欧拉圆盘不同能量耗散机理之间的关联

本文研究了欧拉圆盘运动过程中盘厚度以及盘面与水平面夹角α两因素对能量耗散的影响. 得出圆盘厚度与直径之比x对能量变化中各项因子的影响: x很小时, 质心在竖直方向上的动能变化和重力势能变化是系统能量耗散的主要因素; 当x>0.4142时, 圆盘绕与之平行的轴的转动动能变化成为主要因素, 并给出圆盘厚度可忽略的条件. 模拟了滚动摩擦、空气黏滞等不同能量耗散方式与x,α的关系, 导出各种耗散方式在圆盘运动的过程中的转变规律, 并指出x=0.1733, α>18°时能量耗散形式为纯滚动摩擦, 这修正了文献[26]结论.     

有限深两层流体中内孤立波造波实验及其理论模型

将置于大尺度密度分层水槽上下层流体中的两块垂直板反方向平推, 以基于 Miyata-Choi-Camassa (MCC)理论解的内孤立波诱导上下层流体中的层平均水平速度作为其运动速度, 发展了一种振幅可控的双推板内孤立波实验室造波方法. 在此基础上, 针对有限深两层流体中定态内孤立波 Korteweg-de Vries (KdV), 扩展KdV (eKdV), MCC和修改的Kdv (mKdV)理论的适用性条件等问题, 开展了系列实验研究.结果表明, 对以水深为基准定义的非线性参数ε 和色散参数μ, 存在一个临界色散参数μ₀, 当μ < μ₀ 时, KdV理论适用于ε ≤μ 的情况, eKdV理论适用于μ < ε ≤√μ 的情况, 而MCC理论适用于ε > √μ 的情况, 而且当μ ≥μ₀ 时MCC理论也是适用的.结果进一步表明, 当上下层流体深度比并不接近其临界值时, mKdV理论主要适用于内孤立波振幅接近其理论极限振幅的情况, 但这时MCC理论同样适用.本项研究定量地表征了四类内孤立波理论的适用性条件, 为采用何种理论来表征实际海洋中的内孤立波特征提供了理论依据. 关键词： 两层流体 内孤立波 双板造波 临界色散参数     

波浪破碎气体的卷入过程及相关统计量的估计

基于实验观测,导出了波浪破碎能量耗散ε_ed、气泡云卷入深度z_b、气体卷入速率Q(z)和湍流动能耗散率ε_T(z)的表达式,在此基础上建立了一种简单、实用的气泡粒径谱参数化模式N(a,z),揭示了波浪破碎气泡云卷入过程能量耗散、气泡破碎临界Hinze特征尺度和气泡粒径谱在不同海况下的变化. 研究表明：气泡云卷入过程能量耗 关键词： 波浪破碎能量耗散 气泡云卷入深度 气泡粒径谱     

圆形射流中心线上小尺度湍流的统计特性及其受高频噪声的影响

本文采用热线风速仪测量了出口雷诺数为Re (≡ U_jd/ν) = 20100的圆形射流的中心线轴向速度,其中U_j为动量平均出口速度,d为喷嘴出口直径,ν为运动黏性系数.在有效去除热线测量数据中的高频噪声后,作者对射流中心线上小尺度湍流统计量的变化规律进行了系统的分析.研究发现,射流在经过一定距离的发展后,其小尺度统计量逐渐进入自相似状态,湍动能平均耗散率ε随下游距离的增加以指数形 关键词： 恒温热线 圆形湍射流 耗散率 小尺度     

微平行管道内Jeffrey流体的非定常电渗流动

研究了微平行管道内线性黏弹性流体的非定常电渗流动, 其中线性黏弹性流体的本构关系是由Jeffrey流体模型来描述的. 利用Laplace变换法, 求解了线性化的Poisson-Boltzmann方程、 非定常的柯西动量方程和Jeffrey流体本构方程, 给出了黏弹性Jeffrey流体电渗速度的解析表达式, 分析了无量纲弛豫时间λ₁和滞后时间λ₂对速度剖面的影响. 发现滞后时间为零时, 弛豫时间越小, 速度剖面图越接近牛顿流体的速度剖面图; 随着弛豫时间和滞后时间的增加, 速度振幅也变得越来越大, 随着时间的增加, 速度逐渐趋于恒定. 关键词： 双电层 微平行管道 Jeffrey流体 非定常电渗流动     

