This work is concerned with the Lagrangian formulation of electromagnetic fields. Lagrange differential equation for continuous, nondispersive media is employed. The Lagrangian density for electromagnetic fields is extended to derive jose saletan classical dynamics pdf four Maxwell’s equations by means of electric and magnetic potentials. For the first time, ohmic losses for time and space variant fields are included.
Therefore, a dissipation density function with time dependent and gradient dependent terms is developed. Finally, two examples demonstrate the advantage of describing interacting physical systems by a single Lagrangian density. Check if you have access through your login credentials or your institution. The last decades witnessed a renewal of interest in the Burgers equation.
Much activities focused on extensions of the original one-dimensional pressureless model introduced in the thirties by the Dutch scientist J. Burgers equation with random initial conditions or random forcing. Such work was frequently motivated by new emerging applications of Burgers model to statistical physics, cosmology, and fluid dynamics. Also Burgers turbulence appeared as one of the simplest instances of a nonlinear system out of equilibrium. The study of random Lagrangian systems, of stochastic partial differential equations and their invariant measures, the theory of dynamical systems, the applications of field theory to the understanding of dissipative anomalies and of multiscaling in hydrodynamic turbulence have benefited significantly from progress in Burgers turbulence. The aim of this review is to give a unified view of selected work stemming from these rather diverse disciplines. We are hiring PHP developers.