Kinematical and Dynamical Aspects of Higher-Spin Bound-State Equations in Holographic QCD

In this paper we derive holographic wave equations for hadrons with arbitrary spin starting from an effective action in a higher-dimensional space asymptotic to anti-de Sitter (AdS) space. Our procedure takes advantage of the local tangent frame, and it applies to all spins, including half-integer spins. An essential element is the mapping of the higher-dimensional equations of motion to the light-front Hamiltonian, thus allowing a clear distinction between the kinematical and dynamical aspects of the holographic approach to hadron physics. Accordingly, the non-trivial geometry of pure AdS space encodes the kinematics, and the additional deformations of AdS space encode the dynamics, including confinement. It thus becomes possible to identify the features of holographic QCD which are independent of the specific mechanisms of conformal symmetry breaking. In particular, we account for some aspects of the striking similarities and differences observed in the systematics of the meson and baryon spectra.Comment: 43 page

Light-front holographic QCD and emerging confinement

In this report we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. The light-front holographic methods described here give a precise interpretation of holographic variables and quantities in AdS space in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound-states in physical space-time. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large q(2) the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low q2 the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications. (C)) 2015 Elsevier B.V. All rights reserved

Texture evolution in Ti-6AI-4V

Crystallographic orientation and microstructural morphology control properties in engineering materials. Titanium alloys are used extensively in commercial turbofan aircraft engines, due to their high strength and excellent corrosion resistance. The formation of preferred crystallite orientations during manufacturing must be understood in order to maximise component lifespan and avoid failure. In this thesis, I present a methodology which generates virtual 3D microstructures representing a material, conforming to an approximation of a 2D reference surface characterised by electron backscatter diffraction (EBSD). The subsurface grains of this microstructure are instanced using statistical information taken from the map, controlling grain size and texture. The subsurface texture is controlled through optimisations of an orientation distribution function (ODF) and misorientation distribution function (MDF). The influence of this control is shown through simulating deformation within the DAMASK crystal plasticity fast Fourier transform (CP-FFT) solver, to demonstrate the effect of subsurface texture on the stress and strain partitioning on the reference surface. The textures of Ti-6Al 4V formed through hot-rolling at temperatures between 750 and 950 °C are characterised by EBSD. As this method measures spatial and orientation information describing a 2D surface the material, I investigate the mechanisms through which lattice orientations of crystallites evolve during processing. EBSD maps are segmented by preferred orientation to demonstrate the spatial distribution of texture fibres. By measuring phase composition through direct backscatter spectroscopy (DBS) and elemental composition through energy dispersive x-ray spectroscopy (EDS), I demonstrate the influence of the β phase on the formation of texture fibres during rolling, with weak evolution of all existing texture fibres as the Ti-6Al-4V bar plastically deforms through slip. Through CP-FFT simulations of synthetic textured polycrystals in DAMASK, using the orientations of the texture fibres observed by EBSD, I simulate the texture evolution during deformation by hot rolling. Through examination of lattice rotation, slip shear rates and twinning shear rates, I demonstrate that the texture evolution resulting from plastic deformation at high temperatures is conducted entirely by crystal slip, resulting in only small lattice rotations and weak texture evolution. This is in agreement with the textures obtained through EBSD of hot-rolled Ti-6Al-4V.Open Acces

Similarities and Differences Between Warped Linear Prediction and Laguerre Linear Prediction

Linear prediction has been successfully applied in many speech and audio processing systems. This paper presents the similarities and differences between two classes of linear prediction schemes, namely, Warped Linear Prediction (WLP) and Laguerre Linear Prediction (LLP). It is shown that both systems are closely related. In particular, we show that the LLP is in fact a WLP system where the optimization procedure is adapted such that the whitening property is automatically incorporated. The adaptation consists of a new linear constraint on the parameters. Furthermore, we show that an optimized WLP scheme where whitening is achieved by prefiltering before estimating the optimal coefficients results in a filter having all except the last reflection coefficient equal to those of the optimal LLP filter.

Bayesian Variational Regularisation for Dark Matter Reconstruction with Uncertainty Quantification

Despite the great wealth of cosmological knowledge accumulated since the early 20th century, the nature of dark-matter, which accounts for ~85% of the matter content of the universe, remains illusive. Unfortunately, though dark-matter is scientifically interesting, with implications for our fundamental understanding of the Universe, it cannot be directly observed. Instead, dark-matter may be inferred from e.g. the optical distortion (lensing) of distant galaxies which, at linear order, manifests as a perturbation to the apparent magnitude (convergence) and ellipticity (shearing). Ensemble observations of the shear are collected and leveraged to construct estimates of the convergence, which can directly be related to the universal dark-matter distribution. Imminent stage IV surveys are forecast to accrue an unprecedented quantity of cosmological information; a discriminative partition of which is accessible through the convergence, and is disproportionately concentrated at high angular resolutions, where the echoes of cosmological evolution under gravity are most apparent. Capitalising on advances in probability concentration theory, this thesis merges the paradigms of Bayesian inference and optimisation to develop hybrid convergence inference techniques which are scalable, statistically principled, and operate over the Euclidean plane, celestial sphere, and 3-dimensional ball. Such techniques can quantify the plausibility of inferences at one-millionth the computational overhead of competing sampling methods. These Bayesian techniques are applied to the hotly debated Abell-520 merging cluster, concluding that observational catalogues contain insufficient information to determine the existence of dark-matter self-interactions. Further, these techniques were applied to all public lensing catalogues, recovering the then largest global dark-matter mass-map. The primary methodological contributions of this thesis depend only on posterior log-concavity, paving the way towards a, potentially revolutionary, complete hybridisation with artificial intelligence techniques. These next-generation techniques are the first to operate over the full 3-dimensional ball, laying the foundations for statistically principled universal dark-matter cartography, and the cosmological insights such advances may provide