阻尼作用下一维非线性单原子链中的孤子

利用多重尺度法,研究了弱阻尼作用下一维非线性单原子链中的波动行为,发现在O(ε)级阻尼作用下其格波幅度减小,群速变慢.在晶格动力学中导出了参数耗散型非线性Schrdinger方程,对方程进行解析求解.结果表明在O(ε)级阻尼作用下一维非线性单原子链中的格孤波为传播的包络孤子;在O(ε2)级阻尼作用下,格孤波为钟状或扭结的孤子.     

阻尼作用下一维非线性单原子链中的孤子

利用多重尺度法,研究了弱阻尼作用下一维非线性单原子链中的波动行为,发现在O(ε)级阻尼作用下其格波幅度减小,群速变慢.在晶格动力学中导出了参数耗散型非线性Schr?dinger方程,对方程进行解析求解.结果表明:在O(ε)级阻尼作用下一维非线性单原子链中的格孤波为传播的包络孤子;在O(ε²)级阻尼作用下,格孤波为钟状或扭结的孤子.     

在碰撞等离子体中阿尔芬(ALFVEN)波动力理论计算

本文用预报校正格式求解了非线性复系数复函数抛物型方程,获得了阿尔芬(ALFVEN)波包在碰撞等离子体中随时间的非线性传播的演变图象。结果表明:碰撞粘滞对波包的阻尼作用不容忽视,而非线性朗道(Landau)阻尼对波包的阻尼作用较弱。     

一类广义强阻尼Sine-Gordon方程的整体解

同时考虑黏性效应及外阻尼作用研究了一类广义强阻尼Sine-Gordon方程-利用Galerkin方法,首先证明了该方程在初值u(x,0)∈H¹₀(Ω),u_t(x,0)∈L²(Ω)的条件下初边值问题存在整体弱解u(x,t),并证明了整体弱解关于初始条件具有 关键词： Sine-Gordon型方程 强阻尼 Galerkin方法 整体解     

传质势容耗散极值原理及通风排污过程的优化

为了获得排污效率较高的室内通风方式,本文将传热势容耗散极值原理应用到对流传质过程分析,定义了传质势容耗散函数,并利用变分原理在给定条件下对耗散函数求极值,获得了场协同方程,求解场协同方程获得了最佳流场,使传质势容耗散取得极小值,室内污染物浓度最低.这些结论对通风排污过程的分析与优化设计有重要指导意义.     

统一的对流扩散型可压缩流体力学方程与解法

流体力学的动量方程、能量方程、湍动能方程和耗散方程都具有对流扩散方程的形式,但连续方程却不是对流扩散型的。对于可压缩问题,本文通过合理的数学推导,不作任何近似、假定与简化,得到一个全新的连续方程形式．该连续方程以压力为未知变量,并具有对流扩散型形式,使得所有的流体动力学方程组都具有完全统一的方程形式,给出了这种三维对流扩散方程组的有限精确差分计算格式。对流体力学的进一步发展具有一定意义．     

耗散对孤波与局地地形相互作用的影响

利用扰动法，由包括耗散和地形的准地转位涡度方程导出了强迫mKdV-Burgers方程，求得了小耗散情形下mKdV-Burgers方程的近似分析解，分析了mKdV孤波质量和能量的时间演变特性。对给定的局地地形，利用拟谱法对强迫mKdV-Burgers方程进行了数值求解。结果显示，小耗散的存在使弧波的振幅和移速随时间缓慢地减小，孤波宽度则随时间缓慢增大；在耗散和地形强迫的非线性系统中，在孤波与地形的相互作用中，耗散的存在使孤波在强迫区附近振荡传播，这有利于大振幅扰动的形成。     

耗散与局地地形激发的代数孤立长波（英）

利用包括地形外源和湍流耗散的准地转涡度方程导出了包含强迫项和湍流耗散项的非齐次强迫BDO-Burgers方程，求出了小耗散存在情况下BDO-Burgers方程的近似解析解，讨论了代数孤立波的质量和能量的守恒关系，最后，对给定的弱切变基本气流和避地地形强迫，数据积分强迫BDO-Burgers方程，求得了不同参数下的数值解。     

