Traveling gravity water waves with critical layers

We establish the existence of small-amplitude uni- and bimodal steady periodic gravity waves with an affine vorticity distribution, using a bifurcation argument that differs slightly from earlier theory. The solutions describe waves with critical layers and an arbitrary number of crests and troughs in each minimal period. An important part of the analysis is a fairly complete description of the local geometry of the so-called kernel equation, and of the small-amplitude solutions. Finally, we investigate the asymptotic behavior of the bifurcating solutions.Comment: 31 page

Fermion condensation and super pivotal categories

We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions, and condensing pairs of physical and emergent fermions. There are two distinct types of objects in fermionic theories, which we call "m-type" and "q-type" particles. The endomorphism algebras of q-type particles are complex Clifford algebras, and they have no analogues in bosonic theories. We construct a fermionic generalization of the tube category, which allows us to compute the quasiparticle excitations in fermionic topological phases. We then prove a series of results relating data in condensed theories to data in their parent theories; for example, if $\mathcal{C}$ is a modular tensor category containing a fermion, then the tube category of the condensed theory satisfies $\textbf{Tube}(\mathcal{C}/\psi) \cong \mathcal{C} \times (\mathcal{C}/\psi)$. We also study how modular transformations, fusion rules, and coherence relations are modified in the fermionic setting, prove a fermionic version of the Verlinde dimension formula, construct a commuting projector lattice Hamiltonian for fermionic theories, and write down a fermionic version of the Turaev-Viro-Barrett-Westbury state sum. A large portion of this work is devoted to three detailed examples of performing fermion condensation to produce fermionic topological phases: we condense fermions in the Ising theory, the $SO(3)_6$ theory, and the $\frac{1}{2}\text{E}_6$ theory, and compute the quasiparticle excitation spectrum in each of these examples.Comment: 161 pages; v2: corrected typos (including 18 instances of "the the") and added some reference

Constructing Narcoterrorism as Danger: Afghanistan and the Politics of Security and Representation

Afghanistan has become a country synonymous with danger. Discourses of narcotics, terrorism, and narcoterrorism have come to define the country and the current conflict. However, despite the prevalence of these dangers globally, they are seldom treated as political representations. This project theorizes danger as a political representation by deconstructing and problematizing contemporary discourses of (narco)terrorism in Afghanistan. Despite the globalisation of these two discourses of danger, (narco)terrorism remains largely under-theorised, with the focus placed on how to overcome this problem rather than critically analysing it as a representation. The argument being made here is that (narco)terrorism is not some ‘new’ existential danger, but rather reflects the hegemonic and counterhegemonic use of danger to establish authority over the collective identity. Using the case study of Afghanistan, this project critically analyses representations of danger emerging from the Afghan government and the Taliban. While many studies have looked at terrorism and narcotics as security concerns, there has not been a critical analysis of these two dangers as a political representation in the Afghan context. Therefore, this study will be of great benefit to scholars and practitioners of security as it presents a unique look on how identity is shaped through representations of danger in Afghanistan. Through applying Critical Discourse Analysis to contemporary representations in Afghanistan, this study provides new insight into the aims and objectives of both the Government of the Islamic Republic of Afghanistan and the Taliban

Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order

Foliated fracton order is a qualitatively new kind of phase of matter. It is similar to topological order, but with the fundamental difference that a layered structure, referred to as a foliation, plays an essential role and determines the mobility restrictions of the topological excitations. In this work, we introduce a new kind of field theory to describe these phases: a foliated field theory. We also introduce a new lattice model and string-membrane-net condensation picture of these phases, which is analogous to the string-net condensation picture of topological order.Comment: 22+15 pages, 8 figures; v3 added a summary of our model near the end of the introductio

The EMC of satellite power systems and DoD C-E systems

The solar power satellite (SPS) technical parameters that are needed to accurately assess the electromagnetic compatibility (EMC) between SPS systems and DoD communications-electronics (C-E) systems are identified and assessed. The type of electromagnetic interactions that could degrade the performance of C-E systems are described and the major military installations in the southwestern portions of CONUS where specially sensitive C-E systems are being used for combat training and evaluation are identified. Classes of C-E systems that are generally in the vicinity of these military installations are considered. The Technical parameters that govern the degree of compatibility of the SPS with these C-E systems, and some technical requirements that are necessary to ensure short-term and long-term EMC are identified

Quasiparticle velocities in 2D electron/hole liquids with spin-orbit coupling

We study the influence of spin-orbit interactions on quasiparticle dispersions in two-dimensional electron and heavy-hole liquids in III-V semiconductors. To obtain closed-form analytical results, we restrict ourselves to spin-orbit interactions with isotropic spectrum and work within the screened Hartree-Fock approximation, valid in the high-density limit. For electrons having a linear-in-momentum Rashba (or, equivalently, Dresselhaus) spin-orbit interaction, we show that the screened Hartree-Fock approximation recovers known results based on the random-phase approximation and we extend those results to higher order in the spin-orbit coupling. While the well-studied case of electrons leads only to a weak modification of quasiparticle properties in the presence of the linear-in-momentum spin-orbit interaction, we find two important distinctions for hole systems (with a leading nonlinear-in-momentum spin-orbit interaction). First, the group velocities associated with the two hole-spin branches acquire a significant difference in the presence of spin-orbit interactions, allowing for the creation of spin-polarized wavepackets in zero magnetic field. Second, we find that the interplay of Coulomb and spin-orbit interactions is significantly more important for holes than for electrons and can be probed through the quasiparticle group velocities. These effects should be directly observable in magnetotransport, Raman scattering, and femtosecond-resolved Faraday rotation measurements. Our results are in agreement with a general argument on the velocities, which we formulate for an arbitrary choice of the spin-orbit coupling.Comment: 11 pages, 4 figure

Beregningsprogram for pipesupport

Det er i denne oppgaven blitt laget et beregningsprogram for dimensjonering av pipesupports. Programmet tar for seg en firkantprofil som er festet til en plate, der bolter blir utsatt for skjær-, strekk- og momentbelastninger. Det er også sett på sveisen som er mellom platen og supportprofilen som holder oppe røret. Programmet er skrevet i Mathcad, som er et dataprogram som kan utføre både enkle og avanserte kalkulasjoner. Det er også tegnet og lagt inn enkle modeller i Inventor og ANSYS. Programmet er laget brukervennlig, for en rask innføring i beregning av pipesupports. Rapporten beskriver utgangspunktet for beregningene som er gjort, programmene som er brukt, og tanker rundt. Kapasitetsberegninger av forbindelser er blitt gjort i henhold til retningslinjene gitt i NS-EN 1993-1-8:2005+NA:2009 (Eurokode 3). Dette formelverket skal sikre at forbindelsen har nødvendige kapasiteter. Eurokodene er etter 1. april 2010 gjeldende regelverk for konstruksjoner i Nordsjøen. Tidligere var det de nasjonale standardene som var gjeldende