No description available.

We survey standard topics in elementary differential geometry and complex analysis to build up the necessary theory for studying applications of univalent harmonic function theory to minimal surfaces. We then proceed to consider convex combination harmonic mappings of the form f=sf_1+(1-s) f_2 and give conditions on when f lifts to a one-parameter family of minimal surfaces via the Weierstrauss-Enneper representation formula. Finally, we demand two minimal surfaces M and M' be locally isometric, formulate a system of partial differential equations modeling this constraint, and calculate their symmetry group. The group elements generate transformations that when applied to a prescribed harmonic mapping, lift to locally isometric minimal surfaces with varying graphs embedded in mathbb{R}^3.

No description available.

Thesis advisor: Ian Biringer / We consider the space $\rootedH2$ of all complete hyperbolic surfaces without boundary with a basepoint equipped with the pointed Gromov-Hausdorff topology. Continuous paths within $\rootedH2$ arising from certain deformations on a hyperbolic surface and concrete geometric constructions are studied. These include changing some Fenchel-Nielsen parameters of a subsurface, pinching a simple closed geodesic to a cusp, and inserting an infinite strip along a proper bi-infinite geodesic. We then use these paths to show that $\rootedH2$ is path-connected and that it is locally weakly connected at points whose underlying surfaces are either the hyperbolic plane or hyperbolic surfaces of the first kind. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

The influence of modal interactions on the response of harmonically excited flexible L-shaped metallic and composite structures has been investigated analytically and experimentally. Each metallic structure possesses a two-to-one internal resonance, while each composite structure possesses a three-to-one internal resonance and either a two-to-one or a one-to-·one internal resonance. For the metallic structures, a weakly nonlinear analysis is used to derive the autonomous system of equations which describe the evolution of the amplitudes and phases of the internally resonant modes. These equations are obtained for primary- and secondary-resonant excitations. The excitation frequency or amplitude is used as a control parameter and the resulting bifurcations (saddle-node, pitchfork, and Hopf bifurcations) are studied. Theoretical analyses for internally resonant systems are used to predict and explain the responses of the composite structures. / Ph. D.

Under heterogeneous variance, conventional optimal response surface experimental designs for estimating location models are no longer optimal. To address this deficiency. D and Q criteria appropriate under heterogeneous variance are developed. These criteria are then applied to demonstrate the improved efficiency of a proposed two-stage experimental design procedure. In the proposed procedure the first stage estimates the heterogeneous variance structure and the second stage augments the first stage to produce a total design that is Q or D-optimal for the estimated variance structure. The Q and 0 criteria not only direct the total design, but also suggest optimal designs for estimating dispersion effects in the first stage. The efficiency of the proposed two-stage procedure is further enhanced if certain mild assumptions concerning variance structure are valid. These assumptions are formulated as a prior distribution and effectively stabilize the variance estimation in the first stage through a Bayes estimator. / Ph. D.

The following document serves as a design guidebook to assist landscape architects, designers, planners, engineers, and architects in the practice of developing land while preserving water quality. This guidebook outlines methods for maximizing permeable surfaces by providing examples of ways to minimize impervious surfaces. / Master of Landscape Architecture

Yes / Computer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique together

No / In this work we propose a talking head system for animating facial expressions using a template face generated from partial differential equations (PDE). It uses a set of pre configured curves to calculate an internal template surface face. This surface is then used to associate various facial features with a given 3D face object. Motion retargeting is then used to transfer the deformations in these areas from the template to the target object. The procedure is continued until all the expressions in the database are calculated and transferred to the target 3D human face object. Additionally the system interacts with the user using an artificial intelligence (AI) chatter bot to generate response from a given text. Speech and facial animation are synchronized using the Microsoft Speech API, where the response from the AI bot is converted to speech.

Future wireless networks are envisioned to support a wide range of novel use cases, and connect a massive number of people and devices in an energy efficient way. Several key enabling technologies were considered to support this vision including Internet of Things (IoT) networks, aerial and stratospheric platforms, and reconfigurable intelligent surfaces (RIS). In this dissertation, we study different problems related to the integration between these technologies. First, we propose a cost-effective framework for data collection from IoT sensors using multiple unmanned aerial vehicles (UAVs). This is achieved by effcient clustering of the sensors and optimized deployment of cluster heads (CHs). Then, the number of deployed UAVs and their trajectories will be optimized to minimize the data collection flight time. The impacts of the trajectory approach, environment type, and UAVs' altitude as well as the fairness of UAVs trajectories on the data collection process are investigated. Given that IoT nodes might have different priorities and time deadlines, and respecting the limited battery capacity of UAVs, we enhance the data collection framework to account for these practical constraints. First, an algorithm for finding the minimal number of CHs and their best locations is proposed. Then, the minimal number of UAVs and their trajectories are obtained by solving the associated capacitated vehicle routing problem. The results investigate the impacts of the selected trajectory approach, the battery capacity and time deadlines on the consumed energy, number of visited CHs, and number of deployed UAVs. Next, given the energy issue on aerial platforms, we present our vision for integrating RIS in aerial and stratospheric platforms to provide energy-efficient communications. We propose a control architecture for such integration, discuss its benefits and identify potential use cases and associated research challenges. Then, to substantiate our vision, we study the link budget of RIS-assisted communications under the specular and the scattering reflection paradigms. Specifically, we analyze the characteristics of RIS-equipped stratospheric and aerial platforms and compare their communication performance with that of RIS-assisted terrestrial networks, using standardized channel models. In addition, we derive the optimal aerial platforms placements under both reflection paradigms. The obtained results provide important insights for the design of RIS-assisted communications. For instance, given that a HAPS has a large RIS surface, it provides superior link budget performance in most studied scenarios. In contrast, the limited RIS area on UAVs and the large propagation loss in low Earth orbit (LEO) satellite communications make them unfavorable candidates for supporting terrestrial users. Then, motivated by the demonstrated potential of HAPS equipped with RIS (HAPS-RIS), we propose a solution to support the stranded users in terrestrial networks through a dedicated control station (CS) and HAPS-RIS. We refer to this approach as "beyond-cell" communications. We demonstrate that this approach works in tandem with legacy terrestrial networks to support uncovered or unserved users. Optimal transmit power and RIS unit assignment strategies for the users based on different network objectives are introduced. Furthermore, to increase the percentage of admitted users in an efficient manner, a novel resource-efficient optimization problem is formulated that maximizes the number of connected UEs, while minimizing the total power consumed by the CS and RIS. Since the resulting problem is a mixed-integer nonlinear program (MINLP), a low-complexity two-stage algorithm is developed. Finally, given the different applications and various options of HAPS payload, we envision the use of a multi-mode HAPS that can adaptively switch between different modes so as to reduce energy consumption and extend the HAPS loitering time. These modes comprise a HAPS super macro base station (HAPS-SMBS) mode for enhanced computing, caching, and communication services, a HAPS relay station (HAPS-RS) mode for active communication, and a HAPSRIS mode for passive communication. This multi-mode HAPS ensures that operations rely mostly on the passive communication payload while switching to an energy-greedy active mode only when necessary. We illustrate the envisioned multi-mode HAPS, and discuss its benefits and challenges. Then, we validate the multi-mode efficiency through a case study. At the end of the dissertation, several future research directions are proposed including hybrid orthogonal and non-orthogonal multiple access (OMA/NOMA) beyond-cell communications assisted by HAPS-RIS, configuration of RIS units on stratospheric platforms, energy management for HAPS-RIS, and supporting aerial users through terrestrial RIS.