In the UCNτ experiment, ultracold neutrons (UCN) are confined by magnetic fields and the Earth’s gravitational field. Field-trapping mitigates the problem of UCN loss on material surfaces, which caused the largest correction in prior neutron experiments using material bottles. However, the neutron dynamics in field traps differ qualitatively from those in material bottles. In the latter case, neutrons bounce off material surfaces with significant diffusivity and the population quickly reaches a static spatial distribution with a density gradient induced by the gravitational potential. In contrast, the field-confined UCN—whose dynamics can be described by Hamiltonian mechanics—do not exhibit the stochastic behaviors typical of an ideal gas model as observed in material bottles. In this report, we will describe our efforts to simulate UCN trapping in the UCNτ magneto-gravitational trap. We compare the simulation output to the experimental results to determine the parameters of the neutron detector and the input neutron distribution. The tuned model is then used to understand the phase space evolution of neutrons observed in the UCNτ experiment. We will discuss the implications of chaotic dynamics on controlling the systematic effects, such as spectral cleaning and microphonic heating, for a successful UCN lifetime experiment to reach a 0.01% level of precision.

A Multivalent entity, which could represent a protein, nanoparticle, polymer, virus or a lipid bilayer, has the ability to form multiple bonds to a substrate. Hence, a multivalent interaction can be strong, even if the individual bonds are weak. However, much more interestingly, multivalency enables the design of highly specific interactions using non-specific individual bonds. We attempt to rationalise multivalent effects using simple physical models complemented with numerical simulations. Based on physiochemical characteristics of multivalent binders, we aim to predict the overall strength of interaction and its sensitivity to variation in parameters. We start with a simple model of homo-multivalency, where all bonds are equivalent. Such systems can exhibit a super-selective response, which denotes the high sensitivity of the strength of multivalent binding to the number of accessible binding sites on the target surface. We present a theoretical analysis of systems of multivalent particles and show that a certain degree of disorder is necessary for super-selective behaviour. Moreover, we formulate a set of simple design rules for multivalent interactions that yield optimal selectivity. In the second stage, we expand the model to hetero-multivalency, accounting for multiple distinct types of binding partners. We consider targeting of cells based on a density profile of different membrane receptors types and demonstrate, that speci city towards a desired receptor density profile can be obtained. Hence, cells can be reliably targeted in the absence of specific markers. Crucially, we show that for optimal selectivity, individual bonds must be weak. Finally, we add information about specific geometry and positions of binding sites on the multivalent entity. We focus on molecular imprinting; the process whereby a polymer matrix is cross-linked in the presence of template molecules. The cross-linking process endows the polymer matrix with a chemical ‘memory’, such that the target molecules can subsequently be recognised by the matrix. We show how the binding multivalency and the polymer material properties affect the efficiency and selectivity of molecular imprinting.

<p>This paper examines the pricing of barrier options using Monte Carlo Simulations. MATLAB based software is developed to estimate the price of the option using Monte Carlo simulation. We consider a generalized barrier option of knock out type, but we let the domain take the shape of a rectangular box. We investigate the price of this kind of barrier options. We investigate how the box is placed and what effect it will have on the price of the option. We compare the number of trajectories that are needed in order to achieve the same accuracy between this box barrier option and an ordinary option.</p>

