Study of the Diurnal Variation of Cosmic Rays during Different Phases of Solar Activity

The pressure-corrected hourly counting rate data of ground-based super neutron monitor stations, situated in different latitudes, have been employed to study the characteristics of the long-term variation of cosmic-ray diurnal anisotropy for a long (44-year) period (1965?–?2008). Some of these super neutron monitors are situated in low latitudes with high cutoff rigidity. Annual averages of the diurnal amplitudes and phases have been obtained for each station. It is found that the amplitude of the diurnal anisotropy varies with a period of one solar activity cycle (11 years), whereas the diurnal phase varies with a period of 22 years (one solar magnetic cycle). The average diurnal amplitudes and phases have also been calculated by grouping the days on the basis of ascending and descending periods of each solar cycle (Cycles 20, 21, 22, and 23). Systematic and significant differences are observed in the characteristics of the diurnal variation between the descending periods of the odd and even solar cycles. The overall vector averages of the descending periods of the even solar cycles (20 and 22) show significantly smaller diurnal amplitudes compared to the vector averages of the descending periods of the odd solar cycles (21 and 23). In contrast, we find a large diurnal phase shift to earlier hours only during the descending periods of even solar cycles (20 and 22), as compared to almost no shift in the diurnal phase during the descending periods of odd solar cycles. Further, the overall vector average diurnal amplitudes of the ascending period of odd and even solar cycles remain invariant from one ascending period to the other, or even between the even and odd solar cycles. However, we do find a significant diurnal phase shift to earlier hours during the ascending periods of odd solar cycles (21 and 23) in comparison to the diurnal phase in the ascending periods of even solar cycles (20 and 22).     

Uncertainty propagation in orbital mechanics via tensor decomposition

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker–Planck equation (FPE) is defined on a relatively high dimensional (6-D) state–space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the \(x-y-z\) subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors’ knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral (“super-fast”) convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.     

The general class of Bianchi cosmological models with viscous fluid and particle creation in Brans-Dicke theory

This paper deals with the general class of Bianchi cosmological models with bulk viscosity and particle creation described by full causal thermodynamics in Brans-Dicke theory. We discuss three types of average scale-factor solutions for the general class of Bianchi cosmological models by using a special law for the deceler- ation parameter which is linear in time with a negative slope. The exact solutions to the corresponding field equations are obtained in quadrature form and solutions to the Einstein field equations are obtained for three different physically viable cosmologies. All the physical parameters are calculated and discussed in each model.     

Hidden mass in the solar neighborhood

It is suggested that the minimum mass of a star at the time of its formation is approximately 0.01M . Making use of this fact and the stellar mass functionF(M) M ^–, it is found that the hidden mass (or the missing mass) in the solar neighborhood may be explained by the presence of a large number of invisible stars of very low mass (0.01M M<0.07M ).     

Kaluza-Klein dark energy cosmological model in scale Co-variant Theory of Gravitation

A five dimensional Kaluza-Klein dark energy model with variable EoS parameter is investigated in the scale co-variant theory of gravitation proposed by Canuto et al. (in Phys. Rev. 39:429, 1977) in a five dimensional Kaluza-Klein space-time in the presence of perfect fluid source. Using the special law of variation for Hubble’s parameter proposed by Berman (in Nuovo Cimento B 74:183, 1983), we have obtained a determinate solution which represents a dark energy cosmological model in the theory. We have also used the result that the scalar expansion is proportional to shear scalar of the space-time. It is observed that the EoS parameter, skewness parameter in the model turn out to be functions of cosmic time. Some physical and Kinematical properties of the model are also discussed.     

Core-envelope models for massive fluid spheres

The solution of equation of state corresponding to equality =₃ gives non-terminating solutions for isothermal neutron star cores. Hence, for this equality, core-envelope models have been developed by taking another equation of state, corresponding to the condition ₃, in the envelope. Various static, pulsational, and rotational parameters pertaining to neutron star models are calculated. These models are gravitationally bound and stable for radial perturbations and slow rotations.     

Some Bianchi-type cosmological models in a new scalar-tensor theory

Bianchi type I, III, V, VI₀, and Kantowski-Sachs type models have been investigated in a scalar tensor theory developed by Saez and Ballester (1985) and Saez (1985). The dynamical behaviour of the models has also been analyzed.     

Bianchi II,VIII, and IX viscous fluid cosmology

In this paper we study the exact solutions for a viscous fluid distribution in Bianchi II, VIII, and IX models. The metric is simplified by assuming a relationship between the coefficients of the metric tensor. Solutions are obtained in two special cases: in one an additional assumption is made where the matter density and the expansion scalar have a definite relation and in the other a barotropic equation of state of the formp= is assumed. While the Bianchi II solutions are already found in the literature the other two classes of solutions are apparently new.     

The magnetohydrodynamics of stellar structures

The equation governing the equilibrium of a centrally-symmetric, self-gravitating distribution of matter is obtained by assuming that matter is described by magnetofluid and it is shown that the equation of stellar structure described by an ideal fluid is recovered when magnetic fieldh is vanishing     

Empirical estimate of p-mode frequency shift for solar cycle 23

We have obtained empirical relations between the p-mode frequency shift and the change in solar activity indices. The empirical relations are determined on the basis of frequencies obtained from BBSO and GONG stations during solar cycle 22. These relations are applied to estimate the change in mean frequency for the cycle 21 and 23. A remarkable agreement between the calculated and observed frequency shifts for the ascending phase of cycle 23, indicates that the derived relations are independent of epoch and do not change significantly from cycle to cycle. We propose that these relations could be used to estimate the shift in p-mode frequencies for past, present and future solar activity cycles, if the solar activity index is known. The maximum frequency shift for cycle 23 is estimated to be 265±90 nHz, corresponding to a predicted maximum smoothed sunspot number 118.1±35.