358 research outputs found
Normal Forms for Symplectic Maps with Twist Singularities
We derive a normal form for a near-integrable, four-dimensional symplectic
map with a fold or cusp singularity in its frequency mapping. The normal form
is obtained for when the frequency is near a resonance and the mapping is
approximately given by the time- mapping of a two-degree-of freedom
Hamiltonian flow. Consequently there is an energy-like invariant. The fold
Hamiltonian is similar to the well-studied, one-degree-of freedom case but is
essentially nonintegrable when the direction of the singular curve in action
does not coincide with curves of the resonance module. We show that many
familiar features, such as multiple island chains and reconnecting invariant
manifolds, are retained even in this case. The cusp Hamiltonian has an
essential coupling between its two degrees of freedom even when the singular
set is aligned with the resonance module. Using averaging, we approximately
reduced this case to one degree of freedom as well. The resulting Hamiltonian
and its perturbation with small cusp-angle is analyzed in detail.Comment: LaTex, 27 pages, 21 figure
Vanishing Twist in the Hamiltonian Hopf Bifurcation
The Hamiltonian Hopf bifurcation has an integrable normal form that describes
the passage of the eigenvalues of an equilibrium through the 1: -1 resonance.
At the bifurcation the pure imaginary eigenvalues of the elliptic equilibrium
turn into a complex quadruplet of eigenvalues and the equilibrium becomes a
linearly unstable focus-focus point. We explicitly calculate the frequency map
of the integrable normal form, in particular we obtain the rotation number as a
function on the image of the energy-momentum map in the case where the fibres
are compact. We prove that the isoenergetic non-degeneracy condition of the KAM
theorem is violated on a curve passing through the focus-focus point in the
image of the energy-momentum map. This is equivalent to the vanishing of twist
in a Poincar\'e map for each energy near that of the focus-focus point. In
addition we show that in a family of periodic orbits (the non-linear normal
modes) the twist also vanishes. These results imply the existence of all the
unusual dynamical phenomena associated to non-twist maps near the Hamiltonian
Hopf bifurcation.Comment: 18 pages, 4 figure
Precision Measurement of the Proton and Deuteron Spin Structure Functions g2 and Asymmetries A2
We have measured the spin structure functions g2p and g2d and the virtual
photon asymmetries A2p and A2d over the kinematic range 0.02 < x < 0.8 and 0.7
< Q^2 < 20 GeV^2 by scattering 29.1 and 32.3 GeV longitudinally polarized
electrons from transversely polarized NH3 and 6LiD targets. Our measured g2
approximately follows the twist-2 Wandzura-Wilczek calculation. The twist-3
reduced matrix elements d2p and d2n are less than two standard deviations from
zero. The data are inconsistent with the Burkhardt-Cottingham sum rule if there
is no pathological behavior as x->0. The Efremov-Leader-Teryaev integral is
consistent with zero within our measured kinematic range. The absolute value of
A2 is significantly smaller than the sqrt[R(1+A1)/2] limit.Comment: 12 pages, 4 figures, 2 table
Measurements of the -Dependence of the Proton and Neutron Spin Structure Functions g1p and g1n
The structure functions g1p and g1n have been measured over the range 0.014 <
x < 0.9 and 1 < Q2 < 40 GeV2 using deep-inelastic scattering of 48 GeV
longitudinally polarized electrons from polarized protons and deuterons. We
find that the Q2 dependence of g1p (g1n) at fixed x is very similar to that of
the spin-averaged structure function F1p (F1n). From a NLO QCD fit to all
available data we find at
Q2=5 GeV2, in agreement with the Bjorken sum rule prediction of 0.182 \pm
0.005.Comment: 17 pages, 3 figures. Submitted to Physics Letters
Application-Layer Connector Synthesis
International audienceThe heterogeneity characterizing the systems populating the Ubiquitous Computing environment prevents their seamless interoperability. Heterogeneous protocols may be willing to cooperate in order to reach some common goal even though they meet dynamically and do not have a priori knowledge of each other. Despite numerous e orts have been done in the literature, the automated and run-time interoperability is still an open challenge for such environment. We consider interoperability as the ability for two Networked Systems (NSs) to communicate and correctly coordinate to achieve their goal(s). In this chapter we report the main outcomes of our past and recent research on automatically achieving protocol interoperability via connector synthesis. We consider application-layer connectors by referring to two conceptually distinct notions of connector: coordinator and mediator. The former is used when the NSs to be connected are already able to communicate but they need to be speci cally coordinated in order to reach their goal(s). The latter goes a step forward representing a solution for both achieving correct coordination and enabling communication between highly heterogeneous NSs. In the past, most of the works in the literature described e orts to the automatic synthesis of coordinators while, in recent years the focus moved also to the automatic synthesis of mediators. Within the Connect project, by considering our past experience on automatic coordinator synthesis as a baseline, we propose a formal theory of mediators and a related method for automatically eliciting a way for the protocols to interoperate. The solution we propose is the automated synthesis of emerging mediating connectors (i.e., mediators for short)
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Energetic particle influence on the Earth's atmosphere
This manuscript gives an up-to-date and comprehensive overview of the effects of energetic particle precipitation (EPP) onto the whole atmosphere, from the lower thermosphere/mesosphere through the stratosphere and troposphere, to the surface. The paper summarizes the different sources and energies of particles, principally
galactic cosmic rays (GCRs), solar energetic particles (SEPs) and energetic electron precipitation (EEP). All the proposed mechanisms by which EPP can affect the atmosphere
are discussed, including chemical changes in the upper atmosphere and lower thermosphere, chemistry-dynamics feedbacks, the global electric circuit and cloud formation. The role of energetic particles in Earthâs atmosphere is a multi-disciplinary problem that requires expertise from a range of scientific backgrounds. To assist with this synergy, summary tables are provided, which are intended to evaluate the level of current knowledge of the effects of energetic particles on processes in the entire atmosphere
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