Matching Items (12)
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- Creators: Mechanical and Aerospace Engineering Program
- Creators: School of Mathematical and Statistical Sciences
- Status: Published
Description
Chebfun is a collection of algorithms and an open-source software system in object-oriented Matlab that extends familiar powerful methods of numerical computation involving numbers to continuous or piecewise-continuous functions. The success of this strategy is based on the mathematical fact that smooth functions can be represented very efficiently by polynomial interpolation at Chebyshev points or by trigonometric interpolation at equispaced points for periodic functions. More recently, the system has been extended to handle bivariate functions and vector fields. These two new classes of objects are called Chebfun2 and Chebfun2v, respectively. We will show that Chebfun2 and Chebfun2v, and can be used to accurately and efficiently perform various computations on parametric surfaces in two or three dimensions, including path trajectories and mean and Gaussian curvatures. More advanced surface computations such as mean curvature flows are also explored. This is also the first work to use the newly implemented trigonometric representation, namely Trigfun, for computations on surfaces.
ContributorsPage-Bottorff, Courtney Michelle (Author) / Platte, Rodrigo (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.
ContributorsMcleod, Kristyn Noelle (Author) / Platte, Rodrigo (Thesis director) / Gelb, Anne (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor)
Created2014-05
Description
Monatomic gases are ideal working mediums for Brayton cycle systems due to their favorable thermodynamic properties. Closed Brayton cycle systems make use of these monatomic gases to increase system performance and thermal efficiency. Open Brayton cycles, on the other hand, operate with primarily diatomic and polyatomic gases from air and combustion products, which have less favorable properties. The focus of this study is to determine if monatomic gases can be utilized in an open Brayton cycle system, in a way that increases the overall performance, but is still cost effective.
Two variations on open cycle Brayton systems were analyzed, consisting of an “airborne” thrust producing propulsion system, and a “ground-based” power generation system. Both of these systems have some mole fraction of He, Ne, or Ar injected into the flow path at the inlet, and some fraction of monatomic gas recuperated and at the nozzle exit to be re-circulated through the system. This creates a working medium of an air-monatomic gas mixture before the combustor, and a combustion products-monatomic gas mixture after combustor. The system’s specific compressor work, specific turbine work, specific net power output, and thermal efficiency were analyzed for each case. The most dominant metric for performance is the thermal efficiency (η_sys), which showed a significant increase as the mole fraction of monatomic gas increased for all three gas types. With a mole fraction of 0.15, there was a 2-2.5% increase in the airborne system, and a 1.75% increase of the ground-based system. This confirms that “spiking” any open Brayton system with monatomic gas will lead to an increase in performance. Additionally, both systems showed an increase in compressor and turbine work for a set temperature difference with He and Ne, which can additionally lead to longer component lifecycles with less frequent maintenance checks.
The cost analysis essentially compares the operating cost of a standard system with the operating cost of the monatomic gas “spiked” system, while keeping the internal mass flow rate and total power output the same. This savings is denoted as a percent of the standard system with %NCS. This metric lumps the cost ratio of the monatomic gas and fuel (MGC/FC) with the fraction of recuperated monatomic gas (RF) into an effective cost ratio that represents the cost per second of monatomic gas injected into the system. Without recuperation, the results showed there is no mole fraction of any monatomic gas type that yields a positive %NCS for a reasonable range of current MGC/FC values. Integrating recuperation machinery in an airborne system is hugely impractical, effectively meaning that the use of monatomic gas in this case is not feasible. For a ground-based system on the other hand, recuperation is much more practical. The ground-based system showed that a RF value of at least 50% for He, 89% for Ne, and 94% for Ar is needed for positive savings. This shows that monatomic gas could theoretically be used cost effectively in a ground-based, power-generating open Brayton system. With an injected monatomic gas mole fraction of 0.15, and full 100% recuperation, there is a net cost savings of about 3.75% in this ground-based system.
Two variations on open cycle Brayton systems were analyzed, consisting of an “airborne” thrust producing propulsion system, and a “ground-based” power generation system. Both of these systems have some mole fraction of He, Ne, or Ar injected into the flow path at the inlet, and some fraction of monatomic gas recuperated and at the nozzle exit to be re-circulated through the system. This creates a working medium of an air-monatomic gas mixture before the combustor, and a combustion products-monatomic gas mixture after combustor. The system’s specific compressor work, specific turbine work, specific net power output, and thermal efficiency were analyzed for each case. The most dominant metric for performance is the thermal efficiency (η_sys), which showed a significant increase as the mole fraction of monatomic gas increased for all three gas types. With a mole fraction of 0.15, there was a 2-2.5% increase in the airborne system, and a 1.75% increase of the ground-based system. This confirms that “spiking” any open Brayton system with monatomic gas will lead to an increase in performance. Additionally, both systems showed an increase in compressor and turbine work for a set temperature difference with He and Ne, which can additionally lead to longer component lifecycles with less frequent maintenance checks.
