On the long standing issue of an R phi(2) coupling between gravity and a massless free scalar field

Using 2-body trees on a flat space background, it is shown that the actions A[g, φ] = (Latin small letter esh) d4x√-g [(R/2K) + (1/2)(gμν ∂μφ∂νφ + λRφ2)] and Ā[ḡ, φ̄] = (Latin small letter esh) d4x√ - ḡ [(R̄/2k) + (1/2) ḡμν∂μφ̄∂ νφ] describe the same theory at the tree-level in this case. We also demonstrate the quantum equivalence (at one-loop) of the barred and unbarred systems for λ == -1/6 (conformal coupling).

Tópicos em teoria das perturbações cosmológicas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Synchrotron x ray induced axonal transections in the brain of rats assessed by high-field diffusion tensor imaging tractography

Since approximately two thirds of epileptic patients are non-eligible for surgery, local axonal fiber transections might be of particular interest for them. Micrometer to millimeter wide synchrotron-generated X-ray beamlets produced by spatial fractionation of the main beam could generate such fiber disruptions non-invasively. The aim of this work was to optimize irradiation parameters for the induction of fiber transections in the rat brain white matter by exposure to such beamlets. For this purpose, we irradiated cortex and external capsule of normal rats in the antero-posterior direction with a 4 mm×4 mm array of 25 to 1000 µm wide beamlets and entrance doses of 150 Gy to 500 Gy. Axonal fiber responses were assessed with diffusion tensor imaging and fiber tractography; myelin fibers were examined histopathologically. Our study suggests that high radiation doses (500 Gy) are required to interrupt axons and myelin sheaths. However, a radiation dose of 500 Gy delivered by wide minibeams (1000 µm) induced macroscopic brain damage, depicted by a massive loss of matter in fiber tractography maps. With the same radiation dose, the damage induced by thinner microbeams (50 to 100 µm) was limited to their paths. No macroscopic necrosis was observed in the irradiated target while overt transections of myelin were detected histopathologically. Diffusivity values were found to be significantly reduced. A radiation dose ≤ 500 Gy associated with a beamlet size of < 50 µm did not cause visible transections, neither on diffusion maps nor on sections stained for myelin. We conclude that a peak dose of 500 Gy combined with a microbeam width of 100 µm optimally induced axonal transections in the white matter of the brain.

Improved predictions for μ\to e conversion in nuclei and Higgs-induced lepton flavor violation

Compared to μ→eγ and μ→eee, the process μ→e conversion in nuclei receives enhanced contributions from Higgs-induced lepton flavor violation. Upcoming μ→e conversion experiments with drastically increased sensitivity will be able to put extremely stringent bounds on Higgs-mediated μ→e transitions. We point out that the theoretical uncertainties associated with these Higgs effects, encoded in the couplings of quark scalar operators to the nucleon, can be accurately assessed using our recently developed approach based on SU(2) chiral perturbation theory that cleanly separates two- and three-flavor observables. We emphasize that with input from lattice QCD for the coupling to strangeness fNs, hadronic uncertainties are appreciably reduced compared to the traditional approach where fNs is determined from the pion-nucleon σ term by means of an SU(3) relation. We illustrate this point by considering Higgs-mediated lepton flavor violation in the standard model supplemented with higher-dimensional operators, the two-Higgs-doublet model with generic Yukawa couplings, and the minimal supersymmetric standard model. Furthermore, we compare bounds from present and future μ→e conversion and μ→eγ experiments.

Cosmological perturbations in coherent oscillating scalar field models

The fact that fast oscillating homogeneous scalar fields behave as perfect fluids in average and their intrinsic isotropy have made these models very fruitful in cosmology. In this work we will analyse the perturbations dynamics in these theories assuming general power law potentials V(ϕ) = λ|ϕ|^n /n. At leading order in the wavenumber expansion, a simple expression for the effective sound speed of perturbations is obtained c_eff^ 2  = ω = (n − 2)/(n + 2) with ω the effective equation of state. We also obtain the first order correction in k^ 2/ω_eff^ 2 , when the wavenumber k of the perturbations is much smaller than the background oscillation frequency, ω_eff. For the standard massive case we have also analysed general anharmonic contributions to the effective sound speed. These results are reached through a perturbed version of the generalized virial theorem and also studying the exact system both in the super-Hubble limit, deriving the natural ansatz for δϕ; and for sub-Hubble modes, exploiting Floquet’s theorem.

