Circumstellar nebulae of WR and OB stars with strong winds: Simultaneous excitation by stellar radiation and shocks

We use a two-phase model for the structure of the circumstellar nebulae of hot stars to analyze the radiative cooling of a dense, compact cloud behind the shock produced by the compression of the cloud by hot gas from the stellar wind, taking into account ionization and heating by radiation from the central star. We can distinguish three stages of the evolution of the cloud during its compression. In the first stage, relevant for the entire cloud before compression and the gas ahead of the shock front, the state of the gas is determined purely by ionization by the stellar radiation. The next stage is characterized by the simultaneous action of two gas excitation mechanisms—photoionization by the stellar radiation and shock heating. In this stage, the gas intensively radiates thermal energy received at the shock front. After radiative cooling, in the final stage, ionization and heating of the gas are again determined mainly by the star. To compute the spectrum of the cloud radiation, we solved for the propagation of a plane-parallel, homogeneous flux through the shock front in the radiation field of the hot star. The computations show that a combination of two excitation mechanisms considerably enriches the theoretical spectrum. The relative intensities of emission lines of a single cloud may resemble either those for an HII region or of a supernova remnant.     

A solution for the transition zone isosats in two-phase primary drainage in the presence of gravity

Primary drainage in a water-wet saturated medium in the absence of capillarity is typically a combination of shock (discontinuous) and rarefaction (continuous) waves. Using nonlinear relative permeability functions for the host fluid and the invading fluid leads to the existence of a shock wave front, and the degree of nonlinearity of the relative permeability functions has an inverse relationship with the size of the shock wave (i.e., difference of saturation between upstream and downstream of the shock wave), whereas for linear relative permeability functions, the shock wave size approaches 0. Injection of a lower-viscosity immiscible phase such as gas or solvent into a water-wet porous medium in the presence of large capillary pressure leads to development of an extended and growing saturation transition zone that follows the discontinuous shock wave front. In this article, a semianalytical solution for the position of equisaturation contours (isosats) in the transition zone in the presence of gravity is obtained for a set of linearized relative permeability functions. The capillary (diffusive) and buoyancy terms are neglected, and the generalized convective equation for mass conservation is obtained. The set of equations is then reduced to a one-dimensional steady-state differential equation through forcing the isosat formulation to obey mass conservation. This scheme allows the isosat distribution to be solved, and the case of injection into an axisymmetric geometry for a confined planar configuration is solved and presented. A finite element model was developed to demonstrate the reasonable agreement between analytical and numerical solutions.     

The nonthermal radio emission of WR 140 in a model with colliding two-phase winds

We present a model in which the nonthermal radio emission of binary systems containing Wolf-Rayet and O components is due to collisions between clouds belonging to dense phases of the wind of each star. The relativistic electrons are generated during the propagation of fast shock waves through the clouds and their subsequent de-excitation. The initial injection of superthermal particles is due to photoionization of the de-excited cold gas by hard radiation from the shock front. Therefore, the injection takes place in cloud regions fairly far from the front. Further, the superthermal electrons are accelerated by the betatron mechanism to relativistic energies during the isobaric compression of the cloud material, when most of the gas radiates its energy. Collisions between the clouds can occur far beyond the contact boundary between the rarefied wind components. Thus, the model avoids the problem of strong low-frequency absorption of the radiation.     

Formation of galactic shocks and the vertical structure of the gaseous disk of the galaxy in a “turbulent” interstellar medium

The effects on the formation of Galactic shocks and the vertical structure of the Galactic disk due to thermal processes in a cloudy interstellar medium as it flows through a spiral density wave in the plane of the Galactic disk are considered. The evolution of the gas is fundamentally different, depending on the thermal properties of the medium. For example, if it is compressed in the horizontal direction (parallel to the Galactic plane) by the gravitational forces of the spiral density waves responsible for the formation of spiral arms, an isothermal and adiabatic medium is swept out in the vertical direction. However, on the contrary, a medium whose volume loss function increases fairly rapidly with density and temperature is further compressed under the action of the overall gravitational field of the galaxy. This effect is referred to as “self-focusing,” and may serve as an additional mechanism to explain the recently discovered anticorrelation between the width of the atomic hydrogen layer in the Galaxy and the gas density. The difference in the vertical behavior of media with different thermal properties can be used as an indicator of the thermal properties of a particular component of the interstellar gas (atomic or molecular). Attention is drawn to the fact that Galactic shocks themselves represent a mechanism that can heat the ensemble of clouds, i.e., increase the dispersion of cloud velocities. The vertical structure of a Galactic shock front is constructed, which is in qualitative agreement with the “bow shock” inferred from radio data.     

