Higher-Spin Interactions: four-point functions and beyond

In this work we construct an infinite class of four-point functions for massless higher-spin fields in flat space that are consistent with the gauge symmetry. In the Lagrangian picture, these reflect themselves in a peculiar non-local nature of the corresponding non-abelian higher-spin couplings implied by the Noether procedure that starts from the fourth order. We also comment on the nature of the colored spin-2 excitation present both in the open string spectrum and in the Vasiliev system, highlighting how some aspects of String Theory appear to reflect key properties of Field Theory that go beyond its low energy limit. A generalization of these results to n-point functions, fermions and mixed-symmetry fields is also addressed.Comment: 66 pages, 10 figures, 1 table, LaTex. Several statements clarified. Final version to appear in JHE

Extraction of textual information from image for information retrieval

Ph.DDOCTOR OF PHILOSOPH

Computational Predictions for Boger Fluids and Circular Contraction Flow under Various Aspect Ratios

This work puts forward a modeling study contrasted against experimental, with focus on abrupt circular contraction flow of two highly-elastic constant shear-viscosity Boger fluids, i.e. a polyacrylamide dissolved in corn-syrup PAA/CS (Fluid-1) and a polyisobutylene dissolved in polybutene PIB/PB (Fluid-2), in various contraction-ratio geometries. Moreover, this work goes hand-in-hand with the counterpart matching of experimental pressure-drops observed in such 4:1 and 8:1 aspect-ratio contraction flows, as described experimentally in the literature. In this study, the experimental findings, for Boger fluids with severe strain-hardening features, reveal significant vortex-evolution characteristics, correlated with enhanced pressure-drop phasing and normal-stress response in the corner region. It is shown how such behavior may be replicated through simulation and the rheological dependencies that are necessary to bring this about. Predictive solutions with an advanced hybrid finite-element/volume (fe/fv) algorithm are able to elucidate the rheological properties (extensional viscosity and normal-stress response) that rule such vortex-enhancement evolution. This is accomplished by employing the novel swanINNFM(q) family of fluids, through the swIM model-variant, with its strong and efficient control on elongational properties

FILAMENTS, FIBERS, AND FOLIATIONS IN FRUSTRATED SOFT MATERIALS

Assemblies of one-dimensional filaments appear in a wide range of physical systems: from biopolymer bundles, columnar liquid crystals, and superconductor vortex arrays; to familiar macroscopic materials, like ropes, cables, and textiles. Interactions between the constituent filaments in such systems are most sensitive to the distance of closest approach between the central curves which approximate their configuration, subjecting these distinct assemblies to common geometric constraints. Dual to strong dependence of inter-filament interactions on changes in the distance of closest approach is their relative insensitivity to reptations, translations along the filament backbone. In this dissertation, after briefly reviewing the mechanics and geometry of frustrated elastic materials relevant for the discussion of fiber geometry and elasticity in Chapter 1, we examine in detail the geometry associated with constant spacing between continuous filament fields, and the associated couplings between stretching of lengths between filaments, symmetries of multi-filament energies, and the shapes adopted by filament bundles. In Chapter 2, we consider two distinct notions of constant spacing in multi-filament packings in three Euclidean dimensions, E3: equidistance, where the distance of closest approach is constant along the length of filament pairs; and isometry, where the distances of closest approach between all neighboring filaments are constant and equal. We show that, although any smooth curve in E3 permits one dimensional families of collinear equidistant curves belonging to a ruled surface, there are only two families of tangent fields with mutually equidistant integral curves in E3. The relative shapes and configurations of curves in these families are highly constrained: they must be either (isometric) developable domains, which can bend, but not twist; or (non-isometric) constant-pitch helical bundles, which can twist, but not bend. Thus, filament textures that are simultaneously bent and twisted, such as twisted toroids of condensed DNA plasmids or wire ropes, are doubly frustrated: twist frustrates constant neighbor spacing in the cross-section, while non-equidistance requires additional longitudinal variations of spacing along the filaments. To illustrate the consequences of the failure of equidistance, we compare spacing in three almost equidistant\u27\u27 ansatzes for twisted toroidal bundles and use our formulation of equidistance to construct upper bounds on the growth of longitudinal variations of spacing with bundle thickness. In Chapter 3, we show that because the elastic response of non-equidistant filament bundles is frustrated, it cannot adequately be described by linearized, two-dimensional strains. To describe non-equidistant configurations, we derive a geometrically nonlinear, coordinate invariant, gauge-like theory for the elasticity of filamentous materials. For small strains, we derive the Euler-Lagrange equations for general, non-equidistant filament bundles, and show that, while force balance is qualitatively similar to that for 2D crystals, there are corrections which account for the non-integrability of twisted filament fields. Because of these corrections, force balance along the filament tangents couples to the convective flow tensor, which measures local deviations from equidistance. Within this framework, we discuss the impact of filament texture on bundle elasticity, and extend the analysis of helical filament bundles to the large twist limit. In Chapter 4, we finally turn our attention to longitudinally frustrated, non-equidistant bundles. Taking twisted toroidal filament bundles, which can be found in condensates of nucleic acids under confinement (e.g., inside a viral capsid), as a geometric prototype for the more general class of non-equidistant filament bundles, we derive the linearized force-balance equations in the limit of small central-filament curvature. While we make substantial progress towards a qualitative understanding of the behavior of non-equidistant filaments, the general solution to the Euler-Lagrange equations remains out of reach due to the presence of singularities at the outer boundary that emerge as a result of our perturbation scheme. We conclude by discussing the progress made in this dissertation in understanding the physics of frustrated fibers, and speculating about the ramifications for more general soft-elastic materials

