Lattice dynamical system modelling of molecular clouds

Because a comprehensive microscopic treatment of interstellar molecular clouds is out of reach, an alternative approach is proposed in which most of the crucial ingredients of the problem are considered, but at some 'minimal' level of modelling. This leads to the elaboration of a lattice dynamical system , i.e. a time-dependent, spatially extended, deterministic system of macroscopic cells coupled through radiative transfer. Each cell is characterized by a small set of variables and supports a caricatural chemistry possessing the essential dynamical features of more realistic reaction schemes.   This approach naturally precludes quantitative results, but allows heretofore unavailable insights into some of the basic mechanisms at play. We focus on the response of the transfer process and the chemistry to a frozen 'turbulent' velocity field. It is shown that the system settles generically into a state where the effective coupling between cells is neither local nor global, and for which no single length-scale exists.   The spectral lines reconstructed from the spatiotemporal evolution of our model may, depending on the velocity field, exhibit profiles ranging from Gaussian to bimodal with strong realization effects. In the bimodal case, the model intrinsically displays an energy cascade transport mechanism to the cells that cool most efficiently: the feedback of chemistry on radiative transfer cannot be neglected.   Finally, extensions of this work are discussed and future developments are outlined.     

洪水演算理论与计算方法的若干进展与评论

从洪水波运动的小扰动分析、水力学洪水演算方法及新技术在洪水演算中的应用等方面,总结了近20年来国内外洪水演算理论与计算方法研究的若干进展,并作了简要的评论.     

技术方法的进步与地球科学的发展

地球科学作为自然科学的一大门类,其发展速度十分惊人。地球科学的迅速发展一方面反映了人类生产的发展对资源和环境方面愈来愈高的要求,一方面得益于科学技术的普遍发展为地球科学研究提供的越来越有利的条件。关于技术方法对地球科学研究的推动作用,人们早有认识,而现在更为深刻。当今对地球科学研究影响最大的关键技术,包括空间技术,深部探测技术,高新分析测试技术和数据综合分析技术,均来源于现代科学技术的最新发展。为了推动地球科学研究,不但要注意引进各种高新技术,还要注意将这些技术与地学研究相结合,发展和创造适合于地学研究的高新技术,并善于综合应用它们,使它们在地学研究中发挥最有效的作用。     

Simulations of spheroidal systems with substructure: trees in fields

We present a hybrid technique of N -body simulation to deal with collisionless stellar systems having an inhomogeneous global structure. We combine a treecode and a self-consistent field code such that each of the codes models a different component of the system being investigated. The treecode is suited to treatment of dynamically cold or clumpy components, which may undergo significant evolution within a dynamically hot system. The hot system is appropriately evolved by the self-consistent field code. This combined code is particularly suited to a number of problems in galactic dynamics. Applications of the code to these problems are briefly discussed.     

Evolution of peaks in weakly non-linear density field and dark halo profiles

Using the two-point Edgeworth series up to second order in the linear rms density fluctuation we construct the weakly non-linear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of the skewness parameter S ₃. We test the dependence of the two-point skewness on distance from the peak for scale-free power spectra and Gaussian smoothing. The statistical features of such a conditional distribution are given as the values obtained within linear theory corrected by the terms that arise as a result of weakly non-linear evolution. The expected density around the peak is found to be always below the linear prediction while its dispersion is always larger than in the linear case. For large enough overdensities the weakly non-linear corrections can be more significant than the peak constraint introduced by Bardeen et al. We apply these results to the spherical model of collapse as developed by Hoffman & Shaham and find that in general the effect of weakly non-linear interactions is to decrease the scale from which a peak gathers mass and therefore also the mass itself. In the case of an open universe this results in steepening of the final profile of the virialized proto-object.     

On a time-symmetric Hermite integrator for planetary N-body simulation

We describe a P(EC) ⁿ Hermite scheme for planetary N -body simulation. The fourth-order implicit Hermite scheme is a time-symmetric integrator that has no secular energy error for the integration of periodic orbits with time-symmetric time-steps. In general N -body problems, however, this advantage is of little practical significance, since it is difficult to achieve time-symmetry with individual variable time-steps. However, we can easily enjoy the benefit of the time-symmetric Hermite integrator in planetary N -body systems, where all bodies spend most of the time on nearly circular orbits. These orbits are integrated with almost constant time-steps even if we adopt the individual time-step scheme. The P(EC) ⁿ Hermite scheme and almost constant time-steps reduce the integration error greatly. For example, the energy error of the P(EC)² Hermite scheme is two orders of magnitude smaller than that of the standard PEC Hermite scheme in the case of an N  = 100,  m  = 10²⁵ g planetesimal system with the rms eccentricity 〈 e ²〉^1/2 ≲0.03.     

'Stokes imaging' of the accretion region in magnetic cataclysmic variables — I. Conception and realization

Modelling the polarized cyclotron emission from magnetic cataclysmic variables has been a pivotal technique for determining the structure of the accretion zones on the white dwarf. To date, model solutions have been obtained from trial fits to the intensity and polarization data, which have been constructed from emission regions (for example arcs and spots) put in by hand. These models were all inferred indirectly from arguments based on the polarization and X-ray light curves.   We present a more analytical and objective technique using optimization by a genetic algorithm, Tikhonov regularization and Powell's method that robustly models the details of polarized emission.   To demonstrate the success of this technique, we show the results of several simulations in which we calculated the intensity and polarization curves from arbitrarily shaped emission regions on the surface of a sphere and then applied our code to these curves to recover the original test data. We also show how adding artificial noise affects the outcome of the optimization technique.     

Collapse and fragmentation of rotating, prolate clouds

We present the results of collapse calculations for uniformly rotating, prolate clouds performed using the numerical method: smoothed particle hydrodynamics (SPH). The clouds considered are isothermal, prolate spheroids with different axial ratios ( a/b ), and with different values of β, the ratio of the rotational to gravitational energy. Small density perturbations are added to the clouds, and different initial perturbation spectra are studied. All of the clouds considered are strongly unstable to gravitational contraction, and so collapse to form a spindle configuration. Such a linear structure is unstable to fragmentation, so that the clouds break up into a number of subcondensations. The long-term evolution of the system is then determined by the angular momentum possessed by these fragments.
It is found that a number of the calculations performed result in the formation of orbitally stable binary systems, composed of two rotationally supported discs in orbit about their common centre of mass. Tidal interactions during closest approach, close three-body interactions and the continued accretion of material with high specific angular momentum are all found to increase the orbital separation during these calculations, ensuring that the systems do not merge at later times. The calculations are therefore relevant to the problem of binary star formation, though the systems produced tend to have large orbital separations and periods. One of the strong points of the models presented, however, is their ability to produce systems with a range of mass ratios and orbital eccentricities, without the explicit inclusion of biases in the initial conditions.