UV and NIR-Responsive Layer-by-Layer Films Containing 6-Bromo-7-hydroxycoumarin Photolabile Groups

PubMed Central

2017-01-01

This paper describes polyelectrolyte multilayer films prepared by the layer-by-layer (LbL) technique capable of undergoing dissolution upon exposure to either ultraviolet or near-infrared light. Film dissolution is driven by photochemical deprotection of a random methacrylic copolymer with two types of side chains: (i) 6-bromo-7-hydroxycoumarinyl esters, photocleavable groups that are known to have substantial two-photon photolysis cross sections, and (ii) cationic residues from the commercially available monomer N,N-dimethylaminoethyl methacrylate (DMAEMA). In addition, the dependence of stability of both unirradiated and irradiated films on pH provides experimental evidence for the necessity of disrupting both ion-pairing and hydrophobic interactions between polyelectrolytes to realize film dissolution. This work therefore provides both new fundamental insight regarding photolabile LbL films and expands their applied capabilities to nonlinear photochemical processes. PMID:28967754

Ultra-large nonlinear parameter in graphene-silicon waveguide structures.

PubMed

Donnelly, Christine; Tan, Dawn T H

2014-09-22

Mono-layer graphene integrated with optical waveguides is studied for the purpose of maximizing E-field interaction with the graphene layer, for the generation of ultra-large nonlinear parameters. It is shown that the common approach used to minimize the waveguide effective modal area does not accurately predict the configuration with the maximum nonlinear parameter. Both photonic and plasmonic waveguide configurations and graphene integration techniques realizable with today's fabrication tools are studied. Importantly, nonlinear parameters exceeding 10(4) W(-1)/m, two orders of magnitude larger than that in silicon on insulator waveguides without graphene, are obtained for the quasi-TE mode in silicon waveguides incorporating mono-layer graphene in the evanescent part of the optical field. Dielectric loaded surface plasmon polariton waveguides incorporating mono-layer graphene are observed to generate nonlinear parameters as large as 10(5) W(-1)/m, three orders of magnitude larger than that in silicon on insulator waveguides without graphene. The ultra-large nonlinear parameters make such waveguides promising platforms for nonlinear integrated optics at ultra-low powers, and for previously unobserved nonlinear optical effects to be studied in a waveguide platform.

Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable

ERIC Educational Resources Information Center

du Toit, Stephen H. C.; Cudeck, Robert

2009-01-01

A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…

A predictability study of Lorenz's 28-variable model as a dynamical system

NASA Technical Reports Server (NTRS)

Krishnamurthy, V.

1993-01-01

The dynamics of error growth in a two-layer nonlinear quasi-geostrophic model has been studied to gain an understanding of the mathematical theory of atmospheric predictability. The growth of random errors of varying initial magnitudes has been studied, and the relation between this classical approach and the concepts of the nonlinear dynamical systems theory has been explored. The local and global growths of random errors have been expressed partly in terms of the properties of an error ellipsoid and the Liapunov exponents determined by linear error dynamics. The local growth of small errors is initially governed by several modes of the evolving error ellipsoid but soon becomes dominated by the longest axis. The average global growth of small errors is exponential with a growth rate consistent with the largest Liapunov exponent. The duration of the exponential growth phase depends on the initial magnitude of the errors. The subsequent large errors undergo a nonlinear growth with a steadily decreasing growth rate and attain saturation that defines the limit of predictability. The degree of chaos and the largest Liapunov exponent show considerable variation with change in the forcing, which implies that the time variation in the external forcing can introduce variable character to the predictability.

Numerical simulation of the nonlinear response of composite plates under combined thermal and acoustic loading

NASA Technical Reports Server (NTRS)

Mei, Chuh; Moorthy, Jayashree

1995-01-01

A time-domain study of the random response of a laminated plate subjected to combined acoustic and thermal loads is carried out. The features of this problem also include given uniform static inplane forces. The formulation takes into consideration a possible initial imperfection in the flatness of the plate. High decibel sound pressure levels along with high thermal gradients across thickness drive the plate response into nonlinear regimes. This calls for the analysis to use von Karman large deflection strain-displacement relationships. A finite element model that combines the von Karman strains with the first-order shear deformation plate theory is developed. The development of the analytical model can accommodate an anisotropic composite laminate built up of uniformly thick layers of orthotropic, linearly elastic laminae. The global system of finite element equations is then reduced to a modal system of equations. Numerical simulation using a single-step algorithm in the time-domain is then carried out to solve for the modal coordinates. Nonlinear algebraic equations within each time-step are solved by the Newton-Raphson method. The random gaussian filtered white noise load is generated using Monte Carlo simulation. The acoustic pressure distribution over the plate is capable of accounting for a grazing incidence wavefront. Numerical results are presented to study a variety of cases.

Study of recombination characteristics in MOCVD grown GaN epi-layers on Si

NASA Astrophysics Data System (ADS)

Gaubas, E.; Ceponis, T.; Dobrovolskas, D.; Malinauskas, T.; Meskauskaite, D.; Miasojedovas, S.; Mickevicius, J.; Pavlov, J.; Rumbauskas, V.; Simoen, E.; Zhao, M.

2017-12-01

The radiative and non-radiative recombination carrier decay lifetimes in GaN epi-layers grown by metal-organic chemical vapour deposition technology on Si substrates were measured by contactless techniques of time-resolved photoluminescence and microwave-probed transients of photoconductivity. The lifetime variations were obtained to be dependent on growth regimes. These variations have been related to varied densities of edge dislocations associated with growth temperature. It has been also revealed that the lateral carrier lifetime and photoluminescence intensity distribution is determined by the formation of dislocation clusters dependent on the growth conditions. For low excitation level, the asymptotic component within the excess carrier decay transients is attributed to carrier trapping and anomalous diffusion through random-walk processes within dislocation cluster regions and barriers at dislocation cores. The two-componential decay process at high excitation conditions, where excess carriers may suppress barriers, proceeds through a nonlinear recombination, where band-to-band transitions determine the nonlinearity of the process, while the asymptotic component is ascribed to the impact of D-A pair PL within the long-wavelength wing of the UV-PL band.

Probing nonlinear rheology layer-by-layer in interfacial hydration water.

PubMed

Kim, Bongsu; Kwon, Soyoung; Lee, Manhee; Kim, Q Hwan; An, Sangmin; Jhe, Wonho

2015-12-22

Viscoelastic fluids exhibit rheological nonlinearity at a high shear rate. Although typical nonlinear effects, shear thinning and shear thickening, have been usually understood by variation of intrinsic quantities such as viscosity, one still requires a better understanding of the microscopic origins, currently under debate, especially on the shear-thickening mechanism. We present accurate measurements of shear stress in the bound hydration water layer using noncontact dynamic force microscopy. We find shear thickening occurs above ∼ 10(6) s(-1) shear rate beyond 0.3-nm layer thickness, which is attributed to the nonviscous, elasticity-associated fluidic instability via fluctuation correlation. Such a nonlinear fluidic transition is observed due to the long relaxation time (∼ 10(-6) s) of water available in the nanoconfined hydration layer, which indicates the onset of elastic turbulence at nanoscale, elucidating the interplay between relaxation and shear motion, which also indicates the onset of elastic turbulence at nanoscale above a universal shear velocity of ∼ 1 mm/s. This extensive layer-by-layer control paves the way for fundamental studies of nonlinear nanorheology and nanoscale hydrodynamics, as well as provides novel insights on viscoelastic dynamics of interfacial water.

Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures.

PubMed

Khusnutdinova, Karima R; Samsonov, Alexander M; Zakharov, Alexey S

2009-05-01

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

Photon induced non-linear quantized double layer charging in quaternary semiconducting quantum dots.

PubMed

Nair, Vishnu; Ananthoju, Balakrishna; Mohapatra, Jeotikanta; Aslam, M

2018-03-15

Room temperature quantized double layer charging was observed in 2 nm Cu 2 ZnSnS 4 (CZTS) quantum dots. In addition to this we observed a distinct non-linearity in the quantized double layer charging arising from UV light modulation of double layer. UV light irradiation resulted in a 26% increase in the integral capacitance at the semiconductor-dielectric (CZTS-oleylamine) interface of the quantum dot without any change in its core size suggesting that the cause be photocapacitive. The increasing charge separation at the semiconductor-dielectric interface due to highly stable and mobile photogenerated carriers cause larger electrostatic forces between the quantum dot and electrolyte leading to an enhanced double layer. This idea was supported by a decrease in the differential capacitance possible due to an enhanced double layer. Furthermore the UV illumination enhanced double layer gives us an AC excitation dependent differential double layer capacitance which confirms that the charging process is non-linear. This ultimately illustrates the utility of a colloidal quantum dot-electrolyte interface as a non-linear photocapacitor. Copyright © 2017 Elsevier Inc. All rights reserved.

Third-harmonic generation in tunable nonlinear hyperbolic metamaterial

NASA Astrophysics Data System (ADS)

Wicharn, Surawut; Buranasiri, Prathan

2018-03-01

In this research, a third-harmonic generation (THG) in a tunable nonlinear hyperbolic metamaterial (TNHM) has been investigated numerically. The TNHM is consisted of periodically arranging of multilayered graphene layers system for controlled optical properties purpose, and ordinary nonlinear dielectric layer. The possibility of TNHM permittivity dispersion controlled by number of graphene layers and external bias voltage to graphene layers was satisfied, then the structure has created the nearly perfect phase-matching scheme based on epsilon-near-zero (ENZ) behavior of the nonlinear medium. Finally, the optimal designed TNHM structure with sufficient bias voltage have given the forwardand backward-direction TH pulses, which the backward-forward TH intensity ratio is closely unity. The THG conversion efficiencies have been maximized after increasing the pumping level to 800 MW/cm2 . From this study, the optimal designed TNHM can be applied as a bi-directional nonlinear frequency converters in nanophotonic systems.

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

NASA Astrophysics Data System (ADS)

Williams, P. D.; Haine, T. W. N.; Read, P. L.; Lewis, S. R.; Yamazaki, Y. H.

2008-09-01

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

NASA Astrophysics Data System (ADS)

Williams, P. D.; Haine, T. W. N.; Read, P. L.; Lewis, S. R.; Yamazaki, Y. H.

2009-02-01

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

Nonlinear evolution of the first mode supersonic oblique waves in compressible boundary layers. Part 1: Heated/cooled walls

NASA Technical Reports Server (NTRS)

Gajjar, J. S. B.

1993-01-01

The nonlinear stability of an oblique mode propagating in a two-dimensional compressible boundary layer is considered under the long wave-length approximation. The growth rate of the wave is assumed to be small so that the concept of unsteady nonlinear critical layers can be used. It is shown that the spatial/temporal evolution of the mode is governed by a pair of coupled unsteady nonlinear equations for the disturbance vorticity and density. Expressions for the linear growth rate show clearly the effects of wall heating and cooling and in particular how heating destabilizes the boundary layer for these long wavelength inviscid modes at O(1) Mach numbers. A generalized expression for the linear growth rate is obtained and is shown to compare very well for a range of frequencies and wave-angles at moderate Mach numbers with full numerical solutions of the linear stability problem. The numerical solution of the nonlinear unsteady critical layer problem using a novel method based on Fourier decomposition and Chebychev collocation is discussed and some results are presented.

Some theoretical aspects of boundary layer stability theory

NASA Technical Reports Server (NTRS)

Hall, Philip

1990-01-01

Increased understanding in recent years of boundary layer transition has been made possible by the development of strongly nonlinear stability theories. After some twenty or so years when nonlinear stability theory was restricted to the application of the Stuart-Watson method (or less formal amplitude expansion procedures), there now exist strongly nonlinear theories which can describe processes which have an 0(1) effect on the basic state. These strongly nonlinear theories and their possible role in pushing theoretical understanding of transition ever further into the nonlinear regime are discussed.

Acoustic source for generating an acoustic beam

DOEpatents

Vu, Cung Khac; Sinha, Dipen N.; Pantea, Cristian

2016-05-31

An acoustic source for generating an acoustic beam includes a housing; a plurality of spaced apart piezo-electric layers disposed within the housing; and a non-linear medium filling between the plurality of layers. Each of the plurality of piezoelectric layers is configured to generate an acoustic wave. The non-linear medium and the plurality of piezo-electric material layers have a matching impedance so as to enhance a transmission of the acoustic wave generated by each of plurality of layers through the remaining plurality of layers.

