This paper presents recent work on connections between symmetries and conservation laws. After reviewing Noether’s theorem and its limitations, we present the Direct Construction Method to show how to find directly the conservation laws for any given system of differential equations. This method yields the multipliers for conservation laws as well as an integral formula for corresponding conser...

As a necessary component, regenerator plays an important role in the refrigeration performance of the pulse tube refrigerator. The objective of this research is to investigate the flow characteristics in a porous regenerator of the pulse tube refrigerators, subjected to oscillating flow. The hydrodynamic and thermal behavior of the regenerator is investigated by considering porous media approac...

This paper established a physical axiom system. By the axiom system we can derive important physical laws such as momentum conservation law, Newton’s second law, Newton’s law of gravity, Schrödinger equation and Maxwell’s equations, simplified existing physical theories and explain some physical phenomenons those unresolved by traditional physical theories. We can also derive Schwarzschild solu...

Guilhaumon et al. (1) use an extensive dataset to determine the most appropriate functional form for species–area relationships (SARs) among terrestrial plants and vertebrates. Their discovery that the traditional power-law relationship is not the most appropriate model in the majority of ecoregions raises compelling macroecological questions. However, their subsequent conservation analyses are...

In this paper we discuss the conservation of wave action under numerical discretization by variational and multisymplectic methods. Both the general wave action conservation defined with respect to a smooth, periodic, one-parameter ensemble of flow realizations and the specific wave action based on an approximated and averaged Lagrangian are addressed in the numerical context. It is found that ...

homogeneous locally neutral medium,we have two independent current conservation laws: one law applies to the freecharge current i and another one applies to the displacement current i. Note that in a homogeneous medium i is not necessarily negligible, but the application of the current conservation law on i can be done independently of the existence of i because the two laws are independent. In...

A conservation law and stability, recovering phenomena and characteristic patterns of a nonlinear dynamical system have been studied and applied to biological and ecological systems. In our previous study, we proposed a system of symmetric 2n-dimensional conserved nonlinear differential equations with external perturbations. In this paper, competitive systems described by 2-dimensional nonlinea...

A general kinematic wave model for flood propagation is presented in the form of a scalar conservation law. The corresponding flux function is convex or nearly convex for regular cross-sections of the river. In the presence of pronounced irregularities, however, convexity may fail. Qualitative consequences of the shape of the flux function for typical irregularities are discussed, particularly ...

In this paper we consider bounded weak solutions u of scalar conservation laws, not necessarily of class BV , defined in a subset Ω ⊂ R+×R. We define a strong notion of trace at the boundary of Ω reached by L convergence for a large class of functionals of u, G(u). Those functionals G depend on the flux function of the conservation law and on the boundary of Ω. The result holds for general flux...