用射线踪迹法解黑表面矩形介质耦合换热

本文用射线踪迹-节点分析法研究了二维黑体表面矩形、各向同性散射半透明介质内辐射与导热瞬态耦合换热。采用全隐格式的有限差分法离散二维瞬态微分能量方程,用辐射传递系数来表示辐射源项,结合谱带模型并采用射线踪迹法求解辐射传递系数。采用Patankar线性化方法将辐射源项及不透明边界条件线性化,并采用附加源项法处理边界条件,运用ADI方法求解名以上的线性化方程组,从而解得二维矩形介质内的瞬态温度分布。     

变系数瞬态热传导问题边界元格式的特征正交分解降阶方法

提出了一种基于边界元法求解变系数瞬态热传导问题的特征正交分解(POD)降阶方法,重组并推导出变系数瞬态热传导问题适合降阶的边界元离散积分方程,建立了变系数瞬态热传导问题边界元格式的POD降阶模型,并用常数边界条件下建立的瞬态热传导问题的POD降阶模态,对光滑时变边界条件瞬态热传导问题进行降阶分析.首先,对一个变系数瞬态热传导问题,建立其边界域积分方程,并将域积分转换成边界积分;其次,离散并重组积分方程,获得可用于降阶分析的矩阵形式的时间微分方程组;最后,用POD模态矩阵对该时间微分方程组进行降阶处理,建立降阶模型并对其求解.数值算例验证了本文方法的正确性和有效性.研究表明:1)常数边界条件下建立的低阶POD模态矩阵,能够用来准确预测复杂光滑时变边界条件下的温度场结果;2)低阶模型的建立,解决了边界元法中采用时间差分推进技术求解大型时间微分方程组时求解速度慢、算法稳定性差的问题.     

Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein–Gordon equation and numerical comparisons

We consider a damped, parametrically driven discrete nonlinear Klein–Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of solutions to the discrete nonlinear Schrödinger equation. To illustrate the main results, we consider numerical simulations showing the dynamics of errors made by the discrete nonlinear equation. We consider two types of initial conditions, with one of them being a discrete soliton of the nonlinear Schrödinger equation, that is expectedly approximate discrete breathers of the nonlinear Klein–Gordon equation.     

A Coupled Hybrid Lattice: Its Related Continuous Equation and Symmetries

The hybrid lattice, known as a discrete Korteweg-de Vries (KdV) equation, is found to be a discrete modified Korteweg-de Vries (mKdV) equation in this paper. The coupled hybrid lattice, which is pointed to be a discrete coupled KdV system, is also found to be discrete form of a coupled mKdV systems. Delayed differential reduction system and pure difference systems are derived from the coupled hybrid system by means of the symmetry reduction approach. Cnoidal wave, positon and negaton solutions for the coupled hybrid system are proposed.     

Simulation of Decoherence by Averaged Semiquantum Method for Spin-Boson Model

We investigate the dynamics of a system coupled to an environment byaveraged semiquantum method. The theory origins from the time-dependentvariational principle (TDVP) formulation and contains nondiagonal matrixelements. So it can be applied to study dissipation, measurement, anddecoherence problems in the model (H = h_S + h_E + h_I). In the calculation, the influence of the environment govern by differential dynamical equation is incorporated through a mean field. We have performed averaged semiquantum method for a spin-boson model, which reproduce theresults from stochastic Schrodinger equation method and Hierarchicalapproach quite accurately. The problems, dynamics in nonequilibriumenvironments, have also been studied by our method.     

Exact transverse solitary and periodic wave solutions in a coupled nonlinear inductor-capacitor network

Through two methods, we investigate the solitary and periodic wave solutions of the differential equation describing a nonlinear coupled two-dimensional discrete electrical lattice. The fixed points of our model equation are examined and the bifurcations of phase portraits of this equation for various values of the front wave velocity are presented. Using the sineGordon expansion method and classic integration, we obtain exact transverse solutions including breathers, bright solitons,and periodic solutions.     

