多体相互作用体系中的弛豫与扩散:一个尚未解决的问题

文章目的在于引起国内研究团体对一系列复杂相互作用体系中的弛豫和扩散的普适性进行关注.研究发现,无论是不同的化学结构（如无机物、有机物、聚合物、生物分子、胶体、金属和离子导电材料）,还是不同的物理状态（如晶态、玻璃态、液体、熔体、混合体系和含水系统）,以及不同的尺度（如从块体至纳米）,这种普适性无处不在 ［K.L.Ngai.Relaxation and Diffusion in Complex Systems.New York:Springer,2011］.该现象起源于多体系统的不可逆过程,取决于一些基本物理定律,与非简谐势引发的经典混沌有关.重新认识这种普适性不仅对众多不同领域的发展有利,而且能进一步弄清楚多体系统中的弛豫与扩散问题—— 一个重要而又未解决的物理问题.作者提出的耦合模型尽管不是一个严格而完整的答案,但却能够预测多体系统的弛豫和扩散特征,而且与实验结果吻合.基于该模型,绝大多数多体系统中的弛豫与扩散行为是相似的.该模型有望为这一难题的彻底解决奠定基石.     

多体相互作用体系中的弛豫与扩散:一个尚未解决的问题

文章目的在于引起国内研究团体对一系列复杂相互作用体系中的弛豫和扩散的普适性进行关注.研究发现,无论是不同的化学结构(如无机物、有机物、聚合物、生物分子、胶体、金属和离子导电材料),还是不同的物理状态(如晶态、玻璃态、液体、熔体、混合体系和含水系统),以及不同的尺度(如从块体至纳米),这种普适性无处不在[K.L.Ngai.Relaxation and Diffusion in Complex Systems.NewYork:Springer,2011].该现象起源于多体系统的不可逆过程,取决于一些基本物理定律,与非简谐势引发的经典混沌有关.重新认识这种普适性不仅对众多不同领域的发展有利,而且能进一步弄清楚多体系统中的弛豫与扩散问题——一个重要而又未解决的物理问题.作者提出的耦合模型尽管不是一个严格而完整的答案,但却能够预测多体系统的弛豫和扩散特征,而且与实验结果吻合.基于该模型,绝大多数多体系统中的弛豫与扩散行为是相似的.该模型有望为这一难题的彻底解决奠定基石.     

Universal Long-Time Relaxation on Lattices of Classical Spins: Markovian Behavior on Non-Markovian Timescales

The long-time behavior of certain fast-decaying infinite temperature correlation functions on one-, two-, and three-dimensional lattices of classical spins with various kinds of nearest-neighbor interactions is studied numerically, and evidence is presented that the functional form of this behavior is either simple exponential or exponential multiplied by cosine. Due to the fast characteristic timescale of the long-time decay, such a universality cannot be explained on the basis of conventional Markovian assumptions. It is suggested that this behavior is related to the chaotic properties of the spin dynamics.     

Effects of barrier fluctuation on the tunneling dynamics in the presence of classical chaos in a mixed quantum-classical system

We present a numerical investigation of the tunneling dynamics of a particle moving in a bistable potential with fluctuating barrier which is coupled to a non-integrable classical system and study the interplay between classical chaos and barrier fluctuation in the tunneling dynamics. We found that the coupling of the quantum system with the classical subsystem decreases the tunneling rate irrespective of whether the classical subsystem is regular or chaotic and also irrespective of the fact that whether the barrier fluctuates or not. Presence of classical chaos always enhances the tunneling rate constant. The effect of barrier fluctuation on the tunneling rate in a mixed quantum-classical system is to suppress the tunneling rate. In contrast to the case of regular subsystem, the suppression arising due to barrier fluctuation is more visible when the subsystem is chaotic.      