Dust formation in binaries with OB and WR components in a two-phase stellar-wind model

We describe the formation of carbon dust in binary systems with hot components as a result of the collisions of clouds in a two-phase stellar-wind model. Calculations are made for the well studied system WR 140. The collisions lead to the formation of composite clouds and shock waves, with the temperature at the shock front equal to about 3×10⁸ K along both sides of the interface boundary. During isobaric deexcitation to (0.5–0.7)×10⁴ K, the cloud density increases by a factor of several thousand; its thickness in the direction of the shock decreases by the same factor. After deexcitation, the hydrogen inside the composite cloud is in its atomic state, while the carbon remains ionized. The deexcitation is followed by expansion of the cloud, which moves away from both stars. During the first 10⁶ s, its thickness remains relatively small, so that the expansion is one-dimensional. The radiation field inside the cloud decays, resulting in the recombination of the carbon. Further expansion of the cloud leads to adiabatic cooling, and the formation of dust particles becomes possible. After the dimensions of the cloud have become roughly the same in all directions, its expansion is isotropic, so that it becomes transparent within approximately 10⁶ s, and the dust is heated to (1.0–1.4)×10³ K, observed as an IR “lare.” The time required for the cloud to move from the exciting star and heat the dust is comparable to the observed delay in the increased IR emission relative to the time of periastron.     

Self-similar focusing of rarefaction waves in relativistic collapsing clouds

The development of an inhomogeneous collapse of an initially homogeneous cloud in pressure equilibrium with an external medium is considered in a general-relativistic treatment. It is shown that a rarefaction wave propagating from the outer boundary toward the center of the cloud forms in the initial stage of the collapse. The rarefaction front moves through the collapsing gas at the sound speed, and separates the cloud material into an inner, uniform core and an outer, inhomogeneous envelope. Our analysis distinguishes two possible collapse regimes, depending on the ratio of the focusing time for the rarefaction wave and the free-fall time for the cloud. In massive clouds, the focusing time for the rarefaction wave exceeds the free-fall time, and the collapse of such clouds inevitably leads to the formation of an event horizon and black hole. In low-mass clouds, the focusing time is less than the free-fall time. After the focusing, the collapse of such clouds is fully inhomogeneous, and can be appreciably slowed by the pressure gradient. The compression of a cloud in a transitional regime separating these two scenarios is studied. In this case, a self-similar collapse regime is realized in the central part of the cloud near the focusing time for the rarefaction wave. The constructed self-similar solution describes both early stages in the compression up to the focusing of the rarefaction wave and later stages with the accretion of gas onto the black hole that is formed. Asymptotic distributions of quantities in the inhomogeneous region at large distances from the rarefaction front and in the accreting envelope are found. The structure of space-time in the vicinity of the black hole that is formed at the center of the cloud as a result of the focusing of the rarefaction wave is discussed.     

The nature of peculiar stellar complexes

The nature of stellar complexes with peculiar populations and morphologies is investigated. The existence in the LMC of complexes made up of isolated stars, on the one hand, and consisting exclusively of clusters, on the other hand, could be due to different turbulence patterns in the initial gaseous medium. Arc-shaped stellar complexes are unlikely to be the result of star formation in a gaseous shell swept up by a central source of pressure, and instead probably reflect the shape of a bow shock that develops when a sufficiently dense cloud is subject to dynamical pressure. A peculiar arc-shaped complex in NGC 6946, which contains a young, massive cluster, may be the result of an oblique infall of a high-velocity cloud onto a region of the gaseous disk of the Galaxy with a strong, regular magnetic field; the properties of this complex can be explained as the result of a collision of the resulting shocks. The arc-shaped complexes in the LMC were also probably produced by high-velocity clouds moving obliquely through the more tenuous gas of the LMC disk. A similar complex in NGC 300 may owe its origin to the effect produced on a dense cloud by the shock from an extremely powerful external explosion, whose stellar remnant may have survived as an X-ray source now located along the line of symmetry of the arc of the complex. The rareness of such structures can be explained by the narrow range of conditions under which they can develop.     

The influence of variations of the elemental composition on the thermal properties of gas behind shock fronts

The homogenization of inhomogeneities in the elemental composition of the interstellar medium due to stellar evolution and weak mixing are inevitably related to the action of shocks. This paper considers the influence of variations in the elemental composition on the thermal and ionizational evolution of a collisional gas with the solar metallicity that is cooled behind a shock front with a velocity of 50–120 km/s. The intensities of lines of heavy elements in plasma cooling behind a shock front depend not only on variations in the elemental composition, but also on the shock velocity, due to the different values of the critical density for the transition to the equilibrium level populations in atoms and ions of heavy elements. This circumstance can be used to determine the elemental composition of cool and warm gas of the interstellar medium, as well as the thermal history of the gas.     

