Elimination of cusps in dimension 4 and its applications

We study a class of homotopies between maps from 4-manifolds to surfaces which we call cusp merges. These homotopies naturally appear in the uniqueness problems for certain pictorial descriptions of 4-manifolds derived from maps to the 2-sphere (for example, broken Lefschetz fibrations, wrinkled fibrations, or Morse 2-functions). Our main results provide a classification of cusp merge homotopies in terms of suitably framed curves in the source manifold, as well as a fairly explicit description of a parallel transport diffeomorphism associated to a cusp merge homotopy. The latter is the key ingredient in understanding how the aforementioned pictorial descriptions change under homotopies involving cusp merges. We apply our methods to the uniqueness problem of surface diagrams of 4-manifolds and describe algorithms to obtain surface diagrams for total spaces of (achiral) Lefschetz fibrations and 4-manifolds of the form M×S1, where M is a 3-manifold. Along the way we provide extensive background material about maps to surfaces and homotopies thereof and develop a theory of parallel transport that generalizes the use of gradient flows in Morse theory

Intrabeam Scattering Analysis of ATF Beam Measurements

At the Accelerator Test Facility (ATF) at KEK intrabeam scattering (IBS) is a strong effect for an electron machine. It is an effect that couples all dimensions of the beam, and in April 2000, over a short period of time, all dimensions were measured as functions of current. In this report we derive a simple relation for the growth rates of emittances due to IBS. We apply the theories of Bjorken-Mtingwa, Piwinski, and a formula due to Raubenheimer to the ATF parameters, and find that the results all agree (if in Piwinski's formalism we replace the dispersion squared over beta by the dispersion invariant). Finally, we compare theory, including the effect of potential well bunch lengthening, with the April 2000 measurements, and find reasonably good agreement in the energy spread and horizontal emittance dependence on current. The vertical emittance measurement, however, implies that either: there is error in the measurement (equivalent to an introduction of 0.6% x-y coupling error), or the effect of intrabeam scattering is stronger than predicted (35% stronger in growth rates).Comment: 4 pages, 3 figures, Presented at IEEE Particle Accelerator Conferenc

Formation of Deeply Bound Kaonic Atoms in (K^-,N) Reactions

We study theoretically the (K^-,N) reactions for the formation of the deeply bound kaonic atoms, which were predicted to be quasi--stable with narrow widths, using the Green function method. We consider various cases with different target nuclei and energies systematically and find the clear signals in the theoretical spectra for all cases considered in this article. The signals show very interesting structures, such as the $RESONANCE DIP$ instead of the resonance peak. We discuss the origins of the interesting structures and possibilities to get new information on the existence of the kaonic nuclei from the spectra of the atomic state formations.Comment: 11 pages, 9 figure

Near-infrared Brightness of the Galilean Satellites Eclipsed in Jovian Shadow: A New Technique to Investigate Jovian Upper Atmosphere

We have discovered that Europa, Ganymede and Callisto are bright around 1.5 {\mu}m even when not directly lit by sunlight, based on observations from the Hubble Space Telescope and the Subaru Telescope. The observations were conducted with non-sidereal tracking on Jupiter outside of the field of view to reduce the stray light subtraction uncertainty due to the close proximity of Jupiter. Their eclipsed luminosity was $10^{-6}$-$10^{-7}$ of their uneclipsed brightness, which is low enough that this phenomenon has been undiscovered until now. In addition, Europa in eclipse was <1/10 of the others at 1.5 {\mu}m, a potential clue to the origin of the source of luminosity. Likewise, Ganymede observations were attempted at 3.6 {\mu}m by the Spitzer Space Telescope but it was not detected, suggesting a significant wavelength dependence. The reason why they are luminous even when in the Jovian shadow is still unknown, but forward-scattered sunlight by haze in the Jovian upper atmosphere is proposed as the most plausible candidate. If this is the case, observations of these Galilean satellites while eclipsed by the Jovian shadow provide us a new technique to investigate Jovian atmospheric composition, and investigating the transmission spectrum of Jupiter by this method is important for investigating the atmosphere of extrasolar giant planets by transit spectroscopy.Comment: 7 pages, 3 figures, accepted to Ap