A Time-Transformed Leapfrog Scheme     

Seppo Mikkola  Sverre Aarseth 《Celestial Mechanics and Dynamical Astronomy》2002,84(4):343-354

We present a time-transformed leapfrog scheme combined with the extrapolation method to construct an integrator for orbits in N-body systems with large mass ratios. The basic idea can be used to transform any second-order differential equation into a form which may allow more efficient numerical integration. When applied to gravitating few-body systems this formulation permits extremely close two-body encounters to be considered without significant loss of accuracy. The new scheme has been implemented in a direct N-body code for simulations of super-massive binaries in galactic nuclei. In this context relativistic effects may also be included.  相似文献   

Diffusion in momentum space as a picture of second-order Fermi acceleration     

M. Ostrowski  G. Siemieniec-Ozi b o 《Astroparticle Physics》1997,6(3-4):271-277

Energetic particles in a turbulent medium can be subject to second-order Fermi acceleration due to scattering on moving plasma waves. This mechanism leads to growing particle momentum dispersion and, at the same time, increases the mean particle energy. In the most frequently met situations both processes can be represented by a single momentum diffusion term in the particle kinetic equation. In the present paper we discuss the conditions allowing the additional term for regular acceleration to arise. For forward-backward asymmetric scattering centres, besides the diffusive term one should explicitly consider the regular acceleration term in momentum space, which can consist of the first-order (∝ V), as well as the second-order (∝ V²) part in the wave velocity V. We derive the condition for the scattering probability in the wave rest frame requied for vanishing the regular acceleration term and provide a simple mechanical example illustrating the theoretical concepts. Finally, we address its possible role in cosmic ray acceleration processes.  相似文献   

Estimation of parameters in petrologic materials balance equations     

N. H. Gray 《Mathematical Geology》1973,5(3):225-236

A rigorous treatment of the least-squares estimation of the parameters in petrologic materials balance equations is developed to take into account the uncertainties inherent in the chemical analyses. The choice of the optimal estimation procedure for a particular problem is dependent upon the extent of the petrogenetic understanding of the exact nature of the materials balance involved. Some of the complications entailed in obtaining least-squares estimates are illustrated by the examples of magmatic differentiation and metamorphic reactions.  相似文献   

广义相对论中静态荷电球体的内解     

王行翔 《中国天文和天体物理学报》1988,(3)

本文在假设荷电球体内部物质密度为ρ_m=μγ~α,电荷密度为ρ_e=ρ_0γ~(b_e-λ/2)的情况下,严格求解Einstein-Maxwell场方程,求得了静态荷电球体的一个较为普遍的内部解。这个解可以看作是Wyman得到的内部解推广到荷电情况下的结果,并且将Wilson,李鉴增,Santos,Pant和Sah等人给出的许多结果作为自己的特例包括在内。  相似文献   

On Charged Analogues of Buchdahl’S Type Fluid Spheres     

Y.?K.?Gupta  Mukesh?KumarEmail author 《Astrophysics and Space Science》2005,299(1):43-59

In this article the charged analogues of recently derived Buchdahl’s type fluid spheres have been obtained by considering a particular form of electric field intensity. In this process, Einstein–Maxwell field equations yield eight different classes of solutions, joining smoothly with the exterior Reissner–Nordstrom metric at the pressure free intersurface. Out of the eight solutions only seven could be utilized to represent superdense star models with ultrahigh surface density of the order 2×10¹⁴ gm cm⁻³. The maximum masses of the star models were found to be 8.223931M_Θ and 8.460857M_Θ subject to strong and weak energy conditions, respectively, which are much higher than the maximum masses 3.82M_Θ and 4.57M_Θ allowed in the neutral cases. The velocity of sound seen to be less than that of light throughout the star models.  相似文献   

    

Michael W. D. Davis  Michel David  Jean-Marc Belisle 《Mathematical Geology》1978,10(4):369-374

