671 research outputs found
The Degasperis-Procesi equation as a non-metric Euler equation
In this paper we present a geometric interpretation of the periodic
Degasperis-Procesi equation as the geodesic flow of a right invariant symmetric
linear connection on the diffeomorphism group of the circle. We also show that
for any evolution in the family of -equations there is neither gain nor loss
of the spatial regularity of solutions. This in turn allows us to view the
Degasperis-Procesi and the Camassa-Holm equation as an ODE on the Fr\'echet
space of all smooth functions on the circle.Comment: 17 page
Anti-self-dual conformal structures with null Killing vectors from projective structures
Using twistor methods, we explicitly construct all local forms of
four--dimensional real analytic neutral signature anti--self--dual conformal
structures with a null conformal Killing vector. We show that is
foliated by anti-self-dual null surfaces, and the two-dimensional leaf space
inherits a natural projective structure. The twistor space of this projective
structure is the quotient of the twistor space of by the group action
induced by the conformal Killing vector.
We obtain a local classification which branches according to whether or not
the conformal Killing vector is hyper-surface orthogonal in . We give
examples of conformal classes which contain Ricci--flat metrics on compact
complex surfaces and discuss other conformal classes with no Ricci--flat
metrics.Comment: 43 pages, 4 figures. Theorem 2 has been improved: ASD metrics are
given in terms of general projective structures without needing to choose
special representatives of the projective connection. More examples (primary
Kodaira surface, neutral Fefferman structure) have been included. Algebraic
type of the Weyl tensor has been clarified. Final version, to appear in
Commun Math Phy
Peatland hydrology and carbon release: why small-scale process matters
Peatlands cover over 400 million hectares of the Earth's surface and store between one-third and one-half of the world's soil carbon pool. The long-term ability of peatlands to absorb carbon dioxide from the atmosphere means that they play a major role in moderating global climate. Peatlands can also either attenuate or accentuate flooding. Changing climate or management can alter peatland hydrological processes and pathways for water movement across and below the peat surface. It is the movement of water in peats that drives carbon storage and flux. These small-scale processes can have global impacts through exacerbated terrestrial carbon release. This paper will describe advances in understanding environmental processes operating in peatlands. Recent (and future) advances in high-resolution topographic data collection and hydrological modelling provide an insight into the spatial impacts of land management and climate change in peatlands. Nevertheless, there are still some major challenges for future research. These include the problem that impacts of disturbance in peat can be irreversible, at least on human time-scales. This has implications for the perceived success and understanding of peatland restoration strategies. In some circumstances, peatland restoration may lead to exacerbated carbon loss. This will also be important if we decide to start to create peatlands in order to counter the threat from enhanced atmospheric carbon
Trapped Particle Stability for the Kinetic Stabilizer
A kinetically stabilized axially symmetric tandem mirror (KSTM) uses the
momentum flux of low-energy, unconfined particles that sample only the outer
end-regions of the mirror plugs, where large favorable field-line curvature
exists. The window of operation is determined for achieving MHD stability with
tolerable energy drain from the kinetic stabilizer. Then MHD stable systems are
analyzed for stability of the trapped particle mode. This mode is characterized
by the detachment of the central-cell plasma from the kinetic stabilizer region
without inducing field-line bending. Stability of the trapped particle mode is
sensitive to the electron connection between the stabilizer and the end plug.
