Equipartition of rotational and translational energy in a dense granular gas

Experiments quantifying the rotational and translational motion of particles in a dense, driven, 2D granular gas floating on an air table reveal that kinetic energy is divided equally between the two translational and one rotational degrees of freedom. This equipartition persists when the particle properties, confining pressure, packing density, or spatial ordering are changed. While the translational velocity distributions are the same for both large and small particles, the angular velocity distributions scale with the particle radius. The probability distributions of all particle velocities have approximately exponential tails. Additionally, we find that the system can be described with a granular Boyle's law with a van?der?Waals-like equation of state. These results demonstrate ways in which conventional statistical mechanics can unexpectedly apply to nonequilibrium systems.     

Large eddy simulation of orientation and rotation of ellipsoidal particles in isotropic turbulent flows

The rotational motion and orientational distribution of ellipsoidal particles in turbulent flows are of significance in environmental and engineering applications. Whereas the translational motion of an ellipsoidal particle is controlled by the turbulent motions at large scales, its rotational motion is determined by the fluid velocity gradient tensor at small scales, which raises a challenge when predicting the rotational dispersion of ellipsoidal particles using large eddy simulation (LES) method due to the lack of subgrid scale (SGS) fluid motions. We report the effects of the SGS fluid motions on the orientational and rotational statistics, such as the alignment between the long axis of ellipsoidal particles and the vorticity, the mean rotational energy at various aspect ratios against those obtained with direct numerical simulation (DNS) and filtered DNS. The performances of a stochastic differential equation (SDE) model for the SGS velocity gradient seen by the particles and the approximate deconvolution method (ADM) for LES are investigated. It is found that the missing SGS fluid motions in LES flow fields have significant effects on the rotational statistics of ellipsoidal particles. Alignment between the particles and the vorticity is weakened; and the rotational energy of the particles is reduced in LES. The SGS-SDE model leads to a large error in predicting the alignment between the particles and the vorticity and over-predicts the rotational energy of rod-like particles. The ADM significantly improves the rotational energy prediction of particles in LES.     

CO_2与高振动激发K_2碰撞中的全分辨转动态分布

在K_2+CO_2中,受激发射泵浦得到K_2(E=3 500和4 000cm~(-1))高位振动态,研究了高振动激发K_2与CO_2碰撞产生的CO_2全分辨转动态分布。利用高分辨瞬时激光诱导荧光(LIF)测量了CO_2(0000)J=2~74的转动和平移能量轮廓,利用双高斯函数拟合,分别确定各转动态的产生和倒空线宽,从而得到碰撞产生的Doppler展宽、平移温度和平移能。对于K_2不同的激发能E,能量转移的机制是相似的,为振动-转动/平移弛豫机制。但碰撞出现部分的平移温度均超出池温,而碰撞倒空部分的平移温度均略低于池温,平移能随E的增加而增大,E增加14%,平移能增加40%。CO_2(0000)转动态分布的半对数描绘给出了双指数分布,对于K_2E=3 500cm~(-1),低J态分布T_a=(523±60)K,高J态分布T_b=(1 890±210)K。Ta接近池温,说明低J态为近弹性碰撞,属单量子弛豫过程,而高J态为非弹性碰撞,属多量子驰豫过程。对于K_2E=4 000cm~(-1)同样有双指数行为,低J分布T_a=(620±65)K,高J分布T_b=(2 240±250)K。高振动态K_2(E)与CO_2碰撞,E=4 000cm~(-1)比E=3 500cm~(-1)的Ta和Tb均约高19%,说明转动分布对于K_2不同能量是敏感的,但弹性和非弹性分支比是基本相同的,弱碰撞约占82%,强碰撞约占18%。     

Dynamics of uniaxial hard ellipsoids

We study the dynamics of monodisperse hard ellipsoids via a new event-driven molecular dynamics algorithm as a function of volume fraction phi and aspect ratio X0. We evaluate the translational D(trans) and the rotational D(rot) diffusion coefficients and the associated isodiffusivity lines in the phi-X0 plane. We observe a decoupling of the translational and rotational dynamics which generates an almost perpendicular crossing of the D(trans) and D(rot) isodiffusivity lines. While the self-intermediate scattering function exhibits stretched relaxation, i.e., glassy dynamics, only for large phi and X(0) approximately 1, the second order orientational correlator C2(t) shows stretching only for large and small X0 values. We discuss these findings in the context of a possible prenematic order driven glass transition.     

Computer simulations of a rough sphere fluid I

A molecular dynamics simulation of a rough sphere fluid with variable roughness is presented from which the intermediate scattering function, orientational correlation functions and velocity autocorrelation functions are calculated for several values of the density, roughness and wave number. The dependence of these correlation functions on the parameters is discussed and a comparison with a neutron scattering experiment on neopentane [C(CH₃)₄] is made, which gives good agreement between the two experiments.     

