Rock fracture mean trace length estimation and confidence interval calculation using maximum likelihood methods

There has been a resurgence of interest in the mean trace length estimator of Pahl for window sampling of traces. The estimator has been dealt with by Mauldon and Zhang and Einstein in recent publications. The estimator is a very useful one in that it is non-parametric. However, despite some discussion regarding the statistical distribution of the estimator, none of the recent works or the original work by Pahl provide a rigorous basis for the determination a confidence interval for the estimator or a confidence region for the estimator and the corresponding estimator of trace spatial intensity in the sampling window. This paper shows, by consideration of a simplified version of the problem but without loss of generality, that the estimator is in fact the maximum likelihood estimator (MLE) and that it can be considered essentially unbiased. As the MLE, it possesses the least variance of all estimators and confidence intervals or regions should therefore be available through application of classical ML theory. It is shown that valid confidence intervals can in fact be determined. The results of the work and the calculations of the confidence intervals are illustrated by example. (C) 2003 Elsevier Science Ltd. All rights reserved.

Stereological and other methods applied to rock joint size estimation - Does Crofton's theorem apply?

A number of authors concerned with the analysis of rock jointing have used the idea that the joint areal or diametral distribution can be linked to the trace length distribution through a theorem attributed to Crofton. This brief paper seeks to demonstrate why Crofton's theorem need not be used to link moments of the trace length distribution captured by scan line or areal mapping to the moments of the diametral distribution of joints represented as disks and that it is incorrect to do so. The valid relationships for areal or scan line mapping between all the moments of the trace length distribution and those of the joint size distribution for joints modeled as disks are recalled and compared with those that might be applied were Crofton's theorem assumed to apply. For areal mapping, the relationship is fortuitously correct but incorrect for scan line mapping.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Selecting methods to solve multi-well master equations

There are several competing methods commonly used to solve energy grained master equations describing gas-phase reactive systems. When it comes to selecting an appropriate method for any particular problem, there is little guidance in the literature. In this paper we directly compare several variants of spectral and numerical integration methods from the point of view of computer time required to calculate the solution and the range of temperature and pressure conditions under which the methods are successful. The test case used in the comparison is an important reaction in combustion chemistry and incorporates reversible and irreversible bimolecular reaction steps as well as isomerizations between multiple unimolecular species. While the numerical integration of the ODE with a stiff ODE integrator is not the fastest method overall, it is the fastest method applicable to all conditions.

Influence of magnetically-induced E-fields on cardiac electric activity during MRI: A modeling study

In modern magnetic resonance imaging (MRI), patients are exposed to strong, time-varying gradient magnetic fields that may be able to induce electric fields (E-fields)/currents in tissues approaching the level of physiological significance. In this work we present theoretical investigations into induced E-fields in the thorax, and evaluate their potential influence on cardiac electric activity under the assumption that the sites of maximum E-field correspond to the myocardial stimulation threshold (an abnormal circumstance). Whole-body cylindrical and planar gradient coils were included in the model. The calculations of the induced fields are based on an efficient, quasi-static, finite-difference scheme and an anatomically realistic, whole-body model. The potential for cardiac stimulation was evaluated using an electrical model of the heart. Twelve-lead electrocardiogram (ECG) signals were simulated and inspected for arrhythmias caused by the applied fields for both healthy and diseased hearts. The simulations show that the shape of the thorax and the conductive paths significantly influence induced E-fields. In healthy patients, these fields are not sufficient to elicit serious arrhythmias with the use of contemporary gradient sets. However, raising the strength and number of repeated switching episodes of gradients, as is certainly possible in local chest gradient sets, could expose patients to increased risk. For patients with cardiac disease, the risk factors are elevated. By the use of this model, the sensitivity of cardiac pathologies, such as abnormal conductive pathways, to the induced fields generated by an MRI sequence can be investigated. (C) 2003 Wiley-Liss, Inc.

A comparison of two methods for the calculation of accumulated oxygen deficit

The aim of this study was to compare accumulated oxygen deficit data derived using two different exercise protocols with the aim of producing a less time-consuming test specifically for use with athletes. Six road and four track male endurance cyclists performed two series of cycle ergometer tests. The first series involved five 10 min sub-maximal cycle exercise bouts, a (V) over dotO(2peak) test and a 115% (V) over dotO(2peak) test. Data from these tests were used to estimate the accumulated oxygen deficit according to the calculations of Medbo et al. (1988). In the second series of tests, participants performed a 15 min incremental cycle ergometer test followed, 2 min later, by a 2 min variable resistance test in which they completed as much work as possible while pedalling at a constant rate. Analysis revealed that the accumulated oxygen deficit calculated from the first series of tests was higher (P< 0.02) than that calculated from the second series: 52.3 +/- 11.7 and 43.9 +/- 6.4 ml . kg(-1), respectively (mean +/- s). Other significant differences between the two protocols were observed for (V) over dot O-2peak, total work and maximal heart rate; all were higher during the modified protocol (P

Water table waves in an unconfined aquifer: Experiments and modeling

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics ( in addition to that contained in the driving head) being generated at the interface or in the interior.

