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Articles 1 - 30 of 1019

Full-Text Articles in Engineering

Decoupling Information And Connectivity Via Information-Centric Transport, Hila Ben Abraham, Jyoti Parwatikar, John Dehart, Adam Drescher, Patrick Crowley Aug 2018

Decoupling Information And Connectivity Via Information-Centric Transport, Hila Ben Abraham, Jyoti Parwatikar, John Dehart, Adam Drescher, Patrick Crowley

Computer Science and Engineering Publications and Presentations

The power of Information-Centric Networking (ICN) architectures lies in their abstraction for communication --- the request for named data. This abstraction promises that applications can choose to operate only in the information plane, agnostic to the mechanisms implemented in the connectivity plane. However, despite this powerful promise, the information and connectivity planes are presently coupled in today's incarnations of leading ICNs by a core architectural component, the forwarding strategy. Presently, this component is not sustainable: it implements both the information and connectivity mechanisms without specifying who should choose a forwarding strategy --- an application developer or the network operator. In practice ...


In Vivo Vascular Imaging With Photoacoustic Microscopy, Hsun-Chia Hsu Aug 2018

In Vivo Vascular Imaging With Photoacoustic Microscopy, Hsun-Chia Hsu

Engineering and Applied Science Theses & Dissertations

Photoacoustic (PA) tomography (PAT) has received extensive attention in the last decade for its capability to provide label-free structural and functional imaging in biological tissue with highly scalable spatial resolution and penetration depth. Compared to modern optical modalities, PAT offers speckle-free images and is more sensitive to optical absorption contrast (with 100% relative sensitivity). By implementing different regimes of optical wavelength, PAT can be used to image diverse light-absorbing biomolecules. For example, hemoglobin is of particular interest in the visible wavelength regime owing to its dominant absorption, and lipids and water are more commonly studied in the near-infrared regime.

In ...


Brain-Computer Interfaces Using Electrocorticography And Surface Stimulation, Jesse Wheeler Aug 2018

Brain-Computer Interfaces Using Electrocorticography And Surface Stimulation, Jesse Wheeler

Engineering and Applied Science Theses & Dissertations

The brain connects to, modulates, and receives information from every organ in the body. As such, brain-computer interfaces (BCIs) have vast potential for diagnostics, medical therapies, and even augmentation or enhancement of normal functions. BCIs provide a means to explore the furthest corners of what it means to think, to feel, and to act—to experience the world and to be who you are. This work focuses on the development of a chronic bi-directional BCI for sensorimotor restoration through the use of separable frequency bands for recording motor intent and providing sensory feedback via electrocortical stimulation. Epidural cortical surface electrodes ...


Engineering Robust And Programmable Biological Systems, Tatenda Shopera Aug 2018

Engineering Robust And Programmable Biological Systems, Tatenda Shopera

Engineering and Applied Science Theses & Dissertations

The ability to engineer programmable biological systems using complex artificial gene networks has great potential to unlock important innovative solutions to many biotechnological challenges. While cells have been engineered to implement complex information processing algorithms and to produce food, materials, and pharmaceuticals, many innovative applications are yet to be realized due to our poor understanding of how robust, reliable, and predictable artificial gene circuits are built. In this work, we demonstrate that robust complex cellular behaviors (e.g., bistability and gene expression dynamics) can be achieved by engineering gene regulatory architecture and increasing the complexity of genetic networks. We further ...


Development And Application Of Quadratic Constitutive Relation And Transitional Crossflow Effects In The Wray-Agarwal Turbulence Model, Hakop Jack Nagapetyan Aug 2018

Development And Application Of Quadratic Constitutive Relation And Transitional Crossflow Effects In The Wray-Agarwal Turbulence Model, Hakop Jack Nagapetyan

Engineering and Applied Science Theses & Dissertations

Computational Fluid Dynamics (CFD) has now become an almost indispensable tool for modern engineering analysis of fluid flow over aircrafts, turbomachinery, automobiles, and many other industrial applications. Accurate prediction of turbulent flows remains a challenging problem. The most popular approach for simulating turbulent flows in complex industrial applications is based on the solution of the Reynolds-Averaged Navier-Stokes (RANS) equations. RANS equations introduce the so called “Reynolds or turbulent stresses” which are generally modeled using the Boussinesq approximation known as “Turbulence modeling.” Despite their development over a century, the turbulence models used with RANS equations still need much improvement. The first ...


