Investigação da dinâmica sequêncial Monte Carlo/Mecânica Quântica para sitemas moleculares orgânicos

O principal objetivo deste trabalho é investigar teóricamente as propriedades eletrônicas e óticas de compostos orgânicos em ambiente líquido. A compreensão das interações em sistemas líquidos é muito importante para a descrição de fenômenos em muitas partes da ciência, como Física, Química, Biologia e Materiais, bem como no desenvolvimento de materiais óticos. As flutuações térmicas fazem que inumaram das configurações para os líquidos possam ser gerados. Esta é a razão do comportamento estatístico observado em sistemas líquidos. Considerando estas dificuldades, o tratamento sequencial Monte Carlo / Mecânica Quântica (SMC/QM) é usado neste trabalho. Neste procedimento, a estrutura líquida é gerada primeiramente por simulações clássicas de MC e mais tarde, somente a parte mais importante do sistema é tratada com mecânica quântica. Usando o procedimento acima, os propriedades do quantum o pirazine dimethyl do thiene Methyl da laranja (MO) e do O 2,3-dimetil tieno[3,4-b] pirazina (DTP) foram investigados. O MO é um conhecido indicador de pH e pode ser encontrado sob circunstâncias básicas e acidas. Suas geometrias de mínima energia foram obtidas mediante a Teoria do Funcional da Densidade pelo funcional B3LYP, sendo o sistema descrito pelas bases de Pople com uma função de polarização (6-31G*). Para obter as propriedades médias dos observaveis, cálculos de química quântica foram executados dentro da aproximação semi-empírica de INDO/S-CI. Com respeito ao espectro de absorção, os dados experimentais existentes na literatura científica reportam a existência de uma larga banda localizada na região de baixas energias, mais precisamente entre 400 e 600 nm. Nossos resultados teóricos para a forma alcalina mostram uma transição intensa transição π → π* aproximadamente à 432.4 ± 0.03 nm e, sob condições ácidas, esta transição aparece aproximadamente à 507.4 ± 0.12, 496.4 ± 0.28 ou 545.3 ± 0.10 nm, dependendo da estrutura, mostrando bom acordo com resultados experimentais. O DTP é um sistema particular usado na produção de polímeros de baixo gap. Suas propriedades elétricas e óticas foram obtidas através de um novo procedimento conhecido por Configuração Eletrostática Média do Solvent (ASEC). O procedimento ASEC inclui moléculas do solvente como cargas pontuais e permite o obtenção das quantidades quânticas executando somente poucos cálculos de mecânica quântica. Para o DTP, usando a teoria das perturbações de segunda ordem Mφller-Plesset (MP2) e o conjunto de bases aug-cc-pVDZ, a convergência do momento de dipolo foi alcançada com apenas quatro cálculos de mecânica quântica à 1.16 D, apresentando um aumento de 42% quando comparado ao dipolo isolado. O polarizabilidade corresponde à outra característica elétrica que pôde ser medida. Considerando o mesmo nível empregado ao cálculo do dipolo, o valor médio 132.7 a30 foi observado. A região de mais baixas da energias do espectro de absorption foi investigada também atravé de procedimento de ASEC usando ambos as aproximações, semi-empírico e DFT. Esta região de absorção é motivo de conclusões contraditórias com relação à natureza das transições n → π* e π → π*. Nossos resultados mostram que realmente que essas excitações são realmente observadas simultanemente podendo sobrepôr-se. Como exemplo, nossos resultados para DFT, encontrados usando o funcional B3LYP nos mostra que estas transições aparecem aproximadamente à 360.6 e 351.1 nm.

A Monte Carlo study of the anisotropic N=3 Ashkin-Teller model

The phase diagram of an asymmetric N = 3 Ashkin-Teller model is obtained by a numerical analysis which combines Monte Carlo renormalization group and reweighting techniques. Present results reveal several differences with those obtained by mean-field calculations and a Hamiltonian approach. In particular, we found Ising critical exponents along a line where Goldschmidt has located the Kosterlitz-Thouless multicritical point. On the other hand, we did find nonuniversal exponents along another transition line. Symmetry breaking in this case is very similar to the N = 2 case, since the symmetries associated to only two of the Ising variables are broken. However, for large values of the coupling constant ratio XW = W/K, when the only broken symmetry is of a hidden variable, we detected first-order phase transitions giving evidence supporting the existence of a multicritical point, as suggested by Goldschmidt, but in a different region of the phase diagram. © 2002 Elsevier Science B.V. All rights reserved.

