Related papers: A trajectory map for the pressureless Euler equati…

Starting from a particle model describing self-propelled particles interacting through nematic alignment, we derive a macroscopic model for the particle density and mean direction of motion. We first propose a mean-field kinetic model of…

We develop a general hydrodynamic theory describing a system of interacting actively propelling particles of arbitrary shape suspended in a viscous fluid. We model the active part of the particle motion using a slip velocity prescribed on…

We study closed systems of particles that are subject to stochastic forces in addition to the conservative forces. The stochastic equations of motion are set up in such a way that the energy is strictly conserved at all times. To ensure…

Equations of motion that recognize biochemical patterns are described. The equations are partial differential equations in a continuous multiple component system in which adequate initial and boundary conditions are given. The biochemical…

We consider a two-dimensional model system of Brownian particles in which slow particles are accelerated while fast particles are damped. The motion of the individual particles are described by a Langevin equation with Rayleigh-Helmholtz…

The results of our study of the motion of a three particle, self-gravitating system in general relativistic lineal gravity is presented for an arbitrary ratio of the particle masses. We derive a canonical expression for the Hamiltonian of…

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…

This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The…

We give a proof of the analiticity in time for the particle trajectories associated with the solutions of some transport equations when the initial datum is a patch. These results are obtained from a precise study of the Beurling transform,…

We consider a problem of mass points interacting gravitationally whose motion is subjected to certain holonomic constraints. The motion of points is restricted to certain curves and surfaces. We illustrate the complicated behaviour of…

A conventional derivation of motion equations in mechanics and field equations in field theory is based on the principle of least action with a proper Lagrangian. With a time-independent Lagrangian, a function of coordinates and velocities…

A general framework for performing event-driven simulations of systems with semi-flexible or rigid bodies interacting under impulsive torques and forces is outlined. Two different approaches are presented. In the first, the dynamics and…

The purpose of the article is to derive equations that determine the trajectory of a non-conservative natural system in configuration space in non-stationary external fields. A theorem on the change in the kinetic energy of the system is…

We formulate the laws governing the dynamics of a crystalline solid in which a continuous distribution of dislocations is present. Our formulation is based on new differential geometric concepts, which in particular relate to Lie groups. We…

This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second…

Relativistic action-at-a-distance theories with interactions that propagate at the speed of light in vacuum are investigated. We consider the most general action depending on the velocities and relative positions of the particles. The…

The Einstein-Vlasov equations govern Einstein spacetimes filled with matter which interacts only via gravitation. The matter, described by a distribution function on phase space, evolves under the collisionless Boltzmann equation,…

A Lagrangian formalism is used to study the motion of a spinning massive particle in Friedmann--Robertson--Walker and G\"odel spacetimes, as well as in a general Schwarzschild-like spacetime and in static spherically symmetric conformally…

We study the center-of-mass motion in systems of trapped interacting particles with space- and velocity-dependent friction and anharmonic traps. Our approach, based on a dynamical ansatz assuming a fixed density profile, allows us to obtain…

We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the…