3,083 research outputs found
Pieri rules for Schur functions in superspace
International audienceThe Schur functions in superspace and are the limits and respectively of the Macdonald polynomials in superspace. We present the elementary properties of the bases and (which happen to be essentially dual) such as Pieri rules, dualities, monomial expansions, tableaux generating functions, and Cauchy identities.Les fonctions de Schur dans le superespace et sont les limites et respectivement des polynÎmes de Macdonald dans le superespace. Nous présentons les propriétés élémentaires des bases et (qui sont essentiellement duales l'une de l'autre) tels que les rÚgles de Pieri, la dualité, le développement en fonctions monomiales, les fonctions génératrices de tableaux et les identités de Cauchy
UNLV Percussion Ensemble and UNLV Steel Band
Program listing performers and works performed
Measuring Topological Chaos
The orbits of fluid particles in two dimensions effectively act as
topological obstacles to material lines. A spacetime plot of the orbits of such
particles can be regarded as a braid whose properties reflect the underlying
dynamics. For a chaotic flow, the braid generated by the motion of three or
more fluid particles is computed. A ``braiding exponent'' is then defined to
characterize the complexity of the braid. This exponent is proportional to the
usual Lyapunov exponent of the flow, associated with separation of nearby
trajectories. Measuring chaos in this manner has several advantages, especially
from the experimental viewpoint, since neither nearby trajectories nor
derivatives of the velocity field are needed.Comment: 4 pages, 6 figures. RevTeX 4 with PSFrag macro
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Explaining timescales associated with jet stream variability
Extreme weather events are often the result of slow-moving, large-scale wave patterns. Greater understanding of these large-scale modes of variability would allow us to
anticipate how quasi-stationary modes might depend on changes to the background state
in future climate. In this thesis the Empirical Normal Mode (ENM) technique, a technique for extracting dynamical modes of variability from atmospheric timeseries data, is
utilised to examine the dependence of mode structure and frequency on jet latitude.
The ENM methodology is extended to include the lower troposphere spanned by
isentropic surfaces that can intersect the ground. This involves careful accounting of the
terms in large amplitude pseudomomentum and pseudoenergy associated with this region
of the atmosphere - terms that contribute to the âboundary wave activityâ in the limit
of small amplitude.
In the third chapter, the implementation of the technique itself is validated by testing
the characteristic âintrinsicâ phase speed of the ENMs against an empirical phase speed
derived from the modesâ principal component timeseries, using a set of idealised model
experiments simulated using the Reading IGCM2.2. It is found that the phase speed
matching conditions are met for the dominant freely propagating baroclinic modes, validating the approach to the calculation of wave activity and some approximations used in
deriving relevant wave activity norms.
In the fourth chapter, a new series of idealised experiments are devised that possess
a jetstream with controllable latitude such that the change in behaviour of the modes
of variability with a shift in jet latitude may be examined. The initial and relaxation
temperature field in thermal wind balance with a prescribed zonal wind field with jet
latitudes ranging from ⌠40° to ⌠65° is found, and a sloping tropopause is added in
order to maintain baroclinicity.
Subsequently, in the fifth chapter, the ENM structures of these experiments are found,
and the change in the phase speed of the modes as the jet latitude changes is explored.
A quasi-stationary branch of modes is identified which is associated with the most perturbation energy (for each zonal wavenumber) and therefore can propagate most strongly
westwards against the background state westerly flow. As the jet is shifted polewards,
the wavelength of the most energetic modes remains approximately the same, but they
shift to lower zonal wavenumbers due to reduction in the latitude circle circumference
Pieri rules for Schur functions in superspace
The Schur functions in superspace and are the limits and respectively of the Macdonald polynomials in superspace. We present the elementary properties of the bases and (which happen to be essentially dual) such as Pieri rules, dualities, monomial expansions, tableaux generating functions, and Cauchy identities
Hadamard Regularization
Motivated by the problem of the dynamics of point-particles in high
post-Newtonian (e.g. 3PN) approximations of general relativity, we consider a
certain class of functions which are smooth except at some isolated points
around which they admit a power-like singular expansion. We review the concepts
of (i) Hadamard ``partie finie'' of such functions at the location of singular
points, (ii) the partie finie of their divergent integral. We present and
investigate different expressions, useful in applications, for the latter
partie finie. To each singular function, we associate a partie-finie (Pf)
pseudo-function. The multiplication of pseudo-functions is defined by the
ordinary (pointwise) product. We construct a delta-pseudo-function on the class
of singular functions, which reduces to the usual notion of Dirac distribution
when applied on smooth functions with compact support. We introduce and analyse
a new derivative operator acting on pseudo-functions, and generalizing, in this
context, the Schwartz distributional derivative. This operator is uniquely
defined up to an arbitrary numerical constant. Time derivatives and partial
derivatives with respect to the singular points are also investigated. In the
course of the paper, all the formulas needed in the application to the physical
problem are derived.Comment: 50 pages, to appear in Journal of Mathematical Physic
Two-photon coherent control of femtosecond photoassociation
Photoassociation with short laser pulses has been proposed as a technique to
create ultracold ground state molecules. A broad-band excitation seems the
natural choice to drive the series of excitation and deexcitation steps
required to form a molecule in its vibronic ground state from two scattering
atoms. First attempts at femtosecond photoassociation were, however, hampered
by the requirement to eliminate the atomic excitation leading to trap
depletion. On the other hand, molecular levels very close to the atomic
transition are to be excited. The broad bandwidth of a femtosecond laser then
appears to be rather an obstacle. To overcome the ostensible conflict of
driving a narrow transition by a broad-band laser, we suggest a two-photon
photoassociation scheme. In the weak-field regime, a spectral phase pattern can
be employed to eliminate the atomic line. When the excitation is carried out by
more than one photon, different pathways in the field can be interfered
constructively or destructively. In the strong-field regime, a temporal phase
can be applied to control dynamic Stark shifts. The atomic transition is
suppressed by choosing a phase which keeps the levels out of resonance. We
derive analytical solutions for atomic two-photon dark states in both the
weak-field and strong-field regime. Two-photon excitation may thus pave the way
toward coherent control of photoassociation. Ultimately, the success of such a
scheme will depend on the details of the excited electronic states and
transition dipole moments. We explore the possibility of two-photon femtosecond
photoassociation for alkali and alkaline-earth metal dimers and present a
detailed study for the example of calcium
Numerical investigation of the partial oxidation in a two-stage downdraft gasifyer
International audienceno abstrac
Lorentzian regularization and the problem of point-like particles in general relativity
The two purposes of the paper are (1) to present a regularization of the
self-field of point-like particles, based on Hadamard's concept of ``partie
finie'', that permits in principle to maintain the Lorentz covariance of a
relativistic field theory, (2) to use this regularization for defining a model
of stress-energy tensor that describes point-particles in post-Newtonian
expansions (e.g. 3PN) of general relativity. We consider specifically the case
of a system of two point-particles. We first perform a Lorentz transformation
of the system's variables which carries one of the particles to its rest frame,
next implement the Hadamard regularization within that frame, and finally come
back to the original variables with the help of the inverse Lorentz
transformation. The Lorentzian regularization is defined in this way up to any
order in the relativistic parameter 1/c^2. Following a previous work of ours,
we then construct the delta-pseudo-functions associated with this
regularization. Using an action principle, we derive the stress-energy tensor,
made of delta-pseudo-functions, of point-like particles. The equations of
motion take the same form as the geodesic equations of test particles on a
fixed background, but the role of the background is now played by the
regularized metric.Comment: 34 pages, to appear in J. Math. Phy
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