Monte Carlo simulation of circular grain growth

Monte Carlo simulations have been carried out to study the effect of temperature on the growth kinetics of a circular grain. This work demonstrates the importance of roughening fluctuations on the growth dynamics. Since the effect of thermal fluctuations is stronger in d =2 than in d =3, as predicted by d =3 theories of domain kinetics, the circular domain shrinks linearly with time as A (t)=A(0)-αt, where A (0) and A(t) are the initial and instantaneous areas, respectively. However, in contrast to d =3, the slope α is strongly temperature dependent for T≥0.6TC. An analytical theory which considers the thermal fluctuations agrees with the T dependence of the Monte Carlo data in this regime, and this model show that these fluctuations are responsible for the strong temperature dependence of the growth rate for d =2. Our results are particularly relevant to the problem of domain growth in surface science

Monte Carlo simulation of recrystallization

A Monte Carlo computer simulation technique, in which a continuum system is modeled employing a discrete lattice, has been applied to the problem of recrystallization. Primary recrystallization is modeled under conditions where the degree of stored energy is varied and nucleation occurs homogeneously (without regard for position in the microstructure). The nucleation rate is chosen as site saturated. Temporal evolution of the simulated microstructures is analyzed to provide the time dependence of the recrystallized volume fraction and grain sizes. The recrystallized volume fraction shows sigmoidal variations with time. The data are approximately fit by the Johnson-Mehl-Avrami equation with the expected exponents, however significant deviations are observed for both small and large recrystallized volume fractions. Under constant rate nucleation conditions, the propensity for irregular grain shapes is decreased and the density of two sided grains increases.

Monte Carlo simulation on a system of hard cylinders at a very high packing fraction

Using the Monte Carlo method the behavior of a system of true hard cylinders has been studied. Values of the length-to-breadth ratio L/D and packing fraction η have been chosen similar to those of real nematic liquid crystals. Results include radial distribution function g(r), structure factor S(k), and orientational order parameter M. These results lead to the conclusion that the hard cylinder model may be a useful reference for real mesomorphic phases.

A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation

Stochastic model updating must be considered for quantifying uncertainties inherently existing in real-world engineering structures. By this means the statistical properties,instead of deterministic values, of structural parameters can be sought indicating the parameter variability. However, the implementation of stochastic model updating is much more complicated than that of deterministic methods particularly in the aspects of theoretical complexity and low computational efficiency. This study attempts to propose a simple and cost-efficient method by decomposing a stochastic updating process into a series of deterministic ones with the aid of response surface models and Monte Carlo simulation. The response surface models are used as surrogates for original FE models in the interest of programming simplification, fast response computation and easy inverse optimization. Monte Carlo simulation is adopted for generating samples from the assumed or measured probability distributions of responses. Each sample corresponds to an individual deterministic inverse process predicting the deterministic values of parameters. Then the parameter means and variances can be statistically estimated based on all the parameter predictions by running all the samples. Meanwhile, the analysis of variance approach is employed for the evaluation of parameter variability significance. The proposed method has been demonstrated firstly on a numerical beam and then a set of nominally identical steel plates tested in the laboratory. It is found that compared with the existing stochastic model updating methods, the proposed method presents similar accuracy while its primary merits consist in its simple implementation and cost efficiency in response computation and inverse optimization.

Red Cell Volume Expansion at Altitude: A Meta-analysis and Monte Carlo Simulation

Meta-análisis del volumen de eritrocitos en altitud

FocusDET, a new toolbox for SISCOM analysis. Evaluation of the registration accuracy using monte carlo simulation