<p>Fixed-collision correlated sampling for Monte Carlo (MC) simulations is a method which can be used in order to shorten the simulation time for brachytherapy treatment planning in a 3D patient geometry. The increased efficiency compared to conventional MC simulation is measured by efficiency gain. However, a previous study showed that, in some cases, PDFs (probability density functions) of estimates of the efficiency gain, simulated using resampling and other MC methods, were multimodal with values below 1. This means that the method was less effective than conventional sampling for these cases. The aims of this thesis were to trace the causes of the multimodal distributions and to propose techniques to mitigate the problem caused by photons with high statistical weights.Two simulation environments were used for the study case, a homogeneous and a heterogeneous environment. The homogenous environment consisted of a water sphere with the radius 100mm. For the heterogeneous environment a cylindrical block of tungsten alloy (diameter 15 mm, height 2.5 mm) was placed in the water sphere. The sphere was divided into an array of cubic voxels of size 2.5 mm x 2.5 mm x 2.5 mm for dose calculations. A photon source was positioned in the middle of the water sphere and emitted photons with the energy 400 keV.It was found that the low values and multimodal PDFs for the efficiency gain estimates originated from photons depositing high values of energy in some voxels in the heterogeneous environment. The high energy deposits were due to extremely high statistical weights of photons interacting repeatedly in the highly attenuating tungsten cylinder. When photon histories contributing to the rare events of high energy deposits (outliers) were removed, the PDFs became uni-modal and efficiency gain increased. However, removing outliers will cause results to be biased calling for other techniques to handle the problem with high statistical weights.One way to resolve the problem in the current implementation of the fixed-collision correlated sampling scheme in PTRAN (the MC code used) could be to split photons with high statistical weights into several photons with the same sum weight as the initial photon. The splitting of photons will result in more time consuming simulations in areas with high attenuation coefficients, which may not be the areas of interest. This could be resolved by using Russian roulette, eliminating some of the photons with high statistical weight in such areas.Fixed-collision correlated sampling for Monte Carlo (MC) simulations is a method which can be used in order to shorten the simulation time for brachytherapy treatment planning in a 3D patient geometry. The increased efficiency compared to conventional MC simulation is measured by efficiency gain. However, a previous study showed that, in some cases, PDFs (probability density functions) of estimates of the efficiency gain, simulated using resampling and other MC methods, were multimodal with values below 1. This means that the method was less effective than conventional sampling for these cases. The aims of this thesis were to trace the causes of the multimodal distributions and to propose techniques to mitigate the problem caused by photons with high statistical weights.Two simulation environments were used for the study case, a homogeneous and a heterogeneous environment. The homogenous environment consisted of a water sphere with the radius 100mm. For the heterogeneous environment a cylindrical block of tungsten alloy (diameter 15 mm, height 2.5 mm) was placed in the water sphere. The sphere was divided into an array of cubic voxels of size 2.5 mm x 2.5 mm x 2.5 mm for dose calculations. A photon source was positioned in the middle of the water sphere and emitted photons with the energy 400 keV.It was found that the low values and multimodal PDFs for the efficiency gain estimates originated from photons depositing high values of energy in some voxels in the heterogeneous environment. The high energy deposits were due to extremely high statistical weights of photons interacting repeatedly in the highly attenuating tungsten cylinder. When photon histories contributing to the rare events of high energy deposits (outliers) were removed, the PDFs became uni-modal and efficiency gain increased. However, removing outliers will cause results to be biased calling for other techniques to handle the problem with high statistical weights.One way to resolve the problem in the current implementation of the fixed-collision correlated sampling scheme in PTRAN (the MC code used) could be to split photons with high statistical weights into several photons with the same sum weight as the initial photon. The splitting of photons will result in more time consuming simulations in areas with high attenuation coefficients, which may not be the areas of interest. This could be resolved by using Russian roulette, eliminating some of the photons with high statistical weight in such areas.</p>

<p>The use of process capability indices in the industry is traditionally based on the assumptions that a sample from a process are observations on independently, identically and normally distributed random variables<i>, IIN</i>. However, all three assumptions are open to discussion and in this thesis, the estimation of the indices is studied when the assumption of independence is not fulfilled.</p><p>In five reports, the indices <i>C</i><i>pk</i> and <i>C</i><i>pm </i>are studied, and instead of random samples, samples are regarded as observations on a time series.</p><p>In the first four reports, each index is studied for either an <i>AR(1)</i> or an <i>MA(1)</i> process and the fifth report, both indices are studied for a general <i>ARMA(p,q</i>) process.</p><p>In all reports, alternatives to <i>C</i><i>pk</i><i> </i>and <i>C</i><i>pm</i><i> </i>are suggested as well as point and interval estimators for the suggested indices. The accuracy of interval estimators are evaluated through large Monte Carlo simulations and the difference between empirical coverage rates and nominal confidence limits are calculated.</p><p>It was found in all reports that a dependency among observations has a great impact on the coverage rates. The coverage rate difference depends on both the size of the autocorrelation and the type of time series model and for the original <i>C</i><i>pk</i> and <i>C</i><i>pm</i> the difference can be large. With the suggested alternative indices, however, the differences are always reduced and unless the autocorrelations are close to ±1, the sizes of differences are of little consequence.</p>

