Related papers: A trajectory map for the pressureless Euler equati…
We investigate regular configurations of a small number of particles settling under gravity in a viscous fluid. The particles do not touch each other and can move relative to each other. The dynamics is analyzed in the point-particle…
We use dynamical systems approach and Lagrangian tools to study surface transport and mixing of water masses in a selected coastal region of the Japan Sea with moving mesoscale eddies associated with the Primorskoye Current. Lagrangian…
Dynamics of systems of structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a…
We investigate a one-dimensional system of $N$ particles, initially distributed with random positions and velocities, interacting through binary collisions. The collision rule is such that there is a time after which the $N$ particles do…
The goal of this contribution is to introduce the Hamiltonian formalism of theoretical mechanics for analysing motion in generic linear and non-linear dynamical systems, including particle accelerators. This framework allows the derivation…
We investigate the dynamics of two point-like particles through the third post-Newtonian (3PN) approximation of general relativity. The infinite self-field of each point-mass is regularized by means of Hadamard's concept of ``partie…
A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow, and can be expressed…
The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.
The thermodynamic equilibrium conditions for compact structures composed by mass varying particles are discussed assuming that the so-called dynamical mass behaves like an additional extensive thermodynamic degree of freedom. It then…
We analyze the convergence to equilibrium in a family of Kac-like kinetic equations in multiple space dimensions. These equations describe the change of the velocity distribution in a spatially homogeneous gas due to binary collisions…
A rotating continuum of particles attracted to each other by gravity may be modeled by the Euler-Poisson system. The existence of solutions is a very classical problem. Here it is proven that a curve of solutions exists, parametrized by the…
We investigate particle trajectories in equatorial flows with geophysical corrections caused by the earth's rotation. Particle trajectories in the flows are constructed using pairs of analytic functions defined over the labelling space used…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…
The anomalous (i.e. non-Gaussian) dynamics of particles subject to a deterministic acceleration and a series of 'random kicks' is studied. Based on an extension of the concept of continuous time random walks to position-velocity space, a…
We study the problem of motion of a relativistic, ideal elastic solid with free surface boundary by casting the equations in material form ("Lagrangian coordinates"). By applying a basic theorem due to Koch, we prove short-time existence…
The dynamics of a circular thin vortex ring and a sphere moving along the symmetry axis of the ring in an inviscid incompressible fluid is studied on the basis of Euler's equations of motion. The equations of motion for position and radius…
We present a new, simple, fast algorithm to numerically evolve disks of inelastically colliding particles surrounding a central star. Our algorithm adds negligible computational cost to the fastest existing collisionless N-body codes, and…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…