The Influence of Deformation-Induced Residual Stresses on the Post-Forming Tensile Stress/Strain Behavior of Dual-Phase Steels

It was hypothesized that, in dual-phase (DP) steels, strain partitioning between ferrite and martensite during deformation results in a distribution of post-deformation residual stresses that, in turn, affects the subsequent strength, work hardening behavior and formability when the strain path is changed. The post-forming deformation-induced residual stress state was expected to depend upon the microstructure, the amount of strain and the prestrain path. The primary objective of this research program was to understand the influence of deformation-induced residual stresses on the post-forming tensile stress/strain behavior of DP steels. Three commercially produced sheet steels were considered in this analysis: 1) a DP steel with approximately 15 vol. % martensite, 2) a conventional high-strength, low-alloy (HSLA) steel, and 3) a conventional, ultra-low-carbon interstitial-free (IF) steel. Samples of each steel were subjected to various prestrain levels in various plane-stress forming modes, including uniaxial tension, plane strain and balanced biaxial stretching.Neutron diffraction experiments confirmed the presence of large post-forming deformation-induced residual stresses in the ferrite phase of the DP steel. The deformation-induced residual stress state varied systematically with the prestrain mode, where the principal residual stress components are proportional to the principal strain components of the prestrain mode, but opposite in sign. For the first time, and by direct experimental correlation, it was shown that deformation-induced residual stresses greatly affect the post-forming tensile stress/strain behavior of DP steels. As previously reported in the literature, the formability (residual tensile ductility) of the IF steel and the HSLA steel was adversely affected by strain path changes. The DP steel presents a formability advantage over the conventional IF and HSLA steels, and is expected to be particularly well suited for complex forming operations that involve abrupt strain path changes.Deformation-induced residual stresses were measured in the IF steel and the HSLA steel; however, the magnitudes of which are such that post-forming tensile stress/strain behavior was not significantly affected. Considering the vast differences in mechanical properties, microstructure, and composition, the IF steel and the HSLA steel showed remarkably similar post-forming tensile stress/strain behavior for all prestrain modes considered

C0 beam elements based on the Refined Zigzag Theory for multilayered composite and sandwich laminates

The paper deals with the development and computational assessment of three- and two-node beam finite elements based on the Refined Zigzag Theory (RZT) for the analysis of multilayered composite and sandwich beams. RZT is a recently proposed structural theory that accounts for the stretching, bending, and transverse shear deformations, and which provides substantial improvements over previously developed zigzag and higher-order theories. This new theory is analytically rigorous, variationally consistent, and computationally attractive. The theory is not affected by anomalies of most previous zigzag and higher-order theories, such as the vanishing of transverse shear stress and force at clamped boundaries. In contrast to Timoshenko theory, RZT does not employ shear correction factors to yield accurate results. From the computational mechanics perspective RZT requires C°-continuous shape functions and thus enables the development of efficient displacement-type finite elements. The focus of this paper is to explore several low-order beam finite elements that offer the best compromise between computational efficiency and accuracy. The initial attention is on the choice of shape functions that do not admit shear locking effects in slender beams. For this purpose, anisoparametric (aka interdependent) interpolations are adapted to approximate the four independent kinematic variables that are necessary to model the planar beam deformations. To achieve simple two-node elements, several types of constraint conditions are examined and corresponding deflection shape-functions are derived. It is recognized that the constraint condition requiring a constant variation of the transverse shear force gives rise to a remarkably accurate two-node beam element. The proposed elements and their predictive capabilities are assessed using several elastostatic example problems, where simply supported and cantilevered beams are analyzed over a range of lamination sequences, heterogeneous material properties, and slenderness ratios

An experimental and theoretical investigation of plane-stress fracture of 2024-T351 aluminum alloy

Plane-stress fracture behavior of precracked aluminum alloy

Selected aspects of lunar mare geology from Apollo orbital photography

Crater size-frequency distributions were studied (100-500 m) and are shown to provide significant integrated information concerning mare surface ages, subsurface stratigraphy, and surficial geology. Equilibrium cratering is discussed gradually reducing the relative numbers of craters smaller than 300-400 m in diameter as surfaces age and regolith thickens. Results for surface ages are in good agreement with other published crater ages. The existing correlations of large ring structures among various circular mare basins are shown to be based on criteria that are inconsistent and nonstandardized. A means of comparing equivalent ring structures in the different maria is proposed which takes into account the important characteristics of young unflooded basins (Orientale) as well as the progressive development of tectonic and volcanic features within the older flooded maria. Specific geologic aspects of several of the lunar maria are discussed and especially Mare Smythii, because of its great age and significantly different surface morphology. Lunar photographs and maps are shown

Performance assessment of Timber High-rise Buildings: Structural and Technological Considerations

Nowadays, a renewed momentum on the use of timber material is ensured by the development of high performing engineered wood products, which enables larger and taller structures to be built. Although the design of multi-story timber buildings is still in its early stages, the active interest shown by designers and researchers in advancing awareness and technologies in this field bodes well for the proliferation of an increasing number of tall wooden buildings