Wilson Lines and a Canonical Basis of SU(4) Heterotic Standard Models

The spontaneous breaking of SU(4) heterotic standard models by Z_3 x Z_3 Wilson lines to the MSSM with three right-handed neutrino supermultiplets and gauge group SU(3)_C x SU(2)_L x U(1) x U(1) is explored. The two-dimensional subspace of the Spin(10) Lie algebra that commutes with su(3)_C + su(2)_L is analyzed. It is shown that there is a unique basis for which the initial soft supersymmetry breaking parameters are uncorrelated and for which the U(1) x U(1) field strengths have no kinetic mixing at any scale. If the Wilson lines "turn on" at different scales, there is an intermediate regime with either a left-right or a Pati-Salam type model. We compute their spectra directly from string theory, and adjust the associated mass parameter so that all gauge parameters exactly unify. A detailed analysis of the running gauge couplings and soft gaugino masses is presented.Comment: 59 pages, 9 figure

Creativity as Cognitive design \ud The case of mesoscopic variables in Meta-Structures\ud

Creativity is an open problem which has been differently approached by several disciplines since a long time. In this contribution we consider as creative the constructivist design an observer does on the description levels of complex phenomena, such as the self-organized and emergent ones ( e.g., Bènard rollers, Belousov-Zhabotinsky reactions, flocks, swarms, and more radical cognitive and social emergences). We consider this design as related to the Gestaltian creation of a language fit for representing natural processes and the observer in an integrated way. Organised systems, both artificial and most of the natural ones are designed/ modelled according to a logical closed model which masters all the inter-relation between their constitutive elements, and which can be described by an algorithm or a single formal model. We will show there that logical openness and DYSAM (Dynamical Usage of Models) are the proper tools for those phenomena which cannot be described by algorithms or by a single formal model. The strong correlation between emergence and creativity suggests that an open model is the best way to provide a formal definition of creativity. A specific application relates to the possibility to shape the emergence of Collective Behaviours. Different modelling approaches have been introduced, based on symbolic as well as sub-symbolic rules of interaction to simulate collective phenomena by means of computational emergence. Another approach is based on modelling collective phenomena as sequences of Multiple Systems established by percentages of conceptually interchangeable agents taking on the same roles at different times and different roles at the same time. In the Meta-Structures project we propose to use mesoscopic variables as creative design, invention, good continuity and imitation of the description level. In the project we propose to define the coherence of sequences of Multiple Systems by using the values taken on by the dynamic mesoscopic clusters of its constitutive elements, such as the instantaneous number of elements having, in a flock, the same speed, distance from their nearest neighbours, direction and altitude. In Meta-Structures the collective behaviour’s coherence corresponds, for instance, to the scalar values taken by speed, distance, direction and altitude along time, through statistical strategies of interpolation, quasi-periodicity, levels of ergodicity and their reciprocal relationship. In this case the constructivist role of the observer is considered creative as it relates to neither non-linear replication nor transposition of levels of description and models used for artificial systems, like reductionism. Creativity rather lies in inventing new mesoscopic variables able to identify coherent patterns in complex systems. As it is known, mesoscopic variables represent partial macroscopic properties of a system by using some of the microscopic degrees of freedom possessed by composing elements. Such partial usage of microscopic as well as macroscopic properties allows a kind of Gestaltian continuity and imitation between levels of descriptions for mesoscopic modelling. \ud \u

A Modular Approach to Large-scale Design Optimization of Aerospace Systems.

Gradient-based optimization and the adjoint method form a synergistic combination that enables the efficient solution of large-scale optimization problems. Though the gradient-based approach struggles with non-smooth or multi-modal problems, the capability to efficiently optimize up to tens of thousands of design variables provides a valuable design tool for exploring complex tradeoffs and finding unintuitive designs. However, the widespread adoption of gradient-based optimization is limited by the implementation challenges for computing derivatives efficiently and accurately, particularly in multidisciplinary and shape design problems. This thesis addresses these difficulties in two ways. First, to deal with the heterogeneity and integration challenges of multidisciplinary problems, this thesis presents a computational modeling framework that solves multidisciplinary systems and computes their derivatives in a semi-automated fashion. This framework is built upon a new mathematical formulation developed in this thesis that expresses any computational model as a system of algebraic equations and unifies all methods for computing derivatives using a single equation. The framework is applied to two engineering problems: the optimization of a nanosatellite with 7 disciplines and over 25,000 design variables; and simultaneous allocation and mission optimization for commercial aircraft involving 330 design variables, 12 of which are integer variables handled using the branch-and-bound method. In both cases, the framework makes large-scale optimization possible by reducing the implementation effort and code complexity. The second half of this thesis presents a differentiable parametrization of aircraft geometries and structures for high-fidelity shape optimization. Existing geometry parametrizations are not differentiable, or they are limited in the types of shape changes they allow. This is addressed by a novel parametrization that smoothly interpolates aircraft components, providing differentiability. An unstructured quadrilateral mesh generation algorithm is also developed to automate the creation of detailed meshes for aircraft structures, and a mesh convergence study is performed to verify that the quality of the mesh is maintained as it is refined. As a demonstration, high-fidelity aerostructural analysis is performed for two unconventional configurations with detailed structures included, and aerodynamic shape optimization is applied to the truss-braced wing, which finds and eliminates a shock in the region bounded by the struts and the wing.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111567/1/hwangjt_1.pd