Bifurcation in electrostatic resistive drift wave turbulence

The Hasegawa-Wakatani equations, coupling plasma density and electrostatic potential through an approximation to the physics of parallel electron motions, are a simple model that describes resistive drift wave turbulence. We present numerical analyses of bifurcation phenomena in the model that provide new insights into the interactions between turbulence and zonal flows in the tokamak plasma edge region. The simulation results show a regime where, after an initial transient, drift wave turbulence is suppressed through zonal flow generation. As a parameter controlling the strength of the turbulence is tuned, this zonal flow dominated state is rapidly destroyed and a turbulence-dominated state re-emerges. The transition is explained in terms of the Kelvin-Helmholtz stability of zonal flows. This is the first observation of an upshift of turbulence onset in the resistive drift wave system, which is analogous to the well-known Dimits shift in turbulence driven by ion temperature gradients.Comment: 21 pages, 11 figure

An evaluation of possible mechanisms for anomalous resistivity in the solar corona

A wide variety of transient events in the solar corona seem to require explanations that invoke fast reconnection. Theoretical models explaining fast reconnection often rely on enhanced resistivity. We start with data derived from observed reconnection rates in solar flares and seek to reconcile them with the chaos-induced resistivity model of Numata & Yoshida (2002) and with resistivity arising out of the kinetic Alfv\'en wave (KAW) instability. We find that the resistivities arising from either of these mechanisms, when localized over lengthscales of the order of an ion skin depth, are capable of explaining the observationally mandated Lundquist numbers.Comment: Accepted, Solar Physic

Exponents of 2-multiarrangements and multiplicity lattices

We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.Comment: 14 page

Sub-kHz lasing of a CaF_2 Whispering Gallery Mode Resonator Stabilized Fiber Ring Laser

We utilize a high quality calcium fluoride whispering-gallery-mode resonator to stabilize a simple erbium doped fiber ring laser with an emission frequency of 196 THz (wavelenght 1530 nm) to a linewidth below 650 Hz. This corresponds to a relative stability of 3.3 x 10^(-12) over 16 \mus. In order to characterize the linewidth we use two identical self-built lasers and a commercial laser to determine the individual lasing linewidth via the three-cornered hat method.Comment: 4 pages, 3 figure

Magnetization of alpha\u27 iron nitride produced through the fcc->bct martensitic transformation in high magnetic field

The gamma iron nitride (nitrogen austenite) was subjected to high magnetic field process in order to drive the fcc-->bct martensitic transformation. Molar fraction of martensite monotonically increased with increasing the magnetic field and reached 94% at 35 T. With a combination of magnetization and 57Fe Mössbauer spectroscopy data, magnetization of bulk processed alpha[prime] phase with 9.6 at. % N is determined to be 229 emu/g, the same as that for dc sputtered thin films

Long-distance remote comparison of ultrastable optical frequencies with 1e-15 instability in fractions of a second

We demonstrate a fully optical, long-distance remote comparison of independent ultrastable optical frequencies reaching a short term stability that is superior to any reported remote comparison of optical frequencies. We use two ultrastable lasers, which are separated by a geographical distance of more than 50 km, and compare them via a 73 km long phase-stabilized fiber in a commercial telecommunication network. The remote characterization spans more than one optical octave and reaches a fractional frequency instability between the independent ultrastable laser systems of 3e-15 in 0.1 s. The achieved performance at 100 ms represents an improvement by one order of magnitude to any previously reported remote comparison of optical frequencies and enables future remote dissemination of the stability of 100 mHz linewidth lasers within seconds.Comment: 7 pages, 4 figure

Suppression of extraneous thermal noise in cavity optomechanics

Extraneous thermal motion can limit displacement sensitivity and radiation pressure effects, such as optical cooling, in a cavity-optomechanical system. Here we present an active noise suppression scheme and its experimental implementation. The main challenge is to selectively sense and suppress extraneous thermal noise without affecting motion of the oscillator. Our solution is to monitor two modes of the optical cavity, each with different sensitivity to the oscillator's motion but similar sensitivity to the extraneous thermal motion. This information is used to imprint "anti-noise" onto the frequency of the incident laser field. In our system, based on a nano-mechanical membrane coupled to a Fabry-P\'{e}rot cavity, simulation and experiment demonstrate that extraneous thermal noise can be selectively suppressed and that the associated limit on optical cooling can be reduced.Comment: 27 pages, 14 figure

Nature of Phase Transitions of Superconducting Wire Networks in a Magnetic Field

We study $I$-$V$ characteristics of periodic square Nb wire networks as a function of temperature in a transverse magnetic field, with a focus on three fillings 2/5, 1/2, and 0.618 that represent very different levels of incommensurability. For all three fillings, a scaling behavior of $I$-$V$ characteristics is found, suggesting a finite temperature continuous superconducting phase transition. The low-temperature $I$-$V$ characteristics are found to have an exponential form, indicative of the domain-wall excitations.Comment: 5 pages, also available at http://www.neci.nj.nec.com/homepages/tang.htm

Betti numbers for numerical semigroup rings

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra and Applications (V. Ene, E. Miller Eds.