Effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam

PubMed Central

Thomsen, Jon Juel

2016-01-01

The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation. PMID:27118899

Joint nonlinearity effects in the design of a flexible truss structure control system

NASA Technical Reports Server (NTRS)

Mercadal, Mathieu

1986-01-01

Nonlinear effects are introduced in the dynamics of large space truss structures by the connecting joints which are designed with rather important tolerances to facilitate the assembly of the structures in space. The purpose was to develop means to investigate the nonlinear dynamics of the structures, particularly the limit cycles that might occur when active control is applied to the structures. An analytical method was sought and derived to predict the occurrence of limit cycles and to determine their stability. This method is mainly based on the quasi-linearization of every joint using describing functions. This approach was proven successful when simple dynamical systems were tested. Its applicability to larger systems depends on the amount of computations it requires, and estimates of the computational task tend to indicate that the number of individual sources of nonlinearity should be limited. Alternate analytical approaches, which do not account for every single nonlinearity, or the simulation of a simplified model of the dynamical system should, therefore, be investigated to determine a more effective way to predict limit cycles in large dynamical systems with an important number of distributed nonlinearities.

Chaotic dynamical aperture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, S.Y.; Tepikian, S.

1985-01-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator designs have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipolesmore » should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take a tremendous amount of computing time. In this review the method of determining chaotic orbit and applying the method to nonlinear problems in accelerator physics is discussed. We then discuss the scaling properties and effect of random sextupoles.« less

Giant Kerr response of ultrathin gold films from quantum size effect.

PubMed

Qian, Haoliang; Xiao, Yuzhe; Liu, Zhaowei

2016-10-10

With the size of plasmonic devices entering into the nanoscale region, the impact of quantum physics needs to be considered. In the past, the quantum size effect on linear material properties has been studied extensively. However, the nonlinear aspects have not been explored much so far. On the other hand, much effort has been put into the field of integrated nonlinear optics and a medium with large nonlinearity is desirable. Here we study the optical nonlinear properties of a nanometre scale gold quantum well by using the z-scan method and nonlinear spectrum broadening technique. The quantum size effect results in a giant optical Kerr susceptibility, which is four orders of magnitude higher than the intrinsic value of bulk gold and several orders larger than traditional nonlinear media. Such high nonlinearity enables efficient nonlinear interaction within a microscopic footprint, making quantum metallic films a promising candidate for integrated nonlinear optical applications.

The Nonlinear Magnetosphere: Expressions in MHD and in Kinetic Models

NASA Technical Reports Server (NTRS)

Hesse, Michael; Birn, Joachim

2011-01-01

Like most plasma systems, the magnetosphere of the Earth is governed by nonlinear dynamic evolution equations. The impact of nonlinearities ranges from large scales, where overall dynamics features are exhibiting nonlinear behavior, to small scale, kinetic, processes, where nonlinear behavior governs, among others, energy conversion and dissipation. In this talk we present a select set of examples of such behavior, with a specific emphasis on how nonlinear effects manifest themselves in MHD and in kinetic models of magnetospheric plasma dynamics.

Nonlinear compensation techniques for magnetic suspension systems. Ph.D. Thesis - MIT

NASA Technical Reports Server (NTRS)

Trumper, David L.

1991-01-01

In aerospace applications, magnetic suspension systems may be required to operate over large variations in air-gap. Thus the nonlinearities inherent in most types of suspensions have a significant effect. Specifically, large variations in operating point may make it difficult to design a linear controller which gives satisfactory stability and performance over a large range of operating points. One way to address this problem is through the use of nonlinear compensation techniques such as feedback linearization. Nonlinear compensators have received limited attention in the magnetic suspension literature. In recent years, progress has been made in the theory of nonlinear control systems, and in the sub-area of feedback linearization. The idea is demonstrated of feedback linearization using a second order suspension system. In the context of the second order suspension, sampling rate issues in the implementation of feedback linearization are examined through simulation.

Nonlinear bending-torsional vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.

1986-01-01

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by comparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Nonlinear vibration and stability of rotating, pretwisted, preconed blades including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.; Brown, G. V.; Lawrence, C.

1987-01-01

The coupled bending-bending-torsional equations of dynamic motion of rotating, linearly pretwisted blades are derived including large precone, second degree geometric nonlinearities and Coriolis effects. The equations are solved by the Galerkin method and a linear perturbation technique. Accuracy of the present method is verified by conparisons of predicted frequencies and steady state deflections with those from MSC/NASTRAN and from experiments. Parametric results are generated to establish where inclusion of only the second degree geometric nonlinearities is adequate. The nonlinear terms causing torsional divergence in thin blades are identified. The effects of Coriolis terms and several other structurally nonlinear terms are studied, and their relative importance is examined.

Inducing in situ, nonlinear soil response applying an active source

USGS Publications Warehouse

Johnson, P.A.; Bodin, P.; Gomberg, J.; Pearce, F.; Lawrence, Z.; Menq, F.-Y.

2009-01-01

[1] It is well known that soil sites have a profound effect on ground motion during large earthquakes. The complex structure of soil deposits and the highly nonlinear constitutive behavior of soils largely control nonlinear site response at soil sites. Measurements of nonlinear soil response under natural conditions are critical to advancing our understanding of soil behavior during earthquakes. Many factors limit the use of earthquake observations to estimate nonlinear site response such that quantitative characterization of nonlinear behavior relies almost exclusively on laboratory experiments and modeling of wave propagation. Here we introduce a new method for in situ characterization of the nonlinear behavior of a natural soil formation using measurements obtained immediately adjacent to a large vibrator source. To our knowledge, we are the first group to propose and test such an approach. Employing a large, surface vibrator as a source, we measure the nonlinear behavior of the soil by incrementally increasing the source amplitude over a range of frequencies and monitoring changes in the output spectra. We apply a homodyne algorithm for measuring spectral amplitudes, which provides robust signal-to-noise ratios at the frequencies of interest. Spectral ratios are computed between the receivers and the source as well as receiver pairs located in an array adjacent to the source, providing the means to separate source and near-source nonlinearity from pervasive nonlinearity in the soil column. We find clear evidence of nonlinearity in significant decreases in the frequency of peak spectral ratios, corresponding to material softening with amplitude, observed across the array as the source amplitude is increased. The observed peak shifts are consistent with laboratory measurements of soil nonlinearity. Our results provide constraints for future numerical modeling studies of strong ground motion during earthquakes.

Large Spatial and Temporal Separations of Cause and Effect in Policy Making - Dealing with Non-linear Effects

NASA Astrophysics Data System (ADS)

McCaskill, John

There can be large spatial and temporal separation of cause and effect in policy making. Determining the correct linkage between policy inputs and outcomes can be highly impractical in the complex environments faced by policy makers. In attempting to see and plan for the probable outcomes, standard linear models often overlook, ignore, or are unable to predict catastrophic events that only seem improbable due to the issue of multiple feedback loops. There are several issues with the makeup and behaviors of complex systems that explain the difficulty many mathematical models (factor analysis/structural equation modeling) have in dealing with non-linear effects in complex systems. This chapter highlights those problem issues and offers insights to the usefulness of ABM in dealing with non-linear effects in complex policy making environments.

Soliton compression to few-cycle pulses with a high quality factor by engineering cascaded quadratic nonlinearities.

PubMed

Zeng, Xianglong; Guo, Hairun; Zhou, Binbin; Bache, Morten

2012-11-19

We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency. Numerical results show that compressed pulses with less than three-cycle duration can be achieved even when the compression factor is very large, and in contrast to standard soliton compression, these compressed pulses have minimal pedestal and high quality factor.

The Effect of Crack Orientation on the Nonlinear Interaction of a P-wave with an S-wave

DOE PAGES

TenCate, J. A.; Malcolm, A. E.; Feng, X.; ...

2016-06-06

Cracks, joints, fluids, and other pore-scale structures have long been hypothesized to be the cause of the large elastic nonlinearity observed in rocks. It is difficult to definitively say which pore-scale features are most important, however, because of the difficulty in isolating the source of the nonlinear interaction. In this work, we focus on the influence of cracks on the recorded nonlinear signal and in particular on how the orientation of microcracks changes the strength of the nonlinear interaction. We do this by studying the effect of orientation on the measurements in a rock with anisotropy correlated with the presencemore » and alignment of microcracks. We measure the nonlinear response via the traveltime delay induced in a low-amplitude P wave probe by a high-amplitude S wave pump. We find evidence that crack orientation has a significant effect on the nonlinear signal.« less

Impact of a large density gradient on linear and nonlinear edge-localized mode simulations

DOE PAGES

Xi, P. W.; Xu, X. Q.; Xia, T. Y.; ...

2013-09-27

Here, the impact of a large density gradient on edge-localized modes (ELMs) is studied linearly and nonlinearly by employing both two-fluid and gyro-fluid simulations. In two-fluid simulations, the ion diamagnetic stabilization on high-n modes disappears when the large density gradient is taken into account. But gyro-fluid simulations show that the finite Larmor radius (FLR) effect can effectively stabilize high-n modes, so the ion diamagnetic effect alone is not sufficient to represent the FLR stabilizing effect. We further demonstrate that additional gyroviscous terms must be kept in the two-fluid model to recover the linear results from the gyro-fluid model. Nonlinear simulations show that the density variation significantly weakens the E × B shearing at the top of the pedestal and thus leads to more energy loss during ELMs. The turbulence spectrum after an ELM crash is measured and has the relation ofmore » $$P(k_{z})\\propto k_{z}^{-3.3}$$ .« less

Nonlinear optical effects on the surface of acridine yellow-doped lead-tin fluorophosphate glass

NASA Technical Reports Server (NTRS)

He, K. X.; Bryant, William; Venkateswarlu, Putcha

1991-01-01

The second- and third-order nonlinear optical properties of acridine yellow-doped lead-tin fluorophosphate (LTF) glass have been directly studied by measurement of surface enhanced second harmonic generation and third harmonic generation. The three photon excitation fluorescence is also observed. Based on these results, the large nonlinearities of the acridine LTF system which is a new nonlinear optical material are experimentally demonstrated.

Nonlinear flap-lag-extensional vibrations of rotating, pretwisted, preconed beams including Coriolis effects

NASA Technical Reports Server (NTRS)

Subrahmanyam, K. B.; Kaza, K. R. V.

1985-01-01

The effects of pretwist, precone, setting angle, Coriolis forces and second degree geometric nonlinearities on the natural frequencies, steady state deflections and mode shapes of rotating, torsionally rigid, cantilevered beams were studied. The governing coupled equations of flap lag extensional motion are derived including the effects of large precone and retaining geometric nonlinearities up to second degree. The Galerkin method, with nonrotating normal modes, is used for the solution of both steady state nonlinear equations and linear perturbation equations. Parametric indicating the individual and collective effects of pretwist, precone, Coriolis forces and second degree geometric nonlinearities on the steady state deflection, natural frequencies and mode shapes of rotating blades are presented. It is indicated that the second degree geometric nonlinear terms, which vanish for zero precone, can produce frequency changes of engineering significance. Further confirmation of the validity of including those generated by MSC NASTRAN. It is indicated that the linear and nonlinear Coriolis effects must be included in analyzing thick blades. The Coriolis effects are significant on the first flatwise and the first edgewise modes.

Nonlinear pulse propagation in one-dimensional metal-dielectric multilayer stacks: ultrawide bandwidth optical limiting.

PubMed

Scalora, Michael; Mattiucci, Nadia; D'Aguanno, Giuseppe; Larciprete, MariaCristina; Bloemer, Mark J

2006-01-01

We numerically study the nonlinear optical properties of metal-dielectric photonic band gap structures in the pulsed regime. We exploit the high chi3 of copper metal to induce nonlinear effects such as broadband optical limiting, self-phase modulation, and unusual spectral narrowing of high intensity pulses. We show that in a single pass through a typical, chirped multilayer stack nonlinear transmittance and peak powers can be reduced by nearly two orders of magnitude compared to low light intensity levels across the entire visible range. Chirping dielectric layer thickness dramatically improves the linear transmittance through the stack and achieves large fields inside the copper to access the large nonlinearity. At the same time, the linear properties of the stack block most of the remaining electromagnetic spectrum.

Microscopic cascading of second-order molecular nonlinearity: New design principles for enhancing third-order nonlinearity.

PubMed

Baev, Alexander; Autschbach, Jochen; Boyd, Robert W; Prasad, Paras N

2010-04-12

Herein, we develop a phenomenological model for microscopic cascading and substantiate it with ab initio calculations. It is shown that the concept of local microscopic cascading of a second-order nonlinearity can lead to a third-order nonlinearity, without introducing any new loss mechanisms that could limit the usefulness of our approach. This approach provides a new molecular design protocol, in which the current great successes achieved in producing molecules with extremely large second-order nonlinearity can be used in a supra molecular organization in a preferred orientation to generate very large third-order response magnitudes. The results of density functional calculations for a well-known second-order molecule, (para)nitroaniline, show that a head-to-tail dimer configuration exhibits enhanced third-order nonlinearity, in agreement with the phenomenological model which suggests that such an arrangement will produce cascading due to local field effects.

The chaotic dynamical aperture

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, S.Y.; Tepikian, S.

1985-10-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipolesmore » should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles.« less

Piezoelectric Field Enhanced Second-Order Nonlinear Optical Susceptibilities in Wurtzite GaN/AlGaN Quantum Wells

NASA Technical Reports Server (NTRS)

Liu, Ansheng; Chuang, S.-L.; Ning, C. Z.; Woo, Alex (Technical Monitor)

1999-01-01

Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.

On effective holographic Mott insulators

NASA Astrophysics Data System (ADS)

Baggioli, Matteo; Pujolàs, Oriol

2016-12-01

We present a class of holographic models that behave effectively as prototypes of Mott insulators — materials where electron-electron interactions dominate transport phenomena. The main ingredient in the gravity dual is that the gauge-field dynamics contains self-interactions by way of a particular type of non-linear electrodynamics. The electrical response in these models exhibits typical features of Mott-like states: i) the low-temperature DC conductivity is unboundedly low; ii) metal-insulator transitions appear by varying various parameters; iii) for large enough self-interaction strength, the conductivity can even decrease with increasing doping (density of carriers) — which appears as a sharp manifestation of `traffic-jam'-like behaviour; iv) the insulating state becomes very unstable towards superconductivity at large enough doping. We exhibit some of the properties of the resulting insulator-superconductor transition, which is sensitive to the momentum dissipation rate in a specific way. These models imply a clear and generic correlation between Mott behaviour and significant effects in the nonlinear electrical response. We compute the nonlinear current-voltage curve in our model and find that indeed at large voltage the conductivity is largely reduced.

Enhanced optical limiting effects in a double-decker bis(phthalocyaninato) rare earth complex using radially polarized beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Jia-Lu; Gu, Bing, E-mail: gubing@seu.edu.cn; Liu, Dahui

2014-10-27

Optical limiting (OL) effects can be enhanced by exploiting various limiting mechanisms and by designing nonlinear optical materials. In this work, we present the large enhancement of OL effects by manipulating the polarization distribution of the light field. Theoretically, we develop the Z-scan and nonlinear transmission theories on a two-photon absorber under the excitation of cylindrical vector beams. It is shown that both the sensitivity of Z-scan technique and the OL effect using radially polarized beams have the large enhancement compared with that using linearly polarized beams (LPBs). Experimentally, we investigate the nonlinear absorption properties of a double-decker Pr[Pc(OC{sub 8}H{submore » 17}){sub 8}]{sub 2} rare earth complex by performing Z-scan measurements with femtosecond-pulsed radially polarized beams at 800 nm wavelength. The observed two-photon absorption process, which originates from strong intramolecular π–π interaction, is exploited for OL application. The results demonstrate the large enhancement of OL effects using radially polarized beams instead of LPBs.« less

Nonlinear refractive index measurements and self-action effects in Roselle-Hibiscus Sabdariffa solutions

NASA Astrophysics Data System (ADS)

Henari, F. Z.; Al-Saie, A.

2006-12-01

We report the observation of self-action phenomena, such as self-focusing, self-defocusing, self-phase modulation and beam fanning in Roselle-Hibiscus Sabdariffa solutions. This material is found to be a new type of natural nonlinear media, and the nonlinear reflective index coefficient has been determined using a Z-scan technique and by measuring the critical power for the self-trapping effect. Z-scan measurements show that this material has a large negative nonlinear refractive index, n 2 = 1 × 10-4 esu. A comparison between the experimental n 2 values and the calculated thermal value for n 2 suggests that the major contribution to nonlinear response is of thermal origin.

Perturbation theory for cosmologies with nonlinear structure

NASA Astrophysics Data System (ADS)

Goldberg, Sophia R.; Gallagher, Christopher S.; Clifton, Timothy

2017-11-01

The next generation of cosmological surveys will operate over unprecedented scales, and will therefore provide exciting new opportunities for testing general relativity. The standard method for modelling the structures that these surveys will observe is to use cosmological perturbation theory for linear structures on horizon-sized scales, and Newtonian gravity for nonlinear structures on much smaller scales. We propose a two-parameter formalism that generalizes this approach, thereby allowing interactions between large and small scales to be studied in a self-consistent and well-defined way. This uses both post-Newtonian gravity and cosmological perturbation theory, and can be used to model realistic cosmological scenarios including matter, radiation and a cosmological constant. We find that the resulting field equations can be written as a hierarchical set of perturbation equations. At leading-order, these equations allow us to recover a standard set of Friedmann equations, as well as a Newton-Poisson equation for the inhomogeneous part of the Newtonian energy density in an expanding background. For the perturbations in the large-scale cosmology, however, we find that the field equations are sourced by both nonlinear and mode-mixing terms, due to the existence of small-scale structures. These extra terms should be expected to give rise to new gravitational effects, through the mixing of gravitational modes on small and large scales—effects that are beyond the scope of standard linear cosmological perturbation theory. We expect our formalism to be useful for accurately modeling gravitational physics in universes that contain nonlinear structures, and for investigating the effects of nonlinear gravity in the era of ultra-large-scale surveys.

Evolution of diffraction and self-diffraction phenomena in thin films of Gelite Bloom/Hibiscus Sabdariffa

NASA Astrophysics Data System (ADS)

Cano-Lara, Miroslava; Severiano-Carrillo, Israel; Trejo-Durán, Mónica; Alvarado-Méndez, Edgar

2017-09-01

In this work, we present a study of non-linear optical response in thin films elaborated with Gelite Bloom and extract of Hibiscus Sabdariffa. Non-linear refraction and absorption effects were studied experimentally (Z-scan technique) and numerically, by considering the transmittance as non-linear absorption and refraction contribution. We observe large phase shifts to far field, and diffraction due to self-phase modulation of the sample. Diffraction and self-diffraction effects were observed as time function. The aim of studying non-linear optical properties in thin films is to eliminate thermal vortex effects that occur in liquids. This is desirable in applications such as non-linear phase contrast, optical limiting, optics switches, etc. Finally, we find good agreement between experimental and theoretical results.

Bridgman growth of large-aperture yttrium calcium oxyborate crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wu, Anhua, E-mail: wuanhua@mail.sic.ac.cn; Jiang, Linwen; Qian, Guoxing

2012-09-15

Highlights: ► YCOB is a novel non-linear optical crystal possessing good thermal, mechanical and nonlinear optical properties. ► Large size crystal growth is key technology question for YCOB crystal. ► YCOB crystals 3 in. in diameter were grown with modified vertical Bridgman method. ► It is a more effective growth method to obtain large size and high quality YCOB crystal. -- Abstract: Large-aperture yttrium calcium oxyborate YCa{sub 4}O(BO{sub 3}){sub 3} (YCOB) crystals with 3 in. in diameter were grown with modified vertical Bridgman method, and the large crystal plate (63 mm × 68 mm × 20 mm) was harvested formore » high-average power frequency conversion system. The crack, facet growth and spiral growth can be effectively controlled in the as-grown crystal, and Bridgman method displays more effective in obtain large size and high quality YCOB crystal plate than Czochralski technique.« less

On the benefit of DMT modulation in nonlinear VLC systems.

PubMed

Qian, Hua; Cai, Sunzeng; Yao, Saijie; Zhou, Ting; Yang, Yang; Wang, Xudong

2015-02-09

In a visible light communication (VLC) system, the nonlinear characteristic of the light emitting diode (LED) in transmitter is a limiting factor of system performance. Modern modulation signals with large peak-to-power-ratio (PAPR) suffers uneven distortion. The nonlinear response directly impacts the intensity modulation and direct detection VLC system with pulse-amplitude modulation (PAM). The amplitude of the PAM signal is distorted unevenly and large signal is vulnerable to noise. Orthogonal linear transformations, such as discrete multi-tone (DMT) modulation, can spread the nonlinear effects evenly to each data symbol, thus perform better than PAM signals. In this paper, we provide theoretical analysis on the benefit of DMT modulation in nonlinear VLC system. We show that the DMT modulation is a better choice than the PAM modulation for the VLC system as the DMT modulation is more robust against nonlinearity. We also show that the post-distortion nonlinear elimination method, which is applied at the receiver, can be a reliable solution to the nonlinear VLC system. Simulation results show that the post-distortion greatly improves the system performance for the DMT modulation.

Coriolis effects on nonlinear oscillations of rotating cylinders and rings

NASA Technical Reports Server (NTRS)

Padovan, J.

1976-01-01

The effects which moderately large deflections have on the frequency spectrum of rotating rings and cylinders are considered. To develop the requisite solution, a variationally constrained version of the Lindstedt-Poincare procedure is employed. Based on the solution developed, in addition to considering the effects of displacement induced nonlinearity, the role of Coriolis forces is also given special consideration.

Large-area and highly crystalline MoSe2 for optical modulator

NASA Astrophysics Data System (ADS)

Yin, Jinde; Chen, Hao; Lu, Wei; Liu, Mengli; Li, Irene Ling; Zhang, Min; Zhang, Wenfei; Wang, Jinzhang; Xu, Zihan; Yan, Peiguang; Liu, Wenjun; Ruan, Shuangchen

2017-12-01

Transition metal dichalcogenides (TMDs) have been successfully used as broadband optical modulator materials for pulsed fiber laser systems. However, the nonlinear optical absorptions of exfoliated TMDs are strongly limited by their nanoflakes morphology with uncontrollable lateral size and thickness. In this work, we provide an effective method to fully explore the nonlinear optical properties of MoSe2. Large-area and high quality lattice MoSe2 grown by chemical vapor deposition method was adopted as an optical modulator for the first time. The large-area MoSe2 shows excellent nonlinear optical absorption with a large modulation depth of 21.7% and small saturable intensity of 9.4 MW cm-2. After incorporating the MoSe2 optical modulator into fiber laser cavity as a saturable absorber, a highly stable Q-switching operation with single pulse energy of 224 nJ is achieved. The large-area MoSe2 possessing superior nonlinear optical properties compared to exfoliated nanoflakes affords possibility for the larger-area two-dimensional materials family as high performance optical devices.

A Limited-Memory BFGS Algorithm Based on a Trust-Region Quadratic Model for Large-Scale Nonlinear Equations.

PubMed

Li, Yong; Yuan, Gonglin; Wei, Zengxin

2015-01-01

In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that the method is competitive with the norm method.

Dark energy and modified gravity in the Effective Field Theory of Large-Scale Structure

NASA Astrophysics Data System (ADS)

Cusin, Giulia; Lewandowski, Matthew; Vernizzi, Filippo

2018-04-01

We develop an approach to compute observables beyond the linear regime of dark matter perturbations for general dark energy and modified gravity models. We do so by combining the Effective Field Theory of Dark Energy and Effective Field Theory of Large-Scale Structure approaches. In particular, we parametrize the linear and nonlinear effects of dark energy on dark matter clustering in terms of the Lagrangian terms introduced in a companion paper [1], focusing on Horndeski theories and assuming the quasi-static approximation. The Euler equation for dark matter is sourced, via the Newtonian potential, by new nonlinear vertices due to modified gravity and, as in the pure dark matter case, by the effects of short-scale physics in the form of the divergence of an effective stress tensor. The effective fluid introduces a counterterm in the solution to the matter continuity and Euler equations, which allows a controlled expansion of clustering statistics on mildly nonlinear scales. We use this setup to compute the one-loop dark-matter power spectrum.

A therapy inactivating the tumor angiogenic factors.

PubMed

Morales-Rodrigo, Cristian

2013-02-01

This paper is devoted to a nonlinear system of partial differential equations modeling the effect of an anti-angiogenic therapy based on an agent that binds to the tumor angiogenic factors. The main feature of the model under consideration is a nonlinear flux production of tumor angiogenic factors at the boundary of the tumor. It is proved the global existence for the nonlinear system and the effect in the large time behavior of the system for high doses of the therapeutic agent.

Nonlinear Control of Large Disturbances in Magnetic Bearing Systems

NASA Technical Reports Server (NTRS)

Jiang, Yuhong; Zmood, R. B.

1996-01-01

In this paper, the nonlinear operation of magnetic bearing control methods is reviewed. For large disturbances, the effects of displacement constraints and power amplifier current and di/dt limits on bearing control system performance are analyzed. The operation of magnetic bearings exhibiting self-excited large scale oscillations have been studied both experimentally and by simulation. The simulation of the bearing system has been extended to include the effects of eddy currents in the actuators, so as to improve the accuracy of the simulation results. The results of these experiments and simulations are compared, and some useful conclusions are drawn for improving bearing system robustness.

Isogeometric analysis of free-form Timoshenko curved beams including the nonlinear effects of large deformations

NASA Astrophysics Data System (ADS)

Hosseini, Seyed Farhad; Hashemian, Ali; Moetakef-Imani, Behnam; Hadidimoud, Saied

2018-03-01

In the present paper, the isogeometric analysis (IGA) of free-form planar curved beams is formulated based on the nonlinear Timoshenko beam theory to investigate the large deformation of beams with variable curvature. Based on the isoparametric concept, the shape functions of the field variables (displacement and rotation) in a finite element analysis are considered to be the same as the non-uniform rational basis spline (NURBS) basis functions defining the geometry. The validity of the presented formulation is tested in five case studies covering a wide range of engineering curved structures including from straight and constant curvature to variable curvature beams. The nonlinear deformation results obtained by the presented method are compared to well-established benchmark examples and also compared to the results of linear and nonlinear finite element analyses. As the nonlinear load-deflection behavior of Timoshenko beams is the main topic of this article, the results strongly show the applicability of the IGA method to the large deformation analysis of free-form curved beams. Finally, it is interesting to notice that, until very recently, the large deformations analysis of free-form Timoshenko curved beams has not been considered in IGA by researchers.

Study of large nonlinear change phase in Hibiscus Sabdariffa

NASA Astrophysics Data System (ADS)

Trejo-Durán, M.; Alvarado-Méndez, E.; Andrade-Lucio, J. A.; Rojas-Laguna, R.; Vázquez-Guevara, M. A.

2015-09-01

High intensities electromagnetic energy interacting with organic media gives rise to nonlinear optical effects. Hibiscus Sabdariffa is a flower whose concentrated solution presents interesting nonlinear optical properties. This organic material shows an important self-phase modulation with changes bigger than 2π. We present a diffraction ring patterns study of the Hibiscus Sabdariffa solution. Numerical results of transmittance, with refraction and simultaneous absorption, are shown.

On the analytical modeling of the nonlinear vibrations of pretensioned space structures

NASA Technical Reports Server (NTRS)

Housner, J. M.; Belvin, W. K.

1983-01-01

Pretensioned structures are receiving considerable attention as candidate large space structures. A typical example is a hoop-column antenna. The large number of preloaded members requires efficient analytical methods for concept validation and design. Validation through analyses is especially important since ground testing may be limited due to gravity effects and structural size. The present investigation has the objective to present an examination of the analytical modeling of pretensioned members undergoing nonlinear vibrations. Two approximate nonlinear analysis are developed to model general structural arrangements which include beam-columns and pretensioned cables attached to a common nucleus, such as may occur at a joint of a pretensioned structure. Attention is given to structures undergoing nonlinear steady-state oscillations due to sinusoidal excitation forces. Three analyses, linear, quasi-linear, and nonlinear are conducted and applied to study the response of a relatively simple cable stiffened structure.

Dynamic Nonlinear Elastic Stability of Helicopter Rotor Blades in Hover and in Forward Flight

NASA Technical Reports Server (NTRS)

Friedmann, P.; Tong, P.

1972-01-01

Equations for large coupled flap-lag motion of hingeless elastic helicopter blades are consistently derived. Only torsionally-rigid blades excited by quasi-steady aerodynamic loads are considered. The nonlinear equations of motion in the time and space variables are reduced to a system of coupled nonlinear ordinary differential equations with periodic coefficients, using Galerkin's method for the space variables. The nonlinearities present in the equations are those arising from the inclusion of moderately large deflections in the inertia and aerodynamic loading terms. The resulting system of nonlinear equations has been solved, using an asymptotic expansion procedure in multiple time scales. The stability boundaries, amplitudes of nonlinear response, and conditions for existence of limit cycles are obtained analytically. Thus, the different roles played by the forcing function, parametric excitation, and nonlinear coupling in affecting the solution can be easily identified, and the basic physical mechanism of coupled flap-lag response becomes clear. The effect of forward flight is obtained with the requirement of trimmed flight at fixed values of the thrust coefficient.

Micro-/nanoscale multi-field coupling in nonlinear photonic devices

NASA Astrophysics Data System (ADS)

Yang, Qing; Wang, Yubo; Tang, Mingwei; Xu, Pengfei; Xu, Yingke; Liu, Xu

2017-08-01

The coupling of mechanics/electronics/photonics may improve the performance of nanophotonic devices not only in the linear region but also in the nonlinear region. This review letter mainly presents the recent advances on multi-field coupling in nonlinear photonic devices. The nonlinear piezoelectric effect and piezo-phototronic effects in quantum wells and fibers show that large second-order nonlinear susceptibilities can be achieved, and second harmonic generation and electro-optic modulation can be enhanced and modulated. Strain engineering can tune the lattice structures and induce second order susceptibilities in central symmetry semiconductors. By combining the absorption-based photoacoustic effect and intensity-dependent photobleaching effect, subdiffraction imaging can be achieved. This review will also discuss possible future applications of these novel effects and the perspective of their research. The review can help us develop a deeper knowledge of the substance of photon-electron-phonon interaction in a micro-/nano- system. Moreover, it can benefit the design of nonlinear optical sensors and imaging devices with a faster response rate, higher efficiency, more sensitivity and higher spatial resolution which could be applied in environmental detection, bio-sensors, medical imaging and so on.

Methods for Large-Scale Nonlinear Optimization.

DTIC Science & Technology

1980-05-01

STANFORD, CALIFORNIA 94305 METHODS FOR LARGE-SCALE NONLINEAR OPTIMIZATION by Philip E. Gill, Waiter Murray, I Michael A. Saunden, and Masgaret H. Wright...typical iteration can be partitioned so that where B is an m X m basise matrix. This partition effectively divides the vari- ables into three classes... attention is given to the standard of the coding or the documentation. A much better way of obtaining mathematical software is from a software library

Numerical nonlinear inelastic analysis of stiffened shells of revolution. Volume 1: Theory manual for STARS-2P digital computer program

NASA Technical Reports Server (NTRS)

Svalbonas, V.; Levine, H.

1975-01-01

The theoretical analysis background for the STARS-2P nonlinear inelastic program is discussed. The theory involved is amenable for the analysis of large deflection inelastic behavior in axisymmetric shells of revolution subjected to axisymmetric loadings. The analysis is capable of considering such effects as those involved in nonproportional and cyclic loading conditions. The following are also discussed: orthotropic nonlinear kinematic hardening theory; shell wall cross sections and discrete ring stiffeners; the coupled axisymmetric large deflection elasto-plastic torsion problem; and the provision for the inelastic treatment of smeared stiffeners, isogrid, and waffle wall constructions.

Fully nonlinear Goertler vortices in constricted channel flows and their effect on the onset of separation

NASA Technical Reports Server (NTRS)

Denier, James P.; Hall, Philip

1992-01-01

The development of fully nonlinear Goertler vortices in high Reynolds number flow in a symmetrically constricted channel is investigated. Attention is restricted to the case of 'strongly' constricted channels considered by Smith and Daniels (1981) for which the scaled constriction height is asymptotically large. Such flows are known to develop a Goldstein singularity and subsequently become separated at some downstream station past the point of maximum channel constriction. It is shown that these flows can support fully nonlinear Goertler vortices, of the form elucidated by Hall and Lakin (1988), for constrictions which have an appreciable region of local concave curvature upstream of the position at which separation occurs. The effect on the onset of separation due to the nonlinear Goertler modes is discussed. A brief discussion of other possible nonlinear states which may also have a dramatic effect in delaying (or promoting) separation is given.

Design and verification of a hybrid nonlinear MRE vibration absorber for controllable broadband performance

NASA Astrophysics Data System (ADS)

Sun, S. S.; Yildirim, T.; Wu, Jichu; Yang, J.; Du, H.; Zhang, S. W.; Li, W. H.

2017-09-01

In this work, a hybrid nonlinear magnetorheological elastomer (MRE) vibration absorber has been designed, theoretically investigated and experimentally verified. The proposed nonlinear MRE absorber has the dual advantages of a nonlinear force-displacement relationship and variable stiffness technology; the purpose for coupling these two technologies is to achieve a large broadband vibration absorber with controllable capability. To achieve a nonlinear stiffness in the device, two pairs of magnets move at a rotary angle against each other, and the theoretical nonlinear force-displacement relationship has been theoretically calculated. For the experimental investigation, the effects of base excitation, variable currents applied to the device (i.e. variable stiffness of the MRE) and semi-active control have been conducted to determine the enhanced broadband performance of the designed device. It was observed the device was able to change resonance frequency with the applied current; moreover, the hybrid nonlinear MRE absorber displayed a softening-type nonlinear response with clear discontinuous bifurcations observed. Furthermore, the performance of the device under a semi-active control algorithm displayed the optimal performance in attenuating the vibration from a primary system to the absorber over a large frequency bandwidth from 4 to 12 Hz. By coupling nonlinear stiffness attributes with variable stiffness MRE technology, the performance of a vibration absorber is substantially improved.

Analysis of Three-Dimensional, Nonlinear Development of Wave-Like Structure in a Compressible Round Jet

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Mankbadi, Reda R.

2002-01-01

An analysis of the nonlinear development of the large-scale structures or instability waves in compressible round jets was conducted using the integral energy method. The equations of motion were decomposed into two sets of equations; one set governing the mean flow motion and the other set governing the large-scale structure motion. The equations in each set were then combined to derive kinetic energy equations that were integrated in the radial direction across the jet after the boundary-layer approximations were applied. Following the application of further assumptions regarding the radial shape of the mean flow and the large structures, equations were derived that govern the nonlinear, streamwise development of the large structures. Using numerically generated mean flows, calculations show the energy exchanges and the effects of the initial amplitude on the coherent structure development in the jet.

An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints [Continuum modeling of elasto-plastic media with multiple embedded nonlinearly-compliant joints

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hurley, R. C.; Vorobiev, O. Y.; Ezzedine, S. M.

Here, we present a numerical method for modeling the mechanical effects of nonlinearly-compliant joints in elasto-plastic media. The method uses a series of strain-rate and stress update algorithms to determine joint closure, slip, and solid stress within computational cells containing multiple “embedded” joints. This work facilitates efficient modeling of nonlinear wave propagation in large spatial domains containing a large number of joints that affect bulk mechanical properties. We implement the method within the massively parallel Lagrangian code GEODYN-L and provide verification and examples. We highlight the ability of our algorithms to capture joint interactions and multiple weakness planes within individualmore » computational cells, as well as its computational efficiency. We also discuss the motivation for developing the proposed technique: to simulate large-scale wave propagation during the Source Physics Experiments (SPE), a series of underground explosions conducted at the Nevada National Security Site (NNSS).« less

An algorithm for continuum modeling of rocks with multiple embedded nonlinearly-compliant joints [Continuum modeling of elasto-plastic media with multiple embedded nonlinearly-compliant joints

DOE PAGES

Hurley, R. C.; Vorobiev, O. Y.; Ezzedine, S. M.

2017-04-06

Here, we present a numerical method for modeling the mechanical effects of nonlinearly-compliant joints in elasto-plastic media. The method uses a series of strain-rate and stress update algorithms to determine joint closure, slip, and solid stress within computational cells containing multiple “embedded” joints. This work facilitates efficient modeling of nonlinear wave propagation in large spatial domains containing a large number of joints that affect bulk mechanical properties. We implement the method within the massively parallel Lagrangian code GEODYN-L and provide verification and examples. We highlight the ability of our algorithms to capture joint interactions and multiple weakness planes within individualmore » computational cells, as well as its computational efficiency. We also discuss the motivation for developing the proposed technique: to simulate large-scale wave propagation during the Source Physics Experiments (SPE), a series of underground explosions conducted at the Nevada National Security Site (NNSS).« less

Measurement of large nonlinear refractive index of natural pigment extracted from Hibiscus rosa-sinensis leaves with a low power CW laser and by spatial self-phase modulation technique

NASA Astrophysics Data System (ADS)

Biswas, S.; Kumbhakar, P.

2017-02-01

We have reported here, for the first time, to the best of our knowledge, a high nonlinear refractive index (n2e) of a natural pigment extracted from Hibiscus rosa-sinensis leaves by using spatial self-phase modulation technique (SSPM) with a low power CW He-Ne laser radiation at 632.8 nm. It is found by UV-Vis absorption spectroscopic analysis that chlrophyll-a, chlrophyll-b and carotenoid are present in the pigment extract with 56%, 25% and 19%, respectively. The photoluminescence (PL) emission characteristics of the extracted samples have also been measured at room temperature as well as in the temperature range of 283-333 K to investigate the effect of temperature on luminescent properties of the sample. By analyzing the SSPM experimental data, the nonlinear refractive index value of pigment extract has been determined to be 3.5 × 10- 5 cm2/W. The large nonlinear refractive index has been assigned due to asymmetrical structure, molecular reorientation and thermally induced nonlinearity in the sample. The presented results might open new avenues for the green and economical technique of syntheses of organic dyes with such a large nonlinear optical property.

Effect of polarization self-action in cubic crystals: peculiarities and applications

NASA Astrophysics Data System (ADS)

Boiko, Sergei A.; Lisitsa, Mikhail P.; Tarasov, Georgiy G.; Valakh, Mikhail Y.

1995-04-01

New concepts are developed to describe a wide area of nonlinear systems involving the phase relaxation peculiarities for the degenerate two- level system under the resonant optical excitation. Nonlinear susceptibility of the two-level system becomes anisotropic, and self- induced changes of polarization (SICP) are developed to the large (gigantic) magnitudes. The nonlinearities of two different natures are considered: the saturation of absorption and the resonant optical reorientation of anisotropic defects. For these particular cases, the SICP effects manifest themselves at a field much lower than that in traditional nonlinear optics. The larger magnitudes of the effects offer good possibilities for the development of optical devices based on the new physical principles. Various applications of SICP effects are demonstrated, including the spectroscopic investigations of impure cubic crystals, optical diagnostics, optical storage, information processing, and the development of new optical devices.

Dispersion of Sound in Dilute Suspensions with Nonlinear Particle Relaxation

NASA Technical Reports Server (NTRS)

Kandula, Max

2010-01-01

The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of Omega(Tau)(sub d), where Omega is the circular frequency, and Tau(sub d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction

Mechanical nonlinearity elimination with a micromechanical clamped-free semicircular beams resonator

NASA Astrophysics Data System (ADS)

Chen, Dongyang; Chen, Xuying; Wang, Yong; Liu, Xinxin; Guan, Yangyang; Xie, Jin

2018-04-01

This paper reports a micro-machined clamped-free semicircular beam resonator aiming to eliminate the nonlinearity that widely exists in traditional mechanical resonators. Cubic coefficients over vibration displacement due to axial extension of the beams are analyzed through theoretical modelling, and the corresponding frequency effect is demonstrated. With the device working in the elastic vibration mode, the cubic coefficients are eliminated by using a free end to release the nonlinear extension of beams and thus the inside axial stress. The amplitude-frequency (A-f) effect is overcome in a large region of source power, and the coefficient of frequency softening is linearized in a large region of polarization voltage. As a result, the resonator can be driven at larger vibration amplitude to achieve a high signal to noise ratio and power handling performance.

Tidal alignment of galaxies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blazek, Jonathan; Vlah, Zvonimir; Seljak, Uroš

We develop an analytic model for galaxy intrinsic alignments (IA) based on the theory of tidal alignment. We calculate all relevant nonlinear corrections at one-loop order, including effects from nonlinear density evolution, galaxy biasing, and source density weighting. Contributions from density weighting are found to be particularly important and lead to bias dependence of the IA amplitude, even on large scales. This effect may be responsible for much of the luminosity dependence in IA observations. The increase in IA amplitude for more highly biased galaxies reflects their locations in regions with large tidal fields. We also consider the impact ofmore » smoothing the tidal field on halo scales. We compare the performance of this consistent nonlinear model in describing the observed alignment of luminous red galaxies with the linear model as well as the frequently used "nonlinear alignment model," finding a significant improvement on small and intermediate scales. We also show that the cross-correlation between density and IA (the "GI" term) can be effectively separated into source alignment and source clustering, and we accurately model the observed alignment down to the one-halo regime using the tidal field from the fully nonlinear halo-matter cross correlation. Inside the one-halo regime, the average alignment of galaxies with density tracers no longer follows the tidal alignment prediction, likely reflecting nonlinear processes that must be considered when modeling IA on these scales. Finally, we discuss tidal alignment in the context of cosmic shear measurements.« less

Tidal alignment of galaxies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blazek, Jonathan; Vlah, Zvonimir; Seljak, Uroš, E-mail: blazek@berkeley.edu, E-mail: zvlah@stanford.edu, E-mail: useljak@berkeley.edu

We develop an analytic model for galaxy intrinsic alignments (IA) based on the theory of tidal alignment. We calculate all relevant nonlinear corrections at one-loop order, including effects from nonlinear density evolution, galaxy biasing, and source density weighting. Contributions from density weighting are found to be particularly important and lead to bias dependence of the IA amplitude, even on large scales. This effect may be responsible for much of the luminosity dependence in IA observations. The increase in IA amplitude for more highly biased galaxies reflects their locations in regions with large tidal fields. We also consider the impact ofmore » smoothing the tidal field on halo scales. We compare the performance of this consistent nonlinear model in describing the observed alignment of luminous red galaxies with the linear model as well as the frequently used 'nonlinear alignment model,' finding a significant improvement on small and intermediate scales. We also show that the cross-correlation between density and IA (the 'GI' term) can be effectively separated into source alignment and source clustering, and we accurately model the observed alignment down to the one-halo regime using the tidal field from the fully nonlinear halo-matter cross correlation. Inside the one-halo regime, the average alignment of galaxies with density tracers no longer follows the tidal alignment prediction, likely reflecting nonlinear processes that must be considered when modeling IA on these scales. Finally, we discuss tidal alignment in the context of cosmic shear measurements.« less

Anomalous nonlinear absorption in epsilon-near-zero materials: optical limiting and all-optical control.

PubMed

Vincenti, M A; de Ceglia, D; Scalora, Michael

2016-08-01

We investigate nonlinear absorption in films of epsilon-near-zero materials. The combination of large local electric fields at the fundamental frequency and material losses at the harmonic frequencies induce unusual intensity-dependent phenomena. We predict that the second-order nonlinearity of a low-damping, epsilon-near-zero slab produces an optical limiting effect that mimics a two-photon absorption process. Anomalous absorption profiles that depend on low permittivity values at the pump frequency are also predicted for third-order nonlinearities. These findings suggest new opportunities for all-optical light control and novel ways to design reconfigurable and tunable nonlinear devices.

The dissipation of electromagnetic waves in plasmas

NASA Astrophysics Data System (ADS)

Basov, N. G.

The present anthology includes articles concerning the experimental study of the interaction of high power electromagnetic waves with collisionless plasmas and with electrons. Among the topics covered are the nonlinear dissipation of electromagnetic waves in inhomogeneous collisionless plasmas, the collisionless absorption of electromagnetic waves in plasmas and 'slow' nonlinear phenomena, the nonlinear effects of electron plasma waves propagating in an inhomogeneous plasma layer, and secondary-emission microwave discharges having large electron transit angles.

Robust decentralised stabilisation of uncertain large-scale interconnected nonlinear descriptor systems via proportional plus derivative feedback

NASA Astrophysics Data System (ADS)

Li, Jian; Zhang, Qingling; Ren, Junchao; Zhang, Yanhao

2017-10-01

This paper studies the problem of robust stability and stabilisation for uncertain large-scale interconnected nonlinear descriptor systems via proportional plus derivative state feedback or proportional plus derivative output feedback. The basic idea of this work is to use the well-known differential mean value theorem to deal with the nonlinear model such that the considered nonlinear descriptor systems can be transformed into linear parameter varying systems. By using a parameter-dependent Lyapunov function, a decentralised proportional plus derivative state feedback controller and decentralised proportional plus derivative output feedback controller are designed, respectively such that the closed-loop system is quadratically normal and quadratically stable. Finally, a hypersonic vehicle practical simulation example and numerical example are given to illustrate the effectiveness of the results obtained in this paper.

Syntheses of Octasubstituted Metal Phthalocyanines for Nonlinear Optics

NASA Technical Reports Server (NTRS)

Guo, Huaisong; Townsend, Cheryl; Sanghadasa, Mohan; Amai, Robert L. S.; Clark, Ronald D.; Penn, Benjamin

1998-01-01

Many organic materials can be used as nonlinear optical media. Phthalocyanines are of special interest because they show an unusually large third order nonlinear response, they are thermally and photochemically stable and they can be formed into oriented thin films (Langmuir-Blodgett films). They also can be easily complexed by a large variety of metals, which place them at the interface between organics and organometallics, and allows for fine tuning of the macro cycle electronic properties by the coordinated metal and substituent groups. A series of 1,4,8,11,15,18,22,25-octaalkoxy metal-free and metal phthalocyanines and 2,3,9,10,16,17,23,24-octaalkoxy metal phthalocyanines has been synthesized. Their nonlinear optical properties have been measured. The physical properties of all the phthalocyanines synthesized in this work are subject to both acid and solvent effects.

Spatial nonlinearities: Cascading effects in the earth system

USGS Publications Warehouse

Peters, Debra P.C.; Pielke, R.A.; Bestelmeyer, B.T.; Allen, Craig D.; Munson-McGee, Stuart; Havstad, K. M.; Canadell, Josep G.; Pataki, Diane E.; Pitelka, Louis F.

2006-01-01

Nonlinear behavior is prevalent in all aspects of the Earth System, including ecological responses to global change (Gallagher and Appenzeller 1999; Steffen et al. 2004). Nonlinear behavior refers to a large, discontinuous change in response to a small change in a driving variable (Rial et al. 2004). In contrast to linear systems where responses are smooth, well-behaved, continuous functions, nonlinear systems often undergo sharp or discontinuous transitions resulting from the crossing of thresholds. These nonlinear responses can result in surprising behavior that makes forecasting difficult (Kaplan and Glass 1995). Given that many system dynamics are nonlinear, it is imperative that conceptual and quantitative tools be developed to increase our understanding of the processes leading to nonlinear behavior in order to determine if forecasting can be improved under future environmental changes (Clark et al. 2001).

On the nonlinear three dimensional instability of Stokes layers and other shear layers to pairs of oblique waves

NASA Technical Reports Server (NTRS)

Wu, Xuesong; Lee, Sang Soo; Cowley, Stephen J.

1992-01-01

The nonlinear evolution of a pair of initially oblique waves in a high Reynolds Number Stokes layer is studied. Attention is focused on times when disturbances of amplitude epsilon have O(epsilon(exp 1/3)R) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects. Viscous effects are included by studying the distinguished scaling epsilon = O(R(exp -1)). This leads to a complicated modification of the kernel function in the integro-differential amplitude equation. When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be introduced by nonlinear effects; we suggest that such explosive growth can lead to the bursts observed in experiments. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave vortex approach is identified.

The real evidence of effects from source to freefield as base for nonlinear seismology

NASA Astrophysics Data System (ADS)

Marmureanu, Gheorghe; Marmureanu, Alexandru; Ortanza Cioflan, Carmen-; -Florinela Manea, Elena

2014-05-01

Authors developed in last time the concept of "Nonlinear Seismology-The Seismology of the XXI Century". Prof. P. M. Shearer, California Univ. in last book:(i) Strong ground accelerations from large earthquakes can produce a non-linear response in shallow soils; (ii) The shaking from large earthquakes cannot be predicted by simple scaling of records from small earthquakes; (iii) This is an active area of research in strong motion and engineering seismology. Aki: Nonlinear amplification at sediments sites appears to be more pervasive than seismologists used to think. Any attempt at seismic zonation must take into account the local site condition and this nonlinear amplification (Tectonophysics, 218, 93-111, 1993). The difficulty to seismologists in demonstrating the nonlinear site effects has been due to the effect being overshadowed by the overall patterns of shock generation and propagation. In other words, the seismological detection of the nonlinear site effects requires a simultaneous understanding and splitting up (if it is possible…and if it is necessary!) the effects of earthquake source, propagation path and local geological site conditions. To see the actual influence of nonlinearity of the whole system (seismic source-path propagation-local geological structure) the authors used to study the free field response spectra which are the last in this chain and they are the ones who are taken into account in seismic design of all structures. Soils from last part of this system(source-freefield) exhibit a strong nonlinear behaviour under cyclic loading conditions and although have many common mechanical properties require the use of different models to describe behavior differences. Sands typically have low rheological properties and can be modeled with an acceptable linear elastic model and clays which frequently presents significant changes over time can be modeled by a nonlinear viscoelastic model The real evidence of site effects from source to freefield analysis was conducted by using spectral amplification factors for last strong and deep Vrancea earthquakes (March 04,1977;MW =7.5;h=94.5 km; August 30,1986;MW=7.1;h=134.5 km; May 30 1009;MW=6.0;h=90.9 km; May 31, 1990; MW=6.4 ;h=86.9 km).The amplification factors decrease with increasing the magnitudes of strong Vrancea earthquakes and these values are far of that given by Regulatory Guide 1.60 of the U. S. Atomic Energy Commission and IAEA Vienna. The concept was used for last Stress Test asked by IAEA Vienna for Romanian Cernavoda Nuclear Power Plant.. The spectral amplification factors were: SAF= 4.07 (MW =7.1); 4.74(MW=6.9) and 5.78 (MW=6.4), unction of earthquake magnitude. The analysis indicates that the effect of nonlinearity could be very important and if the analysis is made for peak accelerations, it is 48.87% smaller assuming that response of soil to earthquake with MW=6.4, it is still in elastic domain. In other 25 seismic stations here are values between 14.2% and 55.4%. The authors are coming with new quantitative real and recorded data in extra-Carpathian area with large alluvial deposits / sediments, thick Quaternary layers etc.

Cascading second-order nonlinear processes in a lithium niobate-on-insulator microdisk.

PubMed

Liu, Shijie; Zheng, Yuanlin; Chen, Xianfeng

2017-09-15

Whispering-gallery-mode (WGM) microcavities are very important in both fundamental science and practical applications, among which on-chip second-order nonlinear microresonators play an important role in integrated photonic functionalities. Here we demonstrate resonant second-harmonic generation (SHG) and cascaded third-harmonic generation (THG) in a lithium niobate-on-insulator (LNOI) microdisk resonator. Efficient SHG in the visible range was obtained with only several mW input powers at telecom wavelengths. THG was also observed through a cascading process, which reveals simultaneous phase matching and strong mode coupling in the resonator. Cascading of second-order nonlinear processes gives rise to an effectively large third-order nonlinearity, which makes on-chip second-order nonlinear microresonators a promising frequency converter for integrated nonlinear photonics.

Electrets in soft materials: nonlinearity, size effects, and giant electromechanical coupling.

PubMed

Deng, Qian; Liu, Liping; Sharma, Pradeep

2014-07-01

Development of soft electromechanical materials is critical for several tantalizing applications such as soft robots and stretchable electronics, among others. Soft nonpiezoelectric materials can be coaxed to behave like piezoelectrics by merely embedding charges and dipoles in their interior and assuring some elastic heterogeneity. Such so-called electret materials have been experimentally shown to exhibit very large electromechanical coupling. In this work, we derive rigorous nonlinear expressions that relate effective electromechanical coupling to the creation of electret materials. In contrast to the existing models, we are able to both qualitatively and quantitatively capture the known experimental results on the nonlinear response of electret materials. Furthermore, we show that the presence of another form of electromechanical coupling, flexoelectricity, leads to size effects that dramatically alter the electromechanical response at submicron feature sizes. One of our key conclusions is that nonlinear deformation (prevalent in soft materials) significantly enhances the flexoelectric response and hence the aforementioned size effects.

Two Step Acceleration Process of Electrons in the Outer Van Allen Radiation Belt by Time Domain Electric Field Bursts and Large Amplitude Chorus Waves

NASA Astrophysics Data System (ADS)

Agapitov, O. V.; Mozer, F.; Artemyev, A.; Krasnoselskikh, V.; Lejosne, S.

2014-12-01

A huge number of different non-linear structures (double layers, electron holes, non-linear whistlers, etc) have been observed by the electric field experiment on the Van Allen Probes in conjunction with relativistic electron acceleration in the Earth's outer radiation belt. These structures, found as short duration (~0.1 msec) quasi-periodic bursts of electric field in the high time resolution electric field waveform, have been called Time Domain Structures (TDS). They can quite effectively interact with radiation belt electrons. Due to the trapping of electrons into these non-linear structures, they are accelerated up to ~10 keV and their pitch angles are changed, especially for low energies (˜1 keV). Large amplitude electric field perturbations cause non-linear resonant trapping of electrons into the effective potential of the TDS and these electrons are then accelerated in the non-homogeneous magnetic field. These locally accelerated electrons create the "seed population" of several keV electrons that can be accelerated by coherent, large amplitude, upper band whistler waves to MeV energies in this two step acceleration process. All the elements of this chain acceleration mechanism have been observed by the Van Allen Probes.

Nonlinear Flying Qualities Criteria for Large-Amplitude Maneuvers

DTIC Science & Technology

1984-12-01

theory which are pertinent to the formation of a nonlinear flying qualities methodology. This report surveys nonlinear system theory and describes...the development of an applied flying qualities methodology based on a canonical system theory and using research in relative controllability...The Nonlinear Flying Qualities (NFQ) for Large-Amplitude Maneuvers Program examined promising techniques from nonlinear analysis and nonlinear system

Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

NASA Astrophysics Data System (ADS)

Nadkarni, Neel; Daraio, Chiara; Kochmann, Dennis M.

2014-08-01

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.

Nonlinear Transient Growth and Boundary Layer Transition

NASA Technical Reports Server (NTRS)

Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

2016-01-01

Parabolized stability equations (PSE) are used in a variational approach to study the optimal, non-modal disturbance growth in a Mach 3 at plate boundary layer and a Mach 6 circular cone boundary layer. As noted in previous works, the optimal initial disturbances correspond to steady counter-rotating streamwise vortices, which subsequently lead to the formation of streamwise-elongated structures, i.e., streaks, via a lift-up effect. The nonlinear evolution of the linearly optimal stationary perturbations is computed using the nonlinear plane-marching PSE for stationary perturbations. A fully implicit marching technique is used to facilitate the computation of nonlinear streaks with large amplitudes. To assess the effect of the finite-amplitude streaks on transition, the linear form of plane- marching PSE is used to investigate the instability of the boundary layer flow modified by spanwise periodic streaks. The onset of bypass transition is estimated by using an N- factor criterion based on the amplification of the streak instabilities. Results show that, for both flow configurations of interest, streaks of sufficiently large amplitude can lead to significantly earlier onset of transition than that in an unperturbed boundary layer without any streaks.

Assessment of current state of the art in modeling techniques and analysis methods for large space structures

NASA Technical Reports Server (NTRS)

Noor, A. K.

1983-01-01

Advances in continuum modeling, progress in reduction methods, and analysis and modeling needs for large space structures are covered with specific attention given to repetitive lattice trusses. As far as continuum modeling is concerned, an effective and verified analysis capability exists for linear thermoelastic stress, birfurcation buckling, and free vibration problems of repetitive lattices. However, application of continuum modeling to nonlinear analysis needs more development. Reduction methods are very effective for bifurcation buckling and static (steady-state) nonlinear analysis. However, more work is needed to realize their full potential for nonlinear dynamic and time-dependent problems. As far as analysis and modeling needs are concerned, three areas are identified: loads determination, modeling and nonclassical behavior characteristics, and computational algorithms. The impact of new advances in computer hardware, software, integrated analysis, CAD/CAM stems, and materials technology is also discussed.

A study of the parallel algorithm for large-scale DC simulation of nonlinear systems

NASA Astrophysics Data System (ADS)

Cortés Udave, Diego Ernesto; Ogrodzki, Jan; Gutiérrez de Anda, Miguel Angel

Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries are managed through concurrent processes. This numerical complexity can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the BBD matrix structure. This block-parallel approach may give a considerable profit though it is strongly dependent on the system topology and, of course, on the processor type. This contribution presents the easy-parallelizable decomposition-based algorithm for DC simulation and provides a detailed study of its effectiveness.

Functional Nonlinear Mixed Effects Models For Longitudinal Image Data

PubMed Central

Luo, Xinchao; Zhu, Lixing; Kong, Linglong; Zhu, Hongtu

2015-01-01

Motivated by studying large-scale longitudinal image data, we propose a novel functional nonlinear mixed effects modeling (FN-MEM) framework to model the nonlinear spatial-temporal growth patterns of brain structure and function and their association with covariates of interest (e.g., time or diagnostic status). Our FNMEM explicitly quantifies a random nonlinear association map of individual trajectories. We develop an efficient estimation method to estimate the nonlinear growth function and the covariance operator of the spatial-temporal process. We propose a global test and a simultaneous confidence band for some specific growth patterns. We conduct Monte Carlo simulation to examine the finite-sample performance of the proposed procedures. We apply FNMEM to investigate the spatial-temporal dynamics of white-matter fiber skeletons in a national database for autism research. Our FNMEM may provide a valuable tool for charting the developmental trajectories of various neuropsychiatric and neurodegenerative disorders. PMID:26213453

Numerical modelling of nonlinear full-wave acoustic propagation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx

2015-10-28

The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on amore » GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.« less

Berry curvature dipole in Weyl semimetal materials: An ab initio study

NASA Astrophysics Data System (ADS)

Zhang, Yang; Sun, Yan; Yan, Binghai

2018-01-01

Noncentrosymmetric metals are anticipated to exhibit a dc photocurrent in the nonlinear optical response caused by the Berry curvature dipole in momentum space. Weyl semimetals (WSMs) are expected to be excellent candidates for observing these nonlinear effects because they carry a large Berry curvature concentrated in small regions, i.e., near the Weyl points. We have implemented the semiclassical Berry curvature dipole formalism into an ab initio scheme and investigated the second-order nonlinear response for two representative groups of materials: the TaAs-family type-I WSMs and the MoTe2-family type-II WSMs. Both types of WSMs exhibited a Berry curvature dipole in which type-II Weyl points are usually superior to the type-I WSM because of the strong tilt. Corresponding nonlinear susceptibilities in several materials promise a nonlinear Hall effect in the dc field limit, which is within the experimentally detectable range.

Nonlinear optical response in graphene nanoribbons: The critical role of electron scattering

NASA Astrophysics Data System (ADS)

Karimi, F.; Davoody, A. H.; Knezevic, I.

