Parametrized tests of post-Newtonian theory using Advanced LIGO and Einstein Telescope

General relativity has very specific predictions for the gravitational waveforms from inspiralling compact binaries obtained using the post-Newtonian (PN) approximation. We investigate the extent to which the measurement of the PN coefficients, possible with the second generation gravitational-wave detectors such as the Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and the third generation gravitational-wave detectors such as the Einstein Telescope (ET), could be used to test post-Newtonian theory and to put bounds on a subclass of parametrized-post-Einstein theories which differ from general relativity in a parametrized sense. We demonstrate this possibility by employing the best inspiralling waveform model for nonspinning compact binaries which is 3.5PN accurate in phase and 3PN in amplitude. Within the class of theories considered, Advanced LIGO can test the theory at 1.5PN and thus the leading tail term. Future observations of stellar mass black hole binaries by ET can test the consistency between the various PN coefficients in the gravitational-wave phasing over the mass range of 11-44M(circle dot). The choice of the lower frequency cutoff is important for testing post-Newtonian theory using the ET. The bias in the test arising from the assumption of nonspinning binaries is indicated.

Coupling of surface acoustic waves propagating in two separated piezoelectric media

The coupling of surface acoustic waves propagating in two separated piezoelectric media is studied using the perturbation theory of Auld. The results of the analysis are applied to two configurations using Bi12GeO20 and CdS crystals. It is found that the loss due to coupling is about 7 dB at 50 MHz in the cases of (111)-cut, [110]-prop. Bi12GeO20 and Y-cut, 60°-X prop. CdS combination. On étudie le couplage des ondes acoustiques de surface se propageant sur deux milieux piezo-eléctriques par la théorie de perturbation de Auld. Les resultats d'analyse sont appliqué's aux deux configurations des cristanx Bi12GeO20 et CdS. On trouve que la perte par couplage est environ de 7 dB a 50 MHz dans le cas de combination de (111)-coupe, [110]-prop. Bi12GeO20 et Y-coupe, 60°-X prop. CdS.

Magnetically induced currents and magnetic response properties of molecules

The magnetically induced currents in organic monoring and multiring molecules, in Möbius shaped molecules and in inorganic all-metal molecules have been investigated by means of the Gauge-including magnetically induced currents (GIMIC) method. With the GIMIC method, the ring-current strengths and the ring-current density distributions can be calculated. For open-shell molecules, also the spin current can be obtained. The ring-current pathways and ring-current strengths can be used to understand the magnetic resonance properties of the molecules, to indirectly identify the effect of non-bonded interactions on NMR chemical shifts, to design new molecules with tailored properties and to discuss molecular aromaticity. In the thesis, the magnetic criterion for aromaticity has been adopted. According to this, a molecule which has a net diatropic ring current might be aromatic. Similarly, a molecule which has a net paratropic current might be antiaromatic. If the net current is zero, the molecule is nonaromatic. The electronic structure of the investigated molecules has been resolved by quantum chemical methods. The magnetically induced currents have been calculated with the GIMIC method at the density-functional theory (DFT) level, as well as at the self-consistent field Hartree-Fock (SCF-HF), at the Møller-Plesset perturbation theory of the second order (MP2) and at the coupled-cluster singles and doubles (CCSD) levels of theory. For closed-shell molecules, accurate ring-current strengths can be obtained with a reasonable computational cost at the DFT level and with rather small basis sets. For open-shell molecules, it is shown that correlated methods such as MP2 and CCSD might be needed to obtain reliable charge and spin currents. The basis set convergence has to be checked for open-shell molecules by performing calculations with large enough basis sets. The results discussed in the thesis have been published in eight papers. In addition, some previously unpublished results on the ring currents in the endohedral fullerene Sc3C2@C80 and in coronene are presented. It is shown that dynamical effects should be taken into account when modelling magnetic resonance parameters of endohedral metallofullerenes such as Sc3C2@C80. The ring-current strengths in a series of nano-sized hydrocarbon rings are related to static polarizabilities and to H-1 nuclear magnetic resonance (NMR) shieldings. In a case study on the possible aromaticity of a Möbius-shaped [16]annulene we found that, according to the magnetic criterion, the molecule is nonaromatic. The applicability of the GIMIC method to assign the aromatic character of molecules was confirmed in a study on the ring currents in simple monocylic aromatic, homoaromatic, antiaromatic, and nonaromatic hydrocarbons. Case studies on nanorings, hexaphyrins and [n]cycloparaphenylenes show that explicit calculations are needed to unravel the ring-current delocalization pathways in complex multiring molecules. The open-shell implementation of GIMIC was applied in studies on the charge currents and the spin currents in single-ring and bi-ring molecules with open shells. The aromaticity predictions that are made based on the GIMIC results are compared to other aromaticity criteria such as H-1 NMR shieldings and shifts, electric polarizabilities, bond-length alternation, as well as to predictions provided by the traditional Hückel (4n+2) rule and its more recent extensions that account for Möbius twisted molecules and for molecules with open shells.

