We report on a search for short -period binary systems composed of pairs of evolved stars. The search is being carried out concurrently with a program to characterize the kinematical properties of two different samples of stars. Each sample has produced one close binary candidate for which further spectroscopic observations are planned. We also recapitulate the discovery of a close detached binary system composed of two cool DA white dwarfs, and we discuss the null results of Ha observations of the suspected white dwarf /brown dwarf system G 29-38.

In this study we present photometric predictions for C-type Asymptotic Giant Branch Stars (AGB) stars from Eriksson et al. (2014) for the James Webb Space Telescope (JWST) and the Wide-field Infrared Survey Explorer (WISE) instruments. The photometric predictions we have done are for JWST’s general purpose wide-band filters on NIRCam and MIRI covering wavelengths of 0.7 — 21 microns. AGB stars contribute substantially to the integrated light of intermediate-age stellar popula- tions and is a substantial source of the metals (especially carbon) in galaxies. Studies of AGB stars are (among other reasons) important for the understanding of the chemical evolution and dust cycle of galaxies. Since the JWST is scheduled for launch in 2018 it should be a high priority to prepare observing strategies. With these predictions we hope it will be possible to optimize observing strategies of AGB stars and maximize the science return of JWST. By testing our method on Whitelock et al. (2006) objects from the WISE catalog and comparing them with our photometric results based on Eriksson et al. (2014) we have been able to fit 20 objects with models. The photometric data set can be accessed at: http://www.astro.uu.se/AGBmodels/ / I den här studien har jag gjort fotometriska förutsägelser för asymptotis- ka jättegrensstjärnor (AGB-stjärnor) av C typ från Eriksson et al. (2014) modifierade för instrument ombord på James Webb Space Telescope (JWST) och Wide-field Infrared Survey Explorer (WISE). AGB-stjärnor bidrar kraftigt till det totala ljuset av stjärnor av intermediär ålder och är också en stor källa till metaller (speciellt kol) i galaxer. Studier av AGB stjärnor är viktiga av flera anledningar, däribland för att förstå den kemiska evolutionen och stoftcykler i galaxer. JWST är planerad att skjutas upp 2018 och fram till dess bör det vara en hög prioritet att förbereda observeringsstrategier. Med den fotometriska datan i den här studien hoppas vi att användare av JWST kommer kunna optimera sina observeringsstrategier av AGB-stjärnor och få ut så mycket som möjligt av sin obseravtionstid med teleskopet. Vi har testat metoden genom att titta på objekt från Whitelock et al. (2006) i WISE-katalogen och jämföra dem med de fotometriska resultaten baserade på modellerna från Eriksson et al. (2014). På detta sett har vi lyckats matcha 20 objekt med modeller. Den fotometriska datan går att ladda ner ifrån: http://www.astro.uu.se/AGBmodels/

<b>Asymptotic cones.</b> A finitely generated group has a word metric, which one can scale and thereby view the group from increasingly distant vantage points. The group coalesces to an "asymptotic cone" in the limit (this is made precise using techniques of non-standard analysis). The reward is that in place of the discrete group one has a continuous object "that is amenable to attack by geometric (e.g. topological, infinitesimal) machinery" (to quote Gromov). We give coarse geometric conditions for a metric space X to have N-connected asymptotic cones. These conditions are expressed in terms of certain filling functions concerning filling N-spheres in an appropriately coarse sense. We interpret the criteria in the case where X is a finitely generated group &Gamma; with a word metric. This leads to upper bounds on filling functions for groups with simply connected cones -- in particular they have linearly bounded filling length functions. We prove that if all the asymptotic cones of &Gamma; are N-connected then &Gamma; is of type F_N+1 and we provide N-th order isoperimetric and isodiametric functions. Also we show that the asymptotic cones of a virtually polycyclic group &Gamma; are all contractible if and only if &Gamma; is virtually nilpotent. <b>Combable groups and almost-convex groups.</b> A combing of a finitely generated group &Gamma; is a normal form; that is a choice of word (a combing line) for each group element that satisfies a geometric constraint: nearby group elements have combing lines that fellow travel. An almost-convexity condition concerns the geometry of closed balls in the Cayley graph for &Gamma;. We show that even the most mild combability or almost-convexity restrictions on a finitely presented group already force surprisingly strong constraints on the geometry of its word problem. In both cases we obtain an n! isoperimetric function, and upper bounds of ~ n² on both the minimal isodiametric function and the filling length function.

