Trapped null geodesies in a rotating interior metric

We consider trapped, null geodesies in an interior, rotating metric which matches the Kerr metric on a spheroidal surface. The interior metric is unphysical, but still useful for obtaining a qualitative understandng of the properties of the trapped, interior geodesies. We find, by numerical techniques, that the presence of rotation increases trapping for count-errotating orbits, but decreases it for corotating orbits.     

Null geodesies,caustics and apparent motion of galaxies in a finite rotating universe

Null solutions of the geodesic equation are presented for a universe which can be regarded as a rotating and shearing generalization of the static Einstein universe (the Ozsváth class I model). It is shown how the closest caustic, which in the static case just consists of one point at the antipode, grows to form two interwoven closed surfaces when motion is introduced. It is further shown how they prevent causality violating null-like curves. The observed transversal motion of matter (the global rotation) is calculated. The conclusions concerning the causality of the universe which an observer might draw from the global rotation are discussed.     

Dynamics of differential rotating sphere and pulsar

The dynamics of the differential rotating sphere is worked out. In view of the results, a theory for producing the pulse of pulsars is proposed.     

Radiation reaction for a rotating sphere with rigid surface charge

Radiation reaction in classical electrodynamics is studied using as a simple model a rotating sphere with rigid surface charge. Because of the transparent geometric nature of the problem, we obtain an exact integral expression for the “self-torque”, which depends causally and linearly on the angular speed. This leads to a linear equation of motion, which does not have any runaway solutions, as long as no negative mechanical moment-of-inertia is added to the system. The results are illustrated with a few examples corresponding to predetermined motions and external torques.     

Analytical solutions for the unsteady MHD rotating flow over a rotating sphere near the equator

In this paper we investigate the three-dimensional magnetohydrodynamic (MHD) rotating flow of a viscous fluid over a rotating sphere near the equator. The Navier-Stokes equations in spherical polar coordinates are reduced to a coupled system of nonlinear partial differential equations. Self-similar solutions are obtained for the steady state system, resulting from a coupled system of nonlinear ordinary differential equations. Analytical solutions are obtained and are used to study the effects of the magnetic field and the suction/injection parameter on the flow characteristics. The analytical solutions agree well with the numerical solutions of Chamkha et al. [31]. Moreover, the obtained analytical solutions for the steady state are used to obtain the unsteady state results. Furthermore, for various values of the temporal variable, we obtain analytical solutions for the flow field and present through figures.     

Effect of spatial coherence on radiation forces acting on a Rayleigh dielectric sphere

We show that the radiation forces (RFs) on a Rayleigh dielectric sphere induced by a partially coherent light beam are greatly affected by the spatial coherence. We find that the magnitude of the RFs greatly decreases as the spatial coherence decreases and derive an inequality for the required correlation width sigma(0) (i.e., the spatial coherence of the beam) to stably trap the particles.     

Beam-like gravitational waves and their geodesies

Exact solutions for the gravitational wave produced by an impulsive, massless beam of arbitrary energy profile are constructed in any number of spacetime dimensions. Geodesics can be explicitly computed and, for homogeneous, axisymmetric, finite-size beams, they exactly focus at the location of the curvature singularity found in the infinite shell collision.     

Universal spectrum of two-dimensional turbulence on a rotating sphere and some basic features of atmospheric circulation on giant planets

The Kolmogorov-Batchelor-Kraichnan (KBK) theory of two-dimensional turbulence is generalized for turbulence on the surface of a rotating sphere. The energy spectrum develops considerable anisotropy; a steep -5 slope emerges in the zonal direction, while in all others the classical KBK scaling prevails. This flow regime in robust steady state is reproduced in simulations with linear drag. The conditions favorable for this regime may be common for giant planets' atmospheric circulations; the same steep spectra are found in their observed zonal velocity profiles and utilized to explain their basic characteristics.     

Shearfree congruences of null geodesies and killing tensors

In this communication, the mutual connections between quantities that are generalizations of the notion of a Killing vector field are investigated. A classification of these quantities in terms of a complex vector field _a is given. A common feature of all these quantities is that they imply the existence of a pair of shearfree geodetic null congruences. There are no explicit restrictions posed on the Ricci tensor.     