Lignin Conversion To Value-Added Products Via Heterogeneous Catalysts, Yu Gao Aug 2018

Lignin Conversion To Value-Added Products Via Heterogeneous Catalysts, Yu Gao

Engineering and Applied Science Theses & Dissertations

Increasing world population has led to great demands for fuels, chemicals, and materials, and has raised concerns over the depletion of non-renewable resources and the environmental impacts of their processing and utilization. However, the biorefinery concept suggests lignocellulosic biomass can be used as an alternative resource for producing a range of fuels, chemicals and materials to fulfill these demands in a sustainable way. Hence, fermentation technologies are widely developed to efficiently utilize lignocellulosic carbohydrates. However, the non-carbohydrate fraction of biomass, lignin, is still considered as waste and is under-utilized as low-grade fuel, mainly for local heat and electricity production. Since ...


Development And Application Of Rotation And Curvature Correction To Wray-Agarwal Turbulence Model, Xiao Zhang Aug 2018

Development And Application Of Rotation And Curvature Correction To Wray-Agarwal Turbulence Model, Xiao Zhang

Engineering and Applied Science Theses & Dissertations

Computational Fluid Dynamics (CFD) is increasingly playing a significant role in the analysis and design of aircrafts, turbomachines, automobiles, and in many other industrial applications. In majority of the applications, the fluid flow is generally turbulent. The accurate prediction of turbulent flows to date remains a challenging problem in CFD. In almost all industrial applications, Reynolds-Averaged Navier-Stokes (RANS) equations in conjunction with a turbulence model are employed for simulation and prediction of turbulent flows. Currently the one-equation (namely the Spalart-Allmaras (SA) and Wray-Agarwal (WA) and two-equation (namely the k-ε and Shear Stress Transport k-ω) turbulence models remain the most widely ...


Forward Electrophysiological Modeling And Inverse Problem For Uterine Contractions During Pregnancy, Mengxue Zhang Aug 2018

Forward Electrophysiological Modeling And Inverse Problem For Uterine Contractions During Pregnancy, Mengxue Zhang

Engineering and Applied Science Theses & Dissertations

Uterine contractile dysfunction during pregnancy is a significant healthcare challenge that imposes heavy medical and financial burdens on both human beings and society. In the U.S., about 12% of babies are born prematurely each year, which is a leading cause of neonatal mortality and increases the possibility of having subsequent health problems. Post-term birth, in which a baby is born after 42 weeks of gestation, can cause risks for both the newborn and the mother. Currently, there is a limited understanding of how the uterus transitions from quiescence to excitation, which hampers our ability to detect labor and treat ...


Developing Multi-Scale Models For Water Quality Management In Drinking Water Distribution Systems, Ahmed A. Abokifa Aug 2018

Developing Multi-Scale Models For Water Quality Management In Drinking Water Distribution Systems, Ahmed A. Abokifa

Engineering and Applied Science Theses & Dissertations

Drinking water supply systems belong to the group of critical infrastructure systems that support the socioeconomic development of our modern societies. In addition, drinking water infrastructure plays a key role in the protection of public health by providing a common access to clean and safe water for all our municipal, industrial, and firefighting purposes. Yet, in the United States, much of our national water infrastructure is now approaching the end of its useful life while investments in its replacement and rehabilitation have been consistently inadequate. Furthermore, the aging water infrastructure has often been operated empirically, and the embracement of modern ...


Development And Application Of Hybrid Wray-Agarwal Turbulence Model And Large-Eddy Simulation, Xu Han Aug 2018

Development And Application Of Hybrid Wray-Agarwal Turbulence Model And Large-Eddy Simulation, Xu Han

Engineering and Applied Science Theses & Dissertations

Rapid development in computing power in past five decades along with the development and progress in building blocks of Computational Fluid Dynamics (CFD) technology has made CFD an indispensable tool for modern engineering analysis and design of fluid-based products and systems. For CFD analysis, Reynolds-Averaged Navier-Stokes (RANS) equations are currently the most widely used fluid equations in the industry. RANS methods require modeling of turbulence effect (i.e. turbulence modeling) based on empirical relations and therefore often produce low accuracy results for many flows. In recent years, the Large Eddy Simulation (LES) approach has been developed which has shown promise ...


