Analysis of Nematic Liquid Crystals with Disclination Lines

We investigate the structure of nematic liquid crystal thin films described by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a limiting uniaxial texture forms with disclination lines corresponding to a finite number of defects, all of degree 1/2 or all of degree -1/2. We also state a result on the limiting behavior of minimizers of the Chern-Simons-Higgs model without magnetic field that follows from a similar proof.Comment: 40 pages, 1 figur

Multipoint Variable Cycle Engine Design Using Gradient-based Optimization

Supersonic aircraft are challenging to optimally design due to the widely varying constraints and flight conditions they experience. Additionally, a large number of disciplinary subsystems must be considered due to highly complex design requirements. One subsystem that has a major effect on overall performance is the engine. In this work, we construct a supersonic mixed-flow variable cycle engine and perform multipoint gradient-based optimization using this model. We see that the operational variables allow the optimizer to tailor performance at each individual flight condition, leading to better overall performance. To simulate airframe integration constraints, we run successive optimizations with increasingly restrictive inlet areas and see decreases in engine performance. This work is part of a larger effort to incorporate engine design into aero-thermal-mission optimization of a supersonic aircraft

Halfvortices in flat nanomagnets

We discuss a new type of topological defect in XY systems where the O(2) symmetry is broken in the presence of a boundary. Of particular interest is the appearance of such defects in nanomagnets with a planar geometry. They are manifested as kinks of magnetization along the edge and can be viewed as halfvortices with winding numbers \pm 1/2. We argue that halfvortices play a role equally important to that of ordinary vortices in the statics and dynamics of flat nanomagnets. Domain walls found in experiments and numerical simulations are composite objects containing two or more of these elementary defects. We also discuss a closely related system: the two-dimensional smectic liquid crystal films with planar boundary condition.Comment: 7 pages, 8 figures, To appear as a chapter in Les Houches summer school on Quantum Magnetis

Numerical Model of a Variable-Combined-Cycle Engine for Dual Subsonic and Supersonic Cruise

Efficient high speed propulsion requires exploiting the cooling capability of the cryogenic fuel in the propulsion cycle. This paper presents the numerical model of a combined cycle engine while in air turbo-rocket configuration. Specific models of the various heat exchanger modules and the turbomachinery elements were developed to represent the physical behavior at off-design operation. The dynamic nature of the model allows the introduction of the engine control logic that limits the operation of certain subcomponents and extends the overall engine operational envelope. The specific impulse and uninstalled thrust are detailed while flying a determined trajectory between Mach 2.5 and 5 for varying throttling levels throughout the operational envelope

Ginzburg-Landau vortex dynamics with pinning and strong applied currents

We study a mixed heat and Schr\"odinger Ginzburg-Landau evolution equation on a bounded two-dimensional domain with an electric current applied on the boundary and a pinning potential term. This is meant to model a superconductor subjected to an applied electric current and electromagnetic field and containing impurities. Such a current is expected to set the vortices in motion, while the pinning term drives them toward minima of the pinning potential and "pins" them there. We derive the limiting dynamics of a finite number of vortices in the limit of a large Ginzburg-Landau parameter, or \ep \to 0, when the intensity of the electric current and applied magnetic field on the boundary scale like \lep. We show that the limiting velocity of the vortices is the sum of a Lorentz force, due to the current, and a pinning force. We state an analogous result for a model Ginzburg-Landau equation without magnetic field but with forcing terms. Our proof provides a unified approach to various proofs of dynamics of Ginzburg-Landau vortices.Comment: 48 pages; v2: minor errors and typos correcte

The mimetic politics of lone-wolf terrorism

Written at a time of crisis in the project of social and political modernity, Fyodor Dostoevsky’s 1864 novel Notes from Underground offers an intriguing parallel for the twenty-first century lone-wolf; it portrays an abject, outcast, spiteful unnamed anti-hero boiling with rage, bitter with resentment and on the verge of radicalisation. A Girardian reading of the poetic truths contained in Dostoevsky’s work is able to provide important keys to explain the contemporary transformation from ‘fourth-wave’ religious terrorism to ‘fifth-wave’ lone-wolf terrorism. Such a reading argues that it is mimetic rivalry – rather than much-trumpeted forms of religious violence or cultural differences – that fuels the triangular relation between governments, terrorists and civilian victims at heart of terrorist acts. This approach is further able to blend social inquiry with an account of the individual, in fact anthropological, conditions of lone-wolf terrorism by tracing the globalisation of resentment and the individualisation of violence to the hyper-mimeticism characterising the globalisation of late modernity. Finally, a mimetic reading of ‘fifth-wave’ terrorism accounts for the turbulence of a global politics in which victimhood and scapegoating no longer have the ability to stabilise social order and warns against a future where violence proliferates and escalates unchecked

Feasibility and acceptance of electronic quality of life assessment in general practice: an implementation study

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