579 research outputs found
Transmission properties in waveguides: An optical streamline analysis
A novel approach to study transmission through waveguides in terms of optical
streamlines is presented. This theoretical framework combines the computational
performance of beam propagation methods with the possibility to monitor the
passage of light through the guiding medium by means of these sampler paths. In
this way, not only the optical flow along the waveguide can be followed in
detail, but also a fair estimate of the transmitted light (intensity) can be
accounted for by counting streamline arrivals with starting points
statistically distributed according to the input pulse. Furthermore, this
approach allows to elucidate the mechanism leading to energy losses, namely a
vortical dynamics, which can be advantageously exploited in optimal waveguide
design.Comment: 8 pages, 4 figure
Hierarchical neural networks perform both serial and parallel processing
In this work we study a Hebbian neural network, where neurons are arranged
according to a hierarchical architecture such that their couplings scale with
their reciprocal distance. As a full statistical mechanics solution is not yet
available, after a streamlined introduction to the state of the art via that
route, the problem is consistently approached through signal- to-noise
technique and extensive numerical simulations. Focusing on the low-storage
regime, where the amount of stored patterns grows at most logarithmical with
the system size, we prove that these non-mean-field Hopfield-like networks
display a richer phase diagram than their classical counterparts. In
particular, these networks are able to perform serial processing (i.e. retrieve
one pattern at a time through a complete rearrangement of the whole ensemble of
neurons) as well as parallel processing (i.e. retrieve several patterns
simultaneously, delegating the management of diff erent patterns to diverse
communities that build network). The tune between the two regimes is given by
the rate of the coupling decay and by the level of noise affecting the system.
The price to pay for those remarkable capabilities lies in a network's capacity
smaller than the mean field counterpart, thus yielding a new budget principle:
the wider the multitasking capabilities, the lower the network load and
viceversa. This may have important implications in our understanding of
biological complexity
A Coaxial Vortex Ring Model for Vortex Breakdown
A simple - yet plausible - model for B-type vortex breakdown flows is
postulated; one that is based on the immersion of a pair of slender coaxial
vortex rings in a swirling flow of an ideal fluid rotating around the axis of
symmetry of the rings. It is shown that this model exhibits in the advection of
passive fluid particles (kinematics) just about all of the characteristics that
have been observed in what is now a substantial body of published research on
the phenomenon of vortex breakdown. Moreover, it is demonstrated how the very
nature of the fluid dynamics in axisymmetric breakdown flows can be predicted
and controlled by the choice of the initial ring configurations and their
vortex strengths. The dynamic intricacies produced by the two ring + swirl
model are illustrated with several numerical experiments.Comment: 40 pages, 9 figures, submitted to Physica
Nonequilibrium mesoscopic transport: a genealogy
Models of nonequilibrium quantum transport underpin all modern electronic
devices, from the largest scales to the smallest. Past simplifications such as
coarse graining and bulk self-averaging served well to understand electronic
materials. Such particular notions become inapplicable at mesoscopic
dimensions, edging towards the truly quantum regime. Nevertheless a unifying
thread continues to run through transport physics, animating the design of
small-scale electronic technology: microscopic conservation and nonequilibrium
dissipation. These fundamentals are inherent in quantum transport and gain even
greater and more explicit experimental meaning in the passage to atomic-sized
devices. We review their genesis, their theoretical context, and their
governing role in the electronic response of meso- and nanoscopic systems.Comment: 21p
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