Holographic Superfluids and Solitons

Superfluidity is perhaps one of the most remarkable observed macroscopic quantum effect. Superfluidity appears when a macroscopic number of particles occupies a single quantum state. Using modern experimental techniques one dark solitons) and vortices. There is a large literature on theoretical work studying the properties of such solitons using semiclassical methods. This thesis describes an alternative method for the study of superfluid solitons. The method used here is a holographic duality between a class of quantum field theories and gravitational theories. The classical limit of the gravitational system maps into a strong coupling limit of the quantum field theory. We use a holographic model of superfluidity to study solitons in these systems. One particularly appealing feature of this technique is that it allows us to take into account finite temperature effects in a large range of temperatures.

Noncommutative Quantum Field Theory : Problem of Time and Some Applications

In this thesis the current status and some open problems of noncommutative quantum field theory are reviewed. The introduction aims to put these theories in their proper context as a part of the larger program to model the properties of quantized space-time. Throughout the thesis, special focus is put on the role of noncommutative time and how its nonlocal nature presents us with problems. Applications in scalar field theories as well as in gauge field theories are presented. The infinite nonlocality of space-time introduced by the noncommutative coordinate operators leads to interesting structure and new physics. High energy and low energy scales are mixed, causality and unitarity are threatened and in gauge theory the tools for model building are drastically reduced. As a case study in noncommutative gauge theory, the Dirac quantization condition of magnetic monopoles is examined with the conclusion that, at least in perturbation theory, it cannot be fulfilled in noncommutative space.

Dipolar cross-correlation effects in the nuclear overhauser experiments of weakly and strongly coupled spins

The effect of dipolar cross correlation in 1H---1H nuclear Overhauser effect experiments is investigated by detailed calculation in an ABX spin system. It is found that in weakly coupled spin systems, the cross-correlation effects are limited to single-quantum transition probabilities and decrease in magnitude as ωτc increases. Strong coupling, however, mixes the states and the cross correlations affect the zero-quantum and double-quantum transition probabilities as well. The effect of cross correlation in steady-state and transient NOE experiments is studied as a function of strong coupling and ωτc. The results for steady-state NOE experiments are calculated analytically and those for transient NOE experiments are calculated numerically. The NOE values for the A and B spins have been calculated by assuming nonselective perturbation of all the transitions of the X spin. A significant effect of cross correlation is found in transient NOE experiments of weakly as well as strongly coupled spins when the multiplets are resolved. Cross correlation manifests itself largely as a multiplet effect in the transient NOE of weakly coupled spins for nonselective perturbation of all X transitions. This effect disappears for a measuring pulse of 90° or when the multiplets are not resolved. For steady-state experiments, the effect of cross correlation is analytically zero for weakly coupled spins and small for strongly coupled spins.

