共查询到20条相似文献，搜索用时 703 毫秒
1.
Relaxation times in the spaces of several stellar-motion parameters are obtained for a number of open-cluster models. The differences between the relaxation times in these spaces increase with the degree of nonstationarity of the cluster models. In the course of the cluster’s evolution, the relaxation times increase in all the spaces considered. During violent relaxation, the stars occupy all domains accessible to them, first in absolute velocity and then in clustercentric distance. The dependence of the coarse-grained phase-space density of the cluster on small initial perturbations of the phase-space coordinates of its constituent stars tends to decrease at times exceeding the time scales for violent and “collisional” relaxation. 相似文献
2.
Stellar trajectories in models of open star clusters that are nonstationary in the regular field of the cluster are analyzed. The maximum characteristic Lyapunov exponents λ of the trajectories of the stellar motions in the open cluster are estimated. The mean λ in the open-cluster models considered are \(\bar \lambda \simeq ({\rm M}yr)^{ - 1} \). Cluster cores and halos are regions of highly stochastic and more ordered stellar motions, respectively. The mean Lyapunov exponent, \(\bar \lambda \), increases with the cluster density, as does the size of the highly stochastic region in the cluster core. The stellar trajectories in phase space are “glued” to a domain with a given λ. A Fourier analysis of the stellar trajectories in the open-cluster models is performed. The distributions of the periods of the stellar trajectories with the highest power-spectrum levels are constructed. The distributions of the periods corresponding to the most significant oscillations of the stellar trajectories exhibit peaks with periods commensurable with (or close to) those of the most significant oscillations of the regular field of the system. Specific features of the distributions of the periods of the most significant oscillations of the stellar trajectories and the origins of the formation of these features in the open-cluster models are discussed. 相似文献
3.
V. M. Danilov 《Astronomy Reports》2000,44(5):298-308
In dynamical models for open clusters, virial equilibrium is not achieved over the violent relaxation time scale τvr. The stars form an equilibrium distribution in (?, ?ζ, l) space, where ? and l are the energy and angular momentum per unit stellar mass in the combined field of the Galaxy and cluster and ?ζ is the energy of motion perpendicular to the Galactic plane per unit mass of cluster stars in the gravitational field of the Galaxy. This distribution of stars changes little when t>τvr. The stellar phase-space distribution corresponding to this type of equilibrium and the regular cluster potential vary periodically (or quasi-periodically) with time. This phase-space equilibrium is probably possible due to an approximate balance in the stellar transitions between phase-space cells over times equal to the oscillation period for the regular cluster field. 相似文献
4.
V. M. Danilov 《Astronomy Reports》2011,55(6):473-486
The kinematics of stars in open-cluster models are investigated. The central regions of these model clusters are fairly “cool,
” leading to gravitational instability in the cluster cores. A temporary virilization is observed in the model clusters, during
which an appreciable fraction of the fluctuation energy of the cluster is temporarily transformed into the kinetic energy
of the peculiar motions of stars. The duration of this stage can reach ∼108 yr. The origins of this temporary virialization of the model clusters are discussed. The instability of the intrinsic fluctuations
of the phase density in the centers of six clusters and model clusters is investigated. Several new regions of unstable phase-density
fluctuations are found, in addition to those already known. The observed and model clusters can move toward a stable equilibrium
state when the density of the cluster core both decreases and increases. The structure of regions of instability of the phase-density
fluctuations in the centers of the six clusters is studied. Resonance curves for the amplitudes of steady-state phase-density
fluctuations in the center of NGC 6705 are constructed. Analysis of the structure of the regions of instability indicates
an appreciable rate of fluctuation-energy loss due to relaxation effects. The instability increments and widths of regions
of instability fall off with increasing distance of the cluster from the Galactic center. An important role in the formation
of regions of instability may be played by resonances between the frequency of the orbital motion of the cluster in the Galaxy
and the frequencies of intrinsic phase-density fluctuations in the centers of the clusters considered. 相似文献
5.
