Short-Term Nonlinear Response of Tension Leg Platform in Random Sea Waves

Most of the existing mathematical models for analyzing the dynamic response of TLP are based on explicit or implicit assumptions that motions (translations and rotations) are small magnitude. However, when TLP works in severe adverse conditions, the a priori assumption on small displacements may be inadequate. In such situation, the motions should be regarded as finite magnitude. This paper will study stochastic nonlinear dynamic responses of TLP with finite displacements in random waves. The nonlinearities considered are: large amplitude motions, coupling the six degrees-of-freedom, instantaneous position, instantaneous wet surface, free surface effects and viscous drag force. The nonlinear dynamic responses are calculated by using numerical integration procedure in the time domain. After the time histories of the dynamic responses are obtained, we carry out cycle counting of the stress histories of the tethers with rain-flow counting method to get the stress range distribution.

Einfluss des Tag-Nacht-Verhaltens von Fischen auf das Ergebnis hydroakustischer Messungen

Echo integration is an established method for stock estimation. However, this method is not free of errors like every other measuring method. Especially the variation between day and night behaviour of fish may lead to large measuring errors. A new method is represented detecting such systematic errors, exemplified by investigations during the international hydroacoustic survey on the spring spawning herring in the Norwegian Sea. For this method all measured sA-values are sorted by starting time of the measuring unit distance. In order to reduce random influences a moving average over five time intervals is computed. When displaying these values in a diagram makes it is very easy to detect systematic errors based on the differences in day-night behaviour. For both species, herring and blue whiting, stock estimations are calculated based on the measured sA-values and the results of the analysed trawl catches. The influence of the differnt day and night behaviour of herring on the results of its biomass estimation is rather low. For blue whiting the measured values were about three time higher during day time than during night time. The result of this investigation should initiate a change of the evaluation procedure for stock estimation based on hydroacoustic measurements.

Space-time correlations of fluctuating velocities in turbulent shear flows

Space-time correlations or Eulerian two-point two-time correlations of fluctuating velocities are analytically and numerically investigated in turbulent shear flows. An elliptic model for the space-time correlations in the inertial range is developed from the similarity assumptions on the isocorrelation contours: they share a uniform preference direction and a constant aspect ratio. The similarity assumptions are justified using the Kolmogorov similarity hypotheses and verified using the direct numerical simulation DNS of turbulent channel flows. The model relates the space-time correlations to the space correlations via the convection and sweeping characteristic velocities. The analytical expressions for the convection and sweeping velocities are derived from the Navier-Stokes equations for homogeneous turbulent shear flows, where the convection velocity is represented by the mean velocity and the sweeping velocity is the sum of the random sweeping velocity and the shearinduced velocity. This suggests that unlike Taylor’s model where the convection velocity is dominating and Kraichnan and Tennekes’ model where the random sweeping velocity is dominating, the decorrelation time scales of the space-time correlations in turbulent shear flows are determined by the convection velocity, the random sweeping velocity, and the shear-induced velocity. This model predicts a universal form of the spacetime correlations with the two characteristic velocities. The DNS of turbulent channel flows supports the prediction: the correlation functions exhibit a fair good collapse, when plotted against the normalized space and time separations defined by the elliptic model.

The relationship between otolith increments and time for yellowfin and skipjack tuna marked with tetracycline

ENGLISH: The rate at which increments are deposited on the sagittal otoliths of yellowfin (Thunnus albacares) and skipjack (Katsuwonus p elamis) tunas is determined by a markrecapture experiment using tetracycline. During growth in fork length from 40 to 110 em, and for a period of up to 389 days, yellowfin of the Revillagigedo Islands- Baja California region deposit one increment per day in either the postrostrum or rostrum position of the otolith. For skipjack of the same region, rostrum increments underestimate time by approximately 24 percent during growth from 42 to 64 cm and over the maximum interval of 249 days. The growth rate of each species is estimated from the recapture fork length and the linear change in an otolith dimension following tetracycline injection. Over specific ranges in fork length the rates are 3.06 and 1.15 em per month for yellowfin and skipjack, respectively. SPANISH: La rapidez (tasa) en la que se depositan los incrementos en los otolitos sagitales del aleta amarilla (Thunnus albacares) y el barrilete (Katsuwonus pelamis) se determina mediante un experimento al recapturar los peces que han sido marcados con tetraciclina. Durante el crecimiento de la longitud de horquilla de 40 a 110 cm y por un período hasta de 389 días, se forma en el aleta amarilla de la región de las Islas Revillagigedo-Baja California, un incremento diario ya sea en el parte del postrostrum o rostrum de los otolitos. Con respecto al barrilete de la misma region los incrementos en el rostrum subestiman aproximadamente el tiempo en un 24 por ciento durante el crecimiento de 42 a 64 cm y sobre un intervalo máximo de 249 días. El índice de crecimiento de cada especie se estima en la recaptura según la longitud de horquilla y el cambio lineal en la dimensión de un otolito después de la inyección de tetraciclina. La variación específica sobre la longitud de horquilla de los índices son 3.06 y 1.15 cm por mes para el aleta amarilla y el barrilete, respectivamente. (PDF contains 54 pages.)

