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.     

On fractional kinetic equations

The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with fractional integral equations. The results derived in this paper provide an extension of a result given by Haubold and Mathai in a recent paper (Haubold and Mathai, 2000). This revised version was published online in July 2006 with corrections to the Cover Date.     

Exact solutions: neutral and charged static perfect fluids with pressure

We show in this article that charged fluid with pressure derived by Bijalwan (Astrophys. Space. Sci. doi:, 2011a) can be used to model classical electron, quark, neutron stars and pulsar with charge matter, quasi black hole, white dwarf, super-dense star etc. Recent analysis by Bijalwan (Astrophys. Space. Sci., 2011d) that all charged fluid solutions in terms of pressure mimic the classical electron model are partially correct because solutions by Bijalwan (Astrophys. Space. Sci. doi:, 2011a) may possess a neutral counterpart. In this paper we characterized solutions in terms of pressure for charged fluids that have and do not have a well behaved neutral counter part considering same spatial component of metric e ^λ for neutral and charged fluids. We discussed solution by Gupta and Maurya (Astrophys. Space Sci. 331(1):135–144, 2010a) and solutions by Bijalwan (Astrophys. Space Sci. doi:, 2011b; Astrophys. Space Sci. doi:, 2011c; Astrophys. Space Sci., 2011d) such that charged fluids possess and do not possess a neutral counterpart as special cases, respectively. For brevity, we only present some analytical results in this paper.     

Asteroseismic modelling of the solar-like star β Hydri

We present the results of modelling the subgiant star β Hydri using seismic observational constraints. We have computed several grids of stellar evolutionary tracks using the Aarhus STellar Evolution Code (ASTEC, Christensen-Dalsgaard in Astrophys. Space Sci. 316:13, 2008a), with and without helium diffusion and settling. For those models on each track that are located at the observationally determined position of β Hydri in the Hertzsprung-Russell (HR) diagram, we have calculated the oscillation frequencies using the Aarhus adiabatic pulsation package (ADIPLS, Christensen-Dalsgaard in Astrophys. Space Sci. 316:113, 2008b). Applying the near-surface corrections to the calculated frequencies using the empirical law presented by Kjeldsen et al. (Astrophys. J. 683:L175, 2008), we have compared the corrected model frequencies with the observed frequencies of the star. We show that after correcting the frequencies for the near-surface effects, we have a fairly good fit for both l=0 and l=2 frequencies. We also have good agreement between the observed and calculated l=1 mode frequencies, although there is room for improvement in order to fit all the observed mixed modes simultaneously.     

A general relativistic rotating evolutionary universe—Part II

As a sequel to Berman (Astrophys. Space Sci., 2008b), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker’s metric has been employed with proper-time, in its standard applications; the generalised Gaussian metric implies in the use of a non-constant temporal metric coefficient modifying Robertson-Walker’s standard form. Experimental predictions are made.     

Anisotropic fluid distribution in higher dimensional general theory of relativity

We have obtained static and spherically symmetric self-gravitating solution of the field equations for anisotropic distribution of matter in higher- dimensional in the context of Einstein’s general theory of relativity. This work is an extension of the previous work of Hector Rago (Astrophys. Space Sci. 183:333, 1991) for four dimensional space-time. The solutions are matched to the analytical solutions for spherically symmetric self gravitating distribution of anisotropic matter obtained by Hector Rago (1991) for n=2.     

Increase of the mean Sun–Earth distance caused by a secular mass accumulation

Based on many planetary observations between the years 1971 and 2003, Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267–288, 2004) have estimated a rate of increase in the mean Sun-Earth distance of (15±4) m per century. Together with other anomalous observations in the solar system, this increase appears to be unexplained (Lämmerzahl et al. in Astrophys. Space Sci. Lib., vol. 349, pp. 75–101, 2008). We explain these findings by invoking a recently proposed gravitational impact model (Wilhelm et al. in Astrophys. Space Sci. 343:135–144, 2013) that implies a secular mass increase of all massive bodies. This allows us to formulate a quantitative understanding of the effect within the parameter range of the model with a mass accumulation rate of the Sun of (6.4±1.7)×10¹⁰ kg?s^?1.     

Comment on “Non-vacuum conformally flat space-times: dark energy”

Ibohal, Ishwarchandra and Singh (Ibohal et al., Astrophys. Space Sci. 335, 581, 2011) proposed a class of exact, non-vacuum and conformally flat solutions of Einstein’s equations whose stress tensor T _ab has negative pressure. We show that T _ab corresponds to an anisotropic fluid and the equation of state parameter seems not to be ω=?1/2. We consider the authors’ constant cannot be the mass of a test particle but is related to a Rindler acceleration of a spherical distribution of uniformly accelerating observers.     

