Sobre o comportamento de sequências de monopolos com massas arbitrariamente grandes em dimensões 3 e 7

Orientadores: Henrique Nogueira de Sá Earp, Gonçalo Marques Fernandes de OliveiraTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Estudamos aspectos analíticos de soluções suaves das equaçõs de Yang-Mills-Higgs em variedades riemannianas não-compactas com geometria limitada, focando no problema de compacidade para soluções do tipo monopolo sob um certo regime assintótico de massas arbitrariamente grandes em variedades assintóticamente cônicas (AC) de dimensões 3 e 7. No caso de dimensão 3, as componentes conexas do espaço de módulos de monopolos são indexadas por um inteiro chamado de carga, e consideramos o problema do comportamento limite de sequências de monopolos com carga fixa k e massas arbitrariamente grandes, cf. Fadel-Oliveira (2019). Provamos que a comportamento limite de tais monopolos é caracterizado pela concentração de energia ao longo de um conjunto finito Z, consistindo de no máximo k pontos nos quais os zeros dos campos de Higgs se acumulam e um monopolo em R^3 de massa 1 e carga 1 borbulha. Finalmente, seguindo uma sugestão do artigo seminal de Donaldson-Segal (2009), desenvolvemos o mesmo tipo de análise para monopolos de dimensões mais altas em G2-variedades de dimensão 7 e, sob certas hipóteses brandas, provamos, entre outras coisas, que o conjunto de acumulação dos zeros dos campos de Higgs nesse caso é de medida H^4 finita e está contido em um conjunto H^4-retificável onde a energia intermediária da sequência se concentraAbstract: We study analytical aspects of smooth solutions of the Yang-Mills-Higgs equations on noncompact Riemannian manifolds of bounded geometry, focusing on the compactness problem for monopole solutions under a certain asymptotic regime of arbitrarily large mass on asymptotically conical (AC) 3- and 7- dimensional manifolds. In the 3-dimensional case, the connected components of the moduli space of monopoles are labeled by an integer called the charge, and we consider the problem of the limiting behavior of sequences of monopoles with fixed charge k and arbitrarily large masses, cf. Fadel-Oliveira (2019). We prove that the limiting behavior of such monopoles is characterized by energy concentration along a finite set Z, consisting of at most k points at which the zeros of the Higgs fields accumulate and a mass 1 and charge 1 R^3-monopole bubbles off. We also give some results on the direction of the convergence problem of the sequence outside Z. Finally, following a suggestion of the seminal paper of Donaldson-Segal (2009), we develop the same sort of analysis for higher dimensional monopoles on 7-dimensional AC G2-manifolds and under certain mild assumptions we prove, among other things, that the accumulation set of the Higgs fields zeros in this case is of finite H^4-measure and is included in a H^4-rectifiable set where the intermediate energy of the sequence concentratesDoutoradoMatematicaDoutor em Matemática142267/2017-1CNPQCAPE

The Limit of Large Mass Monopoles

In this paper we consider $\rm SU(2)$ monopoles on an asymptotically conical, oriented, Riemannian $3$-manifold with one end. The connected components of the moduli space of monopoles in this setting are labeled by an integer called the charge. We analyse the limiting behavior of sequences of monopoles with fixed charge, and whose sequence of Yang--Mills--Higgs energies is unbounded. We prove that the limiting behavior of such monopoles is characterized by energy concentration along a certain set, which we call the blow-up set. Our work shows that this set is finite, and using a bubbling analysis obtain effective bounds on its cardinality, with such bounds depending solely on the charge of the monopole. Moreover, for such sequences of monopoles there is another naturally associated set, the zero set, which consists on the set at which the zeros of the Higgs fields accumulate. Regarding this, our results show that for such sequences of monopoles, the zero set and the blow-up set coincide. In particular, proving that in this "large mass" limit, the zero set is a finite set of points. Some of our work extends for sequences of finite mass critical points of the Yang--Mills--Higgs functional for which the Yang--Mills--Higgs energies are $O(m_i)$ as $i\to\infty$, where $m_i$ are the masses of the configurations.Comment: v4: accepted for publication in the Proceedings of the London Mathematical Society. Fully revised, exposition improved; reworked Theorems 4.1 and 5.