2018-06-01

Nonlinear nanophotonics has many potential applications, such as in mode locking, frequency-comb generation, and all-optical switching. The development of materials with large nonlinear susceptibility is key to realizing nonlinear nanophotonics. Nanostructured graphene systems, such as graphene nanoribbons and nanoislands, have been predicted to have a strong plasmon-enhanced nonlinear optical behavior in the nonretarded regime. Plasmons concentrate the light field down to subwavelength scales and can enhance the nonlinear optical effects; however, plasmon resonances are narrowband and sensitive to the nanostructure geometry. Here we show that graphene nanoribbons, particularly armchair graphene nanoribbons, have a remarkably strong nonlinear optical response in the long-wavelength regime and over a broad frequency range, from terahertz to the near infrared. We use a quantum-mechanical master equation with a detailed treatment of scattering and show that, in the retarded regime, electron scattering has a critical effect on the optical nonlinearity of graphene nanoribbons, which cannot be captured via the commonly used relaxation-time approximation. At terahertz frequencies, where intraband optical transitions dominate, the strong nonlinearity (in particular, third-order Kerr nonlinearity) stems from the jagged shape of the electron energy distribution, caused by the interband electron scattering mechanisms along with the intraband inelastic scattering mechanisms. We show that the relaxation-time approximation fails to capture this quantum-mechanical phenomenon and results in a significant underestimation of the intraband nonlinearity. At the midinfrared to near infrared frequencies, where interband optical transitions dominate, the Kerr nonlinearity is significantly overestimated within the relaxation-time approximation. These findings unveil the critical effect of electron scattering on the optical nonlinearity of nanostructured graphene, and also underscore the capability of this class of materials for nonlinear nanophotonic applications.

Simulation and measurement of nonlinear behavior in a high-power test cell.

PubMed

Harvey, Gerald; Gachagan, Anthony

2011-04-01

High-power ultrasound has many diverse uses in process applications in industries ranging from food to pharmaceutical. Because cavitation is frequently a desirable effect within many high-power, low-frequency systems, these systems are commonly expected to feature highly nonlinear acoustic propagation because of the high input levels employed. This generation of harmonics significantly alters the field profile compared with that of a linear system, making accurate field modeling difficult. However, when the short propagation distances involved are considered, it is not unreasonable to assume that these systems may remain largely linear until the onset of cavitation, in terms of classical acoustic propagation. The purpose of this paper is to investigate the possible nonlinear effects within such systems before the onset of cavitation. A theoretical description of nonlinear propagation will be presented and the merits of common analytical models will be discussed. Following this, a numerical model of nonlinearity will be outlined and the advantages it presents for representing nonlinear effects in bounded fields will be discussed. Next, the driving equipment and transducers will be evaluated for linearity to disengage any effects from those formed in the transmission load. Finally, the linearity of the system will be measured using an acoustic hydrophone and compared with finite element analysis to confirm that nonlinear effects are not prevalent in such systems at the onset of cavitation. © 2011 IEEE

Multimodal nonlinear nanophotonics (Conference Presentation)

NASA Astrophysics Data System (ADS)

Kivshar, Yuri S.

2017-05-01

Nonlinear nanophotonics is a rapidly developing field of research with many potential applications for the design of nonlinear nanoantennas, light sources, nanolasers, and ultrafast miniature metadevices. A tight confinement of the local electromagnetic fields in resonant photonic nanostructures can boost nonlinear optical effects, thus offering versatile opportunities for the subwavelength control of light. To achieve the desired functionalities, it is essential to gain flexible control over the near- and far-field properties of nanostructures. To engineer nonlinear scattering from resonant nanoscale elements, both modal and multipolar control of the nonlinear response are widely exploited for enhancing the near-field interaction and optimizing the radiation directionality. Motivated by the recent progress of all-dielectric nanophotonics, where the electric and magnetic multipolar contributions may become comparable, here we review the advances in the recently emerged field of multipolar nonlinear nanophotonics, starting from earlier relevant studies of metallic and metal-dielectric structures supporting localized plasmonic resonances to then discussing the latest results for all-dielectric nanostructures driven by Mie-type multipolar resonances and optically induced magnetic response. These recent developments suggest intriguing opportunities for a design of nonlinear subwavelength light sources with reconfigurable radiation characteristics and engineering large effective optical nonlinearities at the nanoscale, which could have important implications for novel nonlinear photonic devices operating beyond the diffraction limit.

Quantitative analysis of a frequency-domain nonlinearity indicator.

PubMed

Reichman, Brent O; Gee, Kent L; Neilsen, Tracianne B; Miller, Kyle G

2016-05-01

In this paper, quantitative understanding of a frequency-domain nonlinearity indicator is developed. The indicator is derived from an ensemble-averaged, frequency-domain version of the generalized Burgers equation, which can be rearranged in order to directly compare the effects of nonlinearity, absorption, and geometric spreading on the pressure spectrum level with frequency and distance. The nonlinear effect is calculated using pressure-squared-pressure quadspectrum. Further theoretical development has given an expression for the role of the normalized quadspectrum, referred to as Q/S by Morfey and Howell [AIAA J. 19, 986-992 (1981)], in the spatial rate of change of the pressure spectrum level. To explore this finding, an investigation of the change in level for initial sinusoids propagating as plane waves through inviscid and thermoviscous media has been conducted. The decibel change with distance, calculated through Q/S, captures the growth and decay of the harmonics and indicates that the most significant changes in level occur prior to sawtooth formation. At large distances, the inviscid case results in a spatial rate of change that is uniform across all harmonics. For thermoviscous media, large positive nonlinear gains are observed but offset by absorption, which leads to a greater overall negative spatial rate of change for higher harmonics.

Adaptive Neural Networks Decentralized FTC Design for Nonstrict-Feedback Nonlinear Interconnected Large-Scale Systems Against Actuator Faults.

PubMed

Li, Yongming; Tong, Shaocheng

The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.The problem of active fault-tolerant control (FTC) is investigated for the large-scale nonlinear systems in nonstrict-feedback form. The nonstrict-feedback nonlinear systems considered in this paper consist of unstructured uncertainties, unmeasured states, unknown interconnected terms, and actuator faults (e.g., bias fault and gain fault). A state observer is designed to solve the unmeasurable state problem. Neural networks (NNs) are used to identify the unknown lumped nonlinear functions so that the problems of unstructured uncertainties and unknown interconnected terms can be solved. By combining the adaptive backstepping design principle with the combination Nussbaum gain function property, a novel NN adaptive output-feedback FTC approach is developed. The proposed FTC controller can guarantee that all signals in all subsystems are bounded, and the tracking errors for each subsystem converge to a small neighborhood of zero. Finally, numerical results of practical examples are presented to further demonstrate the effectiveness of the proposed control strategy.

Nonlinear silicon photonics

NASA Astrophysics Data System (ADS)

Tsia, Kevin K.; Jalali, Bahram

2010-05-01

An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.

Plastic and Large-Deflection Analysis of Nonlinear Structures

NASA Technical Reports Server (NTRS)

Thomson, R. G.; Hayduk, R. J.; Robinson, M. P.; Durling, B. J.; Pifko, A.; Levine, H. S.; Armen, H. J.; Levy, A.; Ogilvie, P.

1982-01-01

Plastic and Large Deflection Analysis of Nonlinear Structures (PLANS) system is collection of five computer programs for finite-element static-plastic and large deflection analysis of variety of nonlinear structures. System considers bending and membrane stresses, general three-dimensional bodies, and laminated composites.

Nonlinear Finite Element Analysis of a Composite Non-Cylindrical Pressurized Aircraft Fuselage Structure

NASA Technical Reports Server (NTRS)

Przekop, Adam; Wu, Hsi-Yung T.; Shaw, Peter

2014-01-01

The Environmentally Responsible Aviation Project aims to develop aircraft technologies enabling significant fuel burn and community noise reductions. Small incremental changes to the conventional metallic alloy-based 'tube and wing' configuration are not sufficient to achieve the desired metrics. One of the airframe concepts that might dramatically improve aircraft performance is a composite-based hybrid wing body configuration. Such a concept, however, presents inherent challenges stemming from, among other factors, the necessity to transfer wing loads through the entire center fuselage section which accommodates a pressurized cabin confined by flat or nearly flat panels. This paper discusses a nonlinear finite element analysis of a large-scale test article being developed to demonstrate that the Pultruded Rod Stitched Efficient Unitized Structure concept can meet these challenging demands of the next generation airframes. There are specific reasons why geometrically nonlinear analysis may be warranted for the hybrid wing body flat panel structure. In general, for sufficiently high internal pressure and/or mechanical loading, energy related to the in-plane strain may become significant relative to the bending strain energy, particularly in thin-walled areas such as the minimum gage skin extensively used in the structure under analysis. To account for this effect, a geometrically nonlinear strain-displacement relationship is needed to properly couple large out-of-plane and in-plane deformations. Depending on the loading, this nonlinear coupling mechanism manifests itself in a distinct manner in compression- and tension-dominated sections of the structure. Under significant compression, nonlinear analysis is needed to accurately predict loss of stability and postbuckled deformation. Under significant tension, the nonlinear effects account for suppression of the out-of-plane deformation due to in-plane stretching. By comparing the present results with the previously published preliminary linear analysis, it is demonstrated in the present paper that neglecting nonlinear effects for the structure and loads of interest can lead to appreciable loss in analysis fidelity.

The Search for an Effective Clinical Behavior Analysis: The Nonlinear Thinking of Israel Goldiamond

ERIC Educational Resources Information Center

Layng, T. V. Joe

2009-01-01

This paper has two purposes; the first is to reintroduce Goldiamond's constructional approach to clinical behavior analysis and to the field of behavior analysis as a whole, which, unfortunately, remains largely unaware of his nonlinear functional analysis and its implications. The approach is not simply a set of clinical techniques; instead it…

Research on trust-region algorithms for nonlinear programming. Final technical report, 1 January 1990--31 December 1992

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dennis, J.E. Jr.; Tapia, R.A.

Goal of the research was to develop and test effective, robust algorithms for general nonlinear programming (NLP) problems, particularly large or otherwise expensive NLP problems. We discuss the research conducted over the 3-year period Jan. 1990-Dec. 1992. We also describe current and future directions of our research.

Linear and nonlinear 2D finite element analysis of sloshing modes and pressures in rectangular tanks subject to horizontal harmonic motions

NASA Astrophysics Data System (ADS)

Virella, Juan C.; Prato, Carlos A.; Godoy, Luis A.

2008-05-01

The influence of nonlinear wave theory on the sloshing natural periods and their modal pressure distributions are investigated for rectangular tanks under the assumption of two-dimensional behavior. Natural periods and mode shapes are computed and compared for both linear wave theory (LWT) and nonlinear wave theory (NLWT) models, using the finite element package ABAQUS. Linear wave theory is implemented in an acoustic model, whereas a plane strain problem with large displacements is used in NLWT. Pressure distributions acting on the tank walls are obtained for the first three sloshing modes using both linear and nonlinear wave theory. It is found that the nonlinearity does not have significant effects on the natural sloshing periods. For the sloshing pressures on the tank walls, different distributions were found using linear and nonlinear wave theory models. However, in all cases studied, the linear wave theory conservatively estimated the magnitude of the pressure distribution, whereas larger pressures resultant heights were obtained when using the nonlinear theory. It is concluded that the nonlinearity of the surface wave does not have major effects in the pressure distribution on the walls for rectangular tanks.

Efficient Second-Harmonic Generation in Nanocrystalline Silicon Nanoparticles.

PubMed

Makarov, Sergey V; Petrov, Mihail I; Zywietz, Urs; Milichko, Valentin; Zuev, Dmitry; Lopanitsyna, Natalia; Kuksin, Alexey; Mukhin, Ivan; Zograf, George; Ubyivovk, Evgeniy; Smirnova, Daria A; Starikov, Sergey; Chichkov, Boris N; Kivshar, Yuri S

2017-05-10

Recent trends to employ high-index dielectric particles in nanophotonics are motivated by their reduced dissipative losses and large resonant enhancement of nonlinear effects at the nanoscale. Because silicon is a centrosymmetric material, the studies of nonlinear optical properties of silicon nanoparticles have been targeting primarily the third-harmonic generation effects. Here we demonstrate, both experimentally and theoretically, that resonantly excited nanocrystalline silicon nanoparticles fabricated by an optimized laser printing technique can exhibit strong second-harmonic generation (SHG) effects. We attribute an unexpectedly high yield of the nonlinear conversion to a nanocrystalline structure of nanoparticles supporting the Mie resonances. The demonstrated efficient SHG at green light from a single silicon nanoparticle is 2 orders of magnitude higher than that from unstructured silicon films. This efficiency is significantly higher than that of many plasmonic nanostructures and small silicon nanoparticles in the visible range, and it can be useful for a design of nonlinear nanoantennas and silicon-based integrated light sources.

Nonlinear Dynamical Model of a Soft Viscoelastic Dielectric Elastomer

NASA Astrophysics Data System (ADS)

Zhang, Junshi; Chen, Hualing; Li, Dichen

2017-12-01

Actuated by alternating stimulation, dielectric elastomers (DEs) show a behavior of complicated nonlinear vibration, implying a potential application as dynamic electromechanical actuators. As is well known, for a vibrational system, including the DE system, the dynamic properties are significantly affected by the geometrical sizes. In this article, a nonlinear dynamical model is deduced to investigate the geometrical effects on dynamic properties of viscoelastic DEs. The DEs with square and arbitrary rectangular geometries are considered, respectively. Besides, the effects of tensile forces on dynamic performances of rectangular DEs with comparably small and large geometrical sizes are explored. Phase paths and Poincaré maps are utilized to detect the periodicity of the nonlinear vibrations of DEs. The resonance characteristics of DEs incorporating geometrical effects are also investigated. The results indicate that the dynamic properties of DEs, including deformation response, vibrational periodicity, and resonance, are tuned when the geometrical sizes vary.

Strong nonlinear dependence of the spectral amplification factors of deep Vrancea earthquakes magnitude

NASA Astrophysics Data System (ADS)

Marmureanu, Gheorghe; Ortanza Cioflan, Carmen; Marmureanu, Alexandru

2010-05-01

Nonlinear effects in ground motion during large earthquakes have long been a controversial issue between seismologists and geotechnical engineers. Aki wrote in 1993:"Nonlinear amplification at sediments sites appears to be more pervasive than seismologists used to think…Any attempt at seismic zonation must take into account the local site condition and this nonlinear amplification( Local site effects on weak and strong ground motion, Tectonophysics,218,93-111). In other words, the seismological detection of the nonlinear site effects requires a simultaneous understanding of the effects of earthquake source, propagation path and local geological site conditions. The difficulty for seismologists in demonstrating the nonlinear site effects has been due to the effect being overshadowed by the overall patterns of shock generation and path propagation. The researchers from National Institute for Earth Physics ,in order to make quantitative evidence of large nonlinear effects, introduced the spectral amplification factor (SAF) as ratio between maximum spectral absolute acceleration (Sa), relative velocity (Sv) , relative displacement (Sd) from response spectra for a fraction of critical damping at fundamental period and peak values of acceleration(a-max),velocity (v-max) and displacement (d-max),respectively, from processed strong motion record and pointed out that there is a strong nonlinear dependence on earthquake magnitude and site conditions.The spectral amplification factors(SAF) are finally computed for absolute accelerations at 5% fraction of critical damping (β=5%) in five seismic stations: Bucharest-INCERC(soft soils, quaternary layers with a total thickness of 800 m);Bucharest-Magurele (dense sand and loess on 350m); Cernavoda Nuclear Power Plant site (marl, loess, limestone on 270 m) Bacau(gravel and loess on 20m) and Iassy (loess, sand, clay, gravel on 60 m) for last strong and deep Vrancea earthquakes: March 4,1977 (MGR =7.2 and h=95 km);August 30,1986(MGR =7.0 and h=130 km);May 30,1990 (MGR =6.7 and h=90 km) and May 31,1990 (MGR =6.1 and h=87 km). With a view to understand the characteristics of nonlinear soil behavior and the nonlinearity in the seismology and the influence to hazard and risk assessment ,this study examined the ways that nonlinearity would expected to appear on strong motion records made on Romania territory during to last Vrancea earthquake. The effect on nonlinearity is very large. For example, if we maintain the same amplification factor (SAF=5.8942) as for relatively strong earthquake on May 31,1990 with magnitude Ms =6,1 then at Bacau seismic station for earthquake on May 30,1990 (MGR =6.7) the peak acceleration has to be a*max =0.154g( +14.16%) and the actual recorded was only, a max =0.135g. Also, for Vrancea earthquake on August 30,1986, the peak acceleration has to be a*max=0.107g (+45,57%), instead of real value of 0.0736 g recorded at Bacau seismic station. More, the spectral amplification factors(SAF) are function of earthquake magnitude and there is a strong nonlinear dependence of the SAF of earthquake magnitude. The median values of SAF of the last strong Vrancea earthquakes for damping 5% are: 4.16; 3.63 and 3.26 corresponding to May 31,1990 Vrancea earthquake (Ms=6.1),May 30,1990 Vrancea earthquake(Ms=6.7),respectively, August 30,1986 Vrancea one(Ms=7.0). At the same seismic station, for example at Bacau, for 5% damping, SAF for accelerations is 5.22 for May 31,1990 earthquake (Ms =6.1);4.32 for May 30,1990 earthquake (Ms =6.7) and 3,94 for August 30,1986 one (Ms=7.0) etc. Finally, it will be made a comment in connection to U.S. Atomic Energy Commission-Regulatory Guide 1.60 on "Design Response Spectra for seismic design of nuclear power plants " to see spectral amplification factors for deep Vrancea earthquakes are larger and different.

Nonreciprocity in the dynamics of coupled oscillators with nonlinearity, asymmetry, and scale hierarchy

NASA Astrophysics Data System (ADS)

Moore, Keegan J.; Bunyan, Jonathan; Tawfick, Sameh; Gendelman, Oleg V.; Li, Shuangbao; Leamy, Michael; Vakakis, Alexander F.

2018-01-01

In linear time-invariant dynamical and acoustical systems, reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and this can be broken only by odd external biases, nonlinearities, or time-dependent properties. A concept is proposed in this work for breaking dynamic reciprocity based on irreversible nonlinear energy transfers from large to small scales in a system with nonlinear hierarchical internal structure, asymmetry, and intentional strong stiffness nonlinearity. The resulting nonreciprocal large-to-small scale energy transfers mimic analogous nonlinear energy transfer cascades that occur in nature (e.g., in turbulent flows), and are caused by the strong frequency-energy dependence of the essentially nonlinear small-scale components of the system considered. The theoretical part of this work is mainly based on action-angle transformations, followed by direct numerical simulations of the resulting system of nonlinear coupled oscillators. The experimental part considers a system with two scales—a linear large-scale oscillator coupled to a small scale by a nonlinear spring—and validates the theoretical findings demonstrating nonreciprocal large-to-small scale energy transfer. The proposed study promotes a paradigm for designing nonreciprocal acoustic materials harnessing strong nonlinearity, which in a future application will be implemented in designing lattices incorporating nonlinear hierarchical internal structures, asymmetry, and scale mixing.

Parameterization of plume chemistry into large-scale atmospheric models: Application to aircraft NOx emissions

NASA Astrophysics Data System (ADS)

Cariolle, D.; Caro, D.; Paoli, R.; Hauglustaine, D. A.; CuéNot, B.; Cozic, A.; Paugam, R.

2009-10-01

A method is presented to parameterize the impact of the nonlinear chemical reactions occurring in the plume generated by concentrated NOx sources into large-scale models. The resulting plume parameterization is implemented into global models and used to evaluate the impact of aircraft emissions on the atmospheric chemistry. Compared to previous approaches that rely on corrected emissions or corrective factors to account for the nonlinear chemical effects, the present parameterization is based on the representation of the plume effects via a fuel tracer and a characteristic lifetime during which the nonlinear interactions between species are important and operate via rates of conversion for the NOx species and an effective reaction rates for O3. The implementation of this parameterization insures mass conservation and allows the transport of emissions at high concentrations in plume form by the model dynamics. Results from the model simulations of the impact on atmospheric ozone of aircraft NOx emissions are in rather good agreement with previous work. It is found that ozone production is decreased by 10 to 25% in the Northern Hemisphere with the largest effects in the north Atlantic flight corridor when the plume effects on the global-scale chemistry are taken into account. These figures are consistent with evaluations made with corrected emissions, but regional differences are noticeable owing to the possibility offered by this parameterization to transport emitted species in plume form prior to their dilution at large scale. This method could be further improved to make the parameters used by the parameterization function of the local temperature, humidity and turbulence properties diagnosed by the large-scale model. Further extensions of the method can also be considered to account for multistep dilution regimes during the plume dissipation. Furthermore, the present parameterization can be adapted to other types of point-source NOx emissions that have to be introduced in large-scale models, such as ship exhausts, provided that the plume life cycle, the type of emissions, and the major reactions involved in the nonlinear chemical systems can be determined with sufficient accuracy.

fNL‑gNL mixing in the matter density field at higher orders

NASA Astrophysics Data System (ADS)

Gressel, Hedda A.; Bruni, Marco

2018-06-01

In this paper we examine how primordial non-Gaussianity contributes to nonlinear perturbative orders in the expansion of the density field at large scales in the matter dominated era. General Relativity is an intrinsically nonlinear theory, establishing a nonlinear relation between the metric and the density field. Representing the metric perturbations with the curvature perturbation ζ, it is known that nonlinearity produces effective non-Gaussian terms in the nonlinear perturbations of the matter density field δ, even if the primordial ζ is Gaussian. Here we generalise these results to the case of a non-Gaussian primordial ζ. Using a standard parametrization of primordial non-Gaussianity in ζ in terms of fNL, gNL, hNL\\ldots , we show how at higher order (from third and higher) nonlinearity also produces a mixing of these contributions to the density field at large scales, e.g. both fNL and gNL contribute to the third order in δ. This is the main result of this paper. Our analysis is based on the synergy between a gradient expansion (aka long-wavelength approximation) and standard perturbation theory at higher order. In essence, mathematically the equations for the gradient expansion are equivalent to those of first order perturbation theory, thus first-order results convert into gradient expansion results and, vice versa, the gradient expansion can be used to derive results in perturbation theory at higher order and large scales.

Vacuum nonlinear electrodynamic polarization effects in hard emission of pulsars and magnetars

NASA Astrophysics Data System (ADS)

Denisov, V. I.; Sokolov, V. A.; Svertilov, S. I.

2017-09-01

The nonlinear electrodynamics influence of pulsar magnetic field on the electromagnetic pulse polarization is discussed from the point of observation interpretation. The calculations of pulsar magnetic field impact on the electromagnetic pulse polarization are made in such a way to make it easier to interpret these effects in space experiments. The law of hard emission pulse propagation in the pulsar magnetic field according to the vacuum (nonlinear electrodynamics is obtained. It has been shown, that due to the birefringence in the vacuum the front part of any hard emission pulse coming from a pulsar should be linearly polarized and the rest of pulse can have arbitrary polarization. The observational possibilities of vacuum birefringence are discussed. In this paper we give the estimations of detector parameters such as effective area, exposure time and necessity of polarization measurements with high accuracy. The combination of large area and extremely long exposure time gives the good opportunity to search the fine polarization effects like vacuum nonlinear electrodynamics birefringence.

Vacuum nonlinear electrodynamic polarization effects in hard emission of pulsars and magnetars

DOE Office of Scientific and Technical Information (OSTI.GOV)

Denisov, V.I.; Sokolov, V.A.; Svertilov, S.I., E-mail: vid.msu@yandex.ru, E-mail: sokolov.sev@inbox.ru, E-mail: sis@coronas.ru

The nonlinear electrodynamics influence of pulsar magnetic field on the electromagnetic pulse polarization is discussed from the point of observation interpretation. The calculations of pulsar magnetic field impact on the electromagnetic pulse polarization are made in such a way to make it easier to interpret these effects in space experiments. The law of hard emission pulse propagation in the pulsar magnetic field according to the vacuum (nonlinear electrodynamics is obtained. It has been shown, that due to the birefringence in the vacuum the front part of any hard emission pulse coming from a pulsar should be linearly polarized and themore » rest of pulse can have arbitrary polarization. The observational possibilities of vacuum birefringence are discussed. In this paper we give the estimations of detector parameters such as effective area, exposure time and necessity of polarization measurements with high accuracy. The combination of large area and extremely long exposure time gives the good opportunity to search the fine polarization effects like vacuum nonlinear electrodynamics birefringence.« less

Modeling of Nonlinear Optical Response in Gaseous Media and Its Comparison with Experiment

NASA Astrophysics Data System (ADS)

Xia, Yi

This thesis demonstrates the model and application of nonlinear optical response with Metastable Electronic State Approach (MESA) in ultrashort laser propagation and verifies accuracy of MESA through extensive comparison with experimental data. The MESA is developed from quantum mechanics to describe the nonlinear off-resonant optical response together with strong-field ionization in gaseous medium. The conventional light-matter interaction models are based on a piece-wise approach where Kerr effect and multi-photon ionization are treated as independent nonlinear responses. In contrast, MESA is self-consistent as the response from freed electrons and bound electrons are microscopically linked. It also can be easily coupled to the Unidirectional Pulse Propagation Equations (UPPE) for large scale simulation of experiments. This work tests the implementation of MESA model in simulation of nonlinear phase transients of ultrashort pulse propagation in a gaseous medium. The phase transient has been measured through Single-Shot Supercontinuum Spectral Interferometry. This technique can achieve high temporal resolution (10 fs) and spatial resolution (5 mum). Our comparison between simulation and experiment gives a quantitive test of MESA model including post-adiabatic corrections. This is the first time such a comparison was achieved for a theory suitable for large scale numerical simulation of modern nonlinear-optics experiments. In more than one respect, ours is a first-of-a-kind achievement. In particular, • Large amount of data are compared. We compare the data of nonlinear response induced by different pump intensity in Ar and Nitrogen. The data sets are three dimensions including two transverse spacial dimensions and one axial temporal dimension which reflect the whole structure of nonlinear response including the interplay between Kerr and plasma-induced effects. The resolutions of spatial and temporal dimension are about a few micrometer and several femtosecond. • The regime of light-matter interaction investigated here is between the strong and perturbative, where the pulse intensity can induce nonlinear refractive index change and partial ionization of dielectric medium. Obviously, such regimes are difficult to study both experimentally and theoretically. • MESA is a quantum based model, but it retains the same computation complexity as conventional light-matter interaction model. MESA contains the response from both bound and continuum states in a single self-consistent "Package". So, it is fair to say that this experiment-theory comparison sets a new standard for nonlinear light-matter interaction models and their verification in the area of extreme nonlinear optics.

How long time will we go with linear seismology?

NASA Astrophysics Data System (ADS)

Marmureanu, Gheorghe; Cioflan, Carmen; Marmureanu, Alexandru; Apostol, Bogdan

2013-04-01

Motto: The nonlinear seismology is the rule, The linear seismology is the exception. Paraphrasing Tullio Levi-Civita The leading question is: how many cities, villages, metropolitan areas etc. in seismic regions are constructed on rock sites? Most of them are located on alluvial deposits/ sediments, on Quaternary layers or in river valleys. In last book written by Peter M. Shearer, Professor of Geophysics at University of California, we can find, in total, only 12 rows about non-linear seismology(page 176).Among others are the following conclusions:(i)-Strong ground accelerations from large earthquakes can produce a non-linear response in shallow soils; (ii)-When a non-linear site response is present, then the shaking from large earthquakes cannot be predicted by simple scaling of records from small earthquakes; (iii)-This is an active area of research in strong motion and engineering seismology. On the other hand, Aki wrote: Nonlinear amplification at sediments sites appears to be more pervasive than seismologists used to think…Any attempt at seismic zonation must take into account the local site condition and this nonlinear amplification(Aki, A., Local Site Effects on Weak and Strong Ground Motion, Tectonophysics,218,93-111,1993). The difficulty to seismologists in demonstrating the nonlinear site effects has been due to the effect being overshadowed by the overall patterns of shock generation and propagation. In other words, the seismological detection of the nonlinear site effects requires a simultaneous understanding and separating of the effects of earthquake source, propagation path and local geological site conditions. To see the actual influence of nonlinearity of the whole system (seismic source-path propagation-local geological structure) the authors used to study the response spectra because they are the last in this chain and, of course, that they are the ones who are taken into account in seismic design of all structures Stress-strain relationships for soils are usually nonlinear, soil stiffness decreases and internal damping increases with increasing shear strain during of strong earthquakes. There is a strong nonlinear dependence of the spectral amplification factors(SAF) on earthquake magnitude for all seismic stations on Romanian territory on extra-Carpathian area (Iasi, Bacau, Focsani, Bucharest etc.). Median values of SAF for last strong Vrancea earthquakes are decreasing from 4.16(May 31,1990;Mw=6.4),to 3.63 (May 30,1990;Mw=6.9) and to 3.26 (August 30, 1986; Mw=7.1) .The novelty and the complexity degree comes from the fact that for first time, the final decision for NPP Cernavoda site was also based on local strong nonlinear spectral amplifications for strong earthquakes and used in last "STRESS TEST" asked by IAEA Vienna in 2011. The present analysis indicates that the effect of nonlinearity could be very important and if the analysis is made for peak accelerations, it is 48.87% and for stronger earthquakes it will be bigger. The authors are coming with new recorded data which will open up a new challenge for seismologists studying nonlinear site effects in 2-D and 3-D irregular geological structures, leading them to a fascinating research subject in earth physics(Aki,1993, p.108,idem),in nonlinear seismology and,finally, in a real evaluation of earthquake risk and loss estimates.

Numerical Simulations of Vortical Mode Stirring: Effects of Large Scale Shear and Strain

DTIC Science & Technology

2015-09-30

Numerical Simulations of Vortical Mode Stirring: Effects of Large-Scale Shear and Strain M.-Pascale Lelong NorthWest Research Associates...can be implemented in larger-scale ocean models. These parameterizations will incorporate the effects of local ambient conditions including latitude...talk at the 1 DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. Nonlinear Effects in Internal Waves Conference held

Nonlinear effects of a modal domain optical fiber sensor in a vibration suppression control loop for a flexible structure

NASA Technical Reports Server (NTRS)

Lindner, D. K.; Zvonar, G. A.; Baumann, W. T.; Delos, P. L.

1993-01-01

Recently, a modal domain optical fiber sensor has been demonstrated as a sensor in a control system for vibration suppression of a flexible cantilevered beam. This sensor responds to strain through a mechanical attachment to the structure. Because this sensor is of the interferometric type, the output of the sensor has a sinusoidal nonlinearity. For small levels of strain, the sensor can be operated in its linear region. For large levels of strain, the detection electronics can be configured to count fringes. In both of these configurations, the sensor nonlinearity imposes some restrictions on the performance of the control system. In this paper we investigate the effects of these sensor nonlinearities on the control system, and identify the region of linear operation in terms of the optical fiber sensor parameters.

Formation of large-scale structures with sharp density gradient through Rayleigh-Taylor growth in a two-dimensional slab under the two-fluid and finite Larmor radius effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goto, R.; Hatori, T.; Miura, H., E-mail: miura.hideaki@nifs.ac.jp

Two-fluid and the finite Larmor effects on linear and nonlinear growth of the Rayleigh-Taylor instability in a two-dimensional slab are studied numerically with special attention to high-wave-number dynamics and nonlinear structure formation at a low β-value. The two effects stabilize the unstable high wave number modes for a certain range of the β-value. In nonlinear simulations, the absence of the high wave number modes in the linear stage leads to the formation of the density field structure much larger than that in the single-fluid magnetohydrodynamic simulation, together with a sharp density gradient as well as a large velocity difference. Themore » formation of the sharp velocity difference leads to a subsequent Kelvin-Helmholtz-type instability only when both the two-fluid and finite Larmor radius terms are incorporated, whereas it is not observed otherwise. It is shown that the emergence of the secondary instability can modify the outline of the turbulent structures associated with the primary Rayleigh-Taylor instability.« less

Dynamics of Oscillating and Rotating Liquid Drop using Electrostatic Levitator

NASA Astrophysics Data System (ADS)

Matsumoto, Satoshi; Awazu, Shigeru; Abe, Yutaka; Watanabe, Tadashi; Nishinari, Katsuhiro; Yoda, Shinichi

2006-11-01

In order to understand the nonlinear behavior of liquid drop with oscillatory and/or rotational motions, an experimental study was performed. The electrostatic levitator was employed to achieve liquid drop formation on ground. A liquid drop with about 3 mm in diameter was levitated. The oscillation of mode n=2 along the vertical axis was induced by an external electrostatic force. The oscillatory motions were observed to clarify the nonlinearities of oscillatory behavior. A relationship between amplitude and frequency shift was made clear and the effect of frequency shift on amplitude agreed well with the theory. The frequency shift became larger with increasing the amplitude of oscillation. To confirm the nonlinear effects, we modeled the oscillation by employing the mass-spring-damper system included the nonlinear term. The result indicates that the large-amplitude oscillation includes the effect of nonlinear oscillation. The sound pressure was imposed to rotate the liquid drop along a vertical axis by using a pair of acoustic transducers. The drop transited to the two lobed shape due to centrifugal force when nondimensional angular velocity exceeded to 0.58.

Theory of plasmonic effects in nonlinear optics: the case of graphene

NASA Astrophysics Data System (ADS)

Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration

The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).

An impulsive receptance technique for the time domain computation of the vibration of a whole aero-engine model with nonlinear bearings

NASA Astrophysics Data System (ADS)

Hai, Pham Minh; Bonello, Philip

2008-12-01

The direct study of the vibration of real engine structures with nonlinear bearings, particularly aero-engines, has been severely limited by the fact that current nonlinear computational techniques are not well-suited for complex large-order systems. This paper introduces a novel implicit "impulsive receptance method" (IRM) for the time domain analysis of such structures. The IRM's computational efficiency is largely immune to the number of modes used and dependent only on the number of nonlinear elements. This means that, apart from retaining numerical accuracy, a much more physically accurate solution is achievable within a short timeframe. Simulation tests on a realistically sized representative twin-spool aero-engine showed that the new method was around 40 times faster than a conventional implicit integration scheme. Preliminary results for a given rotor unbalance distribution revealed the varying degree of journal lift, orbit size and shape at the example engine's squeeze-film damper bearings, and the effect of end-sealing at these bearings.

Nonlinear Optical Properties of Aluminum Doped Zinc Oxide

NASA Astrophysics Data System (ADS)

Otieno, Calford O.

Nonlinear optical (NLO) materials are crucial to future progress in industrial and technological applications that involve intense light-matter interaction. While ZnO-related materials are known to possess good NLO properties, existing results on ZnO and AZO (Al-doped ZnO) are mostly available at a single wavelength or limited ranges. Therefore, NLO dispersions (wavelength dependences) are not entirely studied, especially at longer wavelengths far below the bandgap. It is important to explore wavelength dependences since doping can induce a drastic change in the NLO responses at varied spectral ranges via doping-induced subgap-state contributions. We present results of our studies on nonlinear harmonic generation from our samples, which include 1) second harmonic generation and 2) third harmonic generation precisely characterized by Maker fringes as a function of both Al doping and wavelength. We exhaustively discuss the possible cause for the modified optical nonlinearities observed in our AZO thin films and give detailed comparisons of our observations with the previous studies. We also present the results of open- and close-aperture Z-scans to characterize the two-photon absorption coefficient (TPA) and the nonlinear refractive index (NLR), respectively, of the AZO films. There was no clearcut evidence of monotonic dependence of TPA and NLR on doping. This presumably indicates that the overall effect is nontrivial and should be understood in terms of combined effects of bandgap shift and crystallinity upon varying the doping level. Most intriguingly, we found that NLR values from the closed-aperture Z-scan are very large by orders of magnitude when compared with the bulk counterparts. Similar observation was made for TPA values from the open-aperture Z-scan. To countercheck very large NLO absorption, we conducted simple intensity scan by varying the incident photon number on each sample but fixing the beam area to eliminate any possible errors related to optical damage at the Z-scan focus. However, we confirmed that the TPA values are also very large and comparable to those obtained by the open-aperture Z-scan. We try to explain this very large nonlinearity by seriously considering the previously proposed models.

Optimizing BAO measurements with non-linear transformations of the Lyman-α forest

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Xinkang; Font-Ribera, Andreu; Seljak, Uroš, E-mail: xinkang.wang@berkeley.edu, E-mail: afont@lbl.gov, E-mail: useljak@berkeley.edu

2015-04-01

We explore the effect of applying a non-linear transformation to the Lyman-α forest transmitted flux F=e{sup −τ} and the ability of analytic models to predict the resulting clustering amplitude. Both the large-scale bias of the transformed field (signal) and the amplitude of small scale fluctuations (noise) can be arbitrarily modified, but we were unable to find a transformation that increases significantly the signal-to-noise ratio on large scales using Taylor expansion up to the third order. In particular, however, we achieve a 33% improvement in signal to noise for Gaussianized field in transverse direction. On the other hand, we explore anmore » analytic model for the large-scale biasing of the Lyα forest, and present an extension of this model to describe the biasing of the transformed fields. Using hydrodynamic simulations we show that the model works best to describe the biasing with respect to velocity gradients, but is less successful in predicting the biasing with respect to large-scale density fluctuations, especially for very nonlinear transformations.« less

Dynamic Time Expansion and Compression Using Nonlinear Waveguides

DOEpatents

Findikoglu, Alp T.; Hahn, Sangkoo F.; Jia, Quanxi

2004-06-22

Dynamic time expansion or compression of a small amplitude input signal generated with an initial scale is performed using a nonlinear waveguide. A nonlinear waveguide having a variable refractive index is connected to a bias voltage source having a bias signal amplitude that is large relative to the input signal to vary the reflective index and concomitant speed of propagation of the nonlinear waveguide and an electrical circuit for applying the small amplitude signal and the large amplitude bias signal simultaneously to the nonlinear waveguide. The large amplitude bias signal with the input signal alters the speed of propagation of the small-amplitude signal with time in the nonlinear waveguide to expand or contract the initial time scale of the small-amplitude input signal.

Dynamic time expansion and compression using nonlinear waveguides

DOEpatents

Findikoglu, Alp T [Los Alamos, NM; Hahn, Sangkoo F [Los Alamos, NM; Jia, Quanxi [Los Alamos, NM

2004-06-22

Dynamic time expansion or compression of a small-amplitude input signal generated with an initial scale is performed using a nonlinear waveguide. A nonlinear waveguide having a variable refractive index is connected to a bias voltage source having a bias signal amplitude that is large relative to the input signal to vary the reflective index and concomitant speed of propagation of the nonlinear waveguide and an electrical circuit for applying the small-amplitude signal and the large amplitude bias signal simultaneously to the nonlinear waveguide. The large amplitude bias signal with the input signal alters the speed of propagation of the small-amplitude signal with time in the nonlinear waveguide to expand or contract the initial time scale of the small-amplitude input signal.

Electromagnetic-continuum-induced nonlinearity

NASA Astrophysics Data System (ADS)

Matsko, Andrey B.; Vyatchanin, Sergey P.

2018-05-01

A nonrelativistic Hamiltonian describing interaction between a mechanical degree of freedom and radiation pressure is commonly used as an ultimate tool for studying system behavior in optomechanics. This Hamiltonian is derived from the equation of motion of a mechanical degree of freedom and the optical wave equation with time-varying boundary conditions. We show that this approach is deficient for studying higher-order nonlinear effects in an open resonant optomechanical system. Optomechanical interaction induces a large mechanical nonlinearity resulting from a strong dependence of the power of the light confined in the optical cavity on the mechanical degrees of freedom of the cavity due to coupling with electromagnetic continuum. This dissipative nonlinearity cannot be inferred from the standard Hamiltonian formalism.

A hybrid linear/nonlinear training algorithm for feedforward neural networks.

PubMed

McLoone, S; Brown, M D; Irwin, G; Lightbody, A

1998-01-01

This paper presents a new hybrid optimization strategy for training feedforward neural networks. The algorithm combines gradient-based optimization of nonlinear weights with singular value decomposition (SVD) computation of linear weights in one integrated routine. It is described for the multilayer perceptron (MLP) and radial basis function (RBF) networks and then extended to the local model network (LMN), a new feedforward structure in which a global nonlinear model is constructed from a set of locally valid submodels. Simulation results are presented demonstrating the superiority of the new hybrid training scheme compared to second-order gradient methods. It is particularly effective for the LMN architecture where the linear to nonlinear parameter ratio is large.

Nonlinear gravitational recoil from the mergers of precessing black-hole binaries

NASA Astrophysics Data System (ADS)

Lousto, Carlos O.; Zlochower, Yosef

2013-04-01

We present results from an extensive study of 88 precessing, equal-mass black-hole binaries with large spins (83 with intrinsic spins |S→i/mi2| of 0.8 and 5 with intrinsic spins of 0.9), and use these data to model new nonlinear contributions to the gravitational recoil imparted to the merged black hole. We find a new effect, the cross kick, that enhances the recoil for partially aligned binaries beyond the hangup kick effect. This has the consequence of increasing the probabilities of recoils larger than 2000kms-1 by nearly a factor of 2, and consequently, of black holes getting ejected from galaxies, as well as the observation of large differential redshifts/blueshifts in the cores of recently merged galaxies.

Nonlinear hybrid modal synthesis based on branch modes for dynamic analysis of assembled structure

NASA Astrophysics Data System (ADS)

Huang, Xing-Rong; Jézéquel, Louis; Besset, Sébastien; Li, Lin; Sauvage, Olivier

2018-01-01

This paper describes a simple and fast numerical procedure to study the steady state responses of assembled structures with nonlinearities along continuous interfaces. The proposed strategy is based on a generalized nonlinear modal superposition approach supplemented by a double modal synthesis strategy. The reduced nonlinear modes are derived by combining a single nonlinear mode method with reduction techniques relying on branch modes. The modal parameters containing essential nonlinear information are determined and then employed to calculate the stationary responses of the nonlinear system subjected to various types of excitation. The advantages of the proposed nonlinear modal synthesis are mainly derived in three ways: (1) computational costs are considerably reduced, when analyzing large assembled systems with weak nonlinearities, through the use of reduced nonlinear modes; (2) based on the interpolation models of nonlinear modal parameters, the nonlinear modes introduced during the first step can be employed to analyze the same system under various external loads without having to reanalyze the entire system; and (3) the nonlinear effects can be investigated from a modal point of view by analyzing these nonlinear modal parameters. The proposed strategy is applied to an assembled system composed of plates and nonlinear rubber interfaces. Simulation results have proven the efficiency of this hybrid nonlinear modal synthesis, and the computation time has also been significantly reduced.

On intrinsic nonlinear particle motion in compact synchrotrons

NASA Astrophysics Data System (ADS)

Hwang, Kyung Ryun

Due to the low energy and small curvature characteristics of compact synchrotrons, there can be unexpected features that were not present or negligible in high energy accelerators. Nonlinear kinetics, fringe field effect, and space charge effect are those features which become important for low energy and small curvature accelerators. Nonlinear kinematics can limit the dynamics aperture for compact machine even if it consists of all linear elements. The contribution of the nonlinear kinematics on nonlinear optics parameters are first derived. As the dipole bending radius become smaller, the dipole fringe field effect become stronger. Calculation of the Lie map generator and corresponding mapping equation of dipole fringe field is presented. It is found that the higher order nonlinear potential is inverse proportional to powers of fringe field extent and correction to focusing and low order nonlinear potential is proportional to powers of fringe field extent. The fringe field also found to cause large closed orbit deviation for compact synchrotrons. The 2:1 and 4:1 space charge resonances are known to cause beam loss, emittance growth and halo formation for low energy high intensity beams. By numerical simulations, we observe a higher order 6:2 space charge resonance, which can successfully be understood by the concatenation of 2:1 and 4:1 resonances via canonical perturbation. We also develop an explicit symplectic tracking method for compact electrostatic storage rings and explore the feasibility of electric dipole moment (EDM) measurements.

The study of micro-inextensible piezoelectric cantilever plate

NASA Astrophysics Data System (ADS)

Chen, L. H.; Xu, J. W.; Zhang, W.

2018-06-01

In this paper, a micro-inextensible piezoelectric cantilever plate is analyzed and its nonlinear dynamic behaviour is studied. The nonlinear oscillation differential equation is established by using Hamilton’s principle with the application of strain gradient theory to consider the size effect, and inextensible theory to consider the large deformation and rotation effect of cantilever plate. Based on MATLAB software, using the Runge-Kuta method, we can obtain the response of the nonlinear oscillation differential equation. The influences of the strain gradient length scale parameter and voltage on the dynamic response of micro piezoelectric cantilever plate are investigated separately. The results confirmed an increase of the stiffness of the system by using the strain gradient theory and the amplitude of the vibration is reduced. The vibration of the system can be controlled by applying an active voltage. The effect of external excitation frequency on nonlinear dynamic behaviour is considered by using Poincare surface of section and diagrams of waveforms, phase and bifurcation.

Weakly Nonlinear Description of Parametric Instabilities in Vibrating Flows

NASA Technical Reports Server (NTRS)

Knobloch, E.; Vega, J. M.

1999-01-01

This project focuses on the effects of weak dissipation on vibrational flows in microgravity and in particular on (a) the generation of mean flows through viscous effects and their reaction on the flows themselves, and (b) the effects of finite group velocity and dispersion on the resulting dynamics in large domains. The basic mechanism responsible for the generation of such flows is nonlinear and was identified by Schlichting [21] and Longuet-Higgins. However, only recently has it become possible to describe such flows self-consistently in terms of amplitude equations for the parametrically excited waves coupled to a mean flow equation. The derivation of these equations is nontrivial because the limit of zero viscosity is singular. This project focuses on various aspects of this singular problem (i.e., the limit C equivalent to (nu)((g)(h(exp 3)))exp -1/2 << 1,where nu is the kinematic viscosity and h is the liquid depth) in the weakly nonlinear regime. A number of distinct cases is identified depending on the values of the Bond number, the size of the nonlinear terms, distance above threshold and the length scales of interest. The theory provides a quantitative explanation of a number of experiments on the vibration modes of liquid bridges and related experiments on parametric excitation of capillary waves in containers of both small and large aspect ratio. The following is a summary of results obtained thus far.

Electron acceleration via magnetic island coalescence

NASA Astrophysics Data System (ADS)

Shinohara, I.; Yumura, T.; Tanaka, K. G.; Fujimoto, M.

2009-06-01

Electron acceleration via fast magnetic island coalescence that happens as quick magnetic reconnection triggering (QMRT) proceeds has been studied. We have carried out a three-dimensional full kinetic simulation of the Harris current sheet with a large enough simulation run for two magnetic islands coalescence. Due to the strong inductive electric field associated with the non-linear evolution of the lower-hybrid-drift instability and the magnetic island coalescence process observed in the non-linear stage of the collisionless tearing mode, electrons are significantly accelerated at around the neutral sheet and the subsequent X-line. The accelerated meandering electrons generated by the non-linear evolution of the lower-hybrid-drift instability are resulted in QMRT, and QMRT leads to fast magnetic island coalescence. As a whole, the reconnection triggering and its transition to large-scale structure work as an effective electron accelerator.

Contributions of changes in climatology and perturbation and the resulting nonlinearity to regional climate change.

PubMed

Adachi, Sachiho A; Nishizawa, Seiya; Yoshida, Ryuji; Yamaura, Tsuyoshi; Ando, Kazuto; Yashiro, Hisashi; Kajikawa, Yoshiyuki; Tomita, Hirofumi

2017-12-20

Future changes in large-scale climatology and perturbation may have different impacts on regional climate change. It is important to understand the impacts of climatology and perturbation in terms of both thermodynamic and dynamic changes. Although many studies have investigated the influence of climatology changes on regional climate, the significance of perturbation changes is still debated. The nonlinear effect of these two changes is also unknown. We propose a systematic procedure that extracts the influences of three factors: changes in climatology, changes in perturbation and the resulting nonlinear effect. We then demonstrate the usefulness of the procedure, applying it to future changes in precipitation. All three factors have the same degree of influence, especially for extreme rainfall events. Thus, regional climate assessments should consider not only the climatology change but also the perturbation change and their nonlinearity. This procedure can advance interpretations of future regional climates.

Noise Response Data Reveal Novel Controllability Gramian for Nonlinear Network Dynamics

PubMed Central

Kashima, Kenji

2016-01-01

Control of nonlinear large-scale dynamical networks, e.g., collective behavior of agents interacting via a scale-free connection topology, is a central problem in many scientific and engineering fields. For the linear version of this problem, the so-called controllability Gramian has played an important role to quantify how effectively the dynamical states are reachable by a suitable driving input. In this paper, we first extend the notion of the controllability Gramian to nonlinear dynamics in terms of the Gibbs distribution. Next, we show that, when the networks are open to environmental noise, the newly defined Gramian is equal to the covariance matrix associated with randomly excited, but uncontrolled, dynamical state trajectories. This fact theoretically justifies a simple Monte Carlo simulation that can extract effectively controllable subdynamics in nonlinear complex networks. In addition, the result provides a novel insight into the relationship between controllability and statistical mechanics. PMID:27264780

Two-Dimensional CH3NH3PbI3 Perovskite Nanosheets for Ultrafast Pulsed Fiber Lasers.

PubMed

Li, Pengfei; Chen, Yao; Yang, Tieshan; Wang, Ziyu; Lin, Han; Xu, Yanhua; Li, Lei; Mu, Haoran; Shivananju, Bannur Nanjunda; Zhang, Yupeng; Zhang, Qinglin; Pan, Anlian; Li, Shaojuan; Tang, Dingyuan; Jia, Baohua; Zhang, Han; Bao, Qiaoliang

2017-04-12

Even though the nonlinear optical effects of solution processed organic-inorganic perovskite films have been studied, the nonlinear optical properties in two-dimensional (2D) perovskites, especially their applications for ultrafast photonics, are largely unexplored. In comparison to bulk perovskite films, 2D perovskite nanosheets with small thicknesses of a few unit cells are more suitable for investigating the intrinsic nonlinear optical properties because bulk recombination of photocarriers and the nonlinear scattering are relatively small. In this research, we systematically investigated the nonlinear optical properties of 2D perovskite nanosheets derived from a combined solution process and vapor phase conversion method. It was found that 2D perovskite nanosheets have stronger saturable absorption properties with large modulation depth and very low saturation intensity compared with those of bulk perovskite films. Using an all dry transfer method, we constructed a new type of saturable absorber device based on single piece 2D perovskite nanosheet. Stable soliton state mode-locking was achieved, and ultrafast picosecond pulses were generated at 1064 nm. This work is likely to pave the way for ultrafast photonic and optoelectronic applications based on 2D perovskites.

Subharmonic response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random excitation.

PubMed

Haiwu, Rong; Wang, Xiangdong; Xu, Wei; Fang, Tong

2009-08-01

The subharmonic response of single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to narrow-band random excitation is investigated. The narrow-band random excitation used here is a filtered Gaussian white noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, or velocity jumps, thereby permitting the applications of asymptotic averaging over the "fast" variables. The averaged stochastic equations are solved exactly by the method of moments for the mean-square response amplitude for the case of linear system with zero offset. A perturbation-based moment closure scheme is proposed and the formula of the mean-square amplitude is obtained approximately for the case of linear system with nonzero offset. The perturbation-based moment closure scheme is used once again to obtain the algebra equation of the mean-square amplitude of the response for the case of nonlinear system. The effects of damping, detuning, nonlinear intensity, bandwidth, and magnitudes of random excitations are analyzed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak amplitudes may be strongly reduced at large detunings or large nonlinear intensity.

Falling films on flexible inclines

NASA Astrophysics Data System (ADS)

Matar, O. K.; Craster, R. V.; Kumar, S.

2007-11-01

The nonlinear stability and dynamic behavior of falling fluid films is studied for flow over a flexible substrate. We use asymptotic methods to deduce governing equations valid in various limits. Long-wave theory is used to derive Benney-like coupled equations for the film thickness and substrate deflection. Weakly nonlinear equations are then derived from these equations that, in the limit of large wall damping and/or large wall tension, reduce to the Kuramoto-Sivashinsky equation. These models break down when inertia becomes more significant, so we also use a long-wave approximation in conjunction with integral theory to derive three strongly coupled nonlinear evolution equations for the film thickness, substrate deflection, and film volumetric flow rate valid at higher Reynolds numbers. These equations, accounting for inertia, capillary, viscous, wall tension, and damping effects, are solved over a wide range of parameters. Our results suggest that decreasing wall damping and/or wall tension can promote the development of chaos in the weakly nonlinear regime and lead to severe substrate deformations in the strongly nonlinear regime; these can give rise to situations in which the free surface and underlying substrate come into contact in finite time.

Supercontinuum generation in quadratic nonlinear waveguides without quasi-phase matching.

PubMed

Guo, Hairun; Zhou, Binbin; Steinert, Michael; Setzpfandt, Frank; Pertsch, Thomas; Chung, Hung-ping; Chen, Yen-Hung; Bache, Morten

2015-02-15

Supercontinuum generation (SCG) is most efficient when the solitons can be excited directly at the pump laser wavelength. Quadratic nonlinear waveguides may induce an effective negative Kerr nonlinearity, so temporal solitons can be directly generated in the normal (positive) dispersion regime overlapping with common ultrafast laser wavelengths. There is no need for waveguide dispersion engineering. Here, we experimentally demonstrate SCG in standard lithium niobate (LN) waveguides without quasi-phase matching (QPM), pumped with femtosecond pulses in the normal dispersion regime. The observed large bandwidths (even octave spanning), together with other experimental data, indicate that negative nonlinearity solitons are indeed excited, which is backed up by numerical simulations. The QPM-free design reduces production complexity, extends the maximum waveguide length, and limits undesired spectral resonances. Finally, nonlinear crystals can be used where QPM is inefficient or impossible, which is important for mid-IR SCG. QPM-free waveguides in mid-IR nonlinear crystals can support negative nonlinearity solitons, as these waveguides have a normal dispersion at the emission wavelengths of mid-IR ultrafast lasers.

Improvement of SPM nonlinear limit by chirped duobinary PolSK transmission

NASA Astrophysics Data System (ADS)

Yang, Lixiu; Fan, Jiayu; Wang, Lutang; Huang, Zhaoming

2005-02-01

In today's terrestrial long-haul optical fiber communication systems, high channel powers are required to obtain a large transmission distance with reasonable optical amplifier spacing. In such systems, however, the presence of nonlinear effects such as the self-phase modulation (SPM) and the fiber dispersion as well as their combined effects, called SPM-induced nonlinear limitation or SPM limit, will seriously degrade the system performances in respect of the effective transmission distance and ultimately become a limiting factor in high-speed, long-haul optical fiber transmission.In this paper, a new transmission format: chirped duobinary PolSK transmission, has been proposed to generate a pre-chirped duobianry signal with fixed polarity (either positive or negative), which is modulated by a PolSK modulator. This format is based on a transmitter setup consisting of a duobinary PolSK Modulation transmitter followed by an additional phase modulator. The chirped duobinary PolSK transmission reduces the signal degradation and spectral broadening in the nonlinear regime significantly. Thus it shifts this SPM nonlinear limit to enable more relaxed dispersion compensation at high optical power compared to the conventional duobinary schemes.The simulation results show chirped duobinary PolSK transmission enlarges the dispersion limited transmission distance, increases the dispersion tolerance and overcome the SPM nonlinear limit.

Finite difference time domain calculation of transients in antennas with nonlinear loads

NASA Technical Reports Server (NTRS)

Luebbers, Raymond J.; Beggs, John H.; Kunz, Karl S.; Chamberlin, Kent

1991-01-01

Determining transient electromagnetic fields in antennas with nonlinear loads is a challenging problem. Typical methods used involve calculating frequency domain parameters at a large number of different frequencies, then applying Fourier transform methods plus nonlinear equation solution techniques. If the antenna is simple enough so that the open circuit time domain voltage can be determined independently of the effects of the nonlinear load on the antennas current, time stepping methods can be applied in a straightforward way. Here, transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain (FDTD) methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case, the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets, including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

Sediment transport under wave groups: Relative importance between nonlinear waveshape and nonlinear boundary layer streaming

USGS Publications Warehouse

Yu, X.; Hsu, T.-J.; Hanes, D.M.

2010-01-01

Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two-phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross-shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one-dimensional vertical (1DV) model by simplifying the two-dimensional vertical (2DV) ensemble-averaged two-phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near-bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high-velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low-wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near-bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape. Copyright 2010 by the American Geophysical Union.

Quasi-phase-matching and second-harmonic generation enhancement in a semiconductor microresonator array using slow-light effects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumeige, Yannick

We theoretically analyze the second-harmonic generation process in a sequence of unidirectionnaly coupled doubly resonant whispering gallery mode semiconductor resonators. By using a convenient design, it is possible to coherently sum the second-harmonic fields generated inside each resonator. We show that resonator coupling allows the bandwidth of the phase-matching curve to be increased with respect to single-resonator configurations simultaneously taking advantage of the resonant feature of the resonators. This quasi-phase-matching technique could be applied to obtain small-footprint nonlinear devices with large bandwidth and limited nonlinear losses. The results are discussed in the framework of the slow-light-effect enhancement of second-order opticalmore » nonlinearities.« less

Computation of Large-Scale Structure Jet Noise Sources With Weak Nonlinear Effects Using Linear Euler

NASA Technical Reports Server (NTRS)

Dahl, Milo D.; Hixon, Ray; Mankbadi, Reda R.

2003-01-01

An approximate technique is presented for the prediction of the large-scale turbulent structure sound source in a supersonic jet. A linearized Euler equations code is used to solve for the flow disturbances within and near a jet with a given mean flow. Assuming a normal mode composition for the wave-like disturbances, the linear radial profiles are used in an integration of the Navier-Stokes equations. This results in a set of ordinary differential equations representing the weakly nonlinear self-interactions of the modes along with their interaction with the mean flow. Solutions are then used to correct the amplitude of the disturbances that represent the source of large-scale turbulent structure sound in the jet.

Nonlinear response of unidirectional boron/aluminum

NASA Technical Reports Server (NTRS)

Pindera, M.-J.; Herakovich, C. T.; Becker, W.; Aboudi, J.

1990-01-01

Experimental results obtained for unidirectional boron/aluminum subjected to combined loading using off-axis tension, compression and Iosipescu shear specimens are correlated with a nonlinear micromechanics model. It is illustrated that the nonlinear response in the principal material directions is markedly influenced by the different loading modes and different ratios of the applied stress components. The observed nonlinear response under pure and combined loading is discussed in terms of initial yielding, subsequent hardening, stress-interaction effects and unloading-reloading characteristics. The micromechanics model is based on the concept of a repeating unit cell representative of the composite-at-large and employs the unified theory of Bodner and Partom to model the inelastic response of the matrix. It is shown that the employed micromechanics model is sufficiently general to predict the observed nonlinear response of unidirectional boron/aluminum with good accuracy.

Non-Linear Dynamics and Emergence in Laboratory Fusion Plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hnat, B.

2011-09-22

Turbulent behaviour of laboratory fusion plasma system is modelled using extended Hasegawa-Wakatani equations. The model is solved numerically using finite difference techniques. We discuss non-linear effects in such a system in the presence of the micro-instabilities, specifically a drift wave instability. We explore particle dynamics in different range of parameters and show that the transport changes from diffusive to non-diffusive when large directional flows are developed.

Prediction of nonlinear optical properties of organic materials. General theoretical considerations

NASA Technical Reports Server (NTRS)

Cardelino, B.; Moore, C.; Zutaut, S.

1993-01-01

The prediction of nonlinear optical properties of organic materials is geared to assist materials scientists in the selection of good candidate molecules. A brief summary of the quantum mechanical methods used for estimating hyperpolarizabilities will be presented. The advantages and limitations of each technique will be discussed. Particular attention will be given to the finite-field method for calculating first and second order hyperpolarizabilities, since this method is better suited for large molecules. Corrections for dynamic fields and bulk effects will be discussed in detail, focusing on solvent effects, conformational isomerization, core effects, dispersion, and hydrogen bonding. Several results will be compared with data obtained from third-harmonic-generation (THG) and dc-induced second harmonic generation (EFISH) measurements. These comparisons will demonstrate the qualitative ability of the method to predict the relative strengths of hyperpolarizabilities of a class of compounds. The future application of molecular mechanics, as well as other techniques, in the study of bulk properties and solid state defects will be addressed. The relationship between large values for nonlinear optical properties and large conjugation lengths is well known, and is particularly important for third-order processes. For this reason, the materials with the largest observed nonresonant third-order properties are conjugated polymers. An example of this type of polymer is polydiacetylene. One of the problems in dealing with polydiacetylene is that substituents which may enhance its nonlinear properties may ultimately prevent it from polymerizing. A model which attempts to predict the likelihood of solid-state polymerization is considered, along with the implications of the assumptions that are used. Calculations of the third-order optical properties and their relationship to first-order properties and energy gaps will be discussed. The relationship between monomeric and polymeric third-order optical properties will also be considered.

