Elliptical motions of stars in close binary systems

The motion of stars in close binary systems with conservative mass transfer is considered. It is shown that the Paczynski-Huang model that is currently used to determine the variations of the semimajor axis of the relative orbit of the stars is not correct, and leads to large errors in the derived semi-major axis. A new model is proposed, suitable for elliptical stellar orbits. The reaction forces and gravitational forces between the stars and the stream of overflowing matter are taken into account. The possibility of mass transfer in the presence of an accretion disk is considered.     

Elliptical motion of a star in a close binary system

The motion of a rotating star in a close binary system with conservative mass exchange is considered. In contrast to the Paczyński-Huang model, the new model applied examines the relative motion of a star along an elliptical orbit in a close binary system, taking into account the mutual gravitation between the stars, reactive forces, the gravitation exered on the stars by the mass-transfer stream, and perturbations due to the rotation of the accreting star. The variations of the semi-major axis and eccentricity of the orbit and the orbital angular velocity of the accreting star as a function of the component-mass ratio q are determined. The results are applied to the BF Aurigae system.     

The planet around the horizontal-branch star HIP 13044

The evolution of the orbit of the planet detected around the horizontal-branch star HIP 13044 is considered. The initial semi-major axis of the planet’s orbit is estimated. A formula for the final result of the common-envelope stage in a close binary systemis used to estimate the mass of the envelope ejected by the red giant. The relatively small mass of this envelope (～0.1M _⊙) facilitated the survival of the planet after the partial dispersal of the envelope material and the transformation of the star into a horizontal-branch star.     

Influence of mass-loss due to stellar wind on the orbits of binary stars to a second order theory

We examine the influence of mass-loss due to stellar wind using the celestial mechanics of variable mass, and derive first-and second-order solutions, taking into account the decreasing mass due to the stellar wind. The theoretical results show that the semi-major axis exhibits secular and periodic variations in the first-and second-order theory. The orbital eccentricity exhibits periodic, but no secular variation or changes. The longitude of periastron exhibits only periodic variations in the first-order solution, but also secular variations in the second-order solution. The theoretical results are applied to the binary star HD 698, and variability of the orbital elements of this star due to stellar-wind mass loss calculated. Published in Russian in Astronomicheskiĭ Zhurnal, 2008, Vol. 85, No. 10, pp. 896–900. The article was translated by the authors.     

Close binaries containing Supermassive Black Holes

We consider the evolution of binary systems formed by a Supermassive Black Hole (SMBH) residing in the center of a galaxy or a globular cluster and a star in its immediate vicinity. The star is assumed to fill its Roche lobe, and the SMBH accretes primarily the matter of this star. The evolution of such a system is mainly determined by the same processes as for an ordinary binary. The main differences are that the donor star is irradiated by hard radiation emitted during accretion onto the SMBH; in a detached system, nearly all the donor wind is captured by the black hole, which strongly affects the evolution of the semi-major axis; it is not possible for companions of the most massive SMBHs to fill their Roche lobes, since the corresponding orbital separations are smaller than the radius of the last stable orbit in the gravitational field of the SMBH. Moreover, there may not be efficient exchange between the orbital angular momentum and the angular momentum of the overflowing matter in such systems. Our computations assumed that, if the characteristic timescale for mass transfer is smaller than the thermal timescale of the star, no momentum exchange occurs. Absorption of incident external radiation in the stellar envelope was treated using the same formalism that was used when computing the radiative transfer in the stellar atmosphere. Numerical simulations show that Roche-lobe overflow is possible for a broad range of initial system parameters. The evolution of semi-detached systems containing a star and a SMBH nearly always ends with the dynamical disruption of the star. Stars with masses close to the solar mass are destroyed immediately after they fill their Roche lobes. During the accretion of matter of disrupted stars, the SMBH can achieve quasar luminosities. If the SMBH accretes ambient gas as well as gas stripped from stars, the star is subject to additional radiation in the detached phase of its evolution, strengthening its stellar wind. This leads to an increase of the semi-major axis and subsequent decrease of the probability of Roche-lobe overflow during the subsequent evolution of the system.     