Random response of nonlinear continuous systems

This thesis presents a technique for obtaining the stochastic response of a nonlinear continuous system. First, the general method of nonstationary continuous equivalent linearization is developed. This technique allows replacement of the original nonlinear system with a time-varying linear continuous system. Next, a numerical implementation is described which allows solution of complex problems on a digital computer. In this procedure, the linear replacement system is discretized by the finite element method. Application of this method to systems satisfying the one-dimensional wave equation with two different types of constitutive nonlinearities is described. Results are discussed for nonlinear stress-strain laws of both hardening and softening types.

Isotopic proxies for microbial and environmental change : insights hydrogen isotopes and the Ediacaran Khufai Formation

Microbes have profoundly influenced the Earth’s environments through time. Records of these interactions come primarily from the development and implementation of proxies that relate known modern processes to chemical signatures in the sedimentary record. This thesis is presented in two parts, focusing first on novel proxy development in the modern and second on interpretation of past environments using well-established methods. Part 1, presented in two chapters, builds on previous observations that different microbial metabolisms produce vastly different lipid hydrogen isotopic compositions. Chapter 1 evaluates the potential environmental expression of metabolism-based fractionation differences by exploiting the natural microbial community gradients in hydrothermal springs. We find a very large range in isotopic composition that can be demonstrably linked to the microbial source(s) of the fatty acids at each sample site. In Chapter 2, anaerobic culturing techniques are used to evaluate the hydrogen isotopic fractionations produced by anaerobic microbial metabolisms. Although the observed fractionation patterns are similar to those reported for aerobic cultures for some organisms, others show large differences. Part 2 changes focus from the modern to the ancient and uses classical stratigraphic methods combined with isotope stratigraphy to interpret microbial and environmental changes during the latest Precambrian Era. Chapter 3 presents a detailed characterization of the facies, parasequence development, and stratigraphic architecture of the Ediacaran Khufai Formation. Chapter 4 presents measurements of carbon, oxygen, and sulfur isotopic ratios in stratigraphic context. Large oscillations in the isotopic composition of sulfate constrain the size of the marine sulfate reservoir and suggest incorporation of an enriched isotopic source. Because this data was measured in stratigraphic context, we can assert with confidence that these isotopic shifts are not related to stratigraphic surfaces or facies type but instead reflect the evolution of the ocean through time. This data integrates into the chemostratigraphic global record and contributes to the emerging picture of changing marine chemistry during the latest Precambrian Era.

Integrating climate change impacts to improve understanding of coastal climate change: heavy rains, strong winds, and high seas in coastal Hawaii, Alaska and the Pacific Northwest

Coastal storms, and the strong winds, heavy rains, and high seas that accompany them pose a serious threat to the lives and livelihoods of the peoples of the Pacific basin, from the tropics to the high latitudes. To reduce their vulnerability to the economic, social, and environmental risks associated with these phenomena (and correspondingly enhance their resiliency), decision-makers in coastal communities require timely access to accurate information that affords them an opportunity to plan and respond accordingly. This includes information about the potential for coastal flooding, inundation and erosion at time scales ranging from hours to years, as well as the longterm climatological context of this information. The Pacific Storms Climatology Project (PSCP) was formed in 2006 with the intent of improving scientific understanding of patterns and trends of storm frequency and intensity - “storminess”- and related impacts of these extreme events. The project is currently developing a suite of integrated information products that can be used by emergency managers, mitigation planners, government agencies and decision-makers in key sectors, including: water and natural resource management, agriculture and fisheries, transportation and communication, and recreation and tourism. The PSCP is exploring how the climate-related processes that govern extreme storm events are expressed within and between three primary thematic areas: heavy rains, strong winds, and high seas. To address these thematic areas, PSCP has focused on developing analyses of historical climate records collected throughout the Pacific region, and the integration of these climatological analyses with near-real time observations to put recent weather and climate events into a longer-term perspective.(PDF contains 4 pages)

