1,950 research outputs found
A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula
Continuing our development of a mathematical theory of stochastic
microlensing, we study the random shear and expected number of random lensed
images of different types. In particular, we characterize the first three
leading terms in the asymptotic expression of the joint probability density
function (p.d.f.) of the random shear tensor at a general point in the lens
plane due to point masses in the limit of an infinite number of stars. Up to
this order, the p.d.f. depends on the magnitude of the shear tensor, the
optical depth, and the mean number of stars through a combination of radial
position and the stars' masses. As a consequence, the p.d.f.s of the shear
components are seen to converge, in the limit of an infinite number of stars,
to shifted Cauchy distributions, which shows that the shear components have
heavy tails in that limit. The asymptotic p.d.f. of the shear magnitude in the
limit of an infinite number of stars is also presented. Extending to general
random distributions of the lenses, we employ the Kac-Rice formula and Morse
theory to deduce general formulas for the expected total number of images and
the expected number of saddle images. We further generalize these results by
considering random sources defined on a countable compact covering of the light
source plane. This is done to introduce the notion of {\it global} expected
number of positive parity images due to a general lensing map. Applying the
result to microlensing, we calculate the asymptotic global expected number of
minimum images in the limit of an infinite number of stars, where the stars are
uniformly distributed. This global expectation is bounded, while the global
expected number of images and the global expected number of saddle images
diverge as the order of the number of stars.Comment: To appear in JM
Accelerator Design for the CHESS-U Upgrade
During the summer and fall of 2018 the Cornell High Energy Synchrotron Source
(CHESS) is undergoing an upgrade to increase high-energy flux for x-ray users.
The upgrade requires replacing one-sixth of the Cornell Electron Storage Ring
(CESR), inverting the polarity of half of the CHESS beam lines, and switching
to single-beam on-axis operation. The new sextant is comprised of six
double-bend achromats (DBAs) with combined-function dipole-quadrupoles.
Although the DBA design is widely utilized and well understood, the constraints
for the CESR modifications make the CHESS-U lattice unique. This paper
describes the design objectives, constraints, and implementation for the CESR
accelerator upgrade for CHESS-U
Large droplet impact on water layers
The impact of large droplets onto an otherwise undisturbed layer of water is considered. The work, which is motivated primarily with regard to aircraft icing, is to try and help understand the role of splashing on the formation of ice on a wing, in particular for large droplets where splash appears, to have a significant effect. Analytical and numerical approaches are used to investigate a single droplet impact onto a water layer. The flow for small times after impact is determined analytically, for both direct and oblique impacts. The impact is also examined numerically using the volume of fluid (VOF) method. At small times there are promising comparisons between the numerical results, the analytical solution and experimental work capturing the ejector sheet. At larger times there is qualitative agreement with experiments and related simulations. Various cases are considered, varying the droplet size to layer depth ratio, including surface roughness, droplet distortion and air effects. The amount of fluid splashed by such an impact is examined and is found to increase with droplet size and to be significantly influenced by surface roughness. The makeup of the splash is also considered, tracking the incoming fluid, and the splash is found to consist mostly of fluid originating in the layer
Measurement and Compensation of Horizontal Crabbing at the Cornell Electron Storage Ring Test Accelerator
In storage rings, horizontal dispersion in the rf cavities introduces
horizontal-longitudinal (xz) coupling, contributing to beam tilt in the xz
plane. This coupling can be characterized by a "crabbing" dispersion term
{\zeta}a that appears in the normal mode decomposition of the 1-turn transfer
matrix. {\zeta}a is proportional to the rf cavity voltage and the horizontal
dispersion in the cavity. We report experiments at the Cornell Electron Storage
Ring Test Accelerator (CesrTA) where xz coupling was explored using three
lattices with distinct crabbing properties. We characterize the xz coupling for
each case by measuring the horizontal projection of the beam with a beam size
monitor. The three lattice configurations correspond to a) 16 mrad xz tilt at
the beam size monitor source point, b) compensation of the {\zeta}a introduced
by one of two pairs of RF cavities with the second, and c) zero dispersion in
RF cavities, eliminating {\zeta}a entirely. Additionally, intrabeam scattering
(IBS) is evident in our measurements of beam size vs. rf voltage.Comment: 5 figures, 10 page
Edge scaling limits for a family of non-Hermitian random matrix ensembles
A family of random matrix ensembles interpolating between the GUE and the
Ginibre ensemble of matrices with iid centered complex Gaussian
entries is considered. The asymptotic spectral distribution in these models is
uniform in an ellipse in the complex plane, which collapses to an interval of
the real line as the degree of non-Hermiticity diminishes. Scaling limit
theorems are proven for the eigenvalue point process at the rightmost edge of
the spectrum, and it is shown that a non-trivial transition occurs between
Poisson and Airy point process statistics when the ratio of the axes of the
supporting ellipse is of order . In this regime, the family of
limiting probability distributions of the maximum of the real parts of the
eigenvalues interpolates between the Gumbel and Tracy-Widom distributions.Comment: 44 page
A relativistically covariant version of Bohm's quantum field theory for the scalar field
We give a relativistically covariant, wave-functional formulation of Bohm's
quantum field theory for the scalar field based on a general foliation of
space-time by space-like hypersurfaces. The wave functional, which guides the
evolution of the field, is space-time-foliation independent but the field
itself is not. Hence, in order to have a theory in which the field may be
considered a beable, some extra rule must be given to determine the foliation.
