Philosophiae Doctor - PhD / Numerical approximations of multiscale problems of important applications in ecology are investigated. One of the class of models considered in this work are singularly perturbed (slow-fast) predator-prey systems which are characterized by the presence of a very small positive parameter representing the separation of time-scales between the fast and slow dynamics. Solution of such problems involve multiple scale phenomenon characterized by repeated switching of slow and fast motions, referred to as relaxationoscillations, which are typically challenging to approximate numerically. Granted with a priori knowledge, various time-stepping methods are developed within the framework of partitioning the full problem into fast and slow components, and then numerically treating each component differently according to their time-scales. Nonlinearities that arise as a result of the application of the implicit parts of such schemes are treated by using iterative algorithms, which are known for their superlinear convergence, such as the Jacobian-Free Newton-Krylov (JFNK) and the Anderson’s Acceleration (AA) fixed point methods.

Compared to single-mode VCSELs, multimode VCSELs have not received much attention in models and characterizations for functional parameters, despite making up the majority of commercially available VCSELs [1]. In particular, the extraction of the linewidth enhancement factor for multimode VCSELs has been overlooked, likely due to difficulties in measurement. Additionally, multimode models for VCSELs have, until recently, omitted spectral characteristics such as linewidth [2]. This is the first work to report a measured linewidth enhancement factor value (lower bound) for a multimode VCSEL. A characterization for the functional parameters of a red multimode vertical-cavity surface-emitting laser (VCSEL) is shown herein. The extracted values form a complete working set of parameters for the laser rate equations. The techniques employed for extracting values include frequency responses, power versus current fittings, and optical spectral measurements. From the frequency responses at various bias currents, the relaxation oscillation frequency and damping factor are found. The power versus current curve is fitted to find parameters including the modal spontaneous emission rate and carrier density at threshold. The spectral measurements are used for evaluating the linewidth enhancement factor (LEF) also known as the alpha factor or Henry factor. These 5 methods have been applied previously to characterizing single-mode VCSELs [3]–[5]. The experimentally extracted parameters herein are important for creating accurate models and simulations for multimode VCSELs. Improved multimode VCSEL models are necessary for improving optical communication, especially for short-range optical interconnects [2]. The measured parameters for the characterized VCSEL are comparable to similar single-mode VCSELs characterized in other works. This is promising because multi-mode VCSELs have higher output power than their single-mode counterparts, thus these results may aid in improving short-range optical interconnects.

This work is inspired by the peculiar behavior of the natural systems, namely the ability to produce self-sustained oscillations in the level of tens of Hertz in constant ambient conditions. This feature is one of the key signatures prescribed to living organisms. The firing rate of neuronal cells, a pulsating heart, or the beating of cilia and flagella are among many biological examples that possess amazing functionalities and unprecedented intelligence solely relying on bio-electro-chemical processes. Exploring shapeable polymeric technologies, new self-oscillating artificial microsystems were developed within this thesis. These microsystems rely on the novel nonlinear architecture that exhibits a negative differential resistance (NDR) within the parametric response that enables periodic oscillations. These systems are made of polymers and metals and were microfabricated in a planar fashion. The electrochemically deposited ionic electroactive polymers act as actuators of the system. Upon the self-assembly process, due to the interlayer strains, the planar device transforms into a three-dimensional soft nonlinear system that is able to perform self-sustained relaxation oscillations when subjected to a constant electric field while consuming extremely low powers (as low as several microwatts). The parameters of these systems were tuned for a high oscillation amplitude and frequency. This electro-mechanical parametric relaxation oscillator (EMPRO) can generate a rhythmic motion at stroke frequencies that are biologically relevant reaching up to ~95 Hz. The EMPRO oscillations at high frequencies generate a flow in the surrounding liquid, which was observed in the form of vortices around the micro actuators. This flow was further studied in ex-vivo conditions by measuring Doppler shifts of ultrasound waves. The EMPRO was made autonomous by integrating an electrochemical voltaic cell. Four different electrochemical batteries were tested to match the power consumption of the EMPRO system and electrochemical compatibility of the surrounding media. An Ag-Mg primary cell was then integrated with the EMPRO for autonomous operation without the need for external power sources, cables or controllers. This biomimicking self-powered self-sustaining oscillating microsystem is envisioned to be useful in novel application scenarios operating at low Reynolds numbers in biologically relevant conditions. Furthermore, as the system is electromechanical in nature, it could be integrated with electronic components such as sensors and communication devices in the next generation of autonomous microsystems.:  Table of contents Acronyms 7 1 Introduction 8 1.1 Motivation 9 1.2 Objectives 9 1.3 Thesis organization 10 2 Background 12 2.1 A brief review on nonlinear self-oscillation 12 2.2 Self-oscillating biological systems 13 2.3 Stimuli responsive materials 15 2.3.1 Electroactive polymers in electrochemical cells 16 2.3.2 Sources of electrical field for electroactive polymers 24 2.4 Self-oscillating synthetic systems 27 2.5 Movement in low Reynolds number regime 33 3 Materials and methods 38 3.1 Deposition methods 38 3.1.1 Photolithography 38 3.1.2 Plasma sputtering 41 3.1.3 Atomic layer deposition 42 3.1.4 Electrochemical polymerization 44 3.2 Shapeable polymeric platform technology 46 3.2.1 Sacrificial layer 46 3.2.2 Hydrogel swelling layer 47 3.2.3 Polyimide reinforcing layer 48 3.3 Characterization methods 49 3.3.1 Profilometry 49 3.3.2 Scanning electron and focused ion beam microscopy 50 3.3.3 Cyclic Voltammetry 52 3.3.4 Ultrasound and Doppler shift measurements 53 4 Electromechanical Parametric Relaxation Oscillators (EMPROs) 56 4.1 Relaxation oscillation in EMPROs 56 4.2 Theory of EMPRO relaxation oscillations 61 4.3 Realization of EMPROs 67 4.3.1 Design parameters of EMPROs 67 4.3.2 EMPRO on-chip battery integration 71 4.4 Fabrication of autonomous EMPROs 76 5 EMPRO performances 84 5.1 Externally biased EMPROs 84 5.2 Autonomous EMPROs 95 6 Conclusions and outlook 98 6.1 Outlook 99 Bibliography i List of Figures and Tables xi Versicherung xiii Acknowledgements xiv Scientific publications and contributions xvi Theses xvii Curriculum Vitae xix