Modeling and Simulation of Linear and Nonlinear MEMS Scale Electromagnetic Energy Harvesters for Random Vibration Environments

PubMed Central

Sassani, Farrokh

2014-01-01

The simulation results for electromagnetic energy harvesters (EMEHs) under broad band stationary Gaussian random excitations indicate the importance of both a high transformation factor and a high mechanical quality factor to achieve favourable mean power, mean square load voltage, and output spectral density. The optimum load is different for random vibrations and for sinusoidal vibration. Reducing the total damping ratio under band-limited random excitation yields a higher mean square load voltage. Reduced bandwidth resulting from decreased mechanical damping can be compensated by increasing the electrical damping (transformation factor) leading to a higher mean square load voltage and power. Nonlinear EMEHs with a Duffing spring and with linear plus cubic damping are modeled using the method of statistical linearization. These nonlinear EMEHs exhibit approximately linear behaviour under low levels of broadband stationary Gaussian random vibration; however, at higher levels of such excitation the central (resonant) frequency of the spectral density of the output voltage shifts due to the increased nonlinear stiffness and the bandwidth broadens slightly. Nonlinear EMEHs exhibit lower maximum output voltage and central frequency of the spectral density with nonlinear damping compared to linear damping. Stronger nonlinear damping yields broader bandwidths at stable resonant frequency. PMID:24605063

Thickness dependence and the role of spin transfer torque in nonlinear giant magnetoresistance of permalloy dual spin valves

NASA Astrophysics Data System (ADS)

Banerjee, N.; Aziz, A.; Ali, M.; Robinson, J. W. A.; Hickey, B. J.; Blamire, M. G.

2010-12-01

The recent discovery of nonlinear current-dependent magnetoresistance in dual spin valve devices [A. Aziz, O. P. Wessely, M. Ali, D. M. Edwards, C. H. Marrows, B. J. Hickey, and M. G. Blamire, Phys. Rev. Lett. 103, 237203 (2009)10.1103/PhysRevLett.103.237203] opens up the possibility for distinct physics which extends the standard model of giant magnetoresistance. When the outer ferromagnetic layers of a dual spin valve are antiparallel, the resulting accumulation of spin in the middle ferromagnetic layer strongly modifies its bulk and interfacial spin asymmetry and resistance. Here, we report experimental evidence of the role of bulk spin accumulation in this nonlinear effect and show that interfacial spin accumulation alone cannot account for the observed dependence of the effect on the thickness of the middle ferromagnetic layer. It is also shown that spin torque acting on the middle ferromagnetic layer combined with the nonlinear effect might be useful in understanding the dynamical features associated with the nonlinear behavior.

Bidirectional Reflectance of Flat, Optically Thick Particulate Layers: An Efficient Radiative Transfer Solution and Applications to Snow and Soil Surfaces

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Dlugach, Janna M.; Yanovitsku, Edgard G.; Zakharova, Nadia T.

1999-01-01

We describe a simple and highly efficient and accurate radiative transfer technique for computing bidirectional reflectance of a macroscopically flat scattering layer composed of nonabsorbing or weakly absorbing, arbitrarily shaped, randomly oriented and randomly distributed particles. The layer is assumed to be homogeneous and optically semi-infinite, and the bidirectional reflection function (BRF) is found by a simple iterative solution of the Ambartsumian's nonlinear integral equation. As an exact Solution of the radiative transfer equation, the reflection function thus obtained fully obeys the fundamental physical laws of energy conservation and reciprocity. Since this technique bypasses the computation of the internal radiation field, it is by far the fastest numerical approach available and can be used as an ideal input for Monte Carlo procedures calculating BRFs of scattering layers with macroscopically rough surfaces. Although the effects of packing density and coherent backscattering are currently neglected, they can also be incorporated. The FORTRAN implementation of the technique is available on the World Wide Web at http://ww,,v.giss.nasa.gov/-crmim/brf.html and can be applied to a wide range of remote sensing, engineering, and biophysical problems. We also examine the potential effect of ice crystal shape on the bidirectional reflectance of flat snow surfaces and the applicability of the Henyey-Greenstein phase function and the 6-Eddington approximation in calculations for soil surfaces.

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.

Broadband ultrafast nonlinear absorption and nonlinear refraction of layered molybdenum dichalcogenide semiconductors.

PubMed

Wang, Kangpeng; Feng, Yanyan; Chang, Chunxia; Zhan, Jingxin; Wang, Chengwei; Zhao, Quanzhong; Coleman, Jonathan N; Zhang, Long; Blau, Werner J; Wang, Jun

2014-09-21

A series of layered molybdenum dichalcogenides, i.e., MoX₂ (X = S, Se and Te), were prepared in cyclohexyl pyrrolidinone by a liquid-phase exfoliation technique. The high quality of the two-dimensional nanostructures was verified by transmission electron microscopy and absorption spectroscopy. Open- and closed-aperture Z-scans were employed to study the nonlinear absorption and nonlinear refraction of the MoX₂ dispersions, respectively. All the three-layered nanostructures exhibit prominent ultrafast saturable absorption (SA) for both femtosecond (fs) and picosecond (ps) laser pulses over a broad wavelength range from the visible to the near infrared. While the dispersions treated with low-speed centrifugation (1500 rpm) have an SA response, and the MoS₂ and MoSe₂ dispersions after higher speed centrifugation (10,000 rpm) possess two-photon absorption for fs pulses at 1030 nm, which is due to the significant reduction of the average thickness of the nanosheets; hence, the broadening of band gap. In addition, all dispersions show obvious nonlinear self-defocusing for ps pulses at both 1064 nm and 532 nm, resulting from the thermally-induced nonlinear refractive index. The versatile ultrafast nonlinear properties imply a huge potential of the layered MoX2 semiconductors in the development of nanophotonic devices, such as mode-lockers, optical limiters, optical switches, etc.

Reservoir computing on the hypersphere

NASA Astrophysics Data System (ADS)

Andrecut, M.

Reservoir Computing (RC) refers to a Recurrent Neural Network (RNNs) framework, frequently used for sequence learning and time series prediction. The RC system consists of a random fixed-weight RNN (the input-hidden reservoir layer) and a classifier (the hidden-output readout layer). Here, we focus on the sequence learning problem, and we explore a different approach to RC. More specifically, we remove the nonlinear neural activation function, and we consider an orthogonal reservoir acting on normalized states on the unit hypersphere. Surprisingly, our numerical results show that the system’s memory capacity exceeds the dimensionality of the reservoir, which is the upper bound for the typical RC approach based on Echo State Networks (ESNs). We also show how the proposed system can be applied to symmetric cryptography problems, and we include a numerical implementation.

Application of a Phase-resolving, Directional Nonlinear Spectral Wave Model

NASA Astrophysics Data System (ADS)

Davis, J. R.; Sheremet, A.; Tian, M.; Hanson, J. L.

2014-12-01

We describe several applications of a phase-resolving, directional nonlinear spectral wave model. The model describes a 2D surface gravity wave field approaching a mildly sloping beach with parallel depth contours at an arbitrary angle accounting for nonlinear, quadratic triad interactions. The model is hyperbolic, with the initial wave spectrum specified in deep water. Complex amplitudes are generated based on the random phase approximation. The numerical implementation includes unidirectional propagation as a special case. In directional mode, it solves the system of equations in the frequency-alongshore wave number space. Recent enhancements of the model include the incorporation of dissipation caused by breaking and propagation over a viscous mud layer and the calculation of wave induced setup. Applications presented include: a JONSWAP spectrum with a cos2s directional distribution, for shore-perpendicular and oblique propagation, a study of the evolution of a single directional triad, and several preliminary comparisons to wave spectra collected at the USACE-FRF in Duck, NC which show encouraging results although further validation with a wider range of beach slopes and wave conditions is needed.

Equivalent Linearization Analysis of Geometrically Nonlinear Random Vibrations Using Commercial Finite Element Codes

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2002-01-01

Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.

Thin layer model for nonlinear evolution of the Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Zhao, K. G.; Wang, L. F.; Xue, C.; Ye, W. H.; Wu, J. F.; Ding, Y. K.; Zhang, W. Y.

2018-03-01

On the basis of the thin layer approximation [Ott, Phys. Rev. Lett. 29, 1429 (1972)], a revised thin layer model for incompressible Rayleigh-Taylor instability has been developed to describe the deformation and nonlinear evolution of the perturbed interface. The differential equations for motion are obtained by analyzing the forces (the gravity and pressure difference) of fluid elements (i.e., Newton's second law). The positions of the perturbed interface are obtained from the numerical solution of the motion equations. For the case of vacuum on both sides of the layer, the positions of the upper and lower interfaces obtained from the revised thin layer approximation agree with that from the weakly nonlinear (WN) model of a finite-thickness fluid layer [Wang et al., Phys. Plasmas 21, 122710 (2014)]. For the case considering the fluids on both sides of the layer, the bubble-spike amplitude from the revised thin layer model agrees with that from the WN model [Wang et al., Phys. Plasmas 17, 052305 (2010)] and the expanded Layzer's theory [Goncharov, Phys. Rev. Lett. 88, 134502 (2002)] in the early nonlinear growth regime. Note that the revised thin layer model can be applied to investigate the perturbation growth at arbitrary Atwood numbers. In addition, the large deformation (the large perturbed amplitude and the arbitrary perturbed distributions) in the initial stage can also be described by the present model.

Reference Models for Multi-Layer Tissue Structures

DTIC Science & Technology

2016-09-01

simulation,  finite   element  analysis 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON USAMRMC...Physiologically realistic, fully specimen-specific, nonlinear reference models. Tasks. Finite element analysis of non-linear mechanics of cadaver...models. Tasks. Finite element analysis of non-linear mechanics of multi-layer tissue regions of human subjects. Deliverables. Partially subject- and

Nonlinear stability of non-stationary cross-flow vortices in compressible boundary layers

NASA Technical Reports Server (NTRS)

Gajjar, J. S. B.

1995-01-01

The nonlinear evolution of long wavelength non-stationary cross-flow vortices in a compressible boundary layer is investigated and the work extends that of Gajjar (1994) to flows involving multiple critical layers. The basic flow profile considered in this paper is that appropriate for a fully three-dimensional boundary layer with O(1) Mach number and with wall heating or cooling. The governing equations for the evolution of the cross-flow vortex are obtained and some special cases are discussed. One special case includes linear theory where exact analytic expressions for the growth rate of the vortices are obtained. Another special case is a generalization of the Bassom & Gajjar (1988) results for neutral waves to compressible flows. The viscous correction to the growth rate is derived and it is shown how the unsteady nonlinear critical layer structure merges with that for a Haberman type of viscous critical layer.

A deep belief network with PLSR for nonlinear system modeling.

PubMed

Qiao, Junfei; Wang, Gongming; Li, Wenjing; Li, Xiaoli

2018-08-01

Nonlinear system modeling plays an important role in practical engineering, and deep learning-based deep belief network (DBN) is now popular in nonlinear system modeling and identification because of the strong learning ability. However, the existing weights optimization for DBN is based on gradient, which always leads to a local optimum and a poor training result. In this paper, a DBN with partial least square regression (PLSR-DBN) is proposed for nonlinear system modeling, which focuses on the problem of weights optimization for DBN using PLSR. Firstly, unsupervised contrastive divergence (CD) algorithm is used in weights initialization. Secondly, initial weights derived from CD algorithm are optimized through layer-by-layer PLSR modeling from top layer to bottom layer. Instead of gradient method, PLSR-DBN can determine the optimal weights using several PLSR models, so that a better performance of PLSR-DBN is achieved. Then, the analysis of convergence is theoretically given to guarantee the effectiveness of the proposed PLSR-DBN model. Finally, the proposed PLSR-DBN is tested on two benchmark nonlinear systems and an actual wastewater treatment system as well as a handwritten digit recognition (nonlinear mapping and modeling) with high-dimension input data. The experiment results show that the proposed PLSR-DBN has better performances of time and accuracy on nonlinear system modeling than that of other methods. Copyright © 2017 Elsevier Ltd. All rights reserved.

Study on Nonlinear Vibration Analysis of Gear System with Random Parameters

NASA Astrophysics Data System (ADS)

Tong, Cao; Liu, Xiaoyuan; Fan, Li

2018-03-01

In order to study the dynamic characteristics of gear nonlinear vibration system and the influence of random parameters, firstly, a nonlinear stochastic vibration analysis model of gear 3-DOF is established based on Newton’s Law. And the random response of gear vibration is simulated by stepwise integration method. Secondly, the influence of stochastic parameters such as meshing damping, tooth side gap and excitation frequency on the dynamic response of gear nonlinear system is analyzed by using the stability analysis method such as bifurcation diagram and Lyapunov exponent method. The analysis shows that the stochastic process can not be neglected, which can cause the random bifurcation and chaos of the system response. This study will provide important reference value for vibration engineering designers.

