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Nonlinear Dynamics of Semiconductor Device Circuits and Characterization of Deep Energy Levels in HgCdTe by Using Magneto-Optical Spectroscopy

Description: The nonlinear dynamics of three physical systems has been investigated. Diode resonator systems are experimentally shown to display a period doubling route to chaos, quasiperiodic states, periodic locking states, and Hopf bifurcation to chaos. Particularly, the transition from quasiperiodic states to chaos in line-coupled systems agrees well with the Curry-Yorke model. The SPICE program has been modified to give realistic models for the diode resonator systems.
Date: May 1994
Creator: Yü, Chi
Partner: UNT Libraries

A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean

Description: The Hamiltonian of a stably stratified incompressible fluid in an internal water wave in a deep ocean is constructed. Studying the ocean internal wave field with its full dynamics is formidable (or unsolvable) so we consider a test-wave Hamiltonian to study the dynamical and statistical properties of the internal water wave field in a deep ocean. Chaos is present in the internal test-wave dynamics using actual coupling coefficients. Moreover, there exists a certain separatrix net that fills the phase space and is covered by a thin stochastic layer for a two-triad pure resonant interaction. The stochastic web implies the existence of diffusion of the Arnold type for the minimum dimension of a non-integrable autonomous system. For non-resonant case, stochastic layer is formed where the separatrix from KAM theory is disrupted. However, the stochasticity does not increase monotonically with increasing energy. Also, the problem of relaxation process is studied via microscopic Hamiltonian model of the test-wave interacting nonlinearly with ambient waves. Using the Mori projection technique, the projected trajectory of the test-wave is transformed to a form which corresponds to a generalized Langevin equation. The mean action of the test-wave grows ballistically for a short time regime, and quenches back to the normal diffusion for a intermediate time regime and regresses linearly to a state of statistical equilibrium. Applying the Nakajima-Zwanzig technique on the test-wave system, we get the generalized master equation on the test-wave system which is non-Markovian in nature. From our numerical study, the distribution of the test-wave has non-Gaussian statistics.
Date: December 1996
Creator: Kim, Won-Gyu, 1962-
Partner: UNT Libraries


Description: Since 1980, under the grant DEFG02-96ER40949, the Department of Energy has supported the educational and research work of the University of Maryland Dynamical Systems and Accelerator Theory (DSAT) Group. The primary focus of this educational/research group has been on the computation and analysis of charged-particle beam transport using Lie algebraic methods, and on advanced methods for the computation of electromagnetic fields and multiparticle phenomena. This Final Report summarizes the accomplishments of the DSAT Group from its inception in 1980 through its end in 2011.
Date: August 31, 2012
Creator: Dragt, Alex J.
Partner: UNT Libraries Government Documents Department

Frequency map analysis of nonlinear dynamics in the NLC main damping rings

Description: To avoid radiation damage, the acceptance of linear collider damping rings must be large enough that injection efficiency close to 100 percent can be achieved. Survival plots based on tracking particles in the NLC Main Damping Ring lattice suggest a dynamic aperture with some margin over the specified injected beam size and energy spread. Here, we apply Frequency Map Analysis to give a more detailed picture of the dynamical stability of particle trajectories in the presence of lattice nonlinearities arising from the sextupoles and the damping wiggler. The techniques that we use are of general applicability to nonlinear elements in beamlines, and in particular will be used for analysis of wiggler effects in future damping ring designs.
Date: October 11, 2004
Creator: Wolski, Andrzej; Venturini, Marco; Wan, Weishi & Marks, Steve
Partner: UNT Libraries Government Documents Department


Description: The NSLS-II storage ring lattice is comprised of 30 DBA cells arranged in 15 superperiods. There are 15 long straight sections (9.3m) for injection, RF and insertion devices and 15 short straights (6.6m) for insertion devices. In the baseline lattice, the short straights have small horizontal and vertical beta functions but the long straights have large horizontal beta function optimized for injection. In this paper, we explore the possibility of maintaining three long straights with large horizontal beta function while providing the other 12 long straights with smaller horizontal beta function to optimize the brightness of insertion devices. Our study considers the possible linear lattice solutions as well as characterizing the nonlinear dynamics. Results are reported on optimization of dynamic aperture required for good injection efficiency and adequate Touschek lifetime. This paper discusses dynamic aperture optimization for the NSLS-II lattice with alternate high and low horizontal beta function in the long straights, which is proposed for the optimization of the brightness of insertion devices. The linear optics is optimized to meet the requirements of lattice function and source properties. Nonlinear optimization for a lattice with working point at (37.18, 16.2) is performed. Considering the realistic magnets errors and physical apertures, we calculate the frequency maps and plot the tune footprint. The results show that the lattice with high-low beta function has adequate dynamic aperture for good injection efficiency and sufficient Touschek lifetime.
Date: March 28, 2011
Creator: Fanglei, L.; Bengtsson, J.; Guo, W.; Krinsky, S.; Li, Y. & Yang, L.
Partner: UNT Libraries Government Documents Department

