Statistical analysis and simulation techniques in wall-bounded turbulence

The present work is devoted to the assessment of the energy fluxes physics in the space of scales and physical space of wall-turbulent flows. The generalized Kolmogorov equation will be applied to DNS data of a turbulent channel flow in order to describe the energy fluxes paths from production to dissipation in the augmented space of wall-turbulent flows. This multidimensional description will be shown to be crucial to understand the formation and sustainment of the turbulent fluctuations fed by the energy fluxes coming from the near-wall production region. An unexpected behavior of the energy fluxes comes out from this analysis consisting of spiral-like paths in the combined physical/scale space where the controversial reverse energy cascade plays a central role. The observed behavior conflicts with the classical notion of the Richardson/Kolmogorov energy cascade and may have strong repercussions on both theoretical and modeling approaches to wall-turbulence. To this aim a new relation stating the leading physical processes governing the energy transfer in wall-turbulence is suggested and shown able to capture most of the rich dynamics of the shear dominated region of the flow. Two dynamical processes are identified as driving mechanisms for the fluxes, one in the near wall region and a second one further away from the wall. The former, stronger one is related to the dynamics involved in the near-wall turbulence regeneration cycle. The second suggests an outer self-sustaining mechanism which is asymptotically expected to take place in the log-layer and could explain the debated mixed inner/outer scaling of the near-wall statistics. The same approach is applied for the first time to a filtered velocity field. A generalized Kolmogorov equation specialized for filtered velocity field is derived and discussed. The results will show what effects the subgrid scales have on the resolved motion in both physical and scale space, singling out the prominent role of the filter length compared to the cross-over scale between production dominated scales and inertial range, lc, and the reverse energy cascade region lb. The systematic characterization of the resolved and subgrid physics as function of the filter scale and of the wall-distance will be shown instrumental for a correct use of LES models in the simulation of wall turbulent flows. Taking inspiration from the new relation for the energy transfer in wall turbulence, a new class of LES models will be also proposed. Finally, the generalized Kolmogorov equation specialized for filtered velocity fields will be shown to be an helpful statistical tool for the assessment of LES models and for the development of new ones. As example, some classical purely dissipative eddy viscosity models are analyzed via an a priori procedure.

Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

A simulation study using the hybrid statistic and the meta-analysis t-test for data with matched and unmatched subjects in the interim analysis of clinical trials

An interim analysis is usually applied in later phase II or phase III trials to find convincing evidence of a significant treatment difference that may lead to trial termination at an earlier point than planned at the beginning. This can result in the saving of patient resources and shortening of drug development and approval time. In addition, ethics and economics are also the reasons to stop a trial earlier. In clinical trials of eyes, ears, knees, arms, kidneys, lungs, and other clustered treatments, data may include distribution-free random variables with matched and unmatched subjects in one study. It is important to properly include both subjects in the interim and the final analyses so that the maximum efficiency of statistical and clinical inferences can be obtained at different stages of the trials. So far, no publication has applied a statistical method for distribution-free data with matched and unmatched subjects in the interim analysis of clinical trials. In this simulation study, the hybrid statistic was used to estimate the empirical powers and the empirical type I errors among the simulated datasets with different sample sizes, different effect sizes, different correlation coefficients for matched pairs, and different data distributions, respectively, in the interim and final analysis with 4 different group sequential methods. Empirical powers and empirical type I errors were also compared to those estimated by using the meta-analysis t-test among the same simulated datasets. Results from this simulation study show that, compared to the meta-analysis t-test commonly used for data with normally distributed observations, the hybrid statistic has a greater power for data observed from normally, log-normally, and multinomially distributed random variables with matched and unmatched subjects and with outliers. Powers rose with the increase in sample size, effect size, and correlation coefficient for the matched pairs. In addition, lower type I errors were observed estimated by using the hybrid statistic, which indicates that this test is also conservative for data with outliers in the interim analysis of clinical trials.^

Physical, biological and chemical characteristics of Canadian and Danish lakes during summer