The use of process capability indices in the industry is traditionally based on the assumptions that a sample from a process are observations on independently, identically and normally distributed random variables, IIN. However, all three assumptions are open to discussion and in this thesis, the estimation of the indices is studied when the assumption of independence is not fulfilled. In five reports, the indices Cpk and Cpm are studied, and instead of random samples, samples are regarded as observations on a time series. In the first four reports, each index is studied for either an AR(1) or an MA(1) process and the fifth report, both indices are studied for a general ARMA(p,q) process. In all reports, alternatives to Cpk and Cpm are suggested as well as point and interval estimators for the suggested indices. The accuracy of interval estimators are evaluated through large Monte Carlo simulations and the difference between empirical coverage rates and nominal confidence limits are calculated. It was found in all reports that a dependency among observations has a great impact on the coverage rates. The coverage rate difference depends on both the size of the autocorrelation and the type of time series model and for the original Cpk and Cpm the difference can be large. With the suggested alternative indices, however, the differences are always reduced and unless the autocorrelations are close to ±1, the sizes of differences are of little consequence.

This paper examines the pricing of barrier options using Monte Carlo Simulations. MATLAB based software is developed to estimate the price of the option using Monte Carlo simulation. We consider a generalized barrier option of knock out type, but we let the domain take the shape of a rectangular box. We investigate the price of this kind of barrier options. We investigate how the box is placed and what effect it will have on the price of the option. We compare the number of trajectories that are needed in order to achieve the same accuracy between this box barrier option and an ordinary option.