It is found that the stability condition for the trapped particle mode is more
constraining than the stability condition for the MHD mode, and it is
challenging to satisfy the required power constraint. Furthermore a severe
power drain may arise from the necessary connection of low-energy electrons in
the kinetic stabilizer to the central region
Simulation of Beam-Beam Effects and Tevatron Experience
Effects of electromagnetic interactions of colliding bunches in the Tevatron
had a variety of manifestations in beam dynamics presenting vast opportunities
for development of simulation models and tools. In this paper the computer code
for simulation of weak-strong beam-beam effects in hadron colliders is
described. We report the collider operational experience relevant to beam-beam
interactions, explain major effects limiting the collider performance and
compare results of observations and measurements with simulations.Comment: 23 pages, 17 figure
Electroproduction of two light vector mesons in next-to-leading BFKL: study of systematic effects
The forward electroproduction of two light vector mesons is the first example
of a collision process between strongly interacting colorless particles for
which the amplitude can be written completely within perturbative QCD in the
Regge limit with next-to-leading accuracy. In a previous paper we have given a
numerical determination of the amplitude in the case of equal photon
virtualities by using a definite representation for the amplitude and a
definite optimization method for the perturbative series. Here we estimate the
systematic uncertainty of our previous determination, by considering a
different representation of the amplitude and different optimization methods of
the perturbative series. Moreover, we compare our result for the differential
cross section at the minimum momentum transfer with a different approach, based
on collinear kernel improvement.Comment: 17 pages, 11 figures; journal version, new figures and discussion
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Flux Phase as a Dynamic Jahn-Teller Phase: Berryonic Matter in the Cuprates?
There is considerable evidence for some form of charge ordering on the
hole-doped stripes in the cuprates, mainly associated with the low-temperature
tetragonal phase, but with some evidence for either charge density waves or a
flux phase, which is a form of dynamic charge-density wave. These three states
form a pseudospin triplet, demonstrating a close connection with the E X e
dynamic Jahn-Teller effect, suggesting that the cuprates constitute a form of
Berryonic matter. This in turn suggests a new model for the dynamic Jahn-Teller
effect as a form of flux phase. A simple model of the Cu-O bond stretching
phonons allows an estimate of electron-phonon coupling for these modes,
explaining why the half breathing mode softens so much more than the full
oxygen breathing mode. The anomalous properties of provide a coupling
(correlated hopping) which acts to stabilize density wave phases.Comment: Major Revisions: includes comparisons with specific cuprate phonon
modes, 16 eps figures, revte
Radiative Corrections to One-Photon Decays of Hydrogenic Ions
Radiative corrections to the decay rate of n=2 states of hydrogenic ions are
calculated. The transitions considered are the M1 decay of the 2s state to the
ground state and the E1(M2) decays of the and states to
the ground state. The radiative corrections start in order , but the method used sums all orders of . The leading
correction for the E1 decays is calculated and compared
with the exact result. The extension of the calculational method to parity
nonconserving transitions in neutral atoms is discussed.Comment: 22 pages, 2 figure
Beam instrumentation for the Tevatron Collider
The Tevatron in Collider Run II (2001-present) is operating with six times
more bunches and many times higher beam intensities and luminosities than in
Run I (1992-1995). Beam diagnostics were crucial for the machine start-up and
the never-ending luminosity upgrade campaign. We present the overall picture of
the Tevatron diagnostics development for Run II, outline machine needs for new
instrumentation, present several notable examples that led to Tevatron
performance improvements, and discuss the lessons for future colliders
Superstrings with Intrinsic Torsion
We systematically analyse the necessary and sufficient conditions for the
preservation of supersymmetry for bosonic geometries of the form R^{1,9-d}
\times M_d, in the common NS-NS sector of type II string theory and also type
I/heterotic string theory. The results are phrased in terms of the intrinsic
torsion of G-structures and provide a comprehensive classification of static
supersymmetric backgrounds in these theories. Generalised calibrations
naturally appear since the geometries always admit NS or type I/heterotic
fivebranes wrapping calibrated cycles. Some new solutions are presented. In
particular we find d=6 examples with a fibred structure which preserve N=1,2,3
supersymmetry in type II and include compact type I/heterotic geometries.Comment: 58 pages, LaTeX; v2: New section on solutions including an example
with N=3 supersymmetry and discussion of heterotic compactifications. Details
on conventions and references added. v3: added an explicit example of
non-integrable product structure in Appendix C; some typos fixe
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