The cost analysis essentially compares the operating cost of a standard system with the operating cost of the monatomic gas “spiked” system, while keeping the internal mass flow rate and total power output the same. This savings is denoted as a percent of the standard system with %NCS. This metric lumps the cost ratio of the monatomic gas and fuel (MGC/FC) with the fraction of recuperated monatomic gas (RF) into an effective cost ratio that represents the cost per second of monatomic gas injected into the system. Without recuperation, the results showed there is no mole fraction of any monatomic gas type that yields a positive %NCS for a reasonable range of current MGC/FC values. Integrating recuperation machinery in an airborne system is hugely impractical, effectively meaning that the use of monatomic gas in this case is not feasible. For a ground-based system on the other hand, recuperation is much more practical. The ground-based system showed that a RF value of at least 50% for He, 89% for Ne, and 94% for Ar is needed for positive savings. This shows that monatomic gas could theoretically be used cost effectively in a ground-based, power-generating open Brayton system. With an injected monatomic gas mole fraction of 0.15, and full 100% recuperation, there is a net cost savings of about 3.75% in this ground-based system.
ContributorsBernaud, Ryan Clark (Author) / Dahm, Werner (Thesis director) / Wells, Valana (Committee member) / Mechanical and Aerospace Engineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.
ContributorsWhitehurst, Ryan David (Author) / Kostelich, Eric (Thesis director) / Jones, Donald (Committee member) / Armbruster, Dieter (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-05
Description
A statistical method is proposed to learn what the diffusion coefficient is at any point in space of a cell membrane. The method used bayesian non-parametrics to learn this value. Learning the diffusion coefficient might be useful for understanding more about cellular dynamics.
ContributorsGallimore, Austin Lee (Author) / Presse, Steve (Thesis director) / Armbruster, Dieter (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Energy efficient optimal formation control of a multiple quadrotor UAV system with uncertain payload
Description
This thesis presents the design and simulation of an energy efficient controller for a system of three drones transporting a payload in a net. The object ensnared in the net is represented as a mass connected by massless stiff springs to each drone. Both a pole-placement approach and an optimal control approach are used to design a trajectory controller for the system. Results are simulated for a single drone and the three drone system both without and with payload.
ContributorsHayden, Alexander (Author) / Grewal, Anoop (Thesis director) / Berman, Spring (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Historical, Philosophical & Religious Studies, Sch (Contributor)
Created2022-05
Description
This paper describes the development of a software tool used to automate the preliminary design of aircraft wing structure. By taking wing planform and aircraft weight as inputs, the tool is able to predict loads that will be experienced by the wing. An iterative process is then used to select optimal material thicknesses for each section of the design to minimize total structural weight. The load analysis checks for tensile failure as well as Euler buckling when considering if a given wing structure is valid. After running a variety of test cases with the tool it was found that wing structure of small-scale aircraft is predominantly buckling driven. This is problematic because commonly used weight estimation equations are based on large scale aircraft with strength driven wing designs. Thus, if these equations are applied to smaller aircraft, resulting weight estimates are often much lower than reality. The use of a physics-based approach to preliminary sizing could greatly improve the accuracy of weight predictions and accelerate the design process.
ContributorsKolesov, Nikolay (Author) / Takahashi, Timothy (Thesis director) / Patel, Jay (Committee member) / Kosaraju, Srinivas (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-12
Description
The purpose of this project was to create an algorithm to improve firearm aiming. In order to do so, a simulation of exterior ballistics – the bullet’s behavior between the firearm muzzle and the target – was created in MATLAB. The simulation of bullet trajectory included consideration of three forces: gravity, air drag, and Coriolis ‘force’. An overall equation of motion for the bullet in flight, comprising the effects of the aforementioned forces, was constructed using formulae and theory given in R. L. McCoy’s Modern Exterior Ballistics. For the project, a reference frame was defined based on firearm muzzle and target positions, and an aim vector described by two angles was defined to describe the direction of the firearm’s barrel. The simulations of bullet trajectory take into account eleven parameters: the two aim angles, initial bullet speed (commonly referred to as muzzle velocity), 3-D Cartesian components of wind velocity, air density, bullet diameter, bullet mass, latitude of the firing area, and azimuth of fire (a quantified compass direction of fire).
