. When making a complex material, there are many different ways to put these pieces together. The self-assembly of complex materials is a search in high-dimensional space for the desired structure. We reduce the dimensionality of the problem by folding 1-D colloidomer chains into compact architectures, analogous to a polypeptide folding into a protein. Folding is triggered by fast temperature quenches, which tune DNA-mediated interactions along the length of the colloidal polymer. Colloidal polymers can be assembled with either a single homogeneous interaction or with an alternating repeated set of interactions. The strength of these interactions is temperature-dependent; we can trigger different interactions in sequence by careful design of a temperature change protocol. We show that, even with simple alternating sequences, we can prune the possible folding pathways of emulsion chains to produce one single final structure. We will also show how equilibrium folding structures differ from kinetically trapped folding structures. This work enables us to synthesize programmable colloidal polymers that will fold to a unique stable structure of a functional complex material that has unique photonic or material properties. This work was supported by the NSF MRSEC Program (DMR-0820341).
Daniele Coslovich: Glass structure through the prism of clustering
This seminar will focus on unsupervised approaches to learn about structure in supercooled liquids and glasses. The key idea is perform a cluster analysis on a suitable structural feature set, which describes the local environments around each particle. As a first example, I will introduce a simple distributional clustering method that groups particles with similar local structure into "communities" using an information-theoretic criterion. The properties of the resulting communities and their connection with particle mobility will be discussed for some models of binary glass-formers. I will then compare this approach to related statistical clustering methods and scrutinize the role of dimensional reduction of the structural feature space.
Olivier Dauchot: Self aligning vs Active Brownian Particles
In this talk I would like to discuss the physics of polar active particles, which align their orientation with their own velocity. When such a self aligning particle (SAP) of this kind is confined in a parabolic potential, it presents an original steady state distribution, distinct from that of the now standard Active Brownian Particles (ABP). How relevant is this observation at the collective level? A first significant difference with repulsive ABP is the absence of equation of state for the mechanical pressure. Concerning collective motion, the self alignment leads to an effective alignment of the velocities, but the mean field behavior is radically different from that of the Vicsek model. There is however yet no evidence of significant differences beyond mean field. The most striking differences take place when such particles are embedded in an elastic medium, a situation which might be of significant importance when modeling biological tissues.
Juan P. Garrahan: Slow quantum dynamics of kinetically constrained models
Classical kinetically constrained models can describe the basic dynamics seen in glass formers, such as super-Arrhenius slowing down, facilitation, dynamic heterogeneity and decoupling. They do so without recourse to putative thermodynamic transitions: due to constraints all complexity is in trajectories of the dynamics which can be quantified by dynamical large deviation techniques. I will discuss how these ideas are also applicable to quantum systems. I will show that under unitary evolution KCMs can display slow thermalisation and dynamical arrest without the need for quenched disorder. I will also consider connections to the problem of many body localisation and to so-called quantum scars.
David Huse: Many-body localization (MBL) as glass
I will discuss some aspects of many-body localization (MBL), with some emphasis on the similarities to and differences from short-range spin glasses and structural glasses.
Jorge Kurchan: Parisi scheme, multithermalization and an important hidden symmetry
In finite dimensions the equilibrium solution and the solution for the long time-dynamics may be shown to be closely related. If a system has a Parisi solution for equilibrium, it has a `multithermalization’ solution for slow dynamics (I will explain what this is), and vice-versa. This has three interesting consequences: (i) the Parisi/multithermalization scenario is a single thing, that now we may understand as a generalization of thermodynamics; (ii) we may check the scenario via dynamics (experiments and simulation), rather than equilibrium, and obtain answers of unprecedented unambiguity; (iii) the role of a group of ‘time reparametrizations’ (I will also explain what that is) as a central object of the theory becomes evident, and spills over from dynamics to statics.
Kirsten Martens: Out-of-equilibrium critical phenomena in sheared yield-stress materials
In this presentation I shall introduce several out-of-equilibrium critical phenomena that are observed in the athermal deformation process of dense disordered materials. Besides the well studied avalanche phenomenon in the vanishing driving limit, I shall discuss how fluidisation (e.g. due to internal activity or external vibrations) combined with self-fluidisation effects (e.g. inertial dynamics on the particle scale), can lead to a finite shear rate critical point with a set of exponents that appear to be general when compared to experiments.