颗粒速度在颗粒流稀疏流-密集流转变中的作用

用实验和计算模拟的方法研究了颗粒流中的颗粒速度与颗粒流特性的关系.实验研究发现当入口流量固定时，在出口上方高速运动的颗粒会使颗粒流由稀疏流向密集流转变的临界出口尺寸变小.当颗粒流转变为密集流后，颗粒速度的作用被出口上方的颗粒堆积区所消耗，最终变得与颗粒速度无关.二维分子动力学模拟计算得到了与实验相同的结论.通过二维分子动力学模拟计算，还给出了不同颗粒速度下体系的密度和速率在空间的分布图.这些分布图显示随着颗粒到达出口上方的瞬间速度的不同，颗粒堆积区的密度和高度均会改变，并最终导致颗粒流流动状态的改变. 关键词： 颗粒流 颗粒气体 分子动力学模拟     

三维颗粒气体相分离现象

颗粒体系是一类复杂的耗散体系.在颗粒气体中,耗散性质会使其内部形成局部的凝聚,类似于真实气体中亚稳分解形成的液滴,因此被认为是颗粒气液两相分离的过程. 零重力环境下二维颗粒气体相分离现象已有成熟的流体静力学理论解释,将该理论模型推广到三维情形,发现相分离现象依然存在且具有同样的不稳定性根源,通过理论计算给出了三维相分离发生的具体条件. 同时,用分子动力学方法模拟检验了理论结果,并给出了三维颗粒气体相分离的新形貌. 关键词： 颗粒气体 耗散 相分离 分子动力学模拟     

利用Ghost Fluid方法模拟激波与柱形界面相互作用

利用GhostFluid方法(后面简称Ghost方法)和γ-model方法,在同样的时空离散精度条件下,对激波与柱形界面相互作用的二维可压缩流场进行了直接模拟,并与实验结果相比较.从模拟结果看,在短时间内,Ghost方法和γ-model方法模拟的结果与实验结果基本相同,两种方法均正确地模拟出界面的位置、激波的强度和速度.但随着时间的发展,具有较大数值耗散的γ-model方法的计算结果与实验差别越来越大;而数值耗散较小的Ghost方法能较为正确地模拟界面的运动.     

垂直振动激励下颗粒材料有效质量和耗散功率的研究

研究了垂直振动激发下钨颗粒的动态有效质量(ω) 和耗散功率p(ω)随频率ω 的依赖关系. 实验发现, 在给定的振动幅度下, 自由表面样品有效质量的实数部分M₁ (ω) 、虚数部分M₂ (ω) 以及耗散功率p(ω)随频率的变化曲线均出现一个尖锐的共振峰. 随着在颗粒上表面施加压强的增大, M₁ (ω), M₂ (ω) 和耗散功率p(ω)曲线的峰值频率向高频移动, 且峰值高度也相应增大. 进一步研究发现, 有效质量实数部分的共振频率f_g 随表面压强P的变化满足分段幂律规律, 当P较小时, 幂指数为0.3, 当P较大时, 幂指数减小为1/6. 颗粒系统的品质因子的倒数1/Q随压强P的变化满足指数衰减规律.     