Simulation studies of bilayers of N2 adsorbed on graphite at 25 and 35 K

Molecular dynamics simulations of bilayers of model nitrogen molecules adsorbed on the graphite basal plane at 25 and 35 K are reported. Systems considered include commensurate bilayers and three uniaxially compressed films, namely, two with different compressions along the X-axis (perpendicular to the herringbone lattice glideline) and one with a compression along the Y-axis, relative to the commensurate spacing. For comparison, commensurate and X-compressed monolayer films were also simulated. Properties simulated include: center-of-mass (COM) molecule-surface densities as a function of separation distance: in-plane COM pair correlation functions; in-plane and out-of-plane distributions of the molecular axis orientations; average potential energies for N₂-surface and for N₂-N₂ interactions; and velocity time-correlation functions for translational and orientational motion perpendicular to and parallel to the surface. These results indicate that the N₂ layers at these temperatures are nearly harmonic oscillator solids, with considerable orientational freedom. Molecules tend to be coplanar with the surface in both layers. The in-plane orientations for the compressed films form a herringbone lattice, in both layers, with variable angles between the molecular axis and the crystal glidliines; the commensurate film does not show herringbone ordering for the potential model used in this work. It is concluded that both the orientational and translational the degrees of freedom strongly coupled, between layers as well as within the layer. It is also shown that the Y-compressed film is unstable and that both layers in the bilayer spontaneously rearrange into a (rotated) uniaxially X-compressed structure.     

Rotational Brownian Motion of a Pair of Dipoles Coupled via a Classical Heisenberg Interaction

The rotational Smoluchowski equation for the orientational distribution function of two dipoles with classical Heisenberg interaction is solved exactly. The equilibrium self- and pair time-correlation functions of the two dipole moments are evaluated. They are shown to be approximated well over a wide range of interaction strength by a superposition of two exponentials.     

Translations and rotations are correlated in granular gases

In a granular gas of rough particles the axis of rotation is shown to be correlated with the translational velocity of the particles. The average relative orientation of angular and linear velocities depends on the parameters which characterize the dissipative nature of the collision. We derive a simple theory for these correlations and validate it with numerical simulations for a wide range of coefficients of normal and tangential restitution. The limit of smooth spheres is shown to be singular: even an arbitrarily small roughness of the particles gives rise to orientational correlations.     

Brownian dynamics simulations with spin Brownian motion on the negative magneto-rheological effect of a rod-like hematite particle suspension

We have investigated the behaviour of a suspension of magnetic rod-like hematite particles in a simple shear flow with the addition of an applied magnetic field. A significant feature of the present hematite particle suspension is the fact that the magnetic moment of the hematite particle lies normal to the particle-axis direction. From simulations, we have attempted to clarify the dependence of the negative magneto-rheological effect on the particle aggregation and orientational distribution of particles. The present Brownian dynamics method has a significant advantage in that it takes into account the spin rotational Brownian motion about the particle axis in addition to the ordinary translational and rotational Brownian motion. The net viscosity is decomposed into three components and discussed at a deeper level and in detail: these three viscosity components arise from (1) the torque due to the magnetic particle–field interaction, (2) the torque and (3) the force due to the interaction between particles. It is found that a slight change in the orientational distribution has a significant influence on the negative magneto-rheological effect. In a relatively dense suspension, the viscosity components arising from an applied magnetic field and the interaction between particles come to change rapidly for a certain strength of the magnetic particle–particle interaction, which is due to the onset of the formation of raft-like clusters.     

Glass transitions in quasi-two-dimensional suspensions of colloidal ellipsoids

We observed a two-step glass transition in monolayers of colloidal ellipsoids by video microscopy. The glass transition in the rotational degree of freedom was at a lower density than that in the translational degree of freedom. Between the two transitions, ellipsoids formed an orientational glass. Approaching the respective glass transitions, the rotational and translational fastest-moving particles in the supercooled liquid moved cooperatively and formed clusters with power-law size distributions. The mean cluster sizes diverge in power law as they approach the glass transitions. The clusters of translational and rotational fastest-moving ellipsoids formed mainly within pseudonematic domains and around the domain boundaries, respectively.     

High-beta equilibria of drift-optimized compact stellarators

Compact stellarator configurations have been obtained with good neoclassical confinement that are stable to both pressure- and current-driven modes for high values of beta. These configurations are drift-optimized tokamak-stellarator hybrids with a high-shear tokamak-like rotational transform profile and /B/ that is approximately poloidally symmetric. The bootstrap current is consistent with the required equilibrium current and, while larger than that in existing stellarators, is typically only a small fraction (1/3-1/5) of that in an equivalent tokamak. These configurations have strong magnetic wells and consequently high interchange stability beta limits up to beta=23%. Because of the reduced bootstrap current, these configurations are stable to low-n ideal MHD kink modes with no wall stabilization for values of beta ( approximately 7%-11%) significantly larger than in an equivalent advanced tokamak.     

