颗粒介质的离散态特性研究

回顾了颗粒介质中应力的分布和传播模式以及物体在颗粒介质中运动所受阻力的研究进展，并报道了我们对颗粒体系中代表离散特性的颗粒尺寸效应对颗粒介质特性影响的研究.研究发现物体由于自身重量在颗粒介质中下沉的深度随着颗粒尺寸的增大单调减小；球体在下陷过程中受到的颗粒床的支撑力，除了在约1 mm范围的表面作用区域以外，与下陷深度之间满足很好的幂率关系，幂值在1.5—1.0之间，并且此幂值随着颗粒尺寸的增大而单调减小.颗粒床的支撑力与下陷深度的幂率关系可解释为颗粒介质内部应力结构重组的宏观反应结果. 关键词： 颗粒物质 离散介质力学     

Levitation and lateral forces between a point magnetic dipole and a superconducting sphere

The dipole–dipole interaction model is employed to investigate the angular dependence of the levitation and lateral forces acting on a small magnet in an anti-symmetric magnet/superconducting sphere system. Breaking the symmetry of the system enables us to study the lateral force which is important in the stability of the magnet above a superconducting sphere in the Meissner state. Under the assumption that the lateral displacement of the magnet is small compared to the physical dimensions of our proposed system, analytical expressions are obtained for the levitation and lateral forces as a function of the geometrical parameters of the superconductor as well as the height, the lateral displacement, and the orientation of the magnetic moment of the magnet. The dependence of the levitation force on the height of the levitating magnet is similar to that in the symmetric magnet/superconducting sphere system within the range of proposed lateral displacements. It is found that the levitation force is linearly dependent on the lateral displacement whereas the lateral force is independent of this displacement. A sinusoidal variation of both forces as a function of the polar and azimuthal angles specifying the orientation of the magnetic moment is observed. The relationship between the stability and the orientation of the magnetic moment is discussed for different orientations.     

Construction of the mass velocity profile for a rarefied molecular gas entrained by a rotating sphere taking into account thermophysical parameters of the gas

The problem of a sphere rotating in a molecular gas is solved in the isothermal approximation. The expression for the velocity of a rarefied molecular gas entrained by a sphere rotating in it is derived for sliding flow conditions taking into account the second-order correction in the Knudsen number. A generalization of the Boltzmann kinetic equation in the BGK model to the case of rotational degrees of freedom of gas molecules is used as the basic equation. The diffusive reflection model is employed as the microscopic boundary condition on the surface of the sphere. It is shown that this approach makes it possible to take into account the dependence of the gas velocity on the Prandtl number and gas temperature.     

Energy of a solid sphere under nonstationary oscillations

Analytical solution for spherically symmetric nonstationary oscillations of acoustic and elastic solid sphere is given. Time dependence of potential, kinetic and internal energy of a solid sphere is analyzed. The received results are of practical importance for a wide range of problems connected to testing of material dynamic strength parameters and to the problems of optimizing (minimizing) energy needed for fracture of solids.     

Axial chiral vortical effect in a sphere with finite size effect

We investigate the axial vortical effect in a uniformly rotating sphere subject to finite size. We use the MIT boundary condition to limit the boundary of the sphere. For massless fermions inside the sphere, we obtain the exact axial vector current far from the boundary that matches the expression obtained in cylindrical coordinates in literature. On the spherical boundary, we find both the longitudinal and transverse (with respect to the rotation axis) components with magnitude depending on the colatitude angle. For massive fermions, we derive an expansion of the axial conductivity far from the boundary to all orders of mass, whose leading order term agrees with the mass correction reported in literature. We also obtain the leading order mass correction on the boundary, which is linear and stronger than the quadratic dependence far from the boundary. The qualitative implications on the phenomenology of heavy ion collisions are speculated.     

