Excitation Thresholds for Nonlinear Localized Modes on Lattices

Breathers are spatially localized and time periodic solutions of extended Hamiltonian dynamical systems. In this paper we study excitation thresholds for (nonlinearly dynamically stable) ground state breather or standing wave solutions for networks of coupled nonlinear oscillators and wave equations of nonlinear Schr\"odinger (NLS) type. Excitation thresholds are rigorously characterized by variational methods. The excitation threshold is related to the optimal (best) constant in a class of discr ete interpolation inequalities related to the Hamiltonian energy. We establish a precise connection among $d$, the dimensionality of the lattice, $2\sigma+1$, the degree of the nonlinearity and the existence of an excitation threshold for discrete nonlinear Schr\"odinger systems (DNLS). We prove that if $\sigma\ge 2/d$, then ground state standing waves exist if and only if the total power is larger than some strictly positive threshold, $\nu_{thresh}(\sigma, d)$. This proves a conjecture of Flach, Kaldko& MacKay in the context of DNLS. We also discuss upper and lower bounds for excitation thresholds for ground states of coupled systems of NLS equations, which arise in the modeling of pulse propagation in coupled arrays of optical fibers.Comment: To appear in Nonlinearit

Observing Gravitational Waves with a Single Detector

A major challenge of any search for gravitational waves is to distinguish true astrophysical signals from those of terrestrial origin. Gravitational-wave experiments therefore make use of multiple detectors, considering only those signals which appear in coincidence in two or more instruments. It is unclear, however, how to interpret loud gravitational-wave candidates observed when only one detector is operational. In this paper, we demonstrate that the observed rate of binary black hole mergers can be leveraged in order to make confident detections of gravitational-wave signals with one detector alone. We quantify detection confidences in terms of the probability $P(S)$ that a signal candidate is of astrophysical origin. We find that, at current levels of instrumental sensitivity, loud signal candidates observed with a single Advanced LIGO detector can be assigned $P(S)\gtrsim0.4$. In the future, Advanced LIGO may be able to observe single-detector events with confidences exceeding $P(S)\sim90\%$.Comment: 8 pages, 4 figures; published in CQG; minor updates to match published versio

Jumping into the 20th century before it is too late: is laboratory robotics still in its infancy?

Successful management of laboratory robotic automation programmes in the environment of research and drug discovery within the pharmaceutical industry may perhaps be best compared to a chef preparing the perfect hollandaise sauce. All the ingredients must be available at the same time and be of highest quality for the right price. However, if components are not added in the right quantities and in the proper order, no amount of whipping together by the product champion will create the best product. In the past, managerial scepticism surrounding useful implementation of cost-effective, high-throughput robotic systems often placed these ‘modern toys’ at low priorities for research development laboratories. Management now recognizes the unique contributions of robotics in the research environment. Although the scientific director must still play the role of product champion, new questions are being proposed and new commitments are being made to bring the potential of robotic automation to every laboratory where repetitive functions can benefit from new applications. Research laboratory directors have become both the key ingredient, as well as the rate-limiting determinant in the development of new applications. Having fulfilled the promise of robotic automation to release talented personnel, the challenge now is for the ‘end users’, the bench scientists, to be provided with opportunities to invest the time and effort required for future applications and new career functions

Charged Rotating Black Holes in Equilibrium

Axially symmetric, stationary solutions of the Einstein-Maxwell equations with disconnected event horizon are studied by developing a method of explicit integration of the corresponding boundary-value problem. This problem is reduced to non-leaner system of algebraic equations which gives relations between the masses, the angular momenta, the angular velocities, the charges, the distance parameters, the values of the electromagnetic field potential at the horizon and at the symmetry axis. A found solution of this system for the case of two charged non-rotating black holes shows that in general the total mass depends on the distance between black holes. Two-Killing reduction procedure of the Einstein-Maxwell equations is also discussed.Comment: LaTeX 2.09, no figures, 15 pages, v2, references added, introduction section slightly modified; v3, grammar errors correcte

Can Long-Range Nuclear Properties Be Influenced By Short Range Interactions? A chiral dynamics estimate

Recent experiments and many-body calculations indicate that approximately 20\% of the nucleons in medium and heavy nuclei ($A\geq12$) are part of short-range correlated (SRC) primarily neutron-proton ($np$) pairs. We find that using chiral dynamics to account for the formation of $np$ pairs due to the effects of iterated and irreducible two-pion exchange leads to values consistent with the 20\% level. We further apply chiral dynamics to study how these correlations influence the calculations of nuclear charge radii, that traditionally truncate their effect, to find that they are capable of introducing non-negligible effects.Comment: 6 pages, 0 figures. This version includes many improvement

Search for color-suppressed B hadronic decay processes at the Υ(4S) resonance

Using 3.1fb^(-1) of data accumulated at the Υ(4S) by the CLEO-II detector, corresponding to 3.3×10^6 BB̅ pairs, we have searched for the color-suppressed B hadronic decay processes B^(0) → D^(0)(D^(*0))X^0, where X^0 is a light neutral meson π^0, ρ^0, η, η′ or ω. The D^(*0) mesons are reconstructed in D^(*0) → D^(0)π^(0) and the D^0 mesons in D^(0) → K^(-)π^(+), K^(-)π^(+)π^(0) and K^(-)π^(+)π^(+)π^(-) decay modes. No obvious signal is observed. We set 90% C.L. upper limits on these modes, varying from 1.2×10^(-4) for B^(0) → D^(0)π^(0) to 1.9×10^(-3) for B^(0) → D^(*0)η′

Measurement of the B Semileptonic Branching Fraction with Lepton Tags

We have used the CLEO II detector and 2.06fb^(-1) of ϒ(4S) data to measure the B-meson semileptonic branching fraction. The B→Xeν momentum spectrum was obtained over nearly the full momentum range by using charge and kinematic correlations in events with a high-momentum lepton tag and an additional electron. We find B(B→Xeν) = (10.49±0.17±0.43)%, with overall systematic uncertainties less than those of untagged single-lepton measurements. We use this result to calculate the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element V_(cb) and to set an upper limit on the fraction of ϒ(4S) decays to final states other than BB̅

Measurement of transparency ratios for protons from short-range correlated pairs

Nuclear transparency, Tp(A), is a measure of the average probability for a struck proton to escape the nucleus without significant re-interaction. Previously, nuclear transparencies were extructed for quasi-elastic A(e,e'p) knockout of protons with momentum below the Fermi momentum, where the spectral functions are well known. In this paper we extract a novel observable, the transparency ratio, Tp(A)/T_p(12C), for knockout of high-missing-momentum protons from the breakup of short range correlated pairs (2N-SRC) in Al, Fe and Pb nuclei relative to C. The ratios were measured at momentum transfer Q^2 > 1.5 (GeV/c)^2 and x_B > 1.2 where the reaction is expected to be dominated by electron scattering from 2N-SRC. The transparency ratios of the knocked-out protons coming from 2N-SRC breakup are 20 - 30% lower than those of previous results for low missing momentum. They agree with Glauber calculations and agree with renormalization of the previously published transparencies as proposed by recent theoretical investigations. The new transparencies scale as A^-1/3, which is consistent with dominance of scattering from nucleons at the nuclear surface.Comment: 6 pages, 4 figure