Related papers: Lagrangian coordinates for the sticky particle sys…
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…
We study a stochastic Hamiltonian system of $N$ particles with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical…
The one-dimensional shallow water equations in Eulerian and Lagrangian coordinates are considered. It is shown the relationship between symmetries and conservation laws in Lagrangian (potential) coordinates and symmetries and conservation…
We consider a degenerate stochastic differential equation that has a sticky point in the Markov process sense. We prove that weak existence and weak uniqueness hold, but that pathwise uniqueness does not hold nor does a strong solution…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
We are interested in a kinetic equation intended to describe the interaction of particles with their environment. The environment is modeled by a collection of local vibrational degrees of freedom. We establish the existence of weak…
This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…
We will prove that, in general, a system formed by several particles moving along relativistic trajectories can not be described by a mechanical system. The contradiction that leads to the previous assertion is due to the fact that a…
In this paper a new approach is proposed to quantize mechanical systems whose equations of motion can not be put into Hamiltonian form. This approach is based on a new type of variational principle, which is adopted to a describe a…
We show that the Lagrangian for interacting nonrelativistic particles can be coupled to an external gauge field and metric tensor in a way that exhibits a nonrelativistic version of general coordinate invariance. We explore the consequences…
A manifestly relativistic-invariant Lellouch-L\"uscher formalism for the three-particle decays is proposed. Similarly to ref.[1], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance…
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…
It is now known that the equations of motion for the contact point during peeling of an adhesive tape mounted on a roll introduced earlier are singular and do not support dynamical jumps across the two stable branches of the peel force…
The Standard Model of particle physics was established based on the equivalence principle and gauge invariance. The Lagrangians were built upon experimental data demonstrating the violation of discrete symmetries together with ideas of…
Around mid-1970s W. M. Tulczyjew discovered an approach which brings the two formalisms under a common geometric roof: the dynamics of a particle with configuration space $X$ is determined by a Lagrangian submanifold $D$ of $TT^*X$ (the…
Pluri-Lagrangian systems are variational systems with the multi-dimensional consistency property. This notion has its roots in the theory of pluriharmonic functions, in the Z-invariant models of statistical mechanics, in the theory of…
Understanding and predicting the dynamical properties of systems involving dry friction is a major concern in physics and engineering. It abounds in many mechanical processes, from the sound produced by a violin to the screeching of chalk…
In a previous work we considered a two-dimensional lattice of particles and calculated its time evolution by using an interaction law based on the spatial position of the particles themselves. The model reproduced the behaviour of…
The sticking of a soft polystyrene colloidal particle to a planar glass plate was studied by a microrheological technique using an optical tweezer to trap the particle and a piezoelectric-stage to position the plate and to sinusoidally…
Stochastic thermodynamics provides a framework for describing small systems like colloids or biomolecules driven out of equilibrium but still in contact with a heat bath. Both, a first-law like energy balance involving exchanged heat and…