A vacancy-modulated self-selective resistive switching memory with pronounced nonlinear behavior

NASA Astrophysics Data System (ADS)

Ma, Haili; Feng, Jie; Gao, Tian; Zhu, Xi

2017-12-01

In this study, we report a self-selective (nonlinear) resistive switching memory cell, with high on-state half-bias nonlinearity of 650, sub-μA operating current, and high On/Off ratios above 100×. Regarding the cell structure, a thermal oxidized HfO x layer in combination with a sputtered Ta2O5 layer was configured as an active stack, with Pt and Hf as top and bottom electrodes, respectively. The Ta2O5 acts as a selective layer as well as a series resistor, which could make the resistive switching happened in HfO x layer. Through the analysis of the physicochemical properties and electrical conduction mechanisms at each state, a vacancy-modulated resistance switching model was proposed to explain the switching behavior. The conductivity of HfO x layer was changed by polarity-dependent drift of the oxygen vacancy ( V o), resulting in an electron hopping distance change during switching. With the help of Ta2O5 selective layer, high nonlinearity observed in low resistance state. The proposed material stack shows a promising prospect to act as a self-selective cell for 3D vertical RRAM application.

Modular representation of layered neural networks.

PubMed

Watanabe, Chihiro; Hiramatsu, Kaoru; Kashino, Kunio

2018-01-01

Layered neural networks have greatly improved the performance of various applications including image processing, speech recognition, natural language processing, and bioinformatics. However, it is still difficult to discover or interpret knowledge from the inference provided by a layered neural network, since its internal representation has many nonlinear and complex parameters embedded in hierarchical layers. Therefore, it becomes important to establish a new methodology by which layered neural networks can be understood. In this paper, we propose a new method for extracting a global and simplified structure from a layered neural network. Based on network analysis, the proposed method detects communities or clusters of units with similar connection patterns. We show its effectiveness by applying it to three use cases. (1) Network decomposition: it can decompose a trained neural network into multiple small independent networks thus dividing the problem and reducing the computation time. (2) Training assessment: the appropriateness of a trained result with a given hyperparameter or randomly chosen initial parameters can be evaluated by using a modularity index. And (3) data analysis: in practical data it reveals the community structure in the input, hidden, and output layers, which serves as a clue for discovering knowledge from a trained neural network. Copyright © 2017 Elsevier Ltd. All rights reserved.

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

NASA Astrophysics Data System (ADS)

Williams, P. D.; Haine, T. W. N.; Read, P. L.; Lewis, S. R.; Yamazaki, Y. H.

2009-04-01

The QUAGMIRE model has recently been made freely available for public use. QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. This presentation describes the model's main features. QUAGMIRE uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

Boundary Layer Effect on Behavior of Discrete Models.

PubMed

Eliáš, Jan

2017-02-10

The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson's ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis.

Layer contributions to the nonlinear acoustic radiation from stratified media.

PubMed

Vander Meulen, François; Haumesser, Lionel

2016-12-01

This study presents the thorough investigation of the second harmonic generation scenario in a three fluid layer system. An emphasis is on the evaluation of the nonlinear parameter B/A in each layer from remote measurements. A theoretical approach of the propagation of a finite amplitude acoustic wave in a multilayered medium is developed. In the frame of the KZK equation, the weak nonlinearity of the media, attenuation and diffraction effects are computed for the fundamental and second harmonic waves propagating back and forth in each of the layers of the system. The model uses a gaussian expansion to describe the beam propagation in order to quantitatively evaluate the contribution of each part of the system (layers and interfaces) to its nonlinearity. The model is validated through measurements on a water/aluminum/water system. Transmission as well as reflection configurations are studied. Good agreement is found between the theoretical results and the experimental data. The analysis of the second harmonic field sources measured by the transducers from outside the stratified medium highlights the factors that favor the cumulative effects. Copyright © 2016 Elsevier B.V. All rights reserved.

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.

Resonant triad in boundary-layer stability. Part 1: Fully nonlinear interaction

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

A first principles theory is developed to study the nonlinear spatial evolution of a near-resonance triad of instability waves in boundary layer transition. This triad consists of a plane wave at fundamental frequency and a pair of symmetrical, oblique waves at the subharmonic frequency. A low frequency, high Reynolds number asymptotic scaling leads to a distinct critical layer where nonlinearity first becomes important; the development of the triad's waves is determined by the critical layer's nonlinear, viscous dynamics. The resulting theory is fully nonlinear in that all nonlinearly generated oscillatory and nonoscillatory components are accounted for. The presence of the plane wave initially causes exponential of exponential growth of the oblique waves. However, the plane wave continues to follow the linear theory, even when the oblique waves' amplitude attains the same order of magnitude as that of the plane wave. A fully interactive stage then comes into effect when the oblique waves exceed a certain level compared to that of the plane wave. The oblique waves react back on the fundamental, slowing its growth rate. The oblique waves' saturation results from their self-interaction - a mechanism that does not require the presence of the plane wave. The oblique waves' saturation level is independent of their initial level, but decreases as the obliqueness angle increases.

Master stability functions reveal diffusion-driven pattern formation in networks

NASA Astrophysics Data System (ADS)

Brechtel, Andreas; Gramlich, Philipp; Ritterskamp, Daniel; Drossel, Barbara; Gross, Thilo

2018-03-01

We study diffusion-driven pattern formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing random walks, while they can be created or destroyed by reactions between or within a layer. We show that the stability of homogeneous steady states can be analyzed with a master stability function approach that reveals a deep analogy between pattern formation in networks and pattern formation in continuous space. For illustration, we consider a generalized model of ecological meta-food webs. This fairly complex model describes the dispersal of many different species across a region consisting of a network of individual habitats while subject to realistic, nonlinear predator-prey interactions. In this example, the method reveals the intricate dependence of the dynamics on the spatial structure. The ability of the proposed approach to deal with this fairly complex system highlights it as a promising tool for ecology and other applications.

Ultralow power switching in a silicon-rich SiNy/SiNx double-layer resistive memory device.

PubMed

Kim, Sungjun; Chang, Yao-Feng; Kim, Min-Hwi; Bang, Suhyun; Kim, Tae-Hyeon; Chen, Ying-Chen; Lee, Jong-Ho; Park, Byung-Gook

2017-07-26

Here we demonstrate low-power resistive switching in a Ni/SiN y /SiN x /p ++ -Si device by proposing a double-layered structure (SiN y /SiN x ), where the two SiN layers have different trap densities. The LRS was measured to be as low as 1 nA at a voltage of 1 V, because the SiN x layer maintains insulating properties for the LRS. The single-layered device suffers from uncontrollability of the conducting path, accompanied by the inherent randomness of switching parameters, weak immunity to breakdown during the reset process, and a high operating current. On the other hand, for a double-layered device, the effective conducting path in each layer, which can determine the operating current, can be well controlled by the I CC during the initial forming and set processes. A one-step forming and progressive reset process is observed for a low-power mode, which differs from the high-power switching mode that shows a two-step forming and reset process. Moreover, nonlinear behavior in the LRS, whose origin can be attributed to the P-F conduction and F-N tunneling driven by abundant traps in the silicon-rich SiN x layer, would be beneficial for next-generation nonvolatile memory applications by using a conventional passive SiN x layer as an active dielectric.

Sub-optimal control of unsteady boundary layer separation and optimal control of Saltzman-Lorenz model

NASA Astrophysics Data System (ADS)

Sardesai, Chetan R.

The primary objective of this research is to explore the application of optimal control theory in nonlinear, unsteady, fluid dynamical settings. Two problems are considered: (1) control of unsteady boundary-layer separation, and (2) control of the Saltzman-Lorenz model. The unsteady boundary-layer equations are nonlinear partial differential equations that govern the eruptive events that arise when an adverse pressure gradient acts on a boundary layer at high Reynolds numbers. The Saltzman-Lorenz model consists of a coupled set of three nonlinear ordinary differential equations that govern the time-dependent coefficients in truncated Fourier expansions of Rayleigh-Renard convection and exhibit deterministic chaos. Variational methods are used to derive the nonlinear optimal control formulations based on cost functionals that define the control objective through a performance measure and a penalty function that penalizes the cost of control. The resulting formulation consists of the nonlinear state equations, which must be integrated forward in time, and the nonlinear control (adjoint) equations, which are integrated backward in time. Such coupled forward-backward time integrations are computationally demanding; therefore, the full optimal control problem for the Saltzman-Lorenz model is carried out, while the more complex unsteady boundary-layer case is solved using a sub-optimal approach. The latter is a quasi-steady technique in which the unsteady boundary-layer equations are integrated forward in time, and the steady control equation is solved at each time step. Both sub-optimal control of the unsteady boundary-layer equations and optimal control of the Saltzman-Lorenz model are found to be successful in meeting the control objectives for each problem. In the case of boundary-layer separation, the control results indicate that it is necessary to eliminate the recirculation region that is a precursor to the unsteady boundary-layer eruptions. In the case of the Saltzman-Lorenz model, it is possible to control the system about either of the two unstable equilibrium points representing clockwise and counterclockwise rotation of the convection roles in a parameter regime for which the uncontrolled solution would exhibit deterministic chaos.

Broadband ultrafast nonlinear absorption and nonlinear refraction of layered molybdenum dichalcogenide semiconductors

NASA Astrophysics Data System (ADS)

Wang, Kangpeng; Feng, Yanyan; Chang, Chunxia; Zhan, Jingxin; Wang, Chengwei; Zhao, Quanzhong; Coleman, Jonathan N.; Zhang, Long; Blau, Werner J.; Wang, Jun

2014-08-01

A series of layered molybdenum dichalcogenides, i.e., MoX2 (X = S, Se and Te), were prepared in cyclohexyl pyrrolidinone by a liquid-phase exfoliation technique. The high quality of the two-dimensional nanostructures was verified by transmission electron microscopy and absorption spectroscopy. Open- and closed-aperture Z-scans were employed to study the nonlinear absorption and nonlinear refraction of the MoX2 dispersions, respectively. All the three-layered nanostructures exhibit prominent ultrafast saturable absorption (SA) for both femtosecond (fs) and picosecond (ps) laser pulses over a broad wavelength range from the visible to the near infrared. While the dispersions treated with low-speed centrifugation (1500 rpm) have an SA response, and the MoS2 and MoSe2 dispersions after higher speed centrifugation (10 000 rpm) possess two-photon absorption for fs pulses at 1030 nm, which is due to the significant reduction of the average thickness of the nanosheets; hence, the broadening of band gap. In addition, all dispersions show obvious nonlinear self-defocusing for ps pulses at both 1064 nm and 532 nm, resulting from the thermally-induced nonlinear refractive index. The versatile ultrafast nonlinear properties imply a huge potential of the layered MoX2 semiconductors in the development of nanophotonic devices, such as mode-lockers, optical limiters, optical switches, etc.A series of layered molybdenum dichalcogenides, i.e., MoX2 (X = S, Se and Te), were prepared in cyclohexyl pyrrolidinone by a liquid-phase exfoliation technique. The high quality of the two-dimensional nanostructures was verified by transmission electron microscopy and absorption spectroscopy. Open- and closed-aperture Z-scans were employed to study the nonlinear absorption and nonlinear refraction of the MoX2 dispersions, respectively. All the three-layered nanostructures exhibit prominent ultrafast saturable absorption (SA) for both femtosecond (fs) and picosecond (ps) laser pulses over a broad wavelength range from the visible to the near infrared. While the dispersions treated with low-speed centrifugation (1500 rpm) have an SA response, and the MoS2 and MoSe2 dispersions after higher speed centrifugation (10 000 rpm) possess two-photon absorption for fs pulses at 1030 nm, which is due to the significant reduction of the average thickness of the nanosheets; hence, the broadening of band gap. In addition, all dispersions show obvious nonlinear self-defocusing for ps pulses at both 1064 nm and 532 nm, resulting from the thermally-induced nonlinear refractive index. The versatile ultrafast nonlinear properties imply a huge potential of the layered MoX2 semiconductors in the development of nanophotonic devices, such as mode-lockers, optical limiters, optical switches, etc. Electronic supplementary information (ESI) available: Electron scattering patterns from TEM characterizations of MX2 nanosheets; CA Z-scan results of graphene dispersions in the ps region. See DOI: 10.1039/c4nr02634a

Initial-boundary layer associated with the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system

NASA Astrophysics Data System (ADS)

Fei, Mingwen; Han, Daozhi; Wang, Xiaoming

2017-01-01

In this paper, we study the vanishing Darcy number limit of the nonlinear Darcy-Brinkman-Oberbeck-Boussinesq system (DBOB). This singular perturbation problem involves singular structures both in time and in space giving rise to initial layers, boundary layers and initial-boundary layers. We construct an approximate solution to the DBOB system by the method of multiple scale expansions. The convergence with optimal convergence rates in certain Sobolev norms is established rigorously via the energy method.

