Three-dimensional geoelectric modelling with optimal work/accuracy rate using an adaptive wavelet algorithm

Despite the ever-increasing power of modern computers, realistic modelling of complex 3-D earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modelling approaches includes either finite difference or non-adaptive finite element algorithms and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behaviour of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modelled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet-based approach that is applicable to a large range of problems, also including nonlinear problems. In comparison with earlier applications of adaptive solvers to geophysical problems we employ here a new adaptive scheme whose core ingredients arose from a rigorous analysis of the overall asymptotically optimal computational complexity, including in particular, an optimal work/accuracy rate. Our adaptive wavelet algorithm offers several attractive features: (i) for a given subsurface model, it allows the forward modelling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient and (iii) the modelling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving 3-D geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best-fitting subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectric modelling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with high spatial variability of electrical conductivities. The linear dependence of the modelling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementatio

Trends in marine dissolved oxygen: Implications for ocean circulation changes and the carbon budget

Recent measurements and model studies have consistently identified a decreasing trend in the concentration of dissolved O2 in the ocean over the last several decades. This trend has important implications for our understanding of anthropogenic climate change. First, the observed oceanic oxygen changes may be a signal of the beginning of a reorganization of large-scale ocean circulation in response to anthropogenic radiative forcing. Second, the repartitioning of oxygen between the ocean and the atmosphere requires a revision of the current atmospheric carbon budget and the estimates of the terrestrial and oceanic carbon sinks as calculated by the Intergovernmental Panel on Climate Change (IPCC) from measurements of atmospheric O2/N2

An Infinite Swapping Approach to the Rare-Event Sampling Problem

We describe a new approach to the rare-event Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and thus more easily sampled than their original, potentially sparse counterparts. After discussing the formal outline of the approach and devising techniques for its practical implementation, we illustrate the utility of the technique with a series of numerical applications to Lennard-Jones clusters of varying complexity and rare-event character.Comment: 24 pages, 16 figure

Hybrid-learning for social design

Underlying causes of conflict, inequity, and injustice remain deeply entrenched in the lives of people ranging from impoverished villages to overpopulated megalopolises. To help address these complex issues, social design brings together designers from varying disciplines to address the needs of the community. While universities across the world recognize the need to introduce social design pedagogy into their curriculum, many programs remain confined within Western post-graduate education. In response, two multidisciplinary professors initiated a team-taught \u27Design for Social Change\u27 course in an undergraduate design program in Dubai, UAE. Open to students across disciplines, the course followed a hybrid-learning approach to planning, conducting, and evaluating learning activities. The methodology empowered students to determine their project interest, cooperatively build research, and value their diverse skills. This paper introduces the notion of hybrid-learning, collabor-active team-teaching in an interdisciplinary classroom, and applies the methodology to a social design course in the MENA region. This paper has been presented as part of the Tasmeem Exploration Platform during Tasmeem Conference, Doha, 2013

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Photochemistry of Furyl- and Thienyldiazomethanes: Spectroscopic Characterization of Triplet 3-Thienylcarbene

Photolysis (λ \u3e 543 nm) of 3-thienyldiazomethane (1), matrix isolated in Ar or N2 at 10 K, yields triplet 3-thienylcarbene (13) and α-thial-methylenecyclopropene (9). Carbene 13 was characterized by IR, UV/vis, and EPR spectroscopy. The conformational isomers of 3-thienylcarbene (s-E and s-Z) exhibit an unusually large difference in zero-field splitting parameters in the triplet EPR spectrum (|D/hc| = 0.508 cm–1, |E/hc| = 0.0554 cm–1; |D/hc| = 0.579 cm–1, |E/hc| = 0.0315 cm–1). Natural Bond Orbital (NBO) calculations reveal substantially differing spin densities in the 3-thienyl ring at the positions adjacent to the carbene center, which is one factor contributing to the large difference in D values. NBO calculations also reveal a stabilizing interaction between the sp orbital of the carbene carbon in the s-Z rotamer of 13 and the antibonding σ orbital between sulfur and the neighboring carbon—an interaction that is not observed in the s-E rotamer of 13. In contrast to the EPR spectra, the electronic absorption spectra of the rotamers of triplet 3-thienylcarbene (13) are indistinguishable under our experimental conditions. The carbene exhibits a weak electronic absorption in the visible spectrum (λmax = 467 nm) that is characteristic of triplet arylcarbenes. Although studies of 2-thienyldiazomethane (2), 3-furyldiazomethane (3), or 2-furyldiazomethane (4) provided further insight into the photochemical interconversions among C5H4S or C5H4O isomers, these studies did not lead to the spectroscopic detection of the corresponding triplet carbenes (2-thienylcarbene (11), 3-furylcarbene (23), or 2-furylcarbene (22), respectively)

Scalable transactions in the cloud: partitioning revisited

Lecture Notes in Computer Science, 6427Cloud computing is becoming one of the most used paradigms to deploy highly available and scalable systems. These systems usually demand the management of huge amounts of data, which cannot be solved with traditional nor replicated database systems as we know them. Recent solutions store data in special key-value structures, in an approach that commonly lacks the consistency provided by transactional guarantees, as it is traded for high scalability and availability. In order to ensure consistent access to the information, the use of transactions is required. However, it is well-known that traditional replication protocols do not scale well for a cloud environment. Here we take a look at current proposals to deploy transactional systems in the cloud and we propose a new system aiming at being a step forward in achieving this goal. We proceed to focus on data partitioning and describe the key role it plays in achieving high scalability.This work has been partially supported by the Spanish Government under grant TIN2009-14460-C03-02 and by the Spanish MEC under grant BES-2007-17362 and by project ReD Resilient Database Clusters (PDTC/EIA-EIA/109044/2008)