Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). In the present work, we follow the method originally proposed by Van Vliet in LRT. The Hamiltonian in this approach is of the form: H = H°(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H° - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H°(E, B) , include the external fields without any limitation on strength. In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0 , t → ∞ , so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices.

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.

Dynamics of ecosystem metabolism and flocculent detritus transport in estuarine Taylor River

Estuaries and estuarine wetlands are ecologically and societally important systems, exhibiting high rates of primary production that fuel offshore secondary production. Hydrological processes play a central role in shaping estuarine ecosystem structure and function by controlling nutrient loading and the relative contributions of marine and terrestrial influences on the estuary. The Comprehensive Everglades Restoration Plan includes plans to restore freshwater delivery to Taylor Slough, a shallow drainage basin in the southern Everglades, ultimately resulting in increased freshwater flow to the downstream Taylor River estuary. The existing seasonal and inter-annual variability of water flow and source in Taylor River affords the opportunity to investigate relationships between ecosystem function and hydrologic forcing. Estimates of aquatic ecosystem metabolism, derived from free-water, diel changes in dissolved oxygen, were combined with assessments of wetland flocculent detritus quality and transport within the context of seasonal changes in Everglades hydrology. Variation in ecosystem gross primary production and respiration were linked to seasonal changes in estuarine water quality using multiple autoregression models. Furthermore, Taylor River was observed to be net heterotrophic, indicating that an allochthonous source of carbon maintained ecosystem respiration in excess of autochthonous primary production. Wetland-derived detritus appears to be an important vector of energy and nutrients across the Everglades landscape; and in Taylor River, is seasonally flushed into ponded segments of the river where it is then respired. Lastly, seasonal water delivery appears to govern feedbacks regulating water column phosphorus availability in the Taylor River estuary.

Examining Seasonally Pulsed Detrital Transport in the Coastal Everglades Using a Sediment Tracing Technique

The Comprehensive Everglades Restoration includes plans to restore freshwater delivery to Taylor Slough, a shallow drainage basin in the Southern Everglades, ultimately resulting in increased freshwater flow to the downstream Taylor River estuary. The effect of altered hydrologic regime on the transport dynamics of flocculent, estuarine detritus is not well understood. We utilized a paramagnetic sediment tracer to examine detrital transport in three Taylor River pond/creek pairs during early wet versus late wet transition season estuarine flow conditions. Flux of floc tracer was greatest in the downstream direction during all observations, and was most pronounced during the early wet season, coincident with shallower water depth and faster discharge from northern Taylor River. Floc tracer was more likely to move upriver during the late wet/dry season. We observed a floc tracer transport velocity of approximately 1.74 to 1.78 m/day across both seasonal hydrologic conditions. Tracer dynamics were also surprisingly site-dependent, which may highlight the importance of channel geomorphology in regulating hydrologic and sediment transport conditions. Our data suggest that restoration of surface water delivery to Taylor River will influence downstream loading of detritus material into riverine ponds. These detrital inputs have the potential to enhance ecosystem primary productivity and/or secondary productivity.

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.

The correlation of structure and electronic properties near the surface of transition metal oxides

The strong couplings between different degrees of freedom are believed to be responsible for novel and complex phenomena discovered in transition metal oxides (TMOs). The physical complexity is directly responsible for their tunability. Creating surfaces/interfaces add an additional ' man-made' twist, approaching the quantum phenomena of correlated materials. ^ The dissertation focused on the structural and electronic properties in proximity of surface of three prototype TMO compounds by using three complementary techniques: scanning tunneling microscopy, angle-resolved photoelectron spectroscopy and low energy electron diffraction, particularly emphasized the effects of broken symmetry and imperfections like defects on the coupling between charge and lattice degrees of freedom. ^ Ca1.5Sr0.5RuO4 is a layered ruthenate with square lattice and at the boundary of magnetic/orbital instability in Ca2-xSrxRuO4. That the substitution of Sr 2+ with Ca2+ causing RuO6 rotation narrows the dxy band width and changes the Fermi surface topology. Particularly, the γ(dxy) Fermi surface sheet exhibited hole-like in Ca1.5Sr0.5RuO4 in contrast to electron-like in Sr2RuO4, showing a strong charge-lattice coupling. ^ Na0.75CoO2 is a layered cobaltite with triangular lattice exhibiting extraordinary thermoelectric properties. The well-ordered CoO2-terminated surface with random Na distribution was observed. However, lattice constants of the surface are smaller than that in bulk. The surface density of states (DOS) showed strong temperature dependence. Especially, an unusual shift of the minimum DOS occurs below 230 K, clearly indicating a local charging effect on the surface. ^ Cd2Re2O7 is the first known pyrochlore oxide superconductor (Tc ∼ 1K). It exhibited an unusual second-order phase transition occurring at TS1 = 200 K and a controversial first-order transition at TS2 = 120 K. While bulk properties display large anomalies at TS1 but rather subtle and sample-dependent changes at TS2, the surface DOS near the EF show no change at T s1 but a substantial increase below TS2---a complete reversal as the signature for the transitions. We argued that crystal imperfections, mainly defects, which were considerably enhanced at the surface, resulted in the transition at TS2. ^