I. Rigid body penetration into brittle materials. II. Phase change effect on shock wave propagation

Part I.

We have developed a technique for measuring the depth time history of rigid body penetration into brittle materials (hard rocks and concretes) under a deceleration of ~ 10⁵ g. The technique includes bar-coded projectile, sabot-projectile separation, detection and recording systems. Because the technique can give very dense data on penetration depth time history, penetration velocity can be deduced. Error analysis shows that the technique has a small intrinsic error of ~ 3-4 % in time during penetration, and 0.3 to 0.7 mm in penetration depth. A series of 4140 steel projectile penetration into G-mixture mortar targets have been conducted using the Caltech 40 mm gas/ powder gun in the velocity range of 100 to 500 m/s.

We report, for the first time, the whole depth-time history of rigid body penetration into brittle materials (the G-mixture mortar) under 10⁵ g deceleration. Based on the experimental results, including penetration depth time history, damage of recovered target and projectile materials and theoretical analysis, we find:

1. Target materials are damaged via compacting in the region in front of a projectile and via brittle radial and lateral crack propagation in the region surrounding the penetration path. The results suggest that expected cracks in front of penetrators may be stopped by a comminuted region that is induced by wave propagation. Aggregate erosion on the projectile lateral surface is < 20% of the final penetration depth. This result suggests that the effect of lateral friction on the penetration process can be ignored.

2. Final penetration depth, P_max, is linearly scaled with initial projectile energy per unit cross-section area, e_s , when targets are intact after impact. Based on the experimental data on the mortar targets, the relation is P_max(mm) 1.15e_s (J/mm² ) + 16.39.

3. Estimation of the energy needed to create an unit penetration volume suggests that the average pressure acting on the target material during penetration is ~ 10 to 20 times higher than the unconfined strength of target materials under quasi-static loading, and 3 to 4 times higher than the possible highest pressure due to friction and material strength and its rate dependence. In addition, the experimental data show that the interaction between cracks and the target free surface significantly affects the penetration process.

4. Based on the fact that the penetration duration, t_max, increases slowly with e_s and does not depend on projectile radius approximately, the dependence of t_max on projectile length is suggested to be described by t_max(μs) = 2.08e_s (J/mm² + 349.0 x m/(πR²), in which m is the projectile mass in grams and R is the projectile radius in mm. The prediction from this relation is in reasonable agreement with the experimental data for different projectile lengths.

5. Deduced penetration velocity time histories suggest that whole penetration history is divided into three stages: (1) An initial stage in which the projectile velocity change is small due to very small contact area between the projectile and target materials; (2) A steady penetration stage in which projectile velocity continues to decrease smoothly; (3) A penetration stop stage in which projectile deceleration jumps up when velocities are close to a critical value of ~ 35 m/s.

6. Deduced averaged deceleration, a, in the steady penetration stage for projectiles with same dimensions is found to be a(g) = 192.4v + 1.89 x 10⁴, where v is initial projectile velocity in m/s. The average pressure acting on target materials during penetration is estimated to be very comparable to shock wave pressure.

7. A similarity of penetration process is found to be described by a relation between normalized penetration depth, P/P_max, and normalized penetration time, t/t_max, as P/P_max = f(t/t_max, where f is a function of t/t_max. After f(t/t_max is determined using experimental data for projectiles with 150 mm length, the penetration depth time history for projectiles with 100 mm length predicted by this relation is in good agreement with experimental data. This similarity also predicts that average deceleration increases with decreasing projectile length, that is verified by the experimental data.