Stability of stationary solutions of the discrete self-trapping equation

The discrete self-trapping equation is a model coupled oscillator system with applications in many areas including the dynamics of small molecules and the study of solitions on alpha-helix proteins. Some simple stability criteria for stationary solutions of this equation are presented, together with some example calculations.     

Solving coupled nonlinear Schrodinger equations via a direct discontinuous Galerkin method

In this work,we present the direct discontinuous Galerkin(DDG) method for the one-dimensional coupled nonlinear Schrdinger(CNLS) equation.We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system.The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge-Kutta method.Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.     

The mechanical and the wave-theoretical aspects of momentum considering discrete action

The mechanical aspect of momentum, basically its role as a tangent vector of the trajectory of the particle, is related to properties of the momentum found in the contexts of Hamilton's optico-mechanical analogy, de Broglie's matter waves, and quantum mechanics. These properties are treated in a systematic way by considering an approximation of the particle mechanical action of the particle by a step function. A special method of discretizing partial differential equations is shown to be required. Using this method, a discrete dynamics is developed. It is shown that particle dynamics can be regarded as the limit case of the discrete dynamics as the step functions tend to the continuous ones. The equation of motion of a free particle in an arbitrary reference system is deduced in two ways: (i) in continuous dynamics by making use of the invariance of action within changes of reference systems, and (ii) by taking the mentioned limit in discrete dynamics of an equation which expresses that the mechanical and wave-theoretical aspects of the momentum are interrelated in specific way.     

Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method

In this work, we present the direct discontinuous Galerkin (DDG) method for the one-dimensional coupled nonlinear Schrödinger (CNLS) equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge-Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.     

Generalized differential transform method to differential-difference equation

In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Padé technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation.     

Localization of Bose-Einstein condensates in optical lattices

The dynamics of repulsive bosons condensed in an optical lattice is effectively described by the Bose-Hubbard model. The classical limit of this model, reproduces the dynamics of Bose-Einstein condensates, in a periodic potential, and in the superfluid regime. Such dynamics is governed by a discrete nonlinear Schrödinger equation. Several papers, addressing the study of the discrete nonlinear Schrödinger dynamics, have predicted the spontaneous generation of (classical) breathers in coupled condensates. In the present contribute, we shall focus on localized solutions (quantum breathers) of the full Bose-Hubbard model. We will show that solutions exponentially localized in space and periodic in time exist also in absence of randomness. Thus, this kind of states, reproduce a novel quantum localization phenomenon due to the interplay between bounded energy spectrum and non-linearity.     

Variational master equation approach to dynamics of magnetic moments

Non-equilibrium properties of a model system comprised of a subsystem of magnetic moments strongly coupled to a selected Bose field mode and weakly coupled to a heat bath made of a plurality of Bose field modes was studied on the basis of non-equilibrium master equation approach combined with the approximating Hamiltonian method. A variational master equation derived within this approach is tractable numerically and can be readily used to derive a set of ordinary differential equations for various relevant physical variables belonging to the subsystem of magnetic moments. Upon further analysis of the thus obtained variational master equation, an influence of the macroscopic filling of the selected Bose field mode at low enough temperatures on the relaxation dynamics of magnetic moments was revealed.     

Modeling of ultrashort pulsed laser ablation in water and?biological tissues in cylindrical coordinates

A numerical model combining the ultrafast radiative transfer and the ablation rate equation is proposed to investigate the transient process of plasma formation during laser plasma-mediated ablation of absorbing-scattering media. The focus beam propagation governed by the transient equation of radiative transfer is solved by the transient discrete ordinates method to account for scattering effect. The temporal evolution of the free-electron density governed by the ablation rate equation is calculated using a fourth-order Runge–Kutta method to examine various effects such as the multiphoton, chromophore, and cascade ionizations. The threshold of optical breakdown, the shape and maximum length of plasma growth for ablation in water are predicted by the present model and compared with the existing experimental and numerical data. Good agreements have been found. The dynamic process of plasma formation for ablation in the model skin tissue is simulated. A parametric study with regard to the influences of the ionization energy and the critical free-electron density on the ablation threshold of the tissue is conducted.     

