Multiple-scale analysis of transport phenomena in porous media with biofilms

This dissertation examines transport phenomena within porous media colonized by biofilms. These sessile communities of microbes can develop within subsurface soils or rocks, or the riverine hyporheic zone and can induce substantial modification to mass and momentum transport dynamics. Biofilms also extensively alter the chemical speciation within freshwater ecosystems, leading to the biodegradation of many pollutants. Consequently, such systems have received a considerable amount of attention from the ecological engineering point of view. Yet, research has been severely limited by our incapacity to (1) directly observe the microorganisms within real opaque porous structures and (2) assess for the complex multiple-scale behavior of the phenomena. This thesis presents theoretical and experimental breakthroughs that can be used to overcome these two difficulties. An innovative strategy, based on X-ray computed microtomography, is devised to obtain three-dimensional images of the spatial distribution of biofilms within porous structures. This topological information can be used to study the response of the biological entity to various physical, chemical and biological parameters at the pore-scale. In addition, these images are obtained from relatively large volumes and, hence, can also be used to determine the influence of biofilms on the solute transport on a larger scale. For this purpose, the boundary-value-problems that describe the pore-scale mass transport are volume averaged to obtain homogenized Darcy-scale equations. Various models, along with their domains of validity, are presented in the cases of passive and reactive transport. This thesis uses the volume averaging technique, in conjunction with spatial moments analyses, to provide a comprehensive macrotransport theory as well as a thorough study of the relationship between the different models, especially between the two-equation and one-equation models. A non-standard average plus perturbation decomposition is also presented to obtain a one-equation model in the case of multiphasic transport with linear reaction rates. Eventually, the connection between the three-dimensional images and the theoretical multiple-scale analysis is established. This thesis also briefly illustrates how the permeability can be calculated numerically by solving the so-called closure problems from the three-dimensional X-ray images

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Modelling of transport in highly heterogeneous porous media, with application to the flushing of waste.

This thesis is concerned with predicting the fate of contaminants using tracer and contaminant flushing datasets in otherwise poorly characterised heterogeneous media. A deductive approach towards constraining prediction uncertainty is adopted, by narrowing a 'pool' of plausible process models and associated parameter sets. Mathematical comparison of simple transport models is used to allow enhanced diagnosis. Transport models are put into a framework. Then they are compared using commonly used measures of breakthrough curves (least squares fitting, method of moments and late-time concentration gradients). Experimental data and models for transport in waste are then reviewed using this framework. Two new tracer datasets, at laboratory and lysimeter scales, are analysed and modelled. Strong evidence is shown of 'dual-porosity' diffusive exchange effects being an important component in transport in municipal solid waste. However, it is not possible to discriminate between contributions to dispersion through advective and diffusive effects. Approaches to enhance the diagnostic capability of future waste experiments are developed. One possible 'entrant' to the 'pool' of models is examined: a stochastic channel network model. Histograms of nodes and average heads are evaluated at different distances from a range of boundary conditions for large ensembles revealing key insights into network flow behaviour near different types of boundary. Key properties of the network are related to typical continuum analyses, including dimensionality of flow and genesis of apparent 'skins' near boundaries. 'Classical' percolation networks (with zero spatial correlation) are also analysed, revealing new insights into their network properties within finite boundaries. In summary, progress towards predicting the fate of contaminants in highly heterogeneous systems is made through a thorough delineation of the behaviour of simple models in tandem with adoption of a fertile approach to adding new conceptual models. The increased rigorousness of using multiple diagnostic criteria in conjunction with adopting a philosophy of working with multiple working hypotheses is commended as a methodology that provides a sound basis from which to employ multiple-model uncertainty analysis for predictive purposes in the future

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity

The Fifteenth Marcel Grossmann Meeting

The three volumes of the proceedings of MG15 give a broad view of all aspects of gravitational physics and astrophysics, from mathematical issues to recent observations and experiments. The scientific program of the meeting included 40 morning plenary talks over 6 days, 5 evening popular talks and nearly 100 parallel sessions on 71 topics spread over 4 afternoons. These proceedings are a representative sample of the very many oral and poster presentations made at the meeting.Part A contains plenary and review articles and the contributions from some parallel sessions, while Parts B and C consist of those from the remaining parallel sessions. The contents range from the mathematical foundations of classical and quantum gravitational theories including recent developments in string theory, to precision tests of general relativity including progress towards the detection of gravitational waves, and from supernova cosmology to relativistic astrophysics, including topics such as gamma ray bursts, black hole physics both in our galaxy and in active galactic nuclei in other galaxies, and neutron star, pulsar and white dwarf astrophysics. Parallel sessions touch on dark matter, neutrinos, X-ray sources, astrophysical black holes, neutron stars, white dwarfs, binary systems, radiative transfer, accretion disks, quasars, gamma ray bursts, supernovas, alternative gravitational theories, perturbations of collapsed objects, analog models, black hole thermodynamics, numerical relativity, gravitational lensing, large scale structure, observational cosmology, early universe models and cosmic microwave background anisotropies, inhomogeneous cosmology, inflation, global structure, singularities, chaos, Einstein-Maxwell systems, wormholes, exact solutions of Einstein's equations, gravitational waves, gravitational wave detectors and data analysis, precision gravitational measurements, quantum gravity and loop quantum gravity, quantum cosmology, strings and branes, self-gravitating systems, gamma ray astronomy, cosmic rays and the history of general relativity