Velocity measurement of a settling sphere

We study experimentally the motion of a solid sphere settling under gravity in a fluid at rest. The particle velocity is measured with a new acoustic method. Variations of the sphere size and density allow measurements at Reynolds numbers, based on limit velocity, between 40 and 7 000. At all Reynolds numbers, our observations are consistent with the presence of a memory-dependent force acting on the particle. At short times it has a t ^-1/2 behaviour as predicted by the unsteady Stokes equations and as observed in numerical simulations. At long times, the decay of the memory (Basset) force is better fitted by an exponential behaviour. Comparison of the dynamics of spheres of different densities for the same Reynolds number show that the density is an important control parameter. Light spheres show transitory oscillations at Re∼ 400, but reach a constant limit speed. Received 12 April 2000 and Received in final form 13 July 2000     

Polarization of two close metal spheres in an external homogeneous electric field

The dipole moment of each of two uncharged conducting spheres with radius R in an external electric field was calculated. The distance between the centers of the spheres is 2l. It was shown that, if R/l≲0.8, the influence of higher multipole moments is negligible.     

Assessing the Exact Muffin-Tin Orbitals method for the Bain path of metals

Abstract

We scrutinise the muffin-tin approximation and the screening within the framework of the Exact Muffin-Tin Orbitals method in the case of cubic and tetragonal crystal symmetries. Systematic total energy calculations are carried out for the Bain path including the body-centred cubic and face-centred cubic structures for a set of simple and transition metals. The present converged results in terms of potential sphere radius (S) and hard sphere radius (b) are in good agreement with previous theoretical calculations. We demonstrate that for all structures considered here, potential sphere radii around and slightly larger than the average Wigner–Seitz radius (w) yield accurate total energy results whereas S values smaller than w give large errors. It is shown that for converged total energies hard spheres with radii b = 0.7–0.8w should be used for an efficient screening within real space clusters consisting typically of 70–90 lattice sites. The less efficient convergence of the total energy in the case of small hard spheres is ascribed to the delocalisation of the screened spherical waves, which leads to inaccurate interstitial overlap matrix. The above conclusions are not significantly affected by the volume of the system.     

广义相对论中负指数多层球的结构及稳定性

本文运用广义相对论讨论了满足负指数多方状态方程的流体多层球。经典引力理论与相对论性理论的差别由σ标志。σ是球体中心处的压力与密度之比。通过数值积分得到了n<0的相对论性Emden函数。在-1ed^*也增大。 关键词：     

Magnetic multilayers on nanosphere arrays with various curvature radius

[Co/Pt]_n multilayers with different Co thickness have been deposited on a silicon (Si) substrate to obtain better perpendicular anisotropy. The 0.5 nm thickness of the Co layer was chosen as the optimized thickness of the multilayer. Magnetic nanostructures with cap configuration were fabricated based on the template of polystyrene (PS) colloid sphere arrays with various curvature radius. Compared to the flat multilayer, the cap multilayer showed an oblique average anisotropy axis. When the curvature radius of the colloidal sphere increased, the shape of the multilayers changed from ellipsoidal to spherical, which led to a different dependence of magnetic properties on the field angles. The varying shape anisotropy, the dipole-dipole interaction between small magnetic caps, and the special nucleation mechanism on the spheres larger than 400 nm caused the M_r/M_s ratio and the coercivity to first increase and then decrease with varying curvature radius of the PS spheres.     

Force-coupling method for particulate two-phase flow: Stokes flow

In this paper we describe a force-coupling method for particle dynamics in fluid flows. The general principles of the model are described and it is tested on three different Stokes flow problems; a single isolated sphere, a pair of otherwise isolated spheres, and a single sphere in a channel. For sphere to sphere or sphere to wall distances larger than 1/4 of the sphere radius the force-coupling results compared well with analytical and accurate numerical values. For smaller distances the results agree qualitatively, but lubrication effects are not included and this leads to a quantitative discrepancy.     

On the proximity relation between two surface-melted clusters involved in inter-cluster mass transfer

We explore the way free particles produced by dissociating “particle-hole pairs” on a surface-melted cluster can be transferred to a second, nearby surface-melted cluster. This mass transport is based on an inter-cluster direct transfer mechanism of the particles. We found that in this particular case one cluster may grow at the expense of another, obeying a temporal power law with the exponent 1/2 for the average radius (R∼t ^1/2). The change from the expected universal power law (R∼t ^1/3) is a consequence of the proximity relation between these two clusters which lead to enhance the effective transport rates. Received 4 December 2000     

Design of a Nanomagnet

We design a two-dimensional ferromagnet of quantum spheres of radius O(10 nm³) made of nonmagneticintrinsic semiconducting material, each connected to its neighbors by nano-cylinders made of identical material. Ferromagnetism ensues if there is precisely one electron trapped in each sphere; this is a direct consequence of a theorem by Elliott Lieb. We analyze and estimate the important materials parameters. At concentrations of less than 1 electron per sphere, ultimate collapse of the ferromagnetic state should yield a paramagnetic Fermi liquid. We point out the need for additional numerical and physical experimentation.     

