11,553 research outputs found
UMSL Bulletin 2023-2024
The 2023-2024 Bulletin and Course Catalog for the University of Missouri St. Louis.https://irl.umsl.edu/bulletin/1088/thumbnail.jp
Slitless spectrophotometry with forward modelling: principles and application to atmospheric transmission measurement
In the next decade, many optical surveys will aim to tackle the question of
dark energy nature, measuring its equation of state parameter at the permil
level. This requires trusting the photometric calibration of the survey with a
precision never reached so far, controlling many sources of systematic
uncertainties. The measurement of the on-site atmospheric transmission for each
exposure, or on average for each season or for the full survey, can help reach
the permil precision for magnitudes. This work aims at proving the ability to
use slitless spectroscopy for standard star spectrophotometry and its use to
monitor on-site atmospheric transmission as needed, for example, by the Vera C.
Rubin Observatory Legacy Survey of Space and Time supernova cosmology program.
We fully deal with the case of a disperser in the filter wheel, which is the
configuration chosen in the Rubin Auxiliary Telescope. The theoretical basis of
slitless spectrophotometry is at the heart of our forward model approach to
extract spectroscopic information from slitless data. We developed a publicly
available software called Spectractor (https://github.com/LSSTDESC/Spectractor)
that implements each ingredient of the model and finally performs a fit of a
spectrogram model directly on image data to get the spectrum. We show on
simulations that our model allows us to understand the structure of
spectrophotometric exposures. We also demonstrate its use on real data, solving
specific issues and illustrating how our procedure allows the improvement of
the model describing the data. Finally, we discuss how this approach can be
used to directly extract atmospheric transmission parameters from data and thus
provide the base for on-site atmosphere monitoring. We show the efficiency of
the procedure on simulations and test it on the limited data set available.Comment: 30 pages, 36 figures, submitted to Astronomy and Astrophysic
Signed tropicalization of polar cones
We study the tropical analogue of the notion of polar of a cone, working over
the semiring of tropical numbers with signs. We characterize the cones which
arise as polars of sets of tropically nonnegative vectors by an invariance
property with respect to a tropical analogue of Fourier-Motzkin elimination. We
also relate tropical polars with images by the nonarchimedean valuation of
classical polars over real closed nonarchimedean fields and show, in
particular, that for semi-algebraic sets over such fields, the operation of
taking the polar commutes with the operation of signed valuation (keeping track
both of the nonarchimedean valuation and sign). We apply these results to
characterize images by the signed valuation of classical cones of matrices,
including the cones of positive semidefinite matrices, completely positive
matrices, completely positive semidefinite matrices, and their polars,
including the cone of co-positive matrices, showing that hierarchies of
classical cones collapse under tropicalization. We finally discuss an
application of these ideas to optimization with signed tropical numbers.Comment: 24 pages, 1 figure. Changes with respect to Version 2: we improved
Introduction and added Examples 3.24 and 3.25 illustrating that "bend
addition" can be considered as a tropical analogue of the Fourier-Motzkin
eliminatio
Southern Adventist University Undergraduate Catalog 2022-2023
Southern Adventist University\u27s undergraduate catalog for the academic year 2022-2023.https://knowledge.e.southern.edu/undergrad_catalog/1121/thumbnail.jp
Application of multi-scale computational techniques to complex materials systems
The applications of computational materials science are ever-increasing, connecting fields far beyond traditional subfields in materials science. This dissertation demonstrates the broad scope of multi-scale computational techniques by investigating multiple unrelated complex material systems, namely scandate thermionic cathodes and the metallic foam component of micrometeoroid and orbital debris (MMOD) shielding. Sc-containing scandate cathodes have been widely reported to exhibit superior properties compared to previous thermionic cathodes; however, knowledge of their precise operating mechanism remains elusive. Here, quantum mechanical calculations were utilized to map the phase space of stable, highly-faceted and chemically-complex W nanoparticles, accounting for both finite temperature and chemical environment. The precise processing conditions required to form the characteristic W nanoparticle observed experimentally were then distilled. Metallic foams, a central component of MMOD shielding, also represent a highly-complex materials system, albeit at a far higher length scale than W nanoparticles. The non-periodic, randomly-oriented constituent ligaments of metallic foams and similar materials create a significant variability in properties that is generally difficult to model. Rather than homogenizing the material such that its unique characteristic structural features are neglected, here, a stochastic modeling approach is applied that integrates complex geometric structure and utilizes continuum calculations to predict the resulting probabilistic distributions of elastic properties. Though different in many aspects, scandate cathodes and metallic foams are united by complexity that is impractical, even dangerous, to ignore and well-suited to exploration with multi-scale computational methods
Aspects Topologiques des Représentations en Analyse Calculable
Computable analysis provides a formalization of algorithmic computations over infinite mathematical objects. The central notion of this theory is the symbolic representation of objects, which determines the computation power of the machine, and has a direct impact on the difficulty to solve any given problem. The friction between the discrete nature of computations and the continuous nature of mathematical objects is captured by topology, which expresses the idea of finite approximations of infinite objects.We thoroughly study the multiple interactions between computations and topology, analysing the information that can be algorithmically extracted from a representation. In particular, we focus on the comparison between two representations of a single family of objects, on the precise relationship between algorithmic and topological complexity of problems, and on the relationship between finite and infinite representations.L’analyse calculable permet de formaliser le traitement algorithmique d’objets mathématiques infinis. La théorie repose sur une représentation symbolique des objets, dont le choix détermine les capacités de calcul de la machine, notamment sa difficulté à résoudre chaque problème donné. La friction entre le caractère discret du calcul et la nature continue des objets est capturée par la topologie, qui exprime l’idée d’approximation finie d’objets infinis.Nous étudions en profondeur les multiples interactions entre calcul et topologie, cherchant à analyser l’information qui peut être extraite algorithmiquement d’une représentation. Je me penche plus particulièrement sur la comparaison entre deux représentations d’une même famille d’objets, sur les liens détaillés entre complexité algorithmique et topologique des problèmes, ainsi que sur les relations entre représentations finies et infinies
Solving time-dependent PDEs with the ultraspherical spectral method
We apply the ultraspherical spectral method to solving time-dependent PDEs by
proposing two approaches to discretization based on the method of lines and
show that these approaches produce approximately same results. We analyze the
stability, the error, and the computational cost of the proposed method. In
addition, we show how adaptivity can be incorporated to offer adequate spatial
resolution efficiently. Both linear and nonlinear problems are considered. We
also explore time integration using exponential integrators with the
ultraspherical spatial discretization. Comparisons with the Chebyshev
pseudospectral method are given along the discussion and they show that the
ultraspherical spectral method is a competitive candidate for the spatial
discretization of time-dependent PDEs
The existence of subspace designs
We prove the existence of subspace designs with any given parameters,
provided that the dimension of the underlying space is sufficiently large in
terms of the other parameters of the design and satisfies the obvious necessary
divisibility conditions. This settles an open problem from the 1970s. Moreover,
we also obtain an approximate formula for the number of such designs.Comment: 61 page
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