基于广义交替数值通量的局部间断Galerkin方法求解二维波动方程

波的传播往往在复杂的地质结构中进行,如何有效地求解非均匀介质中的波动方程一直是研究的热点.本文将局部间断Galekin(local discontinuous Galerkin, LDG)方法引入到数值求解波动方程中.首先引入辅助变量,将二阶波动方程写成一阶偏微分方程组,然后对相应的线性化波动方程和伴随方程构造间断Galerkin格式;为了保证离散格式满足能量守恒,在单元边界上选取广义交替数值通量,理论证明该方法满足能量守恒性.在时间离散上,采用指数积分因子方法,为了提高计算效率,应用Krylov子空间方法近似指数矩阵与向量的乘积.数值实验中给出了带有精确解的算例,验证了LDG方法的数值精度和能量守恒性;此外,也考虑了非均匀介质和复杂计算区域的计算,结果表明LDG方法适合模拟具有复杂结构和多尺度结构介质中的传播.     

A study of Boltzmann energy equations

The formulation, theory, and numerical resolution of physical Boltzmann energy equations are considered. These equations model the time evolution of the energy distribution function for spatially homogeneous isotropic systems of identical particles. Precise statements of the conservation laws and the H-theorem are made. The possibility of solving such equations in Hilbert space settings is considered both from a theoretical and from a computational viewpoint. The structures of the kernels for a variety of physical models are analyzed in detail, and point. The structures of the kernels for a variety of physical models are analyzed in detail, and a new class of models is proposed which is simple yet has all the right physical features. Numerical results show that enhancement phenomena probably occur for a range of different models. In an appendix the connection through an Abel transform for the Bobylev, Krook, and Wu (BKW) and Tjon and Wu (TW) equations is demonstrated by direct integration.     

Modeling three-dimensional elastic wave propagation in circular cylindrical structures using a finite-difference approach

Wave propagation along circular cylindrical structures is important for nondestructive-testing applications and shocks in tubes. To simulate elastic wave propagation phenomena in such structures the governing equations in cylindrical coordinates are solved numerically. To reduce the required amount of computer memory and the computational time, the stress components are eliminated in the equilibrium equations. In the resulting coupled partial differential equations, in which only the three displacement components are involved, the derivatives with respect to spatial coordinates and time are approximated using second order central differences. This leads to the present new approach, which is both accurate and efficient. In order to obtain a stable scheme the displacements must be allocated on a staggered grid. The von Neumann stability analysis is performed and the result is compared with an existing empirical criterion. Mechanical energies are observed in order to validate the finite-difference code. Since no material damping or energy dissipation is taken into account in the equations of motion, the total energy must remain constant over time. Only negligible variations are observed during long-term simulations. Dispersion relations are used to check the physical behavior of the waves calculated with the proposed finite-difference method: Theoretically calculated curves are compared with values obtained by a spectrum estimation method, applied to the results of a simulation.     

Statistical equilibrium solutions of the shallow water equations

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2D fluid flow with a free surface, is described. The model contains a competing acoustic turbulent direct energy cascade, and a 2D turbulent inverse energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrains the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations.     

Vibration of complex structures: The modal constraint method

A method is described for establishing the natural frequencies of an arbitrary structure with arbitrary supports. The method is based on the modal constraint technique described in a previous paper [1]. As shown in the present paper Weinstein's theory for the intermediate problem can be regarded as equivalent to the Lagrangian multiplier method: i.e., both methods result in the same eigenvalue equations. Weinstein's theory deals with modifications of base differential operators whereas the Lagrangian multiplier method deals with modifications of base energy functionals. The modal constraint technique is an extension of Weinstein's theory, or in energy terms the generalized Fourier expansion of the Lagrangian multiplier. The merits of this method lie in the fact that the eigenvalues and eigenfunctions of structures are used as base structures. The coupling of these structures are taken into account by Lagrangian generalized forces of the constraint acting on the base structures. Some examples are given and the results compared with known solutions.     

Analysis of a model of minority charge-carrier distributions generated in a three-layer semiconductor structure by a wide electron beam

Based on the use of a model of independent sources, a method is described for the calculation of minority-charge-carrier distributions generated in three-layer planar semiconductor structures by a wide electron beam with energy typical of electron probe devices (5–30 keV). It is shown that, in limiting cases, equations describing these distributions agree with the data obtained previously for a two-layer semiconductor structure.     

