Phononic Rogue Waves

We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We consider two examples. The first one is the prototypical nonlinear mass-spring system in the form of a homogeneous Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with a polynomial potential. By deriving an approximation based on the nonlinear Schroedinger (NLS) equation, we are able to initialize the FPUT model using a suitably transformed Peregrine soliton solution of the NLS, obtaining dynamics that resembles a rogue wave on the FPUT lattice. We also show that Gaussian initial data can lead to dynamics featuring rogue wave for sufficiently wide Gaussians. The second example is a diatomic granular crystal exhibiting rogue wave like dynamics, which we also obtain through an NLS reduction and numerical simulations. The granular crystal (a chain of particles that interact elastically) is a widely studied system that lends itself to experimental studies. This study serves to illustrate the potential of such dynamical lattices towards the experimental observation of acoustic rogue waves.Comment: 9 pages, 4 figure

Perturbation theory for the two-dimensional abelian Higgs model in the unitary gauge

In the unitary gauge the unphysical degrees of freedom of spontaneously broken gauge theories are eliminated. The Feynman rules are simpler than in other gauges, but it is non-renormalizable by the rules of power counting. On the other hand, it is formally equal to the limit $\xi \to 0$ of the renormalizable R$_{\xi}$-gauge. We consider perturbation theory to one-loop order in the R$_{\xi}$-gauge and in the unitary gauge for the case of the two-dimensional abelian Higgs model. An apparent conflict between the unitary gauge and the limit $\xi \to 0$ of the R$_{\xi}$-gauge is resolved, and it is demonstrated that results for physical quantities can be obtained in the unitary gauge.Comment: 15 pages, LaTeX2e, uses the feynmf package, formulations correcte

Study of Strangeness Condensation by Expanding About the Fixed Point of the Harada-Yamawaki Vector Manifestation

Building on, and extending, the result of a higher-order in-medium chiral perturbation theory combined with renormalization group arguments and a variety of observations of the vector manifestation of Harada-Yamawaki hidden local symmetry theory, we obtain a surprisingly simple description of kaon condensation by fluctuating around the "vector manifestation (VM)" fixed point identified to be the chiral restoration point. Our development establishes that strangeness condensation takes place at about 3 n_0 where n_0 is nuclear matter density. This result depends only on the renoramlization-group (RG) behavior of the vector interactions, other effects involved in fluctuating about the bare vacuum in so many previous calculations being "irrelevant" in the RG about the fixed point. Our results have major effects on the collapse of neutron stars into black holes.Comment: 4 page

On Flux Rope Stability and Atmospheric Stratification in Models of Coronal Mass Ejections Triggered by Flux Emergence

Flux emergence is widely recognized to play an important role in the initiation of coronal mass ejections. The Chen-Shibata (2000) model, which addresses the connection between emerging flux and flux rope eruptions, can be implemented numerically to study how emerging flux through the photosphere can impact the eruption of a pre-existing coronal flux rope. The model's sensitivity to the initial conditions and reconnection micro-physics is investigated with a parameter study. In particular, we aim to understand the stability of the coronal flux rope in the context of X-point collapse and the effects of boundary driving in both unstratified and stratified atmospheres. In the absence of driving, we assess the behavior of waves in the vicinity of the X-point. With boundary driving applied, we study the effects of reconnection micro-physics and atmospheric stratification on the eruption. We find that the Chen-Shibata equilibrium can be unstable to an X-point collapse even in the absence of driving due to wave accumulation at the X-point. However, the equilibrium can be stabilized by reducing the compressibility of the plasma, which allows small-amplitude waves to pass through the X-point without accumulation. Simulations with the photospheric boundary driving evaluate the impact of reconnection micro-physics and atmospheric stratification on the resulting dynamics: we show the evolution of the system to be determined primarily by the structure of the global magnetic fields with little sensitivity to the micro-physics of magnetic reconnection; and in a stratified atmosphere, we identify a novel mechanism for producing quasi-periodic behavior at the reconnection site behind a rising flux rope as a possible explanation of similar phenomena observed in solar and stellar flares.Comment: Submitted Feb 28, 2014 to, accepted Aug 14, 2014 by Astronomy & Astrophysics. 13 pages, 10 figures, 2 table

Field theory in superfluid 3He: What are the lessons for particle physics, gravity and high-temperature superconductivity?

There are several classes of homogeneous Fermi-systems which are characterized by the topology of the energy spectrum of fermionic quasiparticles: (1) Gapless systems with a Fermi-surface; (2) Systems with a gap in their spectrum; (3) Gapless systems with topologically stable point nodes (Fermi points); and (4) Gapless systems with topologically unstable lines of nodes (Fermi lines). Superfluid 3He-A and electroweak vacuum belong to the universality Class (3). The fermionic quasiparticles (particles) in this class are chiral: they are left-handed or right-handed. The collective bosonic modes of systems of Class (3) are the effective gauge and gravitational fields. The great advantage of superfluid 3He-A is that we can perform experiments using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3He-A one can simulate event horizons, Hawking radiation, rotating vacuum, etc. High-temperature superconductors are believed to belong to Class (4). They have gapless fermionic quasiparticles with a "relativistic" spectrum close to gap nodes, which allows application of ideas developed for superfluid 3He-A.Comment: RevTex file, 8 pages, 5 figures, submitted to Proc. Nat. Ac. Sc. US, modified after referee reports, references are adde

Experimental and analytical investigation of axisymmetric supersonic cruise nozzle geometry at Mach numbers from 0.60 to 1.30

Quantitative pressure and force data for five axisymmetric boattail nozzle configurations were examined. These configurations simulate the variable-geometry feature of a single nozzle design operating over a range of engine operating conditions. Five nozzles were tested in the Langley 16-Foot Transonic Tunnel at Mach numbers from 0.60 to 1.30. The experimental data were also compared with theoretical predictions