Leak identification in saturated unsteady flow via a Cauchy problem

This work is an initial study of a numerical method for identifying multiple leak zones in saturated unsteady flow. Using the conventional saturated groundwater flow equation, the leak identification problem is modelled as a Cauchy problem for the heat equation and the aim is to find the regions on the boundary of the solution domain where the solution vanishes, since leak zones correspond to null pressure values. This problem is ill-posed and to reconstruct the solution in a stable way, we therefore modify and employ an iterative regularizing method proposed in [1] and [2]. In this method, mixed well-posed problems obtained by changing the boundary conditions are solved for the heat operator as well as for its adjoint, to get a sequence of approximations to the original Cauchy problem. The mixed problems are solved using a Finite element method (FEM), and the numerical results indicate that the leak zones can be identified with the proposed method.

Dynamic analysis of submerged microscale plates:the effects of acoustic radiation and viscous dissipation

The aim of this paper is to study the dynamic characteristics of micromechanical rectangular plates used as sensing elements in a viscous compressible fluid. A novel modelling procedure for the plate- fluid interaction problem is developed on the basis of linearized Navier-Stokes equations and noslip conditions. Analytical expression for the fluidloading impedance is obtained using a double Fourier transform approach. This modelling work provides us an analytical means to study the effects of inertial loading, acoustic radiation and viscous dissipation of the fluid acting on the vibration of microplates. The numerical simulation is conducted on microplates with different boundary conditions and fluids with different viscosities. The simulation results reveal that the acoustic radiation dominates the damping mechanism of the submerged microplates. It is also proved that microplates offer better sensitivities (Q-factors) than the conventional beam type microcantilevers beingmass sensing platforms in a viscous fluid environment. The frequency response features of microplates under highly viscous fluid loading are studied using the present model. The dynamics of the microplates with all edges clamped are less influenced by the highly viscous dissipation of the fluid than the microplates with other types of boundary conditions.

Universal profile of the vortex condensate in two-dimensional turbulence

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate—a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Weak Langmuir optical turbulence in a fiber cavity

We study theoretically and numerically the dynamics of a passive optical fiber ring cavity pumped by a highly incoherent wave: an incoherently injected fiber laser. The theoretical analysis reveals that the turbulent dynamics of the cavity is dominated by the Raman effect. The forced-dissipative nature of the fiber cavity is responsible for a large diversity of turbulent behaviors: Aside from nonequilibrium statistical stationary states, we report the formation of a periodic pattern of spectral incoherent solitons, or the formation of different types of spectral singularities, e.g., dispersive shock waves and incoherent spectral collapse behaviors. We derive a mean-field kinetic equation that describes in detail the different turbulent regimes of the cavity and whose structure is formally analogous to the weak Langmuir turbulence kinetic equation in the presence of forcing and damping. A quantitative agreement is obtained between the simulations of the nonlinear Schrödinger equation with cavity boundary conditions and those of the mean-field kinetic equation and the corresponding singular integrodifferential reduction, without using adjustable parameters. We discuss the possible realization of a fiber cavity experimental setup in which the theoretical predictions can be observed and studied.

Relationship fading in business-to-consumer context

The objective of this thesis is to develop a better understanding of the relationship fading phenomenon in business-to-consumer context. Fading relates to a gradual decline in consumer’s willingness to continue a relationship with a company. Therefore, understanding the fading process may help to elucidate the ‘unexplained’ relationship dissolution and customer defection. Led by an assumption that a relationship between a consumer and a brand is like the one between individuals, the thesis proposes that the trajectory of relationship fading reflects the disaffection processes similar to the ones suggested in marital and romantic relationships between individuals. The approach taken to answering this research question is a multi-study approach. This type of approach allows addressing each individual research question independently, using the most appropriate research methods. As a result, the thesis comprises three adjacent studies. All three studies are linked and together contribute to a better understanding of the relationship fading process, which is the main topic of the thesis. Based on the results from the first study, a set of boundary conditions of relationship fading is identified. The results of the second study suggest that predictors of relationship fading stage can be uncovered. Thirdly, different restoration techniques are explored, aiming to describe their effectiveness in various relationship fading stages. Individual objectives of the three studies are accomplished. All three studies contribute to achieving the overall objective of the thesis, namely to developing a better understanding of the phenomenon of relationship fading.

Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Development of an enhanced hydro-geochemical model to address mercury-speciation fate and transport in aquatic environments

An awareness of mercury (Hg) contamination in various aquatic environments around the world has increased over the past decade, mostly due to its ability to concentrate in the biota. Because the presence and distribution of Hg in aquatic systems depend on many factors (e.g., pe, pH, salinity, temperature, organic and inorganic ligands, sorbents, etc.), it is crucial to understand its fate and transport in the presence of complexing constituents and natural sorbents, under those different factors. An improved understanding of the subject will support the selection of monitoring, remediation, and restoration technologies. The coupling of equilibrium chemical reactions with transport processes in the model PHREEQC offers an advantage in simulating and predicting the fate and transport of aqueous chemical species of interest. Thus, a great variety of reactive transport problems could be addressed in aquatic systems with boundary conditions of specific interest. Nevertheless, PHREEQC lacks a comprehensive thermodynamic database for Hg. Therefore, in order to use PHREEQC to address the fate and transport of Hg in aquatic environments, it is necessary to expand its thermodynamic database, confirm it and then evaluate it in applications where potential exists for its calibration and continued validation. The objectives of this study were twofold: 1) to develop, expand, and confirm the Hg database of the hydrogeochemical PHREEQC to enhance its capability to simulate the fate of Hg species in the presence of complexing constituents and natural sorbents under different conditions of pH, redox, salinity and temperature; and 2) to apply and evaluate the new database in flow and transport scenarios, at two field test beds: Oak Ridge Reservation, Oak Ridge, TN and Everglades National Park, FL, where Hg is present and is of much concern. Overall, this research enhanced the capability of the PHREEQC model to simulate the coupling of the Hg reactions in transport conditions. It also demonstrated its usefulness when applied to field situations.

What does board capital really bring to the table? Exploring the effect of directors' human and social capital on effective governance during international expansion

What constitutes effective corporate governance? Which director characteristics render boards effective at positively influencing firm-level performance outcomes? This dissertation examines these questions by taking a multilevel, multidisciplinary approach to corporate governance. I explore the individual-, team-, and firm- level factors that enable directors to serve effectively as strategic resources during international expansion. I argue that directors' international experience improves their ability to serve as effective strategic consultants and resource providers to firms during the complex internationalization process. However, unlike prior research, which tends to assume that directors with the potential to provide important resources uniformly do so, I acknowledge contextual factors (i.e. board cohesiveness, strategic relevance of directors' experience) that affect their propensity to actually influence outcomes. I explore these issues in three essays: one review essay and two empirical essays.^ In the first empirical essay, I integrate resource dependence theory with insights from social-psychological research to explore the influence of board capital on firms' cross-border M&A performance. Using a sample of cross-border M&As completed by S&P 500 firms from 2004-2009, I find evidence that directors' depth of international experience is associated with superior pre-deal outcomes. This suggests that boards' deep, market-specific knowledge is valuable during the target selection phase. I further find that directors' breadth of international experience is associated with superior post-deal performance, suggesting that these directors' global mindset helps firms in the post-M&A integration phase. I also find that these relationships are positively moderated by board cohesiveness, measured by boards' internal social ties.^ In the second empirical essay, I explore the boundary conditions of international board capital by examining how the characteristics of firms' internationalization strategy moderate the relationship between board capital and firm performance. Using a panel of 377 S&P 500 firms observed from 2004-2011, I find that boards' depth of international experience and social capital are more important during early stages of internationalization, when firms tend to lack market knowledge and legitimacy in the host markets. On the other hand, I find that breadth of international experience has a stronger relationship with performance when firms' have higher scope of internationalization, when information-processing demands are higher.^

An experimental study of the effects of double-diffusive convention processes during the solification of binary alloys

Experiments were conducted to show the effects of thermal and geometric boundary conditions on the liquid pool of a binary alloy system which is undergoing phase change, solidification. Transparent analogue solutions were selected for study and experimental apparatus were designed and built. Thermal distribution and concentration data were collected and analysed for the melt pool of various selected geometries and boundary conditions of the systems under study. The data indicate-that characteristic flows develop for both Hypereutectic and Hypoeutectic concentration levels and that the development of macrosegregation and microsegregation defects in continuous casting materials can be minimised by the adjustment of the process variables.

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Engineering Analysis in Imprecise Geometric Models

Engineering analysis in geometric models has been the main if not the only credible/reasonable tool used by engineers and scientists to resolve physical boundaries problems. New high speed computers have facilitated the accuracy and validation of the expected results. In practice, an engineering analysis is composed of two parts; the design of the model and the analysis of the geometry with the boundary conditions and constraints imposed on it. Numerical methods are used to resolve a large number of physical boundary problems independent of the model geometry. The time expended due to the computational process are related to the imposed boundary conditions and the well conformed geometry. Any geometric model that contains gaps or open lines is considered an imperfect geometry model and major commercial solver packages are incapable of handling such inputs. Others packages apply different kinds of methods to resolve this problems like patching or zippering; but the final resolved geometry may be different from the original geometry, and the changes may be unacceptable. The study proposed in this dissertation is based on a new technique to process models with geometrical imperfection without the necessity to repair or change the original geometry. An algorithm is presented that is able to analyze the imperfect geometric model with the imposed boundary conditions using a meshfree method and a distance field approximation to the boundaries. Experiments are proposed to analyze the convergence of the algorithm in imperfect models geometries and will be compared with the same models but with perfect geometries. Plotting results will be presented for further analysis and conclusions of the algorithm convergence

