Small-world networks on a sphere

The Small-World Network on a Sphere SWNS is a non-crossing network that has no hubs and presents the small-world property diam ~ log?N with diam being the maximal distance between any two vertices and N being the number of vertices. The SWNS is constructed using a partition of the sphere and the parallels are regular sections of the sphere with constant latitude. The number of cells on the parallels, however, increases exponentially from the pole to the equator of the sphere. We analytically compute the distribution of connectivity, the clustering coefficient and the SWNS distances. The resilience of the model against selective attacks is also discussed.     

Drag on a sphere in a fluid

Summary The possible acceleration dependence of the drag on a sphere, executing a translatory motion in a fluid, is examined in detail. After revisiting the standard derivations of this dependence, it is pointed out that the result might be connected with the scheme of incompressible fluids. That the adoption of this scheme is crucial is made evident by showing that a striking contradiction would arise in compressible fluids. Next a procedure is applied which, in a suitable linear approximation, leads to an explicit expression for the drag in compressible fluids. The drag turns out to depend both on the present value and on the history of the speed of the sphere.

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Riassunto Si considera una sfera in moto traslatorio in un fluido e si esamina il problema dell’eventuale dipendenza della forza resistiva dall’accelerazione. Sulla base delle derivazioni classiche di tale dipendenza, si mette in evidenza che il risultato potrebbe essere conseguenza diretta dell’adozione del modello di fluido incomprimibile. Che tale modello sia realmente cruciale è provato anzitutto osservando che l’analoga trattazione, nel caso di fluidi comprimibili, conduce ad una contraddizione. Successivamente, seguendo un’opportuna approssimazione lineare, si perviene all’espressione esplicita della forza resistiva in un fluido comprimibile. Tale forza risulta dipendente sia dal valore attuale sia dalla storia della velocità della sfera.

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Резюме Рассматривается трансияционное движение сферы в жидкости и исследуется проблема эффективной зависимости силы сопротивления от ускорения. После анализа стандартных подходов для вывода этой зависимости отмечается, что исследуемый результат может быть связан с выбранной моделью несжимаемой жидкости. Тот факт, что выбор модели является сушественнум, иллюстрируется в случае сжимаемых жидкостей, где возникает противоречие. Затем развивается линейное приближение, которое приводит к явному выражению для сопротивления в сжимаемых жидкостях. Оказывается, что сопротивление зависит не только от скорости в данный момент, но и от истории скорости сферы.

     

Dynamics of a monodisperse Lennard-Jones system on a sphere

We investigate by molecular dynamics simulation a system of N particles moving on the surface of a two-dimensional sphere and interacting by a Lennard-Jones potential. We detail the way to account for the changes brought by a nonzero curvature, both at a methodological and at a physical level. When compared to a two-dimensional Lennard-Jones liquid on the Euclidean plane, where a phase transition to an ordered hexagonal phase takes place, we find that the presence of excess defects imposed by the topology of the sphere frustrates the hexagonal order. We observe at high density a rapid increase of the relaxation time when the temperature is decreased, whereas in the same range of temperature the pair correlation function of the system evolves only moderately.     

球在可自由移动的球形空腔内作纯滚动的运动分析

对在光滑水平面上可自由移动的球形空腔内作纯滚动的球的运动进行分析,给出球心及其边缘上任意一点在静止参考系中的运动轨迹方程,并绘出它们相应的轨迹,求出球在球形空腔内平衡位置附近作小振动的周期,并和球在可自由移动的球形空腔内作纯滑动的情况作了比较.     

Statistical geometry of four calottes on a sphere

We calculate the configurational integral and reduced distribution functions for a system of four rigid spherical calottes, a model which allows an exact analysis of excluded-volume effects resulting from the interplay between statistics and geometry.     

High-performance high-resolution semi-Lagrangian tracer transport on a sphere

Current climate models have a limited ability to increase spatial resolution because numerical stability requires the time step to decrease. We describe a semi-Lagrangian method for tracer transport that is stable for arbitrary Courant numbers, and we test a parallel implementation discretized on the cubed sphere. The method includes a fixer that conserves mass and constrains tracers to a physical range of values. The method shows third-order convergence and maintains nonlinear tracer correlations to second order. It shows optimal accuracy at Courant numbers of 10–20, more than an order of magnitude higher than explicit methods. We present parallel performance in terms of strong scaling, weak scaling, and spatial scaling (where the time step stays constant while the resolution increases). For a 0.2° test with 100 tracers, the implementation scales efficiently to 10,000 MPI tasks.     