Los surfactantes son moléculas anfifílicas, con una cabeza solvofílica y una cola solvofóbica. Cuando la concentración de surfactante en solución es suficientemente alta, las moléculas se agregan entre ellas para proteger las partes solvofóbicas del contacto con el medio. Tales agregados pueden tener forma y tamaño muy diferentes, dependiendo del surfactante y de las condiciones del sistema. La auto-organización de los surfactantes (self-assembly), debida a un compromiso energético y entrópico de su estructura molecular, es la clave que permite observar cristales líquidos muy ordenados. En presencia de un precursor inorgánico y dependiendo de las interacciones que este precursor establece con el surfactante, se puede observar la formación del material híbrido. Los materiales híbridos constituyen un paso intermedio fundamental para la síntesis de los materiales mesoporosos ordenados, los cuales se obtienen eliminando la matriz orgánica (surfactante) del substrato inorgánico. El presente estudio tiene como principal objetivo estudiar bajo cuales condiciones los sistemas formados por un surfactante, un precursor inorgánico y un solvente, se auto-organizan para dar lugar a estructuras híbridas muy ordenadas. En particular nos proponemos individuar cuales son las características más importantes que los precursores inorgánicos deberían tener para poder observar la formación de materiales mesoporosos ordenados.Simulaciones Monte Carlo en el colectivo canónico han sido utilizadas para analizar la agregación de los surfactantes en estructuras complejas, como micelas, cilindros organizados en forma hexagonal, o laminas, a partir de configuraciones totalmente desordenadas. Con particular interés hemos analizado el rango de condiciones que llevan a la formación de las estructuras cilíndricas, y estas mismas estructuras han sido comparadas en función de algunas importantes características morfológicas, como el tamaño de poro, el grosor de las paredes, la presencia y accesibilidad de los grupos funcionales en los poros. El modelo usado representa las moléculas de surfactante y de precursor inorgánico como cadenas de segmentos en una red tridimensional que discretiza el espacio en sitios de volumen unitario. Este modelo no entra en el detalle de las características físicas y químicas de las moléculas, pero permite reproducir su agregación en estructuras complejas en un tiempo de cálculo muy razonable. La separación de fase ha sido también evaluada recorriendo a una teoría de campo medio, la quasi-chemical theory, que, aunque no pueda predecir la formación de estructuras ordenadas, ha sido muy útil para confirmar los resultados de las simulaciones, sobretodo cuando no se observa formación de fases ordenadas. El estudio de surfactantes distintos, uno modelado por una cadena lineal y otro con una cabeza ramificada, nos ha permitido evaluar algunas diferencias estructurales de los materiales obtenidos. La ramificación de la cabeza, que merecería un estudio más profundo del que hemos descrito en este trabajo, ha evidenciado unas interesantes consecuencias en el tamaño de los poros. Este mismo surfactante con cabeza ramificada ha sido elegido para la síntesis de agregados cilíndricos utilizados como templates en la formación, agregación, y condensación de una capa de sílica modelada a través de un modelo atomístico. En particular, hemos aislado uno de los cilindros presentes en los cristales líquidos de estructura hexagonal, y a su alrededor hemos simulado la formación de una capa de sílica utilizando un modelo atomístico. De esta forma, hemos obtenido un poro típico de una estructura mesoporosa más realista, sin necesidad de asumir una forma mas o menos cilíndrica del template, por ser este generado de la auto-agregación del surfactante. / Surfactants are amphiphilic molecules with a solvophilic head and a solvophobic tail. When the surfactant concentration in a given solution is high enough, the molecules aggregate between them to shield the solvophobic part from the contact with the solvent. Such aggregates can show very different sizes and shapes, according to the surfactant and the conditions of the system. The surfactants self-assembly, being due to an energetic and entropic compromise of their molecular structure, is fundamental to observe the formation of very ordered liquid crystals. In the presence of an inorganic precursor and depending on the interactions established between such a precursor and the surfactant, it is possible to synthesize a hybrid material. Hybrid materials are the key step for the formation of periodic ordered mesoporous materials, which can be obtained by eliminating the organic soft matter (the surfactants) from the inorganic framework. Periodic ordered mesoporous materials represent an important family of porous materials as they find a large number of applications in several industrial fields, such as separations, catalysis, sensors, etc. In the last decade, the range of potential applications has increased with the possibility of functionalizing the pore walls by incorporating organic groups during the synthesis, or with post-synthesis treatments.In this work, we are interested in studying the formation of ordered materials when hybrid organic-inorganic precursors are used. Lattice Monte Carlo simulations in the NVT ensemble have been used to study the equilibrium phase behavior and the synthesis of self-assembling ordered mesoporous materials formed by an organic template with amphiphilic properties and an inorganic precursor in a model solvent. Three classes of inorganic precursors have been modeled: terminal (R-Si-(OEt)3) and bridging ((EtO)3-Si-R-Si-(OEt)3)) organosilica precursors (OSPs), along with pure silica precursors (Si-(OEt)4). Each class has been studied by analyzing its solubility in the solvent and the solvophobicity of the inorganic group. At high surfactant concentrations, periodic ordered structures, such as hexagonally-ordered cylinders or lamellas, can be obtained depending on the OSPs used. In particular, ordered structures were obtained in a wider range of conditions when bridging hydrophilic OSPs have been used, because a higher surfactant concentration was reached in the phase where the material was formed. Terminal and bridging OSPs produced ordered structures only when the organic group is solvophilic. In this case, a partial solubility between the precursor and the solvent or a lower temperature favored the formation of ordered phases.With particular interest, we have analyzed the range of conditions leaving to the formation of cylindrical structures, which have been evaluated according to the pore size distribution, the pore wall thickness, the distribution and the accessibility of the functional organic groups around the pores. The phase behavior has been also evaluated by applying the quasi-chemical theory, which cannot predict the formation of ordered structures, but was very useful to confirm the results of simulations, especially when no ordered structures were observed.The study of the phase and aggregation behavior of two different surfactants, one modeled by a linear chain of head segments and the other modeled by a branched-head, permitted us to evaluate some structural differences of the materials obtained.