Multimode Analysis of Nanoscale Biomolecular Interactions

Biomolecular interactions, including protein-protein, protein-DNA, and protein-ligand interactions, are of special importance in all biological systems. These interactions may occer during the loading of biomolecules to interfaces, the translocation of biomolecules through transmembrane protein pores, and the movement of biomolecules in a crowded intracellular environment. The molecular interaction of a protein with its binding partners is crucial in fundamental biological processes such as electron transfer, intracellular signal transmission and regulation, neuroprotective mechanisms, and regulation of DNA topology. In this dissertation, a customized surface plasmon resonance (SPR) has been optimized and new theoretical and label free experimental methods with related analytical calculations have been developed for the analysis of biomolecular interactions. Human neuroglobin (hNgb) and cytochrome c from equine heart (Cyt c) proteins have been used to optimize the customized SPR instrument. The obtained Kd value (~13 µM), from SPR results, for Cyt c-hNgb molecular interactions is in general agreement with a previously published result. The SPR results also confirmed no significant impact of the internal disulfide bridge between Cys 46 and Cys 55 on hNgb binding to Cyt c. Using SPR, E. coli topoisomerase I enzyme turnover during plasmid DNA relaxation was found to be enhanced in the presence of Mg2+. In addition, a new theoretical approach of analyzing biphasic SPR data has been introduced based on analytical solutions of the biphasic rate equations. In order to develop a new label free method to quantitatively study protein-protein interactions, quartz nanopipettes were chemically modified. The derived Kd (~20 µM) value for the Cyt c-hNgb complex formations matched very well with SPR measurements (Kd ~16 µM). The finite element numerical simulation results were similar to the nanopipette experimental results. These results demonstrate that nanopipettes can potentially be used as a new class of a label-free analytical method to quantitatively characterize protein-protein interactions in attoliter sensing volumes, based on a charge sensing mechanism. Moreover, the molecule-based selective nature of hydrophobic and nanometer sized carbon nanotube (CNT) pores was observed. This result might be helpful to understand the selective nature of cellular transport through transmembrane protein pores.

A Multi-Criteria GIS-Based Route Selection Tool for Hazardous Material Transport: Consideration of Environmental Consequence, Traffic Congestions and Costs

Hazardous materials are substances that, if not regulated, can pose a threat to human populations and their environmental health, safety or property when transported in commerce. About 1.5 million tons of hazardous material shipments are transported by truck in the US annually, with a steady increase of approximately 5% per year. The objective of this study was to develop a routing tool for hazardous material transport in order to facilitate reduced environmental impacts and less transportation difficulties, yet would also find paths that were still compelling for the shipping carriers as a matter of trucking cost. The study started with identification of inhalation hazard impact zones and explosion protective areas around the location of hypothetical hazardous material releases, considering different parameters (i.e., chemicals characteristics, release quantities, atmospheric condition, etc.). Results showed that depending on the quantity of release, chemical, and atmospheric stability (a function of wind speed, meteorology, sky cover, time and location of accidents, etc.) the consequence of these incidents can differ. The study was extended by selection of other evaluation criteria for further investigation because health risk as an evaluation criterion would not be the only concern in selection of routes. Transportation difficulties (i.e., road blockage and congestion) were incorporated as important factor due to their indirect impact/cost on the users of transportation networks. Trucking costs were also considered as one of the primary criteria in selection of hazardous material paths; otherwise the suggested routes would have not been convincing for the shipping companies. The last but not least criterion was proximity of public places to the routes. The approach evolved from a simple framework to a complicated and efficient GIS-based tool able to investigate transportation networks of any given study area, and capable of generating best routing options for cargos. The suggested tool uses a multi-criteria-decision-making method, which considers the priorities of the decision makers in choosing the cargo routes. Comparison of the routing options based on each criterion and also the overall suitableness of the path in regards to all the criteria (using a multi-criteria-decision-making method) showed that using similar tools as the one proposed by this study can provide decision makers insights in the area of hazardous material transport. This tool shows the probable consequences of considering each path in a very easily understandable way; in the formats of maps and tables, which makes the tradeoffs of costs and risks considerably simpler, as in some cases slightly compromising on trucking cost may drastically decrease the probable health risk and/or traffic difficulties. This will not only be rewarding to the community by making cities safer places to live, but also can be beneficial to shipping companies by allowing them to advertise as environmental friendly conveyors.