Asymptotic solution to the restricted three‐body problem with a mass point moving near a small‐mass body

The motion of a mass point in the gravitational field of two bodies traveling along arbitrary orbits about their center of mass is considered. The mass ratio of the two bodies is equal to ε?1. When the mass point passes close to the smaller mass, the character of its trajectory changes abruptly, and the trajectory asymptotics as ε→0 is complex. The uniform asymptotic expansion of the entire trajectory up to any power of ε is constructed and justified. In particular, an algorithm is presented for finding the limiting turning angle of the trajectory after the mass point passes a neighbourhood of the smaller mass. Copyright © 2010 John Wiley & Sons, Ltd.     

变质量可控力学系统的相对论性变分原理与运动方程*

本文同时考虑经典变质量和相对论变质量情况,建立了基本形式、Lagrange形式,Nielsen形式和APPell形式的变质量可控力学系统的相对论性D'Alembert原理,得到了变质量非完整可控力学系统在准坐标下和广义坐标下的相对论性方程、Nielsen方程和APPell方程,并讨论了完整系统、常质量系统的相对论性可控力学系统的运动方程。     

Investigation of critical influential speed for moving mass problems on beams

A traveling mass due to its mass inertia has significant effects on the dynamic response of the structures. According to recent developments in structural materials and constructional technologies, the structures are likely to be affected by sudden changes of masses and substructure elements, in which the inertia effect of a moving mass is not negligible. The transverse inertia effects have been a topic of interest in bridge dynamics, design of railway tracks, guide way systems and other engineering applications such as modern high-speed precision machinery process. In this study an analytical–numerical method is presented which can be used to determine the dynamic response of beams carrying a moving mass, with various boundary conditions. It has been shown that the Coriolis acceleration, associated with the moving mass as it traverses along the vibrating beam shall be considered as well. Influences regarding the speed of the moving mass on the dynamic response of beams with various boundary conditions were also investigated. Results illustrated that the speed of a moving mass has direct influence on the entire structural dynamic response, depending on its boundary conditions. Critical influential speeds in the moving mass problems were introduced and obtained in numerical examples for various BC’s.     

锚固岩体参数的等效方法研究

利用岩体中结构体与结构面的刚度系数比较严密地推导了裂隙岩体的等效法向及切向刚度系数;基于岩体小变形、变形可叠加性及强度参数C、φ不相关性假定,利用Coulomb强度理论推导了裂隙岩体等效连续体的等效强度参数C、φ值的表达式.其成果在岩体边坡的整体稳定分析方面具有重要的应用价值,对于推动岩体本构关系的研究具有重要意义.     

微血管自律运动对微循环物质交换的影响*

本文分析了管壁运动状况下微循环的渗透现象,着重分析了管壁运动对物质交换的影响.结果表明,管壁运动对于促进物质交换有着重要作用.     

Bartnik’s Mass and Hamilton’s Modified Ricci Flow

We provide estimates on the Bartnik mass of constant mean curvature surfaces which are diffeomorphic to spheres and have positive mean curvature. We prove that the Bartnik mass is bounded from above by the Hawking mass and a new notion we call the asphericity mass. The asphericity mass is defined by applying Hamilton’s modified Ricci flow and depends only upon the restricted metric of the surface and not on its mean curvature. The theorem is proven by studying a class of asymptotically flat Riemannian manifolds foliated by surfaces satisfying Hamilton’s modified Ricci flow with prescribed scalar curvature. Such manifolds were first constructed by the first author in her dissertation conducted under the supervision of M. T. Wang. We make a further study of this class of manifolds which we denote Ham₃, bounding the ADM masses of such manifolds and analyzing the rigid case when the Hawking mass of the inner surface of the manifold agrees with its ADM mass.     

Two-Component Two-Compressible Flow in a Porous Medium

We prove existence of solutions of a two-compressible (liquid and gas) phase flow model in porous media with two components (water and hydrogen). This model is obtained by writing the mass conservation for each component in each phase. We suppose that the mass exchange between dissolved hydrogen and hydrogen in the gas phase is supposed finite. This mass exchange is modeled by a source term on each mass conservation equations.     

Quasi-Local Mass Integrals and the Total Mass

On asymptotically flat and asymptotically hyperbolic manifolds, by evaluating the total mass via the Ricci tensor, we show that the limits of certain Brown–York type and Hawking type quasi-local mass integrals equal the total mass of the manifold in all dimensions.     