Multi-Gpu Acceleration Of Iterative X-Ray Ct Image Reconstruction, Ayan Mitra Aug 2018

Multi-Gpu Acceleration Of Iterative X-Ray Ct Image Reconstruction, Ayan Mitra

Engineering and Applied Science Theses & Dissertations

X-ray computed tomography is a widely used medical imaging modality for screening and diagnosing diseases and for image-guided radiation therapy treatment planning. Statistical iterative reconstruction (SIR) algorithms have the potential to significantly reduce image artifacts by minimizing a cost function that models the physics and statistics of the data acquisition process in X-ray CT. SIR algorithms have superior performance compared to traditional analytical reconstructions for a wide range of applications including nonstandard geometries arising from irregular sampling, limited angular range, missing data, and low-dose CT. The main hurdle for the widespread adoption of SIR algorithms in multislice X-ray CT reconstruction ...


Spin Alignment Generated In Inelastic Nuclear Reactions, Daniel Hoff Aug 2018

Spin Alignment Generated In Inelastic Nuclear Reactions, Daniel Hoff

Arts & Sciences Electronic Theses and Dissertations

The spin alignment of inelastically excited 7Li projectiles, when the target remains in its ground state, was determined through angular-correlation measurements between the breakup fragments of 7Li_ (_ + t). It was found that 7Li_ is largely aligned along the beam axis (longitudinal) in this type of inelastic reaction, regardless of the target. This longitudinal alignment is well described by DWBA calculations, which can be explained by an angular-momentum-excitation-energy mismatch condition. These calculations also explain the longitudinal spin alignment of excited nuclei in several other systems, showing the phenomenon is more general. The experiment involving 7Li was performed at the Texas ...


Super‐Resolution Imaging Of Amyloid Structures Over Extended Times By Using Transient Binding Of Single Thioflavin T Molecules, Kevin Spehar, Tianben Ding, Yuanzi Sun, Niraja Kedia, Jin Lu, George R. Nahass, Matthew D. Lew, Jan Bieschke Jun 2018

Super‐Resolution Imaging Of Amyloid Structures Over Extended Times By Using Transient Binding Of Single Thioflavin T Molecules, Kevin Spehar, Tianben Ding, Yuanzi Sun, Niraja Kedia, Jin Lu, George R. Nahass, Matthew D. Lew, Jan Bieschke

Electrical & Systems Engineering Publications and Presentations

Oligomeric amyloid structures are crucial therapeutic targets in Alzheimer's and other amyloid diseases. However, these oligomers are too small to be resolved by standard light microscopy. We have developed a simple and versatile tool to image amyloid structures by using thioflavin T without the need for covalent labeling or immunostaining. The dynamic binding of single dye molecules generates photon bursts that are used for fluorophore localization on a nanometer scale. Thus, photobleaching cannot degrade image quality, allowing for extended observation times. Super‐resolution transient amyloid binding microscopy promises to directly image native amyloid by using standard probes and record ...


Imaging The Three-Dimensional Orientation And Rotational Mobility Of Fluorescent Emitters Using The Tri-Spot Point Spread Function, Oumeng Zhang, Jin Lu, Tianben Ding, Matthew D. Lew Jun 2018

Imaging The Three-Dimensional Orientation And Rotational Mobility Of Fluorescent Emitters Using The Tri-Spot Point Spread Function, Oumeng Zhang, Jin Lu, Tianben Ding, Matthew D. Lew

Electrical & Systems Engineering Publications and Presentations

Fluorescence photons emitted by single molecules contain rich information regarding their rotational motions, but adapting single-molecule localization microscopy (SMLM) to measure their orientations and rotational mobilities with high precision remains a challenge. Inspired by dipole radiation patterns, we design and implement a Tri-spot point spread function (PSF) that simultaneously measures the three-dimensional orientation and the rotational mobility of dipole-like emitters across a large field of view. We show that the orientation measurements done using the Tri-spot PSF are sufficiently accurate to correct the anisotropy-based localization bias, from 30 nm to 7 nm, in SMLM. We further characterize the emission anisotropy ...


