206 research outputs found
Coherent Beam-Beam Tune Shift of Unsymmetrical Beam-Beam Interactions with Large Beam-Beam Parameter
Coherent beam-beam tune shift of unsymmetrical beam-beam interactions was
studied experimentally and numerically in HERA where the lepton beam has a very
large beam-beam parameter (up to ). Unlike the symmetrical case of
beam-beam interactions, the ratio of the coherent and incoherent beam-beam tune
shift in this unsymmetrical case of beam-beam interactions was found to
decrease monotonically with increase of the beam-beam parameter. The results of
self-consistent beam-beam simulation, the linearized Vlasov equation, and the
rigid-beam model were compared with the experimental measurement. It was found
that the coherent beam-beam tune shifts measured in the experiment and
calculated in the simulation agree remarkably well but they are much smaller
than those calculated by the linearized Vlasov equation with the single-mode
approximation or the rigid-beam model. The study indicated that the single-mode
approximation in the linearization of Vlasov equation is not valid in the case
of unsymmetrical beam-beam interactions. The rigid-beam model is valid only
with a small beam-beam parameter in the case of unsymmetrical beam-beam
interactions.Comment: 32 pages, 13 figure
Nematic Films and Radially Anisotropic Delaunay Surfaces
We develop a theory of axisymmetric surfaces minimizing a combination of
surface tension and nematic elastic energies which may be suitable for
describing simple film and bubble shapes. As a function of the elastic constant
and the applied tension on the bubbles, we find the analogues of the unduloid,
sphere, and nodoid in addition to other new surfaces.Comment: 15 pages, 18 figure
Stability of complex hyperbolic space under curvature-normalized Ricci flow
Using the maximal regularity theory for quasilinear parabolic systems, we
prove two stability results of complex hyperbolic space under the
curvature-normalized Ricci flow in complex dimensions two and higher. The first
result is on a closed manifold. The second result is on a complete noncompact
manifold. To prove both results, we fully analyze the structure of the
Lichnerowicz Laplacian on complex hyperbolic space. To prove the second result,
we also define suitably weighted little H\"{o}lder spaces on a complete
noncompact manifold and establish their interpolation properties.Comment: Some typos in version 2 are correcte
Stability of the selfsimilar dynamics of a vortex filament
In this paper we continue our investigation about selfsimilar solutions of
the vortex filament equation, also known as the binormal flow (BF) or the
localized induction equation (LIE). Our main result is the stability of the
selfsimilar dynamics of small pertubations of a given selfsimilar solution. The
proof relies on finding precise asymptotics in space and time for the tangent
and the normal vectors of the perturbations. A main ingredient in the proof is
the control of the evolution of weighted norms for a cubic 1-D Schr\"odinger
equation, connected to the binormal flow by Hasimoto's transform.Comment: revised version, 36 page
The Cauchy problems for Einstein metrics and parallel spinors
We show that in the analytic category, given a Riemannian metric on a
hypersurface and a symmetric tensor on , the metric
can be locally extended to a Riemannian Einstein metric on with second
fundamental form , provided that and satisfy the constraints on
imposed by the contracted Codazzi equations. We use this fact to study the
Cauchy problem for metrics with parallel spinors in the real analytic category
and give an affirmative answer to a question raised in B\"ar, Gauduchon,
Moroianu (2005). We also answer negatively the corresponding questions in the
smooth category.Comment: 28 pages; final versio
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