Surface stickiness of drops of carbohydrate and organic acid solutions during convective drying: Experiments and modeling

Drying kinetics of low molecular weight sugars such as fructose, glucose, sucrose and organic acid such as citric acid and high molecular weight carbohydrate such as maltodextrin (DE 6) were determined experimentally using single drop drying experiments as well as predicted numerically by solving the mass and heat transfer equations. The predicted moisture and temperature histories agreed with the experimental ones within 6% average relative (absolute) error and average difference of +/- 1degreesC, respectively. The stickiness histories of these drops were determined experimentally and predicted numerically based on the glass transition temperature (T-g) of surface layer. The model predicted the experimental observations with good accuracy. A nonsticky regime for these materials during spray drying is proposed by simulating a drop, initially 120 mum in diameter, in a spray drying environment.

Rates of electronic energy transfer in conformationally flexible bichromophoric macrocyclic complexes: a combined experimental and molecular modeling study

Electronic energy transfer (EET) rate constants between a naphthalene donor and anthracene acceptor in [ZnL4a](ClO4)(2) and [ZnL4b](ClO4)(2) were determined by time-resolved fluorescence where L-4a and L-4b are the trans and cis isomers of 6-((anthracen-9-yl-methyl)amino)-6,13-dimethyl-13-((naphthalen-1-yl-methyl)amino)-1,4,8,11-tetraazacyclotetradecane, respectively. These isomers differ in the relative disposition of the appended chromophores with respect to the macrocyclic plane. The trans isomer has an energy transfer rate constant (k(EET)) of 8.7 x 10(8) s(-1), whereas that of the cis isomer is significantly faster (2.3 x 10(9) s(-1)). Molecular modeling was used to determine the likely distribution of conformations in CH3CN solution for these complexes in an attempt to identify any distance or orientation dependency that may account for the differing rate constants observed. The calculated conformational distributions together with analysis by H-1 NMR for the [ZnL4a](2+) trans complex in the common trans-III N-based isomer gave a calculated Forster rate constant close to that observed experimentally. For the [ZnL4b](2+) cis complex, the experimentally determined rate constant may be attributed to a combination of trans-Ill and trans-I N-based isomeric forms of the complex in solution.

Metodologia para obtenção do hidrograma de escoamento superficial em encostas e canais. Parte II: modelo computacional e análise de sensibilidade

Estimativas de vazão máxima de escoamento superficial são necessárias para o projeto de obras hidráulicas em bacias urbanas e rurais. A dificuldade em aplicar os procedimentos disponíveis para calcular a variação do escoamento superficial com o tempo e de seu valor máximo deve-se à inexatidão dos métodos usados para esse objetivo e à variabilidade nos resultados que podem ser obtidos por profissionais que usem o mesmo procedimento. Dessa forma, a investigação de um método que produza estimativas confiáveis da vazão máxima e do hidrograma de escoamento superficial é de grande interesse. Neste trabalho, desenvolveu-se e avaliou-se a sensibilidade de um software (HIDROGRAMA 2.1) que permite a obtenção do hidrograma de escoamento superficial, da vazão máxima e seu tempo de ocorrência, da altura e da velocidade máximas do escoamento, do volume e da lâmina de escoamento superficial em encosta e em canais. O modelo apresentou grande sensibilidade ao período de retorno, à taxa de infiltração estável e ao comprimento da encosta e do canal.

Comparação de desempenho entre a formulação direta do Método dos Elementos de Contorno com Funções Radiais e o Método dos Elementos Finitos em problemas de Poisson e Helmholtz

O presente trabalho objetiva avaliar o desempenho do MECID (Método dos Elementos de Contorno com Interpolação Direta) para resolver o termo integral referente à inércia na Equação de Helmholtz e, deste modo, permitir a modelagem do Problema de Autovalor assim como calcular as frequências naturais, comparando-o com os resultados obtidos pelo MEF (Método dos Elementos Finitos), gerado pela Formulação Clássica de Galerkin. Em primeira instância, serão abordados alguns problemas governados pela equação de Poisson, possibilitando iniciar a comparação de desempenho entre os métodos numéricos aqui abordados. Os problemas resolvidos se aplicam em diferentes e importantes áreas da engenharia, como na transmissão de calor, no eletromagnetismo e em problemas elásticos particulares. Em termos numéricos, sabe-se das dificuldades existentes na aproximação precisa de distribuições mais complexas de cargas, fontes ou sorvedouros no interior do domínio para qualquer técnica de contorno. No entanto, este trabalho mostra que, apesar de tais dificuldades, o desempenho do Método dos Elementos de Contorno é superior, tanto no cálculo da variável básica, quanto na sua derivada. Para tanto, são resolvidos problemas bidimensionais referentes a membranas elásticas, esforços em barras devido ao peso próprio e problemas de determinação de frequências naturais em problemas acústicos em domínios fechados, dentre outros apresentados, utilizando malhas com diferentes graus de refinamento, além de elementos lineares com funções de bases radiais para o MECID e funções base de interpolação polinomial de grau (um) para o MEF. São geradas curvas de desempenho através do cálculo do erro médio percentual para cada malha, demonstrando a convergência e a precisão de cada método. Os resultados também são comparados com as soluções analíticas, quando disponíveis, para cada exemplo resolvido neste trabalho.

