The main properties and peculiarities of the Earth’s motion relative to the center of mass

The methods of theoretical and celestial mechanics and mathematical statistics have been used to prove that the Earth’s motion relative to the center of mass, the polar wobble, in the principal approximation is a combination of two circumferences with a slow trend in the mean position corresponding to the annual and Chandler components. It has been established that the parameters (amplitude and phase shift) of the annual wobble are stable, while those of the Chandler component are less stable and undergo significant variations over the observed time intervals. It has been proven that the behavior of these polar motion parameters is attributable to the gravitational-tidal mechanisms of their excitation.     

On the treatment of the center of mass motion in nuclear mean field theories

It is shown how the spurious components due to the center of mass motion can be eliminated from general Hartree-Fock-Bogoliubov quasi-particle configurations with the help of projection techniques. The problem how to restore the additional symmetries being broken by such configurations is discussed. An explicit formulation is given for the spherical Hartree-Fock problem with center of mass momentum projection before the variation. As an example for the application of this method the ground state of⁴He is studied using two different interactions, a microscopic two-body one as well as a phenomenological one including a Skyrme-type three-body force. The results are compared to those of the usual approximate treatment of the center of mass motion in Hartree-Fock calculations. It turns out that, at least for the chosen example, the latter yields a rather reasonable approximation to the correct total energy, single particle energy and even the mass density provided that it is calculated from a translationally invariant density operator.     

原子质心运动对二能级原子发射谱的影响

研究了质心做谐振运动的二能级原子的发射谱. 当原子质心运动与光场无关联时，原子质心运动不影响原子发射谱的相位敏感性，随着原子质心运动平均能量的增加，原子发射谱峰间的相对距离变小，峰高的变化与原子质心运动和光场所处的状态有关. 当原子质心运动与光场有关联时，原子发射谱不依赖于光场与原子偶极矩的相对相位，在适当条件下原子发射谱峰的数目减少，峰高增大，峰宽变小. 关键词： 原子质心运动 二能级原子 原子发射谱 SU(2)相干态     

On the new prolonged solar activity minimum

The current 24th solar activity cycle started in 2008 and continuing to the present is anomalous in comparison with previous cycles. Its unusual properties include a low sunspot number R _z for a long time, a weak interplanetary magnetic field, a weak polar photospheric field in the Sun, and others. Beginning in 1000 to the present, five prolonged solar activity minima took place. These minima occurred in time intervals, when the distance between the center of mass of the solar system and the Sun center changed several times from maximum to minimum values for 40–70 years. Since the beginning of the new millennium, exactly such a period started and it can be assumed that we entered a new prolonged minimum which will last for several decades. In the current 24th and subsequent 2–3 solar activity cycles, annual average sunspot numbers will be low, R _zmax ≤ (50–70).     

Prediction of geoeffective solar wind streams near earth according to solar observational data

A semi-empirical model for predicting solar wind (SW) streams is developed based on satellite images of the Sun and corona using a hierarchical approach. The model allows simultaneous calculation of the parameters of all three SW components, i.e., slow SW, high-speed streams from coronal holes, and interplanetary coronal mass ejections, as well as the detection of their possible interaction in the heliosphere.     

Regularities of solar energetic particle events and fluxes

Some regularities related to solar energetic proton (SEP) events and fluxes have been established. It is shown that the rate of SEP events is proportional to the Wolf numbers and that the distribution functions of SEP events related to both different levels and cycle phases, divided by the sums of Wolf numbers, are identical. It is concluded that extremely large SEP events may also occur in periods of minimum solar activity. This conclusion is confirmed by the experimental data obtained at the end of 2004 and in 2005.     

Mechanics of a particle near the center of a rotating ring

The equations of motion of a test particle moving near the center of a massive rotating ring are derived up to the post-post-Newtonian order of approximation, by using the metric tensor for many body system which is Minkowskian at spatial infinity. Logarithmic divergences due to self-interaction of the ring appear in the equations of motion. These divergences can be removed by the procedure which is similar to the renormalization method in particle physics. In the equations of motion there appears a force directing to the rotation axis and depending on the angular velocity of the ring. This force vanishes when the magnitude of the gravitational constant times the mass of the ring divided by the radius of the ring is about one tenth of the square of the velocity of light. Under this condition it is shown that the relative magnitude of the Coriolis force to the centrifugal force in the equations of motion agrees with the expected one from the equations of motion in a rotating reference frame.     