Spherical/gyroid phase diagram of the diblock copolymer in the median selective solvent

The effect of the median selective solution on the lamellar, spherical and gyroid structures is studied. The self-consistent field equations of the diblock copolymer solution are solved by using the reciprocal space method. It is shown that the spherical and gyroid phases have the lowest free energy in the certain range of the solution concentration. Furthermore, the phase diagram of the ordered structures in the diblock copolymer solution with the median selective solvent is calculated, which is consistent with the experimental results. Supported by the National Natural Science Foundation of China (Grant Nos. 10834014, 10674173, and 30770517) and the National Basic Research Program of China (Grant No. 2009CB930704)     

Micromagnetic Studies of Finite Temperature M-H Loops for FePt-C Media

We have recently developed a new micromagnetic method at finite temperature, where the Hybrid Monte Carlo method is employed to realize the Boltzmann distribution with respect to the magnetic free energy. Hence, the hysteresis loops and domain structures at arbitrary temperature below the Curie point T_c can be simulated.The Hamilton equations are used to find the magnetization distributions instead of the Landau-Lifshitz(LL)equations. In our previous work, we applied this method on a simple uniaxial anisotropy nano-particle and compared it with the micromagnetic method using LL equations. In this work, we use this new method to simulate an L10 FePt-C granular thin film at finite temperatures. The polycrystalline Voronoi microstructure is included in the model, and the effects of the misorientation of FePt grains are also simulated.     

A Diffusion Model of Field-Induced Aggregation in Ferrofluid Film

By introducing Arrhenius behaviour to the ferroparticles on the surface of the aggregated columnar structure in a diffusion model, equilibrium equations are set up. The solution of the equations shows that to keep the aggregated structures stable, a characteristic field is needed. The aggregation is enhanced by magnetic fields, yet suppressed as the temperature increases. Analysing the influence of the magnetic field on the interaction energy between the dipolar particles, we estimate the portion of the diffusing particles, and provide the agreeable ratio of the column radius over the centre-to-centre spacing between columns in a hexagonal columnar structure formed under a perpendicular magnetic field.     

Natural frequency split estimation for inextensional vibration of imperfect hemispherical shell

In this study, mathematical model of hemispherical shell is introduced using inextensional vibration mode shapes. Adopting energy equations, the natural frequency of the shell is determined by applying Rayleigh's energy method. Further, the vibration for imperfect shell is investigated with point mass elements representing imperfections on the structures. Also, the effects are considered via energy relations, and the split amount of the natural frequencies can be determined. Finally, the influences of point mass are presented by explicit functions for the split of the natural frequency and shifting angle of mode orientation. Based on the proposed model of imperfect shell with multiple point masses, the structure can be expressed as an equivalent single mass model.     

Incoherent energy transfer within light-harvesting complexes

Rate equations are used to model spectroscopic observation of incoherent energy transfer in light-harvesting antenna systems based upon known structures. A two-parameter two-dimensional model is proposed. The transfer rates obtained, by matching the fluorescent decay, are self-consistent within our model. Received 29 May 1998     

Effective-mass approaches for one-dimensional quantum well structures. Comparison with multi-band results

Exactk-space equations are employed to calculate the energy levels and envelope functions of several one-dimensional quantum well structures having both step and graded-potential profile. We consider finite as well as infinite structures and compare the results obtained with those given by standard effective-mass methods.     

High-frequency vibration analysis of thin elastic plates under heavy fluid loading by an energy finite element formulation

An energy finite element analysis (EFEA) formulation for computing the high frequency behavior of plate structures in contact with a dense fluid is presented. The heavy fluid loading effect is incorporated in the derivation of the EFEA governing differential equations and in the computation of the power transfer coefficients between plate members. The new formulation is validated through comparison of EFEA results to classical techniques such as statistical energy analysis (SEA) method and the modal decomposition method for bodies of revolution. Good correlations are observed and the advantages of the EFEA formulation are identified.     

