Revisiting Noether gauge symmetry for F(R) theory of gravity

Noether gauge symmetry for F(R) theory of gravity has been explored recently. The fallacy is that, even after setting gauge to vanish, the form of F(R)∝R ⁿ (where n≠1 is arbitrary) obtained in the process, has been claimed to be an outcome of gauge Noether symmetry. On the contrary, earlier works proved that any nonlinear form other than $F(R) \propto R^{\frac{3}{2}}$ is obscure. Here, we show that, setting gauge term zero, Noether equations are satisfied only for n=2, which again does not satisfy the field equations. Thus, as noticed earlier, the only form that Noether symmetry admits is $F(R) \propto R^{\frac{3}{2}}$ . Noether symmetry with non-zero gauge has also been studied explicitly here, to show that it does not produce anything new.     

Five dimensional Bianchi type-V cosmological models described by a binary mixture of perfect fluid and dark energy with Λ-term

Some recent experimental observations have been shown that inclusion of electron collisions damping in inertial Alfvén wave (IAW) dynamics may be important for laboratory as well as space plasmas. This paper presents the numerical simulation of model equation governing the nonlinear dynamics of IAW in low-beta plasmas. When the nonlinearity arises due to the ponderomotive force and Joule heating driven density perturbations, the model equation turns out to be a modified nonlinear Schr?dinger equation (MNLS). The electron collisions are introduced only in the electron momentum equation. The damped localized structures of IAW with sidebands are obtained. Also, the effect of collisional damping on power spectra of magnetic fluctuations with different scaling laws has been studied. These turbulent structures may be responsible for particle acceleration in laboratory and space plasmas.     

Investigation on spectral character of ELF electromagnetic radiations during Leonid 2009 meteor shower

The problem of solitary electron acoustic (EA) wave propagation in a plasma with nonthermal hot electrons featuring the Tsallis distribution is addressed. A physically meaningful nonextensive nonthermal velocity distribution is outlined. It is shown that the effect of the nonthermal electron nonextensivity on EA waves can be quite important. Interestingly, we found that the phase speed of the linear EA mode increases as the entropic index q decreases. This enhancement is weak for q>1, and significant for q<1. For a given nonthermal state, the minimum value of the allowable Mach numbers is lowered as the nonextensive nature of the electrons becomes important. This critical limit is shifted towards higher values as the nonthermal character of the plasma is increased. Moreover, our plasma model supports rarefactive EA solitary waves the main quantities of which depend sensitively on q. This dependency (for q>1) becomes less noticeable as the nonthermal parameter decreases. Nevertheless, decreasing α yields for q<0 a different result, a trend which may be attributed to the functional form of the nonthermal nonextensive distribution. Our study (which is not aimed at putting the ad hoc Cairns distribution onto a more rigorous foundation) suggests that a background electron nonextensivity may influence the EA solitons.     

GPS-TEC variations during low solar activity period (2007–2009) at Indian low latitude stations

The paper is based on the ionospheric variations in terms of vertical total electron content (VTEC) for the low solar activity period from May 2007 to April 2009 based on the analysis of dual frequency signals from the Global Positioning System (GPS) satellites recorded at ground stations Varanasi (Geographic latitude 25°16′ N, Longitude 82°59′ E), situated near the equatorial ionization anomaly crest and other two International GNSS Service (IGS) stations Hyderabad (Geographic latitude 17°20′ N, longitude 78°30′ E) and Bangalore (Geographic latitude 12°58′ N, longitude 77°33′ E) in India. We describe the diurnal and seasonal variations of total electron content (TEC), and the effects of a space weather related event i.e. a geomagnetic storm on TEC. The mean diurnal variation during different seasons is brought out. It is found that TEC at all the three stations is maximum during equinoctial months (March, April, September and October), and minimum during the winter months (November, December, January and February), while obtaining intermediate values during summer months (May, June, July and August). TEC shows a semi-annual variation. TEC variation during geomagnetic quiet as well as disturbed days of each month and hence for each season from May 2007 to April 2008 at Varanasi is examined and is found to be more during disturbed period compared to that in the quiet period. Monthly, seasonal and annual variability of GPS-TEC has been compared with those derived from International Reference Ionosphere (IRI)-2007 with three different options of topside electron density, NeQuick, IRI01-corr and IRI 2001. A good agreement is found between the GPS-TEC and IRI model TEC at all the three stations.     

Solution of Lane-Emden type equations using Bernstein operational matrix of differentiation

The purpose of this paper is to propose an efficient numerical method for solving Lane-Emden type equations arising in astrophysics using Bernstein polynomials. First Bernstein operational matrix of differentiation is derived using Bernstein polynomials and then applied to solve the linear and nonlinear differential equations of Lane-Emden type. Some illustrative examples are given to demonstrate the efficiency and validity of the proposed algorithm.     

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).     