评"相对论的质心运动定理"

在相对论情况下,质点系统的质心是一个不确定的概念,在相对论力学中,质心系（质量中心参照系）亦被有确切定义的动量中心系（系统总动量为零的参照系）所代替,本文对《相对论的质心运动定理与质量亏损》一文的论证和结果作出了评论。     

The gravitational influence of Venus,the Earth,and Jupiter on the 11-year cycle of solar activity

This paper presents the calculations of the resulting tidal force of Jupiter, Venus, and Earth, that act on the Sun. Considering the tidal forces as the difference of gravitational forces that act on the extreme points of the Sun’s diameter and on the center of the Sun, it is shown that there are large variations in the resulting tidal force (RTF) at the moments of linear configurations of Venus, the Earth, and Jupiter, and that the maximum variations of the RTF are in a strong agreement with the minimum values of the JEV planetary index, as introduced by the author in previous works.     

Stochastic dynamics of the magneto-optical trap

The cloud of cold atoms obtained from a magneto-optical trap is known to exhibit two types of instabilities in the regime of high atomic densities: stochastic instabilities and deterministic instabilities. In the present paper, the experimentally observed stochastic dynamics is described extensively. It is shown that it exists a variety of dynamical behaviors, which differ by the frequency components appearing in the dynamics. Indeed, some instabilities exhibit only low frequency components, while in other cases, a second time scale, corresponding to a higher frequency, appears in the motion of the center of mass of the cloud. A one-dimensional stochastic model taking into account the shadow effect is shown to be able to reproduce the experimental behavior, linking the existence of instabilities to folded stationary solutions where noise response is enhanced. The different types of regimes are explained by the existence of a relaxation frequency, which in some conditions is excited by noise.Received: 18 June 2003, Published online: 28 October 2003PACS: 32.80.Pj Optical cooling of atoms; trapping - 05.40.Ca Noise - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems     

Possibility of prediction of solar proton events

The dynamic processes in the interplanetary space have been investigated on the basis of the time variations in the parameters of the cosmic-ray rigidity spectrum. It is established that the change in the electromagnetic characteristics of the heliosphere begins before the sporadic phenomena on the Sun. In particular, it is shown that the sporadic phenomena are preceded by generation of local polarization electric fields, a decrease in the magnetic field strength in small-scale heliospheric structures, and an increase in the potential difference between the pole and ecliptic plane. The use of these signs makes it possible to predict solar proton events with a lead time from several hours to several tens of hours with a high degree of confirmation.     

Relativistic effects in many-body systems of finite size,internal structure,and internal motions: I. “Self-acceleration” of astrophysical systems

It is proved that the post-Newtonian general relativistic center of rest mass of a bounded physical system composed of a number of bodies characterized by finite dimensions, arbitrary internal structure, and arbitrary internal motions cannot in general move uniformly, contrary to what was conventionally accepted up to now. Mathematical expressions are derived and discussed describing, in terms of the above characteristics of the bodies, the position and velocity vectors of the center of rest mass of the system and the force, which is responsible for its nonuniform motion, with respect to the uniformly moving post-Newtonian general relativistic center of inertial mass of the physical system. In the special case of a binary star it is shown that the center of rest mass should describe, around the uniformly moving center of inertial mass, an ellipse of the same period and eccentricity as those of the Newtonian elliptical orbit of the relative motion. The length of the axes of this ellipse depends on the internal characteristics of the members of the binary star, and the motion of the center of rest mass becomes important when these characteristics are strong enough. Finally, it is proved that in every effort for describing theoretically a binary system, the internal characteristics of the members of which are ignored, and for accurate measurements of their positions and velocities, the above fictitious motion of the center of rest mass has to be taken into account; otherwise, the results of the measurements will not be consistent with the theoretical predictions.     

Dependence of Forbush-decrease magnitudes on parameters of solar eruptions

By data of the 23^rd solar cycle, it is shown that close statistical relations exist between quantitative parameters of dimmings and arcades caused by solar coronal mass ejections (CMEs), on the one hand, and magnitudes of non-recurrent Forbush-decreases of the galactic cosmic ray flux, as well as the propagation time of disturbances from the Sun to the Earth, on the other hand. Parameters of dimmings and arcades, in particular their summarized magnetic flux of the prolonged field at the photospheric level, were calculated by data of the EUV SOHO/EIT telescope in the 195 Å Received results mean that the scale, characteristics, and propagation time of interplanetary disturbances to the Earth are determined to a large degree by measurable parameters of solar eruptions and may be estimated in advance by observations of dimmings and arcades in the EUV range.     

Characteristic periodic motion of polymers in shear flow

The motion of both free and tethered polymer molecules as well as rigid Brownian rods in unbound shear flow is found to be characterized by a clear periodicity or tumbling frequency. Periodicity is shown using a combination of single molecule DNA experiments and computer simulations. In all cases, we develop scaling laws for this behavior and demonstrate that the frequency of characteristic periodic motion scales sublinearly with flow rate.     

