This dissertation focuses on the relative energy analysis of two-species fluids composed of charged particles. It presents a formal derivation of the relative energy identity for both the bipolar Euler-Maxwell system and the unmagnetized case of the bipolar Euler-Poisson system. Furthermore, the dissertation explores several applications of the relative energy method to Euler-Poisson systems, enabling a comprehensive stability analysis of these systems. The first application establishes the high-friction limit of a bipolar Euler-Poisson system with friction, converging towards a bipolar drift-diffusion system. Moreover, the second application investigates the limits of zero-electron-mass and quasi-neutrality in a bipolar Euler-Poisson system. In the former limit, a non-linear adiabatic electron system is obtained, while the combined limit yields an Euler system. A weak-strong uniqueness principle for a single-species Euler-Poisson system in the whole space is also established. This principle is further extended to an Euler-Riesz system, considering a more general interaction potential. The theory of Riesz potentials, along with representation formulas for the potentials, is employed to overcome the technical challenges in these studies.

This thesis studies mean-field games (MFGs) models of price formation. The thesis focuses explicitly on a MFGs price formation model proposed by Gomes and Saude. The thesis is divided into two parts. The first part examines the deterministic supply case, while the second part extends the model to incorporate a stochastic supply function. We explore different approaches, such as Aubry-Mather theory, to study the properties of the MFGs price formation model and alternative formulations using a convex variational problem with constraints. We propose machine-learning-based numerical methods to approximate the solution of the MFGs price formation model in the deterministic and stochastic setting.

Tilt-series cryo-electron tomography (cryo-ET) is an established imaging technique used in several fields like biology and material science. Despite its success, cryo-ET remains an arduous task. The missing-wedge acquisition, the motion, and the high-level noise are the main challenges existing in this field. In this dissertation, we tackle these challenges through the exploration of three distinct approaches: plug-and-play approach, adaptive differentiable density grids, and adaptive tensorial density field representation. Firstly, using embedded fiducial markers, our framework first estimates the motion field in the sample in order to correct the captured projections, and then reconstructs the sample using an iterative plug-and-play approach. Secondly, we propose an adaptive representation based on an octree structure. Each block of the structure represents a 3D density grid that is optimized from the captured projections. To ensure a denoised output, we update the octree in a multi-scale fashion. We also combined the differentiable image formation model with cross-nodes non-local constraint, total variation, and boundary consistency priors in the loss function. Thirdly, we propose an adaptive tensorial density field representation. Considering that cryo-ET is thin along the z-axis, we use a quadtree structure instead of initializing a nulled octree, and represent each node with a vector-matrix factorization. Combined with total variation, boundary consistency, and an isotropic Fourier prior, our framework allows us to reconstruct clean cryo-ET results. Experiments show considerable improvement in cryo-ET reconstructions.

The extracellular matrix, or ECM, is a three-dimensional network that serves as a structural scaffold for tissue construction. To do so, cells need to attach, proliferate, self-organize, and coordinate biochemical deposition across multiple length and time scales. Hydrogels have been utilized as biomaterials because their chemical and mechanical properties can be designed to mimic those of native ECMs. Short, synthetic, amphiphilic peptides have been used to design scaffolds for tissue engineering because the peptides self-assemble in water and are easy to tune. To date, hydrogels for tissue engineering have typically sacrificed one or more crucial properties in favor of improving others, since nearly all chemical and mechanical properties within a hydrogel are interdependent. The focus of this research is to study the mechanical tunability and viability of ultrashort peptide hydrogels derived from naturally occurring amino acids (IIZR, IIZK, and IZZK), such that ideal concentrations of each peptide can be configured to mimic the mechanical properties of native ECMs for human dermal fibroblasts (HDFns) and primary cortical neurons (CNs). Our results show that IIZR, IIZK, and IZZK hydrogel scaffolds are good candidates for these cell types because their stiffness, elasticity, and biocompatibility are commensurate with those of these cells’ native ECMs. As evidence, the stiffness of the materials generally increased with HDFns across all concentrations, except for 2mg/ml. In particular, HDFns favored hydrogels consisting of higher peptide concentrations, resulting in greater elasticity and higher stiffness. IIZR hydrogels were also well-suited for both HDFns and CNs, which could have been due to the peptides’ positively charged R groups that can facilitate cell adhesion via electrostatics.

Roots are considered an important organ as they transport nutrients and water and provide anchor and support in the plants. The development of roots involves the participation of specific proteins such as RETINOBLASTOMA-RELATED (RBR) which has been found to play a role in cell cycle regulation and stem cell niche maintenance. Additionally, roots can interact with the environment and soil microorganisms that can influence processes in plant growth and development. For instance, plant growth-promoting rhizobacteria (PGPR) have been found to have the ability to alter the root system by their influence on signaling pathways or phytohormones. In this study, we generated RBR mutant lines using CRISPR-Cas9 to determine the role of this protein in early plant growth. We found that the mutant lines contained partial abortion in ovules and mild reduction in siliques suggesting the participation of this protein in the early stages of plant development. Furthermore, we also use beneficial and pathogenic bacteria strains to study their effect on root patterning. We showed that WSC417 beneficial bacteria can influence root structure by promoting the growth of root hairs which might suggest a plant improvement in nutrient uptake. Also, we could observe that WSC417 can exert some protection against DC 3000 pathogenic bacteria when plant seedlings were inoculated with both strains. Overall, we could determine that RBR plays a role in early developmental stages and root development can also be influenced by biotic factors such as microorganisms.

