4 Phenomenologi al Equation Closure. 7 4 1 Examples 8 Example: River Flow 8 Quasi-equilibrium approximation 8 Example: TraÆ Flow 9 Example: Heat Condu tion 10 Fi k's Law 10 Thermal ondu tivity, difusivity, heat equation 10 Example: Granular Flow 11 Example: Invis id Fluid Flow 12 In ompressible Euler Equations 12 In ompressible Navier-Stokes Equations 12 Gas Dynami s 13 Equation of State 13 Ise...

We develop a conservation law for a multi-class GI/GI/1 queue operating under a general work-conserving scheduling discipline. For single-class single-server queues, conservation laws have been obtained for both nonanticipating and anticipating disciplines with general service time distributions. For multi-class single-server queues, conservation laws have been obtained for (i) nonanticipating ...

In this article we illustrate a new method to extend local wellposedness results for dispersive equations to global ones. The main ingredient of this method is the definition of a family of what we call almost conservation laws. In particular we analyze the Korteweg-de Vries initial value problem and we illustrate in general terms how the “algorithm” that we use to formally generate almost cons...

In 1994, Lions, Perthame and Tadmor conjectured the maximal smoothing effect for multidimensional scalar conservation laws in Sobolev spaces. For strictly smooth convex flux and the one-dimensional case we detail the proof of this conjecture in the framework of Sobolev fractional spaces W s,1, and in fractional BV spaces: BV s. The BV s smoothing effect is more precise and optimal. It implies t...

I discuss recent progress in low-energy tests of symmetries and conservation laws, including parity nonconservation in atoms and nuclei, electric dipole moment tests of time-reversal invariance, β-decay correlation studies, and decays violating separate (family) and total lepton number.

Conservation laws are first order systems of quasilinear partial differential equations in divergence form; they express the balance laws of continuum physics for media with "elastic" response, in which internal dissipation is neglected. The absence of internal dissipation is manifested in the emergence of solutions with jump discontinuities across manifolds of codimension one, representing, in...

Conservation laws, i.e. conserved quantities along Euler–Lagrange extremals, which are obtained on the basis of Noether’s theorem, play an prominent role in mathematical analysis and physical applications. In this paper we present a general and constructive method to obtain conserved quantities along the Pontryagin extremals of optimal control problems, which are invariant under a family of tra...

A 1D Reversible Cellular Automata (RCA) with forward and backward radius2 neighborhoods is called Rectangular. It was previously conjectured that the conservation laws in 1D Rectangular RCA can be described as linear combinations of independent constant-speed flows to the right or to the left. This is indeed the case; so is a similar statement about a more general class of Rectangular RCA in an...

In this paper we address the questions of the convergence rate for approximate solutions to conservation laws with piecewise smooth solutions in a weighted W 1,1 space. Convergence rate for the derivative of the approximate solutions is established under the assumption that a weak pointwise-error estimate is given. In other words, we are able to convert weak pointwise-error estimates to optimal...