Misaki Ozawa: Brittle and ductile yielding of amorphous materials
When a material is mechanically deformed from an initial quiescent glassy state, two different types of yielding behaviors are observed. One is “brittle” yielding, where the sample catastrophically breaks as a smartphone screen breaks sharply. The other one is “ductile” yielding, for which the sample deforms significantly, just like when toothpaste is slowly crushed by a toothbrush. It is known that a given material may show brittle or ductile yielding depending on the sample preparation history. The understanding transformation from brittle to ductile behaviors is a major challenge in many fields, from material science to geophysics. We address this problem, performing extensive molecular simulations and mesoscopic elastoplastic models. In the first part of the seminar, I will talk about the presence of critical stability separating brittle and ductile yielding behaviors in various rheological settings, from shear start-up conditions for glasses in slow driving to cyclic deformation protocols, which is relevant for experimental situations from the rheology of soft materials to fatigue failure in metallic glasses. In the second part of the seminar, I will focus on a microscopic description of the brittle failure of amorphous materials and assess the role of rare events and quenched disorder. We argue that brittle yielding originates at rare soft regions. We numerically demonstrate how localized plastic events in such soft regions trigger macroscopic failure via the propagation of a shear band.
Itamar Procaccia: Plasticity and Screening in Amorphous Solids
Amorphous solids appear to react elastically to small external strains, but in contrast to ideal elastic media, plastic responses abound immediately, at any value of the strain. Such plastic responses are quasi-localized in nature, with the ``cheapest" one being a quadrupolar source. The existence of such plastic responses results in {\em screened elasticity} in which strains and stresses can either quantitatively or qualitatively differ from the un-screened theory, depending on the specific screening mechanism. Here we offer a theory of such screening effects by plastic quadrupoles, dipoles and monopoles, explain their natural appearance, and point out the analogy to electrostatic screening by electric charges and dipoles. For low density of quadrupoles the effect is to normalize the elastic moduli without a qualitative change compared to pure elasticity theory; for higher density of quadrupoles the screening effects result in qualitative changes. Predictions for the spatial dependence of displacement fields caused by local sources of strains are provided and compared to numerical simulations. We find that anomalous elasticity is richer than electrostatics in having a screening mode that does not appear in the electrostatic analog.
Giorgio Parisi: Jamming, dynamics and all that
Federico Ricci-Tersenghi: Long-range vector spin glasses in a field at T=0: the Hessian spectrum has a pseudo-gap and a delocalization transition
We study m-component vector spin glasses on fully-connected graphs and sparse random graphs (Bethe lattices), fixing the temperature to zero (T=0) and varying the external field. We consider the dense case with m=3 (Heisenberg) and the sparse case with m=2 (XY). In both cases there is a phase transition from a paramagnetic to a spin glass phase decreasing the intensity of the external random field. We study the low-energy excitations around the ground state via the spectrum of the Hessian matrix, both numerically and analytically via the cavity method. We uncover that in the paramagnetic phase the spectrum is gapless and shows a pseudo-gap, resembling the spectrum of low-frequency modes in glass models. Low-energy excitations turn out to be localized in the paramagnetic phase. At the transition to the spin glass phase these quasi-localized excitations become extended, thus suggesting that the spin glass transition is a delocalization transition for low-energy modes. Work in collaboration with S. Franz, C. Lupo, F. Nicoletti and G. Parisi
Alberto Rosso: Avalanche clustering in presence of long range interactions
Disordered elastic interfaces display avalanche dynamics at the depinning transition. For short-range interactions, avalanches correspond to compact reorganizations of the interface well described by the depinning theory. For long-range elasticity, an avalanche is a collection of spatially disconnected clusters. Here we propose a scaling approach to characterize cluster statistics and relate them to the roughness exponent of the interface. The key observation of our analysis is the identification of a Bienaymé-Galton-Watson process describing the statistics of the number of clusters. Our work has concrete importance for experimental applications where the cluster statistics is a key probe of avalanche dynamics.
C. Patrick Royall: What colloids have done for dynamical arrest: a tale of two spaces
While the basic underlying physics is the same, colloidal particles exhibit two key differences with respect to atoms and molecules: they are larger, and they can be designed. In the mid-1980s, the seminal work of Peter Pusey and Bill van Megen catapulted colloids into the realm of physics, following the design and realisation of hard—sphere like experimental systems. It was now possible to test, directly, in experiment, theoretical predictions pertaining to this key basic model. In addition to a fairly accurate representation of hard spheres, colloidal dispersions exhibit timescales of seconds and lengthscales of microns, which are amenable to laboratory based experiments with light and wristwatches rather than ultrafast x-ray and neutron scattering for molecular systems.
Experimental techniques that obtain structural information on colloidal systems fall into two classes — light scattering which operates in reciprocal space and light microscopy which operates in real space. While the former accesses similar information to scattering techniques for molecular systems, the latter has no direct equivalent in molecular systems. Among the early “success” stories with light scattering in the context of glass physics was the very close quantitative agreement with mode—coupling theory. Later work revealed the discrepancy long known in molecular systems. Real space methods with 3d confocal microscopy began with the pioneering work of Alfons van Blaaderen and Pierre Wiltzius who demonstrated the potential to directly measure higher—order structural correlation functions that are fiendishly hard to measure with the reciprocal space techniques available to molecular systems. This was followed by the work of Eric Weeks et al., which was among the first convincing experimental demonstrations of dynamic heterogeneity.