Despite comprehensive studies addressing the chemical kinetics of butanol isomers, relevant uncertainties associated with the emissions of relevant pollutants persists. Also, a lack of chemistry knowledge of processes designed to produce biofuels limits their implementation at industrial scales. Therefore, the first objective of this thesis was to use cutting-edge kinetic theories to calculate rate constants of propen-2-ol, 1-pronenol, and vinyl alcohol keto-enol tautomerizations, which account for the production of the harmful carbonyl species. The second objective was to use the predictive capabilities of dynamic theories to reveal new chemistry of syngas oxy-combustion in supercritical CO2 and complexities of the zeolite dealumination, two processes involved in coal and biomass conversion. Rate constants computations considered transition state theory with variational effects, tunneling correction, and multistructural torsional anharmonicity. The study also included pressure effects by using and improving the system-specific quantum Rice-Ramsperger-Kassel/modified strong collision model. The atomistic simulations used ReaxFF force fields in hydrogen/oxygen/carbon monoxide/ carbon dioxide mixtures to represent the syngas system and an MFI zeolite with different water loading to model the dealumination. The results show that the studied assisted tautomerizations have much lower energy barriers than the unimolecular process. However, the “catalytic” effect is efficient only if the partner molecule is at high concentrations. Pressure effects are pronounced in the chemically activated tautomerizations, and the improved algorithm to compute pressure-dependent rate constants overcomes the initial difficulties associated with its application to C3 or larger molecules at temperatures above 800-1000 K. Reactive molecular dynamics simulations revealed the role of CO2 as an initiator in the syngas oxy-combustion and a new step involving the formation of formic acid. Those simulations for the zeolite dealumination process also showed that proton transfer, framework flexibility, and aluminum dislodging mediated by silicon reactions are complex dynamic phenomena determining the process. These aspects complement the dealumination theory uncovered so far and establish new paths in the study of water-zeolite interactions. Overall, the rate constants computed in this work reduce relevant uncertainties in the chemical kinetic mechanisms of alcohol oxidation, and the molecular dynamics simulations broaden the chemical knowledge of processes aimed at the utilization of alternative energy resources.

On-site sensing systems provide fast and timely information about a myriad of applications ranging from chemical and biological to physical phenomena in the environment or the human body. Such systems are embedded in our daily life for detecting pollutants, monitoring health, and diagnosing diseases. Especially in the field of health care, the development of portable and affordable diagnosing systems, also known as point-of-care (PoC) devices, is a major challenge. Moreover, to this day, systems for therapeutic drug monitoring (TDM) have remained bulky and highly expensive, mostly due to the need for exceptionally precise, rapid, and highly accurate real-time on-site measurements. This dissertation focuses on the design, development, and implementation of miniaturized PoC devices for achieving high sensitivity, selectivity, and reliability through a combination of hardware and software strategies at the edge. The first part of the dissertation introduces the design of single and multi-channel electrochemical readout platforms with a high voltage range, fast scan rates, and with nano-ampere resolution, covering a broad range of electrochemical excitation techniques. These platforms were paired with electrochemical-based sensors to detect SARS‑CoV‑2, bisphenol A, and ascorbic acid. The low power feature of the proposed platforms is demonstrated by powering the complete detection system with energy harvested from natural and artificial ambient light. The second part of the dissertation introduces the design and development of a miniaturized wearable device with a pico-ampere resolution, high-speed electrochemical frequency interface, and highly stable sensing circuitry. A complete in-vivo system is demonstrated for long-term (>4 hours) measurement, wherein molecules are detected and monitored directly from a probe inserted in the subcutaneous abdomen region of a Sprague-Dawley rat. A solution for sensor drift due to biofouling and interference is demonstrated thought to the integration with real-time processing software. Furthermore, integrating the aforementioned platforms with highly reduced dense neural network models is demonstrated to increase the robustness of the sensors, allowing the detection of contaminants in complex samples, improving the sensor selectivity, and providing timely diagnoses in-situ.