Dynamics of Complex Systems Built as Coupled Physical, Communication and Decision Layers

PubMed Central

Kühnlenz, Florian; Nardelli, Pedro H. J.

2016-01-01

This paper proposes a simple model to capture the complexity of multilayer systems where their constituent layers affect, and are affected by, each other. The physical layer is a circuit composed by a power source and resistors in parallel. Every individual agent aims at maximizing its own delivered power by adding, removing or keeping the resistors it has; the delivered power is in turn a non-linear function that depends on the other agents’ behavior, its own internal state, its global state perception, the information received from its neighbors via the communication network and a randomized selfishness. We develop an agent-based simulation to analyze the effects of number of agents (system size), communication network topology, communication errors and the minimum power gain that triggers a behavioral change on the system dynamic. Our results show that a wave-like behavior at macro-level (caused by individual changes in the decision layer) can only emerge for a specific system size. The ratio between cooperators and defectors depends on the minimum gain assumed—lower minimal gains lead to less cooperation, and vice-versa. Different communication network topologies imply different levels of power utilization and fairness at the physical layer, and a certain level of error in the communication layer induces more cooperation. PMID:26730590

Laminar and orientation-dependent characteristics of spatial nonlinearities: implications for the computational architecture of visual cortex.

PubMed

Victor, Jonathan D; Mechler, Ferenc; Ohiorhenuan, Ifije; Schmid, Anita M; Purpura, Keith P

2009-12-01

A full understanding of the computations performed in primary visual cortex is an important yet elusive goal. Receptive field models consisting of cascades of linear filters and static nonlinearities may be adequate to account for responses to simple stimuli such as gratings and random checkerboards, but their predictions of responses to complex stimuli such as natural scenes are only approximately correct. It is unclear whether these discrepancies are limited to quantitative inaccuracies that reflect well-recognized mechanisms such as response normalization, gain controls, and cross-orientation suppression or, alternatively, imply additional qualitative features of the underlying computations. To address this question, we examined responses of V1 and V2 neurons in the monkey and area 17 neurons in the cat to two-dimensional Hermite functions (TDHs). TDHs are intermediate in complexity between traditional analytic stimuli and natural scenes and have mathematical properties that facilitate their use to test candidate models. By exploiting these properties, along with the laminar organization of V1, we identify qualitative aspects of neural computations beyond those anticipated from the above-cited model framework. Specifically, we find that V1 neurons receive signals from orientation-selective mechanisms that are highly nonlinear: they are sensitive to phase correlations, not just spatial frequency content. That is, the behavior of V1 neurons departs from that of linear-nonlinear cascades with standard modulatory mechanisms in a qualitative manner: even relatively simple stimuli evoke responses that imply complex spatial nonlinearities. The presence of these findings in the input layers suggests that these nonlinearities act in a feedback fashion.

Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer

NASA Astrophysics Data System (ADS)

Pikichyan, H. V.

2017-07-01

In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.

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.

Double layers without current

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

Perkins, F.W.; Sun, Y.C.

1980-11-01

The steady-state solution of the nonlinear Vlasov-Poisson equations is reduced to a nonlinear eigenvalue problem for the case of double-layer (potential drop) boundary conditions. Solutions with no relative electron-ion drifts are found. The kinetic stability is discussed. Suggestions for creating these states in experiments and computer simulations are offered.

Nonlinear random response prediction using MSC/NASTRAN

NASA Technical Reports Server (NTRS)

Robinson, J. H.; Chiang, C. K.; Rizzi, S. A.

1993-01-01

An equivalent linearization technique was incorporated into MSC/NASTRAN to predict the nonlinear random response of structures by means of Direct Matrix Abstract Programming (DMAP) modifications and inclusion of the nonlinear differential stiffness module inside the iteration loop. An iterative process was used to determine the rms displacements. Numerical results obtained for validation on simple plates and beams are in good agreement with existing solutions in both the linear and linearized regions. The versatility of the implementation will enable the analyst to determine the nonlinear random responses for complex structures under combined loads. The thermo-acoustic response of a hexagonal thermal protection system panel is used to highlight some of the features of the program.

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.

Monolithic high voltage nonlinear transmission line fabrication process

DOEpatents

Cooper, Gregory A.

1994-01-01

A process for fabricating sequential inductors and varactor diodes of a monolithic, high voltage, nonlinear, transmission line in GaAs is disclosed. An epitaxially grown laminate is produced by applying a low doped active n-type GaAs layer to an n-plus type GaAs substrate. A heavily doped p-type GaAs layer is applied to the active n-type layer and a heavily doped n-type GaAs layer is applied to the p-type layer. Ohmic contacts are applied to the heavily doped n-type layer where diodes are desired. Multiple layers are then either etched away or Oxygen ion implanted to isolate individual varactor diodes. An insulator is applied between the diodes and a conductive/inductive layer is thereafter applied on top of the insulator layer to complete the process.

Reproduction of exact solutions of Lipkin model by nonlinear higher random-phase approximation

NASA Astrophysics Data System (ADS)

Terasaki, J.; Smetana, A.; Šimkovic, F.; Krivoruchenko, M. I.

2017-10-01

It is shown that the random-phase approximation (RPA) method with its nonlinear higher generalization, which was previously considered as approximation except for a very limited case, reproduces the exact solutions of the Lipkin model. The nonlinear higher RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number N = 2 and numerically for N = 8. This finding indicates that the nonlinear higher RPA is equivalent to the exact Schrödinger equation.

Vibration control of multiferroic fibrous composite plates using active constrained layer damping

NASA Astrophysics Data System (ADS)

Kattimani, S. C.; Ray, M. C.

2018-06-01

Geometrically nonlinear vibration control of fiber reinforced magneto-electro-elastic or multiferroic fibrous composite plates using active constrained layer damping treatment has been investigated. The piezoelectric (BaTiO3) fibers are embedded in the magnetostrictive (CoFe2O4) matrix forming magneto-electro-elastic or multiferroic smart composite. A three-dimensional finite element model of such fiber reinforced magneto-electro-elastic plates integrated with the active constrained layer damping patches is developed. Influence of electro-elastic, magneto-elastic and electromagnetic coupled fields on the vibration has been studied. The Golla-Hughes-McTavish method in time domain is employed for modeling a constrained viscoelastic layer of the active constrained layer damping treatment. The von Kármán type nonlinear strain-displacement relations are incorporated for developing a three-dimensional finite element model. Effect of fiber volume fraction, fiber orientation and boundary conditions on the control of geometrically nonlinear vibration of the fiber reinforced magneto-electro-elastic plates is investigated. The performance of the active constrained layer damping treatment due to the variation of piezoelectric fiber orientation angle in the 1-3 Piezoelectric constraining layer of the active constrained layer damping treatment has also been emphasized.

Density response of the mesospheric sodium layer to gravity wave perturbations

NASA Technical Reports Server (NTRS)

Shelton, J. D.; Gardner, C. S.; Sechrist, C. F., Jr.

1980-01-01

Lidar observations of the mesospheric sodium layer often reveal wavelike features moving through the layer. It is often assumed that these features are a layer density response to gravity waves. Chiu and Ching (1978) described the approximate form of the linear response of atmospheric layers to gravity waves. In this paper, their results are used to predict the response of the sodium layer to gravity waves. These simulations are compared with experimental observations and a good correlation is found between the two. Because of the thickness of the sodium layer and the density gradients found in it, a linear model of the layer response is not always adequate to describe gravity wave-sodium layer interactions. Inclusion of nonlinearities in the layer response is briefly discussed. Experimental data is seen to contain features consistent with the predicted nonlinearities.

Resonant Triad in Boundary-Layer Stability. Part 2; Composite Solution and Comparison with Observations

NASA Technical Reports Server (NTRS)

Mankbadi, Reda R.

1991-01-01

Here, numerical results are computed from an asymptotic near-resonance triad analysis. The analysis considers a resonant triad of instability waves consisting of a plane fundamental wave and a pair of symmetrical oblique subharmonic waves. The relevant scaling ensures that nonlinearity is confined to a distinct critical layer. The analysis is first used to form a composite solution that accounts for both the flow divergence and nonlinear effects. It is shown that the backreaction on the plane Tollmien Schlichting (TS) fundamental wave, although fully accounted for, is of little significance. The observed enhancement at the fundamental frequency disturbance is not in the plane TS wave, but is caused by nonlinearly generated waves at the fundamental frequency that result from nonlinear interactions in the critical layer. The saturation of the oblique waves is caused by their self-interaction. The nonlinear phase-locking phenomenon, the location of resonance with respect to the neutral stability curve, low frequency effects, detuning in the streamwise wave numbers, and nonlinear distortion of the mode shapes are discussed. Nonlinearity modifies the initially two dimensional Blasius profile into a fuller one with spanwise periodicity. The interactions at a wide range of unstable spanwise wave numbers are considered, and the existence of a preferred spanwise wave number is explained by means of the vorticity distribution in the critical layer. Besides presenting novel features of the phenomena and explaining the delicate mechanisms of the interactions, the results of the theory are in excellent agreement with experimental and numerical observations for all stages of the development and for various input parameters.

Linear and nonlinear stability of the Blasius boundary layer

NASA Technical Reports Server (NTRS)

Bertolotti, F. P.; Herbert, TH.; Spalart, P. R.

1992-01-01

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier-Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien-Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearity are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow.

Subdiffraction focusing of scanning beams by a negative-refraction layer combined with a nonlinear layer.

PubMed

Husakou, A; Herrmann, J

2006-11-13

We evaluate the possibility to focus scanning light beams below the diffraction limit by using the combination of a nonlinear material with a Kerr-type nonlinearity or two-photon absorption to create seed evanescent components of the beam and a negative-refraction material to enhance them. Superfocusing to spots with a FWHM in the range of 0.2 lambda is theoretically predicted both in the context of the effective-medium theory and by the direct numerical solution of Maxwell equations for an inhomogeneous pho-tonic crystal. The evolution of the transverse spectrum and the dependence of superfocusing on the parameters of the negative-refraction material are also studied. We show that the use of a Kerr-type nonlinear layer for the creation of seed evanescent components yields focused spots with a higher intensity compared with those obtained by the application of a saturable absorber.

Linear and weakly nonlinear aspects of free shear layer instability, roll-up, subharmonic interaction and wall influence

NASA Technical Reports Server (NTRS)

Cain, A. B.; Thompson, M. W.

1986-01-01

The growth of the momentum thickness and the modal disturbance energies are examined to study the nature and onset of nonlinearity in a temporally growing free shear layer. A shooting technique is used to find solutions to the linearized eigenvalue problem, and pseudospectral weakly nonlinear simulations of this flow are obtained for comparison. The roll-up of a fundamental disturbance follows linear theory predictions even with a 20 percent disturbance amplitude. A weak nonlinear interaction of the disturbance creates a finite-amplitude mean shear stress which dominates the growth of the layer momentum thickness, and the disturbance growth rate changes until the fundamental disturbance dominates. The fundamental then becomes an energy source for the harmonic, resulting in an increase in the growth rate of the subharmonic over the linear prediction even when the fundamental has no energy to give. Also considered are phase relations and the wall influence.

On the instability of a three-dimensional attachment-line boundary layer - Weakly nonlinear theory and a numerical approach

NASA Technical Reports Server (NTRS)

Hall, P.; Malik, M. R.

1986-01-01

The instability of a three-dimensional attachment-line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite-amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time-dependent Navier-Stokes equations for the attachment-line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite-amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment-line boundary layer is also investigated.

On the instability of a 3-dimensional attachment line boundary layer: Weakly nonlinear theory and a numerical approach

NASA Technical Reports Server (NTRS)

Hall, P.; Malik, M. R.

1984-01-01

The instability of a three dimensional attachment line boundary layer is considered in the nonlinear regime. Using weakly nonlinear theory, it is found that, apart from a small interval near the (linear) critical Reynolds number, finite amplitude solutions bifurcate subcritically from the upper branch of the neutral curve. The time dependent Navier-Stokes equations for the attachment line flow have been solved using a Fourier-Chebyshev spectral method and the subcritical instability is found at wavenumbers that correspond to the upper branch. Both the theory and the numerical calculations show the existence of supercritical finite amplitude (equilibrium) states near the lower branch which explains why the observed flow exhibits a preference for the lower branch modes. The effect of blowing and suction on nonlinear stability of the attachment line boundary layer is also investigated.

