Nonlinear dynamics and chaos simulation system analysis for improved design

Small errors proved catastrophic. Our purpose to remark that a very small cause which escapes our notice determined a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. Small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. When dealing with any kind of electrical device specification, it is important to note that there exists a pair of test conditions that define a test: the forcing function and the limit. Forcing functions define the external operating constraints placed upon the device tested. The actual test defines how well the device responds to these constraints. Forcing inputs to threshold for example, represents the most difficult testing because this put those inputs as close as possible to the actual switching critical points and guarantees that the device will meet the Input-Output specifications. ^ Prediction becomes impossible by classical analytical analysis bounded by Newton and Euclides. We have found that non linear dynamics characteristics is the natural state of being in all circuits and devices. Opportunities exist for effective error detection in a nonlinear dynamics and chaos environment. ^ Nowadays there are a set of linear limits established around every aspect of a digital or analog circuits out of which devices are consider bad after failing the test. Deterministic chaos circuit is a fact not a possibility as it has been revived by our Ph.D. research. In practice for linear standard informational methodologies, this chaotic data product is usually undesirable and we are educated to be interested in obtaining a more regular stream of output data. ^ This Ph.D. research explored the possibilities of taking the foundation of a very well known simulation and modeling methodology, introducing nonlinear dynamics and chaos precepts, to produce a new error detector instrument able to put together streams of data scattered in space and time. Therefore, mastering deterministic chaos and changing the bad reputation of chaotic data as a potential risk for practical system status determination. ^

Interaction dynamics in small networks of nonlinear elements

We study a small circuit of coupled nonlinear elements to investigate general features of signal transmission through networks. The small circuit itself is perceived as building block for larger networks. Individual dynamics and coupling are motivated by neuronal systems: We consider two types of dynamical modes for an individual element, regular spiking and chattering and each individual element can receive excitatory and/or inhibitory inputs and is subjected to different feedback types (excitatory and inhibitory; forward and recurrent). Both, deterministic and stochastic simulations are carried out to study the input-output relationships of these networks. Major results for regular spiking elements include frequency locking, spike rate amplification for strong synaptic coupling, and inhibition-induced spike rate control which can be interpreted as a output frequency rectification. For chattering elements, spike rate amplification for low frequencies and silencing for large frequencies is characteristic

Soliton based DPSK encoded sequences:stability and dynamical properties

We study the dynamical properties of the RZ-DPSK encoded sequences of bits, focusing on the instabilities in the train leading to the bit stream corruption. The problem is studied within the framework of the complex Toda chain model for optical solitons. We show how the bit composition of the pattern affects the initial stage of the train dynamics and explain the general mechanisms of the appearance of unstable collective soliton modes. Then we discuss the nonlinear regime using the asymptotic properties of the pulse stream at large propagation distances and analyze the dynamical behavior of the train elucidating different scenarios for the pattern instabilities. ©2010 Crown.

Effect of road quality in structural health monitoring under operational conditions

The effect of unevenness in a bridge deck for the purpose of Structural Health Monitoring (SHM) under operational conditions is studied in this paper. The moving vehicle is modelled as a single degree of freedom system traversing the damaged beam at a constant speed. The bridge is modelled as an Euler-Bernoulli beam with a breathing crack, simply supported at both ends. The breathing crack is treated as a nonlinear system with bilinear stiffness characteristics related to the opening and closing of crack. The unevenness in the bridge deck considered is modelled using road classification according to ISO 8606:1995(E). Numerical simulations are conducted considering the effects of changing road surface classes from class A - very good to class E - very poor. Cumulant based statistical parameters, based on a new algorithm are computed on stochastic responses of the damaged beam due to passages of the load in order to calibrate the damage. Possibilities of damage detection and calibration under benchmarked and non-benchmarked cases are considered. The findings of this paper are important for establishing the expectations from different types of road roughness on a bridge for damage detection purposes using bridge-vehicle interaction where the bridge does not need to be closed for monitoring.