V. M. Danilov 《Astronomy Reports》2002,46(6):443-450
Models of open clusters in a state of equilibrium in the space of the three parameters of the stellar motion and simultaneously far from virial equilibrium are analyzed. A formula for the phase-space stellar number density in such cluster models is derived, as well as formulas for the integrated and differential energy distributions of the phase-space volume occupied by cluster stars per unit stellar mass. These three quantities are computed for several times exceeding the time for violent relaxation of the cluster model. The phase-space density function obtained is used to compute the distribution of the absolute values of stellar velocities for the cluster model considered. 相似文献
6.
We have obtained the stellar velocity dispersion in three mutually perpendicular directions in the halos and cores of clusters as a function of time for several non-stationary open-cluster models. During the dynamical evolution of the open-cluster models, the velocity dispersions undergo oscillations that do not decay during 5–10 violent-relaxation timescales, τ vr . We estimated the time for synchronization of the rotation of the open-cluster models and their motion around the center of the Galaxy, t s , which, depending on the model parameters, is t s ? (5–27)τ vr . Synchronization mechanisms for the models are discussed. The disruption of the systems in the force field of the Galaxy is strongly affected by tidal friction. We have also estimated the time for the formation of a spherical stellar-velocity distribution in the cluster models, t σ ? (6 ? 25)τ vr . The impact of instability in the stellar motions in a cluster on the formation of a spherical velocity distribution in the open-cluster models is discussed. We have noted a tendency for a weakening of the dependence of the coarse phase density of the cluster on small initial perturbations of the stellar phase coordinates in the model cluster cores for times about five times longer than the violent-relaxation time. 相似文献
7.
Two-time and two-point (two-particle) correlations are calculated for several parameters of the stellar motions, the densities, and the phase densities of model open clusters, in the vicinities of the cluster stars. The correlation times and correlation radii are determined in spaces of the parameters considered. The distributions of the two-point correlations for the distances between stars in the coordinate and velocity spaces of the stars are calculated. The local maxima of these distributions are used to determine the parameters of density waves, the potential, and the phase density in the model clusters. Analysis of the fine structure of regions of concentration in the two-point correlations in space of mutual distances between stars suggests the formation of polarization clouds near a number of such distances between stars. The distributions of the phase-density correlations are calculated, and the dynamics of these distributions analyzed. The dispersions of these distributions depend strongly on the presence of broad ??wings?? in the distributions (i.e., of strong correlations in the system). These dispersions are considered as a measure of the degree of correlation of phase-density fluctuations in model clusters. A growth in the correlations with time is observed for 50% of the cluster models considered. Flows of the phase-density correlations are investigated. A dominant correlation flow from the region of strong to the region of weak correlations is identified, leading to a flow of kinetic energy toward the cluster center. The rate at which this flow heats the model cluster core is estimated. Signs of weak turbulence are detected in the stellar motions in the model cluster cores with the highest degree of non-stationary in the regular field. 相似文献
8.
V. M. Danilov 《Astronomy Reports》2005,49(8):604-610
Equations of motion containing a small parameter μ are derived for stars at the peripheries of open star clusters. The parameter μ is obtained for six numerical open-cluster models. The general analytical solution of these equations of motion for μ = 0 is found. An iterative method is used to derive the frequencies of the stellar motions for first-order expansions in μ of the solutions of the equations of motion for stars at the cluster periphery. Applications of the results are discussed. 相似文献
9.
Estimates of a number of dynamical parameters of 103 open star clusters are presented: the density contrast in the cluster core, stellar velocity dispersion, taking into account the influence of the external field of the Galaxy and non-stationarity of the cluster, oscillation periods of the cluster and the cluster core, etc. Analytical solutions to the gross dynamical equations are obtained for simple cluster models. These solutions are used to estimate a number of quantities characterizing the degree of non-stationarity of the cluster, such as the amplitude of oscillations of the cluster virial coefficient and of the radius of the cluster core, etc. Astrophysical applications of these results are discussed. 相似文献
10.
