Developments and extensions of Roth's method of double Fourier series with applications to the solution of electromagnetic field problems

The first part of the thesis compares Roth's method with other methods, in particular the method of separation of variables and the finite cosine transform method, for solving certain elliptic partial differential equations arising in practice. In particular we consider the solution of steady state problems associated with insulated conductors in rectangular slots. Roth's method has two main disadvantages namely the slow rate of con­vergence of the double Fourier series and the restrictive form of the allowable boundary conditions. A combined Roth-separation of variables method is derived to remove the restrictions on the form of the boundary conditions and various Chebyshev approximations are used to try to improve the rate of convergence of the series. All the techniques are then applied to the Neumann problem arising from balanced rectangular windings in a transformer window. Roth's method is then extended to deal with problems other than those resulting from static fields. First we consider a rectangular insulated conductor in a rectangular slot when the current is varying sinusoidally with time. An approximate method is also developed and compared with the exact method.The approximation is then used to consider the problem of an insulated conductor in a slot facing an air gap. We also consider the exact method applied to the determination of the eddy-current loss produced in an isolated rectangular conductor by a transverse magnetic field varying sinusoidally with time. The results obtained using Roth's method are critically compared with those obtained by other authors using different methods. The final part of the thesis investigates further the application of Chebyshdev methods to the solution of elliptic partial differential equations; an area where Chebyshev approximations have rarely been used. A poisson equation with a polynomial term is treated first followed by a slot problem in cylindrical geometry.

Design and analysis of distributed utility maximization algorithm for multihop wireless network with inaccurate feedback

Distributed network utility maximization (NUM) is receiving increasing interests for cross-layer optimization problems in multihop wireless networks. Traditional distributed NUM algorithms rely heavily on feedback information between different network elements, such as traffic sources and routers. Because of the distinct features of multihop wireless networks such as time-varying channels and dynamic network topology, the feedback information is usually inaccurate, which represents as a major obstacle for distributed NUM application to wireless networks. The questions to be answered include if distributed NUM algorithm can converge with inaccurate feedback and how to design effective distributed NUM algorithm for wireless networks. In this paper, we first use the infinitesimal perturbation analysis technique to provide an unbiased gradient estimation on the aggregate rate of traffic sources at the routers based on locally available information. On the basis of that, we propose a stochastic approximation algorithm to solve the distributed NUM problem with inaccurate feedback. We then prove that the proposed algorithm can converge to the optimum solution of distributed NUM with perfect feedback under certain conditions. The proposed algorithm is applied to the joint rate and media access control problem for wireless networks. Numerical results demonstrate the convergence of the proposed algorithm. © 2013 John Wiley & Sons, Ltd.

Design and analysis of distributed utility maximization algorithm for multihop wireless network with inaccurate feedback

Distributed network utility maximization (NUM) is receiving increasing interests for cross-layer optimization problems in multihop wireless networks. Traditional distributed NUM algorithms rely heavily on feedback information between different network elements, such as traffic sources and routers. Because of the distinct features of multihop wireless networks such as time-varying channels and dynamic network topology, the feedback information is usually inaccurate, which represents as a major obstacle for distributed NUM application to wireless networks. The questions to be answered include if distributed NUM algorithm can converge with inaccurate feedback and how to design effective distributed NUM algorithm for wireless networks. In this paper, we first use the infinitesimal perturbation analysis technique to provide an unbiased gradient estimation on the aggregate rate of traffic sources at the routers based on locally available information. On the basis of that, we propose a stochastic approximation algorithm to solve the distributed NUM problem with inaccurate feedback. We then prove that the proposed algorithm can converge to the optimum solution of distributed NUM with perfect feedback under certain conditions. The proposed algorithm is applied to the joint rate and media access control problem for wireless networks. Numerical results demonstrate the convergence of the proposed algorithm. © 2013 John Wiley & Sons, Ltd.

