Related papers: Lagrangian coordinates for the sticky particle sys…
We propose a new classical approach for describing a system composed of $n$ interacting particles with variable mass connected by a single field with no predefined form ($n$-VMVF systems). Instead of assuming any particular nature or…
Scalar conservation laws in one space variable allow a Lagrangian (particle path) formulation. The Lagrangian trajectory in the infinite-dimensional group of diffeomorphisms on the physical space can be written as a system of conservation…
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\'e map provides a splitting of the phase space into regions where…
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…
We define a Chern- Simons Lagrangian for a system of planar particles topologically interacting at a distance. The anyon model appears as a particular case where all the particles are identical. We propose exact N-body eigenstates, set up a…
The Hamiltonian formulation for the mechanical systems with reparametrization-invariant Lagrangians, depending on the worldline external curvatures is given, which is based on the use of moving frame. A complete sets of constraints are…
Particles of low velocity, travelling without dissipation in a superfluid, can interact and emit sound when they collide. We propose a minimal model in which the equations of motion of the particles, including a short-range repulsive force,…
The consequences of coupling of the torsion (highest curvature) term to the Lagrangian of a massive spinless particle in four-dimensional space-time are studied. It is shown that the modified system remains spinless and possesses extended…
The Lagrange--Poincar\'e equations for the mechanical system describing the motion of a scalar particle on a Riemannian manifold with a given free and isometric action of a compact Lie group is obtained. In an arising principle fibre…
The dynamics of supercooled liquid and glassy systems are usually studied within the Lagrangian representation, in which the positions and velocities of distinguishable interacting particles are followed. Within this representation,…
In this paper, we study the clustering of inertial particles using a periodic kinematic simulation. The systematic Lagrangian tracking of particles makes it possible to identify the particles' clustering patterns for different values of…
Inspired by a Chern-Simons description of 2+1D gravity coupled to point particles we propose a new Lagrangian of a multiparticle system living in $\kappa$-Minkowski/$\kappa$-Poincar\'e spacetime. We derive the dynamics of interacting…
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…
We extend the previous work of Olivier Costa de Beauregard regarding the isomorphism between the equation describing the motion of relativistic point particles and the equation describing the static equilibrium of classical elastic strings,…
We have investigated the non-equilibrium nature of a lattice gas system consisting of a regular lattice of charged particles driven by an external electric field. For a big system, an exact solution cannot be obtained using a master…
The Lagrange--Poincar\'{e} equations for a mechanical system which describes the interaction of two scalar particles that move on a special Riemannian manifold, consisting of the product of two manifolds, the total space of a principal…
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
Infinite-dimensional stochastic differential equations (ISDEs) describing systems with an infinite number of particles are considered. Each particle undergoes a L\'evy process, and the interaction between particles is determined by the…
We introduce a new Lagrangian particle tracking algorithm that tracks particles in three dimensions to separations between trajectories approaching contact. The algorithm also detects low Weber number binary collisions that result in…
Here we investigate the Cauchy problem for the inhomogeneous Navier-Stokes equations in the whole $n$-dimensional space. Under some smallness assumption on the data, we show the existence of global-in-time unique solutions in a critical…