Investigation of the spatial distribution of second-order nonlinearity in thermally poled optical fibers.

PubMed

An, Honglin; Fleming, Simon

2005-05-02

The spatial distribution of second-order nonlinearity in thermally poled optical fibers was characterized by second-harmonic microscopy. The second-order nonlinearity was found to be confined to a thin layer close to the anode surface and progressed further into the silica as the poling time increased. Position uncertainty of the anode metal wire was observed to have an effect, as the nonlinear layers were found not always symmetrically located around the nearest points between the anode and cathode. Optical microscopy results were obtained on etched poled fiber cross-sections and compared with those from second-harmonic microscopy.

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.

Multifractal Modeling of Turbulent Mixing

NASA Astrophysics Data System (ADS)

Samiee, Mehdi; Zayernouri, Mohsen; Meerschaert, Mark M.

2017-11-01

Stochastic processes in random media are emerging as interesting tools for modeling anomalous transport phenomena. Applications include intermittent passive scalar transport with background noise in turbulent flows, which are observed in atmospheric boundary layers, turbulent mixing in reactive flows, and long-range dependent flow fields in disordered/fractal environments. In this work, we propose a nonlocal scalar transport equation involving the fractional Laplacian, where the corresponding fractional index is linked to the multifractal structure of the nonlinear passive scalar power spectrum. This work was supported by the AFOSR Young Investigator Program (YIP) award (FA9550-17-1-0150) and partially by MURI/ARO (W911NF-15-1-0562).

Generation Mechanism of Nonlinear Rayleigh Surface Waves for Randomly Distributed Surface Micro-Cracks.

PubMed

Ding, Xiangyan; Li, Feilong; Zhao, Youxuan; Xu, Yongmei; Hu, Ning; Cao, Peng; Deng, Mingxi

2018-04-23

This paper investigates the propagation of Rayleigh surface waves in structures with randomly distributed surface micro-cracks using numerical simulations. The results revealed a significant ultrasonic nonlinear effect caused by the surface micro-cracks, which is mainly represented by a second harmonic with even more distinct third/quadruple harmonics. Based on statistical analysis from the numerous results of random micro-crack models, it is clearly found that the acoustic nonlinear parameter increases linearly with micro-crack density, the proportion of surface cracks, the size of micro-crack zone, and the excitation frequency. This study theoretically reveals that nonlinear Rayleigh surface waves are feasible for use in quantitatively identifying the physical characteristics of surface micro-cracks in structures.

Generation Mechanism of Nonlinear Rayleigh Surface Waves for Randomly Distributed Surface Micro-Cracks

PubMed Central

Ding, Xiangyan; Li, Feilong; Xu, Yongmei; Cao, Peng; Deng, Mingxi

2018-01-01

This paper investigates the propagation of Rayleigh surface waves in structures with randomly distributed surface micro-cracks using numerical simulations. The results revealed a significant ultrasonic nonlinear effect caused by the surface micro-cracks, which is mainly represented by a second harmonic with even more distinct third/quadruple harmonics. Based on statistical analysis from the numerous results of random micro-crack models, it is clearly found that the acoustic nonlinear parameter increases linearly with micro-crack density, the proportion of surface cracks, the size of micro-crack zone, and the excitation frequency. This study theoretically reveals that nonlinear Rayleigh surface waves are feasible for use in quantitatively identifying the physical characteristics of surface micro-cracks in structures. PMID:29690580

Monolithic high voltage nonlinear transmission line fabrication process

DOEpatents

Cooper, G.A.

1994-10-04

A process for fabricating sequential inductors and varistor diodes of a monolithic, high voltage, nonlinear, transmission line in GaAs is disclosed. An epitaxially grown laminate is produced by applying a low doped active n-type GaAs layer to an n-plus type GaAs substrate. A heavily doped p-type GaAs layer is applied to the active n-type layer and a heavily doped n-type GaAs layer is applied to the p-type layer. Ohmic contacts are applied to the heavily doped n-type layer where diodes are desired. Multiple layers are then either etched away or Oxygen ion implanted to isolate individual varistor diodes. An insulator is applied between the diodes and a conductive/inductive layer is thereafter applied on top of the insulator layer to complete the process. 6 figs.

Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings.

PubMed

Tang, Yang; Gao, Huijun; Zou, Wei; Kurths, Jürgen

2013-02-01

In this paper, the distributed synchronization problem of networks of agent systems with controllers and nonlinearities subject to Bernoulli switchings is investigated. Controllers and adaptive updating laws injected in each vertex of networks depend on the state information of its neighborhood. Three sets of Bernoulli stochastic variables are introduced to describe the occurrence probabilities of distributed adaptive controllers, updating laws and nonlinearities, respectively. By the Lyapunov functions method, we show that the distributed synchronization of networks composed of agent systems with multiple randomly occurring nonlinearities, multiple randomly occurring controllers, and multiple randomly occurring updating laws can be achieved in mean square under certain criteria. The conditions derived in this paper can be solved by semi-definite programming. Moreover, by mathematical analysis, we find that the coupling strength, the probabilities of the Bernoulli stochastic variables, and the form of nonlinearities have great impacts on the convergence speed and the terminal control strength. The synchronization criteria and the observed phenomena are demonstrated by several numerical simulation examples. In addition, the advantage of distributed adaptive controllers over conventional adaptive controllers is illustrated.

Active constrained layer damping of geometrically nonlinear vibrations of functionally graded plates using piezoelectric fiber-reinforced composites

NASA Astrophysics Data System (ADS)

Panda, Satyajit; Ray, M. C.

2008-04-01

In this paper, a geometrically nonlinear dynamic analysis has been presented for functionally graded (FG) plates integrated with a patch of active constrained layer damping (ACLD) treatment and subjected to a temperature field. The constraining layer of the ACLD treatment is considered to be made of the piezoelectric fiber-reinforced composite (PFRC) material. The temperature field is assumed to be spatially uniform over the substrate plate surfaces and varied through the thickness of the host FG plates. The temperature-dependent material properties of the FG substrate plates are assumed to be graded in the thickness direction of the plates according to a power-law distribution while the Poisson's ratio is assumed to be a constant over the domain of the plate. The constrained viscoelastic layer of the ACLD treatment is modeled using the Golla-Hughes-McTavish (GHM) method. Based on the first-order shear deformation theory, a three-dimensional finite element model has been developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG substrate plates under the thermal environment. The analysis suggests the potential use of the ACLD treatment with its constraining layer made of the PFRC material for active control of geometrically nonlinear vibrations of FG plates in the absence or the presence of the temperature gradient across the thickness of the plates. It is found that the ACLD treatment is more effective in controlling the geometrically nonlinear vibrations of FG plates than in controlling their linear vibrations. The analysis also reveals that the ACLD patch is more effective for controlling the nonlinear vibrations of FG plates when it is attached to the softest surface of the FG plates than when it is bonded to the stiffest surface of the plates. The effect of piezoelectric fiber orientation in the active constraining PFRC layer on the damping characteristics of the overall FG plates is also discussed.

A theoretical and experimental investigation of nonlinear propagation of ultrasound through tissue mimicking media

NASA Astrophysics Data System (ADS)

Rielly, Matthew Robert

An existing numerical model (known as the Bergen code) is used to investigate finite amplitude ultrasound propagation through multiple layers of tissue-like media. This model uses a finite difference method to solve the nonlinear parabolic KZK wave equation. The code is modified to include an arbitrary frequency dependence of absorption and transmission effects for wave propagation across a plane interface at normal incidence. In addition the code is adapted to calculate the total intensity loss associated with the absorption of the fundamental and nonlinearly generated harmonics. Measurements are also taken of the axial nonlinear pressure field generated from a circular focused, 2.25 MHz source, through single and multiple layered tissue mimicking fluids, for source pressures in the range from 13 kPa to 310 kPa. Two tissue mimicking fluids are developed to provide acoustic properties similar to amniotic fluid and a typical soft tissue. The values of the nonlinearity parameter, sound velocity and frequency dependence of attenuation for both fluids are presented, and the measurement procedures employed to obtain these characteristics are described in detail. These acoustic parameters, together with the measured source conditions are used as input to the numerical model, allowing the experimental conditions to be simulated. Extensive comparisons are made between the model's predictions and the axial pressure field measurements. Results are presented in the frequency domain showing the fundamental and three subsequent harmonic amplitudes on axis, as a function of axial distance. These show that significant nonlinear distortion can occur through media with characteristics typical of tissue. Time domain waveform comparisons are also made. An excellent agreement is found between theory and experiment indicating that the model can be used to predict nonlinear ultrasound propagation through multiple layers of tissue-like media. The numerical code is also used to model the intensity loss through layered tissue mimics and results are presented illustrating the effects of altering the layered medium on the magnitude and spatial distribution of intensity loss.

A Combined Adaptive Neural Network and Nonlinear Model Predictive Control for Multirate Networked Industrial Process Control.

PubMed

Wang, Tong; Gao, Huijun; Qiu, Jianbin

2016-02-01

This paper investigates the multirate networked industrial process control problem in double-layer architecture. First, the output tracking problem for sampled-data nonlinear plant at device layer with sampling period T(d) is investigated using adaptive neural network (NN) control, and it is shown that the outputs of subsystems at device layer can track the decomposed setpoints. Then, the outputs and inputs of the device layer subsystems are sampled with sampling period T(u) at operation layer to form the index prediction, which is used to predict the overall performance index at lower frequency. Radial basis function NN is utilized as the prediction function due to its approximation ability. Then, considering the dynamics of the overall closed-loop system, nonlinear model predictive control method is proposed to guarantee the system stability and compensate the network-induced delays and packet dropouts. Finally, a continuous stirred tank reactor system is given in the simulation part to demonstrate the effectiveness of the proposed method.

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.

Quantitative thickness measurement of polarity-inverted piezoelectric thin-film layer by scanning nonlinear dielectric microscopy

NASA Astrophysics Data System (ADS)

Odagawa, Hiroyuki; Terada, Koshiro; Tanaka, Yohei; Nishikawa, Hiroaki; Yanagitani, Takahiko; Cho, Yasuo

2017-10-01

A quantitative measurement method for a polarity-inverted layer in ferroelectric or piezoelectric thin film is proposed. It is performed nondestructively by scanning nonlinear dielectric microscopy (SNDM). In SNDM, linear and nonlinear dielectric constants are measured using a probe that converts the variation of capacitance related to these constants into the variation of electrical oscillation frequency. In this paper, we describe a principle for determining the layer thickness and some calculation results of the output signal, which are related to the radius of the probe tip and the thickness of the inverted layer. Moreover, we derive an equation that represents the relationship between the output signal and the oscillation frequency of the probe and explain how to determine the thickness from the measured frequency. Experimental results in Sc-doped AlN piezoelectric thin films that have a polarity-inverted layer with a thickness of 1.5 µm fabricated by radio frequency magnetron sputtering showed a fairly good value of 1.38 µm for the thickness of the polarity-inverted layer.

Nonlinear instability and convection in a vertically vibrated granular bed

NASA Astrophysics Data System (ADS)

Shukla, Priyanka; Ansari, I. H.; van der Meer, D.; Lohse, Detlef; Alam, Meheboob

2015-11-01

The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis. Under a quasi-steady ansatz, the base state temperature decreases with increasing height away from from the vibrating plate, but the density profile consists of three distinct regions: (i) a collisional dilute layer at the bottom, (ii) a levitated dense layer at some intermediate height and (iii) a ballistic dilute layer at the top of the granular bed. For the nonlinear stability analysis, the nonlinearities up-to cubic order in perturbation amplitude are retained, leading to the Landau equation. The genesis of granular convection is shown to be tied to a supercritical pitchfork bifurcation from the Leidenfrost state. Near the bifurcation point the equilibrium amplitude is found to follow a square-root scaling law, Ae √{ ▵} , with the distance ▵ from bifurcation point. The strength of convection is maximal at some intermediate value of the shaking strength, with weaker convection both at weaker and stronger shaking. Our theory predicts a novel floating-convection state at very strong shaking.

Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media.

PubMed

Jing, Yuan; Cleveland, Robin O

2007-09-01

A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media.