A PACKING GENERATION SCHEME FOR THE GRANULAR ASSEMBLIES WITH PLANAR ELLIPTICAL PARTICLES

In this paper, a new generator algorithm and a computer program PG2D is introduced for 2D numerical simulation of packing configuration in a granular material composed of elliptical particles of different a/b aspect ratios. Each elliptical particle is approximated by four connected arcs. The centre co-ordinates and radius of each arc and co-ordinates of connecting points can be determined from the formulae derived by entering the major axis length, 2a, and the eccentricity. The domain to be filled with particles can be a polygon of any shape. Given the size of the packing domain, geometrical information and numbers of particles to be generated, the packing location of each particle and the co-ordinates of contact points along with contact normal rose diagram can be generated as outputs. Simulation results show that this new algorithm can provide quite a reasonable packing model in accordance with the initial input required for the analysis of the mechanics of granular material. This generation scheme has the potential to cover packing generation and behaviour analysis of 3D sphere or ellipsoidal shaped granular materials. © 1997 by John Wiley & Sons, Ltd.     

High-pressure properties of diaspore,AlO(OH)

The structural compression mechanism and compressibility of diaspore, AlO(OH), were investigated by in situ single-crystal synchrotron X-ray diffraction at pressures up to 7 GPa using the diamond-anvil cell technique. Complementary density functional theory based model calculations at pressures up to 40 GPa revealed additional information on the pressure-dependence of the hydrogen-bond geometry and the vibrational properties of diaspore. A fit of a second-order Birch–Murnaghan equation of state to the p–V data resulted in the bulk modulus B ₀ = 150(3) GPa and B ₀ = 150.9(4) GPa for the experimental and theoretical data, respectively, while a fit of a third-order Birch–Murnaghan equation of state resulted in B ₀ = 143.7(9) GPa with its pressure derivative B′ = 4.4(6) for the theoretical data. The compression is anisotropic, with the a-axis being most compressible. The compression of the crystal structure proceeds mainly by bond shortening, and particularly by compression of the hydrogen bond, which crosses the channels of the crystal structure in the (001) plane, in a direction nearly parallel to the a-axis, and hence is responsible for the pronounced compression of this axis. While the hydrogen bond strength increases with pressure, a symmetrisation is not reached in the investigated pressure range up to 40 GPa and does not seem likely to occur in diaspore even at higher pressures. The stretching frequencies of the O–H bond decrease approximately linearly with increasing pressure, and therefore also with increasing O–H bond length and decreasing hydrogen bond length. Electronic Supplementary Material The online version of this article () contains supplementary material, which is available to authorized users.     

Effect of sampling and linkage on fault length and length–displacement relationship

The power-law exponent (n) in the equation: D=cL ⁿ , with D = maximum displacement and L = fault length, would be affected by deviations of fault trace length. (1) Assuming n=1, numerical simulations on the effect of sampling and linkage on fault length and length–displacement relationship are done in this paper. The results show that: (a) uniform relative deviations, which means all faults within a dataset have the same relative deviation, do not affect the value of n; (b) deviations of the fault length due to unresolved fault tip decrease the values of n and the deviations of n increase with the increasing length deviations; (c) fault linkage and observed dimensions either increase or decrease the value of n depending on the distribution of deviations within a dataset; (d) mixed deviations of the fault lengths are either negative or positive and cause the values of n to either decrease or increase; (e) a dataset combined from two or more datasets with different values of c and orders of magnitude also cause the values of n to deviate. (2) Data including 19 datasets and spanning more than eight orders of fault length magnitudes (10⁻²–10⁵ m) collected from the published literature indicate that the values of n range from 0.55 to 1.5, the average value being 1.0813, and the peak value of n _d (double regression) is 1.0–1.1. Based on above results from the simulations and published data, we propose that the relationship between the maximum displacement and fault length in a single tectonic environment with uniform mechanical properties is linear, and the value of n deviated from 1 is mainly caused by the sampling and linkage effects.     

隧道开挖对邻近单桩竖向受力特性影响

在分析隧道开挖对邻近单桩竖向受力特性影响时,基于荷载传递法和Winkler地基模型,利用两阶段分析法通过迭代求解给出隧道开挖与邻近单桩相互作用的弹塑性解答。通过与离心机试验的短期和长期试验结果的对比,分析了隧道开挖对邻近单桩的竖向影响,从而验证该方法的合理性和适用性。讨论了隧道开挖情况下隧道中心线距地表的距离、隧道中心线与桩轴线的距离、平均地层损失比、桩长、桩径、桩身强度6种因素对邻近单桩竖向受力特性的影响,提出隧道开挖对邻近单桩的竖向受力特性的影响规律。结果表明：随着隧道中心线距地表距离的增加,桩身沉降和桩身轴力先增大然后逐渐减小;随着隧道轴线与桩轴线距离的增加,桩身沉降逐渐减小,桩身轴力增大到一定值后逐渐减小;随着平均地层损失比的增加桩身沉降不断增大,桩身轴力逐渐增大到稳定值。     