Monte Carlo Neutronics and Thermal-hydraulics coupling applied to Fast Reactors

Un escenario habitualmente considerado para el uso sostenible y prolongado de la energía nuclear contempla un parque de reactores rápidos refrigerados por metales líquidos (LMFR) dedicados al reciclado de Pu y la transmutación de actínidos minoritarios (MA). Otra opción es combinar dichos reactores con algunos sistemas subcríticos asistidos por acelerador (ADS), exclusivamente destinados a la eliminación de MA. El diseño y licenciamiento de estos reactores innovadores requiere herramientas computacionales prácticas y precisas, que incorporen el conocimiento obtenido en la investigación experimental de nuevas configuraciones de reactores, materiales y sistemas. A pesar de que se han construido y operado un cierto número de reactores rápidos a nivel mundial, la experiencia operacional es todavía reducida y no todos los transitorios se han podido entender completamente. Por tanto, los análisis de seguridad de nuevos LMFR están basados fundamentalmente en métodos deterministas, al contrario que las aproximaciones modernas para reactores de agua ligera (LWR), que se benefician también de los métodos probabilistas. La aproximación más usada en los estudios de seguridad de LMFR es utilizar una variedad de códigos, desarrollados a base de distintas teorías, en busca de soluciones integrales para los transitorios e incluyendo incertidumbres. En este marco, los nuevos códigos para cálculos de mejor estimación ("best estimate") que no incluyen aproximaciones conservadoras, son de una importancia primordial para analizar estacionarios y transitorios en reactores rápidos. Esta tesis se centra en el desarrollo de un código acoplado para realizar análisis realistas en reactores rápidos críticos aplicando el método de Monte Carlo. Hoy en día, dado el mayor potencial de recursos computacionales, los códigos de transporte neutrónico por Monte Carlo se pueden usar de manera práctica para realizar cálculos detallados de núcleos completos, incluso de elevada heterogeneidad material. Además, los códigos de Monte Carlo se toman normalmente como referencia para los códigos deterministas de difusión en multigrupos en aplicaciones con reactores rápidos, porque usan secciones eficaces punto a punto, un modelo geométrico exacto y tienen en cuenta intrínsecamente la dependencia angular de flujo. En esta tesis se presenta una metodología de acoplamiento entre el conocido código MCNP, que calcula la generación de potencia en el reactor, y el código de termohidráulica de subcanal COBRA-IV, que obtiene las distribuciones de temperatura y densidad en el sistema. COBRA-IV es un código apropiado para aplicaciones en reactores rápidos ya que ha sido validado con resultados experimentales en haces de barras con sodio, incluyendo las correlaciones más apropiadas para metales líquidos. En una primera fase de la tesis, ambos códigos se han acoplado en estado estacionario utilizando un método iterativo con intercambio de archivos externos. El principal problema en el acoplamiento neutrónico y termohidráulico en estacionario con códigos de Monte Carlo es la manipulación de las secciones eficaces para tener en cuenta el ensanchamiento Doppler cuando la temperatura del combustible aumenta. Entre todas las opciones disponibles, en esta tesis se ha escogido la aproximación de pseudo materiales, y se ha comprobado que proporciona resultados aceptables en su aplicación con reactores rápidos. Por otro lado, los cambios geométricos originados por grandes gradientes de temperatura en el núcleo de reactores rápidos resultan importantes para la neutrónica como consecuencia del elevado recorrido libre medio del neutrón en estos sistemas. Por tanto, se ha desarrollado un módulo adicional que simula la geometría del reactor en caliente y permite estimar la reactividad debido a la expansión del núcleo en un transitorio. éste módulo calcula automáticamente la longitud del combustible, el radio de la vaina, la separación de los elementos de combustible y el radio de la placa soporte en función de la temperatura. éste efecto es muy relevante en transitorios sin inserción de bancos de parada. También relacionado con los cambios geométricos, se ha implementado una herramienta que, automatiza el movimiento de las barras de control en busca d la criticidad del reactor, o bien calcula el valor de inserción axial las barras de control. Una segunda fase en la plataforma de cálculo que se ha desarrollado es la simulació dinámica. Puesto que MCNP sólo realiza cálculos estacionarios para sistemas críticos o supercríticos, la solución más directa que se propone sin modificar el código fuente de MCNP es usar la aproximación de factorización de flujo, que resuelve por separado la forma del flujo y la amplitud. En este caso se han estudiado en profundidad dos aproximaciones: adiabática y quasiestática. El método adiabático usa un esquema de acoplamiento que alterna en el tiempo los cálculos neutrónicos y termohidráulicos. MCNP calcula el modo fundamental de la distribución de neutrones y la reactividad al final de cada paso de tiempo, y COBRA-IV calcula las propiedades térmicas en el punto intermedio de los pasos de tiempo. La evolución de la amplitud de flujo se calcula resolviendo las ecuaciones de cinética puntual. Este método calcula la reactividad estática en cada paso de tiempo que, en general, difiere de la reactividad dinámica que se obtendría con la distribución de flujo exacta y dependiente de tiempo. No obstante, para entornos no excesivamente alejados de la criticidad ambas reactividades son similares y el método conduce a resultados prácticos aceptables. Siguiendo esta línea, se ha desarrollado después un método mejorado para intentar tener en cuenta el efecto de la fuente de neutrones retardados en la evolución de la forma del flujo durante el transitorio. El esquema consiste en realizar un