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To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
With the aim of understanding the emergence of collective motion from local interactions of organisms in a "noisy" environment, we study biologically inspired, inherently non-equilibrium models consisting of self-propelled particles. In…
Numerical simulations of plasma flows are crucial for advancing our understanding of microscopic processes that drive the global plasma dynamics in fusion devices, space, and astrophysical systems. Identifying and classifying particle…
The collectivity in the simultaneous diffusion of many particles, i.e. the interdependence of stochastic forces affecting different particles in the same solution, is a largely overlooked phenomenon with no well-established theory.…
Deformable self-propelled particles provide us with one of the most important nonlinear dissipative systems, which are related, for example, to the motion of microorganisms. It is emphasized that this is a subject of localized objects in…
A fundamental question in complex systems is how to relate interactions between individual components ("microscopic description") to the global properties of the system ("macroscopic description"). Another fundamental question is whether…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…
The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are…
The length-scale dependence of the dynamic entropy is studied in a molecular dynamics simulation of a binary Lennard-Jones liquid above the mode-coupling critical temperature $T_c$. A number of methods exist for estimating the entropy of…
Density-dependent diffusion is a widespread phenomenon in nature. We have examined the density-dependent diffusion behavior of some biological processes such as tumor growth and invasion [23]. Here, we extend our previous work by developing…
We characterize the dynamic non-equilibrium steady state behavior of active particles using density fluctuations in the system. We analyze the effective local density around a particle in the steady state and numerically calculate its mean,…
Collective motion in actively propelled particle systems is triggered on the very local scale by nucleation of coherently moving units consisting of just a handful of particles. These units grow and merge over time, ending up in a…
In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm…
The behavior of particles driven through a narrow constriction is investigated in experiment and simulation. The system of particles adapts to the confining potentials and the interaction energies by a self-consistent arrangement of the…
In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. We consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant…
A small quantum scattering system (the microsystem) is studied in interaction with a large system (the macrosystem) described by unknown stochastic variables. The interaction between the two systems is diagonal for the microsystem in a…
We give an explicit stochastic Hamiltonian model of discontinuous unitary evolution for quantum spontaneous jumps like in a system of atoms in quantum optics, or in a system of quantum particles that interacts singularly with "bubbles"…
Stochasticity is a defining feature of the pairwise forces governing interactions in biological systems-from molecular motors to cell-cell adhesion-yet its consequences on large-scale dynamics remain poorly understood. Here, we show that…
Any continuous curve in a higher dimensional space can be considered a trajectory that can be parameterized by a single variable, usually taken as time. It is well known that a continuous curve can have a fractional dimensionality, which…
We introduce a model of interacting Random Walk, whose hopping amplitude depends on the number of walkers/particles on the link. The mesoscopic counterpart of such a microscopic dynamics is a diffusing system whose diffusivity depends on…