Kinetic theory of hydrodynamic flows,III. the torque on a rotating sphere or cylinder1

The extended Boltzmann equation introduced in previous papers is used to compute the torque exerted on a macroscopic sphere or cylinder placed in a dilute gas, when the mean free path of the gas molecules is small compared to the characteristic dimension of the sphere or cylinder. The usual hydrodynamic results are recovered in this kinetic theory calculation.Work supported in part by the National Science Foundation Grant No. CHE 77-16308.     

Quasi-wetting on a sphere

Wetting phenomena on a sphere of radius R are studied in the context of the Sullivan model. Neither a first nor a continuous transition is found for finite R. Only in the strict limit of R→∞ a second-order transition appears. For temperatures T higher than the wetting temperature in a flat geometry, T^∞_w, the thickness l of the enhanced density layer, which forms on the surface of the sphere, is for large R proportional to In R.     

转动球体的全空间磁场分布

根据(连带)勒让德多项式的性质和加法公式,利用矢势叠加法得到了转动带电球体的空间磁场分布.     

Phase transitions of the energy-relative enstrophy theory for a coupled barotropic fluid–rotating sphere system

The statistical equilibrium of a coupled barotropic fluid–rotating solid sphere system is simulated using a energy-relative enstrophy spherical model in a wide range of parameter space by Monte Carlo (MC) methods [J.M. Hammersley, D.C. Handscomb, Monte Carlo Methods, Methuen & Co, London, Wiley, New York City, 1964; C.C. Lim, J. Nebus, Vorticity, Statistical Mechanics and Simulations, Springer, Berlin, 2006]. The energy-relative enstrophy model does not have the low temperature defect of the classical energy–enstrophy theory [R.H. Kraichnan, Statistical dynamics of two-dimensional flows, J. Fluid Mech. 67 (1975) 155–175] because of its microcanonical constraint on relative enstrophy. This model also differs from previous work in not fixing the angular momentum. A family of spin–lattice models are derived as convergent finite dimensional approximations to the total kinetic energy. MC simulations are used to calculate the mean nearest neighbor parity as order parameter or indicator of phase transitions in the system.     

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.     

A numerical examination of certain null geodesies of a high angular momentum kerr field

An observer situated anywhere but in the equatorial plane of a high angular momentum Kerr field cannot see the ring singularity. In the visual field of such an observer, what demarcates his own universe from that through the ring? The projections onto a certain submanifold of the null geodesics which pass through a point on the symmetry axis of a specific Kerr field are examined numerically. All the distinct projections are obtained by varying one parameter, essentially the quadratic Killing tensor constant. Various interesting features of the geodesics emerge. Through the ring is a region in which there exist closed time-like curves and which can be used to construct closed time-like curves through any non-singular point of the manifold. Only geodesies of negative angular momentum can enter this region.     

Damage detection of cracked thick rotating blades by a spatial wavelet based approach

This paper presents a technique for blade damage detection based on spatial wavelet analysis. The wavelet transform is used to analyze spatially distributed signals (e.g. mode shape) of cracked thick rotating blades. First, a finite element model is applied to the vibration of a thick rotating blade with a single edge crack. The effects of transverse shear deformation and rotatory inertia are taken into account. Then the mode shapes of the cracked rotating blade are analyzed by wavelet transformation. The effects of crack locations and sizes on the wavelet coefficients are studied. It is found that the distributions of the wavelet coefficients can identify the crack position of the rotating blades by showing a peak at the position of the crack. Then the signals are analyzed by wavelet transform. It is found that the distributions of the wavelet coefficients can identify the crack position. Assumed measurement errors are added to nth mode shape for evaluating the effect of measurement errors on the capability of detecting crack position. The moving average method is used to process the data with assumed measurement errors. The crack positions can also be identified when there exist assumed measurement errors.     

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.

---

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.

---

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.

     

Energy and spatial momentum of charged rotating frames in tetrad gravity

We compute the total energy and the spatial momentum of four charged rotating (Kerr-Newman) frames by using the gravitational energy-momentum 3-form within the framework of the tetrad formulation of the general relativity theory. We show how the effect of the inertial always makes the total energy divergent. We use a natural regularization method, which yields the physical value for the total energy of the system. We show how the regularization method works on a number of different rotating frames that are related to each other by the local Lorentz transformation. We also show that the inertial has no effect on the spatial momentum components.