Modeling for Process Control: High-Dimensional Systems

Description: Most of other technologically important systems (among them, powders and other granular systems) are intrinsically nonlinear. This project is focused on building the dynamical models for granular systems as a prototype for nonlinear high-dimensional systems exhibiting complex non-equilibrium phenomena. Granular materials present a unique opportunity to study these issues in a technologically important and yet fundamentally interesting setting. Granular systems exhibit a rich variety of regimes from gas-like to solid-like depending on the external excitation. Based the combination of the rigorous asymptotic analysis, available experimental data and nonlinear signal processing tools, we developed a multi-scale approach to the modeling of granular systems from detailed description of grain-grain interaction on a micro-scale to continuous modeling of large-scale granular flows with important geophysical applications.
Date: September 15, 2008
Creator: Tsimring, Lev S.
Partner: UNT Libraries Government Documents Department

Sliding and Rocking of Unanchored Components and Structures: Chapter 7.6 ASCE 4 Revision 2

Description: Chapter 7.6 of ASCE 4-Rev 2, Seismic Analysis of Safety-Related Nuclear Structures: Standard and Commentary, provides updated guidance for analysis of rocking and sliding of unanchored structures and components subjected to seismic load. This guidance includes provisions both for simplified approximate energy-based approaches, and for detailed probabilistic time history analysis using nonlinear methods. Factors to be applied to the analytical results are also provided with the intent of ensuring achievement of the 80% non-exceedence probability target of the standard. The present paper surveys the published literature supporting these provisions. The results of available testing and analysis are compared to results produced by both simplified and probabilistic approaches. In addition, adequacy of the standard's provisions for analysis methods and factors is assessed. A comparison is made between the achieved level of conservatism and the standard's non-exceedence probability target.
Date: April 1, 2011
Creator: Jensen, S. R.
Partner: UNT Libraries Government Documents Department

Dynamics of Granular Materials and Particle-Laden Flows

Description: Rapid granular flows and particle-laden flows were studied in laboratory experiments, molecular dynamics simulations, and simulations of continuum equations. The research demonstrated that the inclusion of friction is crucial in realistic modeling of granular flows; hence extensive previous analyses and simulations by many researchers for frictionless particles must be reconsidered in the light of our work.
Date: April 18, 2007
Creator: Swinney, Harry L.
Partner: UNT Libraries Government Documents Department

Nonlinear dynamics of fluid-structure systems. Final technical report for period January 5, 1991 - December 31, 1997

Description: The technical research was directed at problems involving the dynamics of fluid flow and elastic structures. Such problems occur in heat-exchange systems in energy generating plants. Fluid excited vibrations of structures can result in unwanted impact forces which can lead to metal fatigue failures. Mathematical theories based on linear models have been used for several decades. In this research the authors explored the phenomena associated with nonlinear effects using experimental models, mathematical models and numerical computation. A number of nonlinear effects were observed experimentally including chaotic dynamics, multi-fractal Poincare maps, quasi-periodic vibrations, subcritical Hopf bifurcations, helical waves in a tube row and spatial localization.
Date: July 20, 1999
Creator: Moon, Francis C.
Partner: UNT Libraries Government Documents Department

Dynamics of Granular Materials and Particle-Laden Flows

Description: Rapid granular flows and particle-laden flows were studied in laboratory experiments, molecular dynamics simulations, and simulations of continuum equations. The research demonstrated that the inclusion of friction is crucial in realistic modeling of granular flows; hence extensive previous analyses and simulations by many researchers for frictionless particles must be reconsidered in the light of our work. We also made the first detailed comparison between experiment and the predictions of continuum theory for granular media (hydrodynamic equations). We found that shock waves easily form in granular flows since the speed of sound waves (pressure fluctuations) in a granular gas is small, typically 10 cm, while flow velocities are easily an order of magnitude larger. Our measurements on vertically oscillating granular layers led to the development of a novel technique for continuously separating particles of different sizes. Our study of craters formed by the impact of a projectile in a granular medium showed, surprisingly, that the time taken for a projectile to come to a rest in the granular layer is independent of the projectile’s impact energy. Another study supported by this grant examined a vertically oscillating layer of a mixture of cornstarch and water. The discovery of stable holes in the mixture was reported widely in the popular press, e.g., Science News [15 May 2004], “Imaging poking a liquid to create holes that persist like the holes in Swiss cheese. Incredible as that might sound, a group of scientists has done it.” Further experiments on glass spheres in an aqueous solution yielded the same holey fluid phenomenon, supporting our conjecture that such holes may occur in dense concentrations of particles in solution in industrial applications.
Date: July 11, 2007
Creator: Swinney, Harry L.
Partner: UNT Libraries Government Documents Department