Local Energy Decay in Even Dimensions for the Wave Equation with a Time-Periodic Non-Trapping Metric and Applications to Strichartz Estimates

2000 Mathematics Subject Classification: 35B40, 35L15.

Paleoenvironments and geochemical signals from the late Barremian to the middle Aptian in a Tethyan marginal basin, northeast Spain: Implications for carbon sequestration in restricted basins

The hallmark of oceanic anoxic event 1a (OAE1a) (early Aptian ~125 Ma) corresponds to worldwide deposition of black shales with total organic carbon (TOC) content > 2% and a δ13C positive excursion up to ~5‰. OAE1a has been related to large igneous province volcanism and dissociation of methane hydrates during the Lower Cretaceous. However, the occurrence of atypical, coeval and diachronous organic-rich deposits associated with OAE1a, which are also characterized by positive spikes of the δ 13C in epicontinental to restricted marine environments of the Tethys Ocean, indicates localized responses decoupled from complex global forcing factors. ^ The present research is a high-resolution, multiproxy approach to assess the paleoenvironmental conditions that led to enhanced carbon sequestration from the late Barremian to the middle Aptian in a restricted, Tethyan marginal basin prior to and during OAE1a. I studied the lower 240 m of the El Pui section, Organyà Basin, Spanish Pyrenees. The basin developed as the result of extensional tectonism linked to the opening of the Atlantic Ocean. At the field scale the section consists of a sequence of alternating beds of cm – m-scale, medium-gray to grayish-black limestones and marlstones with TOC up to ~4%. ^ The results indicate that the lowest 85 m of the section, from latest Barremian -earliest Aptian, characterize a deepening phase of the basin concomitant with sustained riverine flux and intensified primary productivity. These changes induced a shift in the sedimentation pattern and decreased the oxygen levels in the water column through organic matter respiration and limited ventilation of the basin. ^ The upper 155 m comprising the earliest – late-early Aptian document the occurrence of OAE1a and its associated geochemical signatures (TOC up to 3% and a positive shift in δ13C of ~5‰). However, a low enrichment of redox-sensitive trace elements indicates that the basin did not achieve anoxic conditions. The results also suggest that a shallower-phase of the basin, coeval with platform progradation, may have increased ventilation of the basin at the same time that heightened sedimentation rates and additional input of organic matter from terrestrial sources increased the burial and preservation rate of TOC in the sediment.^

Seawater carbonate chemistry, growth rate and PIC and POC production during experiments with Emiliania huxleyi (B92/11), 2011

The coccolithophore Emiliania huxleyi was cultured under a broad range of carbonate chemistry conditions to distinguish the effects of individual carbonate system parameters on growth, primary production, and calcification. In the first experiment, alkalinity was kept constant and the fugacity of CO2(fCO2) varied from 2 to 600 Pa (1Pa ~ 10 µatm). In the second experiment, pH was kept constant (pHfree = 8) with fCO2 varying from 4 to 370 Pa. Results of the constant-alkalinity approach revealed physiological optima for growth, calcification, and organic carbon production at fCO2 values of ~20Pa, ~40 Pa, and ~80 Pa, respectively. Comparing this with the constant-pH approach showed that growth and organic carbon production increased similarly from low to intermediate CO2 levels but started to diverge towards higher CO2 levels. In the high CO2 range, growth rates and organic carbon production decreased steadily with declining pH at constant alkalinity while remaining consistently higher at constant pH. This suggests that growth and organic carbon production rates are directly related to CO2 at low (sub-saturating) concentrations, whereas towards higher CO2 levels they are adversely affected by the associated decrease in pH. A pH dependence at high fCO2 is also indicated for calcification rates, while the key carbonate system parameter determining calcification at low fCO2 remains unclear. These results imply that key metabolic processes in coccolithophores have their optima at different carbonate chemistry conditions and are influenced by different parameters of the carbonate system at both sides of the optimum.

Last Interglacial synthesis of high-latitude temperature: temperature anomalies and associated errors for 4 time slices

