<p>Injection to the subcutaneous (SC) tissue is one of the preferred methods for drug delivery of pharmaceuticals, from small molecules to monoclonal antibodies. Delivery to SC has become widely popular in part thanks to the low cost, ease of use, and effectiveness of drug delivery through the use of auto-injector devices. However, injection physiology, from initial plume formation to the eventual uptake of the drug in the lymphatics, is highly dependent on SC mechanics, poroelastic properties in particular. Yet, the poroelastic properties of SC have been understudied. In this thesis, I present a two-pronged approach to understanding the poroelastic properties of SC. Experimentally, mechanical and fluid transport properties of SC were measured with confined compression experiments and compared against gelatin hydrogels used as SC-phantoms. It was found that SC tissue is a highly non-linear material that has viscoelastic and porohyperelastic dissipation mechanisms. Gelatin hydrogels showed a similar, albeit more linear response, suggesting a micromechanical mechanism may underline the nonlinear behavior. The second part of the thesis focuses on the multiscale modeling of SC to gain a fundamental understanding of how geometry and material properties of the microstructure drive the macroscale response. SC is composed of adipocytes (fat cells) embedded in a collagen network. The geometry can be characterized with Voroni-like tessellations. Adipocytes are fluid-packed, highly deformable and capable of volume change through fluid transport. Collagen is highly nonlinear and nearly incompressible. Representative volume element (RVE) simulations with different Voroni tesselations shows that the different materials, coupled with the geometry of the packing, can contribute to different material response under the different kinds of loading. Further investigation of the effect of geometry showed that cell packing density nonlinearly contributes to the macroscale response. The RVE models can be homogenized to obtain macroscale models useful in large scale finite element simulations of injection physiology. Two types of homogenization were explored: fitting to analytical constitutive models, namely the Blatz-Ko material model, or use of Gaussian process surrogates, a data-driven non-parametric approach to interpolate the macroscale response.</p>

<p dir="ltr">Due to the vast increase and versatility of Additive Manufacturing and 3D-printing, in this study, the mechanical behavior of implementing both continuous and short carbon fiber within Nylon and investigated for its effectiveness within additively manufactured prints. Here, 0.1wt% of pure nylon was combined with carbon nanotubes through both dry and heat mixing to determine the best method and used to create printable filaments. Compression, tensile and short beam shear (SBS) samples were created and tested to determine maximum deformation and were simulated using ANSYS and its ACP Pre tool. SEM imaging was used to analyze CNT integration within the nylon filament, as well as the fractography of tested samples. Experimental testing shows that compressive strength increased by 28%, and the average SBS samples increased by 8% with minimal impacts on the tensile strength. The simulated results for Nylon/CF tensile samples were compared to experimental results and showed that lower amounts of carbon fiber samples tend to have lower errors.</p>

<p dir="ltr">Uncertainty quantification is a science and engineering subject that aims to quantify and analyze the uncertainty arising from mathematical models, simulations, and measurement data. An uncertainty quantification analysis usually consists of conducting experiments to collect data, creating and calibrating mathematical models, predicting through numerical simulation, making decisions using predictive results, and comparing the model prediction with new experimental data.</p><p dir="ltr">The overarching goal of uncertainty quantification is to determine how likely some quantities in this analysis are if some other information is not exactly known and ultimately facilitate decision-making. This dissertation delivers a complete package, including theory, algorithms, and applications of information field theory, a Bayesian uncertainty quantification tool that leverages the state-of-the-art machine learning framework to accelerate solving the classical uncertainty quantification problems specified by differential equations.</p>

<p dir="ltr">This research aims to address these critical challenges in uncertainty quantification. The objective is to employ data-driven approaches for UQ with physics models.</p>

