Curvature Inspired Cosmological Scenario

Using modified gravity with non-linear terms of curvature, $R^2$ and $R^{(r +2)}$ (with $r$ being the positive real number and $R$ being the scalar curvature), cosmological scenario,beginning at the Planck scale, is obtained. Here, a unified picture of cosmology is obtained from $f(R)-$ gravity. In this scenario, universe begins with power-law inflation, followed by deceleration and acceleration in the late universe as well as possible collapse of the universe in future. It is different from $f(R)-$ dark energy models with non-linear curvature terms assumed as dark energy. Here, dark energy terms are induced by linear as well as non-linear terms of curvature in Friedmann equation being derived from modified gravity.It is also interesting to see that, in this model, dark radiation and dark matter terms emerge spontaneously from the gravitational sector. It is found that dark energy, obtained here, behaves as quintessence in the early universe and phantom in the late universe. Moreover, analogous to brane-tension in brane-gravity inspired Friedmann equation, a tension term $\lambda$ arises here being called as cosmic tension. It is found that, in the late universe, Friedmann equation (obtained here) contains a term $- \rho^2/2\lambda$ ($\rho$ being the phantom energy density) analogous to a similar term in Friedmann equation with loop quantum effects, if $\lambda > 0$ and brane-gravity correction when $\lambda < 0.$Comment: 19 Pages. To appear in Int. J. Thro. Phy

Identification of Shocks in the Spectra from Black Holes

We study the spectral properties of a low angular momentum flow as a function of the shock strength, compression ratio, accretion rate and flow geometry. In the absence of a satisfactory description of magnetic fields inside the advective disk, we consider the presence of only stochastic fields and use the ratio of the field energy to the gravitational energy density as a parameter. We not only include `conventional' synchrotron emission and Comptonization by Maxwell-Bolzmann electrons in the gas, but we also compute these effects due to power-law electrons. For strong shocks, a bump is produced due to the post-shock flow. A power-law spectral components due to the thermal and non-thermal electrons appear after this bump.Comment: 8 pages, 5 figures, Astronomy and Space Science (in press), Proceedings of the Hong Kong Conference (2004) Edited by Cheng and Romer

A Simple Geometric Representative for μ\mu of a Point

For $SU(2)$ (or $SO(3)$) Donaldson theory on a 4-manifold $X$, we construct a simple geometric representative for $\mu$ of a point. Let $p$ be a generic point in $X$. Then the set $\{ [A] | F_A^-(p)$ is reducible $\}$, with coefficient -1/4 and appropriate orientation, is our desired geometric representative.Comment: Updated 2018 to published version. 8 pages, AmS-TeX, no figure

Circularly polarized dielectric resonator antenna excited by a conformal wire

A conformal spiral wire has been used to feed a dielectric resonator antenna to obtain a circular polarization. The parameters of the spiral have been optimized numerically so that minimum axial ratio (AR) and return losses are achieved. The method of moments (MoM) has been used in the analysis and the results have been validated against those from a commercial software package with a good agreement

Small scale rural aquaculture in Assam, India: a case study

The state of Assam in northeastern India has an excellent sub-tropical climate for the development of fresh water fish culture in a variety of aquatic bodies. Aquaculture not only plays an important role in nutrition but also in the rural economy of the State. A pilot project conducted with a group of resource poor tribal farmers revealed that a production of about 1 800 kg/ha/yr could be achieved from small seasonal homestead ponds through integrated use of locally available biological resources. This implies an excellent opportunity for improving the rural economy through the development of small-scale fish culture enterprises. In this project, a greater emphasis was placed on improving the knowledge and skills of the farmers and their farming practices so that in the future they would be in a position to expand their activities with financial assistance made available locally. Aquaculture being a new activity in the area, this pilot project was only a start in acquainting the farmers with the practice and potential of aquaculture

A generalized asymptotic extraction solution for antennas in multilayered spherical media

An efficient model is developed to accelerate the convergence of the dyadic Green's function's (DGF) infinite summation when the source and observation points are placed in different layers of a dielectric sphere, thereby expediting computational analysis. The proposed procedure is based on asymptotic extraction principles in which the quasi-static images are extracted from the spectral domain DGF. The effectiveness of the approach is demonstrated in a method of moment model where a microstrip antenna as well as a conformal dipole array have been studied

The dynamics of thin fluid films

Not only are thin fluid films of enormous importance in numerous practical applications, including painting, the manufacture of foodstuffs, and coating processes for products ranging from semi-conductors and magnetic tape to television screens, but they are also of great fundamental interest to mathematicians, physicists and engineers. Thin fluid films can exhibit a wealth of fascinating behaviour, including wave propagation, rupture, and transition to quasi-periodic or chaotic structures. More details of various aspects of thin-film flow can be found in the recent review articles by Oron, Davis and Bankoff (1997) and Myers (1998), and in the volumes edited by Kistler and Schweizer (1997) and Batchelor, Moffatt and Worster (2000)

Electromagnetic radiation by antennas of arbitrary shape in a layered spherical media

A unified method of moments model is developed for the analysis of arbitrarily shaped antennas that are radiating next to a multilayered dielectric sphere. The curvilinear Rao-Wilton-Glisson triangular basis functions and dyadic Green's functions have been used in the model. Antennas of various geometries including spherical, circular and rectangular microstrip antennas as well as hemispherical dielectric resonators have been modeled. Input impedance and radiation pattern results are presented and shown to be in good agreement with published data

Asymptotic extraction approach for antennas in a multilayered spherical media

An efficient algorithm is introduced to enhance the convergence of dyadic Green's functions (DGF) in a layered spherical media where asymptotic expressions have been developed. The formulated expressions involve an infinite series of spherical eigenmodes that can be reduced to the simple homogenous media Green's function using the addition theorem of spherical Hankel functions. Substantial improvements in the convergence speed have been attained by subtracting the asymptotic series representation from the original DGF. The subtracted components are then added to the solution using the homogenous media Green's function format

Moment method analysis of an archimedean spiral printed on a layered dielectric sphere

A method of moments model is presented to analyze Archimedean spirals that are printed on a layered dielectric sphere. The model is derived assuming an arbitrary location of the spiral. Input impedance, current distribution and far-field results are presented and are shown to be in good agreements with other methods