8. Based on the penetration process analysis and the present data, a first principle model for rigid body penetration is suggested. The model incorporates the models for contact area between projectile and target materials, friction coefficient, penetration stop criterion, and normal stress on the projectile surface. The most important assumptions used in the model are: (1) The penetration process can be treated as a series of impact events, therefore, pressure normal to projectile surface is estimated using the Hugoniot relation of target material; (2) The necessary condition for penetration is that the pressure acting on target materials is not lower than the Hugoniot elastic limit; (3) The friction force on projectile lateral surface can be ignored due to cavitation during penetration. All the parameters involved in the model are determined based on independent experimental data. The penetration depth time histories predicted from the model are in good agreement with the experimental data.

9. Based on planar impact and previous quasi-static experimental data, the strain rate dependence of the mortar compressive strength is described by σ_f/σ⁰_f = exp(0.0905(log(έ/έ_0) ^1.14, in the strain rate range of 10^-7/s to 10³/s (σ⁰_f and έ are reference compressive strength and strain rate, respectively). The non-dispersive Hugoniot elastic wave in the G-mixture has an amplitude of ~ 0.14 GPa and a velocity of ~ 4.3 km/s.

Part II.

Stress wave profiles in vitreous GeO₂ were measured using piezoresistance gauges in the pressure range of 5 to 18 GPa under planar plate and spherical projectile impact. Experimental data show that the response of vitreous GeO₂ to planar shock loading can be divided into three stages: (1) A ramp elastic precursor has peak amplitude of 4 GPa and peak particle velocity of 333 m/s. Wave velocity decreases from initial longitudinal elastic wave velocity of 3.5 km/s to 2.9 km/s at 4 GPa; (2) A ramp wave with amplitude of 2.11 GPa follows the precursor when peak loading pressure is 8.4 GPa. Wave velocity drops to the value below bulk wave velocity in this stage; (3) A shock wave achieving final shock state forms when peak pressure is > 6 GPa. The Hugoniot relation is D = 0.917 + 1.711u (km/s) using present data and the data of Jackson and Ahrens [1979] when shock wave pressure is between 6 and 40 GPa for ρ₀ = 3.655 gj cm³ . Based on the present data, the phase change from 4-fold to 6-fold coordination of Ge⁺⁴ with O^-2 in vitreous GeO₂ occurs in the pressure range of 4 to 15 ± 1 GPa under planar shock loading. Comparison of the shock loading data for fused SiO₂ to that on vitreous GeO₂ demonstrates that transformation to the rutile structure in both media are similar. The Hugoniots of vitreous GeO₂ and fused SiO₂ are found to coincide approximately if pressure in fused SiO₂ is scaled by the ratio of fused SiO₂to vitreous GeO₂ density. This result, as well as the same structure, provides the basis for considering vitreous Ge0₂ as an analogous material to fused SiO₂ under shock loading. Experimental results from the spherical projectile impact demonstrate: (1) The supported elastic shock in fused SiO₂ decays less rapidly than a linear elastic wave when elastic wave stress amplitude is higher than 4 GPa. The supported elastic shock in vitreous GeO₂ decays faster than a linear elastic wave; (2) In vitreous GeO₂ , unsupported shock waves decays with peak pressure in the phase transition range (4-15 GPa) with propagation distance, x, as α 1/x^-3.35 , close to the prediction of Chen et al. [1998]. Based on a simple analysis on spherical wave propagation, we find that the different decay rates of a spherical elastic wave in fused SiO₂ and vitreous GeO₂ is predictable on the base of the compressibility variation with stress under one-dimensional strain condition in the two materials.

Predicting the effects of climate change on sea turtle nesting habitat in Florida

