Principal Equatorial Null Geodesic Congruences in the Kerr Metric, and Their Quantum Propagators

Using the Raychaudhuri equation, we associate quantum probability amplitudes (propagators) to equatorial principal ingoing and outgoing null geodesic congruences in the Kerr metric. The expansion scalars diverge at the ring singularity;however, the propagators remain finite, which is an indication that at the quantum level singularities might disappear or, at least, become softened.

On Geodesic E-quasiconvex Functions and Geodesic E-epigraphs

The definition of geodesic E-quasiconvex functions is established in a geodesic metric space. Meanwhile, the relations of geodesic E-quasiconvex functions, geodesic Econvex functions and geodesic E-almostconvex functions are studied. Furthermore, the notion of E-epigraphs is generalized to geodesic E-epigraphs and a characterization of geodesic E-quasiconvex functions in terms of its geodesic E-epigraphs is considered.

Geodesics算法在雷达投影转换中的应用检验

基于上海市气象局布设于临港的X波段移动式双线偏振雷达观测资料,利用反射率因子、差分反射率和相关系数等变量识别出东海大桥固定地物回波位置,进而采用Geodesics和HRAP(Hydrologic Rainfall Analysis Project)投影转换算法将雷达回波的极坐标位置转换至地理坐标。以国家测绘局利用GPS技术测量的沪芦高速(东海大桥段)地理坐标作为真值,将环境大气分为晴空回波-低湿度情况和降水回波-高湿度情况分类检验两种算法的效果。检验算法包含经投影转换后地物回波样本位于桥面主体内部的数目(多边形检验)和样本偏离桥体中心线的距离(中心线检验)。其结果表明:Geodesics算法在多边形和中心线检验方面表现均优于HRAP算法,其在雷达投影转换的实际业务中具备一定的应用价值。

Implementation of a Conservative Two-step Shape-Preserving Advection Scheme on a Spherical Icosahedral Hexagonal Geodesic Grid

An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid） to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid, the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes （a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity） to calculate the fluxes at the cell walls （one scheme corresponds to one cell wall）. The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport （FCT） approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes.

Toroidal component of velocity for geodesic acoustic modes in the edge plasmas of the J-TEXT tokamak

The toroidal component of the velocity for geodesic acoustic modes(GAMs)is first demonstrated.Multiple Langmuir probe arrays set up near the top tokamak of the J-TEXT were utilized for this study.A significant peak at the GAM frequency is observed in Mach number fluctuations.The toroidal velocity for the GAMs is estimated as 10–100 ms-1 and increases with the poloidal velocity.The ratio of toroidal component to the poloidal one of the velocity is mainly located in the interval between 0.3 and 1.0.With higher safety factors q,the ratio almost does not change with decreasing the safety factor,whereas it goes up sharply at low q.The coherencies between poloidal electric fields and Mach number fluctuations in turbulence frequency bands are also evaluated,and are higher than those between radial electric fields and Mach number fluctuations.

Fast Approximate Geodesic Paths on Triangle Mesh

We present a new algorithm to compute a geodesic path over a triangle mesh. Based on Novotni＇s propagating wavefront method which is similar to the well known Dijkstra algorithm, we made some improvements which Novotni had missed and we also gave the method to find out the geodesic path which Novotni had not. It can handle both convex and non-convex surfaces or even with boundaries. Experiment results show that our method works very well both in efficiency and precision.

The properties and geodesics related to the NUT-Taub-like spacetime

Some properties related to the NUT-Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT-Taub-like black hole are discussed. Furthermore, the geodesics in the NUT-Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT-Taub spacetime when m^＊ = 0 and m^＊ 〈〈 M, respectively.

Time-like geodesic structure of a spherically symmetric black hole in the brane-world

Recently Malihe Heydari-Fard obtained a spherically symmetric exterior black hole solution in the brane-world scenario, which can be used to explain the galaxy rotation curves without postulating dark matter. By analysing the particle effective potential, we have investigated the time-like geodesic structure of the spherically symmetric black hole in the brane-world. We mainly take account of how the cosmological constant α and the stellar pressure β affect the time-like geodesic structure of the black hole. We find that the radial particle falls to the singularity from a finite distance or plunges into the singularity, depending on its initial conditions. But the non-radial time-like geodesic structure is more complex than the radial case. We find that the particle moves on the bound orbit or stable （unstable） circle orbit or plunges into the singularity, or reflects to infinity, depending on its energy and initial conditions. By comparing the particle effective potential curves for different values of the stellar pressureβ and the cosmological constant α, we find that the stellar pressure parameter β does not affect the time-like geodesic structure of the black hole, but the cosmological constant a has an impact on its time-like geodesic structure.

MORSE CONCAVITY FOR CLOSED GEODESICS

In this paper, the concavity of closed geodesics proposed by M. Morse in 1930s is studied.

CONNECTIONS AND GEODESIC CHARACTERISTIC OF EQUATIONSOF MOTION FOR CONSTRAINED MECHANICAL SYSTEMS

The geodesic characteristic of equations of motion for nonautonomous constrained mechanical systems is studied in the modern setting of global differential geometry. A necessary and sufficient condition for the dynamical flow of a nonautonomous mechanical system with geodesic characteristic was obtained with respect to a connection of 1-jet bundle. The dynamical flow concerning the non-autonomous case motion of an nonautonomous mechanical system with constraints can be always represented by the motion along the geodesic line of torsion-free connection on 1-jet bundle, which is different from the case in an autonomous mechanical system.

GEODESIC PRECESSION IN THE (Ω,A_(ab))-FIELD THEORY

This paper aims to determine the geodesic precession in Yu's (Ω, Aab)-field the- ory[1], and to compare the result with that of the Schwarzschild orbit.

