基于能量守恒框架下的波动力学理论研究

基于波动力学的基本概念,提出了在能量守恒框架下建立波动力学方程的新思路与方法.首先,回顾了用牛顿第二定律推导波动力学方程,同时回顾并分析了利用Hamilton变分原理,推导了在连续介质中的Lagrange方程、Hamilton正则方程,以及相应的波动力学方程;其次,在能量守恒的框架下,建立了连续介质的Lagrange方程、Hamilton正则方程和波动力学方程,并证明其结果与利用经典力学推导的结果的一致性,特别地,澄清了用Hamilton变分原理建立保守系统下连续介质的Lagrange方程和Hamilton正则方程时在边界条件应用时的一些模糊认识.在能量守恒框架下建立一系列动力学方程,为我们在不涉及泛函求极值的变分原理等基础上刻画和表述复杂介质中波动现象的演化规律提供了另一种途径,也深入探讨了最小作用原理的物理本质.最后,在能量守恒的框架下给出了建立黏弹性介质中的波动力学微分方程的应用.

Mechanism and kinetics analysis of AlN combustion synthesis

Mechanism of AlN combustion synthesis was studied by DSC analysis and “quenching” experiment of combustion wave. In preheating region, Al powder melted at 660 ℃ and became spherical because of surface tension. In reaction region, Al volatilized rapidly at 1 000 ℃ and Al vapor reacted with N2 to form AlN, which nucleated and grew on the surface of AlN formed precedently as a diluent. Based on the experiment analysis, kinetics equations and modeling were established. Analysis showed the dramatic effect of temperature, aluminum particle size and nitrogen pressure on the reaction speed.

Composition Estimation of Reactive Batch Distillation by Using Adaptive Neuro-Fuzzy Inference System

Composition estimation plays very important role in plant operation and control.Extended Kalman filter(EKF) is one of the most common estimators,which has been used in composition estimation of reactive batch distillation,but its performance is heavily dependent on the thermodynamic modeling of vapor-liquid equilibrium,which is difficult to initialize and tune.In this paper an inferential state estimation scheme based on adaptive neuro-fuzzy inference system(ANFIS) ,which is a model base estimator,is employed for composition estimation by using temperature measurements in multicomponent reactive batch distillation.The state estimator is supported by data from a complete dynamic model that includes component and energy balance equations accompanied with thermodynamic relations and reaction kinetics.The mathematical model is verified by pilot plant data.The simulation results show that the ANFIS estimator provides reliable and accurate estimation for component concentrations in reactive batch distillation.The estimated states form a basis for improving the performance of reactive batch distillation either through decision making of an operator or through an automatic closed-loop control scheme.

Fractional Fourier Transformation for Quantum Mechanical Wave Functions Studied by Virtue of IWOP Technique

Starting from the optical fractional Fourier transform (FFT) and using the technique of integration withinan ordered product of operators we establish a formalism of FFT for quantum mechanical wave functions. In doing so, theessence of FFT can be seen more clearly, and the FFT of some wave functions can be derived more directly and concisely.We also point out that different FFT integral kernels correspond to different quantum mechanical representations. Theyare generalized FFT. The relationship between the FFT and the rotated Wigner operator is studied by virtue of theWeyl ordered form of the Wigner operator.

Soliton Solutions in Three-Component Bose-Einstein Condensates

We obtain soliton and plane wave solutions for the coupled nonlinear Schrotinger equations, which describe the dynamics of the three-component Bose-Einstein condensates by using the Hirota method. Meanwhile we find that the system which has attractive atomic interaction will only possess a shape changing （inelastic） collision property due to intensity redistribution in the absence of the spin-exchange interaction. As a discussed example, we investigate the one-soliton, two-soliton solutions and collisional effects between bright two-soliotn solution, which lead to the intensity redistribu tion.

Research on the Correlation of the Fluctuating Density Gradient of the Compressible Flows

This work is to study a role of the fluctuating density gradient in the compressible flows tbr the computational fluid dynamics （CFD）. A new anisotropy tensor with the fluctuating density gradient is introduced, and is used for an invariant modeling technique to model the turbulent density gradient correlation equation derived from the continuity equation. The modeling equation is decomposed into three groups proportional to the mean velocity, proportional to the mean strain rate, and proportional to the mean density. The characteristics of the correlation in a wake are extracted from the results by the two dimensional direct simulation, and shows the strong correlation with the vortices in the wake near the body. Thus, it can be concluded that the correlation of the density gradient is a significant parameter to describe the quick generation of the turbulent property in the compressible flows.

On the Kinetic Formulation of a Nonlinear Hyperbolic Variational Wave Equation

Motivated by [3], [4] and [5], we present the kinetic formulation of a nonlinear variational wave equation corresponding to some specific weak solutions . This equation arises from studies in nematic liquid crystals, long wave on a dipole chain and a few other fields.

The form-invariance of wave equations without requiring a priori relations between field variables

According to the principle of relativity,the equations describing the laws of physics should have the same forms in all admissible frames of reference,i.e.,form-invariance is an intrinsic property of correct wave equations.However,so far in the design of metamaterials by transformation methods,the form-invariance is always proved by using certain relations between field variables before and after coordinate transformation.The main contribution of this paper is to give general proofs of form-invariance of electromagnetic,sound and elastic wave equations in the global Cartesian coordinate system without using any assumption of the relation between field variables.The results show that electromagnetic wave equations and sound wave equations are intrinsically form-invariant,but traditional elastodynamic equations are not.As a by-product,one can naturally obtain new elastodynamic equations in the time domain that are locally accurate to describe the elastic wave propagation in inhomogeneous media.The validity of these new equations is demonstrated by some numerical simulations of a perfect elastic wave rotator and an approximate elastic wave cloak.These findings are important for solving inverse scattering problems in many fields such as seismology,nondestructive evaluation and metamaterials.