Testing isotropy of cosmic microwave background radiation

We introduce new symmetry-based methods to test for isotropy in cosmic microwave background (CMB) radiation. Each angular multipole is factored into unique products of power eigenvectors, related multipoles and singular values that provide two new rotationally invariant measures mode by mode. The power entropy and directional entropy are new tests of randomness that are independent of the usual CMB power. Simulated Galactic plane contamination is readily identified. The ILC– WMAP data maps show seven axes well aligned with one another and the direction Virgo. Parameter free statistics find 12 independent cases of extraordinary axial alignment, low power entropy, or both having 5 per cent probability or lower in an isotropic distribution. Isotropy of the ILC maps is ruled out to confidence levels of better than 99.9 per cent, whether or not coincidences with other puzzles coming from the Virgo axis are included. Our work shows that anisotropy is not confined to the low l region, but extends over a much larger l range.     

Scattered emission from a relativistic outflow and its application to gamma-ray bursts

We investigate a scenario of photon scattering by electrons within a relativistic outflow. The outflow is composed of discrete shells with different speeds. One shell emits radiation for a short duration. Some of this radiation is scattered by the shell(s) behind. We calculate in a simple two-shell model the observed scattered flux density as a function of the observed primary flux density, the normalized arrival time delay between the two emission components, the Lorentz factor ratio of the two shells and the scattering shell's optical depth. Thomson scattering in a cold shell and inverse Compton scattering in a hot shell are both considered. The results of our calculations are applied to the gamma-ray bursts and the afterglows. We find that the scattered flux from a cold slower shell is small and likely to be detected only for those bursts with very weak afterglows. A hot scattering shell could give rise to a scattered emission as bright as the X-ray shallow decay component detected in many bursts, on a condition that the isotropically equivalent total energy carried by the hot electrons is large, ∼10⁵²–10⁵⁶ erg. The scattered emission from a faster shell could appear as a late short γ-ray/MeV flash or become part of the prompt emission depending on the delay of the ejection of the shell.     

Damping of slow magnetoacoustic waves in an inhomogeneous coronal plasma

We study the propagation and dissipation of slow magnetoacoustic waves in an inhomogeneous viscous coronal loop plasma permeated by uniform magnetic field. Only viscosity and thermal conductivity are taken into account as dissipative processes in the coronal loop. The damping length of slow-mode waves exhibit varying behaviour depending upon the physical parameters of the loop in an active region AR8270 observed by TRACE. The wave energy flux associated with slow magnetoacoustic waves turns out to be of the order of 10⁶ erg cm^?2 s^?1 which is high enough to replace the energy lost through optically thin coronal emission and the thermal conduction below to the transition region. It is also found that only those slow-mode waves which have periods more than 240s provide the required heating rate to balance the energy losses in the solar corona. Our calculated wave periods for slow-mode waves nearly match with the oscillation periods of loop observed by TRACE.     

Effect of pedogenesis on the stable isotopic composition of calcretes and n‐alkanes: Implications for palaeoenvironmental reconstruction

In a fluvial system, depending on sub‐aerial exposure, non‐pedogenic pond calcretes can be modified into pedogenic calcretes. The present study attempts to understand the effect of sub‐aerial exposure and pedogenesis on calcretes using carbon and oxygen isotopic composition. For this purpose, two profiles (profile‐A and profile‐B) from the same stratigraphic level in Rayka from the western part of India were selected. The profiles are separated by a distance of 500 m and showed differences in calcrete characteristics. In profile‐A, the calcretes showed pedogenic features (root traces and void filling spar) whereas calcretes in profile‐B showed non‐pedogenic characteristics (fine laminations). However, some of the calcretes in profile‐A exhibited remnants of fine laminations suggesting that initially the calcretes had a non‐pedogenic origin but were modified due to pedogenesis. In profile‐A, the carbon and oxygen isotope values of pedogenic calcrete (δ¹³C_PC and δ¹⁸O_PC) showed more variation compared with non‐pedogenic pond calcretes (δ¹³C_SPC and δ¹⁸O_SPC) in profile‐B. The δ¹³C_PC and δ¹³C_SPC values exhibited a spread of 3·0‰ and 1·3‰, respectively, and δ¹⁸O_PC and δ¹⁸O_SPC values showed a spread of 2·3‰ and 1·3‰, respectively. The differences in the isotopic composition between the two profiles suggest that pedogenesis controlled the isotopic inheritance in calcretes. In addition, the carbon isotopic composition of organic matter (δ¹³C_OM) and n‐alkanes (δ¹³C_n‐alk) that forms the basis of palaeovegetational reconstruction have also been measured to understand the effect of pedogenesis on organic matter in both of the profiles. The average δ¹³C_OM values in profile‐A and profile‐B are ?23·4‰ and ?21·1‰, respectively. The disparity in δ¹³C_OM values is a result of the difference in the sources and preservation of organic matter. However, the δ¹³C_n‐alk values show a similar trend in profile‐A and profile‐B, indicating that sources of n‐alkanes are the same in both of the profiles and δ¹³C_n‐alk values are unaffected by the pedogenic modifications.