An important aspect of colloids is that the very slowness which enables all dynamic events to be accessed on the second timescale leads to the uncomfortable consequence that the equivalent of the experimental glass transition Tg, of a relaxation time of 100s in molecular systems corresponds to millions of years in colloidal systems. We discuss approaches to address this challenge, in short using colloids that are more like molecules, i.e. smaller.
Beyond hard spheres, colloids with a large range of designer interactions have been prepared and arguably the simplest step beyond hard spheres, sticky spheres (with a short—ranged attraction), exhibit a fascinating range of phenomena, such as gelation.
Srikanth Sastry: Yielding of amorphous solids under cyclic deformation
Investigations of plastic deformation and yielding of amorphous solids reveal a strong dependence of their yielding behaviour on the degree of annealing. Above a threshold degree of annealing, the nature of yielding changes qualitatively, becoming progressively more discontinuous. I will first describe simulation investigations of the nature of yielding and the role of annealing in the yielding behaviour of athermal glasses. Theoretical investigations of yielding in amorphous solids have largely focused on uniform deformation, but cyclic deformation reveals intriguing features that remain un-investigated. Focusing on athermal cyclic deformation, I describe a family of models, which reproduce key features observed in simulations, and provide an interpretation for the intriguing presence of a threshold energy. The dynamics of the model has a mapping to a first passage problem in a reformulation, that leads to new insights, which will be discussed. Extension of the models to incorporate interactions among mesoscopic blocks and spatially heterogeneous behaviour will also be discussed.
Samuel Schoenholz: JAX MD: A Framework for Differentiable Molecular Dynamics
I will describe JAX MD, a software package for performing differentiable physics simulations with a focus on molecular dynamics. JAX MD includes a number of statistical physics simulation environments as well as interaction potentials and neural networks that can be integrated into these environments without writing any additional code. Since the simulations themselves are differentiable functions, entire trajectories can be differentiated to perform meta-optimization. These features are built on primitive operations, such as spatial partitioning, that allow simulations to scale to hundreds-of-thousands of particles on a single GPU. These primitives are flexible enough that they can be used to scale up a wide range of molecular dynamics workloads. I will go through a demonstration implementing a recent algorithm popular in glass physics into JAX MD. Code is available at www.github.com/google/jax-md.
Julien Tailleur: The anomalous mechanical properties of active fluids
Active particles dissipate energy to exert self-propelling forces on their environment. This microscopic drive out of equilibrium leads to rich behaviors, from the flocking of birds to the motility-induced phase separation of self-propelled colloids or bacteria, that have attracted a lot of attention in the past. This exchange of momentum with the environment also impacts their collective mechanical properties, a topic which has been much less studied. In this talk, I will review recent developments concerning the mechanical pressure and the surface tension of active systems and show how statistics and mechanics decouple in these non-equilibrium systems, leading to surprising properties.
Eric Vanden-Eijnden: Promises and Challenges of Machine Learning in Scientific Computing
The recent success of machine learning suggests that neural networks may be capable of approximating high-dimensional functions with controllably small errors. As a result, they could outperform standard function interpolation methods that have been the workhorses of current numerical methods. This feat offers exciting prospects for scientific computing, as it may allow us to solve problems in high-dimension once thought intractable. I will discuss some recent results in this direction, focusing on applications related to (i) solving Fokker-Planck equations associated with high-dimensional systems displaying metastability and (ii) sampling Boltzmann-Gibbs distributions using generative models to assist MCMC methods.
Vincenzo Vitelli: Non reciprocal phase transitions
The interaction between a peregrine falcon and a dove is visibly non-reciprocal. What happens to the well established framework of phase transitions in non-reciprocal systems far from equilibrium?
In this talk, I will answer this question by looking at three archetypal classes of self-organization out of equilibrium: synchronization, flocking and pattern formation. Simple demonstrations with robots will be presented along with naturally occurring phenomena from various domains of science that share a common feature: reciprocity has no reason to exist. In all these cases, the emergence of unique time-dependent many-body phases can be captured by combining insights from non-Hermitian quantum mechanics and bifurcation theory. This approach lays the foundation for a general theory of critical phenomena in systems whose dynamics is not governed by an optimization principle.
Matthieu Wyart: Landscape and learning regimes in deep learning
Deep learning algorithms are responsible for a technological revolution in a variety of tasks, yet understanding why they work remains a challenge.
First, learning corresponds to minimizing a loss in high dimension, which is in general not convex and could well get stuck in bad minima. Second, deep learning predicting power increases with the number of fitting parameters, even in a regime where data are perfectly fitted. Third, it is trying to learn a rule in very large dimension, which is provably impossible for data that have little structure. Describing what structure makes data as images learnable remains a challenge. I will discuss recent analogies with physical systems that shed some lights on these puzzles.