• From Gravity to Hopf Algebra Lattice Models 

  Osumanu, Abdulmajid (University of Waterloo, 2019-10-02)

  This thesis addresses three different problems related to quantum gravity. In the first problem we will discuss the two natural ways to encode gravity through geometric structures. One is the much acclaimed Einstein's ...

• Physical Modelling and the Associated Acoustic Behaviour of Trumpets and Trombones 

  Resch, Janelle (University of Waterloo, 2019-09-30)

  Accurately modelling the production of realistic musical notes in brass instruments is no easy task. Compared to woodwind instruments, brass instruments are considerably longer and constructed with bends, valves or coils, ...

• Optimal Actuator Design for Nonlinear Systems 

  Edalatzadeh, M. Sajjad (University of Waterloo, 2019-09-24)

  For systems modeled by partial differential equations (PDE's), the location and shape of the actuators can be regarded as a design variable and included as part of the controller synthesis procedure. Optimal actuator ...

• A walk through quantum noise: a study of error signatures and characterization methods 

  Carignan-Dugas, Arnaud (University of Waterloo, 2019-09-17)

  The construction of large scale quantum computing devices might be one of the most exciting and promising endeavors of the 21st century, but it also comes with many challenges. As quantum computers are supplemented with ...

• The Interactions of Graphene with Ionic Solutions and Their Effects on the Differential Capacitance for Sensing Applications 

  Daniels, Lindsey (University of Waterloo, 2019-08-28)

  Nano-scale devices continue to challenge the theoretical understanding of microscopic systems. Of particular interest is the characterization of the interface electrochemistry of sensors, which operate as field effect ...

• Black Hole to White Hole Quantum Tunnelling 

  Clements, Kate Elizabeth Alexandra (University of Waterloo, 2019-08-26)

  In this thesis, we explore the proposal that near the end of its lifetime, a Schwarzschild black hole will undergo a quantum transition into a 'white hole': an object which is precisely the time-reversal of the black hole. ...

• Numerical Methods for Hamilton-Jacobi-Bellman Equations with Applications 

  Chen, Yangang (University of Waterloo, 2019-08-26)

  Hamilton-Jacobi-Bellman (HJB) equations are nonlinear controlled partial differential equations (PDEs). In this thesis, we propose various numerical methods for HJB equations arising from three specific applications. First, ...

• Model for a cortical circuit associated with childhood absence epilepsy 

  Ahmed, Maliha (University of Waterloo, 2019-08-23)

  Childhood absence epilepsy is suspected to result from mutations in genes which encode ion channels including sodium channels. Our purpose in this thesis is to explore some of the factors that alter the function of neurons ...

• Mathematical Modelling of Cancer Treatments Involving Radiation Therapy and Hypoxia-Activated Prodrugs 

  Meaney, Cameron (University of Waterloo, 2019-08-19)

  Cancer is one of the world's deadliest diseases despite immense investments into oncological research in recent years. Although great strides have been made in our understanding of cancer, much remains unknown regarding ...

• Particle Clustering and Sub-clustering as a Proxy for Mixing in Geophysical Flows 

  Chakraborty, Rishiraj (University of Waterloo, 2019-08-16)

  The Eulerian point of view is the traditional theoretical and numerical tool to describe fluid mechanics. Some modern computational fluid dynamics codes allow for the efficient simulation of particles, in turn facilitating ...

• Prandtl number dependence of stratified turbulence 

  Legaspi, Jesse (University of Waterloo, 2019-08-15)

  Stratified turbulence is affected by buoyancy forces that suppress vertical motion, resulting in a horizontally-layered structure with quasi-two-dimensional vortices. The Prandtl number Pr quantifies the relative strengths ...

• Model for the RE-TC thalamic circuit with application to childhood absence epilepsy 

  Newman, Jennie (University of Waterloo, 2019-08-12)

  Childhood absence epilepsy (CAE) is an idiopathic neurological disorder affecting roughly 2-8 children per 100,000 children worldwide. It is characterized by absence seizures, or short lapses in consciousness, and the ...

• Relativistic Theory of the Interaction of Two-Dimensional Materials with Moving Charged Particles 

  Akbari, Kamran (University of Waterloo, 2019-08-08)

  Prompted by the recent surge of interest in integrating atomically thin layers of conducting materials into nanophotonic and nanoplasmonic devices; we propose, in this thesis, a theoretical framework to analyze the ...

• Correlation and Communication via a Quantum Field 

  Simidzija, Petar (University of Waterloo, 2019-07-15)

  We study the ability of qubit detectors to i) extract correlations from, and ii) transmit quantum information through, a quantum field. We start by perturbatively studying the harvesting of correlations from thermal and ...

• Invariant manifold theory for impulsive functional differential equations with applications 

  Church, Kevin E. M. (University of Waterloo, 2019-07-03)

  The primary contribution of this thesis is a development of invariant manifold theory for impulsive functional differential equations. We begin with an in-depth analysis of linear systems, immersed in a nonautonomous ...

• Kalman Filter Based Sensor Placement For Burgers Equation 

  Zonov, Stanislav (University of Waterloo, 2019-06-03)

  The algorithm used for determining sensor placement in this thesis will be based on the Kalman filter. This filter is very famous and its application are numerous - some examples include aircraft navigation, finance and ...

• Numerical Simulations of Internal Solitary and Solitary-Like Waves: Wave Interactions and Instabilities 

  Xu, Chengzhu (University of Waterloo, 2019-05-31)

  Internal solitary and solitary-like waves (ISWs) are commonly observed in stably stratified fluids such as the Earth's atmosphere and oceans. As these waves interact with other physical processes and/or move through a ...

• Estimation for Linear and Semi-linear Infinite-dimensional Systems 

  Germ, Fabian (University of Waterloo, 2019-05-21)

  Estimating the state of a system that is not fully known or that is exposed to noise has been an intensely studied problem in recent mathematical history. Such systems are often modelled by either ordinary differential ...

• Three Results in Quantum Physics 

  Huq, Jaron Meser (University of Waterloo, 2019-05-09)

  This thesis is split into three disjoint sections. The first deals with two practical issues regarding the use of unitary 2-designs. A simplified description of how to generate elements of the smallest known unitary 2-design ...

• Microswimmer Propulsion by Two Steadily Rotating Helical Flagella 

  Shum, Henry (MDPI, 2019-01-01)

  Many theoretical studies of bacterial locomotion adopt a simple model for the organism consisting of a spheroidal cell body and a single corkscrew-shaped flagellum that rotates to propel the body forward. Motivated by ...

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