受诸多因素影响的水库汛期分期其实质是一个聚类数目未确知的高维时间序列聚类问题,它要求聚类方法具有能处理高维和时序性数据,且能同时回答聚为几类最为合理的能力。鉴于目前常规聚类方法不同时具备这些能力,在模糊C-均值聚类和紧密与分离聚类有效函数的基础上,提出了能够处理高维时序聚类问题的动态模糊C-均值聚类分析方法和相应的时序聚类有效性函数,耦合二者建立了适用于汛期分期的有效模糊聚类分析方法,提出采用实码加速遗传算法优化求解,克服了模糊C-均值聚类方法常规迭代优化求解对初值敏感的困难,并给出了完备的建模步骤和模型的合理性检验。最后,将模型应用于滦河流域潘家口水库汛期分期中,得出了合理的结论。 相似文献
11.
Phillips JD 《The Journal of geology》2000,108(1):91-102
Complex system behaviors such as self-organization are difficult to address in geology. System evolution often cannot be directly observed and, in geology models and theory, must be reconciled with field evidence. However, self-organization can be addressed within the historical-interpretive paradigm by applying a measure of the degree of self-organization of geologic features, using standard interpretive methods to determine the nature of changes, and determining whether those changes result in an increase or decrease in organization. In this way, stable non-self-organizing convergent development can be distinguished from unstable chaotic self-organizing divergent development. Kolmogorov entropy (K-entropy) was used as a measure of the self-organization of soil profiles in eastern North Carolina. In general, the profiles are low in K-entropy, indicating a generally high level of predictability and information in the vertical arrangement of pedogenetic horizons. As a broad generality, the study profiles appear to be decreasing in entropy if or when surface erosion is minimal and increasing in entropy otherwise. However, results show that whether the profiles demonstrate evidence of convergent or divergent behavior is determined by the relative rates or magnitudes of three main processes: (1) horizon differentiation in surficial horizons by the formation of transitional AE or A&E horizons due to secondary podzolization, (2) thickening of the solum at the weathering front, and (3) surface erosion. There is no direct relationship between the degree of pedogenic development and self-organization. The results suggest that complex system behaviors are controlled by, and can be linked to, specific pedologic and geomorphic processes and that soils and regoliths may be characterized by both convergent and divergent developmental pathways. 相似文献
12.
为了研究煤体静载破坏中低频磁场变化特征及其产生机制,进一步完善煤矿动力灾害监测预警技术,通过室内试验、现场试验研究了煤体静载破坏中低频磁场时、频谱特征,并结合微震信号提出了低频磁信号的产生机制。结果表明：煤体静载破坏中所产生低频磁场信号强度为19～156 nT,信号最大幅值、能量与试样强度、加载速度均呈正相关关系。垂直于裂纹扩展面磁场最强,平行于裂纹扩展面磁场最弱。并结果微震信号提出了低频磁场产生机制。低频磁场与微震信号具有时、频域同步性,带电裂纹面随微震信号同频振荡为低频磁场产生机制。现场放炮破煤低频磁信号由簇状脉冲信号及小幅震荡信号组成,其中簇状脉冲成分产生于炮后振动波带动带电壁面的同频振动,而小幅震荡成分是巷帮煤壁趋向新应力平衡状态时发生的横向拉伸破坏及带电煤碎屑运移、摩擦及转动的结果。 相似文献
13.
