1,721,863 research outputs found
Wave propagation in non rectilinear waveguides
No full textWe present a mathematical framework for studying the problem of
electromagnetic wave propagation in a 2-D or 3-D optical waveguide
(optical fiber). We will consider both the case of a rectilinear
waveguide and the one of a waveguide presenting imperfections, with
applications to phenomenons of physical interest. Numerical examples
will be given
A radiation condition for the 2-D Helmholtz equation in stratified media
Full text linkWe study the 2-D Helmholtz equation in perturbed stratified media,
allowing the existence of guided waves. Our assumptions on the
perturbing and source terms are not too restrictive.
We prove two results. Firstly, we introduce a Sommerfeld-Rellich
radiation condition and prove the uniqueness of the solution for the
studied equation. Then, by careful asymptotic estimates, we prove
the existence of a bounded solution satisfying our radiation
condition
A weak comparison principle for solutions of very degenerate elliptic equations
Full text linkWe prove a comparison principle for weak solutions of elliptic quasilinear equations in divergence form whose ellipticity constants degenerate at every point where , where is a Borel set containing the origin
A method of variation of boundaries for waveguide grating couplers
Full text linkWe describe a method for calculating the solution of the
electromagnetic field in a non-rectilinear open waveguide by using a
series expansion, starting from the field of a rectilinear
waveguide. Our approach is based on a method of variation of
boundaries. We prove that the obtained series expansion converges
and we provide a radiation condition at infinity in such a way that
the problem has a unique solution.
Our approach can model several kinds of optical devices which are
used in optical integrated circuits. Numerical examples will be
shown for the case of finite aperiodic waveguide grating couplers
Tools and datasets for unmanned aerial system applications
No full textUnmanned aerial systems (UASs) have rapidly transformed environmental monitoring by affording distributed and frequent observations at high spatial resolutions. The pervasive use of such platforms is impressive and UASs have rapidly become an indispensable addition to the toolkit available to researchers and practitioners globally. However, the ubiquitous spread of UASs has also been paralleled by a plethora of platforms and techniques to process data and extracts environmental variables. From off-the-shelf commercial toolboxes to custom-built routines, UAS end users have to orient themselves among innumerable platforms and resources, and this hampers accurate comparisons to more established approaches. In this chapter, we identify a common workflow for most popular UAS applications from raw data to output benchmarking and comprehensively report available protocols and software tools. Further, we present several data resources for a thorough comparison of existing techniques. Finally, we illustrate state of the art and challenges of multisource studies that merge data from diverse monitoring platforms. This work represents an important effort towards the harmonization of existing UAS methodologies and the standardization of UAS-based measurements
Symmetry for positive critical points of Caffarelli–Kohn–Nirenberg inequalities
Full text linkWe consider positive critical points of Caffarelli–Kohn–Nirenberg inequalities and prove a Liouville type result which allows us to give a complete classification of the solutions in a certain range of parameters, providing a symmetry result for positive solutions. The governing operator is a weighted p-Laplace operator, which we consider for a general p∈(1,d). For p=2, the symmetry breaking region for extremals of Caffarelli–Kohn–Nirenberg inequalities was completely characterized in Dolbeault et al. (2016). Our results extend this result to a general p and are optimal in some cases
Serrin’s type overdetermined problems in convex cones
Full text linkWe consider overdetermined problems of Serrin’s type in convex cones for (possibly) degenerate operators in the Euclidean space as well as for a suitable generalization to space forms. We prove rigidity results by showing that the existence of a solution implies that the domain is a spherical sector
Wulff shape characterizations in overdetermined anisotropic elliptic problems
Full text linkWe study some overdetermined problems for possibly anisotropic degenerate elliptic PDEs, including the well-known Serrin's overdetermined problem, and we prove the corresponding Wulff shape characterizations by using some integral identities and just one pointwise inequality. Our techniques provide a somehow unified approach to this variety of problems
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