Exact solutions: classical electron model

Rahaman et al. (Astrophys. Space. Sci. 331:191–197, 2010) discussed some classical electron models (CEM) in general relativity. Bijalwan (Astrophys. Space. Sci. 334:139–143, 2011) present a general exact solution of the Einstein-Maxwell equations in terms of pressure. We showed that charged fluid solutions in terms of pressure are not reducible to a well behaved neutral counter part for a spatial component of metrice ^λ . Hence, these solutions represent an electron model in general relativity. We illustrated solutions in terms of pressure briefly with de-Sitter equation of state and charged analogues of Kohler Chao interior solution as a special cases.     

Evidences to the pulse like origin of double spicules based on Hinode/SOT observations

Motivated by the recent work of Rastkar et al. (in Astrophys. Space Sci. 337:487, 2012) the present study has attempted to study the role of f(G) gravity in the emergent universe. Different energy conditions are examined for the effective energy density and violation of strong energy condition is observed. Also, the behavior of the equation of state parameter is studied for the effective energy density and dark energy density. It is found that the equation of state parameter behaves like phantom in both of the cases.     

Implementation and Comparison of Acoustic Travel-Time Measurement Procedures for the Solar Dynamics Observatory/Helioseismic and Magnetic Imager Time?–?Distance Helioseismology Pipeline

The Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO) satellite is designed to produce high-resolution Doppler-velocity maps of oscillations at the solar surface with high temporal cadence. To take advantage of these high-quality oscillation data, a?time?–?distance helioseismology pipeline (Zhao et al., Solar Phys. submitted, 2010) has been implemented at the Joint Science Operations Center (JSOC) at Stanford University. The aim of this pipeline is to generate maps of acoustic travel times from oscillations on the solar surface, and to infer subsurface 3D flow velocities and sound-speed perturbations. The wave travel times are measured from cross-covariances of the observed solar oscillation signals. For implementation into the pipeline we have investigated three different travel-time definitions developed in time?–?distance helioseismology: a Gabor-wavelet fitting (Kosovichev and Duvall, SCORE’96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997), a?minimization relative to a reference cross-covariance function (Gizon and Birch, Astrophys. J. 571, 966, 2002), and a linearized version of the minimization method (Gizon and Birch, Astrophys. J. 614, 472, 2004). Using Doppler-velocity data from the Michelson Doppler Imager (MDI) instrument onboard SOHO, we tested and compared these definitions for the mean and difference travel-time perturbations measured from reciprocal signals. Although all three procedures return similar travel times in a quiet-Sun region, the method of Gizon and Birch (Astrophys. J. 614, 472, 2004) gives travel times that are significantly different from the others in a magnetic (active) region. Thus, for the pipeline implementation we chose the procedures of Kosovichev and Duvall (SCORE’96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997) and Gizon and Birch (Astrophys. J. 571, 966, 2002). We investigated the relationships among these three travel-time definitions, their sensitivities to fitting parameters, and estimated the random errors that they produce.     

Reply to: “Comment on the paper ‘On the triangular libration points in photogravitational restricted three-body problem with variable mass’’’ by Varvoglis, H. and Hadjidemetriou, J.D.

Recently Varvoglis and Hadjidemetriou (Astrophys. Space Sci. doi:, 2012; hereafter referred to as paper VH) have raised two points concerning the model of the restricted three-body problem with variable mass presented in our paper (Zhang et al. in Astrophys. Space Sci. 337:107, 2012; hereafter referred to as paper ZZX) and made intensive investigations of this model. These points and investigations are very useful and here we provide some explanation and supplementary specification regarding the model presented in the paper ZZX.     

An electrodynamic model of the solar wind interaction with the ionospheres of Mars and Venus

The electrodynamic model for the solar wind interaction with non-magnetic planets. (Cloutier and Daniell, Planet. Space Sci.21, 463, 1973; Daniell and Cloutier, Planet. Space Sci.25, 621, 1977) is modified to include the effects of non-ohmic currents in the upper ionosphere. The model is then used to calculate convection patterns induced by the solar wind in the ionospheres of Mars and Venus. For Mars the observations of the neutral mass spectrometer or Vikings 1 and 2 provided the neutral atmosphere. Model calculations reproduced the retarding potential analyzer data and indicate that the ionosphere above about 200 km is probably controlled by convection rather than chemistry or diffusion. For Venus a model atmosphere based on Dickenson and Ridley, J. Atmos. Sci.32, 1219 (1975) and Mayr et al., J. geophys. Res.83, 4411 (1978) was used. The resulting model calculations were compared to radio occultation data from Mariners 5 and 10 and Venera 9 which represent extremes in the variability of the upper Cytherean ionosphere. The model calculations are shown to fall within this variation. These results represent the state of the theory immediately prior to the Pioneer-Venus encounter.     

