牛顿摆衰减的建模与探究

通过Hertz碰撞模型,推导出了牛顿摆体系的演化方程并进行数值模拟,重现了非理想牛顿摆的衰减特征,并定性分析了非对心碰撞和小球固有摆动因素对牛顿摆非理想行为的作用.在小球排列相对整齐的情况下,黏滞耗散和框架耗散是主要的能量耗散因素;在小球排列相对不够整齐的情况下,非对心碰撞引起的能量耗散占主要地位.同时定量说明了空气阻尼并非衰减的主要因素.     

微液滴动力学特性的耗散粒子动力学模拟

对传统的耗散粒子动力学方法进行了改进.改进的耗散粒子动力学方法采用了包含远程吸引力和近距排斥力的保守力势函数,从而使得用耗散粒子动力学方法模拟多相流动成为可能.应用改进的耗散粒子动力学方法,对微尺度下液滴的形成及液滴在微重力下的大幅度振荡变形进行了数值模拟.计算结果表明,改进的耗散粒子动力学(DPD)方法能够有效地描述微尺度下液滴的动力学特性,对研究复杂流体多相流动有着重要的意义. 关键词： 多相流 微液滴 耗散粒子动力学(DPD)方法 保守力势函数     

轻系统耗散碰撞的动力学

用包含六个自由度的运动学方程对轻系统耗散碰撞的动力学进行了计算.对角分布和反应时间,能量耗散和碎片形变等问题进行了讨论.     

费米型级联运动方程的绝热截断方案

研究开放量子系统的量子耗散动力学对于理解许多新奇量子现象背后的机制和实现量子器件的精确量子态控制具有重要意义. 级联运动方程方法已成为研究这类量子耗散动力学最常用的数值方法之一. 然而，在处理强电子关联系统时，准确描述强关联效应需要高的级联截断层数. 这导致级联运动方程方法需要耗费大量物理内存和计算时间. 为了解决该问题，将具有最快耗散速率的耗散模式与其他较慢的耗散模式分离，提出了一种级联运动方程的绝热截断方案. 在单杂质安德森模型上进行的数值测试表明，与传统的方案相比，该截断方案显著地降低了级联运动方程收敛需要的截断层数. 此外，该截断方案缓解了长时间耗散动力学中的数值不稳定性.     

重离子碰撞两体关联输运理论Ⅲ.半经典近似下的数值计算

为了验证由相干单粒子波函数和两体关联动力学所建立的非相对论条件下的重离子碰撞两体关联输运理论的有效性,利用没有碰撞项的量子分子动力学,即时间相关的Hartree-Fock方法的经典近似,实现了两体关联输运理论在半经典近似下的数值计算.计算结果表明:这种两体关联输运理论的确能够有效地描述重离子碰撞过程中的输运和耗散过程.     

旋转体系中湍流的LBM模拟

采用基于多松弛时间因子的格子Boltzmann方法对旋转体系中的湍流进行数值研究,考察Rossby数和Ekman数对湍流的影响,包括湍流能量及其耗散率、速度、涡结构及湍流的耗散尺度即Kolmorogov尺度和积分尺度等.研究表明,系统的旋转延缓了湍流能量的衰减速率,逐步破坏初始涡结构的均匀性,与旋转方向相反的涡逐步被抑制,并最终形成若干与旋转同向的涡柱.结果还表明,系统旋转越快,湍流的耗散尺度越小而积分尺度越大.     

三体相互作用下三势阱中玻色-爱因斯坦凝聚体的稳定性研究

着重研究受到非弹性碰撞相互作用,即考虑有三体复合耗散和原子填充时三势阱中玻色-爱因斯坦凝聚体的动力学性质.运用三模近似,得到三个耦合的GP方程,用数值的方法得到不同散射长度的数值结果,展示了玻色-爱因斯坦凝聚体在零相位和π相位时,会出现自俘获及量子隧穿现象,且定态解的稳定性与相位有关.     