文中讨论了作为极复杂巨系统的固体地球内部运动规律的 3条推论 :(1)地球系统在偏离平衡态时 ,有选择能量耗散最小方式的“惯性” ,在系统内禀熵急增时或者回到一种准稳定的定态 ,或者通过自组织迅速减少内禀熵增加率。换言之 ,地球系统可能有种尽量保存自身内能不受大量耗散的惯性 ,使其总体内禀熵产生率对时空的积分取极小值。我们把这一认识称为总体熵产生率取极小准则 ,对于孤立与渐变的地质过程 ,它等同于热力学第二定律与普里高津最小熵产生原理 ,对于极复杂地球巨系统及远离平衡态情况加了“总体”两字 ,意思是在局部或短期突变时熵产生率可能是大的 ,但它对全球与长时间的积分而言仍然取极小。换句话说 ,作为一个巨系统 ,固体地球在其局部远离平衡状态时 ,仍然能保持总体上内能消耗取极小的惯性 ,维持对全部固体地球时空系统总体熵产生率取极小准则。 (2 )关于地质作用过程演化的定态遍历准则。地球系统的复杂性不仅表现在其非线性 ,即同时存在着多种可能的定态作为其演化的趋势 ,而且表现在其时空发展过程中将经历尽可能多的定态。非线性非平衡态动力学的一般规律符合大多数包含激变事件的地质作用过程。将来在地球系统偏离平衡态足够远时 ,它可能会具有无穷多个耗散结构 ,因而使系统进入完全? 相似文献
14.
Mark S. Ghiorso Ian S. E. Carmichael Mark L. Rivers Richard O. Sack 《Contributions to Mineralogy and Petrology》1983,84(2-3):107-145
The compositions of liquids coexisting with experimentally grown crystals of olivine, plagioclase, clinopyroxene, orthopyroxene, leucite, spinel, rhombohedral oxide, melilite and potassium feldspar are used to define, through mass action expressions of liquid/solid equilibrium, compositional derivatives of the Gibbs free energy of mixing of naturally occuring silicate liquids as a function of temperature, pressure and the fugacity of oxygen. The available experimental data describe these derivatives over a range of compositions which includes basic magmas. Therefore, for silicate liquids in this composition range, the topology of the Gibbs free energy of mixing can be approximated from experimental determinations of its derivatives. The majority of the existing thermodynamic data on the liquid phase is consistent with the application of regular solution theory to model the free energy of mixing. Strictly symmetric, temperature and pressure independent, regular solution interaction parameters are calibrated from this phase equilibrium data using regression techniques which have their basis in inverse theory. These techniques generate numerically stable interaction parameters which incorporate inter-variable correlation and account for experimental uncertainty. The regular solution model fits the available data on anhydrous silicate liquids to within the accuracy of the thermodynamic database +/?550 cals). Extensions to regular solution theory allow water solubility in more silica rich liquids to be modelled somewhat less accurately (+/?750 cals). The topology of the excess free energy of mixing surface is strongly asymmetric, possessing a single multicomponent saddle point which defines a spinodal locus. Given this prediction of a multicomponent spinode, a mathematical procedure based upon minimisation of the Gibbs free energy of mixing is developed for the calculation of the compositions of coexisting immiscible liquids. Predicted binodal compositions substantially agree with elemental liquid/liquid partitioning trends observed in lavas. Calculations suggest that an immiscible dome, in temperature-composition space, intersects the liquidus field of the magma type tholeiite. Immiscible phenomena are predicted at sub-liquidus temperatures for the bulk compositions of more basic or alkalic lavas, but are absent in more siliceous rock types for temperatures of the metastable liquid down to 900 K. The regular solution model is used in four petrological applications. The first concerns a prediction of the binary olivine-liquid phase diagram. The calculated geometry exhibits a minimum near Fa75, which, though not in accord with experimental results on the pseudobinary system, compares quite favorably with olivine-liquid phase equilibria interpreted from rhyolites, namely that the olivine phenocrysts of rhyolites are more iron rich than their coexisting liquids. The second petrological example concerns estimating the depth of the source regions of several basic lavas whose compositions cover a range from ugandite to basaltic andesite. The third application is a calculation of the saturation temperatures and compositions of plagioclase and olivine in four experimental basaltic liquids and a prediction of the liquidus temperatures and first phenocryst compositions of the Thingmuli lava series of Eastern Iceland. Lastly, enthalpies of fusion are computed for a variety of stoichiometric compounds of geologic interest. These demonstrate good agreement with calorimetrically measured quantities 相似文献
15.