Superposition of elliptic functions as solutions for a large number of nonlinear equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khare, Avinash; Saxena, Avadh

2014-03-15

For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ{sup 4}, the discrete MKdV as well asmore » for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn{sup 2}(x, m), it also admits solutions in terms of dn {sup 2}(x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations.« less

Enhancing Thermoelectric Performance Using Nonlinear Transport Effects

NASA Astrophysics Data System (ADS)

Jiang, Jian-Hua; Imry, Yoseph

2017-06-01

We study nonlinear transport effects on the maximum efficiency and power for both inelastic and elastic thermoelectric generators. The former device refers to phonon-assisted hopping in double quantum dots, while the latter device is represented by elastic tunneling through a single quantum dot. We find that nonlinear thermoelectric transport can lead to enhanced efficiency and power for both types of devices. A comprehensive survey of various quantum-dot energy, temperature, and parasitic heat conduction reveals that the nonlinear transport-induced improvements of the maximum efficiency and power are overall much more significant for inelastic devices than for elastic devices, even for temperature biases as small as Th=1.2 Tc (Th and Tc are the temperatures of the hot and cold reservoirs, respectively). The underlying mechanism is revealed as due to the fact that, unlike the Fermi distribution, the Bose distribution is not bounded when the temperature bias increases. A large flux density of absorbed phonons leads to a great enhancement of the electrical current, output power, and energy efficiency, dominating over the concurrent increase of the parasitic heat current. Our study reveals that nonlinear transport effects can be a useful tool for improving thermoelectric performance.

Nonlinear Kerr enhancement of the Sagnac effect in a coherently coupled array of optical microresonators

NASA Astrophysics Data System (ADS)

Wang, Chao; Search, Christopher

2013-03-01

Optical gyroscopes based on the Sagnac effect are of great interest both theoretically and practically. Previously it has been suggested a nonlinear Kerr medium inserted into a ring resonator gyroscope can largely increase the rotation sensitivity due to an instability caused by the non-reciprocal self-phase and cross-phase modulations. Recently, coupled microresonator arrays such as Side-Coupled Integrated Spaced Sequence of Resonators (SCISSOR) and Coupled Resonator Optical Waveguides (CROW) have drawn interest as potential integrated gyroscopes due to the sensitivity enhancement resulting from distributed interference between resonators. Here we analyze a SCISSOR system, which consists of an array of microresonators evanescently coupled to two parallel bus waveguides in the presence of a strong intra-resonator Kerr nonlinearity. We show that the distributed interference in the waveguides combined with the nonlinearly enhanced Sagnac effect in the resonators can further improve the sensitivity compared with either a single resonator of equal footprint or SCISSOR without a Kerr nonlinearity. Numerical simulation shows that bistability in the SCISSOR occurs and the rotation sensitivity dIoutput/dω can go to infinity near the boundaries of the bistable region.

Deterministic quantum nonlinear optics with single atoms and virtual photons

NASA Astrophysics Data System (ADS)

Kockum, Anton Frisk; Miranowicz, Adam; Macrı, Vincenzo; Savasta, Salvatore; Nori, Franco

2017-06-01

We show how analogs of a large number of well-known nonlinear-optics phenomena can be realized with one or more two-level atoms coupled to one or more resonator modes. Through higher-order processes, where virtual photons are created and annihilated, an effective deterministic coupling between two states of such a system can be created. In this way, analogs of three-wave mixing, four-wave mixing, higher-harmonic and -subharmonic generation (i.e., up- and down-conversion), multiphoton absorption, parametric amplification, Raman and hyper-Raman scattering, the Kerr effect, and other nonlinear processes can be realized. In contrast to most conventional implementations of nonlinear optics, these analogs can reach unit efficiency, only use a minimal number of photons (they do not require any strong external drive), and do not require more than two atomic levels. The strength of the effective coupling in our proposed setups becomes weaker the more intermediate transition steps are needed. However, given the recent experimental progress in ultrastrong light-matter coupling and improvement of coherence times for engineered quantum systems, especially in the field of circuit quantum electrodynamics, we estimate that many of these nonlinear-optics analogs can be realized with currently available technology.

Strongly nonlinear composite dielectrics: A perturbation method for finding the potential field and bulk effective properties

NASA Astrophysics Data System (ADS)

Blumenfeld, Raphael; Bergman, David J.

1991-10-01

A class of strongly nonlinear composite dielectrics is studied. We develop a general method to reduce the scalar-potential-field problem to the solution of a set of linear Poisson-type equations in rescaled coordinates. The method is applicable for a large variety of nonlinear materials. For a power-law relation between the displacement and the electric fields, it is used to solve explicitly for the value of the bulk effective dielectric constant ɛe to second order in the fluctuations of its local value. A simlar procedure for the vector potential, whose curl is the displacement field, yields a quantity analogous to the inverse dielectric constant in linear dielectrics. The bulk effective dielectric constant is given by a set of linear integral expressions in the rescaled coordinates and exact bounds for it are derived.

Nonlinear Radiation Heat Transfer Effects in the Natural Convective Boundary Layer Flow of Nanofluid Past a Vertical Plate: A Numerical Study

PubMed Central

Mustafa, Meraj; Mushtaq, Ammar; Hayat, Tasawar; Ahmad, Bashir

2014-01-01

The problem of natural convective boundary layer flow of nanofluid past a vertical plate is discussed in the presence of nonlinear radiative heat flux. The effects of magnetic field, Joule heating and viscous dissipation are also taken into consideration. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations via similarity transformations and then solved numerically using the Runge–Kutta fourth-fifth order method with shooting technique. The results reveal an existence of point of inflection for the temperature distribution for sufficiently large wall to ambient temperature ratio. Temperature and thermal boundary layer thickness increase as Brownian motion and thermophoretic effects intensify. Moreover temperature increases and heat transfer from the plate decreases with an increase in the radiation parameter. PMID:25251242

Nonlinear crack analysis with finite elements

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Saleme, E.; Pifko, A.; Levine, H. S.

1973-01-01

The application of finite element techniques to the analytic representation of the nonlinear behavior of arbitrary two-dimensional bodies containing cracks is discussed. Specific methods are proposed using which it should be possible to obtain information concerning: the description of the maximum, minimum, and residual near-tip stress and strain fields; the effects of crack closure on the near-tip behavior of stress and strain fields during cyclic loading into the plastic range; the stress-strain and displacement field behavior associated with a nonstationary crack; and the effects of large rotation near the crack tip.

Non-linear coherent mode interactions and the control of shear layers

NASA Technical Reports Server (NTRS)

Nikitopoulos, D. E.; Liu, J. T. C.

1990-01-01

A nonlinear integral formulation, based on local linear stability considerations, is used to study the collective interactions between discrete wave-modes associated with large-scale structures and the mean flow in a developing shear layer. Aspects of shear layer control are examined in light of the sensitivity of these interactions to the initial frequency parameter, modal energy contents and modal phases. Manipulation of the large-scale structure is argued to be an effective means of controlling the flow, including the small-scale turbulence dominated region far downstream. Cases of fundamental, 1st and 2nd subharmonic forcing are discussed in conjunction with relevant experiments.

Test particle simulation study of whistler wave packets observed near Comet Giacobini-Zinner

NASA Astrophysics Data System (ADS)

Kaya, N.; Matsumoto, H.; Tsurutani, B. T.

1989-01-01

Nonlinear interactions of water group ions with large-amplitude whistler wave packets detected at the leading edge of steepened magnetosonic waves observed near Comet Giacobini-Zinner (GZ) are studied using test particle simulations of water-ion interactions with a model wave based on GZ data. Some of the water ions are found to be decelerated in the steepened portion of the magnetosonic wave to the resonance velocity with the whistler wave packets. Through resonance and related nonlinear interaction with the large-amplitude whistler waves, the water ions become trapped by the packet. An energy balance calculation demonstrates that the trapped ions lose their kinetic energy during the trapped motion in the packet. Thus, the nonlinear trapping motion in the wave structure leads to effective energy transfer from the water group ions to the whistler wave packets in the leading edge of the steepened MHD waves.

Benzothiazolium Single Crystals: A New Class of Nonlinear Optical Crystals with Efficient THz Wave Generation.

PubMed

Lee, Seung-Heon; Lu, Jian; Lee, Seung-Jun; Han, Jae-Hyun; Jeong, Chan-Uk; Lee, Seung-Chul; Li, Xian; Jazbinšek, Mojca; Yoon, Woojin; Yun, Hoseop; Kang, Bong Joo; Rotermund, Fabian; Nelson, Keith A; Kwon, O-Pil

2017-08-01

Highly efficient nonlinear optical organic crystals are very attractive for various photonic applications including terahertz (THz) wave generation. Up to now, only two classes of ionic crystals based on either pyridinium or quinolinium with extremely large macroscopic optical nonlinearity have been developed. This study reports on a new class of organic nonlinear optical crystals introducing electron-accepting benzothiazolium, which exhibit higher electron-withdrawing strength than pyridinium and quinolinium in benchmark crystals. The benzothiazolium crystals consisting of new acentric core HMB (2-(4-hydroxy-3-methoxystyryl)-3-methylbenzo[d]thiazol-3-ium) exhibit extremely large macroscopic optical nonlinearity with optimal molecular ordering for maximizing the diagonal second-order nonlinearity. HMB-based single crystals prepared by simple cleaving method satisfy all required crystal characteristics for intense THz wave generation such as large crystal size with parallel surfaces, moderate thickness and high optical quality with large optical transparency range (580-1620 nm). Optical rectification of 35 fs pulses at the technologically very important wavelength of 800 nm in 0.26 mm thick HMB crystal leads to one order of magnitude higher THz wave generation efficiency with remarkably broader bandwidth compared to standard inorganic 0.5 mm thick ZnTe crystal. Therefore, newly developed HMB crystals introducing benzothiazolium with extremely large macroscopic optical nonlinearity are very promising materials for intense broadband THz wave generation and other nonlinear optical applications. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Highly efficient flexible piezoelectric nanogenerator and femtosecond two-photon absorption properties of nonlinear lithium niobate nanowires

NASA Astrophysics Data System (ADS)

Gupta, Manoj Kumar; Aneesh, Janardhanakurup; Yadav, Rajesh; Adarsh, K. V.; Kim, Sang-Woo

2017-05-01

We present a high performance flexible piezoelectric nanogenerator (NG) device based on the hydrothermally grown lead-free piezoelectric lithium niobate (LiNbO3) nanowires (NWs) for scavenging mechanical energies. The non-linear optical coefficient and optical limiting properties of LiNbO3 were analyzed using femtosecond laser pulse assisted two photon absorption techniques for the first time. Further, a flexible hybrid type NG using a composite structure of the polydimethylsiloxane polymer and LiNbO3 NWs was fabricated, and their piezoelectric output signals were measured. A large output voltage of ˜4.0 V and a recordable large current density of about 1.5 μA cm-2 were obtained under the cyclic compressive force of 1 kgf. A subsequent UV-Vis analysis of the as-prepared sample provides a remarkable increase in the optical band gap (UV absorption cut-off, ˜251 nm) due to the nanoscale size effect. The high piezoelectric output voltage and current are discussed in terms of large band gap, significant nonlinear optical response, and electric dipole alignments under poling effects. Such high performance and unique optical properties of LiNbO3 show its great potential towards various next generation smart electronic applications and self-powered optoelectronic devices.

All-optical tunable dual Fano resonance in nonlinear metamaterials in optical communication range

NASA Astrophysics Data System (ADS)

Zhou, Yi; Hu, Xiaoyong; Li, Chong; Yang, Hong; Gong, Qihuang

2018-01-01

Low-power, ultra-fast all-optical tunable dual Fano resonance was realized in a metamaterial coated with a non-linear nanocomposite layer composed of gold nanoparticle-doped polycrystalline barium strontium titanate and multilayer tungsten disulphide microsheets. A high non-linear refractive index of -2.148 × 10-11 m2/W was achieved in the nanocomposite material that originated in the non-linearity enhancement associated with the quantum confinement effect, the local-field enhancement effect, and reinforced interactions between photons and the multilayer tungsten disulphide microsheets. An ultra-low threshold pump intensity of 600 kW/cm2 was obtained. An ultra-fast response time of 25.4 ps was maintained because of the fast relaxation dynamics of the bound electrons in the nanoscale polycrystalline barium strontium titanate grains. The large third-order non-linear responses of the metamaterial were confirmed with a high third harmonic generation conversion efficiency of 5.4 × 10-5. This work may help to pave the way towards realization of ultra-high-speed information processing chips and multifunctional integrated photonic devices based on metamaterials.

Influence of asymmetric magnetic perturbation on the nonlinear evolution of double tearing modes

NASA Astrophysics Data System (ADS)

Xiong, G. Z.; Wang, L.; Li, X. Q.; Liu, H. F.; Tang, C. J.; Huang, J.; Zhang, X.; Wang, X. Q.

2017-06-01

The effects of asymmetric magnetic perturbation on the triggering and evolution of double tearing modes (DTMs) are investigated using nonlinear magnetohydrodynamics simulations in a slab geometry. We find that for reversed magnetic shear plasmas the resistive reconnection process induced by the initial perturbation at one rational surface can drive a new island at the other rational surface with the same mode number. The four typical states of the mode for the time evolution are found, and include: (i) a linear growth stage; (ii) a linear/nonlinear stable stage; (iii) an interactively driving stage; and (iv) a symmetric DTM stage. These differ from previous simulation results. Moreover, nonlinear DTM growth is found to strongly depend on the asymmetric magnetic perturbation, particularly in the early nonlinear phase. The initial perturbation strength scale of island width suggests that the left island enters into a Sweet-Parker growth process when the right island is sufficiently large to effectively drive the other. These results predict that although externally applied magnetic perturbations can suppress the neoclassical tearing mode they can also trigger new instabilities such as asymmetric DTMs.

Investigation of giant Kerr nonlinearity in quantum cascade lasers using mid-infrared femtosecond pulses

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Hong; Liu, Sheng; Department of Physics, University of Maryland, Baltimore County

2015-02-02

We study the Kerr nonlinearity of quantum cascade lasers (QCLs) by coupling resonant and off-resonant mid-infrared (mid-IR) femtosecond (fs) pulses into an active QCL waveguide. We observe an increase in the spectral width of the transmitted fs pulses as the coupled mid-infrared (mid-IR) pulse power increases. This is explained by the self-phase modulation effect due to the large Kerr nonlinearity of QCL waveguides. We further confirm this effect by observing the intensity dependent far-field profile of the transmitted mid-IR pulses, showing the pulses undergo self-focusing as they propagate through the active QCL due to the intensity dependent refractive index. Wemore » experimentally estimate the nonlinear refractive index n{sub 2} of a QCL to be ∼8 × 10{sup −9 }cm{sup 2}/W using the far-field beam profile of the transmitted pulses. The finite-difference time-domain simulations of QCL waveguides with Kerr nonlinearity incorporated show similar behavior to the experimental results.« less

Tackling non-linearities with the effective field theory of dark energy and modified gravity

NASA Astrophysics Data System (ADS)

Frusciante, Noemi; Papadomanolakis, Georgios

2017-12-01

We present the extension of the effective field theory framework to the mildly non-linear scales. The effective field theory approach has been successfully applied to the late time cosmic acceleration phenomenon and it has been shown to be a powerful method to obtain predictions about cosmological observables on linear scales. However, mildly non-linear scales need to be consistently considered when testing gravity theories because a large part of the data comes from those scales. Thus, non-linear corrections to predictions on observables coming from the linear analysis can help in discriminating among different gravity theories. We proceed firstly by identifying the necessary operators which need to be included in the effective field theory Lagrangian in order to go beyond the linear order in perturbations and then we construct the corresponding non-linear action. Moreover, we present the complete recipe to map any single field dark energy and modified gravity models into the non-linear effective field theory framework by considering a general action in the Arnowitt-Deser-Misner formalism. In order to illustrate this recipe we proceed to map the beyond-Horndeski theory and low-energy Hořava gravity into the effective field theory formalism. As a final step we derived the 4th order action in term of the curvature perturbation. This allowed us to identify the non-linear contributions coming from the linear order perturbations which at the next order act like source terms. Moreover, we confirm that the stability requirements, ensuring the positivity of the kinetic term and the speed of propagation for scalar mode, are automatically satisfied once the viability of the theory is demanded at linear level. The approach we present here will allow to construct, in a model independent way, all the relevant predictions on observables at mildly non-linear scales.

Thermal effects on nonlinear vibration of a carbon nanotube-based mass sensor using finite element analysis

NASA Astrophysics Data System (ADS)

Kang, Dong-Keun; Kim, Chang-Wan; Yang, Hyun-Ik

2017-01-01

In the present study we carried out a dynamic analysis of a CNT-based mass sensor by using a finite element method (FEM)-based nonlinear analysis model of the CNT resonator to elucidate the combined effects of thermal effects and nonlinear oscillation behavior upon the overall mass detection sensitivity. Mass sensors using carbon nanotube (CNT) resonators provide very high sensing performance. Because CNT-based resonators can have high aspect ratios, they can easily exhibit nonlinear oscillation behavior due to large displacements. Also, CNT-based devices may experience high temperatures during their manufacture and operation. These geometrical nonlinearities and temperature changes affect the sensing performance of CNT-based mass sensors. However, it is very hard to find previous literature addressing the detection sensitivity of CNT-based mass sensors including considerations of both these nonlinear behaviors and thermal effects. We modeled the nonlinear equation of motion by using the von Karman nonlinear strain-displacement relation, taking into account the additional axial force associated with the thermal effect. The FEM was employed to solve the nonlinear equation of motion because it can effortlessly handle the more complex geometries and boundary conditions. A doubly clamped CNT resonator actuated by distributed electrostatic force was the configuration subjected to the numerical experiments. Thermal effects upon the fundamental resonance behavior and the shift of resonance frequency due to attached mass, i.e., the mass detection sensitivity, were examined in environments of both high and low (or room) temperature. The fundamental resonance frequency increased with decreasing temperature in the high temperature environment, and increased with increasing temperature in the low temperature environment. The magnitude of the shift in resonance frequency caused by an attached mass represents the sensing performance of a mass sensor, i.e., its mass detection sensitivity, and it can be seen that this shift is affected by the temperature change and the amount of electrostatic force. The thermal effects on the mass detection sensitivity are intensified in the linear oscillation regime and increase with increasing CNT length; this intensification can either improve or worsen the detection sensitivity.

Differences between direct current and alternating current capacitance nonlinearities in high-k dielectrics and their relation to hopping conduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khaldi, O.; Kassmi, M.; El Manar University, LMOP, 2092 Tunis

2014-08-28

Capacitance nonlinearities were studied in atomic layer deposited HfO{sub 2} films using two types of signals: a pure ac voltage of large magnitude (ac nonlinearities) and a small ac voltage superimposed to a large dc voltage (dc nonlinearities). In theory, ac and dc nonlinearities should be of the same order of magnitude. However, in practice, ac nonlinearities are found to be an order of magnitude higher than dc nonlinearities. Besides capacitance nonlinearities, hopping conduction is studied using low-frequency impedance measurements and is discussed through the correlated barrier hopping model. The link between hopping and nonlinearity is established. The ac nonlinearitiesmore » are ascribed to the polarization of isolated defect pairs, while dc nonlinearities are attributed to electrode polarization which originates from defect percolation paths. Both the ac and dc capacitance nonlinearities display an exponential variation with voltage, which results from field-induced lowering of the hopping barrier energy.« less

The optimal density of cellular solids in axial tension.

PubMed

Mihai, L Angela; Alayyash, Khulud; Wyatt, Hayley

2017-05-01

For cellular bodies with uniform cell size, wall thickness, and shape, an important question is whether the same volume of material has the same effect when arranged as many small cells or as fewer large cells. To answer this question, for finite element models of periodic structures of Mooney-type material with different structural geometry and subject to large strain deformations, we identify a nonlinear elastic modulus as the ratio between the mean effective stress and the mean effective strain in the solid cell walls, and show that this modulus increases when the thickness of the walls increases, as well as when the number of cells increases while the volume of solid material remains fixed. Since, under the specified conditions, this nonlinear elastic modulus increases also as the corresponding mean stress increases, either the mean modulus or the mean stress can be employed as indicator when the optimum wall thickness or number of cells is sought.

Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

PubMed Central

Eshraghi, Iman; Jalali, Seyed K.; Pugno, Nicola Maria

2016-01-01

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ) method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs. PMID:28773911

Finite-amplitude, pulsed, ultrasonic beams

NASA Astrophysics Data System (ADS)

Coulouvrat, François; Frøysa, Kjell-Eivind

An analytical, approximate solution of the inviscid KZK equation for a nonlinear pulsed sound beam radiated by an acoustic source with a Gaussian velocity distribution, is obtained by means of the renormalization method. This method involves two steps. First, the transient, weakly nonlinear field is computed. However, because of cumulative nonlinear effects, that expansion is non-uniform and breaks down at some distance away from the source. So, in order to extend its validity, it is re-written in a new frame of co-ordinates, better suited to following the nonlinear distorsion of the wave profile. Basically, the nonlinear coordinate transform introduces additional terms in the expansion, which are chosen so as to counterbalance the non-uniform ones. Special care is devoted to the treatment of shock waves. Finally, comparisons with the results of a finite-difference scheme turn out favorable, and show the efficiency of the method for a rather large range of parameters.

Precluding nonlinear ISI in direct detection long-haul fiber optic systems

NASA Technical Reports Server (NTRS)

Swenson, Norman L.; Shoop, Barry L.; Cioffi, John M.

1991-01-01

Long-distance, high-rate fiber optic systems employing directly modulated 1.55-micron single-mode lasers and conventional single-mode fiber suffer severe intersymbol interference (ISI) with a large nonlinear component. A method of reducing the nonlinearity of the ISI, thereby making linear equalization more viable, is investigated. It is shown that the degree of nonlinearity is highly dependent on the choice of laser bias current, and that in some cases the ISI nonlinearity can be significantly reduced by biasing the laser substantially above threshold. Simulation results predict that an increase in signal-to-nonlinear-distortion ratio as high as 25 dB can be achieved for synchronously spaced samples at an optimal sampling phase by increasing the bias current from 1.2 times threshold to 3.5 times threshold. The high SDR indicates that a linear tapped delay line equalizer could be used to mitigate ISI. Furthermore, the shape of the pulse response suggests that partial response precoding and digital feedback equalization would be particularly effective for this channel.

Transmission Measurement of the Third-Order Susceptibility of Gold

NASA Technical Reports Server (NTRS)

Smith, David D.; Yoon, Youngkwon; Boyd, Robert W.; Crooks, Richard M.; George, Michael

1999-01-01

Gold nanoparticle composites are known to display large optical nonlinearities. In order to assess the validity of generalized effective medium theories (EMT's) for describing the linear and nonlinear optical properties of metal nanoparticle composites, knowledge of the linear and nonlinear susceptibilities of the constituent materials is a prerequisite. In this study the inherent nonlinearity of the metal is measured directly (rather than deduced from a suitable EMT) using a very thin gold film. Specifically, we have used the z-scan technique at a wavelength near the transmission window of bulk gold to measure the third-order susceptibility of a continuous thin gold film deposited on a quartz substrate surface-modified with a self-assembled monolayer to promote adhesion and uniformity without affecting the optical properties. We compare our results with predictions which ascribe the nonlinear response to a Fermi-smearing mechanism. Further, we note that the sign of the nonlinear susceptibility is reversed from that of gold nanoparticle composites.

A new impedance accounting for short- and long-range effects in mixed substructured formulations of nonlinear problems

NASA Astrophysics Data System (ADS)

Negrello, Camille; Gosselet, Pierre; Rey, Christian

2018-05-01

An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is often too expensive to be computed exactly in practice: an approximate version has to be sought for, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.

Experimental and theoretical studies of spectral alteration in ultrasonic waves resulting from nonlinear elastic response in rock

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr.

1993-11-01

Experiments in rock show a large nonlinear elastic wave response, far greater than that of gases, liquids and most other solids. The large response is attributed to structural defects in rock including microcracks and grain boundaries. In the earth, a large nonlinear response may be responsible for significant spectral alteration at amplitudes and distances currently considered to be well within the linear elastic regime.

Strongly nonlinear dynamics of electrolytes in large ac voltages.

PubMed

Højgaard Olesen, Laurits; Bazant, Martin Z; Bruus, Henrik

2010-07-01

We study the response of a model microelectrochemical cell to a large ac voltage of frequency comparable to the inverse cell relaxation time. To bring out the basic physics, we consider the simplest possible model of a symmetric binary electrolyte confined between parallel-plate blocking electrodes, ignoring any transverse instability or fluid flow. We analyze the resulting one-dimensional problem by matched asymptotic expansions in the limit of thin double layers and extend previous work into the strongly nonlinear regime, which is characterized by two features--significant salt depletion in the electrolyte near the electrodes and, at very large voltage, the breakdown of the quasiequilibrium structure of the double layers. The former leads to the prediction of "ac capacitive desalination" since there is a time-averaged transfer of salt from the bulk to the double layers, via oscillating diffusion layers. The latter is associated with transient diffusion limitation, which drives the formation and collapse of space-charge layers, even in the absence of any net Faradaic current through the cell. We also predict that steric effects of finite ion sizes (going beyond dilute-solution theory) act to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids, and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional nonlinear responses to large ac voltages, such as Faradaic reactions, electro-osmotic instabilities, and induced-charge electrokinetic phenomena.

Robust decentralized hybrid adaptive output feedback fuzzy control for a class of large-scale MIMO nonlinear systems and its application to AHS.

PubMed

Huang, Yi-Shao; Liu, Wel-Ping; Wu, Min; Wang, Zheng-Wu

2014-09-01

This paper presents a novel observer-based decentralized hybrid adaptive fuzzy control scheme for a class of large-scale continuous-time multiple-input multiple-output (MIMO) uncertain nonlinear systems whose state variables are unmeasurable. The scheme integrates fuzzy logic systems, state observers, and strictly positive real conditions to deal with three issues in the control of a large-scale MIMO uncertain nonlinear system: algorithm design, controller singularity, and transient response. Then, the design of the hybrid adaptive fuzzy controller is extended to address a general large-scale uncertain nonlinear system. It is shown that the resultant closed-loop large-scale system keeps asymptotically stable and the tracking error converges to zero. The better characteristics of our scheme are demonstrated by simulations. Copyright © 2014. Published by Elsevier Ltd.

Parametrically excited motion of a levitated rigid bar over high- Tc superconducting bulks

NASA Astrophysics Data System (ADS)

Shimizu, T.; Sugiura, T.; Ogawa, S.

2006-10-01

High-Tc superconducting levitation systems achieve, under no contact support, stable levitation without control. This feature can be applied to flywheels, magnetically levitated trains, and so on. But no contact support has small damping. So these mechanisms can show complicated phenomena of dynamics due to nonlinearity in their magnetic force. For application to large-scale machines, we need to analyze dynamics of a large levitated body supported at multiple points. This research deals with nonlinearly coupled oscillation of a homogeneous and symmetric rigid bar supported at its both ends by equal electromagnetic forces between superconductors and permanent magnets. In our past study, using a rigid bar, we found combination resonance. Combination resonance happens owing to the asymmetry of the system. But, even if support forces are symmetric, parametric resonance can happen. With a simple symmetric model, this research focuses on especially the parametric resonance, and evaluates nonlinear effect of the symmetric support forces by experiment and numerical analysis. Obtained results show that two modes, caused by coupling of horizontal translation and roll motion, can be excited nonlinearly when the superconductor is excited vertically in the neighborhood of twice the natural frequencies of those modes. We confirmed these resonances have nonlinear characteristics of soft-spring, hysteresis and so on.

Geometrically Nonlinear Finite Element Analysis of a Composite Space Reflector

NASA Technical Reports Server (NTRS)

Lee, Kee-Joo; Leet, Sung W.; Clark, Greg; Broduer, Steve (Technical Monitor)

2001-01-01

Lightweight aerospace structures, such as low areal density composite space reflectors, are highly flexible and may undergo large deflection under applied loading, especially during the launch phase. Accordingly, geometrically nonlinear analysis that takes into account the effect of finite rotation may be needed to determine the deformed shape for a clearance check and the stress and strain state to ensure structural integrity. In this study, deformation of the space reflector is determined under static conditions using a geometrically nonlinear solid shell finite element model. For the solid shell element formulation, the kinematics of deformation is described by six variables that are purely vector components. Because rotational angles are not used, this approach is free of the limitations of small angle increments. This also allows easy connections between substructures and large load increments with respect to the conventional shell formulation using rotational parameters. Geometrically nonlinear analyses were carried out for three cases of static point loads applied at selected points. A chart shows results for a case when the load is applied at the center point of the reflector dish. The computed results capture the nonlinear behavior of the composite reflector as the applied load increases. Also, they are in good agreement with the data obtained by experiments.

Modeling and control of a dielectric elastomer actuator

NASA Astrophysics Data System (ADS)

Gupta, Ujjaval; Gu, Guo-Ying; Zhu, Jian

2016-04-01

The emerging field of soft robotics offers the prospect of applying soft actuators as artificial muscles in the robots, replacing traditional actuators based on hard materials, such as electric motors, piezoceramic actuators, etc. Dielectric elastomers are one class of soft actuators, which can deform in response to voltage and can resemble biological muscles in the aspects of large deformation, high energy density and fast response. Recent research into dielectric elastomers has mainly focused on issues regarding mechanics, physics, material designs and mechanical designs, whereas less importance is given to the control of these soft actuators. Strong nonlinearities due to large deformation and electromechanical coupling make control of the dielectric elastomer actuators challenging. This paper investigates feed-forward control of a dielectric elastomer actuator by using a nonlinear dynamic model. The material and physical parameters in the model are identified by quasi-static and dynamic experiments. A feed-forward controller is developed based on this nonlinear dynamic model. Experimental evidence shows that this controller can control the soft actuator to track the desired trajectories effectively. The present study confirms that dielectric elastomer actuators are capable of being precisely controlled with the nonlinear dynamic model despite the presence of material nonlinearity and electromechanical coupling. It is expected that the reported results can promote the applications of dielectric elastomer actuators to soft robots or biomimetic robots.

Semiconductor Nonlinear Waveguide Devices and Integrated-Mirror Etalons

NASA Astrophysics Data System (ADS)

Chuang, Chih-Li.

This dissertation investigates different III-V semiconductor devices for applications in nonlinear photonics. These include passive and active nonlinear directional couplers, current-controlled optical phase shifter, and integrated -mirror etalons. A novel method to find the propagation constants of an optical waveguide is introduced. The same method is applied, with minor modifications, to find the coupling length of a directional coupler. The method presented provides a tool for the design of optical waveguide devices. The design, fabrication, and performance of a nonlinear directional coupler are presented. This device uses light intensity to control the direction of light coming out. This is achieved through photo-generated-carriers mechanism in the picosecond regime and through the optical Stark effect in the femtosecond regime. A two-transverse -dimensions beam-propagation computation is used to model the switching behavior in the nonlinear directional coupler. It is found that, by considering the pulse degradation effect, the computation agrees well with experiments. The possibility of operating a nonlinear directional coupler with gain is investigated. It is concluded that by injecting current into the nonlinear directional coupler does not provide the advantages hoped for and the modelling using 2-D beam -propagation methods verifies that. Using current injection to change the refractive index of a waveguide, an optical phase shifter is constructed. This device has the merit of delivering large phase shift with almost no intensity modulation. A phase shift as large as 3pi is produced in a waveguide 400 μm in length. Finally, a new structure, grown by the molecular beam epitaxy machine, is described. The structure consists of two quarter-wave stacks and a spacer layer to form an integrated-mirror etalon. The theory, design principles, spectral analyses are discussed with design examples to clarify the ideas. Emphasis is given to the vertical-cavity surface-emitting laser constructed from this structure. Here we demonstrated the cw operation of the VCSEL at room temperature.

Equivalent reduced model technique development for nonlinear system dynamic response

NASA Astrophysics Data System (ADS)

Thibault, Louis; Avitabile, Peter; Foley, Jason; Wolfson, Janet

2013-04-01

The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled system. However, the assembly of linear components using highly nonlinear connection elements or contact regions causes the entire system to become nonlinear. Conventional transient nonlinear integration of the equations of motion can be extremely computationally intensive, especially when the finite element models describing the components are very large and detailed. In this work, the equivalent reduced model technique (ERMT) is developed to address complicated nonlinear contact problems. ERMT utilizes a highly accurate model reduction scheme, the System equivalent reduction expansion process (SEREP). Extremely reduced order models that provide dynamic characteristics of linear components, which are interconnected with highly nonlinear connection elements, are formulated with SEREP for the dynamic response evaluation using direct integration techniques. The full-space solution will be compared to the response obtained using drastically reduced models to make evident the usefulness of the technique for a variety of analytical cases.

Second order nonlinear QED processes in ultra-strong laser fields

NASA Astrophysics Data System (ADS)

Mackenroth, Felix

2017-10-01

In the interaction of ultra-intense laser fields with matter the ever increasing peak laser intensities render nonlinear QED effects ever more important. For long, ultra-intense laser pulses scattering large systems, like a macroscopic plasma, the interaction time can be longer than the scattering time, leading to multiple scatterings. These are usually approximated as incoherent cascades of single-vertex processes. Under certain conditions, however, this common cascade approximation may be insufficient, as it disregards several effects such as coherent processes, quantum interferences or pulse shape effects. Quantifying deviations of the full amplitude of multiple scatterings from the commonly employed cascade approximations is a formidable, yet unaccomplished task. In this talk we are going to discuss how to compute second order nonlinear QED amplitudes and relate them to the conventional cascade approximation. We present examples for typical second order processes and benchmark the full result against common approximations. We demonstrate that the approximation of multiple nonlinear QED scatterings as a cascade of single interactions has certain limitations and discuss these limits in light of upcoming experimental tests.

On the Effect of Variability on Fermi, Pasta and Ulam Matrices

NASA Astrophysics Data System (ADS)

Nelson, Heather; Choubey, Bhaskar

The first numerical experiment by Fermi, Pasta, Ulam and Tsingou in 1955 observed recurrence in an array of non-linear systems. This has led to a large number of nonlinear numerical experiments with various new results from a chain of ideal oscillators. FPUT arrays consists of linear oscillators connected nonlinearly which leads to recurrence of energy mode with time. However, if such a system were to be physically constructed, inherent process variations would introduce a manufacturing tolerance into the parameters of the system. This abstract reports investigation into the effects of these tolerances on the FPU matrices. It has been observed that tolerance in the oscillators can degrade the observance of recurrence and with a chain of even 64 oscillators, recurrence cannot be observed with tolerances more than 10%. It has also been observed that linear oscillators tolerances have more effects on recurrence than those of the nonlinear coupling. Even with very small tolerances of +/- 1% on the linear components, one start to observe variations in the quality and magnitude of the recurrence and at +/- 5%, recurrence is starting to break down.

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

PubMed

Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G

2016-12-02

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

Nonlinear equations for dynamics of pretwisted beams undergoing small strains and large rotations

NASA Technical Reports Server (NTRS)

Hodges, D. H.

1985-01-01

Nonlinear beam kinematics are developed and applied to the dynamic analysis of a pretwisted, rotating beam element. The common practice of assuming moderate rotations caused by structural deformation in geometric nonlinear analyses of rotating beams was abandoned in the present analysis. The kinematic relations that described the orientation of the cross section during deformation are simplified by systematically ignoring the extensional strain compared to unity in those relations. Open cross section effects such as warping rigidity and dynamics are ignored, but other influences of warp are retained. The beam cross section is not allowed to deform in its own plane. Various means of implementation are discussed, including a finite element formulation. Numerical results obtained for nonlinear static problems show remarkable agreement with experiment.

Nonlinear Solver Approaches for the Diffusive Wave Approximation to the Shallow Water Equations

NASA Astrophysics Data System (ADS)

Collier, N.; Knepley, M.

2015-12-01

The diffusive wave approximation to the shallow water equations (DSW) is a doubly-degenerate, nonlinear, parabolic partial differential equation used to model overland flows. Despite its challenges, the DSW equation has been extensively used to model the overland flow component of various integrated surface/subsurface models. The equation's complications become increasingly problematic when ponding occurs, a feature which becomes pervasive when solving on large domains with realistic terrain. In this talk I discuss the various forms and regularizations of the DSW equation and highlight their effect on the solvability of the nonlinear system. In addition to this analysis, I present results of a numerical study which tests the applicability of a class of composable nonlinear algebraic solvers recently added to the Portable, Extensible, Toolkit for Scientific Computation (PETSc).

Disentangling Redshift-Space Distortions and Nonlinear Bias using the 2D Power Spectrum

DOE PAGES

Jennings, Elise; Wechsler, Risa H.

2015-08-07

We present the nonlinear 2D galaxy power spectrum, P(k, µ), in redshift space, measured from the Dark Sky simulations, using galaxy catalogs constructed with both halo occupation distribution and subhalo abundance matching methods, chosen to represent an intermediate redshift sample of luminous red galaxies. We find that the information content in individual µ (cosine of the angle to the line of sight) bins is substantially richer then multipole moments, and show that this can be used to isolate the impact of nonlinear growth and redshift space distortion (RSD) effects. Using the µ < 0.2 simulation data, which we show ismore » not impacted by RSD effects, we can successfully measure the nonlinear bias to an accuracy of ~ 5% at k < 0.6hMpc-1 . This use of individual µ bins to extract the nonlinear bias successfully removes a large parameter degeneracy when constraining the linear growth rate of structure. We carry out a joint parameter estimation, using the low µ simulation data to constrain the nonlinear bias, and µ > 0.2 to constrain the growth rate and show that f can be constrained to ~ 26(22)% to a kmax < 0.4(0.6)hMpc-1 from clustering alone using a simple dispersion model, for a range of galaxy models. Our analysis of individual µ bins also reveals interesting physical effects which arise simply from different methods of populating halos with galaxies. We also find a prominent turnaround scale, at which RSD damping effects are greater then the nonlinear growth, which differs not only for each µ bin but also for each galaxy model. These features may provide unique signatures which could be used to shed light on the galaxy–dark matter connection. Furthermore, the idea of separating nonlinear growth and RSD effects making use of the full information in the 2D galaxy power spectrum yields significant improvements in constraining cosmological parameters and may be a promising probe of galaxy formation models.« less

Evaluation of crack status in a meter-size concrete structure using the ultrasonic nonlinear coda wave interferometry.

PubMed

Legland, Jean-Baptiste; Zhang, Yuxiang; Abraham, Odile; Durand, Olivier; Tournat, Vincent

2017-10-01

The field of civil engineering is in need of new methods of non-destructive testing, especially in order to prevent and monitor the serious deterioration of concrete structures. In this work, experimental results are reported on fault detection and characterization in a meter-scale concrete structure using an ultrasonic nonlinear coda wave interferometry (NCWI) method. This method entails the nonlinear mixing of strong pump waves with multiple scattered probe (coda) waves, along with analysis of the net effect using coda wave interferometry. A controlled damage protocol is implemented on a post-tensioned, meter-scale concrete structure in order to generate cracking within a specific area being monitored by NCWI. The nonlinear acoustic response due to the high amplitude of acoustic modulation yields information on the elastic nonlinearities of concrete, as evaluated by two specific nonlinear observables. The increase in nonlinearity level corresponds to the creation of a crack with a network of microcracks localized at its base. In addition, once the crack closes as a result of post-tensioning, the residual nonlinearities confirm the presence of the closed crack. Last, the benefits and applicability of this NCWI method to the characterization and monitoring of large structures are discussed.

Simulation of Vortex Structure in Supersonic Free Shear Layer Using Pse Method

NASA Astrophysics Data System (ADS)

Guo, Xin; Wang, Qiang

The method of parabolized stability equations (PSE) are applied in the analysis of nonlinear stability and the simulation of flow structure in supersonic free shear layer. High accuracy numerical techniques including self-similar basic flow, high order differential method, appropriate transformation and decomposition of nonlinear terms are adopted and developed to solve the PSE effectively for free shear layer. The spatial evolving unstable waves which dominate the flow structure are investigated through nonlinear coupling spatial marching methods. The nonlinear interactions between harmonic waves are further analyzed and instantaneous flow field are obtained by adding the harmonic waves into basic flow. Relevant data agree well with that of DNS. The results demonstrate that T-S wave does not keeping growing exponential as the linear evolution, the energy transfer to high order harmonic modes and finally all harmonic modes get saturation due to the nonlinear interaction; Mean flow distortion is produced by the nonlinear interaction between the harmonic and its conjugate harmonic, makes great change to the average flow and increases the thickness of shear layer; PSE methods can well capture the large scale nonlinear flow structure in the supersonic free shear layer such as vortex roll-up, vortex pairing and nonlinear saturation.

Modeling and simulation of thermally actuated bilayer plates

NASA Astrophysics Data System (ADS)

Bartels, Sören; Bonito, Andrea; Muliana, Anastasia H.; Nochetto, Ricardo H.

2018-02-01

We present a mathematical model of polymer bilayers that undergo large bending deformations when actuated by non-mechanical stimuli such as thermal effects. The simple model captures a large class of nonlinear bending effects and can be discretized with standard plate elements. We devise a fully practical iterative scheme and apply it to the simulation of folding of several practically useful compliant structures comprising of thin elastic layers.

Nonlinear Dynamics of Electroelastic Dielectric Elastomers

DTIC Science & Technology

2018-01-30

research will significantly advance the basic science and fundamental understanding of how rate- dependent material response couples to large, nonlinear...experimental studies of constrained dielectric elastomer films, a transition in the surface instability mechanism depending on the elastocapillary number...fundamental understanding of how rate- dependent material response couples to large, nonlinear material deformation under applied electrostatic loading to

Compounding nonlinearities in the climate and wildfire system contribute to high uncertainty in estimates of future burned area in the western United State

NASA Astrophysics Data System (ADS)

Williams, P.

2015-12-01

Ecological studies are increasingly recognizing the importance of atmospheric vapor-pressure deficit (VPD) as a driver of forest drought stress and disturbance processes such as wildfire. Because of the nonlinear Clausius-Clapeyron relationship between temperature and saturation vapor pressure, small variations in temperature can have large impacts on VPD, and therefore drought, particularly in warm, dry areas and particularly during the warm season. It is also clear that VPD and drought affect forest fire nonlinearly, as incremental drying leads to increasingly large burned areas. Forest fire is also affected by fuel amount and connectivity, which are promoted by vegetation growth in previous years, which is in turn promoted by lack of drought, highlighting the importance of nuances in the sequencing of natural interannual climate variations in modulating the impacts of drought on wildfire. The many factors affecting forest fire, and the nonlinearities embedded within the climate and wildfire systems, cause interannual variability in forest-fire area and frequency to be wildly variable and strongly affected by internal climate variability. In addition, warming over the past century has produced a background increase in forest fire frequency and area in many regions. In this talk I focus on the western United States and will explore whether the relationships between internal climate variability on forest fire area have been amplified by the effects of warming as a result of the compounding nonlinearities described above. I will then explore what this means for future burned area in the western United States and make the case that uncertainties in the future global greenhouse gas emissions trajectory, model projections of mean temperatures, model projections of precipitation, and model projections of natural climate variability translate to very large uncertainties in the effects of future climate variability on forest fire area in the United States and globally.

Nonlocal nonlinear refraction in Hibiscus sabdariffa with large phase shifts.

PubMed

Ramírez-Martínez, D; Alvarado-Méndez, E; Trejo-Durán, M; Vázquez-Guevara, M A

2014-10-20

In this work we present a study of nonlinear optical properties in organic materials (hibiscus sabdariffa). Our results demonstrate that the medium exhibits a highly nonlocal nonlinear response. We show preliminary numerical results of the transmittance as nonlocal response by considering, simultaneously, the nonlinear absorption and refraction in media. Numerical results are accord to measurement obtained by Z- scan technique where we observe large phase shifts. We also analyze the far field diffraction ring patterns of the sample.

Vowel selection and its effects on perturbation and nonlinear dynamic measures.

PubMed

Maccallum, Julia K; Zhang, Yu; Jiang, Jack J

2011-01-01

Acoustic analysis of voice is typically conducted on recordings of sustained vowel phonation. This study applied perturbation and nonlinear dynamic analyses to the vowels /a/, /i/, and /u/ in order to determine vowel selection effects on analysis. Forty subjects (20 males and 20 females) with normal voices participated in recording. Traditional parameters of fundamental frequency, signal-to-noise ratio, percent jitter, and percent shimmer were calculated for the signals using CSpeech. Nonlinear dynamic parameters of correlation dimension and second-order entropy were also calculated. Perturbation analysis results were largely incongruous in this study and in previous research. Fundamental frequency results corroborated previous work, indicating higher fundamental frequency for /i/ and /u/ and lower fundamental frequency for /a/. Signal-to-noise ratio results showed that /i/ and /u/ have greater harmonic levels than /a/. Results of nonlinear dynamic analysis suggested that more complex activity may be evident in /a/ than in /i/ or /u/. Percent jitter and percent shimmer may not be useful for description of acoustic differences between vowels. Fundamental frequency, signal-to-noise ratio, and nonlinear dynamic parameters may be applied to characterize /a/ as having lower frequency, higher noise, and greater nonlinear components than /i/ and /u/. Copyright © 2010 S. Karger AG, Basel.

Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels.

PubMed

Steinacher, Arno; Bates, Declan G; Akman, Ozgur E; Soyer, Orkun S

2016-01-01

Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for the ubiquity of nonlinear dynamics in gene expression networks, and generate useful guidelines for the design of synthetic gene circuits.

Sorption of selected organic compounds from water to a peat soil and its humic-acid and humin fractions: Potential sources of the sorption nonlinearity

USGS Publications Warehouse

Chiou, C.T.; Kile, D.E.; Rutherford, D.W.; Sheng, G.; Boyd, S.A.

2000-01-01

The sorption isotherms of ethylene dibromide (EDB), diuron (DUN), and 3,5-dichlorophenol (DCP) from water on the humic acid and humin fractions of a peat soil and on the humic-acid of a muck soil have been measured. The data were compared with those of the solutes with the whole peat from which the humic-acid (HA) and humin (HM) fractions were derived and on which the sorption of the solutes exhibited varying extents of nonlinear capacities at low relative concentrations (C(e)/S(w)). The HA fraction as prepared by the density-fractionated method is relatively pure and presumably free of high- surface-area carbonaceous material (HSACM) that is considered to be responsible for the observed nonlinear sorption for nonpolar solutes (e.g., EDB) on the peat; conversely, the base-insoluble HM fraction as prepared is presumed to be enriched with HSACM, as manifested by the greatly higher BET- (N2) surface area than that of the whole peat. The sorption of EDB on HA exhibits no visible nonlinear effect, whereas the sorption on HM shows an enhanced nonlinearity over that on the whole peat. The sorption of polar DUN and DCP on HA and HM display nonlinear effects comparable with those on the whole peat; the effects are much more significant than those with nonpolar EDB. These results conform to the hypothesis that adsorption onto a small amount of strongly adsorbing HSACM is largely responsible for the nonlinear sorption of nonpolar solutes on soils and that additional specific interactions with the active groups of soil organic matter are responsible for the generally higher nonlinear sorption of the polar solutes.

Finite element modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, A. K.; Andersen, C. M.

1983-01-01

Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.

Double layers and double wells in arbitrary degenerate plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akbari-Moghanjoughi, M.

Using the generalized hydrodynamic model, the possibility of variety of large amplitude nonlinear excitations is examined in electron-ion plasma with arbitrary electron degeneracy considering also the ion temperature effect. A new energy-density relation is proposed for plasmas with arbitrary electron degeneracy which reduces to the classical Boltzmann and quantum Thomas-Fermi counterparts in the extreme limits. The pseudopotential method is employed to find the criteria for existence of nonlinear structures such as solitons, periodic nonlinear structures, and double-layers for different cases of adiabatic and isothermal ion fluids for a whole range of normalized electron chemical potential, η{sub 0}, ranging from dilutemore » classical to completely degenerate electron fluids. It is observed that there is a Mach-speed gap in which no large amplitude localized or periodic nonlinear excitations can propagate in the plasma under consideration. It is further revealed that the plasma under investigation supports propagation of double-wells and double-layers the chemical potential and Mach number ranges of which are studied in terms of other plasma parameters. The Mach number criteria for nonlinear waves are shown to significantly differ for cases of classical with η{sub 0} < 0 and quantum with η{sub 0} > 0 regimes. It is also shown that the localized structure propagation criteria possess significant dissimilarities for plasmas with adiabatic and isothermal ions. Current research may be generalized to study the nonlinear structures in plasma containing positrons, multiple ions with different charge states, and charged dust grains.« less

Non-linear Frequency Shifts, Mode Couplings, and Decay Instability of Plasma Waves

NASA Astrophysics Data System (ADS)

Affolter, Mathew; Anderegg, F.; Driscoll, C. F.; Valentini, F.

2015-11-01

We present experiments and theory for non-linear plasma wave decay to longer wavelengths, in both the oscillatory coupling and exponential decay regimes. The experiments are conducted on non-neutral plasmas in cylindrical Penning-Malmberg traps, θ-symmetric standing plasma waves have near acoustic dispersion ω (kz) ~kz - αkz2 , discretized by kz =mz (π /Lp) . Large amplitude waves exhibit non-linear frequency shifts δf / f ~A2 and Fourier harmonic content, both of which are increased as the plasma dispersion is reduced. Non-linear coupling rates are measured between large amplitude mz = 2 waves and small amplitude mz = 1 waves, which have a small detuning Δω = 2ω1 -ω2 . At small excitation amplitudes, this detuning causes the mz = 1 mode amplitude to ``bounce'' at rate Δω , with amplitude excursions ΔA1 ~ δn2 /n0 consistent with cold fluid theory and Vlasov simulations. At larger excitation amplitudes, where the non-linear coupling exceeds the dispersion, phase-locked exponential growth of the mz = 1 mode is observed, in qualitative agreement with simple 3-wave instability theory. However, significant variations are observed experimentally, and N-wave theory gives stunningly divergent predictions that depend sensitively on the dispersion-moderated harmonic content. Measurements on higher temperature Langmuir waves and the unusual ``EAW'' (KEEN) waves are being conducted to investigate the effects of wave-particle kinetics on the non-linear coupling rates. Department of Energy Grants DE-SC0002451and DE-SC0008693.

Tunable phonon-cavity coupling in graphene membranes.

PubMed

De Alba, R; Massel, F; Storch, I R; Abhilash, T S; Hui, A; McEuen, P L; Craighead, H G; Parpia, J M

2016-09-01

A major achievement of the past decade has been the realization of macroscopic quantum systems by exploiting the interactions between optical cavities and mechanical resonators. In these systems, phonons are coherently annihilated or created in exchange for photons. Similar phenomena have recently been observed through phonon-cavity coupling-energy exchange between the modes of a single system mediated by intrinsic material nonlinearity. This has so far been demonstrated primarily for bulk crystalline, high-quality-factor (Q > 10(5)) mechanical systems operated at cryogenic temperatures. Here, we propose graphene as an ideal candidate for the study of such nonlinear mechanics. The large elastic modulus of this material and capability for spatial symmetry breaking via electrostatic forces is expected to generate a wealth of nonlinear phenomena, including tunable intermodal coupling. We have fabricated circular graphene membranes and report strong phonon-cavity effects at room temperature, despite the modest Q factor (∼100) of this system. We observe both amplification into parametric instability (mechanical lasing) and the cooling of Brownian motion in the fundamental mode through excitation of cavity sidebands. Furthermore, we characterize the quenching of these parametric effects at large vibrational amplitudes, offering a window on the all-mechanical analogue of cavity optomechanics, where the observation of such effects has proven elusive.

Multi-linear model set design based on the nonlinearity measure and H-gap metric.

PubMed

Shaghaghi, Davood; Fatehi, Alireza; Khaki-Sedigh, Ali

2017-05-01

This paper proposes a model bank selection method for a large class of nonlinear systems with wide operating ranges. In particular, nonlinearity measure and H-gap metric are used to provide an effective algorithm to design a model bank for the system. Then, the proposed model bank is accompanied with model predictive controllers to design a high performance advanced process controller. The advantage of this method is the reduction of excessive switch between models and also decrement of the computational complexity in the controller bank that can lead to performance improvement of the control system. The effectiveness of the method is verified by simulations as well as experimental studies on a pH neutralization laboratory apparatus which confirms the efficiency of the proposed algorithm. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear radiative peristaltic flow of hydromagnetic fluid through porous medium

NASA Astrophysics Data System (ADS)

Hussain, Q.; Latif, T.; Alvi, N.; Asghar, S.

2018-06-01

The radiative heat and mass transfer in wall induced flow of hydromagnetic fluid through porous medium in an asymmetric channel is analyzed. The fluid viscosity is considered temperature dependent. In the theory of peristalsis, the radiation effects are either ignored or taken as linear approximation of radiative heat flux. Such approximation is only possible when there is sufficiently small temperature differences in the flow field; however, nonlinear radiation effects are valid for large temperature differences as well (the new feature added in the present study). Mathematical modeling of the problems include the complicated system of highly nonlinear differential equations. Semi-analytical solutions are established in the wave reference frame. Results are displayed graphically and discussed in detail for the variation of various physical parameters with the special attention to viscosity, radiation, and temperature ratio parameters.

A Non-linear Lifting Line Model for Design and Analysis of Trochoidal Propulsors

NASA Astrophysics Data System (ADS)

Roesler, Bernard; Epps, Brenden

2014-11-01

Flapping wing propulsors may increase the propulsive efficiency of large shipping vessels. A comparison of the design of a notional propulsor for a large shipping vessel with (a) a conventional ducted propeller versus (b) a flapping wing propulsor is presented. Calculations for flapping wing propulsors are performed using an open-source MATLAB software suite developed by the authors, CyROD, implementing an unsteady lifting-line model with free vortex wake roll-up to study the non-linear effects of foil-wake, and foil-foil interactions. Improvements to the traditional lifting line theory are made using further discretization of the wake vortex ring spacing near the trailing edge. Considerations of packaging options for a flapping wing propulsor on a large shipping vessel are presented, and compared with those for a conventional ducted propeller.

Three-dimensional boundary layer stability and transition

NASA Technical Reports Server (NTRS)

Malik, M. R.; Li, F.

1992-01-01

Nonparallel and nonlinear stability of a three-dimensional boundary layer, subject to crossflow instability, is investigated using parabolized stability equations (PSEs). Both traveling and stationary disturbances are considered and nonparallel effect on crossflow instability is found to be destabilizing. Our linear PSE results for stationary disturbances agree well with the results from direct solution of Navier-Stokes equations obtained by Spalart (1989). Nonlinear calculations have been carried out for stationary vortices and the computed wall vorticity pattern results in streamwise streaks which resemble remarkably well with the surface oil-flow visualizations in swept-wing experiments. Other features of the stationary vortex development (half-mushroom structure, inflected velocity profiles, vortex doubling, etc.) are also captured in our nonlinear calculations. Nonlinear interaction of the stationary amplitude of the stationary vortex is large as compared to the traveling mode, and the stationary vortex dominates most of the downstream development. When the two modes have the same initial amplitude, the traveling mode dominates the downstream development owing to its higher growth rate, and there is a tendency for the stationary mode to be suppressed. The effect of nonlinear wave development on the skin-friction coefficient is also computed.

Automatic control: the vertebral column of dogfish sharks behaves as a continuously variable transmission with smoothly shifting functions.

PubMed

Porter, Marianne E; Ewoldt, Randy H; Long, John H

2016-09-15

During swimming in dogfish sharks, Squalus acanthias, both the intervertebral joints and the vertebral centra undergo significant strain. To investigate this system, unique among vertebrates, we cyclically bent isolated segments of 10 vertebrae and nine joints. For the first time in the biomechanics of fish vertebral columns, we simultaneously characterized non-linear elasticity and viscosity throughout the bending oscillation, extending recently proposed techniques for large-amplitude oscillatory shear (LAOS) characterization to large-amplitude oscillatory bending (LAOB). The vertebral column segments behave as non-linear viscoelastic springs. Elastic properties dominate for all frequencies and curvatures tested, increasing as either variable increases. Non-linearities within a bending cycle are most in evidence at the highest frequency, 2.0 Hz, and curvature, 5 m -1 Viscous bending properties are greatest at low frequencies and high curvatures, with non-linear effects occurring at all frequencies and curvatures. The range of mechanical behaviors includes that of springs and brakes, with smooth transitions between them that allow for continuously variable power transmission by the vertebral column to assist in the mechanics of undulatory propulsion. © 2016. Published by The Company of Biologists Ltd.

A penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography.

PubMed

Shang, Shang; Bai, Jing; Song, Xiaolei; Wang, Hongkai; Lau, Jaclyn

2007-01-01

Conjugate gradient method is verified to be efficient for nonlinear optimization problems of large-dimension data. In this paper, a penalized linear and nonlinear combined conjugate gradient method for the reconstruction of fluorescence molecular tomography (FMT) is presented. The algorithm combines the linear conjugate gradient method and the nonlinear conjugate gradient method together based on a restart strategy, in order to take advantage of the two kinds of conjugate gradient methods and compensate for the disadvantages. A quadratic penalty method is adopted to gain a nonnegative constraint and reduce the illposedness of the problem. Simulation studies show that the presented algorithm is accurate, stable, and fast. It has a better performance than the conventional conjugate gradient-based reconstruction algorithms. It offers an effective approach to reconstruct fluorochrome information for FMT.

Geometrically nonlinear analysis of adhesively bonded joints

NASA Technical Reports Server (NTRS)

Dattaguru, B.; Everett, R. A., Jr.; Whitcomb, J. D.; Johnson, W. S.

1982-01-01

A geometrically nonlinear finite element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode 1, crack opening, and mode 2, inplane shear, strain-energy-release rates. The ratio of the mode 1 to mode 2 strain-energy-relase rates (G1/G2) was found to be strongly affected by he adhesive modulus and the adherend thickness. The ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode 1 strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements.

Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

Subcritical transition scenarios via linear and nonlinear localized optimal perturbations in plane Poiseuille flow

NASA Astrophysics Data System (ADS)

Farano, Mirko; Cherubini, Stefania; Robinet, Jean-Christophe; De Palma, Pietro

2016-12-01

Subcritical transition in plane Poiseuille flow is investigated by means of a Lagrange-multiplier direct-adjoint optimization procedure with the aim of finding localized three-dimensional perturbations optimally growing in a given time interval (target time). Space localization of these optimal perturbations (OPs) is achieved by choosing as objective function either a p-norm (with p\\gg 1) of the perturbation energy density in a linear framework; or the classical (1-norm) perturbation energy, including nonlinear effects. This work aims at analyzing the structure of linear and nonlinear localized OPs for Poiseuille flow, and comparing their transition thresholds and scenarios. The nonlinear optimization approach provides three types of solutions: a weakly nonlinear, a hairpin-like and a highly nonlinear optimal perturbation, depending on the value of the initial energy and the target time. The former shows localization only in the wall-normal direction, whereas the latter appears much more localized and breaks the spanwise symmetry found at lower target times. Both solutions show spanwise inclined vortices and large values of the streamwise component of velocity already at the initial time. On the other hand, p-norm optimal perturbations, although being strongly localized in space, keep a shape similar to linear 1-norm optimal perturbations, showing streamwise-aligned vortices characterized by low values of the streamwise velocity component. When used for initializing direct numerical simulations, in most of the cases nonlinear OPs provide the most efficient route to transition in terms of time to transition and initial energy, even when they are less localized in space than the p-norm OP. The p-norm OP follows a transition path similar to the oblique transition scenario, with slightly oscillating streaks which saturate and eventually experience secondary instability. On the other hand, the nonlinear OP rapidly forms large-amplitude bent streaks and skips the phases of streak saturation, providing a contemporary growth of all of the velocity components due to strong nonlinear coupling.