Nonlinear optics with cold Rb atoms using tapered optical nanofibres

Optical nanofibres (ONFs) are very thin optical waveguides with sub-wavelength diameters. ONFs have very high evanescent fields and the guided light is confined strongly in the transverse direction. These fibres can be used to achieve strong light-matter interactions. Atoms around the waist of an ONF can be probed by collecting the atomic fluorescence coupling or by measuring the transmission (or the polarisation) of the probe beam sent through it. This thesis presents experiments using ONFs for probing and manipulating laser-cooled 87Rb atoms. As an initial experiment, a single mode ONF was integrated into a magneto-optical trap (MOT) and used for measuring the characteristics of the MOT, such as the loading time and the average temperature of the atom cloud. The effect of a near-resonant probe beam on the local temperature of the cold atoms has been studied. Next, the ONF was used for manipulating the atoms in the evanescent fields region in order to generate nonlinear optical effects. Four-wave mixing, ac Stark effect (Autler-Townes splitting) and electromagnetically induced transparency have been observed at unprecedented ultralow power levels. In another experiment, a few-mode ONF, supporting only the fundamental mode and the first higher order mode group, has been used for studying cold atoms. A higher pumping rate of the atomic fluorescence into the higher order fibreguided modes and more interactions with the surrounding atoms for higher order mode evanescent light, when compared to signals for the fundamental mode, have been identified. The results obtained in the thesis are particularly for a fundamental understanding of light-atom interactions when atoms are near a dielectric surface and also for the development of fibre-based quantum information technologies. Atoms coupled to ONFs could be used for preparing intrinsically fibre-coupled quantum nodes for quantum computing and the studies presented here are significant for a detailed understanding of such a system.

Nonlinear soil-structure interaction for buried pressure pipes under differential ground motion

Pipelines extend thousands of kilometers across wide geographic areas as a network to provide essential services for modern life. It is inevitable that pipelines must pass through unfavorable ground conditions, which are susceptible to natural disasters. This thesis investigates the behaviour of buried pressure pipelines experiencing ground distortions induced by normal faulting. A recent large database of physical modelling observations on buried pipes of different stiffness relative to the surrounding soil subjected to normal faults provided a unique opportunity to calibrate numerical tools. Three-dimensional finite element models were developed to enable the complex soil-structure interaction phenomena to be further understood, especially on the subjects of gap formation beneath the pipe and the trench effect associated with the interaction between backfill and native soils. Benchmarked numerical tools were then used to perform parametric analysis regarding project geometry, backfill material, relative pipe-soil stiffness and pipe diameter. Seismic loading produces a soil displacement profile that can be expressed by isoil, the distance between the peak curvature and the point of contraflexure. A simplified design framework based on this length scale (i.e., the Kappa method) was developed, which features estimates of longitudinal bending moments of buried pipes using a characteristic length, ipipe, the distance from peak to zero curvature. Recent studies indicated that empirical soil springs that were calibrated against rigid pipes are not suitable for analyzing flexible pipes, since they lead to excessive conservatism (for design). A large-scale split-box normal fault simulator was therefore assembled to produce experimental data for flexible PVC pipe responses to a normal fault. Digital image correlation (DIC) was employed to analyze the soil displacement field, and both optical fibres and conventional strain gauges were used to measure pipe strains. A refinement to the Kappa method was introduced to enable the calculation of axial strains as a function of pipe elongation induced by flexure and an approximation of the longitudinal ground deformations. A closed-form Winkler solution of flexural response was also derived to account for the distributed normal fault pattern. Finally, these two analytical solutions were evaluated against the pipe responses observed in the large-scale laboratory tests.

Multiscale Analysis for Field-Effect Penetration through Two-Dimensional Materials

Gate-tunable two-dimensional (2D) materials-based quantum capacitors (QCs) and van der Waals heterostructures involve tuning transport or optoelectronic characteristics by the field effect. Recent studies have attributed the observed gate-tunable characteristics to the change of the Fermi level in the first 2D layer adjacent to the dielectrics, whereas the penetration of the field effect through the one-molecule-thick material is often ignored or oversimplified. Here, we present a multiscale theoretical approach that combines first-principles electronic structure calculations and the Poisson–Boltzmann equation methods to model penetration of the field effect through graphene in a metal–oxide–graphene–semiconductor (MOGS) QC, including quantifying the degree of “transparency” for graphene two-dimensional electron gas (2DEG) to an electric displacement field. We find that the space charge density in the semiconductor layer can be modulated by gating in a nonlinear manner, forming an accumulation or inversion layer at the semiconductor/graphene interface. The degree of transparency is determined by the combined effect of graphene quantum capacitance and the semiconductor capacitance, which allows us to predict the ranking for a variety of monolayer 2D materials according to their transparency to an electric displacement field as follows: graphene > silicene > germanene > WS2 > WTe2 > WSe2 > MoS2 > phosphorene > MoSe2 > MoTe2, when the majority carrier is electron. Our findings reveal a general picture of operation modes and design rules for the 2D-materials-based QCs.

