Related papers: Euler-Lagrangian dynamics to the physical interpre…
This paper expands on previous work to derive and motivate the Lagrangian formulation of field theories. In the process, we take three deliberate steps. First, we give the definition of the action and derive Euler-Lagrange equations for…
Molecular dynamics (MD) simulations allow investigating the structural dynamics of biomolecular systems with unrivaled time and space resolution. However, in order to compensate for the inaccuracies of the utilized empirical force fields,…
A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction…
Realistic models of physical world rely on differentiable symmetries that, in turn, correspond to conservation laws. Recent works on Lagrangian and Hamiltonian neural networks show that the underlying symmetries of a system can be easily…
We apply the physics-learning duality to molecular systems by complementing the physical description of interacting particles with a dual learning description, where each particle is modeled as an agent minimizing a loss function. In the…
The expansion of a classical Hamilton formalism consisting in adaptation of it to describe the nonequilibrium systems is offered. Expansion is obtained by construction of formalism on the basis of the dynamics equation of the equilibrium…
An interplay between electromagnetic and gravitational interactions is studied with particular emphasis on the particles mass dependence of amplitudes. The cancellations between diagrams due to the gauge invarinace are explicitly…
A discrete theory for implicit nonholonomic Lagrangian systems undergoing elastic collisions is developed. It is based on the discrete Lagrange-d'Alembert-Pontryagin variational principle and the dynamical equations thus obtained are the…
In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently…
This is a survey highlighting several recent results concerning well/ill posedness of the Euler system of gas dynamics. Solutions of the system are identified as limits of consistent approximations generated either by physically more…
The Heisenberg dynamics of the energy, momentum, and particle densities for fermions with short-range pair interactions is shown to converge to the compressible Euler equations in the hydrodynamic limit. The pressure function is given by…
A new theory for determining the mass function of cosmic structures is presented. It relies on a realistic treatment of collapse dynamics. Gravitational collapse is analyzed in the Lagrangian perturbative framework. Lagrangian perturbations…
A new method is proposed for switching on interactions that are compatible with global symmetries and conservation laws of the original free theory. The method is applied to the control of stability in Lagrangian and non-Lagrangian theories…
In this paper, we show how to study the evolution of a system, given imprecise knowledge about the state of the system and the dynamics laws. Our approach is based on Fuzzy Set Theory, and it will be shown that the \emph{Fuzzy Dynamics} of…
In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating…
We consider non-Lorentzian expansions, Galilean and Carrollian, of the Lorentz force equation in which both the particle position and the electro-magnetic field are expanded. There are two well-known limits in the case of a constant field,…
The Lagrangian theory of structure formation in cosmological fluids, restricted to the matter model ``dust'', provides successful models of large-scale structure in the Universe in the laminar regime, i.e., where the fluid flow is…
We consider a new variant of cosmological perturbation theory that has been designed specifically to include non-linear density contrasts on scales 100 Mpc, while still allowing for linear fluctuations on larger scales. This theory is used…
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…
The present paper is devoted to the group classification of magnetogasdynamics equations in which dependent variables in Euler coordinates depend on time and two spatial coordinates. It is assumed that the continuum is inviscid and…