Solution of Generalized Fractional Reaction-Diffusion Equations

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.     

Fractional Reaction-Diffusion Equations

In a series of papers, Saxena et al. (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen et al. (1999) for anomalous diffusion and del-Castillo-Negrete et al. (2003) for reaction-diffusion systems with Lévy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.     

A Certain Class of Laplace Transforms with Applications to Reaction and Reaction-Diffusion Equations

A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables and the concept of Laplacianness in statistics, α-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations.     

Nonlinear Interactions Between Kinetic Alfvén and Ion-Sound Waves

The resonant interaction between kinetic Alfvén and ion-acoustic waves is considered using the Hall-MHD theory. The results of previous authors are generalized to cover both finite Larmor radius as well as the ideal MHD results. It is found that the three-wave coupling is strongest when the wavelength is comparable to the ion-sound gyroradius. Applications of our work to weak turbulence theories as well as to the heating of the solar corona are pointed out.     

Acoustic-Gravity Waves from Bolide Sources

We have developed a new approach to modeling the acoustic-gravity wave (AGW) radiation from bolide sources. This first effort involves entry modeling of bolide sources that have available satellite data through procedures developed in ReVelle (Earth Moon Planets 95, 441–476, 2004a; in: A. Milani, G. Valsecchi, D. Vokrouhlicky (eds) NEO Fireball Diversity: Energetics-based Entry Modeling and Analysis Techniques, Near-earth Objects: Our Celestial Neighbors (IAU S236), 2007b). Results from the entry modeling are directly coupled to AGW production through line source blast wave theory for the initial wave amplitude and period at (at 10 blast wave radii and perpendicular to the trajectory). The second effort involves the prediction of the formation and or dominance of the propagation of the atmospheric Lamb, edge-wave composite mode in a viscous fluid (Pierce, J. Acoust. Soc. Amer. 35, 1798–1807, 1963) as a function of the source energy, horizontal range and source altitude using the Lamb wave frequency that was deduced directly during the entry modeling and that is used as a surrogate for the source energy. We have also determined that Lamb wave production by bolides at close range decreases dramatically as either the source energy decreases or the source altitude increases. Finally using procedures in Gill (Atmospheric-Ocean Dynamics, 1982) and in Tolstoy (Wave Propagation, 1973), we have analyzed two simple dispersion relationships and have calculated the expected dispersion for the Lamb edge-wave mode and for the excited, propagating internal acoustic waves. Finally, we have used the above formalism to fully evaluate these techniques for four large bolides, namely: the Tunguska bolide of June 30, 1908; the Revelstoke bolide of March 31, 1965; the Crete bolide of June 6, 2002 and the Antarctic bolide of September 3, 2004. Due to page limitations, we will only present results in detail for the Revelstoke bolide.     

Coronal Shock Waves,EUV Waves,and Their Relation to CMEs. II. Modeling MHD Shock Wave Propagation Along the Solar Surface,Using Nonlinear Geometrical Acoustics

We model the propagation of a coronal shock wave, using nonlinear geometrical acoustics. The method is based on the Wentzel–Kramers–Brillouin (WKB) approach and takes into account the main properties of nonlinear waves: i) dependence of the wave front velocity on the wave amplitude, ii) nonlinear dissipation of the wave energy, and iii) progressive increase in the duration of solitary shock waves. We address the method in detail and present results of the modeling of the propagation of shock-associated extreme-ultraviolet (EUV) waves as well as Moreton waves along the solar surface in the simplest solar corona model. The calculations reveal deceleration and lengthening of the waves. In contrast, waves considered in the linear approximation keep their length unchanged and slightly accelerate.     

Gravitational Waves and Gravitational-wave Sourcestwo

The recent discovery of gravitational-wave burst GW150914 marks the coming of a new era of gravitational-wave astronomy, which provides a new window to study the physics of strong gravitational field, extremely massive stars, extremely high energy processes, and extremely early universe. In this article, we introduce the basic characters of gravitational waves in the Einstein's general relativity, their observational effects and main generation mechanisms, including the rotation of neutron stars, evolution of binary systems, and spontaneous generation in the inflation universe. Different sources produce the gravitational waves at quite different frequencies, which can be detected by different methods. In the lowest frequency range (f < 10^?15 Hz), the detection is mainly dependent of the observation of B-mode polarization of cosmic microwave background radiation. In the middle frequency range (10^?9 < f < 10^?6 Hz), the gravitational waves are detected by analyzing the timing residuals of millisecond pulsars. And in the high frequency range (10 ? 4 < f < 10⁴ Hz), they can be detected by the space-based and ground-based laser interferometers. In particular, we focus on the main features, detection methods, detection status, and the future prospects for several important sources, including the continuous sources (e.g., the spinning neutron stars, and stable binary systems), the burst sources (e.g., the supernovae, and the merge of binary system), and the stochastic backgrounds generated by the astrophysical and cosmological process. In addition, we forecast the potential breakthroughs in gravitational-wave astronomy in the near future, and the Chinese projects which might involve in these discoveries.     

