Figures of equilibrium inside a gravitating ring and the limiting oblateness of elliptical galaxies

A new class of figures of equilibrium for a rotating gravitating fluid located inside a gravitating ring or torus is studied. These figures form a family of sequences of generalized oblate spheroids, in which there is for any value of the tidal parameter α in the interval 0 ≤ \(0 \leqslant \frac{\alpha }{{\pi G\rho }} \leqslant 0.1867\) ≤ 0.1867 a sequence of spheroids with oblatenesses emin (α) ≤ e ≤ e_max (α). A series of classicalMaclaurin spheroids from a sphere to a flat disk is obtained for α = 0. At intermediate values 0 < α ≤ α_max, there are two limiting non-rotating spheroids in each sequence. When α = α_max, the sequence degenerates into a single non-rotating spheroid with e_cr ≈ 0.9600, corresponding to the maximum oblateness of E7 elliptical galaxies. The second part of the paper considers the influence of rings of dark matter on the dynamics of elliptical galaxies. It is proposed that the equilibrium of an oblate isolated non-rotating galaxy is unstable, and it cannot be supported purely by anisotropy of the stellar velocity dispersion. A ring of dark matter can stabilize a weakly rotating galaxy, supplementing standard dynamical models for such stellar systems. In order for a galaxy to acquire appreciable oblateness, the mass of the ring must be an order of magnitude higher than the mass of the galaxy itself, consistent with the ratios of the masses of dark and baryonic matter in the Universe. The influence of massive external rings could shed light on the existence of galaxies with the critical oblateness E7.     

Observed effects of gravitational microlensing of stars by a spatial-temporal tunnel

We consider microlensing of stars by a spacetime tunnel (wormhole), which is manifest as a gravitational lens with negative mass and a circular caustic in the source plane. If a source with a small angular size does not cross the circular caustic, it is impossible to discriminate between gravitational lenses with positive and negative mass. Even for comparatively large stellar angular diameters, differences from a Schwarzschild lensing curve are on the order of the observational errors. When the angular size of a star is comparable to the radius of the Einstein cone, for a sufficiently large impact parameter, the shape of the observed light curves can be similar to that due to microlensing of a compact object surrounded by an extended gaseous envelope. Such an object can be easily distinguished from a negative-mass gravitational lens via analysis of chromatic and polarization effects of the lensing.     

A unified theory for the formation of galactic structures

A new theory for the formation of the main structures of galaxies is proposed: these structures are viewed as low-frequency normal modes in disks consisting of precessing stellar orbits. Mathematically, the theory is based on an integral equation in the form of a classical eigenvalue problem, with the eigenvalues being equal to the angular velocities Ω_p of the modes. Analysis of the general properties of the master integral equation (without finding concrete solutions) shows that it admits two types of solutions: barlike and spiral. The numerical algorithms are discussed and particular solutions of the integral equation are presented. If resonance interaction can be neglected, the bar mode represents a neutral perturbation of the disk. This mode can be amplified by the effect of the long-range gravitational field of the mode on stars located in the vicinity of the corotation and outer-Lindblad resonances. Spiral perturbations are waves with zero total angular momentum, and spiral modes are excited at the inner-Lindblad resonance. The approach proposed is compared to currently accepted mechanisms for the formation of galactic structures. In particular, Toomre's application of the swing amplification mechanism to explain the formation of global modes is critically discussed. In addition, we show that it is not correct to simulate the real stellar velocity dispersion in a galaxy using softened gravity.     