Cavitation shedding dynamics around a hydrofoil simulated using a filter-based density corrected model

The unsteady turbulent cloud cavitation around a NACA66 hydrofoil was simulated using the filter-based density corrected model(FBDCM). The cloud cavitation was treated as a homogeneous liquid-vapor mixture and the effects of turbulent eddy viscosity were reduced in cavitation regions near the hydrofoil and in the wake. The numerical results(in terms of the vapor shedding structure and transient pressure pulsation due to cavitation evolution) agree well with the available experimental data, showing the validity of the FBDCM method. Furthermore, the interaction of vortex and cavitation was analyzed based on the vorticity transport equation, revealing that the cavitation evolution has a strong connection with vortex dynamics. A detailed analysis shows that the cavitation could promote the vortex production and flow unsteadiness by the dilatation and baroclinic torque terms in the vorticity transport equation.

Shock Wave in Supersonic Moist Air Jet for a Low Pressure Ratio

In the present study,a computational fluid dynamics work was performed to investigate the occurrence of the shock wave by condensation in supersonic moist air jet.The unsteady,compressible axisymmetric Navier-Stokes equation is solved by TVD(Total Variation Diminishing) scheme in this study.The numerical simulations have been performed for low pressure ratio and various humidities.The results show the occurrence of the shock wave in supersonic moist air jet for a low pressure ratio when Mach disk does not occur,depending on humidity of the air.

A Theoretical Model to Explain the Mechanism of Electromagnetic Wave Propagation Along Cylindrical Micelles

A theoretical model to explain the mechanism of the electromagnetic wave propagation in the quasi two-dimensional layer of counterions adjacent to the surface of a charged cylindrical membrane is presented. By using Maxwell and hydrodynamic equations with appropriate boundary conditions, general expression of dispersion relation is obtained for the electromagnetic wave with mixed TE and TM modes.

Influence of Non-Maxwellian Particles on Dust Acoustic Waves in a Dusty Magnetized Plasma

In this paper an investigation into dust acoustic sofitary waves （DASWs） in the presence of superthermM electrons and ions in a magnetized plasma with cold dust gains and trapped electrons is discussed. The dynamic of both electrons and ions is simulated by the generalized Lorentzian （κ） distribution function （DF）. The dust grains are cold and their dynamics are studied by hydrodynamic equations. The basic set of fluid equations is reduced to modified Korteweg-de Vries （mKdV） equation using Reductive Perturbation Theory （RPT）. Two types of solitary waves, fast and slow dust acoustic soliton （DAS） exist in this plasma. Caiculations reveal that compressive solitary structures are possibly propagated in the plasma where dust grains are negatively （or positively） charged. The properties of DASs are also investigated numerically.

Stability of planar diffusion wave for nonlinear evolution equation Dedicated to the NSFC-CNRS Chinese-French summer institute on fluid mechanics in 2010

It is known that the one-dimensional nonlinear heat equation ut ： f（u）x1x1, f＇（u） 〉 0, u（±∞, t） ： u, u＋ ≠ u- has a unique self-similar solution u（x1/√1＋t）. In multi-dimensional space, （x1/√1＋t） is called a planar diffusion wave. In the first part of the present paper, it is shown that under some smallness conditions, such a planar diffusion wave is nonlinearly stable for the nonlinear heat equation： ut -△f（u） = 0, x ∈ R^n. The optimal time decay rate is obtained. In the second part of this paper, it is further shown that this planar diffusion wave is still nonlinearly stable for the quasilinear wave equation with damping： utt ＋ ut - △f（u） = 0, x ∈ R^n. The time decay rate is also obtained. The proofs are given by an elementary energy method.

Localization and shock waves in curved manifolds

The investigation of the interplay between geometry and nonlinearity may open the road to the control of extreme waves. We study three-dimensional localization and dispersive shocks in a bent cigar shaped potential by the nonlinear Schro¨ dinger equation. At high bending and high nonlinearity, topological trapping is frustrated by the generation of curved wave-breaking. Four-dimensional parallel simulations confirm the theoretical model. This work may contribute to novel devices based on geometrically constrained highly nonlinear dynamics and tests and analogs of fundamental physical theories in curved space.

Dynamic Response of Warship Structure under Air Non-contact Explosion

The ship hull is simplified as a free beam with varying sections. Based on hydroelasticity and explosion mechanics theory,mechanical model and kinetic equation for hull girder vibration under non-contact explosion are established. The equation is solved by Wilson-θ algorithm. On the basis of the above principles,a structure kinetics analysis program is compiled. The dynamic response of supposed warship under air explosion is calculated conveniently and quickly. Under the explosion condition designed in the paper,the positive pressure period of non-contact explosion wave is much less than the natural periods of the first four modes of hull girder and the resonance of ship girder overall vibration can be avoided. The ratio of midship maximum moment to ultimate bearing strength under non-contact explosion accelerates with the increment of impact factor.