1,043 research outputs found
Classification of resonance Regge trajectories and a modified Mulholland formula
We employ a simple potential model to analyse the effects which a Regge
trajectory, correlating with a bound or a metastable state at zero angular
momentum, has on an integral cross section. A straightforward modification of
the Mulholland formula of Macek et al is proposed for more efficient separation
of the resonance contribution.Comment: 4 pages, 5 figure
Weak vorticity formulation for the incompressible Euler equations in domains with boundary
In this article we examine the interaction of incompressible 2D flows with
compact material boundaries. Our focus is the dynamic behavior of the
circulation of velocity around boundary components and the possible exchange
between flow vorticity and boundary circulation in flows with vortex sheet
initial data We begin by showing that the velocity can be uniquely
reconstructed from the vorticity and boundary component circulations, which
allows to recast 2D Euler evolution using vorticity and the circulations as
dynamic variables. The weak form of this vortex dynamics formulation of the
equations is called the weak vorticity formulation. The main result in this
article is the equivalence between the weak velocity and weak vorticity
formulations, without sign assumptions. Next, we focus on weak solutions
obtained by mollifying initial data and passing to the limit, with the portion
of vorticity singular with respect to the Lebesgue measure assumed to be
nonnegative. For these solutions we prove that the circulations around each
boundary component cannot be smaller than the initial data circulation, so that
nonnegative vorticity may be absorbed by the boundary, but not produced by the
boundary. In addition, we prove that if the weak solution conserves circulation
at the boundary components it is a boundary coupled weak solution, a stronger
version of the weak vorticity formulation. We prove existence of a weak
solution which conserves circulation at the boundary components if the initial
vorticity is integrable. In addition, we discuss the definition of the
mechanical force which the flow exerts on material boundary components and its
relation with conservation of circulation. Finally, we describe the
corresponding results for a bounded domain with holes, and the adaptations
required in the proofs.Comment: 37 page
The quest for three-color entanglement: experimental investigation of new multipartite quantum correlations
We experimentally investigate quadrature correlations between pump, signal,
and idler fields in an above-threshold optical parametric oscillator. We
observe new quantum correlations among the pump and signal or idler beams, as
well as among the pump and a combined quadrature of signal and idler beams. A
further investigation of unforeseen classical noise observed in this system is
presented, which hinders the observation of the recently predicted tripartite
entanglement. In spite of this noise, current results approach the limit
required to demonstrate three-color entanglement.Comment: 10 pages, 5 figures, submitted to Opt. Expres
Large time behavior for vortex evolution in the half-plane
In this article we study the long-time behavior of incompressible ideal flow
in a half plane from the point of view of vortex scattering. Our main result is
that certain asymptotic states for half-plane vortex dynamics decompose
naturally into a nonlinear superposition of soliton-like states. Our approach
is to combine techniques developed in the study of vortex confinement with weak
convergence tools in order to study the asymptotic behavior of a self-similar
rescaling of a solution of the incompressible 2D Euler equations on a half
plane with compactly supported, nonnegative initial vorticity.Comment: 30 pages, no figure
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