Closed form Vaidya-Tikekar type charged fluid spheres with pressure

Recently, Bijalwan (Astrophys. Space Sci. doi:, 2011) discussed all important solutions of charged fluid spheres with pressure and Gupta et al. (Astrophys. Space Sci. doi:, 2010) found first closed form solutions of charged Vaidya-Tikekar (V-T) type super-dense star. We extend here the approach evolved by Bijalwan (Astrophys. Space Sci. doi:, 2011) to find all possible closed form solutions of V-T type super-dense stars. The existing solutions of Vaidya-Tikekar type charged fluid spheres considering particular form of electric field intensity are being used to model massive stars. Infact at present maximum masses of the star models are found to be 8.223931M _Θ and 8.460857M _Θ subject to ultra-relativistic and non-relativistic conditions respectively. But these stars with such are large masses are not well behaved due to decreasing velocity of sound in the interior of star. We present new results concerning the existence of static, electrically charged perfect fluid spheres that have a regular interior. It is observed that electric intensity used in this article can be used to model superdense stars with ultrahigh surface density of the order 2×10¹⁴ gm/cm³ which may have maximum mass 7.26368240M _Θ for ultra-relativistic condition and velocity of sound found to be decreasing towards pressure free interface. We solve the Einstein-Maxwell equations considering a general barotropic equation of state with pressure. For brevity we don’t present a detailed analysis of the derived solutions in this paper.     

Time-resolved high-resolution spectroscopy of the pulsating sdB star QQ Vir (PG1325+101)

In this work, a standard solar model is computed with new reaction rates that take into account the exact astrophysical S-factor, S _e for the ³He(³He,2p)⁴He, ³He(α,γ)⁷Be and ⁷Be(p,γ)⁸B reactions. The exact S-factor which is valid for all energies is an improved version of the S-factor in the lower-energy approximation (Yusof and Kassim in Astrophys. Space Sci., 2009b). The effects of these new nuclear reaction rates on the solar neutrino fluxes are then discussed by comparing this model to a solar model computed with the standard NACRE reaction rates (Angulo et al. in Nucl. Phys. A. 656:3, 1999). The new reaction rates are found to decrease the neutrinos flux for ⁷Be and ⁸B by about 6% and 16%, respectively. A solar model is also computed with the reaction rates of the LUNA collaboration for ¹⁴N(p,γ)¹⁵O (Formicola et al. in Phys. Lett. B 591:61, 2004). In this case, a clear decrease of the fluxes for ¹³N and ¹⁵O is observed to be in good agreement with previous results (see e.g. Bahcall et al. in Astrophys. J. 621:L88, 2005).     

New face in the spectral behavior of Capella in the UV

We present low and high resolution ultraviolet spectra of the Capella spectroscopic binary system from the observations taken by the International Ultraviolet Explorer (IUE) during the period between 1978–1990 and 1978–1995. Thirteen profile of Capella showing variations of line fluxes at different orbital phases are presented. This paper focuses on the C IV emission line at 1550 Å produced in the transition region of the secondary star and Mg II emission lines at 2800 Å produced in the stellar chromosphere of the secondary star by calculating spectral line fluxes. Our results show that there are significant variations of line fluxes with time. These spectral variations are similar to that found in the EUV by Dupree and Brickhouse (in Int. Astron. Union Symp. 176P:184D, 1995) in the UV for H 1 Ly?α by Ayres et al. (in Astrophys. J. 402:710A, 1993), and in the near IR by Katsova (in Astrophys. Space Sci. 252:427K, 1997). We attribute these variations in line fluxes to the variations of both density and temperature in the line emitting regions as a result of the intermediate-scale magnetic fields responsible for stellar activity leading to these spectral variations.     