Nonlinear Drift–Alfvén Waves in Relativistically Hot Multicomponent Plasmas and Their Relevance to the Fine Structure of Pulsar Radioemissions

A set of equations which governs the nonlinear dynamics of drift–Alfvén waves in an inhomogeneous relativistic electron-positron plasma with a small admixture of heavy ions is derived. It is shown that these equations admit a stationary solution in the form of a two-scale dipolar vortex. The conditions for the existence of such structures are discussed. It is shown that the presence of heavy ions in are lativistic electron-positron plasma significantly reinforces the spatial localization of the solitary waves which results in the appearance of exponentially localized vortex structures. It is also shown that the small scale micropulse structure of radio pulsar radiation (e.g., in the case of the pulsar PSR 0905+08) can be interpreted as a signature of the vortex structure in the outer region of the pulsar polar magnetosphere. This revised version was published online in July 2006 with corrections to the Cover Date.     

天体物理中的重力波和磁重力波

本文简要综述重力波和磁重力波在各种天体物理场合中的应用 ,我们描述在具有开放径向磁场的恒星大气各种磁流体波之间的相互转换过程 ,强调磁重力波被束缚在恒星冕内的可能性 ,并探讨恒星内部高频的声波模 (p -模 )被低频的重力波模 (g -模 )所调制的过程 ,一旦有了足够长时间未间断高质量的日震数据 ,太阳内部的重力波模对声波模的调制效应—即每一个分立声波模的频率精细结构—则可被用来寻找深陷于太阳内部的重力波模或进一步独立地约束重力波模的振幅上限     

Completely Integrable Systems Connected with Lie Algebras

In a recent paper Ballersteros and Ragnisco (1998) have proposed a new method of constructing integrable Hamiltonian systems. A new class of integrable systems may be devised using the following sequence: , where A is a Lie algebra is a Lie–Poisson structure on R ₃, C is a Casimir for is a reduced Poisson bracket and (A, ▵) is a bialgebra. We study the relation between a Lie-Poisson stucture Λ and a reduced Poisson bracket , which is a key element in using the Lie algebra A to constructing this sequence. New examples of Lie algebras and their related integrable Hamiltonian systems are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

Analytical treatment of air drag and earth oblateness effects upon an artificial satellite

A development of an analytical solution for the motion of an artificial Earth satellite subject to the combined effects of Earth gravity and air drag is presented. The atmospheric model takes into account a linear variation of the density scale height with altitude, the rotation and the oblateness of the atmosphere. The perturbation theory is based upon Lie transforms. The secular and long-periodic terms as well as the short-periodic effects are included in the theory which is valid for small to moderate eccentricities and for all values of the inclination.Belgian National Fund for Scientific Research     

电离层与电波传播路径

电离层从猜想到证实完全是无线电技术发展的结果。通过地面无线电探测和火箭、卫星的空间探测、证实了Ｃｈａｐｍａｎ的理论。由于太阳紫外线，Ｘ射线辐射致使高空上层大气电离。电离层介质是电子、正负离子和中性粒子全体的混合物。它们构成了地磁场中磁离子介质。本文根据磁离子理论，研究了电离层中等离子体的频率特性，从而解释了Ｄ、Ｅ、Ｆ１和Ｆ２层的电波反射特性。最后计算了陕西天文台至云南天文台电离层波导的传播时延，获得了有意义的结果。     

引力波理论和实验的新进展

引力波的存在是爱因斯坦在广义相对论理论中提出的一个重要预言．由于目前技术水平的限制,无法在实验室产生足以被探测到的引力波,因此宇宙中大量的大质量剧烈活动的天体成为科学家研究引力波的首选,从而诞生了引力波天文学．引力波探测将开启研究宇宙的新窗口,是继电磁辐射、宇宙线和中微子探测后探索宇宙奥秘的又一重要手段,对天文学研究有着极为重要的意义.新一代应用了高灵敏度的迈克耳逊干涉仪装置的长基线引力波探测仪正在建造中．该综述从引力波理论出发,阐述了目前研究较多的可探测引力波源,给出了目前观测上的最新进展,并展望了今后的发展前景．     

Velocities of Magneto-Elastic and Magneto-Electron Waves in Dark Molecular Clouds

We present analytic and numerical estimates for group velocity of wave motions in two models of cold interstellar medium presumably constituting the interior of cores of magnetically supported dark molecular clouds. Namely, in the model of gas-based ferrocolloidal soft matter and in the model of noncompensated electron magnetoplasma. The predictions of these models are given in juxtaposition with data on recent Zeeman measurements of the molecular linewidths detected from dark central regions of star-forming interstellar clouds.     

