Related papers: Inherent Structures, Configurational Entropy and S…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
Configurational entropy has been revealed as a reliable method for constraining some parameters of a given model [Phys. Rev. D \textbf{92} (2015) 126005, Eur. Phys. J. C \textbf{76} (2016) 100]. In this letter we calculate the…
The ability to continuously learn remains elusive for deep learning models. Unlike humans, models cannot accumulate knowledge in their weights when learning new tasks, mainly due to an excess of plasticity and the low incentive to reuse…
We give a notion of entropy for general gemetric structures, which generalizes well-known notions of topological entropy of vector fields and geometric entropy of foliations, and which can also be applied to singular objects, e.g. singular…
Topological constraint theory has become an increasingly popular tool to predict the compositional dependence of glass properties or pinpoint promising compositions with tailored functionalities. This approach reduces complex disordered…
This paper is concerned with reconstruction issue of inverse obstacle problems governed by partial differential equations and consists of two parts. (i) The first part considers the foundation of the probe and enclosure methods for an…
We present new results reflecting the analogies between the Kob-Andersen model and other glassy systems. Studying the stability of the blocked configurations above and below the transition we also give arguments that supports their…
We introduce a class of dissipative quantum spin models with local interactions and without quenched disorder that show glassy behaviour. These models are the quantum analogs of the classical facilitated spin models. Just like their…
We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree, such as the replica method, the Thouless-Anderson-Palmer formalism, the cavity method,…
The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field…
We explore several potential issues that have been raised over the years regarding the "entropic droplet" scenario of activated transport in liquids, due to Wolynes and coworkers, with the aim of clarifying the status of various…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
The random first order transition theory of the dynamics of supercooled liquids is extended to treat aging phenomena in nonequilibrium structural glasses. A reformulation of the idea of ``entropic droplets'' in terms of libraries of local…
We establish the global existence of weak entropy solutions for 1D isentropic gas dynamics with general pressure laws ($\gamma > 1$). To address vacuum degeneracy, we introduce a novel structural regularization via a "Synchronized Dual…
We develop a method of obtaining a hierarchy of new higher-order entropies in the context of compressible models with local and non-local diffusion and isentropic pressure. The local viscosity is allowed to degenerate as the density…
This key-issues review is a plea for a new focus on simpler and more realistic models of glass-forming fluids. It seems to me that we have too often been led astray by sophisticated mathematical models that beautifully capture some of the…
Identifying the conditions under which glass formation occurs is crucial for a fundamental understanding of the glass transition mechanism. Pure liquids devoid of any frustration avoid glass transition and undergo crystallization. In this…
The complex dynamics of an increasing number of systems is attributed to the emergence of a rugged energy landscape with an exponential number of metastable states. To develop this picture into a predictive dynamical theory I discuss how to…
By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations we explicitly construct a constrained replica free energy functional that maps directly…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…