<p dir="ltr">The need for reducing reliance on fossil fuels to meet ever-increasing energy demands and minimizing global climate change due to greenhouse gas emissions has led to an increase in investments in Variable Energy Resources (VREs), such as wind and solar. But due to the unreliable nature of VREs, an energy storage system must be coupled with it which drives up the investment cost.</p><p dir="ltr">Lithium-ion batteries are compact, modular, and have high cyclic efficiency, making them an ideal choice for energy storage systems. However, they are susceptible to capacity loss over the years, limiting the total life of the batteries to 15-18 years only, after which they must be safely discarded or recycled. Hence, designing a Battery Energy Storage System (BESS) should consider all aspects, such as battery life, investment cost, energy efficiency, etc.</p><p dir="ltr">Most of the available studies on cost and lifetime of BESS either consider a steady degradation rate over years, or do not account for it at all, they take constant charge/discharge cycles, and sometimes do not consider ambient temperature too. This may result in an error in estimation of the cost of energy storage. The location where the BESS is supposed to be installed can also impact its life, given that each location has its own power consumption trend and temperature profile. In this work, we attempt to simulate a BESS by considering the ambient temperature, degradation rate and energy usage. This will help in getting an insight of a more realistic estimate of levelized cost of storage and for estimating the thermal energy needed to keep them within a certain temperature range, so that they can last longer.</p>

<p dir="ltr">The kinetic-based lattice Boltzmann method (LBM) is a specialized computational fluid dynamics (CFD) technique that resolves intricate flow phenomena at the mesoscale level. The LBM is particularly suited for large-scale parallel computing on Graphic Processing Units (GPU) and simulating multi-phase flows. By incorporating a volume fraction parameter, LBM becomes a volumetric lattice Boltzmann method (VLBM), leading to advantages such as easy handling of complex geometries with/without movement. These capabilities render VLBM an effective tool for modeling various complex flows. In this study, we investigated the computational modeling of complex flows using VLBM, focusing particularly on pulsatile flows, the transition to turbulent flows, and pore-scale porous media flows. Furthermore, a new discrete dynamical system (DDS) is derived and validated for potential integration into large eddy simulations (LES) aimed at enhancing modeling for turbulent and pulsatile flows. Pulsatile flows are prevalent in nature, engineering, and the human body. Understanding these flows is crucial in research areas such as biomedical engineering and cardiovascular studies. However, the characteristics of oscillatory, variability in Reynolds number (Re), and shear stress bring difficulties in the numerical modeling of pulsatile flows. To analyze and understand the shear stress variability in pulsatile flows, we first developed a unique computational method using VLBM to quantify four-dimensional (4-D) wall stresses in image-based pulsatile flows. The method is validated against analytical solutions and experimental data, showing good agreement. Additionally, an application study is presented for the non-invasive quantification of 4-D hemodynamics in human carotid and vertebral arteries. Secondly, the transition to turbulent flows is studied as it plays an important role in the understanding of pulsatile flows since the flow can shift from laminar to transient and then to turbulent within a single flow cycle. We conducted direct numerical simulations (DNS) using VLBM in a three-dimensional (3-D) pipe and investigated the flow at Re ranging from 226 to 14066 in the Lagrangian description. Results demonstrate good agreement with analytical solutions for laminar flows and with open data for turbulent flows. Key observations include the disappearance of parabolic velocity profiles when Re>2300, the fluctuation of turbulent kinetic energy (TKE) between laminar and turbulent states within the range 2300</p>

<p dir="ltr">Counterflow diffusion flames have been studied in depth as a one-dimensional flame, and are often used to study chemical kinetics, soot formation, and extinction and ignition characteristics of flames because of the low computing costs associated with one dimensional computations. Further, strained flames have been used in models of turbulent flames with the assumption that the underlying chemistry can be represented by a limited number of variables. Detailed three dimensional simulations of H₂/CH₄/air counterflow diffusion flames are performed using CONVERGE CFD [41] and compared to one dimensional simulation and experimental Dual-Pump Coherent anti-Stokes Raman Scattering (DPCARS) measurements of temperature and normalized mole fractions of H₂ and O₂[37]. The multi-dimensional effects of differential and advective diffusion are explored. The effects of boundary conditions far from the centerline axis of the burner one flow field and flame shape are investigated.</p>

