In this paper we have studied the anisotropic Kantowski-Sachs, locally rotationally symmetric (LRS) Bianchi type-I and LRS Bianchi type-III geometries filled with dark energy and one dimensional cosmic string in the Saez-Ballester theory of gravitation. To get physically valid solution we take hybrid expansion law of the average scale factor which is a product of power and exponential type of functions that results in time dependent deceleration parameter (\(q\)). The equation of state parameter of dark energy (\(\omega _{\mathit{de}}\)) has been discussed and we have observed that for the three models it crosses the phantom divide line (\(\omega _{\mathit{de}} = -1\)) and shows quintom like behavior. The density of dark energy (\(\rho _{\mathit{de}}\)) is an increasing function of redshift and remains positive throughout the evolution of the universe for the three models. Moreover in Kantowski-Sachs and LRS Bianchi type-I geometries the dark energy density dominates the string tension density (\(\lambda \)) and proper density (\(\rho \)) throughout the evolution of the universe. The physical and geometrical aspects of the statefinder parameters (\(r,s\)), squared speed of sound (\(v_{s}^{2} \)) and \(\omega _{\mathit{de}}\)–\(\omega ^{\prime }_{\mathit{de}}\) plane are also discussed. 相似文献
ABSTRACTEffective public transit planning needs to address realistic travel demands, which can be illustrated by corridors across major residential areas and activity centers. It is vital to identify public transit corridors that contain the most significant transit travel demand patterns. We propose a two-stage approach to discover primary public transit corridors at high spatio-temporal resolutions using massive real-world smart card and bus trajectory data, which manifest rich transit demand patterns over space and time. The first stage was to reconstruct chained trips for individual passengers using multi-source massive public transit data. In the second stage, a shared-flow clustering algorithm was developed to identify public transit corridors based on reconstructed individual transit trips. The proposed approach was evaluated using transit data collected in Shenzhen, China. Experimental results demonstrated that the proposed approach is a practical tool for extracting time-varying corridors for many potential applications, such as transit planning and management. 相似文献
Atlantic salmon reared in recirculating aquaculture system (RAS) may lead to inappropriately high stocking density, because fish live in a limited space. Finding the suitable stocking density of Atlantic salmon reared in RAS is very important for RAS industry. In this paper, the influence of stocking density on growth and some stress related physiological factors were investigated to evaluate the effects of stocking density. The fish were reared for 220 days at five densities (A: 24 kg/m3; B: 21 kg/m3; C: 15 kg/m3; D: 9 kg/ m3 and E: 6 kg/m3 ). The results show that 30 kg/m3 might be the maximum density which RAS can afford in China. The stocking densities under 30 kg/m3 have no effect on mortality of Atlantic salmon reared in RAS. However, the specific growth rate (SGR), final weight and weight gain in the high density group were significantly lower than the lower density groups and middle density groups. Moreover, feed conversion rate (FCR) had a negative correlation with density. Plasma hormone T3 and GH showed significant decrease with the increase of the stocking density of the experiment. Furthermore, thyroid hormone (T3), GH (growth hormone) activities were decreased with stocking density increase. However, plasma cortisol, GOT (glutamic oxalacetic transaminase) and GPT (glutamic pyruvic transaminase) activities were increase with stocking density increase. And the stocking density has no effects on plasma lysozyme of Atlantic salmon reared in RAS. These investigations would also help devise efficient ways to rear adult Atlantic salmon in China and may, in a way, help spread salmon mariculture in China.
We study the neighborhood of the equal mass regular polygon relative equilibria in the N-body probem, and show that this relative equilibirum is isolated among the co-circular configurations (in which each point lies on a common circle) for which the center of mass is located at the center of the common circle. It is also isolated in the sense that a sufficiently small mass cannot be added to the common circle to form a \(N+1\)-body relative equilibrium. These results provide strong evidence for a conjecture that the equal mass regular polygon is the only co-circular relative equilibrium with its center of mass located at the center of the common circle. 相似文献
The analysis of relative motion of two spacecraft in Earth-bound orbits is usually carried out on the basis of simplifying assumptions. In particular, the reference spacecraft is assumed to follow a circular orbit, in which case the equations of relative motion are governed by the well-known Hill–Clohessy–Wiltshire equations. Circular motion is not, however, a solution when the Earth’s flattening is accounted for, except for equatorial orbits, where in any case the acceleration term is not Newtonian. Several attempts have been made to account for the \(J_2\) effects, either by ingeniously taking advantage of their differential effects, or by cleverly introducing ad-hoc terms in the equations of motion on the basis of geometrical analysis of the \(J_2\) perturbing effects. Analysis of relative motion about an unperturbed elliptical orbit is the next step in complexity. Relative motion about a \(J_2\)-perturbed elliptic reference trajectory is clearly a challenging problem, which has received little attention. All these problems are based on either the Hill–Clohessy–Wiltshire equations for circular reference motion, or the de Vries/Tschauner–Hempel equations for elliptical reference motion, which are both approximate versions of the exact equations of relative motion. The main difference between the exact and approximate forms of these equations consists in the expression for the angular velocity and the angular acceleration of the rotating reference frame with respect to an inertial reference frame. The rotating reference frame is invariably taken as the local orbital frame, i.e., the RTN frame generated by the radial, the transverse, and the normal directions along the primary spacecraft orbit. Some authors have tried to account for the non-constant nature of the angular velocity vector, but have limited their correction to a mean motion value consistent with the \(J_2\) perturbation terms. However, the angular velocity vector is also affected in direction, which causes precession of the node and the argument of perigee, i.e., of the entire orbital plane. Here we provide a derivation of the exact equations of relative motion by expressing the angular velocity of the RTN frame in terms of the state vector of the reference spacecraft. As such, these equations are completely general, in the sense that the orbit of the reference spacecraft need only be known through its ephemeris, and therefore subject to any force field whatever. It is also shown that these equations reduce to either the Hill–Clohessy–Wiltshire, or the Tschauner–Hempel equations, depending on the level of approximation. The explicit form of the equations of relative motion with respect to a \(J_2\)-perturbed reference orbit is also introduced. 相似文献
Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker–Planck equation (FPE) is defined on a relatively high dimensional (6-D) state–space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the \(x-y-z\) subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors’ knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral (“super-fast”) convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations. 相似文献