Completing Cooperative Task By Utilizing Eeg-Based Brain Computer Interface, Jongwoon Kim May 2018

Completing Cooperative Task By Utilizing Eeg-Based Brain Computer Interface, Jongwoon Kim

Engineering and Applied Science Theses & Dissertations

We sought to design a cooperative brain computer interface (BCI), wherein multiple users contribute brain activities that are decoded towards a common goal. We used a base design involving collection of electroencephalographic (EEG) brain activity from a low-cost consumer system (the Muse Headband), then classified the ensuing signals into different mental states as either relaxed or focused. The goal of the cooperative BCI was to have two subjects drive a cursor on the screen to some acceptance range given a prescribed path. Each subject was responsible for controlling either the direction or the displacement of the ball. EEG patterns for ...


Inferring Intent From Interaction With Visualization, Ran Wan May 2018

Inferring Intent From Interaction With Visualization, Ran Wan

Engineering and Applied Science Theses & Dissertations

Today's state-of-the-art analysis tools combine the human visual system and domain knowledge, with the machine's computational power. The human performs the reasoning, deduction, hypothesis generation, and judgment. The entire burden of learning from the data usually rests squarely on the human user's shoulders. This model, while successful in simple scenarios, is neither scalable nor generalizable. In this thesis, we propose a system that integrates advancements from artificial intelligence within a visualization system to detect the user's goals. At a high level, we use hidden unobservable states to represent goals/intentions of users. We automatically infer these ...


Exploiting Click-Chemistry And Microfluidics To Map The Neuronal Itinerary Of App Processing And Amyloid-Beta Generation, Namratha Srinivas May 2018

Exploiting Click-Chemistry And Microfluidics To Map The Neuronal Itinerary Of App Processing And Amyloid-Beta Generation, Namratha Srinivas

Engineering and Applied Science Theses & Dissertations

Alzheimer’s disease (AD) is a chronic neurodegenerative disease and is the sixth leading cause of death in the United States with approximately 5.5 million Americans diagnosed with it. The neuropathological hallmark includes extracellular senile plaques and intraneuronal neurofibrillary tangles. Recent GWAS studies have identified genes associated with AD, and have revealed several classes of genes implicated in disease pathogenesis. In particular, three general pathways associated with an increased risk of AD included: 1) cholesterol metabolism, innate immune system, and the membrane trafficking. Our lab has focused on intracellular trafficking as it relates to the processing of amyloid precursor ...


Optimization Of Gpu-Accelerated Iterative Ct Reconstruction Algorithm For Clinical Use, Tao Ge May 2018

Optimization Of Gpu-Accelerated Iterative Ct Reconstruction Algorithm For Clinical Use, Tao Ge

Engineering and Applied Science Theses & Dissertations

In order to transition the GPU-accelerated CT reconstruction algorithm to a more clinical environment, a graphical user interface is implemented. Some optimization methods on the implementation are presented. We describe the alternating minimization (AM) algorithm as the updating algorithm, and the branchless distance-driven method for the system forward operator. We introduce a version of the Feldkamp-Davis-Kress algorithm to generate the initial image for our alternating minimization algorithm and compare it to a choice of a constant initial image. For the sake of better rate of convergence, we introduce the ordered-subsets method, find the optimal number of ordered subsets, and discuss ...


Modeling Of Swimming Cells From Nano-Scale To Micro-Scale, Yicheng Zhao May 2018

Modeling Of Swimming Cells From Nano-Scale To Micro-Scale, Yicheng Zhao

Engineering and Applied Science Theses & Dissertations

Certain human genetic diseases -- primary ciliary dyskinesia, infertility, and hydrocephalus -- are characterized by changes in beat frequency and waveform of cilia and flagella. Chlamydomonas reinhardtii, which is a single-cell green alga about ten micrometers in diameter that swims with two flagella, serves as an excellent biological model because its flagella share the same structure and genetic background as mammalian cilia and flagella. This study uses the finite element method to investigate the behavior of C. reinhardtii swimming from nano-scale to micro-scale. At the device-level, micro-scale modeling indicates that well-designed acoustic microfluidic devices can be used to trap groups of C ...


