The tensor structure on the representation category of the Wp\mathcal{W}_p triplet algebra

We study the braided monoidal structure that the fusion product induces on the abelian category $\mathcal{W}_p$-mod, the category of representations of the triplet $W$-algebra $\mathcal{W}_p$. The $\mathcal{W}_p$-algebras are a family of vertex operator algebras that form the simplest known examples of symmetry algebras of logarithmic conformal field theories. We formalise the methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch, that are widely used in the physics literature and illustrate a systematic approach to calculating fusion products in non-semi-simple representation categories. We apply these methods to the braided monoidal structure of $\mathcal{W}_p$-mod, previously constructed by Huang, Lepowsky and Zhang, to prove that this braided monoidal structure is rigid. The rigidity of $\mathcal{W}_p$-mod allows us to prove explicit formulae for the fusion product on the set of all simple and all projective $\mathcal{W}_p$-modules, which were first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and Runkel.Comment: 58 pages; edit: added references and revisions according to referee reports. Version to appear on J. Phys.

Free-standing all-polymer microring resonator optical filter

Free-standing all-polymer microring resonator optical filters as prototypical elements in flexible integrated lightwave circuits are demonstrated. The fabrication and measurement methods are discussed. The measured spectrum shows good agreement with theoretical expectations. The crucial 'critical' coupling condition is achieved, resulting in a measurement limited -27 dB extinction of the filter output on resonances

Zoology of a non-local cross-diffusion model for two species

We study a non-local two species cross-interaction model with cross-diffusion. We propose a positivity preserving finite volume scheme based on the numerical method introduced in Ref. [15] and explore this new model numerically in terms of its long-time behaviours. Using the so gained insights, we compute analytical stationary states and travelling pulse solutions for a particular model in the case of attractive-attractive/attractive-repulsive cross-interactions. We show that, as the strength of the cross-diffusivity decreases, there is a transition from adjacent solutions to completely segregated densities, and we compute the threshold analytically for attractive-repulsive cross-interactions. Other bifurcating stationary states with various coexistence components of the support are analysed in the attractive-attractive case. We find a strong agreement between the numerically and the analytically computed steady states in these particular cases, whose main qualitative features are also present for more general potentials

Nonlinear stability of flock solutions in second-order swarming models

In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one of the typical patterns emerging from such dynamics. We provide an analysis showing that the nonlinear stability of flocks in second-order models entirely depends on the linear stability of the first-order aggregation equation. Flocks are shown to be nonlinearly stable as a family of states under reasonable assumptions on the interaction potential. Furthermore, we numerically verify that commonly used potentials satisfy these hypotheses and investigate the nonlinear stability of flocks by an extensive case-study of uniform perturbations.Comment: 22 pages, 1 figure, 1 tabl

High-pressure study of the basal-plane anisotropy of the upper critical field of the topological superconductor SrxBi2Se3

We report a high-pressure transport study of the upper-critical field, $B_{c2}(T)$, of the topological superconductor Sr$_{0.15}$Bi$_2$Se$_3$ ($T_c = 3.0$ K). $B_{c2}(T)$ was measured for magnetic fields directed along two orthogonal directions, $a$ and $a^*$, in the trigonal basal plane. While superconductivity is rapidly suppressed at the critical pressure $p_c \sim 3.5$ GPa, the pronounced two-fold basal-plane anisotropy $B_{c2}^a/B_{c2}^{a^*} = 3.2$ at $T=0.3$ K, recently reported at ambient pressure (Pan et al., 2016), is reinforced and attains a value of $\sim 5$ at the highest pressure (2.2 GPa). The data reveal that the unconventional superconducting state with broken rotational symmetry is robust under pressure

Anomalous Nonlocal Resistance and Spin-charge Conversion Mechanisms in Two-Dimensional Metals

We uncover two anomalous features in the nonlocal transport behavior of two-dimensional metallic materials with spin-orbit coupling. Firstly, the nonlocal resistance can have negative values and oscillate with distance, even in the absence of a magnetic field. Secondly, the oscillations of the nonlocal resistance under an applied in-plane magnetic field (Hanle effect) can be asymmetric under field reversal. Both features are produced by direct magnetoelectric coupling, which is possible in materials with broken inversion symmetry but was not included in previous spin diffusion theories of nonlocal transport. These effects can be used to identify the relative contributions of different spin-charge conversion mechanisms. They should be observable in adatom-functionalized graphene, and may provide the reason for discrepancies in recent nonlocal transport experiments on graphene.Comment: 5 pages, 3 figures, and Supplementary Materials, to appear in Phys. Rev. Let

Symbol error rate analysis for M-QAM modulated physical-layer network coding with phase errors

Recent theoretical studies of physical-layer network coding (PNC) show much interest on high-level modulation, such as M-ary quadrature amplitude modulation (M-QAM), and most related works are based on the assumption of phase synchrony. The possible presence of synchronization error and channel estimation error highlight the demand of analyzing the symbol error rate (SER) performance of PNC under different phase errors. Assuming synchronization and a general constellation mapping method, which maps the superposed signal into a set of M coded symbols, in this paper, we analytically derive the SER for M-QAM modulated PNC under different phase errors. We obtain an approximation of SER for general M-QAM modulations, as well as exact SER for quadrature phase-shift keying (QPSK), i.e. 4-QAM. Afterwards, theoretical results are verified by Monte Carlo simulations. The results in this paper can be used as benchmarks for designing practical systems supporting PNC. © 2012 IEEE

v4 for identified particles at RHIC from viscous hydrodynamics

Using ideal and viscous hydrodynamics, the ratio of azimuthal moments v4/(v2)^2 is calculated for pions, protons, and kaons in sqrt{s}=200 A*GeV Au+Au collisions. For any value of viscosity here is little dependence on particle species. Ideal hydrodynamics and data show a flat curve as a function of pt. Adding viscosity in the standard way destroys this flatness. However, it can be restored by replacing the standard quadratic ansatz for delta f (the viscous correction to the distribution function at freeze-out) with a weaker momentum dependence.Comment: Proceedings of Hot Quarks 2010, 21-26 June 2010 La Londe Les Maures, 4 pages, 2 figure