Subtraction of Ictal SPECT Co-registered to MRI (SISCOM) is an imaging technique used to localize the epileptogenic focus in patients with intractable partial epilepsy. The aim of this study was to determine the accuracy of registration algorithms involved in SISCOM analysis using FocusDET, a new user-friendly application. To this end, Monte Carlo simulation was employed to generate realistic SPECT studies. Simulated sinograms were reconstructed by using the Filtered BackProjection (FBP) algorithm and an Ordered Subsets Expectation Maximization (OSEM) reconstruction method that included compensation for all degradations. Registration errors in SPECT-SPECT and SPECT-MRI registration were evaluated by comparing the theoretical and actual transforms. Patient studies with well-localized epilepsy were also included in the registration assessment. Global registration errors including SPECT-SPECT and SPECT-MRI registration errors were less than 1.2 mm on average, exceeding the voxel size (3.32 mm) of SPECT studies in no case. Although images reconstructed using OSEM led to lower registration errors than images reconstructed with FBP, differences after using OSEM or FBP in reconstruction were less than 0.2 mm on average. This indicates that correction for degradations does not play a major role in the SISCOM process, thereby facilitating the application of the methodology in centers where OSEM is not implemented with correction of all degradations. These findings together with those obtained by clinicians from patients via MRI, interictal and ictal SPECT and video-EEG, show that FocusDET is a robust application for performing SISCOM analysis in clinical practice.

Monte-Carlo dosimetry on a realistic cell monolayer geometry exposed to alpha particles

The energy and specific energy absorbed in the main cell compartments (nucleus and cytoplasm) in typical radiobiology experiments are usually estimated by calculations as they are not accessible for a direct measurement. In most of the work, the cell geometry is modelled using the combination of simple mathematical volumes. We propose a method based on high resolution confocal imaging and ion beam analysis (IBA) in order to import realistic cell nuclei geometries in Monte-Carlo simulations and thus take into account the variety of different geometries encountered in a typical cell population. Seventy-six cell nuclei have been imaged using confocal microscopy and their chemical composition has been measured using IBA. A cellular phantom was created from these data using the ImageJ image analysis software and imported in the Geant4 Monte-Carlo simulation toolkit. Total energy and specific energy distributions in the 76 cell nuclei have been calculated for two types of irradiation protocols: a 3 MeV alpha particle microbeam used for targeted irradiation and a 239Pu alpha source used for large angle random irradiation. Qualitative images of the energy deposited along the particle tracks have been produced and show good agreement with images of DNA double strand break signalling proteins obtained experimentally. The methodology presented in this paper provides microdosimetric quantities calculated from realistic cellular volumes. It is based on open-source oriented software that is publicly available.

Simulation of academic performance rates, estimation of indicators of subjects and of a complete degree

The purpose of this paper is to present a program written in Matlab-Octave for the simulation of the time evolution of student curricula, i.e, how students pass their subjects along time until graduation. The program computes, from the simulations, the academic performance rates for the subjects of the study plan for each semester as well as the overall rates, which are a) the efficiency rate defined as the ratio of the number of students passing the exam to the number of students who registered for it and b) the success rate, defined as the ratio of the number of students passing the exam to the number of students who not only registered for it but also actually took it. Additionally, we compute the rates for the bachelor academic degree which are established for Spain by the National Quality Evaluation and Accreditation Agency (ANECA) and which are the graduation rate (measured as the percentage of students who finish as scheduled in the plan or taking an extra year) and the efficiency rate (measured as the percentage of credits which a student who graduated has really taken). The simulation is done in terms of the probabilities of passing all the subjects in their study plan. The application of the simulator to Polytech students in Madrid, where requirements for passing are specially stiff in first and second year subjects, is particularly relevant to analyze student cohorts and the probabilities of students finishing in the minimum of four years, or taking and extra year or two extra years, and so forth. It is a very useful tool when designing new study plans. The calculation of the probability distribution of the random variable "number of semesters a student has taken to complete the curricula and graduate" is difficult or even unfeasible to obtain analytically, and this is even truer when we incorporate uncertainty in parameter estimation. This is why we apply Monte Carlo simulation which not only provides illustration of the stochastic process but also a method for computation. The stochastic simulator is proving to be a useful tool for identification of the subjects most critical in the distribution of the number of semesters for curriculum vitae (CV) completion and subsequently for a decision making process in terms of CV planning and passing standards in the University. Simulations are performed through a graphical interface where also the results are presented in appropriate figures. The Project has been funded by the Call for Innovation in Education Projects of Universidad Politécnica de Madrid (UPM) through a Project of its school Escuela Técnica Superior de Ingenieros Industriales ETSII during the period September 2010-September 2011.

