Nonlinear Dynamics in a New Double Chain-Model of DNA

We investigate the mechanics ofa new double chain-model of DNA. The model consists of two long elastic homogeneous strands (or rods), which represent two polynucleotide chains of the DNA molecule, connected with each other by an elastic membrane (or some linear springs) representing the hydrogen bonds between the base pairs of the two chains. The nonlinear dynamical equations are derived and some solitary wave solutions are discussed. By the way,our model can be regarded as the mechanical model of cubic nonlinear Klein-Gordon equation and 4-field equation.     

黏性流体中超细长弹性杆的动力学不稳定性

基于坐标基矢摄动的方法研究了黏性流体中超细长弹性杆动力学稳定性判据与失稳后的模态选择,推导出了黏性介质中超细长弹性杆Kirchoff动力学方程的一阶摄动表示,即线性的二阶偏微分方程组.以平面扭转DNA环为例,说明了以上结果的应用,得到了平面扭转DNA环的稳定性判据及其稳定的临界区域,讨论了其失稳后的模态选择及黏性阻力对其的影响.     

DNA单分子弹性理论

随着单分子操纵技术的发明与发展，人们已经可以对单个生物大分子施以力或力矩，并测量它们的物理性质，DNA单分子的力学实验表明，在分子尺度上理解生物大分子的生化过程，力与能量是同等重要的结构与功能参数。一个梯子模型被用来描述双链DNA的外力拉伸曲线，在这个模型中，DNA是由许多碱基对(梯子的横杆，横杆之间存在吸引势)连接两条聚核苷酸虫链(梯子的两侧)形成的高分子，利用路径积分法得出的理论曲线与实验曲线吻合得很好，对于单链DNA，用分立的杂化高分子链统计理论的母函数方法来计算其弹性行为，得出与实验相符合的外力引起的解链相变结果。此外，对于抑瘤蛋白p53识别序列DNA微环弹性进行分析，发现其弹性模量只是通常随机序列的三分之一。     

Jourdain Principle of a Super-Thin Elastic Rod Dynamics

A super thin elastic rod is modeled with a background of DNA super coiling structure, and its dynamics is discussed based on the Jourdain variation. The cross section of the rod is taken as the object of this study and two velocity spaces about are coordinate and the time are obtained respectively. Virtual displacements of the section on the two velocity spaces are defined and can be expressed in terms of Jourdain variation. JourdMn principles of a super thin elastic rod dynamics on arc coordinate and the time velocity space are established, respectively, which show that there are two ways to realize the constraint conditions. If the constitutive relation of the rod is linear, the Jourdain principle takes the Euler-Lagrange form with generalized coordinates. The Kirchhoff equation, Lagrange equation and Appell equation can be derived from the present Jourdain principle. While the rod subjected to a surface constraint, Lagrange equation with undetermined multipliers may be derived.     

Homogenization of multicoated inclusion-reinforced linear elastic composites with eigenstrains: Application to thermoelastic behavior

A new micromechanical approach for arbitrary multicoated ellipsoidal elastic inclusions with general eigenstrains is developed. We start from the integral equation of the linear elastic medium with eigenstrains adopting the Green's function technique and we apply an ‘(n+1)-phase’ model with a self-consistent condition to determine the homogenized behavior of multicoated inclusion-reinforced composites. The effective elastic moduli and eigenstrains are obtained as well as the residual stresses through the local stress concentration equations. The effective eigenstrains are determined either with the concentration tensors obtained here by the present model, or, more classically, with Levin's formula. In order to assess our micromechanical model, some applications to the isotropic thermoelastic behavior of composites with and without interphase are given. In particular, ‘four-phase’ and ‘three-phase’ models are derived for isotropic homothetic spherical inclusion-reinforced materials, and the results are successfully compared to exact analytical solutions regarding the effective elastic moduli and the effective thermal expansion.     

Vibration characteristic analysis of buried pipes using the wave propagation approach

A theoretical analysis for the free vibration of simply supported buried pipes has been investigated using the wave propagation approach. The pipe modeled as a thin cylindrical shell of linear homogeneous isotropic elastic material buried in a linear isotropic homogeneous elastic medium of infinite extent. The vibrations of the pipe are examined by using Flüggle shell equation. The natural frequencies are obtained for the pipes surrounded by vacuo or elastic medium. The results are compared with those available in the literature and agreement is found with them. It is found that the free vibration frequency of the pipe does not appear for some of the axial or circular vibration modes and the real natural frequencies of the pipe are significantly dependent on the rigidity of the surrounding medium.     