The user inputs target position, muzzle position, and estimated environmental parameters to the system. Then, an aim vector would be calculated to hit the target under estimated conditions. Because the eleven trajectory parameters likely cannot all be precisely known, this solution will have some error. In real life, the system would use feedback from real shots of a firearm to correct for this error. For this project, a real-world proxy simulation was created that had built-in random error and variations in the parameters. The correction algorithm uses the error data from all previous shots to calculate adjustments to the original aim vector, so that each successive shot becomes more accurate. The system was tested with specifications of a common rifle platform, with estimated parameters and variations for a location in Tempe, AZ (since data for an urban area is readily available compared to a point in the wilderness). Results from this testing revealed that the system can “hit” a 2-meter-radius circular target in under 30 shots. When the errors and variations in parameters were halved for the real-world stand-in simulation, the system could “hit” a circular target with 0.55 meter radius in less than 25 shots. After analysis, it was found that the corrected aim angles converged on values, suggesting that the correction algorithm functions as intended (taking into account all past shots). Generally, it was found that any reduction of the means and standard deviations of parameter error improved the ability of the system to hit smaller targets, or hit the same target with less shots.
The user inputs target position, muzzle position, and estimated environmental parameters to the system. Then, an aim vector would be calculated to hit the target under estimated conditions. Because the eleven trajectory parameters likely cannot all be precisely known, this solution will have some error. In real life, the system would use feedback from real shots of a firearm to correct for this error. For this project, a real-world proxy simulation was created that had built-in random error and variations in the parameters. The correction algorithm uses the error data from all previous shots to calculate adjustments to the original aim vector, so that each successive shot becomes more accurate. The system was tested with specifications of a common rifle platform, with estimated parameters and variations for a location in Tempe, AZ (since data for an urban area is readily available compared to a point in the wilderness). Results from this testing revealed that the system can “hit” a 2-meter-radius circular target in under 30 shots. When the errors and variations in parameters were halved for the real-world stand-in simulation, the system could “hit” a circular target with 0.55 meter radius in less than 25 shots. After analysis, it was found that the corrected aim angles converged on values, suggesting that the correction algorithm functions as intended (taking into account all past shots). Generally, it was found that any reduction of the means and standard deviations of parameter error improved the ability of the system to hit smaller targets, or hit the same target with less shots.
ContributorsReyes, Joshua De Leon (Author) / Grewal, Anoop Singh (Thesis director) / Murthy, Raghavendra N. (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
This Creative Project was carried out in coordination with the capstone project, Around the Corner Imaging with Terahertz Waves. This capstone project deals with a system designed to implement Around the Corner, or Non Line-of-Sight (NLoS) Imaging. This document discusses the creation of a GUI using MATLAB to control the Terahertz Imaging system. The GUI was developed in response to a need for synchronization, ease of operation, easy parameter modification, and data management. Along the way, many design decisions were made ranging from choosing a software platform to determining how variables should be passed. These decisions and considerations are discussed in this document. The resulting GUI has measured up to the design criteria and will be able to be used by anyone wishing to use the Terahertz Imaging System for further research in the field of Around the Corner or NLoS Imaging.
ContributorsWood, Jacob Cannon (Author) / Trichopoulos, Georgios (Thesis director) / Aberle, James (Committee member) / Electrical Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
This honors thesis explores and models the flow of air around a cylindrical arrow that is rotating as it moves through the air. This model represents the airflow around an archery arrow after it is released from the bow and rotates while it flies through the air. This situation is important in archery because an understanding of the airflow allows archers to predict the flight of the arrow. As a result, archers can improve their accuracy and ability to hit targets. However, not many computational fluid dynamic simulations modeling the airflow around a rotating archery arrow exist. This thesis attempts to further the understanding of the airflow around a rotating archery arrow by creating a mathematical model to numerically simulate the airflow around the arrow in the presence of this rotation. This thesis uses a linearized approximation of the Navier Stokes equations to model the airflow around the arrow and explains the reasoning for using this simplification of the fully nonlinear Navier Stokes equations. This thesis continues to describe the discretization of these linearized equations using the finite difference method and the boundary conditions used for these equations. A MATLAB code solves the resulting system of equations in order to obtain a numerical simulation of this airflow around the rotating arrow. The results of the simulation for each velocity component and the pressure distribution are displayed. This thesis then discusses the results of the simulation, and the MATLAB code is analyzed to verify the convergence of the solution. Appendix A includes the full MATLAB code used for the flow simulation. Finally, this thesis explains potential future research topics, ideas, and improvements to the code that can help further the understanding and create more realistic simulations of the airflow around a flying archery arrow.
ContributorsCholinski, Christopher John (Author) / Tang, Wenbo (Thesis director) / Herrmann, Marcus (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05