Dynamical calculation of direct muon-transfer rates from thermalized muonic hydrogen to C6+ and O8+

Moun-transfer reactions from muonic hydrogen to carbon and oxygen nuclei employing a full quantum-mechanical few-body description of rearrangement scattering were studied by solving the Faddeev-Hahn-type equations using close-coupling approximation. The application of a close-coupling-type ansatz led to satisfactory results for direct muon-transfer reactions from muonic hydrogen to C6+ and O8+.

General method for reducing the two-body Dirac equation

A semirelativistic two-body Dirac equation with an enlarged set of phenomenological potentials, including Breit-type terms, is investigated for the general case of unequal masses. Solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each one being obtained by solving a system of four coupled first-order radial differential equations. The reduction of each of these systems to a pair of coupled Schrödinger-type equations is also discussed. © 1992 American Institute of Physics.

Intersections on moduli spaces of curves

We present a new approach to perform calculations with the certain standard classes in cohomology of the moduli spaces of curves. It is based on an important lemma of Ionel relating the intersection theoriy of the moduli space of curves and that of the space of admissible coverings. As particular results, we obtain expressions of Hurwitz numbers in terms of the intersections in the tautological ring, expressions of the simplest intersection numbers in terms of Hurwitz numbers, an algorithm of calculation of certain correlators which are the subject of the Witten conjecture, an improved algorithm for intersections related to the Boussinesq hierarchy, expressions for the Hodge integrals over two-pointed ramification cycles, cut-and-join type equations for a large class of intersection numbers, etc.

Non-Markovian stochastic processes and their applications: from anomalous diffusion to time series analysis

This work provides a forward step in the study and comprehension of the relationships between stochastic processes and a certain class of integral-partial differential equation, which can be used in order to model anomalous diffusion and transport in statistical physics. In the first part, we brought the reader through the fundamental notions of probability and stochastic processes, stochastic integration and stochastic differential equations as well. In particular, within the study of H-sssi processes, we focused on fractional Brownian motion (fBm) and its discrete-time increment process, the fractional Gaussian noise (fGn), which provide examples of non-Markovian Gaussian processes. The fGn, together with stationary FARIMA processes, is widely used in the modeling and estimation of long-memory, or long-range dependence (LRD). Time series manifesting long-range dependence, are often observed in nature especially in physics, meteorology, climatology, but also in hydrology, geophysics, economy and many others. We deepely studied LRD, giving many real data examples, providing statistical analysis and introducing parametric methods of estimation. Then, we introduced the theory of fractional integrals and derivatives, which indeed turns out to be very appropriate for studying and modeling systems with long-memory properties. After having introduced the basics concepts, we provided many examples and applications. For instance, we investigated the relaxation equation with distributed order time-fractional derivatives, which describes models characterized by a strong memory component and can be used to model relaxation in complex systems, which deviates from the classical exponential Debye pattern. Then, we focused in the study of generalizations of the standard diffusion equation, by passing through the preliminary study of the fractional forward drift equation. Such generalizations have been obtained by using fractional integrals and derivatives of distributed orders. In order to find a connection between the anomalous diffusion described by these equations and the long-range dependence, we introduced and studied the generalized grey Brownian motion (ggBm), which is actually a parametric class of H-sssi processes, which have indeed marginal probability density function evolving in time according to a partial integro-differential equation of fractional type. The ggBm is of course Non-Markovian. All around the work, we have remarked many times that, starting from a master equation of a probability density function f(x,t), it is always possible to define an equivalence class of stochastic processes with the same marginal density function f(x,t). All these processes provide suitable stochastic models for the starting equation. Studying the ggBm, we just focused on a subclass made up of processes with stationary increments. The ggBm has been defined canonically in the so called grey noise space. However, we have been able to provide a characterization notwithstanding the underline probability space. We also pointed out that that the generalized grey Brownian motion is a direct generalization of a Gaussian process and in particular it generalizes Brownain motion and fractional Brownain motion as well. Finally, we introduced and analyzed a more general class of diffusion type equations related to certain non-Markovian stochastic processes. We started from the forward drift equation, which have been made non-local in time by the introduction of a suitable chosen memory kernel K(t). The resulting non-Markovian equation has been interpreted in a natural way as the evolution equation of the marginal density function of a random time process l(t). We then consider the subordinated process Y(t)=X(l(t)) where X(t) is a Markovian diffusion. The corresponding time-evolution of the marginal density function of Y(t) is governed by a non-Markovian Fokker-Planck equation which involves the same memory kernel K(t). We developed several applications and derived the exact solutions. Moreover, we considered different stochastic models for the given equations, providing path simulations.