The Last Interglacial (LIG, 129-116 thousand of years BP, ka) represents a test bed for climate model feedbacks in warmer-than-present high latitude regions. However, mainly because aligning different palaeoclimatic archives and from different parts of the world is not trivial, a spatio-temporal picture of LIG temperature changes is difficult to obtain. Here, we have selected 47 polar ice core and sub-polar marine sediment records and developed a strategy to align them onto the recent AICC2012 ice core chronology. We provide the first compilation of high-latitude temperature changes across the LIG associated with a coherent temporal framework built between ice core and marine sediment records. Our new data synthesis highlights non-synchronous maximum temperature changes between the two hemispheres with the Southern Ocean and Antarctica records showing an early warming compared to North Atlantic records. We also observe warmer than present-day conditions that occur for a longer time period in southern high latitudes than in northern high latitudes. Finally, the amplitude of temperature changes at high northern latitudes is larger compared to high southern latitude temperature changes recorded at the onset and the demise of the LIG. We have also compiled four data-based time slices with temperature anomalies (compared to present-day conditions) at 115 ka, 120 ka, 125 ka and 130 ka and quantitatively estimated temperature uncertainties that include relative dating errors. This provides an improved benchmark for performing more robust model-data comparison. The surface temperature simulated by two General Circulation Models (CCSM3 and HadCM3) for 130 ka and 125 ka is compared to the corresponding time slice data synthesis. This comparison shows that the models predict warmer than present conditions earlier than documented in the North Atlantic, while neither model is able to produce the reconstructed early Southern Ocean and Antarctic warming. Our results highlight the importance of producing a sequence of time slices rather than one single time slice averaging the LIG climate conditions.

Temperature, salinity, methane concentration, oxidation rates and methanotrophic cell number at Svalbard seeps in summer 2011 and 2012 (cruises POS419 and MSM21/4)

Large amounts of the greenhouse gas methane are released from the seabed to the water column where it may be consumed by aerobic methanotrophic bacteria. This microbial filter is consequently the last marine sink for methane before its liberation to the atmosphere. The size and activity of methanotrophic communities, which determine the capacity of the water column methane filter, are thought to be mainly controlled by nutrient and redox dynamics, but little is known about the effects of ocean currents. Here, we report measurements of methanotrophic activity and biomass (CARD-FISH) at methane seeps west of Svalbard, and related them to physical water mass properties (CTD) and modelled current dynamics. We show that cold bottom water containing a large number of aerobic methanotrophs was rapidly displaced by warmer water with a considerably smaller methanotrophic community. This water mass exchange, caused by short-term variations of the West Spitsbergen Current, constitutes a rapid oceanographic switch severely reducing methanotrophic activity in the water column. Strong and fluctuating currents are widespread oceanographic features common at many methane seep systems and are thus likely to globally affect methane oxidation in the ocean water column.

Compilation of 220 sediment core d13C data from the glacial Atlantic Ocean

We compare a compilation of 220 sediment core d13C data from the glacial Atlantic Ocean with three-dimensional ocean circulation simulations including a marine carbon cycle model. The carbon cycle model employs circulation fields which were derived from previous climate simulations. All sediment data have been thoroughly quality controlled, focusing on epibenthic foraminiferal species (such as Cibicidoides wuellerstorfi or Planulina ariminensis) to improve the comparability of model and sediment core carbon isotopes. The model captures the general d13C pattern indicated by present-day water column data and Late Holocene sediment cores but underestimates intermediate and deep water values in the South Atlantic. The best agreement with glacial reconstructions is obtained for a model scenario with an altered freshwater balance in the Southern Ocean that mimics enhanced northward sea ice export and melting away from the zone of sea ice production. This results in a shoaled and weakened North Atlantic Deep Water flow and intensified Antarctic Bottom Water export, hence confirming previous reconstructions from paleoproxy records. Moreover, the modeled abyssal ocean is very cold and very saline, which is in line with other proxy data evidence.

Mineralogy of sea-floor surface sediments, Sonne cruise SO202/1 to the North Pacific and Bering Sea

During expedition 202 of research vessel SONNE in 2009, 39 sea-floor surface sediments were sampled over a wide area across the North Pacific and the Bering Sea, which are well suited as reference archives of modern environmental processes. In this study, we used the samples to infer the documentation of land-ocean linkages of terrigenous sediment supply. We followed an integrated approach of grain-size analysis, bulk mineralogy, and clay mineralogy in combination with statistical data evaluation (end-member modelling of grain-size data, fuzzy-cluster analysis of mineralogical data), in order to identify the significant sources and modes of sediment transport in an overregional context. We also compiled literature data on clay mineralogy and updated those with the new data. Today, two processes of terrigenous sediment supply prevail in the study area: far-distant aeolian sediment supply to the pelagic North Pacific as well as hemipelagic sediment dispersal from nearby land sources by ocean currents along the continental margins and island arcs of the study area. The aeolian particles show the finest grain sizes (clay and fine silt), while the hemipelagic sediments have high abundances of sortable silt, particles >10 microns.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