Unfolding of Plasmodium falciparum triosephosphate isomerase in urea and guanidinium chloride solutions. Evidence for a novel disulfide exchange reaction in a covalently crosslinked mutant

The conformational stability of Plasmodium falciparum triosephosphate isomerase (TIMWT) enzyme has been investigated in urea and guanidinium chloride (GdmCl) solutions using circular dichroism, fluorescence, and size-exclusion chromatography. The dimeric enzyme is remarkably stable in urea solutions. It retains considerable secondary, tertiary, and quaternary structure even in 8 M urea. In contrast, the unfolding transition is complete by 2.4 M GdmCl. Although the secondary as well as the tertiary interactions melt before the perturbation of the quaternary structure, these studies imply that the dissociation of the dimer into monomers ultimately leads to the collapse of the structure, suggesting that the interfacial interactions play a major role in determining multimeric protein stability. The Cm(urea)/Cm(GdmCl) ratio (where Cm is the concentration of the denaturant required at the transition midpoint) is unusually high for triosephosphate isomerase as compared to other monomeric and dimeric proteins. A disulfide cross-linked mutant protein (Y74C) engineered to form two disulfide cross-links across the interface (13-74‘) and (13‘-74) is dramatically destablized in urea. The unfolding transition is complete by 6 M urea and involves a novel mechanism of dimer dissociation through intramolecular thiol−disulfide exchange.

Embracing Integrability in Stellar and Planetary Dynamics

Hamiltonian systems in stellar and planetary dynamics are typically near integrable. For example, Solar System planets are almost in two-body orbits, and in simulations of the Galaxy, the orbits of stars seem regular. For such systems, sophisticated numerical methods can be developed through integrable approximations. Following this theme, we discuss three distinct problems. We start by considering numerical integration techniques for planetary systems. Perturbation methods (that utilize the integrability of the two-body motion) are preferred over conventional "blind" integration schemes. We introduce perturbation methods formulated with Cartesian variables. In our numerical comparisons, these are superior to their conventional counterparts, but, by definition, lack the energy-preserving properties of symplectic integrators. However, they are exceptionally well suited for relatively short-term integrations in which moderately high positional accuracy is required. The next exercise falls into the category of stability questions in solar systems. Traditionally, the interest has been on the orbital stability of planets, which have been quantified, e.g., by Liapunov exponents. We offer a complementary aspect by considering the protective effect that massive gas giants, like Jupiter, can offer to Earth-like planets inside the habitable zone of a planetary system. Our method produces a single quantity, called the escape rate, which characterizes the system of giant planets. We obtain some interesting results by computing escape rates for the Solar System. Galaxy modelling is our third and final topic. Because of the sheer number of stars (about 10^11 in Milky Way) galaxies are often modelled as smooth potentials hosting distributions of stars. Unfortunately, only a handful of suitable potentials are integrable (harmonic oscillator, isochrone and Stäckel potential). This severely limits the possibilities of finding an integrable approximation for an observed galaxy. A solution to this problem is torus construction; a method for numerically creating a foliation of invariant phase-space tori corresponding to a given target Hamiltonian. Canonically, the invariant tori are constructed by deforming the tori of some existing integrable toy Hamiltonian. Our contribution is to demonstrate how this can be accomplished by using a Stäckel toy Hamiltonian in ellipsoidal coordinates.