Joule heating of Io's ionosphere by unipolar induction currents

The unexpectedly large scale height of Io's ionosphere (Kliore, A., et al., 1975, Icarus24, 407–410) together with the relatively large molecular weight of the likely principal constituent, SO₂ (Pearl, J., et al., 1979, Nature280, 755–758), suggest a high ionospheric temperature. Electrical induction in Io's ionosphere due to the corotating plasma bound to the Jovian magnetosphere is one possible source for attainment of such high temperatures. Accordingly, unipolar induction models were constructed to calculate ionospheric joule heating numerically. Heating rates produced by highly simplified models lie in the range 10^?9 to 10^?8 W/m³. These heating rates are lower than those determined from uv photodissociative heating models (Kumar, S., 1980, Geophys. Res. Lett.7, 9–12) at low levels in the ionosphere but are comparable in the upper ionosphere. The low electrical heating rate throughout most of the ionosphere is due to the power limitation imposed by the Alfvén wings which complete the electrical circuit (Neubauer, F.M., 1980, J. Geophys. Res.85, 1171–1178). Contrary to the pre-Voyager calculations of Cloutier, P. A., et al. (1978, Astrophys. Space Sci.55, 93–112), our numerical results show that the J × B force density due to unipolar induction currents in the ionosphere is much less than the gravitational force density when the combined mass of the neutral species is included. The binding and coupling of the ionosphere is principally due to the relatively dense (possibly localized) neutral SO₂ atmosphere. In regions where the ions and neutrals are collisionally coupled the ionosphere will not be stripped off by the J × B forces. However at a level above that (to which the ions move by diffusion only) the charged species would be removed. Thus there appears to be no need to postulate the existence of an intrinsic Ionian magnetic field as suggested by Kivelson, M. G., et al. (79, Science 205, 491–493) and Southwood, S. J., et al. (1980, J. Geophys. Res., in press) in order to retain the observed ionosphere.     

Reconstructing CME Structures from IPS Observations Using a Phenomenological Model

We present an extension of the Tappin?–?Howard (TH) phenomenological model (Tappin and Howard, Space Sci. Rev. 147, 55, 2009) for coronal mass ejection reconstruction to use interplanetary scintillation g-map data. The necessary changes to the model are discussed. We then use the modified model to reconstruct two major interplanetary disturbances observed using the Cambridge 3.6 ha Array in September 1980. We find that despite the lower cadence of IPS observations compared with white-light imagers, a consistent reconstruction can be generated which is in agreement with in-situ measurements and solar observations.     

An electrodynamic model of electric currents and magnetic fields in the dayside ionosphere of Venus

The electric current configuration induced in the ionosphere of Venus by the interaction of the solar wind has been calculated in previous papers (Cloutier and Daniell, Planet. Space Sci. 21, 463, 1973; Daniell and Cloutier. Planet. Space Sci.25, 621, 1977; Cloutier and Daniell, Planet. Space Sci.27, 1111, 1979) for average steady-state solar wind conditions and interplanetary magnetic field. This model is generalized to include the effects of (a) plasma depletion and magnetic field enhancement near the ionopause, (b) velocity-shear-induced MHD instabilities of the Kelvin-Helmholtz type within the ionosphere, and (c) variations in solar wind parameters and interplanetary magnetic field. It is shown that the magnetic field configuration resulting from the model varies in response to changes in solar wind and interplanetary field conditions, and that these variations produce magnetic field profiles in excellent agreement with those seen by the PIONEER-VENUS Orbiter. The formation of “flux-ropes” by the Kelvin-Helmholtz instability is shown to be a natural consequence of the model, with the spatial distribution and size of the flux-ropes determined by the magnetic Reynolds number.     

Eigenfrequencies of rotationally and tidally distorted white dwarf models of stars

In the present paper we have studied the eigenfrequencies of small adiabatic barotropic pseudo-radial and nonradial modes of oscillations of the white dwarf models of rotating stars in binary systems. In this work the methodology of Mohan and Saxena (in Astrophys. Space Sci. 113:155, 1985) has been used that utilizes the averaging technique of Kippenhahn and Thomas (in Proc. IAU Colloq., vol. 4, p. 20, 1970) and certain results on Roche equipotential as that given by Kopal (in Advances in Astronomy and Astrophysics, Academic Press, 1972). The objective of this study is to investigate the effects of rotation and/or tidal distortion on the periods of oscillations of rotationally and/or tidally distorted white dwarf models of stars assuming it to be the primary component of the binary system and rotating uniformly. The results of present study show that the eigenfrequencies (both radial and nonradial modes) of the rotationally distorted and rotationally and tidally distorted white dwarf model of stars in binary systems tend to decrease under the influence of rotational distortions and rotational and tidal distortions, respectively. However, results are contrary for tidally distorted white dwarf model of stars.