A fast tracking mirror for adaptive optics

A piezo driven tilt mirror was developed and built as one component of an image motion compensation system for a solar telescope. The bandwidth of the mirror with a diameter of 60 mm is about 1 kHz with negligible phase shift between input signal and mirror response up to 900 Hz. The tilt range is 1.6 mrad. Special care was taken to maintain the surface quality of the mirror to better than /15 after fixing it to the substrate.     

Model of VLBI observation within the relativistic framework

In this paper we derive the post-newtonian expressions for the VLBI time delay and gravitational delay in the barycentric coordinate system of the solar system. We discuss the effect of the various bodies and their range of action. From the transformation between the barycentric and the geocentric systems we then give the VLBI observational model in the geocentric system. Our final results are given by formula (16) for the gravitational delay and by formula (25) for the VLBI time delay.     

Design of 2-M to 6-M Liquid Mirror Containers

A new design is proposed for large (up to 6-m) liquid mirror containers. The design uses Kevlar, foam and aluminum, as in previous designs, but with a different configuration that makes the container lighter, stronger and more rigid. The results of finite element analysis are presented, consisting in the deformations due to temperature changes and to weight, and in the security factor for each material when maximum constraints are applied. Tilt rigidity is also analyzed. They show that the composite material construction technique gives a good performance up to 6 m diameters. The figures and tables contained in this paper can be used as recipes to build containers having diameters between 2 and 6 m. This revised version was published online in July 2006 with corrections to the Cover Date.     

A relativistic model of the movement of apparent superluminal radio sources

Based on the relativistic model of the apparent superluminal motion and under the condition that the center of mass of a superluminal radio source remains in motion relative to the observer, the equation of the apparent velocity between nucleus and component is derived. Assuming that the directions of jet and movement of superluminal radio source are opposite, then, supposing that the velocities of nucleus and components of SLS are equal and the nucleus is fixed, the equations of real velocity are respectively derived. With the data of V_app and θ substituted in the equation of real velocity, the velocity of the components of SLS is obtained. Comparing the real velocity with the velocity of Hubble redshift of SLS, it is concluded that the movement of SLS has no influence on the velocity of components.     

相对论多方球的稳定性

本文从理论的角度，讨论了静态相对论多方球的稳定性问题，给出稳定性对球体物质的绝热指数的依赖关系．     

Propagation of plane relativistic shock waves in a slowly moving medium

Similarity solutions for the propagation of plane relativistic shock waves in a slowly moving medium, where the nucleon number density obeys an exponential law ofx/t, is obtained in this paper. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium.     

The Wilkinson Microwave Anisotropy Probe (WMAP) confirmed the model of our observed relativistic universe

The Wilkinson Microwave Anisotropy Probe (WMAP) confirmed the model of flat expansive homogeneous and isotropic relativistic universe, which describes the properties of our observed flat expansive homogeneous and isotropic relativistic Universe in the first (linear, Newtonian or classical-mechanical) approximation.     

On the relativistic magnetic reconnection

Reconnection of the magnetic lines of force is considered in case the magnetic energy exceeds the rest energy of the matter. It is shown that the classical Sweet–Parker and Petschek models are generalized straightforwardly to this case and the reconnection rate may be estimated by substituting the Alfven velocity in the classical formulae with the speed of light. The outflow velocity in the Sweet–Parker configuration is mildly relativistic. In the Petschek configuration, the outflow velocity is ultrarelativistic whereas the angle between the slow shocks is very small. As a result of the strong compression, the plasma outflow in the Petschek configuration may become strongly magnetized if the reconnecting fields are not exactly antiparallel.     

On the relativistic formulation of matter

A critical analysis of the relativistic formulation of matter reveals some surprising inconsistencies and paradoxes. Corrections are discovered which lead to the long-sought-after equality of the gravitational and inertial masses, which are otherwise different in general relativity.     

On the Stability of Equilibrium Points in the Relativistic Restricted Three-Body Problem

The equilibrium points of the relativistic restricted three-body problem are considered. The stability of the triangular points is determined and contrary to recent results of other authors a region of linear stability in the parameter space is obtained. The positions of the collinear points are approximated by series by expansions and their stability is similarly determined. It is found that these are always unstable.This revised version was published online in October 2005 with corrections to the Cover Date.     

