A mechanism for the injection of very low energy particles into the magnetosphere

A mechanism for the injection of very low energy particles into the magnetosphere is suggested. Protons in the solar plasma accelerate neutral hydrogen atoms in the interplanetary gas by charge exchange; these hydrogen atoms are stripped by the gas in the exosphere to give protons. The rate of such injection into the magnetosphere during a geomagnetic storm is calculated and is found to be about 10²² protons per second of energy ～20 KeV.     

Space Research: Particles and their Fields A Brief Introduction for Mathematicians

The use of vectors in describing the motion of charged particles is illustrated by applying the results of an elementary analysis to the motions of charged particles in Earth's ionosphere and magnetosphere. In the ionosphere electric fields give rise to ‘E x B’ drifts which cause bulk motion of the ionization away from the equator near midday. This is evident in world contours of the isolines of electron density which exhibit an equatorial trough near noon and in the early afternoon. In the magnetosphere, drifts caused by particle pressures, together with inhomogeneity and curvature drifts, cause the charged particles there to form a geomagnetic ring current whose effects have been observed by satellite. This ring current may affect the topology of the magnetosphere.     

Multiscale behavior and fractional kinetics from the data of solar wind–magnetosphere coupling

Multiscale phenomena are ubiquitous in nature as well as in laboratories. A broad range of interacting space and time scales determines the dynamics of many systems which are inherently multiscale. In many systems multiscale phenomena are not only prominent, but also they often play the dominant role. In the solar wind–magnetosphere interaction, multiscale features coexist along with the global or coherent features. Underlying these phenomena are the mathematical and theoretical approaches such as phase transitions, turbulence, self-organization, fractional kinetics, percolation, etc. The fractional kinetic equations provide a suitable mathematical framework for multiscale behavior. In the fractional kinetic equations the multiscale nature is described through fractional derivatives and the solutions of these equations yield infinite moments, showing strong multiscale behavior. Using a Lévy flights approach, we analyze the correlated data of the solar wind–magnetosphere coupling. Based on this analysis a model of the multiscale features is proposed and compared with the solutions of diffusion-type equations. The equation with fractional spatial derivative shows strong multiscale behavior with infinite moments. On the other hand, the equation with space dependent diffusion coefficients yield finite moments, indicating Gaussian type solutions and absence of long tails typically associated with multiscale behavior.     

A model for the interaction of the solar wind with a plasma layer (Statement of the model)

We consider a model for the generation of an electric field in the tail of the magnetosphere as a result of a viscous interaction of the solar wind with the magneto sphere plasma. We propose a way of determining the parameters of the model-the Hartman number G and the conductivity . We carry out a detailed analysis of the consequences of the model and a comparison with the existing experimental data.Translated fromDinamicheskie Sistemy, No. 6, 1987, pp. 54–59.     

Collision of a solar wind shock wave with the Earth’s bow shock. Wave flow pattern

The wave pattern of the flow developed when a solar wind shock wave propagates along the surface of the Earth’s bow shock is studied. The investigation is carried out in the three-dimensional non-plane-polarized formulation within the framework of the ideal magnetohydrodynamic model in which the medium is assumed to be inviscid and non-heat-conducting and to have the infinite conductivity. The global three-dimensional pattern of the interaction which is a function of the latitude and longitude of elements on the surface of the bow shock is constructed as a mosaic of solutions to the problem of breakdown of a discontinuity developed between the states behind the impinging and bow shocks on the moving curve of intersection of their fronts. The investigation is carried out for typical solar wind parameters and interplanetary magnetic field strength in the Earth’s orbit and for several Mach numbers of the interplanetary shock wave, which makes it possible to trace the evolution of the flow developed as a function of the intensity of the shock perturbation of the solar wind. The solution obtained is necessary for interpreting measurements carried out by spacecraft located in the neighborhood of the Lagrange point and the Earth’s magnetosphere.     

