Monte-Carlo-Simulationen zum Phasenverhalten binärer Polymerbürsten

Diese Arbeit beschäftigt sich mit Strukturbildung im schlechten Lösungsmittel bei ein- und zweikomponentigen Polymerbürsten, bei denen Polymerketten durch Pfropfung am Substrat verankert sind. Solche Systeme zeigen laterale Strukturbildungen, aus denen sich interessante Anwendungen ergeben. Die Bewegung der Polymere erfolgt durch Monte Carlo-Simulationen im Kontinuum, die auf CBMC-Algorithmen sowie lokalen Monomerverschiebungen basieren. Eine neu entwickelte Variante des CBMC-Algorithmus erlaubt die Bewegung innerer Kettenteile, da der bisherige Algorithmus die Monomere in Nähe des Pfropfmonomers nicht gut relaxiert. Zur Untersuchung des Phasenverhaltens werden mehrere Analysemethoden entwickelt und angepasst: Dazu gehören die Minkowski-Maße zur Strukturuntersuchung binären Bürsten und die Pfropfkorrelationen zur Untersuchung des Einflusses von Pfropfmustern. Bei einkomponentigen Bürsten tritt die Strukturbildung nur beim schwach gepfropften System auf, dichte Pfropfungen führen zu geschlossenen Bürsten ohne laterale Struktur. Für den graduellen Übergang zwischen geschlossener und aufgerissener Bürste wird ein Temperaturbereich bestimmt, in dem der Übergang stattfindet. Der Einfluss des Pfropfmusters (Störung der Ausbildung einer langreichweitigen Ordnung) auf die Bürstenkonfiguration wird mit den Pfropfkorrelationen ausgewertet. Bei unregelmäßiger Pfropfung sind die gebildeten Strukturen größer als bei regelmäßiger Pfropfung und auch stabiler gegen höhere Temperaturen. Bei binären Systemen bilden sich Strukturen auch bei dichter Pfropfung aus. Zu den Parametern Temperatur, Pfropfdichte und Pfropfmuster kommt die Zusammensetzung der beiden Komponenten hinzu. So sind weitere Strukturen möglich, bei gleicher Häufigkeit der beiden Komponenten bilden sich streifenförmige, lamellare Muster, bei ungleicher Häufigkeit formt die Minoritätskomponente Cluster, die in der Majoritätskomponente eingebettet sind. Selbst bei gleichmäßig gepfropften Systemen bildet sich keine langreichweitige Ordnung aus. Auch bei binären Bürsten hat das Pfropfmuster großen Einfluss auf die Strukturbildung. Unregelmäßige Pfropfmuster führen schon bei höheren Temperaturen zur Trennung der Komponenten, die gebildeten Strukturen sind aber ungleichmäßiger und etwas größer als bei gleichmäßig gepfropften Systemen. Im Gegensatz zur self consistent field-Theorie berücksichtigen die Simulationen Fluktuationen in der Pfropfung und zeigen daher bessere Übereinstimmungen mit dem Experiment.

Monte Carlo simulations of nucleation of colloidal crystals

A crystal nucleus in a finite volume may exhibit phase coexistence with a surrounding fluid. The thermodynamic properties of the coexisting fluid (pressure and chemical potential) are enhanced relative to their coexistence values. This enhancement is uniquely related to the surface excess free energy. rnA model for weakly attractive soft colloidal particles is investigated, the so called Asakura-Oosawa model. In simulations, this model allows for the calculation of the pressure in the liquid using the virial formula directly. The phase coexistence pressure in the thermodynamic limit is obtained from the interface velocity method. We introduce a method by which the chemical potential in dense liquids can be measured. There is neither a need to locate the interface nor to compute the anisotropic interfacial tension to obtain nucleation barriers. Therefore, our analysis is appropriate for nuclei of arbitrary shape. Monte Carlo simulations over a wide range of nucleus volumes yield to nucleation barriers independent from the total system volume. The interfacial tension is determined via the ensemble-switch method, hence a detailed test of classical nucleation theory is possible. The anisotropy of the interfacial tension and the resulting non-spherical shape has only a minor effect on the barrier for the Asakura-Oosawa model.