Semi-parametric geolocation estimation in NLOS environments

The position of a stationary target can be determined using triangulation in combination with time of arrival measurements at several sensors. In urban environments, none-line-of-sight (NLOS) propagation leads to biased time estimation and thus to inaccurate position estimates. Here, a semi-parametric approach is proposed to mitigate the effects of NLOS propagation. The degree of contamination by NLOS components in the observations, which result in asymmetric noise statistics, is determined and incorporated into the estimator. The proposed method is adequate for environments where the NLOS error plays a dominant role and outperforms previous approaches that assume a symmetric noise statistic.

A Study of How Economic Attitudes Are Shaped by Environmental Shocks and Life Experiences

Social attitudes, attitudes toward financial risk and attitudes toward deferred gratification are thought to influence many important economic decisions over the life-course. In economic theory, these attitudes are key components in diverse models of behavior, including collective action, saving and investment decisions and occupational choice. The relevance of these attitudes have been confirmed empirically. Yet, the factors that influence them are not well understood. This research evaluates how these attitudes are affected by large disruptive events, namely, a natural disaster and a civil conflict, and also by an individual-specific life event, namely, having children.

By implementing rigorous empirical strategies drawing on rich longitudinal datasets, this research project advances our understanding of how life experiences shape these attitudes. Moreover, compelling evidence is provided that the observed changes in attitudes are likely to reflect changes in preferences given that they are not driven just by changes in financial circumstances. Therefore the findings of this research project also contribute to the discussion of whether preferences are really fixed, a usual assumption in economics.

In the first chapter, I study how altruistic and trusting attitudes are affected by exposure to the 2004 Indian Ocean tsunami as long as ten years after the disaster occurred. Establishing a causal relationship between natural disasters and attitudes presents several challenges as endogenous exposure and sample selection can confound the analysis. I take on these challenges by exploiting plausibly exogenous variation in exposure to the tsunami and by relying on a longitudinal dataset representative of the pre-tsunami population in two districts of Aceh, Indonesia. The sample is drawn from the Study of the Tsunami Aftermath and Recovery (STAR), a survey with data collected both before and after the disaster and especially designed to identify the impact of the tsunami. The altruistic and trusting attitudes of the respondents are measured by their behavior in the dictator and trust games. I find that witnessing closely the damage caused by the tsunami but without suffering severe economic damage oneself increases altruistic and trusting behavior, particularly towards individuals from tsunami affected communities. Having suffered severe economic damage has no impact on altruistic behavior but may have increased trusting behavior. These effects do not seem to be caused by the consequences of the tsunami on people’s financial situation. Instead they are consistent with how experiences of loss and solidarity may have shaped social attitudes by affecting empathy and perceptions of who is deserving of aid and trust.

In the second chapter, co-authored with Ryan Brown, Duncan Thomas and Andrea Velasquez, we investigate how attitudes toward financial risk are affected by elevated levels of insecurity and uncertainty brought on by the Mexican Drug War. To conduct our analysis, we pair the Mexican Family Life Survey (MxFLS), a rich longitudinal dataset ideally suited for our purposes, with a dataset on homicide rates at the month and municipality-level. The homicide rates capture well the overall crime environment created by the drug war. The MxFLS elicits risk attitudes by asking respondents to choose between hypothetical gambles with different payoffs. Our strategy to identify a causal effect has two key components. First, we implement an individual fixed effects strategy which allows us to control for all time-invariant heterogeneity. The remaining time variant heterogeneity is unlikely to be correlated with changes in the local crime environment given the well-documented political origins of the Mexican Drug War. We also show supporting evidence in this regard. The second component of our identification strategy is to use an intent-to-treat approach to shield our estimates from endogenous migration. Our findings indicate that exposure to greater local-area violent crime results in increased risk aversion. This effect is not driven by changes in financial circumstances, but may be explained instead by heightened fear of victimization. Nonetheless, we find that having greater economic resources mitigate the impact. This may be due to individuals with greater economic resources being able to avoid crime by affording better transportation or security at work.

