Related papers: Interacting Particle Systems in Time-Dependent Geo…
This study in centered on models accounting for stochastic deformations of sample paths of random walks, embedded either in $\mathbb{Z}^2$ or in $\mathbb{Z}^3$. These models are immersed in multi-type particle systems with exclusion.…
From tumour invasion to cell sorting and animal territoriality, many biological systems rely on nonlocal interactions that drive complex spatial organisation. Partial differential equations (PDEs) with nonlocal advection are increasingly…
Quantum collision models allow for the dynamics of open quantum systems to be described by breaking the environment into small segments, typically consisting of non-interacting harmonic oscillators or two-level systems. This work introduces…
We present a systematic way to analyze and model systems having many characteristic time-scales. The method we propose is employed for a test-case of a meandering jet model manifesting chaotic tracer dispersion with long time-correlations.…
Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental…
The quasi-coherent effects in two-dimensional incompressible turbulence are analyzed starting from the test particle trajectories. They can acquire coherent aspects when the stochastic potential has slow time variation and the motion is not…
Alignment interactions in active matter are typically modeled as relaxational dynamics toward local consensus. In unbounded systems, this makes alignment effectively decoupled from local density and therefore unable to sustain self-confined…
Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly…
We review recent work on systems with multiple interacting-particles having the dynamical feature of stochastic resetting. The interplay of time scales related to inter-particle interactions and resetting leads to a rich behavior, both…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes one we developed previously (Phys. Rev. E v.79, 011110, 2009) in order to describe the Levy type stochastic processes in terms of continuous…
The relationship between a driven extended system and an autonomous spatiotemporal system is investigated in the context of coupled map lattice models. Specifically, a locally coupled map lattice subjected to an external drive is compared…
Impact induced attrition processes are, beyond being essential models of industrial ore processing, broadly regarded as the key to decipher the provenance of sedimentary particles. A detailed understanding of single impact phenomena of…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
We consider the dynamics of a collisional model in which both the system and environment are embodied by spin-$1/2$ particles. In order to include non-Markovian features in our model we introduce interactions among the environmental qubits…
Temporal coherence-persistent alignment across time-can arise between agents with fundamentally distinct dynamics, a behavior that classical diffusion models (e.g., Brownian motion, fractional Brownian motion, generalized Langevin equation)…
Intracellular protein patterns regulate many vital cellular functions, such as the processing of spatiotemporal information or the control of shape deformations. To do so, pattern-forming systems can be sensitive to the cell geometry by…
We consider a general framework for multi-type interacting particle systems on graphs, where particles move one at a time by random walk steps, different types may have different speeds, and may interact, possibly randomly, when they meet.…
The dynamic of complex ordering systems with active rotational degrees of freedom exemplified by protein self-assembly is explored using a machine learning workflow that combines deep learning-based semantic segmentation and rotationally…