STUDIES ON SCATTERING AND QUASI-NORMAL MODES IN BLACK HOLE SPACE-TIMES

The question of stability of black hole was first studied by Regge and Wheeler who investigated linear perturbations of the exterior Schwarzschild spacetime. Further work on this problem led to the study of quasi-normal modes which is believed as a characteristic sound of black holes. Quasi-normal modes (QNMs) describe the damped oscillations under perturbations in the surrounding geometry of a black hole with frequencies and damping times of oscillations entirely fixed by the black hole parameters.In the present work we study the influence of cosmic string on the QNMs of various black hole background spacetimes which are perturbed by a massless Dirac field.

On the relationship of normal modes to local modes in molecular vibrations

A simple model for the effective vibrational hamiltonian of the XH stretching vibrations in H2O, NH3 and CH4 is considered, based on a morse potential function for the bond stretches plus potential and kinetic energy coupling between pairs of bond oscillators. It is shown that this model can be set up as a matrix in local mode basis functions, or as a matrix in normal mode basis functions, leading to identical results. The energy levels obtained exhibit normal mode patterns at low vibrational excitation, and local mode patterns at high excitation. When the hamiltonian is set up in the normal mode basis it is shown that Darling-Dennison resonances must be included, and simple relations are found to exist between the xrs, gtt, and Krrss anharmonic constants (where the Darling-Dennison coefficients are denoted K) due to their contributions from morse anharmonicity in the bond stretches. The importance of the Darling-Dennison resonances is stressed. The relationship of the two alternative representations of this local mode/normal mode model are investigated, and the potential uses and limitations of the model are discussed.

Normal Modes Using Maple (Water)

The normal modes of water are obtained using Maple

Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation

The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

Quasinormal modes of brane-localized standard model fields in Gauss-Bonnet theory

We study the massless scalar, Dirac, and electromagnetic fields propagating on a 4D-brane, which is embedded in higher-dimensional Gauss-Bonnet space-time. We calculate, in the time domain, the fundamental quasinormal modes of a spherically symmetric black hole for such fields. Using WKB approximation we study quasinormal modes in the large multipole limit. We observe also a universal behavior, independent on a field and value of the Gauss-Bonnet parameter, at an asymptotically late time.

Functional dynamics of PDZ binding domains: a normal-mode analysis.

Postsynaptic density-95/disks large/zonula occludens-1 (PDZ) domains are relatively small (80-120 residues) protein binding modules central in the organization of receptor clusters and in the association of cellular proteins. Their main function is to bind C-terminals of selected proteins that are recognized through specific amino acids in their carboxyl end. Binding is associated with a deformation of the PDZ native structure and is responsible for dynamical changes in regions not in direct contact with the target. We investigate how this deformation is related to the harmonic dynamics of the PDZ structure and show that one low-frequency collective normal mode, characterized by the concerted movements of different secondary structures, is involved in the binding process. Our results suggest that even minimal structural changes are responsible for communication between distant regions of the protein, in agreement with recent NMR experiments. Thus, PDZ domains are a very clear example of how collective normal modes are able to characterize the relation between function and dynamics of proteins, and to provide indications on the precursors of binding/unbinding events.

The vibrational spectra and the normal coordinate analysis of thiocarbonye halides /|nby C. R. Subramaniam. -- 260 St. Catharines, Ont. : [s. n.],

The infrared and the Raman spectra of eSelF has been obtained for the first time and has been analysed to give the in-plane normal vibrational frequencies of the molecule, in the ground state. A normal co-ordinate analysis has been carried out for the molecules CSF2, CSClF and eSel 2 using a Urey-Bradley type of potential function and the elements of the [L] matrix elements, the distribution of the potential energy in Urey-Bradley space, and the displacement vector diagrams for the normal modes of vibration for these molecules, have been obtained. The bond for~e constants obtained through the normal co-ordinate analysis, have given some interesting results. The stretching force constant, Kes ' varies markedly with halogen substitution and the force constants KeF and Keel also vary with substitution.