Macro Monte Carlo for dose calculation of proton beams

Although the Monte Carlo (MC) method allows accurate dose calculation for proton radiotherapy, its usage is limited due to long computing time. In order to gain efficiency, a new macro MC (MMC) technique for proton dose calculations has been developed. The basic principle of the MMC transport is a local to global MC approach. The local simulations using GEANT4 consist of mono-energetic proton pencil beams impinging perpendicularly on slabs of different thicknesses and different materials (water, air, lung, adipose, muscle, spongiosa, cortical bone). During the local simulation multiple scattering, ionization as well as elastic and inelastic interactions have been taken into account and the physical characteristics such as lateral displacement, direction distributions and energy loss have been scored for primary and secondary particles. The scored data from appropriate slabs is then used for the stepwise transport of the protons in the MMC simulation while calculating the energy loss along the path between entrance and exit position. Additionally, based on local simulations the radiation transport of neutrons and the generated ions are included into the MMC simulations for the dose calculations. In order to validate the MMC transport, calculated dose distributions using the MMC transport and GEANT4 have been compared for different mono-energetic proton pencil beams impinging on different phantoms including homogeneous and inhomogeneous situations as well as on a patient CT scan. The agreement of calculated integral depth dose curves is better than 1% or 1 mm for all pencil beams and phantoms considered. For the dose profiles the agreement is within 1% or 1 mm in all phantoms for all energies and depths. The comparison of the dose distribution calculated using either GEANT4 or MMC in the patient also shows an agreement of within 1% or 1 mm. The efficiency of MMC is up to 200 times higher than for GEANT4. The very good level of agreement in the dose comparisons demonstrate that the newly developed MMC transport results in very accurate and efficient dose calculations for proton beams.

More than just Good Luck. How to Explain the Success of Monte Carlo Simulations

Monte Carlo simulation is a powerful method in many natural and social sciences. But what sort of method is it? And where does its power come from? Are Monte Carlo simulations experiments, theories or something else? The aim of this talk is to answer these questions and to explain the power of Monte Carlo simulations. I provide a classification of Monte Carlo techniques and defend the claim that Monte Carlo simulation is a sort of inference.

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.

Feasibility assessment of the interactive use of a Monte Carlo algorithm in treatment planning for intraoperative electron radiation therapy

This work analysed the feasibility of using a fast, customized Monte Carlo (MC) method to perform accurate computation of dose distributions during pre- and intraplanning of intraoperative electron radiation therapy (IOERT) procedures. The MC method that was implemented, which has been integrated into a specific innovative simulation and planning tool, is able to simulate the fate of thousands of particles per second, and it was the aim of this work to determine the level of interactivity that could be achieved. The planning workflow enabled calibration of the imaging and treatment equipment, as well as manipulation of the surgical frame and insertion of the protection shields around the organs at risk and other beam modifiers. In this way, the multidisciplinary team involved in IOERT has all the tools necessary to perform complex MC dosage simulations adapted to their equipment in an efficient and transparent way. To assess the accuracy and reliability of this MC technique, dose distributions for a monoenergetic source were compared with those obtained using a general-purpose software package used widely in medical physics applications. Once accuracy of the underlying simulator was confirmed, a clinical accelerator was modelled and experimental measurements in water were conducted. A comparison was made with the output from the simulator to identify the conditions under which accurate dose estimations could be obtained in less than 3 min, which is the threshold imposed to allow for interactive use of the tool in treatment planning. Finally, a clinically relevant scenario, namely early-stage breast cancer treatment, was simulated with pre- and intraoperative volumes to verify that it was feasible to use the MC tool intraoperatively and to adjust dose delivery based on the simulation output, without compromising accuracy. The workflow provided a satisfactory model of the treatment head and the imaging system, enabling proper configuration of the treatment planning system and providing good accuracy in the dosage simulation.

Mean-value identities as an opportunity for Monte Carlo error reduction

In the Monte Carlo simulation of both lattice field theories and of models of statistical mechanics, identities verified by exact mean values, such as Schwinger-Dyson equations, Guerra relations, Callen identities, etc., provide well-known and sensitive tests of thermalization bias as well as checks of pseudo-random-number generators. We point out that they can be further exploited as control variates to reduce statistical errors. The strategy is general, very simple, and almost costless in CPU time. The method is demonstrated in the twodimensional Ising model at criticality, where the CPU gain factor lies between 2 and 4.

A New Algorithm for Monte Carlo for American Options

2000 Mathematics Subject Classification: 91B28, 65C05.

Avaliação da dose absorvida na tiróide, em cintigrafias com 123I e Na99mTcO4 utilizando modelos biocinéticos e métodos de Monte Carlo

Mestrado em Radiações Aplicadas às Tecnologias da Saúde. Área de especialização: Protecção contra Radiações

Monte Carlo modeling and simulations of the High Definition (HD120) micro MLC and validation against measurements for a 6 MV beam