Exact solutions of the Boltzmann equation in the VHP model with removal interaction

The linear and nonlinear Boltzmann equation for very hard particles (VHP) is considered in the case when the collision between two particles may lead not only to elastic scattering, but also to a removal event with the disappearance of the molecules. The extended transport equation is solved for arbitrary initial distributions. The computations are carried out explicitly for a special class of initial distributions and for various removal rates. The results are demonstrated graphically. Finally, source terms fulfilling physically reasonable conditions are introduced into the VHP model, and the time-dependent particle number is calculated.     

On the existence conditions of localized states in linear chains

The existence conditions of localized states in linear chains with one or two impurities, are investigated in the tight-binding model. The influence of the coupling between impurity and its neighbour is stressed, in the cases of infinite and semi-infinite chains.     

An equation of state for the isotropic phase of linear,partially flexible and fully flexible tangent hard-sphere chain fluids

A new equation of state is developed that accurately describes the isotropic phase behaviour of linear, partially flexible and fully flexible tangent hard-sphere chain fluids and their mixtures. The equation of state is based on the equation of state of Liu and Hu [H. Liu and Y. Hu, Fluid Phase Equilibr. 122, 75 (1996)] for fully flexible chain fluids. The effect of molecular flexibility is described by a pure-component parameter that is introduced in the theory at the level of the cavity correlation function of next-to-nearest neighbour segments in a chain molecule. The equation of state contains a total of three adjustable model constants. The extension to partially flexible- and linear chain fluids is based on a refitting of the first model constant to numerical data of the second virial coefficient of partially flexible and linear tangent hard-sphere chain fluids. The numerical data were obtained from an analytical approximation for the pair-excluded volume. The other two parameters were adjusted to molecular simulation data for the pressure of linear tangent hard-sphere chain fluids. For both, pure component systems and mixtures of chains of variable flexibility, the pressure and second virial coefficient obtained from the equation of state, are in excellent agreement with the results from Monte Carlo simulations. A significant improvement to TPT1, TPT2, generalised Flory-dimer theory and scaled particle theory is observed.     

Quantal description of inelastic heavy-ion scattering

A model Schrödinger equation for scattering with energy loss is discussed. The equation is linear and is closely related to the coupled-channels approach to elastic and inelastic scattering. A possible parametrization of the model for applications to heavy-ion scattering is considered.     

Kirchhoff弹性杆动力学建模的分析力学方法

以杆的横截面为研究对象，讨论了其自由度，给出了截面虚位移定义，并定义变分和偏微分运算对独立坐标服从交换关系. 给出了曲面约束的基本假设，讨论了约束对截面自由度的影响以及加在虚位移上的限制方程. 从D'Alembert原理出发结合虚功原理，建立了弹性杆动力学的D'Alembert-Lagrange原理，当杆的材料服从线性本构关系时，化作Euler-Lagrange形式、Nielsen形式和Appell形式. 由此导出了Kirchhoff方程以及Lagrange方程、Nielsen方程和Appell方程，得到 关键词： 超细长弹性杆 分析力学方法 Kirchhoff动力学比拟 变分原理     

弹性压扭直杆的Greenhill公式对精确模型的推广

将圆截面Kirchhoff弹性压扭直杆的Greenhill公式推广到精确模型.基于平面截面假定,在弯扭的基础上增加了拉压和剪切变形,将弹性杆的位形表达为截面的弧坐标历程.由弹性杆精确模型的平衡微分方程,得到了两端受力螺旋作用时对应于直线平衡状态的特解,导出了线性化扰动方程及其通解,再根据两端为铰支时的边界条件以及积分常数存在非零解的条件导出弹性直杆精确模型的Greenhill公式.结果表明,由力螺旋表示的稳定域为一对称的封闭区域,拉压和剪切对稳定性的影响取决于拉压柔度与剪切柔度之差、抗弯刚度和杆长这三个因素.     

A Theory of Non-Linear Elasticity Compatible With the Murnaghan Equation of State

We present an equation of state for a cubic non-linear elastic material in a general state of finite strain. For hydrostatic pressure, the predictions closely follow Murnaghan's well-known equation of state. At 170 kbar, our model differs from Murnaghan's equation by only 1.3%, which contrasts with the currently accepted non-linear elasticity theory that differs by 10% at this pressure. The theory is based on expressing the variation of the elastic constants as a linear function of stress rather than strain. We define a different set of third-order elastic constants, which involve a derivative with respect to stress, and relate these to the conventional third-order elastic constants. We apply the model to GaAs under hydrostatic pressure and we compare the predictions of the conventional non-linear theory with those of the model we present.     

