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As an injury heals, an embryo develops, or a carcinoma spreads, epithelial cells systematically change their shape. In each of these processes cell shape is studied extensively, whereas variation of shape from cell-to-cell is dismissed most…

Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…

When we try to solve a system of linear equations, we can consider a simple iterative algorithm in which an equation including only one variable is chosen at each step, and the variable is fixed to the value satisfying the equation. The…

An electro-chemo-mechanical phase-field formulation is developed to simulate pitting and stress corrosion in polycrystalline materials. The formulation incorporates dependencies of mechanical properties and corrosion potential on…

In these lecture notes I describe some of the main theoretical ideas emerged to explain the aging dynamics. This is meant to be a very short introduction to aging dynamics and no previous knowledge is assumed. I will go through simple…

We study the long-time behaviour of the first-moment semigroup of a non conservative piecewise deterministic measure-valued stochastic process with support on R 2 + driven by a deterministic flow between random jump times, with a transition…

Projection-based embedding offers a simple framework for embedding correlated wavefunction methods in density functional theory. Partitioning between the correlated wavefunction and density functional subsystems is performed in the space of…

Given a quantum many-body system and the expectation-value dynamics of some operator, we study how this reference dynamics is altered due to a perturbation of the system's Hamiltonian. Based on projection operator techniques, we unveil that…

We investigate aging in glassy systems based on a simple model, where a point in configuration space performs thermally activated jumps between the minima of a random energy landscape. The model allows us to show explicitly a subaging…

We introduce a high dimensional symplectic map, modeling a large system consisting of weakly interacting chaotic subsystems, as a toy model to analyze the interplay between single-particle chaotic dynamics and particles interactions in…

Aging remains a fundamental open problem in modern biology. Although there exist a number of theories on aging on the cellular scale, nearly nothing is known about how microscopic failures cascade to macroscopic failures of tissues, organs…

Numerical studies are providing novel information on the physical processes associated to physical aging. The process of aging has been shown to consist in a slow process of explorations of deeper and deeper minima of the system potential…

This work deals with the average scattering entropy of quantum graphs. We explore this concept in several distinct scenarios that involve periodic, aperiodic and random distribution of vertices of distinct degrees. In particular, we compare…

Molten metallic nanoparticles have recently been used to construct graphene nanostructures with crystallographic edges. The mechanism by which this happens, however, remains unclear. Here, we present a simple model that explains how a…

Recent experiments at the level of a single cell have shown that gene expression occurs in abrupt stochastic bursts. Further, in an ensemble of cells, the levels of proteins produced have a bimodal distribution. In a large fraction of…

Localized growth in driven materials is often governed by intermittent failure, yet how a material's history biases failure sites remains poorly understood. Using pause-restart experiments on chemical precipitate membranes, we quantify the…

Battery degradation is governed by complex and randomized cyclic conditions, yet existing modeling and prediction frameworks usually rely on rigid, unchanging protocols that fail to capture real-world dynamics. The stochastic electrical…

Laboratory and numerical corrosion experiments impose an electric potential on the metal surface, differing from natural corrosion conditions, where corrosion typically occurs in the absence of external current sources. In this work, we…

Although species longevity is subject to a diverse range of selective forces, the mortality curves of a wide variety of organisms are rather similar. We argue that aging and its universal characteristics may have evolved by means of a…

Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not…