Adjoint analysis of Buckley-Leverett and two-phase flow equations

This paper analyzes the adjoint equations and boundary conditions for porous media flow models, specifically the Buckley-Leverett equation, and the compressible two-phase flow equations in mass conservation form. An adjoint analysis of a general scalar hyperbolic conservation law whose primal solutions include a shock jump is initially presented, and the results are later specialized to the Buckley-Leverett equation. The non-convexity of the Buckley-Leverett flux function results in adjoint characteristics that are parallel to the shock front upstream of the shock and emerge from the shock front downstream of the shock. Thus, in contrast to the behavior of Burgers’ equation where the adjoint is continuous at a shock, the Buckley-Leverett adjoint, in general, contains a discontinuous jump across the shock. Discrete adjoint solutions from space-time discontinuous Galerkin finite element approximations of the Buckley-Leverett equation are shown to be consistent with the derived closed-form analytical solutions. Furthermore, a general result relating the adjoint equations for different (though equivalent) primal equations is used to relate the two-phase flow adjoints to the Buckley-Leverett adjoint. Adjoint solutions from space-time discontinuous Galerkin finite element approximations of the two-phase flow equations are observed to obey this relationship.     

松辽盆地保乾三角洲前缘带演变及其勘探意义

岩性油藏是松辽盆地最主要油藏类型之一,而三角洲前缘带是形成岩性油藏的有利相带。通过保乾三角洲沉积体系在不同地质时期沉积微相和沉积模式的深入研究,动态再现了保乾三角洲前缘带的演化过程。前缘带砂体经历了退积、进积和大规模迁移三个过程,物源方向总体由西南向西北方向逐步迁移,三角洲朵体形态由“深湖型”朵叶式逐步转变为“浅湖型”树枝式。保乾三角洲前缘带不同沉积时期的迁移规律对岩性油藏的勘探具有重要指导意义。     

深层岩体松动爆破中不耦合装药效应的探讨

基于冲击波在交界面两侧压力和速度必须各自相等的连续性条件,求解爆轰产物中适用的反射波方程和介质中适用的冲击波方程,得到药包周围介质中冲击波的初始参数.通过波的传播机理,把集中药包应力波随距离的衰减公式扩展到延长药包,并计算耦合与不耦合装药爆破时距爆心相同距离处岩石中冲击波的参数.由计算结果可知:(1)耦合装药爆破时形成的冲击波压力超过岩石抗压强度极限几十倍以上,药包周围岩石形成粉碎区;(2)与耦合装药爆破相比,不耦合装药爆破可以降低孔壁处岩石中冲击波初始压力,但可以增加孔壁后岩石中的冲击波压力.合理的不耦合系数,可使岩石不形成粉碎区,大幅度减少能量耗散;(3)水一般认为是非线性弹性介质,因此水介质成为炸药爆轰产物与岩石间的弹性缓冲层,增加了能量传递,延长了冲击波作用时间,加大了爆炸的作用范围.     

Acceleration of multiply charged ions of the anomalous cosmic-ray component at the heliosphere boundary

The formation of the energy spectra of heavy ions at the front of a parallel shock is considered taking into account ionization and recombination during the acceleration. An analytic solution for ions with three possible charge states is obtained and applied to the acceleration of the anomalous cosmic-ray component at the boundary of the heliosphere. In addition, a more general numerical model for such acceleration at a spherical shock front is developed and used to obtain the energy dependence of the mean charges for C, N, O, Ne, Si, S, Ar, and Fe ions. The model implies that highly excited ions begin to dominate over ions with low charges at energies above 1 MeV/nucleon, in agreement with observational data.     

Traveling waves in a finite condensation rate model for steam injection

Steam drive recovery of oil is an economical way of producing oil even in times of low oil prices and is used worldwide. This paper focuses on the one-dimensional setting, where steam is injected into a core initially containing oil and connate water while oil and water are produced at the other end. A three-phase (oil, water, steam) hot zone develops, which is abruptly separated from the two-phase (oil + water) cold zone by the steam condensation front. The oil, water and energy balance equations (Rankine–Hugoniot conditions) cannot uniquely solve the system of equations at the steam condensation front. In a previous study, we showed that two additional constraints follow from an analysis of the traveling wave equation representing the shock; however, within the shock, we assumed local thermodynamic equilibrium. Here we extend the previous study and include finite condensation rates; using that appropriate scaling requires that the Peclet number and the Damkohler number are of the same order of magnitude. We give a numerical proof, using a color-coding technique, that, given the capillary diffusion behavior and the rate equation, a unique solution can be obtained. It is proven analytically that the solution for large condensation rates tends to the solution obtained assuming local thermodynamic equilibrium. Computations with realistic values to describe the viscous and capillary effects show that the condensation rate can have a significant effect on the global saturation profile, e.g. the oil saturation just upstream of the steam condensation front.     

