Related papers: Modeling Flocks and Prices: Jumping Particles with…
We study a microscopic limit order book model, in which the order dynamics depend on the current best bid and ask price and the current volume density functions, simultaneously, and derive its macroscopic high-frequency dynamics. As opposed…
The goal of this paper is to provide mathematically rigorous tools for modelling the evolution of a community of interacting individuals. We model the population by a measure space where the measure determines the abundance of individual…
Direct numerical simulations are used to investigate the individual dynamics of large spherical particles suspended in a developed homogeneous turbulent flow. A definition of the direction of the particle motion relative to the surrounding…
In this paper we derive the continuum limit of a multiple-species, interacting particle system by proving a $\Gamma$-convergence result on the interaction energy as the number of particles tends to infinity. As the leading application, we…
A catalytic branching random walk on a multidimensional lattice, with arbitrary finite number of catalysts, is studied in supercritical regime. The dynamics of spatial spread of the particles population is examined, upon normalization. The…
We introduce a simple model of diffusive jump process where a fee is charged for each jump. The nonlinear cost function is such that slow jumps incur a flat fee, while for fast jumps the cost is proportional to the velocity of the jump. The…
We study the collective dynamics of a population of particles/organisms subject to self-consistent attraction-repulsion interactions and an external velocity field. The starting point of our analysis is a mean-field kinetic model and we…
The article considers systems of interacting particles on networks with adaptively coupled dynamics. Such processes appear frequently in natural processes and applications. Relying on the notion of graph convergence, we prove that for large…
Fluctuations may govern the fate of an interacting particle system even on the mean-field level. This is demonstrated via a three species cyclic trapping reaction with a large, yet finite number of particles, where the final number of…
We study interacting particle systems on the real line which generalize the Hammersley process [D. Aldous and P. Diaconis, Prob. Theory Relat. Fields 103, 199-213 (1995)]. Particles jump to the right to a randomly chosen point between their…
Recently, we proposed a self-propelled particle model with competing alignment interactions: nearby particles tend to align their velocities whereas they anti-align their direction of motion with particles which are further away [R.…
A non--linear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additonal repulsive and attractive forces leading to a changed local mobiltiy. The…
We consider a two type (red and blue or $R$ and $B$) particle population that evolves on the $d$-dimensional lattice according to some reaction-diffusion process $R+B\to 2R$ and starts with a single red particle and a density $\rho$ of blue…
A central limit theorem is shown for moderately interacting particles in the whole space. The interaction potential approximates singular attractive or repulsive potentials of sub-Coulomb type. It is proved that the fluctuations become…
For any system $\{i\}$ of particles with the trajectories $x_{i}(t)$ in $R^{d}$ on a finite time interval $[0,\tau]$ we define the interaction graph $G$. Vertices of $G$ are the particles, there is an edge between two particles $i,j$ iff…
Quantum escapes of a particle from an end of a one-dimensional finite region to $N$ number of semi-infinite leads are discussed by a scattering theoretical approach. Depending on a potential barrier amplitude at the junction, the…
We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
The lift and drag forces acting on a small spherical particle moving with a finite slip in single-wall-bounded flows are investigated via direct numerical simulations. The effect of slip velocity on the particle force is analysed as a…
The dynamical system for inertial particles in fluid flow has both attracting and repelling regions, the interplay of which can localize particles. In laminar flow experiments we find that particles, initially moving throughout the fluid…