Simulação do equilíbrio: o método de Monte Carlo

We make several simulations using the Monte Carlo method in order to obtain the chemical equilibrium for several first-order reactions and one second-order reaction. We study several direct, reverse and consecutive reactions. These simulations show the fluctuations and relaxation time and help to understand the solution of the corresponding differential equations of chemical kinetics. This work was done in an undergraduate physical chemistry course at UNIFIEO.

Simulação Monte Carlo no ensino de luminescência e cinética de decaimento de estados excitados

A software based in the Monte Carlo method have been developed aiming the teaching of important cases of mechanisms found in luminescence and in excited states decay kinetics, including: multiple decays, consecutive decays and coupled systems decays. The Monte Carlo Method allows the student to easily simulate and visualize the luminescence mechanisms, focusing on the probabilities of the related steps. The software CINESTEX was written for FreeBASIC compiler; it assumes first-order kinetics and any number of excited states, where the pathways are allowed with probabilities assigned by the user.

Simulação Monte Carlo de mecanismo de transferência de energia de excitação eletrônica: modelo de Perrin para a supressão estática da luminescência

A software based in the Monte Carlo method has been developed aiming the teaching of the Perrin´s model for static luminescence quenching. This software allows the student to easily simulate the luminescence decays of emissive molecules in the presence of quenching ones. The software named PERRIN was written for FreeBASIC compiler and it can be applied for systems where the molecules remain static during its excited state lifetime. The good agreement found between the simulations and the expected theoretical results shows that it can be used for the luminescence and excited states decay kinetic teaching.

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.

Monte Carlo -reaktorifysiikkalaskennan ja laskennallisen virtausmekaniikan kytkentä kuulakekoreaktorissa

Monte Carlo -reaktorifysiikkakoodit nykyisin käytettävissä olevilla laskentatehoilla tarjoavat mielenkiintoisen tavan reaktorifysiikan ongelmien ratkaisuun. Neljännen sukupolven ydinreaktoreissa käytettävät uudet rakenteet ja materiaalit ovat haasteellisia nykyisiin reaktoreihin suunnitelluille laskentaohjelmille. Tässä työssä Monte Carlo -reaktorifysiikkakoodi ja CFD-koodi yhdistetään kytkettyyn laskentaan kuulakekoreaktorissa, joka on yksi korkealämpötilareaktorityyppi. Työssä käytetty lähestymistapa on uutta maailmankin mittapuussa ajateltuna.

Direct Simulation Monte Carlo Method Applied to Aerothermodynamics

An axisymmetric supersonic flow of rarefied gas past a finite cylinder was calculated applying the direct simulation Monte Carlo method. The drag force, the coefficients of pressure, of skin friction, and of heat transfer, the fields of density, of temperature, and of velocity were calculated as function of the Reynolds number for a fixed Mach number. The variation of the Reynolds number is related to the variation of the Knudsen number, which characterizes the gas rarefaction. The present results show that all quantities in the transition regime (Knudsen number is about the unity) are significantly different from those in the hydrodynamic regime, when the Knudsen number is small.

Neutron tomography using projection data obtained by Monte Carlo simulation for nondestructive evaluation

This work present the application of a computer package for generating of projection data for neutron computerized tomography, and in second part, discusses an application of neutron tomography, using the projection data obtained by Monte Carlo technique, for the detection and localization of light materials such as those containing hydrogen, concealed by heavy materials such as iron and lead. For tomographic reconstructions of the samples simulated use was made of only six equal projection angles distributed between 0º and 180º, with reconstruction making use of an algorithm (ARIEM), based on the principle of maximum entropy. With the neutron tomography it was possible to detect and locate polyethylene and water hidden by lead and iron (with 1cm-thick). Thus, it is demonstrated that thermal neutrons tomography is a viable test method which can provide important interior information about test components, so, extremely useful in routine industrial applications.

Variational Monte Carlo study of core-valence separation schemes for first-row atoms and positive ions /

All-electron partitioning of wave functions into products ^core^vai of core and valence parts in orbital space results in the loss of core-valence antisymmetry, uncorrelation of motion of core and valence electrons, and core-valence overlap. These effects are studied with the variational Monte Carlo method using appropriately designed wave functions for the first-row atoms and positive ions. It is shown that the loss of antisymmetry with respect to interchange of core and valence electrons is a dominant effect which increases rapidly through the row, while the effect of core-valence uncorrelation is generally smaller. Orthogonality of the core and valence parts partially substitutes the exclusion principle and is absolutely necessary for meaningful calculations with partitioned wave functions. Core-valence overlap may lead to nonsensical values of the total energy. It has been found that even relatively crude core-valence partitioned wave functions generally can estimate ionization potentials with better accuracy than that of the traditional, non-partitioned ones, provided that they achieve maximum separation (independence) of core and valence shells accompanied by high internal flexibility of ^core and Wvai- Our best core-valence partitioned wave function of that kind estimates the IP's with an accuracy comparable to the most accurate theoretical determinations in the literature.