膜孔多向交汇入渗湿润体特性试验研究

通过大量膜孔多向交汇入渗试验资料.分析了膜孔多向交汇入渗湿润体形状、湿润锋运移和湿润体内土壤含水率,该研究成果可为进一步研究膜孔交汇入渗规律和膜孔灌技术提供参考.     

Squeezing a Sponge: A Three-Dimensional Solution in Poroelasticity

A three-dimensional solution is derived for the fluid flow in a deformable porous medium. It is assumed that the deformation of the medium is described by Hooke's law and the flow of the fluid by Darcy's law, i.e. the theory of poroelasticity applies. The governing equations are completed by suitable boundary conditions such that a compressed saturated cubic sponge is modelled. The solution is a three-dimensional generalisation of the one-dimensional solution of Terzaghi. A two-dimensional plane strain solution is derived also. Both solutions give excellent possibilities to test numerical codes.     

基于Mein-Larson入渗模型的凹形边坡稳定性分析

坡面形态对边坡表面应力状态影响显著,而应力状态与边坡稳定性密切相关。以往的降雨入渗模型仅考虑直线形态的边坡,并没有考虑边坡为曲线形态的情况。将Mein-Larson入渗模型与坡形函数相结合,推导降雨作用下凹形边坡的入渗函数,结合极限平衡分析方法,提出一种凹形边坡稳定性计算模型。同时根据坡形拟合与坡形简化的思路,将实际边坡分别当作成凹形边坡和直线边坡进行研究。研究结果表明:湿润锋入渗深度与降雨时间呈线性关系,湿润锋面在不同降雨时刻下均与坡面平行。将实际边坡当作凹形边坡进行分析时,其降雨入渗规律更符合实际情况;当降雨时间为10天时,浅层斜坡模型得到的计算结果为0.95,而本文计算模型与数值模拟得到的稳定性系数分别为1.004和1.003,相对误差不超过1%。因此与以往提出的计算模型相比,该模型不仅考虑了实际边坡的坡面形态,而且具有计算简便、可靠度较高等特点。     

Self-similar regimes for the collapse of magnetic protostellar clouds

Self-similar solutions describing the homogeneous, free, isothermal collapse of protostellar clouds are considered. One such solution correponds to the critical case of the propagation of a rarefaction wave near the time when it is focused in the central region of the cloud. The speed of the rarefaction front is finite and equal to three times the isothermal sound speed. The asymptotic distributions of gas-dynamical quantities in the central part of the collapsing cloud and the surrounding envelopes are considered at both early and late stages of compression, after the formation of an opaque core (protostar). These solutions are used in a magneto-kinematic approximation to study the geometry and evolution of the large-scale magnetic fields of collapsing protostellar clouds. All the solutions are verified using direct numerical simulations. It is shown that an initially uniform magnetic field acquires an “hourglass” geometry with time. The characteristic opening angles in the self-similar solutions are in satisfactory agreement with observations.     

长江下游上河口段北岸无凝聚性砂岸的变形破坏规律

长江下游上河口段北岸,属南通市城港口范围,岸线在平面上是反“S” 型,大部分处于凹岸的顶冲区,尽管江岸的演变受诸如河型,迳流、潮汐、科氏力等主要因素的影响,但其变形破坏规律恰受以细粉砂层为主体的这一江岸介质条件的制约。文中分析了发生于近数十年来江岸的各种变形破坏形式和规律。对是否存在砂体的渗透变形问题,据水位观测,室内渗透变形试验和现场调查所得,亦作了较详细的分析。     

颗粒形状对粒状材料破碎演化规律及强度准则影响

为探讨颗粒形状对粒状材料的颗粒破碎演化规律及强度特征的影响,提出了一个新的粒状材料颗粒形状量化参数,设计了一种考虑三维颗粒形状的人工试样制备方法,随即进行了常规三轴压缩试验,并分析了颗粒破碎和强度特征,最终建立了一个二元介质强度准则,具体的研究成果为：建立颗粒形状量化参数——球形模量GM,在此基础上制备了5种不同形状的可破碎粒状材料三轴试样,并发现球形模量影响着粒状材料的三轴压缩强度特征;通过筛分确定试样的颗粒破碎情况,对试样的颗粒破碎演化规律和临界状态进行探讨,发现颗粒形状通过影响颗粒破碎规律而控制着宏观强度的非线性演化特征;以二元介质理论为基础,建立了考虑颗粒形状的可破碎粒状材料强度准则,并通过试验对其适用性进行了验证。     

Self‐similar solution of a plane‐strain fracture driven by a power‐law fluid

This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power‐law rheology and behaviour index n?0. The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self‐similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self‐similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed. Copyright © 2002 John Wiley & Sons, Ltd.