Study of Love-type wave propagation in an isotropic tri layers elastic medium overlying a semi-infinite elastic medium structure

This paper deals with the propagation of Love-type wave in a composite isotropic structure embraced of tri layers elastic medium overlying a semi-infinite elastic medium. The heterogeneity is caused due to the variation of linear, exponential, and quadratic with respect to the depth. Modified Bessel function with Debye Asymptotic Expansion approach is used to achieve closed form of dispersion equation analytically and found to be in well agreement to the classical Love wave equation. Numerical computation has been carried out to accomplish the graphical demonstration to unravel some important peculiarities of wave number associated in presence or absence of layers medium and effect of heterogeneities on phase velocity of Love-type wave.     

Perturbed soliton-like molecular excitations in a deformed DNA chain

We study the nonlinear dynamics of a deformed Deoxyribonucleic acid (DNA) molecular chain which is governed by a perturbed sine-Gordon equation coupled with a linear wave equation representing the lattice deformation. The DNA chain considered here is assumed to be deformed periodically which is the energetically favourable configuration, and the periodic deformation is due to the repulsive force between base pairs, stress in the helical backbones and due to the elastic strain force in both the strands. A multiple scale soliton perturbation analysis is carried out to solve the perturbed sine-Gordon equation and the resultant perturbed kink and antikink solitons represent open state configuration with small fluctuation. The perturbation due to periodic deformation of the lattice changes the velocity of the soliton. However, the width of the soliton remains unchanged.     

Analytical modeling of squeeze film damping for rectangular elastic plates using Green's functions

An analytical method for the solution of squeeze film damping based on Green's function to the nonlinear Reynolds equation considering an elastic plate is presented. This allows calculating the stiffness and damping forces rapidly for various boundary conditions. The elastic plate velocity is applied to the nonlinear Reynolds equation as a forcing term. The nonlinear Reynolds equation is divided into multiple linear nonhomogeneous Helmholtz equations, which then can be solvable using the presented approach. Approximate mode shapes of a rectangular elastic plate are used, enabling the calculation of the damping ratio and frequency shift for the linear case, as well as the complex resistant pressure, for both linear and nonlinear cases.     

Multicanonical Monte Carlo simulations on intramolecular micelle formation in copolymers

The formation of intramolecular micelles in copolymers with periodic sequence, where hydrophobic units (stickers) are periodically placed along the chain, is studied by using multicanonical Monte Carlo computer simulations for an off-lattice bead-rod model in three dimensions. With decreasing the temperature, a transition from random-coil conformations to micelles occurs and flower-type micelles are formed via the transition. The number of stickers forming a micelle core is limited by the excluded-volume effect of loop chains around micelle cores. By this effect, two intramolecular micelles are formed for long polymer chains with 60 bonds via the coil-to-micelle transition. By further decreasing the temperature, we find that another transition, i.e., a micelle-to-micelle transition, takes place. At this transition point, the two intramolecular micelles merge into one micelle. Furthermore, we extend the multicanonical MC method to study elastic properties of single polymer chains with strong attractive interactions under external force fields, and study how the intramolecular micellization affects the elastic property of single polymer chains.     

Linear superposition solutions to nonlinear wave equations

The solutions to a linear wave equation can satisfy the principle of superposition,i.e.,the linear superposition of two or more known solutions is still a solution of the linear wave equation.We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic,triangle,and exponential functions,and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics.The linear superposition solutions to the generalized KdV equation K(2,2,1),the Oliver water wave equation,and the k(n,n) equation are given.The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed,and the reason why the solutions with the forms of hyperbolic,triangle,and exponential functions can form the linear superposition solutions is also discussed.     

A note on the spheroidal modes vibration of an elastic sphere in linear viscoelastic fluid

Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing, and also to investigate materials mechanical properties. An analytical approach based on the exact theory has been developed in this paper, to establish a new accurate and simple generalized frequency equation to predict spheroidal vibration of an elastic nanosphere, in a compressible viscoelastic fluid using linear Maxwell fluid model. To demonstrate the accuracy of the present approach, a comparison is made with the published theoretical results in the literature in some particular cases, which shows a very good agreement. Thus, the obtained frequency equation can be very useful to interpret the experimental measurements of vibrational dynamics of nanospheres and can serve as benchmark solution in design of liquid sensors.     

Kinetic Description of a Rayleigh Gas with Annihilation

In this paper, we consider the dynamics of a tagged point particle in a gas of moving hard-spheres that are non-interacting among each other. This model is known as the ideal Rayleigh gas. We add to this model the possibility of annihilation (ideal Rayleigh gas with annihilation), requiring that each obstacle is either annihilating or elastic, which determines whether the tagged particle is elastically reflected or removed from the system. We provide a rigorous derivation of a linear Boltzmann equation with annihilation from this particle model in the Boltzmann–Grad limit. Moreover, we give explicit estimates for the error in the kinetic limit by estimating the contributions of the configurations which prevent the Markovianity. The estimates show that the system can be approximated by the Boltzmann equation on an algebraically long time scale in the scaling parameter.