Studies on scattering and thermodynamics of black holes in f(R) theory and Einstein's theory

One of the interesting consequences of Einstein's General Theory of Relativity is the black hole solutions. Until the observation made by Hawking in 1970s, it was believed that black holes are perfectly black. The General Theory of Relativity says that black holes are objects which absorb both matter and radiation crossing the event horizon. The event horizon is a surface through which even light is not able to escape. It acts as a one sided membrane that allows the passage of particles only in one direction i.e. towards the center of black holes. All the particles that are absorbed by black hole increases the mass of the black hole and thus the size of event horizon also increases. Hawking showed in 1970s that when applying quantum mechanical laws to black holes they are not perfectly black but they can emit radiation. Thus the black hole can have temperature known as Hawking temperature. In the thesis we have studied some aspects of black holes in f(R) theory of gravity and Einstein's General Theory of Relativity. The scattering of scalar field in this background space time studied in the first chapter shows that the extended black hole will scatter scalar waves and have a scattering cross section and applying tunneling mechanism we have obtained the Hawking temperature of this black hole. In the following chapter we have investigated the quasinormal properties of the extended black hole. We have studied the electromagnetic and scalar perturbations in this space-time and find that the black hole frequencies are complex and show exponential damping indicating the black hole is stable against the perturbations. In the present study we show that not only the black holes exist in modified gravities but also they have similar properties of black hole space times in General Theory of Relativity. 2 + 1 black holes or three dimensional black holes are simplified examples of more complicated four dimensional black holes. Thus these models of black holes are known as toy models of black holes in four dimensional black holes in General theory of Relativity. We have studied some properties of these types of black holes in Einstein model (General Theory of Relativity). A three dimensional black hole known as MSW is taken for our study. The thermodynamics and spectroscopy of MSW black hole are studied and obtained the area spectrum which is equispaced and different thermo dynamical properties are studied. The Dirac perturbation of this three dimensional black hole is studied and the resulting quasinormal spectrum of this three dimensional black hole is obtained. The different quasinormal frequencies are tabulated in tables and these values show an exponential damping of oscillations indicating the black hole is stable against the mass less Dirac perturbation. In General Theory of Relativity almost all solutions contain singularities. The cosmological solution and different black hole solutions of Einstein's field equation contain singularities. The regular black hole solutions are those which are solutions of Einstein's equation and have no singularity at the origin. These solutions possess event horizon but have no central singularity. Such a solution was first put forward by Bardeen. Hayward proposed a similar regular black hole solution. We have studied the thermodynamics and spectroscopy of Hay-ward regular black holes. We have also obtained the different thermodynamic properties and the area spectrum. The area spectrum is a function of the horizon radius. The entropy-heat capacity curve has a discontinuity at some value of entropy showing a phase transition.

Low-Energy Scattering of Heavy-Light Mesons from Nucleons

We study the low-energy scattering of charmed (D) and strange (K) mesons by nucleons. The short-distance part of the interaction is due to quark-gluon interchanges derived from a model that realizes dynamical chiral symmetry breaking and confines color. The quark-gluon interaction incorporates a confining Coulomb-like potential extracted from lattice QCD simulations in Coulomb gauge and a transverse hyperfine interaction consistent with a finite gluon propagator in the infrared. The long-distance part of the interaction is due to single vector (rho, omega) and scalar (sigma) meson exchanges. We show results for scattering cross-sections for isospin I = 0 and I = 1.

Relativistic Coulomb scattering of spinless bosons

Coordena����o de Aperfei��oamento de Pessoal de N��vel Superior (CAPES)

An example of cognitive obstacles in advanced integration: the case of scalar line integrals

Cognitive obstacles that arise in the teaching and learning of scalar line integrals, derived from cognitive aids provided to students when first learning about integration of single variable functions are described. A discussion of how and why the obstacles cause students problems is presented and possible strategies to overcome the obstacles are outlined.

Scattering of electromagnetic waves from chirally coated cylinders

The problem of electromagnetic scattering from an isotropic homogeneous chirally coated conducting cylinder is analysed. The cylinder is assumed to be illuminated by either a transverse magnetic or a transverse electric wave. Mie's analysis is used to evaluate the scattering characteristics. The computed results include the evaluation of the normalized scattering width and the absorption efficiency. The results show that there is a significant reduction in the normalized scattering width as compared to a RAM coated cylinder. This reduction has been attributed to increased absorption.

Surface-enhanced Raman scattering of molecules adsorbed on nanocrystalline Au and Ag films formed at the organic-aqueous interface

Surface-enhanced Raman scattering (SERS) of pyridine adsorbed on ultrathin nanocrystalline Au and Ag films generated at the liquid-liquid interface has been investigated. The shifts and intensification of bands formed with these films comprising metal nanoparticles are comparable to those found with other types of Au and Ag substrates. SERS of rhodamine 6G adsorbed on Ag films has also been studied. The results demonstrate that nanocrystalline metal films prepared by the simple method involving the organic-aqueous interface can be used effectively for SERS investigations.

Search for the Production of Scalar Bottom Quarks in pp�� Collisions at ���s=1.96������TeV

We report on a search for direct scalar bottom quark (sbottom) pair production in $p \bar{p}$ collisions at $\sqrt{s}=1.96$~TeV, in events with large missing transverse energy and two jets of hadrons in the final state, where at least one of the jets is required to be identified as originating from a $b$ quark. The study uses a CDF Run~II data sample corresponding to 2.65~fb${}^{-1}$ of integrated luminosity. The data are in agreement with the standard model. In an R-parity conserving minimal supersymmetric scenario, and assuming that the sbottom decays exclusively into a bottom quark and a neutralino, 95$\%$ confidence-level upper limits on the sbottom pair production cross section of 0.1~pb are obtained. For neutralino masses below 70~GeV/$c^2$, sbottom masses up to 230~GeV/$c^2$ are excluded at 95$\%$ confidence level.

