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).

An irregular lattice model to simulate crack paths in bonded granular assemblies

Peer reviewed

An irregular lattice model to simulate crack paths in bonded granular assemblies

Peer reviewed

Galois lattice dynamics

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

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.

Lattice Engineering of III-Nitride Heterostructures and Their Applications

III-Nitride materials have recently become a promising candidate for superior applications over the current technologies. However, certain issues such as lack of native substrates, and high defect density have to be overcome for further development of III-Nitride technology. This work presents research on lattice engineering of III-Nitride materials, and the structural, optical, and electrical properties of its alloys, in order to approach the ideal material for various applications. We demonstrated the non-destructive and quantitative characterization of composition modulated nanostructure in InAlN thin films with X-ray diffraction. We found the development of the nanostructure depends on growth temperature, and the composition modulation has impacts on carrier recombination dynamics. We also showed that the controlled relaxation of a very thin AlN buffer (20 ~ 30 nm) or a graded composition InGaN buffer can significantly reduce the defect density of a subsequent epitaxial layer. Finally, we synthesized an InAlGaN thin films and a multi-quantum-well structure. Significant emission enhancement in the UVB range (280 – 320 nm) was observed compared to AlGaN thin films. The nature of the enhancement was investigated experimentally and numerically, suggesting carrier confinement in the In localization centers.

Physics of Hexagonal Limit-Periodic Phases: Thermodynamics, Formation and Vibrational Modes

Limit-periodic (LP) structures exhibit a type of nonperiodic order yet to be found in a natural material. A recent result in tiling theory, however, has shown that LP order can spontaneously emerge in a two-dimensional (2D) lattice model with nearest-and next-nearest-neighbor interactions. In this dissertation, we explore the question of what types of interactions can lead to a LP state and address the issue of whether the formation of a LP structure in experiments is possible. We study emergence of LP order in three-dimensional (3D) tiling models and bring the subject into the physical realm by investigating systems with realistic Hamiltonians and low energy LP states. Finally, we present studies of the vibrational modes of a simple LP ball and spring model whose results indicate that LP materials would exhibit novel physical properties.

A 2D lattice model defined on a triangular lattice with nearest- and next-nearest-neighbor interactions based on the Taylor-Socolar (TS) monotile is known to have a LP ground state. The system reaches that state during a slow quench through an infinite sequence of phase transitions. Surprisingly, even when the strength of the next-nearest-neighbor interactions is zero, in which case there is a large degenerate class of both crystalline and LP ground states, a slow quench yields the LP state. The first study in this dissertation introduces 3D models closely related to the 2D models that exhibit LP phases. The particular 3D models were designed such that next-nearest-neighbor interactions of the TS type are implemented using only nearest-neighbor interactions. For one of the 3D models, we show that the phase transitions are first order, with equilibrium structures that can be more complex than in the 2D case.

In the second study, we investigate systems with physical Hamiltonians based on one of the 2D tiling models with the goal of stimulating attempts to create a LP structure in experiments. We explore physically realizable particle designs while being mindful of particular features that may make the assembly of a LP structure in an experimental system difficult. Through Monte Carlo (MC) simulations, we have found that one particle design in particular is a promising template for a physical particle; a 2D system of identical disks with embedded dipoles is observed to undergo the series of phase transitions which leads to the LP state.

LP structures are well ordered but nonperiodic, and hence have nontrivial vibrational modes. In the third section of this dissertation, we study a ball and spring model with a LP pattern of spring stiffnesses and identify a set of extended modes with arbitrarily low participation ratios, a situation that appears to be unique to LP systems. The balls that oscillate with large amplitude in these modes live on periodic nets with arbitrarily large lattice constants. By studying periodic approximants to the LP structure, we present numerical evidence for the existence of such modes, and we give a heuristic explanation of their structure.

Galois lattice dynamics

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Lipoprotein-associated phospholipase A2 (Lp-PLA2) as a therapeutic target to prevent retinal vasopermeability during diabetes

Lipoprotein-associated phospholipase A2 (Lp-PLA2) hydrolyses oxidized low-density lipoproteins into proinflammatory products, which can have detrimental effects on vascular function. As a specific inhibitor of Lp-PLA2, darapladib has been shown to be protective against atherogenesis and vascular leakage in diabetic and hypercholesterolemic animal models. This study has investigated whether Lp-PLA2 and its major enzymatic product, lysophosphatidylcholine (LPC), are involved in blood-retinal barrier (BRB) damage during diabetic retinopathy. We assessed BRB protection in diabetic rats through use of species-specific analogs of darapladib. Systemic Lp-PLA2 inhibition using SB-435495 at 10 mg/kg (i.p.) effectively suppressed BRB breakdown in streptozotocin-diabetic Brown Norway rats. This inhibitory effect was comparable to intravitreal VEGF neutralization, and the protection against BRB dysfunction was additive when both targets were inhibited simultaneously. Mechanistic studies in primary brain and retinal microvascular endothelial cells, as well as occluded rat pial microvessels, showed that luminal but not abluminal LPC potently induced permeability, and that this required signaling by the VEGF receptor 2 (VEGFR2). Taken together, this study demonstrates that Lp-PLA2 inhibition can effectively prevent diabetes-mediated BRB dysfunction and that LPC impacts on the retinal vascular endothelium to induce vasopermeability via VEGFR2. Thus, Lp-PLA2 may be a useful therapeutic target for patients with diabetic macular edema (DME), perhaps in combination with currently administered anti-VEGF agents.