Boundary Layer Effect on Behavior of Discrete Models

PubMed Central

Eliáš, Jan

2017-01-01

The paper studies systems of rigid bodies with randomly generated geometry interconnected by normal and tangential bonds. The stiffness of these bonds determines the macroscopic elastic modulus while the macroscopic Poisson’s ratio of the system is determined solely by the normal/tangential stiffness ratio. Discrete models with no directional bias have the same probability of element orientation for any direction and therefore the same mechanical properties in a statistical sense at any point and direction. However, the layers of elements in the vicinity of the boundary exhibit biased orientation, preferring elements parallel with the boundary. As a consequence, when strain occurs in this direction, the boundary layer becomes stiffer than the interior for the normal/tangential stiffness ratio larger than one, and vice versa. Nonlinear constitutive laws are typically such that the straining of an element in shear results in higher strength and ductility than straining in tension. Since the boundary layer tends, due to the bias in the elemental orientation, to involve more tension than shear at the contacts, it also becomes weaker and less ductile. The paper documents these observations and compares them to the results of theoretical analysis. PMID:28772517

Analytical framework for modeling of long-range transport of fungal plant epidemics

NASA Astrophysics Data System (ADS)

Kogan, Oleg; O'Keeffe, Kevin; Schneider, David; Myers, Christopher; Analytical FrameworksInfectious Disease Dynamics Team

2015-03-01

A new framework for the study of long-range transport of fungal plant epidemics is proposed. The null nonlinear model includes advective transport through the free atmosphere, spore production on the ground, and transfer of spores between the ground and the advective atmospheric layer. The competition between the growth wave on the ground and the effect of the wind is most strongly reflected in upwind fronts, which can propagate into the wind for exponential initial conditions. If the rate of spore transfer into the advective layer is below critical, this happens for initital conditions with arbitrary steepness. Upwind fronts from localized initial conditions will propagate in the direction of the wind above this critical parameter, and will not propagate below it. On the other hand, the speed of the downwind front does not have a strong dependence on the rate of spore transfer between the advective layer and the ground. Thus, even vanishingly small, but finite transfer rates result in a substantial epidemic wave in the direction of the wind. We also consider the effect of an additional, random-walk like mechanism of transport through the near-ground atmospheric boundary layer, and attempt to understand which route dominates the transport over long distances.

Nonlinear digital out-of-plane waveguide coupler based on nonlinear scattering of a single graphene layer

NASA Astrophysics Data System (ADS)

Asadi, Reza; Ouyang, Zhengbiao

2018-03-01

A new mechanism for out-of-plane coupling into a waveguide is presented and numerically studied based on nonlinear scattering of a single nano-scale Graphene layer inside the waveguide. In this mechanism, the refractive index nonlinearity of Graphene and nonhomogeneous light intensity distribution occurred due to the interference between the out-of-plane incident pump light and the waveguide mode provide a virtual grating inside the waveguide, coupling the out-of-plane pump light into the waveguide. It has been shown that the coupling efficiency has two distinct values with high contrast around a threshold pump intensity, providing suitable condition for digital optical applications. The structure operates at a resonance mode due to band edge effect, which enhances the nonlinearity and decreases the required threshold intensity.

Second-order non-linear optical studies on CdS microcrystallite-doped alkali borosilicate glasses

NASA Astrophysics Data System (ADS)

Liu, Hao; Liu, Qiming; Wang, Mingliang; Zhao, Xiujian

2007-05-01

CdS microcrystal-doped alkali borosilicate glasses were prepared by conventional fusion and heat-treatment method. Utilizing Maker fringe method, second-harmonic generation (SHG) was both observed from CdS-doped glasses before and after certain thermal/electrical poling. While because the direction of polarization axes of CdS crystals formed in the samples is random or insufficient interferences of generated SH waves occur, the fringe patterns obtained in samples without poling treatments showed no fine structures. For the poled samples, larger SH intensity has been obtained than that of the samples without any poling treatments. It was considered that the increase of an amount of hexagonal CdS in the anode surface layer caused by the applied dc field increased the SH intensity. The second-order non-linearity χ(2) was estimated to be 1.23 pm/V for the sample poled with 2.5 kV at 360 °C for 30 min.

Mathematical nonlinear optics

NASA Astrophysics Data System (ADS)

McLaughlin, David W.

1995-08-01

The principal investigator, together with a post-doctoral fellows Tetsuji Ueda and Xiao Wang, several graduate students, and colleagues, has applied the modern mathematical theory of nonlinear waves to problems in nonlinear optics and to equations directly relevant to nonlinear optics. Projects included the interaction of laser light with nematic liquid crystals and chaotic, homoclinic, small dispersive, and random behavior of solutions of the nonlinear Schroedinger equation. In project 1, the extremely strong nonlinear response of a continuous wave laser beam in a nematic liquid crystal medium has produced striking undulation and filamentation of the laser beam which has been observed experimentally and explained theoretically. In project 2, qualitative properties of the nonlinear Schroedinger equation (which is the fundamental equation for nonlinear optics) have been identified and studied. These properties include optical shocking behavior in the limit of very small dispersion, chaotic and homoclinic behavior in discretizations of the partial differential equation, and random behavior.

Nonlinear Excitation of Inviscid Stationary Vortex in a Boundary-Layer Flow

NASA Technical Reports Server (NTRS)

Choudhari, Meelan; Duck, Peter W.

1996-01-01

We examine the excitation of inviscid stationary crossflow instabilities near an isolated surface hump (or indentation) underneath a three-dimensional boundary layer. As the hump height (or indentation depth) is increased from zero, the receptivity process becomes nonlinear even before the stability characteristics of the boundary layer are modified to a significant extent. This behavior contrasts sharply with earlier findings on the excitation of the lower branch Tollmien-Schlichting modes and is attributed to the inviscid nature of the crossflow modes, which leads to a decoupling between the regions of receptivity and stability. As a result of this decoupling, similarity transformations exist that allow the nonlinear receptivity of a general three-dimensional boundary layer to be studied with a set of canonical solutions to the viscous sublayer equations. The parametric study suggests that the receptivity is likely to become nonlinear even before the hump height becomes large enough for flow reversal to occur in the canonical solution. We also find that the receptivity to surface humps increases more rapidly as the hump height increases than is predicted by linear theory. On the other hand, receptivity near surface indentations is generally smaller in comparison with the linear approximation. Extension of the work to crossflow receptivity in compressible boundary layers and to Gortler vortex excitation is also discussed.

Nonlinear critical-layer evolution of a forced gravity wave packet

NASA Astrophysics Data System (ADS)

Campbell, L. J.; Maslowe, S. A.

2003-10-01

In this paper, numerical simulations are presented of the nonlinear critical-layer evolution of a forced gravity wave packet in a stratified shear flow. The wave packet, localized in the horizontal direction, is forced at the lower boundary of a two-dimensional domain and propagates vertically towards the critical layer. The wave mean-flow interactions in the critical layer are investigated numerically and contrasted with the results obtained using a spatially periodic monochromatic forcing. With the horizontally localized forcing, the net absorption of the disturbance at the critical layer continues for large time and the onset of the nonlinear breakdown is delayed compared with the case of monochromatic forcing. There is an outward flux of momentum in the horizontal direction so that the horizontal extent of the packet increases with time. The extent to which this happens depends on a number of factors including the amplitude and horizontal length of the forcing. It is also seen that the prolonged absorption of the disturbance stabilizes the solution to the extent that it is always convectively stable; the local Richardson number remains positive well into the nonlinear regime. In this respect, our results for the localized forcing differ from those in the case of monochromatic forcing where significant regions with negative Richardson number appear.

Geometrically nonlinear analysis of layered composite plates and shells

NASA Technical Reports Server (NTRS)

Chao, W. C.; Reddy, J. N.

1983-01-01

A degenerated three dimensional finite element, based on the incremental total Lagrangian formulation of a three dimensional layered anisotropic medium was developed. Its use in the geometrically nonlinear, static and dynamic, analysis of layered composite plates and shells is demonstrated. A two dimenisonal finite element based on the Sanders shell theory with the von Karman (nonlinear) strains was developed. It is shown that the deflections obtained by the 2D shell element deviate from those obtained by the more accurate 3D element for deep shells. The 3D degenerated element can be used to model general shells that are not necessarily doubly curved. The 3D degenerated element is computationally more demanding than the 2D shell theory element for a given problem. It is found that the 3D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion.

Dynamical processes and epidemic threshold on nonlinear coupled multiplex networks

NASA Astrophysics Data System (ADS)

Gao, Chao; Tang, Shaoting; Li, Weihua; Yang, Yaqian; Zheng, Zhiming

2018-04-01

Recently, the interplay between epidemic spreading and awareness diffusion has aroused the interest of many researchers, who have studied models mainly based on linear coupling relations between information and epidemic layers. However, in real-world networks the relation between two layers may be closely correlated with the property of individual nodes and exhibits nonlinear dynamical features. Here we propose a nonlinear coupled information-epidemic model (I-E model) and present a comprehensive analysis in a more generalized scenario where the upload rate differs from node to node, deletion rate varies between susceptible and infected states, and infection rate changes between unaware and aware states. In particular, we develop a theoretical framework of the intra- and inter-layer dynamical processes with a microscopic Markov chain approach (MMCA), and derive an analytic epidemic threshold. Our results suggest that the change of upload and deletion rate has little effect on the diffusion dynamics in the epidemic layer.

Dynamical continuous time random Lévy flights

NASA Astrophysics Data System (ADS)

Liu, Jian; Chen, Xiaosong

2016-03-01

The Lévy flights' diffusive behavior is studied within the framework of the dynamical continuous time random walk (DCTRW) method, while the nonlinear friction is introduced in each step. Through the DCTRW method, Lévy random walker in each step flies by obeying the Newton's Second Law while the nonlinear friction f(v) = - γ0v - γ2v3 being considered instead of Stokes friction. It is shown that after introducing the nonlinear friction, the superdiffusive Lévy flights converges, behaves localization phenomenon with long time limit, but for the Lévy index μ = 2 case, it is still Brownian motion.

Problems in nonlinear acoustics: Pulsed finite amplitude sound beams, nonlinear acoustic wave propagation in a liquid layer, nonlinear effects in asymmetric cylindrical sound beams, effects of absorption on the interaction of sound beams, and parametric receiving arrays

NASA Astrophysics Data System (ADS)

Hamilton, Mark F.

1990-12-01

This report discusses five projects all of which involve basic theoretical research in nonlinear acoustics: (1) pulsed finite amplitude sound beams are studied with a recently developed time domain computer algorithm that solves the KZK nonlinear parabolic wave equation; (2) nonlinear acoustic wave propagation in a liquid layer is a study of harmonic generation and acoustic soliton information in a liquid between a rigid and a free surface; (3) nonlinear effects in asymmetric cylindrical sound beams is a study of source asymmetries and scattering of sound by sound at high intensity; (4) effects of absorption on the interaction of sound beams is a completed study of the role of absorption in second harmonic generation and scattering of sound by sound; and (5) parametric receiving arrays is a completed study of parametric reception in a reverberant environment.

On buffer layers as non-reflecting computational boundaries

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Turkel, Eli L.

1996-01-01

We examine an absorbing buffer layer technique for use as a non-reflecting boundary condition in the numerical simulation of flows. One such formulation was by Ta'asan and Nark for the linearized Euler equations. They modified the flow inside the buffer zone to artificially make it supersonic in the layer. We examine how this approach can be extended to the nonlinear Euler equations. We consider both a conservative and a non-conservative form modifying the governing equations in the buffer layer. We compare this with the case that the governing equations in the layer are the same as in the interior domain. We test the effectiveness of these buffer layers by a simulation of an excited axisymmetric jet based on a nonlinear compressible Navier-Stokes equations.

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.

Nonlinear Convective Flows in a Laterally Heated Two-Layer System with a Temperature-Dependent Heat Release/Consumption at the Interface

NASA Astrophysics Data System (ADS)

Simanovskii, Ilya; Viviani, Antonio; Dubois, Frank; Queeckers, Patrick

2018-01-01

Nonlinear convective flows developed under the joint action of buoyant and thermocapillary effects in a laterally heated two-layer system filling the closed cavity, have been investigated. The influence of a temperature-dependent interfacial heat release/consumption on nonlinear steady and oscillatory regimes, has been studied. It is shown that sufficiently strong temperature dependence of interfacial heat sinks and heat sources can change the sequence of bifurcations and lead to the development of specific oscillatory regimes in the system.

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

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

NASA Astrophysics Data System (ADS)

Aver'yanov, M. V.; Khokhlova, V. A.; Sapozhnikov, O. A.; Blanc-Benon, Ph.; Cleveland, R. O.

2006-12-01

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption.