Locally Anisotropic Kinetic Processes and Thermodynamics in Curved Spaces

The kinetic theory is formulated with respect to anholonomic frames of reference on curved spacetimes. By using the concept of nonlinear connection we develop an approach to modelling locally anisotropic kinetic processes and, in corresponding limits, the relativistic nonequilibrium thermodynamics with local anisotropy. This leads to a unified formulation of the kinetic equations on (pseudo) Riemannian spaces and in various higher dimensional models of Kaluza–Klein type and/or generalized Lagrange and Finsler spaces. The transition rate considered for the locally anisotropic transport equations is related to the differential cross section and spacetime parameters of anisotropy. The equations of states for pressure and energy in locally anisotropic thermodynamics are derived. The obtained general expressions for heat conductivity, shear, and volume viscosity coefficients are applied to determine the transport coefficients of cosmic fluids in spacetimes with generic local anisotropy. We emphasize that such local anisotropic structures are induced also in general relativity if we are modelling physical processes with respect to frames with mixed sets of holonomic and anholonomic basis vectors which naturally admits an associated nonlinear connection structure.     

FINITE ELEMENT MODELLING OF LAMINATED PIEZO-ELASTIC STRUCTURES: LYAPUNOV STABILITY ANALYSIS

In this study, the dynamic stability of finite element modelling of laminated piezo-elastic structures is investigated. The criteria for stability are established based on the second method of Lyapunov, which considers the energy of the system. The results show that the equations of motion are asymptotically stable. However, energy dissipation through the piezoelectric effect continued at zero feedback gain. This implied that the structure was controlled unconditionally. Subsequently, a control strategy that satisfies the condition of no piezoelectric effects when the gain set to zero is developed.     

Application of the intersecting spheres model to periodic structures: Computation of the energy bands of diamond

The intersecting spheres model is an asymptotically exact method for the solution of the X_α equations which has already been applied to molecules with satisfactory results. This success led us to extend the model to the case of periodic structures. The results of a calculation of the self-consistent energy bands of diamond are reported here in order to show the capability of the model to deal with crystalline structures.     

Intermittent dissipation and lack of universality in one-dimensional Alfvénic turbulence

The randomly driven Cohen–Kulsrud–Burgers equation is used to study the influence of viscous intermediate shocks (IS) on Alfvénic turbulence. Some of these structures are unstable and undergo gradient collapse leading, as the viscosity is reduced, to increasingly intermittent dissipation bursts. The slow decay at intermediate scales of stable IS prevents the existence of a usual inertial range. Furthermore, the dissipation is unable to adiabatically compensate for the energy injection, making the total energy sensitive to the viscosity parameter. Turbulence thus looses its universal character. Preliminary simulations extend these conclusions to magnetohydrodynamic equations with anisotropic viscosity, typical of strongly magnetized plasmas.     

复杂结构的损耗因子和耦合损耗因子的测量方法

本文介绍利用测量结构振动能量比,测量组装结构的损耗因子和耦合损耗因子的方法。这种方法既适合于保守耦合结构,也适合于非保守耦合结构。这种方法的优点是同时可测量得到结构损耗因子、耦合损耗因子和间接耦合损耗因子,而不需要知道各子结构的模态密度。耦合损耗因子不仅包括共振传输而且也包含低频的非共振传输的影响。利用这种方法测量了转动机械系统的损耗因子和耦合损耗因子并用修正的统计能量分析平衡方程预测了结构振动响应。然后与实测的结构振动平均响应比较,一致性非常好。     

Transient magnetic reconnection and unstable shear layers

We study three-dimensional magnetic reconnection caused by the Kelvin-Helmholtz (KH) instability and differential rotation in subsonic and sub-Alfvenic flows. The flows, which are modeled by the resistive magnetohydrodynamic equations with constant resistivity, are stable in the direction of the magnetic field but unstable perpendicular to the magnetic field. Localized transient reconnection is observed on the KH time scale, and kinetic energy increases with decreasing resistivity. As in flux-transfer events in the Earth's magnetopause boundary layer, bipolar structures in the normal flux and bidirectional jetting away from reconnection zones are observed.     

Exact Solutions of the Equilibrium Shape Equations in a General WLC Model for DNA Forms

In this letter,we are going to use a geometrical approach to describe the free energy of DNA structures.The exact solutions of the equilibrium shape equations in a general WLC model for DNA forms by using the Feoli's formalism [A.Feoli,et al.,Nucl.Phys.B 705(2005) 577] are studied.Then,the free energy of transition between Band Z-DNA is calculated in this formalism.