Method to improve near-field nonlinearity of a high-power diode laser array on a microchannel cooler

NASA Astrophysics Data System (ADS)

Zhang, Hongyou; Jia, Yangtao; Cai, Wanshao; Tao, Chunhua; Zah, Chung-en; Liu, Xingsheng

2018-03-01

Due to thermal stress, each emitter in a semiconductor laser bar or array is vertically displaced along the p-n junction; the result is that each emitter is not in a line, called near-field nonlinearity. Near-field nonlinearity along a laser bar (also known as "SMILE" effect) degrades the laser beam brightness, which causes an adverse effect on optical coupling and beam shaping. A large SMILE value causes a large divergence angle after collimation and a wider line after collimation and focusing. We simulate the factors affecting the SMILE value of a high-power diode laser array on a microchannel cooler (MCC). According to the simulation results, we have fabricated a series of laser bars bonded on MCCs with lower SMILE value. After simulation and experiment analysis, we found the key factor to affect SMILE is the deformation of the thin MCC because of the distribution of strain and stress in it. We also decreased the SMILE value of 1-cm-wide full bar AuSn bonded on MCCs from 12 to 1 μm by balancing force on MCC to minimize the deformation.

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions

PubMed Central

Hayat, T.; Hussain, Zakir; Alsaedi, A.; Farooq, M.

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ—perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears. PMID:27280883

The interplay between the kinetic nonlinear frequency shift and the flowing gradient in stimulated Brillouin scattering

NASA Astrophysics Data System (ADS)

Wang, Q.; Y Zheng, C.; Liu, Z. J.; Xiao, C. Z.; Feng, Q. S.; Zhang, H. C.; He, X. T.

2018-02-01

The effect of the kinetic nonlinear frequency shift (KNFS) on backward stimulated Brillouin scattering (SBS) in homogeneous plasmas and inhomogeneous flowing plasmas is investigated by three-wave coupled-mode equations. When the positive contribution to the KNFS from electrons as well as the negative contribution from ions is included, the net KNFS can become positive at a large electron-ion temperature ratio {{ZT}}e/{T}i. In homogeneous plasmas, KNFS can greatly reduce the SBS reflectivity at low or large {{ZT}}e/{T}i but has a weak effect on SBS at {{ZT}}e/{T}i where the positive frequency shifts from electrons almost cancels out the negative shifts from ions. In inhomogeneous plasmas, the net negative frequency shift can enhance the backward SBS reflectivity for the negative gradient of the plasma flowing, and can suppress the reflectivity for the positive case. On the contrary, the net positive frequency can suppress the reflectivity for the negative case of the flowing gradient and enhance the reflectivity for the positive case. This indicates that the SBS in inhomogeneous flowing plasmas can be controlled by changing the sign of the nonlinear frequency shift.

Magnetohydrodynamic Flow by a Stretching Cylinder with Newtonian Heating and Homogeneous-Heterogeneous Reactions.

PubMed

Hayat, T; Hussain, Zakir; Alsaedi, A; Farooq, M

2016-01-01

This article examines the effects of homogeneous-heterogeneous reactions and Newtonian heating in magnetohydrodynamic (MHD) flow of Powell-Eyring fluid by a stretching cylinder. The nonlinear partial differential equations of momentum, energy and concentration are reduced to the nonlinear ordinary differential equations. Convergent solutions of momentum, energy and reaction equations are developed by using homotopy analysis method (HAM). This method is very efficient for development of series solutions of highly nonlinear differential equations. It does not depend on any small or large parameter like the other methods i. e., perturbation method, δ-perturbation expansion method etc. We get more accurate result as we increase the order of approximations. Effects of different parameters on the velocity, temperature and concentration distributions are sketched and discussed. Comparison of present study with the previous published work is also made in the limiting sense. Numerical values of skin friction coefficient and Nusselt number are also computed and analyzed. It is noticed that the flow accelerates for large values of Powell-Eyring fluid parameter. Further temperature profile decreases and concentration profile increases when Powell-Eyring fluid parameter enhances. Concentration distribution is decreasing function of homogeneous reaction parameter while opposite influence of heterogeneous reaction parameter appears.

Lifting primordial non-Gaussianity above the noise

DOE Office of Scientific and Technical Information (OSTI.GOV)

Welling, Yvette; Woude, Drian van der; Pajer, Enrico, E-mail: welling@strw.leidenuniv.nl, E-mail: D.C.vanderWoude@uu.nl, E-mail: enrico.pajer@gmail.com

2016-08-01

Primordial non-Gaussianity (PNG) in Large Scale Structures is obfuscated by the many additional sources of non-linearity. Within the Effective Field Theory approach to Standard Perturbation Theory, we show that matter non-linearities in the bispectrum can be modeled sufficiently well to strengthen current bounds with near future surveys, such as Euclid. We find that the EFT corrections are crucial to this improvement in sensitivity. Yet, our understanding of non-linearities is still insufficient to reach important theoretical benchmarks for equilateral PNG, while, for local PNG, our forecast is more optimistic. We consistently account for the theoretical error intrinsic to the perturbative approachmore » and discuss the details of its implementation in Fisher forecasts.« less

Large-Signal Lyapunov-Based Stability Analysis of DC/AC Inverters and Inverter-Based Microgrids

NASA Astrophysics Data System (ADS)

Kabalan, Mahmoud

Microgrid stability studies have been largely based on small-signal linearization techniques. However, the validity and magnitude of the linearization domain is limited to small perturbations. Thus, there is a need to examine microgrids with large-signal nonlinear techniques to fully understand and examine their stability. Large-signal stability analysis can be accomplished by Lyapunov-based mathematical methods. These Lyapunov methods estimate the domain of asymptotic stability of the studied system. A survey of Lyapunov-based large-signal stability studies showed that few large-signal studies have been completed on either individual systems (dc/ac inverters, dc/dc rectifiers, etc.) or microgrids. The research presented in this thesis addresses the large-signal stability of droop-controlled dc/ac inverters and inverter-based microgrids. Dc/ac power electronic inverters allow microgrids to be technically feasible. Thus, as a prelude to examining the stability of microgrids, the research presented in Chapter 3 analyzes the stability of inverters. First, the 13 th order large-signal nonlinear model of a droop-controlled dc/ac inverter connected to an infinite bus is presented. The singular perturbation method is used to decompose the nonlinear model into 11th, 9th, 7th, 5th, 3rd and 1st order models. Each model ignores certain control or structural components of the full order model. The aim of the study is to understand the accuracy and validity of the reduced order models in replicating the performance of the full order nonlinear model. The performance of each model is studied in three different areas: time domain simulations, Lyapunov's indirect method and domain of attraction estimation. The work aims to present the best model to use in each of the three domains of study. Results show that certain reduced order models are capable of accurately reproducing the performance of the full order model while others can be used to gain insights into those three areas of study. This will enable future studies to save computational effort and produce the most accurate results according to the needs of the study being performed. Moreover, the effect of grid (line) impedance on the accuracy of droop control is explored using the 5th order model. Simulation results show that traditional droop control is valid up to R/X line impedance value of 2. Furthermore, the 3rd order nonlinear model improves the currently available inverter-infinite bus models by accounting for grid impedance, active power-frequency droop and reactive power-voltage droop. Results show the 3rd order model's ability to account for voltage and reactive power changes during a transient event. Finally, the large-signal Lyapunov-based stability analysis is completed for a 3 bus microgrid system (made up of 2 inverters and 1 linear load). The thesis provides a systematic state space large-signal nonlinear mathematical modeling method of inverter-based microgrids. The inverters include the dc-side dynamics associated with dc sources. The mathematical model is then used to estimate the domain of asymptotic stability of the 3 bus microgrid. The three bus microgrid system was used as a case study to highlight the design and optimization capability of a large-signal-based approach. The study explores the effect of system component sizing, load transient and generation variations on the asymptotic stability of the microgrid. Essentially, this advancement gives microgrid designers and engineers the ability to manipulate the domain of asymptotic stability depending on performance requirements. Especially important, this research was able to couple the domain of asymptotic stability of the ac microgrid with that of the dc side voltage source. Time domain simulations were used to demonstrate the mathematical nonlinear analysis results.

Behavioural and neurobiological implications of linear and non-linear features in larynx phonations of horseshoe bats

PubMed Central

Kobayasi, Kohta I.; Hage, Steffen R.; Berquist, Sean; Feng, Jiang; Zhang, Shuyi; Metzner, Walter

2012-01-01

Mammalian vocalizations exhibit large variations in their spectrotemporal features, although it is still largely unknown which result from intrinsic biomechanical properties of the larynx and which are under direct neuromuscular control. Here we show that mere changes in laryngeal air flow yield several non-linear effects on sound production, in an isolated larynx preparation from horseshoe bats. Most notably, there are sudden jumps between two frequency bands used for either echolocation or communication in natural vocalizations. These jumps resemble changes in “registers” as in yodelling. In contrast, simulated contractions of the main larynx muscle produce linear frequency changes, but are limited to echolocation or communication frequencies. Only by combining non-linear and linear properties can this larynx therefore produce sounds covering the entire frequency range of natural calls. This may give behavioural meaning to yodelling-like vocal behaviour and reshape our thinking about how the brain controls the multitude of spectral vocal features in mammals. PMID:23149729

Utilizing strongly absorbing materials for low-loss surface-wave nonlinear optics

NASA Astrophysics Data System (ADS)

Grosse, Nicolai B.; Franz, Philipp; Heckmann, Jan; Pufahl, Karsten; Woggon, Ulrike

2018-04-01

Optical media endowed with large nonlinear susceptibilities are highly prized for their employment in frequency conversion and the generation of nonclassical states of light. Although the presence of an optical resonance can greatly increase the nonlinear response (e.g., in epsilon-near-zero materials), the non-negligible increase in linear absorption often precludes the application of such materials in nonlinear optics. Absorbing materials prepared as thin films, however, can support a low-loss surface wave: the long-range surface exciton polariton (LRSEP). Its propagation lifetime increases with greater intrinsic absorption and reduced film thickness, provided that the film is embedded in a transparent medium (symmetric cladding). We explore LRSEP propagation in a molybdenum film by way of a prism-coupling configuration. Our observations show that excitation of the LRSEP mode leads to a dramatic increase in the yield of second-harmonic generation. This implies that the LRSEP mode is an effective vehicle for utilizing the nonlinear response of absorbing materials.

Multi-fluid Approach to High-frequency Waves in Plasmas. III. Nonlinear Regime and Plasma Heating

NASA Astrophysics Data System (ADS)

Martínez-Gómez, David; Soler, Roberto; Terradas, Jaume

2018-03-01

The multi-fluid modeling of high-frequency waves in partially ionized plasmas has shown that the behavior of magnetohydrodynamic waves in the linear regime is heavily influenced by the collisional interaction between the different species that form the plasma. Here, we go beyond linear theory and study large-amplitude waves in partially ionized plasmas using a nonlinear multi-fluid code. It is known that in fully ionized plasmas, nonlinear Alfvén waves generate density and pressure perturbations. Those nonlinear effects are more pronounced for standing oscillations than for propagating waves. By means of numerical simulations and analytical approximations, we examine how the collisional interaction between ions and neutrals affects the nonlinear evolution. The friction due to collisions dissipates a fraction of the wave energy, which is transformed into heat and consequently raises the temperature of the plasma. As an application, we investigate frictional heating in a plasma with physical conditions akin to those in a quiescent solar prominence.

Reverse saturable absorption studies in polymerized indole - Effect of polymerization in the phenomenal enhancement of third order optical nonlinearity

NASA Astrophysics Data System (ADS)

Jayakrishnan, K.; Joseph, Antony; Bhattathiripad, Jayakrishnan; Ramesan, M. T.; Chandrasekharan, K.; Siji Narendran, N. K.

2016-04-01

We report our results on the identification of large order enhancement in nonlinear optical coefficients of polymerized indole and its comparative study with reference to its monomer counterpart. Indole monomer shows virtually little third order effects whereas its polymerized version exhibits phenomenal increase in its third order nonlinear optical parameters such as nonlinear refractive index and nonlinear absorption. Open aperture Z-scan trace of polyindole done with Q-switched Nd:YAG laser source (532 nm, 7 ns), shows β value as high as 89 cm/GW at a beam energy of 0.83 GW/cm2. Closed aperture Z-scan done at identical energies reveals nonlinear refractive index of the order of -3.55 × 10-17 m2/W. Band gap measurement of polyindole was done with UV-Vis absorption spectra and compared with that of Indole. FTIR spectra of the monomer and polymerized versions were recorded and relevant bond formations were confirmed from the characteristic peaks. Photo luminescent spectra were investigated to know the emission features of both molecules. Beam energy (I0) versus nonlinear absorption coefficient (β) plot indicates reverse saturable type of absorption behaviour in polyindole molecules. Degenerate Four Wave Mixing (DFWM) plot of polyindole reveals quite a cubic dependence between probe and phase conjugate signal and the resulting χ(3) is comparable with Z-scan results. Optical limiting efficiency of polyindole is comparable with certain derivatives of porphyrins, phthalocyanines and graphene oxides.

The role of finite displacements in vocal fold modeling.

PubMed

Chang, Siyuan; Tian, Fang-Bao; Luo, Haoxiang; Doyle, James F; Rousseau, Bernard

2013-11-01

Human vocal folds experience flow-induced vibrations during phonation. In previous computational models, the vocal fold dynamics has been treated with linear elasticity theory in which both the strain and the displacement of the tissue are assumed to be infinitesimal (referred to as model I). The effect of the nonlinear strain, or geometric nonlinearity, caused by finite displacements is yet not clear. In this work, a two-dimensional model is used to study the effect of geometric nonlinearity (referred to as model II) on the vocal fold and the airflow. The result shows that even though the deformation is under 1 mm, i.e., less than 10% of the size of the vocal fold, the geometric nonlinear effect is still significant. Specifically, model I underpredicts the gap width, the flow rate, and the impact stress on the medial surfaces as compared to model II. The study further shows that the differences are caused by the contact mechanics and, more importantly, the fluid-structure interaction that magnifies the error from the small-displacement assumption. The results suggest that using the large-displacement formulation in a computational model would be more appropriate for accurate simulations of the vocal fold dynamics.

The Natural Neighbour Radial Point Interpolation Meshless Method Applied to the Non-Linear Analysis

NASA Astrophysics Data System (ADS)

Dinis, L. M. J. S.; Jorge, R. M. Natal; Belinha, J.

2011-05-01

In this work the Natural Neighbour Radial Point Interpolation Method (NNRPIM), is extended to large deformation analysis of elastic and elasto-plastic structures. The NNPRIM uses the Natural Neighbour concept in order to enforce the nodal connectivity and to create a node-depending background mesh, used in the numerical integration of the NNRPIM interpolation functions. Unlike the FEM, where geometrical restrictions on elements are imposed for the convergence of the method, in the NNRPIM there are no such restrictions, which permits a random node distribution for the discretized problem. The NNRPIM interpolation functions, used in the Galerkin weak form, are constructed using the Radial Point Interpolators, with some differences that modify the method performance. In the construction of the NNRPIM interpolation functions no polynomial base is required and the used Radial Basis Function (RBF) is the Multiquadric RBF. The NNRPIM interpolation functions posses the delta Kronecker property, which simplify the imposition of the natural and essential boundary conditions. One of the scopes of this work is to present the validation the NNRPIM in the large-deformation elasto-plastic analysis, thus the used non-linear solution algorithm is the Newton-Rapson initial stiffness method and the efficient "forward-Euler" procedure is used in order to return the stress state to the yield surface. Several non-linear examples, exhibiting elastic and elasto-plastic material properties, are studied to demonstrate the effectiveness of the method. The numerical results indicated that NNRPIM handles large material distortion effectively and provides an accurate solution under large deformation.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jennings, Elise; Wechsler, Risa H.

We present the nonlinear 2D galaxy power spectrum, P(k, µ), in redshift space, measured from the Dark Sky simulations, using galaxy catalogs constructed with both halo occupation distribution and subhalo abundance matching methods, chosen to represent an intermediate redshift sample of luminous red galaxies. We find that the information content in individual µ (cosine of the angle to the line of sight) bins is substantially richer then multipole moments, and show that this can be used to isolate the impact of nonlinear growth and redshift space distortion (RSD) effects. Using the µ < 0.2 simulation data, which we show ismore » not impacted by RSD effects, we can successfully measure the nonlinear bias to an accuracy of ~ 5% at k < 0.6hMpc-1 . This use of individual µ bins to extract the nonlinear bias successfully removes a large parameter degeneracy when constraining the linear growth rate of structure. We carry out a joint parameter estimation, using the low µ simulation data to constrain the nonlinear bias, and µ > 0.2 to constrain the growth rate and show that f can be constrained to ~ 26(22)% to a kmax < 0.4(0.6)hMpc-1 from clustering alone using a simple dispersion model, for a range of galaxy models. Our analysis of individual µ bins also reveals interesting physical effects which arise simply from different methods of populating halos with galaxies. We also find a prominent turnaround scale, at which RSD damping effects are greater then the nonlinear growth, which differs not only for each µ bin but also for each galaxy model. These features may provide unique signatures which could be used to shed light on the galaxy–dark matter connection. Furthermore, the idea of separating nonlinear growth and RSD effects making use of the full information in the 2D galaxy power spectrum yields significant improvements in constraining cosmological parameters and may be a promising probe of galaxy formation models.« less

Fuzzy Adaptive Decentralized Optimal Control for Strict Feedback Nonlinear Large-Scale Systems.

PubMed

Sun, Kangkang; Sui, Shuai; Tong, Shaocheng

2018-04-01

This paper considers the optimal decentralized fuzzy adaptive control design problem for a class of interconnected large-scale nonlinear systems in strict feedback form and with unknown nonlinear functions. The fuzzy logic systems are introduced to learn the unknown dynamics and cost functions, respectively, and a state estimator is developed. By applying the state estimator and the backstepping recursive design algorithm, a decentralized feedforward controller is established. By using the backstepping decentralized feedforward control scheme, the considered interconnected large-scale nonlinear system in strict feedback form is changed into an equivalent affine large-scale nonlinear system. Subsequently, an optimal decentralized fuzzy adaptive control scheme is constructed. The whole optimal decentralized fuzzy adaptive controller is composed of a decentralized feedforward control and an optimal decentralized control. It is proved that the developed optimal decentralized controller can ensure that all the variables of the control system are uniformly ultimately bounded, and the cost functions are the smallest. Two simulation examples are provided to illustrate the validity of the developed optimal decentralized fuzzy adaptive control scheme.

A comparative study of the effects of cone-plate and parallel-plate geometries on rheological properties under oscillatory shear flow

NASA Astrophysics Data System (ADS)

Song, Hyeong Yong; Salehiyan, Reza; Li, Xiaolei; Lee, Seung Hak; Hyun, Kyu

2017-11-01

In this study, the effects of cone-plate (C/P) and parallel-plate (P/P) geometries were investigated on the rheological properties of various complex fluids, e.g. single-phase (polymer melts and solutions) and multiphase systems (polymer blend and nanocomposite, and suspension). Small amplitude oscillatory shear (SAOS) tests were carried out to compare linear rheological responses while nonlinear responses were compared using large amplitude oscillatory shear (LAOS) tests at different frequencies. Moreover, Fourier-transform (FT)-rheology method was used to analyze the nonlinear responses under LAOS flow. Experimental results were compared with predictions obtained by single-point correction and shear rate correction. For all systems, SAOS data measured by C/P and P/P coincide with each other, but results showed discordance between C/P and P/P measurements in the nonlinear regime. For all systems except xanthan gum solutions, first-harmonic moduli were corrected using a single horizontal shift factor, whereas FT rheology-based nonlinear parameters ( I 3/1, I 5/1, Q 3, and Q 5) were corrected using vertical shift factors that are well predicted by single-point correction. Xanthan gum solutions exhibited anomalous corrections. Their first-harmonic Fourier moduli were superposed using a horizontal shift factor predicted by shear rate correction applicable to highly shear thinning fluids. The distinguished corrections were observed for FT rheology-based nonlinear parameters. I 3/1 and I 5/1 were superposed by horizontal shifts, while the other systems displayed vertical shifts of I 3/1 and I 5/1. Q 3 and Q 5 of xanthan gum solutions were corrected using both horizontal and vertical shift factors. In particular, the obtained vertical shift factors for Q 3 and Q 5 were twice as large as predictions made by single-point correction. Such larger values are rationalized by the definitions of Q 3 and Q 5. These results highlight the significance of horizontal shift corrections in nonlinear oscillatory shear data.

Broad band nonlinear optical absorption measurements of the laser dye IR26 using white light continuum Z-scan

NASA Astrophysics Data System (ADS)

Dey, Soumyodeep; Bongu, Sudhakara Reddy; Bisht, Prem Ballabh

2017-03-01

We study the nonlinear optical response of a standard dye IR26 using the Z-scan technique, but with the white light continuum. The continuum source of wavelength from 450 nm to 1650 nm has been generated from the photonic crystal fiber on pumping with 772 nm of Ti:Sapphire oscillator. The use of broadband incident pulse enables us to probe saturable absorption (SA) and reverse saturable absorption (RSA) over the large spectral range with a single Z-scan measurement. The system shows SA in the resonant region while it turns to RSA in the non-resonant regions. The low saturation intensity of the dye can be explained based on the simultaneous excitation from ground states to various higher energy levels with the help of composite energy level diagram. The cumulative effects of excited state absorption and thermal induced nonlinear optical effects are responsible for the observed RSA.

Hidden dynamics in models of discontinuity and switching

NASA Astrophysics Data System (ADS)

Jeffrey, Mike R.

2014-04-01

Sharp switches in behaviour, like impacts, stick-slip motion, or electrical relays, can be modelled by differential equations with discontinuities. A discontinuity approximates fine details of a switching process that lie beyond a bulk empirical model. The theory of piecewise-smooth dynamics describes what happens assuming we can solve the system of equations across its discontinuity. What this typically neglects is that effects which are vanishingly small outside the discontinuity can have an arbitrarily large effect at the discontinuity itself. Here we show that such behaviour can be incorporated within the standard theory through nonlinear terms, and these introduce multiple sliding modes. We show that the nonlinear terms persist in more precise models, for example when the discontinuity is smoothed out. The nonlinear sliding can be eliminated, however, if the model contains an irremovable level of unknown error, which provides a criterion for systems to obey the standard Filippov laws for sliding dynamics at a discontinuity.

Nonlinear energy transfer and current sheet development in localized Alfvén wavepacket collisions in the strong turbulence limit

NASA Astrophysics Data System (ADS)

Verniero, J. L.; Howes, G. G.; Klein, K. G.

2018-02-01

In space and astrophysical plasmas, turbulence is responsible for transferring energy from large scales driven by violent events or instabilities, to smaller scales where turbulent energy is ultimately converted into plasma heat by dissipative mechanisms. The nonlinear interaction between counterpropagating Alfvén waves, denoted Alfvén wave collisions, drives this turbulent energy cascade, as recognized by early work with incompressible magnetohydrodynamic (MHD) equations. Recent work employing analytical calculations and nonlinear gyrokinetic simulations of Alfvén wave collisions in an idealized periodic initial state have demonstrated the key properties that strong Alfvén wave collisions mediate effectively the transfer of energy to smaller perpendicular scales and self-consistently generate current sheets. For the more realistic case of the collision between two initially separated Alfvén wavepackets, we use a nonlinear gyrokinetic simulation to show here that these key properties persist: strong Alfvén wavepacket collisions indeed facilitate the perpendicular cascade of energy and give rise to current sheets. Furthermore, the evolution shows that nonlinear interactions occur only while the wavepackets overlap, followed by a clean separation of the wavepackets with straight uniform magnetic fields and the cessation of nonlinear evolution in between collisions, even in the gyrokinetic simulation presented here which resolves dispersive and kinetic effects beyond the reach of the MHD theory.

The Effects of Hydrogen Band EMIC Waves on Ring Current H+ Ions

NASA Astrophysics Data System (ADS)

Wang, Zhiqiang; Zhai, Hao; Gao, Zhuxiu

2017-12-01

Hydrogen band electromagnetic ion cyclotron (EMIC) waves have received much attention recently because they are found to frequently span larger spatial areas than the other band EMIC waves. Using test particle simulations, we study the nonlinear effects of hydrogen band EMIC waves on ring current H+ ions. A dimensionless parameter R is used to characterize the competition between wave-induced and adiabatic motions. The results indicate that there are three regimes of wave-particle interactions for typical 35 keV H+ ions at L = 5: diffusive (quasi-linear) behavior when αeq ≤ 35° (R ≥ 2.45), the nonlinear phase trapping when 35° < αeq < 50° (0.75 < R < 2.45), and both the nonlinear phase bunching and phase trapping when αeq ≥ 50° (R ≤ 0.75). The phase trapping can transport H+ ions toward large pitch angle, while the phase bunching has the opposite effect. The phase-trapped H+ ions can be significantly accelerated (from 35 keV to over 500 keV) in about 4 min and thus contribute to the formation of high energy components of ring current ions. The results suggest that the effect of hydrogen band EMIC waves is not ignorable in the nonlinear acceleration and resonance scattering of ring current H+ ions.

Suppression of the Nonlinear Zeeman Effect and Heading Error in Earth-Field-Range Alkali-Vapor Magnetometers.

PubMed

Bao, Guzhi; Wickenbrock, Arne; Rochester, Simon; Zhang, Weiping; Budker, Dmitry

2018-01-19

The nonlinear Zeeman effect can induce splitting and asymmetries of magnetic-resonance lines in the geophysical magnetic-field range. This is a major source of "heading error" for scalar atomic magnetometers. We demonstrate a method to suppress the nonlinear Zeeman effect and heading error based on spin locking. In an all-optical synchronously pumped magnetometer with separate pump and probe beams, we apply a radio-frequency field which is in phase with the precessing magnetization. This results in the collapse of the multicomponent asymmetric magnetic-resonance line with ∼100  Hz width in the Earth-field range into a single peak with a width of 22 Hz, whose position is largely independent of the orientation of the sensor within a range of orientation angles. The technique is expected to be broadly applicable in practical magnetometry, potentially boosting the sensitivity and accuracy of Earth-surveying magnetometers by increasing the magnetic-resonance amplitude, decreasing its width, and removing the important and limiting heading-error systematic.

Long-term, correlated emittance decrease in intense, high-brightness induction linacs

NASA Astrophysics Data System (ADS)

Carlsten, Bruce E.

1999-09-01

Simulations of high-brightness induction linacs often show a slow, long-term emittance decrease as the beam is matched from the electron gun into the linac. Superimposed on this long-term decrease are rapid emittance oscillations. These effects can be described in terms of correlations in the beam's radial phase space. The rapid emittance oscillations are due to transverse plasma oscillations, which stay nearly in phase for different radial positions within the beam. The initial emittance, just after the electron gun, is dominated by nonlinear focusing within the gun introduced by the anode exit hole. Due to the large space-charge force of an intense electron beam, the focusing of the beam through the matching section introduces an effective nonlinear force (from the change in the particles' potential energies) which counteracts the nonlinearities from the electron gun, leading to an average, long-term emittance decrease. Not all of the initial nonlinearity is removed by the matching procedure, and there are important consequences both for emittance measurements using solenoid focal length scans and for focusing the electron beam to a target.

Nonlinear Diamagnetic Stabilization of Double Tearing Modes in Cylindrical MHD Simulations

NASA Astrophysics Data System (ADS)

Abbott, Stephen; Germaschewski, Kai

2014-10-01

Double tearing modes (DTMs) may occur in reversed-shear tokamak configurations if two nearby rational surfaces couple and begin reconnecting. During the DTM's nonlinear evolution it can enter an ``explosive'' growth phase leading to complete reconnection, making it a possible driver for off-axis sawtooth crashes. Motivated by similarities between this behavior and that of the m = 1 kink-tearing mode in conventional tokamaks we investigate diamagnetic drifts as a possible DTM stabilization mechanism. We extend our previous linear studies of an m = 2 , n = 1 DTM in cylindrical geometry to the fully nonlinear regime using the MHD code MRC-3D. A pressure gradient similar to observed ITB profiles is used, together with Hall physics, to introduce ω* effects. We find the diamagnetic drifts can have a stabilizing effect on the nonlinear DTM through a combination of large scale differential rotation and mechanisms local to the reconnection layer. MRC-3D is an extended MHD code based on the libMRC computational framework. It supports nonuniform grids in curvilinear coordinates with parallel implicit and explicit time integration.

Initial Alignment of Large Azimuth Misalignment Angles in SINS Based on Adaptive UPF

PubMed Central

Sun, Jin; Xu, Xiao-Su; Liu, Yi-Ting; Zhang, Tao; Li, Yao

2015-01-01

The case of large azimuth misalignment angles in a strapdown inertial navigation system (SINS) is analyzed, and a method of using the adaptive UPF for the initial alignment is proposed. The filter is based on the idea of a strong tracking filter; through the introduction of the attenuation memory factor to effectively enhance the corrections of the current information residual error on the system, it reduces the influence on the system due to the system simplification, and the uncertainty of noise statistical properties to a certain extent; meanwhile, the UPF particle degradation phenomenon is better overcome. Finally, two kinds of non-linear filters, UPF and adaptive UPF, are adopted in the initial alignment of large azimuth misalignment angles in SINS, and the filtering effects of the two kinds of nonlinear filter on the initial alignment were compared by simulation and turntable experiments. The simulation and turntable experiment results show that the speed and precision of the initial alignment using adaptive UPF for a large azimuth misalignment angle in SINS under the circumstance that the statistical properties of the system noise are certain or not have been improved to some extent. PMID:26334277

Enhancing a slow and weak optomechanical nonlinearity with delayed quantum feedback

PubMed Central

Wang, Zhaoyou; Safavi-Naeini, Amir H.

2017-01-01

A central goal of quantum optics is to generate large interactions between single photons so that one photon can strongly modify the state of another one. In cavity optomechanics, photons interact with the motional degrees of freedom of an optical resonator, for example, by imparting radiation pressure forces on a movable mirror or sensing minute fluctuations in the position of the mirror. Here, we show that the optical nonlinearity arising from these effects, typically too small to operate on single photons, can be sufficiently enhanced with feedback to generate large interactions between single photons. We propose a protocol that allows photons propagating in a waveguide to interact with each other through multiple bounces off an optomechanical system. The protocol is analysed by evolving the full many-body quantum state of the waveguide-coupled system, illustrating that large photon–photon interactions mediated by mechanical motion may be within experimental reach. PMID:28677674

Enhancing a slow and weak optomechanical nonlinearity with delayed quantum feedback

NASA Astrophysics Data System (ADS)

Wang, Zhaoyou; Safavi-Naeini, Amir H.

2017-07-01

A central goal of quantum optics is to generate large interactions between single photons so that one photon can strongly modify the state of another one. In cavity optomechanics, photons interact with the motional degrees of freedom of an optical resonator, for example, by imparting radiation pressure forces on a movable mirror or sensing minute fluctuations in the position of the mirror. Here, we show that the optical nonlinearity arising from these effects, typically too small to operate on single photons, can be sufficiently enhanced with feedback to generate large interactions between single photons. We propose a protocol that allows photons propagating in a waveguide to interact with each other through multiple bounces off an optomechanical system. The protocol is analysed by evolving the full many-body quantum state of the waveguide-coupled system, illustrating that large photon-photon interactions mediated by mechanical motion may be within experimental reach.

Direct heuristic dynamic programming for damping oscillations in a large power system.

PubMed

Lu, Chao; Si, Jennie; Xie, Xiaorong

2008-08-01

This paper applies a neural-network-based approximate dynamic programming method, namely, the direct heuristic dynamic programming (direct HDP), to a large power system stability control problem. The direct HDP is a learning- and approximation-based approach to addressing nonlinear coordinated control under uncertainty. One of the major design parameters, the controller learning objective function, is formulated to directly account for network-wide low-frequency oscillation with the presence of nonlinearity, uncertainty, and coupling effect among system components. Results include a novel learning control structure based on the direct HDP with applications to two power system problems. The first case involves static var compensator supplementary damping control, which is used to provide a comprehensive evaluation of the learning control performance. The second case aims at addressing a difficult complex system challenge by providing a new solution to a large interconnected power network oscillation damping control problem that frequently occurs in the China Southern Power Grid.

New solitary wave solutions of (3 + 1)-dimensional nonlinear extended Zakharov-Kuznetsov and modified KdV-Zakharov-Kuznetsov equations and their applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun

In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.

Enhanced nonlinear interactions in quantum optomechanics via mechanical amplification

PubMed Central

Lemonde, Marc-Antoine; Didier, Nicolas; Clerk, Aashish A.

2016-01-01

The quantum nonlinear regime of optomechanics is reached when nonlinear effects of the radiation pressure interaction are observed at the single-photon level. This requires couplings larger than the mechanical frequency and cavity-damping rate, and is difficult to achieve experimentally. Here we show how to exponentially enhance the single-photon optomechanical coupling strength using only additional linear resources. Our method is based on using a large-amplitude, strongly detuned mechanical parametric drive to amplify mechanical zero-point fluctuations and hence enhance the radiation pressure interaction. It has the further benefit of allowing time-dependent control, enabling pulsed schemes. For a two-cavity optomechanical set-up, we show that our scheme generates photon blockade for experimentally accessible parameters, and even makes the production of photonic states with negative Wigner functions possible. We discuss how our method is an example of a more general strategy for enhancing boson-mediated two-particle interactions and nonlinearities. PMID:27108814

Toward high-speed 3D nonlinear soft tissue deformation simulations using Abaqus software.

PubMed

Idkaidek, Ashraf; Jasiuk, Iwona

2015-12-01

We aim to achieve a fast and accurate three-dimensional (3D) simulation of a porcine liver deformation under a surgical tool pressure using the commercial finite element software Abaqus. The liver geometry is obtained using magnetic resonance imaging, and a nonlinear constitutive law is employed to capture large deformations of the tissue. Effects of implicit versus explicit analysis schemes, element type, and mesh density on computation time are studied. We find that Abaqus explicit and implicit solvers are capable of simulating nonlinear soft tissue deformations accurately using first-order tetrahedral elements in a relatively short time by optimizing the element size. This study provides new insights and guidance on accurate and relatively fast nonlinear soft tissue simulations. Such simulations can provide force feedback during robotic surgery and allow visualization of tissue deformations for surgery planning and training of surgical residents.

Nonlinear Generation of shear flows and large scale magnetic fields by small scale

NASA Astrophysics Data System (ADS)

Aburjania, G.

2009-04-01

EGU2009-233 Nonlinear Generation of shear flows and large scale magnetic fields by small scale turbulence in the ionosphere by G. Aburjania Contact: George Aburjania, g.aburjania@gmail.com,aburj@mymail.ge

Nonlinear effects of group size on the success of wolves hunting elk

USGS Publications Warehouse

MacNulty, Daniel R.; Smith, Douglas W.; Mech, L. David; Vucetich, John A.; Packer, Craig

2012-01-01

Despite the popular view that social predators live in groups because group hunting facilitates prey capture, the apparent tendency for hunting success to peak at small group sizes suggests that the formation of large groups is unrelated to prey capture. Few empirical studies, however, have tested for nonlinear relationships between hunting success and group size, and none have demonstrated why success trails off after peaking. Here, we use a unique dataset of observations of individually known wolves (Canis lupus) hunting elk (Cervus elaphus) in Yellowstone National Park to show that the relationship between success and group size is indeed nonlinear and that individuals withholding effort (free riding) is why success does not increase across large group sizes. Beyond 4 wolves, hunting success leveled off, and individual performance (a measure of effort) decreased for reasons unrelated to interference from inept hunters, individual age, or size. But performance did drop faster among wolves with an incentive to hold back, i.e., nonbreeders with no dependent offspring, those performing dangerous predatory tasks, i.e., grabbing and restraining prey, and those in groups of proficient hunters. These results suggest that decreasing performance was free riding and that was why success leveled off in groups with >4 wolves that had superficially appeared to be cooperating. This is the first direct evidence that nonlinear trends in group hunting success reflect a switch from cooperation to free riding. It also highlights how hunting success per se is unlikely to promote formation and maintenance of large groups.

Nonlinear model and attitude dynamics of flexible spacecraft with large amplitude slosh

NASA Astrophysics Data System (ADS)

Deng, Mingle; Yue, Baozeng

2017-04-01

This paper is focused on the nonlinearly modelling and attitude dynamics of spacecraft coupled with large amplitude liquid sloshing dynamics and flexible appendage vibration. The large amplitude fuel slosh dynamics is included by using an improved moving pulsating ball model. The moving pulsating ball model is an equivalent mechanical model that is capable of imitating the whole liquid reorientation process. A modification is introduced in the capillary force computation in order to more precisely estimate the settling location of liquid in microgravity or zero-g environment. The flexible appendage is modelled as a three dimensional Bernoulli-Euler beam and the assumed modal method is employed to derive the nonlinear mechanical model for the overall coupled system of liquid filled spacecraft with appendage. The attitude maneuver is implemented by the momentum transfer technique, and a feedback controller is designed. The simulation results show that the liquid sloshing can always result in nutation behavior, but the effect of flexible deformation of appendage depends on the amplitude and direction of attitude maneuver performed by spacecraft. Moreover, it is found that the liquid sloshing and the vibration of flexible appendage are coupled with each other, and the coupling becomes more significant with more rapid motion of spacecraft. This study reveals that the appendage's flexibility has influence on the liquid's location and settling time in microgravity. The presented nonlinear system model can provide an important reference for the overall design of the modern spacecraft composed of rigid platform, liquid filled tank and flexible appendage.

Nonlinear magnetoelectric effects at high magnetic field amplitudes in composite multiferroics

NASA Astrophysics Data System (ADS)

Fetisov, L. Y.; Burdin, D. A.; Ekonomov, N. A.; Chashin, D. V.; Zhang, J.; Srinivasan, G.; Fetisov, Y. K.

2018-04-01

Magnetoelectric effects (ME) in ferromagnetic-ferroelectric layered composites arise due to magnetostriction and piezoelectric effect in the ferroic phases and are mediated by mechanical strain. The ME coupling strength in such composites could be measured by electrical response to an applied ac magnetic field h and a bias magnetic field H. The coupling, in general, is linear for small ac field amplitudes, but one expects nonlinear ME interactions for high field strengths since the dependence of magnetostriction λ on magnetic fields is nonlinear. Here we report on nonlinear voltage response of a composite of ferromagnetic Metglas and piezoelectric lanthanum gallium tantalate (langatate) subjected to an ac and a bias magnetic fields, resulting in the generation of voltages at harmonics of the frequency of h. The dependences of the ME voltage of the first four harmonics on the magnetic fields for H  =  0–20 Oe and h  =  0–50 Oe were measured. Up to a hundred harmonics were observed in the voltage versus frequency spectra and was indicative of high nonlinearity of the ME coupling in the multiferroic structure. It is shown that for h smaller than the saturation magnetic field H S for magnetostriction in the ferromagnetic layer, the amplitudes of the ME voltages are proportional to the derivatives of λ with respect to H and show a power-law dependence on the pumping field amplitude A n (H) ~ λ (n)(H)h n . We discuss a procedure for estimating the amplitudes of the harmonics for large pumping fields h, on the order of H S. The nonlinear ME effects in the composites are of interest for application in signal processing devices and highly sensitive magnetic field sensors.

Nonlinear characterization of a bolted, industrial structure using a modal framework

NASA Astrophysics Data System (ADS)

Roettgen, Daniel R.; Allen, Matthew S.

2017-02-01

This article presents measurements from a sub assembly of an off-the-shelf automotive exhaust system containing a bolted-flange connection and uses a recently proposed modal framework to develop a nonlinear dynamic model for the structure. The nonlinear identification and characterization methods used are reviewed to highlight the strengths of the current approach and the areas where further development is needed. This marks the first use of these new testing and nonlinear identification tools, and the associated modal framework, on production hardware with a realistic joint and realistic torque levels. To screen the measurements for nonlinearities, we make use of a time frequency analysis routine designed for transient responses called the zeroed early-time fast Fourier transform (ZEFFT). This tool typically reveals the small frequency shifts and distortions that tend to occur near each mode that is affected by the nonlinearity. The damping in this structure is found to be significantly nonlinear and a Hilbert transform is used to characterize the damping versus amplitude behavior. A model is presented that captures these effects for each mode individually (e.g. assuming negligible nonlinear coupling between modes), treating each mode as a single degree-of-freedom oscillator with a spring and viscous damping element in parallel with a four parameter Iwan model. The parameters of this model are identified for each of the structure's modes that exhibited nonlinearity and the resulting nonlinear model is shown to capture the stiffness and damping accurately over a large range of response amplitudes.

Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations

NASA Astrophysics Data System (ADS)

Indekeu, Joseph O.; Smets, Ruben

2017-08-01

Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.

Second order nonlinear equations of motion for spinning highly flexible line-elements. [for spacecraft solar sail

NASA Technical Reports Server (NTRS)

Salama, M.; Trubert, M.

1979-01-01

A formulation is given for the second order nonlinear equations of motion for spinning line-elements having little or no intrinsic structural stiffness. Such elements have been employed in recent studies of structural concepts for future large space structures such as the Heliogyro solar sailer. The derivation is based on Hamilton's variational principle and includes the effect of initial geometric imperfections (axial, curvature, and twist) on the line-element dynamics. For comparison with previous work, the nonlinear equations are reduced to a linearized form frequently found in the literature. The comparison has revealed several new spin-stiffening terms that have not been previously identified and/or retained. They combine geometric imperfections, rotary inertia, Coriolis, and gyroscopic terms.

Design of a 6 TeV muon collider

DOE PAGES

Wang, M-H.; Nosochkov, Y.; Cai, Y.; ...

2016-09-09

Here, a preliminary design of a muon collider ring with the center of mass (CM) energy of 6 TeV is presented. The ring circumference is 6.3 km, and themore » $$\\beta$$ functions at collision point are 1 cm in each plane. The ring linear optics, the non-linear chromaticity compensation in the Interaction Region (IR), and the additional non-linear orthogonal correcting knobs are described. Magnet specifications are based on the maximum pole-tip field of 20T in dipoles and 15T in quadrupoles. Careful compensation of the non-linear chromatic and amplitude dependent effects provide a sufficiently large dynamic aperture for the momentum range of up to $$\\pm$$0.5% without considering magnet errors.« less

Lipschitz regularity results for nonlinear strictly elliptic equations and applications

NASA Astrophysics Data System (ADS)

Ley, Olivier; Nguyen, Vinh Duc

2017-10-01

Most of Lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic growth power in gradient, one usually uses weak Bernstein-type arguments which require regularity and/or convex-type assumptions on the gradient nonlinearity. In this article, we obtain new Lipschitz regularity results for a large class of nonlinear strictly elliptic equations with possibly arbitrary growth power of the Hamiltonian with respect to the gradient variable using some ideas coming from Ishii-Lions' method. We use these bounds to solve an ergodic problem and to study the regularity and the large time behavior of the solution of the evolution equation.

Transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation under the influence of nonlinear gain and higher-order effects

NASA Astrophysics Data System (ADS)

Uzunov, Ivan M.; Georgiev, Zhivko D.; Arabadzhiev, Todor N.

2018-05-01

In this paper we study the transitions of stationary to pulsating solutions in the complex cubic-quintic Ginzburg-Landau equation (CCQGLE) under the influence of nonlinear gain, its saturation, and higher-order effects: self-steepening, third-order of dispersion, and intrapulse Raman scattering in the anomalous dispersion region. The variation method and the method of moments are applied in order to obtain the dynamic models with finite degrees of freedom for the description of stationary and pulsating solutions. Having applied the first model and its bifurcation analysis we have discovered the existence of families of subcritical Poincaré-Andronov-Hopf bifurcations due to the intrapulse Raman scattering, as well as some small nonlinear gain and the saturation of the nonlinear gain. A phenomenon of nonlinear stability has been studied and it has been shown that long living pulsating solutions with relatively small fluctuations of amplitude and frequencies exist at the bifurcation point. The numerical analysis of the second model has revealed the existence of Poincaré-Andronov-Hopf bifurcations of Raman dissipative soliton under the influence of the self-steepening effect and large nonlinear gain. All our theoretical predictions have been confirmed by the direct numerical solution of the full perturbed CCQGLE. The detailed comparison between the results obtained by both dynamic models and the direct numerical solution of the perturbed CCQGLE has proved the applicability of the proposed models in the investigation of the solutions of the perturbed CCQGLE.

An added-mass partition algorithm for fluid–structure interactions of compressible fluids and nonlinear solids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Banks, J.W., E-mail: banksj3@rpi.edu; Henshaw, W.D., E-mail: henshw@rpi.edu; Kapila, A.K., E-mail: kapila@rpi.edu

We describe an added-mass partitioned (AMP) algorithm for solving fluid–structure interaction (FSI) problems involving inviscid compressible fluids interacting with nonlinear solids that undergo large rotations and displacements. The computational approach is a mixed Eulerian–Lagrangian scheme that makes use of deforming composite grids (DCG) to treat large changes in the geometry in an accurate, flexible, and robust manner. The current work extends the AMP algorithm developed in Banks et al. [1] for linearly elasticity to the case of nonlinear solids. To ensure stability for the case of light solids, the new AMP algorithm embeds an approximate solution of a nonlinear fluid–solidmore » Riemann (FSR) problem into the interface treatment. The solution to the FSR problem is derived and shown to be of a similar form to that derived for linear solids: the state on the interface being fundamentally an impedance-weighted average of the fluid and solid states. Numerical simulations demonstrate that the AMP algorithm is stable even for light solids when added-mass effects are large. The accuracy and stability of the AMP scheme is verified by comparison to an exact solution using the method of analytical solutions and to a semi-analytical solution that is obtained for a rotating solid disk immersed in a fluid. The scheme is applied to the simulation of a planar shock impacting a light elliptical-shaped solid, and comparisons are made between solutions of the FSI problem for a neo-Hookean solid, a linearly elastic solid, and a rigid solid. The ability of the approach to handle large deformations is demonstrated for a problem of a high-speed flow past a light, thin, and flexible solid beam.« less

Coarse-grained incompressible magnetohydrodynamics: Analyzing the turbulent cascades

DOE PAGES

Aluie, Hussein

2017-02-21

Here, we formulate a coarse-graining approach to the dynamics of magnetohydrodynamic (MHD) fluids at a continuum of length-scales. In this methodology, effective equations are derived for the observable velocity and magnetic fields spatially-averaged at an arbitrary scale of resolution. The microscopic equations for the bare velocity and magnetic fields are renormalized by coarse-graining to yield macroscopic effective equations that contain both a subscale stress and a subscale electromotive force (EMF) generated by nonlinear interaction of eliminated fields and plasma motions. At large coarse-graining length-scales, the direct dissipation of invariants by microscopic mechanisms (such as molecular viscosity and Spitzer resistivity) ismore » shown to be negligible. The balance at large scales is dominated instead by the subscale nonlinear terms, which can transfer invariants across scales, and are interpreted in terms of work concepts for energy and in terms of topological flux-linkage for the two helicities. An important application of this approach is to MHD turbulence, where the coarse-graining length ℓ lies in the inertial cascade range. We show that in the case of sufficiently rough velocity and/or magnetic fields, the nonlinear inter-scale transfer need not vanish and can persist to arbitrarily small scales. Although closed expressions are not available for subscale stress and subscale EMF, we derive rigorous upper bounds on the effective dissipation they produce in terms of scaling exponents of the velocity and magnetic fields. These bounds provide exact constraints on phenomenological theories of MHD turbulence in order to allow the nonlinear cascade of energy and cross-helicity. On the other hand, we show that the forward cascade of magnetic helicity to asymptotically small scales is impossible unless 3rd-order moments of either velocity or magnetic field become infinite.« less

Effect of magnetic quantization on ion acoustic waves ultra-relativistic dense plasma

NASA Astrophysics Data System (ADS)

Javed, Asif; Rasheed, A.; Jamil, M.; Siddique, M.; Tsintsadze, N. L.

2017-11-01

In this paper, we have studied the influence of magnetic quantization of orbital motion of the electrons on the profile of linear and nonlinear ion-acoustic waves, which are propagating in the ultra-relativistic dense magneto quantum plasmas. We have employed both Thomas Fermi and Quantum Magneto Hydrodynamic models (along with the Poisson equation) of quantum plasmas. To investigate the large amplitude nonlinear structure of the acoustic wave, Sagdeev-Pseudo-Potential approach has been adopted. The numerical analysis of the linear dispersion relation and the nonlinear acoustic waves has been presented by drawing their graphs that highlight the effects of plasma parameters on these waves in both the linear and the nonlinear regimes. It has been noticed that only supersonic ion acoustic solitary waves can be excited in the above mentioned quantum plasma even when the value of the critical Mach number is less than unity. Both width and depth of Sagdeev potential reduces on increasing the magnetic quantization parameter η. Whereas the amplitude of the ion acoustic soliton reduces on increasing η, its width appears to be directly proportional to η. The present work would be helpful to understand the excitation of nonlinear ion-acoustic waves in the dense astrophysical environments such as magnetars and in intense-laser plasma interactions.

Adaptive Neural Network Based Control of Noncanonical Nonlinear Systems.

PubMed

Zhang, Yanjun; Tao, Gang; Chen, Mou

2016-09-01

This paper presents a new study on the adaptive neural network-based control of a class of noncanonical nonlinear systems with large parametric uncertainties. Unlike commonly studied canonical form nonlinear systems whose neural network approximation system models have explicit relative degree structures, which can directly be used to derive parameterized controllers for adaptation, noncanonical form nonlinear systems usually do not have explicit relative degrees, and thus their approximation system models are also in noncanonical forms. It is well-known that the adaptive control of noncanonical form nonlinear systems involves the parameterization of system dynamics. As demonstrated in this paper, it is also the case for noncanonical neural network approximation system models. Effective control of such systems is an open research problem, especially in the presence of uncertain parameters. This paper shows that it is necessary to reparameterize such neural network system models for adaptive control design, and that such reparameterization can be realized using a relative degree formulation, a concept yet to be studied for general neural network system models. This paper then derives the parameterized controllers that guarantee closed-loop stability and asymptotic output tracking for noncanonical form neural network system models. An illustrative example is presented with the simulation results to demonstrate the control design procedure, and to verify the effectiveness of such a new design method.

A NASTRAN primer for the analysis of rotating flexible blades

NASA Technical Reports Server (NTRS)

Lawrence, Charles; Aiello, Robert A.; Ernst, Michael A.; Mcgee, Oliver G.

1987-01-01

This primer provides documentation for using MSC NASTRAN in analyzing rotating flexible blades. The analysis of these blades includes geometrically nonlinear (large displacement) analysis under centrifugal loading, and frequency and mode shape (normal modes) determination. The geometrically nonlinear analysis using NASTRAN Solution sequence 64 is discussed along with the determination of frequencies and mode shapes using Solution Sequence 63. A sample problem with the complete NASTRAN input data is included. Items unique to rotating blade analyses, such as setting angle and centrifugal softening effects are emphasized.

Finite element analysis of steady and transiently moving/rolling nonlinear viscoelastic structure. I - Theory

NASA Technical Reports Server (NTRS)

Padovan, Joe

1987-01-01

In a three-part series of papers, a generalized finite element analysis scheme is developed to handle the steady and transient response of moving/rolling nonlinear viscoelastic structure. This paper considers the development of the moving/rolling element strategy, including the effects of large deformation kinematics and viscoelasticity modeled by fractional integrodifferential operators. To improve the solution strategy, a special hierarchical constraint procedure is developed for the case of steady rolling/translating, as well as a transient scheme involving the use of a Grunwaldian representation of the fractional operator.

Proposed solution methodology for the dynamically coupled nonlinear geared rotor mechanics equations

NASA Technical Reports Server (NTRS)

Mitchell, L. D.; David, J. W.

1983-01-01

The equations which describe the three-dimensional motion of an unbalanced rigid disk in a shaft system are nonlinear and contain dynamic-coupling terms. Traditionally, investigators have used an order analysis to justify ignoring the nonlinear terms in the equations of motion, producing a set of linear equations. This paper will show that, when gears are included in such a rotor system, the nonlinear dynamic-coupling terms are potentially as large as the linear terms. Because of this, one must attempt to solve the nonlinear rotor mechanics equations. A solution methodology is investigated to obtain approximate steady-state solutions to these equations. As an example of the use of the technique, a simpler set of equations is solved and the results compared to numerical simulations. These equations represent the forced, steady-state response of a spring-supported pendulum. These equations were chosen because they contain the type of nonlinear terms found in the dynamically-coupled nonlinear rotor equations. The numerical simulations indicate this method is reasonably accurate even when the nonlinearities are large.

Off-resonant third-order optical nonlinearities of squarylium and croconium dyes

NASA Astrophysics Data System (ADS)

Li, Zhongyu; Xu, Song; Niu, Lihong; Zhang, Zhi; Chen, Zihui; Zhang, Fushi

2008-01-01

The magnitude and dynamic response of the third-order optical nonlinearities of squarylium and croconium dyes in methanol solution were measured by femtosecond degenerate four-wave mixing (DFWM) technique at 800 nm. Ultrafast nonlinear optical responses have been observed, and the magnitude of the second-order hyperpolarizabilities was evaluated to be 5.80 × 10 -31 esu for the squarylium dye and 8.69 × 10 -31 esu for the croconium dye, respectively. The large optical nonlinearities of the dyes can be attributed to their rigid and intramolecular charge transfer structure, and the instantaneous NLO responses of dyes are shorter than the experimental time resolution (50 fs), which is mainly contributed from the electron delocalization. The fast nonlinear response and large third-order optical nonlinearities show that the studied squarylium and croconium dyes might a kind of promising materials for the applications in all-optical switching and modulator.

Unified nonlinear analysis for nonhomogeneous anisotropic beams with closed cross sections

NASA Technical Reports Server (NTRS)

Atilgan, Ali R.; Hodges, Dewey H.

1991-01-01

A unified methodology for geometrically nonlinear analysis of nonhomogeneous, anisotropic beams is presented. A 2D cross-sectional analysis and a nonlinear 1D global deformation analysis are derived from the common framework of a 3D, geometrically nonlinear theory of elasticity. The only restrictions are that the strain and local rotation are small compared to unity and that warping displacements are small relative to the cross-sectional dimensions. It is concluded that the warping solutions can be affected by large deformation and that this could alter the incremental stiffnes of the section. It is shown that sectional constants derived from the published, linear analysis can be used in the present nonlinear, 1D analysis governing the global deformation of the beam, which is based on intrinsic equations for nonlinear beam behavior. Excellent correlation is obtained with published experimental results for both isotropic and anisotropic beams undergoing large deflections.

Why the soliton wavelet transform is useful for nonlinear dynamic phenomena

NASA Astrophysics Data System (ADS)

Szu, Harold H.

1992-10-01

If signal analyses were perfect without noise and clutters, then any transform can be equally chosen to represent the signal without any loss of information. However, if the analysis using Fourier transform (FT) happens to be a nonlinear dynamic phenomenon, the effect of nonlinearity must be postponed until a later time when a complicated mode-mode coupling is attempted without the assurance of any convergence. Alternatively, there exists a new paradigm of linear transforms called wavelet transform (WT) developed for French oil explorations. Such a WT enjoys the linear superposition principle, the computational efficiency, and the signal/noise ratio enhancement for a nonsinusoidal and nonstationary signal. Our extensions to a dynamic WT and furthermore to an adaptive WT are possible due to the fact that there exists a large set of square-integrable functions that are special solutions of the nonlinear dynamic medium and could be adopted for the WT. In order to analyze nonlinear dynamics phenomena in ocean, we are naturally led to the construction of a soliton mother wavelet. This common sense of 'pay the nonlinear price now and enjoy the linearity later' is certainly useful to probe any nonlinear dynamics. Research directions in wavelets, such as adaptivity, and neural network implementations are indicated, e.g., tailoring an active sonar profile for explorations.

Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration.

PubMed

Chen, Yunjin; Pock, Thomas

2017-06-01

Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image restoration problems. By embodying recent improvements in nonlinear diffusion models, we propose a dynamic nonlinear reaction diffusion model with time-dependent parameters (i.e., linear filters and influence functions). In contrast to previous nonlinear diffusion models, all the parameters, including the filters and the influence functions, are simultaneously learned from training data through a loss based approach. We call this approach TNRD-Trainable Nonlinear Reaction Diffusion. The TNRD approach is applicable for a variety of image restoration tasks by incorporating appropriate reaction force. We demonstrate its capabilities with three representative applications, Gaussian image denoising, single image super resolution and JPEG deblocking. Experiments show that our trained nonlinear diffusion models largely benefit from the training of the parameters and finally lead to the best reported performance on common test datasets for the tested applications. Our trained models preserve the structural simplicity of diffusion models and take only a small number of diffusion steps, thus are highly efficient. Moreover, they are also well-suited for parallel computation on GPUs, which makes the inference procedure extremely fast.

On the Theory of Solitons of Fluid Pressure and Solute Density in Geologic Porous Media, with Applications to Shale, Clay and Sandstone

NASA Astrophysics Data System (ADS)

Caserta, A.; Kanivetsky, R.; Salusti, E.

2017-11-01

We here analyze a new model of transients of pore pressure p and solute density ρ in geologic porous media. This model is rooted in the nonlinear wave theory, its focus is on advection and effect of large pressure jumps on strain. It takes into account nonlinear and also time-dependent versions of the Hooke law about stress, rate and strain. The model solutions strictly relate p and ρ evolving under the effect of a strong external stress. As a result, the presence of quick and sharp transients in low permeability rocks is unveiled, i.e., the nonlinear "Burgers solitons". We, therefore, show that the actual transport process in porous rocks for large signals is not only the linear diffusion, but also a solitons presence could control the process. A test of a presence of solitons is applied to Pierre shale, Bearpaw shale, Boom clay and Oznam-Mugu silt and clay. An application about the presence of solitons for nuclear waste disposal and salt water intrusions is also discussed. Finally, in a kind of "theoretical experiment" we show that solitons could also be present in higher permeability rocks (Jordan and St. Peter sandstones), thus supporting the idea of a possible occurrence of osmosis also in sandstones.

Optimal control in adaptive optics modeling of nonlinear systems

NASA Astrophysics Data System (ADS)

Herrmann, J.

The problem of using an adaptive optics system to correct for nonlinear effects like thermal blooming is addressed using a model containing nonlinear lenses through which Gaussian beams are propagated. The best correction of this nonlinear system can be formulated as a deterministic open loop optimal control problem. This treatment gives a limit for the best possible correction. Aspects of adaptive control and servo systems are not included at this stage. An attempt is made to determine that control in the transmitter plane which minimizes the time averaged area or maximizes the fluence in the target plane. The standard minimization procedure leads to a two-point-boundary-value problem, which is ill-conditioned in the case. The optimal control problem was solved using an iterative gradient technique. An instantaneous correction is introduced and compared with the optimal correction. The results of the calculations show that for short times or weak nonlinearities the instantaneous correction is close to the optimal correction, but that for long times and strong nonlinearities a large difference develops between the two types of correction. For these cases the steady state correction becomes better than the instantaneous correction and approaches the optimum correction.

Frequency chirpings in Alfven continuum

NASA Astrophysics Data System (ADS)

Wang, Ge; Berk, Herb; Breizman, Boris; Zheng, Linjin

2017-10-01

We have used a self-consistent mapping technique to describe both the nonlinear wave-energetic particle resonant interaction and its spatial mode structure that depends upon the resonant energetic particle pressure. At the threshold for the onset of the energetic particle mode (EPM), strong chirping emerges in the lower continuum close to the TAE gap and then, driven by strong continuum damping, chirps rapidly to lower frequencies in the Alfven continuum. An adiabatic theory was developed that accurately replicated the results from the simulation where the nonlinearity was only due to the EPM resonant particles. The results show that the EPM-trapped particles have their action conserved during the time of rapid chirping. This adiabaticity enabled wave trapped particles to be confined within their separatrix, and produce even larger resonant structures, that can produce a large amplitude mode far from linearly predicted frequencies. In the present work we describe the effect of additional MHD nonlinearity to this calculation. We studied how the zonal flow component and its nonlinear feedback to the fundamental frequency and found that the MHD nonlinearity doesn't significantly alter the frequency chirping response that is predicted by the calculation that neglects the MHD nonlinearity.

Integration of system identification and finite element modelling of nonlinear vibrating structures

NASA Astrophysics Data System (ADS)

Cooper, Samson B.; DiMaio, Dario; Ewins, David J.