Applicability of prevailing gravity thickening theories to activated sludge /

Vita.

Applications of differential geometry to high spin field theories

The main aim of this thesis is to investigate the application of methods of differential geometry to the constraint analysis of relativistic high spin field theories. As a starting point the coordinate dependent descriptions of the Lagrangian and Dirac-Bergmann constraint algorithms are reviewed for general second order systems. These two algorithms are then respectively employed to analyse the constraint structure of the massive spin-1 Proca field from the Lagrangian and Hamiltonian viewpoints. As an example of a coupled field theoretic system the constraint analysis of the massive Rarita-Schwinger spin-3/2 field coupled to an external electromagnetic field is then reviewed in terms of the coordinate dependent Dirac-Bergmann algorithm for first order systems. The standard Velo-Zwanziger and Johnson-Sudarshan inconsistencies that this coupled system seemingly suffers from are then discussed in light of this full constraint analysis and it is found that both these pathologies degenerate to a field-induced loss of degrees of freedom. A description of the geometrical version of the Dirac-Bergmann algorithm developed by Gotay, Nester and Hinds begins the geometrical examination of high spin field theories. This geometric constraint algorithm is then applied to the free Proca field and to two Proca field couplings; the first of which is the minimal coupling to an external electromagnetic field whilst the second is the coupling to an external symmetric tensor field. The onset of acausality in this latter coupled case is then considered in relation to the geometric constraint algorithm.

Real - time prediction of rainfall induced instability of residual soil slopes associated with deep cracks