Recurrent solar wind streams

A new approach to investigating the statistical relationship between certain solar features and recurrent wind streams is presented. This approach is based, on a comparative analysis of the distributions of lifetimes of a set of solar features, recurrent geomagnetic disturbances, and geomagnetic “calms.” Correlation coefficients of 0.81, 0.85, 0.79, and 0.77 are found for the distributions of several solar features—filaments, large-scale magnetic fields, coronal features, and coronal holes, respectively—and recurrent geomagnetic disturbances. A correlation factor of 0.97 between the distributions of geomagnetic “calms” and active regions is found. The combined evidence indicates that no specific type of solar feature is responsible for the recurrent stream activity. Rather, the configuration of the large-scale magnetic field of the Sun appears to control the permanently existing corpuscular activity. Since prominences trace polarity division lines of the large-scale magnetic field structure of the Sun, they have been checked as a possible general predictor of recurrent corpuscular activity; their parameters could present the most reliable indices that relate closely with trends in geomagnetic disturbances. A comparative analysis of cyclic variations of sunspot numbers, the total number of prominences, the relative number of low-height (<-20″) prominences, and recurrent geomagnetic storms is made for solar cycle N16. The relative number of low-height prominences is found to correlate broadly (0.83) with recurrent wind streams. P. K. Shternberg State Astronomical Institute, Moscow, Russia; National Solar Observatory, Sacramento Peak, U.S. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 2, pp. 145–151, February, 1998.     

Relativistic aspects of the motion of two-particle model molecule oscillating perpendicularly to the direction of its translation

On solving exactly relativistic equations of motion for the model molecule of two particles coupled elastically, it has been shown that in the framework of relativistic mechanics this system, and in general any closed system of interacting particles, is not inertial. In particular, the translational velocity of the mass center of such a system has, as a consequence of the nonlinearity of the equations, oscillatory components reflecting its internal transverse oscillations—it is a pulsed motion. This effect can in principle be seen in the time-of-flight experiments. The force constant of elastic coupling in the system, as seen by the observer at rest, is shown to decline with increase of the total momentum of the system.     

Falling paper: Navier-Stokes solutions, model of fluid forces, and center of mass elevation

We investigate the problem of falling paper by solving the two dimensional Navier-Stokes equations subject to the motion of a free-falling body at Reynolds numbers around 10(3). The aerodynamic lift on a tumbling plate is found to be dominated by the product of linear and angular velocities rather than velocity squared, as appropriate for an airfoil. This coupling between translation and rotation provides a mechanism for a brief elevation of center of mass near the cusplike turning points. The Navier-Stokes solutions further provide the missing quantity in the classical theory of lift, the instantaneous circulation, and suggest a revised model for the fluid forces.     

Plasma motion in a filtered cathodic vacuum arc

A model is proposed for the flow of a plasma originating from a cathodic vacuum arc into a curvilinear magnetic field. The model gives good agreement with measurements obtained from a filtered cathodic-arc thin film deposition system. The important parameters involved in the motion of a vacuum arc plasma beam through a magnetic filter are examined. The analysis is based on the use of the guiding center approximation to describe the motion of the charged particles produced in the plasma where the thermal energy is negligible compared to the mass flow energy. Electron-ion collision effects are included within the framework of the drift model. It is shown that under the limiting condition of a collision frequency which is much higher than the cyclotron frequency of the electron, the motion of the plasma ions around the bend becomes independent of the magnetic field, with the number of ions traversing the filter significantly reduced. However, in the collisionless plasma case (cyclotron frequency higher than the collision frequency), the model predicts a square-law relationship between ion-saturation current and magnetic field , I_p ∞B²     

原子质心运动的量子效应对光场量子噪声压缩的影响

考虑JaynesCummings模型中与光场相互作用的原子为超冷原子,讨论了原子质心运动的量子效应对光场两正交分量量子噪声压缩的影响,结果表明,在JaynesCummings模型中,原子质心运动的量子效应增加光场两正交分量的量子噪声,使其压缩效应消失 关键词： 超冷原子 质心运动的量子效应 光场量子噪声压缩     

Scattering parameters of a waveguide cross junction loaded with a metallic post in the center

In this paper, the scattering parameters of a waveguide cross junction loaded with a metallic post in the center are analyzed for the first time by using the Method of Lines. The homogeneous boundary condition of the third kind and curved boundary are introduced in the formulation. Numerical results are in good agreement with the experimental data. The scattering parameters at Ka-band and W-band of the cross junctions loaded with metallic posts of different radii are presented. It is shown from the numerical results that loaded with metallic posts is an effective means for adjusting the network parameters of the waveguide cross junction to satisfy some special requirements in the design of millimeter wave components.