The Chirality-Flow Formalism and Optimising Scattering Amplitudes

This thesis is composed of five papers, which all attempt to optimise calculations of scattering amplitudes in high-energy-physics collisions. These scattering amplitudes are a key part of theoretical predictions for particle-physics experiments like the Large Hadron Collider at CERN. The first four papers are the main topic of the thesis, and describe a novel method called chirality flow. Chirality flow simplifies Feynman-diagram calculations and makes them more intuitive. Papers I, II, and IV describe chirality flow in detail at both tree-level and one-loop level, while paper III shows a first implementation of it in the event generator MadGraph5_aMC@NLO. The final paper instead explores the speed, accuracy, and precision of an approximation of the colour part of a scattering amplitude.Paper I introduces the chirality-flow formalism, a new pictorial method used to calculate tree-level helicity amplitudes by drawing lines and connecting them to find spinor inner products, instead of doing algebraic manipulations. This method makes calculations more transparent, and often allows one to go from Feynman diagram to spinor inner products in a single line. Massless QED and QCD are treated in full. Paper II extends the chirality-flow formalism of paper I to deal with massive particles, and therefore allows chirality flow to be used for any tree-level Standard Model calculation. Paper III describes our implementation of chirality flow in massless QED in MadGraph5_aMC@NLO. A speed comparison is made showing up to a factor of 10 increase in evaluation speed. Paper IV extends the chirality-flow formalism to the one-loop level for any Standard Model calculation, showing the simplifications in the numerator algebra and the tensor reduction. Paper V describes an extension to the MadGraph5_aMC@NLO event generator in which the kinematics are calculated using Berends-Giele recursions instead of Feynman diagrams, and the colour matrix can be expanded in the number of colours Nc. The speed of the extension, and the accuracy and precision of the colour expansion are explored

A study of characteristics of intercity transportation systems. Phase 1: Definition of transportation comparison methodology

Decision making in early transportation planning must be responsive to complex value systems representing various policies and objectives. The assessment of alternative transportation concepts during the early initial phases of the system life cycle, when supportive research and technology development activities are defined, requires estimates of transportation, environmental, and socio-economic impacts throughout the system life cycle, which is a period of some 40 or 50 years. A unified methodological framework for comparing intercity passenger and freight transportation systems is described and is extended to include the comparison of long term transportation trends arising from implementation of the various R & D programs. The attributes of existing and future transportation systems are reviewed in order to establish measures for comparison, define value functions, and attribute weightings needed for comparing alternative policy actions for furthering transportation goals. Comparison criteria definitions and an illustrative example are included

Enforcing Femininity: How Jespersen v. Harrah\u27s Operating Co. Leaves Women in Typically Female Jobs Vulnerable to Workplace Sex Discrimination

This Comment argues that the Ninth Circuit was mistaken in concluding that Jespersen fell outside of the Supreme Court\u27s rule on sex-stereotyping discrimination under Title VII of the Civil Rights Act of 1964

Neuroanatomical Asymmetry, Handedness, and Family History of Handedness : A Study of the Markers of Structural and Functional Lateralization

This study investigated the associations between (1) handedness (demonstrated preference of one hand for the performance of most unimanual tasks) and neuroanatomical asymmetry (measurable differences in width between the cerebral hemispheres) and (2) familial history of handedness (the presence of a left-handed sibling or parent of a right-handed subject) as an intervening factor in the relation between handedness and neuroanatomical asymmetry. Width measurements of the brain were derived from computerized tomographic ( CT) films and grouped in to categories by hand preference (measured by the Edinburgh Handedness Inventory) and family history. The measurements of right (n=68), right with left-· handed relatives (n=24), and left-handed (n=16) groups were then compared by width and other transformations of the brain measurements. Subjects were adults of both sexes who had been referred for neurologic examination and were diagnosed as free of major distorting brain pathology. Hemispheric widths were compared by group, as ratios (left÷right) and as differences (left-right). Analysis of variance revealed significant differences between right-hemisphere widths at three percentages of brain length in the posterior occipital and temporal-parietal portion of the right hemisphere. The two right-handed groups had significantly smaller right-hemisphere measurements than the left group at 80% (p=.03), 75% (p= .012), and 60% (p= .029) of brain length. There were no significant left-hemisphere differences between the groups. In terms of ratios of sides and differences between sides in the same brain region, the left - handed group was different from the right-handed group at the p Handedness appears to be moderately associated with neuroanatomical asymmetry. The differences in sizes of brain structures and their relation to functionally lateralized abilities may shed light on the processes by which each hemisphere becomes specialized to perform specific tasks and other aspects of individual differences