V. Kress 《Contributions to Mineralogy and Petrology》2000,139(3):316-325
We present a new formulation to describe the thermodynamics of liquids in the system O-S-Fe. The model is based on an associated
regular solution formulation. According to this model, liquids in the O-S-Fe ternary are made up of an equilibrium solution
of the six melt species S, Fe, FeO, FeO1.5, FeS and FeOS. The model presented here represents oxygen and sulfur fugacities as well as phase equilibria with stoichiometric
solid phases better than models from the literature on O-Fe and S-Fe binaries. Furthermore, this model represents a substantial
improvement on the model of Kress (1997), which is the only other thermodynamic model available in the ternary system. Asymmetric
regular solution parameters are required along the FeO join in order to reproduce experimental data with the chosen list of
species. Symmetric regular solution parameters are required along the Fe-S binary. Mixing between any of the species considered
and FeOS close to ideal. The associated solution model presented here will serve as a more solid foundation for future models
in O-S-Fe- Ni-Cu liquids. Efficient and robust strategies for calculating equilibrium speciation and estimating model parameters
are presented.
Received: 15 June 1999 / Accepted: 5 February 2000 相似文献
16.
We formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter-grains elongation/compression energy from inter-grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model. 相似文献
17.
Order-disorder theory has been used to treat ion-exchange equilibrium for ions of A and B on a uniform group of exchange sites more numerous than the number of monovalent cations required for electrical neutrality. The method allowed consideration of the effects of extra relaxation energy terms arising from one, two or three of the pairs AA, AB and BB on two nearest neighbour sites. These energies are additional to the energies of 2(OA), (OA + OB) and 2(OB) respectively where O denotes an empty site. Isotherms and thermodynamic equilibrium constants have been compared for different site co-ordination numbers, ion valences, and choices of the three extra energies and of the ratio, n, of the total number of sites to the number of cationic charges needed for electrical neutrality. Miscibility gaps in the isotherms occurred less readily the larger the value of n and the smaller the co-ordination number. Such gaps were also less in evidence when the two exchange ions carried different charges. The model has been considered in relation to the random interstratification of cation layers sometimes observed in clay minerals. 相似文献
18.
L. P. Osipkov 《Astronomy Reports》2006,50(2):116-122
The tensor virial theorem is used to analyze the conditions for the existence of an equilibrium cluster moving in a circular orbit in a stationary axisymmetric galaxy. A general necessary condition is derived, which, for uniform models, coincides with the Bok stability condition. Generalized Mineur ellipsoids are constructed for nonuniform systems with anisotropic velocity distributions. The Hill stability of the cluster is analyzed. 相似文献
19.
矿物在超临界溶液中的溶解度理论计算 总被引：10，自引：0，他引：10
本文概述了矿物在超临界溶液中的溶解度理论计算。讨论了平衡常数法和自由能法的热力学原理和计算机方法。两种方法都需要热力学数据,所不同的是平衡常数法需要的是反应平衡常数,而自由能法需要物种自由能数据。方法确定以后这些数据具备与否及其精度是这项研究的关键。此外当溶液中离子强度较大时,寻求一种适当的活度系数算法对溶解度理论计算也至关重要。 相似文献
20.
V. M. Danilov 《Astronomy Reports》2010,54(6):514-527
Instability of proper fluctuations of the phase density at the centers of six open clusters is demonstrated. The boundaries
of the region of instability in terms of the mean mass densities of the cluster cores are determined. Estimates for a number
of dynamical parameters (the potential, velocity dispersion of the stellar motions, mass density, phase-density fluctuation
period, time for the development of instability of the fluctuations, etc.) are obtained for the central parts of these clusters,
as well as for numerical dynamical models for open clusters. Equation that can be used to estimate the dynamical mass of a
cluster taking into account the influence of the external field of the Galaxy and the non-stationarity of the cluster is derived.
Allowance for these effects makes it possible to decrease the dynamical masses of clusters compared to the virial masses assuming
isolated systems. Astrophysical applications of the results are discussed. 相似文献