A static model of the universe

It is shown that the observational data of cosmology and the universe evolution can be explained in the framework of static (non-expanding) models of the universe without singularity by introducing in the time part of the metrics the scale factor, dependent on time. The latter can be interpreted as a function of the light velocity evolution or the rate of cosmic time relative to the linear atomic time.Expressions for these functions have been obtained on the basis of the Einstein equation solution with the use of conformal metrics.The theory is consistent with the test of dependence of the angular galaxy dimension on the redshift.     

Perturbation of mass accretion rate,associated acoustic geometry and stability analysis

We investigate the stability of stationary integral solutions of an ideal irrotational fluid in a general static and spherically symmetric background, by studying the profile of the perturbation of the mass accretion rate. We consider low angular momentum axisymmetric accretion flows for three different accretion disk models and consider time dependent and radial linear perturbation of the mass accretion rate. First we show that the propagation of such perturbation can be determined by an effective 2 × 2 matrix, which has qualitatively similar acoustic causal properties as one obtains via the perturbation of the velocity potential. Next, using this matrix we analytically address the stability issues, for both standing and travelling wave configurations generated by the perturbation. Finally, based on this general formalism we briefly discuss the explicit example of the Schwarzschild spacetime and compare our results of stability with the existing literature, which instead address this problem via the perturbation of the velocity potential.     

Evolution of the energy density in the static universe

The Einstein static model of the universe as a whole is considered. The Hubble law is explained by the Doppler effect due to the downward inertial acceleration along a certain radius experienced by an observer in the center of the universe, with the total acceleration over all radii being equal zero. Evolution of the universe is introduced through the wave function of the universe dependent on time. This yields the energy density of the universe hence the temperature of the universe dependent on time. On the contrary, the energy, forth and intensity of radiation are fixed with time that allows to develop the Newtonian physics in the whole universe. The time-temperature relation of the universe in the model considered is the same as in the radiation dominated universe in the Friedmann model that allows to explain primordial nucleosynthesis as it is in the standard scenario. The modern parameters of the universe in the model considered are consistent with the observations.     

Dark energy models with anisotropic fluid in Bianchi Type-VI 0 space-time with time dependent deceleration parameter

We present two dark energy (DE) models with an anisotropic fluid in Bianchi type-VI ₀ space-time by considering time dependent deceleration parameter (DP). The equation of state (EoS) for dark energy ω is found to be time dependent and its existing range for derived models is in good agreement with the recent observations. Under the suitable condition, the anisotropic models approach to isotropic scenario. We also find that during the evolution of the universe, the EoS parameter for DE changes from ω>−1 to ω=−1 in first model whereas from ω>−1 to ω<−1 in second model which is consistent with recent observations. The cosmological constant Λ is found to be a positive decreasing function of time and it approaches a small positive value at late time (i.e. the present epoch) which is corroborated by results from recent type Ia supernovae observations. The cosmic jerk parameter in our derived models is also found to be in good agreement with the recent data of astrophysical observations. The physical and geometric aspects of both the models are also discussed in detail.     

Universe with Time Dependent Deceleration Parameter and Λ Term in General Relativity

A new class of exact solutions of Einstein's field equations with perfect fluid for an LRS Bianchi type-I spacetime is obtained by using a time dependent deceleration parameter. We have obtained a general solution of the field equations from which three models of the universe are derived: exponential, polynomial and sinusoidal form respectively. The behaviour of these models of the universe are also discussed in the frame of reference of recent supernovae Ia observations.     

Molecular line profiles as diagnostics of protostellar collapse: modelling the 'blue asymmetry' in inside-out infall

The evolution of star-forming core analogues undergoing inside-out collapse is studied with a multipoint chemodynamical model which self-consistently computes the abundance distribution of chemical species in the core. For several collapse periods the output chemistry of infalling tracer species such as HCO⁺, CS and N₂H⁺ is then coupled to an accelerated Λ-iteration radiative transfer code, which predicts the emerging molecular line profiles using two different input gas/dust temperature distributions. We investigate the sensitivity of the predicted spectral line profiles and line asymmetry ratios to the core temperature distribution, the time-dependent model chemistry, as well as to ad hoc abundance distributions. The line asymmetry is found to be strongly dependent on the adopted chemical abundance distribution. In general, models with a warm central region show higher values of blue asymmetry in optically thick HCO⁺ and CS lines than models with a starless core temperature profile. We find that in the formal context of Shu-type inside-out infall, and in the absence of rotation or outflows, the relative blue asymmetry of certain HCO⁺ and CS transitions is a function of time and, subject to the foregoing caveats, can act as a collapse chronometer. The sensitivity of simulated HCO⁺ line profiles to linear radial variations, subsonic or supersonic, of the internal turbulence field is investigated in the separate case of static cores.     

