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Sparse inversion and classification problems are ubiquitous in modern data science and imaging. They are often formulated as non-smooth minimisation problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity term and an…
We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…
Performing molecular dynamics simulations, we investigate the enormous slowdowns of water dynamics when approaching a glass transition or a solid interface. We show that both effects can be described on common grounds within a theoretical…
Besides the dynamical slowing down signaled by an enormous increase of the viscosity approaching the glass transition, structural glasses show interesting anomalous thermodynamic features at low temperatures that hint at peculiar deviations…
We study the dynamics of a one-dimensional fluid of orientable hard rectangles with a non-coarse-grained microscopic mechanism of facilitation. The length occupied by a rectangle depends on its orientation, which is coupled to an external…
Aging dynamics in glassy systems is investigated by considering the hopping motion in a rugged energy landscape whose deep minima are characterized by an exponential density of states. In particular we explore the behavior of a generic…
We study locally interacting processes in discrete time, often called probabilistic cellular automata, indexed by locally finite graphs. For infinite regular trees and certain generalized Galton-Watson trees, we show that the marginal…
The dynamical glass transition is typically taken to be the temperature at which a glassy liquid is no longer able to equilibrate on experimental timescales. Consequently, the physical properties of these systems just above or below the…
The effects of floppy modes in the thermodynamical properties of a system are studied. From thermodynamical arguments, we deduce that floppy modes are not at zero frequency and thus a modified Debye model is used to take into account this…
We study a discrete-time asynchronous midpoint dynamics on the circle in which, at each step, a uniformly chosen neighboring pair moves to the midpoint along the shortest arc. Although the update rule is locally contractive, we show that…
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way,…
Recent observations demonstrate that densely packed tissues exhibit features of glassy dynamics, such as caging behavior and dynamical heterogeneities, although it has remained unclear how single-cell properties control this behavior. Here…
A model system with fast and slow processes is introduced. After integrating out the fast ones, the considered dynamics of the slow variables is exactly solvable. In statics the system undergoes a Kauzmann transition to a glassy state. The…
We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a…
Stretched-exponential relaxation is a widely observed phenomenon found in ordered ferromagnets as well as glassy systems. One modeling approach connects this behavior to a droplet dynamics described by an effective Langevin equation for the…
The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the…
The requirement that packings of hard particles, arguably the simplest structural glass, cannot be compressed by rearranging their network of contacts is shown to yield a new constraint on their microscopic structure. This constraint takes…
We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical…
In this article we study a simple spin model which has a non-interacting Hamiltonian but constrained dynamics. The model, which is a simplification of a purely toplogical cellular model, displays glassy behaviour, involves activated…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…