On the r-mode spectrum of relativistic stars

We present a mathematically rigorous proof that the r-mode spectrum of relativistic stars to the rotational lowest order has a continuous part. A rigorous definition of this spectrum is given in terms of the spectrum of a continuous linear operator. This study verifies earlier results by Kojima concerning the nature of the r-mode spectrum.     

On the internal structure of relativistic jets

A magnetohydrodynamic model is constructed for a cylindrical jet embedded in an external uniform magnetic field. It is shown that, as in the force-free case, the total electric current within the jet can be zero. The particle energetics and the magnetic-field structure are determined in a self-consistent way; all jet parameters depend markedly on the physical conditions in the external medium. In particular, we show that a region with subsonic flow can exist in the central jet regions. In real relativistic jets, most of the energy is transferred by the electromagnetic field only at a sufficiently large magnetization parameter σ>10⁶. We also show that, in general, the well-known solution with a central core B _Z =B ₀/(1+?²/? _c ² ) cannot be realized in the presence of an external medium.     

On the physics of relativistic double layers

A model of a strong, time-independent, and relativistic double layer is studied. Besides double layers having the electric field parallel to the current the model also describes a certain type of oblique double layers. The Langmuir condition (ratio of ion current density to electron current density) as well as an expression for the potential drop of the double layer are derived. Furthermore, the distributions of charged particles, electric field, and potential within the double layer are clarified and discussed. It is found that the properties of relativistic double layers differ substantially from the properties of corresponding non-relativistic double layers.     

On the existence of cosmological evolutionary effects

Parameters of the distant galaxy clusters of 3C295 (z=0.46) and Cl 0024+1654 (z=0.39) are compared with the predictions made using galaxies of the local clusters Coma (z=0.023) and DC 0329–52 (z=0.057) taking theK-effect into account. The distributions of colour and morphological type, and the amplitudesF ⁺/F^– of the ₀ 4000 discontinuity are examined and no evidence for evolution of the galaxies and the clusters can be seen.     

On the existence of cosmological evolutionary effects

At the beginning of a series of papers concerning reality of various suggested cosmological evolutionary effects, the counts of quasars are examined. The recently reported counts of optically selected quasars (Green and Schmidt, 1978) probably have been biased by the use of distance-dependent morphological criteria of selection. The influence of this bias is to mimic cosmological evolution. The application of theK-correction for the counts of quasars is discussed. TheK-corrected, presumably unbiased counts of objects with ultraviolet excess and broad emission lines, including quasars and type 1 Seyfert galaxies, give the slopeb=0.6, i.e. a uniform radial distribution. Correctness of the latter sampling of data is dependent on the solution of the redshift problem and presupposes an inverse correlation between luminosity and intrinsic redshift.     

On the existence of long-term periodicities in solar activity

Solar Physics - Application of the non-integer technique of power spectral analysis has yielded evidence for long-term periodicities in the Zürich sunspot series. Although the spectrum shows...     

On the r-mode spectrum of relativistic stars in the low-frequency approximation

The axial modes for non-barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow-rotation formalism together with the low-frequency approximation, first investigated by Kojima. The time-independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for     , it is nevertheless also possible to find discrete mode solutions (the r modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time-dependent equations. For stellar models admitting a physical r-mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of l it seems that in certain cases there are no mode solutions at all.     

On the spectrum of relativistic electrons accelerated in cosmic-ray sources

The data on the spectrum of the cosmic-ray electron component near the earth, on the radio-spectra of radio-galaxies, quasars and the Crab Nebula, as well as the data pertaining to the X-ray spectrum of the cosmic background, all agree that the sources of cosmic-ray electrons (such as supernovae and galactic nuclei) inject particles characterized by a power spectrumN(E)=KE ^–0, with 01.5–2.5. A mechanism is known in which the source emits a proton-nuclear component of cosmic rays with a spectrumN _n (E)=K _n E ^– _n, _n = + 2, =w cr/(w–w cr), wherew cr is the cosmic-ray energy density in the source, andw=w cr+w n+w _turb, the total energy density. We obtain =2.5 in agreement with observations on the natural assumption that =0.5. Within the framework of the same model with some additional assumptions, the electrons in the source, as well as those ejected by the source, are shown to have a power-spectrum characterized with _{0 n} = + 2. Thus the model discussed gives an adequate spectrum for both the proton-nuclear and the electron components of cosmic rays.