The correlations in a star molecule fluid. Integral equation theory and Monte Carlo study

The structure of a starlike molecule (SLM) fluid with four arms of different length is studied by applying the associative Percus–Yevick integral equation (IE) theory and canonical Monte Carlo (MC) simulations. In the IE study the SLM fluid is modelled by a fluid of hard spheres with four associative sites on each sphere while the MC has been performed for a freely-joined tangent hard sphere fluid. The total radial distribution functions have been calculated in both approaches for different volume fraction regimes and different arm lengths. It is shown that the associative IE theory predicts the structure of SLM fluid best for relatively long arms and at high densities. Additionally, the dependence of the SLM centre–centre correlations on the functionality and fluid particle density has been analysed using the MC results.     

Modeling of short-range order in a defect square lattice

The short-range order and pair correlations in a square lattice in which some part of sites are occupied by A atoms and the other are vacant have been investigated by computer simulation. It is shown that, in the presence of interactions in the first coordination sphere of an A _y □_{1 ? y} solid solution with a square lattice, induced pair correlations damp only in the ninth coordination sphere. A functional dependence between the correlation in the first coordination sphere and the induced correlations in the next coordination spheres has been established for different compositions of the solid solution.     

Biminimal hypersurfaces in a sphere

In this paper, we mainly concentrate on the biminimal hypersurfaces in a sphere. First, we obtain some rigidity theorems for biminimal hypersurfaces. Then we give a classification of non-minimal biminimal isoparametric hypersurfaces in a sphere.     

Contact force resulting from rolling on a self-affine fractal rough surface

The time dependence of the contact force resulting from the rolling of a sphere on self-affine fractal rough surfaces was investigated using the method of reduction of dimensionality. The main focus was on the part of the spectrum corresponding to the short wavelength corrugation (with a wavelength much smaller than the nominal contact radius). It has been shown that in this domain, the spectral density of the normal force is a power function of frequency. This result can be used for calculation of high frequency acoustic emission of rolling contacts in various technical systems as well as for development of diagnostic systems.     

Capillary aging of the contacts between glass spheres and a quartz resonator surface

The strength of the contacts between small glass spheres and the surface of a quartz crystal resonator has been probed based on the increase of resonance frequency induced upon sphere contact. The acoustic interaction between the sphere and the plate is modeled as a low-frequency coupled resonance; the dependence of the resonant parameters on overtone order lends support to this model. After exposing the sample to humid air and drying it again, the contact strength increases at least tenfold due to capillary forces--we observe a hysteretic form of the sand-castle effect. Repeated wet-dry cycles reveal logarithmic capillary aging with time. The experiments suggest that the drying of the liquid bridges leads to a contraction of small voids in the contact zone, subsequently increasing cohesion.     

Inelastic scattering of slow electrons by molecules adsorbed on a small metal sphere

The differential cross section for inelastic scattering of slow electrons by dipole excitation of molecules adsorbed on a small metal sphere is calculated. The significance of the exact hard core wave functions in calculating the cross section is shown by comparison with the corresponding plane-wave result. A strong radius dependence is obtained for the cross section at low energies. We conclude from our results that the scattering process studied provides a promising testing ground for the quantum dynamics of slow electrons near a small metal sphere.     

Calculation of the force characteristics of a multi-coil suspension of a superconducting sphere

The theory presented in the accompanying paper [Ref. 1: Zh. Tekh. Fiz. 67(1), 3 (1997); Tech. Phys. 42, 1 (1997)] for the calculation of the magnetic field and the force characteristics of an electromagnetic suspension for a superconducting body is used to carry out specific calculations of the force characteristics of a multi-coil suspension of a superconducting sphere. Formulas are obtained for the dependence of the force and the stiffness, from which it is possible to approach the problem of the stable suspension of a superconducting sphere in the field of a system of circular currents. The problem of determining the magnetic field at the sphere is analyzed and the conditions are found for which it is less than the critical field. Zh. Tekh. Fiz. 67, 10–16 (January 1997)     