Stellar structure of irregular galaxies: Edge-on galaxies

Stellar photometry obtained using the Hubble Space Telescope is used to study the distributions of the number densities of stars of various ages in 12 irregular and dwarf spiral galaxies viewed edge-on. Two subsystems can be distinguished in all the galaxies: a thin disk comprised of young stars and a thick disk containing a large fraction of old stars (primarily red giants) in the system. Variations of the stellar number density in the thin and thick disks in the Z direction perpendicular to the plane of the galaxy follow an exponential law. The size of the thin disk corresponds to the visible size of the galaxy at the μ = 25 mag/arcsec² isophote, while the thick disk is a factor of two to three larger. In addition to a thick disk, the massive irregular galaxy M82 also has a more extended stellar halo that is flattened at the galactic poles. The results of our previous study of 12 face-on galaxies are used together with the new results presented here to construct an empirical model for the stellar structure of irregular galaxies. Original Russian Text ? N.A. Tikhonov, 2006, published in Astronomicheskiĭ Zhurnal, 2006, Vol. 83, No. 7, pp. 579–588.     

塔里木盆地柯坪塔格构造带南缘古溶洞特征及主控因素分析

中加里东运动时期,塔里木盆地柯坪地区遭受广泛的水平挤压和构造抬升,奥陶系一间房组和鹰山组顶部地层3次暴露并发生岩溶化,形成多种类型古溶洞,并在喜马拉雅运动中抬升出露地表,现今成为形态各异的露头。通过大量露头观察,依据古溶洞发育形态和空间结构,划分了古溶洞类型,研究了不同类型古溶洞特征及主控因素,以期对岩溶型储层勘探开发提供借鉴意义。研究表明：古溶洞可划分为4种类型,其中管状分支型溶洞为细长管道,可发育多个分支,横剖面近于圆形或椭圆形,受地下暗河控制;单一孤立型溶洞受断层、裂缝、顺层溶蚀等因素控制,横剖面上可出现漏斗形、倒漏斗形、板形和复合型等形态;溶洞群型溶洞受古潜水面和地下暗河的共同控制,纵向上具有分层性,平面上呈片状集中发育,且溶洞之间通过断层、裂缝、小型溶蚀通道相互连通;厅堂型溶洞由宽阔的厅和多个规模较小的堂组成,主控因素是顺层溶蚀。     

The stellar population and evolution of galaxies of the NGC 80 group

Seven early-type galaxies that are members of the massive X-ray group containing NGC 80 have been studied using two-dimensional spectroscopy with the 6-m telescope of the Special Astrophysical Observatory. We searched for evidence for the synchronous secular evolution of the galaxies in the group. The bulges of five of the seven galaxies appear to be old, with the average age of the bulge stars being 10–15 billion years. Signs of a relatively recent star-formation burst are observed in the small S0 galaxy IC 1548, whose average bulge age is 3 billion years and average core age is 1.5 billion years. A circumnuclear polar gas ring was also detected in this galaxy; in its outer regions, it makes a smooth transition to a gas disk that counter-rotates relative to the stars. IC 1548 probably underwent a close interaction, which resulted in its transformation from a spiral to a lenticular galaxy; the same interaction may also have induced the central burst of star formation. In the giant E0 galaxy NGC 83, a compact massive stellar-gas disk with a radius of about 2 kpc and very rapid rotation is observed, with ongoing star formation; the so-called “minor merger” is likely to have occurred there. We conclude that the NGC 80 group is in a state of formation, with the small NGC 83 subgroup “falling into” the large, old NGC 80 subgroup.     

矩形壁板桩群桩竖直承载特性的理论分析

矩形壁板桩不具有圆形桩的轴对称性,因此壁板桩群桩的承载特性及群桩效应不仅受桩间距的影响,而且受桩身截面形状以及群桩布置方式的影响。为分析这些因素,利用Mindlin方程和静力平衡条件建立了求解有无刚性承台时壁板桩群桩的荷载沉降计算方法。分析结果表明,在设计群桩时壁板桩应尽可能沿其纵向布置（即沿壁板桩的长边方向布置）;对于具有常规截面尺寸的壁板桩,桩的对边距应超过2 m,以减小群桩效应。     

Determination of the principal axes of elliptic cross sections in strain ellipsoids by a variational method

A method is presented for the determination of the shape and orientation of the ellipse on a central plane section across a triaxial ellipsoid (such as a strain ellipsoid) of known orientation and magnitude. Conditional extremal values of longitudinal strain (λ) are obtained in the plane section and these are the principal axes of the strain ellipse. In solving this variational problem, the arbitrary cosntants (two undetermined Lagrange multipliers) are found to have physical meaning in themselves as proved in a complementary geometric solution. The two roots of the first constant directly determine the magnitude of the principal axes of the strain ellipse in terms of the normal to the cross section. The two arbitrary constants together define shear strains and orientation of these axes.

