Recovering the nonlinear density field from the galaxy distribution with a Poisson-Lognormal filter

We present a general expression for a lognormal filter given an arbitrary nonlinear galaxy bias. We derive this filter as the maximum a posteriori solution assuming a lognormal prior distribution for the matter field with a given mean field and modeling the observed galaxy distribution by a Poissonian process. We have performed a three-dimensional implementation of this filter with a very efficient Newton-Krylov inversion scheme. Furthermore, we have tested it with a dark matter N-body simulation assuming a unit galaxy bias relation and compared the results with previous density field estimators like the inverse weighting scheme and Wiener filtering. Our results show good agreement with the underlying dark matter field for overdensities even above delta~1000 which exceeds by one order of magnitude the regime in which the lognormal is expected to be valid. The reason is that for our filter the lognormal assumption enters as a prior distribution function, but the maximum a posteriori solution is also conditioned on the data. We find that the lognormal filter is superior to the previous filtering schemes in terms of higher correlation coefficients and smaller Euclidean distances to the underlying matter field. We also show how it is able to recover the positive tail of the matter density field distribution for a unit bias relation down to scales of about >~2 Mpc/h.Comment: 17 pages, 9 figures, 1 tabl

Parameter Estimation for the Finite Fourier Distribution in Civil Engineering Application.

A solution to a one dimensional diffusion equation applicable to a finite interval was adapted to be a probability distribution function. This distribution function can accommodate various shapes of distribution such as those similar to the uniform, single-modal, and bi-modal distributions. This distribution is bounded at both boundaries. It was named the finite Fourier distribution (FFD) to recognize the form of the distribution. The FFD was extended to include a linear combination of the FFD termed two-component FFD. Monte Carlo simulation technique was used to evaluate four parameter estimation techniques, Method of Maximum Likelihood Estimator (MLE), Method of Moments (MOM), Method of L-Moments (LMM), and Method of Least Square (LSQ). Robustness evaluation and other goodness-of-fit measures of these parameter estimation techniques are discussed. Both FFD and two-component FFD were applied to the field measured dissolved oxygen (DO) concentrations, laboratory measured hydraulic conductivity of clay liners, river quality data, and pore size distribution of compacted clays. Goodness-of-fit tests were performed to evaluate the models. The FFD provides similar or slightly better fit than the traditional distributions for certain sample data. Two-component FFD performed very well modeling the pore size distributions in compacted clays

Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis:version 4.0 developers manual.

The DAKOTA (Design Analysis Kit for Optimization and Terascale Applications) toolkit provides a flexible and extensible interface between simulation codes and iterative analysis methods. DAKOTA contains algorithms for optimization with gradient and nongradient-based methods; uncertainty quantification with sampling, reliability, and stochastic finite element methods; parameter estimation with nonlinear least squares methods; and sensitivity/variance analysis with design of experiments and parameter study methods. These capabilities may be used on their own or as components within advanced strategies such as surrogate-based optimization, mixed integer nonlinear programming, or optimization under uncertainty. By employing object-oriented design to implement abstractions of the key components required for iterative systems analyses, the DAKOTA toolkit provides a flexible and extensible problem-solving environment for design and performance analysis of computational models on high performance computers. This report serves as a developers manual for the DAKOTA software and describes the DAKOTA class hierarchies and their interrelationships. It derives directly from annotation of the actual source code and provides detailed class documentation, including all member functions and attributes

Advances in the Modeling of Time-Resolved Laser-Induced Incandescence

Aerosolized nanoparticles represent both great potential for the development of emerging technologies and one of the biggest challenges currently facing our planet. In the former case, aerosol-based synthesis techniques represent one of the most cost-effective approaches to generating engineered nanoparticles having applications that range from medicine to energy. In the latter case, aerosolized soot is the second largest forcing factor after carbon dioxide in climate change models and contributes significantly to asthma, bronchitis, and various other respiratory illnesses. The increased predominance of engineered nanoparticles also presents significant environmental and health risks due to various toxicological effects. In any of these cases, robust characterization is critical to the function and regulation of these nanoaerosols. Time-resolved laser-induced incandescence (TiRe-LII) is well-suited to meeting this challenge. Since its inception in the 1980s, TiRe-LII has matured into a standard diagnostic for characterizing soot in combustion applications and, increasingly, engineered nanoparticles synthesized as an aerosol. The in situ nature of the technique makes it well-suited to probe in-flame soot formation and the fundamentals of nanoparticle formation. Moreover, its cost-effectiveness and real-time capabilities make TiRe-LII particularly well-suited as an avenue for online control of nanoparticle synthesis. TiRe-LII involves heating nanoparticles within a sample volume of aerosol to incandescent temperatures using a short laser-pulse. Following the laser pulse, the nanoparticles return to the ambient gas temperature via conductive and evaporative cooling. The magnitude of the peak spectral incandescence signal can be used to derive the particle volume fraction, while the temperature decay of the nanoparticles can be used to infer thermophysical properties, including the nanoparticle size, thermal accommodation coefficient (TAC), and latent heat of vaporization. Data analysis requires the use of spectroscopic models, used to convert the observed incandescence to a volume fraction or nanoparticle temperature, and heat transfer models, used to model the changes in the nanoparticle temperature over the duration of a signal. These models have evolved considerably over the past two decades, increasing the interpretive power of TiRe-LII. Nevertheless, there are several factors that impede further improvements to the reliability of TiRe-LII derived quantities. Several anomalies have been observed in measured signals collected from both engineered nanoparticle and soot, ranging from faster-than-expected temperature decays to inconsistencies in measurements between laboratories and experimental conditions. Resolving these differences is crucial to improving the robustness of TiRe-LII both as a combustion and engineered nanoparticle diagnostic. However, this first requires the development of advanced analysis tools that allow for a better understanding of nanoscale physics and the uncertainties associated with model development. This thesis presents several advances in the modeling and interpretation of TiRe-LII signals. The current state-of-the-art in TiRe-LII models is first established and the process of model inversion is discussed, with particular reference to uncertainty quantification within the Bayesian perspective. This lays the foundation for analysis of the measurement errors associated with TiRe-LII signals, providing practitioners with another source of information to characterize measurement devices and fluctuations in observed processes. Next, a novel approach to describe the relationship between the peak nanoparticle temperature and the laser fluence is derived. This allows the first comparison of fluence curves obtained using different instrumentation and under different measurement conditions. This dissertation proceeds by examining inversion of the spectroscopic model to determine both the nanoparticle temperature decay and the factor that scales emission from the nanoparticles to the observed signal. Unexpected temporal effects in the latter quantity are examined as an additional source of information that TiRe-LII practitioners can use for nanoparticle characterization and for diagnosing problems with measurement devices. Molecular dynamics simulations are employed to calculate the thermal accommodation coefficient, a parameter fundamental to the heat transfer model used in interpreting the inferred nanoparticle temperature decay, using the results are used in an analysis of TiRe-LII collected from iron, silver, and molybdenum nanoparticles. The cross-comparison of these materials highlights the utility of the developed analysis tools and provides fundamental insights into both nanoscale physics and bulk thermophysical properties. This dissertation concludes with a critical discussion of model development, emphasizing the importance of complexity and uncertainty in model selection. This is particularly important in the context of the context of the increasingly divergent set of TiRe-LII models available in the literature, indicative of model tuning. In summary, this dissertation not only presents direct improvements to the spectroscopic and heat transfer models used in traditional TiRe-LII analysis but also presents a set of new approaches by which the remaining challenges in TiRe-LII analysis can be resolved