Approximate equations of rotational motion of a rigid body carrying a movable point mass

The dynamics of a compound system, consisting of a rigid body and a point mass, which moves in a specified way along a curve, rigidly attached to the body is investigated. The system performs free motion in a uniform gravity field. Differential equations are derived which describe the rotation of the body about its centre of mass. In two special cases, which allow of the introduction of a small parameter, an approximate system of equations of motion is obtained using asymptotic methods. The accuracy with which the solutions of the approximate system approach the solutions of the exact equations of motion is indicated. In one case, it is assumed that the point mass has a mass that is small compared with the mass of the body, and performs rapid motion with respect to the rigid body. It is shown that in this case the approximate system is integrable. A number of special motions of the body, described by the approximate system, are indicated, and their stability is investigated. In the second case, no limitations are imposed on the mass of the point mass, but it is assumed that the relative motion of the point is rapid and occurs near a specified point of the body. It is shown that, in the approximate system, the motion of the rigid body about its centre of mass is Euler–Poinsot motion.     

The rate of concentration for the radially symmetric solution to a degenerate drift-diffusion equation with the mass critical exponent

We consider the concentration rate of the total mass for radially symmetric blow-up solutions to the Cauchy problem of a degenerate drift-diffusion system with the mass critical exponent. We proved that the radially symmetric solution blows up in finite time when the initial data has negative free energy. We show that the mass concentration phenomenon occurs with the sharp lower constant related to the best constant of the Hardy–Littlewood–Sobolev inequality and the concentration rate of the total mass.     

The Wightman axioms and the mass gap for strong interactions of exponential type in two-dimensional space-time

We construct boson models in two space-time dimensions which satisfy all the Wightman axioms with mass gap. The interactions are exponential and no restriction on the size of the coupling constant is made. The Schwinger functions for the space cut-off interaction are shown to be non-negative and to decrease monotonically to their unique, non zero, infinite volume limit, as the space cut-off is removed. The correspondent Wightman functions satisfy all the Wightman axioms. The mass gap of the space cut-off Hamiltonian is non decreasing as the space cut-off is removed and the Hamiltonian for the infinite volume limit has mass gap at least as large as the bare mass. The infinite volume Schwinger functions and the mass gap depend monotonically on the coupling constant and the bare mass. The coupling of the first power of the field to the first excited state is proven and an equation of motion for the interacting field is derived.     

Measure-valued Markov processes and stochastic flows on abstract spaces

We consider measure-valued processes with constant mass in Hilbert space. The stochastic flow which carries the mass satisfies a stochastic differential equation with coefficients depending on the mass distribution. This mass distribution can be considered as the conditional distribution of the solution of a certain SDE. In contrast to the filtration equation, in our case the random measure cannot diffuse: a single particle cannot break up or turn into clouds. The Markov structure of the measure-valued processes obtained is studied and a comparison with Fleming–Viot processes is presented.     

Simulation of mass transfer at free liquid/liquid interfaces

A numerical scheme for the simulation of mass transfer processes at free liquid/liquid interfaces using the interface tracking method is presented. Due to comparable diffusion coefficients in liquid/liquid systems, the mass transfer resistance in both phases is relevant for the entire transient mass transfer process. Exemplary, the extraction process from a free rising spherical droplet of constant shape is used. The presented approach can be used in general for any multiphase steady-state mass transfer system. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rigid–flexible coupling dynamic analysis on a mass attached to a rotating flexible rod

A rigid–flexible coupling dynamic analysis is presented where a mass is attached to a massless flexible rod which rotates about an axis. The rod is limited to small deformation so that the mass is constrained to move in the plane of rotation. A strongly nonlinear model of the system is established based on the couplings between the elastic deflections of the mass and rigid rotation, in which the mass deflection and rigid rotation are both treated as unknown variables. The additional inertia forces on the mass and coupling mechanism are elucidated in the system model. In the case of varied but prescribed rigid rotation, a set of time-varying differential equations governing mass motion is obtained. The trajectories of mass motion are examined for the spin-up and spin-down rotation. Under constant rigid rotation, a set of ordinary differential equations is further attained, and the issues with dynamic frequencies and critical angular velocity of the system are analyzed. The effects of the centrifugal, Coriolis and tangential inertia forces on the dynamic responses are discussed.     