2018-03-01

The Finite Element Method (FEM), Experimental modal analysis (EMA) and other linear analysis techniques have been established as reliable tools for the dynamic analysis of engineering structures. They are often used to provide solutions to small and large structures and other variety of cases in structural dynamics, even those exhibiting a certain degree of nonlinearity. Unfortunately, when the nonlinear effects are substantial or the accuracy of the predicted response is of vital importance, a linear finite element model will generally prove to be unsatisfactory. As a result, the validated linear FE model requires further enhancement so that it can represent and predict the nonlinear behaviour exhibited by the structure. In this paper, a pragmatic approach to integrating test-based system identification and FE modelling of a nonlinear structure is presented. This integration is based on three different phases: the first phase involves the derivation of an Underlying Linear Model (ULM) of the structure, the second phase includes experiment-based nonlinear identification using measured time series and the third phase covers augmenting the linear FE model and experimental validation of the nonlinear FE model. The proposed case study is demonstrated on a twin cantilever beam assembly coupled with a flexible arch shaped beam. In this case, polynomial-type nonlinearities are identified and validated with force-controlled stepped-sine test data at several excitation levels.

Parametric and nonparametric Granger causality testing: Linkages between international stock markets

NASA Astrophysics Data System (ADS)

De Gooijer, Jan G.; Sivarajasingham, Selliah

2008-04-01

This study investigates long-term linear and nonlinear causal linkages among eleven stock markets, six industrialized markets and five emerging markets of South-East Asia. We cover the period 1987-2006, taking into account the on-set of the Asian financial crisis of 1997. We first apply a test for the presence of general nonlinearity in vector time series. Substantial differences exist between the pre- and post-crisis period in terms of the total number of significant nonlinear relationships. We then examine both periods, using a new nonparametric test for Granger noncausality and the conventional parametric Granger noncausality test. One major finding is that the Asian stock markets have become more internationally integrated after the Asian financial crisis. An exception is the Sri Lankan market with almost no significant long-term linear and nonlinear causal linkages with other markets. To ensure that any causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of VAR filtered residuals and VAR filtered squared residuals for the post-crisis sample. We find quite a few remaining significant bi- and uni-directional causal nonlinear relationships in these series. Finally, after filtering the VAR-residuals with GARCH-BEKK models, we show that the nonparametric test statistics are substantially smaller in both magnitude and statistical significance than those before filtering. This indicates that nonlinear causality can, to a large extent, be explained by simple volatility effects.

Nonlinear Control and Discrete Event Systems

NASA Technical Reports Server (NTRS)

Meyer, George; Null, Cynthia H. (Technical Monitor)

1995-01-01

As the operation of large systems becomes ever more dependent on extensive automation, the need for an effective solution to the problem of design and validation of the underlying software becomes more critical. Large systems possesses much detailed structure, typically hierarchical, and they are hybrid. Information processing at the top of the hierarchy is by means of formal logic and sentences; on the bottom it is by means of simple scalar differential equations and functions of time; and in the middle it is by an interacting mix of nonlinear multi-axis differential equations and automata, and functions of time and discrete events. The lecture will address the overall problem as it relates to flight vehicle management, describe the middle level, and offer a design approach that is based on Differential Geometry and Discrete Event Dynamic Systems Theory.

Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region.

PubMed

Alam, M Zahirul; De Leon, Israel; Boyd, Robert W

2016-05-13

Nonlinear optical phenomena are crucial for a broad range of applications, such as microscopy, all-optical data processing, and quantum information. However, materials usually exhibit a weak optical nonlinearity even under intense coherent illumination. We report that indium tin oxide can acquire an ultrafast and large intensity-dependent refractive index in the region of the spectrum where the real part of its permittivity vanishes. We observe a change in the real part of the refractive index of 0.72 ± 0.025, corresponding to 170% of the linear refractive index. This change in refractive index is reversible with a recovery time of about 360 femtoseconds. Our results offer the possibility of designing material structures with large ultrafast nonlinearity for applications in nanophotonics. Copyright © 2016, American Association for the Advancement of Science.

Probing the nuclear susceptibility of mesoionic compounds using two-beam coupling with chirp-controlled pulses

NASA Astrophysics Data System (ADS)

Bosco, Carlos A. C.; Maciel, Glauco S.; Rakov, Nikifor; de Araújo, Cid B.; Acioli, Lúcio H.; Simas, Alfredo M.; Athayde-Filho, Petrônio F.; Miller, Joseph

2007-11-01

The third-order non-linear optical response of mesoionic compounds (MIC) in dimethylsulfoxide (DMSO) and methanol solutions was investigated by use of collinear pump and probe technique with chirp-controlled femtosecond pulses. The experiments allowed the investigation of non-instantaneous nuclear processes and thermal effects induced by two-photon absorption (TPA). We found that the nuclear non-linearity of MIC in DMSO is ˜1/5 the benzene, which was used as a reference material. This result is attributed to the large inertia of MIC to rotation, compared to benzene. The results for MIC in methanol indicate the influence of thermal effects due to TPA.

Sound Propagation in Gas-Vapor-Droplet Suspensions with Evaporation and Nonlinear Particle Relaxation

NASA Technical Reports Server (NTRS)

Kandula, Max

2012-01-01

The Sound attenuation and dispersion in saturated gas-vapor-droplet mixture in the presence of evaporation has been investigated theoretically. The theory is based on an extension of the work of Davidson to accommodate the effects of nonlinear particle relaxation processes of mass, momentum and energy transfer on sound attenuation and dispersion. The results indicate the existence of a spectral broadening effect in the attenuation coefficient (scaled with respect to the peak value) with a decrease in droplet mass concentration. It is further shown that for large values of the droplet concentration the scaled attenuation coefficient is characterized by a universal spectrum independent of droplet mass concentration.

Inflight characterization and correction of Planck/HFI analog to digital converter nonlinearity

NASA Astrophysics Data System (ADS)

Sauvé, A.; Couchot, F.; Patanchon, G.; Montier, L.

2016-07-01

The Planck Satellite launched in 2009 was targeted to observe the anisotropies of the Cosmic Microwave Back-ground (CMB) to an unprecedented sensitivity. While the Analog to Digital Converter of the HFI (High Frequency Instrument) readout electronics had not been properly characterized on ground, it has been shown to add a systematic nonlinearity effect up to 2% of the cosmological signal. This was a limiting factor for CMB science at large angular scale. We will present the in-flight analysis and method used to characterize and correct this effect down to 0.05% level. We also discuss how to avoid this kind of complex issue for future missions.

Large optical nonlinearity of ITO nanorods for sub-picosecond all-optical modulation of the full-visible spectrum

NASA Astrophysics Data System (ADS)

Guo, Peijun; Schaller, Richard D.; Ocola, Leonidas E.; Diroll, Benjamin T.; Ketterson, John B.; Chang, Robert P. H.

2016-09-01

Nonlinear optical responses of materials play a vital role for the development of active nanophotonic and plasmonic devices. Optical nonlinearity induced by intense optical excitation of mobile electrons in metallic nanostructures can provide large-amplitude, dynamic tuning of their electromagnetic response, which is potentially useful for all-optical processing of information and dynamic beam control. Here we report on the sub-picosecond optical nonlinearity of indium tin oxide nanorod arrays (ITO-NRAs) following intraband, on-plasmon-resonance optical pumping, which enables modulation of the full-visible spectrum with large absolute change of transmission, favourable spectral tunability and beam-steering capability. Furthermore, we observe a transient response in the microsecond regime associated with slow lattice cooling, which arises from the large aspect-ratio and low thermal conductivity of ITO-NRAs. Our results demonstrate that all-optical control of light can be achieved by using heavily doped wide-bandgap semiconductors in their transparent regime with speed faster than that of noble metals.

Nonlinear wavenumber shift of large amplitude Langmuir waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Dehui, E-mail: dhli@ipp.ac.cn; Wang, Shaojie

2016-07-15

Nonlinear particle-in-cell simulation is carried out to investigate the nonlinear behavior of the Langmuir wave launched with a fixed frequency in a uniform plasma. It is found that in the strong driving case, the launched wave propagates in a phase velocity larger than that predicted by the linear theory; there appears a nonlinear down-shift of wavenumber. The phase velocity of the nonlinear wave and the down-shift of the wavenumber are demonstrated to be determined by the velocity of nonlinearly accelerated resonant electrons.

Stochastic Integration H∞ Filter for Rapid Transfer Alignment of INS.

PubMed

Zhou, Dapeng; Guo, Lei

2017-11-18

The performance of an inertial navigation system (INS) operated on a moving base greatly depends on the accuracy of rapid transfer alignment (RTA). However, in practice, the coexistence of large initial attitude errors and uncertain observation noise statistics poses a great challenge for the estimation accuracy of misalignment angles. This study aims to develop a novel robust nonlinear filter, namely the stochastic integration H ∞ filter (SIH ∞ F) for improving both the accuracy and robustness of RTA. In this new nonlinear H ∞ filter, the stochastic spherical-radial integration rule is incorporated with the framework of the derivative-free H ∞ filter for the first time, and the resulting SIH ∞ F simultaneously attenuates the negative effect in estimations caused by significant nonlinearity and large uncertainty. Comparisons between the SIH ∞ F and previously well-known methodologies are carried out by means of numerical simulation and a van test. The results demonstrate that the newly-proposed method outperforms the cubature H ∞ filter. Moreover, the SIH ∞ F inherits the benefit of the traditional stochastic integration filter, but with more robustness in the presence of uncertainty.

A Large-Particle Monte Carlo Code for Simulating Non-Linear High-Energy Processes Near Compact Objects

NASA Technical Reports Server (NTRS)

Stern, Boris E.; Svensson, Roland; Begelman, Mitchell C.; Sikora, Marek

1995-01-01

High-energy radiation processes in compact cosmic objects are often expected to have a strongly non-linear behavior. Such behavior is shown, for example, by electron-positron pair cascades and the time evolution of relativistic proton distributions in dense radiation fields. Three independent techniques have been developed to simulate these non-linear problems: the kinetic equation approach; the phase-space density (PSD) Monte Carlo method; and the large-particle (LP) Monte Carlo method. In this paper, we present the latest version of the LP method and compare it with the other methods. The efficiency of the method in treating geometrically complex problems is illustrated by showing results of simulations of 1D, 2D and 3D systems. The method is shown to be powerful enough to treat non-spherical geometries, including such effects as bulk motion of the background plasma, reflection of radiation from cold matter, and anisotropic distributions of radiating particles. It can therefore be applied to simulate high-energy processes in such astrophysical systems as accretion discs with coronae, relativistic jets, pulsar magnetospheres and gamma-ray bursts.

Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays.

PubMed

Tong, Shao Cheng; Li, Yong Ming; Zhang, Hua-Guang

2011-07-01

In this paper, two adaptive neural network (NN) decentralized output feedback control approaches are proposed for a class of uncertain nonlinear large-scale systems with immeasurable states and unknown time delays. Using NNs to approximate the unknown nonlinear functions, an NN state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping technique with decentralized control design principle, an adaptive NN decentralized output feedback control approach is developed. In order to overcome the problem of "explosion of complexity" inherent in the proposed control approach, the dynamic surface control (DSC) technique is introduced into the first adaptive NN decentralized control scheme, and a simplified adaptive NN decentralized output feedback DSC approach is developed. It is proved that the two proposed control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the observer errors and the tracking errors converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approaches.

Multibody dynamic analysis using a rotation-free shell element with corotational frame

NASA Astrophysics Data System (ADS)

Shi, Jiabei; Liu, Zhuyong; Hong, Jiazhen

2018-03-01

Rotation-free shell formulation is a simple and effective method to model a shell with large deformation. Moreover, it can be compatible with the existing theories of finite element method. However, a rotation-free shell is seldom employed in multibody systems. Using a derivative of rigid body motion, an efficient nonlinear shell model is proposed based on the rotation-free shell element and corotational frame. The bending and membrane strains of the shell have been simplified by isolating deformational displacements from the detailed description of rigid body motion. The consistent stiffness matrix can be obtained easily in this form of shell model. To model the multibody system consisting of the presented shells, joint kinematic constraints including translational and rotational constraints are deduced in the context of geometric nonlinear rotation-free element. A simple node-to-surface contact discretization and penalty method are adopted for contacts between shells. A series of analyses for multibody system dynamics are presented to validate the proposed formulation. Furthermore, the deployment of a large scaled solar array is presented to verify the comprehensive performance of the nonlinear shell model.

Direct numerical simulations of premixed autoignition in compressible uniformly-sheared turbulence

NASA Astrophysics Data System (ADS)

Towery, Colin; Darragh, Ryan; Poludnenko, Alexei; Hamlington, Peter

2017-11-01

High-speed combustion systems, such as scramjet engines, operate at high temperatures and pressures, extremely short combustor residence times, very high rates of shear stress, and intense turbulent mixing. As a result, the reacting flow can be premixed and have highly-compressible turbulence fluctuations. We investigate the effects of compressible turbulence on the ignition delay time, heat-release-rate (HRR) intermittency, and mode of autoignition of premixed Hydrogen-air fuel in uniformly-sheared turbulence using new three-dimensional direct numerical simulations with a multi-step chemistry mechanism. We analyze autoignition in both the Eulerian and Lagrangian reference frames at eight different turbulence Mach numbers, Mat , spanning the quasi-isentropic, linear thermodynamic, and nonlinear compressibility regimes, with eddy shocklets appearing in the nonlinear regime. Results are compared to our previous study of premixed autoignition in isotropic turbulence at the same Mat and with a single-step reaction mechanism. This previous study found large decreases in delay times and large increases in HRR intermittency between the linear and nonlinear compressibility regimes and that detonation waves could form in both regimes.

Topologically nontrivial black holes in Lovelock-Born-Infeld gravity

NASA Astrophysics Data System (ADS)

Farhangkhah, N.

2018-04-01

We present the black hole solutions possessing horizon with nonconstant-curvature and additional scalar restrictions on the base manifold in Lovelock gravity coupled to Born-Infeld (BI) nonlinear electrodynamics. The asymptotic and near origin behavior of the metric is presented and we analyze different behaviors of the singularity. We find that, in contrast to the case of black hole solutions of BI-Lovelock gravity with constant curvature horizon and Maxwell-Lovelock gravity with non constant horizon which have only timelike singularities, spacelike, and timelike singularities may exist for BI-Lovelock black holes with nonconstant curvature horizon. By calculating the thermodynamic quantities, we study the effects of nonlinear electrodynamics via the Born-Infeld action. Stability analysis shows that black holes with positive sectional curvature, κ , possess an intermediate unstable phase and large and small black holes are stable. We see that while Ricci flat Lovelock-Born-Infeld black holes having exotic horizons are stable in the presence of Maxwell field or either Born Infeld field with large born Infeld parameter β , unstable phase appears for smaller values of β , and therefore nonlinearity brings in the instability.

Evaluation of on-line pulse control for vibration suppression in flexible spacecraft

NASA Technical Reports Server (NTRS)

Masri, Sami F.

1987-01-01

A numerical simulation was performed, by means of a large-scale finite element code capable of handling large deformations and/or nonlinear behavior, to investigate the suitability of the nonlinear pulse-control algorithm to suppress the vibrations induced in the Spacecraft Control Laboratory Experiment (SCOLE) components under realistic maneuvers. Among the topics investigated were the effects of various control parameters on the efficiency and robustness of the vibration control algorithm. Advanced nonlinear control techniques were applied to an idealized model of some of the SCOLE components to develop an efficient algorithm to determine the optimal locations of point actuators, considering the hardware on the SCOLE project as distributed in nature. The control was obtained from a quadratic optimization criterion, given in terms of the state variables of the distributed system. An experimental investigation was performed on a model flexible structure resembling the essential features of the SCOLE components, and electrodynamic and electrohydraulic actuators were used to investigate the applicability of the control algorithm with such devices in addition to mass-ejection pulse generators using compressed air.

Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

NASA Astrophysics Data System (ADS)

Squire, J.; Quataert, E.; Kunz, M. W.

2017-12-01

In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are very small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI saturates into strong turbulence. Our goal is to better understand how the saturation of the MRI in a low-collisionality plasma might differ from that in the collisional regime. We focus on two key effects: (i) the direct impact of self-induced pressure-anisotropy nonlinearities on the evolution of an MRI mode, and (ii) the influence of pressure anisotropy on the `parasitic instabilities' that are suspected to cause the mode to break up into turbulence. Our main conclusions are: (i) The mirror instability regulates the pressure anisotropy in such a way that the linear MRI in a collisionless plasma is an approximate nonlinear solution once the mode amplitude becomes larger than the background field (just as in magnetohyrodynamics). This implies that differences between the collisionless and collisional MRI become unimportant at large amplitudes. (ii) The break up of large-amplitude MRI modes into turbulence via parasitic instabilities is similar in collisionless and collisional plasmas. Together, these conclusions suggest that the route to magnetorotational turbulence in a collisionless plasma may well be similar to that in a collisional plasma, as suggested by recent kinetic simulations. As a supplement to these findings, we offer guidance for the design of future kinetic simulations of magnetorotational turbulence.

A discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions

NASA Astrophysics Data System (ADS)

Rahmouni, A.; Beidouri, Z.; Benamar, R.

2013-09-01

The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the previously developed models of geometrically nonlinear vibrations of Euler-Bernoulli continuous beams, and multidof system models made of N masses placed at the end of elastic bars connected by linear spiral springs, presenting the beam flexural rigidity. The validation of the new model via the analysis of the convergence conditions of the nonlinear frequencies obtained by the N-dof system, when N increases, and those obtained in previous works using a continuous description of the beam. In addition to the above points, the models developed in the present work, may constitute, in our opinion, a good illustration, from the didactic point of view, of the origin of the geometrical nonlinearity induced by large transverse vibration amplitudes of constrained continuous beams, which may appear as a Pythagorean Theorem effect. The first step of the work presented here was the formulation of the problem of nonlinear vibrations of the discrete system shown in Fig. 1 in terms of the semi-analytical method, denoted as SAA, developed in the early 90's by Benamar and coauthors [3], and discussed for example in [6,7]. This method has been applied successfully to various types of geometrically nonlinear problems of structural dynamics [1-3,6-8,10-12] and the objective here was to use it in order to develop a flexible discrete nonlinear model which may be useful for presenting in further works geometrically nonlinear vibrations of real beams with discontinuities in the mass, the section, or the stiffness distributions. The purpose in the present work was restricted to developing and validating the model, via comparison of the obtained dependence of the resonance frequencies of such a system on the amplitude of vibration, with the results obtained previously by continuous beams nonlinear models. In the SAA method, the dynamic system under consideration is described by the mass matrix [M], the rigidity matrix [K], and the nonlinear rigidity matrix [B], which depends on the amplitude of vibration, and involves a fourth-order nonlinearity tensor bijkl. Details are given below, corresponding to the definition of the tensors mentioned above. The analogy between the classical continuous Euler-Bernoulli model of beams and the present discrete model is developed, leading to the expressions for the equivalent spiral and axial stiffness, in terms of the continuous beam geometrical and mechanical characteristics. Some numerical results are also given, showing the amplitude dependence of the frequencies on the amplitude of vibration, and compared to the backbone curves obtained previously by the continuous nonlinear classical beam theory, presented for example in [3,5,8,15-22]. A convergence study is performed by increasing the number of masses and bars, showing a good convergence to the theoretical values of continuous beams.

Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1988-01-01

The nonlinear reaction between two oblique 3-D Tollmein-Schlichting (TS) waves and their induced streamwise-vortex flow is considered theoretically for an imcompressible boundary layer. The same theory applies to the destabilization of an incident vortex motion by subharmonic TS waves, followed by interaction. The scales and flow structure involved are addressed for high Reynolds numbers. The nonlionear interaction is powerful, starting at quite low amplitudes with a triple-deck structure for the TS waves but a large-scale structure for the induced vortex, after which strong nonlinear amplification occurs. This includes nonparallel-flow effects. The nonlinear interaction is governed by a partial differential system for the vortex flow coupled with an ordinary-differential one for the TS pressure. The solution properties found sometimes produce a breakup within a finite distance and sometimes further downstream, depending on the input amplitudes upstream and on the wave angles, and that then leads to the second stages of interaction associated with higher amplitudes, the main second stages giving either long-scale phenomena significantly affected by nonparallelism or shorter quasi-parallel ones governed by the full nonlinear triple-deck response.

Dynamic modeling of moment wheel assemblies with nonlinear rolling bearing supports

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Luo, Ruizhi; Qing, Tao

2017-10-01

Moment wheel assemblies (MWA) have been widely used in spacecraft attitude control and large angle slewing maneuvers over the years. Understanding and controlling vibration of MWAs is a crucial factor to achieving the desired level of payload performance. Dynamic modeling of a MWA with nonlinear rolling bearing supports is conducted. An improved load distribution analysis is proposed to more accurately obtain the contact deformations and angles between the rolling balls and raceways. Then, the bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. The effects of preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication could all be reflected in the nonlinear bearing forces. Considering the mass imbalances of the flywheel, flexibility of supporting structures and rolling bearing nonlinearity, the dynamic model of a typical MWA is established based upon the energy theorem. Dynamic tests are conducted to verify the nonlinear dynamic model. The influences of flywheel mass eccentricity and inner/outer waviness amplitudes on the dynamic responses are discussed in detail. The obtained results would be useful for the design and vibration control of the MWA system.

Influence of mechanically-induced dilatation on the shape memory behavior of amorphous polymers at large deformation

NASA Astrophysics Data System (ADS)

Hanzon, Drew W.; Lu, Haibao; Yakacki, Christopher M.; Yu, Kai

2018-01-01

In this study, we explore the influence of mechanically-induced dilatation on the thermomechanical and shape memory behavior of amorphous shape memory polymers (SMPs) at large deformation. The uniaxial tension, glass transition, stress relaxation and free recovery behaviors are examined with different strain levels (up to 340% engineering strain). A multi-branched constitutive model that incorporates dilatational effects on the polymer relaxation time is established and applied to assist in discussions and understand the nonlinear viscoelastic behaviors of SMPs. It is shown that the volumetric dilatation results in an SMP network with lower viscosity, faster relaxation, and lower Tg. The influence of the dilatational effect on the thermomechanical behaviors is significant when the polymers are subject to large deformation or in a high viscosity state. The dilation also increases the free recovery rate of SMP at a given recovery temperature. Even though the tested SMPs are far beyond their linear viscoelastic region when a large programming strain is applied, the free recovery behavior still follows the time-temperature superposition (TTSP) if the dilatational effect is considered during the transformation of time scales; however, if the programming strain is different, TTSP fails in predicting the recovery behavior of SMPs because the network has different entropy state and driving force during shape recovery. Since most soft active polymers are subject to large deformation in practice, this study provides a theoretical basis to better understand their nonlinear viscoelastic behaviors, and optimize their performance in engineering applications.

Nonlinear effects on electrophoresis of a charged dielectric nanoparticle in a charged hydrogel medium

NASA Astrophysics Data System (ADS)

Bhattacharyya, S.; De, Simanta

2016-09-01

The impact of the solid polarization of a charged dielectric particle in gel electrophoresis is studied without imposing a weak-field or a thin Debye length assumption. The electric polarization of a dielectric particle due to an external electric field creates a non-uniform surface charge density, which in turn creates a non-uniform Debye layer at the solid-gel interface. The solid polarization of the particle, the polarization of the double layer, and the electro-osmosis of mobile ions within the hydrogel medium create a nonlinear effect on the electrophoresis. We have incorporated those nonlinear effects by considering the electrokinetics governed by the Stokes-Brinkman-Nernst-Planck-Poisson equations. We have computed the governing nonlinear coupled set of equations numerically by adopting a finite volume based iterative algorithm. Our numerical method is tested for accuracy by comparing with several existing results on free-solution electrophoresis as well as results based on the Debye-Hückel approximation. Our computed result shows that the electrophoretic velocity decreases with the rise of the particle dielectric permittivity constant and attains a saturation limit at large values of permittivity. A significant impact of the solid polarization is found in gel electrophoresis compared to the free-solution electrophoresis.

Alcohol outlet density and assault: a spatial analysis.

PubMed

Livingston, Michael

2008-04-01

A large number of studies have found links between alcohol outlet densities and assault rates in local areas. This study tests a variety of specifications of this link, focusing in particular on the possibility of a non-linear relationship. Cross-sectional data on police-recorded assaults during high alcohol hours, liquor outlets and socio-demographic characteristics were obtained for 223 postcodes in Melbourne, Australia. These data were used to construct a series of models testing the nature of the relationship between alcohol outlet density and assault, while controlling for socio-demographic factors and spatial auto-correlation. Four types of relationship were examined: a normal linear relationship between outlet density and assault, a non-linear relationship with potential threshold or saturation densities, a relationship mediated by the socio-economic status of the neighbourhood and a relationship which takes into account the effect of outlets in surrounding neighbourhoods. The model positing non-linear relationships between outlet density and assaults was found to fit the data most effectively. An increasing accelerating effect for the density of hotel (pub) licences was found, suggesting a plausible upper limit for these licences in Melbourne postcodes. The study finds positive relationships between outlet density and assault rates and provides evidence that this relationship is non-linear and thus has critical values at which licensing policy-makers can impose density limits.

A parametrisation of modified gravity on nonlinear cosmological scales

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lombriser, Lucas, E-mail: llo@roe.ac.uk

2016-11-01

Viable modifications of gravity on cosmological scales predominantly rely on screening mechanisms to recover Einstein's Theory of General Relativity in the Solar System, where it has been well tested. A parametrisation of the effects of such modifications in the spherical collapse model is presented here for the use of modelling the modified nonlinear cosmological structure. The formalism allows an embedding of the different screening mechanisms operating in scalar-tensor theories through large values of the gravitational potential or its first or second derivatives as well as of linear suppression effects or more general transitions between modified and Einstein gravity limits. Eachmore » screening or suppression mechanism is parametrised by a time, mass, and environment dependent screening scale, an effective modified gravitational coupling in the fully unscreened limit that can be matched to linear theory, the exponent of a power-law radial profile of the screened coupling, determined by derivatives, symmetries, and potentials in the scalar field equation, and an interpolation rate between the screened and unscreened limits. Along with generalised perturbative methods, the parametrisation may be used to formulate a nonlinear extension to the linear parametrised post-Friedmannian framework to enable generalised tests of gravity with the wealth of observations from the nonlinear cosmological regime.« less

Design rules for quasi-linear nonlinear optical structures

NASA Astrophysics Data System (ADS)

Lytel, Richard; Mossman, Sean M.; Kuzyk, Mark G.

2015-09-01

The maximization of the intrinsic optical nonlinearities of quantum structures for ultrafast applications requires a spectrum scaling as the square of the energy eigenstate number or faster. This is a necessary condition for an intrinsic response approaching the fundamental limits. A second condition is a design generating eigenstates whose ground and lowest excited state probability densities are spatially separated to produce large differences in dipole moments while maintaining a reasonable spatial overlap to produce large off-diagonal transition moments. A structure whose design meets both conditions will necessarily have large first or second hyperpolarizabilities. These two conditions are fundamental heuristics for the design of any nonlinear optical structure.

Resonant and Nonresonant Nonlinear Optical Spectroscopy of CDSE Quantum Dots for Nonlinear Photonic Applications

DTIC Science & Technology

2006-11-01

Temple D., Yoo K. P., Kim S. Y., Mott A., Namkung M., and Jung S. S., 2003: Large and pure refractive nonlinearity of nanostructure silica ... aerogel , Appl. Phys. Lett., 82(25), 4444-4446. [18] Sun W., Patton T., Stultz L., andClaude J. P., 2003: Resonant third-order nonlinearities of tetrakis

A first approach to the distortion analysis of nonlinear analog circuits utilizing X-parameters

NASA Astrophysics Data System (ADS)

Weber, H.; Widemann, C.; Mathis, W.

2013-07-01

In this contribution a first approach to the distortion analysis of nonlinear 2-port-networks with X-parameters1 is presented. The X-parameters introduced by Verspecht and Root (2006) offer the possibility to describe nonlinear microwave 2-port-networks under large signal conditions. On the basis of X-parameter measurements with a nonlinear network analyzer (NVNA) behavioral models can be extracted for the networks. These models can be used to consider the nonlinear behavior during the design process of microwave circuits. The idea of the present work is to extract the behavioral models in order to describe the influence of interfering signals on the output behavior of the nonlinear circuits. Hereby, a simulator is used instead of a NVNA to extract the X-parameters. Assuming that the interfering signals are relatively small compared to the nominal input signal, the output signal can be described as a superposition of the effects of each input signal. In order to determine the functional correlation between the scattering variables, a polynomial dependency is assumed. The required datasets for the approximation of the describing functions are simulated by a directional coupler model in Cadence Design Framework. The polynomial coefficients are obtained by a least-square method. The resulting describing functions can be used to predict the system's behavior under certain conditions as well as the effects of the interfering signal on the output signal. 1 X-parameter is a registered trademark of Agilent Technologies, Inc.

Fully nonlinear development of the most unstable goertler vortex in a three dimensional boundary layer

NASA Technical Reports Server (NTRS)

Otto, S. R.; Bassom, Andrew P.

1992-01-01

The nonlinear development is studied of the most unstable Gortler mode within a general 3-D boundary layer upon a suitably concave surface. The structure of this mode was first identified by Denier, Hall and Seddougui (1991) who demonstrated that the growth rate of this instability is O(G sup 3/5) where G is the Gortler number (taken to be large here), which is effectively a measure of the curvature of the surface. Previous researchers have described the fate of the most unstable mode within a 2-D boundary layer. Denier and Hall (1992) discussed the fully nonlinear development of the vortex in this case and showed that the nonlinearity causes a breakdown of the flow structure. The effect of crossflow and unsteadiness upon an infinitesimal unstable mode was elucidated by Bassom and Hall (1991). They demonstrated that crossflow tends to stabilize the most unstable Gortler mode, and for certain crossflow/frequency combinations the Gortler mode may be made neutrally stable. These vortex configurations naturally lend themselves to a weakly nonlinear stability analysis; work which is described in a previous article by the present author. Here we extend the ideas of Denier and Hall (1992) to the three-dimensional boundary layer problem. It is found that the numerical solution of the fully nonlinear equations is best conducted using a method which is essentially an adaption of that utilized by Denier and Hall (1992). The influence of crossflow and unsteadiness upon the breakdown of the flow is described.

Topology optimization of hyperelastic structures using a level set method

NASA Astrophysics Data System (ADS)

Chen, Feifei; Wang, Yiqiang; Wang, Michael Yu; Zhang, Y. F.

2017-12-01

Soft rubberlike materials, due to their inherent compliance, are finding widespread implementation in a variety of applications ranging from assistive wearable technologies to soft material robots. Structural design of such soft and rubbery materials necessitates the consideration of large nonlinear deformations and hyperelastic material models to accurately predict their mechanical behaviour. In this paper, we present an effective level set-based topology optimization method for the design of hyperelastic structures that undergo large deformations. The method incorporates both geometric and material nonlinearities where the strain and stress measures are defined within the total Lagrange framework and the hyperelasticity is characterized by the widely-adopted Mooney-Rivlin material model. A shape sensitivity analysis is carried out, in the strict sense of the material derivative, where the high-order terms involving the displacement gradient are retained to ensure the descent direction. As the design velocity enters into the shape derivative in terms of its gradient and divergence terms, we develop a discrete velocity selection strategy. The whole optimization implementation undergoes a two-step process, where the linear optimization is first performed and its optimized solution serves as the initial design for the subsequent nonlinear optimization. It turns out that this operation could efficiently alleviate the numerical instability and facilitate the optimization process. To demonstrate the validity and effectiveness of the proposed method, three compliance minimization problems are studied and their optimized solutions present significant mechanical benefits of incorporating the nonlinearities, in terms of remarkable enhancement in not only the structural stiffness but also the critical buckling load.

Algebraic and adaptive learning in neural control systems

NASA Astrophysics Data System (ADS)

Ferrari, Silvia

A systematic approach is developed for designing adaptive and reconfigurable nonlinear control systems that are applicable to plants modeled by ordinary differential equations. The nonlinear controller comprising a network of neural networks is taught using a two-phase learning procedure realized through novel techniques for initialization, on-line training, and adaptive critic design. A critical observation is that the gradients of the functions defined by the neural networks must equal corresponding linear gain matrices at chosen operating points. On-line training is based on a dual heuristic adaptive critic architecture that improves control for large, coupled motions by accounting for actual plant dynamics and nonlinear effects. An action network computes the optimal control law; a critic network predicts the derivative of the cost-to-go with respect to the state. Both networks are algebraically initialized based on prior knowledge of satisfactory pointwise linear controllers and continue to adapt on line during full-scale simulations of the plant. On-line training takes place sequentially over discrete periods of time and involves several numerical procedures. A backpropagating algorithm called Resilient Backpropagation is modified and successfully implemented to meet these objectives, without excessive computational expense. This adaptive controller is as conservative as the linear designs and as effective as a global nonlinear controller. The method is successfully implemented for the full-envelope control of a six-degree-of-freedom aircraft simulation. The results show that the on-line adaptation brings about improved performance with respect to the initialization phase during aircraft maneuvers that involve large-angle and coupled dynamics, and parameter variations.

Application of nonlinear rheology to assess the effect of secondary nanofiller on network structure of hybrid polymer nanocomposites

NASA Astrophysics Data System (ADS)

Kamkar, Milad; Aliabadian, Ehsan; Shayesteh Zeraati, Ali; Sundararaj, Uttandaraman

2018-02-01

Carbon nanotube (CNT)/polymer nanocomposites exhibit excellent electrical properties by forming a percolated network. Adding a secondary filler can significantly affect the CNTs' network, resulting in changing the electrical properties. In this work, we investigated the effect of adding manganese dioxide nanowires (MnO2NWs) as a secondary nanofiller on the CNTs' network structure inside a poly(vinylidene fluoride) (PVDF) matrix. Incorporating MnO2NWs to PVDF/CNT samples produced a better state of dispersion of CNTs, as corroborated by light microscopy and transmission electron microscopy. The steady shear and oscillatory shear flows were employed to obtain a better insight into the nanofiller structure and viscoelastic behavior of the nanocomposites. The transient response under steady shear flow revealed that the stress overshoot of hybrid nanocomposites (two-fillers), PVDF/CNT/MnO2NWs, increased dramatically in comparison to binary nanocomposites (single-filler), PVDF/CNT and PVDF/MnO2NWs. This can be attributed to microstructural changes. Large amplitude oscillatory shear characterization was also performed to further investigate the effect of the secondary nanofiller on the nonlinear viscoelastic behavior of the samples. The nonlinear rheological observations were explained using quantitative nonlinear parameters [strain-stiffening ratio (S) and shear-thickening ratio (T)] and Lissajous-Bowditch plots. Results indicated that a more rigid nanofiller network was formed for the hybrid nanocomposites due to the better dispersion state of CNTs and this led to a more nonlinear viscoelastic behavior.

Mechano-optic logic gate controlled by third-order nonlinear optical properties in a rotating ZnO:Au thin film

NASA Astrophysics Data System (ADS)

Carrillo-Delgado, C.; García-Gil, C. I.; Trejo-Valdez, M.; Torres-Torres, C.; García-Merino, J. A.; Martínez-Gutiérrez, H.; Khomenko, A. V.; Torres-Martínez, R.

2016-01-01

Measurements of the third-order nonlinear optical properties exhibited by a ZnO thin solid film deposited on a SnO2 substrate are presented. The samples were prepared by a spray pyrolysis processing route. Scanning electron microscopy analysis and UV-Vis spectroscopy studies were carried out. The picosecond response at 1064 nm was explored by the z-scan technique. A large optical Kerr effect with two-photon absorption was obtained. The inhibition of the nonlinear optical absorption together with a noticeable enhancement in the optical Kerr effect in the sample was achieved by the incorporation of Au nanoparticles into the ZnO film. Additionally, a two-wave mixing configuration at 532 nm was performed and an optical Kerr effect was identified as the main cause of the nanosecond third-order optical nonlinearity. The relaxation time of the photothermal response of the sample was estimated to be about 1 s when the sample was excited by nanosecond single-shots. The rotation of the sample during the nanosecond two-wave mixing experiments was analyzed. It was stated that a non-monotonic relation between rotating frequency and pulse repetition rate governs the thermal contribution to the nonlinear refractive index exhibited by a rotating film. Potential applications for switching photothermal interactions in rotating samples can be contemplated. A rotary logic system dependent on Kerr transmittance in a two-wave mixing experiment was proposed.

An effective description of dark matter and dark energy in the mildly non-linear regime

DOE PAGES

Lewandowski, Matthew; Maleknejad, Azadeh; Senatore, Leonardo

2017-05-18

In the next few years, we are going to probe the low-redshift universe with unprecedented accuracy. Among the various fruits that this will bear, it will greatly improve our knowledge of the dynamics of dark energy, though for this there is a strong theoretical preference for a cosmological constant. We assume that dark energy is described by the so-called Effective Field Theory of Dark Energy, which assumes that dark energy is the Goldstone boson of time translations. Such a formalism makes it easy to ensure that our signatures are consistent with well-established principles of physics. Since most of the informationmore » resides at high wavenumbers, it is important to be able to make predictions at the highest wavenumber that is possible. Furthermore, the Effective Field Theory of Large-Scale Structure (EFTofLSS) is a theoretical framework that has allowed us to make accurate predictions in the mildly non-linear regime. In this paper, we derive the non-linear equations that extend the EFTofLSS to include the effect of dark energy both on the matter fields and on the biased tracers. For the specific case of clustering quintessence, we then perturbatively solve to cubic order the resulting non-linear equations and construct the one-loop power spectrum of the total density contrast.« less

Dynamic updating atlas for heart segmentation with a nonlinear field-based model.

PubMed

Cai, Ken; Yang, Rongqian; Yue, Hongwei; Li, Lihua; Ou, Shanxing; Liu, Feng

2017-09-01

Segmentation of cardiac computed tomography (CT) images is an effective method for assessing the dynamic function of the heart and lungs. In the atlas-based heart segmentation approach, the quality of segmentation usually relies upon atlas images, and the selection of those reference images is a key step. The optimal goal in this selection process is to have the reference images as close to the target image as possible. This study proposes an atlas dynamic update algorithm using a scheme of nonlinear deformation field. The proposed method is based on the features among double-source CT (DSCT) slices. The extraction of these features will form a base to construct an average model and the created reference atlas image is updated during the registration process. A nonlinear field-based model was used to effectively implement a 4D cardiac segmentation. The proposed segmentation framework was validated with 14 4D cardiac CT sequences. The algorithm achieved an acceptable accuracy (1.0-2.8 mm). Our proposed method that combines a nonlinear field-based model and dynamic updating atlas strategies can provide an effective and accurate way for whole heart segmentation. The success of the proposed method largely relies on the effective use of the prior knowledge of the atlas and the similarity explored among the to-be-segmented DSCT sequences. Copyright © 2016 John Wiley & Sons, Ltd.

An effective description of dark matter and dark energy in the mildly non-linear regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewandowski, Matthew; Maleknejad, Azadeh; Senatore, Leonardo

In the next few years, we are going to probe the low-redshift universe with unprecedented accuracy. Among the various fruits that this will bear, it will greatly improve our knowledge of the dynamics of dark energy, though for this there is a strong theoretical preference for a cosmological constant. We assume that dark energy is described by the so-called Effective Field Theory of Dark Energy, which assumes that dark energy is the Goldstone boson of time translations. Such a formalism makes it easy to ensure that our signatures are consistent with well-established principles of physics. Since most of the informationmore » resides at high wavenumbers, it is important to be able to make predictions at the highest wavenumber that is possible. Furthermore, the Effective Field Theory of Large-Scale Structure (EFTofLSS) is a theoretical framework that has allowed us to make accurate predictions in the mildly non-linear regime. In this paper, we derive the non-linear equations that extend the EFTofLSS to include the effect of dark energy both on the matter fields and on the biased tracers. For the specific case of clustering quintessence, we then perturbatively solve to cubic order the resulting non-linear equations and construct the one-loop power spectrum of the total density contrast.« less

An effective description of dark matter and dark energy in the mildly non-linear regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewandowski, Matthew; Senatore, Leonardo; Maleknejad, Azadeh, E-mail: matthew.lewandowski@cea.fr, E-mail: azade@ipm.ir, E-mail: senatore@stanford.edu

In the next few years, we are going to probe the low-redshift universe with unprecedented accuracy. Among the various fruits that this will bear, it will greatly improve our knowledge of the dynamics of dark energy, though for this there is a strong theoretical preference for a cosmological constant. We assume that dark energy is described by the so-called Effective Field Theory of Dark Energy, which assumes that dark energy is the Goldstone boson of time translations. Such a formalism makes it easy to ensure that our signatures are consistent with well-established principles of physics. Since most of the informationmore » resides at high wavenumbers, it is important to be able to make predictions at the highest wavenumber that is possible. The Effective Field Theory of Large-Scale Structure (EFTofLSS) is a theoretical framework that has allowed us to make accurate predictions in the mildly non-linear regime. In this paper, we derive the non-linear equations that extend the EFTofLSS to include the effect of dark energy both on the matter fields and on the biased tracers. For the specific case of clustering quintessence, we then perturbatively solve to cubic order the resulting non-linear equations and construct the one-loop power spectrum of the total density contrast.« less

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.

PubMed

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-01

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential.

SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

1999-03-01

This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples ofmore » the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.« less

DEPENDENCE OF STELLAR MAGNETIC ACTIVITY CYCLES ON ROTATIONAL PERIOD IN A NONLINEAR SOLAR-TYPE DYNAMO

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pipin, V. V.; Kosovichev, A. G.

2016-06-01

We study the turbulent generation of large-scale magnetic fields using nonlinear dynamo models for solar-type stars in the range of rotational periods from 14 to 30 days. Our models take into account nonlinear effects of dynamical quenching of magnetic helicity, and escape of magnetic field from the dynamo region due to magnetic buoyancy. The results show that the observed correlation between the period of rotation and the duration of activity cycles can be explained in the framework of a distributed dynamo model with a dynamical magnetic feedback acting on the turbulent generation from either magnetic buoyancy or magnetic helicity. Wemore » discuss implications of our findings for the understanding of dynamo processes operating in solar-like stars.« less

Achieving nonlinear optical modulation via four-wave mixing in a four-level atomic system

NASA Astrophysics Data System (ADS)

Li, Hai-Chao; Ge, Guo-Qin; Zubairy, M. Suhail

2018-05-01

We propose an accessible scheme for implementing tunable nonlinear optical amplification and attenuation via a synergetic mechanism of four-wave mixing (FWM) and optical interference in a four-level ladder-type atomic system. By constructing a cyclic atom-field interaction, we show that two reverse FWM processes can coexist via optical transitions in different branches. In the suitable input-field conditions, strong interference effects between the input fields and the generated FWM fields can be induced and result in large amplification and deep attenuation of the output fields. Moreover, such an optical modulation from enhancement to suppression can be controlled by tuning the relative phase. The quantum system can be served as a switchable optical modulator with potential applications in quantum nonlinear optics.

A parametric study of variables that affect fiber microbuckling initiation in composite laminates. I - Analyses. II - Experiments

NASA Technical Reports Server (NTRS)

Guynn, E. G.; Ochoa, Ozden O.; Bradley, Walter L.

1992-01-01

The effects of the stacking sequence (orientation of plies adjacent to the 0-deg plies), free surfaces, fiber/matrix interfacial bond strength, initial fiber waviness, resin-rich regions, and nonlinear shear constitutive behavior of the resin on the initiation of fiber microbuckling in thermoplastic composites were investigated using nonlinear geometric and nonlinear 2D finite-element analyses. Results show that reductions in the resin shear tangent modulus, large amplitudes of the initial fiber waviness, and debonds each cause increases in the localized matrix shear strains; these increases lead in turn to premature initiation of fiber microbuckling. The numerical results are compared to experimental data obtained using three thermoplastic composite material systems: (1) commercial APC-2, (2) QUADRAX Unidirectional Interlaced Tape, and AU4U/PEEK.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Yunliang; International Centre for Advanced Studies in Physical Sciences and Institute for Theoretical Physics, Faculty of Physics and Astronomy, Ruhr University Bochum, D-44780 Bochum; Lü, Xiaoxia

A theoretical and numerical study of the modulational instability of large amplitude quantum magnetosonic waves (QMWs) in a relativistically degenerate plasma is presented. A modified nonlinear Schrödinger equation is derived by using the reductive perturbation method. The modulational instability regions of the QMWs and the corresponding growth rates are significantly affected by the relativistic degeneracy parameter, the Pauli spin magnetization effects, and the equilibrium magnetic field. The dynamics and nonlinear saturation of the modulational instability of QMWs are investigated numerically. It is found that the increase of the relativistic degeneracy parameter can increase the growth rate of the instability, andmore » the system is saturated nonlinearly by the formation of envelope solitary waves. The current investigation may have relevance to astrophysical magnetized compact objects, such as white dwarfs and pulsar magnetospheres.« less

Ultra-flattened nearly-zero dispersion and ultrahigh nonlinear slot silicon photonic crystal fibers with ultrahigh birefringence

NASA Astrophysics Data System (ADS)

Liao, Jianfei; Xie, Yingmao; Wang, Xinghua; Li, Dongbo; Huang, Tianye

2017-07-01

A slot silicon photonic crystal fiber (PCF) is proposed to simultaneously achieve ultrahigh birefringence, large nonlinearity and ultra-flattened nearly-zero dispersion over a wide wavelength range. By taking advantage on the slot effect, ultrahigh birefringence up to 0.0736 and ultrahigh nonlinear coefficient up to 211.48 W-1 m-1 for quasi-TE mode can be obtained at the wavelength of 1.55 μm. Moreover, ultra-flattened dispersion of 0.49 ps/(nm km) for quasi-TE mode can be achieved over a 180 nm wavelength range with low dispersion slope of 1.85 × 10-3 ps/(nm2 km) at 1.55 μm. Leveraging on these advantages, the proposed slot PCF has great potential for efficient all-optical signal processing applications.

Nonlinear effects of group size on the success of wolves hunting elk

USGS Publications Warehouse

MacNulty, D.R.; Smith, D.W.; Mech, L.D.; Vucetich, J.A.; Packer, C.

2012-01-01

Despite the popular view that social predators live in groups because group hunting facilitates prey capture, the apparent tendency for hunting success to peak at small group sizes suggests that the formation of large groups is unrelated to prey capture. Few empirical studies, however, have tested for nonlinear relationships between hunting success and group size, and none have demonstrated why success trails off after peaking. Here, we use a unique dataset of observations of individually known wolves (Canis lupus) hunting elk (Cervus elaphus) in Yellowstone National Park to show that the relationship between success and group size is indeed nonlinear and that individuals withholding effort (free riding) is why success does not increase across large group sizes. Beyond 4 wolves, hunting success leveled off, and individual performance (a measure of effort) decreased for reasons unrelated to interference from inept hunters, individual age, or size. But performance did drop faster among wolves with an incentive to hold back, i.e., nonbreeders with no dependent offspring, those performing dangerous predatory tasks, i.e., grabbing and restraining prey, and those in groups of proficient hunters. These results suggest that decreasing performance was free riding and that was why success leveled off in groups with >4 wolves that had superficially appeared to be cooperating. This is the first direct evidence that nonlinear trends in group hunting success reflect a switch from cooperation to free riding. It also highlights how hunting success per se is unlikely to promote formation and maintenance of large groups. ?? 2011 The Author.

Current-Nonlinear Hall Effect and Spin-Orbit Torque Magnetization Switching in a Magnetic Topological Insulator

NASA Astrophysics Data System (ADS)

Yasuda, K.; Tsukazaki, A.; Yoshimi, R.; Kondou, K.; Takahashi, K. S.; Otani, Y.; Kawasaki, M.; Tokura, Y.

2017-09-01

The current-nonlinear Hall effect or second harmonic Hall voltage is widely used as one of the methods for estimating charge-spin conversion efficiency, which is attributed to the magnetization oscillation by spin-orbit torque (SOT). Here, we argue the second harmonic Hall voltage under a large in-plane magnetic field with an in-plane magnetization configuration in magnetic-nonmagnetic topological insulator (TI) heterostructures, Crx (Bi1 -ySby )2 -xTe3 /(Bi1 -ySby )2Te3 , where it is clearly shown that the large second harmonic voltage is governed not by SOT but mainly by asymmetric magnon scattering without macroscopic magnetization oscillation. Thus, this method does not allow an accurate estimation of charge-spin conversion efficiency in TI. Instead, the SOT contribution is exemplified by current pulse induced nonvolatile magnetization switching, which is realized with a current density of 2.5 ×1010 A m-2 , showing its potential as a spintronic material.

Current-Nonlinear Hall Effect and Spin-Orbit Torque Magnetization Switching in a Magnetic Topological Insulator.

PubMed

Yasuda, K; Tsukazaki, A; Yoshimi, R; Kondou, K; Takahashi, K S; Otani, Y; Kawasaki, M; Tokura, Y

2017-09-29

The current-nonlinear Hall effect or second harmonic Hall voltage is widely used as one of the methods for estimating charge-spin conversion efficiency, which is attributed to the magnetization oscillation by spin-orbit torque (SOT). Here, we argue the second harmonic Hall voltage under a large in-plane magnetic field with an in-plane magnetization configuration in magnetic-nonmagnetic topological insulator (TI) heterostructures, Cr_{x}(Bi_{1-y}Sb_{y})_{2-x}Te_{3}/(Bi_{1-y}Sb_{y})_{2}Te_{3}, where it is clearly shown that the large second harmonic voltage is governed not by SOT but mainly by asymmetric magnon scattering without macroscopic magnetization oscillation. Thus, this method does not allow an accurate estimation of charge-spin conversion efficiency in TI. Instead, the SOT contribution is exemplified by current pulse induced nonvolatile magnetization switching, which is realized with a current density of 2.5×10^{10}  A m^{-2}, showing its potential as a spintronic material.

On the secondary instability of Taylor-Goertler vortices to Tollmien-Schlichting waves in fully developed flows

NASA Technical Reports Server (NTRS)

Bennett, James; Hall, Philip

1988-01-01

There are many flows of practical importance where both Tollmien-Schlichting waves and Taylor-Goertler vortices are possible causes of transition to turbulence. The effect of fully nonlinear Taylor-Goertler vortices on the growth of small amplitude Tollmien-Schlichting waves is investigated. The basic state considered is the fully developed flow between concentric cylinders driven by an azimuthal pressure gradient. It is hoped that an investigation of this problem will shed light on the more complicated external boundary layer problem where again both modes of instability exist in the presence of concave curvature. The type of Tollmien-Schlichting waves considered have the asymptotic structure of lower branch modes of plane Poiseuille flow. Whilst instabilities at lower Reynolds number are possible, the latter modes are simpler to analyze and more relevant to the boundary layer problem. The effect of fully nonlinear Taylor-Goertler vortices on both two-dimensional and three-dimensional waves is determined. It is shown that, whilst the maximum growth as a function of frequency is not greatly affected, there is a large destabilizing effect over a large range of frequencies.

On the secondary instability of Taylor-Goertler vortices to Tollmien-Schlichting waves in fully-developed flows

NASA Technical Reports Server (NTRS)

Bennett, James; Hall, Philip

1986-01-01

There are many flows of practical importance where both Tollmien-Schlichting waves and Taylor-Goertler vortices are possible causes of transition to turbulence. The effect of fully nonlinear Taylor-Goertler vortices on the growth of small amplitude Tollmien-Schlichting waves is investigated. The basic state considered is the fully developed flow between concentric cylinders driven by an azimuthal pressure gradient. It is hoped that an investigation of this problem will shed light on the more complicated external boundary layer problem where again both modes of instability exist in the presence of concave curvature. The type of Tollmein-Schlichting waves considered have the asymptotic structure of lower branch modes of plane Poisseulle flow. Whilst instabilities at lower Reynolds number are possible, the latter modes are simpler to analyze and more relevant to the boundary layer problem. The effect of fully nonlinear Taylor-Goertler vortices on both two-dimensional and three-dimensional waves is determined. It is shown that, whilst the maximum growth as a function of frequency is not greatly affected, there is a large destabilizing effect over a large range of frequencies.

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

NASA Technical Reports Server (NTRS)

Buttrill, Carey S.

1989-01-01

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Nonlinear observation of internal states of fuel cell cathode utilizing a high-order sliding-mode algorithm

NASA Astrophysics Data System (ADS)

Xu, Liangfei; Hu, Junming; Cheng, Siliang; Fang, Chuan; Li, Jianqiu; Ouyang, Minggao; Lehnert, Werner

2017-07-01

A scheme for designing a second-order sliding-mode (SOSM) observer that estimates critical internal states on the cathode side of a polymer electrolyte membrane (PEM) fuel cell system is presented. A nonlinear, isothermal dynamic model for the cathode side and a membrane electrolyte assembly are first described. A nonlinear observer topology based on an SOSM algorithm is then introduced, and equations for the SOSM observer deduced. Online calculation of the inverse matrix produces numerical errors, so a modified matrix is introduced to eliminate the negative effects of these on the observer. The simulation results indicate that the SOSM observer performs well for the gas partial pressures and air stoichiometry. The estimation results follow the simulated values in the model with relative errors within ± 2% at stable status. Large errors occur during the fast dynamic processes (<1 s). Moreover, the nonlinear observer shows good robustness against variations in the initial values of the internal states, but less robustness against variations in system parameters. The partial pressures are more sensitive than the air stoichiometry to system parameters. Finally, the order of effects of parameter uncertainties on the estimation results is outlined and analyzed.

Investigation of local strain distribution and linear electro-optic effect in strained silicon waveguides.

PubMed

Chmielak, Bartos; Matheisen, Christopher; Ripperda, Christian; Bolten, Jens; Wahlbrink, Thorsten; Waldow, Michael; Kurz, Heinrich

2013-10-21

We present detailed investigations of the local strain distribution and the induced second-order optical nonlinearity within strained silicon waveguides cladded with a Si₃N₄ strain layer. Micro-Raman Spectroscopy mappings and electro-optic characterization of waveguides with varying width w(WG) show that strain gradients in the waveguide core and the effective second-order susceptibility χ(2)(yyz) increase with reduced w(WG). For 300 nm wide waveguides a mean effective χ(2)(yyz) of 190 pm/V is achieved, which is the highest value reported for silicon so far. To gain more insight into the origin of the extraordinary large optical second-order nonlinearity of strained silicon waveguides numerical simulations of edge induced strain gradients in these structures are presented and discussed.

Non-linear unsteady wing theory, part 1. Quasi two-dimensional behavior: Airfoils and slender wings

NASA Technical Reports Server (NTRS)

Mccune, J. E.

1987-01-01

The initial phases of a study of the large-amplitude unsteady aerodynamics of wings in severe maneuver are reported. The research centers on vortex flows, their initiation at wing surfaces, their subsequent convection, and interaction dynamically with wings and control surfaces. The focus is on 2D and quasi-2D aspects of the problem and features the development of an exact nonlinear unsteady airfoil theory as well as an approach to the crossflow problem for slender wing applications including leading-edge separation. The effective use of interactive on-line computing in quantifying and visualizing the nonsteady effects of severe maneuver is demonstrated. Interactive computational work is now possible, in which a maneuver can be initiated and its effects observed and analyzed immediately.

Design and calibration of a scanning tunneling microscope for large machined surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grigg, D.A.; Russell, P.E.; Dow, T.A.

During the last year the large sample STM has been designed, built and used for the observation of several different samples. Calibration of the scanner for prope dimensional interpretation of surface features has been a chief concern, as well as corrections for non-linear effects such as hysteresis during scans. Several procedures used in calibration and correction of piezoelectric scanners used in the laboratorys STMs are described.

The Buoyancy Budget With a Nonlinear Equation of State

NASA Astrophysics Data System (ADS)

Hieronymus, M. H.; Nycander, J.

2012-12-01

There has been a number of studies focusing on different aspects of having a nonlinear equation of state for seawater. Amongst other things it has been shown that the nonlinear equation of state has implications for the oceanic energy budget and that nonlinear processes can be a significant source of dense water production. This presentation will focus on the oceanic buoyancy budget. The nonlinear equation of state of seawater can introduce a sink or source of buoyancy when water parcels of unequal salinities and temperatures are mixed. A common example is the process known as cabbeling, which is responsible for forming a water mass that is denser than the original constituents in a mixture of two water masses with equal densities but different salinities and temperatures. This presentation will contain quantitative estimates of these nonlinear effects on the buoyancy budget of the global ocean. Because of these nonlinear effects there is a net sink of buoyancy in the oceans interior and the size of this sink can be determined from the buoyancy fluxes at the ocean boundaries. These boundary buoyancy fluxes are calculated using two surface heat flux climatologies one based on in situ measurements, the other on a reanalysis and in both cases using a nonlinear equation of state. The presentation also treats the buoyancy budget in the State of the art ocean model Nucleus for European Modelling of the Ocean (NEMO) and the results from NEMO are seen to be in good agreement with the buoyancy budgets based on the heat flux climatologies. Using the ocean model is a good complement to the surface flux climatologies, because in NEMO the buoyancy fluxes can be evaluated at all vertical model levels. This means that the vertical distribution of the buoyancy sink can be looked into. The results from NEMO shows that in large parts of the ocean the nonlinear buoyancy sink is the largest contribution to the buoyancy budget.

Development of a nonlinear vortex method. [steady and unsteady aerodynamic loads of highly sweptback wings

NASA Technical Reports Server (NTRS)

Kandil, O. A.

1981-01-01

Progress is reported in the development of reliable nonlinear vortex methods for predicting the steady and unsteady aerodynamic loads of highly sweptback wings at large angles of attack. Abstracts of the papers, talks, and theses produced through this research are included. The modified nonlinear discrete vortex method and the nonlinear hybrid vortex method are highlighted.

Application of the concept of dynamic trim control and nonlinear system inverses to automatic control of a vertical attitude takeoff and landing aircraft

NASA Technical Reports Server (NTRS)

Smith, G. A.; Meyer, G.

1981-01-01

A full envelope automatic flight control system based on nonlinear inverse systems concepts has been applied to a vertical attitude takeoff and landing (VATOL) fighter aircraft. A new method for using an airborne digital aircraft model to perform the inversion of a nonlinear aircraft model is presented together with the results of a simulation study of the nonlinear inverse system concept for the vertical-attitude hover mode. The system response to maneuver commands in the vertical attitude was found to be excellent; and recovery from large initial offsets and large disturbances was found to be very satisfactory.

Effect of homogenous-heterogeneous reactions on MHD Prandtl fluid flow over a stretching sheet

NASA Astrophysics Data System (ADS)

Khan, Imad; Malik, M. Y.; Hussain, Arif; Salahuddin, T.

An analysis is performed to explore the effects of homogenous-heterogeneous reactions on two-dimensional flow of Prandtl fluid over a stretching sheet. In present analysis, we used the developed model of homogeneous-heterogeneous reactions in boundary layer flow. The mathematical configuration of presented flow phenomenon yields the nonlinear partial differential equations. Using scaling transformations, the governing partial differential equations (momentum equation and homogenous-heterogeneous reactions equations) are transformed into non-linear ordinary differential equations (ODE's). Then, resulting non-linear ODE's are solved by computational scheme known as shooting method. The quantitative and qualitative manners of concerned physical quantities (velocity, concentration and drag force coefficient) are examined under prescribed physical constrained through figures and tables. It is observed that velocity profile enhances verses fluid parameters α and β while Hartmann number reduced it. The homogeneous and heterogeneous reactions parameters have reverse effects on concentration profile. Concentration profile shows retarding behavior for large values of Schmidt number. Skin fraction coefficient enhances with increment in Hartmann number H and fluid parameter α .

Analysis of Composite Panels Subjected to Thermo-Mechanical Loads

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Peters, Jeanne M.

1999-01-01

The results of a detailed study of the effect of cutout on the nonlinear response of curved unstiffened panels are presented. The panels are subjected to combined temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order, shear deformation, Sanders-Budiansky-type shell theory with the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, as well as in the material properties of the individual layers. Numerical results are presented for cylindrical panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities as well as their sensitivity to changes in the various panel, layer, and micromechanical parameters.