Strain computation uses simple, single-line equations in either frames of strained or unstrained states.     

Avoiding Singularities in the Numerical Solution of the Motion of a Deformable Ellipse Immersed in a Viscous Fluid

Geological materials are largely heterogeneous and are typically comprised of approximately ellipsoidal objects immersed in a matrix with different physical properties. Methodologies for the identification of ancient regional tectonic patterns may be developed based on an understanding of the behaviour of heterogeneous materials. In this contribution, the differential equation governing the rotation of a deformable ellipse immersed in a viscous fluid is considered and is found to contain a singularity when the ellipse becomes circular in shape. This problem is avoided by reformulating the equations using the standard algebraic representation of an ellipse. Thus, the equations can be numerically solved without difficulty.     

不同截面形态的空心抗滑桩支挡效果对比研究

为了研究矩形截面空心桩和圆形截面空心桩的支挡效果及破坏模式,文章利用压力盒、应变片、钢筋计等传感器装置,开展室内模型试验。研究表明:矩形截面空心桩和圆形截面空心桩桩身最大弯矩分布在滑面上下约5 cm处,分布范围约占桩体自由段长度的1/4~1/2;空心桩桩身集水孔的布置会导致桩体承载能力有所降低,交错布置集水孔时,承载力约降低10%,竖排直线布置承载力约降低25%;圆形截面空心桩破坏时表现为沿滑面受剪破坏,而矩形截面空心桩表现为受压破坏。结果显示矩形截面空心桩的承载能力和抗弯能力优于圆形截面空心桩,在空心抗滑桩设计中应加强桩底至滑面以上1/2范围内的结构配筋,空心桩集水孔宜采用交错布置。     

丹麦法稳健估计在隧道椭圆拟合中的应用

隧道断面在设计时为一标准圆形,受到施工及外部环境的影响变形为偏心率很小的椭圆。减小粗差影响、精确确定椭圆的几何参数是其研究的重点。通过对上海某一隧道断面的测量试验,得出用丹麦法稳健估计可以有效减小粗差的影响,而且拟合值可以很好地逼近无粗差情况下的最小二乘拟合值。采用Matlab 语言实现算法,并详细介绍了用二项式变换求解椭圆参数的方法。     

Stellar subsystems of the galaxy NGC 2366

Hubble Space Telescope archive data are used to perform photometry of stars in seven fields at the center and periphery of the galaxy NGC 2366. The variation of the number density of stars of various ages with galactocentric radius and along the minor axis of the galaxy are determined. The boundaries of the thin and thick disks of the galaxy are found. The inferred sizes of the subsystems of NGC 2366 (Z _thin = 4 kpc and Z _thick = 8 kpc for the thin and thick disks, respectively) are more typical for spiral galaxies. Evidence for a stellar halo is found at the periphery of NGC 2366 beyond the thick disk of the galaxy.     