Conformal Klein-Gordon equations and quasinormal modes

Using conformal coordinates associated with conformal relativity-associated with de Sitter spacetime homeomorphic projection into Minkowski spacetime-we obtain a conformal Klein-Gordon partial differential equation, which is intimately related to the production of quasi-normal modes (QNMs) oscillations, in the context of electromagnetic and/or gravitational perturbations around, e.g., black holes. While QNMs arise as the solution of a wave-like equation with a Poschl-Teller potential, here we deduce and analytically solve a conformal 'radial' d'Alembert-like equation, from which we derive QNMs formal solutions, in a proposed alternative to more completely describe QNMs. As a by-product we show that this 'radial' equation can be identified with a Schrodinger-like equation in which the potential is exactly the second Poschl-Teller potential, and it can shed some new light on the investigations concerning QNMs.

A física do violino

Neste artigo apresentamos uma descrição geral da física do violino, analisando os conceitos que lhes dão sustentação física e que revelam toda a riqueza e o potencial pedagógico do assunto. Destacamos as contribuições de físicos como Helmholtz, Savart, Raman e Saunders no esforço para descrever a vibração produzida pelo arco nas cordas, e por compreender as propriedades acústicas do instrumento. Descrevemos a função de cada uma das componentes do instrumento e discutimos a importância dos modos normais de vibração dos tampos e do cavalete na resposta acústica do violino. A ressonância acústica da caixa do violino (ressonância de Helmholtz) será discutida fazendo-se um paralelo entre osciladores mecânico, elétrico e acústico. Discutiremos a resposta acústica do violino e descreveremos a produção de seu som caraterístico, que resulta da forma de onda originada pela excitação das cordas pelo arco, influenciada pelas vibrações e ressonâncias do corpo do violino, seus tampos e o cavalete.

Gravitational signature of Schwarzschild black holes in dynamical Chern-Simons gravity

Dynamical Chern-Simons gravity is an extension of general relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard general relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.

Phase transitions and regions of stability in Reissner-Nordstrom holographic superconductors

The phase transition of Reissner-Nordstrom AdS(4) interacting with a massive charged scalar field has been further revisited. We found exactly one stable and one unstable quasinormal mode region for the scalar field. The two of them are separated by the first marginally stable solution.

Long life of Gauss-Bonnet corrected black holes

Dictated by the string theory and various higher dimensional scenarios, black holes in D > 4-dimensional space-times must have higher curvature corrections. The first and dominant term is quadratic in curvature, and called the Gauss-Bonnet (GB) term. We shall show that although the Gauss-Bonnet correction changes black hole's geometry only softly, the emission of gravitons is suppressed by many orders even at quite small values of the GB coupling. The huge suppression of the graviton emission is due to the multiplication of the two effects: the quick cooling of the black hole when one turns on the GB coupling and the exponential decreasing of the gray-body factor of the tensor type of gravitons at small and moderate energies. At higher D the tensor gravitons emission is dominant, so that the overall lifetime of black holes with Gauss-Bonnet corrections is many orders larger than was expected. This effect should be relevant for the future experiments at the Large Hadron Collider (LHC).

Passage of radiation through wormholes of arbitrary shape

We study quasinormal modes and scattering properties via calculation of the S matrix for scalar and electromagnetic fields propagating in the background of spherically symmetric and axially symmetric traversable Lorentzian wormholes of a generic shape. Such wormholes are described by the general Morris-Thorne ansatz. The properties of quasinormal ringing and scattering are shown to be determined by the behavior of the wormhole's shape function b(r) and shift factor Phi(r) near the throat. In particular, wormholes with the shape function b(r), such that b(dr) approximate to 1, have very long-lived quasinormal modes in the spectrum. We have proved that the axially symmetric traversable Lorentzian wormholes, unlike black holes and other compact rotating objects, do not allow for superradiance. As a by-product we have shown that the 6th order WKB formula used for scattering problems of black or wormholes gives quite high accuracy and thus can be used for quite accurate calculations of the Hawking radiation processes around various black holes.

Gravitational stability of simply rotating Myers-Perry black holes: Tensorial perturbations

We study the stability of D >= 7 asymptotically flat black holes rotating in a single two-plane against tensor-type gravitational perturbations. The extensive search of quasinormal modes for these black holes did not indicate any presence of growing modes, implying the stability of simply rotating Myers-Perry black holes against tensor-type perturbations.