Browsing Applied Mathematics by Title
Now showing items 329-348 of 491
-
On Perturbative Methods in Spectral Geometry
(University of Waterloo, 2017-08-28)The goal of spectral geometry is to establish how much information about the geometry of compact Riemannian manifolds is contained in the spectra of natural differential operators, especially Laplacians, defined on them. ... -
On Realistic Errors in Quantum Computers
(University of Waterloo, 2021-05-27)In this thesis, we are concerned with the problem of characterizing noise associated with implementations of quantum circuits. We first explore the notion of error rates of quantum circuits and argue that the semantic ... -
On Stability and Stabilization of Hybrid Systems
(University of Waterloo, 2015-12-23)The thesis addresses the stability, input-to-state stability (ISS), and stabilization problems for deterministic and stochastic hybrid systems with and without time delay. The stabilization problem is achieved by reliable, ... -
On the Application of Bandlimitation and Sampling Theory to Quantum Field Theory
(University of Waterloo, 2020-10-07)It is widely believed that combining the uncertainty principle with gravity will lead to an effective minimum length scale. A particular challenge is to specify this scale in a coordinate-independent manner so that covariance ... -
On the evaluation of quantum instruments with a consideration to measurements in trapped ion systems
(University of Waterloo, 2022-12-20)Trapped ion chains have shown promise in their application as quantum simulators. However, the close proximity of ions in the trap leads to operations such as state detection causing loss of coherence of other ions due to ... -
On the Geometry of IFS Fractals and its Applications
(University of Waterloo, 2014-01-23)Visually complex objects with infinitesimally fine features, naturally call for mathematical representations. The geometrical property of self-similarity - the whole similar to its parts - when iterated to infinity generates ... -
On the optimal CFL number of SSP methods for hyperbolic problems
(Elsevier, 2019-01-01)We show that the theory for strong stability preserving (SSP) time stepping methods employed with the method of lines-type discretizations of hyperbolic conservation laws may result in overly stringent time step restrictions. ... -
On the Relation between Quantum Discord and Purified Entanglement
(University of Waterloo, 2013-08-30)In this thesis, I study bipartite discord between A and B in terms of the structure formed by the bipartite and tripartite entanglement found in the purified system ABC. I find that discord manifests itself only when there ... -
On the Solution of the Hamilton-Jacobi Equation by the Method of Separation of Variables
(University of Waterloo, 2000)The method of separation of variables facilitates the integration of the Hamilton-Jacobi equation by reducing its solution to a series of quadratures in the separable coordinates. The case in which the metric tensor is ... -
On the TVD property of second order methods for 2D scalar conservation laws
(arXiv, 2021-10-05)The total variation diminishing (TVD) property is an important tool for ensuring nonlinear stability and convergence of numerical solutions of one-dimensional scalar conservation laws. However, it proved to be challenging ... -
One-Dimensional Population Density Approaches To Recurrently Coupled Networks Of Neurons With Noise
(Society for Industrial and Applied Mathematics, 2015)Mean-field systems have been previously derived for networks of coupled, two-dimensional, integrate-and-fire neurons such as the Izhikevich, adapting exponential, and quartic integrate-and-fire, among others. Unfortunately, ... -
Optimal Actuator Design for Nonlinear Systems
(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 ... -
Optimal Actuator Location for Semi-Linear Systems
(2018)Actuator location and design are important choices in controller design for distributed parameter systems. Semi-linear partial differential equations model a wide spectrum of physical systems with distributed parameters. ... -
Optimal Controller and Actuator Design for Nonlinear Parabolic Systems
(2019-10-08)Many physical systems are modeled by nonlinear parabolic differential equations, such as the Kuramoto-Sivashinsky (KS) equation. In this paper, the existence of a concurrent optimal controller and actuator design is ... -
Optimal Direction-Dependent Path Planning for Autonomous Vehicles
(University of Waterloo, 2014-04-24)The focus of this thesis is optimal path planning. The path planning problem is posed as an optimal control problem, for which the viscosity solution to the static Hamilton-Jacobi-Bellman (HJB) equation is used to determine ... -
Optimal Dither and Noise Shaping in Image Processing
(University of Waterloo, 2008-08-20)Dithered quantization and noise shaping is well known in the audio community. The image processing community seems to be aware of this same theory only in bits and pieces, and frequently under conflicting terminology. ... -
Optimal Experimental Design Applied to Models of Microbial Gene Regulation
(University of Waterloo, 2020-12-22)Microbial gene expression is a comparatively well understood process, but regulatory interactions between genes can give rise to complicated behaviours. Regulatory networks can exhibit strong context dependence, time-varying ... -
Optimal Locations of Sensors and Actuators for Control of a Pedestrian Bridge
(University of Waterloo, 2021-12-22)Lightweight structures have been increasing in popularity in structural designs. However, they are more prone to disturbances. Therefore, a controller device can be placed on the structure to control the excessive vibrations. ... -
Optimal Sensor Location for the Estimation of a Linear Dispersive Wave Equation
(University of Waterloo, 2015-08-07)The problem of optimal sensor location for the estimation of a linear dispersive wave equation is considered in this work. A steady-state Kalman filter was used as an optimal state observer with localized velocity information ... -
Optimal trajectory calculation using neural networks
(University of Waterloo, 2024-01-08)Optimal control methods for linear systems have reached a substantial level of maturity, both in terms of conceptual understanding and scalable computational implementation. For non-linear systems, an open-loop feedback ...