变质量耗散系统的Lagrange方程

本文由方程Ｄ’Ａｌｅｍｂｅｒｔ原理导出了变质量耗散系统的Ｌａｇｒａｎｇｅ方程，给出了耗散函数的一般式，并讨论其应用。     

单个守恒型方程熵耗散格式中熵耗散函数的构造

对于一维单个守恒律方程,文[8]设计了一种非线性守恒型差分格式.此格式为二阶Godunov型的,用的是分片线性重构(reconstruction),重构函数的斜率是根据熵耗散得到的.格式满足熵条件.与传统的守恒格式不同的是此格式在计算过程中不仅用到了数值解还用到了数值熵.在此格式中一个所谓的熵耗散函数起到了很重要的作用,它在每一个网格的计算中耗散熵,以保证格式满足熵条件.文[8]中设计的熵耗散函数比较复杂,并且不是很完善.故数值地分析了在格式的构造中为何应给熵以一定的耗散,及应耗散多少.并且给出了一个新的以数值解的二阶差分作为基本模块的熵耗散函数.最后给出了相应的数值算例.     

Parametrically Driven Solitons in a Chain of Nonlinear Coupled Pendula with an Impurity

The system consisting of a chain of parametrically driven and damped nonlinear coupled pendula with a mass impurity is studied by means of a discrete version of the envelope function approach. An analogue of the parametrically driven damped nonlinear Schodinger equation with an impurity term is derived from the original lattice equation. Analytical solutions of impurity pinned high-frequency breathers and kinks are obtained. The results show that the mass impurity has striking influence on the high-frequency modes. In addition, we perform numerical simulations, showing that the light mass impurity has a stabilizing effect on the chain. The breathers seeding chaos in the homogeneous chain are pinned on a suitable light impurity to pull the chain from the chaotic state.     

The nonlinear dynamics of the damped and driven Toda chain: I. Energy bifurcation diagrams

The dynamics of a periodically driven damped Toda chain with periodic boundary conditions is investigated. With the help of energy cross sections it can be shown that besides periodic motions of different periodicity quasiperiodic and aperiodic (chaotic) motions exist. The method of energy bifurcation diagrams is introduced which allows a survey of the resonance properties of the chain.     

Polymers in a vacuum

In a variety of situations, isolated polymer molecules are found in a vacuum, and here we examine their properties. Angular momentum conservation is shown to significantly alter the average size of a chain and its conservation is only broken slowly by thermal radiation. For an ideal chain, the time autocorrelation for monomer position oscillates with a period proportional to chain length. The oscillations and damping are analyzed in detail. Short-range repulsive interactions suppress oscillations and speed up relaxation, but stretched chains still show damped oscillatory correlations.     

Generalized Bloch's theorem for viscous metamaterials: Dispersion and effective properties based on frequencies and wavenumbers that are simultaneously complex

It is common for dispersion curves of damped periodic materials to be based on real frequencies as a function of complex wavenumbers or, conversely, real wavenumbers as a function of complex frequencies. The former condition corresponds to harmonic wave motion where a driving frequency is prescribed and where attenuation due to dissipation takes place only in space alongside spatial attenuation due to Bragg scattering. The latter condition, on the other hand, relates to free wave motion admitting attenuation due to energy loss only in time while spatial attenuation due to Bragg scattering also takes place. Here, we develop an algorithm for 1D systems that provides dispersion curves for damped free wave motion based on frequencies and wavenumbers that are permitted to be simultaneously complex. This represents a generalized application of Bloch's theorem and produces a dispersion band structure that fully describes all attenuation mechanisms, in space and in time. The algorithm is applied to a viscously damped mass-in-mass metamaterial exhibiting local resonance. A frequency-dependent effective mass for this damped infinite chain is also obtained.     

