Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations

We consider a dynamical system described by a system of ordinary differential equations which possesses a compact attracting set Λ of arbitrary shape. Under the assumption of uniform asymptotic stability of Λ in the sense of Lyapunov, we show that discretized versions of the dynamical system involving one-step numerical methods have nearby attracting sets Λ(h), which are also uniformly asymptotically stable. Our proof uses the properties of a Lyapunov function which characterizes the stability of Λ

Statistics of the General Circulation from Cumulant Expansions

Large-scale atmospheric flows may not be so nonlinear as to preclude their statistical description by systematic expansions in cumulants. I extend previous work by examining a two-layer baroclinic model of the general circulation. The fixed point of the cumulant expansion describes the statistically steady state of the out-of-equilibrium model. Equal-time statistics so obtained agree well with those accumulated by direct numerical simulation.Comment: 1 page paper with 4 figures that accompanies one of the winning entries in the APS gallery of nonlinear images competitio

Survey and Experimental Testing of Nongravimetric Mass Measurement Devices

Documentation presented describes the design, testing, and evaluation of an accelerated gravimetric balance, a low mass air bearing oscillator of the spring-mass type, and a centrifugal device for liquid mass measurement. A direct mass readout method was developed to replace the oscillation period readout method which required manual calculations to determine mass. A protoype 25 gram capacity micro mass measurement device was developed and tested

Get the gist? The effects of processing depth on false recognition in short-term and long-term memory

Gist-based processing has been proposed to account for robust false memories in the converging-associates task. The deep-encoding processes known to enhance verbatim memory also strengthen gist memory and increase distortions of long-term memory (LTM). Recent research has demonstrated that compelling false memory illusions are relatively delay-invariant, also occurring under canonical short-term memory (STM) conditions. To investigate the contributions of gist to false memory at short and long delays, processing depth was manipulated as participants encoded lists of four semantically related words and were probed immediately, following a filled 3- to 4-s retention interval, or approximately 20 min later, in a surprise recognition test. In two experiments, the encoding manipulation dissociated STM and LTM on the frequency, but not the phenomenology, of false memory. Deep encoding at STM increases false recognition rates at LTM, but confidence ratings and remember/know judgments are similar across delays and do not differ as a function of processing depth. These results suggest that some shared and some unique processes underlie false memory illusions at short and long delays

Observations of Very High Energy Gamma-Rays during Moonlight and Twilight with the MAGIC Telescope

We study the capability of the MAGIC telescope to observe under moderate moonlight. TeV gamma-ray signals from the Crab nebula were detected with the MAGIC telescope during periods when the Moon was above the horizon and during twilight. This was accomplished by increasing the trigger discriminator thresholds. No change is necessary in the high voltage settings since the camera PMTs were especially designed to avoid high currents. We characterize the telescope performance by studying the effect of the moonlight on the gamma-ray detection efficiency and sensitivity, as well as on the energy threshold.Comment: Contribution to the 30th ICRC, Merida Mexico, July 2007 on behalf of the MAGIC Collaboratio

Enhanced many-body effects in the excitation spectrum of a weakly-interacting rotating Bose-Einstein condensate

The excitation spectrum of a highly-condensed two-dimensional trapped Bose-Einstein condensate (BEC) is investigated within the rotating frame of reference. The rotation is used to transfer high-lying excited states to the low-energy spectrum of the BEC. We employ many-body linear-response theory and show that, once the rotation leads to a quantized vortex in the ground state, already the low-energy part of the excitation spectrum shows substantial many-body effects beyond the realm of mean-field theory. We demonstrate numerically that the many-body effects grow with the vorticity of the ground state, meaning that the rotation enhances them even for very weak repulsion. Furthermore, we explore the impact of the number of bosons $N$ in the condensate on a low-lying single-particle excitation, which is describable within mean-field theory. Our analysis shows deviations between the many-body and mean-field results which clearly persist when $N$ is increased up to the experimentally relevant regime, typically ranging from several thousand up to a million bosons in size. Implications are briefly discussed

A simple closure approximation for slow dynamics of a multiscale system: nonlinear and multiplicative coupling

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical simulations of such systems often require relatively small time discretization step to resolve fast dynamics, which, in turn, increases computational expense. As a result, it became a popular approach in applications to develop a closed approximate model for slow variables alone, which both effectively reduces the dimension of the phase space of dynamics, as well as allows for a longer time discretization step. In this work we develop a new method for approximate reduced model, based on the linear fluctuation-dissipation theorem applied to statistical states of the fast variables. The method is suitable for situations with quadratically nonlinear and multiplicative coupling. We show that, with complex quadratically nonlinear and multiplicative coupling in both slow and fast variables, this method produces comparable statistics to what is exhibited by an original multiscale model. In contrast, it is observed that the results from the simplified closed model with a constant coupling term parameterization are consistently less precise