H$lt;sub$gt;2$lt;/sub$gt;$lt;sup$gt;+$lt;/sup$gt;在强激光场中的解离及其量子调控的理论研究

利用非波恩-奥本海默近似的三维含时量子波包法,理论研究了氢分子离子在强激光场中的解离动力学.通过分析H₂⁺在不同的初始振动态（ν=0–9）和激光场强度下的解离核动能谱,得到了H₂⁺的光解离机理及其随激光场的变化规律.研究结果表明：当激光场的强度I₁=5.0×10¹³ W/cm²时,分子的解离来源于高振动态ν=5–9,其解离机理主要是通过键软化、键硬化和阈下解离过程.当激光场的强度I₂=1.0×10¹⁴ W/cm² 时,H₂⁺在低振动态ν=3–4上的阈上解离起主导作用,而高振动态的键软化、键硬化和阈下解离所占的比重明显地下降了.研究结果为后续的量子调控的实验研究提供了科学的理论预测和指导. 关键词： 光解离 氢分子离子 含时波包法 核动能谱     

冲击荷载下颗粒物质缓冲性能的试验研究

颗粒物质是一种复杂的能量耗散体系. 颗粒间的摩擦和黏滞作用可使冲击荷载引起的能量有效衰减, 颗粒间的力链结构又可将瞬时局部冲击荷载进行空间扩展和时间延长, 达到良好的缓冲效果. 为研究颗粒物质对冲击荷载的缓冲性能, 本文采用重力作用下球体冲击筒内颗粒物质的试验系统, 研究了筒体底部作用力在颗粒材料、颗粒厚度等因素影响下的变化规律. 试验结果表明: 非规则颗粒具有更加良好的缓冲性能, 粗颗粒的缓冲性能略高于细颗粒. 颗粒厚度H是影响缓冲性能的重要因素, 并存在一个临界厚度H_c. 当H<H_c时, 缓冲性能随H的增加而增强; 当H>H_c时, H对缓冲效果的影响不再显著. 以上研究是在同一冲击能量下进行的, 而对于不同冲击能量下的H_c还需要深入开展. 通过颗粒物质对冲击荷载缓冲性能的试验研究, 可揭示颗粒材料的基本物理力学行为, 为其在缓冲减振领域中的应用提供依据.     

Free cooling phase-diagram of hard-spheres with short- and long-range interactions

We study the stability, the clustering and the phase-diagram of free cooling granular gases. The systems consist of mono-disperse particles with additional non-contact (long-range) interactions, and are simulated here by the event-driven molecular dynamics algorithm with discrete (short-range shoulders or wells) potentials (in both 2D and 3D). Astonishingly good agreement is found with a mean field theory, where only the energy dissipation term is modified to account for both repulsive or attractive non-contact interactions. Attractive potentials enhance cooling and structure formation (clustering), whereas repulsive potentials reduce it, as intuition suggests. The system evolution is controlled by a single parameter: the non-contact potential strength scaled by the fluctuation kinetic energy (granular temperature). When this is small, as expected, the classical homogeneous cooling state is found. However, if the effective dissipation is strong enough, structure formation proceeds, before (in the repulsive case) non-contact forces get strong enough to undo the clustering (due to the ongoing dissipation of granular temperature). For both repulsive and attractive potentials, in the homogeneous regime, the cooling shows a universal behaviour when the (inverse) control parameter is used as evolution variable instead of time. The transition to a non-homogeneous regime, as predicted by stability analysis, is affected by both dissipation and potential strength. This can be cast into a phase diagram where the system changes with time, which leaves open many challenges for future research.     

Cumulative author index of Volumes 351 to 360

The dynamic evolution of granular gases is fundamentally different from molecular gases due to the energy loss during collisions. Nevertheless techniques of kinetic theory are useful in a regime, when the granular particles are moving rapidly and the gas is sufficiently dilute. In these lecture notes we analyse in detail the collision of two rough particles which is inelastic due to incomplete normal and tangential restitution as well as Coulomb friction. Based on the Walton model a time evolution operator for the many particle system is introduced, a formalism which is well suited for simple approximations. We discuss free cooling of granular particles with particular emphasis on the exchange of energy between rotational and translational degrees of freedom.     