Nonlinear geometries in liquid crystals and liquid crystalline polymers

NASA Astrophysics Data System (ADS)

Dingemans, Theo Jacobus

The thermodynamic properties of thermotropic liquid crystals (LCs), and polymeric LCs are strongly dependent on mesogenic shape and in order to explore the relationships between shape and physical properties new, nonlinear geometries were examined. Symmetric oxadiazole based model compounds were synthesized and despite an internal exocyclic bond angle of 134sp° the model compounds exhibit a variety of mesophases. Conoscopic studies on bis(p-hexyloxyphenyl) 4,4sp'- (1,3,4-oxadiazole-2,5-diyl) dicarboxylate in its phase Ssb{A} phase are not consistent with the uniaxial Ssb{A} phase, but rather a biaxial Ssb{CM} phase. Uniaxial and biaxial mesogenic monomers were incorporated in main-chain polyesters. Transition temperatures of the interfacially prepared polymers were higher than materials that were melt polymerized. sp{13}C NMR showed that all polymers prepared by melt condensation have random monomer sequence distributions at the diad level. Thiophene and 1,3-phenylene modified p-quinquephenyls were synthesized in order to investigate the effects of mesogen nonlinearity and dipole direction on the LC thermodynamic properties. Results indicate that shape asymmetry favors mesophase formation and stability; the thiophene dipole moment appears to have no effect. The 120sp° exocyclic bond angle disrupts liquid crystallinity in 1,3-phenylene derivatives. Additionally the placement of 2,5-thiophene in "p-quinquephenyls" affects a red shift in its UV absorption. This was exploited in single layer light emitting diodes (LEDs) to tune the electroluminescence emission. In double layer LEDs these compounds function as efficient hole transport materials with high light outputs. Ferroelectric LCs derived from isoleucine were synthesized and shown to have spontaneous polarizations that are a strong function of halogen size (F > Cl > Br).

Synchronism of nonlinear internal waves in a three-layer fluid

NASA Astrophysics Data System (ADS)

Talipova, Tatiana; Kurkina, Oxana; Terletska, Katerina; Rouvinskaya, Ekaterina

2017-04-01

In a three layer fluid with arbitrary layer widths and densities the existence of long internal solitons and breathers is proven theoretically and numerically, see for example (Pelinovsky et al., 2007; Lamb et al., 2007). The existence of breather-like waves of the intermediate length is also shown in numerical simulations (Terletska et al., 2016). For such waves conditions of synchronism are valid when a breather of the first mode and a soliton of the second mode move together with the same speed and form an asymmetric solitary wave of the second mode. The process of strong interaction of long nonlinear internal waves in the framework of three-layer Camassa-Choi model demonstrates the same effect (Jo&Choi, 2014; Barros, 2016). We analyze possible synchronism conditions for steady-state internal waves in a three-layer fluid analytically the framework of the Gardner equation, which is valid for long weakly nonlinear internal waves. The equations for synchronism conditions are derived and considered in terms of wave amplitudes, layer widths and density jumps. The configurations of three-layer fluid are found for which such a synchronism is possible. References: Barros R. Large amplitude internal waves in three-layer flows. The forth international conference "Nonlinear Waves - Theory and Applications", MS7, Beijing, China, June 25 - 28, 2016 Pelinovsky E., Polukhina O., Slunyaev A., Talipova T. Internal solitary waves // Chapter 4 in the book "Solitary Waves in Fluids". WIT Press. Southampton, Boston. 2007. P. 85 - 110. K. Terletska., K. T. Jung, T. Talipova, V. Maderich, I. Brovchenko and R. Grimshaw Internal breather-like wave generation by the second mode solitary wave interaction with a step// Physics of Fluids, 2016, accepted

Nonlinear interactions in mixing layers and compressible heated round jets. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

Jarrah, Yousef Mohd

1989-01-01

The nonlinear interactions between a fundamental instability mode and both its harmonics and the changing mean flow are studied using the weakly nonlinear stability theory of Stuart and Watson, and numerical solutions of coupled nonlinear partial differential equations. The first part focuses on incompressible cold (or isothermal; constant temperature throughout) mixing layers, and for these, the first and second Landau constants are calculated as functions of wavenumber and Reynolds number. It is found that the dominant contribution to the Landau constants arises from the mean flow changes and not from the higher harmonics. In order to establish the range of validity of the weakly nonlinear theory, the weakly nonlinear and numerical solutions are compared and the limitation of each is discussed. At small amplitudes and at low-to-moderate Reynolds numbers, the two results compare well in describing the saturation of the fundamental, the distortion of the mean flow, and the initial stages of vorticity roll-up. At larger amplitudes, the interaction between the fundamental, second harmonic, and the mean flow is strongly nonlinear and the numerical solution predicts flow oscillations, whereas the weakly nonlinear theory yields saturation. In the second part, the weakly nonlinear theory is extended to heated (or nonisothermal; mean temperature distribution) subsonic round jets where quadratic and cubic nonlinear interactions are present, and the Landau constants also depend on jet temperature ratio, Mach number and azimuthal mode number. Under exponential growth and nonlinear saturation, it is found that heating and compressibility suppress the growth of instability waves, that the first azimuthal mode is the dominant instability mode, and that the weakly nonlinear solution describes the early stages of the roll-up of an axisymmetric shear layer. The receptivity of a typical jet flow to pulse type input disturbance is also studied by solving the initial value problem and then examining the behavior of the long-time solution.

Theory of multiple quantum dot formation in strained-layer heteroepitaxy

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

Du, Lin; Maroudas, Dimitrios, E-mail: maroudas@ecs.umass.edu

2016-07-11

We develop a theory for the experimentally observed formation of multiple quantum dots (QDs) in strained-layer heteroepitaxy based on surface morphological stability analysis of a coherently strained epitaxial thin film on a crystalline substrate. Using a fully nonlinear model of surface morphological evolution that accounts for a wetting potential contribution to the epitaxial film's free energy as well as surface diffusional anisotropy, we demonstrate the formation of multiple QD patterns in self-consistent dynamical simulations of the evolution of the epitaxial film surface perturbed from its planar state. The simulation predictions are supported by weakly nonlinear analysis of the epitaxial filmmore » surface morphological stability. We find that, in addition to the Stranski-Krastanow instability, long-wavelength perturbations from the planar film surface morphology can trigger a nonlinear instability, resulting in the splitting of a single QD into multiple QDs of smaller sizes, and predict the critical wavelength of the film surface perturbation for the onset of the nonlinear tip-splitting instability. The theory provides a fundamental interpretation for the observations of “QD pairs” or “double QDs” and other multiple QDs reported in experimental studies of epitaxial growth of semiconductor strained layers and sets the stage for precise engineering of tunable-size nanoscale surface features in strained-layer heteroepitaxy by exploiting film surface nonlinear, pattern forming phenomena.« less

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.

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.

Simulation of Nonlinear Instabilities in an Attachment-Line Boundary Layer

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.

1996-01-01

The linear and the nonlinear stability of disturbances that propagate along the attachment line of a three-dimensional boundary layer is considered. The spatially evolving disturbances in the boundary layer are computed by direct numerical simulation (DNS) of the unsteady, incompressible Navier-Stokes equations. Disturbances are introduced either by forcing at the in ow or by applying suction and blowing at the wall. Quasi-parallel linear stability theory and a nonparallel theory yield notably different stability characteristics for disturbances near the critical Reynolds number; the DNS results con rm the latter theory. Previously, a weakly nonlinear theory and computations revealed a high wave-number region of subcritical disturbance growth. More recent computations have failed to achieve this subcritical growth. The present computational results indicate the presence of subcritically growing disturbances; the results support the weakly nonlinear theory. Furthermore, an explanation is provided for the previous theoretical and computational discrepancy. In addition, the present results demonstrate that steady suction can be used to stabilize disturbances that otherwise grow subcritically along the attachment line.

Formation Learning Control of Multiple Autonomous Underwater Vehicles With Heterogeneous Nonlinear Uncertain Dynamics.

PubMed

Yuan, Chengzhi; Licht, Stephen; He, Haibo

2017-09-26

In this paper, a new concept of formation learning control is introduced to the field of formation control of multiple autonomous underwater vehicles (AUVs), which specifies a joint objective of distributed formation tracking control and learning/identification of nonlinear uncertain AUV dynamics. A novel two-layer distributed formation learning control scheme is proposed, which consists of an upper-layer distributed adaptive observer and a lower-layer decentralized deterministic learning controller. This new formation learning control scheme advances existing techniques in three important ways: 1) the multi-AUV system under consideration has heterogeneous nonlinear uncertain dynamics; 2) the formation learning control protocol can be designed and implemented by each local AUV agent in a fully distributed fashion without using any global information; and 3) in addition to the formation control performance, the distributed control protocol is also capable of accurately identifying the AUVs' heterogeneous nonlinear uncertain dynamics and utilizing experiences to improve formation control performance. Extensive simulations have been conducted to demonstrate the effectiveness of the proposed results.

Sublayer of Prandtl Boundary Layers

NASA Astrophysics Data System (ADS)

Grenier, Emmanuel; Nguyen, Toan T.

2018-03-01

The aim of this paper is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit {ν \\to 0} . In Grenier (Commun Pure Appl Math 53(9):1067-1091, 2000), one of the authors proved that there exists no asymptotic expansion involving one of Prandtl's boundary layer, with thickness of order {√{ν}} , which describes the inviscid limit of Navier-Stokes equations. The instability gives rise to a viscous boundary sublayer whose thickness is of order {ν^{3/4}} . In this paper, we point out how the stability of the classical Prandtl's layer is linked to the stability of this sublayer. In particular, we prove that the two layers cannot both be nonlinearly stable in L^∞. That is, either the Prandtl's layer or the boundary sublayer is nonlinearly unstable in the sup norm.

Investigation of Second- and Third-Harmonic Generation in Few-Layer Gallium Selenide by Multiphoton Microscopy

PubMed Central

Karvonen, Lasse; Säynätjoki, Antti; Mehravar, Soroush; Rodriguez, Raul D.; Hartmann, Susanne; Zahn, Dietrich R. T.; Honkanen, Seppo; Norwood, Robert A.; Peyghambarian, N.; Kieu, Khanh; Lipsanen, Harri; Riikonen, Juha

2015-01-01

Gallium selenide (GaSe) is a layered semiconductor and a well-known nonlinear optical crystal. The discovery of graphene has created a new vast research field focusing on two-dimensional materials. We report on the nonlinear optical properties of few-layer GaSe using multiphoton microscopy. Both second- and third-harmonic generation from few-layer GaSe flakes were observed. Unexpectedly, even the peak at the wavelength of 390 nm, corresponding to the fourth-harmonic generation or the sum frequency generation from third-harmonic generation and pump light, was detected during the spectral measurements in thin GaSe flakes. PMID:25989113

Triplex molecular layers with nonlinear nanomechanical response

NASA Astrophysics Data System (ADS)

Tsukruk, V. V.; Ahn, H.-S.; Kim, D.; Sidorenko, A.

2002-06-01

The molecular design of surface structures with built-in mechanisms for mechanical energy dissipation under nanomechanical deformation and compression resistance provided superior nanoscale wear stability. We designed robust, well-defined trilayer surface nanostructures chemically grafted to a silicon oxide surface with an effective composite modulus of about 1 GPa. The total thickness was within 20-30 nm and included an 8 nm rubber layer sandwiched between two hard layers. The rubber layer provides an effective mechanism for energy dissipation, facilitated by nonlinear, giant, reversible elastic deformations of the rubber matrix, restoring the initial status due to the presence of an effective nanodomain network and chemical grafting within the rubber matrix.

Convection and reaction in a diffusive boundary layer in a porous medium: nonlinear dynamics.

PubMed

Andres, Jeanne Therese H; Cardoso, Silvana S S

2012-09-01

We study numerically the nonlinear interactions between chemical reaction and convective fingering in a diffusive boundary layer in a porous medium. The reaction enhances stability by consuming a solute that is unstably distributed in a gravitational field. We show that chemical reaction profoundly changes the dynamics of the system, by introducing a steady state, shortening the evolution time, and altering the spatial patterns of velocity and concentration of solute. In the presence of weak reaction, finger growth and merger occur effectively, driving strong convective currents in a thick layer of solute. However, as the reaction becomes stronger, finger growth is inhibited, tip-splitting is enhanced and the layer of solute becomes much thinner. Convection enhances the mass flux of solute consumed by reaction in the boundary layer but has a diminishing effect as reaction strength increases. This nonlinear behavior has striking differences to the density fingering of traveling reaction fronts, for which stronger chemical kinetics result in more effective finger merger owing to an increase in the speed of the front. In a boundary layer, a strong stabilizing effect of reaction can maintain a long-term state of convection in isolated fingers of wavelength comparable to that at onset of instability.

Nonlinear Stability and Structure of Compressible Reacting Mixing Layers

NASA Technical Reports Server (NTRS)

Day, M. J.; Mansour, N. N.; Reynolds, W. C.