Purpose: The most recent Varian® micro multileaf collimator(MLC), the High Definition (HD120) MLC, was modeled using the BEAMNRCMonte Carlo code. This model was incorporated into a Varian medical linear accelerator, for a 6 MV beam, in static and dynamic mode. The model was validated by comparing simulated profiles with measurements. Methods: The Varian® Trilogy® (2300C/D) accelerator model was accurately implemented using the state-of-the-art Monte Carlo simulation program BEAMNRC and validated against off-axis and depth dose profiles measured using ionization chambers, by adjusting the energy and the full width at half maximum (FWHM) of the initial electron beam. The HD120 MLC was modeled by developing a new BEAMNRC component module (CM), designated HDMLC, adapting the available DYNVMLC CM and incorporating the specific characteristics of this new micro MLC. The leaf dimensions were provided by the manufacturer. The geometry was visualized by tracing particles through the CM and recording their position when a leaf boundary is crossed. The leaf material density and abutting air gap between leaves were adjusted in order to obtain a good agreement between the simulated leakage profiles and EBT2 film measurements performed in a solid water phantom. To validate the HDMLC implementation, additional MLC static patterns were also simulated and compared to additional measurements. Furthermore, the ability to simulate dynamic MLC fields was implemented in the HDMLC CM. The simulation results of these fields were compared with EBT2 film measurements performed in a solid water phantom. Results: Overall, the discrepancies, with and without MLC, between the opened field simulations and the measurements using ionization chambers in a water phantom, for the off-axis profiles are below 2% and in depth-dose profiles are below 2% after the maximum dose depth and below 4% in the build-up region. On the conditions of these simulations, this tungsten-based MLC has a density of 18.7 g cm− 3 and an overall leakage of about 1.1 ± 0.03%. The discrepancies between the film measured and simulated closed and blocked fields are below 2% and 8%, respectively. Other measurements were performed for alternated leaf patterns and the agreement is satisfactory (to within 4%). The dynamic mode for this MLC was implemented and the discrepancies between film measurements and simulations are within 4%. Conclusions: The Varian® Trilogy® (2300 C/D) linear accelerator including the HD120 MLC was successfully modeled and simulated using the Monte CarloBEAMNRC code by developing an independent CM, the HDMLC CM, either in static and dynamic modes.

Properties of patchy colloidal particles close to a surface: a Monte Carlo and density functional study

We investigate the behavior of a patchy particle model close to a hard-wall via Monte Carlo simulation and density functional theory (DFT). Two DFT approaches, based on the homogeneous and inhomogeneous versions of Wertheim's first order perturbation theory for the association free energy are used. We evaluate, by simulation and theory, the equilibrium bulk phase diagram of the fluid and analyze the surface properties for two isochores, one of which is close to the liquid side of the gas-liquid coexistence curve. We find that the density profile near the wall crosses over from a typical high-temperature adsorption profile to a low-temperature desorption one, for the isochore close to coexistence. We relate this behavior to the properties of the bulk network liquid and find that the theoretical descriptions are reasonably accurate in this regime. At very low temperatures, however, an almost fully bonded network is formed, and the simulations reveal a second adsorption regime which is not captured by DFT. We trace this failure to the neglect of orientational correlations of the particles, which are found to exhibit surface induced orientational order in this regime.

Monte Carlo valuation of worst-of auto-callable equity swaps

This thesis proposes a Monte Carlo valuation method for Worst-of Auto-callable equity swaps. The valuation of this type of swap usually requires complex numerical methods which are implemented in “black-box” valuation systems. The method proposed is an alternative benchmark tool that is relatively simple to implement and customize. The performance of the method was evaluated according to the variance and bias of the output and to the accuracy when compared to a leading valuation system in the market.

Example of Monte Carlo uncertainty assessment in the field of radionuclide metrology

This chapter presents possible uses and examples of Monte Carlo methods for the evaluation of uncertainties in the field of radionuclide metrology. The method is already well documented in GUM supplement 1, but here we present a more restrictive approach, where the quantities of interest calculated by the Monte Carlo method are estimators of the expectation and standard deviation of the measurand, and the Monte Carlo method is used to propagate the uncertainties of the input parameters through the measurement model. This approach is illustrated by an example of the activity calibration of a 103Pd source by liquid scintillation counting and the calculation of a linear regression on experimental data points. An electronic supplement presents some algorithms which may be used to generate random numbers with various statistical distributions, for the implementation of this Monte Carlo calculation method.

Monte Carlo thermodynamic and structural properties of the TIP4P water model: dependence on the computational conditions

Classical Monte Carlo simulations were carried out on the NPT ensemble at 25°C and 1 atm, aiming to investigate the ability of the TIP4P water model [Jorgensen, Chandrasekhar, Madura, Impey and Klein; J. Chem. Phys., 79 (1983) 926] to reproduce the newest structural picture of liquid water. The results were compared with recent neutron diffraction data [Soper; Bruni and Ricci; J. Chem. Phys., 106 (1997) 247]. The influence of the computational conditions on the thermodynamic and structural results obtained with this model was also analyzed. The findings were compared with the original ones from Jorgensen et al [above-cited reference plus Mol. Phys., 56 (1985) 1381]. It is notice that the thermodynamic results are dependent on the boundary conditions used, whereas the usual radial distribution functions g(O/O(r)) and g(O/H(r)) do not depend on them.

Estudo de reações químicas homogêneas via método de Monte Carlo

By using the Monte Carlo simulation platform with probabilistic mathematical functions of the Boltzmann type, , having activation energy and temperature as parameters, it was possible to assess important dynamic aspects of homogeneous chemical reactions of the types A → B and A B. The protocol proved a useful tool in work with the basic concepts of Kinetics and Thermodynamics allowing its application both in class activities and for assisting experimental procedures.