Dispersive flow of disks through a two-dimensional Galton board

We report here an experimental and numerical study of the flow properties of disks driven by gravity through a hexagonal lattice of obstacles, i.e. a Galton board. During the fall, particles experience dissipative collisions that scatter them in random directions. A driven-diffusion regime can be achieved under certain conditions. A characteristic length of the motion and its dependence on geometrical parameters of the system is analyzed in the steady regime. The influence of collective effects on the dispersion process is investigated by comparison between single- and many-particle flows. The characterization of the dynamics and the diffusive properties of the flow in a system like a Galton board can be expanded to other granular systems, particularly static solid particle mixers and will give some insight in understanding granular mixing.     

Singular Energy Distributions in Driven and Undriven Granular Media

We study the kinetic theory of driven and undriven granular gases, taking into account both translational and rotational degrees of freedom. We obtain the high-energy tail of the stationary bivariate energy distribution, depending on the total energy E and the ratio of rotational energy E _w to total energy. Extremely energetic particles have a unique and well-defined distribution f(x) which has several remarkable features: x is not uniformly distributed as in molecular gases; f(x) is not smooth but has multiple singularities. The latter behavior is sensitive to material properties such as the collision parameters, the moment of inertia and the collision rate. Interestingly, there are preferred ratios of rotational-to-total energy. In general, f(x) is strongly correlated with energy and the deviations from a uniform distribution grow with energy. We also solve for the energy distribution of freely cooling Maxwell Molecules and find qualitatively similar behavior.     

Brownian motion in granular gases of viscoelastic particles

A theory is developed of Brownian motion in granular gases (systems of many macroscopic particles undergoing inelastic collisions), where the energy loss in inelastic collisions is determined by a restitution coefficient ɛ. Whereas previous studies used a simplified model with ɛ = const, the present analysis takes into account the dependence of the restitution coefficient on relative impact velocity. The granular temperature and the Brownian diffusion coefficient are calculated for a granular gas in the homogeneous cooling state and a gas driven by a thermostat force, and their variation with grain mass and size and the restitution coefficient is analyzed. Both equipartition principle and fluctuation-dissipation relations are found to break down. One manifestation of this behavior is a new phenomenon of “relative heating” of Brownian particles at the expense of cooling of the ambient granular gas.     

Cooling kinetics of a granular gas of viscoelastic particles

The evolution of a granular gas of viscoelastic particles in the homogeneous cooling state is studied. The velocity distribution function of granular particles and the time dependence of the mean kinetic energy of particles (granular temperature) are found. The noticeable deviation of the distribution function from the Maxwell distribution and its non-monotonous evolution are established. The perturbation theory with respect to the small dispersion parameter is elaborated and the analytical expressions for the asymptotic time dependence of the velocity distribution function and the granular gas temperature are derived.     

Cluster formation, pressure and density measurements in a granular medium fluidized by vibrations

We report experimental results on the behavior of an ensemble of inelastically colliding particles, excited by a vibrated piston in a vertical cylinder. When the particle number is increased, we observe a transition from a regime where the particles have erratic motions (“granular gas”) to a collective behavior where all the particles bounce like a nearly solid body. In the gas-like regime, we measure the density of particles as a function of the altitude and the pressure as a function of the number N of particles. The atmosphere is found to be exponential far enough from the piston, and the “granular temperature”, T, dependence on the piston velocity, V, is of the form , where is a decreasing function of N. This may explain previous conflicting numerical results. Received 1 February 1999     

Thermodynamics of two-parameter quantum group Bose and Fermi gases

The high and low temperature thermodynamical properties of the two-parameter deformed quantum group Bose and Fermi gases with SU _p/q (2) symmetry are studied. Starting with a SU _p/q (2)-invariant bosonic as well as fermionic Hamiltonian, several thermodynamical functions of the system such as the average number of particles, internal energy and equation of state are derived. The effects of two real independent deformation parameters p and q on the properties of the systems are discussed. Particular emphasis is given to a discussion of the Bose-Einstein condensation phenomenon for the two-parameter deformed quantum group Bose gas. The results are also compared with earlier undeformed and one-parameter deformed versions of Bose and Fermi gas models. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.