Solutions of mKdV in classes of functions unbounded at infinity

In 1974 P. Lax introduced an algebro-analytic mechanism similar to the Lax L-A pair. Using it we prove global existence and uniqueness for solutions of the initial value problem for mKdV in classes of smooth functions which can be unbounded at infinity, and may even include functions which tend to infinity with respect to the space variable. Moreover, we establish the invariance of the spectrum and the unitary type of the Schr{\"o}dinger operator under the KdV flow and the invariance of the spectrum and the unitary type of the impedance operator under the mKdV flow for potentials in these classes.Comment: 35 pages, new results about spectra and eigenfunctions of Schr\"odinger operators added, new references adde

Multiple metamagnetic quantum criticality in Sr3_3Ru2_2O7_7

Bilayer strontium ruthenate Sr$_3$Ru$_2$O$_7$ displays pronounced non-Fermi liquid behavior at magnetic fields around 8 T, applied perpendicular to the ruthenate planes, which previously has been associated with an itinerant metamagnetic quantum critical end point (QCEP). We focus on the magnetic Gr\"uneisen parameter $\Gamma_{\rm H}$, which is the most direct probe to characterize field-induced quantum criticality. We confirm quantum critical scaling due to a putative two-dimensional QCEP near 7.845(5) T, which is masked by two ordered phases A and B, identified previously by neutron scattering. In addition we find evidence for a QCEP at 7.53(2) T and determine the quantum critical regimes of both instabilities and the effect of their superposition

Optical generation and wireless transmission of 60 GHz OOK signals using gain switched laser

We present a novel, simple and cost effective system for optical millimeter-wave generation and transmission of 3 Gbps data based on gain switching. System performance has been investigated, including wireless transmission and power budget analysis

Demonstration of wavelength packet switched radio-over-fiber system

The authors present a novel concept of employing optical wavelength packet switching in radio-over-fiber access networks. In such a system, the tunable laser (TL) would be employed as a transmitter in the central station. The optical carrier generated by this device would be externally modulated with the data signal upconverted to an RF frequency before being sent to the appropriate base station (BS). If each of the BSs is assigned a unique wavelength, the addressing and routing of traffic could be performed on a packet-by-packet basis with the TL switching between the wavelength assigned to different BS

Initial bound state studies in light-front QCD

We present the first numerical QCD bound state calculation based on a renormalization group-improved light-front Hamiltonian formalism. The QCD Hamiltonian is determined to second order in the coupling, and it includes two-body confining interactions. We make a momentum expansion, obtaining an equal-time-like Schrodinger equation. This is solved for quark-antiquark constituent states, and we obtain a set of self-consistent parameters by fitting B meson spectra.Comment: 38 pages, latex, 5 latex figures include

Context Dependence, MOPs,WHIMs and procedures Recanati and Kaplan on Cognitive Aspects in Semantics

After presenting Kripke’s criticism to Frege’s ideas on context dependence of thoughts, I present two recent attempts of considering cognitive aspects of context dependent expressions inside a truth conditional pragmatics or semantics: Recanati’s non-descriptive modes of presentation (MOPs) and Kaplan’s ways of having in mind (WHIMs). After analysing the two attempts and verifying which answers they should give to the problem discussed by Kripke, I suggest a possible interpretation of these attempts: to insert a procedural or algorithmic level in semantic representations of indexicals. That a function may be computed by different procedures might suggest new possibilities of integrating contextual cognitive aspects in model theoretic semanti

A finite element based formulation for sensitivity studies of piezoelectric systems

Sensitivity Analysis is a branch of numerical analysis which aims to quantify the affects that variability in the parameters of a numerical model have on the model output. A finite element based sensitivity analysis formulation for piezoelectric media is developed here and implemented to simulate the operational and sensitivity characteristics of a piezoelectric based distributed mode actuator (DMA). The work acts as a starting point for robustness analysis in the DMA technology

Photon Statistics of a Single Atom Laser

We consider a laser model consisting of a single four-level or three-level atom, an optical cavity, and an incoherent pump. Results for photon statistics for varying pump levels are obtained using a quantum trajectory algorithm. In particular, we calculate the mean photon number, Fano factor (which is the variance over the mean). We examine that the behavior of the single-atom device as β, the fraction of spontaneous emission into the lasing mode, is varied. Typical values considered for β are 0.01\u3cβ\u3c1.0. We find that for large enough β, lasing action, with properties similar to those predicted by semiclassical theories that factorize atom-field correlations and use a small-noise approximation, can occur. Squeezing can occur as β is increased. There is no evidence of a sharp phase transition from weakly excited thermal light to coherent light at a particular pump power. This is consistent with work on many-atom lasers with β values in the range considered here. As β is increased, the output goes from quasithermal light to coherent and finally to squeezed light, progressing into a fully quantum-mechanical regime. We also consider the effects of cavity damping and spontaneous emission rates on these results

Kleinian Geometry and the N=2 Superstring

This paper is devoted to the exploration of some of the geometrical issues raised by the $N=2$ superstring. We begin by reviewing the reasons that $\beta$-functions for the $N=2$ superstring require it to live in a four-dimensional self-dual spacetime of signature $(--++)$, together with some of the arguments as to why the only degree of freedom in the theory is that described by the gravitational field. We then move on to describe at length the geometry of flat space, and how a real version of twistor theory is relevant to it. We then describe some of the more complicated spacetimes that satisfy the $\beta$-function equations. Finally we speculate on the deeper significance of some of these spacetimes.Comment: 30 pages, AMS-Te