cálculo cuasiestacionario por cada paso de tiempo con MCNP. La simulación cuasiestacionaria se basa EN la aproximación de fuente constante de neutrones retardados, y consiste en dar un determinado peso o importancia a cada ciclo computacial del cálculo de criticidad con MCNP para la estimación del flujo final. Ambos métodos se han verificado tomando como referencia los resultados del código de difusión COBAYA3 frente a un ejercicio común y suficientemente significativo. Finalmente, con objeto de demostrar la posibilidad de uso práctico del código, se ha simulado un transitorio en el concepto de reactor crítico en fase de diseño MYRRHA/FASTEF, de 100 MW de potencia térmica y refrigerado por plomo-bismuto. ABSTRACT Long term sustainable nuclear energy scenarios envisage a fleet of Liquid Metal Fast Reactors (LMFR) for the Pu recycling and minor actinides (MAs) transmutation or combined with some accelerator driven systems (ADS) just for MAs elimination. Design and licensing of these innovative reactor concepts require accurate computational tools, implementing the knowledge obtained in experimental research for new reactor configurations, materials and associated systems. Although a number of fast reactor systems have already been built, the operational experience is still reduced, especially for lead reactors, and not all the transients are fully understood. The safety analysis approach for LMFR is therefore based only on deterministic methods, different from modern approach for Light Water Reactors (LWR) which also benefit from probabilistic methods. Usually, the approach adopted in LMFR safety assessments is to employ a variety of codes, somewhat different for the each other, to analyze transients looking for a comprehensive solution and including uncertainties. In this frame, new best estimate simulation codes are of prime importance in order to analyze fast reactors steady state and transients. This thesis is focused on the development of a coupled code system for best estimate analysis in fast critical reactor. Currently due to the increase in the computational resources, Monte Carlo methods for neutrons transport can be used for detailed full core calculations. Furthermore, Monte Carlo codes are usually taken as reference for deterministic diffusion multigroups codes in fast reactors applications because they employ point-wise cross sections in an exact geometry model and intrinsically account for directional dependence of the ux. The coupling methodology presented here uses MCNP to calculate the power deposition within the reactor. The subchannel code COBRA-IV calculates the temperature and density distribution within the reactor. COBRA-IV is suitable for fast reactors applications because it has been validated against experimental results in sodium rod bundles. The proper correlations for liquid metal applications have been added to the thermal-hydraulics program. Both codes are coupled at steady state using an iterative method and external files exchange. The main issue in the Monte Carlo/thermal-hydraulics steady state coupling is the cross section handling to take into account Doppler broadening when temperature rises. Among every available options, the pseudo materials approach has been chosen in this thesis. This approach obtains reasonable results in fast reactor applications. Furthermore, geometrical changes caused by large temperature gradients in the core, are of major importance in fast reactor due to the large neutron mean free path. An additional module has therefore been included in order to simulate the reactor geometry in hot state or to estimate the reactivity due to core expansion in a transient. The module automatically calculates the fuel length, cladding radius, fuel assembly pitch and diagrid radius with the temperature. This effect will be crucial in some unprotected transients. Also related to geometrical changes, an automatic control rod movement feature has been implemented in order to achieve a just critical reactor or to calculate control rod worth. A step forward in the coupling platform is the dynamic simulation. Since MCNP performs only steady state calculations for critical systems, the more straight forward option without modifying MCNP source code, is to use the flux factorization approach solving separately the flux shape and amplitude. In this thesis two options have been studied to tackle time dependent neutronic simulations using a Monte Carlo code: adiabatic and quasistatic methods. The adiabatic methods uses a staggered time coupling scheme for the time advance of neutronics and the thermal-hydraulics calculations. MCNP computes the fundamental mode of the neutron flux distribution and the reactivity at the end of each time step and COBRA-IV the thermal properties at half of the the time steps. To calculate the flux amplitude evolution a solver of the point kinetics equations is used. This method calculates the static reactivity in each time step that in general is different from the dynamic reactivity calculated with the exact flux distribution. Nevertheless, for close to critical situations, both reactivities are similar and the method leads to acceptable practical results. In this line, an improved method as an attempt to take into account the effect of delayed neutron source in the transient flux shape evolutions is developed. The scheme performs a quasistationary calculation per time step with MCNP. This quasistationary simulations is based con the constant delayed source approach, taking into account the importance of each criticality cycle in the final flux estimation. Both adiabatic and quasistatic methods have been verified against the diffusion code COBAYA3, using a theoretical kinetic exercise. Finally, a transient in a critical 100 MWth lead-bismuth-eutectic reactor concept is analyzed using the adiabatic method as an application example in a real system.