Coupling between equatorial and auroral ionospheres during polar substorms

The intense substorm activity following the geomagnetic sudden commencement on 8 August 1972 at 2354 UT and on 9 August 1972 at 0037 UT had reversed the eastward electric field at the equatorial station Jicamarca between 0700 and 1200 UT, and this was preceded by similar changes in the westward electric field in the auroral region. This abnormal change at the equatorial latitudes in the American zone (in the night-time) was closely associated with the westward electric field in the Indian zone (in the day-time) causing the counter-electrojet and the sudden disappearance of theq type of equatorialEs. The reversal of the electric field at Jicamarca had caused the generation of theF region irregularities associated with range spreadF. It is suggested that on some occasions the counter equatorial electrojet currents are caused due to the reversal of the equatorial electric fields by the spreading of the auroral electrojet currents to the low latitudes following geomagnetic storms. This suggests a possible link between the equatorial ionosphere and the magnetosphere through the auroral latitudes.     

Features of electron density and temperature in the 500–3500 km region of the plasmasphere—(1) Dawn and dusk sectors

Dawn-dusk features of the plasmasphere are examined for intervals in February and September 1969, using electrostatic probe data ofN _e andT _e from the ISIS-I satellite. Clear plasmatrough formation is seen in the vicinity of 70° geomagnetic latitude in both dawn and dusk sectors in the 1500–3500 km region, but the plasmatrough is absent in the altitude range 500–1500 km. The plasmatrough minimum near 70°φ exhibits no asymmetry between dawn and dusk sectors in its latitudinal position. TheT _e peak associated with the plasmatrough is more pronounced in the dawn sector. DawnN _e is less than duskN _e, but dawnT _e exceeds duskT _e. The influence of processes in the magnetosphere in causing these features is examined.     

Hybrid Simulation of Space Plasmas: Models with Massless Fluid Representation of Electrons. III. Shockless Discontinuities

This is the third article in a series of reviews on hybrid simulation of low-frequency processes in space plasmas. It deals with shockless (contact, tangential, and rotational) discontinuities. A hybrid model is described with ions represented by particles and electrons by a massless fluid. The Hamiltonian scheme for the numerical implementation of this model is discussed in detail. The first part of the article provides basic background information, which covers MHD models (ideal, resistive, and Hall models) as well as a classification of shockless discontinuities and their main properties. The review part of the article surveys the literature on simulation of the structure and properties of nonpropagating (contact and tangential) discontinuities and the structure of the magnetopause as a complex domain consisting of multiple discontinuities and waves. We also review the literature on hybrid simulation of rotational discontinuities and the structure of the reconnection layer—the configuration of the reconnecting magnetic forcelines in the dayside magnetopause and in the distant magnetotail. The concluding sections examine studies on hybrid simulation of the penetration of plasma inhomogeneities from the solar wind into the magnetosphere. The following issues are considered: the interaction of the bow shock with interplanetary discontinuities; the "hot flow anomaly"; the interaction of pressure pulses with the bow shock; impulsive plasma penetration through a tangential discontinuity (the magnetopause) as a result of a "collision" of a magnetosheath plasmoid (plasma current sheet) with the magnetopause.     

Dynamic fractal unifying interaction confirmed with magnetospheric behavior and orbital data

The solar wind makes the magnetosphere to expand and contract as indicated by the expansions and contractions of the auroral oval due to balancing of the dynamic pressure of the ambient space plasma at inner and outer magnetic lines. This self‐similar magnetospheric behavior elucidates the controversial magnetic storm‐substorm relationship and reveals the 3D‐spiral structure of magnetic interaction. The found self‐similarly evolving structure of one seen as fundamental interaction suggests dynamic fractal unifying interaction that builds a firework universe having 3D‐spiral code. The unifying interaction is described with equation drawn in new fundamental dynamic fractal framework. The equation of unifying interaction converges to the inverse square laws and the principle of uncertainty at laboratory scales. The dynamic fractal fundamental framework is made of one 3D‐spirally‐faster‐inward contracting and expanding, oscillating, basic matter. It simply accounts for observed constant speed of light and for the creation of bright and dark bands on a screen behind a tiny slit. The dynamic fractal framework is quantitatively confirmed with the orbital data for the Milky Way Galaxy, the Sun, the Earth, and the triple asteroid system 87 Sylvia. Many testable predictions are also made. The presented new fundamental dynamic fractal framework allows qualitative and quantitative modeling and simplification. © 2007 Wiley Periodicals, Inc. Complexity 12: 61–76, 2007     