A New Approach to the Problem of Scattering of Water Waves by Vertical Barriers

Using a modified Green's function technique the two well-known basic problems of scattering of surface water waves by vertical barriers are reduced to the problem of solving a pair of uncoupled integral equations involving the ���jump��� and ���sum��� of the limiting values of the velocity potential on the two sides of the barriers in each case. These integral equations are then solved, in closed form, by the aid of an integral transform technique involving a general trigonometric kernel as applicable to the problems associated with a radiation condition.

On the solution of the problem of scattering of surface water waves by a sharp discontinuity in the surface boundary conditions

Closed-form analytical expressions are derived for the reflection and transmission coefficients for the problem of scattering of surface water waves by a sharp discontinuity in the surface-boundary-conditions, for the case of deep water. The method involves the use of the Havelock-type expansion of the velocity potential along with an analysis to solve a Carleman-type singular integral equation over a semi-infinite range. This method of solution is an alternative to the Wiener-Hopf technique used previously.

Development of novel multiple quantummethodologies for the analyses of complex protonNMR spectra of scalar coupled spins

One of the significant advancements in Nuclear Magnetic Resonance spectroscopy (NMR) in combating the problem of spectral complexity for deriving the structure and conformational information is the incorporation of additional dimension and to spread the information content in a two dimensional space. This approach together with the manipulation of the dynamics of nuclear spins permitted the designing of appropriate pulse sequences leading to the evolution of diverse multidimensional NMR experiments. The desired spectral information can now be extracted in a simplified and an orchestrated manner. The indirect detection of multiple quantum (MQ) NMR frequencies is a step in this direction. The MQ technique has been extensively used in the study of molecules aligned in liquid crystalline media to reduce spectral complexity and to determine molecular geometries. Unlike in dipolar coupled systems, the size of the network of scalar coupled spins is not big in isotropic solutions and the MQ 1H detection is not routinely employed,although there are specific examples of spin topology filtering. In this brief review, we discuss our recent studies on the development and application of multiple quantum correlation and resolved techniques for the analyses of proton NMR spectra of scalar coupled spins.

Layer-dependent resonant Raman scattering of a few layer MoS2

We report resonant Raman scattering of MoS2 layers comprising of single, bi, four and seven layers, showing a strong dependence on the layer thickness. Indirect band gap MoS2 in bulk becomes a direct band gap semiconductor in the monolayer form. New Raman modes are seen in the spectra of single- and few-layer MoS2 samples which are absent in the bulk. The Raman mode at similar to 230 cm(-1) appears for two, four and seven layers. This mode has been attributed to the longitudinal acoustic phonon branch at the M point (LA(M)) of the Brillouin zone. The mode at similar to 179 cm(-1) shows asymmetric character for a few-layer sample. The asymmetry is explained by the dispersion of the LA(M) branch along the G-M direction. The most intense spectral region near 455 cm(-1) shows a layer-dependent variation of peak positions and relative intensities. The high energy region between 510 and 645 cm(-1) is marked by the appearance of prominent new Raman bands, varying in intensity with layer numbers. Resonant Raman spectroscopy thus serves as a promising non invasive technique to accurately estimate the thickness of MoS2 layers down to a few atoms thick. Copyright (C) 2012 John Wiley & Sons, Ltd.

Selective excitation and detection of maximum quantum coherence of a group of scalar coupled protons in chiral molecules: an NMR experiment for enantiodiscrimination

The H-1 NMR spectroscopic discrimination of enantiomers in the solution state and the measurement of enantiomeric composition is most often hindered due to either very small chemical shift differences between the discriminated peaks or severe overlap of transitions from other chemically non-equivalent protons. In addition the use of chiral auxiliaries such as, crown ether and chiral lanthanide shift reagent may often cause enormous line broadening or give little degree of discrimination beyond the crown ether substrate ratio, hampering the discrimination. In circumventing such problems we are proposing the utilization of the difference in the additive values of all the chemical shifts of a scalar coupled spin system. The excitation and detection of appropriate highest quantum coherence yields the measurable difference in the frequencies between two transitions, one pertaining to each enantiomer in the maximum quantum dimension permitting their discrimination and the F-2 cross section at each of these frequencies yields an enantiopure spectrum. The advantage of the utility of the proposed method is demonstrated on several chiral compounds where the conventional one dimensional H-1 NMR spectra fail to differentiate the enantiomers.

Scattering of carriers by charged dislocations in semiconductors

The scattering of carriers by charged dislocations in semiconductors is studied within the framework of the linearized Boltzmann transport theory with an emphasis on examining consequences of the extreme anisotropy of the cylindrically symmetric scattering potential. A new closed-form approximate expression for the carrier mobility valid for all temperatures is proposed. The ratios of quantum and transport scattering times are evaluated after averaging over the anisotropy in the relaxation time. The value of the Hall scattering factor computed for charged dislocation scattering indicates that there may be a factor of two error in the experimental mobility estimates using the Hall data. An expression for the resistivity tensor when the dislocations are tilted with respect to the plane of transport is derived. Finally, an expression for the isotropic relaxation time is derived when the dislocations are located within the sample with a uniform angular distribution.