Estudo da resistência não drenada de solo de baixa consistência por meio de ensaios de campo e laboratório

A variabilidade natural dos solos torna complexo o conhecimento de suas propriedades na elaboração de projetos geotécnicos, sendo a determinação da resistência ao cisalhamento não drenada um parâmetro importante nas análises de estabilidade de solos moles. Os ensaios de laboratório de cone e palheta, não convencionais, os ensaios de campo de palheta e piezocone e os ensaios de compressão simples e triaxial não adensado e não drenado foram utilizados para mensurar a resistência não drenada de uma camada de argila marinha mole localizada na planície costeira central brasileira. Os ensaios de laboratório foram realizados em amostras indeformadas coletadas com amostradores de pistão estacionário em vertical próxima à realização dos ensaios de campo. O sítio foi investigado preliminarmente por sondagens de simples reconhecimento, sendo apresentado o perfil estratigráfico por meio de modelagem computacional. Foram também realizados ensaios para caracterização física (análise granulométrica, teor de umidade, limites de liquidez e plasticidade, densidade real dos grãos) e mineralógica (difração de raios X), e ensaios de adensamento para obtenção do histórico de tensões e classificação de qualidade das amostras indeformadas. Os valores de resistência não drenada obtidos pelos ensaios de laboratório foram comparados ao perfil contínuo de resistência determinado empiricamente pelo ensaio de piezocone, com fator de cone Nkt calibrado pelo ensaio de palheta de campo, apresentando boa concordância, com a variabilidade natural do solo influenciando de forma preponderante a qualidade das amostras na variação entre os resultados. Os valores de resistência obtidos pelos ensaios de laboratório de cone e palheta foram comparados entre si, apresentando boa compatibilidade. Ambos, quando comparados ao ensaio de palheta de campo, não apresentaram boa concordância. Os resultados de resistência obtidos pelos ensaios de compressão simples e triaxial apresentaram boa compatibilidade com os resultados do ensaio de laboratório de cone, o que não ocorreu com os resultados do ensaio de laboratório de palheta. Na comparação entre a resistência normalizada pela tensão de sobreadensamento obtida pelos diversos métodos e algumas correlações empíricas da literatura internacional, foi observado para as amostras de solo com índice de plasticidade superior a 60% boa concordância com as correlações de Mesri (1975) e Jamiolkowski et al (1985). Os ensaios não convencionais apresentaram boa confiabilidade, que aliado a simplicidade e agilidade de execução, justificam a difusão destes na prática da investigação geotécnica brasileira como método alternativo para complementar e dar suporte às estimativas de resistência não drenada de solos moles.

Estudo do efeito da face sobre o equilíbrio de estruturas de contenção de solo reforçado sob condições de trabalho

Os métodos de análise de estruturas de contenção de solo reforçado sob condições de trabalho, em geral, desconsideram a contribuição da face para o equilíbrio da estrutura. Visando estudar a influência do peso específico da face e das propriedades relacionadas à rigidez da mesma sobre o desempenho das estruturas de solo reforçado, são realizadas simulações numéricas de diversas estruturas, utilizando a versão de dupla precisão do programa CRISP92-SC. Avalia-se, também, o emprego de diferentes tipos de elementos para a representação da face. Verifica-se que a face rígida impõe redução significativa das solicitações máximas de tração nos reforços e dos deslocamentos das estruturas de solo reforçado. A influência do peso específico da face sobre a estabilidade interna dos maciços reforçados mostrase desprezível e constata-se que a rigidez à flexão e a rigidez axial da face, função da sua geometria e do seu módulo de Young, são parâmetros influentes no comportamento das estruturas de contenção de solo reforçado. As variações da tração no reforço e da resultante de força cortante na face, em decorrência do enrijecimento da face, são analisadas e propõe-se uma relação entre elas. Quanto à forma de representação de uma face com rigidez expressiva, na simulação de uma estrutura de solo reforçado com o CRISP92-SC, é observado que a representação da face, seja por elementos de viga, seja por elementos quadriláteros, não altera os resultados da análise.

Modeling Carbon Nanotube Electrical Properties in CNT/Polymer Composites

In this work it is demonstrated that the capacitance between two cylinders increases with the rotation angle and it has a fundamental influence on the composite dielectric constant. The dielectric constant is lower for nematic materials than for isotropic ones and this can be attributed to the effect of the filler alignment in the capacitance. The effect of aspect ratio in the conductivity is also studied in this work. Finally, based on previous work and by comparing to results from the literature it is found that the electrical conductivity in this type of composites is due to hopping between nearest fillers resulting in a weak disorder regime that is similar to the single junction expression.