Maximally Entangled States of a Two-Qubit System

Entanglement has been explored as one of the key resources required for quantum computation, the functional dependence of the entanglement measures on spin correlation functions has been established, correspondence between evolution of maximally entangled states (MES) of two-qubit system and representation of SU(2) group has been worked out and the evolution of MES under a rotating magnetic field has been investigated. Necessary and sufficient conditions for the general two-qubit state to be maximally entangled state (MES) have been obtained and a new set of MES constituting a very powerful and reliable eigen basis (different from magic bases) of two-qubit systems has been constructed. In terms of the MES constituting this basis, Bell’s States have been generated and all the qubits of two-qubit system have been obtained. It has shown that a MES corresponds to a point in the SO(3) sphere and an evolution of MES corresponds to a trajectory connecting two points on this sphere. Analysing the evolution of MES under a rotating magnetic field, it has been demonstrated that a rotating magnetic field is equivalent to a three dimensional rotation in real space leading to the evolution of a MES.     

The Motion of a Nonholonomic Chaplygin Sphere in a Magnetic Field,the Grioli Problem,and the Barnett–London Effect

Doklady Physics - In this paper, we consider the motion of a nonholonomic Chaplygin sphere on a plane in a constant magnetic field under the assumption that the sphere has dielectric and...     

Structure sensitivity in third-harmonic generation microscopy

We characterize experimentally the influence of sample structure and beam focusing on signal level in third-harmonic generation (THG) microscopy. In the case of a homogeneous spherical sample, the dependence of the signal on the size of the sphere can be controlled by modifying the Rayleigh length of the excitation beam. More generally, the influence of excitation focusing on the signal depends on sample geometry, allowing one to highlight certain structures within a complex system. We illustrate this point by focusing-based contrast modulation in THG images of Drosophila embryos.     

Absorption of electromagnetic radiation by electrons of a nanosphere

The electrodynamic response of an electron gas on the surface of a nanosphere is investigated. An analytical relationship for the absorption of electromagnetic radiation by the nanosphere is derived. It is demonstrated that the absorption curve at low temperatures has two resonance peaks. The shape, position, and intensity of the peaks are examined. The dependence of the absorption on the radiation frequency exhibits kinks associated with the degeneracy of the electron gas. The number and position of the kinks and the absorption jumps at these kinks are analyzed. Consideration is given to the cases of an isolated sphere and a sphere exchanging electrons with a reservoir.     

Photon diffusion in a relativistically expanding sphere

A relativistically expanding sphere exists ill many explosive astrophysical systelns, including gamma ray bursts, neutron star mergers, and some supernovae. In this paper we investigate the photon diffusion process in a relativistically expanding sphere, which is important for understanding the energetic and radiative characters of the above inentioned explosive systenls. The following contents are discussed in the frame work of special relativity： random walks of photons by scattering witti electrons, photospheres, photon diffusion, and the energy flux density emerging from the surface of the expanding sphere. Some of the results are also applicable to the Universe since the Universe is also a spherical expanding system.     

积分球内的铷原子激光冷却

研究了积分球内激光冷却原理,设计积分球时对积分球的反射率、尺寸及球上开孔大小对于激光冷却的影响进行了讨论. 进行了积分球冷却⁸⁷Rb实验,实验结果表明积分球有效的冷却了球腔中的铷原子,获得了积分球内冷原子的吸收信号以及冷原子随冷却光失谐的变化曲线. 关键词： 漫反射光场 积分球 全光冷却     

Nonlinear dynamics of a flexible mechanism with impact

The nonlinear dynamics of a slider-crank mechanism with a flexible rod is considered in this study. The flexible rod is modeled with lumped masses and periodically impacted by an external flexible sphere. The impact is modeled using a kinematic coefficient of restitution. Nonlinear dynamics tools are applied to analyze the simulated data captured from the connecting rod of the mechanism. The chaotic behavior of the system is analyzed. The stability of the motion is studied using the Lyapunov exponents. The dependence between the Lyapunov exponents and the corresponding angular velocity of the driver link of the mechanism is investigated.