Ultrashort pulses and short-pulse equations in (2+1)−(2+1)-dimensions

In this paper, we derive and study two versions of the short pulse equation (SPE) in $(2+1)-$dimensions. Using Maxwell's equations as a starting point, and suitable Kramers-Kronig formulas for the permittivity and permeability of the medium, which are relevant, e.g., to left-handed metamaterials and dielectric slab waveguides, we employ a multiple scales technique to obtain the relevant models. General properties of the resulting $(2+1)$-dimensional SPEs, including fundamental conservation laws, as well as the Lagrangian and Hamiltonian structure and numerical simulations for one- and two-dimensional initial data, are presented. Ultrashort 1D breathers appear to be fairly robust, while rather general two-dimensional localized initial conditions are transformed into quasi-one-dimensional dispersing waveforms

Velocity selection problem for combined motion of melting and solidification fronts

We discuss a free boundary problem for two moving solid-liquid interfaces that strongly interact via the diffusion field in the liquid layer between them. This problem arises in the context of liquid film migration (LFM) during the partial melting of solid alloys. In the LFM mechanism the system chooses a more efficient kinetic path which is controlled by diffusion in the liquid film, whereas the process with only one melting front would be controlled by the very slow diffusion in the mother solid phase. The relatively weak coherency strain energy is the effective driving force for LFM. As in the classical dendritic growth problems, also in this case an exact family of steady-state solutions with two parabolic fronts and an arbitrary velocity exists if capillary effects are neglected. We develop a velocity selection theory for this problem, including anisotropic surface tension effects. The strong diffusion interaction and coherency strain effects in the solid near the melting front lead to substantial changes compared to classical dendritic growth.Comment: submitted to PR

The turbulent spectrum created by non-Abelian plasma instabilities

Recent numerical work on the fate of plasma instabilities in weakly-coupled non-Abelian gauge theory has shown the development of a cascade of energy from long to short wavelengths. This cascade has a steady-state spectrum, analogous to the Kolmogorov spectrum for turbulence in hydrodynamics or for energy cascades in other systems. In this paper, we theoretically analyze processes responsible for this cascade and find a steady-state spectrum f_k ~ k^-2, where f_k is the phase-space density of particles with momentum k. The exponent -2 is consistent with results from numerical simulations. We also discuss implications of the emerging picture of instability development on the "bottom-up" thermalization scenario for (extremely high energy) heavy ion collisions, emphasizing fundamental questions that remain to be answered.Comment: 17 pages, 5 figure

The Nambu sum rule and the relation between the masses of composite Higgs bosons

We review the known results on the bosonic spectrum in various NJL models both in the condensed matter physics and in relativistic quantum field theory including $^3$He-B, $^3$He-A, the thin films of superfluid He-3, and QCD (Hadronic phase and the Color Flavor Locking phase). Next, we calculate bosonic spectrum in the relativistic model of top quark condensation suggested in \cite{Miransky}. In all considered cases the sum rule appears that relates the masses (energy gaps) $M_{boson}$ of the bosonic excitations in each channel with the mass (energy gap) of the condensed fermion $M_f$ as $\sum M_{boson}^2 = 4 M_f^2$. Previously this relation was established by Nambu in \cite{Nambu} for $^3$He-B and for the s - wave superconductor. We generalize this relation to the wider class of models and call it the Nambu sum rule. We discuss the possibility to apply this sum rule to various models of top quark condensation. In some cases this rule allows to calculate the masses of extra Higgs bosons that are the Nambu partners of the 125 GeV Higgs.Comment: Latex, 15 page

Glass state of superfluid 3He-A in aerogel

Glass states formed in the superfluid $^3$He confined in aerogel are discussed. If the short range order corresponds to the A-phase state, the glass state is nonsuperfluid in the long wave length limit. The superfluidity can be restored by application of a small mass current. Transitions between the superfluid and nonsuperfluid glass states can be triggered by small magnetic field and by the change of the tipping angle of magnetization in NMR experiments.Comment: 6 pages, LaTeX file, no figures, submitted to JETP Letter

Charge carrier interaction with a purely electronic collective mode: Plasmarons and the infrared response of elemental bismuth

We present a detailed optical study of single crystal bismuth using infrared reflectivity and ellipsometry. Colossal changes in the plasmon frequency are observed as a function of temperature due to charge transfer between hole and electron Fermi pockets. In the optical conductivity, an anomalous temperature dependent mid-infrared absorption feature is observed. An extended Drude model analysis reveals that it can be connected to a sharp upturn in the scattering rate, the frequency of which exactly tracks the temperature dependent plasmon frequency. We interpret this absorption and increased scattering as the first direct optical evidence for a charge carrier interaction with a collective mode of purely electronic origin; here electron-plasmon scattering. The observation of a \emph{plasmaron} as such is made possible only by the unique coincidence of various energy scales and exceptional properties of semi-metal bismuth.Comment: 4 pages, 4 figure

Rotating vortex core: An instrument for detecting the core excitations

Effects of fermionic zero modes (bound states in a vortex core) on the rotational dynamics of vortices with sponaneously broken axisymmetry are considered. The results are compared with the Helsinki experiments where the vortex cores were driven to a fast rotation and torsional oscillations by an NMR r.f. field (Kondo et al, Phys. Rev. Lett. 67, 81 (1991)). We predict a resonance NMR absorption on localized states at the external frequency comparable with the interelevel distance, which is similar to the cyclotron Landau damping. The resonances can experimentally resolve the localized levels in vortex cores. For a pure rotation of the core, the effect depends on the relative signs of the vortex winding number and of the core rotation; thus it is sensitive to the direction of rotation of the container. The similarity with the fermionic zero modes on the fundamental strings, which simulate the thermodynamics of black holes, is discussed.Comment: RevTex file, 7 pages, 1 Figure, extended and clarified after referee Reports, to appear in Phys. Rev.

Theoretically Efficient Parallel Graph Algorithms Can Be Fast and Scalable

There has been significant recent interest in parallel graph processing due to the need to quickly analyze the large graphs available today. Many graph codes have been designed for distributed memory or external memory. However, today even the largest publicly-available real-world graph (the Hyperlink Web graph with over 3.5 billion vertices and 128 billion edges) can fit in the memory of a single commodity multicore server. Nevertheless, most experimental work in the literature report results on much smaller graphs, and the ones for the Hyperlink graph use distributed or external memory. Therefore, it is natural to ask whether we can efficiently solve a broad class of graph problems on this graph in memory. This paper shows that theoretically-efficient parallel graph algorithms can scale to the largest publicly-available graphs using a single machine with a terabyte of RAM, processing them in minutes. We give implementations of theoretically-efficient parallel algorithms for 20 important graph problems. We also present the optimizations and techniques that we used in our implementations, which were crucial in enabling us to process these large graphs quickly. We show that the running times of our implementations outperform existing state-of-the-art implementations on the largest real-world graphs. For many of the problems that we consider, this is the first time they have been solved on graphs at this scale. We have made the implementations developed in this work publicly-available as the Graph-Based Benchmark Suite (GBBS).Comment: This is the full version of the paper appearing in the ACM Symposium on Parallelism in Algorithms and Architectures (SPAA), 201