The 11-year cycle of solar activity and configurations of the planets

In this paper a parameter was used, viz., the average difference between the heliocentric longitudes (ADL) of the planets Venus, Earth, and Jupiter. For the minimum ADL (the planets are in conjunction), as well as at the minimum deviation of the planets from a line passing through them and the Sun at the location of the planets on opposite sides from the Sun, an index was composed that uniquely describes the 11-year cycle of solar activity.     

Existential theorem of conserved quantities and its inverse for the dynamics of nonholonomic relativistic systems

We present a general approach to the construction of conservation laws for the dynamics of nonholonomic relativistic systems.Firstly,we give the definition of integrating factors for the differential equations of motion of a mechanical system.Next,the necessary conditions for the existemce of the conserved quantities are studied in detail.Then,we establish the existential theorem for the conserved quantities and its inverse for the equations of motion of a nonholonomic relativistic system.Finally,an exampled is given to illustrate the application of the result.     

Relationship of solar activity cycles to planetary configurations

A single-valued relation of the 22-year and 11-year solar activity cycles is calculated with allowance for the minimum values of the average difference between the heliocentric longitudes of Venus, Earth, and Jupiter. The envelope curve of the minimum values of this parameter describes both conjunctions of the three planets when they are positioned in an almost straight line from the Sun (causing peak solar activity) and the far more frequent assemblies in a broader longitudinal sector (25–30 degrees) that are characterized by different combinations of planets on opposite sides of the Sun, also eliciting peak solar activity.     

Cycles of solar activity and the configurations of planets

In this paper, using the parameter??the average difference between the heliocentric longitudes of the planets Venus, Earth and Jupiter??the strong link found 22-year and 11-year cycles of solar activity with the lowest values of the parameter. The envelope curve of the minimum values of this parameter is well described as the conjunctions of the three planets, when they are almost in a straight line from the sun, which causes the maximum of solar activity, and the conjunctions in the larger longitudinal sector (25?C30 degrees), which occur much more frequently and are accompanied by different combinations of planets on the opposite side of the Sun, which also cause the maximum of solar activity. Location of these planets on opposite sides of the Sun in various combinations is very well compatible with the parameter used.     

Integrating factors and conservation theorem for holonomic nonconservative dynamical systems in generalized classical mechanics

In this paper,we present a general approach to the construction of conservation laws for generalized classical dynamical systems.Firstly,we give the definition of integrating factors and ,secondly,we study in detail the necessary conditions for the existence of conserved quantities.Then we establish the conservation theorem and its inverse for the hamilton‘s canonical equations of motion of holonomic nonconservative dynamical systems in generalized classical mechanics.Finally,we give an example to illustrate the application of the results.     

Classical geometry of bosonic string dynamics

We develop a treatment of bosonic strings on a general curved background in which the volume element and the coordinates of the worldsheet are related in a similar way as canonically conjugate quantities in mechanics. The resultant formalism is a particular variant of the multi-phase-space approach to classical field theory put forward by Kijowski, Tulczyjew, and others. We study conservation laws within this framework and find that all conserved quantities are related to point symmetries, i.e., isometries of the underlying spacetime. Thus, the symmetries of relativistic mechanics coming from Killing tensors have no analogue here. We furthermore deduce from the present scheme the covariant version of the usual phase space.     

Integrating factors and conservation theorems for Hamilton‘s canonical equations of motion of variable mass nonholonmic nonconservative dynamical systems

We present a general approach to the construction of conservation laws for variable mass noholonmic nonconservative systems.First,we give the definition of integrating factors,and we study in detail the necessary conditions for the existence of the conserved quantities,Then,we establish the conservatioin theorem and its inverse theorem for Hamilton‘s canonical equations of motion of variable mass nonholonomic nonocnservative dynamical systems.Finally,we give an example to illustrate the application of the results.     

事件空间中非完整非保守系统的守恒量存在定理及其逆定理

提出了事件空间中非完整非保守系统守恒定律构成的一般途径.首先，列写系统的运动微分方程，给出积分因子的定义.其次，详细地研究了守恒量存在的必要条件，并建立了事件空间中非完整非保守系统的守恒量存在定理及其逆定理.最后，举例说明结果的应用. 关键词： 事件空间 非完整非保守系统 积分因子 守恒定理     

不同惯性系中的力学规律

由力学相对性原理可知，在不同惯性系中，一切力学规律（如牛顿运动定律、动量定理、动量守恒定律、角动量定理等）的形式都相同．但在一个惯性系中机械能（或角动量）守恒，在另一惯性系中观察机械能（或角动量）却不一定守恒．     

A review of the effects of light scattering on the dynamics of irregularly shaped dust grains in the Solar System

The various aspects of the interaction of electromagnetic radiation with cosmic dust particles are discussed. In particular, attention is paid to discrepancies between optical and physical behavior of realistically shaped particles and volume equivalent homogeneous spheres. The dynamical evolution of morphologically non-identical particles which are driven by gravity, electromagnetic radiation and the Lorentz forces can dramatically differ. Although spherical particles often enable analytical calculations, an orbital evolution of spheres cannot be considered as a representative evolution for real cosmic dust particles. The effect of electromagnetic radiation on the motion of dust grains plays a crucial role here. While irregularly shaped interstellar dust particles may be captured in the Solar System, the spherical particles will not survive due to close encounters with the Sun. Spherical grains can be captured almost only in the evaporation region (in the vicinity of the Sun), where they are destroyed due to high temperatures. The spherical dust particles ejected from comets will monotonously inspiral toward the Sun subject to the Poynting-Robertson effect. However, the non-spherical particles of the same origin may be temporarily stabilized at some heliocentric distances and thus their lifetime may be much longer than that for the Mie spheres. Some dust particles may also be captured in mean-motion resonances with planets (commensurability resonances). While spherical particles are always characterized by the secular decrease of the semi-major axes near mean-motion resonances, this may not be true for non-spherical particles. Resonant captures of arbitrarily shaped dust grains exist for exterior and interior mean-motion resonances with planets.     

