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.

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.

Lattice Boltzmann Method for Flow and Heat Transfer in Microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Use of active power filter to reduce the effects of harmonics in solid oxide fuel cells

The Solid Oxide Fuel Cell (SOFC) is a class of fuel cells that is capable of generating very high levels of power at high temperatures. SOFCs are used for stationary power generation and as Combined Heat and Power (CHP) systems. In spite of all the beneficial features of the SOFC, the propagation of ripple currents, due to nonlinear loads, is a challenging problem, as it interferes with the physical operation of the fuel cell. The purpose of this thesis is to identify the cause of ripples and attempt to eliminate or reduce the ripple propagation through the use of Active Power Filters (APF). To this end, a systematic approach to modeling the fuel cell to account for its nonlinear behavior in the presence of current ripples is presented. A model of a small fuel cell power system which consists of a fuel cell, a DC-DC converter, a single-phase inverter and a nonlinear load is developed in MATLAB/Simulink environment. The extent of ripple propagation, due to variations in load magnitude and frequency, are identified using frequency spectrum analysis. In order to reduce the effects of ripple propagation, an APF is modeled to remove ripples from the DC fuel cell current. The emphasis of this thesis is based on the idea that small fuel cell systems cannot implement large passive filters to cancel the effects of ripple propagation and hence, the compact APF topology effectively protects the fuel cell from propagating ripples and improves its electrical performance.

Dispersion and energy relations in periodic chains and grids

In this study wave propagation, dispersion relations, and energy relations for linear elastic periodic systems are analyzed. In particular, the dispersion relations for monoatomic chain of infinite dimension are obtained analytically by writing the Block-type wave equation for a unit cell in order to capture the dynamic behavior for chains under prescribed vibration. By comparing the discretized model (mass-spring chain) with the solid bar system, the nonlinearity of the dispersion relation for chain indicates that the periodic lattice is dispersive in contrast to the continuous rod, which is non dispersive. Further investigations have been performed considering one-dimensional diatomic linear elastic mass-spring chain. The dispersion relations, energy velocity, and group velocity have been derived. At certain range of frequencies harmonic plane waves do not propagate in contrast with monoatomic chain. Also, since the diatomic chain considered is a linear elastic chain, both of the energy velocity and the group velocity are identical. As long as the linear elastic condition is considered the results show zero flux condition without residual energy. In addition, this paper shows that the diatomic chain dispersion relations are independent on the unit cell scheme. Finally, an extension for the study covers the dispersion and energy relations for 2D- grid system. The 2x2 grid system show a periodicity of the dispersion surface in the wavenumber domain. In addition, the symmetry of the surface can be exploited to identify an Irreducible Brillouin Zone (IBZ). Compact representations of the dispersion properties of multidimensional periodic systems are obtained by plotting frequency as the wave vector’s components vary along the boundary of the IBZ, which leads to a widely accepted and effective visualization of bandgaps and overall dispersion properties.

Pore water and solid-phase measurements on sediment cores from the Black Sea

The surface sediments in the Black Sea are underlain by extensive deposits of iron (Fe) oxide-rich lake sediments that were deposited prior to the inflow of marine Mediterranean Sea waters ca. 9000 years ago. The subsequent downward diffusion of marine sulfate into the methane-bearing lake sediments has led to a multitude of diagenetic reactions in the sulfate-methane transition zone (SMTZ), including anaerobic oxidation of methane (AOM) with sulfate. While the sedimentary cycles of sulfur (S), methane and Fe in the SMTZ have been extensively studied, relatively little is known about the diagenetic alterations of the sediment record occurring below the SMTZ. Here we combine detailed geochemical analyses of the sediment and pore water with multicomponent diagenetic modeling to study the diagenetic alterations below the SMTZ at two sites in the western Black Sea. We focus on the dynamics of Fe, S and phosphorus (P) and demonstrate that diagenesis has strongly overprinted the sedimentary burial records of these elements. Our results show that sulfate-mediated AOM substantially enhances the downward diffusive flux of sulfide into the deep limnic deposits. During this downward sulfidization, Fe oxides, Fe carbonates and Fe phosphates (e.g. vivianite) are converted to sulfide phases, leading to an enrichment in solid phase S and the release of phosphate to the pore water. Below the sulfidization front, high concentrations of dissolved ferrous Fe (Fe2+) lead to sequestration of downward diffusing phosphate as authigenic vivianite, resulting in a transient accumulation of total P directly below the sulfidization front. Our model results further demonstrate that downward migrating sulfide becomes partly re-oxidized to sulfate due to reactions with oxidized Fe minerals, fueling a cryptic S cycle and thus stimulating slow rates of sulfate-driven AOM (~ 1-100 pmol/cm**3/d) in the sulfate-depleted limnic deposits. However, this process is unlikely to explain the observed release of dissolved Fe2+ below the SMTZ. Instead, we suggest that besides organoclastic Fe oxide reduction, AOM coupled to the reduction of Fe oxides may also provide a possible mechanism for the high concentrations of Fe2+ in the pore water at depth. Our results reveal that methane plays a key role in the diagenetic alterations of Fe, S and P records in Black Sea sediments. The downward sulfidization into the limnic deposits is enhanced through sulfate-driven AOM with sulfate and AOM with Fe oxides may provide a deep source of dissolved Fe2+ that drives the sequestration of P in vivianite below the sulfidization front.