On the existence of planets around the pulsar PSR B0329+54

Results of timing measurements of the pulsar PSR B0329+54 obtained in 1968–2012 using the Big Scanning Antenna of the Pushchino Radio Astronomy Observatory (at 102 and 111 MHz), the DSS 13 and DSS 14 telescopes of the Jet Propulsion Laboratory (2388 MHz), and the 64 m telescope of the Kalyazin Radio Astronomy Observatory (610 MHz) are presented. The astrometric and rotational parameters of the pulsar are derived at a new epoch. Periodic variations in the barycentric timing residuals have been found, which can be explained by the presence of a planet orbiting the pulsar, with an orbital period P₁ = 27.8 yr, mass m _c sin i = 2M_?, and orbital semi-major axis a = 10.26 AU. The results of this study do not confirm existence of a proposed second planet with orbital period P₂ = 3 yr.     

基于多尺度分割的岩石图像矿物特征提取及分析

针对传统岩石薄片鉴定以肉眼观察和描述为主,存在主观性强、定量困难等问题,将数字图像处理方法引入岩石矿物研究,提出了基于多尺度分割的岩石图像矿物特征信息提取方法。以铁质石英砂岩薄片显微镜下单偏光图像为实验对象,获取了石英颗粒的边界及其体积分数、大小、周长、长轴长度和方位、长轴和短轴比、圆度和形态指数等信息。其中：石英颗粒的体积分数为47.07%,小于基质的体积分数,在基质中呈漂浮状,为杂基支撑结构, 表明形成于沉积同生期;长轴的范围为50～604像素,表明石英颗粒大小不均、分选性差;颗粒的圆度为0.27～1.82,形态指数值为1.19～2.46,圆度和形态指数值较小,表明石英颗粒有一定的磨圆度。这种信息的获取和定量分析方法有助于对岩石图像的地学理解。     

A New Theropod Dinosaur from the Middle Jurassic of Lufeng,Yunnan, China

A new theropod dinosaur, Shidaisaurus jinae gen. et sp. nov., has been described on the basis of an incomplete skeleton. The specimen was found near the base of the Upper Lufeng Formation (early Middle Jurassic) in Yunnan, China. It is the first theropod dinosaur from the Middle Jurassic of Yunnan. Shidaisaurus jinae is distinguishable from other Jurassic theropods by certain features from the braincase, axis, and pelvic girdle. The absence of any pleurocoels in the axis or in any anterior dorsal vertebrae suggests that the new Lufeng theropod is relatively primitive and more plesiomorphic than most of the Middle to Late Jurassic theropods from China. Most Chinese taxa of Jurassic theropod dinosaurs have not been well described; a further detailed study will be necessary for us to determine their phylogenetic relationships with Shidaisaurus jinae.     

Statistical analysis in classification of bituminous coal

Hundreds of samples and 17 variables collected from coalfields of major coal-bearing strata over China except for Tibet and Taiwan, were used in this study. The dry, ash-free basis volatile matter (V ^r) and caking index (G _(RI)) were chosen by means of correlation analysis and stepwise discriminatory analysis as major indices of a new classification. By means of the optimum section, the boundary value of the axis of ordinate (G _(RI)) and axis of abscissas (V ^r) can be determined in the classification system. Thus, aV ^r –G _(RI) classification scheme diagram was formed and bituminous coal was divided into nine classes. Use of correspondence analysis reduced dimensions of sample-expressive space without losing initial information. The trend on the factor surface of samples shows that the classification obtained from correspondence analysis conforms to theV ^r –G _(RI) classification result and further verified the dependability of classification by two indices. At the same time, a certain relationship between the properties of a great variety of coal and their attributes can be explained. Hence, bituminous coal classification becomes more scientific, reasonable, and practical than before.     

Surface Photometry of Proplyds in the Vicinity of θ1 Ori C

Results of studies of the surface-brightness distributions of a group of young stellar objects located within 16″ of the star θ₁ Ori C are presented. Isophotes around each proplyd are constructed using violet, red, and near-infrared images. No regularity in the sizes of the diametral cross sections of the proplyds in the various photometric bands is observed. The measured relative intensities are converted to absolute fluxes, and the absolute luminosities of the brightest parts of the disks and of the disk peripheries are estimated. The ratio of the semi-major to the semi-minor axes of the objects range from 1.5 to 2.5. The maximum lengths of the proplyd tails in various filters range from 300 to 700 AU. They become shorter with decreasing distance from the illuminating star, possibly due to enhanced dissipation of the disk, due to the growth in the role of photovaporization.