锂离子动力电池高倍率充放电过程中弛豫行为的仿真

基于电化学热耦合模型研究了动力锂离子电池高倍率充放电过程中的弛豫行为, 分析对比了不同充放电机制对电池弛豫行为的影响. 研究发现: 充放电过程中, 欧姆极化是造成电压骤变的主要原因; 而恒流-恒压的充电模式能够缓慢消除欧姆极化, 避免电池电压的骤变; 利用恒流恒压对电池进行充电能够充进更多的电量, 有利于电池性能的完全发挥; 固相锂离子浓度的弛豫时间比液相锂离子浓度的弛豫时间长, 并且在放电后期, 固相扩散的特征时间与液相扩散特征时间的比值不断增大, 固相扩散造成的极化在整个放电过程不可忽略.     

一类动力学系统通过函数耦合实现混沌同步

非线性动力学系统的混沌同步, 一般采用单向线性耦合的控制方式, 对于函数耦合方式研究的比较少. 这就存在一个问题, 对于非线性动力学系统, 在线性耦合实现混沌同步后, 是否其他函数的耦合方式都可以实现混沌同步? 本文对于一类非线性动力学系统, 研究了其线性耦合同步与函数耦合同步的关系, 证明当线性耦合实现同步后, 函数在满足一定的条件下, 可以通过函数耦合实现系统的混沌同步. 最后对于Duffing系统采用两种函数耦合进行了仿真计算, 证明了结论的正确性.     

A Lennard—Jones embedded—atom potential and its application to the study of melting

The nearest-neighbour Lennard-Jones potential from the embedded-atom method is extended to a form that includes more than nearest neighbours.The model has been applied to study melting with molecular dynamics.The calculated melting point,fractional volume change on melting,heat of fusion and linear coefficients of thermal expansion are in good agreement with experimental data.We have found that the second and third neighbours influence the melting point distinctly.     

微粗糙结构表面液滴浸润特性的多体耗散粒子动力学研究

超疏水表面因其优异的自洁作用一直是表面科学领域关注的重点.本文使用多体耗散粒子动力学(many-body dissipative particle dynamics, MDPD)方法模拟研究了不同粗糙结构下液滴的浸润特性, 并与Cassie-Baxter理论进行了对比. 研究使用了一种具有长吸短斥作用的流固作用函数来获得不同的液滴浸润性, 并利用一种简洁的数值方法来测量接触角. 模拟结果表明本研究方法能够稳定地捕捉到液滴在粗糙表面的静态和动态特性. 模拟了粗糙结构对三相接触线运动的黏滞作用, 与物理实验结果相符合, 表明Cassie-Baxter理论在实际应用中尚存在一定局限性. 研究分析了在动态铺展过程中的能量转化关系, 并指出在低值表面容易引起液滴反弹.     

Amide proton relaxation measurements employing a highly deuterated protein

Proton NMR longitudinal and transverse relaxation rates of unlabelled proteins are generally dominated by the many 1H-1H dipolar interactions so that spin diffusion, rather than molecular or internal motions, governs longitudinal relaxation. Here, relaxation measurements of backbone amide proton (1H(N)) magnetisations have been carried out employing the 99% 2H, 98% 15N labelled, small 2F2 protein domain in 10%/90% H(2)O/D(2)O solution. Under these conditions, the longitudinal relaxation rates exhibit time constants, T(1)*=1/R(1)* if described by a mono-exponential, within the range of 3.0 to 18.7s-a wide range which indicates that the phenomenon of spin diffusion has been greatly reduced. The majority of 1H(N) nuclei in this sample (pH 4.0 and 5 degrees C) exhibit chemical exchange with solvent that couples their longitudinal relaxation to that of the solvent. For the subset of 1H(N) nuclei not undergoing detectable solvent chemical exchange, the R(1)* rates correlate well with their individual 1H(N,O)/2H(N,O) structural environments. The correlation for corresponding transverse relaxation rates, R(2)* was found to be less good. Longitudinal relaxation measurements in 1%/99% H(2)O/D(2)O solution identify a further subset of 1H(N) nuclei which exhibit essentially indistinguishable R(1)* rates in both 1% and 10% H(2)O, implying that averaging of rates from spin diffusion processes and different 2F2 isotopomer populations are negligible for these 1H(N) sites. In addition to a high sensitivity to structural parameters, model calculations predict 1H(N) relaxation rates to exhibit pronounced sensitivity to internal dynamics.     