Dynamic stability of elastically supported pipes conveying pulsating fluid

The effect of support flexibility on the dynamic behaviour of pipes conveying fluid is investigated for both steady and pulsatile flows. The pipes are built-in at the upstream end and supported at the other by both a translational and a rotational spring. For the steady flow condition, the critical flow velocities, the frequencies and flow induced damping patterns that are associated with the different vibration modes of selected pipe systems are determined as functions of the flow velocity. The results from steady flow cases show that the pipes may first lose stability by either buckling or flutter, depending on the values of the rotational and translational spring constants and their relative magnitudes. In the case of pulsatile flow, the Floquet theory is utilized for the stability analysis of the selected pipe-fluid systems. Numerical results are presented to illustrate the effects of the amount of translational and rotational resiliences at the elastic support on the regions of parametric and combination resonances of the pipes. The results more of the interesting aspects of the behaviour of non-conservative systems.     

Disclination motion in liquid crystalline films

We theoretically study a single disclination motion in a thin free-standing liquid crystalline film. Backflow effects and the own dynamics of the orientational degree of freedom (bond or director angle) are taken into account. We find the orientation field and the hydrodynamic velocity distribution around the moving disclination, which allows us to relate the disclination velocity to the angle gradient far from the disclination. Different cases are examined depending on the ratio of the rotational and shear viscosity coefficients.     

Depolarization of second-order intensity correlation tensor of light scattered by random orientation of asymmetric particles

Investigation of second-order intensity correlation tensor elements (SOICT) by depolarization measurement of light scattered on orientational fluctuations of asymmetric particles is shown to yield new information on translational and rotational molecular motions.     

Theory of phonon linewidth in orientationally disordered crystals

The dynamics of coupled translational (T) and rotational (R) modes is studied with special reference to the experimental situation in the alkali cyanides. The dynamic equations are extended and, in addition to the bilinear T-R coupling, anharmonic interactions of the form T-T-R are considered. These interactions lead to additional friction coefficients for translational and rotational motion. Transport coefficients are evaluated with mode-mode coupling theory. The validity of orientational relaxation models coupled to lattice vibration is confirmed as a particular case of the present theory at low frequencies. An extension to the high frequency regime is proposed.Dedicated to Prof. Dr. H.E. Müser ob the occasion of his 60th birthday     

非球形颗粒布朗运动的涨落-格子Boltzmann数值研究

采用涨落-格子Boltzmann方法对非球形颗粒(二维)的布朗运动进行直接数值模拟.数值结果包括椭圆形、矩形颗粒的速度均方值及速度自相关函数等.研究发现,对于非球形颗粒,其方向性并没有影响能量均分原理的适用性,每个自由度的能量由其速度或角速度的均方值确定,而且计算的颗粒平动温度和转动温度一致.此外,颗粒的速度自相关函数在相对长的时间内以~ct^-1的规律衰减,其系数c与颗粒的形状无关.     

Lattice models of advection-diffusion

We present a synthesis of theoretical results concerning the probability distribution of the concentration of a passive tracer subject to both diffusion and to advection by a spatially smooth time-dependent flow. The freely decaying case is contrasted with the equilibrium case. A computationally efficient model of advection-diffusion on a lattice is introduced, and used to test and probe the limits of the theoretical ideas. It is shown that the probability distribution for the freely decaying case has fat tails, which have slower than exponential decay. The additively forced case has a Gaussian core and exponential tails, in full conformance with prior theoretical expectations. An analysis of the magnitude and implications of temporal fluctuations of the conditional diffusion and dissipation is presented, showing the importance of these fluctuations in governing the shape of the tails. Some results concerning the probability distribution of dissipation, and concerning the spatial scaling properties of concentration fluctuation, are also presented. Though the lattice model is applied only to smooth flow in the present work, it is readily applicable to problems involving rough flow, and to chemically reacting tracers. (c) 2000 American Institute of Physics.     

Tensor analysis of the refraction distortions dynamics of a sounding optical beam

The capabilities of dynamics analysis of the sounding-beam intensity profile at the output of an atmospheric path on the basis of the chronogram structure tensor are considered. The spatio–temporal structure of the velocity field of refraction distortions is investigated. The characteristic dimensions of the regions of the translational and rotational types of flow motions are determined. The profiles of local velocity projections are obtained, as well as their statistical properties under the conditions of weak variations of meteoparameters in the output flow recording interval. Comparison of the characteristic values of wind velocity that is recorded with an array of anemometers and those calculated with the suggested method allowed us to elaborate an approach to the rough estimation of the translational and fluctuation components of aerodynamic flows at the path.