Cylindrical effects on Richtmyer-Meshkov instability for arbitrary Atwood numbers in weakly nonlinear regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, W. H.; He, X. T.; LCP, Institute of Applied Physics and Computational Mathematics, Beijing 100088

2012-07-15

When an incident shock collides with a corrugated interface separating two fluids of different densities, the interface is prone to Richtmyer-Meshkov instability (RMI). Based on the formal perturbation expansion method as well as the potential flow theory, we present a simple method to investigate the cylindrical effects in weakly nonlinear RMI with the transmitted and reflected cylindrical shocks by considering the nonlinear corrections up to fourth order. The cylindrical results associated with the material interface show that the interface expression consists of two parts: the result in the planar system and that from the cylindrical effects. In the limit ofmore » the cylindrical radius tending to infinity, the cylindrical results can be reduced to those in the planar system. Our explicit results show that the cylindrical effects exert an inward velocity on the whole perturbed interface, regardless of bubbles or spikes of the interface. On the one hand, outgoing bubbles are constrained and ingoing spikes are accelerated for different Atwood numbers (A) and mode numbers k'. On the other hand, for ingoing bubbles, when |A|k'{sup 3/2} Less-Than-Or-Equivalent-To 1, bubbles are considerably accelerated especially at the small |A| and k'; otherwise, bubbles are decelerated. For outgoing spikes, when |A|k' Greater-Than-Or-Equivalent-To 1, spikes are dramatically accelerated especially at large |A| and k'; otherwise, spikes are decelerated. Furthermore, the cylindrical effects have a significant influence on the amplitudes of the ingoing spike and bubble for large k'. Thus, it should be included in applications where the cylindrical effects play a role, such as inertial confinement fusion ignition target design.« less

The reduced space Sequential Quadratic Programming (SQP) method for calculating the worst resonance response of nonlinear systems

NASA Astrophysics Data System (ADS)

Liao, Haitao; Wu, Wenwang; Fang, Daining

2018-07-01

A coupled approach combining the reduced space Sequential Quadratic Programming (SQP) method with the harmonic balance condensation technique for finding the worst resonance response is developed. The nonlinear equality constraints of the optimization problem are imposed on the condensed harmonic balance equations. Making use of the null space decomposition technique, the original optimization formulation in the full space is mathematically simplified, and solved in the reduced space by means of the reduced SQP method. The transformation matrix that maps the full space to the null space of the constrained optimization problem is constructed via the coordinate basis scheme. The removal of the nonlinear equality constraints is accomplished, resulting in a simple optimization problem subject to bound constraints. Moreover, second order correction technique is introduced to overcome Maratos effect. The combination application of the reduced SQP method and condensation technique permits a large reduction of the computational cost. Finally, the effectiveness and applicability of the proposed methodology is demonstrated by two numerical examples.

Manipulating Nonlinear Emission and Cooperative Effect of CdSe/ZnS Quantum Dots by Coupling to a Silver Nanorod Complex Cavity

PubMed Central

Nan, Fan; Cheng, Zi-Qiang; Wang, Ya-Lan; Zhang, Qing; Zhou, Li; Yang, Zhong-Jian; Zhong, Yu-Ting; Liang, Shan; Xiong, Qihua; Wang, Qu-Quan

2014-01-01

Colloidal semiconductor quantum dots have three-dimensional confined excitons with large optical oscillator strength and gain. The surface plasmons of metallic nanostructures offer an efficient tool to enhance exciton-exciton coupling and excitation energy transfer at appropriate geometric arrangement. Here, we report plasmon-mediated cooperative emissions of approximately one monolayer of ensemble CdSe/ZnS quantum dots coupled with silver nanorod complex cavities at room temperature. Power-dependent spectral shifting, narrowing, modulation, and amplification are demonstrated by adjusting longitudinal surface plasmon resonance of silver nanorods, reflectivity and phase shift of silver nanostructured film, and mode spacing of the complex cavity. The underlying physical mechanism of the nonlinear excitation energy transfer and nonlinear emissions are further investigated and discussed by using time-resolved photoluminescence and finite-difference time-domain numerical simulations. Our results suggest effective strategies to design active plasmonic complex cavities for cooperative emission nanodevices based on semiconductor quantum dots. PMID:24787617

Effects of joints in truss structures

NASA Technical Reports Server (NTRS)

Ikegami, R.

1988-01-01

The response of truss-type structures for future space applications, such as Large Deployable Reflector (LDR), will be directly affected by joint performance. Some of the objectives of research at BAC were to characterize structural joints, establish analytical approaches that incorporate joint characteristics, and experimentally establish the validity of the analytical approaches. The test approach to characterize joints for both erectable and deployable-type structures was based upon a Force State Mapping Technique. The approach pictorially shows how the nonlinear joint results can be used for equivalent linear analysis. Testing of the Space Station joints developed at LaRC (a hinged joint at 2 Hz and a clevis joint at 2 Hz) successfully revealed the nonlinear characteristics of the joints. The Space Station joints were effectively linear when loaded to plus or minus 500 pounds with a corresponding displacement of about plus or minus 0.0015 inch. It was indicated that good linear joints exist which are compatible with errected structures, but that difficulty may be encountered if nonlinear-type joints are incorporated in the structure.

Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings

NASA Astrophysics Data System (ADS)

Cunha, Americo; Soize, Christian; Sampaio, Rubens

2015-11-01

This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bit-rock interaction model are taken into account using a parametric probabilistic approach. Numerical simulations have shown that the mechanical system of interest has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits.

Tunneling induced absorption with competing Nonlinearities.

PubMed

Peng, Yandong; Yang, Aihong; Xu, Yan; Wang, Peng; Yu, Yang; Guo, Hongju; Ren, Tingqi

2016-12-13

We investigate tunneling induced nonlinear absorption phenomena in a coupled quantum-dot system. Resonant tunneling causes constructive interference in the nonlinear absorption that leads to an increase of more than an order of magnitude over the maximum absorption in a coupled quantum dot system without tunneling. Resonant tunneling also leads to a narrowing of the linewidth of the absorption peak to a sublinewidth level. Analytical expressions show that the enhanced nonlinear absorption is largely due to the fifth-order nonlinear term. Competition between third- and fifth-order nonlinearities leads to an anomalous dispersion of the total susceptibility.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seljak, Uroš, E-mail: useljak@berkeley.edu

On large scales a nonlinear transformation of matter density field can be viewed as a biased tracer of the density field itself. A nonlinear transformation also modifies the redshift space distortions in the same limit, giving rise to a velocity bias. In models with primordial nongaussianity a nonlinear transformation generates a scale dependent bias on large scales. We derive analytic expressions for the large scale bias, the velocity bias and the redshift space distortion (RSD) parameter β, as well as the scale dependent bias from primordial nongaussianity for a general nonlinear transformation. These biases can be expressed entirely in termsmore » of the one point distribution function (PDF) of the final field and the parameters of the transformation. The analysis shows that one can view the large scale bias different from unity and primordial nongaussianity bias as a consequence of converting higher order correlations in density into 2-point correlations of its nonlinear transform. Our analysis allows one to devise nonlinear transformations with nearly arbitrary bias properties, which can be used to increase the signal in the large scale clustering limit. We apply the results to the ionizing equilibrium model of Lyman-α forest, in which Lyman-α flux F is related to the density perturbation δ via a nonlinear transformation. Velocity bias can be expressed as an average over the Lyman-α flux PDF. At z = 2.4 we predict the velocity bias of -0.1, compared to the observed value of −0.13±0.03. Bias and primordial nongaussianity bias depend on the parameters of the transformation. Measurements of bias can thus be used to constrain these parameters, and for reasonable values of the ionizing background intensity we can match the predictions to observations. Matching to the observed values we predict the ratio of primordial nongaussianity bias to bias to have the opposite sign and lower magnitude than the corresponding values for the highly biased galaxies, but this depends on the model parameters and can also vanish or change the sign.« less

Nonlinear optical microscopy for immunoimaging: a custom optimized system of high-speed, large-area, multicolor imaging

PubMed Central

Li, Hui; Cui, Quan; Zhang, Zhihong; Luo, Qingming

2015-01-01

Background The nonlinear optical microscopy has become the current state-of-the-art for intravital imaging. Due to its advantages of high resolution, superior tissue penetration, lower photodamage and photobleaching, as well as intrinsic z-sectioning ability, this technology has been widely applied in immunoimaging for a decade. However, in terms of monitoring immune events in native physiological environment, the conventional nonlinear optical microscope system has to be optimized for live animal imaging. Generally speaking, three crucial capabilities are desired, including high-speed, large-area and multicolor imaging. Among numerous high-speed scanning mechanisms used in nonlinear optical imaging, polygon scanning is not only linearly but also dispersion-freely with high stability and tunable rotation speed, which can overcome disadvantages of multifocal scanning, resonant scanner and acousto-optical deflector (AOD). However, low frame rate, lacking large-area or multicolor imaging ability make current polygonbased nonlinear optical microscopes unable to meet the requirements of immune event monitoring. Methods We built up a polygon-based nonlinear optical microscope system which was custom optimized for immunoimaging with high-speed, large-are and multicolor imaging abilities. Results Firstly, we validated the imaging performance of the system by standard methods. Then, to demonstrate the ability to monitor immune events, migration of immunocytes observed by the system based on typical immunological models such as lymph node, footpad and dorsal skinfold chamber are shown. Finally, we take an outlook for the possible advance of related technologies such as sample stabilization and optical clearing for more stable and deeper intravital immunoimaging. Conclusions This study will be helpful for optimizing nonlinear optical microscope to obtain more comprehensive and accurate information of immune events. PMID:25694951

Approaches to nonlinear cointegration with a view towards applications in SHM

NASA Astrophysics Data System (ADS)

Cross, E. J.; Worden, K.

2011-07-01

One of the major problems confronting the application of Structural Health Monitoring (SHM) to real structures is that of divorcing the effect of environmental changes from those imposed by damage. A recent development in this area is the import of the technique of cointegration from the field of econometrics. While cointegration is a mature technology within economics, its development has been largely concerned with linear time-series analysis and this places a severe constraint on its application - particularly in the new context of SHM where damage can often make a given structure nonlinear. The objective of the current paper is to introduce two possible approaches to nonlinear cointegration: the first is an optimisation-based method; the second is a variation of the established Johansen procedure based on the use of an augmented basis. Finally, the ideas of nonlinear cointegration will be explored through application to real SHM data from the benchmark project on the Z24 Highway Bridge.

How Artificial Should the Treatment of a Plasma's Viscosity Be?

NASA Astrophysics Data System (ADS)

Whitney, K. G.; Velikovich, A. L.; Thornhill, J. W.; Davis, J.

1999-11-01

Electron viscosity dominates over ion viscosity and is important in describing the generation of shock fronts in highly ionizable plasmas. The sizes of shock front jumps in electron and ion temperature are determined from the magnitudes of the heat flow vector and pressure tensor, which, in turn, acquire non-negligible nonlinear contributions from the temperature and density gradients when these gradients are large. Thus, a consistent treatment of steep gradient formation in plasmas must come from investigations that include the effects of these nonlinear contributions to heat and momentum transport. Coefficients for each of five nonlinear contributions to the pressure tensor for an (r,z) Z-pinch geometry are presented and discussed in this talk. Hydrodynamic code calculations generally are not designed to provide a testbed for directly evaluating the kinetic energy dissipation that occurs at shock fronts; therefore, the strength of these nonlinear pressure tensor terms will be estimated by post-processing a Z-pinch hydrodynamics calculation and a steady-state planar shock wave calculation.

Electromagnetic fields with vanishing quantum corrections

NASA Astrophysics Data System (ADS)

Ortaggio, Marcello; Pravda, Vojtěch

2018-04-01

We show that a large class of null electromagnetic fields are immune to any modifications of Maxwell's equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any generalized classical electrodynamics containing both non-linear terms and higher derivatives, including, e.g., non-linear electrodynamics as well as QED- and string-motivated effective theories. This result holds not only in a flat or (anti-)de Sitter background, but also in a larger subset of Kundt spacetimes, which allow for the presence of aligned gravitational waves and pure radiation.

Linear and nonlinear acoustic wave propagation in the atmosphere

NASA Technical Reports Server (NTRS)

Hariharan, S. I.; Yu, Ping

1988-01-01

The investigation of the acoustic wave propagation theory and numerical implementation for the situation of an isothermal atmosphere is described. A one-dimensional model to validate an asymptotic theory and a 3-D situation to relate to a realistic situation are considered. In addition, nonlinear wave propagation and the numerical treatment are included. It is known that the gravitational effects play a crucial role in the low frequency acoustic wave propagation. They propagate large distances and, as such, the numerical treatment of those problems become difficult in terms of posing boundary conditions which are valid for all frequencies.

Enhancing the nonlinear thermoelectric response of a correlated quantum dot in the Kondo regime by asymmetrical coupling to the leads

NASA Astrophysics Data System (ADS)

Pérez Daroca, Diego; Roura-Bas, Pablo; Aligia, Armando A.

2018-04-01

We study the low-temperature properties of the differential response of the current to a temperature gradient at finite voltage in a single-level quantum dot including electron-electron interaction, nonsymmetric couplings to the leads, and nonlinear effects. The calculated response is significantly enhanced in setups with large asymmetries between the tunnel couplings. In the investigated range of voltages and temperatures with corresponding energies up to several times the Kondo energy scale, the maximum response is enhanced nearly an order of magnitude with respect to symmetric coupling to the leads.

Renormalization-group theory for the eddy viscosity in subgrid modeling

NASA Technical Reports Server (NTRS)

Zhou, YE; Vahala, George; Hossain, Murshed

1988-01-01

Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.

Nonlinear mechanism for the generation of electromagnetic fields in a magnetized plasma by the beatings of waves

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aburjania, G. D.; Machabeli, G. Z.; Kharshiladze, O. A.

2006-07-15

The modulational instability in a plasma in a strong constant external magnetic field is considered. The plasmon condensate is modulated not by conventional low-frequency ion sound but by the beatings of two high-frequency transverse electromagnetic waves propagating along the magnetic field. The instability reduces the spatial scales of Langmuir turbulence along the external magnetic field and generates electromagnetic fields. It is shown that, for a pump wave with a sufficiently large amplitude, the effect described in the present paper can be a dominant nonlinear process.

Large-scale structure in brane-induced gravity. I. Perturbation theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scoccimarro, Roman

2009-11-15

We study the growth of subhorizon perturbations in brane-induced gravity using perturbation theory. We solve for the linear evolution of perturbations taking advantage of the symmetry under gauge transformations along the extra-dimension to decouple the bulk equations in the quasistatic approximation, which we argue may be a better approximation at large scales than thought before. We then study the nonlinearities in the bulk and brane equations, concentrating on the workings of the Vainshtein mechanism by which the theory becomes general relativity (GR) at small scales. We show that at the level of the power spectrum, to a good approximation, themore » effect of nonlinearities in the modified gravity sector may be absorbed into a renormalization of the gravitational constant. Since the relation between the lensing potential and density perturbations is entirely unaffected by the extra physics in these theories, the modified gravity can be described in this approximation by a single function, an effective gravitational constant for nonrelativistic motion that depends on space and time. We develop a resummation scheme to calculate it, and provide predictions for the nonlinear power spectrum. At the level of the large-scale bispectrum, the leading order corrections are obtained by standard perturbation theory techniques, and show that the suppression of the brane-bending mode leads to characteristic signatures in the non-Gaussianity generated by gravity, generic to models that become GR at small scales through second-derivative interactions. We compare the predictions in this work to numerical simulations in a companion paper.« less

Nonlinear Delta-f Simulations of Collective Effects in Intense Charged Particle Beams

NASA Astrophysics Data System (ADS)

Qin, Hong

2002-11-01

A nonlinear delta-f particle simulation method based on the Vlasov-Maxwell equations has been recently developed to study collective processes in high-intensity beams, where space-charge and magnetic self-field effects play a critical role in determining the nonlinear beam dynamics. Implemented in the Beam Equilibrium, Stability and Transport (BEST) code, the nonlinear delta-f method provides a low-noise and self-consistent tool for simulating collective interactions and nonlinear dynamics of high-intensity beams in modern and next- generation accelerators and storage rings, such as the Spallation Neutron Source, and heavy ion fusion drivers. Simulation results for the electron-proton two-stream instability in the Proton Storage Ring (PSR) experiment at Los Alamos National Laboratory agree well with experimental observations. Large-scale parallel simulations have also been carried out for the ion-electron two-stream instability in the very high-intensity heavy ion beams envisioned for heavy ion fusion applications. In both cases, the simulation results indicate that the dominant two-stream instability has a dipole-mode (hose-like) structure and can be stabilized by a modest axial momentum spread of the beam particles of less than 0.25collective processes in high-intensity beams, such as anisotropy-driven instabilities, collective eigenmode excitations for perturbations about stable beam equilibria, and the Darwin model for fully electromagnetic perturbations will also be discussed.

Nonlinear coupling of flow harmonics: Hexagonal flow and beyond

NASA Astrophysics Data System (ADS)

Giacalone, Giuliano; Yan, Li; Ollitrault, Jean-Yves

2018-05-01

Higher Fourier harmonics of anisotropic flow (v4 and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one and allows us to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at s =2.76 TeV, we perform an application of our formalism to hexagonal flow, v6, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient χ624, which couples v6 to v2 and v4. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, and higher order moments recently analyzed by the ALICE Collaboration. The value of χ624 extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher order harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of v7 and v8.

Curved Displacement Transfer Functions for Geometric Nonlinear Large Deformation Structure Shape Predictions

NASA Technical Reports Server (NTRS)

Ko, William L.; Fleischer, Van Tran; Lung, Shun-Fat

2017-01-01

For shape predictions of structures under large geometrically nonlinear deformations, Curved Displacement Transfer Functions were formulated based on a curved displacement, traced by a material point from the undeformed position to deformed position. The embedded beam (depth-wise cross section of a structure along a surface strain-sensing line) was discretized into multiple small domains, with domain junctures matching the strain-sensing stations. Thus, the surface strain distribution could be described with a piecewise linear or a piecewise nonlinear function. The discretization approach enabled piecewise integrations of the embedded-beam curvature equations to yield the Curved Displacement Transfer Functions, expressed in terms of embedded beam geometrical parameters and surface strains. By entering the surface strain data into the Displacement Transfer Functions, deflections along each embedded beam can be calculated at multiple points for mapping the overall structural deformed shapes. Finite-element linear and nonlinear analyses of a tapered cantilever tubular beam were performed to generate linear and nonlinear surface strains and the associated deflections to be used for validation. The shape prediction accuracies were then determined by comparing the theoretical deflections with the finiteelement- generated deflections. The results show that the newly developed Curved Displacement Transfer Functions are very accurate for shape predictions of structures under large geometrically nonlinear deformations.

Highly nonlinear sub-micron silicon nitride trench waveguide coated with gold nanoparticles

NASA Astrophysics Data System (ADS)

Huang, Yuewang; Zhao, Qiancheng; Sharac, Nicholas; Ragan, Regina; Boyraz, Ozdal

2015-05-01

We demonstrate the fabrication of a highly nonlinear sub-micron silicon nitride trench waveguide coated with gold nanoparticles for plasmonic enhancement. The average enhancement effect is evaluated by measuring the spectral broadening effect caused by self-phase-modulation. The nonlinear refractive index n2 was measured to be 7.0917×10-19 m2/W for a waveguide whose Wopen is 5 μm. Several waveguides at different locations on one wafer were measured in order to take the randomness of the nanoparticle distribution into consideration. The largest enhancement is measured to be as high as 10 times. Fabrication of this waveguide started with a MEMS grade photomask. By using conventional optical lithography, the wide linewidth was transferred to a <100> wafer. Then the wafer was etched anisotropically by potassium hydroxide (KOH) to engrave trapezoidal trenches with an angle of 54.7º. Side wall roughness was mitigated by KOH etching and thermal oxidation that was used to generate a buffer layer for silicon nitride waveguide. The guiding material silicon nitride was then deposited by low pressure chemical vapor deposition. The waveguide was then patterned with a chemical template, with 20 nm gold particles being chemically attached to the functionalized poly(methyl methacrylate) domains. Since the particles attached only to the PMMA domains, they were confined to localized regions, therefore forcing the nanoparticles into clusters of various numbers and geometries. Experiments reveal that the waveguide has negligible nonlinear absorption loss, and its nonlinear refractive index can be greatly enhanced by gold nano clusters. The silicon nitride trench waveguide has large nonlinear refractive index, rendering itself promising for nonlinear applications.

Optics and Nonlinear Buckling Mechanics in Large-Area, Highly Stretchable Arrays of Plasmonic Nanostructures.

PubMed

Gao, Li; Zhang, Yihui; Zhang, Hui; Doshay, Sage; Xie, Xu; Luo, Hongying; Shah, Deesha; Shi, Yan; Xu, Siyi; Fang, Hui; Fan, Jonathan A; Nordlander, Peter; Huang, Yonggang; Rogers, John A

2015-06-23

Large-scale, dense arrays of plasmonic nanodisks on low-modulus, high-elongation elastomeric substrates represent a class of tunable optical systems, with reversible ability to shift key optical resonances over a range of nearly 600 nm at near-infrared wavelengths. At the most extreme levels of mechanical deformation (strains >100%), nonlinear buckling processes transform initially planar arrays into three-dimensional configurations, in which the nanodisks rotate out of the plane to form linear arrays with "wavy" geometries. Analytical, finite-element, and finite-difference time-domain models capture not only the physics of these buckling processes, including all of the observed modes, but also the quantitative effects of these deformations on the plasmonic responses. The results have relevance to mechanically tunable optical systems, particularly to soft optical sensors that integrate on or in the human body.

Persistent model order reduction for complex dynamical systems using smooth orthogonal decomposition

NASA Astrophysics Data System (ADS)

Ilbeigi, Shahab; Chelidze, David

2017-11-01

Full-scale complex dynamic models are not effective for parametric studies due to the inherent constraints on available computational power and storage resources. A persistent reduced order model (ROM) that is robust, stable, and provides high-fidelity simulations for a relatively wide range of parameters and operating conditions can provide a solution to this problem. The fidelity of a new framework for persistent model order reduction of large and complex dynamical systems is investigated. The framework is validated using several numerical examples including a large linear system and two complex nonlinear systems with material and geometrical nonlinearities. While the framework is used for identifying the robust subspaces obtained from both proper and smooth orthogonal decompositions (POD and SOD, respectively), the results show that SOD outperforms POD in terms of stability, accuracy, and robustness.

Mixed Models and Reduction Techniques for Large-Rotation, Nonlinear Analysis of Shells of Revolution with Application to Tires

NASA Technical Reports Server (NTRS)

Noor, A. K.; Andersen, C. M.; Tanner, J. A.

1984-01-01

An effective computational strategy is presented for the large-rotation, nonlinear axisymmetric analysis of shells of revolution. The three key elements of the computational strategy are: (1) use of mixed finite-element models with discontinuous stress resultants at the element interfaces; (2) substantial reduction in the total number of degrees of freedom through the use of a multiple-parameter reduction technique; and (3) reduction in the size of the analysis model through the decomposition of asymmetric loads into symmetric and antisymmetric components coupled with the use of the multiple-parameter reduction technique. The potential of the proposed computational strategy is discussed. Numerical results are presented to demonstrate the high accuracy of the mixed models developed and to show the potential of using the proposed computational strategy for the analysis of tires.

Focusing high-squint and large-baseline one-stationary bistatic SAR data using keystone transform and enhanced nonlinear chirp scaling based on an ellipse model

NASA Astrophysics Data System (ADS)

Zhong, Hua; Zhang, Song; Hu, Jian; Sun, Minhong

2017-12-01

This paper deals with the imaging problem for one-stationary bistatic synthetic aperture radar (BiSAR) with high-squint, large-baseline configuration. In this bistatic configuration, accurate focusing of BiSAR data is a difficult issue due to the relatively large range cell migration (RCM), severe range-azimuth coupling, and inherent azimuth-geometric variance. To circumvent these issues, an enhanced azimuth nonlinear chirp scaling (NLCS) algorithm based on an ellipse model is investigated in this paper. In the range processing, a method combining deramp operation and keystone transform (KT) is adopted to remove linear RCM completely and mitigate range-azimuth cross-coupling. In the azimuth focusing, an ellipse model is established to analyze and depict the characteristic of azimuth-variant Doppler phase. Based on the new model, an enhanced azimuth NLCS algorithm is derived to focus one-stationary BiSAR data. Simulating results exhibited at the end of this paper validate the effectiveness of the proposed algorithm.

Generation of dual-wavelength square pulse in a figure-eight erbium-doped fiber laser with ultra-large net-anomalous dispersion.

PubMed

Shao, Zhihua; Qiao, Xueguang; Rong, Qiangzhou; Su, Dan

2015-08-01

A type of wave-breaking-free mode-locked dual-wavelength square pulse was experimentally observed in a figure-eight erbium-doped fiber laser with ultra-large net-anomalous dispersion. A 2.7 km long single-mode fiber (SMF) was incorporated as a nonlinear optical loop mirror (NOLM) and provided largely nonlinear phase accumulation and anomalous dispersion, which enhanced the four-wave-mixing effect to improve the stability of the dual-wavelength operation. In the NOLM, the long SMF with small birefringence supported the Sagnac interference as a filter to manage the dual-wavelength lasing. The dual-wavelength operation was made switchable by adjusting the intra-cavity polarization loss and phase delay corresponding to two square pulses. When the pump power was increased, the duration of the square pulse increased continuously while the peak pulse power gradually decreased. This square-type pulse can potentially be utilized for signal transmission and sensing.

Do large rate coefficients for ion-polar neutral reactions have a serious effect on chemical models of dense clouds?

NASA Technical Reports Server (NTRS)

Herbst, E.; Leung, C. M.

1986-01-01

In order to incorporate large ion-polar neutral rate coefficients into existing gas phase reaction networks, it is necessary to utilize simplified theoretical treatments because of the significant number of rate coefficients needed. The authors have used two simple theoretical treatments: the locked dipole approach of Moran and Hamill for linear polar neutrals and the trajectory scaling approach of Su and Chesnavich for nonlinear polar neutrals. The former approach is suitable for linear species because in the interstellar medium these are rotationally relaxed to a large extent and the incoming charged reactants can lock their dipoles into the lowest energy configuration. The latter approach is a better approximation for nonlinear neutral species, in which rotational relaxation is normally less severe and the incoming charged reactants are not as effective at locking the dipoles. The treatments are in reasonable agreement with more detailed long range theories and predict an inverse square root dependence on kinetic temperature for the rate coefficient. Compared with the locked dipole method, the trajectory scaling approach results in rate coefficients smaller by a factor of approximately 2.5.

Time-sliced perturbation theory for large scale structure I: general formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blas, Diego; Garny, Mathias; Sibiryakov, Sergey

2016-07-01

We present a new analytic approach to describe large scale structure formation in the mildly non-linear regime. The central object of the method is the time-dependent probability distribution function generating correlators of the cosmological observables at a given moment of time. Expanding the distribution function around the Gaussian weight we formulate a perturbative technique to calculate non-linear corrections to cosmological correlators, similar to the diagrammatic expansion in a three-dimensional Euclidean quantum field theory, with time playing the role of an external parameter. For the physically relevant case of cold dark matter in an Einstein-de Sitter universe, the time evolution ofmore » the distribution function can be found exactly and is encapsulated by a time-dependent coupling constant controlling the perturbative expansion. We show that all building blocks of the expansion are free from spurious infrared enhanced contributions that plague the standard cosmological perturbation theory. This paves the way towards the systematic resummation of infrared effects in large scale structure formation. We also argue that the approach proposed here provides a natural framework to account for the influence of short-scale dynamics on larger scales along the lines of effective field theory.« less

Waveguide structures in anisotropic nonlinear crystals

NASA Astrophysics Data System (ADS)

Li, Da; Hong, Pengda; Meissner, Helmuth E.

2017-02-01

We report on the design and manufacturing parameters of waveguiding structures of anisotropic nonlinear crystals that are employed for harmonic conversions, using Adhesive-Free Bonding (AFB®). This technology enables a full range of predetermined refractive index differences that are essential for the design of single mode or low-mode propagation with high efficiency in anisotropic nonlinear crystals which in turn results in compact frequency conversion systems. Examples of nonlinear optical waveguides include periodically bonded walk-off corrected nonlinear optical waveguides and periodically poled waveguide components, such as lithium triborate (LBO), beta barium borate (β-BBO), lithium niobate (LN), potassium titanyl phosphate (KTP), zinc germanium phosphide (ZGP) and silver selenogallate (AGSE). Simulation of planar LN waveguide shows that when the electric field vector E lies in the k-c plane, the power flow is directed precisely along the propagation direction, demonstrating waveguiding effect in the planar waveguide. Employment of anisotropic nonlinear optical waveguides, for example in combination with AFB® crystalline fiber waveguides (CFW), provides access to the design of a number of novel high power and high efficiency light sources spanning the range of wavelengths from deep ultraviolet (as short as 200 nm) to mid-infrared (as long as about 18 μm). To our knowledge, the technique is the only generally applicable one because most often there are no compatible cladding crystals available to nonlinear optical cores, especially not with an engineer-able refractive index difference and large mode area.

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

NASA Technical Reports Server (NTRS)

Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.

1998-01-01

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Redox control of ferrocene-based complexes with systematically extended π-conjugated connectors: switchable and tailorable second order nonlinear optics.

PubMed

Wang, Wen-Yong; Ma, Na-Na; Sun, Shi-Ling; Qiu, Yong-Qing

2014-03-14

The studies of geometrical structures, thermal stabilities, redox properties, nonlinear responses and optoelectronic properties have been carried out on a series of novel ferrocenyl (Fc) chromophores with the view of assessing their switchable and tailorable second order nonlinear optics (NLO). The use of a constant Fc donor and a 4,4'-bipyridinium acceptor and varied conjugated bridges makes it possible to systematically determine the contribution of organic connectors to chromophore nonlinear optical activities. The structures reveal that both the reduction reactions and organic connectors have a significant influence on 4,4'-bipyridinium. The potential energy surface maps along with plots of reduced density gradient mirror the thermal stabilities of the Fc-based chromophores. The first and second reductions take place preferentially at the 4,4'-bipyridinium moieties. Significantly, the reduction processes result in the molecular switches with large NLO contrast varying from zero or very small to a large value. Moreover, time-dependent density functional theory results indicate that the absorption peaks are mainly attributed to Fc to 4,4'-bipyridinium charge transfer and the mixture of intramolecular charge transfer within the two respective 4,4'-bipyridinium moieties coupled with interlayer charge transfer between the two 4,4'-bipyridinium moieties. This provides us with comprehensive information on the effect of organic connectors on the NLO properties.

An Adaptive Moving Target Imaging Method for Bistatic Forward-Looking SAR Using Keystone Transform and Optimization NLCS.

PubMed

Li, Zhongyu; Wu, Junjie; Huang, Yulin; Yang, Haiguang; Yang, Jianyu

2017-01-23

Bistatic forward-looking SAR (BFSAR) is a kind of bistatic synthetic aperture radar (SAR) system that can image forward-looking terrain in the flight direction of an aircraft. Until now, BFSAR imaging theories and methods for a stationary scene have been researched thoroughly. However, for moving-target imaging with BFSAR, the non-cooperative movement of the moving target induces some new issues: (I) large and unknown range cell migration (RCM) (including range walk and high-order RCM); (II) the spatial-variances of the Doppler parameters (including the Doppler centroid and high-order Doppler) are not only unknown, but also nonlinear for different point-scatterers. In this paper, we put forward an adaptive moving-target imaging method for BFSAR. First, the large and unknown range walk is corrected by applying keystone transform over the whole received echo, and then, the relationships among the unknown high-order RCM, the nonlinear spatial-variances of the Doppler parameters, and the speed of the mover, are established. After that, using an optimization nonlinear chirp scaling (NLCS) technique, not only can the unknown high-order RCM be accurately corrected, but also the nonlinear spatial-variances of the Doppler parameters can be balanced. At last, a high-order polynomial filter is applied to compress the whole azimuth data of the moving target. Numerical simulations verify the effectiveness of the proposed method.

β-Octakis(methylthio)porphycenes: synthesis, characterisation and third order nonlinear optical studies.

PubMed

Rana, Anup; Lee, Sangsu; Kim, Dongho; Panda, Pradeepta K

2015-05-04

A novel electron deficient β-octakis(methylthio)porphycene, along with its Zn(ii) and Ni(ii) derivatives, was synthesized for the first time. The macrocyclic structure exhibits core ruffling with a largely red shifted absorption band (∼750 nm) and also a large enhancement in the third order nonlinear optical response.

The nonlinear evolution of modes on unstable stratified shear layers

NASA Technical Reports Server (NTRS)

Blackaby, Nicholas; Dando, Andrew; Hall, Philip

1993-01-01

The nonlinear development of disturbances in stratified shear flows (having a local Richardson number of value less than one quarter) is considered. Such modes are initially fast growing but, like related studies, we assume that the viscous, non-parallel spreading of the shear layer results in them evolving in a linear fashion until they reach a position where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. Four different basic integro-differential amplitude equations are possible, including one due to a novel mechanism; the relevant choice of amplitude equation, at a particular instance, being dependent on the relative sizes of the disturbance amplitude, the growth rate of the disturbance, its wavenumber, and the viscosity of the fluid. This richness of choice of possible nonlinearities arises mathematically from the indicial Frobenius roots of the governing linear inviscid equation (the Taylor-Goldstein equation) not, in general, differing by an integer. The initial nonlinear evolution of a mode will be governed by an integro-differential amplitude equations with a cubic nonlinearity but the resulting significant increase in the size of the disturbance's amplitude leads on to the next stage of the evolution process where the evolution of the mode is governed by an integro-differential amplitude equations with a quintic nonlinearity. Continued growth of the disturbance amplitude is expected during this stage, resulting in the effects of nonlinearity spreading to outside the critical level, by which time the flow has become fully nonlinear.

Engineered Multifunctional Nanophotonic Materials for Ultrafast Optical Switching

DTIC Science & Technology

2012-11-02

and Co3 + placed at tetrahedral and octahedral sites, respectively. Single -layer thin films of Co3O4 nanoparticles have large optical nonlinearity and...the first two methodologies in systems having weakly resonant structures, including 3-D and/or 1-D photonic crystal structures (i.e. nonlinear Bragg...Nonlinear optical transmission of lead phthalocyanine-doped nematic liquid crystal composites for multiscale nonlinear switching from nanosecond to

Theoretical investigation of the force and dynamically coupled torsional-axial-lateral dynamic response of eared rotors

NASA Technical Reports Server (NTRS)

David, J. W.; Mitchell, L. D.

1982-01-01

Difficulties in solution methodology to be used to deal with the potentially higher nonlinear rotor equations when dynamic coupling is included. A solution methodology is selected to solve the nonlinear differential equations. The selected method was verified to give good results even at large nonlinearity levels. The transfer matrix methodology is extended to the solution of nonlinear problems.

NR-code: Nonlinear reconstruction code

NASA Astrophysics Data System (ADS)

Yu, Yu; Pen, Ue-Li; Zhu, Hong-Ming

2018-04-01

NR-code applies nonlinear reconstruction to the dark matter density field in redshift space and solves for the nonlinear mapping from the initial Lagrangian positions to the final redshift space positions; this reverses the large-scale bulk flows and improves the precision measurement of the baryon acoustic oscillations (BAO) scale.

Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults.

PubMed

Li, Yongming; Ma, Zhiyao; Tong, Shaocheng

2017-09-01

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.

Nonlinear saturation amplitude of cylindrical Rayleigh—Taylor instability

NASA Astrophysics Data System (ADS)

Liu, Wan-Hai; Yu, Chang-Ping; Ye, Wen-Hua; Wang, Li-Feng

2014-09-01

The nonlinear saturation amplitude (NSA) of the fundamental mode in the classical Rayleigh—Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface (r0) and the Atwood number (A) play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the r0/λ (λ is the perturbation wavelength), the larger the NSA of the fundamental mode. When r0/λ is large enough (r0 ≫ λ), the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.

An efficient nonlinear Feshbach engine

NASA Astrophysics Data System (ADS)

Li, Jing; Fogarty, Thomás; Campbell, Steve; Chen, Xi; Busch, Thomas

2018-01-01

We investigate a thermodynamic cycle using a Bose-Einstein condensate (BEC) with nonlinear interactions as the working medium. Exploiting Feshbach resonances to change the interaction strength of the BEC allows us to produce work by expanding and compressing the gas. To ensure a large power output from this engine these strokes must be performed on a short timescale, however such non-adiabatic strokes can create irreversible work which degrades the engine’s efficiency. To combat this, we design a shortcut to adiabaticity which can achieve an adiabatic-like evolution within a finite time, therefore significantly reducing the out-of-equilibrium excitations in the BEC. We investigate the effect of the shortcut to adiabaticity on the efficiency and power output of the engine and show that the tunable nonlinearity strength, modulated by Feshbach resonances, serves as a useful tool to enhance the system’s performance.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Opanchuk, B.; Drummond, P. D.

2013-04-01

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

Symmetry-Breaking Bifurcation in the Nonlinear Schrödinger Equation with Symmetric Potentials

NASA Astrophysics Data System (ADS)

Kirr, E.; Kevrekidis, P. G.; Pelinovsky, D. E.

2011-12-01

We consider the focusing (attractive) nonlinear Schrödinger (NLS) equation with an external, symmetric potential which vanishes at infinity and supports a linear bound state. We prove that the symmetric, nonlinear ground states must undergo a symmetry breaking bifurcation if the potential has a non-degenerate local maxima at zero. Under a generic assumption we show that the bifurcation is either a subcritical or supercritical pitchfork. In the particular case of double-well potentials with large separation, the power of nonlinearity determines the subcritical or supercritical character of the bifurcation. The results are obtained from a careful analysis of the spectral properties of the ground states at both small and large values for the corresponding eigenvalue parameter.

Nonlinear absorption in biological tissue for high intensity focused ultrasound.

PubMed

Liu, Xiaozhou; Li, Junlun; Gong, Xiufen; Zhang, Dong

2006-12-22

In recent years the propagation of the high intensity focused ultrasound (HIFU) in biological tissue is an interesting area due to its potential applications in non-invasive treatment of disease. The base principle of these applications is the heat effect generated by ultrasound absorption. In order to control therapeutic efficiency, it is important to evaluate the heat generation in biological tissue irradiated by ultrasound. In his paper, based on the Khokhlov-Zabolotkaya-Kuznetsov (KZK) equation in frequency-domain, the numerical simulations of nonlinear absorption in biological tissues for high intensity focused ultrasound are performed. We find that ultrasound thermal transfer effect will be enhanced with the increasing of initial acoustic intensity due to the high harmonic generation. The concept of extra absorption factor is introduced to describe nonlinear absorption in biological tissue for HIFU. The theoretical results show that the heat deposition induced by the nonlinear theory can be nearly two times as large as that predicated by linear theory. Then, the influence of the diffraction effect on the position of the focus in HIFU is investigated. It is shown that the sound focus moves toward the transducer compared with the geometry focus because of the diffraction of the sound wave. The position of the maximum heat deposition is shifted to the geometry focus with the increase of initial acoustic intensity because the high harmonics are less diffraction. Finally, the temperature in the porcine fat tissue changing with the time is predicated by Pennes' equation and the experimental results verify the nonlinear theoretical prediction.

Capillary waves in the subcritical nonlinear Schroedinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kozyreff, G.

2010-01-15

We expand recent results on the nonlinear Schroedinger equation with cubic-quintic nonlinearity to show that some solutions are described by the Bernoulli equation in the presence of surface tension. As a consequence, capillary waves are predicted and found numerically at the interface between regions of large and low amplitude.

Linearization of Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.

2009-01-01

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

Tunneling induced absorption with competing Nonlinearities

PubMed Central

Peng, Yandong; Yang, Aihong; Xu, Yan; Wang, Peng; Yu, Yang; Guo, Hongju; Ren, Tingqi

2016-01-01

We investigate tunneling induced nonlinear absorption phenomena in a coupled quantum-dot system. Resonant tunneling causes constructive interference in the nonlinear absorption that leads to an increase of more than an order of magnitude over the maximum absorption in a coupled quantum dot system without tunneling. Resonant tunneling also leads to a narrowing of the linewidth of the absorption peak to a sublinewidth level. Analytical expressions show that the enhanced nonlinear absorption is largely due to the fifth-order nonlinear term. Competition between third- and fifth-order nonlinearities leads to an anomalous dispersion of the total susceptibility. PMID:27958303

Annual Review of Research Under the Joint Service Electronics Program.

DTIC Science & Technology

1979-10-01

Contents: Quadratic Optimization Problems; Nonlinear Control; Nonlinear Fault Analysis; Qualitative Analysis of Large Scale Systems; Multidimensional System Theory ; Optical Noise; and Pattern Recognition.

Faraday effect in a short pulse propagating in a resonant medium under an ultra-strong magnetic field

NASA Astrophysics Data System (ADS)

Huang, J. G.; Slavcheva, G.; Hess, O.

2008-04-01

We propose a dynamical model for description of the nonlinear Faraday rotation experienced by a short pulse propagating in a resonant medium subject to an ultra-strong static magnetic field. Under the assumptions of a sufficiently strong external magnetic field, such that the Zeeman splitting of the quantum system energy levels is large compared to the linewidth of the optical transitions involved and the bandwidth of the incident light, the light effectively interacts with a two-level system. Our numerical simulations show that the Faraday effect under these conditions is significantly distinctive from the one caused by weak to moderately strong magnetic field. Nonlinear coherent effects such as inhomogeneous polarization rotation along the pulse duration and an onset of a circularly polarized stimulated emission and coherent ringing have been demonstrated. Some views on the experimental observation of the predicted phenomena are given.

Nonlinear stability of the 1D Boltzmann equation in a periodic box

NASA Astrophysics Data System (ADS)

Wu, Kung-Chien

2018-05-01

We study the nonlinear stability of the Boltzmann equation in the 1D periodic box with size , where is the Knudsen number. The convergence rate is for small time region and exponential for large time region. Moreover, the exponential rate depends on the size of the domain (Knudsen number). This problem is highly nonlinear and hence we need more careful analysis to control the nonlinear term.

Pressure fluctuations beneath turbulent spots and instability wave packets in a hypersonic boundary layer.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beresh, Steven Jay; Casper, Katya M.; Schneider, Steven P.

2010-12-01

The development of turbulent spots in a hypersonic boundary layer was studied on the nozzle wall of the Boeing/AFOSR Mach-6 Quiet Tunnel. Under quiet flow conditions, the nozzle wall boundary layer remains laminar and grows very thick over the long nozzle length. This allows the development of large turbulent spots that can be readily measured with pressure transducers. Measurements of naturally occurring wave packets and developing turbulent spots were made. The peak frequencies of these natural wave packets were in agreement with second-mode computations. For a controlled study, the breakdown of disturbances created by spark and glow perturbations were studiedmore » at similar freestream conditions. The spark perturbations were the most effective at creating large wave packets that broke down into turbulent spots. The flow disturbances created by the controlled perturbations were analyzed to obtain amplitude criteria for nonlinearity and breakdown as well as the convection velocities of the turbulent spots. Disturbances first grew into linear instability waves and then quickly became nonlinear. Throughout the nonlinear growth of the wave packets, large harmonics are visible in the power spectra. As breakdown begins, the peak amplitudes of the instability waves and harmonics decrease into the rising broad-band frequencies. Instability waves are still visible on either side of the growing turbulent spots during this breakdown process.« less

Nonlinear viscoelastic characterization of human vocal fold tissues under large-amplitude oscillatory shear (LAOS)

PubMed Central

Chan, Roger W.

2018-01-01

Viscoelastic shear properties of human vocal fold tissues were previously quantified by the shear moduli (G′ and G″). Yet these small-strain linear measures were unable to describe any nonlinear tissue behavior. This study attempted to characterize the nonlinear viscoelastic response of the vocal fold lamina propria under large-amplitude oscillatory shear (LAOS) with a stress decomposition approach. Human vocal fold cover and vocal ligament specimens from eight subjects were subjected to LAOS rheometric testing with a simple-shear rheometer. The empirical total stress response was decomposed into elastic and viscous stress components, based on odd-integer harmonic decomposition approach with Fourier transform. Nonlinear viscoelastic measures derived from the decomposition were plotted in Pipkin space and as rheological fingerprints to observe the onset of nonlinearity and the type of nonlinear behavior. Results showed that both the vocal fold cover and the vocal ligament experienced intercycle strain softening, intracycle strain stiffening, as well as shear thinning both intercycle and intracycle. The vocal ligament appeared to demonstrate an earlier onset of nonlinearity at phonatory frequencies, and higher sensitivity to changes in frequency and strain. In summary, the stress decomposition approach provided much better insights into the nonlinear viscoelastic behavior of the vocal fold lamina propria than the traditional linear measures. PMID:29780189

Nonlinear viscoelastic characterization of human vocal fold tissues under large-amplitude oscillatory shear (LAOS).

PubMed

Chan, Roger W

2018-05-01

Viscoelastic shear properties of human vocal fold tissues were previously quantified by the shear moduli ( G' and G″ ). Yet these small-strain linear measures were unable to describe any nonlinear tissue behavior. This study attempted to characterize the nonlinear viscoelastic response of the vocal fold lamina propria under large-amplitude oscillatory shear (LAOS) with a stress decomposition approach. Human vocal fold cover and vocal ligament specimens from eight subjects were subjected to LAOS rheometric testing with a simple-shear rheometer. The empirical total stress response was decomposed into elastic and viscous stress components, based on odd-integer harmonic decomposition approach with Fourier transform. Nonlinear viscoelastic measures derived from the decomposition were plotted in Pipkin space and as rheological fingerprints to observe the onset of nonlinearity and the type of nonlinear behavior. Results showed that both the vocal fold cover and the vocal ligament experienced intercycle strain softening, intracycle strain stiffening, as well as shear thinning both intercycle and intracycle. The vocal ligament appeared to demonstrate an earlier onset of nonlinearity at phonatory frequencies, and higher sensitivity to changes in frequency and strain. In summary, the stress decomposition approach provided much better insights into the nonlinear viscoelastic behavior of the vocal fold lamina propria than the traditional linear measures.

Stability investigations of relaxing molecular gas flows. Results and perspectives

NASA Astrophysics Data System (ADS)

Grigor'ev, Yurii N.; Ershov, Igor V.

2017-10-01

This article presents results of systematic investigations of a dissipative effect which manifests itself as the growth of hydrodynamic stability and suppression of turbulence in relaxing molecular gas flows. The effect can be a new way for control stability and laminar turbulent transition in aerodynamic flows. The consideration of suppression of inviscid acoustic waves in 2D shear flows is presented. Nonlinear evolution of large-scale vortices and Kelvin — Helmholtz waves in relaxing shear flows are studied. Critical Reynolds numbers in supersonic Couette flows are calculated analytically and numerically within the framework of both classical linear and nonlinear energy hydrodynamic stability theories. The calculations clearly show that the relaxation process can appreciably delay the laminar-turbulent transition. The aim of this article is to show the new dissipative effect, which can be used for flow control and laminarization.

Nonlinear synthesis of infrasound propagation through an inhomogeneous, absorbing atmosphere.

PubMed

de Groot-Hedlin, C D

2012-08-01

An accurate and efficient method to predict infrasound amplitudes from large explosions in the atmosphere is required for diverse source types, including bolides, volcanic eruptions, and nuclear and chemical explosions. A finite-difference, time-domain approach is developed to solve a set of nonlinear fluid dynamic equations for total pressure, temperature, and density fields rather than acoustic perturbations. Three key features for the purpose of synthesizing nonlinear infrasound propagation in realistic media are that it includes gravitational terms, it allows for acoustic absorption, including molecular vibration losses at frequencies well below the molecular vibration frequencies, and the environmental models are constrained to have axial symmetry, allowing a three-dimensional simulation to be reduced to two dimensions. Numerical experiments are performed to assess the algorithm's accuracy and the effect of source amplitudes and atmospheric variability on infrasound waveforms and shock formation. Results show that infrasound waveforms steepen and their associated spectra are shifted to higher frequencies for nonlinear sources, leading to enhanced infrasound attenuation. Results also indicate that nonlinear infrasound amplitudes depend strongly on atmospheric temperature and pressure variations. The solution for total field variables and insertion of gravitational terms also allows for the computation of other disturbances generated by explosions, including gravity waves.

Nonlinear ultrasonic imaging with X wave

NASA Astrophysics Data System (ADS)

Du, Hongwei; Lu, Wei; Feng, Huanqing

2009-10-01

X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.

Matrix completion by deep matrix factorization.

PubMed

Fan, Jicong; Cheng, Jieyu

2018-02-01

Conventional methods of matrix completion are linear methods that are not effective in handling data of nonlinear structures. Recently a few researchers attempted to incorporate nonlinear techniques into matrix completion but there still exists considerable limitations. In this paper, a novel method called deep matrix factorization (DMF) is proposed for nonlinear matrix completion. Different from conventional matrix completion methods that are based on linear latent variable models, DMF is on the basis of a nonlinear latent variable model. DMF is formulated as a deep-structure neural network, in which the inputs are the low-dimensional unknown latent variables and the outputs are the partially observed variables. In DMF, the inputs and the parameters of the multilayer neural network are simultaneously optimized to minimize the reconstruction errors for the observed entries. Then the missing entries can be readily recovered by propagating the latent variables to the output layer. DMF is compared with state-of-the-art methods of linear and nonlinear matrix completion in the tasks of toy matrix completion, image inpainting and collaborative filtering. The experimental results verify that DMF is able to provide higher matrix completion accuracy than existing methods do and DMF is applicable to large matrices. Copyright © 2017 Elsevier Ltd. All rights reserved.

Enhanced optical nonlinearity and fiber-optical frequency comb controlled by a single atom in a whispering-gallery-mode microtoroid resonator

NASA Astrophysics Data System (ADS)

Li, Jiahua; Zhang, Suzhen; Yu, Rong; Zhang, Duo; Wu, Ying

2014-11-01

Based on a single atom coupled to a fiber-coupled, chip-based microresonator [B. Dayan et al., Science 319, 1062 (2008), 10.1126/science.1152261], we put forward a scheme to generate optical frequency combs at driving laser powers as low as a few nanowatts. Using state-of-the-art experimental parameters, we investigate in detail the influences of different atomic positions and taper-resonator coupling regimes on optical-frequency-comb generation. In addition to numerical simulations demonstrating this effect, a physical explanation of the underlying mechanism is presented. We find that the combination of the atom and the resonator can induce a large third-order nonlinearity which is significantly stronger than Kerr nonlinearity in Kerr frequency combs. Such enhanced nonlinearity can be used to generate optical frequency combs if driven with two continuous-wave control and probe lasers and significantly reduce the threshold of nonlinear optical processes. The comb spacing can be well tuned by changing the frequency beating between the driving control and probe lasers. The proposed method is versatile and can be adopted to different types of resonators, such as microdisks, microspheres, microtoroids or microrings.

Nonlinear optical studies of curcumin metal derivatives with cw laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henari, F. Z., E-mail: fzhenari@rcsi-mub.com; Cassidy, S.

2015-03-30

We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10{sup −7} cm{sup 2}/W and negative nonlinear absorption of the order of 10{sup −6} cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition modelmore » with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated.« less

Improvements in mode-based waveform modeling and application to Eurasian velocity structure

NASA Astrophysics Data System (ADS)

Panning, M. P.; Marone, F.; Kim, A.; Capdeville, Y.; Cupillard, P.; Gung, Y.; Romanowicz, B.

2006-12-01

We introduce several recent improvements to mode-based 3D and asymptotic waveform modeling and examine how to integrate them with numerical approaches for an improved model of upper-mantle structure under eastern Eurasia. The first step in our approach is to create a large-scale starting model including shear anisotropy using Nonlinear Asymptotic Coupling Theory (NACT; Li and Romanowicz, 1995), which models the 2D sensitivity of the waveform to the great-circle path between source and receiver. We have recently improved this approach by implementing new crustal corrections which include a non-linear correction for the difference between the average structure of several large regions from the global model with further linear corrections to account for the local structure along the path between source and receiver (Marone and Romanowicz, 2006; Panning and Romanowicz, 2006). This model is further refined using a 3D implementation of Born scattering (Capdeville, 2005). We have made several recent improvements to this method, in particular introducing the ability to represent perturbations to discontinuities. While the approach treats all sensitivity as linear perturbations to the waveform, we have also experimented with a non-linear modification analogous to that used in the development of NACT. This allows us to treat large accumulated phase delays determined from a path-average approximation non-linearly, while still using the full 3D sensitivity of the Born approximation. Further refinement of shallow regions of the model is obtained using broadband forward finite-difference waveform modeling. We are also integrating a regional Spectral Element Method code into our tomographic modeling, allowing us to move beyond many assumptions inherent in the analytic mode-based approaches, while still taking advantage of their computational efficiency. Illustrations of the effects of these increasingly sophisticated steps will be presented.

Limitations and tradeoffs in synchronization of large-scale networks with uncertain links

PubMed Central

Diwadkar, Amit; Vaidya, Umesh

2016-01-01

The synchronization of nonlinear systems connected over large-scale networks has gained popularity in a variety of applications, such as power grids, sensor networks, and biology. Stochastic uncertainty in the interconnections is a ubiquitous phenomenon observed in these physical and biological networks. We provide a size-independent network sufficient condition for the synchronization of scalar nonlinear systems with stochastic linear interactions over large-scale networks. This sufficient condition, expressed in terms of nonlinear dynamics, the Laplacian eigenvalues of the nominal interconnections, and the variance and location of the stochastic uncertainty, allows us to define a synchronization margin. We provide an analytical characterization of important trade-offs between the internal nonlinear dynamics, network topology, and uncertainty in synchronization. For nearest neighbour networks, the existence of an optimal number of neighbours with a maximum synchronization margin is demonstrated. An analytical formula for the optimal gain that produces the maximum synchronization margin allows us to compare the synchronization properties of various complex network topologies. PMID:27067994

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows.

PubMed

Herault, J; Rincon, F; Cossu, C; Lesur, G; Ogilvie, G I; Longaretti, P-Y

2011-09-01

The nature of dynamo action in shear flows prone to magnetohydrodynamc instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and nonaxisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large-scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understanding the transitional and statistical properties of subcritical magnetorotational turbulence.

Effects of biasing on the galaxy power spectrum at large scales

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beltran Jimenez, Jose; Departamento de Fisica Teorica, Universidad Complutense de Madrid, 28040, Madrid; Durrer, Ruth

2011-05-15

In this paper we study the effect of biasing on the power spectrum at large scales. We show that even though nonlinear biasing does introduce a white noise contribution on large scales, the P(k){proportional_to}k{sup n} behavior of the matter power spectrum on large scales may still be visible and above the white noise for about one decade. We show, that the Kaiser biasing scheme which leads to linear bias of the correlation function on large scales, also generates a linear bias of the power spectrum on rather small scales. This is a consequence of the divergence on small scales ofmore » the pure Harrison-Zeldovich spectrum. However, biasing becomes k dependent if we damp the underlying power spectrum on small scales. We also discuss the effect of biasing on the baryon acoustic oscillations.« less

The Impact of Family Income on Child Achievement: Evidence from the Earned Income Tax Credit. NBER Working Paper No. 14599

ERIC Educational Resources Information Center

Dahl, Gordon; Lochner, Lance

2008-01-01

Past estimates of the effect of family income on child development have often been plagued by endogeneity and measurement error. In this paper, we use two simulated instrumental variables strategies to estimate the causal effect of income on children's math and reading achievement. Our identification derives from the large, non-linear changes in…

Space cryogenics components based on the thermomechanical effect - Vapor-liquid phase separation

NASA Technical Reports Server (NTRS)

Yuan, S. W. K.; Frederking, T. H. K.

1989-01-01

Applications of the thermomechanical effect has been qualified including incorporation in large-scale space systems in the area of vapor-liquid phase separation (VLPS). The theory of the porous-plug phase separator is developed for the limit of a high thermal impedance of the solid-state grains. Extensions of the theory of nonlinear turbulent flow are presented based on experimental results.

Free Electron Laser Theoretical Study.

DTIC Science & Technology

1981-11-30

8217 1 oscillator; 4) finite electron beam pulse effects and parasitic instability growth and saturation. The results of these investigations are...quite large in an oscillator. In order to study these effects as well as those due to the possible growth of parasitic (trapped particles...study harmonic growth and sideband instability in detail has been included in the codo recently. In addition, the nonlinear mechanisms which limit the

The Impact of Family Income on Child Achievement: Evidence from the Earned Income Tax Credit. Discussion Paper No. 1361-09

ERIC Educational Resources Information Center

Dahl, Gordon; Lochner, Lance

2009-01-01

Past estimates of the effect of family income on child development have often been plagued by endogeneity and measurement error. In this paper, we use two simulated instrumental variables strategies to estimate the causal effect of income on children's math and reading achievement. Our identification derives from the large, non-linear changes…

Complex magnetic behaviour and evidence of a superspin glass state in the binary intermetallic compound Er5Pd2

NASA Astrophysics Data System (ADS)

Sharma, Mohit K.; Yadav, Kavita; Mukherjee, K.

2018-05-01

The binary intermetallic compound Er5Pd2 has been investigated using dc and ac magnetic susceptibilities, magnetic memory effect, isothermal magnetization, non-linear dc susceptibility, heat capacity and magnetocaloric effect studies. Interestingly, even though the compound does not show geometrical frustration it undergoes glassy magnetic phase transition below 17.2 K. Investigation of dc magnetization and heat capacity data divulged absence of long-ranged magnetic ordering. Through the magnetic memory effect, time dependent magnetization and ac susceptibility studies it was revealed that the compound undergoes glass-like freezing below 17.2 K. Analysis of frequency dependence of this transition temperature through scaling and Arrhenius law; along with the Mydosh parameter indicate, that the dynamics in Er5Pd2 are due to the presence of strongly interacting superspins rather than individual spins. This phase transition was further investigated by non-linear dc susceptibility and was characterized by static critical exponents γ and δ. Our results indicate that this compound shows the signature of superspin glass at low temperature. Additionally, both conventional and inverse magnetocaloric effect was observed with a large value of magnetic entropy change and relative cooling power. Our results suggest that Er5Pd2 can be classified as a superspin glass system with large magnetocaloric effect.

Global strength assessment in oblique waves of a large gas carrier ship, based on a non-linear iterative method

NASA Astrophysics Data System (ADS)

Domnisoru, L.; Modiga, A.; Gasparotti, C.

2016-08-01

At the ship's design, the first step of the hull structural assessment is based on the longitudinal strength analysis, with head wave equivalent loads by the ships' classification societies’ rules. This paper presents an enhancement of the longitudinal strength analysis, considering the general case of the oblique quasi-static equivalent waves, based on the own non-linear iterative procedure and in-house program. The numerical approach is developed for the mono-hull ships, without restrictions on 3D-hull offset lines non-linearities, and involves three interlinked iterative cycles on floating, pitch and roll trim equilibrium conditions. Besides the ship-wave equilibrium parameters, the ship's girder wave induced loads are obtained. As numerical study case we have considered a large LPG liquefied petroleum gas carrier. The numerical results of the large LPG are compared with the statistical design values from several ships' classification societies’ rules. This study makes possible to obtain the oblique wave conditions that are inducing the maximum loads into the large LPG ship's girder. The numerical results of this study are pointing out that the non-linear iterative approach is necessary for the computation of the extreme loads induced by the oblique waves, ensuring better accuracy of the large LPG ship's longitudinal strength assessment.

A globally convergent LCL method for nonlinear optimization.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Friedlander, M. P.; Saunders, M. A.; Mathematics and Computer Science

2005-01-01

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form 'minimize an augmented Lagrangian function subject to linearized constraints.' Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. Nevertheless, the well-known software package MINOS has proved effective on many large problems. Its success motivates us to derive a related LCL algorithm that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. The new algorithm has been implemented in Matlab, with an optionmore » to use either MINOS or SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a subset of the COPS, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.« less

Generation of 1.5-octave intense infrared pulses by nonlinear interactions in DAST crystal

NASA Astrophysics Data System (ADS)

Vicario, C.; Monoszlai, B.; Arisholm, G.; Hauri, C. P.