Análisis comparativo y nuevas estimaciones de las tasas de rebase en obras marítimas en grandes profundidades

El rebase se define como el transporte de una cantidad importante de agua sobre la coronación de una estructura. Por tanto, es el fenómeno que, en general, determina la cota de coronación del dique dependiendo de la cantidad aceptable del mismo, a la vista de condicionantes funcionales y estructurales del dique. En general, la cantidad de rebase que puede tolerar un dique de abrigo desde el punto de vista de su integridad estructural es muy superior a la cantidad permisible desde el punto de vista de su funcionalidad. Por otro lado, el diseño de un dique con una probabilidad de rebase demasiado baja o nula conduciría a diseños incompatibles con consideraciones de otro tipo, como son las estéticas o las económicas. Existen distintas formas de estudiar el rebase producido por el oleaje sobre los espaldones de las obras marítimas. Las más habituales son los ensayos en modelo físico y las formulaciones empíricas o semi-empíricas. Las menos habituales son la instrumentación en prototipo, las redes neuronales y los modelos numéricos. Los ensayos en modelo físico son la herramienta más precisa y fiable para el estudio específico de cada caso, debido a la complejidad del proceso de rebase, con multitud de fenómenos físicos y parámetros involucrados. Los modelos físicos permiten conocer el comportamiento hidráulico y estructural del dique, identificando posibles fallos en el proyecto antes de su ejecución, evaluando diversas alternativas y todo esto con el consiguiente ahorro en costes de construcción mediante la aportación de mejoras al diseño inicial de la estructura. Sin embargo, presentan algunos inconvenientes derivados de los márgenes de error asociados a los ”efectos de escala y de modelo”. Las formulaciones empíricas o semi-empíricas presentan el inconveniente de que su uso está limitado por la aplicabilidad de las fórmulas, ya que éstas sólo son válidas para una casuística de condiciones ambientales y tipologías estructurales limitadas al rango de lo reproducido en los ensayos. El objetivo de la presente Tesis Doctoral es el contrate de las formulaciones desarrolladas por diferentes autores en materia de rebase en distintas tipologías de diques de abrigo. Para ello, se ha realizado en primer lugar la recopilación y el análisis de las formulaciones existentes para estimar la tasa de rebase sobre diques en talud y verticales. Posteriormente, se llevó a cabo el contraste de dichas formulaciones con los resultados obtenidos en una serie de ensayos realizados en el Centro de Estudios de Puertos y Costas. Para finalizar, se aplicó a los ensayos de diques en talud seleccionados la herramienta neuronal NN-OVERTOPPING2, desarrollada en el proyecto europeo de rebases CLASH (“Crest Level Assessment of Coastal Structures by Full Scale Monitoring, Neural Network Prediction and Hazard Analysis on Permissible Wave Overtopping”), contrastando de este modo la tasa de rebase obtenida en los ensayos con este otro método basado en la teoría de las redes neuronales. Posteriormente, se analizó la influencia del viento en el rebase. Para ello se han realizado una serie de ensayos en modelo físico a escala reducida, generando oleaje con y sin viento, sobre la sección vertical del Dique de Levante de Málaga. Finalmente, se presenta el análisis crítico del contraste de cada una de las formulaciones aplicadas a los ensayos seleccionados, que conduce a las conclusiones obtenidas en la presente Tesis Doctoral. Overtopping is defined as the volume of water surpassing the crest of a breakwater and reaching the sheltered area. This phenomenon determines the breakwater’s crest level, depending on the volume of water admissible at the rear because of the sheltered area’s functional and structural conditioning factors. The ways to assess overtopping processes range from those deemed to be most traditional, such as semi-empirical or empirical type equations and physical, reduced scale model tests, to others less usual such as the instrumentation of actual breakwaters (prototypes), artificial neural networks and numerical models. Determining overtopping in reduced scale physical model tests is simple but the values obtained are affected to a greater or lesser degree by the effects of a scale model-prototype such that it can only be considered as an approximation to what actually happens. Nevertheless, physical models are considered to be highly useful for estimating damage that may occur in the area sheltered by the breakwater. Therefore, although physical models present certain problems fundamentally deriving from scale effects, they are still the most accurate, reliable tool for the specific study of each case, especially when large sized models are adopted and wind is generated Empirical expressions obtained from laboratory tests have been developed for calculating the overtopping rate and, therefore, the formulas obtained obviously depend not only on environmental conditions – wave height, wave period and water level – but also on the model’s characteristics and are only applicable in a range of validity of the tests performed in each case. The purpose of this Thesis is to make a comparative analysis of methods for calculating overtopping rates developed by different authors for harbour breakwater overtopping. First, existing equations were compiled and analysed in order to estimate the overtopping rate on sloping and vertical breakwaters. These equations were then compared with the results obtained in a number of tests performed in the Centre for Port and Coastal Studies of the CEDEX. In addition, a neural network model developed in the European CLASH Project (“Crest Level Assessment of Coastal Structures by Full Scale Monitoring, Neural Network Prediction and Hazard Analysis on Permissible Wave Overtopping“) was also tested. Finally, the wind effects on overtopping are evaluated using tests performed with and without wind in the physical model of the Levante Breakwater (Málaga).