Numerical Simulations And Studies On Round Jet Impingement, Twin Jet Impingement And Helicopter Rotor Blades Ground Effect, Han Gao May 2018

Numerical Simulations And Studies On Round Jet Impingement, Twin Jet Impingement And Helicopter Rotor Blades Ground Effect, Han Gao

Engineering and Applied Science Theses & Dissertations

In this thesis, the whole materials can be divided in to three parts. The first part focused on single round jet impingement. The convention air jet impingement on ground surface was compared to air jet impingement on water surface in the range of Mach number from 0 to 0.3. Currently the studies on round jet impingement on water surface are very few. The goal of this research is to study the difference of aerodynamics and flow physics between air jet impinging on water surface and ground surface at different low Mach number and Non-dimensional height. The incompressible Reynolds-Averaged Navier-Stokes ...


Computational Fluid Dynamics Analysis Of Arteriovenous Graft Configurations, Dillon Williams May 2018

Computational Fluid Dynamics Analysis Of Arteriovenous Graft Configurations, Dillon Williams

Engineering and Applied Science Theses & Dissertations

Hemodialysis is a process of external blood filtration that becomes necessary in the event of end stage renal disease. The most common method of the treatment is the creation of an arteriovenous fistula, which is a surgically created connection between a vein and an artery. For patients who are unable to have an arteriovenous fistula, an arteriovenous graft is required. This graft serves to provide an access site for the removal on unfiltered blood and the return of filtered blood. The design and placement of this graft has not yet been optimized based upon mechanical principles. The aim of this ...


An Evaluation Of Proposed And Current Cardiovascular Stent Design Approaches To Aortoiliac Occlusive Disease, Alexander Wirtz May 2018

An Evaluation Of Proposed And Current Cardiovascular Stent Design Approaches To Aortoiliac Occlusive Disease, Alexander Wirtz

Engineering and Applied Science Theses & Dissertations

Aortoiliac occlusive disease is a subsequent disease of atherosclerosis involving the accumulation of plaque on the lining of the artery wall causing the artery lumen to narrow at the site of the aortic bifurcation. To prevent foreseeable embolization threats or ischemia, revascularization of the aortic bifurcation is commonly treated by arterial stenting. The most common practice of arterial stenting of aortoiliac occlusive disease is using balloon expandable stents. Traditionally, in order to prevent encroachment and/or occlusion of one iliac system by the stenting of the other, two balloon expandable stents are placed in the aortic bifurcation adjacently (kissing) at ...


Chronic Nerve Interfacing Utilizing Graft-Embedded Regenerative Macro-Sieve Electrodes, Amrita Nishtala May 2018

Chronic Nerve Interfacing Utilizing Graft-Embedded Regenerative Macro-Sieve Electrodes, Amrita Nishtala

Engineering and Applied Science Theses & Dissertations

Custom-designed macro-sieve electrodes represent a novel means of facilitating chronic high specificity nerve stimulation needed to control distal nerve musculature and restore sensorimotor function. Implantation of these electrodes requires the transection of the nerve, which has shown to disrupt muscle fiber distribution. This present study assesses the feasibility of implementing these electrodes in an end-to-side nerve graft. The macro-sieve electrodes were fabricated and micro-surgically implanted into 3.2 cm nerve autografts harvested from the sciatic nerve of 12 male Lewis rats. Electrode-enabled nerve grafts were micro-surgically implanted in an end-to-side manner into donor rat sciatic nerves without the need for ...


Fundamental Studies Of Solid-Fuel Combustion Using A Two-Stage Flat-Flame Burner, Adewale Ayodeji Adeosun May 2018

Fundamental Studies Of Solid-Fuel Combustion Using A Two-Stage Flat-Flame Burner, Adewale Ayodeji Adeosun

Engineering and Applied Science Theses & Dissertations

Innovative coal technologies are essential for addressing concerns about air pollution and global climate change. A key pathway to advancing these technologies is through developing a thorough understanding of the fundamental physical and chemical processes that occur during coal combustion. Ignition influences many aspects of coal combustion, including flame stability, submicron aerosol evolution, and char burnout. As important as ignition and these associated processes are, they are challenging to study because they depend on many factors, such as the combustion environment, particle size, and particle-particle interactions.

While there have been many studies of coal ignition, none have studied the process ...


