27,647 research outputs found
q-series and L-functions related to half-derivatives of the Andrews--Gordon identity
Studied is a generalization of Zagier's q-series identity. We introduce a
generating function of L-functions at non-positive integers, which is regarded
as a half-differential of the Andrews--Gordon q-series. When q is a root of
unity, the generating function coincides with the quantum invariant for the
torus knot.Comment: 21 pages, related papers can be found from
http://gogh.phys.s.u-tokyo.ac.jp/~hikami
Identifying the development in phase and amplitude of dipole and multipole radiation
The spatial variation in phase and the propagating wave-front of plane wave electromagnetic radiation are widely familiar text-book territory. In contrast, the developing amplitude and phase of radiation emitted by a dipole or multipole source generally receive less attention, despite the prevalence of these systems. There is additional complexity in such cases where, in consequence of retardation, the character and features significantly and progressively change as radiation propagates onwards, from the near-field and out towards the wave-zone. Readily developed analytical representations of the electric field, cast as a function of distance from the source, provide illuminating insights into the most prominent and distinctive properties of radiant electromagnetic emission. Graphical implementations and animations of the results prove particularly instructive in revealing the spatial form and temporal evolution of the emergent electromagnetic fields
Interparticle interactions:Energy potentials, energy transfer, and nanoscale mechanical motion in response to optical radiation
In the interactions between particles of material with slightly different electronic levels, unusually large shifts in the pair potential can result from photoexcitation, and on subsequent electronic excitation transfer. To elicit these phenomena, it is necessary to understand the fundamental differences between a variety of optical properties deriving from dispersion interactions, and processes such as resonance energy transfer that occur under laser irradiance. This helps dispel some confusion in the recent literature. By developing and interpreting the theory at a deeper level, one can anticipate that in suitable systems, light absorption and energy transfer will be accompanied by significant displacements in interparticle separation, leading to nanoscale mechanical motion
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The measurement of the velocities of particles in an air-solid flow
Theoretical investigations of two-phase flows have not so far produced a useful model since the interdependence of the many variables has been difficult to predict. Progress towards such a model is dependent on accurate experimental work on two-phase flows. Particle velocity is an especially important property, but most available techniques either disturb the flow or are slow or inaccurate.
The laser-Doppler velocity meter, LDV, was developed for measurements in single-phase flows, but it has been demonstrated by a few authors to be practical for particle velocity measurements in air-solid flows. The aim of the investigation was to find the range for which the LDV was suitable, and also to make useful measurements in a pipe conveying a dilute suspension of solids pneumatically.
Air and solid velocity distributions across the diameter of a vertically upward flowing air-solid suspension in a 50 mm diameter pipe were made using an LDV. The solids conveyed were spherical glass balls, mean diameter 455 um, and sand, mean diameters 176 um and 366 um. The maximum ratio of solids to air mass flow rate was 2.5 and the maximum mean air velocity was 50 ms. Significant slip between the phases was found. Some of the correlations postulated between the particle velocity and other flow properties, such as the pressure drop, were investigated.
Velocity measurements were also attempted with an LDV on plastic pellets, with effective diameters of 2 to 3 mm and varying degrees of success were achieved. The optical properties of the particles appears to be important when applying the laser-Doppler particle measuring technique to flows conveying particles of this size
Asymmetric Ejecta of Cool Supergiants and Hypergiants in the Massive Cluster Westerlund 1
We report new 5.5 GHz radio observations of the massive star cluster Westerlund 1, taken by the Australia Telescope Compact Array, detecting nine of the ten yellow hypergiants (YHGs) and red supergiants (RSGs) within the cluster. Eight of nine sources are spatially resolved. The nebulae associated with the YHGs Wd1-4a, -12a and -265 demonstrate a cometary morphology - the first time this phenomenon has been observed for such stars. This structure is also echoed in the ejecta of the RSGs Wd1-20 and -26; in each case the cometary tails are directed away from the cluster core. The nebular emission around the RSG Wd1-237 is less collimated than these systems but once again appears more prominent in the hemisphere facing the cluster. Considered as a whole, the nebular morphologies provide compelling evidence for sculpting via a physical agent associated with Westerlund 1, such as a cluster wind
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