1,364 research outputs found
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 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
Production of Low Mass Electron Pairs Due to the Photon-Photon Mechanism in Central Collisions
We calculate the probability for dilepton production in central relativistic
heavy ion collisions due to the gamma-gamma mechanism. This is a potential
background to more interesting mechanisms. We find that this mechanism is
negligible in the CERES experiments. Generally, the contribution due to this
mechanism is small in the central region, while it can be large for small
invariant masses and forward or backward rapidities. A simple formula based on
the equivalent photon approximation and applications to a possible scenario at
RHIC are also given.Comment: 10 pages REVTeX, 5 Figures, for related work see
http://quasar.physik.unibas.ch/~hencken
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