Collective motion of polar active particles on a sphere

Collective motion of active particles with polar alignment is investigated on a sphere. We discussed the factors that affect particle swarm motion and define an order parameter that can show the degree of particle swarm motion. In the model, we added a polar alignment strength, along with Gaussian curvature, affecting particles swarm motion. We find that when the force exceeds a certain limit, the order parameter will decrease with the increase of the force. Combined with our definition of order parameter and observation of the model, the reason is that particles begin to move side by side under the influence of polar forces. In addition, the effects of velocity, rotational diffusion coefficient, and packing fraction on particle swarm motion are discussed. It is found that the rotational diffusion coefficient and the packing fraction have a great influence on the clustering motion of particles, while the velocity has little influence on the clustering motion of particles.     

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.     

A mechanical model of Brownian motion in half-space

We consider the motion of a heavy mass in an ideal gas in a semi-infinite system, with elastic collisions at the boundary. The motion is determined by elastic collisions. We prove in the Brownian motion limit the convergence of the position and velocity process of the heavy particle to a diffusion process in which velocity and position remain coupled.     

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.     

Rotational dynamics of propylene inside Na-Y zeolite cages

We report here the quasielastic neutron scattering (QENS) studies on the dynamics of propylene inside Na-Y zeolite using triple axis spectrometer (TAS) at Dhruva reactor, Trombay. Molecular dynamics (MD) simulations performed on the system had shown that the rotational motion involves energy larger than that involved in the translational motion. Therefore, rotational motion was not observed in our earlier QENS studies on propylene adsorbed Na-Y zeolite using a higher resolution spectrometer at Dhruva. Analysis of the TAS spectra revealed that the quasielastic broadening observed in propylene-loaded zeolite spectra is due to the rotational motion of the propylene molecules. This is consistent with our simulation result. Further, the rotational motion is found to be isotropic. The rotational diffusion coefficient has been obtained.      

Dynamics of individuals and swarms with shot noise induced by stochastic food supply

We study the Brownian dynamics of individual particles with energy depot in two dimensions and extend the model to swarms of such particles. We assume that the elements (energy depots) are provided at discrete times with packets of chemical energy which is subsequently converted into acceleration of motion. In contrast to the mechanical white noise which is incorporated in the equations of mechanical motion and has no preferred direction, the energetic noise, as discussed in this study, is directed and it does not reverse the direction of mechanical motion. We characterize the effective noise acting on the particles and show that the stochastic energy supply may be modeled as a shot-noise driven Ornstein-Uhlenbeck process in energy which finally results in fluctuations of the velocity. We study the energy and velocity distributions for different regimes and estimate the crossover time from ballistic to diffusion motion. Further we investigate the dynamics of swarms and find a transition from translational to rotational motion depending on the rate of the shot noise.     

On steady and pulsatile motion of blood

A mathematical model has been developed to study the effect of magnetic field on steady and pulsatile motion of blood through a small, rigid, circular tube by microcontinuum approach. The numerical solutions for velocity and cell rotational velocity are obtained and their nature is shown graphically.     

Derivation of microscopic uni-axial unified adiabatic Bohr–Mottelson rotational model

For a rotational motion about a single axis, we derive a microscopic, quantum version of the phenomenological Bohr–Mottelson unified adiabatic rotational model without using redundant coordinates, imposing constraints on the intrinsic state or the particle coordinates, or assuming explicitly a deformed intrinsic state. The model Schrödinger equation is derived from the direct action of the multi-particle Hamiltonian operator on the rotational-model wavefunction. We show that the Coriolis-coupling terms in the derived Schrödinger equation vanish exactly only for a choice of the Euler angle that is consistent with the rotational model requirement that the intrinsic wavefunction be invariant under rotation. For this angle, which also satisfies the conjugate commutation relation, the kinematic moment-of-inertia tensor, collective-rotation velocity field, and flow vorticity have the rigid-flow characteristics. Pairing interaction and fluctuations in the rigid-flow moment of inertia are shown to reduce the rigid-flow value of the kinematic moment of inertia in closer agreement with the experimental value. The derivation shows that a multi-fermion system with unpaired or paired (quasi) particles rotates nearly rigidly and a single-particle system rotates irrotationally if the intrinsic system is rotationally invariant, regardless of the value of the moment of inertia and the nature of the rotationally-invariant momentum-independent interaction.     

Reciprocity in electrohydrodynamics

We consider a rigid body of arbitrary shape with a permanent charge distribution and a permanent dielectric profile immersed in a fluid with a frequency dependent dielectric constant. The body performs small oscillatory translational and rotational motions and the whole system is subjected to an applied electric field oscillating at the same frequency. The force and torque on the body and its external dipole moment are related by a resistance matrix to the translational and rotational velocity and the applied electric field. We show on the basis of the equations of linear electrohydrodynamics that the resistance matrix is symmetric. This may be regarded as an example of Onsager symmetry.     

Theoretical prediction of a rotating magnon wave packet in ferromagnets

We theoretically show that the magnon wave packet has a rotational motion in two ways: a self-rotation and a motion along the boundary of the sample (edge current). They are similar to the cyclotron motion of electrons, but unlike electrons the magnons have no charge and the rotation is not due to the Lorentz force. These rotational motions are caused by the Berry phase in momentum space from the magnon band structure. Furthermore, the rotational motion of the magnon gives an additional correction term to the magnon Hall effect. We also discuss the Berry curvature effect in the classical limit of long-wavelength magnetostatic spin waves having macroscopic coherence length.     