Geomagnetic plasma probe for solar wind

Magnetograms from Alibag reveal that the range Δ H of the daily variation of the horizontal component is negatively correlated with the minimum value ΔH_min. during a day. This relationship is largely unaffected by the degree of geomagnetic disturbance and holds good during all phases of the 11-year cycle of solar activity. From the nature of the relationship between ΔH and ΔH_min. it is concluded that the daily variation of the geomagnetic field at a low latitude station outside the influence of the equatorial electroject must be regarded as largely due to a weakening of the ambient field on the night side rather than an enhancement of the field on the day side due to ionospheric currents. There exists a good correlation between (ΔH)² and the kinetic energy density of the solar wind in interplanetary space measured by IMP-1 satellite. It is suggested that ΔH is largely the result of the partial ring currents related to the convective drift of the plasma from the tail of the magnetosphere. Moreover, using the relationships established during the IMP-1 period, the annual mean kinetic energy density of solar wind for geomagnetically quiet days for the past 11-year cycle is estimated, treating the earth as a plasma probe.     

Modular-function representation of the solutions of the problem of two fixed centres

The problem of two fixed centres can be integrated in quadratures by using Stoeckel's theorem in spheroidal coordinates. The elliptic coordinates of the meridian plane satisfy equations that define a complex elliptic curve. The solution can be written down by using the uniformization formula of the elliptic curve. The constants defining the result in terms of doubly periodic functions are calculated successively from the initial data. The half-period ratio is determined by solving a complex transcendental equation using modular functions. The magnitude of the half-period of least absolute value is determined using -functions of the zero argument, using invariants of the Weierstrass -function.     

On the construction and investigation of solutions of boundary value problems of thermoviscoelasticity

The uncoupled mixed boundary value problem of thermoviscoelasticity is considered in a quasistatic formulation. The temperature distribution is assumed nonstationary and inhomogeneous. The influence of the temperature on the viscoelastic properties of the material is taken into account by the introduction of a reduced time. The equations of state of the material are written in differential form as a system of kinetic equations in some tensor-type strain parameters. The system mentioned is equivalent to a Volterra integral equation with kernel in the form of a sum of exponents. The differential approach used is apparently more convenient for numerical realization /1/ (especially in nonuniform problems) and results in a substantially different mathematical formulation as compared with that based on the integral form of writing the equations of state investigated in /2,3/. Precisely for going over to the boundary value problem are the kinetic differential equations converted into an operator differential equation in Hubert space. The existence, uniqueness, and stability of the solution of the problem formulated are established, and conditions for the convergence of the Galerkin approximations and the stability of the difference approximations in time are formulated.     

On the solution of certain integral equations of mixed problems of plate bending theory

The problem of the bending of a Kirchhoff-Love plate in the shape of a strip under the impression of a thin linear rigid inclusion fastened at one of the edges of the plate when the other edge of the plate is rigidly clamped is considered. The problem is reduced by a Fourier integral transform to the solution of a convolution-type integral equation of the first kind in a finite segment with a regular kernel. The exact inversion of the principal part of the corresponding integral operator is constructed in the class of functions with non-integrable singularities on the segment edges. An effective asymptotic solution is given for the integral equation under investigation in this class of functions in the whole range of variation of the characteristic parameter λ. The results obtained are verified numerically. Analogous integral equations were examined in /1, 2/. The mode of investigation is similar to that proposed in /3/.     