Domain walls in Lyra geometry

In this paper we have discussed two models of domain walls within the framework of Lyra geometry. An exact solution is obtained for a thick non static domain wall. The space time is non singular both in its spatial and temporal behavior and the gravitational field experienced by a test particle is attractive. It is found that these exists no particle horizon in our case. Also we have presented a spherical domain wall with nonvanishing stress components in the direction perpendicular to the plane of the wall. The gravitational field of the domain wall is shown to be attractive in nature. This revised version was published online in July 2006 with corrections to the Cover Date.     

Undamped oscillations of collisionless stellar systems: Spheres,spheroids and discs

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed     

Time-dependent flexure of the lithospheres on the icy satellites of Jupiter and Saturn

Previous analyses into flexural deformation on the icy satellites of Jupiter and Saturn have assumed static, elastic lithospheres. Viscous creep within the lithosphere, however, can cause evolution over time. Here, we apply a finite-element model that employs a time-dependent elastic–viscous-plastic rheology in order to investigate flexure on icy satellites. Factors that affect this time-dependent response are those that control creep rates; surface temperature, heat flow, and grain size. Our results show that surface temperature is by far the dominant factor. At higher surface temperatures (100–130 K), the evolution of the deformation is such that the thickness of a modeled elastic lithosphere could vary by up to an order of magnitude, depending on the time scale over which the deformation occurred. Because the flexure observed on icy satellites generally indicates transient high heat flow events, our results indicate that the duration of the heat pulse is an important factor. For the icy worlds of Jupiter and Saturn, static models of lithospheric flexure should be used with caution.     

Bianchi type-I cosmological models with time dependent q and Λ-term in general relativity

On getting motivation from increasing evidence for the need of a geometry that resembles Bianchi morphology to explain the observed anisotropy in the WMAP data, Einstein’s field equations with variable cosmological “constant” are considered in presence of perfect fluid for a homogeneous and anisotropic Bianchi type-I space-time. Einstein’s field equations are solved by considering a time dependent deceleration parameter which affords a late time acceleration in the universe. The cosmological constant Λ is found to be a decreasing function of time and it approaches a small positive value at the present epoch which is corroborated by consequences from recent supernovae Ia observations. From recently developed Statefinder pair, the behavior of different stages of the evolution of the universe has been studied. The physical significance of the cosmological models have also been discussed.     

Impact of Limitations in Geophysical Background Models on Follow-on Gravity Missions

Purpose of this article is to demonstrate the effect of background geophysical corrections on a follow-on gravity mission. We investigate the quality of two effects, tides and atmospheric pressure variations, which both act as a surface load on the lithosphere. In both cases direct gravitational attraction of the mass variations and the secondary potential caused by the deformation of the lithosphere are sensed by a gravity mission. In order to assess the current situation we have simulated GRACE range-rate errors which are caused by differences in present day tide and atmospheric pressure correction models. Both geophysical correction models are capable of generating range-rate errors up to 10 μm/s and affect the quality of the recovered temporal and static gravity fields. Unlike missions such as TOPEX/Poseidon where tides can be estimated with the altimeter, current gravity missions are only to some degree capable of resolving these (geo)physical limitations. One of the reasons is the use of high inclination low earth orbits without a repeating ground track strategy. The consequence is that we will face a contamination of the gravity solution, both in the static and the time variable part. In the conclusions of this paper we provide suggestions for improving this situation, in particular in view of follow-on gravity missions after GRACE and GOCE, which claim an improved capability of estimating temporal variations in the Earth’s gravity field.     

Isotropic Homogeneous Universe with a Bulk Viscous Fluid in Lyra Geometry

Exact solutions are obtained for an isotropic homogeneous universe with a bulk viscous fluid in the cosmological theory based on Lyra’s geometry. The viscosity coefficient of the bulk viscous fluid is assumed to be a power function of the mass density. Cosmological models with time dependent displacement field have been discussed for a constant value of the deceleration parameter. Finally some possibilities of further problems and their investigations have been pointed out.     

LAMOST观测控制系统体系结构设计

由于大天区面积多目标光纤光谱天文望远镜(LAMOST)系统非常复杂,系统研制的时间比较长,系统建成后有相当长的使用年限,就要求观测控制系统(OCS)有足够长的生命周期(使用、维护及升级),可扩展性和良好的可维护性,因此系统需要一个合理健全、内在一致的体系结构。根据OCS的建模和体系结构的概念,在对OCS建模及参考各种体系结构模式的基础上完成了基于构件的层状的OCS系统体系构架,融合了MVC,代理等体系结构模式。详细讨论了OCS体系结构的静态模型和动态模型,并在OCS的1级系统实现了此体系结构。     

Center-to-Limb Variations of the Ca II H and K Lines in Sunspot Umbrae

A comparison of theoretical and observed Caii H and K line profiles in sunspot umbrae has been made for different sunspot positions on the solar disk. Four semi-empirical static umbral models were used in calculations: the SUNSPOT model of Avrett (1981), and the models of Staude (1982), Maltby et al. (1986), and Severino, Gomez, and Caccin (1994). The models suggested by Avrett, Maltby et al., and Severino, Gomez, and Caccin reproduce the center-to-limb evolution of the shape of observed profiles. The best agreement with profile parameters obtained from observations is given by the Severino, Gomez, and Caccin model.     