Periodic and solitary states of the driven sine-Gordon chain

We show that the propagation velocity of driven kinks in the damped and forced sine-Gordon chain is related to a universal function, which also determines the onset of running solutions in the single-particle case.     

A polyene chain of canthaxanthin investigated by temperature-dependent resonance Raman spectra and density functional theory （DFT） calculations

We report on a temperature-dependent resonance Raman spectral characterization of the polyene chain of canthax- anthin. It is observed that all vibrational intensities of the polyene chain are inversely proportional to temperature, which is analyzed by the resonance Raman effect and the coherent weakly damped electron/lattice vibrations. The increase in intensity of the CC overtone/combination relative to the fundamental with temperature decreasing is detected and discussed in terms of electron/phonon coupling and the activation energy Uop. Moreover, the polyene chain studies using the density functional theory B3LYP/6-31 G＊ level reveal a prominent peak at 1525 cm-1 consisting of two closely spaced modes that are both dominated by C=C stretching coordinates of the polyene chain.     

Semiflexible polymer confined to a spherical surface

We develop a formalism for describing the kinematics of a wormlike chain confined to the surface of a sphere that simultaneously satisfies the spherical confinement and the inextensibility of the chain contour. We use this formalism to study the statistical behavior of the wormlike chain on a spherical surface. In particular, we provide an exact, closed-form expression for the mean square end-to-end distance that is valid for any value of chain length L, persistence length l(p), and sphere radius R. We predict two qualitatively different behaviors for a long polymer depending on the ratio R/l(p). For R/l(p)>4, the mean square end-to-end distance increases monotonically with the chain length, whereas for R/l(p)<4, a damped oscillatory behavior is predicted.     

Kinematics of the forced and overdamped sine-Gordon soliton gas

Motion of a driven and heavily damped sine-Gordon chain with a low density of kinks and tight coupling between particles is controlled by the nucleation and subsequent annihilation of pairs of kinks and antikinks. We show that in the steady state there are no spatial correlations between kinks or between kinks and antikinks. For a given number of kinks and antikinks all geometrical distributions are equally alike, as in equilibrium. A master equation for the probability distribution for the number of kinks on a finite chain is solved, and substantiates the physical reasoning in previous work. The probability distribution characterizing the spread along the direction of particle motion of a finite chain in equilibrium as well as in the driven overdamped case is derived by simple combinatorial considerations. The spatial spread of a driven chain in the thermodynamic limit does not approach a steady state; a given particle followed in time deviates as t^1/2 from its average forced motion. This result follows from the hydrodynamic equations for the dilute kink gas. Comparison is made with other recent results.     

Dynamics of linear discrete systems connected to local, essentially non-linear attachments

The dynamics of a linear periodic substructure, weakly coupled to an essentially non-linear attachment are studied. The essential (non-linearizable) non-linearity of the attachment enables it to resonate with any of the linearized modes of the subtructure leading to energy pumping phenomena, e.g., passive, one-way, irreversible transfer of energy from the substructure to the attachment. As a specific application the dynamics of a finite linear chain of coupled oscillators with a non-linear end attachment is examined. In the absence of damping, it is found that the dynamical effect of the non-linear attachment is predominant in neighborhoods of internal resonances between the attachment and the chain. When damping exists energy pumping phenomena are realized in the system. It is shown that energy pumping strongly depends on the topological structure of the non-linear normal modes (NNMs) of the underlying undamped system. This is due to the fact that energy pumping is caused by the excitation of certain damped invariant NNM manifolds that are analytic continuations for weak damping of NNMs of the underlying undamped system. The bifurcations of the NNMs of the undamped system help explain resonance capture cascades in the damped system. This is a series of energy pumping phenomena occurring at different frequencies, with sudden lower frequency transitions between sequential events. The observed multi-frequency energy pumping cascades are particularly interesting from a practical point of view, since they indicate that non-linear attachments can be designed to resonate and extract energy from an a priori specified set of modes of a linear structure, in compatibility with the design objectives.