Diffusion Monte Carlo study of electronic properties for H and Be atoms /

We examined three different algorithms used in diffusion Monte Carlo (DMC) to study their precisions and accuracies in predicting properties of isolated atoms, which are H atom ground state, Be atom ground state and H atom first excited state. All three algorithms — basic DMC, minimal stochastic reconfiguration DMC, and pure DMC, each with future-walking, are successfully impletmented in ground state energy and simple moments calculations with satisfactory results. Pure diffusion Monte Carlo with future-walking algorithm is proven to be the simplest approach with the least variance. Polarizabilities for Be atom ground state and H atom first excited state are not satisfactorily estimated in the infinitesimal differentiation approach. Likewise, an approach using the finite field approximation with an unperturbed wavefunction for the latter system also fails. However, accurate estimations for the a-polarizabilities are obtained by using wavefunctions that come from the time-independent perturbation theory. This suggests the flaw in our approach to polarizability estimation for these difficult cases rests with our having assumed the trial function is unaffected by infinitesimal perturbations in the Hamiltonian.

Histogram filtering as a tool in variational Monte Carlo optimization

Optimization of wave functions in quantum Monte Carlo is a difficult task because the statistical uncertainty inherent to the technique makes the absolute determination of the global minimum difficult. To optimize these wave functions we generate a large number of possible minima using many independently generated Monte Carlo ensembles and perform a conjugate gradient optimization. Then we construct histograms of the resulting nominally optimal parameter sets and "filter" them to identify which parameter sets "go together" to generate a local minimum. We follow with correlated-sampling verification runs to find the global minimum. We illustrate this technique for variance and variational energy optimization for a variety of wave functions for small systellls. For such optimized wave functions we calculate the variational energy and variance as well as various non-differential properties. The optimizations are either on par with or superior to determinations in the literature. Furthermore, we show that this technique is sufficiently robust that for molecules one may determine the optimal geometry at tIle same time as one optimizes the variational energy.

Monte Carlo study of the XY-model on quasi-periodic lattices

Monte Carlo Simulations were carried out using a nearest neighbour ferromagnetic XYmodel, on both 2-D and 3-D quasi-periodic lattices. In the case of 2-D, both the unfrustrated and frustrated XV-model were studied. For the unfrustrated 2-D XV-model, we have examined the magnetization, specific heat, linear susceptibility, helicity modulus and the derivative of the helicity modulus with respect to inverse temperature. The behaviour of all these quatities point to a Kosterlitz-Thouless transition occuring in temperature range Te == (1.0 -1.05) JlkB and with critical exponents that are consistent with previous results (obtained for crystalline lattices) . However, in the frustrated case, analysis of the spin glass susceptibility and EdwardsAnderson order parameter, in addition to the magnetization, specific heat and linear susceptibility, support a spin glass transition. In the case where the 'thin' rhombus is fully frustrated, a freezing transition occurs at Tf == 0.137 JlkB , which contradicts previous work suggesting the critical dimension of spin glasses to be de > 2 . In the 3-D systems, examination of the magnetization, specific heat and linear susceptibility reveal a conventional second order phase transition. Through a cumulant analysis and finite size scaling, a critical temperature of Te == (2.292 ± 0.003) JI kB and critical exponents of 0:' == 0.03 ± 0.03, f3 == 0.30 ± 0.01 and I == 1.31 ± 0.02 have been obtained.

Quantum Monte Carlo : some theoretical and numerical studies

In Part I, theoretical derivations for Variational Monte Carlo calculations are compared with results from a numerical calculation of He; both indicate that minimization of the ratio estimate of Evar , denoted EMC ' provides different optimal variational parameters than does minimization of the variance of E MC • Similar derivations for Diffusion Monte Carlo calculations provide a theoretical justification for empirical observations made by other workers. In Part II, Importance sampling in prolate spheroidal coordinates allows Monte Carlo calculations to be made of E for the vdW molecule var He2' using a simplifying partitioning of the Hamiltonian and both an HF-SCF and an explicitly correlated wavefunction. Improvements are suggested which would permit the extension of the computational precision to the point where an estimate of the interaction energy could be made~

Exact property estimation from diffusion Monte Carlo with minimal stochastic reconfiguration /

Our objective is to develop a diffusion Monte Carlo (DMC) algorithm to estimate the exact expectation values, ($o|^|^o), of multiplicative operators, such as polarizabilities and high-order hyperpolarizabilities, for isolated atoms and molecules. The existing forward-walking pure diffusion Monte Carlo (FW-PDMC) algorithm which attempts this has a serious bias. On the other hand, the DMC algorithm with minimal stochastic reconfiguration provides unbiased estimates of the energies, but the expectation values ($o|^|^) are contaminated by ^, an user specified, approximate wave function, when A does not commute with the Hamiltonian. We modified the latter algorithm to obtain the exact expectation values for these operators, while at the same time eliminating the bias. To compare the efficiency of FW-PDMC and the modified DMC algorithms we calculated simple properties of the H atom, such as various functions of coordinates and polarizabilities. Using three non-exact wave functions, one of moderate quality and the others very crude, in each case the results are within statistical error of the exact values.

Mesures de risque d'inflation: estimations et étude de Monte Carlo.

Rapport de recherche

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.