The Plastic Coupled Map Lattice: a Novel Image‐processing Paradigm

Coupled map lattices (CML) can describe many relaxation and optimization algorithms currently used in image processing. We recently introduced the ‘‘plastic‐CML’’ as a paradigm to extract (segment) objects in an image. Here, the image is applied by a set of forces to a metal sheet which is allowed to undergo plastic deformation parallel to the applied forces. In this paper we present an analysis of our ‘‘plastic‐CML’’ in one and two dimensions, deriving the nature and stability of its stationary solutions. We also detail how to use the CML in image processing, how to set the system parameters and present examples of it at work. We conclude that the plastic‐CML is able to segment images with large amounts of noise and large dynamic range of pixel values, and is suitable for a very large scale integration(VLSI) implementation.

Aspects of Chiral Symmetry Breaking in Lattice QCD

Thesis (Ph.D.)--University of Washington, 2016-08

The lipid- and lipoprotein- [LDL-Lp(a)] apheresis techniques. Updating

Therapeutic plasmapheresis allows the extracorporeal removal of plasmatic lipoproteins (Lipid-apheresis) (LA). It can be non selective (non specific), semi - selective or selective low density lipoprotein-lipoprotein(a) (specific [LDL- Lp(a)] apheresis) (Lipoprotein apheresis, LDLa). The LDL removal rate is a perfect parameter to assess the system efficiency. Plasma-Exchange (PEX) cannot be considered either specific nor, selective. In PEX the whole blood is separated into plasma and its corpuscular components usually through centrifugation or rather filtration. The corpuscular components mixed with albumin solution plus saline (NaCl 0.9%) solution at 20%-25%, are then reinfused to the patient, to substitute the plasma formerly removed. PEX eliminates atherogenic lipoproteins, but also other essential plasma proteins, such as albumin, immunoglobulins, and hemocoagulatory mediators. Cascade filtration (CF) is a method based on plasma separation and removal of plasma proteins through double filtration. During the CF two hollow–fiber filters with pores of different diameter are used to eliminate the plasma components of different weight and molecular diameter. A CF system uses a first polypropylene filter with 0.55 µm diameter pores and a second one of diacetate of cellulose with 0.02 µm pores. The first filter separates the whole blood, and the plasma is then perfused through a second filter which allows the recovery of molecules with a diameter lower than 0.02 µm, and the removal of molecules larger in diameter as apoB100–containing lipoproteins. Since both albumin and immunoglobulins are not removed, or to a negligible extent, plasma-expanders, substitution fluids, and in particular albumin, as occurs in PEX are not needed. CF however, is characterized by lower selectivity since removes also high density lipoprotein (HDL) particles which have an antiatherogenic activity. In the 80’s, a variation of Lipid-apheresis has been developed which allows the LDL-cholesterol (LDLC) (-61%) and Lp(a) (-60%) removal from plasma through processing 3 liters of filtered plasma by means of lipid-specific thermofiltration, LDL immunoadsorption, heparin-induced LDL precipitation, LDL adsorption through dextran sulphate. More recently (90’s) the DALI®, and the Liposorber D® hemoperfusion systems, effective for apoB100- containing lipoproteins removal have been developed. All the above mentioned systems are established LDL-apheresis techniques referable to the generic definition of LDLa. However, this last definition cannot describe in an appropriate manner the removal of another highly atherogenic lipoprotein particle: the Lp(a). Thus it would be better to refer the above mentioned techniques to the wider scientific and technical concept of lipoprotein apheresis. Lipid apheresis - Lipoprotein apheresis - LDL-apheresis - Severe Dyslipidemia.

Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice

We determine numerically the single-particle and the two-particle spectrum of the three-state quantum Potts model on a lattice by using the density matrix renormalization group method, and extract information on the asymptotic (small momentum) S-matrix of the quasiparticles. The low energy part of the finite size spectrum can be understood in terms of a simple effective model introduced in a previous work, and is consistent with an asymptotic S-matrix of an exchange form below a momentum scale p*. This scale appears to vanish faster than the Compton scale, mc, as one approaches the critical point, suggesting that a dangerously irrelevant operator may be responsible for the behaviour observed on the lattice.

Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a eduction to a cubic nonlinear Schr{\"o}dinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher-order analysis yielding a generalised NLS, which includes known stabilising terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, symptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximised for stationary breathers, and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt \& Wattis, {\em J Phys A}, {\bf 39}, 4955, (2006)), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalised NLS equation.