Cooperative Chiral Order in Copolymers of Chiral and Achiral Units

Polyisocyanates can be synthesized with chiral and achiral pendant groups distributed randomly along the chains. The overall chiral order, measured by optical activity, is strongly cooperative and depends sensitively on the concentration of chiral pendant groups. To explain this cooperative chiral order theoretically, we map the random copolymer onto the one-dimensional random-field Ising model. We show that the optical activity as a function of composition is well-described by the predictions of this theory.Comment: 13 pages, including 3 postscript figures, uses REVTeX 3.0 and epsf.st

Prototyping Operational Autonomy for Space Traffic Management

Current state of the art in Space Traffic Management (STM) relies on a handful of providers for surveillance and collision prediction, and manual coordination between operators. Neither is scalable to support the expected 10x increase in spacecraft population in less than 10 years, nor does it support automated manuever planning. We present a software prototype of an STM architecture based on open Application Programming Interfaces (APIs), drawing on previous work by NASA to develop an architecture for low-altitude Unmanned Aerial System Traffic Management. The STM architecture is designed to provide structure to the interactions between spacecraft operators, various regulatory bodies, and service suppliers, while maintaining flexibility of these interactions and the ability for new market participants to enter easily. Autonomy is an indispensable part of the proposed architecture in enabling efficient data sharing, coordination between STM participants and safe flight operations. Examples of autonomy within STM include syncing multiple non-authoritative catalogs of resident space objects, or determining which spacecraft maneuvers when preventing impending conjunctions between multiple spacecraft. The STM prototype is based on modern micro-service architecture adhering to OpenAPI standards and deployed in industry standard Docker containers, facilitating easy communication between different participants or services. The system architecture is designed to facilitate adding and replacing services with minimal disruption. We have implemented some example participant services (e.g. a space situational awareness provider/SSA, a conjunction assessment supplier/CAS, an automated maneuver advisor/AMA) within the prototype. Different services, with creative algorithms folded into then, can fulfil similar functional roles within the STM architecture by flexibly connecting to it using pre-defined APIs and data models, thereby lowering the barrier to entry of new players in the STM marketplace. We demonstrate the STM prototype on a multiple conjunction scenario with multiple maneuverable spacecraft, where an example CAS and AMA can recommend optimal maneuvers to the spacecraft operators, based on a predefined reward function. Such tools can intelligently search the space of potential collision avoidance maneuvers with varying parameters like lead time and propellant usage, optimize a customized reward function, and be implemented as a scheduling service within the STM architecture. The case study shows an example of autonomous maneuver planning is possible using the API-based framework. As satellite populations and predicted conjunctions increase, an STM architecture can facilitate seamless information exchange related to collision prediction and mitigation among various service applications on different platforms and servers. The availability of such an STM network also opens up new research topics on satellite maneuver planning, scheduling and negotiation across disjoint entities

The chirality-flow formalism

We take a fresh look at Feynman diagrams in the spinor-helicity formalism. Focusing on tree-level massless QED and QCD, we develop a new and conceptually simple graphical method for their calculation. In this pictorial method, which we dub the chirality-flow formalism, Feynman diagrams are directly represented in terms of chirality-flow lines corresponding to spinor inner products, without the need to resort to intermediate algebraic manipulations.Comment: 44 pages, 3 figure

Counterion-Mediated Weak and Strong Coupling Electrostatic Interaction between Like-Charged Cylindrical Dielectrics

We examine the effective counterion-mediated electrostatic interaction between two like-charged dielectric cylinders immersed in a continuous dielectric medium containing neutralizing mobile counterions. We focus on the effects of image charges induced as a result of the dielectric mismatch between the cylindrical cores and the surrounding dielectric medium and investigate the counterion-mediated electrostatic interaction between the cylinders in both limits of weak and strong electrostatic couplings (corresponding, e.g., to systems with monovalent and multivalent counterions, respectively). The results are compared with extensive Monte-Carlo simulations exhibiting good agreement with the limiting weak and strong coupling results in their respective regime of validity.Comment: 19 pages, 10 figure