Stability and Dynamics of Spatio-Temporal Structures

Description: This document constitutes the final report for the grant. It provides a complete list of publications and presentations that arose from the project as well as a brief description of the highlights of the research results. The research funded by this grant has provided insights into the spontaneous formation of structures of increasing complexity in systems driven far from thermodynamic equilibrium. A classic example of such a system is thermally driven convection in a horizontal fluid layer. Highlights of the research are: (1) explanation of the localized traveling wave pulses observed in binary-mixture convection, (2) explanation of the localized waves in electroconvection, (3) introduction of a new diagnostics for spatially and temporally chaotic states, which is based on the statistics of defect trajectories, (4) prediction of complex states in thermally driven convection in rotating systems. Additional contributions provided insight into the localization mechanism for oscillons, the prediction of a new localization mechanism for traveling waves based on a resonant periodic forcing, and an analysis of the stability of quasi-periodic patterns.
Date: October 21, 2005
Creator: Riecke, Hermann
Partner: UNT Libraries Government Documents Department

A Cumulant-based Analysis of Nonlinear Magnetospheric Dynamics

Description: Understanding magnetospheric dynamics and predicting future behavior of the magnetosphere is of great practical interest because it could potentially help to avert catastrophic loss of power and communications. In order to build good predictive models it is necessary to understand the most critical nonlinear dependencies among observed plasma and electromagnetic field variables in the coupled solar wind/magnetosphere system. In this work, we apply a cumulant-based information dynamical measure to characterize the nonlinear dynamics underlying the time evolution of the Dst and Kp geomagnetic indices, given solar wind magnetic field and plasma input. We examine the underlying dynamics of the system, the temporal statistical dependencies, the degree of nonlinearity, and the rate of information loss. We find a significant solar cycle dependence in the underlying dynamics of the system with greater nonlinearity for solar minimum. The cumulant-based approach also has the advantage that it is reliable even in the case of small data sets and therefore it is possible to avoid the assumption of stationarity, which allows for a measure of predictability even when the underlying system dynamics may change character. Evaluations of several leading Kp prediction models indicate that their performances are sub-optimal during active times. We discuss possible improvements of these models based on this nonparametric approach.
Date: January 28, 2004
Creator: Johnson, Jay R. & Wing, Simon
Partner: UNT Libraries Government Documents Department

Nonlinear Dynamics and Control of Large Arrays of Coupled Oscillators: Application to Fluid-Elastic Problems

Description: Large numbers of fluid elastic structures are part of many power plant systems and vibration of these systems sometimes are responsible for plant shut downs. Earlier research at Cornell in this area had centered on nonlinear dynamics of fluid-elastic systems with low degrees of freedom. The focus of current research is the study of the dynamics of thousands of closely arrayed structures in a cross flow under both fluid and impact forces. This research is relevant to two areas: (1) First, fluid-structural problems continue to be important in the power industry, especially in heat exchange systems where up to thousands of pipe-like structures interact with a fluid medium. [Three years ago in Japan for example, there was a shut down of the Monju nuclear power plant due to a failure attributed to flow induced vibrations.] (2) The second area of relevance is to nonlinear systems and complexity phenomena; issues such as spatial temporal dynamics, localization and coherent patterns entropy measures as well as other complexity issues. Early research on flow induced vibrations in tube row and array structures in cross flow goes back to Roberts in 1966 and Connors in 1970. These studies used linear models as have many of the later work in the 1980's. Nonlinear studies of cross flow induced vibrations have been undertaken in the last decade. The research at Cornell sponsored by DOE has explored nonlinear phenomena in fluid-structure problems. In the work at Cornell we have documented a subcritical Hopf bifurcation for flow around a single row of flexible tubes and have developed an analytical model based on nonlinear system identification techniques. (Thothadri, 1998, Thothadri and Moon, 1998, 1999). These techniques have been applied to a wind tunnel experiment with a row of seven cylinders in a cross flow. These system identification methods have been ...
Date: April 1, 2002
Creator: Moon, Francis C.
Partner: UNT Libraries Government Documents Department