Filamentation in Air and Water and Nonlinear Optical Characterization of Biopolymer Using Ultrashort Laser Pulses

Important issues related to femtosecond (fs) pulses and its relevance to this thesis are discussed. A fundamental characteristic, like the timebandwidth product for fs pulses is decribed in detail. A brief review of generation of ultrashort pulses and its propagation through an optically transparent media are presented. Interaction of strong pulses with matter and different ionization processes are also described. An overview of the thesis is presented at the end

Machine learning and data decompositions for complex networked dynamical systems

Thesis (Ph.D.)--University of Washington, 2016-08

Efficient split eld FDTD analysis of third-order nonlinear materials in two-dimensionally periodic media

In this work the split-field finite-difference time-domain method (SF-FDTD) has been extended for the analysis of two-dimensionally periodic structures with third-order nonlinear media. The accuracy of the method is verified by comparisons with the nonlinear Fourier Modal Method (FMM). Once the formalism has been validated, examples of one- and two-dimensional nonlinear gratings are analysed. Regarding the 2D case, the shifting in resonant waveguides is corroborated. Here, not only the scalar Kerr effect is considered, the tensorial nature of the third-order nonlinear susceptibility is also included. The consideration of nonlinear materials in this kind of devices permits to design tunable devices such as variable band filters. However, the third-order nonlinear susceptibility is usually small and high intensities are needed in order to trigger the nonlinear effect. Here, a one-dimensional CBG is analysed in both linear and nonlinear regime and the shifting of the resonance peaks in both TE and TM are achieved numerically. The application of a numerical method based on the finite- difference time-domain method permits to analyse this issue from the time domain, thus bistability curves are also computed by means of the numerical method. These curves show how the nonlinear effect modifies the properties of the structure as a function of variable input pump field. When taking the nonlinear behaviour into account, the estimation of the electric field components becomes more challenging. In this paper, we present a set of acceleration strategies based on parallel software and hardware solutions.

Seasonal changes of heat and moisture fluxes from the Caspian Sea surface and its effect on synoptic systems with heavy rainfalls in southern shores of the sea during 2005-2010

Caspian Sea with its unique characteristics is a significant source to supply required heat and moisture for passing weather systems over the north of Iran. Investigation of heat and moisture fluxes in the region and their effects on these systems that could lead to floods and major financial and human losses is essential in weather forecasting. Nowadays by improvement of numerical weather and climate prediction models and the increasing need to more accurate forecasting of heavy rainfall, the evaluation and verification of these models has been become much more important. In this study we have used the WRF model as a research-practical one with many valuable characteristics and flexibilities. In this research, the effects of heat and moisture fluxes of Caspian Sea on the synoptic and dynamical structure of 20 selective systems associated with heavy rainfall in the southern shores of Caspian Sea are investigated. These systems are selected based on the rainfall data gathered by three local stations named: Rasht, Babolsar and Gorgan in different seasons during a five-year period (2005-2010) with maximum amount of rainfall through the 24 hours of a day. In addition to synoptic analyses of these systems, the WRF model with and without surface flues was run using the two nested grids with the horizontal resolutions of 12 and 36 km. The results show that there are good consistencies between the predicted distribution of rainfall field, time of beginning and end of rainfall by the model and the observations. But the model underestimates the amounts of rainfall and the maximum difference with the observation is about 69%. Also, no significant changes in the results are seen when the domain and the resolution of computations are changed. The other noticeable point is that the systems are severely weakened by removing heat and moisture fluxes and thereby the amounts of large scale rainfall are decreased up to 77% and the convective rainfalls tend to zero.

Effects of an asymmetric friction on the nonlinear equilibration of a baroclinic system

Following some recent linear and nonlinear studies the authors examine, using numerical simulations of a classical two-layer model, the effect of an asymmetric friction on the nonlinear equilibrium of moderately unstable baroclinic systems, The results show that the presence of an asymmetric friction leads to a significant wave scale selection: ''long'' waves (in terms of their zonal wavelengths) emerge with a traditional asymmetric friction (with the upper layer less viscous than the lower layer), while only ''short'' waves dominate with a nontraditional asymmetric friction (with the lower layer less viscous than the upper layer). The role of the nonlinear interactions and. more precisely, the effects of an asymmetric friction on the wave-mean flow and wave-wave interactions; and their consequences on the wave scale selection are examined.