Homogeneous cosmological solutions of the Einstein equation

Homogeneous solutions in the framework of general relativity form the basis to understand the properties of gravitation on global scale. Presently favoured models describe the evolution of the universe by an expansion of space, governed by a scale function, which depends on a global time parameter. Dropping the restriction that a global time parameter exists, and instead assuming that the time scale depends on spatial distance, leads to static solutions, which exhibit no singularities, need no unobserved dark energy and which can explain the cosmological red shift without expansion. In contrast to the expanding world model energy is globally conserved. Observations of high energy emission and absorption from the intergalactic medium, which can scarcely be understood in the ‘concordance model’, find a natural explanation.     

Comparison between Different Models of Galactic Tidal Effects on Cometary Orbits

Different models of the action of the galactic tide are compared. Each model is a substitute for direct numerical integrations allowing a drastic decrease of the computation time. The models are built using two different techniques, (i) averaging of the fast variable (the mean anomaly) over one cometary period and (ii) fixing the comet in its aphelion direction. Moreover, we consider two different formalisms (Lagrangian and Hamiltonian) and also two different sets of variables. As expected, we find that the model results are independent of the formalism and the set of variables considered, and are highly accurate, whereas mathematical technique leads to poor results. In order to further reduce the computation time, mappings are built from the development of the solution of the models. We show that for these mappings, the set of variables giving the most accurate results is strongly dependent on the cometary eccentricity, e, and semimajor axis, a.     

Axially symmetric cosmological models in a scalar tensor theory based on Lyra manifold

Axially symmetric cosmological models are obtained in a scalar tensor theory proposed by Sen (Z. Phys. 149:311, 1957) based on Lyra manifold with time dependent β in the presence of string source, perfect fluid distribution, dust distribution and thick domain walls. Some physical and geometrical properties of these models are discussed.     

Future Satellite Gravimetry for Geodesy

After GRACE and GOCE there will still be need and room for improvement of the knowledge (1) of the static gravity field at spatial scales between 40 km and 100 km, and (2) of the time varying gravity field at scales smaller than 500 km. This is shown based on the analysis of spectral signal power of various gravity field components and on the comparison with current knowledge and expected performance of GRACE and GOCE. Both, accuracy and resolution can be improved by future dedicated gravity satellite missions. For applications in geodesy, the spectral omission error due to the limited spatial resolution of a gravity satellite mission is a limiting factor. The recommended strategy is to extend as far as possible the spatial resolution of future missions, and to improve at the same time the modelling of the very small scale components using terrestrial gravity information and topographic models.We discuss the geodetic needs in improved gravity models in the areas of precise height systems, GNSS levelling, inertial navigation and precise orbit determination. Today global height systems with a 1 cm accuracy are required for sea level and ocean circulation studies. This can be achieved by a future satellite mission with higher spatial resolution in combination with improved local and regional gravity field modelling. A similar strategy could improve the very economic method of determination of physical heights by GNSS levelling from the decimeter to the centimeter level. In inertial vehicle navigation, in particular in sub-marine, aircraft and missile guidance, any improvement of global gravity field models would help to improve reliability and the radius of operation.     

Ultra‐cool dwarf variability

Ultra‐cool dwarf variability studies have matured into a multi‐wavelength, multi‐method probe of ultra‐cool atmospheres. They have the unique potential to address the question of heterogeneity on the ultra‐cool dwarf surface. The constraints on the models that we can gain though time‐sensitive observations are however hampered by the weak signal detected so far, and the limitations of current atmospheric models, otherwise quite successful, to predict dynamical, or even static 2‐D atmosphere characteristics. Here I review the situation of the ultra‐cool dwarf variability studies: possible sources of variability; methods, their limitations and their results; tentative interpretation and prospects. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Early Cosmological Models with Bulk Viscosity in Brans-Dicke Theory

The effect of time dependent bulk viscosity on the evolution of Friedmann models with zero curvature in Brans-Dicke theory is studied. The solutions of the field equations with ‘gamma-law’ equation of state p = (γ-1) ρ, where γ varies continuously as the Universe expands, are obtained by using the power-law relation φ = bR ⁿ , which lead to models with constant deceleration parameter. We obtain solutions for the inflationary period and radiation dominated era of the universe. The physical properties of cosmological solutions are also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.