     

Pressure-induced migration of zeolitic water in laumontite

A polycrystalline sample of natural laumontite (Pleasant Valley, Connecticut) was studied up to 6.8 (1) GPa at room temperature using monochromatic synchrotron X-ray powder diffraction and a diamond-anvil cell. A methanol: ethanol: water mixture was used as a penetrating pressure-transmitting fluid. A dry sample measured before adding the pressure fluid inside the diamond-anvil cell contained ~12 H₂O per formula unit, consistent with the water content of partially dehydrated laumontite. Upon increasing the pressure to 0.2 (1) GPa, fully hydrated laumontite with 18 H₂O per unit cell formed and the unit-cell volume expanded by 2.6%. Further pressure increase up to 2.4 (1) GPa resulted in a gradual contraction of the unit-cell volume and individual cell lengths. During this process, a successive order–disorder transition of hydrogen-bonded water molecules from their symmetry sites was observed, concomittent with an inflectional behavior of the monoclinic beta angle and the channel ellipticity. Above 3 GPa, a tripling of the b axis was detected. Thereafter, up to 6.8 (1) GPa, the compression behavior was reversed for the c axis length and the monoclinic beta angle which showed a gradual increase and decrease, respectively, without any apparent volume discontinuity. We suspect that different ordering of the water molecules or Ca cations inside the channels along the b axis may be responsible for the observed supercell transition above 3 GPa.     

Structure of the 30-sectored polygonal serpentine. A model based on TEM and SAED studies

 Polygonal serpentine (PS) from selected serpentinite were studied using transmission electron microscopy. Fiber axis selected-area electron diffraction (SAED) patterns and electron micrographs reveal orthogonal and monoclinic lizardite polytypes. The PS models by Chisholm (1992) and Baronnet et al. (1994) do not fit SAED measurements. Experimental results are matched with calculated diffraction geometry and intensities, as well as with simulated images, indicating inversion of the tetrahedral layer at sector boundaries. The structural relationships between chrysotile and PS are discussed. Two types of 30-sectored PS are distinguished. In “regular PS” the fiber axis is [100], in “helical PS” the fiber axis points into a [uν0] direction with large u value (u≫ν). Helical PS can be regarded as a lizardite analogue of helical chrysotile. Received December 6, 1995/Revised, accepted May 8, 1996     

Shape and distribution analysis of Merensky Reef potholing, Northam Platinum Mine, western Bushveld Complex: implications for pothole formation and growth

Syn-magmatic removal of the cumulate pile during the formation of the Bushveld Complex resulted in “potholes”. Erosion progressed downward in the cumulate pile, resulting in a series of steep, transgressive contacts between locally conformable potholed reefs in the regional pothole sub-facies of the Swartklip Facies in the western limb of the Bushveld Complex. The deepest of these potholes, “third-order” or “FWP2” potholing, occurs where the base of the Merensky Cyclic Unit transgresses the Upper Pseudo-Reef Chromitite marker horizon. The base of a FWP2 pothole on Northam Platinum Mine consists of an unconformable stringer Merensky Chromitite overlain by a medium-grained, poikilitic orthopyroxenite and underlain by either a pegmatitic harzburgite or the medium-grained Lower Pseudo-Reef Anorthosite. Detailed shape and distribution analysis of FWP2 potholes reveals underlying patterns in their shape and distribution which, in turn, suggest a structural control. The ratio between pothole short vs long axes is 0.624 (N=1,385), although the ratio increases from 0.48 to 0.61 in the long axis range 10 to 60 m, then decreases from 0.61 to 0.57 from 61 to 100 m, increasing again from 0.57 to 0.61 from 101 to 400 m, suggesting that there is not a simple relationship between pothole shape and size. Shape (circularity, eccentricity, and dendricity) analysis of a subset of 638 potholes indicates that potholes with long axes <100 m have an elliptical, average normalized shape, elongate on a 120–150° orientation. Potholes with long axis lengths >100 m have an average normalized shape that is bilobate and elongate on a 120° orientation. The average aspect ratio (short axis length divided by long axis length) of potholes is highest for potholes with long axis lengths >100 m and lowest for potholes with long axis lengths between 35 and 60 m. The most common long axis orientation for potholes with long axis lengths <100 m is 150° but 120° for long axis lengths >100 m. Fractal analysis indicates that the distribution of pothole centers is controlled neither by a single nor several interacting fractal dimensions. Autocorrelation (Fry) analysis of the distribution of pothole centers shows recurring pothole distribution trends at 038, 070, and 110° for potholes over the full range of long axis lengths, while the trends of 008 and 152° occur in potholes with long axes lengths between 60 and 100 m. Chi-squared (X ²) analysis of the locations of pothole centers suggests that the distribution of small potholes is highly non-uniform but becomes exponentially more uniform with increasing pothole size. The model which best fits the observed shape and distribution analysis is a combination of protracted independent growth and “nearest neighbor” merging along specific orientations. For instance, the clustered distribution of original pothole centers resulted in merged potholes with long axes lengths of up to 60 m, exhibiting short vs long axes ratios of 0.61, preferred orientations of 150°, and alignment along 010 and 150° trends. Further independent growth allowed for merging of similar-sized (and smaller) neighboring potholes, generating potholes with long axes of up to 100 m in length, a preferred long axis orientation of 150°, and alignment along 010, 040, 075, and 150°. Subsequent preferential merging occurred along a 120° trend, thereby preserving a bilobate form. This implies that while pothole initiation and enlargement may be driven by a “top-down” (i.e., possibly thermomechanical) process, an underlying linear or structural catalyst/control is revealed in changes in pothole shape during enlargement and, furthermore, in the preferred trends along which potholes merged over a considerable period, possibly concomitant with adjustment of major structures in the footwall to the Bushveld Complex and pulses into the magma chamber.     