The asymptotic behaviour of an elastically supported infinite string and an elastic isotropic half plane (in frames of specific asymptotic model) under a moving point load are studied. The main results of this work are uniform asymptotic formulae and the asymptotic profile for the string and the exact solution and uniform asymptotic formulae for a half plane. The crucial assumption for both structures is that the acceleration is sufficiently small. In order to describe asymptotically the oscillations of an infinite string auxiliary canonical functions are introduced, asymptotically analyzed and tabulated. Using these functions uniform asymptotic formulae for the string under constant accelerating and decelerating point loads are obtained. Approximate formulae for the displacement in the vicinity of the point load and the singularity area behind the shock wave using the steady speed asymptotic expansion with additional contributions from stationary points where appropriate are derived. It is shown how to generalise uniform asymptotic results to the arbitrary acceleration case. As an example these results are applied for the case of sinusoidal load speed. It is shown that the canonical functions can successfully be used in the arbitrary acceleration case as well. The graphical comparative analysis of numerical solu- tion and approximations is provided for different moving load speed intervals and values of the parameters. Vibrations of an elastic half plane are studied within the framework of the asymp- totic model suggested by J. Kaplunov et al. in 2006. Boundary conditions for the main problem are obtained as a solution for the problem of a string on the surface of a half plane subject to uniformly accelerated moving load. The exact solution over the interior of the half plane is derived with respect to boundary conditions. Steady speed and Rayleigh wave speed asymptotic expansions are obtained. In the neighborhood of the Rayleigh speed the uniform asymptotic formulae are derived. Some of their interesting properties are discovered and briefly studied. The graphical comparative analysis of the exact solution and approximations is provided for different moving load speed intervals and values of the parameters.

Master of Science / Department of Statistics / Paul I. Nelson / Capture-Recaputre (CR) experiments stemmed from the study of wildlife and are widely used in areas such as ecology, epidemiology, evaluation of census undercounts, and software testing, to estimate population size, survival rate, and other population parameters. The basic idea of the design is to use “overlapping” information contained in multiple samples from the population. In this report, we focus on the simplest form of Capture-Recapture experiments, namely, a two-sample Capture-Recapture design, which is conventionally called the “Petersen Method.” We study and compare the performance of three methods of constructing confidence intervals for the population size based on a Capture-Recapture design, asymptotic normality estimation, Chapman estimation, and “inverting a chi-square test” estimation, in terms of coverage rate and mean interval width. Simulation studies are carried out and analyzed using R and SAS. It turns out that the “inverting a chi-square test” estimation is better than the other two methods. A possible solution to the “zero recapture” problem is put forward. We find that if population size is at least a few thousand, two-sample CR estimation provides reasonable estimates of the population size.

In this thesis, we study re-weighting when estimating totals in survey sampling. The purpose of re-weighting is to adjust the structure of the sample in order to comply with the structure of the population (with respect to given auxiliary variables). We sum up some known results for methods of the traditional desin-based approach, more attention is given to the model-based approach. We generalize known asymptotic results in the model-based theory to a wider class of weighted estimators. Further, we propose a consistent estimator of asymptotic variance, which takes into consideration weights used in estimator of the total. This is in contrast to usually recommended variance estimators derived from the design-based approach. Moreover, the estimator is robust againts particular model misspecifications. In a simulation study, we investigate how the proposed estimator behaves in comparison with variance estimators which are usually recommended in the literature or used in practice. 1

Ripple marks and oscillation marks are undesirable defects which occur on the surface of solidified steel produced industrially in the ingot and the continuous casting processes, respectively; these defects are characterized by more or less evenly spaced indentations on the metal surface. Although the mechanisms for their formation are thought to be qualitatively understood, there is still considerable scope for improvement as regards quantitative mathematical modeling. In this thesis, models for the two processes are developed. For the case of ripple marks, transient twodimensional (2D) momentum and heat transfer in ingot casting is considered, and a criterion is derived, in terms of the process parameters, that can help to inform how to avoid such marks. For the case of oscillation marks in continuous casting, a novel numerical formulation for a transient 2D model is developed with the aim of tracking the spatial location of the first point of molten steel to solidify, since this determines the profile of the final oscillation mark. In both cases, the models are nondimensionalized, and the sizes of the dimensionless parameters that appear are used to derive asymptotically reduced models, with a view to not only clarifying the qualitative behavior, but also as a means to reducing the computational expense; both finite-difference and finite-element methods are used to solve the resulting model equations. One of the conclusions is that, although experimentalists and metallurgists have, in the past, treated the two cases as being linked, the present modeling approach shows quite clearly, and perhaps for the first time, how they quantitatively differ. / Marcas de ondulação e marcas de oscilação são defeitos indesejáveis que ocorrem na superfície do lingote de aço solidificado produzido industrialmente; esses defeitos são caracterizados por recortes mais ou menos uniformemente espaçados na superfície do metal. Embora se acredite que os mecanismos para sua formação sejam entendidos qualitativamente, ainda há considerável espaço para melhorias no que diz respeito à modelagem matemática quantitativa. Nesta tese, os modelos para os dois processos são desenvolvidos. Para o caso de marcas de ondulação, considera-se a transferência bidimensional e transitória (2D) de calor e de momento no lingotamento, e um critério é derivado, em termos dos parâmetros do processo, que pode ajudar a informar como evitar tais marcas. Para o caso de marcas de oscilação em lingotamento contínuo, uma nova formulação numérica para um modelo 2D transiente é desenvolvida com o objetivo de rastrear a localização espacial do primeiro ponto de aço fundido para solidificar, pois isso determina o perfil da marca final de oscilação. Em ambos os casos, os modelos são adimensionalizados, e os tamanhos dos parâmetros adimensionais que aparecem são usados para derivar modelos assintoticamente reduzidos, visando não apenas esclarecer o comportamento qualitativo, mas também como meio de reduzir o gasto computacional; ambos os métodos de diferenças finitas e elementos finitos são usados para resolver as equações do modelos resultantes. Uma das conclusões é que, embora os experimentalistas e metalúrgicos tenham, no passado, tratado os dois casos como estando ligados, a presente abordagem de modelagem mostra claramente, e talvez pela primeira vez, como eles diferem quantitativamente.

<div>Non-stationary point processes are often used to model systems whose rates vary over time. Estimating underlying rate functions is important for input to a discrete-event simulation along with various statistical analyses. We study nonparametric estimators to the marked point process, the infinite-server queueing model, and the transitory queueing model. We conduct statistical inference for these estimators by establishing a number of asymptotic results.</div><div><br></div><div>For the marked point process, we consider estimating the offered load to the system over time. With direct observations of the offered load sampled at fixed intervals, we establish asymptotic consistency, rates of convergence, and asymptotic covariance through a Functional Strong Law of Large Numbers, a Functional Central Limit Theorem, and a Law of Iterated Logarithm. We also show that there exists an asymptotically optimal interval width as the sample size approaches infinity.</div><div><br></div><div>The infinite-server queueing model is central in many stochastic models. Specifically, the mean number of busy servers can be used as an estimator for the total load faced to a multi-server system with time-varying arrivals and in many other applications. Through an omniscient estimator based on observing both the arrival times and service requirements for n samples of an infinite-server queue, we show asymptotic consistency and rate of convergence. Then, we establish the asymptotics for a nonparametric estimator based on observations of the busy servers at fixed intervals.</div><div><br></div><div>The transitory queueing model is crucial when studying a transitory system, which arises when the time horizon or population is finite. We assume we observe arrival counts at fixed intervals. We first consider a natural estimator which applies an underlying nonhomogeneous Poisson process. Although the estimator is asymptotically unbiased, we see that a correction term is required to retrieve an accurate asymptotic covariance. Next, we consider a nonparametric estimator that exploits the maximum likelihood estimator of a multinomial distribution to see that this estimator converges appropriately to a Brownian Bridge.</div>