Optimized Monte Carlo method for glasses

A new Monte Carlo algorithm is introduced for the simulation of supercooled liquids and glass formers, and tested in two model glasses. The algorithm thermalizes well below the Mode Coupling temperature and outperforms other optimized Monte Carlo methods.

Monte Carlo Algorithms for Linear Problems

MSC Subject Classification: 65C05, 65U05.

A nonparametric ensemble transform method for Bayesian inference

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables. © 2013, Society for Industrial and Applied Mathematics

Bayesian model comparison with un-normalised likelihoods

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalizing constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes’ factors for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates.

Identifying stationary series in panels: A Monte Carlo evaluation of sequential panel selection methods

Sequential panel selection methods (spsms — procedures that sequentially use conventional panel unit root tests to identify I(0)I(0) time series in panels) are increasingly used in the empirical literature. We check the reliability of spsms by using Monte Carlo simulations based on generating directly the individual asymptotic pp values to be combined into the panel unit root tests, in this way isolating the classification abilities of the procedures from the small sample properties of the underlying univariate unit root tests. The simulations consider both independent and cross-dependent individual test statistics. Results suggest that spsms may offer advantages over time series tests only under special conditions.

Application of Reptation Quantum Monte Carlo and Related Methods to LiH

This work investigates mathematical details and computational aspects of Metropolis-Hastings reptation quantum Monte Carlo and its variants, in addition to the Bounce method and its variants. The issues that concern us include the sensitivity of these algorithms' target densities to the position of the trial electron density along the reptile, time-reversal symmetry of the propagators, and the length of the reptile. We calculate the ground-state energy and one-electron properties of LiH at its equilibrium geometry for all these algorithms. The importance sampling is performed with a single-determinant large Slater-type orbitals (STO) basis set. The computer codes were written to exploit the efficiencies engineered into modern, high-performance computing software. Using the Bounce method in the calculation of non-energy-related properties, those represented by operators that do not commute with the Hamiltonian, is a novel work. We found that the unmodified Bounce gives good ground state energy and very good one-electron properties. We attribute this to its favourable time-reversal symmetry in its target density's Green's functions. Breaking this symmetry gives poorer results. Use of a short reptile in the Bounce method does not alter the quality of the results. This suggests that in future applications one can use a shorter reptile to cut down the computational time dramatically.

Portmanteau model diagnostics and tests for nonlinearity: a comparative Monte Carlo study of two alternative methods

This paper employs an extensive Monte Carlo study to test the size and power of the BDS and close return methods of testing for departures from independent and identical distribution. It is found that the finite sample properties of the BDS test are far superior and that the close return method cannot be recommended as a model diagnostic. Neither test can be reliably used for very small samples, while the close return test has low power even at large sample sizes

Comparison of monte carlo collimator transport methods for photon treatment planning in radiotherapy

The aim of this work was a Monte Carlo (MC) based investigation of the impact of different radiation transport methods in collimators of a linear accelerator on photon beam characteristics, dose distributions, and efficiency. Thereby it is investigated if it is possible to use different simplifications in the radiation transport for some clinical situations in order to save calculation time.

Review and comparison of effective delayed neutron fraction calculation methods with Monte Carlo codes

The calculation of the effective delayed neutron fraction, beff , with Monte Carlo codes is a complex task due to the requirement of properly considering the adjoint weighting of delayed neutrons. Nevertheless, several techniques have been proposed to circumvent this difficulty and obtain accurate Monte Carlo results for beff without the need of explicitly determining the adjoint flux. In this paper, we make a review of some of these techniques; namely we have analyzed two variants of what we call the k-eigenvalue technique and other techniques based on different interpretations of the physical meaning of the adjoint weighting. To test the validity of all these techniques we have implemented them with the MCNPX code and we have benchmarked them against a range of critical and subcritical systems for which either experimental or deterministic values of beff are available. Furthermore, several nuclear data libraries have been used in order to assess the impact of the uncertainty in nuclear data in the calculated value of beff .

Methods in Monte Carlo solution of the radiation transport equation /

"UNC-5014 (Volume A) Final Report covering the period 20 March 1961 - 31 May 1962."