Absence of Critical Mass Densities for a Vibrating Membrane

We study the dependence of the eigenvalues of a N-dimensional vibrating membrane upon variation of the mass density. We prove that the elementary symmetric functions of the eigenvalues depend real-analytically on the mass density and that such functions have no critical points with constant mass constraint. In particular, the elementary symmetric functions of the eigenvalues, hence all simple eigenvalues, have no local maxima or minima on the set of those mass densities with a prescribed total mass.     

Mathematical modeling and validation of mass transfer phenomenon in homogeneous charge compression ignition engines based on a thermodynamic multi zone model

The main purpose of the current study is mathematical modelling and validation of mass transfer phenomenon in homogeneous charge compression ignition engines. A validated multi-zone model coupled to a semi-detailed chemical kinetics is used to predict homogeneous charge compression ignition combustion and emissions. Heat and Mass transfer submodels are linked to the multi-zone model. Bulk flow and diffusion mass transfer between zones are considered. The results indicate that the diffusion mass transfer is negligible in homogeneous charge compression ignition engines. Bulk flow mass transfer plays a critical role in homogeneous charge compression ignition simulation and applying it in the multi-zone model leads to accurate prediction of the start of combustion, peak pressure and exhaust emissions. The results show that the maximum error changes from 90% to 5% in carbon monoxide prediction and from 98% to 14% in unburned hydrocarbons prediction, using the mass transfer submodel.     

Time Flat Surfaces and the Monotonicity of the Spacetime Hawking Mass II

In this sequel paper, we give a shorter, second proof of the monotonicity of the Hawking mass for time flat surfaces under spacelike uniformly area expanding flows in spacetimes that satisfy the dominant energy condition. We also include a third proof which builds on a known formula and describe a class of sufficient conditions of divergence type for the monotonicity of the Hawking mass. These flows of surfaces may have connections to the problem in general relativity of bounding the total mass of a spacetime from below by the quasi-local mass of spacelike 2-surfaces in the spacetime.     

Phase trajectory portrait of the vibro-impact forced dynamics of two heavy mass particles motions along rough circle

Forced vibro-impact dynamics of the two heavy mass particle motions, in vertical plane, along rough circle with Coulomb’s type friction and one, one side impact limiter is considered in combinations of applied analytical and numerical methods. System of two differential double equations, each for one of two heavy mass particle motions along same rough circle are composed with corresponding initial conditions as well as impact conditions. By use software package tools differential double equations are numerically integrated for obtaining phase portrait of phase trajectory branches for different mass particles initial kinetic states. By series of the phase trajectory branches for each mass particle motion between two impacts or between impact and alternation of the Coulomb’s friction force direction, two phase trajectory graphs of the system vibro-impact non-linear dynamics are composed. Different software tools are used as helping tools for calculate time moments of the series of the impacts between mass particles, as well as positions of the impacts, necessary for calculations of the impact velocities of the mass particles before and after impacts. Some comparison between forced and free vibro-impact dynamics of the two heavy mass particles in vertical plane, along rough circle with Coulomb’s type friction and one, one side impact limiter is done. Trigger of coupled one side singularities in phase portraits are identified.     

Steady boundary layer flow and reactive mass transfer past an exponentially stretching surface in an exponentially moving free stream

An analysis is made to study the steady two-dimensional boundary layer flow and reactive mass transfer past an exponentially stretching sheet in an exponentially moving free stream. The reaction rate of solute and the wall concentration distribution are taken variable. The governing equations are transformed and then solved numerically. The study reveals that the momentum boundary layer thickness is considerably smaller than that of stagnation point flow over stretching sheet. Due to increase of Schmidt number and reaction rate parameter the mass transfer considerably enhances. Importantly, for solute distribution, in addition to mass transfer, mass absorption occurs in certain situations.     

闭合圆柱壳在冲击荷载下的动力计算

本文讨论闭合圆柱形壳体在冲击荷载作用下的动力计算.文中分析冲击过程各阶段的动量及能量的变化,并计入冲击物和被冲击的闭合圆柱壳系统质量的影响;用相当质量法将整个圆柱形壳体的分布质量转化为只有一个集中的“相当质量”,从而导出闭合圆柱形壳体在冲击力作用下的动力因数.本文的特点是具有实用价值,计算比较简便.