Ergodic properties and thermodynamic behavior of elementary reversible cellular automata. I. Basic properties

This is the first part of a series devoted to the study of thermodynamic behavior of large dynamical systems with the use of a family of fully-discrete and conservative models named elementary reversible cellular automata (ERCAs). In this paper, basic properties such as conservation laws and phase space structure are investigated in preparation for the later studies. ERCAs are a family of one-dimensional reversible cellular automata having two Boolean variables on each site. Reflection and Boolean conjugation symmetries divide them into 88 equivalence classes. For each rule, additive conserved quantities written in a certain form are regarded as a kind of energy, if they exist. By the aid of the discreteness of the variables, every ERCA satisfies the Liouville theorem or the preservation of phase space volume. Thus, if an energy exists in the above sense, statistical mechanics of the model can formally be constructed. If a locally defined quantity is conserved, however, it prevents the realization of statistical mechanics. The existence of such a quantity is examined for each class and a number of rules which have at least one energy but no local conservation laws are selected as hopeful candidates for the realization of thermodynamic behavior. In addition, the phase space structure of ERCAs is analyzed by enumerating cycles exactly in the phase space for systems of comparatively small sizes. As a result, it is revealed that a finite ERCA is not ergodic, that is, a large number of orbits coexist on an energy surface. It is argued that this fact does not necessarily mean the failure of thermodynamic behavior on the basis of an analogy with the ergodic nature of infinite systems.     

CONSERVATION LAWS FOR HEATED LAMINAR RADIAL LIQUID AND FREE JETS

The conserved quantities for the heated radial liquid jet and the heated radial free jet are established by using conservation laws. The flow in a heated radial jet is described by Prandtl's momentum boundary layer equation, the continuity equation and the energy equation. Viscous dissipation is neglected. The multiplier approach is used to derive the conservation laws for the system of three equations for the velocity components and the temperature and three conserved vectors are obtained. The conservation laws for the system of two partial differential equations for the stream function formulation are also computed by the multiplier approach and three conserved vectors are obtained. One of these is a non-local conserved vector for the system. The conserved quantities for the heated radial liquid jet and the heated radial free jet, emitted into a stationary fluid of uniform temperature θ_∞, are derived by integrating the conservation laws across the jet.     

Current Symmetries for Particle Systems with Several Conservation Laws

We consider stochastic interacting particle systems with more than one conservation law in a regime far from equilibrium. Using time reversal we derive symmetry relations for the stationary currents of the conserved quantities that are reminiscent of Onsager’s reciprocity relations. These relations are valid for a very large class of particles with only some mild assumption on the decay of stationary relations and imply that the coarse-grained macroscopic dynamics is governed by a system of hyperbolic conservation laws. An explicit expression for the conserved Lax entropy is obtained.     

两个力学量算符具有共同本征态系的条件

量子力学是人们了解微观世界的一门重要的课程.在量子力学中,由于任何实物体都具有波粒二象性,必须用算符来表示力学量,因此算符理论显得尤为重要.在研究多个算符时,有一个非常重要的定理:两个力学量算符能够具有共同本征函数系的充分必要条件是这两个个力学量算符能够互相对易.本文分析了在使用该定理时可能存在的一些问题,并对这些问题进行了澄清.     

Occam’s Razor as a Formal Basis for a Physical Theory

We introduce the principle of Occam's Razor in a form that can be used as a basis for economical formulations of physics. This allows us to explain the general structure of the Lagrangian for a composite physical system, as well as some other artificial postulates behind the variational formulations of physical laws. As an example, we derive Hamilton's principle of stationary action together with the Lagrangians for the cases of Newtonian mechanics, relativistic mechanics and a relativistic particle in an external gravitational field.     

On the Inclination of Planetary Orbits

Assuming that planets were formed in the equatorial plane of the Sun and that there was a small perturbation at the start, it is shown that relativistic effects could lead to the planetary orbit tilting observed. On the baais of this analysis, a prediction is made for the velocity of the planet Mercury out of its orbital 'plane'. This prediction is a lower limit. Further, this explanation may possibly provide a method for determining the solar angular momentum.     

Warm cascade states in a forced-dissipated Boltzmann gas of hard spheres

We study the homogeneous isotropic Boltzmann equation for an open system. For the case of a hard spheres gas, we look for nonequilibrium steady solutions in the presence of forcing and dissipation. Using the language of weak turbulence theory, we analyze the possibility of observing the Kolmogorov-Zakharov steady distributions, i.e. solutions characterized by constant fluxes of conserved quantities. We derive a differential approximation model and we find that the expected nonequilibrium steady solutions have always the form of warm cascades. We propose an analytical prediction for the relation between the forcing and dissipation and the thermodynamic quantities of the system. Specifically, we find that the temperature of the system is independent of the forcing amplitude and determined only by the forcing and dissipation scales. Finally, we perform direct numerical simulations of the Boltzmann equation finding consistent results with our theoretical predictions.