As Organic solar cells (OSCs) become a promising complementary to traditional inorganic solar cells, studying the optical properties of OSCs plays a critical role to understand and improve the performance of organic solar cells. Studying optical properties is essential because it can help to understand how light interacts with the materials used in organic solar cells, which can help to improve the efficiency of organic solar cells. In this work, the optical properties of the organic photovoltaic system PM6:Y6 prepared from two different solvents, namely, chloroform and o-xylene, were investigated. The optical constants, specifically the refractive index and absorption coefficient of thin films of these materials, and the effects of thermal annealing on the optical properties were studied. The optical properties of isotropic and anisotropic organic materials were also compared, and the obtained optical constants were used to simulate the optical properties of the devices using the transfer matrix approach. The results suggest that more accurate measurements and analysis of the optical constants help to achieve more accurate simulations. This, in turn, provides more information about how the molecular orientation affects the optical properties of OSCs. However, it is important to note that the optical properties of PM6:Y6 blends that were studied are limited to those obtained under the conditions used to prepare the films. In fact, changes in the thickness or concentrations of solutions will need to be considered as well. Lastly, the glass transition temperature was determined using the change in the ellipsometric data (Ψ). This helps to select and test different thermal annealing temperatures for the material system, which could improve the efficiency of the respective solar cells.

Ammonia and hydrogen are two alternative fuels that can help decarbonization as they can be produced using renewable energy. Ammonia has transportation, handling, and storage advantages over hydrogen even though its combustion characteristics are worse. One intermediate strategy to use ammonia or hydrogen as a fuel is to co-fire it with hydrocarbons. However, co-firing with hydrocarbons may emit harmful pollutants such as NOx and soot. This study investigates the effects of ammonia and hydrogen addition on soot formation in laminar coflow nitrogen-diluted-ethylene normal diffusion flames using experimental techniques. Ammonia and hydrogen were added separately to the fuel flow. Flame conditions from 0 to 50 vol% of the added species (ammonia or hydrogen) were tested. Laser diagnostics for measuring the distributions of polycyclic aromatic hydrocarbons (PAHs) and soot volume fraction (SVF), and intrusive measurements (using a thermocouple and probe sampling) were performed. Based on the results, ammonia addition suppressed soot formation while hydrogen addition enhanced it. In conditions with ammonia addition, the temperature measurements with a Type S thermocouple and adiabatic flame temperature simulations using CHEMKIN PRO showed similar temperature profiles and negligible adiabatic flame temperature differences respectively. The qualitative PAH measurements using planar laser induced fluorescence (PLIF) showed that the concentration of PAHs of four or larger rings reduced with ammonia addition. Soot volume fraction (SVF) measurements using planar laser induced incandescence (PLII) showed that the peak SVF decreased exponentially with ammonia addition. Particle size distributions showed that the incipient particles were formed, however growth to mature primary particles was limited with 25% or higher ammonia addition in the flame. Based on similar temperature profiles and decreasing trends in the distribution of PAHs and SVF, soot suppression with ammonia addition was linked to chemical effects. PLIF measurements with hydrogen addition could be affected by the temperature difference between the flames, therefore further investigation is needed. PLII measurements, however, showed that the soot volume fraction increased linearly with hydrogen addition.

Deep Neural Networks (DNNs) find widespread applications across various domains, including computer vision, recommendation systems, and natural language processing. Despite their versatility, training DNNs can be a time-consuming process, and accommodating large models and datasets on a single machine is often impractical. To tackle these challenges, distributed deep learning (DDL) training workloads have gained increasing significance. However, DDL training introduces synchronization requirements among nodes, and the mini-batch stochastic gradient descent algorithm heavily burdens network connections. This dissertation proposes, analyzes, and evaluates three solutions addressing the communication bottleneck in DDL learning workloads. The first solution, SwitchML, introduces an in-network aggregation (INA) primitive that accelerates DDL workloads. By aggregating model updates from multiple workers within the network, SwitchML reduces the volume of exchanged data. This approach, which incorporates switch processing, end-host protocols, and Deep Learning frameworks, enhances training speed by up to 5.5 times for real-world benchmark models. The second solution, OmniReduce, is an efficient streaming aggregation system designed for sparse collective communication. It optimizes performance for parallel computing applications, such as distributed training of large-scale recommendation systems and natural language processing models. OmniReduce achieves maximum effective bandwidth utilization by transmitting only nonzero data blocks and leveraging fine-grained parallelization and pipelining. Compared to state-of-the-art TCP/IP and RDMA network solutions, OmniReduce outperforms them by 3.5 to 16 times, delivering significantly better performance for network-bottlenecked DNNs, even at 100 Gbps. The third solution, CoInNetFlow, addresses congestion in shared data centers, where multiple DNN training jobs compete for bandwidth on the same node. The study explores the feasibility of coflow scheduling methods in hierarchical and multi-tenant in-network aggregation communication patterns. CoInNetFlow presents an innovative utilization of the Sincronia priority assignment algorithm. Through packet-level DDL job simulation, the research demonstrates that appropriate weighting functions, transport layer priority scheduling, and gradient compression on low-priority tensors can significantly improve the median Job Completion Time Inflation by over $70\%$. Collectively, this dissertation contributes to mitigating the network communication bottleneck in distributed deep learning. The proposed solutions can enhance the efficiency and speed of distributed deep learning systems, ultimately improving the performance of DNN training across various domains.