Exchange interaction and acoustical phonon modes in CdTe nanocrystals

Photoluminescence of CdTe nanocrystals (NC) is excited resonantly in the lowest energy absorption peak. The spectrum shows a luminescence line shifted to a lower energy and acoustical and optical phonon replica. The Stokes shift between the luminescence and excitation lines is attributed to the electron-hole exchange energy in the nanocrystal. By tuning the laser line inside the absorption peak, we are able to measure the Stokes shift as a function of the excitation energy. Calculation of the absorption gap and the Stokes shift is done in a tight-binding theory. It allows us to determine the radius R of NC excited at a given wavelength and to compare the experimental and theoretical values of the exchange energy as a function of R. A very good agreement is obtained. The observed size dependence of the acoustical phonon mode energy provides a further confirmation of our analysis.     

Shear stress correlations in hard and soft sphere fluids

The shear stress autocorrelation function has been studied by molecular dynamics simulation using the q^?n potential for very large n. The results are analysed and interpreted here by comparing them with the shear stress response function for hard spheres. It is shown that the hard sphere response function has a singular contribution, and that this is reproduced accurately by the simulations for large n. A simple model for the stress autocorrelation function at finite n is proposed, based on the required hard sphere limiting form.     

Spherical polyelectrolyte block copolymer micelles: Structural change in presence of monovalent salt

Spherical polyelectrolyte block copolymer micelles were investigated as a function of added NaCl salt concentration using Small-Angle Neutron Scattering (SANS) and Light Scattering (LS). The micelles are formed by the self-association of charged-neutral copolymers made of a long deuterated polyelectrolyte moiety (NaPSS_d)₂₅₁ and a short hydrophobic moiety (PEP)₅₂. In presence of salt, the core shape and the aggregation number of the micelles are not affected. The hydrodynamic radius of the micelle is found to be identical to the radius of the whole micelle deduced from neutron scattering and thus the hydrodynamic radius is a valid measure of the corona thickness. At the lowest salt concentrations investigated the thickness of the corona, R_s, remains essentially constant and a contraction is observed above an added-salt concentration c_s of 2×10^-2 M where this crossover concentration corresponds to the average ionic strength of the free counterions in the corona. The contraction takes place while maintaining a rod-like behavior of the chains at short scale and obeys to: R_s c_s^-0.18. The exponent 0.18 suggests an electrostatic persistence length proportional to the Debye screening length.     

Electromagnetic properties of random material

Abstract

This work addresses the relationship between grain properties and the permeability and permittivity spectra of non-crystalline materials or aerosols.

The scattered multipolar fields about a single sphere are related to the polarizability of a random collection of such spheres. Using the Clausius–Mossotti relation the effective permeability and permittivity spectra of an amorphous material is determined for arbitrary permittivity and permeability of the individual spheres, packing density, and sphere size. Although the author considers the spectra over a range where the product of the external wavevector and sphere radius is kept small, typically less than one-tenth, the product of the internal wavevector and sphere radius is unconstrained and seen to have a large effect on predicted spectra.

The result is a variety of possible spectral types which include resonances, relaxations and certain complex. conglomerate spectra that have been measured and far which no direct explanation is otherwise available.     

Discotic molecules in cylindrical nanopores: A Monte Carlo study

We report Monte Carlo simulations of a model discotic molecule embedded in cylindrical pores. We consider a planar anchoring of the molecules on the surface for two different cylinder radii: R ^* = 5 and R ^* = 10 , in units of the molecular diameter. For both radii, we note that the system is progressively structured in concentric shells when decreasing the temperature. With the small radius, we observe continuous transitions from an isotropic to a nematic phase and then to a crystal one. The radius of the pores is sufficiently small to force the crystal to grow along their main axis. However some orientational discrepancies are observed: some samples present a zigzag configuration. With the big radius, the situation is more complex and it is likely that different scenarios are available. The crystals can be built along the main axis of the cylinders, as for the small radius, but also in any other direction. Thus we observe samples with different orientational domains. In the case of crystals oriented along the nanopore axis, we note that only the first 5 shells close to the wall are sensitive to it.     

