An experimental study of a population of phase-repelling relaxation oscillators

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 1995.Includes bibliographical references (leaves 100-103).by Adam Alexander Brailove.Ph.D

Phaselocked patterns and amplitude death in a ring of delay coupled limit cycle oscillators

We study the existence and stability of phaselocked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical Hopf bifurcation. The coupling is limited to nearest neighbors and is linear. We analyze a model set of discrete dynamical equations using the method of plane waves. The resultant dispersion relation, which is valid for any arbitrary number of oscillators, displays important differences from similar relations obtained from continuum models. We discuss the general characteristics of the equilibrium states including their dependencies on various system parameters. We next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay. Time delay is found to expand the range of possible phaselocked patterns and to contribute favorably toward their stability. The amplitude death state is studied in the parameter space of time delay and coupling strength. It is shown that death island regions can exist for any number of oscillators N in the presence of finite time delay. A particularly interesting result is that the size of an island is independent of N when N is even but is a decreasing function of N when N is odd.Comment: 23 pages, 12 figures (3 of the figures in PNG format, separately from TeX); minor additions; typos correcte

Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation

We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation diagram obtained by numerical and analytical solutions shows significant changes in the stability boundaries of the amplitude death, phase locked and incoherent regions. A novel result is the occurrence of amplitude death even in the absence of a frequency mismatch between the two oscillators. Similar results are obtained for an array of N oscillators with a delayed mean field coupling and the regions of such amplitude death in the parameter space of the coupling strength and time delay are quantified. Some general analytic results for the N tending to infinity (thermodynamic) limit are also obtained and the implications of the time delay effects for physical applications are discussed.Comment: 20 aps formatted revtex pages (including 13 PS figures); Minor changes over the previous version; To be published in Physica

Experimental Evidence of Time Delay Induced Death in Coupled Limit Cycle Oscillators

Experimental observations of time delay induced amplitude death in a pair of coupled nonlinear electronic circuits that are individually capable of exhibiting limit cycle oscillations are described. In particular, the existence of multiply connected death islands in the parameter space of the coupling strength and the time delay parameter for coupled identical oscillators is established. The existence of such regions was predicted earlier on theoretical grounds in [Phys. Rev. Lett. 80, 5109 (1998); Physica 129D, 15 (1999)]. The experiments also reveal the occurrence of multiple frequency states, frequency suppression of oscillations with increased time delay and the onset of both in-phase and anti-phase collective oscillations.Comment: 4 aps formatted RevTeX pages; 6 figures; to appear in Phys. Rev. Let

Synchronization in light-controlled oscillators

We have built light-controlled oscillators (LCOs) that mimic gregarious fireflies in the sense that their interactions are episodic and almost pulse-like. The ability of the LCOs to synchronize their light emission constitutes a good experimental setup to validate different models of populations of integrate-and-fire oscillators and to analyze the role of the interactions and the spatial distribution of the LCOs. Experimental measurements on two and three interacting LCOs enable us to find synchronization ranges despite intrinsic differences among the oscillators. We develop a mathematical model that we have used to solve analytically the simplified case of two identical oscillators in which we have found synchronous and anti-synchronous states. We have constructed the phase response curve for an LCO. Finally, we solved the model numerically finding that it reproduces our different experimental results with two LCOs (master-slave interaction and mutual interaction) and three interacting LCOs in a linear configuration. © 2003 Elsevier Science B.V. All rights reserved.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Wafer processing

Artificially grown crystals have to be cut into wafers for further applications. The current wafering techniques are described with a major focus on the dominant multi-wire sawing method. After sawing the wafers may have to be further treated by grinding, lapping, polishing, and etching procedures. The requirements on the processes and wafer qualities depend on the material and the application. The most advanced techniques have been developed for silicon, which is the major material for photovoltaic and microelectronic applications. Multi-wire sawing and the subsequent processes use abrasive particles for material removal. The fine-tuning and optimization of the wafer processes require an understanding of the micromechanical interactions between abrasive particles and crystal. The current status of research and development will be described for the major methods and materials. Finally, a brief overview will be given for alternative wafer processing techniques