Bell correlations in a many-body system with finite statistics

A recent experiment reported the first violation of a Bell correlation witness in a many-body system [Science 352, 441 (2016)]. Following discussions in this paper, we address here the question of the statistics required to witness Bell correlated states, i.e. states violating a Bell inequality, in such experiments. We start by deriving multipartite Bell inequalities involving an arbitrary number of measurement settings, two outcomes per party and one- and two-body correlators only. Based on these inequalities, we then build up improved witnesses able to detect Bell-correlated states in many-body systems using two collective measurements only. These witnesses can potentially detect Bell correlations in states with an arbitrarily low amount of spin squeezing. We then establish an upper bound on the statistics needed to convincingly conclude that a measured state is Bell-correlated.Comment: 5+12 pages, 3+4 figure

The asymptotic geometry of G2\rm G_2-monopoles

This article investigates the asymptotics of $\rm G_2$-monopoles. First, we prove that when the underlying $\rm G_2$-manifold has polynomial volume growth strictly faster than $r^{7/2}$, finite intermediate energy monopoles with bounded curvature have finite mass. The second main result restricts to the case when the underlying $\rm G_2$-manifold is asymptotically conical. In this situation, we deduce sharp decay estimates and that the connection converges, along the end, to a pseudo-Hermitian--Yang--Mills connection over the asymptotic cone. Finally, our last result exhibits a Fredholm setup describing the moduli space of finite intermediate energy monopoles on an asymptotically conical $\rm G_2$-manifold.Comment: 80 pages. v2: added 4 new sections, new results, including a third main result; previous sections fully revised, exposition improved, corrected typos and reworked some proof

Ejemplares tipo de Cactaceae depositados en el Museo Argentino de Ciencias Naturales (Herbario BA), Buenos Aires, Argentina

The Herbarium of the Museo Argentino de ciencias naturales “Bernardino rivadavia” (BA Herbarium) was the first official herbarium in Argentina. Initiated in 1853, it holds about 150,000 herbarium specimens at present, most of them collected all over Argentina, but also obtained by exchange with other national and international botanical institutions. About 100,000 correspond to vascular plants, and 800 represent nomenclatural type specimens. cactaceae type material deposited at BA is presented. this article includes a list of the 57 type specimens alphabetically arranged; scientific names with author of taxon, original publication data and type category are transcribed from the original labels. currently accepted scientific names are also included. under observations, ecological information or additional comments written by the author of the description are given. under notes some consideration of our own, most regarding to the current synonymy, are given. these type specimens are kept in special metal cabinets, separated from the rest of the herbarium material and documented with a copy of the original diagnosis or publication. As part of the digitization of Biological collections Project carried out by the museum, the complete information of each specimen was digitized and is available online through the website of the Sistema nacional de datos Biológicos (SndB) and the Global Biodiversity Information Facility (GBIF).El Herbario del Museo Argentino de ciencias naturales “Bernardino rivadavia” (Herbario BA) fue el primer herbario oficial de Argentina. Iniciado en el año 1853, alberga actualmente unos 150.000 especímenes de herbario, la mayoría de ellos colectados a lo largo y ancho de Argentina pero también obtenidos por intercambio con otras instituciones botánicas tanto na-cionales como internacionales. de todos ellos, aproximadamente 100.000 corresponden a especímenes de plantas vasculares y 800 representan especímenes tipo. continuando con la publicación de los datos de los ejemplares tipo depositados en BA, se presenta un catálogo del material tipo de cactaceae. El presente artículo incluye un listado de los 57 especímenes tipo alfabéticamente ordenados; se transcribe para cada uno de ellos el nombre científico y autor del taxón, así como la información original de etiqueta. En las observaciones se incluye la información ecológica o comentarios adicionales redactadas por el autor de la descripción. En cuanto a las notas provistas por los autores de este trabajo, se incluyen algunas consideraciones acerca de la sinonimia actual. Los ejemplares tipo son guardados en gabinetes metálicos especiales, separados de resto de material del herbario y documentados con una copia de la diagnosis original o su publicación. como parte del Proyecto de digitalización de las colecciones Biológicas llevado a cabo por el Museo, la información completa de cada especimen fue digitalizada y se encuentra disponible a través del portal web del Sistema nacional de datos Biológicos (SndB) y la Infraestructura Mundial de Información en Biodiversidad (GBIF).Fil: Fadel, Valentín Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Alvarenga, Eugenia Celeste. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; ArgentinaFil: Arriaga, Mirta Olga. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Museo Argentino de Ciencias Naturales "Bernardino Rivadavia"; Argentin