2015-09-01

Infrared pulses with large spectral width extending from 1.2 to 3.4 μm are generated in the organic crystal DAST (4-N, N-dimethylamino-4‧-N‧-methylstilbazolium tosylate). The input pulse has a central wavelength of 1.5 μm and 65 fs duration. With 2.8 mJ input energy we obtained up to 700 μJ in the broadened spectrum. The output can be easily scaled up in energy by increasing the crystal size together with the energy and the beam size of the pump. The ultra-broad spectrum is ascribed to cascaded second order processes mediated by the exceptionally large effective χ 2 nonlinearity of DAST, but the shape of the spectrum indicates that a delayed χ 3 process may also be involved. Numerical simulations reproduce the experimental results qualitatively and provide an insight in the mechanisms underlying the asymmetric spectral broadening.

200-W single frequency laser based on short active double clad tapered fiber

NASA Astrophysics Data System (ADS)

Pierre, Christophe; Guiraud, Germain; Yehouessi, Jean-Paul; Santarelli, Giorgio; Boullet, Johan; Traynor, Nicholas; Vincont, Cyril

2018-02-01

High power single frequency lasers are very attractive for a wide range of applications such as nonlinear conversion, gravitational wave sensing or atom trapping. Power scaling in single frequency regime is a challenging domain of research. In fact, nonlinear effect as stimulated Brillouin scattering (SBS) is the primary power limitation in single frequency amplifiers. To mitigate SBS, different well-known techniques has been improved. These techniques allow generation of several hundred of watts [1]. Large mode area (LMA) fibers, transverse acoustically tailored fibers [2], coherent beam combining and also tapered fiber [3] seem to be serious candidates to continue the power scaling. We have demonstrated the generation of stable 200W output power with nearly diffraction limited output, and narrow linewidth (Δν<30kHz) by using a tapered Yb-doped fiber which allow an adiabatic transition from a small purely single mode input to a large core output.

Cosmological Ohm's law and dynamics of non-minimal electromagnetism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hollenstein, Lukas; Jain, Rajeev Kumar; Urban, Federico R., E-mail: lukas.hollenstein@cea.fr, E-mail: jain@cp3.dias.sdu.dk, E-mail: furban@ulb.ac.be

2013-01-01

The origin of large-scale magnetic fields in cosmic structures and the intergalactic medium is still poorly understood. We explore the effects of non-minimal couplings of electromagnetism on the cosmological evolution of currents and magnetic fields. In this context, we revisit the mildly non-linear plasma dynamics around recombination that are known to generate weak magnetic fields. We use the covariant approach to obtain a fully general and non-linear evolution equation for the plasma currents and derive a generalised Ohm law valid on large scales as well as in the presence of non-minimal couplings to cosmological (pseudo-)scalar fields. Due to the sizeablemore » conductivity of the plasma and the stringent observational bounds on such couplings, we conclude that modifications of the standard (adiabatic) evolution of magnetic fields are severely limited in these scenarios. Even at scales well beyond a Mpc, any departure from flux freezing behaviour is inhibited.« less

A Large Signal Model for CMUT Arrays with Arbitrary Membrane Geometries Operating in Non-Collapsed Mode

PubMed Central

Satir, Sarp; Zahorian, Jaime; Degertekin, F. Levent

2014-01-01

A large signal, transient model has been developed to predict the output characteristics of a CMUT array operated in the non-collapse mode. The model is based on separation of the nonlinear electrostatic voltage-to-force relation and the linear acoustic array response. For linear acoustic radiation and crosstalk effects, the boundary element method is used. The stiffness matrix in the vibroacoustics calculations is obtained using static finite element analysis of a single membrane which can have arbitrary geometry and boundary conditions. A lumped modeling approach is used to reduce the order of the system for modeling the transient nonlinear electrostatic actuation. To accurately capture the dynamics of the non-uniform electrostatic force distribution over the CMUT electrode during large deflections, the membrane electrode is divided into patches shaped to match higher order membrane modes, each introducing a variable to the system model. This reduced order nonlinear lumped model is solved in the time domain using Simulink. The model has two linear blocks to calculate the displacement profile of the electrode patches and the output pressure for a given force distribution over the array, respectively. The force to array displacement block uses the linear acoustic model, and the Rayleigh integral is evaluated to calculate the pressure at any field point. Using the model, the transient transmitted pressure can be simulated for different large signal drive signal configurations. The acoustic model is verified by comparison to harmonic FEA in vacuum and fluid for high and low aspect ratio membranes as well as mass-loaded membranes. The overall Simulink model is verified by comparison to transient 3D FEA and experimental results for different large drive signals; and an example for a phased array simulation is given. PMID:24158297

SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.

1998-09-01

This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

A method for exponential propagation of large systems of stiff nonlinear differential equations

NASA Technical Reports Server (NTRS)

Friesner, Richard A.; Tuckerman, Laurette S.; Dornblaser, Bright C.; Russo, Thomas V.

1989-01-01

A new time integrator for large, stiff systems of linear and nonlinear coupled differential equations is described. For linear systems, the method consists of forming a small (5-15-term) Krylov space using the Jacobian of the system and carrying out exact exponential propagation within this space. Nonlinear corrections are incorporated via a convolution integral formalism; the integral is evaluated via approximate Krylov methods as well. Gains in efficiency ranging from factors of 2 to 30 are demonstrated for several test problems as compared to a forward Euler scheme and to the integration package LSODE.

A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

PubMed

Xu, Zhengfu; Bao, Gang

2010-11-01

A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.

NOLM-based all-optical 40 Gbit/s format conversion through sum-frequency generation (SFG) in a PPLN waveguide

NASA Astrophysics Data System (ADS)

Wang, Jian; Sun, Junqiang

2005-11-01

A novel all-optical format conversion scheme from NRZ to RZ based on sum-frequency generation (SFG) in a periodically poled LiNbO 3 (PPLN) waveguide is proposed, using a nonlinear optical loop mirror (NOLM). The conversion mechanism relies on the combination of attenuation and nonlinear phase shift induced on the clockwise signal field during the SFG process. The SFG between pump, and co- and counter- propagating signals in the PPLN waveguide are numerically studied, showing that counter-propagating SFG can be ignored when quasi-phase matching (QPM) for SFG during co-propagating interaction. The nonlinear phase shift induced on the clockwise signal field is analyzed in detail, showing that it is more effective to yield large values for nonlinear phase shift when appropriately phase mismatched for the SFG process. Two tuning schemes are proposed depend on whether the sum-frequency wavelength is variable or fixed. It is found that the latter has a rather wide 3dB signal conversion bandwidth approximately 154nm. Finally, the influence of reversible process of SFG is discussed and the optimum arrangement of pump and signal peak powers is theoretically demonstrated. The result shows that proper power arrangement, pump width, and waveguide length are necessary for achieving a good conversion effect.

Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits.

PubMed

Maiden, Michelle D; Lowman, Nicholas K; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A

2016-04-29

Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.

Sensitivity to Mental Effort and Test-Retest Reliability of Heart Rate Variability Measures in Healthy Seniors

PubMed Central

Mukherjee, Shalini; Yadav, Rajeev; Yung, Iris; Zajdel, Daniel P.; Oken, Barry S.

2011-01-01

Objectives To determine 1) whether heart rate variability (HRV) was a sensitive and reliable measure in mental effort tasks carried out by healthy seniors and 2) whether non-linear approaches to HRV analysis, in addition to traditional time and frequency domain approaches were useful to study such effects. Methods Forty healthy seniors performed two visual working memory tasks requiring different levels of mental effort, while ECG was recorded. They underwent the same tasks and recordings two weeks later. Traditional and 13 non-linear indices of HRV including Poincaré, entropy and detrended fluctuation analysis (DFA) were determined. Results Time domain (especially mean R-R interval/RRI), frequency domain and, among nonlinear parameters- Poincaré and DFA were the most reliable indices. Mean RRI, time domain and Poincaré were also the most sensitive to different mental effort task loads and had the largest effect size. Conclusions Overall, linear measures were the most sensitive and reliable indices to mental effort. In non-linear measures, Poincaré was the most reliable and sensitive, suggesting possible usefulness as an independent marker in cognitive function tasks in healthy seniors. Significance A large number of HRV parameters was both reliable as well as sensitive indices of mental effort, although the simple linear methods were the most sensitive. PMID:21459665

Constant envelope OFDM scheme for 6PolSK-QPSK

NASA Astrophysics Data System (ADS)

Li, Yupeng; Ding, Ding

2018-03-01

A constant envelope OFDM scheme with phase modulator (PM-CE-OFDM) for 6PolSK-QPSK modulation was demonstrated. Performance under large fiber launch power is measured to check its advantages in counteracting fiber nonlinear impairments. In our simulation, PM-CE-OFDM, RF-assisted constant envelope OFDM (RF-CE-OFDM) and conventional OFDM (Con-OFDM) are transmitted through 80 km standard single mode fiber (SSMF) single channel and WDM system. Simulation results confirm that PM-CE-OFDM has best performance in resisting fiber nonlinearity. In addition, benefiting from the simple system structure, the complexity and cost of PM-CE-OFDM system could be reduced effectively.

Vector rectangular-shape laser based on reduced graphene oxide interacting with a long fiber taper.

PubMed

Gao, Lei; Zhu, Tao; Huang, Wei; Zeng, Jing

2014-10-01

A vector dual-wavelength rectangular-shape laser (RSL) based on a long fiber taper deposited with reduced graphene oxide is proposed, where nonlinearity is enhanced due to a large evanescent-field-interacting length and strong field confinement of an 8 mm fiber taper with a waist diameter of 4 μm. Graphene flakes are deposited uniformly on the taper waist with light pressure effect, so this structure guarantees both excellent saturable absorption and high nonlinearity. The RSL with a repetition rate of 7.9 MHz shows fast polarization switching in two orthogonal polarization directions, and temporal and spectral characteristics are investigated.

Large planar maneuvers for articulated flexible manipulators

NASA Technical Reports Server (NTRS)

Huang, Jen-Kuang; Yang, Li-Farn

1988-01-01

An articulated flexible manipulator carried on a translational cart is maneuvered by an active controller to perform certain position control tasks. The nonlinear dynamics of the articulated flexible manipulator are derived and a transformation matrix is formulated to localize the nonlinearities within the inertia matrix. Then a feedback linearization scheme is introduced to linearize the dynamic equations for controller design. Through a pole placement technique, a robust controller design is obtained by properly assigning a set of closed-loop desired eigenvalues to meet performance requirements. Numerical simulations for the articulated flexible manipulators are given to demonstrate the feasibility and effectiveness of the proposed position control algorithms.

The research of radar target tracking observed information linear filter method

NASA Astrophysics Data System (ADS)

Chen, Zheng; Zhao, Xuanzhi; Zhang, Wen

2018-05-01

Aiming at the problems of low precision or even precision divergent is caused by nonlinear observation equation in radar target tracking, a new filtering algorithm is proposed in this paper. In this algorithm, local linearization is carried out on the observed data of the distance and angle respectively. Then the kalman filter is performed on the linearized data. After getting filtered data, a mapping operation will provide the posteriori estimation of target state. A large number of simulation results show that this algorithm can solve above problems effectively, and performance is better than the traditional filtering algorithm for nonlinear dynamic systems.

Nonlinear Analysis in Counseling Research

ERIC Educational Resources Information Center

Balkin, Richard S.; Richey Gosnell, Katelyn M.; Holmgren, Andrew; Osborne, Jason W.

2017-01-01

Nonlinear effects are both underreported and underrepresented in counseling research. We provide a rationale for evaluating nonlinear effects and steps to evaluate nonlinear relationships in counseling research. Two heuristic examples are provided along with discussion of the results and advantages to evaluating nonlinear effects.

Estimating Ω from Galaxy Redshifts: Linear Flow Distortions and Nonlinear Clustering

NASA Astrophysics Data System (ADS)

Bromley, B. C.; Warren, M. S.; Zurek, W. H.

1997-02-01

We propose a method to determine the cosmic mass density Ω from redshift-space distortions induced by large-scale flows in the presence of nonlinear clustering. Nonlinear structures in redshift space, such as fingers of God, can contaminate distortions from linear flows on scales as large as several times the small-scale pairwise velocity dispersion σv. Following Peacock & Dodds, we work in the Fourier domain and propose a model to describe the anisotropy in the redshift-space power spectrum; tests with high-resolution numerical data demonstrate that the model is robust for both mass and biased galaxy halos on translinear scales and above. On the basis of this model, we propose an estimator of the linear growth parameter β = Ω0.6/b, where b measures bias, derived from sampling functions that are tuned to eliminate distortions from nonlinear clustering. The measure is tested on the numerical data and found to recover the true value of β to within ~10%. An analysis of IRAS 1.2 Jy galaxies yields β=0.8+0.4-0.3 at a scale of 1000 km s-1, which is close to optimal given the shot noise and finite size of the survey. This measurement is consistent with dynamical estimates of β derived from both real-space and redshift-space information. The importance of the method presented here is that nonlinear clustering effects are removed to enable linear correlation anisotropy measurements on scales approaching the translinear regime. We discuss implications for analyses of forthcoming optical redshift surveys in which the dispersion is more than a factor of 2 greater than in the IRAS data.

Waveform Design for Wireless Power Transfer

NASA Astrophysics Data System (ADS)

Clerckx, Bruno; Bayguzina, Ekaterina

2016-12-01

Far-field Wireless Power Transfer (WPT) has attracted significant attention in recent years. Despite the rapid progress, the emphasis of the research community in the last decade has remained largely concentrated on improving the design of energy harvester (so-called rectenna) and has left aside the effect of transmitter design. In this paper, we study the design of transmit waveform so as to enhance the DC power at the output of the rectenna. We derive a tractable model of the non-linearity of the rectenna and compare with a linear model conventionally used in the literature. We then use those models to design novel multisine waveforms that are adaptive to the channel state information (CSI). Interestingly, while the linear model favours narrowband transmission with all the power allocated to a single frequency, the non-linear model favours a power allocation over multiple frequencies. Through realistic simulations, waveforms designed based on the non-linear model are shown to provide significant gains (in terms of harvested DC power) over those designed based on the linear model and over non-adaptive waveforms. We also compute analytically the theoretical scaling laws of the harvested energy for various waveforms as a function of the number of sinewaves and transmit antennas. Those scaling laws highlight the benefits of CSI knowledge at the transmitter in WPT and of a WPT design based on a non-linear rectenna model over a linear model. Results also motivate the study of a promising architecture relying on large-scale multisine multi-antenna waveforms for WPT. As a final note, results stress the importance of modeling and accounting for the non-linearity of the rectenna in any system design involving wireless power.

An Analysis of the Macroscopic Tensile Behavior of a Nonlinear Nylon Reinforced Elastomeric Composite System Using MAC/GMC

NASA Technical Reports Server (NTRS)

Assaad, Mahmoud; Arnold, Steven M.

1999-01-01

A special class of composite laminates composed of soft rubbery matrices and stiff reinforcements made of steel wires or synthetic fibers is examined, where each constituent behaves in a nonlinear fashion even in the small strain domain. Composite laminates made of piles stacked at alternating small orientation angles with respect to the applied axial strain are primarily dominated by the nonlinear behavior of the reinforcing fibers. However; composites with large ply orientations or those perpendicular to the loading axis, will approximate the behavior of the matrix phase and respond in even a more complex fashion for arbitrarily stacked piles. The geometric nonlinearity due to small cord rotations during loading was deemed here to have a second order effect and consequently dropped from any consideration. The user subroutine USRMAT within the Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC), was utilized to introduce the constituent material nonlinear behavior. Stress-strain behavior at the macro level was experimentally generated for single and multi ply composites comprised of continuous Nylon-66 reinforcements embedded in a carbon black loaded rubbery matrix. Comparisons between the predicted macro composite behavior and experimental results are excellent when material nonlinearity is included in the analysis. In this paper, a brief review of GMC is provided, along with a description of the nonlinear behavior of the constituents and associated constituent constitutive relations, and the improved macro (or composite) behavior predictions are documented and illustrated.

Nonlinear dynamics of planetary gears using analytical and finite element models

NASA Astrophysics Data System (ADS)

Ambarisha, Vijaya Kumar; Parker, Robert G.

2007-05-01

Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.

Long-term effects of prescribed fire on mixed conifer forest structure in the Sierra Nevada, California

USGS Publications Warehouse

van Mantgem, Phillip J.; Stephenson, Nathan L.; Knapp, Eric; Keeley, Jon E.

2011-01-01

The capacity of prescribed fire to restore forest conditions is often judged by changes in forest structure within a few years following burning. However, prescribed fire might have longer-term effects on forest structure, potentially changing treatment assessments. We examined annual changes in forest structure in five 1 ha old-growth plots immediately before prescribed fire and up to eight years after fire at Sequoia National Park, California. Fire-induced declines in stem density (67% average decrease at eight years post-fire) were nonlinear, taking up to eight years to reach a presumed asymptote. Declines in live stem biomass were also nonlinear, but smaller in magnitude (32% average decrease at eight years post-fire) as most large trees survived the fires. The preferential survival of large trees following fire resulted in significant shifts in stem diameter distributions. Mortality rates remained significantly above background rates up to six years after the fires. Prescribed fire did not have a large influence on the representation of dominant species. Fire-caused mortality appeared to be spatially random, and therefore did not generally alter heterogeneous tree spatial patterns. Our results suggest that prescribed fire can bring about substantial changes to forest structure in old-growth mixed conifer forests in the Sierra Nevada, but that long-term observations are needed to fully describe some measures of fire effects.

Widely-pulsewidth-tunable ultrashort pulse generation from a birefringent carbon nanotube mode-locked fiber laser.

PubMed

Liu, Ya; Zhao, Xin; Liu, Jiansheng; Hu, Guoqing; Gong, Zheng; Zheng, Zheng

2014-08-25

We demonstrate the generation of soliton pulses covering a nearly one order-of-magnitude pulsewidth range from a simple carbon nanotube (CNT) mode-locked fiber laser with birefringence. A polarization-maintaining-fiber-pigtailed, inline polarization beam splitter and its associated birefringence is leveraged to either enable additional nonlinear polarization evolution (NPE) mode-locking effect or result in a bandwidth-tunable Lyot filter, through adjusting the intracavity polarization settings. The large pulsewidth tuning range is achieved by exploiting both the nonlinear CNT-NPE hybrid mode-locking mechanism that narrows the pulses and the linear filtering effect that broadens them. Induced vector soliton pulses with pulsewidth from 360 fs to 3 ps can be generated, and their time-bandwidth products indicate they are close to transform-limited.

Modelling a stochastic HIV model with logistic target cell growth and nonlinear immune response function

NASA Astrophysics Data System (ADS)

Wang, Yan; Jiang, Daqing; Alsaedi, Ahmed; Hayat, Tasawar

2018-07-01

A stochastic HIV viral model with both logistic target cell growth and nonlinear immune response function is formulated to investigate the effect of white noise on each population. The existence of the global solution is verified. By employing a novel combination of Lyapunov functions, we obtain the existence of the unique stationary distribution for small white noises. We also derive the extinction of the virus for large white noises. Numerical simulations are performed to highlight the effect of white noises on model dynamic behaviour under the realistic parameters. It is found that the small intensities of white noises can keep the irregular blips of HIV virus and CTL immune response, while the larger ones force the virus infection and immune response to lose efficacy.

Robust control of the DC-DC boost converter based on the uncertainty and disturbance estimator

NASA Astrophysics Data System (ADS)

Oucheriah, Said

2017-11-01

In this paper, a robust non-linear controller based on the uncertainty and disturbance estimator (UDE) scheme is successfully developed and implemented for the output voltage regulation of the DC-DC boost converter. System uncertainties, external disturbances and unknown non-linear dynamics are lumped as a signal that is accurately estimated using a low-pass filter and their effects are cancelled by the controller. This methodology forms the basis of the UDE-based controller. A simple procedure is also developed that systematically determines the parameters of the controller to meet certain specifications. Using simulation, the effectiveness of the proposed controller is compared against the sliding-mode control (SMC). Experimental tests also show that the proposed controller is robust to system uncertainties, large input and load perturbations.

Large daily stock variation is associated with cardiovascular mortality in two cities of Guangdong, China.

PubMed

Lin, Hualiang; Zhang, Yonghui; Xu, Yanjun; Liu, Tao; Xiao, Jianpeng; Luo, Yuan; Xu, Xiaojun; He, Yanhui; Ma, Wenjun

2013-01-01

The current study aimed to examine the effects of daily change of the Shenzhen Stock Exchange Index on cardiovascular mortality in Guangzhou and Taishan, China. Daily mortality and stock performance data during 2006-2010 were collected to construct the time series for the two cities. A distributed lag non-linear model was utilized to examine the effect of daily stock index changes on cardiovascular mortality after controlling for potential confounding factors. We observed a delayed non-linear effect of the stock index change on cardiovascular mortality: both rising and declining of the stock index were associated with increased cardiovascular deaths. In Guangzhou, the 15-25 lag days cumulative relative risk of an 800 index drop was 2.08 (95% CI: 1.38-3.14), and 2.38 (95% CI: 1.31-4.31) for an 800 stock index increase on the cardiovascular mortality, respectively. In Taishan, the cumulative relative risk over 15-25 days lag was 1.65 (95% CI: 1.13-2.42) for an 800 index drop and 2.08 (95% CI: 1.26-3.42) for an 800 index rising, respectively. Large ups and downs in daily stock index might be important predictor of cardiovascular mortality.

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

NASA Technical Reports Server (NTRS)

Mohler, R. R.

1992-01-01

Research leading to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle of attack aircraft such as the F-18 is discussed. The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis, and simulation were studied in some detail as well. Studies indicated that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in angle of attack. Included here are studies on nonlinear model algorithmic controller design and an analysis of nonlinear system stability using robust stability analysis for linear systems.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Minissale, S.; Yerci, S.; Dal Negro, L.

We investigate the nonlinear optical properties of Si-rich silicon oxide (SRO) and Si-rich silicon nitride (SRN) samples as a function of silicon content, annealing temperature, and excitation wavelength. Using the Z-scan technique, we measure the non-linear refractive index n{sub 2} and the nonlinear absorption coefficient {beta} for a large number of samples fabricated by reactive co-sputtering. Moreover, we characterize the nonlinear optical parameters of SRN in the broad spectral region 1100-1500 nm and show the strongest nonlinearity at 1500 nm. These results demonstrate the potential of the SRN matrix for the engineering of compact devices with enhanced Kerr nonlinearities formore » silicon photonics applications.« less

Nonlinear 2D arm dynamics in response to continuous and pulse-shaped force perturbations.

PubMed

Happee, Riender; de Vlugt, Erwin; van Vliet, Bart

2015-01-01

Ample evidence exists regarding the nonlinearity of the neuromuscular system but linear models are widely applied to capture postural dynamics. This study quantifies the nonlinearity of human arm postural dynamics applying 2D continuous force perturbations (0.2-40 Hz) inducing three levels of hand displacement (5, 15, 45 mm RMS) followed by force-pulse perturbations inducing large hand displacements (up to 250 mm) in a position task (PT) and a relax task (RT) recording activity of eight shoulder and elbow muscles. The continuous perturbation data were used to analyze the 2D endpoint dynamics in the frequency domain and to identify reflexive and intrinsic parameters of a linear neuromuscular shoulder-elbow model. Subsequently, it was assessed to what extent the large displacements in response to force pulses could be predicted from the 'small amplitude' linear neuromuscular model. Continuous and pulse perturbation responses with varying amplitudes disclosed highly nonlinear effects. In PT, a larger continuous perturbation induced stiffening with a factor of 1.5 attributed to task adaptation evidenced by increased co-contraction and reflexive activity. This task adaptation was even more profound in the pulse responses where reflexes and displacements were strongly affected by the presence and amplitude of preceding continuous perturbations. In RT, a larger continuous perturbation resulted in yielding with a factor of 3.8 attributed to nonlinear mechanical properties as no significant reflexive activity was found. Pulse perturbations always resulted in yielding where a model fitted to the preceding 5-mm continuous perturbations predicted only 37% of the recorded peak displacements in RT and 79% in PT. This demonstrates that linear neuromuscular models, identified using continuous perturbations with small amplitudes, strongly underestimate displacements in pulse-shaped (e.g., impact) loading conditions. The data will be used to validate neuromuscular models including nonlinear muscular (e.g., Hill and Huxley) and reflexive components.

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications☆

PubMed Central

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-01-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer. PMID:24829517

Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

PubMed

Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

2014-05-01

An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.

Cascading for Large Effective Third Order Nonlinearities

DTIC Science & Technology

1997-12-18

edited by T. Tamir, H. Bertoni and G. Griffel , (Plenum Press, New York, 1995), p381-9 9. G.I. Stegeman, R. Schiek, G. Krijnen, W. Torruellas, M...Guided Wave Optoelectronics, edited by T. Tamir, H. Bertoni and G. Griffel , (Plenum Press, New York, 1995), 371-9. 10. W.E. Torruellas, Z. Wang, L

Oblique interaction of spatial dark-soliton stripes in nonlocal media.

PubMed

Fischer, Robert; Neshev, Dragomir N; Krolikowski, Wieslaw; Kivshar, Yuri S; Iturbe-Castillo, David; Chavez-Cerda, Sabino; Meneghetti, Mario R; Caetano, Dilson P; Hickman, Jandir M

2006-10-15

We report what we believe to be the first experimental observation of a large spatial lateral shift in the interaction of obliquely oriented spatial dark-soliton stripes. We demonstrate by numerical simulations that this new effect can be attributed to the specific features of optical media with a nonlocal nonlinear response.

Large Enhancement of the Sagnac Effect Based on Nonlinearly Induced Nonreciprocity.

DTIC Science & Technology

1983-05-30

Og4 ,, % 20. ABSTRACT (Continue on reverse side It ne c,&aty and Identify by block number) LL On Back -°. La . -k. DD 1JAN73 1473 EDITION OF ’NOV6S...be published. 8. L. A. Hackel, R. P. Hackel, and S. Ezekiel, Metrologia 13, 141 (1977). Ř. .4

Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.

2001-01-01

Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.

Fluctuations in the DNA double helix

NASA Astrophysics Data System (ADS)

Peyrard, M.; López, S. C.; Angelov, D.

2007-08-01

DNA is not the static entity suggested by the famous double helix structure. It shows large fluctuational openings, in which the bases, which contain the genetic code, are temporarily open. Therefore it is an interesting system to study the effect of nonlinearity on the physical properties of a system. A simple model for DNA, at a mesoscopic scale, can be investigated by computer simulation, in the same spirit as the original work of Fermi, Pasta and Ulam. These calculations raise fundamental questions in statistical physics because they show a temporary breaking of equipartition of energy, regions with large amplitude fluctuations being able to coexist with regions where the fluctuations are very small, even when the model is studied in the canonical ensemble. This phenomenon can be related to nonlinear excitations in the model. The ability of the model to describe the actual properties of DNA is discussed by comparing theoretical and experimental results for the probability that base pairs open an a given temperature in specific DNA sequences. These studies give us indications on the proper description of the effect of the sequence in the mesoscopic model.

Blobs and drift wave dynamics

DOE PAGES

Zhang, Yanzeng; Krasheninnikov, S. I.

2017-09-29

The modified Hasegawa-Mima equation retaining all nonlinearities is investigated from the point of view of the formation of blobs. The linear analysis shows that the amplitude of the drift wave packet propagating in the direction of decreasing background plasma density increases and eventually saturates due to nonlinear effects. Nonlinear modification of the time averaged plasma density profile results in the formation of large amplitude modes locked in the radial direction, but still propagating in the poloidal direction, which resembles the experimentally observed chain of blobs propagating in the poloidal direction. Such specific density profiles, causing the locking of drift waves,more » could form naturally at the edge of tokamak due to a neutral ionization source. Thus, locked modes can grow in situ due to plasma instabilities, e.g., caused by finite resistivity. Furthermore, the modulation instability (in the poloidal direction) of these locked modes can result in a blob-like burst of plasma density.« less

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Opanchuk, B.; Drummond, P. D.

2013-04-15

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such asmore » quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.« less

Optical solitons in nematic liquid crystals: model with saturation effects

NASA Astrophysics Data System (ADS)

Borgna, Juan Pablo; Panayotaros, Panayotis; Rial, Diego; de la Vega, Constanza Sánchez F.

2018-04-01

We study a 2D system that couples a Schrödinger evolution equation to a nonlinear elliptic equation and models the propagation of a laser beam in a nematic liquid crystal. The nonlinear elliptic equation describes the response of the director angle to the laser beam electric field. We obtain results on well-posedness and solitary wave solutions of this system, generalizing results for a well-studied simpler system with a linear elliptic equation for the director field. The analysis of the nonlinear elliptic problem shows the existence of an isolated global branch of solutions with director angles that remain bounded for arbitrary electric field. The results on the director equation are also used to show local and global existence, as well as decay for initial conditions with sufficiently small L 2-norm. For sufficiently large L 2-norm we show the existence of energy minimizing optical solitons with radial, positive and monotone profiles.

Large-Amplitude Long-Wave Instability of a Supersonic Shear Layer

NASA Technical Reports Server (NTRS)

Messiter, A. F.

1995-01-01

For sufficiently high Mach numbers, small disturbances on a supersonic vortex sheet are known to grow in amplitude because of slow nonlinear wave steepening. Under the same external conditions, linear theory predicts slow growth of long-wave disturbances to a thin supersonic shear layer. An asymptotic formulation is given here which adds nonzero shear-layer thickness to the weakly nonlinear formulation for a vortex sheet. Spatial evolution is considered, for a spatially periodic disturbance having amplitude of the same order, in Reynolds number, as the shear-layer thickness. A quasi-equilibrium inviscid nonlinear critical layer is found, with effects of diffusion and slow growth appearing through nonsecularity condition. Other limiting cases are also considered, in an attempt to determine a relationship between the vortex-sheet limit and the long-wave limit for a thin shear layer; there appear to be three special limits, corresponding to disturbances of different amplitudes at different locations along the shear layer.

The application of nonlinear programming and collocation to optimal aeroassisted orbital transfers

NASA Astrophysics Data System (ADS)

Shi, Y. Y.; Nelson, R. L.; Young, D. H.; Gill, P. E.; Murray, W.; Saunders, M. A.

1992-01-01

Sequential quadratic programming (SQP) and collocation of the differential equations of motion were applied to optimal aeroassisted orbital transfers. The Optimal Trajectory by Implicit Simulation (OTIS) computer program codes with updated nonlinear programming code (NZSOL) were used as a testbed for the SQP nonlinear programming (NLP) algorithms. The state-of-the-art sparse SQP method is considered to be effective for solving large problems with a sparse matrix. Sparse optimizers are characterized in terms of memory requirements and computational efficiency. For the OTIS problems, less than 10 percent of the Jacobian matrix elements are nonzero. The SQP method encompasses two phases: finding an initial feasible point by minimizing the sum of infeasibilities and minimizing the quadratic objective function within the feasible region. The orbital transfer problem under consideration involves the transfer from a high energy orbit to a low energy orbit.

Nonlinear waves and shocks in relativistic two-fluid hydrodynamics

NASA Astrophysics Data System (ADS)

Haim, L.; Gedalin, M.; Spitkovsky, A.; Krasnoselskikh, V.; Balikhin, M.

2012-06-01

Relativistic shocks are present in a number of objects where violent processes are accompanied by relativistic outflows of plasma. The magnetization parameter σ = B2/4πnmc2 of the ambient medium varies in wide range. Shocks with low σ are expected to substantially enhance the magnetic fields in the shock front. In non-relativistic shocks the magnetic compression is limited by nonlinear effects related to the deceleration of flow. Two-fluid analysis of perpendicular relativistic shocks shows that the nonlinearities are suppressed for σ<<1 and the magnetic field reaches nearly equipartition values when the magnetic energy density is of the order of the ion energy density, Beq2 ~ 4πnmic2γ. A large cross-shock potential eφ/mic2γ0 ~ B2/Beq2 develops across the electron-ion shock front. This potential is responsible for electron energization.

Enhanced absorption in a reverse saturable absorbing dye blended with carbon nanotubes.

PubMed

Webster, Scott; Reyes-Reyes, Marisol; Williams, Richard; Carroll, David L

2008-12-01

Using nonlinear absorption at 532 nm in the nanosecond temporal regime, we have measured the low fluence nonlinear transmittance properties of the reverse saturable absorbing carbocyanine dye, 1,1',3,3,3',3'-hexamethylindotricarbocyanine iodide (HITCI), blended with well dispersed carbon nanotubes. The nonlinear optical properties of the blends are strongly dependent on the ratio of dye to nanotubes in solution. In the case where the nanotubes per dye molecule ratio is large, we see a distinctive enhancement in optical fluence limiting properties of the system, suggesting enhanced absorption of the excited states. However, when the nanotube to dye ratio decreases, the system's response is dominated by the behavior of the dye. We suggest that this can be understood as a two component system in which sensitized dye molecules associated with the nanotubes have an effectively different optical cross-section from the dye molecules far from the nanotubes. From classical antennae considerations, this is expected.

Intelligent robust control for uncertain nonlinear time-varying systems and its application to robotic systems.

PubMed

Chang, Yeong-Chan

2005-12-01

This paper addresses the problem of designing adaptive fuzzy-based (or neural network-based) robust controls for a large class of uncertain nonlinear time-varying systems. This class of systems can be perturbed by plant uncertainties, unmodeled perturbations, and external disturbances. Nonlinear H(infinity) control technique incorporated with adaptive control technique and VSC technique is employed to construct the intelligent robust stabilization controller such that an H(infinity) control is achieved. The problem of the robust tracking control design for uncertain robotic systems is employed to demonstrate the effectiveness of the developed robust stabilization control scheme. Therefore, an intelligent robust tracking controller for uncertain robotic systems in the presence of high-degree uncertainties can easily be implemented. Its solution requires only to solve a linear algebraic matrix inequality and a satisfactorily transient and asymptotical tracking performance is guaranteed. A simulation example is made to confirm the performance of the developed control algorithms.

Monte Carlo Simulation of THz Multipliers

NASA Technical Reports Server (NTRS)

East, J.; Blakey, P.

1997-01-01

Schottky Barrier diode frequency multipliers are critical components in submillimeter and Thz space based earth observation systems. As the operating frequency of these multipliers has increased, the agreement between design predictions and experimental results has become poorer. The multiplier design is usually based on a nonlinear model using a form of harmonic balance and a model for the Schottky barrier diode. Conventional voltage dependent lumped element models do a poor job of predicting THz frequency performance. This paper will describe a large signal Monte Carlo simulation of Schottky barrier multipliers. The simulation is a time dependent particle field Monte Carlo simulation with ohmic and Schottky barrier boundary conditions included that has been combined with a fixed point solution for the nonlinear circuit interaction. The results in the paper will point out some important time constants in varactor operation and will describe the effects of current saturation and nonlinear resistances on multiplier operation.

GA-optimized feedforward-PID tracking control for a rugged electrohydraulic system design.

PubMed

Sarkar, B K; Mandal, P; Saha, R; Mookherjee, S; Sanyal, D

2013-11-01

Rugged electrohydraulic systems are preferred for remote and harsh applications. Despite the low bandwidth, large deadband and flow nonlinearities in proportional valves valve and highly nonlinear friction in industry-grade cylinders that comprise rugged systems, their maintenance are much easier than very sophisticated and delicate servocontrol and servocylinder systems. With the target of making the easily maintainable system to perform comparably to a servosystem, a feedforward control has been designed here for compensating the nonlinearities. A PID feedback of the piston displacement has been employed in tandem for absorbing the unmodeled effects. All the controller parameters have been optimized by a real-coded genetic algorithm. The agreement between the achieved real-time responses for step and sinusoidal demands with those achieved by modern servosystems clearly establishes the acceptability of the controller design. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

5D Tempest simulations of kinetic edge turbulence

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Xiong, Z.; Cohen, B. I.; Cohen, R. H.; Dorr, M. R.; Hittinger, J. A.; Kerbel, G. D.; Nevins, W. M.; Rognlien, T. D.; Umansky, M. V.; Qin, H.

2006-10-01

Results are presented from the development and application of TEMPEST, a nonlinear five dimensional (3d2v) gyrokinetic continuum code. The simulation results and theoretical analysis include studies of H-mode edge plasma neoclassical transport and turbulence in real divertor geometry and its relationship to plasma flow generation with zero external momentum input, including the important orbit-squeezing effect due to the large electric field flow-shear in the edge. In order to extend the code to 5D, we have formulated a set of fully nonlinear electrostatic gyrokinetic equations and a fully nonlinear gyrokinetic Poisson's equation which is valid for both neoclassical and turbulence simulations. Our 5D gyrokinetic code is built on 4D version of Tempest neoclassical code with extension to a fifth dimension in binormal direction. The code is able to simulate either a full torus or a toroidal segment. Progress on performing 5D turbulence simulations will be reported.

Magnetic-sensor performance evaluated from magneto-conductance curve in magnetic tunnel junctions using in-plane or perpendicularly magnetized synthetic antiferromagnetic reference layers

NASA Astrophysics Data System (ADS)

Nakano, T.; Oogane, M.; Furuichi, T.; Ando, Y.

2018-04-01

The automotive industry requires magnetic sensors exhibiting highly linear output within a dynamic range as wide as ±1 kOe. A simple model predicts that the magneto-conductance (G-H) curve in a magnetic tunnel junction (MTJ) is perfectly linear, whereas the magneto-resistance (R-H) curve inevitably contains a finite nonlinearity. We prepared two kinds of MTJs using in-plane or perpendicularly magnetized synthetic antiferromagnetic (i-SAF or p-SAF) reference layers and investigated their sensor performance. In the MTJ with the i-SAF reference layer, the G-H curve did not necessarily show smaller nonlinearities than those of the R-H curve with different dynamic ranges. This is because the magnetizations of the i-SAF reference layer start to rotate at a magnetic field even smaller than the switching field (Hsw) measured by a magnetometer, which significantly affects the tunnel magnetoresistance (TMR) effect. In the MTJ with the p-SAF reference layer, the G-H curve showed much smaller nonlinearities than those of the R-H curve, thanks to a large Hsw value of the p-SAF reference layer. We achieved a nonlinearity of 0.08% FS (full scale) in the G-H curve with a dynamic range of ±1 kOe, satisfying our target for automotive applications. This demonstrated that a reference layer exhibiting a large Hsw value is indispensable in order to achieve a highly linear G-H curve.

Acoustic nonreciprocity in a lattice incorporating nonlinearity, asymmetry, and internal scale hierarchy: Experimental study

NASA Astrophysics Data System (ADS)

Bunyan, Jonathan; Moore, Keegan J.; Mojahed, Alireza; Fronk, Matthew D.; Leamy, Michael; Tawfick, Sameh; Vakakis, Alexander F.

2018-05-01

In linear time-invariant systems acoustic reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and it can be broken only by odd external biases, nonlinearities, or time-dependent properties. Recently it was shown that one-dimensional lattices composed of a finite number of identical nonlinear cells with internal scale hierarchy and asymmetry exhibit nonreciprocity both locally and globally. Considering a single cell composed of a large scale nonlinearly coupled to a small scale, local dynamic nonreciprocity corresponds to vibration energy transfer from the large to the small scale, but absence of energy transfer (and localization) from the small to the large scale. This has been recently proven both theoretically and experimentally. Then, considering the entire lattice, global acoustic nonreciprocity has been recently proven theoretically, corresponding to preferential energy transfer within the lattice under transient excitation applied at one of its boundaries, and absence of similar energy transfer (and localization) when the excitation is applied at its other boundary. This work provides experimental validation of the global acoustic nonreciprocity with a one-dimensional asymmetric lattice composed of three cells, with each cell incorporating nonlinearly coupled large and small scales. Due to the intentional asymmetry of the lattice, low impulsive excitations applied to one of its boundaries result in wave transmission through the lattice, whereas when the same excitations are applied to the other end, they lead in energy localization at the boundary and absence of wave transmission. This global nonreciprocity depends critically on energy (i.e., the intensity of the applied impulses), and reduced-order models recover the nonreciprocal acoustics and clarify the nonlinear mechanism generating nonreciprocity in this system.

Nonlinear modeling, strength-based design, and testing of flexible piezoelectric energy harvesters under large dynamic loads for rotorcraft applications

NASA Astrophysics Data System (ADS)

Leadenham, Stephen; Erturk, Alper

2014-04-01

There has been growing interest in enabling wireless health and usage monitoring for rotorcraft applications, such as helicopter rotor systems. Large dynamic loads and acceleration fluctuations available in these environments make the implementation of vibration-based piezoelectric energy harvesters a very promising choice. However, such extreme loads transmitted to the harvester can also be detrimental to piezoelectric laminates and overall system reliability. Particularly flexible resonant cantilever configurations tuned to match the dominant excitation frequency can be subject to very large deformations and failure of brittle piezoelectric laminates due to excessive bending stresses at the root of the harvester. Design of resonant piezoelectric energy harvesters for use in these environments require nonlinear electroelastic dynamic modeling and strength-based analysis to maximize the power output while ensuring that the harvester is still functional. This paper presents a mathematical framework to design and analyze the dynamics of nonlinear flexible piezoelectric energy harvesters under large base acceleration levels. A strength-based limit is imposed to design the piezoelectric energy harvester with a proof mass while accounting for material, geometric, and dissipative nonlinearities, with a focus on two demonstrative case studies having the same linear fundamental resonance frequency but different overhang length and proof mass values. Experiments are conducted at different excitation levels for validation of the nonlinear design approach proposed in this work. The case studies in this work reveal that harvesters exhibiting similar behavior and power generation performance at low excitation levels (e.g. less than 0.1g) can have totally different strength-imposed performance limitations under high excitations (e.g. above 1g). Nonlinear modeling and strength-based design is necessary for such excitation levels especially when using resonant cantilevers with no geometric constraint.

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2017-03-29

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Reconstructing Information in Large-Scale Structure via Logarithmic Mapping

NASA Astrophysics Data System (ADS)

Szapudi, Istvan

We propose to develop a new method to extract information from large-scale structure data combining two-point statistics and non-linear transformations; before, this information was available only with substantially more complex higher-order statistical methods. Initially, most of the cosmological information in large-scale structure lies in two-point statistics. With non- linear evolution, some of that useful information leaks into higher-order statistics. The PI and group has shown in a series of theoretical investigations how that leakage occurs, and explained the Fisher information plateau at smaller scales. This plateau means that even as more modes are added to the measurement of the power spectrum, the total cumulative information (loosely speaking the inverse errorbar) is not increasing. Recently we have shown in Neyrinck et al. (2009, 2010) that a logarithmic (and a related Gaussianization or Box-Cox) transformation on the non-linear Dark Matter or galaxy field reconstructs a surprisingly large fraction of this missing Fisher information of the initial conditions. This was predicted by the earlier wave mechanical formulation of gravitational dynamics by Szapudi & Kaiser (2003). The present proposal is focused on working out the theoretical underpinning of the method to a point that it can be used in practice to analyze data. In particular, one needs to deal with the usual real-life issues of galaxy surveys, such as complex geometry, discrete sam- pling (Poisson or sub-Poisson noise), bias (linear, or non-linear, deterministic, or stochastic), redshift distortions, pro jection effects for 2D samples, and the effects of photometric redshift errors. We will develop methods for weak lensing and Sunyaev-Zeldovich power spectra as well, the latter specifically targetting Planck. In addition, we plan to investigate the question of residual higher- order information after the non-linear mapping, and possible applications for cosmology. Our aim will be to work out practical methods, with the ultimate goal of cosmological parameter estimation. We will quantify with standard MCMC and Fisher methods (including DETF Figure of merit when applicable) the efficiency of our estimators, comparing with the conventional method, that uses the un-transformed field. Preliminary results indicate that the increase for NASA's WFIRST in the DETF Figure of Merit would be 1.5-4.2 using a range of pessimistic to optimistic assumptions, respectively.

Numerical study of nonlinear full wave acoustic propagation

NASA Astrophysics Data System (ADS)

Velasco-Segura, Roberto; Rendon, Pablo L.

2013-11-01

With the aim of describing nonlinear acoustic phenomena, a form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A CLAWPACK based, 2D finite-volume method using Roe's linearization has been implemented to obtain numerically the solution of the proposed equations. In order to validate the code, two different tests have been performed: one against a special Taylor shock-like analytic solution, the other against published results on a HIFU system, both with satisfactory results. The code is written for parallel execution on a GPU and improves performance by a factor of over 50 when compared to the standard CLAWPACK Fortran code. This code can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from modest models of diagnostic and therapeutic HIFU, parametric acoustic arrays, to acoustic wave guides. A couple of examples will be presented showing shock formation and oblique interaction. DGAPA PAPIIT IN110411, PAEP UNAM 2013.

Chemical reaction for Carreau-Yasuda nanofluid flow past a nonlinear stretching sheet considering Joule heating

NASA Astrophysics Data System (ADS)

Khan, Mair; Shahid, Amna; Malik, M. Y.; Salahuddin, T.

2018-03-01

Current analysis has been made to scrutinize the consequences of chemical response against magneto-hydrodynamic Carreau-Yasuda nanofluid flow induced by a non-linear stretching surface considering zero normal flux, slip and convective boundary conditions. Joule heating effect is also considered. Appropriate similarity approach is used to convert leading system of PDE's for Carreau-Yasuda nanofluid into nonlinear ODE's. Well known mathematical scheme namely shooting method is utilized to solve the system numerically. Physical parameters, namely Weissenberg number We , thermal slip parameter δ , thermophoresis number NT, non-linear stretching parameter n, magnetic field parameter M, velocity slip parameter k , Lewis number Le, Brownian motion parameter NB, Prandtl number Pr, Eckert number Ec and chemical reaction parameter γ upon temperature, velocity and concentration profiles are visualized through graphs and tables. Numerical influence of mass and heat transfer rates and friction factor are also represented in tabular as well as graphical form respectively. Skin friction coefficient reduces when Weissenberg number We is incremented. Rate of heat transfer enhances for large values of Brownian motion constraint NB. By increasing Lewis quantity Le rate of mass transfer declines.

Inflation from a nonlinear magnetic monopole field nonminimally coupled to curvature

NASA Astrophysics Data System (ADS)

Otalora, Giovanni; Övgün, Ali; Saavedra, Joel; Videla, Nelson

2018-06-01

In the context of nonminimally coupled f(R) gravity theories, we study early inflation driven by a nonlinear monopole magnetic field which is nonminimally coupled to curvature. In order to isolate the effects of the nonminimal coupling between matter and curvature we assume the pure gravitational sector to have the Einstein-Hilbert form. Thus, we study the most simple model with a nonminimal coupling function which is linear in the Ricci scalar. From an effective fluid description, we show the existence of an early exponential expansion regime of the Universe, followed by a transition to a radiation-dominated era. In particular, by applying the most recent results of the Planck collaboration we set the limits on the parameter of the nonminimal coupling, and the quotient of the nonminimal coupling and the nonlinear monopole magnetic scales. We found that these parameters must take large values in order to satisfy the observational constraints. Furthermore, by obtaining the relation for the graviton mass, we show the consistency of our results with the recent gravitational wave data GW170817 of LIGO and Virgo.

Self-consistent theory for the linear and nonlinear propagation of a sinusoidal electron plasma wave. Application to stimulated Raman scattering in a non-uniform and non-stationary plasma

NASA Astrophysics Data System (ADS)

Bénisti, Didier

2018-01-01

In this paper, we address the theoretical resolution of the Vlasov-Gauss system from the linear regime to the strongly nonlinear one, when significant trapping has occurred. The electric field is that of a sinusoidal electron plasma wave (EPW) which is assumed to grow from the noise level, and to keep growing at least up to the amplitude when linear theory in no longer valid (while the wave evolution in the nonlinear regime may be arbitrary). The ions are considered as a neutralizing fluid, while the electron response to the wave is derived by matching two different techniques. We make use of a perturbation analysis similar to that introduced to prove the Kolmogorov-Arnold-Moser theorem, up to amplitudes large enough for neo-adiabatic results to be valid. Our theory is applied to the growth and saturation of the beam-plasma instability, and to the three-dimensional propagation of a driven EPW in a non-uniform and non-stationary plasma. For the latter example, we lay a special emphasis on nonlinear collisionless dissipation. We provide an explicit theoretical expression for the nonlinear Landau-like damping rate which, in some instances, is amenable to a simple analytic formula. We also insist on the irreversible evolution of the electron distribution function, which is nonlocal in the wave amplitude and phase velocity. This makes trapping an effective means of dissipation for the electrostatic energy, and also makes the wave dispersion relation nonlocal. Our theory is generalized to allow for stimulated Raman scattering, which we address up to saturation by accounting for plasma inhomogeneity and non-stationarity, nonlinear kinetic effects, and interspeckle coupling.

Fluid nonlinear frequency shift of nonlinear ion acoustic waves in multi-ion species plasmas in the small wave number region

NASA Astrophysics Data System (ADS)

Feng, Q. S.; Xiao, C. Z.; Wang, Q.; Zheng, C. Y.; Liu, Z. J.; Cao, L. H.; He, X. T.

2016-08-01

The properties of the nonlinear frequency shift (NFS), especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas, have been researched by Vlasov simulation. Pictures of the nonlinear frequency shift from harmonic generation and particle trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given, and the results of Vlasov simulation are consistent with the theoretical result of multi-ion species plasmas. When the wave number k λD e is small, such as k λD e=0.1 , the fluid NFS dominates in the total NFS and will reach as large as nearly 15 % when the wave amplitude |e ϕ / Te|˜0.1 , which indicates that in the condition of small k λD e , the fluid NFS dominates in the saturation of stimulated Brillouin scattering, especially when the nonlinear IAW amplitude is large.

Fluid nonlinear frequency shift of nonlinear ion acoustic waves in multi-ion species plasmas in the small wave number region.

PubMed

Feng, Q S; Xiao, C Z; Wang, Q; Zheng, C Y; Liu, Z J; Cao, L H; He, X T

2016-08-01

The properties of the nonlinear frequency shift (NFS), especially the fluid NFS from the harmonic generation of the ion-acoustic wave (IAW) in multi-ion species plasmas, have been researched by Vlasov simulation. Pictures of the nonlinear frequency shift from harmonic generation and particle trapping are shown to explain the mechanism of NFS qualitatively. The theoretical model of the fluid NFS from harmonic generation in multi-ion species plasmas is given, and the results of Vlasov simulation are consistent with the theoretical result of multi-ion species plasmas. When the wave number kλ_{De} is small, such as kλ_{De}=0.1, the fluid NFS dominates in the total NFS and will reach as large as nearly 15% when the wave amplitude |eϕ/T_{e}|∼0.1, which indicates that in the condition of small kλ_{De}, the fluid NFS dominates in the saturation of stimulated Brillouin scattering, especially when the nonlinear IAW amplitude is large.

Nonlinear model-order reduction for compressible flow solvers using the Discrete Empirical Interpolation Method

NASA Astrophysics Data System (ADS)

Fosas de Pando, Miguel; Schmid, Peter J.; Sipp, Denis

2016-11-01

Nonlinear model reduction for large-scale flows is an essential component in many fluid applications such as flow control, optimization, parameter space exploration and statistical analysis. In this article, we generalize the POD-DEIM method, introduced by Chaturantabut & Sorensen [1], to address nonlocal nonlinearities in the equations without loss of performance or efficiency. The nonlinear terms are represented by nested DEIM-approximations using multiple expansion bases based on the Proper Orthogonal Decomposition. These extensions are imperative, for example, for applications of the POD-DEIM method to large-scale compressible flows. The efficient implementation of the presented model-reduction technique follows our earlier work [2] on linearized and adjoint analyses and takes advantage of the modular structure of our compressible flow solver. The efficacy of the nonlinear model-reduction technique is demonstrated to the flow around an airfoil and its acoustic footprint. We could obtain an accurate and robust low-dimensional model that captures the main features of the full flow.

Nonlinear Excitation of Acoustic Modes by Large Amplitude Alfvén waves in the Large Plasma Device (LAPD)

NASA Astrophysics Data System (ADS)

Dorfman, S.; Carter, T.; Pribyl, P.; Tripathi, S. K. P.; van Compernolle, B.; Vincena, S.; Sydora, R.

2013-10-01

Alfvén waves, a fundamental mode of magnetized plasmas, are ubiquitous in lab and space. While the linear behavior of these waves has been extensively studied, non-linear effects are important in many real systems, including the solar wind and solar corona. In particular, a parametric decay process in which a large amplitude Alfvén wave decays into an ion acoustic wave and backward propagating Alfvén wave may play an important role in coronal heating and/or in establishing the spectrum of solar wind turbulence. Recent counter-propagating Alfvén wave experiments have recorded the first laboratory observation of the Alfvén-acoustic mode coupling at the heart of this parametric decay instability. The resonance in the observed beat process has several features consistent with ponderomotive coupling to an ion acoustic mode, including the measured dispersion relation and spatial profile. Strong damping observed after the pump Alfvén waves are turned off is under investigation. New experiments and simulations also aim to identify decay instabilities from a single large-amplitude Alfvén wave. Supported by DOE and NSF.

Analytical modeling of large amplitude free vibration of non-uniform beams carrying a both transversely and axially eccentric tip mass

NASA Astrophysics Data System (ADS)

Malaeke, Hasan; Moeenfard, Hamid

2016-03-01

The objective of this paper is to study large amplitude flexural-extensional free vibration of non-uniform cantilever beams carrying a both transversely and axially eccentric tip mass. The effects of variable axial force is also taken into account. Hamilton's principle is utilized to obtain the partial differential equations governing the nonlinear vibration of the system as well as the corresponding boundary conditions. A numerical finite difference scheme is proposed to find the natural frequencies and mode shapes of the system which is validated specifically for a beam with linearly varying cross section. Using a single mode approximation in conjunction with the Lagrange method, the governing equations are reduced to a set of two nonlinear ordinary differential equations in terms of end displacement components of the beam which are coupled due to the presence of the transverse eccentricity. These temporal coupled equations are then solved analytically using the multiple time scales perturbation technique. The obtained analytical results are compared with the numerical ones and excellent agreement is observed. The qualitative and quantitative knowledge resulting from this research is expected to enable the study of the effects of eccentric tip mass and non-uniformity on the large amplitude flexural-extensional vibration of beams for improved dynamic performance.

Self-tuning bistable parametric feedback oscillator: Near-optimal amplitude maximization without model information

NASA Astrophysics Data System (ADS)

Braun, David J.; Sutas, Andrius; Vijayakumar, Sethu

2017-01-01

Theory predicts that parametrically excited oscillators, tuned to operate under resonant condition, are capable of large-amplitude oscillation useful in diverse applications, such as signal amplification, communication, and analog computation. However, due to amplitude saturation caused by nonlinearity, lack of robustness to model uncertainty, and limited sensitivity to parameter modulation, these oscillators require fine-tuning and strong modulation to generate robust large-amplitude oscillation. Here we present a principle of self-tuning parametric feedback excitation that alleviates the above-mentioned limitations. This is achieved using a minimalistic control implementation that performs (i) self-tuning (slow parameter adaptation) and (ii) feedback pumping (fast parameter modulation), without sophisticated signal processing past observations. The proposed approach provides near-optimal amplitude maximization without requiring model-based control computation, previously perceived inevitable to implement optimal control principles in practical application. Experimental implementation of the theory shows that the oscillator self-tunes itself near to the onset of dynamic bifurcation to achieve extreme sensitivity to small resonant parametric perturbations. As a result, it achieves large-amplitude oscillations by capitalizing on the effect of nonlinearity, despite substantial model uncertainties and strong unforeseen external perturbations. We envision the present finding to provide an effective and robust approach to parametric excitation when it comes to real-world application.

Magnetoelectric Current Sensors

PubMed Central

Bichurin, Mirza; Petrov, Roman; Leontiev, Viktor; Semenov, Gennadiy; Sokolov, Oleg

2017-01-01

In this work a magnetoelectric (ME) current sensor design based on a magnetoelectric effect is presented and discussed. The resonant and non-resonant type of ME current sensors are considered. Theoretical calculations of the ME current sensors by the equivalent circuit method were conducted. The application of different sensors using the new effects, for example, the ME effect, is made possible with the development of new ME composites. A large number of studies conducted in the field of new composites, allowed us to obtain a high magnetostrictive-piezoelectric laminate sensitivity. An optimal ME structure composition was matched. The characterization of a non-resonant current sensor showed that in the operation range to 5 A, the sensor had a sensitivity of 0.34 V/A, non-linearity less than 1% and for a resonant current sensor in the same operation range, the sensitivity was of 0.53 V/A, non-linearity less than 0.5%. PMID:28574486

Synchronisation and stability in river metapopulation networks.

PubMed

Yeakel, J D; Moore, J W; Guimarães, P R; de Aguiar, M A M

2014-03-01

Spatial structure in landscapes impacts population stability. Two linked components of stability have large consequences for persistence: first, statistical stability as the lack of temporal fluctuations; second, synchronisation as an aspect of dynamic stability, which erodes metapopulation rescue effects. Here, we determine the influence of river network structure on the stability of riverine metapopulations. We introduce an approach that converts river networks to metapopulation networks, and analytically show how fluctuation magnitude is influenced by interaction structure. We show that river metapopulation complexity (in terms of branching prevalence) has nonlinear dampening effects on population fluctuations, and can also buffer against synchronisation. We conclude by showing that river transects generally increase synchronisation, while the spatial scale of interaction has nonlinear effects on synchronised dynamics. Our results indicate that this dual stability - conferred by fluctuation and synchronisation dampening - emerges from interaction structure in rivers, and this may strongly influence the persistence of river metapopulations. © 2013 John Wiley & Sons Ltd/CNRS.

Parametric Excitation of Electrostatic Dust-Modes by Ion-Cyclotron Waves in a Dusty Plasma

NASA Astrophysics Data System (ADS)

Islam, M. K.; Salahuddin, M.; Ferdous, T.; Salimullah, M.

A large amplitude electrostatic ion-cyclotron wave propagating through a magnetized and collisional dusty plasma undergoes strong parametric instability off the low-frequency dust-modes. The presence of the dust-component has effect on the nonlinear coupling via the dust-modes. The ion-neutral collisions are seen to have significant effect on the damping and consequent overall growth of the parametric excitation process.

Holes generation in glass using large spot femtosecond laser pulses

NASA Astrophysics Data System (ADS)

Berg, Yuval; Kotler, Zvi; Shacham-Diamand, Yosi

2018-03-01

We demonstrate high-throughput, symmetrical, holes generation in fused silica glass using a large spot size, femtosecond IR-laser irradiation which modifies the glass properties and yields an enhanced chemical etching rate. The process relies on a balanced interplay between the nonlinear Kerr effect and multiphoton absorption in the glass which translates into symmetrical glass modification and increased etching rate. The use of a large laser spot size makes it possible to process thick glasses at high speeds over a large area. We have demonstrated such fabricated holes with an aspect ratio of 1:10 in a 1 mm thick glass samples.

New evidence and impact of electron transport non-linearities based on new perturbative inter-modulation analysis

NASA Astrophysics Data System (ADS)

van Berkel, M.; Kobayashi, T.; Igami, H.; Vandersteen, G.; Hogeweij, G. M. D.; Tanaka, K.; Tamura, N.; Zwart, H. J.; Kubo, S.; Ito, S.; Tsuchiya, H.; de Baar, M. R.; LHD Experiment Group

2017-12-01

A new methodology to analyze non-linear components in perturbative transport experiments is introduced. The methodology has been experimentally validated in the Large Helical Device for the electron heat transport channel. Electron cyclotron resonance heating with different modulation frequencies by two gyrotrons has been used to directly quantify the amplitude of the non-linear component at the inter-modulation frequencies. The measurements show significant quadratic non-linear contributions and also the absence of cubic and higher order components. The non-linear component is analyzed using the Volterra series, which is the non-linear generalization of transfer functions. This allows us to study the radial distribution of the non-linearity of the plasma and to reconstruct linear profiles where the measurements were not distorted by non-linearities. The reconstructed linear profiles are significantly different from the measured profiles, demonstrating the significant impact that non-linearity can have.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Nonlinear Finite Element Analysis of Shells with Large Aspect Ratio

NASA Technical Reports Server (NTRS)

Chang, T. Y.; Sawamiphakdi, K.