碎片云问题的三维欧拉数值模拟

针对材料超高速碰撞产生碎片云问题进行了多介质弹塑性流体力学欧拉方法数值模拟,介绍了所采用的数学模型、材料模型及相应的计算方法,模拟了铝球超高速碰撞铝板和斜铜柱高速撞击铝板形成碎片云的实验现象。进行了不同碰撞速度下模拟的碎片云形状和实验结果比较,利用经验公式对数值模拟的板靶开孔尺寸进行了分析。数值结果与实验结果、经验公式结果比较,说明多介质弹塑性流体力学欧拉方法能够较好地模拟超高速碰撞产生的碎片云问题,验证了数值方法的有效性。     

中能重离子碰撞中库仑相互作用对动量耗散的同位旋效应

利用同位旋相关的量子分子动力学模型，研究了中能重离子碰撞过程中的库仑相互作用对于 动量耗散的同位旋效应.计算结果表明: 由于库仑相互作用的存在，使得碰撞过程中的化学 不稳定区和力学不稳定区减小，明显地减弱了动量耗散；其减弱的程度与对称势的形式及强 度有关，对称势越强则动量耗散的减弱幅度越大.动量耗散灵敏地依赖于核子-核子碰撞截 面的同位旋相关性而较弱地依赖于对称势，这一特征不论有无库仑相互作用均存在. 关键词： 中能重离子碰撞 库仑相互作用 动量耗散 同位旋效应     

基于大密度差多相流SPH方法的二维液滴碰撞数值模拟

该文结合了Ott提出的修正连续性方程和Adami改进的动量方程, 对空气中的液滴碰撞问题进行了二维数值模拟. 为有效提高计算精度, 推导了适用于大密度差多相流的人工黏性和人工应力方程. 通过表面张力作用下方形液滴自然变化和空气中两液滴互溶的算例, 验证了算法的有效性; 对不同韦伯数 (8.8, 19.8)、不同碰撞参数 (0, 0.5)下的液滴碰撞过程进行了数值模拟, 并与VOF方法对比,取得了较为一致的结果; 进一步计算多个韦伯数、多个碰撞参数下的液滴碰撞, 得到了空气中二维液滴碰撞结果分布图,与实验结果相符合. 结果表明, 该算法对于求解涉及大密度差多相流的液滴碰撞破碎问题十分有效,而且该方法容易拓展到三维, 从而为进一步模拟火箭发动机的二次雾化过程奠定了基础. 关键词： 光滑粒子流体动力学 大密度差 多相流 液滴碰撞     

Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

晶体离子质量差异对激活离子声子参助能量传递几率的影响

在已有理论模型的基础上讨论了基质晶体离子质量差异对激活离子声子参助能量传递几率的影响。结果表明基质离子的质量差异除了导致声子频率的变化从而影响其声子参助能量传递几率,还直接改变其传递几率的显式。对单声子参助能量传递过程,其传递几率必须乘以质量差异因子D²,对双声子参助能量传递过程其传递几率则乘以因子D⁴。文中给出了两种不同质量离子组成的晶体的因子D的表示式和p种不同质量的离子组成的晶体的因子D的一般表达式。     

SimGen(m+n=9)团簇结构和电子性质的计算研究

硅锗团簇结构与电子性质的研究对于研发新型微电子材料具有重要意义. 将遗传算法和基于密度泛函理论的紧束缚方法相结合, 研究了Si_mGe_n(m+n=9)团簇的原子堆积结构和电子性质. 计算结果发现, Si_mGe_n(m+n=9) 团簇存在两种低能原子堆积稳定构型: 带小金字塔的五边形双锥堆积和带桥位Ge原子的四面体紧密堆积. 随着团簇内锗原子数目的逐渐增加, 两种堆积结构均出现明显的转变, 其中最低能量的几何结构由单侧带相邻双金字塔的五边形双锥结构转变为双侧带相邻单金字塔的五边形双锥结构. 随着原子堆积结构的变化, 团簇内原子电荷分布及电子最高占据轨道与电子最低未占据轨道的能隙随团簇内所含硅和锗元素组分的不同呈现出明显的差异.     

Vector semi-rational rogon-solitons and asymptotic analysis for any multi-component Hirota equations with mixed backgrounds

The Hirota equation can be used to describe the wave propagation of an ultrashort optical field. In this paper, the multi-component Hirota (alias n-Hirota, i.e. n-component third-order nonlinear Schrödinger) equations with mixed non-zero and zero boundary conditions are explored. We employ the multiple roots of the characteristic polynomial related to the Lax pair and modified Darboux transform to find vector semi-rational rogon-soliton solutions (i.e. nonlinear combinations of rogon and soliton solutions). The semi-rational rogon-soliton features can be modulated by the polynomial degree. For the larger solution parameters, the first m (m < n) components with non-zero backgrounds can be decomposed into rational rogons and grey-like solitons, and the last n − m components with zero backgrounds can approach bright-like solitons. Moreover, we analyze the accelerations and curvatures of the quasi-characteristic curves, as well as the variations of accelerations with the distances to judge the interaction intensities between rogons and grey-like solitons. We also find the semi-rational rogon-soliton solutions with ultra-high amplitudes. In particular, we can also deduce vector semi-rational solitons of the n-component complex mKdV equation. These results will be useful to further study the related nonlinear wave phenomena of multi-component physical models with mixed background, and even design the related physical experiments.     