Calculating and Testing Nonlinear Force-Free Fields

Improvements to an existing method for calculating nonlinear force-free magnetic fields (Wheatland, Solar Phys. 238, 29, 2006) are described. In particular a solution of the 3-D Poisson equation using 2-D Fourier transforms is presented. The improved nonlinear force-free method is demonstrated in application to linear force-free test cases with localized nonzero values of the normal component of the field in the boundary. These fields provide suitable test cases for nonlinear force-free calculations because the boundary conditions involve localized nonzero values of the normal components of the field and of the current density, and because (being linear force-free fields) they have more direct numerical solutions. Despite their simplicity, fields of this kind have not been recognized as test cases for nonlinear methods before. The examples illustrate the treatment of the boundary conditions on current in the nonlinear force-free method, and in particular the limitations imposed by field lines that connect outside of the boundary region.     

Triple and Multiple Systems

The triple systems display several interesting effects; and are also important for understanding the origin and evolution of binaries. Namely mutual inclination of two orbits, changes of observed inclination, and problems with the third light will be discussed in this contribution.     

Fine Structure of Solar Radio Bursts Observed at Decametric and Hectometric Waves

The analysis of WIND/WAVES RAD2 spectra with fine structure in the form of different fibers in 14 events covering 1997?–?2005 is carried out. A splitting of broad bands of the interplanetary (IP) type II bursts into narrow band fibers of different duration is observed. The instantaneous-frequency bandwidth of fibers is stable: 200?–?300 kHz for slow-drifting fibers in type II bursts, and 700?–?1000 kHz for fast-drifting fibers in type II?+?IV (continuum). Intermediate drift bursts (IDB or fiber bursts) and zebra patterns with variable frequency drift of stripes, typical for the metric range, were not found. Comparison of spectra with the Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph (SOHO/LASCO C2) images shows a connection of the generation of the fiber structures with the passage of shock fronts through narrow jets in the wake of Coronal Mass Ejections (CME). Therefore the most probable emission mechanism of fibers in IP type II bursts appears to be resonance transition radiation (RTR) of fast particles at the boundary of two media with different refractive indices. The same mechanism is also valid for striae in the type III bursts. Taking into account a high-density contrast in the CME wake and the actually observed small-scale inhomogeneities, the effectiveness of the RTR mechanism in IP space must be considerably higher than in the meter or decimeter wavelengths. For the most part the fibers in the type IV continuum at frequencies of 14?–?8 MHz were seen as the direct expansion of similar fine structure (as fibers or “herringbone” structure) in the decametric range observed with the Nançay and IZMIRAN spectrographs.     

Waves in Jupiter's atmosphere observed by the Cassini ISS and CIRS instruments

The Cassini Imaging Science Subsystem (ISS) and Composite Infrared Spectrometer (CIRS) reported a North Equatorial Belt (NEB) wave in Jupiter's atmosphere from optical images [Porco, C.C., and 23 colleagues, 2003. Science 299, 1541-1547] and thermal maps [Flasar, F.M., and 39 colleagues, 2004. Nature 427, 132-135], respectively. The connection between the two waves remained uncertain because the two observations were not simultaneous. Here we report on simultaneous ISS images and CIRS thermal maps that confirm that the NEB wave shown in the ISS ultraviolet (UV1) and strong methane band (MT3) images is correlated with the thermal wave in the CIRS temperature maps, with low temperatures in the CIRS maps (upwelling) corresponding to dark regions in the UV1 images (UV-absorbing particles) and bright regions in the MT3 images (high clouds and haze). The long period of the NEB wave suggests that it is a planetary (Rossby) wave. The combined observations from the ISS and CIRS are utilized to discuss the vertical and meridional propagation of the NEB wave, which offers a possible explanation for why the NEB wave is confined to specific latitudes and altitudes. Further, the ISS UV1 images reveal a circumpolar wave centered at 48.5° S (planetocentric) and probably located in the stratosphere, as suggested by the ISS and CIRS observations. The simultaneous comparison between the ISS and CIRS also implies that the large dark oval in the polar stratosphere of Jupiter discovered in the ISS UV1 images [Porco, C.C., and 23 colleagues, 2003. Science 299, 1541-1547] is the same feature as the warm regions at high northern latitudes in the CIRS 1-mbar temperature maps [Flasar, F.M., and 39 colleagues, 2004. Nature 427, 132-135]. This comparison supports a previous suggestion that the dark oval in the ISS UV1 images is linked to auroral precipitation and heating [Porco, C.C., and 23 colleagues, 2003. Science 299, 1541-1547].     

Nonlinear models of pulsation and mass loss

We briefly discuss the current status of our radiation-hydrodynamical models of pulsation in various stellar objects and of dust-driven mass loss in LPVs. We emphasize the importance of a future combined modelling of pulsation and mass loss in AGB stars which has to be based on reliable physical and numerical methods.