Some new results on the two-dimensional kinetic Ising model in the phase coexistence region

We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of sideL with open boundary conditions, in the absence of an external field and at large inverse temperature . We prove that the gap in the spectrum of the generator restricted to the invariant subspace of functions which are even under global spin flip is much larger than the true gap. As a consequence we are able to show that there exists a new time scalet _even, much smaller than the global relaxation timet _rel, such that, with large probability, any initial configuration first relaxes to one of the two phases in a time scale of ordert _even and only after a time scale of the order oft _rel does it reach the final equilibrium by jumping, via a large deviation, to the opposite phase. It also follows that, with large probability, the time spent by the system during the first jump from one phase to the opposite one is much shorter than the relaxation time.     

一个简单硬球碰撞问题中的混沌

对于一个在铅垂线上的两个硬球及刚性地面组成的硬球碰撞体系,计算了它的Lyapunov指数．因为该Lyapunov指数的正定性,所以该体系是一个混沌体系．     

The Electrodynamic 2-Body Problem and the Origin of Quantum Mechanics

We numerically solve the functional differential equations (FDEs) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard–Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODEs). The ODE formulation is mathematically suspect since FDEs and ODEs are known to be incompatible; however, the Coulomb approximation to the full electrodynamic force has been believed to be adequate for physics. We can now test this long-standing belief by comparing the FDE solution with the ODE solution, in the historically interesting case of the classical hydrogen atom. The solutions differ. A key qualitative difference is that the full force involves a delay torque. Our existing code is inadequate to calculate the detailed interaction of the delay torque with radiative damping. However, a symbolic calculation provides conditions under which the delay torque approximately balances (3rd order) radiative damping. Thus, further investigations are required, and it was prematurely concluded that radiative damping makes the classical hydrogen atom unstable. Solutions of FDEs naturally exhibit an infinite spectrum of discrete frequencies. The conclusion is that (a) the Coulomb force is not a valid approximation to the full electrodynamic force, so that (b) the n-body interaction needs to be reformulated in various current contexts such as molecular dynamics.     

Quantum chaos

A quantum system which is allowed to interact with its boundary in a self-consistent way is shown to exhibit chaos. We conjecture that in general genuine wave chaos (decaying autocorrelation functions, exponential sensitivity of wavefunctions to initial wavefunction configurations) can be obtained whenever a wavefield is allowed to modify its confining boundaries in a self-consistent way. We suggest to test this conjecture in the acoustic regime.     

Coarse-grain modelling using an equation-of-state many-body potential: application to fluid mixtures at high temperature and high pressure

ABSTRACT

A many-body, coarse-grain model, termed the product gas mixture model, is presented that accurately describes the thermodynamic behaviour of molecular mixtures. The coarse-grain model is developed by first approximating the mixture as a van der Waals one-fluid, and subsequently applying an exponential-6 equation-of-state to describe the forces and energies between particles in the spirit of the many-body model pioneered by Pagonabarraga and Frenkel. Isothermal dissipative particle dynamics simulations are carried out at thermochemical states that occur during decomposition of a prototypical energetic material, RDX (1,3,5-trinitro-1,3,5-triazinane). The product gas mixture model performance is assessed by comparing to an explicit-molecule model and a hard-core coarse-grain model based on the exponential-6 pair potential. Overall, the many-body, coarse-grain model is shown to accurately capture the structural and thermodynamic properties for the wide variety of thermochemical states considered, while the hard-core coarse-grain model cannot. The many-body, coarse-grain model overcomes the issues of transferability, scaling consistency and unphysical ordered phase behaviour that often afflict coarse-grain models. While specific thermochemical conditions related to RDX decomposition are considered, the results are generally applicable to the thermodynamic behaviour of other fluid mixtures at both moderate and extreme conditions.