Kinetics of the thallic ion oxidation of olefins

The kinetics of oxidation of chalkone (phenyl styryl ketone) and cinnamaldehyde by T1 (III) acetate in aqueous acetic acid is of the first order in olefin and first order with respect to the oxidant. The parameters of the transition state theory have been computed. The rate of the reaction is strongly accelerated by increasing acid concentration. The reaction rate is also retarded by added sodium chloride and sodium acetate. The results have been interpreted in the light of the ionic mechanism considering T1 (OAc)₃ to be the active oxidant in aqueous acetic acid.     

Asymptotic solution of the first boundary-value problem of the theory of elasticity of the forced vibrations of an isotropic strip

The first boundary-value problem of the theory of elasticity of the forced vibrations of an isotropic strip is solved by an asymptotic method. The asymptotic form of the components of the stress tensor and the displacement vector, which differ in principle from the asymptotic form in the corresponding static problem, is established. All the required quantities in the inner problem are determined and the conditions for resonance to occur are established. The solution in the dynamic boundary layer is constructed and the fundamental (inner) and boundary solutions are matched.     

Studies on efficiencies of electrochemiluminescence of rubrene

The electrochemiluminescence efficiencies of rubrene system has been obtained by using the transient method in a variety of solvents. The efficiencies are in the range of 0·11 × 10^?3?4·1×10^?2. The mixed system efficiencies are less at least by an order of magnitude in all the solvents except in dimethylsulphoxide. The variation in efficiencies of the pure and mixed systems is explained on the basis of mechanistic differences. In the applied magnetic field, the electrochemiluminescence efficiency of the pure system increases by about 7% and of the mixed system by about 18–25%.     

Impact of the cost of the time resource on efficiency of economic processes

The objective of the paper is to simulate behavior of economic agents with a special emphasis on the use of the time resource in economic processes. The case studied is from the fishing industry. With simulations, the study analyzes the behavior of economic agents as they lead their processes through time. The paper estimates the value of time in a fishery operation, and shows that the time cost is essential in clarifying some phenomena in the economic behavior of agents. Among the conclusions is that the difference in economic efficiency between strong and weak ownership is due to difference in time costs. The secondary goal of the paper is to develop a simulation tool for analyzing a range of problems in the fishing industry, ranging from decision situations onboard fishing vessels to serving as a tool for fishery managers and legislators.     

Economical and ecological utility oriented analysis of the process of anaerobic digestion of waste waters

A problem which has been constantly emphasized is the creation of criteria adequate to characterize the complexity of ecological analysis. The objective of the present paper is to demonstrate the capabilities of multiattribute utility theory in difficult-to-formalize problems. The multiattribute utility and the proposed algorithms provide a logically and operationally tested method which includes value in complex ecological problems. The results obtained and the constructed utility functions should be accepted as an iterative stage in real investigations, rather than as complete research that offer a final decision. The value estimations of the decision maker are the basis for interest in a given ecological problem. But they are often not explicitly or consistently addressed in the real investigations. The proposed methods account for otherwise uninterpretable information. The constructed value function can be used for automatic computer control and monitoring of anaerobic waste water digestion, which could reveal a new potential from the practical point of view.     

碾压混凝土坝施工层面变形分析模型

针对碾压混凝土坝施工层面对大坝变形产生显著影响的问题,深入研究了施工层面的变化性质及规律,提出了层面不同阶段变形的模拟方法,建立了施工层面有厚度和无厚度分析模型,提出的模型能反映层面的弹性变形、衰减蠕变、不可逆变形以及加速蠕变等变形状态．实例分析表明:所提出的碾压混凝土坝施工层面有厚度和无厚度分析模型能较客观地模拟大坝的结构变化形态,尤其是施工层面有厚度分析模型较完整地模拟了层面的渐变规律,其计算结果与原位监测成果吻合较好．同时,提出的方法和建立的分析模型可推广应用于常规混凝土坝,特别是坝基内断层和夹层等变形规律的分析．