Q-factor of spherical optical silicon dioxide nanoresonators

The Q-factor of the bound optical modes of silicon dioxide spheres with a radius smaller than one micron has been studied in the visible spectrum, showing that local photonic states with a nonzero orbital momentum yield a thin structure in glow spectra, whose maxima positions depend on the diameters of SiO₂ nanospheres. A theoretical model to calculate the Q-factor of nanoresonators depending on the wavelengths of bound modes and the radius value of spheres has been proposed. It has been shown that the quality of an optical resonator increases as its diameter grows. The Q-factor values have been calculated for the visible light of the order of 10 for spheres smaller than 1 μm in diameter and 10⁶ for spheres of more than 7 μm in diameter. A dependence of bound modes’ radiation propagation outside of the sphere on their wavelengths and orbital momenta has been detected.     

Three-dimensional Wigner molecules formed from an assembly of confined but Coulombically repelling electrons

We first consider N Coulombically interacting electrons confined within a sphere of radius R by an infinite potential barrier. Scaling properties of the Hamiltonian are first discussed, followed by the virial theorem. In the limit of large R and N, it is shown that the problem can be reduced to the solution of N point charges −|e| constrained to move on the surface of a sphere of radius R_W here defined as Wigner radius. Finally, the results of the above model are compared with those of harmonically confined electrons.     

Light scattering and absorption by densely packed groups of spherical particles

Light scattering by clusters of spheres is investigated using numerical light scattering simulations. We consider clusters with density of 0.1-30%. Simulations are carried out for various real part of refractive indices (i.e., 1.01, 1.10, 1.31, 1.60, and 2.00) and for two values of the imaginary part of the refractive index (0 and 0.01) of spheres in the cluster. All spheres in the cluster have the same size (kr=4, k=2π/λ, r is the radius of the sphere, λ is the wavelength of the incident light).The obtained results include behaviors of cross sections as functions of densities (up to 30%), investigation of the influence of multiple scattering inside the media on the cross sections, and influence of densities on phase matrix elements (PMEs) and parameters obtained from the PMEs such as the cross polarization ratio, degree of linear depolarization, entropy, etc.In addition, we also investigate the influence of particle size for the same total volume of the cluster on cross sections. The outer radius R of the cluster of spheres was constant and equal to 40/k in all calculations.     

Spatial ordering and Coulomb interaction energy of d-holes in a system of iron ions with mixed valence in HgSe:Fe crystals

Spatial ordering of d-holes in a system of iron ions with mixed valence Fe²⁺-Fe³⁺ in HgSe:Fe crystals at low temperatures is analyzed. The equation of balance is obtained for the d-holes that have migrated out of the correlation sphere into the spherical shell bounded by the first correlation sphere. The radius of the correlation sphere is determined as a function of the iron content. The change in the Coulomb interaction energy of the correlated system of Fe³⁺ ions as a function of their degree of order is analyzed. Fiz. Tverd. Tela (St. Petersburg) 39, 250–255 (February 1997)     

排列形状及阵列数目对纳米导线阵列场发射性能的影响

为了进一步研究纳米导线阵列的排列形状以及阵列数目对其场发射行为的影响，利用镜像悬浮球模型对正方形以及六边形排列的纳米导线阵列的场发射行为进行计算与模拟，近似的得到纳米导线阵列的场发射增强因子满足如下的变化趋势：β=h/ρ(1/1+W)+1/2(1/1+W)²+3,其中h为纳米导线的高度，ρ为纳米导线的半径，W是以R为自变量的函数，R为纳米导线阵列的间距.结果显示纳米导线阵列的排列形状对其场发射性能的影响较小，而阵列间距则是影响场发射性能的关键因素：当R<R₀时，场发射增强因子随着阵列间距的减小而急剧减小；当R>R₀时，场发射增强因子基本不变，其中R₀为导线阵列场发射的最佳间距.进一步研究表明改变纳米导线阵列的数目基本不会改变阵列的场发射性能随间距的变化趋势，但是随着阵列数目的增加，R₀会有一定程度的减小，场发射增强因子也会降低. 关键词： 纳米导线 场发射 增强因子 阵列数目     

栅极调制纳米线的场增强因子计算

利用悬浮球模型和镜像电荷法计算了栅极调制纳米线的顶端表面电场,给出了场发射增强因子表达式β=1/2（3.5+L/r₀+W）,式中L与r₀分别是纳米线长度与顶端表面曲率半径,W是由栅孔半径R、阴极与栅极间距d以及纳米线自身几何参数所决定的函数．结果表明,纳米线长径比对场增强因子的影响很显著;当阴极与栅极间距较近时,场增强因子随d的增加而减小 关键词： 栅极调制纳米线 场增强因子 悬浮球     

Zero modes for Dirac fermions on a sphere with fractional vortex

Normalized zero-energy states are shown to emerge for massless Dirac fermions in an external gauge field that gives rise to nonquantized vortices on a sphere. A field-theory model is used to describe electronic states of a fullerene-like molecule. In particular, we predict the existence of exactly one zero-energy mode due to a disclination. For 60° disclination, the normalized electron density at zero energy is found to behave as R ^?5/3, with R being the fullerene radius.