Temperature effects on the static, dynamic and fatigue behaviour of composite materials used in wind turbine blades

Many Canadian regions have strong winds that are interesting for wind energy production. However, these same regions are often quite remote and the Canadian climate is atypical for the wind energy industry. The high level of uncertainty about the turbines durability and the profitability of wind plants under such environments thus hinders the development of wind energy projects in Canada. Among the many uncertainties related to Canadian operating conditions, one specific concern is about the durability of wind turbine blades in Northern climates. The goal of this thesis is thus to clarify the effects of temperature and strain rate on the strength, stiffness and fatigue performance of composite materials as used in the wind energy sector. It thus focuses on glass fibre reinforced composites, which is the mainstream material for wind turbine blades. Wind turbine blades are basically beam exposed to a combination of axial, bending (in and out of the rotor plane) and torsional loads. In order to resist these loads, laminates used in the different parts of the blade are mostly made of a combination of longitudinal and ±45◦ plies. In order to improve the basic understanding of the mechanics of failure, two simple laminate configurations are studied, namely: • The unidirectional laminate loaded in the fibre direction, which is the main load bearing component of the blade structure. • The [±45]s bias-ply laminate, which provides shear stiffness to the blades structure. The temperatures considered are limited to those that could realistically be encountered in Canada’s climate, namely an extreme wintertime low of -40℃ to a summertime high of 60℃, which is deemed representative of a part exposed to direct sunlight in the summer. Similarly, fatigue frequencies are limited to a maximum of 24 Hz. It was found that the static strength and stiffness of both laminate configurations were strongly affected by both low and high temperatures. A significant increase of both properties was measured at low temperature, while high temperature strongly degraded them. However, while the high temperature fatigue durability followed the same trend as the static strength, the low temperature fatigue performance was only slightly affected, and even less so for unidirectional laminates. Both a vertical shift and a change in slope of the S–N curve with temperature was observed. At low temperature, this change of slope favours the fatigue strength under a high fatigue load, but reduces expected lives at lower load levels. This finding may be particularly significant in the context of wind turbine blade durability since they generally need to operate at low fatigue stresses, but over very long periods. Frequency effects were mostly not significant within the range explored. Nevertheless, experiments suggest that higher frequencies may have a slightly deleterious effect. An approach to predict the effect of temperature on the probabilistic S–N curve of fibre dominated composites with minimal experimental requirements is also proposed. This method is based on a cyclic strength degradation model, for which the parameters change with temperature is correlated with temperature effect on static strength. Since the latter is also an input for the cyclic strength degradation model, a function describing its temperature dependence is also suggested. The predictions obtained by the model are very good for both strength and fatigue life. Finally, models are developed for describing the static strength as well as the storage and loss modulus as a function of temperature across multiple transitions. The latter model also has provision for evaluating frequency effects on the storage modulus and glass transition temperature. These models provide a very good description of the dynamic response of polymers and composites on which they were validated (epoxies and epoxy based composites). Moreover, they provide a unambiguous definition of the glass transition temperature and allows for the evaluation of temperature and frequency effects on both the storage modulus without using the time-temperature superposition principle. Results show that if the time-temperature shift factors are calculated from the model, they are continuous across the glass transition. This suggests that the commonly expected discontinuity in this region may actually only be a side effect of neglecting the glass transition frequency dependence in conventional time-temperature superposition approaches

Ninth European Powder Diffraction Conference – Prague, September 2-5, 2004

Zeitschrift für Kristallographie. Supplement Volume 23 presents the complete Proceedings of all contributions to the IX European Powder Diffraction Conference in Prague 2004: Method Development and Application, Instrumental, Software Development, Materials Supplement Series of Zeitschrift für Kristallographie publishes Proceedings and Abstracts of international conferences on the interdisciplinary field of crystallography