Inner approximated reachability analysis

International audienceComputing a tight inner approximation of the range of a function over some set is notoriously di cult, way beyond obtaining outer approximations. We propose here a new method to compute a tight inner approximation of the set of reachable states of non-linear dynamical systems on a bounded time interval. This approach involves a ne forms and Kaucher arithmetic, plus a number of extra ingredients from set-based methods. An implementation of the method is discussed, and illustrated on representative numerical schemes, discrete-time and continuous-time dynamical systems

A High-resolution Adaptive Moving Mesh Hydrodynamic Algorithm

An algorithm for simulating self-gravitating cosmological astrophysical fluids is presented. The advantages include a large dynamic range, parallelizability, high resolution per grid element and fast execution speed. The code is based on a finite volume flux conservative Total-Variation-Diminishing (TVD) scheme for the shock capturing hydro, and an iterative multigrid solver for the gravity. The grid is a time dependent field, whose motion is described by a generalized potential flow. Approximately constant mass per cell can be obtained, providing all the advantages of a Lagrangian scheme. The grid deformation combined with appropriate limiting and smoothing schemes guarantees a regular and well behaved grid geometry, where nearest neighbor relationships remain constant. The full hydrodynamic fluid equations are implemented in the curvilinear moving grid, allowing for arbitrary fluid flow relative to the grid geometry. This combination retains all the advantages of the grid based schemes including high speed per fluid element and a rapid gravity solver. The current implementation is described, and empirical simulation results are presented. Accurate execution speed calculations are given in terms of floating point operations per time step per grid cell. This code is freely available to the community.Comment: 53 pages including 14 figures, submitted to ApJ

Unconventional motional narrowing in the optical spectrum of a semiconductor quantum dot

Motional narrowing refers to the striking phenomenon where the resonance line of a system coupled to a reservoir becomes narrower when increasing the reservoir fluctuation. A textbook example is found in nuclear magnetic resonance, where the fluctuating local magnetic fields created by randomly oriented nuclear spins are averaged when the motion of the nuclei is thermally activated. The existence of a motional narrowing effect in the optical response of semiconductor quantum dots remains so far unexplored. This effect may be important in this instance since the decoherence dynamics is a central issue for the implementation of quantum information processing based on quantum dots. Here we report on the experimental evidence of motional narrowing in the optical spectrum of a semiconductor quantum dot broadened by the spectral diffusion phenomenon. Surprisingly, motional narrowing is achieved when decreasing incident power or temperature, in contrast with the standard phenomenology observed for nuclear magnetic resonance

Fluid-structure interaction simulation of prosthetic aortic valves : comparison between immersed boundary and arbitrary Lagrangian-Eulerian techniques for the mesh representation

In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary Lagrangian-Eulerian) or an Eulerian formulation. The majority of the reported 3D heart valve FSI simulations are performed with the Eulerian formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an Eulerian-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations' outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results

Ultrafast Coherent Generation of Hot Electrons Studied via Band-to-Acceptor Luminescence in GaAs

The distribution of hot electrons excited with femtosecond laser pulses is studied via spectrally resolved band-to-acceptor luminescence. Our data demonstrate for the first time that the coherent coupling between the laser pulse and the interband polarization strongly influences the initial carrier distribution. The energetic width of carrier generation is broadened due to rapid phase-breaking scattering events. Theoretical results from a Monte Carlo solution of the semiconductor Bloch equations including on the same kinetic level coherent and incoherent phenomena, are in excellent agreement with the experimental data

First Observation of Υ(1S)→γππ\Upsilon(1S)\to \gamma\pi\pi

We report on a study of exclusive radiative decays of the Upsilon(1S) resonance collected with the CLEO-II detector operating at CESR. We present the first observation of the radiative decays Upsilon(1S)->gamma pi+pi- and Upsilon(1S)->gamma pi0pi0. For the dipion mass regime m(pipi)>1.0 GeV, we obtain Br(Upsilon(1S)->gamma pi+pi-=(6.3+/-1.2+/-1.3) x 10^(-5), and Br(Upsilon(1S)->gamma pi0pi0=(1.7+/-0.6+/-0.3) x 10^(-5). The observed gamma pipi events are consistent with the hypothesis Upsilon(1S)->gamma f2(1270).Comment: 9 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Further Search for the Two-Photon Production of the Glueball Candidate fJ(2220)f_{J}(2220)

The CLEOII detector at the Cornell e+ e- storage ring CESR has been used to search for the two-photon production of the $f_J(2220)$ decaying into pi+ pi-. No evidence for a signal is found in data corresponding to an integrated luminosity of 4.77/fb and a 95% CL upper limit on $\Gamma_{two-photon} * BR{pi+ pi-}$ of 2.5 eV is set. If this result is combined with the BES Collaboration's measurement of $f_J(2220) -> pi+ pi-$ in radiative $J/\psi$ decay, a 95% CL lower limit on the stickiness of the $f_J(2220)$ of 73 is obtained. If the recent CLEO result for \Gamma_{two-photon} * BR{\K_S K_S} is combined with the present result, the stickiness of the $f_J(2220)$ is found to be larger than 102 at the 95% CL. These results for the stickiness (the ratio of the probabilities for two-gluon coupling and two-photon coupling) provide further support for a substantial neutral parton content in the $f_J(2220)$.Comment: 8 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Update of the Search for the Neutrinoless Decay τ→μγ\tau\to \mu\gamma

We present an update of the search for the lepton family number violating decay $\tau \to \mu\gamma$ using a complete CLEO II data sample of 12.6 million $\tau^+\tau^-$ pairs. No evidence of a signal has been found and the corresponding upper limit is \BR(\tau \to \mu\gamma) < 1.0 \times 10^{-6} at 90% CL, significantly smaller than previous limits. All quoted results are preliminary.Comment: 9 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Flavor-Specific Inclusive B Decays to Charm

We have measured the branching fractions for B -> D_bar X, B -> D X, and B -> D_bar X \ell^+ \nu, where ``B'' is an average over B^0 and B^+, ``D'' is a sum over D^0 and D^+, and``D_bar'' is a sum over D^0_bar and D^-. From these results and some previously measured branching fractions, we obtain Br(b -> c c_bar s) = (21.9 $\pm$ 3.7)%, Br(b -> s g) K^- \pi^+) = (3.69 $\pm$ 0.20)%. Implications for the ``B semileptonic decay problem'' (measured branching fraction being below theoretical expectations) are discussed. The increase in the value of Br(b -> c c_bar s) due to $B -> D X$ eliminates 40% of the discrepancy.Comment: 12 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN