Central limit theorems for Poisson hyperplane tessellations

We derive a central limit theorem for the number of vertices of convex polytopes induced by stationary Poisson hyperplane processes in $\mathbb{R}^d$. This result generalizes an earlier one proved by Paroux [Adv. in Appl. Probab. 30 (1998) 640--656] for intersection points of motion-invariant Poisson line processes in $\mathbb{R}^2$. Our proof is based on Hoeffding's decomposition of $U$-statistics which seems to be more efficient and adequate to tackle the higher-dimensional case than the ``method of moments'' used in [Adv. in Appl. Probab. 30 (1998) 640--656] to treat the case $d=2$. Moreover, we extend our central limit theorem in several directions. First we consider $k$-flat processes induced by Poisson hyperplane processes in $\mathbb{R}^d$ for $0\le k\le d-1$. Second we derive (asymptotic) confidence intervals for the intensities of these $k$-flat processes and, third, we prove multivariate central limit theorems for the $d$-dimensional joint vectors of numbers of $k$-flats and their $k$-volumes, respectively, in an increasing spherical region.Comment: Published at http://dx.doi.org/10.1214/105051606000000033 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Limit theorems for functionals on the facets of stationary random tessellations

We observe stationary random tessellations $X=\{\Xi_n\}_{n\ge1}$ in $\mathbb{R}^d$ through a convex sampling window $W$ that expands unboundedly and we determine the total $(k-1)$-volume of those $(k-1)$-dimensional manifold processes which are induced on the $k$-facets of $X$ ($1\le k\le d-1$) by their intersections with the $(d-1)$-facets of independent and identically distributed motion-invariant tessellations $X_n$ generated within each cell $\Xi_n$ of $X$. The cases of $X$ being either a Poisson hyperplane tessellation or a random tessellation with weak dependences are treated separately. In both cases, however, we obtain that all of the total volumes measured in $W$ are approximately normally distributed when $W$ is sufficiently large. Structural formulae for mean values and asymptotic variances are derived and explicit numerical values are given for planar Poisson--Voronoi tessellations (PVTs) and Poisson line tessellations (PLTs).Comment: Published at http://dx.doi.org/10.3150/07-BEJ6131 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks

We consider spatially homogeneous marked point patterns in an unboundedly expanding convex sampling window. Our main objective is to identify the distribution of the typical mark by constructing an asymptotic $\chi^2$-goodness-of-fit test. The corresponding test statistic is based on a natural empirical version of the Palm mark distribution and a smoothed covariance estimator which turns out to be mean square consistent. Our approach does not require independent marks and allows dependences between the mark field and the point pattern. Instead we impose a suitable $\beta$-mixing condition on the underlying stationary marked point process which can be checked for a number of Poisson-based models and, in particular, in the case of geostatistical marking. In order to study test performance, our test approach is applied to detect anisotropy of specific Boolean models.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ523 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm). arXiv admin note: substantial text overlap with arXiv:1205.504

Effekte molekularer Symmetrien in der Elektronenemission bei langsamen He2-plus-He-Stößen : eine kinematisch vollständige experimentelle Untersuchung

In dieser Arbeit wird die Elektronenemission aus langsamen He 2 ­He­Stößen, d.h. bei Stoßenergien unterhalb von 25 keV/u, experimentell untersucht. Dabei wird auf den Vergleich der Einfachionisation (He 2 He ! He 2 He e \Gamma ) mit der Transferionisation (He 2 He ! He He 2 e \Gamma ) besonderes Gewicht gelegt. Die hier verwendete Meßtechnik ist von verschiedenen Arbeitsgruppen in den letzten Jahren entwickelt worden und unter dem Schlagwort COLTRIMS (Cold Target Recoil Ion Momentum Spectroscopy) [1, 2, 3] in der Literatur zu finden. Bei COLTRIMS werden die bei einer Reaktion in einem kalten Gastarget gebildeten Ionen in einem schwachen elektrischen Feld abgesaugt. Durch den ortsaufgelösten Nachweis und die Messung der Flugzeit von der Targetzone bis zum Detektor kann die Anfangsbedingung der Bewegung im Feld, d.h. der Vektor des auf das Targetatom übertragenen Impulses, berechnet werden. Diese Methode kommt ohne Blenden aus, so daß im relevanten Teil des Phasenraumes 4ß Raumwinkel erreicht werden. Der Nachweis des Elektrons erfolgt nach demselben Prinzip, jedoch stößt man dabei an die Grenzen der Flugzeitauflösung. Deshalb wurden in allen früheren Experimenten zu ähnlichen Reaktionen [4, 5, 6, 7, 8, 9] nur zwei der drei Impulskomponenten des Elektrons bestimmt. Die Konzipierung eines Spektrometers, welches in der Lage ist, den relevanten Phasenraum lückenlos zu erfassen und dabei alle drei Impulskomponenten der Elektronen zu bestimmen, war der wesentliche Teil der apparativen Entwicklung. Das durchgeführte Experiment ist nicht nur kinematisch vollständig, sondern erlaubt durch Anwendung des Energieerhaltungssatzes auch die Bestimmung der Schale, in der das Elektron im Endzustand gebunden ist. Die beiden oben genannten Reaktionen können somit getrennt nach Ereignissen mit und ohne Anregung untersucht werden, d.h., es wurden gleichzeitig vier verschiedene Ionisationskanäle vermessen. Für den Ionisationsmechanismus bei Stößen mit einer Projektilgeschwindigkeit unterhalb der klassischen Bahngeschwindigkeit der Elektronen hat sich in den letzten Jahren der Begriff ''Sattelpunkt''­Prozeß durchgesetzt [10]. Quantenmechanische Beschreibungen für Einelektronensysteme, wie das Stoßsystem p H, wurden u.a. mit der semiklassischen Gekoppelte­Kanäle­Methode [11] in einem speziellen Basissatz [12, 13] und der ''Hidden­Crossings''­Theorie [14, 15] gegeben. Beide Modelle beschreiben das System aus Projektil und Target als Quasimolekül. Si sind lediglich in der Lage, die groben Strukturen in den Spektren zu erklären. Das gewählte Stoßsystem He 2 He, welches zwei Elektronen besitzt, erlaubt die Untersuchung von Korrelationseffekten. Die Messungen haben ergeben, daß die Impulsverteilung des emittierten Elektrons stark davon abhängt, wo und in welchem Bindungszustand das zweite Elektron nachgewiesen wird. Die gleiche Kernladung von Projektil und Target bedingt, da alle Eigenzustände des gebildeten Quasimoleküls die Symmetrie des Hamiltonoperators gegenüber Raumspiegelung besitzen, und durch diese Spiegeloperation gehen die Endzustände der Transferionisation und der Einfachionisation ineinander über. Durch die gleichzeitige Messung der differentiellen Wirkungsquerschnitte der verschiedenen Reaktionskanäle und deren Vergleich erhält man Einblick in die zugrundeliegenden Prozesse

Avaliação de técnicas de medição de tenacidade à fratura

Análises de tenacidade à fratura proveem meios de auxiliar na economia e segurança em projetos que envolvam integridade estrutural. Um dos ensaios que abrangem esta perspectiva é o ensaio de CTOD, que envolve a medição da abertura da ponta da trinca durante uma propagação estática e é mais adequado para aplicações onde a plasticidade nessa região é considerável. O objetivo deste trabalho é determinar e comparar resultados de tenacidade à fratura, na forma do ensaio de CTOD, utilizando diferentes metodologias de análise, de forma a identificar a adequação de métodos inovadores a resultados obtidos por ensaios normalizados. Para tanto, foram estudadas metodologias que visam à obtenção de valores de CTOD por medições superficiais, durante a realização dos ensaios, assim como foram realizadas medições nas superfícies de fratura, sem a necessidade de aquisição de dados durante os ensaios. Os resultados, evidenciados por técnicas de análise estatística, comprovam a equivalência entre os valores obtidos por ensaios normalizados e os valores obtidos nas demais metodologias estudadas, permitindo assim, a utilização destes métodos em substituição aos ensaios normalizados, no caso particular do material de estudo.Fracture toughness analyzes provide means of assisting in economics and safety on projects that involve structural integrity. One of the assays covering this perspective is the CTOD test, which implicates measuring the crack tip opening during a static propagation and it is best suited for applications where plasticity on that region is considerable. The aim of this work is to determine and compare fracture toughness results, by the form of the CTOD test, using different analyses methodologies, in order to identify the adequacy of innovative methods with results obtained by standardized tests. In order to do so, different methodologies were studied to obtain CTOD values by surface measurements during the tests, as well as measurements were made on the fracture surfaces, without the need to acquire data during the tests. The results, evidenced by statistical analysis techniques, indicates the equivalence between values obtained by standardized tests and those obtained through other methodologies analyzed, thus allowing the use of these methods instead of the standardized tests in the particular case of the analyzed material

Emotionspsychologie und Musik

While the problem of definition still remains unsolved there is some agreement that an emotion consists of three distinctive responses. Research on these response modes - subjective feelings, expressive behavior, and physiological responses - is reported. The description and differentiation of these emotional phenomena is followed by the question of why we have or do not have certain emotions. Neurophysiological as well as cognitive explanations are discussed. From the standpoint of psychology, music can be seen as an emotional stimulus as well as a means to communicate ones feelings. Both perspectives may be fruitful for research and instruction. Finally the paradigm of classical conditioning, which may explain how music can become an emotional stimulus, is described, together with methods to measure the emotional impact of music. (DIPF/Orig.

Determinação experimental de curvas J-R para um tubo de aço Q125 sob carregamentos monotônico e dinâmico

Metodologias para a execução de projetos que envolvem a necessidade da avaliação da integridade estrutural fornecem segurança, economia e maior confiança em projetos de engenharia, que consideram o efeito de um defeito prévio na estrutura em aplicação. Porém, ao se utilizar apenas a abordagem de projeto por carregamento estático pode-se causar um superdimensionamento estrutural, caso o material esteja suscetível a carregamentos dinâmicos, principalmente em poços de petróleo, onde a competitividade gera uma demanda por custos de processo cada vez menores. Este trabalho possui como meta determinar e avaliar a tenacidade à fratura de um tubo de aço Q125 submetido à carregamentos monotônicos e dinâmicos através da determinação de curvas-R pela abordagem de integral-J, tanto para a metodologia de ensaio por múltiplos corpos de prova, quanto para corpos de prova individuais. Os resultados, sob a forma do parâmetro JIC, evidenciam uma maior energia para fratura em corpos de prova submetidos a carregamentos dinâmicos, o que justifica a aplicação desta metodologia de análise para aplicações que envolvam carregamentos dinâmicos, ao se tomar uma abordagem menos conservadora e que vise a economia em custos de fabricaçãoMethodologies for the execution of projects that involve the need for structural integrity assessment provide security, economic benefits and reliability in engineering projects, that consider the effect of a previous defect on the structure. However, when using only the static loading approach, structural oversizing might be caused if the material is susceptible to dynamic loading, especially in oil wells, where competitiveness generates a demand for increasingly lower process costs. This study aims to determine and evaluate the fracture toughness of a Q125 steel tube subjected to monotonic and dynamic loads through the determination of R-curves by the J-integral approach, both for the test method of multiple specimens, as for individual specimens. The results, in the form of the JIC parameter, show a greater energy for fracture in specimens subjected to dynamic loading, which justifies the application of this methodology for applications involving dynamic loading, if a less conservative approach is taken and aim at saving manufacturing costs