A geometric classical model of collective motion in nuclei

A collective phase space of dimension 12 is introduced to study a classical model of nuclear collective motion. The model employs the 6 components of the coordinate quadrupole and 6 corresponding generalized momenta and can be related to properties of closed-shell nuclei. Vibrational and rotational coordinates are introduced, and purely rotational solutions are studied. The model demonstrates hamiltonian non-rigid motion with a fixed shape of the nucleus. The relation between the coordinate quadrupole tensor and the ellipsoids related to the angular momentum and angular velocity is analyzed for simple forms of the collective potential.     

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.     

Molecular dynamics calculations for HCl in a matrix of solid Ar

We present the results of molecular dynamics calculations on HCl molecules, matrix-isolated in solid fcc argon, using the recently proposed M2 potential of Hutson and Howard. The power spectrum of the centre of mass velocity autocorrelation function of the HCl molecules is in good agreement with the experimental far infrared spectrum. Although there is considerable rotational motion of the HCl molecules, the Cl-H bond vector shows a preference for the crystallographic ?111? direction rather than the ?110? direction suggested by the dimer structure.     

An approximate global solution of Einstein’s equations for a differentially rotating compact body

We obtain an approximate global stationary and axisymmetric solution of Einstein’s equations which can be thought of as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the post-Minkowskian formalism (weak-field approximation) and considering rotation as a perturbation (slow-rotation approximation), we find approximate interior and exterior (asymptotically flat) solutions to this problem in harmonic coordinates. Interior and exterior solutions are matched, in the sense described by Lichnerowicz, on the surface of zero pressure, to obtain a global solution. The resulting metric depends on four arbitrary constants: mass density; rotational velocity at \(r=0\); a parameter that accounts for the change in rotational velocity through the star; and the star radius in the non-rotation limit. The mass, angular momentum, quadrupole moment and other constants of the exterior metric are determined in terms of these four parameters.     

Instability of the Y string baryon model within classical dynamics

For the three-string baryon model (Y configuration), the known exact solution to the classical equations of motion that describes the rotational motion of the system at a constant speed is investigated for stability. In the spectrum of small perturbations of this solution, modes growing exponentially with time are found, whereby the instability of rotational motion is proven for the Y configuration. This result is confirmed within an alternative approach that makes it possible to determine the classical motion of the system from a specific initial position and initial velocities of string points. A comparison of the Y configuration with the model of a relativistic string with massive ends, in which case rotational motion is stable in the linear approximation, aids in revealing the most adequate string model from the point of view of describing baryon excitations on Regge trajectories.     

Membranes with rotating motors

We study collections of rotatory motors confined to two-dimensional manifolds. These systems show a nontrivial collective behavior since the rotational motion leads to a repulsive hydrodynamic interaction between motors. While for high rotation speed motors might exhibit crystalline order, they form at low speed a disordered phase where diffusion is enhanced by velocity fluctuations. These effects should be experimentally observable for motors driven by external fields and for dipolar biological motors embedded into lipid membranes in a viscoelastic solvent.     

Simultaneous control of longitudinal and transverse vibrations of an axially moving string with velocity tracking

In this paper, an active control scheme for an axially moving string system that suppresses both longitudinal and transverse vibrations and regulates the transport velocity of the string to track a desired moving velocity profile is investigated. The control scheme utilizes three inputs: one control force at the right boundary, which is exerted by a hydraulic actuator equipped with a damper, and two control torques applied at the left and right rollers. The equations of motion are derived by using Hamilton's principle. Two nonlinear partial differential equations govern the longitudinal and transverse motions, where the variation of the tension of the string due to the transverse and longitudinal vibrations is considered. Among four boundary conditions, two describe the rotational dynamics of the left and right rollers; one determines the dynamics of the hydraulic actuator at the right boundary, and the last one denotes that the left boundary is fixed. The Lyapunov method is employed to generate control laws. Asymptotic stability of the transverse and longitudinal dynamics and the velocity tracking error is achieved. The effectiveness of the proposed control scheme is illustrated via numerical simulations.     

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.     

基于气体动理论的二维Karman涡街数值模拟

基于从稀薄流到连续流的跨流域气体动理论统一算法(gas-kinetic unified algorithm,GKUA),通过数值求解考虑转动自由度激发的Boltzmann-Rykov模型方程,得到了一种跨流域非定常流动数值模拟的方法.该求解方法以Boltzmann模型方程为控制方程,在常温状态下如果考虑转动能激发的情况...     

Thermally induced effects on the diffraction pattern of a dye doped nematic film

We investigate the effects produced on the diffraction pattern of a dyed nematic thin film under the action of an optical field and a low frequency AC electric field. For a homeotropically aligned mixture of the nematic E7 doped with a dichroic dye, a sequence of dynamical regimes of the far field diffraction pattern is observed. For specific values of the beam's power, frequency and amplitude of the AC field, a uniform steady rotational motion (SR) of the pattern sets in with a measured angular velocity ν_exp =2.58 Hz. To account for this and other observed features of the diffraction pattern an analytical model is proposed. This allows us to describe quantitatively the reorientation of the film, to calculate some specific structural features of the diffraction pattern, as well as its angular velocity. We find that the predicted angular velocity ν_theor=5.7 Hz, is in quite good agreement with the measured value.