The use of driven equilibrium conditions in the measurement of NMR relaxation times

The further development of the use of NMR relaxation times in chemical, biological and medical research has perhaps been curtailed by the length of time these measurements often take. The DESPOT (Driven Equilibrium Single Pulse Observation of T1) method has been developed, which reduces the time required to make a T1 measurement by a factor of up to 100. The technique has been studied extensively herein and the thesis contains recommendations for its successful experimental application. Modified DESPOT type equations for use when T2 relaxation is incomplete or where off-resonance effects are thought to be significant are also presented. A recently reported application of the DESPOT technique to MR imaging gave good initial results but suffered from the fact that the images were derived from spin systems that were not driven to equilibrium. An approach which allows equilibrium to be obtained with only one non-acquisition sequence is presented herein and should prove invaluable in variable contrast imaging. A DESPOT type approach has also been successfully applied to the measurement of T1. T_1's can be measured, using this approach significantly faster than by the use of the classical method. The new method also provides a value for T1 simultaneously and therefore the technique should prove valuable in intermediate energy barrier chemical exchange studies. The method also gives rise to the possibility of obtaining simultaneous T1 and T1 MR images. The DESPOT technique depends on rapid multipulsing at nutation angles, normally less than 90^o. Work in this area has highlighted the possible time saving for spectral acquisition over the classical technique (90^o-5T_1)_n. A new method based on these principles has been developed which permits the rapid multipulsing of samples to give T_1 and M_0 ratio information. The time needed, however, is only slightly longer than would be required to determine the M_0 ratio alone using the classical technique. In ^1H decoupled ^13C spectroscopy the method also gives nOe ratio information for the individual absorptions in the spectrum.

Instantons on Calabi–Yau cones

The Hermitian Yang–Mills equations on certain vector bundles over Calabi–Yau cones can be reduced to a set of matrix equations; in fact, these are Nahm-type equations. The latter can be analysed further by generalising arguments of Donaldson and Kronheimer used in the study of the original Nahm equations. Starting from certain equivariant connections, we show that the full set of instanton equations reduce, with a unique gauge transformation, to the holomorphicity condition alone.

A simultaneous equations model of crash frequency by collision type for rural intersections

Safety at roadway intersections is of significant interest to transportation professionals due to the large number of intersections in transportation networks, the complexity of traffic movements at these locations that leads to large numbers of conflicts, and the wide variety of geometric and operational features that define them. A variety of collision types including head-on, sideswipe, rear-end, and angle crashes occur at intersections. While intersection crash totals may not reveal a site deficiency, over exposure of a specific crash type may reveal otherwise undetected deficiencies. Thus, there is a need to be able to model the expected frequency of crashes by collision type at intersections to enable the detection of problems and the implementation of effective design strategies and countermeasures. Statistically, it is important to consider modeling collision type frequencies simultaneously to account for the possibility of common unobserved factors affecting crash frequencies across crash types. In this paper, a simultaneous equations model of crash frequencies by collision type is developed and presented using crash data for rural intersections in Georgia. The model estimation results support the notion of the presence of significant common unobserved factors across crash types, although the impact of these factors on parameter estimates is found to be rather modest.

Adams-Type Methods for the Numerical Solution of Stochastic Ordinary Differential Equations

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively. (C) 2000 Elsevier Science B.V. All rights reserved.

A Fredholm-type theory for third-kind linear integral equations

The third-kind linear integral equation Image where g(t) vanishes at a finite number of points in (a, b), is considered. In general, the Fredholm Alternative theory [[5.]] does not hold good for this type of integral equation. However, imposing certain conditions on g(t) and K(t, t′), the above integral equation was shown [[1.], 49–57] to obey a Fredholm-type theory, except for a certain class of kernels for which the question was left open. In this note a theory is presented for the equation under consideration with some additional assumptions on such kernels.

UNIQUENESS OF SOLUTIONS TO SCHRODINGER EQUATIONS ON H-TYPE GROUPS

This paper deals with the Schrodinger equation i partial derivative(s)u(z, t; s) - Lu(z, t; s) = 0; where L is the sub-Laplacian on the Heisenberg group. Assume that the initial data f satisfies vertical bar f(z, t)vertical bar less than or similar to q(alpha)(z, t), where q(s) is the heat kernel associated to L. If in addition vertical bar u(z, t; s(0))vertical bar less than or similar to q(beta)(z, t), for some s(0) is an element of R \textbackslash {0}, then we prove that u(z, t; s) = 0 for all s is an element of R whenever alpha beta < s(0)(2). This result holds true in the more general context of H-type groups. We also prove an analogous result for the Grushin operator on Rn+1.

The mixed-type integral equations for transient elastodynamic plane crack problems

In the present paper, by use of the boundary integral equation method and the techniques of Green fundamental solution and singularity analysis, the dynamic infinite plane crack problem is investigated. For the first time, the problem is reduced to solving a system of mixed-typed integral equations in Laplace transform domain. The equations consist of ordinary boundary integral equations along the outer boundary and Cauchy singular integral equations along the crack line. The equations obtained are strictly proved to be equivalent with the dual integral equations obtained by Sih in the special case of dynamic Griffith crack problem. The mixed-type integral equations can be solved by combining the numerical method of singular integral equation with the ordinary boundary element method. Further use the numerical method for Laplace transform, several typical examples are calculated and their dynamic stress intensity factors are obtained. The results show that the method proposed is successful and can be used to solve more complicated problems.