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

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

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

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

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

Topological Defects on the Lattice I: The Ising model

In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect commutation relations, cousins of the Yang-Baxter equation. These relations and their solutions can be extended to allow defect lines to branch and fuse, again with properties depending only on topology. In this part I, we focus on the simplest example, the Ising model. We define lattice spin-flip and duality defects and their branching, and prove they are topological. One useful consequence is a simple implementation of Kramers-Wannier duality on the torus and higher genus surfaces by using the fusion of duality defects. We use these topological defects to do simple calculations that yield exact properties of the conformal field theory describing the continuum limit. For example, the shift in momentum quantization with duality-twisted boundary conditions yields the conformal spin 1/16 of the chiral spin field. Even more strikingly, we derive the modular transformation matrices explicitly and exactly.Comment: 45 pages, 9 figure

Nest building behavior in birds: cross-fostered individuals resemble their own species and not their foster species

Variation in behavioral traits may be genetically or environmentally determined, or both. Previous studies on nest building behaviour in captive birds have proposed that nest building is mainly genetically determined. However, to settle this question, cross-fostering experiments in the wild has been recommended. The focus of the present study has been nest building behavior in blue tits (Cyanistes caeruleus) and great tits (Parus major) studied in a woodland near Oslo in Norway, where respectively, 95 and 79 nests of the two species were observed. Both build nests of mosses, lined with hair and wool. Blue tits also often apply feathers, which are only occasionally used by great tits. Some individuals of both species were interspecifically cross-fostered, i.e. blue tit nestlings were raised by great tit parents, and great tit nestlings were raised by blue tit parents. This provided the opportunity to study, in a natural environment, whether the interspecific variation in use of nest materials is primarily genetically or environmentally determined (due to learning from conspecifics, i.e. cultural transmission). The results show that, with regard to nest building, cross-fostered blue tits and great tits resemble members of their own species and not members of their foster species. This held true even when accounting for possible confounding variables such as laying date of first egg, clutch size, egg volume, and age. This implies that the variation in nest building behavior between these species is largely genetically determined. We suggest that nest building is a conservative trait that has evolved differently in blue tits and great tits

Interaction effects in superconductor/quantum spin Hall devices: universal transport signatures and fractional Coulomb blockade

Interfacing s-wave superconductors and quantum spin Hall edges produces time-reversal-invariant topological superconductivity of a type that can not arise in strictly 1D systems. With the aim of establishing sharp fingerprints of this novel phase, we use renormalization group methods to extract universal transport characteristics of superconductor/quantum spin Hall heterostructures where the native edge states serve as leads. We determine scaling forms for the conductance through a grounded superconductor and show that the results depend sensitively on the interaction strength in the leads, the size of the superconducting region, and the presence or absence of time-reversal-breaking perturbations. We also study transport across a floating superconducting island isolated by magnetic barriers. Here we predict e-periodic Coulomb-blockade peaks, as recently observed in nanowire devices [Albrecht et al., Nature 531, 206 (2016)], with the added feature that the island can support fractional charge tunable via the relative orientation of the barrier magnetizations. As an interesting corollary, when the magnetic barriers arise from strong interactions at the edge that spontaneously break time-reversal symmetry, the Coulomb-blockade periodicity changes from e to e/2. These findings suggest several future experiments that probe unique characteristics of topological superconductivity at the quantum spin Hall edge.Comment: 18 pages, 7 figure