Análisis y diseño de multiplicadores y mezcladores mediante el método de Monte Carlo en la banda de THz = Analysis and design of multipliers and mixers via Monte Carlo modelling at THz bands

La región del espectro electromagnético comprendida entre 100 GHz y 10 THz alberga una gran variedad de aplicaciones en campos tan dispares como la radioastronomía, espectroscopíamolecular, medicina, seguridad, radar, etc. Los principales inconvenientes en el desarrollo de estas aplicaciones son los altos costes de producción de los sistemas trabajando a estas frecuencias, su costoso mantenimiento, gran volumen y baja fiabilidad. Entre las diferentes tecnologías a frecuencias de THz, la tecnología de los diodos Schottky juega un importante papel debido a su madurez y a la sencillez de estos dispositivos. Además, los diodos Schottky pueden operar tanto a temperatura ambiente como a temperaturas criogénicas, con altas eficiencias cuando se usan como multiplicadores y con moderadas temperaturas de ruido en mezcladores. El principal objetivo de esta tesis doctoral es analizar los fenómenos físicos responsables de las características eléctricas y del ruido en los diodos Schottky, así como analizar y diseñar circuitos multiplicadores y mezcladores en bandas milimétricas y submilimétricas. La primera parte de la tesis presenta un análisis de los fenómenos físicos que limitan el comportamiento de los diodos Schottky de GaAs y GaN y de las características del espectro de ruido de estos dispositivos. Para llevar a cabo este análisis, un modelo del diodo basado en la técnica de Monte Carlo se ha considerado como referencia debido a la elevada precisión y fiabilidad de este modelo. Además, el modelo de Monte Carlo permite calcular directamente el espectro de ruido de los diodos sin necesidad de utilizar ningún modelo analítico o empírico. Se han analizado fenómenos físicos como saturación de la velocidad, inercia de los portadores, dependencia de la movilidad electrónica con la longitud de la epicapa, resonancias del plasma y efectos no locales y no estacionarios. También se ha presentado un completo análisis del espectro de ruido para diodos Schottky de GaAs y GaN operando tanto en condiciones estáticas como variables con el tiempo. Los resultados obtenidos en esta parte de la tesis contribuyen a mejorar la comprensión de la respuesta eléctrica y del ruido de los diodos Schottky en condiciones de altas frecuencias y/o altos campos eléctricos. También, estos resultados han ayudado a determinar las limitaciones de modelos numéricos y analíticos usados en el análisis de la respuesta eléctrica y del ruido electrónico en los diodos Schottky. La segunda parte de la tesis está dedicada al análisis de multiplicadores y mezcladores mediante una herramienta de simulación de circuitos basada en la técnica de balance armónico. Diferentes modelos basados en circuitos equivalentes del dispositivo, en las ecuaciones de arrastre-difusión y en la técnica de Monte Carlo se han considerado en este análisis. El modelo de Monte Carlo acoplado a la técnica de balance armónico se ha usado como referencia para evaluar las limitaciones y el rango de validez de modelos basados en circuitos equivalentes y en las ecuaciones de arrastredifusión para el diseño de circuitos multiplicadores y mezcladores. Una notable característica de esta herramienta de simulación es que permite diseñar circuitos Schottky teniendo en cuenta tanto la respuesta eléctrica como el ruido generado en los dispositivos. Los resultados de las simulaciones presentados en esta parte de la tesis, tanto paramultiplicadores comomezcladores, se han comparado con resultados experimentales publicados en la literatura. El simulador que integra el modelo de Monte Carlo con la técnica de balance armónico permite analizar y diseñar circuitos a frecuencias superiores a 1 THz. ABSTRACT The terahertz region of the electromagnetic spectrum(100 GHz-10 THz) presents a wide range of applications such as radio-astronomy, molecular spectroscopy, medicine, security and radar, among others. The main obstacles for the development of these applications are the high production cost of the systems working at these frequencies, highmaintenance, high volume and low reliability. Among the different THz technologies, Schottky technology plays an important rule due to its maturity and the inherent simplicity of these devices. Besides, Schottky diodes can operate at both room and cryogenic temperatures, with high efficiency in multipliers and moderate noise temperature in mixers. This PhD. thesis is mainly concerned with the analysis of the physical processes responsible for the characteristics of the electrical response and noise of Schottky diodes, as well as the analysis and design of frequency multipliers and mixers at millimeter and submillimeter wavelengths. The first part of the thesis deals with the analysis of the physical phenomena limiting the electrical performance of GaAs and GaN Schottky diodes and their noise performance. To carry out this analysis, a Monte Carlo model of the diode has been used as a reference due to the high accuracy and reliability of this diode model at millimeter and submillimter wavelengths. Besides, the Monte Carlo model provides a direct description of the noise spectra of the devices without the necessity of any additional analytical or empirical model. Physical phenomena like velocity saturation, carrier inertia, dependence of the electron mobility on the epilayer length, plasma resonance and nonlocal effects in time and space have been analysed. Also, a complete analysis of the current noise spectra of GaAs and GaN Schottky diodes operating under static and time varying conditions is presented in this part of the thesis. The obtained results provide a better understanding of the electrical and the noise responses of Schottky diodes under high frequency and/or high electric field conditions. Also these results have helped to determine the limitations of numerical and analytical models used in the analysis of the electrical and the noise responses of these devices. The second part of the thesis is devoted to the analysis of frequency multipliers and mixers by means of an in-house circuit simulation tool based on the harmonic balance technique. Different lumped equivalent circuits, drift-diffusion and Monte Carlo models have been considered in this analysis. The Monte Carlo model coupled to the harmonic balance technique has been used as a reference to evaluate the limitations and range of validity of lumped equivalent circuit and driftdiffusion models for the design of frequency multipliers and mixers. A remarkable feature of this reference simulation tool is that it enables the design of Schottky circuits from both electrical and noise considerations. The simulation results presented in this part of the thesis for both multipliers and mixers have been compared with measured results available in the literature. In addition, the Monte Carlo simulation tool allows the analysis and design of circuits above 1 THz.