NONLINEAR EFFECTS IN MAGNETIC GARNET FILMS AND NONRECIPROCAL OPTICAL BLOCH OSCILLATIONS IN WAVEGUIDE ARRAYS

This dissertation presents detailed experimental and theoretical investigations of nonlinear and nonreciprocal effects in magnetic garnet films. The dissertation thus comprises two major sections. The first section concentrates on the study of a new class of nonlinear magneto-optic thin film materials possessing strong higher order magnetic susceptibility for nonlinear optical applications. The focus was on enlarging the nonlinear performance of ferrite garnet films by strain generation and compositional gradients in the sputter-deposition growth of these films. Under this project several bismuth-substituted yttrium iron garnet (Bi,Y) 3 (Fe,Ga)5 O12(acronym as Bi:YIG) films have been sputter-deposited over gadolinium gallium garnet (Gd 3 Ga5 O12 ) substrates and characterized for their nonlinear optical response. One of the important findings of this work is that lattice mismatch strain drives the second harmonic (SH) signal in the Bi:YIG films, in agreement with theoretical predictions; whereas micro-strain was found not to correlate significantly with SH signal at the micro-strain levels present in these films. This study also elaborates on the role of the film's constitutive elements and their concentration gradients in nonlinear response of the films. Ultrahigh sensitivity delivered by second harmonic generation provides a new exciting tool for studying magnetized surfaces and buried interfaces, making this work important from both a fundamental and application point of view. The second part of the dissertation addresses an important technological need; namely the development of an on-chip optical isolator for use in photonic integrated circuits. It is based on two related novel effects, nonreciprocal and unidirectional optical Bloch oscillations (BOs), recently proposed and developed by Professor Miguel Levy and myself. This dissertation work has established a comprehensive theoretical background for the implementation of these effects in magneto-optic waveguide arrays. The model systems we developed consist of photonic lattices in the form of one-dimensional waveguide arrays where an optical force is introduced into the array through geometrical design turning the beam sideways. Laterally displaced photons are periodically returned to a central guide by photonic crystal action. The effect leads to a novel oscillatory optical phenomenon that can be magnetically controlled and rendered unidirectional. An on-chip optical isolator was designed based on the unidirectionality of the magneto-opticBloch oscillatory motion. The proposed device delivers an isolation ratio as high as 36 dB that remains above 30 dB in a 0.7 nm wavelength bandwidth, at the telecommunication wavelength 1.55 μm. Slight modifications in isolator design allow one to achieve an even more impressive isolation ratio ~ 55 dB, but at the expense of smaller bandwidth. Moreover, the device allows multifunctionality, such as optical switching with a simultaneous isolation function, well suited for photonic integrated circuits.

Buy three but get only two: The smallest effect in a 2 × 2 ANOVA is always uninterpretable

Loftus (Memory & Cognition 6:312-319, 1978) distinguished between interpretable and uninterpretable interactions. Uninterpretable interactions are ambiguous, because they may be due to two additive main effects (no interaction) and a nonlinear relationship between the (latent) outcome variable and its indicator. Interpretable interactions can only be due to the presence of a true interactive effect in the outcome variable, regardless of the relationship that it establishes with its indicator. In the present article, we first show that same problem can arise when an unmeasured mediator has a nonlinear effect on the measured outcome variable. Then we integrate Loftus's arguments with a seemingly contradictory approach to interactions suggested by Rosnow and Rosenthal (Psychological Bulletin 105:143-146, 1989). We show that entire data patterns, not just interaction effects alone, produce interpretable or noninterpretable interactions. Next, we show that the same problem of interpretability can apply to main effects. Lastly, we give concrete advice on what researchers can do to generate data patterns that provide unambiguous evidence for hypothesized interactions.

Surfing the high energy output branch of nonlinear energy harvesters

Hysteresis and multistability are fundamental phenomena of driven nonlinear oscillators, which, however, restrict many applications such as mechanical energy harvesting. We introduce an electrical control mechanism to switch from the low to the high energy output branch of a nonlinear energy harvester by exploiting the strong interplay between its electrical and mechanical degrees of freedom. This method improves the energy conversion efficiency over a wide bandwidth in a frequency-amplitude-varying environment using only a small energy budget. The underlying effect is independent of the device scale and the transduction method and is explained using a modified Duffing oscillator model.