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Lattice relaxation profoundly reshapes electronic structures in twisted materials. Prevailing treatments, however, typically rely on large-scale density functional theory (DFT), which is computationally costly and mechanistically opaque.…
This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…
A general kind of models with hierarchically constrained dynamics is shown to exhibit logarithmic anomalous relaxation, similarly to a variety of complex strongly interacting materials. The logarithmic behavior describes most of the decay…
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector…
We investigate the heterogeneous dynamics in a model, where chemical gelation and glass transition interplay, focusing on the dynamical susceptibility. Two independent mechanisms give raise to the correlations, which are manifested in the…
Some stochastic systems are particularly interesting as they exhibit critical behavior without fine-tuning of a parameter, a phenomenon called self-organized criticality. In the context of driven-dissipative steady states, one of the main…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
One considers linearly thermoelastic composite media, which consist of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated inclusions. Effective properties (such as compliance and thermal…
The vibrational anomalies of glasses, in particular the boson peak, are addressed from the standpoint of heterogeneous elasticity, namely the spatial fluctuations of elastic constants caused by the structural disorder of the amorphous…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…
Elastic turbulence is a chaotic regime that emerges in polymer solutions at low Reynolds numbers. A common way to ensure stability in numerical simulations of polymer solutions is to add artificially large polymer-stress diffusion. In order…
In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and…
Stochastic processes offer a fundamentally different paradigm of dynamics than deterministic processes, the most prominent example of the latter being Newton's laws of motion. Here, we discuss in a pedagogical manner a simple and…
We investigate the relaxation dynamics of a dense monolayer of bidisperse beads by analyzing the experimental data previously obtained in a fluidized bed. We show that the dynamics is formed by elementary relaxation events called cage…
We identify the dynamical heterogeneities as an essential prerequisite for stretched exponential relaxation in dynamically frustrated systems. This heterogeneity takes the form of ordered domains of finite but diverging lifetime for…
We study charge fluctuations of a family of stochastic charged cellular automata away from the deterministic single-file limit and obtain the exact typical charge probability distributions, known to be anomalous, using hydrodynamics. The…
Prestress in amorphous solids bears the memory of their formation, and plays a profound role in their mechanical properties, from stiffening or softening elastic moduli to shifting frequencies of vibrational modes, as well as directing…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
Many complex systems respond to a continuous input of energy by an accumulation of stress over time, interrupted by sudden energy releases called avalanches. Recently, it has been pointed out that several basic features of avalanche…
Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…