The early warning based on real-time prediction of rain-induced instability of natural residual slopes helps to minimise human casualties due to such slope failures. Slope instability prediction is complicated, as it is influenced by many factors, including soil properties, soil behaviour, slope geometry, and the location and size of deep cracks in the slope. These deep cracks can facilitate rainwater infiltration into the deep soil layers and reduce the unsaturated shear strength of residual soil. Subsequently, it can form a slip surface, triggering a landslide even in partially saturated soil slopes. Although past research has shown the effects of surface-cracks on soil stability, research examining the influence of deep-cracks on soil stability is very limited. This study aimed to develop methodologies for predicting the real-time rain-induced instability of natural residual soil slopes with deep cracks. The results can be used to warn against potential rain-induced slope failures. The literature review conducted on rain induced slope instability of unsaturated residual soil associated with soil crack, reveals that only limited studies have been done in the following areas related to this topic: - Methods for detecting deep cracks in residual soil slopes. - Practical application of unsaturated soil theory in slope stability analysis. - Mechanistic methods for real-time prediction of rain induced residual soil slope instability in critical slopes with deep cracks. Two natural residual soil slopes at Jombok Village, Ngantang City, Indonesia, which are located near a residential area, were investigated to obtain the parameters required for the stability analysis of the slope. A survey first identified all related field geometrical information including slope, roads, rivers, buildings, and boundaries of the slope. Second, the electrical resistivity tomography (ERT) method was used on the slope to identify the location and geometrical characteristics of deep cracks. The two ERT array models employed in this research are: Dipole-dipole and Azimuthal. Next, bore-hole tests were conducted at different locations in the slope to identify soil layers and to collect undisturbed soil samples for laboratory measurement of the soil parameters required for the stability analysis. At the same bore hole locations, Standard Penetration Test (SPT) was undertaken. Undisturbed soil samples taken from the bore-holes were tested in a laboratory to determine the variation of the following soil properties with the depth: - Classification and physical properties such as grain size distribution, atterberg limits, water content, dry density and specific gravity. - Saturated and unsaturated shear strength properties using direct shear apparatus. - Soil water characteristic curves (SWCC) using filter paper method. - Saturated hydraulic conductivity. The following three methods were used to detect and simulate the location and orientation of cracks in the investigated slope: (1) The electrical resistivity distribution of sub-soil obtained from ERT. (2) The profile of classification and physical properties of the soil, based on laboratory testing of soil samples collected from bore-holes and visual observations of the cracks on the slope surface. (3) The results of stress distribution obtained from 2D dynamic analysis of the slope using QUAKE/W software, together with the laboratory measured soil parameters and earthquake records of the area. It was assumed that the deep crack in the slope under investigation was generated by earthquakes. A good agreement was obtained when comparing the location and the orientation of the cracks detected by Method-1 and Method-2. However, the simulated cracks in Method-3 were not in good agreement with the output of Method-1 and Method-2. This may have been due to the material properties used and the assumptions made, for the analysis. From Method-1 and Method-2, it can be concluded that the ERT method can be used to detect the location and orientation of a crack in a soil slope, when the ERT is conducted in very dry or very wet soil conditions. In this study, the cracks detected by the ERT were used for stability analysis of the slope. The stability of the slope was determined using the factor of safety (FOS) of a critical slip surface obtained by SLOPE/W using the limit equilibrium method. Pore-water pressure values for the stability analysis were obtained by coupling the transient seepage analysis of the slope using finite element based software, called SEEP/W. A parametric study conducted on the stability of an investigated slope revealed that the existence of deep cracks and their location in the soil slope are critical for its stability. The following two steps are proposed to predict the rain-induced instability of a residual soil slope with cracks. (a) Step-1: The transient stability analysis of the slope is conducted from the date of the investigation (initial conditions are based on the investigation) to the preferred date (current date), using measured rainfall data. Then, the stability analyses are continued for the next 12 months using the predicted annual rainfall that will be based on the previous five years rainfall data for the area. (b) Step-2: The stability of the slope is calculated in real-time using real-time measured rainfall. In this calculation, rainfall is predicted for the next hour or 24 hours and the stability of the slope is calculated one hour or 24 hours in advance using real time rainfall data. If Step-1 analysis shows critical stability for the forthcoming year, it is recommended that Step-2 be used for more accurate warning against the future failure of the slope. In this research, the results of the application of the Step-1 on an investigated slope (Slope-1) showed that its stability was not approaching a critical value for year 2012 (until 31st December 2012) and therefore, the application of Step-2 was not necessary for the year 2012. A case study (Slope-2) was used to verify the applicability of the complete proposed predictive method. A landslide event at Slope-2 occurred on 31st October 2010. The transient seepage and stability analyses of the slope using data obtained from field tests such as Bore-hole, SPT, ERT and Laboratory tests, were conducted on 12th June 2010 following the Step-1 and found that the slope in critical condition on that current date. It was then showing that the application of the Step-2 could have predicted this failure by giving sufficient warning time.

A strain-based failure criterion for pillar stability analysis

Strain-based failure criteria have several advantages over stress-based failure criteria: they can account for elastic and inelastic strains, they utilise direct, observables effects instead of inferred effects (strain gauges vs. stress estimates), and model complete stress-strain curves including pre-peak, non-linear elasticity and post-peak strain weakening. In this study, a strain-based failure criterion derived from thermodynamic first principles utilising the concepts of continuum damage mechanics is presented. Furthermore, implementation of this failure criterion into a finite-element simulation is demonstrated and applied to the stability of underground mining coal pillars. In numerical studies, pillar strength is usually expressed in terms of critical stresses or stress-based failure criteria where scaling with pillar width and height is common. Previous publications have employed the finite-element method for pillar stability analysis using stress-based failure criterion such as Mohr-Coulomb and Hoek-Brown or stress-based scalar damage models. A novel constitutive material model, which takes into consideration anisotropy as well as elastic strain and damage as state variables has been developed and is presented in this paper. The damage threshold and its evolution are strain-controlled, and coupling of the state variables is achieved through the damage-induced degradation of the elasticity tensor. This material model is implemented into the finite-element software ABAQUS and can be applied to 3D problems. Initial results show that this new material model is capable of describing the non-linear behaviour of geomaterials commonly observed before peak strength is reached as well as post-peak strain softening. Furthermore, it is demonstrated that the model can account for directional dependency of failure behaviour (i.e. anisotropy) and has the potential to be expanded to environmental controls like temperature or moisture.