A modelagem matemática por meio de equações diferenciais é uma importante ferramenta para prever o comportamento de baterias redox de vanádio, pois ela pode contribuir para o aperfeiçoamento do produto e melhor entendimento dos princípios da sua operação. Os estudos de modelagem podem ser aliados à análise assintótica no intuito de promover reduções ou simplificações que tornem os modelos menos complexos, isso é feito a partir da observação da importância que cada termo exerce sobre as equações. Tais simplificações são úteis neste contexto, visto que os modelos geralmente abordam uma célula apenas - a menor unidade operacional da bateria - enquanto aplicações reais exigem o uso de dezenas ou centenas delas implicando em uma maximização do uso de recursos computacionais. Neste trabalho, foram investigadas múltiplas formas de reduções assintóticas que empregadas na construção dos modelos puderam acelerar o tempo de processamento em até 2,46 vezes ou reduzir os requisitos de memória principal em até 11,39%. As simulações computacionais foram executadas pelo software COMSOL Multiphysics v. 4.4, e também por scripts desenvolvidos em ambiente de programação MATLAB. A validação dos resultados foi feita comparando-os a dados experimentais presentes na literatura. Tal abordagem permitiu também validar as rotinas implementadas para a simulação dos modelos comparando suas soluções com aquelas providas pelo COMSOL. / Mathematical modelling using differential equations is an important tool to predict the behavior of vanadium redox batteries, since it may contribute to improve the device performance and lead to a better understanding of the principles of its operation. Modelling can be complemented by asymptotic analysis as a mean to promote reductions or simplifications that make models less complex. Such simplifications are useful in this context, whereas these models usually addresses one cell only the smallest operating unit while real applications demand tens or hundreds cells implying on larger computational requirements. In this research, several options for asymptotic reductions were investigated and, applied to different models, were able to speed up the processing time in 2.46× or reduce the memory requirements up to 11.39%. The computational simulations were executed by COMSOL Multiphysics v.4.4, also by in-house code developed in MATLAB. The validation of results was done by comparing it to experimental results available in literature. Additionally, correlating the results provided by COMSOL with the ones arising from the implemented sub-routines allowed to validate the developed algorithm.

Cette thèse est consacrée à l’enrichissement du modèle mathématique classique des structures intelligentes, en tenant compte des effets thermiques, et à son étude analytique et numérique. Il s'agit typiquement de structures se présentant sous forme de capteurs ou actionneurs, piézoélectriques et/ou magnétostrictifs, dont les propriétés dépendent de la température. On présente d'abord des résultats d'existence et unicité concernant deux problèmes posés sur un domaine tridimensionnel : le problème dynamique et le problème quasi-statique. A partir du problème quasi-statique on déduit un modèle bidimensionnel de plaque grâce à la méthode des développements asymptotiques en considérant quatre types différents de conditions aux limites, chacun visant à modéliser un comportement de type capteur et/ou actionneur. Chacun des quatre problèmes se découple en un problème membranaire et un problème de flexion. Ce dernier est un problème d'évolution qui tient compte d'un effet d'inertie de rotation. On focalise ensuite notre attention sur ce problème et on en présente une étude mathématique et numérique. L'analyse numérique est complétée avec des tests effectués sous l'environnement FreeFEM++. / This thesis is devoted to the enrichment of the usual mathematical model of smart structures, by taking into account thermal effects, and to its mathematical and numerical study. By the expression "smart structures" we refer to structures acting as sensors or actuators, whose properties depend on the temperature. We present at first the results of existence and uniqueness concerning two problems posed on a three-dimensional domain: the dynamic problem and the quasi-static problem. Based on the quasi-static problem, we infer a two-dimensional plate model by means of the asymptotic expansion method by considering four different sets of boundary conditions, each one featuring a sensor-like or an actuator-like behavior. Each of the four problems decouples into a membrane problem and a flexural problem. The latter is an evolution problem that accounts for a rotational inertia effect. Attention is then focused on this problem by presenting a mathematical and numerical study of it. Our numerical analysis is complemented with numerical tests carried out under the FreeFEM++ environment.