Related papers: Counting metastable states in a kinetically constr…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
The Mackey-Glass system is a paradigmatic example of a delayed model whose dynamics is particularly complex due to, among other factors, its multistability involving the coexistence of many periodic and chaotic attractors. The prediction of…
In this review we define and discuss metastates, mathematical tools with general applicability to thermodynamic systems which are particularly useful when working with disordered or inhomogeneous short-range systems. In an infinite such…
Motivated by the large strain shear of loose granular materials we introduced a model which consists of consecutive optimization and restructuring steps leading to a self organization of a density field. The extensive connections to other…
Glass-forming systems, which are characterized by a highly disordered energy landscape, have been studied in physics by a simulation-based state space aggregation. The purpose of this article is to develop a path-independent approach within…
The East model is a particular one dimensional interacting particle system in which certain transitions are forbidden according to some constraints depending on the configuration of the system. As such it has received particular attention…
We extend the method of time delay proposed by Eisenbud and Wigner, to search for unstable states formed by eta mesons and the 3He nucleus. Using few body equations to describe eta-3He elastic scattering, we predict resonances and unstable…
We consider a simple analytically tractable model of metastability and ageing. In this model, a particle can jump left or right by two steps to an unoccupied site, but only if the the site in between is occupied. We show that the model is…
In this paper we study the metastable behavior of one of the simplest disordered spin system, the random field Curie-Weiss model. We will show how the potential theoretic approach can be used to prove sharp estimates on capacities and…
Using large-scale molecular dynamics simulations for a system of $10^6$ particles, the response of a dense amorphous solid to the continuous expansion of its volume is investigated. We find that the spatially uniform glassy state becomes…
Intensity-based multistate models provide a useful framework for characterizing disease processes, the introduction of interventions, loss to follow-up, and other complications arising in the conduct of randomized trials studying complex…
A one-dimensional Ising model with nearest neighbour interactions is applied to study compaction processes in granular media. An equivalent particle-hole picture is introduced, with the holes being associated to the domain walls of the…
In this letter, we develop a framework to study the mechanical response of athermal amorphous solids via a coupling of mesoscale and microscopic models. Using measurements of coarse grained quantities from simulations of dense disordered…
Understanding how multi-component liquid mixtures undergo phase separation is central to elucidating biophysical organization in the cell. Here, combining analytical and numerical results, we characterise the dynamics of mixtures with…
The East model has a dynamical phase transition between an active (fluid) and inactive (glass) state. We show that this phase transition generalizes to "softened" systems where constraint violations are allowed with small but finite…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
Understanding the role that structure plays in the dynamical arrest observed in glassy systems remains an open challenge. Over the last decade, machine learning (ML) strategies have emerged as an important tool for probing this…
Hybrid multiscale modelling has emerged as a useful framework for modelling complex biological phenomena. However, when accounting for stochasticity in the internal dynamics of agents, these models frequently become computationally…
We offer an alternative real-space description, based purely on activated processes, for the understanding of relaxation dynamics in hierarchical landscapes. To this end, we use the cluster model, a coarse-grained lattice model of a jammed…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…