Related papers: A trajectory map for the pressureless Euler equati…
The motion of a particle carried by a liquid is described by the differential equation equating the velocity of the particle at time t to the the Eulerian velocity field at time t and at the location of the particle at that time. Assuming…
Eulerian-Lagrangian models of particle-laden (multiphase) flows describe fluid flow and particle dynamics in the Eulerian and Lagrangian frameworks respectively. Regardless of whether the flow is turbulent or laminar, the particle dynamics…
We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when…
In this paper, we present a novel Eulerian-Lagrangian formulation for the compressible isentropic Euler equations with vaccum. Using the developed Lagrangian flow map formulation, we show a short-time solution for a general pressure law. A…
By means of a novel variational approach we study ergodic properties of a model of a multi lane traffic flow, considered as a (deterministic) wandering of interacting particles on an infinite lattice. For a class of initial configurations…
The dynamics of a tagged particle immersed in a fluid of particles of the same size but different mass is studied when the system is confined between two hard parallel plates separated a distance smaller than twice the diameter of the…
We derive a master equation for the motion of a polarizable particle weakly interacting with one or several strongly pumped cavity modes. We focus here on massive particles with complex internal structure such as large molecules and…
We study the stability in finite times of the trajectories of interacting particles. Our aim is to show that in average and uniformly in the number of particles, two trajectories whose initial positions in phase space are close, remain…
We establish a result concerning the so-called Lagrangian controllability of the Euler equation for incompressible perfect fluids in dimension 3. More precisely we consider a connected bounded domain of R^3 and two smooth contractible sets…
We consider Lagrangian systems in the limit of infinitely many particles. It is shown that the corresponding discrete action functionals Gamma-converge to a continuum action functional acting on probability measures of particle…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
We discuss the relation between three recent approaches of describing the dynamics and the spatial distribution of particles suspended in turbulent flows: phase-space singularities in the inertial particle dynamics (caustics), real-space…
We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves…
This paper is devoted to the analysis of random motions on the line and in the space R^d (d > 1) performed at finite velocity and governed by a non-homogeneous Poisson process with rate \lambda(t). The explicit distributions p(x,t) of the…
We consider the planar circular equilateral restricted four body-problem where a test particle of infinitesimal mass is moving under the gravitational attraction of three primary bodies which move on circular orbits around their common…
We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…
We consider fairly general class of dynamical systems under the assumptions guaranteeing the existence of Lyapunov function around some nontrivial stationary point. Moreover, the existence of heteroclinic trajectory is proved motivated by…
Working in the lagrangian framework, we develop a geometric theory in vacuum with propagating torsion; the antisymmetric and trace parts of the torsion tensor, considered as derived from local potential fields, are taken and, using the…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
The dynamics of inertial particles in fluid flows have been the focus of extensive research due to their relevance in a wide range of industrial and environmental processes. Earlier studies have examined the dynamics of aerosols and bubbles…