Comparative study of tall building response to synoptic and non-synoptic wind action

Until the beginning of the 21st Century, the characteristics of wind for purposes of structural analysis and design, as reflected in wind codes worldwide, were based on the behavior of wind currents in the vicinity of the ground surface observed in so-called synoptic events. It was only recently recognized that the latter are not the only cause of wind damage to buildings and structures, not even its main cause. In view of the absence of any reference to non-synoptic winds in most South American wind codes, their urgent revision to include the effects on non-synoptic winds is badly needed. The downburst is a relevant meteorological phenomenon that causes extreme winds in the lower atmospheric boundary layer. The present article briefly describes an introduction to an simplified approach recently proposed by the second author to describe the wind velocity field in this type of meteorological phenomenon, that is, downbursts within instability lines. The method is examined by a comparative study of tall building response to synoptic and non-synoptic wind action

Sobre lugares de blow-up de instantons em dimensões superiores

Orientador: Henrique Nogueira de Sá EarpDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: Estudamos aspectos analíticos fundamentais de conexões Yang-Mills em dimensões superiores ou iguais a quatro, seguindo o célebre artigo de G. Tian nos Annals of Mathematics (2000). O objetivo central é fornecer uma apresentação auto-suficiente à análise fundamental de Tian sobre o fenômeno de não-compacidade dos espaços de moduli de conexões Yang-Mills com energia L^2 uniformemente limitada. Isto culmina em uma relação notável entre teoria de calibres e geometria calibrada: sob hipóteses adequadas, verifica-se que os lugares de 'blow-up' de sequências de conexões Yang-Mills definem ciclos calibradosAbstract: We study fundamental analytical aspects of Yang-Mills connections in dimensions higher than or equal to four, following the famous work by G. Tian in the Annals of Mathematics (2000). The main objective is to provide a self-contained introduction to the fundamental analysis of Tian on the noncompactness phenomenon of moduli spaces of Yang-Mills connections with uniformly bounded L^2-energy. This culminates in a remarkable relation between gauge theory and calibrated geometry: under suitable conditions, one verifies that the 'blow-up' sets of sequences of Yang-Mills connections define calibrated cyclesMestradoMatematicaMestre em Matemática131468/2014-6CNP

Probabilistic assessment of the seismic Peak Ground Acceleration (PGA) at seven Colombian cities

This paper presents a probabilistic assessment of peak ground acceleration (PGA) observations at seven Colombian cities located in regions with intermediate and high seismic activity. Frequency histograms of the annual exceedance rates were determined using historical data of the annual rate of exceedance for pre-established values of PGA. After determining distribution parameters by means of the method of moments, several probability density functions were examined in order to evaluate the performance of each function. In most sites, the maximum annual PGA appears to be best modeled by a lognormal distribution, which led to its adoption as parent distribution for the entire group of cities. Once the lognormal function is selected as parent distribution, series of PGA values for arbitrary periods of time may be generated through random simulation. Next, series of maximum values in fifty years of observation were simulated for the seven cities, assuming a Lognormal parent distribution. Analytical solutions for extreme values of different sample sizes of lognormal random variables are not known to the authors. However, since extreme values for large samples of lognormal random variables tend asymptotically to a Type I (Gumbel) probability distribution, the latter was adopted as a possible model for the 50 years PGA distributions suggested in the paper for several Colombian cities, as a useful tool for engineering design, whenever the PGA is regarded as an appropriate seismic intensity measure