The relation between microfabric and strain in a progressively deformed quartzite sequence from Central Australia

In the Ormiston Nappe Complex, west of Alice Springs, central Australia, a deformed zone up to 0.7 km thick is developed in the sedimentary Heavitree Quartzite. The deformed zone is adjacent to a major thrust fault and is defined by mylonitic foliation, which is parallel to the thrust plane and by isoclinal folds. Recognition of original detrital quartz grains allows strain ellipsoids to be measured across the zone. The strain generally plots in the flattening field and many specimens show pure flattening strain. The mylonitic foliation is an axial-plane structure to the folds and is parallel to the XY-plane of the strain ellipsoid. A quartz elongation lineation may be present within the foliation and is parallel to the principal extension direction (the X-axis) of the strain ellipsoid.Strain is accommodated principally by intracrystalline plastic deformation of the quartz grains. In detail the strain is not homogeneous and may vary even between adjacent grains of the same specimen. Quartz optic axis fabrics reflect this strain inhomogeneity. If the strain ellipsoid is an oblate spheroid, c-axes lie in small-circle girdles about the principal shortening axis (the Z-axis). With general triaxial strain, the c-axes lie in a great-circle girdle or girdles which intersect the foliation parallel to the intermediate strain axis (the Y-axis) and lie symmetrically about the Z-axis. A random population of grains from a specimen often shows a composite c-axis pattern between these two types.With approach to the thrust there is an increase in the amount of strain within the specimens. The increasing strain correlates with an increase in the degree of c-axis preferred orientation of the deformed detrital grains and in the amount of new strain-free grains present in the deformed quartzite. Adjacent to the thrust the quartzite is completely composed of polygonal new grains. The new grains probably formed under syntectonic conditions caused by movement along the thrust. The bulk of the new grains developed by increasing misorientation between the subareas of an initially polygonized old grain. There is no evidence of any marked host control on new-grain orientation, but new grain c-axis plots are generally similar to the corresponding old-grain plots from the same specimen.     

A search for Keplerian periods in the brightness variations of T Tauri and Ae Herbig stars

Long-term, uniform series of U BV R observations of T Tauri and Ae Herbig stars obtained over 20 yr at the Maidanak Observatory as part of the ROTOR program are analyzed. We find a linear relationship between the characteristic variability time scale and the bolometric luminosity of the star+disk system: the higher the luminosity, the slower the brightness variations. This dependence is valid over a wide range of masses and luminosities, from T Tauri stars to Ae Herbig stars. On average, the variability time scale is one-quarter the Keplerian period at the dust-sublimation radius, which is known from interferometric observations. Some T Tauri stars have periods from 25 to 120 days, which are preserved over several observing seasons. These periods correspond to Keplerian orbits with semi-major axes from 0.14 to 0.52 AU. The results obtained provide indirect evidence for the existence of protoplanets in the gas-dust disks of stars in early stages of their evolution toward the main sequence.