1. Winter temperatures differ markedly on the Canadian prairies compared with Denmark. Between 1 January 1998 and 31 December 2002, average weekly and monthly temperatures did not drop below 0 °C in the vicinity of Silkeborg, Denmark. Over this same time, weekly average temperatures near Calgary, Alberta, Canada, often dropped below -10 °C for 3-5 weeks and the average monthly temperature was below 0 °C for 2-4 months. Accordingly, winter ice conditions in shallow lakes in Canada and Denmark differed considerably. 2. To assess the implications of winter climate for lake biotic structure and function we compared a number of variables that describe the chemistry and biology of shallow Canadian and Danish lakes that had been chosen to have similar morphometries. 3. The Danish lakes had a fourfold higher ratio of chlorophyll-a: total phosphorus (TP). Zooplankton : phytoplankton carbon was related to TP and fish abundance in Danish lakes but not in Canadian lakes. There was no significant difference in the ratio log total zooplankton biomass : log TP and the Canadian lakes had a significantly higher proportion of cladocerans that were Daphnia. These differences correspond well with the fact that the Danish lakes have more abundant and diverse fish communities than the Canadian lakes. 4. Our results suggest that severe Canadian winters lead to anoxia under ice and more depauperate fish communities, and stronger zooplankton control on phytoplankton in shallow prairie lakes compared with shallow Danish lakes. If climate change leads to warmer winters and a shorter duration of ice cover, we predict that shallow Canadian prairie lakes will experience increased survivorship of planktivores and stronger control of zooplankton. This, in turn, might decrease zooplankton control on phytoplankton, leading to 'greener' lakes on the Canadian prairies.

Electrical resistivity, formation factors, and sound velocity at DSDP Holes 75-530A and 75-530B

From 0 to 277 m at Site 530 are found Holocene to Miocene diatom ooze, nannofossil ooze, marl, clay, and debrisflow deposits; from 277 to 467 m are Miocene to Oligocene mud; from 467 to 1103 m are Eocene to late Albian Cenomanian interbedded mudstone, marlstone, chalk, clastic limestone, sandstone, and black shale in the lower portion; from 1103 to 1121 m are basalts. In the interval from 0 to 467 m, in Holocene to Oligocene pelagic oozes, marl, clay, debris flows, and mud, velocities are 1.5 to 1.8 km/s; below 200 m velocities increase irregularly with increasing depth. From 0 to 100 m, in Holocene to Pleistocene diatom and nannofossil oozes (excluding debris flows), velocities are approximately equivalent to that of the interstitial seawater, and thus acoustic reflections in the upper 100 m are primarily caused by variations in density and porosity. Below 100 or 200 m, acoustic reflections are caused by variations in both velocity and density. From 100 to 467 m, in Miocene-Oligocene nannofossil ooze, clay, marl, debris flows, and mud, acoustic anisotropy irregularly increases to 10%, with 2 to 5% being typical. From 467 to 1103 m in Paleocene to late Albian Cenomanian interbedded mudstone, marlstone, chalk, clastic limestone, and black shale in the lower portion of the hole, velocities range from 1.6 to 5.48 km/s, and acoustic anisotropies are as great as 47% (1.0 km/s) faster horizontally. Mudstone and uncemented sandstone have anisotropies which irregularly increase with increasing depth from 5 to 10% (0.2 km/s). Calcareous mudstones have the greatest anisotropies, typically 35% (0.6 km/s). Below 1103 m, basalt velocities ranged from 4.68 to 4.98 km/s. A typical value is about 4.8 km/s. In situ velocities are calculated from velocity data obtained in the laboratory. These are corrected for in situ temperature, hydrostatic pressure, and porosity rebound (expansion when the overburden pressure is released). These corrections do not include rigidity variations caused by overburden pressures. These corrections affect semiconsolidated sedimentary rocks the most (up to 0.25 km/s faster). These laboratory velocities appear to be greater than the velocities from the sonic log. Reflection coefficients derived from the laboratory data, in general, agree with the major features on the seismic profiles. These indicate more potential reflectors than indicated from the reflection coefficients derived using the Gearhart-Owen Sonic Log from 625 to 940 m, because the Sonic Log data average thin beds. Porosity-density data versus depth for mud, mudstone, and pelagic oozes agree with data for similar sediments as summarized in Hamilton (1976). At depths of about 400 m and about 850 m are zones of relatively higher porosity mudstones, which may suggest anomalously high pore pressure; however, they are more probably caused by variations in grain-size distribution and lithology. Electrical resistivity (horizontal) from 625 to 950 m ranged from about 1.0 to 4.0 ohm-m, in Maestrichtian to Santonian- Coniacian mudstone, marlstone, chalk, clastic limestone, and sandstone. An interstitial-water resistivity curve did not indicate any unexpected lithology or unusual fluid or gas in the pores of the rock. These logs were above the black shale beds. From 0 to 100 m at Sites 530 and 532, the vane shear strength on undisturbed samples of Holocene-Pleistocene diatom and nannofossil ooze uniformly increases from about 80 g/cm**2 to about 800 g/cm**2. From 100 to 300 m, vane shear strength of Pleistocene-Miocene nannofossil ooze, clay, and marl are irregular versus depth with a range of 500 to 2300 g/cm**2; and at Site 532 the vane shear strength appears to decrease irregularly and slightly with increasing depth (gassy zone). Vane shear strength values of gassy samples may not be valid, for the samples may be disturbed as gas evolves, and the sediments may not be gassy at in situ depths.

Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega) the averages [equation, see text] converge for almost every omicron in. Our result implies that sequences like ([ndelta]), where delta > 1 and not an integer, ([n log n]), and ([n2/log n]) are good averaging sequences for L2. In fact, all the sequences we examine will turn out to be good averaging for Lp, p > 1; and even for L log L. We will also establish necessary and sufficient growth conditions on a(x) so that the sequence ([a(n)]) is good averaging for mean convergence. Note that for some a(x) (e.g., a(x) = log2 x), ([a(n)]) may be good for mean convergence without being good for pointwise convergence.

A nova família de distribuições odd log-logística: teoria e aplicações

Neste trabalho, foi proposta uma nova família de distribuições, a qual permite modelar dados de sobrevivência quando a função de risco tem formas unimodal e U (banheira). Ainda, foram consideradas as modificações das distribuições Weibull, Fréchet, half-normal generalizada, log-logística e lognormal. Tomando dados não-censurados e censurados, considerou-se os estimadores de máxima verossimilhança para o modelo proposto, a fim de verificar a flexibilidade da nova família. Além disso, um modelo de regressão locação-escala foi utilizado para verificar a influência de covariáveis nos tempos de sobrevida. Adicionalmente, conduziu-se uma análise de resíduos baseada nos resíduos deviance modificada. Estudos de simulação, utilizando-se de diferentes atribuições dos parâmetros, porcentagens de censura e tamanhos amostrais, foram conduzidos com o objetivo de verificar a distribuição empírica dos resíduos tipo martingale e deviance modificada. Para detectar observações influentes, foram utilizadas medidas de influência local, que são medidas de diagnóstico baseadas em pequenas perturbações nos dados ou no modelo proposto. Podem ocorrer situações em que a suposição de independência entre os tempos de falha e censura não seja válida. Assim, outro objetivo desse trabalho é considerar o mecanismo de censura informativa, baseado na verossimilhança marginal, considerando a distribuição log-odd log-logística Weibull na modelagem. Por fim, as metodologias descritas são aplicadas a conjuntos de dados reais.

Magnetic activity and differential rotation in the young Sun-like stars KIC 7985370 and KIC 7765135