Ergodic Properties of the Non-Markovian Langevin Equation

We discuss the dissipative dynamics of a classical particle coupled to an infinitely extended heat reservoir. We announce a number of results concerning the ergodic properties of this model. The novelty of our approach is that it extends beyond Markovian dynamics to the case where the Langevin equation is driven by colored noise. Our method works in arbitrary space dimension, and for fully nonlinear systems.     

脉冲电流冲击力对电极间距的影响

利用时变场理论和瞬态动力学方程建立了电极及其支撑结构的瞬态耦合模型,分析了瞬态电磁场各参数的分布特点,并求解了电极及其支撑结构的动态响应状态参数。计算结果表明:玻璃钢支撑结构对于脉冲电流形成的冲击力载荷具有很好的缓冲作用;低弹性模量支撑材料在脉冲上升沿和峰值阶段均会产生波动性形变,但该波动性形变对电极间距不会造成太大的影响。     

Dynamics of oscillator chains from high frequency initial conditions: comparison of phi4 and FPU-beta models

The dynamics of oscillator chains are studied, starting from high frequency initial conditions (h.f.i.c.). In particular, the formation and evolution of chaotic breathers (CB's) of the Klein-Gordon chain with quartic nonlinearity in the Hamiltonian (the phi(4) model) are compared to the results of the previously studied Fermi-Pasta-Ulam (FPU-beta) chain. We find an important difference for h.f.i.c. is that the quartic nonlinearity, which drives the high frequency phenomena, being a self-force on each individual oscillator in the phi(4) model is significantly weaker than the quartic term in the FPU-beta model, which acts between neighboring oscillators that are nearly out-of-phase. The addition of a self-force breaks the translational invariance and adds a parameter. We compare theoretical results, using the envelope approximation to reduce the discrete coupled equations to a partial differential equation for each chain, indicating that various scalings can be used to predict the relative energies at which the basic phenomena of parametric instability, breather formation and coalescence, and ultimately breather decay to energy equipartition, will occur. Detailed numerical results, comparing the two chains, are presented to verify the scalings.     

Transient transport equations for high-frequency power flow in heterogeneous cylindrical shells

We use some recent mathematical results obtained for the high-frequency asymptotics of hyperbolic partial differential equations to derive exact transient power flow equations for vibrations of randomly heterogeneous cylindrical shells. The theory shows that the angularly resolved energy densities of an heterogeneous, elastic medium satisfy transient transport equations at higher frequencies. The behaviour of solutions of such equations short of their diffusion limit—if any—is fundamentally different from that of the solution of a diffusion equation, although the latter one is often invoked in the analyses of high-frequency vibrations of elastic structures. A condition by which diffusion equations can be obtained from transport equations is the presence of reflectors or heterogeneities such that scattering mean free paths are short with respect to the characteristic dimensions of the structure. The diffusion limit is reached in this study taking account of scattering by random heterogeneities of the background medium at the scale of the wavelength. This approach fills the gap between transport theory and the diffusion approach in structural dynamics, and clarifies the range of validity of the latter. Our results can be extended to fully coupled dynamic equations for compression, shear and bending of Timoshenko beams or Mindlin plates.     

Numerical Solution of Fractional Partial Differential Equations by Discrete Adomian Decomposition Method

In this paper we find the solution of linear as well as nonlinear fractional partial differential equations using discrete Adomian decomposition method. Here we develop the discrete Adomian decomposition method to find the solution of fractional discrete diffusion equation, nonlinear fractional discrete Schrodinger equation, fractional discrete Ablowitz-Ladik equation and nonlinear fractional discrete Burger's equation. The obtained solution is verified by comparison with exact solution when $\alpha=1$.