<p dir="ltr">Acoustic guitar soundboard material selection is based on selective evaluations that have been developed over centuries. These traditional practices are not conducive to the guitar industry we experience today because the supply of traditionally acceptable soundboard wood has decreased greatly. The purpose of this research was to develop an objective wood selection metric to determine the sound quality of an acoustic guitar’s soundboard. The metric would replace the subjective evaluations traditionally used to select materials for acoustic guitar soundboards.</p><p dir="ltr">The acoustic properties of sound radiation coefficient, material’s speed of sound, resonance and damping and the material properties of longitudinal and radial elastic modulus, density, and specific modulus were used in an attempt to construct a material selection metric. These variables were selected because the literature review revealed that these were the most critical variables in determining sound quality. The gaps in the literature were testing and analyzing samples that represented the true dimensions of an acoustic guitar soundboard blank and forming the metric. The literature revealed that the previous experimental studies did not have the appropriate test sample dimensions that correspond to the test samples evaluated by the subjective methods.</p><p dir="ltr">The methodology was carried out by using the objective testing counterparts to the subjective assessments found in the literature review. Instrumented hammer tap testing collected data to determine damping and resonance frequencies. A three-point static bending test collected data for longitudinal and radial elastic modulus. Mass and dimension measurements were recorded to calculate density. Calculations were done to compute the acoustic properties and specific modulus of the test samples. These variables were put into a table and underwent statistical analysis in the form of predictor correlation and logistical regression. The experimental variables were modeled against the subjective evaluation of an expert on the usability of the test samples.</p><p dir="ltr">Statistical analysis proved that the dataset did not show any significant separation between “good” or “bad” test samples or a significant correlation between the usability of the test sample and the variables in the dataset. The methodology did not produce an objective material selection metric to determine the sound quality of an acoustic guitar’s soundboard. Future research should include a wider range of measured frequencies and the collection of time domain data.</p>

<p dir="ltr">The goal of this thesis is to develop a method of evaluating long-term IAQ performance of an industrial facility and use machine-learning to model the relationship between critical air pollutants and the facility’s HVAC systems and processes. The facility under study for this thesis is an electroplating manufacturer. The air pollutants at this facility that were studied were particulate matter, total-volatile organic compounds, and carbon-dioxide. Upon sensor installation, seven “zones” were identified to isolate areas of the plant for measurement and analysis. A statistical review of the long-term data highlighted how this facility performed in terms of compliance. Their gaseous pollutants were well within regulation. Particulate matter, however, was found to be a pressing issue. PM10 was outside of compliance more than 15% of the time in five out of seven of the zones of study. Some zones were out of compliance up to 80% of the total collection period. The six pollutants that met these criteria were deemed critical and moved on to machine learning modeling. Our model of best fit for each pollutant used a gaussian process regression model, which fits best for non-linear rightly skewed datasets. The performance of each of our models was deemed significant. Every model had at least a regression coefficient of 0.935 and above for both validation and testing. The maximum average error was 12.64 ug.m^3, which is less than 10% of the average PM10 concentration. Through our modeling, we were able to study how HVAC and production played a role in particulate matter presence for each zone. Exhaust systems of the west side of the plant were found to be insufficient at removing particulates from their facility. Overall, the methods developed in this thesis project were able to meet the goal of analyzing IAQ compliance, modeling critical pollutants using machine learning, and identifying a relationship between these pollutants and an industrial facility’s HVAC and production systems.</p>

<p dir="ltr">There is a growing trend towards the development of parsimonious surrogate models for studying physical phenomena. While they typically offer less accuracy, these models bypass the computational costs of numerical methods, usually by multiple orders of magnitude, allowing statistical applications such as sensitivity analysis, stochastic treatments, parametric problems, and uncertainty quantification. Researchers have explored generalized surrogate frameworks leveraging Gaussian processes, various basis function expansions, support vector machines, and neural networks. Dynamical fields, represented through time-dependent partial differential equation, pose a particular hardship for existing frameworks due to their high dimensional representation, and possibly multi-scale solutions.</p><p dir="ltr">In this work, we present a novel architecture for solving time-dependent partial differential equations using co-ordinate neural networks and time-marching updates through hyper-networks. We show that it provides a temporally meshed and spatially mesh-free solution which are causally coherent as justified through a theoretical treatment of Lie groups. We showcase results on some benchmark problems in computational physics while discussing their performance against similar physics-informed approaches like physics-informed DeepOnets and Physics informed neural networks.</p>