Fluorescence Guided Tumor Imaging: Foundations For Translational Applications, Jessica P. Miller May 2018

Fluorescence Guided Tumor Imaging: Foundations For Translational Applications, Jessica P. Miller

Engineering and Applied Science Theses & Dissertations

Optical imaging for medical applications is a growing field, and it has the potential to improve medical outcomes through its increased sensitivity and specificity, lower cost, and small instrumentation footprint as compared to other imaging modalities. The method holds great promise, ranging from direct clinical use as a diagnostic or therapeutic tool, to pre-clinical applications for increased understanding of pathology. Additionally, optical imaging uses non-ionizing radiation which is safe for patients, so it can be used for repeated imaging procedures to monitor therapy, guide treatment, and provide real-time feedback. The versatile features of fluorescence-based optical imaging make it suited for ...


Functional Electrical Stimulation Of Peripheral Nerve Tissue Via Regenerative Sieve Microelectrodes, Matthew Reagan Macewan May 2018

Functional Electrical Stimulation Of Peripheral Nerve Tissue Via Regenerative Sieve Microelectrodes, Matthew Reagan Macewan

Engineering and Applied Science Theses & Dissertations

Functional electrical stimulation (FES) of peripheral nervous tissue offers a promising method for restoring motor function in patients suffering from complex neurological injuries. However, existing microelectrodes designed to stimulate peripheral nerve are unable to provide the type of stable, selective interface required to achieve near-physiologic control of peripheral motor axons and distal musculature. Regenerative sieve electrodes offer a unique alternative to such devices, achieving a highly stable, selective electrical interface with independent groups of regenerated nerve fibers integrated into the electrode. Yet, the capability of sieve electrodes to functionally recruit regenerated motor axons for the purpose of muscle activation remains ...


Application Of Metabolic Modeling And Machine Learning For Investigating Microbial Systems, Ni Wan May 2018

Application Of Metabolic Modeling And Machine Learning For Investigating Microbial Systems, Ni Wan

Engineering and Applied Science Theses & Dissertations

Metabolic modeling is an important tool to interpret the comprehensive cell metabolism and dynamic relationship between substrates and biomass/bioproducts. Genome-scale flux balance model and 13C-metabolic flux analysis are metabolic models which can reveal the theoretical yield and central carbon metabolism under various environmental conditions. Kinetic model is able to capture the complex principles between the change of biomass growth and bioproducts accumulation with the time series. Machine learning model is a data driven approach to reveal fermentation behavior and further predict cell performance under complex circumstances. In my PhD study, modeling analysis and machine learning method have been used ...


Developing Photoacoustic Tomography Devices For Translational Medicine And Basic Science Research, Tsz Wai Wong May 2018

Developing Photoacoustic Tomography Devices For Translational Medicine And Basic Science Research, Tsz Wai Wong

Engineering and Applied Science Theses & Dissertations

Photoacoustic (PA) tomography (PAT) provides volumetric images of biological tissue with scalable spatial resolutions and imaging depths, while preserving the same imaging contrast—optical absorption. Taking the advantage of its 100% sensitivity to optical absorption, PAT has been widely applied in structural, functional, and molecular imaging, with both endogenous and exogenous contrasts, at superior depths than pure optical methods. Intuitively, hemoglobin has been the most commonly studied biomolecule in PAT due to its strong absorption in the visible wavelength regime.

One of the main focuses of this dissertation is to investigate an underexplored wavelength regime—ultraviolet (UV), which allows us ...


Design And Preliminary Testing Of An Improved Abdomen Testing Device For Use In Hernia Repair Modeling, Alexandra Dunbar May 2018

Design And Preliminary Testing Of An Improved Abdomen Testing Device For Use In Hernia Repair Modeling, Alexandra Dunbar

Engineering and Applied Science Theses & Dissertations

No abstract provided.


Validation Of Cfd Simulations For Hypersonic Flow Over A Yawed Cone, Julian Cecil May 2018

Validation Of Cfd Simulations For Hypersonic Flow Over A Yawed Cone, Julian Cecil

Engineering and Applied Science Theses & Dissertations

This study aims to numerically simulate the wind tunnel results for hypersonic flow over a circular cone of semi-apex angle of 10 degrees yawed from 0° to 20° using the commercial computational fluid dynamics software ANSYS Fluent. The ANSYS workbench is used to create the 10° semi-apex circular cone with a shock aligned structured mesh of 3.05 million cells surrounding the cone. Simulation boundary conditions for pressure and temperature in the far field correspond to Tracy’s wind tunnel experiment at Cal Tech. The six simulations cases are conducted for yaw angles of 0, 8, 12, 16, 20 and ...