A UNIQUENESS THEOREM FOR HOLOMORPHIC MAPPINGS IN THE DISK SHARING TOTALLY GEODESIC HYPERSURFACES

In this paper,we prove a Second Main Theorem for holomorphic mappings in a disk whose image intersects some families of nonlinear hypersurfaces(totally geodesic hypersurfaces with respect to a meromorphic connection) in the complex projective space P^(k).This is a generalization of Cartan’s Second Main Theorem.As a consequence,we establish a uniqueness theorem for holomorphic mappings which intersect O(k^(3)) many totally geodesic hypersurfaces.

Kinetic Theories of Geodesic Acoustic Modes：Radial Structure,Linear Excitation by Energetic Particles and Nonlinear Saturation＇

Geodesic acoustic modes（GAMs）are oscillating zonal mode structures unique to toroidal plasmas and are capable of regulating microscopic turbulence and associated transports.Inthispaper,three important aspects of GAM dynamics are investigated,namely（1） GAM continuous spectrum and its mode conversion to kinetic GAM （KGAM）;（2） 1inear excitation of energetic particle induced GAM （EGAM） and its coupling to the GAM continuum, and （3） nonlinear saturationofEGAMviawaveparticletrapping.TheanalogybetweentheGAM

Nonlinear excitation of a geodesic acoustic mode by reversed shear Alfvén eignemodes

The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.

Damping of Geodesic Acoustic Mode by Trapped Electrons

We study the Landau resonance between geodesic acoustic mode（GAM） and trapped electrons as a GAM’s collisionless damping. The assumption of ˉωde 〈〈ωbeis adopted.The damping rate induced by trapped electrons is found to be an increasing function of q. In low q range, circulating-ion-induced damping rate is larger than that induced by trapped electrons.As q increases, the latter becomes larger than the former. The reason is that trapped electrons’ resonant velocity is close to vtefrom the lower side, whiles circulating ions’ resonant velocity gets bigger further from vti. So the number of resonant trapped electrons increases, whiles the number of resonant circulating ions decreases. The amplitude of damping rate induced by trapped electrons in the edge plasma can be comparable to that induced by circulating ions in the low q range.Another phenomenon we found is that in the chosen range of, the damping caused by trapped electrons has a maximum value at point εq for different q. The reason is that as is close to q,trapped electorns’ resonant velocity is close to vte.

A Mathematical Model for the Geodesic Winding of Surfaces of Rotation

ＡＭａｔｈｅｍａｔｉｃａｌＭｏｄｅｌｆｏｒｔｈｅＧｅｏｄｅｓｉｃＷｉｎｄｉｎｇｏｆＳｕｒｆａｃｅｓｏｆＲｏｔａｔｉｏｎＨＵＡＮＧＫａｉｂａｎｇ；ＷＡＮＧＹｏｎｇｚｈａｎｇ；ＦＵＨｏｎｇｙａ；ＣＨＵＲｅｎｘｉｎ；ＳＵＮＧｕｏｑｉａｎｇ黄开榜，王永章，富...

Analytical Theory of the Geodesic Acoustic Mode in the Small and Large Orbit Drift Width Limits and its Application in a Study of Plasma Shaping Effect

Analytical theories of the geodesic acoustic mode （GAM） are reviewed in the small- and large-orbit drift width limits, respectively. Different physics pictures in these two limits are displayed. As an example, these two analytical methods are employed to investigate the plasma shaping effect on the frequency and collisionless damping rate of the GAM.

Influence of dark energy on time-like geodesic motion in Schwarzschild spacetime

In this paper we investigate the influence of the dark energy on the time-like geodesic motion of a particle in Schwarzschild spacetime by analysing the behaviour of the effective potential which appears in an equation of motion. For the non-radial time-like geodesics, we find a bound orbit when the particle energy is in an appropriate range, and also find another possible orbit, which is that the particle drops straightly into the singularity of a black hole or escapes to infinity. For the radial time-like geodesics, we find an unstable circular orbit when the particle energy is the critical value, in which case it is possible for the particle to escape to infinity.

Kinetic theory of geodesic acoustic modes in toroidal plasmas:a brief review

Geodesic acoustic modes（GAM） are oscillating zonal structures unique to toroidal plasmas,and have been extensively studied in the past decades due to their potential capabilities of regulating microscopic turbulences and associated anomalous transport.This article reviews linear and nonlinear theories of GAM;with emphases on kinetic treatment,system nonuniformity and realistic magnetic geometry,in order to reflect the realistic experimental conditions.Specifically,in the linear physics,the resonant wave-particle interactions are discussed,with the application to resonant excitation by energetic particles（EPs）.The theory of EP-induced GAM（EGAM） is applied to realistic devices for the interpretation of experimental observations,and global effects due to coupling to GAM continuum are also discussed.Meanwhile,in the nonlinear physics,the spontaneous GAM excitation by microscale turbulences is reviewed,including the effects of various system nonuniformities.A unified theoretical framework of GAM/EGAM is then constructed based on our present understandings.The first-principle-based GAM/EGAM theories reviewed here,thus,provide the tools needed for the understanding and interpretation of experimental/numerical results.

The Motion of a Gyroscope Freely Falling Along the Radial Geodesic in the Space-Time of a Black Hole with a Global Monopole

By means of the orthonormal frame,the motion of the axis of a gyroscope freely falling along the radial geodesic in the space-time of a black hole with a global monopole is investigated.It is shown that the axis of the gyroscope rotates about the radial direction as it falls into the black hole.