Aims. We present a detailed study of the two Sun-like stars KIC 7985370 and KIC 7765135, to determine their activity level, spot distribution, and differential rotation. Both stars were previously discovered by us to be young stars and were observed by the NASA Kepler mission. Methods. The fundamental stellar parameters (vsini, spectral type, T_eff, log g, and [Fe/H]) were derived from optical spectroscopy by comparison with both standard-star and synthetic spectra. The spectra of the targets allowed us to study the chromospheric activity based on the emission in the core of hydrogen Hα and Ca ii infrared triplet (IRT) lines, which was revealed by the subtraction of inactive templates. The high-precision Kepler photometric data spanning over 229 days were then fitted with a robust spot model. Model selection and parameter estimation were performed in a Bayesian manner, using a Markov chain Monte Carlo method. Results. We find that both stars are Sun-like (of G1.5 V spectral type) and have an age of about 100–200 Myr, based on their lithium content and kinematics. Their youth is confirmed by their high level of chromospheric activity, which is comparable to that displayed by the early G-type stars in the Pleiades cluster. The Balmer decrement and flux ratio of their Ca ii-IRT lines suggest that the formation of the core of these lines occurs mainly in optically thick regions that are analogous to solar plages. The spot model applied to the Kepler photometry requires at least seven persistent spots in the case of KIC 7985370 and nine spots in the case of KIC 7765135 to provide a satisfactory fit to the data. The assumption of the longevity of the star spots, whose area is allowed to evolve with time, is at the heart of our spot-modelling approach. On both stars, the surface differential rotation is Sun-like, with the high-latitude spots rotating slower than the low-latitude ones. We found, for both stars, a rather high value of the equator-to-pole differential rotation (dΩ ≈ 0.18 rad d^-1), which disagrees with the predictions of some mean-field models of differential rotation for rapidly rotating stars. Our results agree instead with previous works on solar-type stars and other models that predict a higher latitudinal shear, increasing with equatorial angular velocity, that can vary during the magnetic cycle.

Investigating the Eastern Extent of the Seattle Fault Zone through Depth to Bedrock and Borehole Analysis in Bellevue, Washington

This study identifies lineaments that indicate fault activity and strengthens previous interpretations of structures within the eastern extent of the Seattle Fault zone in Bellevue, WA. My investigation has compiled geotechnical subsurface data, high-resolution LiDAR imagery, and ground-penetrating radar to produce strip log sections transecting identified lineaments and depth-to-bedrock maps exposing fault structure. My work incorporates field investigation, multiple publicly available datasets, and subsurface modeling. My results include a map showing twenty-eight identified surface lineaments, five strip-log sections, and interpolated depth-to-bedrock and minimum-depth-to-bedrock maps. Several lineaments identified in the minimum-depth-to-bedrock raster are parallel to the Seattle Fault zone and suggest the presence of small splay faults beneath east Bellevue. These results strengthen previous interpretations of seismic profile data located in the study area. Another lineament identified in the minimum-depth-to-bedrock raster suggest an unmapped tear fault accommodating differential offset along fault strike between Mercer Island and Bellevue. This work also demonstrates the utility of publicly available datasets such as geotechnical subsurface explorations and LiDAR imagery in supplementing geologic investigations in the eastern extent of the Seattle Fault zone.

The role of large woody debris and riparian forest in channel avulsion in the Carbon River, Mount Rainier National Park, Washington

A specific type of natural log jam in the upper alluvial reach of the Carbon River was found to influence secondary channel avulsion, causing flooding hazards to the adjacent Carbon River Road in the northwest quadrant of Mount Rainier National Park, Washington. The fence-like natural log jam was characterized by large woody debris buttressed horizontally against standing riparian trees (i.e. ìfence railsî and ìfence postî). The objectives of this report are two-fold. First, physical characteristics and spatial distribution were documented to determine the geomorphic controls on the fence-like log jams. Second, the function and timing of the natural log jam in relation to channel avulsion was determined to provide insight into flooding hazards along the Carbon River Road. The fence-like log jams are most abundant in the upper reaches of the Carbon River between 3.0 and 5.5 kilometers from the Carbon Glacier terminus, where longitudinal gradient significantly decreases from about 0.06 to 0.03. Sediment impoundment can occur directly upstream of the fence-like log jam, creating vertical bed elevation difference as high as 1.32 meters, and can form during low magnitude, high frequency flood event (3.5-year recurrence interval). In some locations, headcuts and widening of secondary channel were observed directly to the side of the log jams, suggesting its role in facilitating secondary channel avulsions. Areas along the Carbon River Road more prone to damages from avulsion hazards were identified by coupling locations of the log jams and Relative Water Surface Elevation map created using the 1-meter 2012 Light Detection and Ranging Digital Elevation Map. Ultimately, the results of this report may provide insight to flooding hazards along the Carbon River Road from log jam-facilitated channel avulsion.

Putting teeth into the developmental origins hypothesis: A longitudinal study of early childhood malnutrition, enamel hypoplasia and adolescent health in Amazonian Bolivia

Thesis (Ph.D.)--University of Washington, 2016-06