Strong spin-two interaction and general relativity

The concept of short range strong spin-two (f) field (mediated by massive f-mesons) and interacting directly with hadrons was introduced along with the infinite range (g) field in early seventies. In the present review of this growing area (often referred to as strong gravity) we give a general relativistic treatment in terms of Einstein-type (non-abelian gauge) field equations with a coupling constant Gf reverse similar, equals 1038 GN (GN being the Newtonian constant) and a cosmological term λf ƒ;μν (ƒ;μν is strong gravity metric and λf not, vert, similar 1028 cm− is related to the f-meson mass). The solutions of field equations linearized over de Sitter (uniformly curves) background are capable of having connections with internal symmetries of hadrons and yielding mass formulae of SU(3) or SU(6) type. The hadrons emerge as de Sitter “microuniverses” intensely curved within (radius of curvature not, vert, similar10−14 cm).The study of spinor fields in the context of strong gravity has led to Heisenberg's non-linear spinor equation with a fundamental length not, vert, similar2 × 10−14 cm. Furthermore, one finds repulsive spin-spin interaction when two identical spin-Image particles are in parallel configuration and a connection between weak interaction and strong gravity.Various other consequences of strong gravity embrace black hole (solitonic) solutions representing hadronic bags with possible quark confinement, Regge-like relations between spins and masses, connection with monopoles and dyons, quantum geons and friedmons, hadronic temperature, prevention of gravitational singularities, providing a physical basis for Dirac's two metric and large numbers hypothesis and projected unification with other basic interactions through extended supergravity.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

The velocity dispersion of giant molecular clouds. II - Mathematical and numerical refinements

The energy input to giant molecular clouds is recalculated, using the proper linearized equations of motion, including the Coriolis force and allowing for changes in the guiding center. Perturbation theory yields a result in the limit of distant encounters and small initial epicyclic amplitudes. Direct integration of the motion equations allows the strong encounter regime to be studied. The present perturbation theory result differs by a factor of order unity from that of Jog and Ostriker (1988). The result of present numerical integrations for the 2D (planar) velocity dispersion is presented. The accretion rate for a molecular cloud in the Galactic disk is calculated.

Head-on infall of two compact objects: Third post-Newtonian energy flux

Head-on infall of two compact objects with arbitrary mass ratio is investigated using the multipolar post-Minkowskian approximation method. At the third post-Newtonian order the energy flux, in addition to the instantaneous contributions, also includes hereditary contributions consisting of the gravitational-wave tails, tails-of-tails, and the tail-squared terms. The results are given both for infall from infinity and also for infall from a finite distance. These analytical expressions should be useful for the comparison with the high accuracy numerical relativity results within the limit in which post-Newtonian approximations are valid.

A new creation cosmology

A new conformal creation field cosmology is considered and it is found that a negative energy scalar field nonminimally coupled to the gravitational field gives rise to creation and, in contrast to Hoyle-Narlikar theory, no a priori assumption about the rate of creation is required to solve the field equations.

Homonuclear NOE in spatially periodic spin systems

The nuclear Overhauser effect equations are solved analytically for a homonuclear group of spins whose sites are periodically arranged, including the special cases where the spins lie at the vertices of a regular polygon and on a one-dimensional lattice. t is shown that, for long correlation times, the equations governing magnetization transfer resemble a diffusion equation. Furthermore the deviation from exact diffusion is quantitatively related to the molecular tumbling correlation time. Equations are derived for the range of magnetization travel subsequent to the perturbation of a single spin in a lattice for both the case of strictly dipolar relaxation and the more general situation where additional T1 mechanisms may be active. The theory given places no restrictions on the delay (or mixing) times, and it includes all the spins in the system. Simulations are presented to confirm the theory.

Stability of synchronization in a multi-cellular system

Networks of biochemical reactions regulated by positive-and negative-feedback processes underlie functional dynamics in single cells. Synchronization of dynamics in the constituent cells is a hallmark of collective behavior in multi-cellular biological systems. Stability of the synchronized state is required for robust functioning of the multi-cell system in the face of noise and perturbation. Yet, the ability to respond to signals and change functional dynamics are also important features during development, disease, and evolution in living systems. In this paper, using a coupled multi-cell system model, we investigate the role of system size, coupling strength and its topology on the synchronization of the collective dynamics and its stability. Even though different coupling topologies lead to synchronization of collective dynamics, diffusive coupling through the end product of the pathway does not confer stability to the synchronized state. The results are discussed with a view to their prevalence in biological systems. Copyright (C) EPLA, 2010