地质勘探用膨胀波纹管截面设计与选择

膨胀波纹管技术是将圆管制成异形截面管,下入孔内后胀圆维护孔壁稳定的一种新兴钻探技术。针对地质勘探的行业需求,提出了一套膨胀波纹管截面形状的设计理论,系统地阐述了膨胀波纹管截面设计的相关步骤和细节,设计出了6种花形不同尺寸的膨胀波纹管截面设计图。在此基础上,利用ANSYS14.0数值模拟软件对不同的设计截面进行了对比分析,得出了膨胀波纹管选择的3条原则：六瓣梅花形是最佳截面形式;设计截面的波峰和波谷的半径、弧度应尽量接近;在满足护壁压力要求的情况,壁厚应尽量的小。     

The role of close passages of galaxies and the asymmetry of their dark haloes in the formation of their spiral patterns

The influence of close passages of galaxies on the shapes of disk galaxies and the distribution of stars in them is studied for several types of interactions in the framework of the restricted N-body problem. Depending on the conditions adopted, either two spiral density waves or ring structures are formed in the stellar disk of the galaxy. These structures can generate star formation fronts with the corresponding shape, as are observed in disk galaxies. Our calculations can also be applied to study the influence of the passage of a nearby star on a protoplanetary disk. The formation of ring structures there could specify the type of planet formation in the outer regions of the planetary system and the distribution of semimajor axes for the planetary orbits. We use the same model to study the generation and evolution of spiral density waves in the stellar disks of galaxies as a result of the recently found asymmetry of the gravitational potential in the massive dark haloes in disk galaxies. The dipole component of the gravitational field of the halo can continuously permanently generate the spiral structure in disk galaxies.     

基于钻孔形态分析的地应力测量方法研究

地应力作用下的钻孔孔壁会发生一定程度的变形,导致钻孔横截面形状会发生变化,变形后的钻孔几何形态也反映了钻孔受力状态。在经典岩石力学理论的基础上,研究钻孔在平面二维应力作用下的几何形态,建立应力与变形后圆孔几何参数的关系,实现基于钻孔椭圆参数的应力解算,并提出钻孔椭圆参数的测量方法和测量技术,形成一种新的基于钻孔形态分析的地应力测量方法。结果表明,（1）在平面二维应力作用下圆孔变形后的几何形态为椭圆,推导了椭圆参数与应力的关系表达式;（2）利用3个不同方向的孔径值可以实现椭圆参数的解算,研发触头式显微光学孔径测量技术,实现了钻孔形态的测量,从原理上分析了技术实现的可行性,并就该技术进行地应力测量过程中可能存在的问题进行了探讨;（3）通过室内模拟试验,验证了技术原理的可行性,并通过误差分析和实例计算对该方法测量结果的准确性进行了讨论。     

大位移井悬链线剖面设计的数值计算

悬链线剖面是大位移井轨道的经典类型,在进行设计时需要求解一个以悬链线初始井斜角为未知数的非线性方程。由于未知数包含在多个三角函数和对数函数中,计算工作量较大,而且常用的迭代求解方法存在一些问题。通过数学变换将该方程转换成一个只包含对数函数和多项式函数的新方程,对新方程的函数性态做了几何分析,进而提出了寻找求解区间的步长搜索算法和自适应步长搜索算法。利用二分法在求解区间上能够快速求出新方程的数值解。利用大位移井设计实例验证了本文算法的有效性,并对圆弧井段井眼曲率与方程解的关系进行了讨论。本文提出的算法可用于大位移井轨道设计的计算机软件开发中。     

The nature hypervelocity stars

We list and analyze the main currently known mechanisms for accelerating the space motions of stars. A high space velocity of a star can be a consequence of its formation in the early stages of the evolution of a massive galaxy, when it was spheroidal and non-stationary, so that stars were born with velocities close to the escape velocity for the galaxy. Another possibility is that the star arrived from another galaxy with a velocity that is high for our Galaxy. The decay of unstable close multiple stars or supernova explosions in close binaries can also provide velocities of up to several hundreds of km/s to main-sequence stars and velocities of up to ∼1000 km/s to degenerate stars, neutron stars, and stellar-mass black holes. The merger of components of a binary system containing two neutron stars or a neutron star and a black hole due to gravitational-wave radiation can accelerate the nascent black hole to a velocity∼1000 km/s. Hypervelocity relativistic stars can be born due to asymmetric neutrino ejection during a supernova explosion. Stars can be efficiently accelerated by single and binary supermassive black holes (with masses from several millions to several billions of solar masses) in the nuclei of galaxies. Thanks to their gravitational field and fast orbital motion (in the case of binary objects), supermassive black holes are able to accelerate even main-sequence stars to relativistic velocities.     