1984-01-01

A higher order degenerated shell element with nine nodes was selected for large deformation and post-buckling analysis of thick or thin shells. Elastic-plastic material properties are also included. The post-buckling analysis algorithm is given. Using a square plate, it was demonstrated that the none-node element does not have shear locking effect even if its aspect ratio was increased to the order 10 to the 8th power. Two sample problems are given to illustrate the analysis capability of the shell element.

Formulation of the aeroelastic stability and response problem of coupled rotor/support systems

NASA Technical Reports Server (NTRS)

Warmbrodt, W.; Friedmann, P.

1979-01-01

The consistent formulation of the governing nonlinear equations of motion for a coupled rotor/support system is presented. Rotor/support coupling is clearly documented by enforcing dynamic equilibrium between the rotor and the moving flexible support. The nonlinear periodic coefficient equations of motion are applicable to both coupled rotor/fuselage aeroelastic problems of helicopters in hover or forward flight and coupled rotor/tower dynamics of a large horizontal axis wind turbine (HAWT). Finally, the equations of motion are used to study the influence of flexible supports and nonlinear terms on rotor aeroelastic stability and response of a large two-bladed HAWT.

Photodeposition of Thin Polydiacetylene Films from Solution that Exhibit Large Third-Order Optical Nonlinearities

NASA Technical Reports Server (NTRS)

Paley, M. S.; Frazier, D. O.; Abdeldayem, H.; McManus, S. P.

1994-01-01

One promising class of organic compounds for applications in the field of nonlinear optics (NLO) are polydiacetylenes, which are of interest because they are highly conjugated polymers capable of exhibiting very large optical nonlinearities with fast response times. During the course of crystal growth studies in anticipation of a space experiment, we discovered a novel, simple method for the formation of polydiacetylene thin films by photodeposition from monomer solutions onto quartz or glass substrates. Characterization of these PDAMNA films is not trivial; they are not soluble in common organic solvents, which makes the standard solution-based methods of polymer analysis useless.

Nonlinearity and Scaling Behavior in Lead Zirconate Titanate Piezoceramic

NASA Astrophysics Data System (ADS)

Mueller, V.

1998-03-01

The results of a comprehensive study of the nonlinear dielectric and electromechanical response of lead zirconate titanate (PZT) piezoceramics are presented. The piezoelectric strain of a series of donor doped (soft PZT) and acceptor doped (hard PZT) polycrystalline systems was measured under quasistatic (nonresonant) conditions. The measuring field was applied both parallel and perpendicular to the poling direction of the ceramic in order to investigate the influence of different symmetry conditions. Dielectric properties were studied in addition to the electromechanical measurements which enables us to compare piezoelectric and dielectric nonlinearities. Due to the different level and type of dopants, the piezoceramics examined differ significantly with regard to its Curie temperature (190^o CE_c2 the nonlinearity can be described in the same way as in soft PZT. The results indicate that irreversible motion of (ferroelastic) non-180^o walls causes the nonlinearity of PZT and that the contribution of (non-ferroelastic) 180^o walls to the linear and nonlinear coefficients is negligibly small. The experimentally observed non-analytic scaling behavior is qualitatively inconsistent with the assumption that the nonlinearity is related to the anharmonicity of the domain wall potential. We suggest that the dynamics of the domain wall in a randomly pinned medium dominates the piezoelectric and dielectric nonlinearity at field strengths well below the limiting field necessary to depole the piezoceramic. The analysis of results obtained at different ceramic systems indicates that linear and nonlinear coefficients are not independent from each other. The observed relationship between linear and nonlinear properties leads us to the suggestion that another extrinsic contribution to the permittivity exists in PZT which may not be attributed to domain wall motion but related to the dielectric dispersion at microwave frequencies.

Broad-band simulation of M7.2 earthquake on the North Tehran fault, considering non-linear soil effects

NASA Astrophysics Data System (ADS)

Majidinejad, A.; Zafarani, H.; Vahdani, S.

2018-05-01

The North Tehran fault (NTF) is known to be one of the most drastic sources of seismic hazard on the city of Tehran. In this study, we provide broad-band (0-10 Hz) ground motions for the city as a consequence of probable M7.2 earthquake on the NTF. Low-frequency motions (0-2 Hz) are provided from spectral element dynamic simulation of 17 scenario models. High-frequency (2-10 Hz) motions are calculated with a physics-based method based on S-to-S backscattering theory. Broad-band ground motions at the bedrock level show amplifications, both at low and high frequencies, due to the existence of deep Tehran basin in the vicinity of the NTF. By employing soil profiles obtained from regional studies, effect of shallow soil layers on broad-band ground motions is investigated by both linear and non-linear analyses. While linear soil response overestimate ground motion prediction equations, non-linear response predicts plausible results within one standard deviation of empirical relationships. Average Peak Ground Accelerations (PGAs) at the northern, central and southern parts of the city are estimated about 0.93, 0.59 and 0.4 g, respectively. Increased damping caused by non-linear soil behaviour, reduces the soil linear responses considerably, in particular at frequencies above 3 Hz. Non-linear deamplification reduces linear spectral accelerations up to 63 per cent at stations above soft thick sediments. By performing more general analyses, which exclude source-to-site effects on stations, a correction function is proposed for typical site classes of Tehran. Parameters for the function which reduces linear soil response in order to take into account non-linear soil deamplification are provided for various frequencies in the range of engineering interest. In addition to fully non-linear analyses, equivalent-linear calculations were also conducted which their comparison revealed appropriateness of the method for large peaks and low frequencies, but its shortage for small to medium peaks and motions with higher than 3 Hz frequencies.

Large eddy simulations of compressible magnetohydrodynamic turbulence

NASA Astrophysics Data System (ADS)

Grete, Philipp

2017-02-01

Supersonic, magnetohydrodynamic (MHD) turbulence is thought to play an important role in many processes - especially in astrophysics, where detailed three-dimensional observations are scarce. Simulations can partially fill this gap and help to understand these processes. However, direct simulations with realistic parameters are often not feasible. Consequently, large eddy simulations (LES) have emerged as a viable alternative. In LES the overall complexity is reduced by simulating only large and intermediate scales directly. The smallest scales, usually referred to as subgrid-scales (SGS), are introduced to the simulation by means of an SGS model. Thus, the overall quality of an LES with respect to properly accounting for small-scale physics crucially depends on the quality of the SGS model. While there has been a lot of successful research on SGS models in the hydrodynamic regime for decades, SGS modeling in MHD is a rather recent topic, in particular, in the compressible regime. In this thesis, we derive and validate a new nonlinear MHD SGS model that explicitly takes compressibility effects into account. A filter is used to separate the large and intermediate scales, and it is thought to mimic finite resolution effects. In the derivation, we use a deconvolution approach on the filter kernel. With this approach, we are able to derive nonlinear closures for all SGS terms in MHD: the turbulent Reynolds and Maxwell stresses, and the turbulent electromotive force (EMF). We validate the new closures both a priori and a posteriori. In the a priori tests, we use high-resolution reference data of stationary, homogeneous, isotropic MHD turbulence to compare exact SGS quantities against predictions by the closures. The comparison includes, for example, correlations of turbulent fluxes, the average dissipative behavior, and alignment of SGS vectors such as the EMF. In order to quantify the performance of the new nonlinear closure, this comparison is conducted from the subsonic (sonic Mach number M s ≈ 0.2) to the highly supersonic (M s ≈ 20) regime, and against other SGS closures. The latter include established closures of eddy-viscosity and scale-similarity type. In all tests and over the entire parameter space, we find that the proposed closures are (significantly) closer to the reference data than the other closures. In the a posteriori tests, we perform large eddy simulations of decaying, supersonic MHD turbulence with initial M s ≈ 3. We implemented closures of all types, i.e. of eddy-viscosity, scale-similarity and nonlinear type, as an SGS model and evaluated their performance in comparison to simulations without a model (and at higher resolution). We find that the models need to be calculated on a scale larger than the grid scale, e.g. by an explicit filter, to have an influence on the dynamics at all. Furthermore, we show that only the proposed nonlinear closure improves higher-order statistics.

Properties of Nonlinear Dynamo Waves

NASA Technical Reports Server (NTRS)

Tobias, S. M.

1997-01-01

Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.

Strongly nonlinear theory of rapid solidification near absolute stability

NASA Astrophysics Data System (ADS)

Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the morphological number, as well as the amplitude. The critical amplitude, at which solutions loose periodicity, depends on a single combination of parameters independent of the morphological number that indicate that non-periodic growth is most commonly present for moderate disequilibrium parameters. The spatial distribution of the interface develops deepening roots at late times. Similar spatial distributions are also seen in the limit in which both the cellular and oscillatory modes are close to absolute stability, and the roots deepen with larger departures from the two absolute stability boundaries.

Optical Nonlinearities in Semiconductors for Limiting.

NASA Astrophysics Data System (ADS)

Wu, Yuan-Yen

I have conducted detailed experimental and theoretical studies of the nonlinear optical properties of semiconductor materials useful for optical limiting. I have constructed optical limiters utilizing two-photon absorption along with photogenerated carrier defocusing as well as the bound electronic nonlinearity using the semiconducting material ZnSe. I have optimized the focusing geometry to achieve a large dynamic range while maintaining a low limiting energy for the device. The ZnSe monolithic optical limiter has achieved a limiting energy as low as 13 nJ (corresponding to 300W peak power) and a dynamic range as large as 10 ^5 at 532 nm using psec pulses. Theoretical analysis showed that the ZnSe device has a broad-band response covering the wavelength range from 550 nm to 800 nm. Moreover, I found that existing theoretical models (e.g. the Auston model and the band-resonant model using Boltzmann statistics) adequately describe the photo-generated carriers refractive nonlinearity in ZnSe. Material nonlinear optical parameters, such as the two-photon absorption coefficient beta _2 = 5.5 cm/GW, the refraction per unit carrier density sigma_{rm n} = -0.8cdot 10^ {-21}cm^3 and the bound electronic refraction n_2 = -4cdot 10^{ -11}esu, have been measured via time-integrated beam distortion experiments in the near field. A numerical code has been written to simulate the beam distortion in order to extract the previously mentioned material parameters. In addition, I have performed time-resolved distortion measurements that provide an intuitive picture of the carrier generation process via two-photon absorption. I also characterized the optical nonlinearities in a ZnSe Fabry-Perot thin film structure (an interference filter). I concluded that the nonlinear absorption alone in the thin film is insufficient to build an effective optical limiter, as it did not show a net change in refraction using psec pulses. An innovative numerical program was developed to simulate the nonlinear beam propagation inside the Fabry-Perot structure. For comparison, pump-probe experiments were performed using both thin film and bulk ZnSe. The results showed relatively long carrier lifetimes (>300 psec) in both samples. A numerical code was written to fit the pump-probe experimental results. The fitting yielded that carrier lifetimes (recombination through traps), radiative decay rate, two-photon absorption coefficient as well as the free carrier absorption coefficient for ZnSe bulk material.

EFFECTS OF LARGE-SCALE NON-AXISYMMETRIC PERTURBATIONS IN THE MEAN-FIELD SOLAR DYNAMO

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pipin, V. V.; Kosovichev, A. G.

2015-11-10

We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R{sub ⊙} has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution ofmore » the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number R{sub m}. In the range of R{sub m} = 10{sup 4}–10{sup 6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process.« less

Nonlinear aeroelastic analysis, flight dynamics, and control of a complete aircraft

NASA Astrophysics Data System (ADS)

Patil, Mayuresh Jayawant

The focus of this research was to analyze a high-aspect-ratio wing aircraft flying at low subsonic speeds. Such aircraft are designed for high-altitude, long-endurance missions. Due to the high flexibility and associated wing deformation, accurate prediction of aircraft response requires use of nonlinear theories. Also strong interactions between flight dynamics and aeroelasticity are expected. To analyze such aircraft one needs to have an analysis tool which includes the various couplings and interactions. A theoretical basis has been established for a consistent analysis which takes into account, (i) material anisotropy, (ii) geometrical nonlinearities of the structure, (iii) rigid-body motions, (iv) unsteady flow behavior, and (v) dynamic stall. The airplane structure is modeled as a set of rigidly attached beams. Each of the beams is modeled using the geometrically exact mixed variational formulation, thus taking into account geometrical nonlinearities arising due to large displacements and rotations. The cross-sectional stiffnesses are obtained using an asymptotically exact analysis, which can model arbitrary cross sections and material properties. An aerodynamic model, consisting of a unified lift model, a consistent combination of finite-state inflow model and a modified ONERA dynamic stall model, is coupled to the structural system to determine the equations of motion. The results obtained indicate the necessity of including nonlinear effects in aeroelastic analysis. Structural geometric nonlinearities result in drastic changes in aeroelastic characteristics, especially in case of high-aspect-ratio wings. The nonlinear stall effect is the dominant factor in limiting the amplitude of oscillation for most wings. The limit cycle oscillation (LCO) phenomenon is also investigated. Post-flutter and pre-flutter LCOs are possible depending on the disturbance mode and amplitude. Finally, static output feedback (SOF) controllers are designed for flutter suppression and gust alleviation. SOF controllers are very simple and thus easy to implement. For the case considered, SOF controllers with proper choice of sensors give results comparable to full state feedback (linear quadratic regulator) designs.

Fabrication and characterization of THUNDER actuators—pre-stress-induced nonlinearity in the actuation response

NASA Astrophysics Data System (ADS)

Kim, Younghoon; Cai, Ling; Usher, Timothy; Jiang, Qing

2009-09-01

This paper documents an experimental and theoretical investigation into characterizing the mechanical configurations and performances of THUNDER actuators, a type of piezoelectric actuator known for their large actuation displacements, through fabrication, measurements and finite element analysis. Five groups of such actuators with different dimensions were fabricated using identical fabrication parameters. The as-fabricated arched configurations, resulting from the thermo-mechanical mismatch among the constituent layers, and their actuation performances were characterized using an experimental set-up based on a laser displacement sensor and through numerical simulations with ANSYS, a widely used commercial software program for finite element analysis. This investigation shows that the presence of large residual stresses within the piezoelectric ceramic layer, built up during the fabrication process, leads to significant nonlinear electromechanical coupling in the actuator response to the driving electric voltage, and it is this nonlinear coupling that is responsible for the large actuation displacements. Furthermore, the severity of the residual stresses, and thus the nonlinearity, increases with increasing substrate/piezoelectric thickness ratio and, to a lesser extent, with decreasing in-plane dimensions of the piezoelectric layer.

Hysteresis modeling and identification of a dielectric electro-active polymer actuator using an APSO-based nonlinear Preisach NARX fuzzy model

NASA Astrophysics Data System (ADS)

Truong, Bui Ngoc Minh; Nam, Doan Ngoc Chi; Ahn, Kyoung Kwan

2013-09-01

Dielectric electro-active polymer (DEAP) materials are attractive since they are low cost, lightweight and have a large deformation capability. They have no operating noise, very low electric power consumption and higher performance and efficiency than competing technologies. However, DEAP materials generally have strong hysteresis as well as uncertain and nonlinear characteristics. These disadvantages can limit the efficiency in the use of DEAP materials. To address these limitations, this research will present the combination of the Preisach model and the dynamic nonlinear autoregressive exogenous (NARX) fuzzy model-based adaptive particle swarm optimization (APSO) identification algorithm for modeling and identification of the nonlinear behavior of one typical type of DEAP actuator. Firstly, open loop input signals are applied to obtain nonlinear features and to investigate the responses of the DEAP actuator system. Then, a Preisach model can be combined with a dynamic NARX fuzzy structure to estimate the tip displacement of a DEAP actuator. To optimize all unknown parameters of the designed combination, an identification scheme based on a least squares method and an APSO algorithm is carried out. Finally, experimental validation research is carefully completed, and the effectiveness of the proposed model is evaluated by employing various input signals.

Estimating the Volterra Series Transfer Function over coherent optical OFDM for efficient monitoring of the fiber channel nonlinearity.

PubMed

Shulkind, Gal; Nazarathy, Moshe

2012-12-17

We present an efficient method for system identification (nonlinear channel estimation) of third order nonlinear Volterra Series Transfer Function (VSTF) characterizing the four-wave-mixing nonlinear process over a coherent OFDM fiber link. Despite the seemingly large number of degrees of freedom in the VSTF (cubic in the number of frequency points) we identified a compressed VSTF representation which does not entail loss of information. Additional slightly lossy compression may be obtained by discarding very low power VSTF coefficients associated with regions of destructive interference in the FWM phased array effect. Based on this two-staged VSTF compressed representation, we develop a robust and efficient algorithm of nonlinear system identification (optical performance monitoring) estimating the VSTF by transmission of an extended training sequence over the OFDM link, performing just a matrix-vector multiplication at the receiver by a pseudo-inverse matrix which is pre-evaluated offline. For 512 (1024) frequency samples per channel, the VSTF measurement takes less than 1 (10) msec to complete with computational complexity of one real-valued multiply-add operation per time sample. Relative to a naïve exhaustive three-tone-test, our algorithm is far more tolerant of ASE additive noise and its acquisition time is orders of magnitude faster.

A review of human factors challenges of complex adaptive systems: discovering and understanding chaos in human performance.

PubMed

Karwowski, Waldemar

2012-12-01

In this paper, the author explores a need for a greater understanding of the true nature of human-system interactions from the perspective of the theory of complex adaptive systems, including the essence of complexity, emergent properties of system behavior, nonlinear systems dynamics, and deterministic chaos. Human performance, more often than not, constitutes complex adaptive phenomena with emergent properties that exhibit nonlinear dynamical (chaotic) behaviors. The complexity challenges in the design and management of contemporary work systems, including service systems, are explored. Examples of selected applications of the concepts of nonlinear dynamics to the study of human physical performance are provided. Understanding and applications of the concepts of theory of complex adaptive and dynamical systems should significantly improve the effectiveness of human-centered design efforts of a large system of systems. Performance of many contemporary work systems and environments may be sensitive to the initial conditions and may exhibit dynamic nonlinear properties and chaotic system behaviors. Human-centered design of emergent human-system interactions requires application of the theories of nonlinear dynamics and complex adaptive system. The success of future human-systems integration efforts requires the fusion of paradigms, knowledge, design principles, and methodologies of human factors and ergonomics with those of the science of complex adaptive systems as well as modern systems engineering.

Second-harmonic generation in substoichiometric silicon nitride layers

NASA Astrophysics Data System (ADS)

Pecora, Emanuele; Capretti, Antonio; Miano, Giovanni; Dal Negro, Luca

2013-03-01

Harmonic generation in optical circuits offers the possibility to integrate wavelength converters, light amplifiers, lasers, and multiple optical signal processing devices with electronic components. Bulk silicon has a negligible second-order nonlinear optical susceptibility owing to its crystal centrosymmetry. Silicon nitride has its place in the microelectronic industry as an insulator and chemical barrier. In this work, we propose to take advantage of silicon excess in silicon nitride to increase the Second Harmonic Generation (SHG) efficiency. Thin films have been grown by reactive magnetron sputtering and their nonlinear optical properties have been studied by femtosecond pumping over a wide range of excitation wavelengths, silicon nitride stoichiometry and thermal processes. We demonstrate SHG in the visible range (375 - 450 nm) using a tunable 150 fs Ti:sapphire laser, and we optimize the SH emission at a silicon excess of 46 at.% demonstrating a maximum SHG efficiency of 4x10-6 in optimized films. Polarization properties, generation efficiency, and the second order nonlinear optical susceptibility are measured for all the investigated samples and discussed in terms of an effective theoretical model. Our findings show that the large nonlinear optical response demonstrated in optimized Si-rich silicon nitride materials can be utilized for the engineering of nonlinear optical functions and devices on a Si chip.

Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method.

PubMed

Treeby, Bradley E; Jaros, Jiri; Rendell, Alistair P; Cox, B T

2012-06-01

The simulation of nonlinear ultrasound propagation through tissue realistic media has a wide range of practical applications. However, this is a computationally difficult problem due to the large size of the computational domain compared to the acoustic wavelength. Here, the k-space pseudospectral method is used to reduce the number of grid points required per wavelength for accurate simulations. The model is based on coupled first-order acoustic equations valid for nonlinear wave propagation in heterogeneous media with power law absorption. These are derived from the equations of fluid mechanics and include a pressure-density relation that incorporates the effects of nonlinearity, power law absorption, and medium heterogeneities. The additional terms accounting for convective nonlinearity and power law absorption are expressed as spatial gradients making them efficient to numerically encode. The governing equations are then discretized using a k-space pseudospectral technique in which the spatial gradients are computed using the Fourier-collocation method. This increases the accuracy of the gradient calculation and thus relaxes the requirement for dense computational grids compared to conventional finite difference methods. The accuracy and utility of the developed model is demonstrated via several numerical experiments, including the 3D simulation of the beam pattern from a clinical ultrasound probe.

Oscillating solutions for nonlinear Helmholtz equations

NASA Astrophysics Data System (ADS)

Mandel, Rainer; Montefusco, Eugenio; Pellacci, Benedetta

2017-12-01

Existence results for radially symmetric oscillating solutions for a class of nonlinear autonomous Helmholtz equations are given and their exact asymptotic behaviour at infinity is established. Some generalizations to nonautonomous radial equations as well as existence results for nonradial solutions are found. Our theorems prove the existence of standing waves solutions of nonlinear Klein-Gordon or Schrödinger equations with large frequencies.

Interactions of large amplitude solitary waves in viscous fluid conduits

NASA Astrophysics Data System (ADS)

Lowman, Nicholas K.; Hoefer, M. A.; El, G. A.

2014-07-01

The free interface separating an exterior, viscous fluid from an intrusive conduit of buoyant, less viscous fluid is known to support strongly nonlinear solitary waves due to a balance between viscosity-induced dispersion and buoyancy-induced nonlinearity. The overtaking, pairwise interaction of weakly nonlinear solitary waves has been classified theoretically for the Korteweg-de Vries equation and experimentally in the context of shallow water waves, but a theoretical and experimental classification of strongly nonlinear solitary wave interactions is lacking. The interactions of large amplitude solitary waves in viscous fluid conduits, a model physical system for the study of one-dimensional, truly dissipationless, dispersive nonlinear waves, are classified. Using a combined numerical and experimental approach, three classes of nonlinear interaction behavior are identified: purely bimodal, purely unimodal, and a mixed type. The magnitude of the dispersive radiation due to solitary wave interactions is quantified numerically and observed to be beyond the sensitivity of our experiments, suggesting that conduit solitary waves behave as "physical solitons." Experimental data are shown to be in excellent agreement with numerical simulations of the reduced model. Experimental movies are available with the online version of the paper.

On the nonlinear forced response of the North Atlantic atmosphere to meridional shifts of the Gulf Stream path

NASA Astrophysics Data System (ADS)

Seo, H.; Kwon, Y. O.; Joyce, T. M.; Ummenhofer, C.

2016-12-01

This study examines the North Atlantic atmospheric circulation response to the meridional shift of Gulf Stream path using a large-ensemble, high-resolution, and hemispheric-scale WRF simulations. The model is forced with wintertime SST anomalies derived from a wide range of Gulf Stream shift scenarios. The key result of the model experiments, supported in part by an independent analysis of a reanalysis data set, is that the large-scale, quasi-steady North Atlantic circulation response is unambiguously nonlinear about the sign and amplitude of chosen SST anomalies. This nonlinear response prevails over the weak linear response and resembles the negative North Atlantic Oscillation, the leading intrinsic mode of variability in the model and the observations. Further analysis of the associated dynamics reveals that the nonlinear responses are accompanied by the anomalous southward shift of the North Atlantic eddy-driven jet stream, which is reinforced nearly equally by the high-frequency transient eddy feedback and the low-frequency high-latitude wave breaking events. The result highlights the importance of the intrinsically nonlinear transient eddy dynamics and eddy-mean flow interactions in generating the nonlinear forced response to the meridional shift in the Gulf Stream.

Vectorial control of nonlinear emission via chiral butterfly nanoantennas: generation of pure high order nonlinear vortex beams.

PubMed

Lesina, Antonino Cala'; Berini, Pierre; Ramunno, Lora

2017-02-06

We report on a chiral gap-nanostructure, which we term a "butterfly nanoantenna," that offers full vectorial control over nonlinear emission. The field enhancement in its gap occurs for only one circular polarization but for every incident linear polarization. As the polarization, phase and amplitude of the linear field in the gap are highly controlled, the linear field can drive nonlinear emitters within the gap, which behave as an idealized Huygens source. A general framework is thereby proposed wherein the butterfly nanoantennas can be arranged in a metasurface, and the nonlinear Huygens sources exploited to produce a highly structured far-field optical beam. Nonlinearity allows us to shape the light at shorter wavelengths, not accessible by linear plasmonics, and resulting in high purity beams. The chirality of the butterfly allows us to create orbital angular momentum states using a linearly polarized excitation. A third harmonic Laguerre-Gauss beam carrying an optical orbital angular momentum of 41 is demonstrated as an example, through large-scale simulations on a high-performance computing platform of the full plasmonic metasurface with an area large enough to contain up to 3600 nanoantennas.

Analysis of the Nonlinear Characteristics of Microwave Power Heterojunction Bipolar Transistors and Optoelectronic Integrated Circuits.

NASA Astrophysics Data System (ADS)

Samelis, Apostolos

A physical basis for large-signal HBT modeling was established in terms of transit times using a Monte Carlo analysis of AlGaAs/GaAs and GaInP/GaAs designs. Static carriers located in the collector-subcollector interface were found to prohibit accurate evaluation of transit times from electron velocity profiles. These carriers also influence the bias dependence of device capacitances. Analytical parameter extraction techniques for DC, thermal and high frequency HBT parameters were developed and applied to HBT large-signal modeling. The "impedance block" conditioned optimization technique was introduced to facilitate parameter extraction. Physical analysis of HBTs by means of Volterra Series techniques showed that C_{bc } dominates nonlinear distortion in high gain amplifiers. Designs with that C_{bc }-V_{cb} characteristics i.e. p -n collector HBTs lead to more than 10 dB IP3 improvement over n-collector HBTs. Nonlinear current cancellation was found to improve intermodulation distortion. A Gummel -Poon-based HBT large-signal model incorporating self-heating effects was developed and applied to AlGaAs/GaAs HBTs. Maximum power drive was shown to occur using constant V _{be} father than I_ {b} bias. The device temperature of constant I_{b} biased HBTs decreases at increased rf-drive levels ensuring in this case safer device operation. A large-signal model incorporating "soft" -breakdown effects typical of InP/InGaAs HBTs was developed and found to model succesfully the power characteristics of OEICs built with them. The effective large-signal transimpedance of a cascode transimpedance preamplifier was evaluated using this model and found to degrade by 3dBOmega for a variation of P_{in} from -65 to -5 dBm. Self-bias of individual transistors was studied and found to be related to variations of the amplifier characteristics at higher rf-drive levels. The power characteristics of CE and CB AlGaAs/GaAs HBTs were investigated using an on -wafer source/load pull setup developed for this purpose. The load-pull power, intermodulation and efficiency contours of power CE HBTs are eccentric due to the feedback provided by C_{bc} between the input and output of the device. Concentric contours were found for P_{out} and PAE of CB HBTs.

A novel nonlinear damage resonance intermodulation effect for structural health monitoring

NASA Astrophysics Data System (ADS)

Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

2017-04-01

This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

Progressive Mid-latitude Afforestation: Local and Remote Climate Impacts in the Framework of Two Coupled Earth System Models

NASA Astrophysics Data System (ADS)

Lague, Marysa

Vegetation influences the atmosphere in complex and non-linear ways, such that large-scale changes in vegetation cover can drive changes in climate on both local and global scales. Large-scale land surface changes have been shown to introduce excess energy to one hemisphere, causing a shift in atmospheric circulation on a global scale. However, past work has not quantified how the climate response scales with the area of vegetation. Here, we systematically evaluate the response of climate to linearly increasing the area of forest cover over the northern mid-latitudes. We show that the magnitude of afforestation of the northern mid-latitudes determines the climate response in a non-linear fashion, and identify a threshold in vegetation-induced cloud feedbacks - a concept not previously addressed by large-scale vegetation manipulation experiments. Small increases in tree cover drive compensating cloud feedbacks, while latent heat fluxes reach a threshold after sufficiently large increases in tree cover, causing the troposphere to warm and dry, subsequently reducing cloud cover. Increased absorption of solar radiation at the surface is driven by both surface albedo changes and cloud feedbacks. We identify how vegetation-induced changes in cloud cover further feedback on changes in the global energy balance. We also show how atmospheric cross-equatorial energy transport changes as the area of afforestation is incrementally increased (a relationship which has not previously been demonstrated). This work demonstrates that while some climate effects (such as energy transport) of large scale mid-latitude afforestation scale roughly linearly across a wide range of afforestation areas, others (such as the local partitioning of the surface energy budget) are non-linear, and sensitive to the particular magnitude of mid-latitude forcing. Our results highlight the importance of considering both local and remote climate responses to large-scale vegetation change, and explore the scaling relationship between changes in vegetation cover and the resulting climate impacts.

Non-linear interactions between CO_2 radiative and physiological effects on Amazonian evapotranspiration in an Earth system model

NASA Astrophysics Data System (ADS)

Halladay, Kate; Good, Peter

2017-10-01

We present a detailed analysis of mechanisms underlying the evapotranspiration response to increased CO_2 in HadGEM2-ES, focussed on western Amazonia. We use three simulations from CMIP5 in which atmospheric CO_2 increases at 1% per year reaching approximately four times pre-industrial levels after 140 years. Using 3-hourly data, we found that evapotranspiration (ET) change was dominated by decreased stomatal conductance (g_s), and to a lesser extent by decreased canopy water and increased moisture gradient (specific humidity difference between surface and near-surface). There were large, non-linear decreases in ET in the simulation in which radiative and physiological forcings could interact. This non-linearity arises from non-linearity in the conductance term (includes aerodynamic and stomatal resistance and partitioning between the two, which is determined by canopy water availability), the moisture gradient, and negative correlation between these two terms. The conductance term is non-linear because GPP responds non-linearly to temperature and GPP is the dominant control on g_s in HadGEM2-ES. In addition, canopy water declines, mainly due to increases in potential evaporation, which further decrease the conductance term. The moisture gradient responds non-linearly owing to the non-linear response of temperature to CO_2 increases, which increases the Bowen ratio. Moisture gradient increases resulting from ET decline increase ET and thus constitute a negative feedback. This analysis highlights the importance of the g_s parametrisation in determining the ET response and the potential differences between offline and online simulations owing to feedbacks on ET via the atmosphere, some of which would not occur in an offline simulation.

Numerical simulation and comparison of nonlinear self-focusing based on iteration and ray tracing

NASA Astrophysics Data System (ADS)

Li, Xiaotong; Chen, Hao; Wang, Weiwei; Ruan, Wangchao; Zhang, Luwei; Cen, Zhaofeng

2017-05-01

Self-focusing is observed in nonlinear materials owing to the interaction between laser and matter when laser beam propagates. Some of numerical simulation strategies such as the beam propagation method (BPM) based on nonlinear Schrödinger equation and ray tracing method based on Fermat's principle have applied to simulate the self-focusing process. In this paper we present an iteration nonlinear ray tracing method in that the nonlinear material is also cut into massive slices just like the existing approaches, but instead of paraxial approximation and split-step Fourier transform, a large quantity of sampled real rays are traced step by step through the system with changing refractive index and laser intensity by iteration. In this process a smooth treatment is employed to generate a laser density distribution at each slice to decrease the error caused by the under-sampling. The characteristics of this method is that the nonlinear refractive indices of the points on current slice are calculated by iteration so as to solve the problem of unknown parameters in the material caused by the causal relationship between laser intensity and nonlinear refractive index. Compared with the beam propagation method, this algorithm is more suitable for engineering application with lower time complexity, and has the calculation capacity for numerical simulation of self-focusing process in the systems including both of linear and nonlinear optical media. If the sampled rays are traced with their complex amplitudes and light paths or phases, it will be possible to simulate the superposition effects of different beam. At the end of the paper, the advantages and disadvantages of this algorithm are discussed.

Homogenized description and retrieval method of nonlinear metasurfaces

NASA Astrophysics Data System (ADS)

Liu, Xiaojun; Larouche, Stéphane; Smith, David R.

2018-03-01

A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry and material composition, across the electromagnetic spectrum.

NONLINEARITIES IN THE SULFATE SECONDARY FINE PARTICULATE RESPONSE TO NOX EMISSIONS REDUCTIONS AS MODELED BY THE REGIONAL ACID DEPOSITION MODEL

EPA Science Inventory

Attention is increasingly being devoted to the health effects of fine particulates. In regions that have a large production of sulfate, sulfuric acid and nitric acid compete for the available ammonia to form aerosols. In addition, the available nitric acid is the result of ur...

Forced cubic Schrödinger equation with Robin boundary data: large-time asymptotics

PubMed Central

Kaikina, Elena I.

2013-01-01

We consider the initial-boundary-value problem for the cubic nonlinear Schrödinger equation, formulated on a half-line with inhomogeneous Robin boundary data. We study traditionally important problems of the theory of nonlinear partial differential equations, such as the global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behaviour of solutions for large time. PMID:24204185

Electromechanical quantum simulators

NASA Astrophysics Data System (ADS)

Tacchino, F.; Chiesa, A.; LaHaye, M. D.; Carretta, S.; Gerace, D.

2018-06-01

Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It is shown that very high operational fidelities for single- and two-qubits gates can be achieved in a minimal architecture, where qubits are encoded in the anharmonic vibrational modes of mechanical nanoresonators, whose effective coupling is mediated by virtual fluctuations of an intermediate superconducting artificial atom. An effective scheme to induce large single-phonon nonlinearities in nanoelectromechanical devices is explicitly discussed, thus opening the route to experimental investigation in this direction. Finally, we explicitly show the very high fidelities that can be reached for the digital quantum simulation of model Hamiltonians, by using realistic experimental parameters in state-of-the-art devices, and considering the transverse field Ising model as a paradigmatic example.

Real-time photonic sampling with improved signal-to-noise and distortion ratio using polarization-dependent modulators

NASA Astrophysics Data System (ADS)

Liang, Dong; Zhang, Zhiyao; Liu, Yong; Li, Xiaojun; Jiang, Wei; Tan, Qinggui

2018-04-01

A real-time photonic sampling structure with effective nonlinearity suppression and excellent signal-to-noise ratio (SNR) performance is proposed. The key points of this scheme are the polarization-dependent modulators (P-DMZMs) and the sagnac loop structure. Thanks to the polarization sensitive characteristic of P-DMZMs, the differences between transfer functions of the fundamental signal and the distortion become visible. Meanwhile, the selection of specific biases in P-DMZMs is helpful to achieve a preferable linearized performance with a low noise level for real-time photonic sampling. Compared with the quadrature-biased scheme, the proposed scheme is capable of valid nonlinearity suppression and is able to provide a better SNR performance even in a large frequency range. The proposed scheme is proved to be effective and easily implemented for real time photonic applications.

Trampoline Effect: Observations and Modeling

NASA Astrophysics Data System (ADS)

Guyer, R.; Larmat, C. S.; Ulrich, T. J.

2009-12-01

The Iwate-Miyagi earthquake at site IWTH25 (14 June 2008) had large, asymmetric at surface vertical accelerations prompting the sobriquet trampoline effect (Aoi et. al. 2008). In addition the surface acceleration record showed long-short waiting time correlations and vertical-horizontal acceleration correlations. A lumped element model, deduced from the equations of continuum elasticity, is employed to describe the behavior at this site in terms of a surface layer and substrate. Important ingredients in the model are the nonlinear vertical coupling between the surface layer and the substrate and the nonlinear horizontal frictional coupling between the surface layer and the substrate. The model produces results in qualitative accord with observations: acceleration asymmetry, Fourier spectrum, waiting time correlations and vertical acceleration-horizontal acceleration correlations. [We gratefully acknowledge the support of the U. S. Department of Energy through the LANL/LDRD Program for this work].

Efficient L1 regularization-based reconstruction for fluorescent molecular tomography using restarted nonlinear conjugate gradient.

PubMed

Shi, Junwei; Zhang, Bin; Liu, Fei; Luo, Jianwen; Bai, Jing

2013-09-15

For the ill-posed fluorescent molecular tomography (FMT) inverse problem, the L1 regularization can protect the high-frequency information like edges while effectively reduce the image noise. However, the state-of-the-art L1 regularization-based algorithms for FMT reconstruction are expensive in memory, especially for large-scale problems. An efficient L1 regularization-based reconstruction algorithm based on nonlinear conjugate gradient with restarted strategy is proposed to increase the computational speed with low memory consumption. The reconstruction results from phantom experiments demonstrate that the proposed algorithm can obtain high spatial resolution and high signal-to-noise ratio, as well as high localization accuracy for fluorescence targets.

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

NASA Astrophysics Data System (ADS)

Do, K. D.

2018-05-01

Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

Jump phenomena. [large amplitude responses of nonlinear systems

NASA Technical Reports Server (NTRS)

Reiss, E. L.

1980-01-01

The paper considers jump phenomena composed of large amplitude responses of nonlinear systems caused by small amplitude disturbances. Physical problems where large jumps in the solution amplitude are important features of the response are described, including snap buckling of elastic shells, chemical reactions leading to combustion and explosion, and long-term climatic changes of the earth's atmosphere. A new method of rational functions was then developed which consists of representing the solutions of the jump problems as rational functions of the small disturbance parameter; this method can solve jump problems explicitly.

An Integrated, Optimization-Based Approach to the Design and Control of Large Space Structures.

DTIC Science & Technology

1984-05-01

investigator.s shall use a nonlinear beam model for the large motions, and they shall use a linear beam model to describe the small displacements as a... use a nonlinear beam model for the large motions, and we shall use a linear beam model to describe the small displacements as a perturbation around the...of the angular velocity, wt as follows 0 = 0 - 0 (2. ) -01 G,𔃼 - f- 0. The use of a quaternion avoids singularities which are often encountered in

A numerical study of nonlinear infrasound propagation in a windy atmosphere.

PubMed

Sabatini, R; Marsden, O; Bailly, C; Bogey, C

2016-07-01

Direct numerical simulations of the two-dimensional unsteady compressible Navier-Stokes equations are performed to study the acoustic field generated by an infrasonic source in a realistic atmosphere. Some of the main phenomena affecting the propagation of infrasonic waves at large distances from the source are investigated. The effects of thermal and wind-related refraction on the signals recorded at ground level are highlighted, with particular emphasis on the phase shift induced by the presence of caustics in the acoustic field. Nonlinear waveform steepening associated with harmonic generation, and period lengthening, both of which are typical of large source amplitudes, are illustrated, and the importance of thermoviscous absorption in the upper atmosphere is clearly demonstrated. The role of diffraction in the shadow zone, around caustics and at stratospheric altitudes is also pointed out. The Navier-Stokes equations are solved using high-order finite-differences and a Runge-Kutta time integration method both originally developed for aeroacoustic applications, along with an adaptive shock-capturing algorithm which allows high-intensity acoustic fields to be examined. An improvement to the shock detection procedure is also proposed in order to meet the specificities of nonlinear propagation at long range. The modeling as well as the numerical results are reported in detail and discussed.

Stationary solutions for the nonlinear Schrödinger equation modeling three-dimensional spherical Bose-Einstein condensates in general potentials.

PubMed

Mallory, Kristina; Van Gorder, Robert A

2015-07-01

Stationary solutions for the cubic nonlinear Schrödinger equation modeling Bose-Einstein condensates (BECs) confined in three spatial dimensions by general forms of a potential are studied through a perturbation method and also numerically. Note that we study both repulsive and attractive BECs under similar frameworks in order to deduce the effects of the potentials in each case. After outlining the general framework, solutions for a collection of specific confining potentials of physical relevance to experiments on BECs are provided in order to demonstrate the approach. We make several observations regarding the influence of the particular potentials on the behavior of the BECs in these cases, comparing and contrasting the qualitative behavior of the attractive and repulsive BECs for potentials of various strengths and forms. Finally, we consider the nonperturbative where the potential or the amplitude of the solutions is large, obtaining various qualitative results. When the kinetic energy term is small (relative to the nonlinearity and the confining potential), we recover the expected Thomas-Fermi approximation for the stationary solutions. Naturally, this also occurs in the large mass limit. Through all of these results, we are able to understand the qualitative behavior of spherical three-dimensional BECs in weak, intermediate, or strong confining potentials.

Circumpolar dynamics of a marine top-predator track ocean warming rates.

PubMed

Descamps, Sébastien; Anker-Nilssen, Tycho; Barrett, Robert T; Irons, David B; Merkel, Flemming; Robertson, Gregory J; Yoccoz, Nigel G; Mallory, Mark L; Montevecchi, William A; Boertmann, David; Artukhin, Yuri; Christensen-Dalsgaard, Signe; Erikstad, Kjell-Einar; Gilchrist, H Grant; Labansen, Aili L; Lorentsen, Svein-Håkon; Mosbech, Anders; Olsen, Bergur; Petersen, Aevar; Rail, Jean-Francois; Renner, Heather M; Strøm, Hallvard; Systad, Geir H; Wilhelm, Sabina I; Zelenskaya, Larisa

2017-09-01

Global warming is a nonlinear process, and temperature may increase in a stepwise manner. Periods of abrupt warming can trigger persistent changes in the state of ecosystems, also called regime shifts. The responses of organisms to abrupt warming and associated regime shifts can be unlike responses to periods of slow or moderate change. Understanding of nonlinearity in the biological responses to climate warming is needed to assess the consequences of ongoing climate change. Here, we demonstrate that the population dynamics of a long-lived, wide-ranging marine predator are associated with changes in the rate of ocean warming. Data from 556 colonies of black-legged kittiwakes Rissa tridactyla distributed throughout its breeding range revealed that an abrupt warming of sea-surface temperature in the 1990s coincided with steep kittiwake population decline. Periods of moderate warming in sea temperatures did not seem to affect kittiwake dynamics. The rapid warming observed in the 1990s may have driven large-scale, circumpolar marine ecosystem shifts that strongly affected kittiwakes through bottom-up effects. Our study sheds light on the nonlinear response of a circumpolar seabird to large-scale changes in oceanographic conditions and indicates that marine top predators may be more sensitive to the rate of ocean warming rather than to warming itself. © 2017 John Wiley & Sons Ltd.

Studies of the linear and nonlinear properties of Alfvén waves in LAPD

NASA Astrophysics Data System (ADS)

Carter, Troy; Dorfman, Seth; Gekelman, Walter; Tripathi, Shreekrishna; van Compernolle, Bart; Vincena, Steve; Rossi, Giovanni; Jenko, Frank

2015-11-01

An overview will be given of recent experimental research into linear and nonlinear properties of Alfvén waves in the Large Plasma Device (LAPD). The nonlinear three-wave interaction process at the heart of the parametric decay instability is studied by launching counter-propagating Alfvén waves from antennas placed at either end of LAPD, producing a damped ion acoustic mode. The decay of a lone, large amplitude Alfvén wave has been observed, producing co-propagating daughter waves with characteristics consistent with kinetic Alfvén waves. The process has an amplitude threshold and the frequency of the daughter modes varies with the amplitude of the pump. A new plasma source based on LaB6 cathode has been added to LAPD, enabling much higher density (x50), electron temperature (x2) and ion temperature (x6). This provides the opportunity to study the physics of waves and instabilities with space and astrophysically relevant β. Topics under investigation include the physics of Alfvén waves in increased β plasmas, electromagnetic effects in drift-Alfvén wave turbulence and the excitation of ion-temperature-anisotropy driven modes such as the mirror and firehose. Supported by NSF and DOE.

Evaluation of bias associated with capture maps derived from nonlinear groundwater flow models

USGS Publications Warehouse

Nadler, Cara; Allander, Kip K.; Pohll, Greg; Morway, Eric D.; Naranjo, Ramon C.; Huntington, Justin

2018-01-01

The impact of groundwater withdrawal on surface water is a concern of water users and water managers, particularly in the arid western United States. Capture maps are useful tools to spatially assess the impact of groundwater pumping on water sources (e.g., streamflow depletion) and are being used more frequently for conjunctive management of surface water and groundwater. Capture maps have been derived using linear groundwater flow models and rely on the principle of superposition to demonstrate the effects of pumping in various locations on resources of interest. However, nonlinear models are often necessary to simulate head-dependent boundary conditions and unconfined aquifers. Capture maps developed using nonlinear models with the principle of superposition may over- or underestimate capture magnitude and spatial extent. This paper presents new methods for generating capture difference maps, which assess spatial effects of model nonlinearity on capture fraction sensitivity to pumping rate, and for calculating the bias associated with capture maps. The sensitivity of capture map bias to selected parameters related to model design and conceptualization for the arid western United States is explored. This study finds that the simulation of stream continuity, pumping rates, stream incision, well proximity to capture sources, aquifer hydraulic conductivity, and groundwater evapotranspiration extinction depth substantially affect capture map bias. Capture difference maps demonstrate that regions with large capture fraction differences are indicative of greater potential capture map bias. Understanding both spatial and temporal bias in capture maps derived from nonlinear groundwater flow models improves their utility and defensibility as conjunctive-use management tools.

Large predispersion for reduction of intrachannel nonlinear impairments in strongly dispersion-managed transmissions

NASA Astrophysics Data System (ADS)

Cao, Wenhua

2016-05-01

Predispersion for reduction of intrachannel nonlinear impairments in quasi-linear strongly dispersion-managed transmission system is analyzed in detail by numerical simulations. We show that for moderate amount of predispersion there is an optimal value at which reduction of the nonlinear impairments can be obtained, which is consistent with previous well-known predictions. However, we found that much better transmission performance than that of the previous predictions can be obtained if predispersion is increased to some extent. For large predispersion, the nonlinear impairments reduce monotonically with increasing predispersion and then they tend to be stabilized when predispersion is further increased. Thus, transmission performance can be efficiently improved by inserting a high-dispersive element, such as a chirped fiber bragg grating (CFBG), at the input end of the transmission link to broaden the signal pulses while, at the output end, using another CFBG with the opposite dispersion to recompress the signal.

Nonlinear finite amplitude torsional vibrations of cantilevers in viscous fluids

NASA Astrophysics Data System (ADS)

Aureli, Matteo; Pagano, Christopher; Porfiri, Maurizio

2012-06-01

In this paper, we study torsional vibrations of cantilever beams undergoing moderately large oscillations within a quiescent viscous fluid. The structure is modeled as an Euler-Bernoulli beam, with thin rectangular cross section, under base excitation. The distributed hydrodynamic loading experienced by the vibrating structure is described through a complex-valued hydrodynamic function which incorporates added mass and fluid damping elicited by moderately large rotations. We conduct a parametric study on the two dimensional computational fluid dynamics of a pitching rigid lamina, representative of a generic beam cross section, to investigate the dependence of the hydrodynamic function on the governing flow parameters. As the frequency and amplitude of the oscillation increase, vortex shedding and convection phenomena increase, thus resulting into nonlinear hydrodynamic damping. We derive a handleable nonlinear correction to the classical hydrodynamic function developed for small amplitude torsional vibrations for use in a reduced order nonlinear modal model and we validate theoretical results against experimental findings.

Nonlinear MHD simulations of QH-mode DIII-D plasmas and implications for ITER high Q scenarios

NASA Astrophysics Data System (ADS)

Liu, F.; Huijsmans, G. T. A.; Loarte, A.; Garofalo, A. M.; Solomon, W. M.; Hoelzl, M.; Nkonga, B.; Pamela, S.; Becoulet, M.; Orain, F.; Van Vugt, D.

2018-01-01

In nonlinear MHD simulations of DIII-D QH-mode plasmas it has been found that low n kink/peeling modes (KPMs) are unstable and grow to a saturated kink-peeling mode. The features of the dominant saturated KPMs, which are localised toroidally by nonlinear coupling of harmonics, such as mode frequencies, density fluctuations and their effect on pedestal particle and energy transport, are in good agreement with the observations of the edge harmonic oscillation typically present in DIII-D QH-mode experiments. The nonlinear evolution of MHD modes including both kink-peeling modes and ballooning modes, is investigated through MHD simulations by varying the pedestal current and pressure relative to the initial conditions of DIII-D QH-mode plasma. The edge current and pressure at the pedestal are key parameters for the plasma either saturating to a QH-mode regime or a ballooning mode dominant regime. The influence of E × B flow and its shear on the QH-mode plasma has been investigated. E × B flow shear has a strong stabilisation effect on the medium to high-n modes but is destabilising for the n = 2 mode. The QH-mode extrapolation results of an ITER Q = 10 plasma show that the pedestal currents are large enough to destabilise n = 1-5 KPMs, leading to a stationary saturated kink-peeling mode.

Nonlinear spin current generation in noncentrosymmetric spin-orbit coupled systems

NASA Astrophysics Data System (ADS)

Hamamoto, Keita; Ezawa, Motohiko; Kim, Kun Woo; Morimoto, Takahiro; Nagaosa, Naoto

2017-06-01

Spin current plays a central role in spintronics. In particular, finding more efficient ways to generate spin current has been an important issue and has been studied actively. For example, representative methods of spin-current generation include spin-polarized current injections from ferromagnetic metals, the spin Hall effect, and the spin battery. Here, we theoretically propose a mechanism of spin-current generation based on nonlinear phenomena. By using Boltzmann transport theory, we show that a simple application of the electric field E induces spin current proportional to E2 in noncentrosymmetric spin-orbit coupled systems. We demonstrate that the nonlinear spin current of the proposed mechanism is supported in the surface state of three-dimensional topological insulators and two-dimensional semiconductors with the Rashba and/or Dresselhaus interaction. In the latter case, the angular dependence of the nonlinear spin current can be manipulated by the direction of the electric field and by the ratio of the Rashba and Dresselhaus interactions. We find that the magnitude of the spin current largely exceeds those in the previous methods for a reasonable magnitude of the electric field. Furthermore, we show that application of ac electric fields (e.g., terahertz light) leads to the rectifying effect of the spin current, where dc spin current is generated. These findings will pave a route to manipulate the spin current in noncentrosymmetric crystals.

GPU simulation of nonlinear propagation of dual band ultrasound pulse complexes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kvam, Johannes, E-mail: johannes.kvam@ntnu.no; Angelsen, Bjørn A. J., E-mail: bjorn.angelsen@ntnu.no; Elster, Anne C., E-mail: elster@ntnu.no

In a new method of ultrasound imaging, called SURF imaging, dual band pulse complexes composed of overlapping low frequency (LF) and high frequency (HF) pulses are transmitted, where the frequency ratio LF:HF ∼ 1 : 20, and the relative bandwidth of both pulses are ∼ 50 − 70%. The LF pulse length is hence ∼ 20 times the HF pulse length. The LF pulse is used to nonlinearly manipulate the material elasticity observed by the co-propagating HF pulse. This produces nonlinear interaction effects that give more information on the propagation of the pulse complex. Due to the large difference inmore » frequency and pulse length between the LF and the HF pulses, we have developed a dual level simulation where the LF pulse propagation is first simulated independent of the HF pulse, using a temporal sampling frequency matched to the LF pulse. A separate equation for the HF pulse is developed, where the the presimulated LF pulse modifies the propagation velocity. The equations are adapted to parallel processing in a GPU, where nonlinear simulations of a typical HF beam of 10 MHz down to 40 mm is done in ∼ 2 secs in a standard GPU. This simulation is hence very useful for studying the manipulation effect of the LF pulse on the HF pulse.« less

Sensitivity to mental effort and test-retest reliability of heart rate variability measures in healthy seniors.

PubMed

Mukherjee, Shalini; Yadav, Rajeev; Yung, Iris; Zajdel, Daniel P; Oken, Barry S

2011-10-01

To determine (1) whether heart rate variability (HRV) was a sensitive and reliable measure in mental effort tasks carried out by healthy seniors and (2) whether non-linear approaches to HRV analysis, in addition to traditional time and frequency domain approaches were useful to study such effects. Forty healthy seniors performed two visual working memory tasks requiring different levels of mental effort, while ECG was recorded. They underwent the same tasks and recordings 2 weeks later. Traditional and 13 non-linear indices of HRV including Poincaré, entropy and detrended fluctuation analysis (DFA) were determined. Time domain, especially mean R-R interval (RRI), frequency domain and, among non-linear parameters - Poincaré and DFA were the most reliable indices. Mean RRI, time domain and Poincaré were also the most sensitive to different mental effort task loads and had the largest effect size. Overall, linear measures were the most sensitive and reliable indices to mental effort. In non-linear measures, Poincaré was the most reliable and sensitive, suggesting possible usefulness as an independent marker in cognitive function tasks in healthy seniors. A large number of HRV parameters was both reliable as well as sensitive indices of mental effort, although the simple linear methods were the most sensitive. Copyright © 2011 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

Dynamical mean-field theory and weakly non-linear analysis for the phase separation of active Brownian particles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Speck, Thomas; Menzel, Andreas M.; Bialké, Julian

2015-06-14

Recently, we have derived an effective Cahn-Hilliard equation for the phase separation dynamics of active Brownian particles by performing a weakly non-linear analysis of the effective hydrodynamic equations for density and polarization [Speck et al., Phys. Rev. Lett. 112, 218304 (2014)]. Here, we develop and explore this strategy in more detail and show explicitly how to get to such a large-scale, mean-field description starting from the microscopic dynamics. The effective free energy emerging from this approach has the form of a conventional Ginzburg-Landau function. On the coarsest scale, our results thus agree with the mapping of active phase separation ontomore » that of passive fluids with attractive interactions through a global effective free energy (motility-induced phase transition). Particular attention is paid to the square-gradient term necessary for the phase separation kinetics. We finally discuss results from numerical simulations corroborating the analytical results.« less

A class of non-linear exposure-response models suitable for health impact assessment applicable to large cohort studies of ambient air pollution.

PubMed

Nasari, Masoud M; Szyszkowicz, Mieczysław; Chen, Hong; Crouse, Daniel; Turner, Michelle C; Jerrett, Michael; Pope, C Arden; Hubbell, Bryan; Fann, Neal; Cohen, Aaron; Gapstur, Susan M; Diver, W Ryan; Stieb, David; Forouzanfar, Mohammad H; Kim, Sun-Young; Olives, Casey; Krewski, Daniel; Burnett, Richard T

2016-01-01

The effectiveness of regulatory actions designed to improve air quality is often assessed by predicting changes in public health resulting from their implementation. Risk of premature mortality from long-term exposure to ambient air pollution is the single most important contributor to such assessments and is estimated from observational studies generally assuming a log-linear, no-threshold association between ambient concentrations and death. There has been only limited assessment of this assumption in part because of a lack of methods to estimate the shape of the exposure-response function in very large study populations. In this paper, we propose a new class of variable coefficient risk functions capable of capturing a variety of potentially non-linear associations which are suitable for health impact assessment. We construct the class by defining transformations of concentration as the product of either a linear or log-linear function of concentration multiplied by a logistic weighting function. These risk functions can be estimated using hazard regression survival models with currently available computer software and can accommodate large population-based cohorts which are increasingly being used for this purpose. We illustrate our modeling approach with two large cohort studies of long-term concentrations of ambient air pollution and mortality: the American Cancer Society Cancer Prevention Study II (CPS II) cohort and the Canadian Census Health and Environment Cohort (CanCHEC). We then estimate the number of deaths attributable to changes in fine particulate matter concentrations over the 2000 to 2010 time period in both Canada and the USA using both linear and non-linear hazard function models.

The MICE grand challenge lightcone simulation - I. Dark matter clustering

NASA Astrophysics Data System (ADS)

Fosalba, P.; Crocce, M.; Gaztañaga, E.; Castander, F. J.

2015-04-01

We present a new N-body simulation from the Marenostrum Institut de Ciències de l'Espai (MICE) collaboration, the MICE Grand Challenge (MICE-GC), containing about 70 billion dark matter particles in a (3 Gpc h-1)3 comoving volume. Given its large volume and fine spatial resolution, spanning over five orders of magnitude in dynamic range, it allows an accurate modelling of the growth of structure in the universe from the linear through the highly non-linear regime of gravitational clustering. We validate the dark matter simulation outputs using 3D and 2D clustering statistics, and discuss mass-resolution effects in the non-linear regime by comparing to previous simulations and the latest numerical fits. We show that the MICE-GC run allows for a measurement of the BAO feature with per cent level accuracy and compare it to state-of-the-art theoretical models. We also use sub-arcmin resolution pixelized 2D maps of the dark matter counts in the lightcone to make tomographic analyses in real and redshift space. Our analysis shows the simulation reproduces the Kaiser effect on large scales, whereas we find a significant suppression of power on non-linear scales relative to the real space clustering. We complete our validation by presenting an analysis of the three-point correlation function in this and previous MICE simulations, finding further evidence for mass-resolution effects. This is the first of a series of three papers in which we present the MICE-GC simulation, along with a wide and deep mock galaxy catalogue built from it. This mock is made publicly available through a dedicated web portal, http://cosmohub.pic.es.

Optical Limiting Based on Liquid-Liquid Immiscibility

DOE Office of Scientific and Technical Information (OSTI.GOV)

Exarhos, Gregory J.; Ferris, Kim F.; Samuels, William D.

A nonionic surfactant is used to stabilize a dispersed droplet phase in a continuous liquid phase when two immiscible liquids are mixed. As both liquid phases approach the index matched condition, interfacial scattering is suppressed, and the mixture takes on the characteristics of a Christiansen-Shelyubskii filter. If, in addition, one of the liquids exhibits a substantial nonlinear optical response, then interfacial light scattering can be reversibly turned on when a laser beam incident upon the filter exceeds a critical fluence. To demonstrate this effect, an organic phase (dichloroethane) was dispersed in an aqueous phase containing sodium thiocyanate (NaSCN) using anmore » alkyl end-capped polyethylene glycol ether. The salt concentration was adjusted so that the index-matched mixture exhibited a large pass band. Marked optical limiting was observed through this transparent medium under conditions where the focused second-harmonic output of a Q-Switched Nd:YAG laser was on the order of about 50 mJ/cm2. An open-aperture Z-scan technique was used to quantify the limiting behavior. Since the thiocyanate anion is both isostructural and isoelectronic with carbon disulfide which exhibits a large optical nonlinearity, the mechanism of optical limiting is thought to be a nonlinear shift in the aqueous fluid index of refraction, resulting in an index mismatch between the disparate phases at high laser fluence. Index mismatch between the two phases leads to multiple reflections, loss of coherence, and a significant transmission decrease due to Mie scattering. The presence of many boundaries significantly amplifies the effect. Experiments also were conducted on the phase-inverted system (aqueous phase in organic liquid). Fundamental studies of such systems are used to verify theoretical predictions of the limiting effect, and aid in the design and development of improved limiters based upon this optical deflection approach.« less

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

PubMed

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series

NASA Astrophysics Data System (ADS)

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Film thickness measurement based on nonlinear phase analysis using a Linnik microscopic white-light spectral interferometer.

PubMed

Guo, Tong; Chen, Zhuo; Li, Minghui; Wu, Juhong; Fu, Xing; Hu, Xiaotang

2018-04-20

Based on white-light spectral interferometry and the Linnik microscopic interference configuration, the nonlinear phase components of the spectral interferometric signal were analyzed for film thickness measurement. The spectral interferometric signal was obtained using a Linnik microscopic white-light spectral interferometer, which includes the nonlinear phase components associated with the effective thickness, the nonlinear phase error caused by the double-objective lens, and the nonlinear phase of the thin film itself. To determine the influence of the effective thickness, a wavelength-correction method was proposed that converts the effective thickness into a constant value; the nonlinear phase caused by the effective thickness can then be determined and subtracted from the total nonlinear phase. A method for the extraction of the nonlinear phase error caused by the double-objective lens was also proposed. Accurate thickness measurement of a thin film can be achieved by fitting the nonlinear phase of the thin film after removal of the nonlinear phase caused by the effective thickness and by the nonlinear phase error caused by the double-objective lens. The experimental results demonstrated that both the wavelength-correction method and the extraction method for the nonlinear phase error caused by the double-objective lens improve the accuracy of film thickness measurements.