Rising global temperatures threaten the survival of many plant and animal species. Having already risen at an unprecedented rate in the past century, temperatures are predicted to rise between 0.3 and 7.5C in North America over the next 100 years (Hawkes et al. 2007). Studies have documented the effects of climate warming on phenology (timing of seasonal activities), with observations of early arrival at breeding grounds, earlier ends to the reproductive season, and delayed autumnal migrations (Pike et al. 2006). In addition, for species not suited to the physiological demands of cold winter temperatures, increasing temperatures could shift tolerable habitats to higher latitudes (Hawkes et al. 2007). More directly, climate warming will impact thermally sensitive species like sea turtles, who exhibit temperature-dependent sexual determination. Temperatures in the middle third of the incubation period determine the sex of sea turtle offspring, with higher temperatures resulting in a greater abundance of female offspring. Consequently, increasing temperatures from climate warming would drastically change the offspring sex ratio (Hawkes et al. 2007). Of the seven extant species of sea turtles, three (leatherback, Kemp’s ridley, and hawksbill) are critically endangered, two (olive ridley and green) are endangered, and one (loggerhead) is threatened. Considering the predicted scenarios of climate warming and the already tenuous status of sea turtle populations, it is essential that efforts are made to understand how increasing temperatures may affect sea turtle populations and how these species might adapt in the face of such changes. In this analysis, I seek to identify the impact of changing climate conditions over the next 50 years on the availability of sea turtle nesting habitat in Florida given predicted changes in temperature and precipitation. I predict that future conditions in Florida will be less suitable for sea turtle nesting during the historic nesting season. This may imply that sea turtles will nest at a different time of year, in more northern latitudes, to a lesser extent, or possibly not at all. It seems likely that changes in temperature and precipitation patterns will alter the distribution of sea turtle nesting locations worldwide, provided that beaches where the conditions are suitable for nesting still exist. Hijmans and Graham (2006) evaluate a range of climate envelope models in terms of their ability to predict species distributions under climate change scenarios. Their results suggested that the choice of species distribution model is dependent on the specifics of each individual study. Fuller et al. (2008) used a maximum entropy approach to model the potential distribution of 11 species in the Arctic Coastal Plain of Alaska under a series of projected climate scenarios. Recently, Pike (in press) developed Maxent models to investigate the impacts of climate change on green sea turtle nest distribution and timing. In each of these studies, a set of environmental predictor variables (including climate variables), for which ‘current’ conditions are available and ‘future’ conditions have been projected, is used in conjunction with species occurrence data to map potential species distribution under the projected conditions. In this study, I will take a similar approach in mapping the potential sea turtle nesting habitat in Florida by developing a Maxent model based on environmental and climate data and projecting the model for future climate data. (PDF contains 5 pages)

The Health Effects of Climate Change: A Survey of Recent Quantitative Research

44 p.

Random propagation in complex systems : nonlinear matrix recursions and epidemic spread

This dissertation studies long-term behavior of random Riccati recursions and mathematical epidemic model. Riccati recursions are derived from Kalman filtering. The error covariance matrix of Kalman filtering satisfies Riccati recursions. Convergence condition of time-invariant Riccati recursions are well-studied by researchers. We focus on time-varying case, and assume that regressor matrix is random and identical and independently distributed according to given distribution whose probability distribution function is continuous, supported on whole space, and decaying faster than any polynomial. We study the geometric convergence of the probability distribution. We also study the global dynamics of the epidemic spread over complex networks for various models. For instance, in the discrete-time Markov chain model, each node is either healthy or infected at any given time. In this setting, the number of the state increases exponentially as the size of the network increases. The Markov chain has a unique stationary distribution where all the nodes are healthy with probability 1. Since the probability distribution of Markov chain defined on finite state converges to the stationary distribution, this Markov chain model concludes that epidemic disease dies out after long enough time. To analyze the Markov chain model, we study nonlinear epidemic model whose state at any given time is the vector obtained from the marginal probability of infection of each node in the network at that time. Convergence to the origin in the epidemic map implies the extinction of epidemics. The nonlinear model is upper-bounded by linearizing the model at the origin. As a result, the origin is the globally stable unique fixed point of the nonlinear model if the linear upper bound is stable. The nonlinear model has a second fixed point when the linear upper bound is unstable. We work on stability analysis of the second fixed point for both discrete-time and continuous-time models. Returning back to the Markov chain model, we claim that the stability of linear upper bound for nonlinear model is strongly related with the extinction time of the Markov chain. We show that stable linear upper bound is sufficient condition of fast extinction and the probability of survival is bounded by nonlinear epidemic map.

Time and tide wait for no man: pioneers and laggards in the deployment of CCS

19 p.

Modelling the Effect of Climate Change on Environmental Pollution Losses from Dairy Systems in the UK

21 p.

How are Italian and Spanish cities tackling climate change? A local comparative study

27 p.

Hunting spectro-temporal information in unevenly spaced paleoclimate time series

18 p.