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Frictional interfaces exhibits a very rich dynamical behavior due to frictional interactions. This work focuses on the transition between spatially localized and propagating stick-slip motion. To overcome the difficulties related to the…
These are lecture notes for a short course given at the Les Houches Summer School on ``Integrability in Atomic and Condensed Matter Physics'', in summer 2018. Here, I pedagogically discuss recent advances in the study of the entanglement…
The flow in a Hele-Shaw cell with a time-increasing gap poses a unique shrinking interface problem. When the upper plate of the cell is lifted perpendicularly at a prescribed speed, the exterior less viscous fluid penetrates the interior…
Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and…
We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model by a low-dimensional system of equations permitting analytical…
Although viral spreading processes taking place in networks are often analyzed using Markovian models in which both the transmission and the recovery times follow exponential distributions, empirical studies show that, in many real…
Many studies investigated the application of statistical mechanics to damage phenomena. However, so far the association of damage with statistical mechanics is far from completely developed. One of the most successful approaches maps the…
We explore in the mean-field approximation the robustness with respect to dissipation of self-organized criticality in sandpile models. To this end, we generalize a recently introduced self-organized branching process, and show that the…
We study time continuous branching processes with exponentially distributed lifetimes, with two types of cells that proliferate according to binary fission. A range of possible system dynamics are considered, each of which is characterized…
We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The…
Time-independent scattering methods are widely employed to analyze transport in non-Hermitian systems. Their application, however, rests on a critical yet often overlooked assumption: that an incident wave is a pure superposition of…
Nonequilibrium kinetic Ising models evolving under the competing effect of spin flips at zero temperature and nearest neighbour spin exchanges at $T=\infty$ are investigated numerically from the point of view of a phase transition.…
We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of…
The early dynamics in heavy-ion collisions involves a rapid, far from equilibrium evolution. This early pre-equilibrium stage of the dynamics can be modeled using kinetic equations. The effect of this pre-equilibrium stage on final…
Epidemic spreading often occurs in spatially heterogeneous environments, yet how quenched heterogeneity reshapes its onset and critical dynamics remains poorly understood. The diffusive epidemic process, a minimal reaction-diffusion model…
This study presents a neural network-enhanced approach to modeling disease spread dynamics over time and space. Neural networks are used to estimate time-varying parameters, with two calibration methods explored: Approximate Bayesian…
Diffusion processes are central to human interactions. One common prediction of the current modeling frameworks is that initial spreading dynamics follow exponential growth. Here, we find that, ranging from mobile handsets to automobiles,…
We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished as t tends to infinity, the first being a regime ahead of the…
This short paper concerns a diffusive logistic equation with the heterogeneous environment and a free boundary, which is formulated to study the spread of an invasive species, where the free boundary represents the expanding front. A…
Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks…