Branes are Waves and Monopoles

In a recent paper it was shown that fundamental strings are null waves in Double Field Theory. Similarly, membranes are waves in exceptional extended geometry. Here the story is continued by showing how various branes are Kaluza-Klein monopoles of these higher dimensional theories. Examining the specific case of the E7 exceptional extended geometry, we see that all branes are both waves and monopoles. Along the way we discuss the O(d; d) transformation of localized brane solutions not associated to an isometry and how true T-duality emerges in Double Field Theory when the background possesses isometries.Comment: 32 pages, Latex, v2, typos correcte

Quasilinear spin voltage profiles in spin thermoelectrics

Recent experiments show that spin thermoelectrics is a promising approach to generate spin voltages. While spin chemical potentials are often limited to a surface layer of the order of the spin diffusion length, we show that thermoelectrically induced spin chemical potentials can extend much further in itinerant ferromagnets with paramagnetic impurities. In some cases, conservation laws, e.g., for a combination of spin and heat currents, give rise to a linear spin voltage profile. More generally, we find quasilinear profiles involving a spin thermoelectric length scale which far exceeds the spin diffusion length.Comment: 4+ page

Structure and dynamics of binary liquid mixtures near their continuous demixing transitions

The dynamic and static critical behavior of five binary Lennard-Jones liquid mixtures, close to their continuous demixing points (belonging to the so-called model H' dynamic universality class), are studied computationally by combining semi-grand canonical Monte Carlo simulations and large-scale molecular dynamics (MD) simulations, accelerated by graphic processing units (GPU). The symmetric binary liquid mixtures considered cover a variety of densities, a wide range of compressibilities, and various interactions between the unlike particles. The static quantities studied here encompass the bulk phase diagram (including both the binodal and the $\lambda$-line), the correlation length, the concentration susceptibility, the compressibility of the finite-sized systems at the bulk critical temperature $T_c$, and the pressure. Concerning the collective transport properties, we focus on the Onsager coefficient and the shear viscosity. The critical power-law singularities of these quantities are analyzed in the mixed phase (above $T_c$) and non-universal critical amplitudes are extracted. Two universal amplitude ratios are calculated. The first one involves static amplitudes only and agrees well with the expectations for the three-dimensional Ising universality class. The second ratio includes also dynamic critical amplitudes and is related to the Einstein--Kawasaki relation for the interdiffusion constant. Precise estimates of this amplitude ratio are difficult to obtain from MD simulations, but within the error bars our results are compatible with theoretical predictions and experimental values for model H'. Evidence is reported for an inverse proportionality of the pressure and the isothermal compressibility at the demixing transition, upon varying either the number density or the repulsion strength between unlike particles.Comment: 15 pages, 12 figure

Graded Lie algebras with finite polydepth

If A is a graded connected algebra then we define a new invariant, polydepth A, which is finite if $Ext_A^*(M,A) \neq 0$ for some A-module M of at most polynomial growth. Theorem 1: If f : X \to Y is a continuous map of finite category, and if the orbits of H_*(\Omega Y) acting in the homology of the homotopy fibre grow at most polynomially, then H_*(\Omega Y) has finite polydepth. Theorem 2: If L is a graded Lie algebra and polydepth UL is finite then either L is solvable and UL grows at most polynomially or else for some integer d and all r, $\sum_{i=k+1}^{k+d} {dim} L_i \geq k^r$, $k\geq$ some $k(r)$

Sparsity-Sensitive Finite Abstraction

Abstraction of a continuous-space model into a finite state and input dynamical model is a key step in formal controller synthesis tools. To date, these software tools have been limited to systems of modest size (typically $\leq$ 6 dimensions) because the abstraction procedure suffers from an exponential runtime with respect to the sum of state and input dimensions. We present a simple modification to the abstraction algorithm that dramatically reduces the computation time for systems exhibiting a sparse interconnection structure. This modified procedure recovers the same abstraction as the one computed by a brute force algorithm that disregards the sparsity. Examples highlight speed-ups from existing benchmarks in the literature, synthesis of a safety supervisory controller for a 12-dimensional and abstraction of a 51-dimensional vehicular traffic network

Time Dependent Modeling of the Markarian 501 X-ray and TeV Gamma-Ray Data Taken During March and April, 1997

If the high-energy emission from TeV blazars is produced by the Synchrotron Self-Compton (SSC) mechanism, then simultaneous X-ray and Gamma-ray observations of these objects are a powerful probe of the electron (and/or positron) populations responsible for this emission. Understanding the emitting particle distributions and their evolution in turn allow us to probe physical conditions in the inner blazar jet and test, for example, various acceleration scenarios. By constraining the SSC emission model parameters, such observations also allow us to predict the intrinsic (unabsorbed) Gamma-ray spectra of these sources, a major uncertainty in current attempts to use the observed Gamma-ray spectra to constrain the intensity of the extragalactic background at optical/infrared wavelengths. As a next step in testing the SSC model and as a demonstration of the potential power of coordinated X-ray and Gamma-ray observations, we attempt to model in detail the X-ray and Gamma-ray light curves of the TeV Blazar Mrk 501 during its April-May 1997 outburst using a time dependent SSC emission model. Extensive, quasi-simultaneous X-ray and gamma-ray coverage exists for this period. We discuss and explore quantitatively several of the flare scenarios presented in the literature. We show that simple two-component models (with a soft, steady X-ray component plus a variable SSC component) involving substantial pre-acceleration of electrons to Lorentz factors on the order of 1E+5 describe the data train surprisingly well. All considered models imply an emission region that is strongly out of equipartition and low radiative efficiencies (ratio between kinetic jet luminosity and comoving radiative luminosity) of 1 per-mill and less.Comment: 16 pages, Refereed Manuscript. Minor changes to previous versio