Higher-order corrections to the short-pulse equation

Using renormalization group techniques, we derive an extended short- pulse equation as approximation to a nonlinear wave equation. We investigate the new equation numerically and show that the new equation captures efficiently higher- order effects on pulse propagation in cubic nonlinear media. We illustrate our findings using one- and two-soliton solutions of the first-order short-pulse equation as initial conditions in the nonlinear wave equation

Polarization-induced distortion in stimulated Brillouin scattering slow-light systems

The vector analysis of stimulated Brillouin scattering amplification in birefringent fibers is extended to include signal pulses. The analysis finds that the different slow-light delays experienced by the states of polarization corresponding to maximum and minimum gain may result in severe pulse distortion. Thus, a generally polarized pulse, experiencing only a moderate gain, can become broader than a pulse aligned for maximum gain and delay. The effect is demonstrated in both numerical simulations and experiments

Extension of an Exponential Light Curve GRB Pulse Model Across Energy Bands

A simple mathematical model of GRB pulses in time, suggested in Norris et al. (2005), is extended across energy. For a class of isolated pulses, two of those parameters appear effectively independent of energy. Specifically, statistical fits indicate that pulse amplitude $A$ and pulse width $\tau$ are energy dependent, while pulse start time and pulse shape are effectively energy independent. These results bolster the Pulse Start and Pulse Scale conjectures of Nemiroff (2000) and add a new Pulse Shape conjecture which states that a class of pulses all have the same shape. The simple resulting pulse counts model is $P(t,E) = A(E) \ {\rm exp} (-t/\tau(E) - \tau(E)/t)$, where $t$ is the time since the start of the pulse. This pulse model is found to be an acceptable statistical fit to many of the fluent separable BATSE pulses listed in Norris et al. (2005). Even without theoretical interpretation, this cross-energy extension may be immediately useful for fitting prompt emission from GRB pulses across energy channels with a minimal number of free parameters.Comment: 11 pages, 5 figures. Accepted by MNRA

Advisory Succession in Real Estate Investment Trusts

Adaptation is crucial to realise high data rate transmission in multicarrier communication systems over dispersive channels. Apart from rate/power adaptation enabled by orthogonal frequency division multiplexing (OFDM), OFDM/offset QAM (OFDM/OQAM) systems provide possibility to adjust pulse shapes depending on the channel characteristics. In this paper we discuss and evaluate pulse shape adaptivity in OFDM/OQAM systems with focus on the extended Gaussian functions (EGF) which have been shown to be good candidates for pulse shape adaptation. By investigating the time frequency dispersion robustness and carrier frequency offset sensitivity, both analysis and simulation results show that pulse shape adaptation with respect to the channel state information can improve the system performance.QC 20111108</p

The Pulse Scale Conjecture and the Case of BATSE Trigger 2193

The pulses that compose gamma-ray bursts (GRBs) are hypothesized to have the same shape at all energies, differing only by scale factors in time and amplitude. This "Pulse Scale Conjecture" is confirmed here between energy channels of the dominant pulse in GRB 930214c (BATSE trigger 2193), the single most fluent single-pulsed GRB that occurred before May 1998. Furthermore, pulses are hypothesized to start at the same time independent of energy. This "Pulse Start Conjecture" is also confirmed in GRB 930214c. Analysis of GRB 930214c also shows that, in general, higher energy channels show shorter temporal scale factors. Over the energy range 100 KeV - 1 MeV, it is found that the temporal scale factors between a pulse measured at different energies are related to that energy by a power law, possibly indicating a simple relativistic mechanism is at work. To test robustness, the Pulse Start and Pulse Scale Conjectures were also tested on the four next most fluent single-pulse GRBs. Three of the four clearly passed, with a second smaller pulse possibly confounding the discrepant test. Models where the pulse rise and decay are created by different phenomena do not typically predict pulses that satisfy both the Pulse Start Conjecture and the Pulse Scale Conjecture, unless both processes are seen to undergo common time dilation.Comment: 19 pages, 9 figures, analysis revised and extended, accepted to Ap

Analytical studies of ultrashort optical pulse propagation in a resonant absorbing medium

Resonant absorption in a laser pulse can be reduced to zero if the trailing part induces stimulated emission and returns the absorbed energy back to the pulse. This kind of effect is called Self-Induced Transparency (SIT). Analytic descriptions of short pulse propagation in a resonant medium, based on Slowly Varying Envelope Approximation (SVEA) and in linear media, have been extended in studies of SIT along two principal directions: First, to improve the SVEA by introducing Short Pulse Approximation (SPA); and second, to consider the effect of nonlinear refractive index