Triplectic Gauge Fixing for N=1 Super Yang-Mills Theory

The Sp(2)-gauge fixing of N = 1 super-Yang-Mills theory is considered here. We thereby apply the triplectic scheme, where two classes of gauge-fixing bosons are introduced. The first one depends only on the gauge field, whereas the second boson depends on this gauge field and also on a pair of Majorana fermions. In this sense, we build up the BRST extended (BRST plus antiBRST) algebras for the model, for which the nilpotency relations, s^2_1=s^2_2=s_1s_2+s_2s_1=0, hold.Comment: 10 pages, no figures, latex forma

Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis

Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation. Explicit expressions for the transport coefficients are given, as a function of the microscopic parameters of the model. We show that the homogeneous state with zero hydrodynamic velocity is unstable above a critical density (which depends on the microscopic parameters), signaling the onset of a collective motion. Comparison with numerical simulations on a standard model of self-propelled particles shows that the phase diagram we obtain is robust, in the sense that it depends only slightly on the precise definition of the model. While the homogeneous flow is found to be stable far from the transition line, it becomes unstable with respect to finite-wavelength perturbations close to the transition, implying a non trivial spatio-temporal structure for the resulting flow. We find solitary wave solutions of the hydrodynamic equations, quite similar to the stripes reported in direct numerical simulations of self-propelled particles.Comment: 33 pages, 11 figures, submitted to J. Phys.

Triplectic Quantization of W2 gravity

The role of one loop order corrections in the triplectic quantization is discussed in the case of W2 theory. This model illustrates the presence of anomalies and Wess Zumino terms in this quantization scheme where extended BRST invariance is represented in a completely anticanonical form.Comment: 10 pages, no figure

Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice

The antiferromagnetic Ising model on a checkerboard lattice has an ice-like ground state manifold with extensive degeneracy. and, to leading order in J_xy, deconfined spinon excitations. We explore the role of cyclic exchange arising at order J^2_xy/J_z on the ice states and their associated spinon excitations. By mapping the original problem onto an equivalent quantum six--vertex model, we identify three different phases as a function of the chemical potential for flippable plaquettes - a phase with long range Neel order and confined spinon excitations, a non-magnetic state of resonating square plaquettes, and a quasi-collinear phase with gapped but deconfined spinon excitations. The relevance of the results to the square--lattice quantum dimer model is also discussed.Comment: 4 pages, 5 figure

Irreducible Hamiltonian BRST-anti-BRST symmetry for reducible systems

An irreducible Hamiltonian BRST-anti-BRST treatment of reducible first-class systems based on homological arguments is proposed. The general formalism is exemplified on the Freedman-Townsend model.Comment: LaTeX 2.09, 35 page

Quantum Dimer Model on the triangular lattice: Semiclassical and variational approaches to vison dispersion and condensation

After reviewing the concept of vison excitations in Z_2 dimer liquids, we study the liquid-crystal transition of the Quantum Dimer Model on the triangular lattice by means of a semiclassical spin-wave approximation to the dispersion of visons in the context of a "soft-dimer" version of the model. This approach captures some important qualitative features of the transition: continuous nature of the transition, linear dispersion at the critical point, and \sqrt{12}x\sqrt{12} symmetry-breaking pattern. In a second part, we present a variational calculation of the vison dispersion relation at the RK point which reproduces the qualitative shape of the dispersion relation and the order of magnitude of the gap. This approach provides a simple but reliable approximation of the vison wave functions at the RK point.Comment: 12 pages, 10 figures. v2: minor changes, to appear in Phys. Rev.

Criterion for purely elastic Taylor-Couette instability in the flows of shear-banding fluids

In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In micellar solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Recently, it has been suggested that those fluctuations originate from a purely elastic instability of the flow. In cylindrical Couette geometry, the instability is reminiscent of the Taylor-like instability observed in viscoelastic polymer solutions. In this letter, we describe how the criterion for purely elastic Taylor-Couette instability should be adapted to shear-banding flows. We derive three categories of shear-banding flows with curved streamlines, depending on their stability.Comment: 6 pages, 3 figure

Potential "ways of thinking" about the shear-banding phenomenon

Shear-banding is a curious but ubiquitous phenomenon occurring in soft matter. The phenomenological similarities between the shear-banding transition and phase transitions has pushed some researchers to adopt a 'thermodynamical' approach, in opposition to the more classical 'mechanical' approach to fluid flows. In this heuristic review, we describe why the apparent dichotomy between those approaches has slowly faded away over the years. To support our discussion, we give an overview of different interpretations of a single equation, the diffusive Johnson-Segalman (dJS) equation, in the context of shear-banding. We restrict ourselves to dJS, but we show that the equation can be written in various equivalent forms usually associated with opposite approaches. We first review briefly the origin of the dJS model and its initial rheological interpretation in the context of shear-banding. Then we describe the analogy between dJS and reaction-diffusion equations. In the case of anisotropic diffusion, we show how the dJS governing equations for steady shear flow are analogous to the equations of the dynamics of a particle in a quartic potential. Going beyond the existing literature, we then draw on the Lagrangian formalism to describe how the boundary conditions can have a key impact on the banding state. Finally, we reinterpret the dJS equation again and we show that a rigorous effective free energy can be constructed, in the spirit of early thermodynamic interpretations or in terms of more recent approaches exploiting the language of irreversible thermodynamics.Comment: 14 pages, 6 figures, tutorial revie

Cross-Lingual Classification of Crisis Data

Many citizens nowadays flock to social media during crises to share or acquire the latest information about the event. Due to the sheer volume of data typically circulated during such events, it is necessary to be able to efficiently filter out irrelevant posts, thus focusing attention on the posts that are truly relevant to the crisis. Current methods for classifying the relevance of posts to a crisis or set of crises typically struggle to deal with posts in different languages, and it is not viable during rapidly evolving crisis situations to train new models for each language. In this paper we test statistical and semantic classification approaches on cross-lingual datasets from 30 crisis events, consisting of posts written mainly in English, Spanish, and Italian. We experiment with scenarios where the model is trained on one language and tested on another, and where the data is translated to a single language. We show that the addition of semantic features extracted from external knowledge bases improve accuracy over a purely statistical model