The origin of intergalactic stars in galaxy clusters

The paper analyzes possible origins of stars located in intergalactic space that are not bound to specific galaxies, which comprise 15–50% of all stars in galaxy clusters. Some such stars can form in streams of intergalactic gas flowing around gas-rich disk galaxies moving in the cluster. Others may be the products of the decay of young, low-mass, spheroidal galaxies after the loss of their gaseous components during an initial burst of star formation. The decay of low-mass disk galaxies moving at high speeds after they have lost their gaseous components due to the pressure of the incident flow of dense intergalactic gas is possible in the cluster core. The largest fraction of intergalactic stars are probably produced by the partial disruption of galaxies as a result of close passages, collisions, or mergers. Collisions of low-mass, gas-rich galaxies are especially good suppliers of intergalactic stars. Both stars from decaying stellar components of galaxies and stars arising in the gaseous components of colliding galaxies can be supplied to the intergalactic medium. The merger of galaxies harboring supermassive black holes in their nuclei could lead to the partial or total disruption of these galaxies during the deceleration of the binary black hole that is formed during the merger. An enhanced density of intergalactic stars is observed in the cores of galaxy clusters, underscoring the role of galaxy collisions in the formation of the intergalactic stellar population, since the frequency of galaxy collisions grows with their density.     

塔里木盆地西北缘露头区奥陶系古溶洞地质建模

塔里木盆地西北缘奥陶系大型古溶洞广泛出露,为古溶洞露头地质建模提供了优越的条件。综合野外资料和Google Earth影像分析,将大型古溶洞以形态结构特征为依据划分成管道—厅堂连通型溶洞、单一管道孤立型溶洞、流线型溶洞3种类型;以存在形式划分成单一溶洞和溶洞群。其中,管道—厅堂连通型溶洞以潜流带型为主,在平面上沿主方位通过岩溶管道连接厅堂分布,厅堂大小不等,在50～50000m³之间变化;单一管道孤立型溶洞以渗流带型为主,平面上呈现单一管道线条状;流线型溶洞分布在潜流带中,从剖面上看呈近圆形、椭圆形和豆荚状等多种形状,包括顺层和斜交地层2种类型。结合各露头剖面中构造、地层条件及发育溶洞类型,明确管道—厅堂联通型溶洞受不整合面控制,分布在三间房、五道班和西克尔剖面中;单一管道孤立型溶洞受断裂系统控制,分布在一间房和硫磺沟剖面中;流线型溶洞主要分布在西克尔剖面,沿溶蚀沟道两侧分布;多种不同因素的耦合控制了溶洞群的分布。以此建立了综合大型古溶洞特征及其控制因素的古溶洞发育概念地质模型,以溶洞群为主要体积计算单元,通过与塔北奥陶系串珠进行体积对比,明确了地质模型的油气勘探意义。     

新星云假说下地球扁率变化上限及影响因素

地球的形状变化是地球演化研究的基本问题之一。为了确定地球形状的变化需要了解各个地质历史时期地球扁率的变化。根据位场球函数理论导出地球的扁率公式,研究扁率与地球的半径、质量和角速度的关系。基于新星云假说推测地球的半径、质量和角速度的变化量,计算出地球在各个时期的扁率并作为上限并画出曲线,各地质历史时期中地球扁率的真实值应该小于计算的扁率值。地球的扁率自地球形成以来脉动变化的情况下总体趋势在减小。影响地球扁率的因素有平均半径、质量和角速度,分析发现地球形成后5亿年为时间起点计算,到现在(共41亿年)为止平均半径变化对扁率的总影响约为3%,质量变化的总影响没有超过百万分之三。而角速度的减小对扁率变化的贡献超过97%。地球扁率共减少了74.3%。