Numerical study of the enlarged O(5) symmetry of the 3D antiferromagnetic RP^(2) spin model

We investigate by means of Monte Carlo simulation and finite-size scaling analysis the critical properties of the three dimensional O (5) non-linear σ model and of the antiferromagnetic RP^(2) model, both of them regularized on a lattice. High accuracy estimates are obtained for the critical exponents, universal dimensionless quantities and critical couplings. It is concluded that both models belong to the same universality class, provided that rather non-standard identifications are made for the momentum-space propagator of the RP^(2) model. We have also investigated the phase diagram of the RP^(2) model extended by a second-neighbor interaction. A rich phase diagram is found, where most of the phase transitions are of the first order.

Phase diagram of the bosonic double-exchange model

The phase diagram of the simplest approximation to double-exchange systems, the bosonic double-exchange model with antiferromagnetic (AFM) superexchange coupling, is fully worked out by means of Monte Carlo simulations, large-N expansions, and variational mean-field calculations. We find a rich phase diagram, with no first-order phase transitions. The most surprising finding is the existence of a segmentlike ordered phase at low temperature for intermediate AFM coupling which cannot be detected in neutron-scattering experiments. This is signaled by a maximum (a cusp) in the specific heat. Below the phase transition, only short-range ordering would be found in neutron scattering. Researchers looking for a quantum critical point in manganites should be wary of this possibility. Finite-size scaling estimates of critical exponents are presented, although large scaling corrections are present in the reachable lattice sizes.

Monte Carlo determination of the phase diagram of the double-exchange model

We study the phase diagram of the double exchange model, with antiferromagnetic interactions, in a cubic lattice both at zero and finite temperature. There is a rich variety of magnetic phases, combined with regions where phase separation takes place. We identify phases, intrinsic to the cubic lattice, which are stable for realistic values of the interactions and dopings. Some of these phases break chiral symmetry, leading to unusual features.

Lattice approach to the dynamics of the DPSK-encoded soliton trains

We study the dynamical properties of the RZ-DPSK encoded sequences, focusing on the instabilities in the soliton train leading to the distortions of the information transmitted. The problem is reformulated within the framework of complex Toda chain model which allows one to carry out the simplified description of the optical soliton dynamics. We elucidate how the bit composition of the pattern affects the initial (linear) stage of the train dynamics and explain the general mechanisms of the appearance of unstable collective soliton modes. Then we discuss the nonlinear regime using asymptotic properties of the pulse stream at large propagation distances and analyze the dynamical behavior of the train classifying different scenarios for the pattern instabilities. Both approaches are based on the machinery of Hermitian and non-Hermitian lattice analysis. © 2010 IEEE.

Organometallic derivatives of cyclotriphosphazene as precursors of nanostructured metallic materials: a new solid state method

The cyclic phosphazene trimers [N3P3(OC6H5)5OC5H4N·Ti(Cp)2Cl][PF6] (3), [N3P3(OC6H4CH2CN·Ti(Cp)2Cl)6][PF6]6 (4), [N3P3(OC6H4-But)5(OC6H4CH2CN·Ti(Cp)2Cl)][PF6] (5), [N3P3(OC6H5)5C6H4CH2CN·Ru(Cp)(PPh3)2][PF6] (6), [N3P3(OC6H5)5C6H4CH2CN·Fe(Cp)(dppe)][PF6] (7) and N3P3(OC6H5)5OC5H4N·W(CO)5 (8) were prepared and characterized. As a model, the simple compounds [HOC5H5N·Ti(Cp)2Cl]PF6 (1) and [HOC6H4CH2CN·Ti(Cp)2Cl]PF6 (2) were also prepared and characterized. Pyrolysis of the organometallic cyclic trimers in air yields metallic nanostructured materials, which according to transmission and scanning electron microscopy (TEM/SEM), energy-dispersive X-ray microanalysis (EDX), and IR data, can be formulated as either a metal oxide, metal pyrophosphate or a mixture in some cases, depending on the nature and quantity of the metal, characteristics of the organic spacer and the auxiliary substituent attached to the phosphorus cycle. Atomic force microscopy (AFM) data indicate the formation of small island and striate nanostructures. A plausible formation mechanism which involves the formation of a cyclomatrix is proposed, and the pyrolysis of the organometallic cyclic phosphazene polymer as a new and general method for obtaining metallic nanostructured materials is discussed.

[N]pT ensemble and finite-size-scaling study of the critical isostructural transition in the generalized exponential model of index 4.

First-order transitions of system where both lattice site occupancy and lattice spacing fluctuate, such as cluster crystals, cannot be efficiently studied by traditional simulation methods, which necessarily fix one of these two degrees of freedom. The difficulty, however, can be surmounted by the generalized [N]pT ensemble [J. Chem. Phys. 136, 214106 (2012)]. Here we show that histogram reweighting and the [N]pT ensemble can be used to study an isostructural transition between cluster crystals of different occupancy in the generalized exponential model of index 4 (GEM-4). Extending this scheme to finite-size scaling studies also allows us to accurately determine the critical point parameters and to verify that it belongs to the Ising universality class.