Comparison of fractional and geodesic anisotropy in diffusion tensor images of 90 monozygotic and dizygotic twins

We used diffusion tensor magnetic resonance imaging (DTI) to reveal the extent of genetic effects on brain fiber microstructure, based on tensor-derived measures, in 22 pairs of monozygotic (MZ) twins and 23 pairs of dizygotic (DZ) twins (90 scans). After Log-Euclidean denoising to remove rank-deficient tensors, DTI volumes were fluidly registered by high-dimensional mapping of co-registered MP-RAGE scans to a geometrically-centered mean neuroanatomical template. After tensor reorientation using the strain of the 3D fluid transformation, we computed two widely used scalar measures of fiber integrity: fractional anisotropy (FA), and geodesic anisotropy (GA), which measures the geodesic distance between tensors in the symmetric positive-definite tensor manifold. Spatial maps of intraclass correlations (r) between MZ and DZ twins were compared to compute maps of Falconer's heritability statistics, i.e. the proportion of population variance explainable by genetic differences among individuals. Cumulative distribution plots (CDF) of effect sizes showed that the manifold measure, GA, comparably the Euclidean measure, FA, in detecting genetic correlations. While maps were relatively noisy, the CDFs showed promise for detecting genetic influences on brain fiber integrity as the current sample expands.

Tensor-based analysis of genetic influences on brain integrity using DTI in 100 twins

Information from the full diffusion tensor (DT) was used to compute voxel-wise genetic contributions to brain fiber microstructure. First, we designed a new multivariate intraclass correlation formula in the log-Euclidean framework. We then analyzed used the full multivariate structure of the tensor in a multivariate version of a voxel-wise maximum-likelihood structural equation model (SEM) that computes the variance contributions in the DTs from genetic (A), common environmental (C) and unique environmental (E) factors. Our algorithm was tested on DT images from 25 identical and 25 fraternal twin pairs. After linear and fluid registration to a mean template, we computed the intraclass correlation and Falconer's heritability statistic for several scalar DT-derived measures and for the full multivariate tensors. Covariance matrices were found from the DTs, and inputted into SEM. Analyzing the full DT enhanced the detection of A and C effects. This approach should empower imaging genetics studies that use DTI.

Phase transitions and gravity

Einstein's gravitational field is non-minimally coupled to a self-interacting scalar field in the presence of radiation. Such a theory can give rise to a phase transition associated with a change of sign of the gravitational “constant”. In our approach, the criterion for stability is formulated in terms of an effective potential, the phase-transition takes place due to temperature dependence of the scalar self-interaction coupling constant.

Instabilities induced by variation of Brunt-Vaisala frequency in compressible stratified shear flows

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible fluid in the presence of a lower rigid boundary are studied. A jump in the Brunt-Vaisala frequency at a level different from the shear zone is introduced and the variation of the Brunt-Vaisala frequency with respect to the vertical coordinate in the middle layer of the three-layered model is considered. An analytic solution in each of the layers is obtained, and the dispersion relation is solved numerically for parameters relevant to the model. The effect of shear in the lowermost layer of the three-layered model for a Boussinesq fluid is discussed. The results are compared with the earlier studies of Lindzen and Rosenthal, and Sachdev and Satya Narayanan. In the present model, new unstable modes with larger growth rates are obtained and the most unstable gravity wave modes are found to agree closely with the observed ones at various heights. Physics of Fluids is copyrighted by The American Institute of Physics.