The third chapter, co-authored with Duncan Thomas, evaluates whether attitudes toward deferred gratification change after having children. For this study we also exploit the MxFLS, which elicits attitudes toward deferred gratification (commonly known as time discounting) by asking individuals to choose between hypothetical payments at different points in time. We implement a difference-in-difference estimator to control for all time-invariant heterogeneity and show that our results are robust to the inclusion of time varying characteristics likely correlated with child birth. We find that becoming a mother increases time discounting especially in the first two years after childbirth and in particular for those women without a spouse at home. Having additional children does not have an effect and the effect for men seems to go in the opposite direction. These heterogeneous effects suggest that child rearing may affect time discounting due to generated stress or not fully anticipated spending needs.

Dahlak coral d18O record (DGII) from the southern Red Sea

Coral palaeoclimatic studies are under way at many sites throughout the wet tropics. However, arid environments have received less attention. Here we report a high-resolution, 63 yr record of coral d18O and d13C extracted from a Porites colony from the Dahlak Archipelago, off the Eritrean coast, in the southern Red Sea. The annual cycles of the coral d18O and d13C are inversely related while their inter-annual variations show a strong positive correlation, with similar inter-decadal trends. Inter-annual variations in coral d18O show a relatively weak correlation with the southern Red Sea SST, but are strongly correlated with the Indian Ocean SST, especially on the decadal time-scale. The range of the inter-annual variations in the coral d18O is high compared to changes in local SST, due to the amplifying effect of simultaneous changes in water isotopic composition. Due to this amplification of the climate signal the coral provides a better indication of regional oceangraphic behaviour than the local SST record. The norrtheast monsoon signal in the coral d18O dominates the mean annual signal and shows the best correlation with the instrumental data sets. It appears that variations in the coral d18O are controlled mainly by variations in the intensity of surface water influx from the Indian Ocean to the Red Sea during the winter northeast monsoon. Of particular significance is that the decadal time-scale variations in the coral skeletal d18O are closely correlated with both the Indian Ocean SST and with variations in the Pacific-based Southern Oscillation index. That is, isotopically light coral skeleton, indicating strong NE monsoon Red Sea inflow, correlates with periods of high Indian Ocean SST and with predominantly negative (El Nino) phases of the Southern Oscillation. The simultaneous nature of inter-decadal changes in Asian monsoon and ENSO behaviour suggest pan-Indo-Pacific tropical climate reorganisation and evolution.

(Table 1) Chemical and isotopic composition of pore fluids in cores TGC-1 and TGC-6

The role of sediment diagenesis in the marine cycles of Li and B is poorly understood. Because Li and B are easily mobilized during burial and are consumed in authigenic clay mineral formation, their abundance in marine pore waters varies considerably. Exchange with the overlying ocean through diffusive fluxes should thus be common. Nevertheless, only a minor Li sink associated with the low-temperature alteration of volcanic ash has been observed. We describe a low-temperature diagenetic environment in the Black Sea dominated by the alteration of detrital plagioclase feldspars. Fluids expelled from the Odessa mud volcano in the Sorokin Trough originate from shallow (~100-400 m deep) sediments which are poor in volcanic materials but rich in anorthite. These fluids are depleted in Na+, K+, Li+, B, and 18O and enriched in Ca2+ and Sr2+, indicating that anorthite is dissolving and authigenic clays are forming. Using a simple chemical model, we calculate the pH and the partial pressure of CO2 (PCO2) in fluids associated with this alteration process. Our results show that the pH of these fluids is up to 1.5 pH units lower than in most deep marine sediments and that PCO2 levels are up to several hundred times higher than in the atmosphere. These conditions are similar to those which favor the weathering of silicate minerals in subaerial soil environments. We propose that in Black Sea sediments enhanced organic matter preservation favors CO2 production through methanogenesis and results in a low pore water pH, compared to most deep sea sediments. As a result, silicate mineral weathering, which is a sluggish process in most marine diagenetic environments, proceeds rapidly in Black Sea sediments. There is a potential for organic matter-rich continental shelf environments to host this type of diagenesis. Should such environments be widespread, this new Li and B sink could help balance the marine Li and Li isotope budgets but would imply an apparent imbalance in the B cycle.