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http://hdl.handle.net/11141/3130
Optimal Control of Coefficients for the Second Order Parabolic Free Boundary Problems
Hagverdiyev, Ali
Dissertation aims to analyze inverse Stefan type free boundary problem for the second
order parabolic PDE with unknown parameters based on the additional information given
in the form of the distribution of the solution of the PDE and the position of the free
boundary at the final moment. This type of ill-posed inverse free boundary problems
arise in many applications such as biomedical engineering problem about the laser ablation of biomedical tissues, in-flight ice accretion modeling in aerospace industry, and
various phase transition processes in thermophysics and fluid mechanics. The set of unknown parameters include a space-time dependent diffusion, convection and reaction coefficients, density of the sources, time-dependent boundary flux and the free boundary.
New PDE constrained optimal control framework in Hilbert-Besov spaces introduced in
U.G. Abdulla, Inverse Problems and Imaging, 7, 2(2013), 307-340; 10, 4(2016), 869-898
is employed, where the missing data and the free boundary are components of the control
vector, and optimality criteria are based on the final moment measurement of the temperature and position of the free boundary, and available information on the phase transition
temperature on the free boundary. The latter presents a key advantage in dealing with applications, where phase transition temperature is not known explicitly, but involve some
measurement error. Another advantage of the new variational approach is based on the
fact that for a given control parameter, Stefan boundary condition turns into Neumann
boundary condition on the given boundary, and parabolic PDE problem is solved in a
fixed domain, and therefore a perspective opens for the development of numerical methods of least computational cost. Discretization of the optimal control problem via method
of finite differences is pursued and the sequence of finite-dimensional optimal control
problems are introduced. The results of the dissertation are different depending on the
structure of the unknown diffusion coefficient. In the case if it is only time-dependent,
the well-posedness of the optimal control problem is established in Hilbert-Besov spaces.
Existence of the optimal control and convergence of the sequence of the discrete optimal
control problems to the continuous optimal control problem both with respect to functional and control is proved. The methods of the proof are based on uniform H
1
-energy
estimates in discrete Sobolev-Hilbert norms, weak compactness argument, Weierstrass
theorem in weak topology and weak convergence of the bilinear interpolations of the solutions of the discrete PDE problems to the solution of the optimal PDE problem in the
class of weakly differentiable functions. To prove similar results in the case when unknown diffusion coefficient is space-time dependent, a new Banach space is introduced.
The motivation for the new space is dictated with the optimal result on the convergence
of the bilinear interpolations of the grid functions in the class of weakly differentiable
functions, and establishment of the discrete H
1
-energy estimate under minimal assumptions on the diffusion coefficient. Existence of the optimal control and convergence of the
sequence of discrete optimal control problems to the continuous optimal control problem
both with respect to functional and control is proved in the setting of the new Banach
space.
Thesis - (Ph.D.) - Florida Institute of Technology, 2020.
Fri, 01 May 2020 00:00:00 GMThttp://hdl.handle.net/11141/31302020-05-01T00:00:00ZCharacterization of Written Text Using Data and Network Science
http://hdl.handle.net/11141/3129
Characterization of Written Text Using Data and Network Science
Hamoodat, Harith A. Hamdon
The success of humans cannot be attributed to language, but it is certainly true
that language and humans are inseparable. Since the first language appeared, we
have seen that language continually evolving over space and social gatherings to
formed around 7,000 languages today. The origin and evolution of languages still
vague, and state-of-the-art in languages evolution still lack a comprehensive characterization. In general, this problem is mainly tackled by statistical measuring the
changes on the part of the language ( e.g., words and sounds). Given the current
availability of data and computational power, this dissertation proposes a comprehensive data-driven characterization of language evolution using vocabulary in
two main fields. First, extracted and classified the structural and chronological
relations between the languages using its vocabulary. Second, studied the Spatio-temporal effect on language vocabulary and its relation with socio-economic factors ( i.e., educational attainment). The results demonstrated that the proposed
method is capable of uncovering the relation between languages from both structural and chronological aspects, also we found that the vocabulary levels can reveal
the educational attainment of a resident population for specific areas and times.
Thesis (Ph.D.) - Florida Institute of Technology, 2020.
Fri, 01 May 2020 00:00:00 GMThttp://hdl.handle.net/11141/31292020-05-01T00:00:00ZDesign, Analysis, and Demonstration of a Multipurpose Fluid Tank Dynamics Characterization Platform
http://hdl.handle.net/11141/3128
Design, Analysis, and Demonstration of a Multipurpose Fluid Tank Dynamics Characterization Platform
Hume, Cameron Ian
The development of a highly versatile multiphase fluid tank characterization platform is
essential to the analysis and improvement of propellant storage tanks. The performance of
these tanks is highly critical to the safety and performance of their carriers, especially in
the space industry where the propellant makes up the overwhelming majority of the mass
of the vehicle. This thesis outlines the design and development of a linear stage used to test
and validate the characteristic of multiphase fluids inside moving specific tanks. This
document will walk through the steps taken to bring a new linear stage to life, from the
development of effective requirements, through design and analysis to the demonstration
of the final product. The final product is a powerfully yet precise piece of machinery that
will add value to the area of fluids research for years to come.
Thesis (M.S.) - Florida Institute of Technology, 2020.
Fri, 01 May 2020 00:00:00 GMThttp://hdl.handle.net/11141/31282020-05-01T00:00:00ZExamining the Impact of Student Motivation on Performance in Mechanical Engineering Design Courses
http://hdl.handle.net/11141/3127
Examining the Impact of Student Motivation on Performance in Mechanical Engineering Design Courses
Kames, Elisabeth
Design courses are an integral component of undergraduate engineering education.
Design is recognized as one of the primary responsibilities of an engineer in industry. New
designs are responsible for stimulating sales and company growth.1 This dissertation
outlines a study seeking to explore the impact of student motivation factors on course
performance of mechanical engineering students in design courses. The first design course,
cornerstone design, takes place during the first semester of freshman year. The second
course, capstone design, takes place during the student’s final year of undergraduate study.
An adapted version of the Motivated Strategies for Learning Questionnaire (MSLQ) is
used to measure five motivation factors: cognitive value, self-regulation, test/presentation
anxiety, intrinsic value, and self-efficacy. Motivation is measured against the final grade in
the course, which is used as the performance metric.
The major contribution of this research is the ability to examine the impact of
motivation on performance in design courses. The motivation and performance is also
measured against student demographic information with regard to student gender, residency (domestic or international), family income, and highest degree attained by
parents to determine if a correlation is realized. Additionally, the longitudinal study
focuses on a single cohorts of students. This affords the ability for the examination of the
differences in motivation between the students’ freshman and senior year to determine if
this can be correlated to student gender, residency (domestic or international), family
income, and degree attained by parents.
The results indicate that motivation is a key factor in the students’ performance in
design curriculum. All five of the motivation factors are found to impact the students’
performance; however, different motivation factors are found to impact the students’
performance at different points in time. This proves the multidimensional and dynamic
nature of motivation. The quantitative findings are further explored through qualitative
data analysis to explore variables impacting the students’ motivation and performance
throughout their capstone design sequence. A total of 69 unique codes were identified
through the student interviews, providing useful feedback on student experiences in senior
capstone design at Florida Institute of Technology.
Thesis (Ph.D.) - Florida Institute of Technology, 2020.
Fri, 01 May 2020 00:00:00 GMThttp://hdl.handle.net/11141/31272020-05-01T00:00:00Z