The Risk of Using the Q Heterogeneity Estimator for Software Engineering Experiments

All meta-analyses should include a heterogeneity analysis. Even so, it is not easy to decide whether a set of studies are homogeneous or heterogeneous because of the low statistical power of the statistics used (usually the Q test). Objective: Determine a set of rules enabling SE researchers to find out, based on the characteristics of the experiments to be aggregated, whether or not it is feasible to accurately detect heterogeneity. Method: Evaluate the statistical power of heterogeneity detection methods using a Monte Carlo simulation process. Results: The Q test is not powerful when the meta-analysis contains up to a total of about 200 experimental subjects and the effect size difference is less than 1. Conclusions: The Q test cannot be used as a decision-making criterion for meta-analysis in small sample settings like SE. Random effects models should be used instead of fixed effects models. Caution should be exercised when applying Q test-mediated decomposition into subgroups.

Comparative analysis of meta-analysis methods: when to use which?

Background: Several meta-analysis methods can be used to quantitatively combine the results of a group of experiments, including the weighted mean difference, statistical vote counting, the parametric response ratio and the non-parametric response ratio. The software engineering community has focused on the weighted mean difference method. However, other meta-analysis methods have distinct strengths, such as being able to be used when variances are not reported. There are as yet no guidelines to indicate which method is best for use in each case. Aim: Compile a set of rules that SE researchers can use to ascertain which aggregation method is best for use in the synthesis phase of a systematic review. Method: Monte Carlo simulation varying the number of experiments in the meta analyses, the number of subjects that they include, their variance and effect size. We empirically calculated the reliability and statistical power in each case Results: WMD is generally reliable if the variance is low, whereas its power depends on the effect size and number of subjects per meta-analysis; the reliability of RR is generally unaffected by changes in variance, but it does require more subjects than WMD to be powerful; NPRR is the most reliable method, but it is not very powerful; SVC behaves well when the effect size is moderate, but is less reliable with other effect sizes. Detailed tables of results are annexed. Conclusions: Before undertaking statistical aggregation in software engineering, it is worthwhile checking whether there is any appreciable difference in the reliability and power of the methods. If there is, software engineers should select the method that optimizes both parameters.

Differential algebra techniques for space applications

This project investigates the utility of differential algebra (DA) techniques applied to the problem of orbital dynamics with initial uncertainties in the orbital determination of the involved bodies. The use of DA theory allows the splitting of a common Monte Carlo simulation in two parts: the generation of a Taylor map of the final states with regard to the perturbation in the initial coordinates, and the evaluation of the map for many points. A propagator is implemented exploiting DA techniques, and tested in the field of asteroid impact risk monitoring with the potentially hazardous 2011 AG5 and 2007 VK184 as test cases. Results show that the new method is able to simulate 2.5 million trajectories with a precision good enough for the impact probability to be accurately reproduced, while running much faster than a traditional Monte Carlo approach (in 1 and 2 days, respectively).

Aspectos metodológicos para la evaluación de sistemas de tomografía por emisión de positrones empleando técnicas Montecarlo, protocolos estandarizados y diferentes trazadores

Esta tesis analiza los elementos que afectan a la evaluación del rendimiento dentro de la técnica de radiodiagnóstico mediante tomografía por emisión de positrones (PET), centrándose en escáneres preclínicos. Se exploran las posibilidades de los protocolos estándar de evaluación sobre los siguientes aspectos: su uso como herramienta para validar programas de simulación Montecarlo, como método para la comparación de escáneres y su validez en el estudio del efecto sobre la calidad de imagen al utilizar radioisótopos alternativos. Inicialmente se estudian los métodos de evaluación orientados a la validación de simulaciones PET, para ello se presenta el programa GAMOS como entorno de simulación y se muestran los resultados de su validación basada en el estándar NEMA NU 4-2008 para escáneres preclínicos. Esta validación se ha realizado mediante la comparación de los resultados simulados frente a adquisiciones reales en el equipo ClearPET, describiendo la metodología de evaluación y selección de los parámetros NEMA. En este apartado también se mencionan las aportaciones desarrolladas en GAMOS para aplicaciones PET, como la inclusión de herramientas para la reconstrucción de imágenes. Por otro lado, la evaluación NEMA del ClearPET es utilizada para comparar su rendimiento frente a otro escáner preclínico: el sistema rPET-1. Esto supone la primera caracterización NEMA NU 4 completa de ambos equipos; al mismo tiempo que se analiza cómo afectan las importantes diferencias de diseño entre ellos, especialmente el tamaño axial del campo de visión y la configuración de los detectores. El 68Ga es uno de los radioisótopos no convencionales en imagen PET que está experimentando un mayor desarrollo, sin embargo, presenta la desventaja del amplio rango o distancia recorrida por el positrón emitido. Además del rango del positrón, otra propiedad física característica de los radioisótopos PET que puede afectar a la imagen es la emisión de fotones gamma adicionales, tal como le ocurre al isótopo 48V. En esta tesis se evalúan dichos efectos mediante estudios de resolución espacial y calidad de imagen NEMA. Finalmente, se analiza el alcance del protocolo NEMA NU 4-2008 cuando se utiliza para este propósito, adaptándolo a tal fin y proponiendo posibles modificaciones. Abstract This thesis analyzes the factors affecting the performance evaluation in positron emission tomography (PET) imaging, focusing on preclinical scanners. It explores the possibilities of standard protocols of assessment on the following aspects: their use as tools to validate Monte Carlo simulation programs, their usefulness as a method for comparing scanners and their validity in the study of the effect of alternative radioisotopes on image quality. Initially we study the methods of performance evaluation oriented to validate PET simulations. For this we present the GAMOS program as a simulation framework and show the results of its validation based on the standard NEMA NU 4-2008 for preclinical PET scanners. This has been accomplished by comparing simulated results against experimental acquisitions in the ClearPET scanner, describing the methodology for the evaluation and selection of NEMA parameters. This section also mentions the contributions developed in GAMOS for PET applications, such as the inclusion of tools for image reconstruction. Furthermore, the evaluation of the ClearPET scanner is used to compare its performance against another preclinical scanner, specifically the rPET-1 system. This is the first complete NEMA NU 4 based characterization study of both systems. At the same time we analyze how do the significant design differences of these two systems, especially the size of the axial field of view and the detectors configuration affect their performance characteristics. 68Ga is one of the unconventional radioisotopes in PET imaging the use of which is currently significantly increasing; however, it presents the disadvantage of the long positron range (distance traveled by the emitted positron before annihilating with an electron). Besides the positron range, additional gamma photon emission is another physical property characteristic of PET radioisotopes that can affect the reconstructed image quality, as it happens to the isotope 48V. In this thesis we assess these effects through studies of spatial resolution and image quality. Finally, we analyze the scope of the NEMA NU 4-2008 to carry out such studies, adapting it and proposing possible modifications.

