Browsing Applied Mathematics by Title
Now showing items 345-364 of 499
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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 ... -
Orthogonal Separation of The Hamilton-Jacobi Equation on Spaces of Constant Curvature
(University of Waterloo, 2014-04-24)What is in common between the Kepler problem, a Hydrogen atom and a rotating black- hole? These systems are described by different physical theories, but much information about them can be obtained by separating an ... -
Outlook On A Worldwide Forest Transition
(Public Library of Science, 2013-10-09)It is not clear whether a worldwide "forest transition" to net reforestation will ever occur, and the need to address the main driver-agriculture-is compelling. We present a mathematical model of land use dynamics based ... -
A parallel, adaptive discontinuous Galerkin method for hyperbolic problems on unstructured meshes
(University of Waterloo, 2018-09-04)This thesis is concerned with the parallel, adaptive solution of hyperbolic conservation laws on unstructured meshes. First, we present novel algorithms for cell-based adaptive mesh refinement (AMR) on unstructured ... -
Parameterizing a dynamic influenza model using longitudinal versus age-stratified case notifications yields different predictions of vaccine impacts
(2018-09-06)Dynamic transmission models of influenza are often used in decision-making to identify which vaccination strategies might best reduce influenza-associated health and economic burdens. Our goal was to use laboratory confirmed ... -
Particle Clustering and Sub-clustering as a Proxy for Mixing in Geophysical Flows
(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 ... -
Persistent oscillations in the Aplysia bag cell network
(University of Waterloo, 2017-08-24)Persistence is a phenomena by which a resting neuron enters a state of persistent behavior following a brief stimulus. Persistent neural systems can exhibit long-term responses that remain after the stimulus is removed, ... -
A Phase Model with Large Time Delayed Coupling
(Elsevier, 2020-10)We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting ... -
Phase models and clustering in networks of oscillators with delayed coupling
(Elsevier, 2017-09-19)We consider a general model for a network of oscillators with time delayed coupling where the coupling matrix is circulant. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations ... -
Physical Modelling and the Associated Acoustic Behaviour of Trumpets and Trombones
(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, ... -
PID Control of Systems with Hysteresis
(University of Waterloo, 2009-04-29)Hysteresis is exhibited by many physical systems. Smart materials such as piezoelectrics, magnetostrictives and shape memory alloys possess useful properties, especially in the field of micropositioning, but the control ...