In mineral deposit evaluation, the estimation of block values can involve the solution of as many as 100,000 systems of linear equations. To minimize computing costs it is important that the program to solve the linear systems be as efficient as possible. Standard library routines tend to contain very general stable methods using pivoting and iteration to ensure high accuracy solutions. Here, a particular method has been developed that gives a substantial improvement in run time at the occasional expense of accuracy and stability. The method is not new—just a simple application of Gaussian elimination in the symmetric case.  相似文献   

Stochastic Hill's equations for the study of errant rocket burns in orbit     

Martin Ostoja-Starzewski  James M. Longuski 《Celestial Mechanics and Dynamical Astronomy》1992,54(4):295-303

The problem of errant rocket burns in low Earth orbit is of growing interest, especially in the area of safety analysis of nuclear powered spacecraft. The development of stochastic Hill's equations provides a rigorous mathematical tool for the study of such errant rocket maneuvers. These equations are analyzed within the context of a theory of linear dynamical systems driven by a random white noise. It is established that the trajectories of an errant rocket are realizations of a Gauss-Markov process, whose mean vector is given by the solution of a deterministic rocket problem. The time-dependent covariance matrix of the process is derived in an explicit form.  相似文献   

Theory of Basin Scale Dynamics of a Stratified Rotating Fluid     

Leo R. M. Maas 《Surveys in Geophysics》2004,25(3-4):249-279

The dynamics of a stratified fluid contained in a rotating rectangular box is described in terms of the evolution of the lowest moments of its density and momentum fields. The first moment of the density field also gives the position of the fluids centre-of-mass. The resulting low-order model allows for fast assessment both of adopted parameterisations, as well as of particular values of parameters. In the ideal fluid limit (neglect of viscous and diffusive effects), in the absence of wind, the equations have a Hamiltonian structure that is integrable (non-integrable) in the absence (presence) of differential heating. In a non-rotating convective regime, dynamically rich behaviour and strong dependence on the single (lumped) parameter are established. For small values of this parameter, in a self-similar regime, further reduction to an explicit map is discussed in an Appendix. Introducing rotation in a nearly geostrophic regime leads through a Hopf bifurcation to a limit cycle, and under the influence of wind and salt to multiple equilibria and chaos, respectively.  相似文献   

Subgrid-Scale Dynamics of Water Vapour, Heat, and Momentum over a Lake     

Nikki Vercauteren  Elie Bou-Zeid  Marc B. Parlange  Ulrich Lemmin  Hendrik Huwald  John Selker  Charles Meneveau 《Boundary-Layer Meteorology》2008,128(2):205-228

We examine the dynamics of turbulence subgrid (or sub-filter) scales over a lake surface and the implications for large-eddy simulations (LES) of the atmospheric boundary layer. The analysis is based on measurements obtained during the Lake-Atmosphere Turbulent EXchange (LATEX) field campaign (August–October, 2006) over Lake Geneva, Switzerland. Wind velocity, temperature and humidity profiles were measured at 20 Hz using a vertical array of four sonic anemometers and open-path gas analyzers. The results indicate that the observed subgrid-scale statistics are very similar to those observed over land surfaces, suggesting that the effect of the lake waves on surface-layer turbulence during LATEX is small. The measurements allowed, for the first time, the study of subgrid-scale turbulent transport of water vapour, which is found to be well correlated with the transport of heat, suggesting that the subgrid-scale modelling of the two scalars may be coupled to save computational resources during LES.  相似文献   

Duality properties of Gorringe–Leach equations     

Yves Grandati  Alain Bérard  Hervé Mohrbach 《Celestial Mechanics and Dynamical Astronomy》2009,103(2):133-141

In the category of motions preserving the angular momentum direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold–Vassiliev type. The specific associated conserved quantities (Laplace–Runge–Lenz vector and Fradkin–Jauch–Hill tensor) are then dual reflections of each other.  相似文献