Non-threshold (F, Dp) bound states

In the previous paper [hep-th/9904112], we argued that there exist BPS bound states of Dp branes carrying certain units of quantized constant electric field for every p (with 1 p 8). Each of these bound states preserves one half of the spacetime supersymmetries. In this paper, we construct these bound state configurations explicitly for 2 p 7 from Schwarz's (m, n)-string or (F, D1) bound state in type IIB string theory by T-dualities along the transverse directions. We calculate the charge per of (p − 1)-dimensional area for F-strings in (F,Dp) and the tension for each of these bound states. The results agree precisely with those obtained previously from the worldvolume study. We study the decoupling limit for the (F, D3) bound state and find that Maldacena's AdS₅/CFT₄ correspondence may hold true even with respect to this bound state but now with an effective string coupling rather than the usual string coupling. This coupling is quantized and can be independent of the usual string coupling in a certain limit.     

On nonanalytic solitary waves formed by a nonlinear dispersion

We study the prototypical, genuinely nonlinear, K(m, n) equation, u_t ± a(u^m)_x + (uⁿ)_xxx = 0, a = const, which exhibits a number of remarkable dispersive effects. In particular, the distinguished subclass wherein m = n + 2 is transformed into a new, purely dispersive equation free of convection. In addition to compactons, the K(m, n) can support both kinks and solitons with an infinite slope(s), periodic waves and dark solitons with cusp(s) all being manifestations of nonlinear dispersion in action. For n < 0 the enhanced dispersion at the tail may generate algebraically decaying patterns.     

Remarks on stochastic non-linear birth and death models

The first part of this paper is an attempt to formulate and motivate additional work on the important problem of obtaining global bounds applicable to the controlled truncation of the paper relates specifically to the linear birth, quadratic death model. Asymptotic results are given for the first finite difference ΔT_m where T_m is the exactly known mean time to extinction starting from state m (m= 0,1,…). These results are in terms of the environmental carrying capacity n^* taken to be large. For m near zero ΔT_me^n*/(n^*)²; whereas, for m near n^*ΔT_m ≈ (π/2)^1/2/(n^*)^3/2. This indicates the vastly different time scales in those two regions of state space - with considerably slower action near extinction than near n^*.     

色散方程的一类具任意稳定性的显格式

本文对色散方程u_r=au_xxx构造了一类中间层包含四个结点,带两个参数m和θ的三层显式差分格式。当m和θ满足一定的关系时,其稳定性条件为|γ|≤(m+1)/(4(m-1))(|m|>1),从而当取m充分接近1时,可得到任意大的稳定性条件,并且保持截断误差阶不变。数值例子验证了理论分析的结果。     

Inverse full state hybrid projective synchronization for chaotic maps with different dimensions

A new synchronization scheme for chaotic(hyperchaotic) maps with different dimensions is presented.Specifically,given a drive system map with dimension n and a response system with dimension m,the proposed approach enables each drive system state to be synchronized with a linear response combination of the response system states.The method,based on the Lyapunov stability theory and the pole placement technique,presents some useful features:(i) it enables synchronization to be achieved for both cases of n m and n m;(ii) it is rigorous,being based on theorems;(iii) it can be readily applied to any chaotic(hyperchaotic) maps defined to date.Finally,the capability of the approach is illustrated by synchronization examples between the two-dimensional H′enon map(as the drive system) and the three-dimensional hyperchaotic Wang map(as the response system),and the three-dimensional H′enon-like map(as the drive system) and the two-dimensional Lorenz discrete-time system(as the response system).     

The basic principle of m × n resistor networks

The unified processing and research of multiple network models are implemented,and a new theoretical advance has been made,which sets up two new theorems on evaluating the exact electrical characteristics (potential and resistance) of the complex m×n resistor networks by the recursion-transform method with potential parameters,and applies to a variety of different types of lattice structure with arbitrary boundaries such as the nonregular m×n rectangular networks and the nonregular m×n cylindrical networks.Our research gives the analytical solutions of electrical characteristics of the complex networks (finite,semi-infinite and infinite),which has not been solved before.As applications of the theorems,a series of analytical solutions of potential and resistance of the complex resistor networks are discovered.