No description available.

Fixed-collision correlated sampling for Monte Carlo (MC) simulations is a method which can be used in order to shorten the simulation time for brachytherapy treatment planning in a 3D patient geometry. The increased efficiency compared to conventional MC simulation is measured by efficiency gain. However, a previous study showed that, in some cases, PDFs (probability density functions) of estimates of the efficiency gain, simulated using resampling and other MC methods, were multimodal with values below 1. This means that the method was less effective than conventional sampling for these cases. The aims of this thesis were to trace the causes of the multimodal distributions and to propose techniques to mitigate the problem caused by photons with high statistical weights.Two simulation environments were used for the study case, a homogeneous and a heterogeneous environment. The homogenous environment consisted of a water sphere with the radius 100mm. For the heterogeneous environment a cylindrical block of tungsten alloy (diameter 15 mm, height 2.5 mm) was placed in the water sphere. The sphere was divided into an array of cubic voxels of size 2.5 mm x 2.5 mm x 2.5 mm for dose calculations. A photon source was positioned in the middle of the water sphere and emitted photons with the energy 400 keV.It was found that the low values and multimodal PDFs for the efficiency gain estimates originated from photons depositing high values of energy in some voxels in the heterogeneous environment. The high energy deposits were due to extremely high statistical weights of photons interacting repeatedly in the highly attenuating tungsten cylinder. When photon histories contributing to the rare events of high energy deposits (outliers) were removed, the PDFs became uni-modal and efficiency gain increased. However, removing outliers will cause results to be biased calling for other techniques to handle the problem with high statistical weights.One way to resolve the problem in the current implementation of the fixed-collision correlated sampling scheme in PTRAN (the MC code used) could be to split photons with high statistical weights into several photons with the same sum weight as the initial photon. The splitting of photons will result in more time consuming simulations in areas with high attenuation coefficients, which may not be the areas of interest. This could be resolved by using Russian roulette, eliminating some of the photons with high statistical weight in such areas.Fixed-collision correlated sampling for Monte Carlo (MC) simulations is a method which can be used in order to shorten the simulation time for brachytherapy treatment planning in a 3D patient geometry. The increased efficiency compared to conventional MC simulation is measured by efficiency gain. However, a previous study showed that, in some cases, PDFs (probability density functions) of estimates of the efficiency gain, simulated using resampling and other MC methods, were multimodal with values below 1. This means that the method was less effective than conventional sampling for these cases. The aims of this thesis were to trace the causes of the multimodal distributions and to propose techniques to mitigate the problem caused by photons with high statistical weights.Two simulation environments were used for the study case, a homogeneous and a heterogeneous environment. The homogenous environment consisted of a water sphere with the radius 100mm. For the heterogeneous environment a cylindrical block of tungsten alloy (diameter 15 mm, height 2.5 mm) was placed in the water sphere. The sphere was divided into an array of cubic voxels of size 2.5 mm x 2.5 mm x 2.5 mm for dose calculations. A photon source was positioned in the middle of the water sphere and emitted photons with the energy 400 keV.It was found that the low values and multimodal PDFs for the efficiency gain estimates originated from photons depositing high values of energy in some voxels in the heterogeneous environment. The high energy deposits were due to extremely high statistical weights of photons interacting repeatedly in the highly attenuating tungsten cylinder. When photon histories contributing to the rare events of high energy deposits (outliers) were removed, the PDFs became uni-modal and efficiency gain increased. However, removing outliers will cause results to be biased calling for other techniques to handle the problem with high statistical weights.One way to resolve the problem in the current implementation of the fixed-collision correlated sampling scheme in PTRAN (the MC code used) could be to split photons with high statistical weights into several photons with the same sum weight as the initial photon. The splitting of photons will result in more time consuming simulations in areas with high attenuation coefficients, which may not be the areas of interest. This could be resolved by using Russian roulette, eliminating some of the photons with high statistical weight in such areas.