Energy transmission in the forbidden bandgap of a nonlinear chain

A nonlinear chain driven by one end may propagate energy in the forbidden band gap by means of nonlinear modes. For harmonic driving at a given frequency, the process ocurs at a threshold amplitude by sudden large energy flow, that we call nonlinear supratransmission. The bifurcation of energy transmission is demonstrated numerically and experimentally on the chain of coupled pendula (sine-Gordon and nonlinear Klein-Gordon equations) and sustained by an extremely simple theory.Comment: LaTex file, 6 figures, published in Phys Rev Lett 89 (2002) 13410

Tristability in the pendula chain

Experiments on a chain of coupled pendula driven periodically at one end demonstrate the existence of a novel regime which produces an output frequency at an odd fraction of the driving frequency. The new stationary state is then obtained on numerical simulations and modeled with an analytical solution of the continuous sine-Gordon equation that resembles a kink-like motion back and forth in the restricted geometry of the chain. This solution differs from the expressions used to understand nonlinear bistability where the synchronization constraint was the basic assumption. As a result the short pendula chain is shown to possess tristable stationary states and to act as a frequency divider.Comment: To appear in PR

Gap soliton dynamics in an optical lattice as a parametrically driven pendulum

A long wavelength optical lattice is generated in a two-level medium by low-frequency contrapropagating beams. Then a short wave length gap soliton generated by evanescent boundary instability (supratransmission) undergoes a dynamics shown to obey the Newton equation of the parametrically driven pendulum, hence presenting extremely rich, possibly chaotic, dynamical behavior. The theory is sustained by numerical simulations and provides an efficient tool to study soliton trajectories

Use of cumulative incidence of novel influenza A/H1N1 in foreign travelers to estimate lower bounds on cumulative incidence in Mexico

Background: An accurate estimate of the total number of cases and severity of illness of an emerging infectious disease is required both to define the burden of the epidemic and to determine the severity of disease. When a novel pathogen first appears, affected individuals with severe symptoms are more likely to be diagnosed. Accordingly, the total number of cases will be underestimated and disease severity overestimated. This problem is manifest in the current epidemic of novel influenza A/H1N1. Methods and Results: We used a simple approach to leverage measures of incident influenza A/H1N1 among a relatively small and well observed group of US, UK, Spanish and Canadian travelers who had visited Mexico to estimate the incidence among a much larger and less well surveyed population of Mexican residents. We estimate that a minimum of 113,000 to 375,000 cases of novel influenza A/H1N1 have occurred in Mexicans during the month of April, 2009. Such an estimate serves as a lower bound because it does not account for underreporting of cases in travelers or for nonrandom mixing between Mexican residents and visitors, which together could increase the estimates by more than an order of magnitude. Conclusions: We find that the number of cases in Mexican residents may exceed the number of confirmed cases by two to three orders of magnitude. While the extent of disease spread is greater than previously appreciated, our estimate suggests that severe disease is uncommon since the total number of cases is likely to be much larger than those of confirmed cases

Multiscale reduction of discrete nonlinear Schroedinger equations

We use a discrete multiscale analysis to study the asymptotic integrability of differential-difference equations. In particular, we show that multiscale perturbation techniques provide an analytic tool to derive necessary integrability conditions for two well-known discretizations of the nonlinear Schroedinger equation.Comment: 12 page

University of Maine Williams Hall Dedication Ceremony

Video of the dedication ceremony of Beryl Warner Williams Hall at the University of Maine held on April 28 to honor the legacy of the Bangor native and UMaine’s first Black graduate to earn a degree in mathematics. Williams went on to have a distinguished academic career at Morgan State University and become an active civic leader in Baltimore

Discrete Multiscale Analysis: A Biatomic Lattice System

We discuss a discrete approach to the multiscale reductive perturbative method and apply it to a biatomic chain with a nonlinear interaction between the atoms. This system is important to describe the time evolution of localized solitonic excitations. We require that also the reduced equation be discrete. To do so coherently we need to discretize the time variable to be able to get asymptotic discrete waves and carry out a discrete multiscale expansion around them. Our resulting nonlinear equation will be a kind of discrete Nonlinear Schr\"odinger equation. If we make its continuum limit, we obtain the standard Nonlinear Schr\"odinger differential equation

Therapist effects in outpatient psychotherapy: A three-level growth curve approach

Evidence suggests that a moderate amount of variance in patient outcomes is attributable to therapist differences. However, explained variance estimates vary widely, perhaps because some therapists achieve greater success with certain kinds of patients. This study assessed the amount of variance in across-session change in symptom intensity scores explained by therapist differences in a large naturalistic data set (1,198 patients and 60 therapists, who each treated 10 -77 of the patients). Results indicated that approximately 8% of the total variance and approximately 17% of the variance in rates of patient improvement could be attributed to the therapists. Cross-validation and extreme group analyses validated the existence of these therapist effects

GNOSIS: the first instrument to use fibre Bragg gratings for OH suppression

GNOSIS is a prototype astrophotonic instrument that utilizes OH suppression fibres consisting of fibre Bragg gratings and photonic lanterns to suppress the 103 brightest atmospheric emission doublets between 1.47-1.7 microns. GNOSIS was commissioned at the 3.9-meter Anglo-Australian Telescope with the IRIS2 spectrograph to demonstrate the potential of OH suppression fibres, but may be potentially used with any telescope and spectrograph combination. Unlike previous atmospheric suppression techniques GNOSIS suppresses the lines before dispersion and in a manner that depends purely on wavelength. We present the instrument design and report the results of laboratory and on-sky tests from commissioning. While these tests demonstrated high throughput and excellent suppression of the skylines by the OH suppression fibres, surprisingly GNOSIS produced no significant reduction in the interline background and the sensitivity of GNOSIS and IRIS2 is about the same as IRIS2. It is unclear whether the lack of reduction in the interline background is due to physical sources or systematic errors as the observations are detector noise-dominated. OH suppression fibres could potentially impact ground-based astronomy at the level of adaptive optics or greater. However, until a clear reduction in the interline background and the corresponding increasing in sensitivity is demonstrated optimized OH suppression fibres paired with a fibre-fed spectrograph will at least provide a real benefits at low resolving powers.Comment: 15 pages, 13 figures, accepted to A