The international legal thought of Carl Schmitt : towards a critique of the contemporary international order

The aim of the thesis is to develop a critique of current liberal conceptualizations of international order. In order to conduct this critique, this thesis revisits the arguments first put forth by the German legal and political theorist Carl Schmitt. Schmitt conceptualizes a tripartite unity between law, order, and place. This unity, established at the constituent moment of land-appropriation, forms a concrete nomos, which subsequently creates the contours of the legal and political order. The establishment of the concrete order is necessarily the construction of a territorial boundary that designates an inside and an outside of the polity. By speaking of a nomos of the earth, Schmitt globalized this understanding of concrete order by looking at the various historical developments that created a "line" between the concrete applicability of interstate norms and a region where the exceptional situation prevails. The critique presented in this thesis is concerned with the lack of concrete boundary conditions within the current international legal order. It is argued that this lack of a well-defined boundary condition is what results in extreme forms of violence that were traditionally bracketed.

Global compilation of benthic data sets I

Approaches to quantify the organic carbon accumulation on a global scale generally do not consider the small-scale variability of sedimentary and oceanographic boundary conditions along continental margins. In this study, we present a new approach to regionalize the total organic carbon (TOC) content in surface sediments (<5 cm sediment depth). It is based on a compilation of more than 5500 single measurements from various sources. Global TOC distribution was determined by the application of a combined qualitative and quantitative-geostatistical method. Overall, 33 benthic TOC-based provinces were defined and used to process the global distribution pattern of the TOC content in surface sediments in a 1°x1° grid resolution. Regional dependencies of data points within each single province are expressed by modeled semi-variograms. Measured and estimated TOC values show good correlation, emphasizing the reasonable applicability of the method. The accumulation of organic carbon in marine surface sediments is a key parameter in the control of mineralization processes and the material exchange between the sediment and the ocean water. Our approach will help to improve global budgets of nutrient and carbon cycles.

Helicopter-borne sea ice thickness measurements in the Storfjord, Spitsbergen from flight HEM_STJ06_01

Results from electromagnetic induction surveys of sea-ice thickness in Storfjorden, Svalbard, reveal large interannual ice-thickness variations in a region which is typically characterized by a reoccurring polynya. The surveys were performed in March 2003, May 2006 and March 2007 with helicopter- and ship-based sensors. The thickness distributions are influenced by sea-ice and atmospheric boundary conditions 2 months prior to the surveys, which are assessed with synthetic aperture radar (SAR) images, regional QuikSCAT backscatter maps and wind information from the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis dataset. Locally formed thin ice from the Storfjorden polynya was frequently observed in 2003 and 2007 (mean thickness 0.55 and 0.37 m, respectively) because these years were characterized by prevailing northeasterly winds. In contrast, the entire fjord was covered with thick external sea ice in 2006 (mean thickness 2.21 m), when ice from the Barents Sea was driven into the fjord by predominantly southerly winds. The modal thickness of this external ice in 2006 increased from 1.2 m in the northern fjord to 2.4 m in the southern fjord, indicating stronger deformation in the southern part. This dynamically thickened ice was even thicker than multi-year ice advected from the central Arctic Ocean in 2003 (mean thickness 1.83 m). The thermodynamic ice thickness of fast ice as boundary condition is investigated with a one-dimensional sea-ice growth model (1DICE) forced with meteorological data from the weather station at the island of Hopen, southeast of Storfjorden. The model results are in good agreement with the modal thicknesses of fast-ice measurements in all years.

Individual foraminifera variability from the western and eastern equatorial Pacific during the Late Holocene and Last Glacial Maximum

El Niño-Southern Oscillation (ENSO) is a major source of global interannual variability, but its response to climate change is uncertain. Paleoclimate records from the Last Glacial Maximum (LGM) provide insight into ENSO behavior when global boundary conditions (ice sheet extent, atmospheric partial pressure of CO2) were different from those today. In this work, we reconstruct LGM temperature variability at equatorial Pacific sites using measurements of individual planktonic foraminifera shells. A deep equatorial thermocline altered the dynamics in the eastern equatorial cold tongue, resulting in reduced ENSO variability during the LGM compared to the Late Holocene. These results suggest that ENSO was not tied directly to the east-west temperature gradient, as previously suggested. Rather, the thermocline of the eastern equatorial Pacific played a decisive role in the ENSO response to LGM climate.