Terapia por láser de baja potencia: consideraciones óptico-físicas y biológicas determinantes en su aplicación clínica.

Objetivos : Analizar la distribución de energía en un tejido cuando se emplea terapia por láser de baja potencia y estudiar las especificaciones mínimas de equipos de terapia láser para estimar la dosis. Material y métodos: Se ha empleado el método de Monte Carlo para obtener la distribución de energía absorbida por la piel para dos tipos de láser y la teoría de la difusión para estimar la longitud de penetración y el recorrido libre medio. Se ha estudiado la variación de esa distribución en función de la raza (caucásico, asiático, afroamericano) y para dos localizaciones anatómicas distintas. Se ha analizado la información facilitada por diversos fabricantes de equipos comerciales para determinar si es necesario adaptar la dosimetría recomendada. Resultados: La radiación láser infrarroja (810nm) se absorbe mayoritariamente en un espesor de piel de 1,9±0,2mm para caucásicos, entre 1,73±0,08mm (volar del antebrazo) y 1,80±0,11mm (palma) para asiáticos y entre 1,25±0,09mm (volar del antebrazo) y 1,65±0,2mm (palma) para afroamericanos. El recorrido libre medio de la luz siempre es menor que 0,69±0,09mm. Para los equipos comerciales analizados la única característica geométrica del haz láser que se menciona es la superficie que oscila entre 0,08 y 1cm2, pero no se especifica cómo es la distribución de energía, la divergencia del haz, forma de la sección transversal, etc. Conclusiones:Dependiendo del equipo de terapia por láser de baja potencia utilizado, el tipo de paciente y la zona a tratar, el clínico debe adaptar las dosis recomendadas. Abstract: Objectives: To analyze the distribution of energy deposited in a tissue when this is irradiated with a low power laser and to study the minimum characteristics that manufacturers of low power laser therapy equipments should include to estimate the dosage. Material and methods: Monte Carlo simulation was performed to determine the absorption location of the laser energy. The diffusion theory was used to estimate penetration depth and mean free path. Variation of this distribution was studied based on three different skin types (Caucasians, Asians and Afroamericans) and for two different anatomic locations: palm and volar forearm. Information given by several manufactures of low power laser therapy equipments has been analyzed. Results: Infrared (810 nm) laser radiation is mainly absorbed in a skin layer of thickness 1.9±0.2mm for Caucasians, from 1.73±0.08mm (volar forearm) to 1.80±0.11mm (palm) for Asians, and from 1.25±0.09mm (volar forearm) to 1.65±0.2mm (palm) for Afroamericans. The light mean free path is lower than 0.69±0.09mm for all cases. The laser beam characteristics (beam shape, energy distribution on a transversal section, divergence, incidence angle,etc.) are not usually specified by the manufacturers. Only beam size (ranging from 0.08 to 1cm2) is given in some cases. Discussion and conclusions: Depending on the low power laser therapy equipment, on the patient and on the anatomic area to be treated, the staff should adapt the recommended dosage for each individual case.

Extreme flood abatement in large dams with fixed-crest spillways

This study characterises the abatement effect of large dams with fixed-crest spillways under extreme design flood conditions. In contrast to previous studies using specific hydrographs for flow into the reservoir and simplifications to obtain analytical solutions, an automated tool was designed for calculations based on a Monte Carlo simulation environment, which integrates models that represent the different physical processes in watersheds with areas of 150?2000 km2. The tool was applied to 21 sites that were uniformly distributed throughout continental Spain, with 105 fixed-crest dam configurations. This tool allowed a set of hydrographs to be obtained as an approximation for the hydrological forcing of a dam and the characterisation of the response of the dam to this forcing. For all cases studied, we obtained a strong linear correlation between the peak flow entering the reservoir and the peak flow discharged by the dam, and a simple general procedure was proposed to characterise the peak-flow attenuation behaviour of the reservoir. Additionally, two dimensionless coefficients were defined to relate the variables governing both the generation of the flood and its abatement in the reservoir. Using these coefficients, a model was defined to allow for the estimation of the flood abatement effect of a reservoir based on the available information. This model should be useful in the hydrological design of spillways and the evaluation of the hydrological safety of dams. Finally, the proposed procedure and model were evaluated and representative applications were presented