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

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

Excitonic and free-carrier polarizations of bulk GaAs studied by femtosecond coherent spectroscopy

The transient third-order polarization at the band gap of undoped and p-doped GaAs is investigated by spectrally and temporally resolved four-wave mixing. Excitonic and free-carrier contributions simultaneously excited within the bandwidth of the 100-fs pulses are clearly distinguished by their different spectral envelopes. The excitonic part dominates at carrier densities below 1016 cm-3 and shows a time evolution governed by exciton-free-carrier scattering and by many-body effects. At higher density, the free-carrier polarization has a strength similar to the exciton contribution and exhibits a spectrum resonant to the femtosecond pulses with a photon-echo-like temporal behavior. The data are analyzed by a numerical solution of the semiconductor Bloch equations including an ensemble Monte Carlo simulation of the scattering dynamics of the carriers. The theoretical model is in good agreement with the experimental results

Observation of the Isospin-Violating Decay Ds∗+→Ds+π0D_s^{*+}\to D_s^+\pi^0

Using data collected with the CLEO~II detector, we have observed the isospin-violating decay $D_s^{*+}\to D_s^+\pi^0$. The decay rate for this mode, relative to the dominant radiative decay, is found to be $\Gamma(D_s^{*+}\to D_s^+\pi^0)/\Gamma(D_s^{*+}\to D_s^+\gamma)= 0.062^{+0.020}_{-0.018}\pm0.022$.Comment: 8 page uuencoded postscript file, also available through http://w4.lns.cornell.edu/public/CLN

Observation of a New Charmed Strange Meson

Using the CLEO-II detector, we have obtained evidence for a new meson decaying to $D^0 K^+$. Its mass is $2573.2^{+1.7}_{-1.6}\pm 0.8\pm 0.5$ {}~MeV/$c^2$ and its width is $16^{+5}_{-4}\pm 3$~MeV/$c^2$. Although we do not establish its spin and parity, the new meson is consistent with predictions for an $L=1$, $S=1$, $J_P=2^+$ charmed strange state.Comment: 9 pages uuencoded compressed postscript (process with uudecode then gunzip). hardcopies with figures can be obtained by sending mail to: [email protected]

Study of Gluon versus Quark Fragmentation in Υ→ggγ\Upsilon\to gg\gamma and e+e−→qqˉγe^{+}e^{-}\to q\bar{q}\gamma Events at \sqrt{s}=10 GeV

Using data collected with the CLEO II detector at the Cornell Electron Storage Ring, we determine the ratio R(chrg) for the mean charged multiplicity observed in Upsilon(1S)->gggamma events, to the mean charged multiplicity observed in e+e- -> qqbar gamma events. We find R(chrg)=1.04+/-0.02+/-0.05 for jet-jet masses less than 7 GeV.Comment: 15 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Precision Measurement of the Ds∗+−Ds+D_s^{*+}- D_s^+ Mass Difference

We have measured the vector-pseudoscalar mass splitting $M(D_s^{*+})-M(D_s^+) = 144.22\pm 0.47\pm 0.37 MeV$, significantly more precise than the previous world average. We minimize the systematic errors by also measuring the vector-pseudoscalar mass difference $M(D^{*0})-M(D^0)$ using the radiative decay $D^{*0}\rightarrow D^0\gamma$, obtaining $[M(D_s^{*+})-M(D_s^+)]-[M(D^{*0})-M(D^0)] = 2.09\pm 0.47\pm 0.37 MeV$. This is then combined with our previous high-precision measurement of $M(D^{*0})-M(D^0)$, which used the decay $D^{*0}\rightarrow D^0\pi^0$. We also measure the mass difference $M(D_s^+)-M(D^+)=99.5\pm 0.6\pm 0.3$ MeV, using the $\phi\pi^+$ decay modes of the $D_s^+$ and $D^+$ mesons.Comment: 18 pages uuencoded compressed postscript (process with uudecode then gunzip). hardcopies with figures can be obtained by sending mail to: [email protected]

Measurement of the Inclusive Semi-electronic D0D^0 Branching Fraction

Using the angular correlation between the $\pi^+$ emitted in a $D^{*+} \rightarrow D^0 \pi^+$ decay and the $e^+$ emitted in the subsequent $D^0 \rightarrow Xe^+\nu$ decay, we have measured the branching fraction for the inclusive semi-electronic decay of the $D^0$ meson to be: {\cal B}(D^0 \rightarrow X e^+ \nu) = [6.64 \pm 0.18 (stat.) \pm 0.29 (syst.)] \%. The result is based on 1.7 fb$^{-1}$ of $e^+e^-$ collisions recorded by the CLEO II detector located at the Cornell Electron Storage Ring (CESR). Combining the analysis presented in this paper with previous CLEO results we find, \frac{{\cal B} (D^0 \rightarrow X e^+ \nu)} {{\cal B} (D^0 \rightarrow K^- \pi^+)} = 1.684 \pm 0.056 (stat.) \pm 0.093(syst.) and \frac{{\cal B}(D\rightarrow K^-e^+\nu)} {{\cal B}(D\rightarrow Xe^+\nu)} = 0.581 \pm 0.023 (stat.) \pm 0.028(syst.). The difference between the inclusive rate and the sum of the measured exclusive branching fractions (measured at CLEO and other experiments) is $(3.3 \pm 7.2) \%$ of the inclusive rate.Comment: Latex file, 33pages, 4 figures Submitted to PR