Related papers: Euler-Lagrangian dynamics to the physical interpre…
The Liouville equation is of fundamental importance in the derivation of continuum models for physical systems which are approximated by interacting particles. However, when particles undergo instantaneous interactions such as collisions,…
The aim of the present paper is to introduce and to discuss inconsistencies errors that may arise when Eulerian and Lagrangian models are coupled for the simulations of turbulent poly-dispersed two-phase flows. In these hydrid models, two…
Motivated by theoretical studies of gravitational clustering in the Universe, we compute propagators (response functions) in the adhesion model. This model, which is able to reproduce the skeleton of the cosmic web and includes nonlinear…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between…
We consider classical closed string with $N$ particles inside. Taking collisions into account, we consider dynamics of this $N$-particle system under the influence of constant external force. We get Euler equations and explicit formula for…
We make use of the Lagrangian description of fluid motion to highlight certain features in the context of spacetime geometry as emergent phenomena in fluid systems. We find by using Lagrangian Perturbation Theory (LPT), that not all kind of…
The creation of large scale magnetic fields is studied in an inflationary universe where electrodynamics is assumed to be nonlinear. After inflation ends electrodynamics becomes linear and thus the description of reheating and the…
The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative…
We study the dynamics of two particles that interact only when in contact. In this sense, although not in every particular, the interactions mimic those in granular materials. The detailed solution of the dynamics allows an analysis of the…
The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling - from the…
A novel approach to account for hard-body interactions in (overdamped) Brownian dynamics simulations is proposed for systems with non-vanishing force fields. The scheme exploits the analytically known transition probability for a Brownian…
By introducing the divergence of a vector potential into the Lagrangian, a Lagrangian framework is developed to incorporate surface energy into elasticity. Besides the Euler-Lagrange equation and natural boundary condition, a new boundary…
A relation between variational principles for equations of continuum mechanics in Eulerian and Lagrangian descriptions is considered. It is shown that for a system of differential equations in Eulerian variables corresponding Lagrangian…
Using effective-lagrangian techniques we perform a systematic survey of the lowest-dimension effective interactions through which heavy physics might manifest itself in present experiments. We do not restrict ourselves to special classes of…
We explore the relationship between mechanical systems describing the motion of a particle with the mechanical systems describing a continuous medium. More specifically, we will study how the so-called intermediate integrals or fields of…
We consider relativistic charged particle dynamics and relativistic magnetohydrodynamics using symplectic structures and actions given in terms of co-adjoint orbits of the Poincar\'e group. The particle case is meant to clarify some points…
Einstein's famous equation $E_{\rm rest}=mc^2$ for the rest energy of a system with mass $m$ requires that the internal energy of the system be included in $m$. Pursuing this idea using Lagrangian and Hamiltonian dynamics yields a…
Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…