球面上皱褶花样的演化

文章从理论和实验两方面研究了通过控制柔性衬底的曲率来调控球面上应力诱导之皱褶花样的可行性.研究以Ag内核/SiO2壳层微结构为对象.结果表明,当球形衬底的曲率较小且应力刚超过临界值时,皱褶花样为三角铺排的凹痕结构;而当应力进一步增大和/或衬底的半径增大时,则出现迷宫形的花样.皱褶的周期长度和临界屈曲应力都随衬底半径的增大而增大.此方向上的研究对于理解大自然中许多花样(比如花叶序与皱纹)的产生和演化具有重要的意义.     

球面上皱褶花样的演化

文章从理论和实验两方面研究了通过控制柔性衬底的曲率来调控球面上应力诱导之皱褶花样的可行性.研究以Ag内核/SiO2壳层微结构为对象.结果表明,当球形衬底的曲率较小且应力刚超过临界值时,皱褶花样为三角铺排的凹痕结构;而当应力进一步增大和/或衬底的半径增大时,则出现迷宫形的花样.皱褶的周期长度和临界屈曲应力都随衬底半径的增大而增大.此方向上的研究对于理解大自然中许多花样(比如花叶序与皱纹)的产生和演化具有重要的意义.     

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.     

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.     

Electrostatic charging of a conducting sphere using another conducting sphere at constant voltage

This study uses results of classical electrostatics to predict the resulting voltage of a conducting sphere that is charged by a second sphere maintained at a constant voltage. The voltage of the charged sphere is calculated as a function of the charging voltage and the size ratio of the two spheres. Theoretical predictions are verified experimentally using conducting spheres of various sizes and a Faraday ice pail apparatus. The results may seem somewhat counterintuitive. For example, a charging sphere held at 100 V will charge another sphere of equal size only to 69.3 V by contact.     

The pressure of a hard sphere fluid on a curved surface

Utilizing the integral equation approach to the hard sphere fluid system developed in the preceding paper, the hard sphere-hard wall interaction is studied. For the case of a flat wall, perturbation solutions of the integral equation valid to second and third order in the packing fraction,y, are derived. For a surface of arbitrary curvature, an equation of state valid to second order in the packing fraction is also derived. When applied to very small cavities, it is found that the pressure at high densities is significantly higher than it would be for a flat wall.     

Acoustic radiation force of a Bessel beam on a porous sphere

The possibility of using acoustic Bessel beams to produce an axial pulling force on porous particles is examined in an exact manner. The mathematical model utilizes the appropriate partial-wave expansion method in spherical coordinates, while Biot's model is used to describe the wave motion within the poroelastic medium. Of particular interest here is to examine the feasibility of using Bessel beams for (a) acoustic manipulation of fine porous particles and (b) suppression of particle resonances. To verify the viability of the technique, the radiation force and scattering form-function are calculated for aluminum and silica foams at various porosities. Inspection of the results has shown that acoustic manipulation of low porosity (<0.3) spheres is similar to that of solid elastic spheres, but this behavior significantly changes at higher porosities. Results have also shown a strong correlation between the backscattered form-function and the regions of negative radiation force. It has also been observed that the high-order resonances of the particle can be effectively suppressed by choosing the beam conical angle such that the acoustic contribution from that particular mode vanishes. This investigation may be helpful in the development of acoustic tweezers for manipulation of micro-porous drug delivery carrier and contrast agents.     

Radiation pressure on a lossy sphere in a quasi-standing plane wave

The radiation pressure forces on a sphere with radially symmetric properties are considered as functions of the sphere size with respect to the wavelength in the quasi-standing plane wave field with a constant frequency in the presence of loss in the inclusion. It is shown that the presence of loss in the inclusion positioned in an ideal fluid medium enhances the filtering properties of the traveling component of a quasistanding wave. With an increase in attenuation, the inclusion size intervals in which such a filtering is possible are progressively shifted toward the smaller wave size region. As the attenuation grows, this leads to the predominance of forces caused by the traveling component of the quasi-standing wave over the forces caused by its standing component even for small coefficients of traveling for a wide range of wave sizes of the inclusion. In turn, this effect determines the filtering properties of the quasi-standing wave. A numerical experiment is carried out to confirm the conclusions of the theoretical analysis.