This paper studies the asymptotic stability of traveling relaxation shock profiles for hyperbolic systems of conservation laws. Under a stability condition of subcharacteristic type the large time relaxation dynamics on the level of shocks is shown to be determined by the equilibrium conservation laws. The proof is due to the energy principle, using the weighted norms, the interaction of waves ...

The conservation of energy, mass, and momentum are three governing laws physics that regularly uttered in teaching engineering courses. Mechanical energies the form kinetic potential forms most common energy dynamics. Fluid flow relating to pressure, velocity, elevation, fluid friction, pump, turbine covered In thermodynamics course, first law deals with heat work can alter internal a system. a...

The process of coagulation is associated with scalar conservation laws, where the adhesion particle dynamics results from shock waves. Conversely, the fragmentation of a massive particle into a number of smaller ones, or into a continuous (dust) distribution, is associated with refraction waves. It is generally agreed that a reversible solution of a conservation law cannot include neither shock...

We outline a story line that introduces Newtonian mechanics by employing conservation of energy to predict the motion of a particle in a one-dimensional potential. We show that incorporating constraints and constants of the motion into the energy expression allows us to analyze more complicated systems. A heuristic transition embeds kinetic and potential energy into the still more powerful prin...

In this paper we prove in a rigorous mathematical way (using the Clifford bundle formalism) that the energies and momenta of two distinct and arbitrary free Maxwell fields (of finite energies and momenta) that are superposed are additive and thus that there is no incompatibility between the principle of superposition of fields and the principle of energy-momentum conservation, contrary to some ...

Nonequilibrium statistical mechanics helps to estimate corrections to the entropy and energy of the fluid with heat flux in terms of the nonequilibrium distribution function, f. This leads to the coefficients of wave model of heat: relaxation time, propagation speed and thermal inertia. With these data a quadratic Lagrangian and a variational principle of Hamilton’s type follows for the fluid i...

The THǫμ formalism was developed to study nonmetric theories of gravitation. In this letter we show that theories that violate Local Lorentz Invariance (LLI) or Local Position Invariance (LPI) also violate charge conservation. Using upper bounds on this violation we can put very stringent limits to violations of Einstein Equivalence Principle (EEP). These limits, in turn, severely restrict stri...