力学中守恒定律的统一公式

经典力学中与时空均匀性和各向同性相联系的有3个极为重要的守恒定律,本文证明,利用张量方法,可将这3个分立的守恒定律统一表述成一个公式。

对《机械能守恒定律》编排的思考

《机械能守恒定律》的设置是追求守恒量的研究源泉，体现了教材编写的一般思路，也是物理体系承上启下的关键。

Extended Conservation Laws of Some Nonlinear Partial Differential Equations

Self-adjoint theorem is introduced to match the corresponding functional of the given differential equations,and then Noether＇s theorem is used to determine the extended conservation laws of the original equations. Finally, as the application of the method, the conservation laws of Drinfel＇d-Sokolov-Wilson equation and Benjamin-Bona-Mahony equation are constructed.

Thermodynamic Analysis of Double Effect Absorption System along with Boiler and Cooling Tower

Many researchers have studied single and double effect absorption cycles based on first and second lows of thermodynamics But so far the relation of different parameters inside these cycles to the second law of thermodynamics in boiler and cooling tower has not been investigated. In this paper, a system comprised of a series flow double effect water-Lithium bromide absorption chiller, a boiler and a cooling tower is studied based on the first and second laws of thermodynamics, and also exergy analysis is investigated. For this purpose, mass and energy conservation laws governing the system are written, and coefficient of performance of the system, exergy destruction （loss） of each component and exergy efficiency have been calculated.

Global Structure Stability of Riemann Solution of Quasilinear Hyperbolic System of Conservation Law in Presence of Boundary:Shocks and Contact Discontinuities

In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the pieeewise C^1 solution u = u（t, x） of the problem, which can be regarded as a perturbation of the corresponding Riemann problem, is globally similar to that of the solution u = U（x/t） of the corresponding Riemann problem. The piecewise C^1 solution u = u（t, x） to this kind of problems is globally structure-stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities.

Thermodynamic Equilibrium

The arguments in this paper lead to a new definition of thermodynamic equilibrium that remedies the deficiencies of the current forms. This definition relates thermodynamic equilibrium to its physical causes and accounts for all factors that determine it for all types of equilibrium. Standard definitions of thermodynamic equilibrium are incomplete. They do not take account of all factors that determine such equilibriums, discuss the impediments which may prevent them being reached or relate the properties that define equilibriums to the physical reasons that determine them when impediments are present. The laws of thermodynamics determine the requirements for equilibrium. These laws arise from the physical behaviour of the molecules in molecular systems and are consequences of the conservation of energy, the energies of molecules, statistics, Newton＇s laws of motion, and the equi-partition of energy. The standard definition of thermodynamic equilibrium correctly defines equilibrium whenever impediments are not factors. The discussion demonstrates how impediments arise, accounts for their role in defining equilibrium and how they relate to the energies of molecules at the conditions of the system. The new definition applies to all types of equilibrium.

Noether symmetries of the nonconservative and nonholonomic systems on time scales

In this paper we give a new method to investigate Noether symmetries and conservation laws of nonconservative and nonholonomic mechanical systems on time scales , which unifies the Noether's theories of the two cases for the continuous and the discrete nonconservative and nonholonomic systems. Firstly, the exchanging relationships between the isochronous variation and the delta derivatives as well as the relationships between the isochronous variation and the total variation on time scales are obtained. Secondly, using the exchanging relationships, the Hamilton's principle is presented for nonconservative systems with delta derivatives and then the Lagrange equations of the systems are obtained. Thirdly, based on the quasi-invariance of Hamiltonian action of the systems under the infinitesimal transformations with respect to the time and generalized coordinates, the Noether's theorem and the conservation laws for nonconservative systems on time scales are given. Fourthly, the d'Alembert-Lagrange principle with delta derivatives is presented, and the Lagrange equations of nonholonomic systems with delta derivatives are obtained. In addition, the Noether's theorems and the conservation laws for nonholonomic systems on time scales are also obtained. Lastly, we present a new version of Noether's theorems for discrete systems. Several examples are given to illustrate the application of our results.

Feedback Stabilization for a Scalar Conservation Law with PID Boundary Control

This paper deals with a scalar conservation law in 1-D space dimension, and in particular, the focus is on the stability analysis for such an equation. The problem of feedback stabilization under proportional-integral-derivative(PID for short) boundary control is addressed. In the proportional-integral(PI for short) controller case, by spectral analysis, the authors provide a complete characterization of the set of stabilizing feedback parameters, and determine the corresponding time delay stability interval. Moreover, the stability of the equilibrium is discussed by Lyapunov function techniques, and by this approach the exponential stability when a damping term is added to the classical PI controller scheme is proved. Also, based on Pontryagin results on stability for quasipolynomials, it is shown that the closed-loop system sub ject to PID control is always unstable.

Modified Nonlinear Model of Arcsin-Electrodynamics

A new modified model of nonlinear arcsin-electrodynamics with two parameters is proposed and analyzed.We obtain the corrections to the Coulomb law. The effect of vacuum birefringence takes place when the external constant magnetic field is present. We calculate indices of refraction for two perpendicular polarizations of electromagnetic waves and estimate bounds on the parameter γ from the BMV and PVLAS experiments. It is shown that the electric field of a point-like charge is finite at the origin. We calculate the finite static electric energy of point-like particles and demonstrate that the electron mass can have the pure electromagnetic nature. The symmetrical Belinfante energy-momentum tensor and dilatation current are found. We show that the dilatation symmetry and dual symmetry are broken in the model suggested. We have investigated the gauge covariant quantization of the nonlinear electrodynamics fields as well as the gauge fixing approach based on Dirac's brackets.

An Energy Stable Monolithic Eulerian Fluid-Structure Numerical Scheme

The conservation laws of continuum mechanics, written in an Eulerian frame,do not distinguish fluids and solids, except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials of energy for hyperelastic solids. By taking the velocities as unknown monolithic methods for fluid structure interactions(FSI for short) are built. In this paper such a formulation is analysed when the solid is compressible and the fluid is incompressible. The idea is not new but the progress of mesh generators and numerical schemes like the Characteristics-Galerkin method render this approach feasible and reasonably robust. In this paper the method and its discretisation are presented, stability is discussed through an energy estimate. A numerical section discusses implementation issues and presents a few simple tests.

Auxiliary Lagrangian and Conservation Laws for a Wave Equation Incorporating Dissipation

In this work we study the Lagrangian and the conservation laws for a wave equation with a dissipative source. Using semi-inverse method, we show that the equation possesses a nonlocal Lagrangian with an auxiliary function.As a result, from a modified Noether's theorem and the nonclassical Noether symmetry generators, we construct some conservation laws for this equation, which are different from the ones obtained by Ibragimov's theorem in [Y. Wang and L. Wei, Abstr. App. Anal. 2013(2013) 407908]. The results show that our method work for arbitrary functions f(u)and g(u) rather than special ones.