In keeping with the current interest in tests of conservation laws, we collect together a Table of experimental limits on all weak and electromagnetic decays, mass differences, and moments, and on a few reactions, whose observation would violate conservation laws. The Table is given only in the full Review of Particle Physics, not in the Particle Physics Booklet. For the benefit of Booklet read...

In this paper we construct fundamental solutions of a scalar conservation law in one space dimension. These source-type solutions are well known for a convex case and hence our focus is on a general non-convex case which may have a finite number of inflection points. Signed fundamental solutions are constructed first and then under an extra hypothesis on nonnegativity of the flux two parameter ...

In this paper, we apply the invariant region theory [1] and the compensated compactness method [2] to study the singular limits of stiff relaxation and dominant diffusion for the Cauchy problem of a system of quadratic flux and the Le Roux system, and obtain the convergence of the solutions to the equilibrium states of these systems.

We give a relatively simple algorithm to do Hodge decomposition on the variational bicomplex based on the imbedding of the total differentiation operator in a Heisenberg algebra. The method is illustrated with several examples taken from the literature. It has been implemented by the authors in the computer algebra system Form [Ver91].

If X is a discrete abelian group and A a finite set, then a cellular automaton (CA) is a continuous map F : A −→ A that commutes with all X-shifts. If φ : A −→ R, then, for any a ∈ A, we define Σφ(a) = ∑ x∈X φ(ax) (if finite); φ is conserved by F if Σφ is constant under the action of F. We characterize such conservation laws in several ways, deriving both theoretical consequences and practical ...

We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The derivations are based on the principle of relativity and on its direct consequence, the addition law of relativistic velocities.

In recent years a variety of high{order schemes for the numerical solution of conservation laws has been developed. In general, these numerical methods involve expensive ux evaluations in order to resolve discontinuities accurately. But in large parts of the ow domain the solution is smooth. Hence in these regions an unexpen-sive nite diierence scheme suuces. In order to reduce the number of ex...

The objective of this investigation is the establishment of governing balance and conservation laws in elastodynamics. The feature of the approach employed here consists in placing time on the same level as the space coordinates, as is done in the theory of relativity, i.e., pursuing a 4 · 4 formalism. Both the Lagrangian and the Eulerian descriptions of the postulated Lagrangian function are f...

It has been known for some time that for a large class of nonlinear field theories in Minkowski space with two-dimensional target space the complex eikonal equation defines integrable submodels with infinitely many conservation laws. These conservation laws are related to the area-preserving diffeomorphisms on target space. Here we demonstrate that for all these theories there exists, in fact, ...

Some aspects of recent developments in the study of the Euler equations for compressible fluids and related hyperbolic conservation laws are analyzed and surveyed. Basic features and phenomena including convex entropy, symmetrization, hyperbolicity, genuine nonlinearity, singularities, BV bound, concentration, and cavitation are exhibited. Global well-posedness for discontinuous solutions, incl...