2,559 research outputs found
Characterisation and representation of non-dissipative electromagnetic medium with a double light cone
We study Maxwell's equations on a 4-manifold N with a medium that is
non-dissipative and has a linear and pointwise response. In this setting, the
medium can be represented by a suitable (2,2)-tensor on the 4-manifold N.
Moreover, in each cotangent space on N, the medium defines a Fresnel surface.
Essentially, the Fresnel surface is a tensorial analogue of the dispersion
equation that describes the response of the medium for signals in the geometric
optics limit. For example, in isotropic medium the Fresnel surface is at each
point a Lorentz light cone. In a recent paper, I. Lindell, A. Favaro and L.
Bergamin introduced a condition that constrains the polarisation for plane
waves. In this paper we show (under suitable assumptions) that a slight
strengthening of this condition gives a pointwise characterisation of all
medium tensors for which the Fresnel surface is the union of two distinct
Lorentz null cones. This is for example the behaviour of uniaxial medium like
calcite. Moreover, using the representation formulas from Lindell et al. we
obtain a closed form representation formula that pointwise parameterises all
medium tensors for which the Fresnel surface is the union of two distinct
Lorentz null cones. Both the characterisation and the representation formula
are tensorial and do not depend on local coordinates
Drifting instabilities of cavity solitons in vertical cavity surface-emitting lasers with frequency selective feedback
In this paper we study the formation and dynamics of self-propelled cavity
solitons (CSs) in a model for vertical cavity surface-emitting lasers (VCSELs)
subjected to external frequency selective feedback (FSF), and build their
bifurcation diagram for the case where carrier dynamics is eliminated. For low
pump currents, we find that they emerge from the modulational instability point
of the trivial solution, where traveling waves with a critical wavenumber are
formed. For large currents, the branch of self-propelled solitons merges with
the branch of resting solitons via a pitchfork bifurcation. We also show that a
feedback phase variation of 2\pi can transform a CS (whether resting or moving)
into a different one associated to an adjacent longitudinal external cavity
mode. Finally, we investigate the influence of the carrier dynamics, relevant
for VCSELs. We find and analyze qualitative changes in the stability properties
of resting CSs when increasing the carrier relaxation time. In addition to a
drifting instability of resting CSs, a new kind of instability appears for
certain ranges of carrier lifetime, leading to a swinging motion of the CS
center position. Furthermore, for carrier relaxation times typical of VCSELs
the system can display multistability of CSs.Comment: 11 pages, 12 figure
A survey on structured deformations
In this work we briefly describe the theory of (first-order) structured deformations of continua as well as the variational problems arising from this theory.
Bayesian stochastic blockmodeling
This chapter provides a self-contained introduction to the use of Bayesian
inference to extract large-scale modular structures from network data, based on
the stochastic blockmodel (SBM), as well as its degree-corrected and
overlapping generalizations. We focus on nonparametric formulations that allow
their inference in a manner that prevents overfitting, and enables model
selection. We discuss aspects of the choice of priors, in particular how to
avoid underfitting via increased Bayesian hierarchies, and we contrast the task
of sampling network partitions from the posterior distribution with finding the
single point estimate that maximizes it, while describing efficient algorithms
to perform either one. We also show how inferring the SBM can be used to
predict missing and spurious links, and shed light on the fundamental
limitations of the detectability of modular structures in networks.Comment: 44 pages, 16 figures. Code is freely available as part of graph-tool
at https://graph-tool.skewed.de . See also the HOWTO at
https://graph-tool.skewed.de/static/doc/demos/inference/inference.htm
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