We suggest one such rule based on the eigen vectors of the energy-momentum
tensor of the field itself.Comment: 1 figure. Submitted to J Phys A. 20/05/04 replacement has additional
references and a few minor changes made for clarity. Accepted by J Phys
Capacity Market for Distribution System Operator – with Reliability Transactions – Considering Critical Loads and Microgrids
Conventional distribution system (DS) asset planning methods consider energy only from transmission
systems (TS) and not from distributed energy resources (DER), leading to expensive plans. Newer transactive energy DS (TEDS) asset planning models, built on capacity market mechanisms, consider energy from both TS and DERs, leading to lower-cost plans and maximizing social welfare.
However, in both methods the cost of higher reliability requirements for some users are socialized across all users, leading to lower social welfare. In this paper, a novel transactive energy capacity market (TECM) model is proposed for DS asset planning. It builds on TEDS incremental capacity auction models by provisioning for critical loads to bid and receive superior reliability as a service. The TECM model considers these reliability transactions, in addition, to selling energy transactions from
TS and DERs, buying energy transactions from loads, and asset upgrade transactions from the network operator. The TECM model allows for islanded microgrids and network reconfiguration to maximize social welfare. The TECM model is assessed on several case studies, demonstrating that
it achieves higher social welfare and a lower plan cost
Análise de endemismo de táxons neotropicais de Pentatomidae (Hemiptera: Heteroptera)
The definition of areas of endemism is central to studies of historical biogeography, and their interrelationships are fundamental questions. Consistent hypotheses for the evolution of Pentatomidae in the Neotropical region depend on the accuracy of the units employed in the analyses, which in the case of studies of historical biogeography, may be areas of endemism. In this study, the distribution patterns of 222 species, belonging to 14 Pentatomidae (Hemiptera) genera, predominantly neotropical, were studied with the Analysis of Endemicity (NDM) to identify possible areas of endemism and to correlate them to previously delimited areas. The search by areas of endemism was carried out using grid-cell units of 2.5° and 5° latitude-longitude. The analysis based on groupings of grid-cells of 2.5° of latitude-longitude allowed the identification of 51 areas of endemism, the consensus of these areas resulted in four clusters of grid-cells. The second analysis, with grid-cells units of 5° latitude-longitude, resulted in 109 areas of endemism. The flexible consensus employed resulted in 17 areas of endemism. The analyses were sensitive to the identification of areas of endemism in different scales in the Atlantic Forest. The Amazonian region was identified as a single area in the area of consensus, and its southeastern portion shares elements with the Chacoan and Paraná subregions. The distribution data of the taxa studied, with different units of analysis, did not allow the identification of individual areas of endemism for the Cerrado and Caatinga. The areas of endemism identified here should be seen as primary biogeographic hypotheses.A definição de áreas de endemismo é central aos estudos de Biogeografia Histórica e suas inter-relações são questões fundamentais. Hipóteses consistentes sobre a evolução de Pentatomidae (Hemiptera) na Região Neotropical dependem da acuidade das unidades empregadas nas análises, que no caso de estudos de biogeografia histórica, podem ser áreas endêmicas. Neste trabalho foram estudados os padrões de distribuição de 222 espécies, pertencentes a 14 gêneros de Pentatomidae, com ocorrência predominantemente neotropical, com base em uma Análise de Endemicidade (NDM) a fim de inferir possíveis áreas endêmicas e relacioná-las a áreas previamente delimitadas. A busca por áreas endêmicas foi realizada com quadrículas de 2,5° e 5° latitude-longitude. A análise com base em agrupamentos de 2,5° latitude-longitude permitiu identificar 51 áreas de endemismo, sendo que o consenso destas áreas resultou em quatro agrupamentos de quadrículas. A segunda análise, com quadrículas de 5° latitude-longitude, resultou em 109 áreas de endemismo. O consenso flexível empregado resultou em 17 áreas de endemismo. As análises foram sensíveis à identificação de áreas de endemismo na Mata Atlântica em diferentes escalas. A região Amazônica foi identificada como uma área única no consenso, sendo que a porção sudeste compartilha elementos com as sub-regiões do Chaco e Paraná. Os dados de distribuição dos táxons estudados, com diferentes unidades de análises, não permitiram a identificação de áreas endêmicas para o Cerrado e a Caatinga. As áreas de endemismo aqui identificadas devem ser tratadas como hipóteses biogeográficas primárias.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Universidade Federal do Rio Grande do Sul Laboratório de Entomologia Sistemática Departamento de ZoologiaUniversidade Federal do Paraná Departamento de Zoologia Programa de Pós-Graduação em EntomologiaUniversidade Federal de São Paulo (UNIFESP) Departamento de Ciências BiológicasUNIFESP, Depto. de Ciências BiológicasSciEL
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