2000-01-01

The parabolized stability equations (PSE) are used to investigate issues of nonlinear flow development and mixing in compressible reacting shear layers. Particular interest is placed on investigating the change in flow structure that occurs when compressibility and heat release are added to the flow. These conditions allow the 'outer' instability modes- one associated with each of the fast and slow streams-to dominate over the 'central', Kelvin-Helmholtz mode that unaccompanied in incompressible nonreacting mixing layers. Analysis of scalar probability density functions in flows with dominant outer modes demonstrates the ineffective, one-sided nature of mixing that accompany these flow structures. Colayer conditions, where two modes have equal growth rate and the mixing layer is formed by two sets of vortices, offer some opportunity for mixing enhancement. Their extent, however, is found to be limited in the mixing layer's parameter space. Extensive validation of the PSE technique also provides a unique perspective on central- mode vortex pairing, further supporting the view that pairing is primarily governed perspective sheds insight on how linear stability theory is able to provide such an accurate prediction of experimentally-observed, fully nonlinear flow phenomenon.

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Amplitude Equations

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented. In this part of the analysis, the system of partial differential critical-layer equations derived in Part I is solved analytically to yield the amplitude equations which are analyzed using a combination of asymptotic and numerical methods. Numerical solutions of the inviscid non-equilibrium oblique-mode amplitude equations show that the frequency-detuned self-interaction enhances the growth of the lower-frequency oblique modes more than the higher-frequency ones. All amplitudes become singular at the same finite downstream position. The frequency detuning delays the occurrence of the singularity. The spanwise-periodic mean-flow distortion and low-frequency nonlinear modes are generated by the critical-layer interaction between frequency-detuned oblique modes. The nonlinear mean flow and higher harmonics as well as the primary instabilities become as large as the base mean flow in the inviscid wall layer in the downstream region where the distance from the singularity is of the order of the wavelength scale.

Development and Breakdown of Goertler Vortices in High Speed Boundary Layers

NASA Technical Reports Server (NTRS)

Li, Fei; Choudhari, Meelan; Chang, Chau-Lyan; Wu, Minwei; Greene, Ptrick T.

2010-01-01

The nonlinear development of G rtler instability over a concave surface gives rise to a highly distorted stationary flow in the boundary layer that has strong velocity gradients in both spanwise and wall-normal directions. This distorted flow is susceptible to strong, high frequency secondary instability that leads to the onset of transition. For high Mach number flows, the boundary layer is also subject to the second mode instability. The nonlinear development of G rtler vortices and the ensuing growth and breakdown of secondary instability, the G rtler vortex interactions with second mode instabilities as well as oblique second mode interactions are examined in the context of both internal and external hypersonic configurations using nonlinear parabolized stability equations, 2-D eigenvalue analysis and direct numerical simulation. For G rtler vortex development inside the Purdue Mach 6 Ludwieg tube wind tunnel, multiple families of unstable secondary eigenmodes are identified and their linear and nonlinear evolution is examined. The computation of secondary instability is continued past the onset of transition to elucidate the physical mechanisms underlying the laminar breakdown process. Nonlinear breakdown scenarios associated with transition over a Mach 6 compression cone configuration are also explored.

Current structure of strongly nonlinear interfacial solitary waves

NASA Astrophysics Data System (ADS)

Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor

2015-04-01

The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr, M., Berntsen, J., and Davies, P.A. Numerical simulation of internal solitary wave-induced reverse flow and associated vortices in a shallow, two-layer fluid benthic boundary layer. Ocean Dynamics, 2011, vol. 61, No. 6, 857 - 872.

Enhancing Security of Double Random Phase Encoding Based on Random S-Box

NASA Astrophysics Data System (ADS)

Girija, R.; Singh, Hukum

2018-06-01

In this paper, we propose a novel asymmetric cryptosystem for double random phase encoding (DRPE) using random S-Box. While utilising S-Box separately is not reliable and DRPE does not support non-linearity, so, our system unites the effectiveness of S-Box with an asymmetric system of DRPE (through Fourier transform). The uniqueness of proposed cryptosystem lies on employing high sensitivity dynamic S-Box for our DRPE system. The randomness and scalability achieved due to applied technique is an additional feature of the proposed solution. The firmness of random S-Box is investigated in terms of performance parameters such as non-linearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities etc. S-Boxes convey nonlinearity to cryptosystems which is a significant parameter and very essential for DRPE. The strength of proposed cryptosystem has been analysed using various parameters such as MSE, PSNR, correlation coefficient analysis, noise analysis, SVD analysis, etc. Experimental results are conferred in detail to exhibit proposed cryptosystem is highly secure.

Non-linear continuous time random walk models★

NASA Astrophysics Data System (ADS)

Stage, Helena; Fedotov, Sergei

2017-11-01

A standard assumption of continuous time random walk (CTRW) processes is that there are no interactions between the random walkers, such that we obtain the celebrated linear fractional equation either for the probability density function of the walker at a certain position and time, or the mean number of walkers. The question arises how one can extend this equation to the non-linear case, where the random walkers interact. The aim of this work is to take into account this interaction under a mean-field approximation where the statistical properties of the random walker depend on the mean number of walkers. The implementation of these non-linear effects within the CTRW integral equations or fractional equations poses difficulties, leading to the alternative methodology we present in this work. We are concerned with non-linear effects which may either inhibit anomalous effects or induce them where they otherwise would not arise. Inhibition of these effects corresponds to a decrease in the waiting times of the random walkers, be this due to overcrowding, competition between walkers or an inherent carrying capacity of the system. Conversely, induced anomalous effects present longer waiting times and are consistent with symbiotic, collaborative or social walkers, or indirect pinpointing of favourable regions by their attractiveness. Contribution to the Topical Issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by Ryszard Kutner and Jaume Masoliver.

A method for reducing the order of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Masri, S. F.; Miller, R. K.; Sassi, H.; Caughey, T. K.

1984-06-01

An approximate method that uses conventional condensation techniques for linear systems together with the nonparametric identification of the reduced-order model generalized nonlinear restoring forces is presented for reducing the order of discrete multidegree-of-freedom dynamic systems that possess arbitrary nonlinear characteristics. The utility of the proposed method is demonstrated by considering a redundant three-dimensional finite-element model half of whose elements incorporate hysteretic properties. A nonlinear reduced-order model, of one-third the order of the original model, is developed on the basis of wideband stationary random excitation and the validity of the reduced-order model is subsequently demonstrated by its ability to predict with adequate accuracy the transient response of the original nonlinear model under a different nonstationary random excitation.

Model of large volumetric capacitance in graphene supercapacitors based on ion clustering

NASA Astrophysics Data System (ADS)

Skinner, Brian; Fogler, M. M.; Shklovskii, B. I.

2011-12-01

Electric double-layer supercapacitors (SCs) are promising devices for high-power energy storage based on the reversible absorption of ions into porous conducting electrodes. Graphene is a particularly good candidate for the electrode material in SCs due to its high conductivity and large surface area. In this paper, we consider SC electrodes made from a stack of graphene sheets with randomly inserted spacer molecules. We show that the large volumetric capacitances C≳100F/cm3 observed experimentally can be understood as a result of collective intercalation of ions into the graphene stack and the accompanying nonlinear screening by graphene electrons that renormalizes the charge of the ion clusters.

A model of large volumetric capacitance in graphene supercapacitors based on ion clustering

NASA Astrophysics Data System (ADS)

Skinner, Brian; Fogler, Michael; Shklovskii, Boris

2012-02-01

Electric double layer supercapacitors are promising devices for high-power energy storage based on the reversible absorption of ions into porous, conducting electrodes. Graphene is a particularly good candidate for the electrode material in supercapacitors due to its high conductivity and large surface area. In this paper we consider supercapacitor electrodes made from a stack of graphene sheets with randomly-inserted ``spacer" molecules. We show that the large volumetric capacitances C > 100 F/cm^3 observed experimentally can be understood as a result of collective intercalation of ions into the graphene stack and the accompanying nonlinear screening by graphene electrons that renormalizes the charge of the ion clusters.

A Shear Deformable Shell Element for Laminated Composites

NASA Technical Reports Server (NTRS)

Chao, W. C.; Reddy, J. N.

1984-01-01

A three-dimensional element based on the total Lagrangian description of the motion of a layered anisotropic composite medium is developed, validated, and used to analyze layered composite shells. The element contains the following features: geometric nonlinearity, dynamic (transient) behavior, and arbitrary lamination scheme and lamina properties. Numerical results of nonlinear bending, natural vibration, and transient response are presented to illustrate the capabilities of the element.

Relationships between nonlinear normal modes and response to random inputs

NASA Astrophysics Data System (ADS)

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

2017-02-01

The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). This work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing. Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.

Theory of multinonlinear media and its application to the soliton processes in ferrite–ferroelectric structures

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

Cherkasskii, M. A., E-mail: macherkasskii@hotmail.com; Nikitin, A. A.; Kalinikos, B. A.

A theory is developed to describe the wave processes that occur in waveguide media having several types of nonlinearity, specifically, multinonlinear media. It is shown that the nonlinear Schrödinger equation can be used to describe the general wave process that occurs in such media. The competition between the electric wave nonlinearity and the magnetic wave nonlinearity in a layered multinonlinear ferrite–ferroelectric structure is found to change a total repulsive nonlinearity into a total attractive nonlinearity.

Non-linear boundary-layer receptivity due to distributed surface roughness

NASA Technical Reports Server (NTRS)

Amer, Tahani Reffet

1995-01-01

The process by which a laminar boundary layer internalizes the external disturbances in the form of instability waves is known as boundary-layer receptivity. The objective of the present research was to determine the effect of acoustic excitation on boundary-layer receptivity for a flat plate with distributed variable-amplitude surface roughness through measurements with a hot-wire probe. Tollmien-Schlichting mode shapes due to surface roughness receptivity have also been determined, analyzed, and shown to be in agreement with theory and other experimental work. It has been shown that there is a linear relationship between the surface roughness and receptivity for certain roughness configurations with constant roughness wavelength. In addition, strong non-linear receptivity effects exist for certain surface roughness configurations over a band where the surface roughness and T-S wavelength are matched. The results from the present experiment follow the trends predicted by theory and other experimental work for linear receptivity. In addition, the results show the existence of non-linear receptivity effects for certain combinations of surface roughness elements.

Negative refraction, gain and nonlinear effects in hyperbolic metamaterials.

PubMed

Argyropoulos, Christos; Estakhri, Nasim Mohammadi; Monticone, Francesco; Alù, Andrea

2013-06-17

The negative refraction and evanescent-wave canalization effects supported by a layered metamaterial structure obtained by alternating dielectric and plasmonic layers is theoretically analyzed. By using a transmission-line analysis, we formulate a way to rapidly analyze the negative refraction operation for given available materials over a broad range of frequencies and design parameters, and we apply it to broaden the bandwidth of negative refraction. Our analytical model is also applied to explore the possibility of employing active layers for loss compensation. Nonlinear dielectrics can also be considered within this approach, and they are explored in order to add tunability to the optical response, realizing positive-to-zero-to-negative refraction at the same frequency, as a function of the input intensity. Our findings may lead to a better physical understanding and improvement of the performance of negative refraction and subwavelength imaging in layered metamaterials, paving the way towards the design of gain-assisted hyperlenses and tunable nonlinear imaging devices.

Impact of Nonlinearity of The Contact Layer Between Elements Joined in a Multi-Bolted System on Its Preload

NASA Astrophysics Data System (ADS)

Grzejda, R.

2017-12-01

The paper deals with modelling and calculations of asymmetrical multi-bolted joints at the assembly stage. The physical model of the joint is based on a system composed of four subsystems, which are: a couple of joined elements, a contact layer between the elements, and a set of bolts. The contact layer is assumed as the Winkler model, which can be treated as a nonlinear or linear model. In contrast, the set of bolts are modelled using simplified beam models, known as spider bolt models. The theorem according to which nonlinearity of the contact layer has a negligible impact on the final preload of the joint in the case of its sequential tightening has been verified. Results of sample calculations for the selected multi-bolted system, in the form of diagrams of preloads in the bolts as well as normal contact pressure between the joined elements during the assembly process and at its end, are presented.

Comparative analysis of ferroelectric domain statistics via nonlinear diffraction in random nonlinear materials.

PubMed

Wang, B; Switowski, K; Cojocaru, C; Roppo, V; Sheng, Y; Scalora, M; Kisielewski, J; Pawlak, D; Vilaseca, R; Akhouayri, H; Krolikowski, W; Trull, J

2018-01-22

We present an indirect, non-destructive optical method for domain statistic characterization in disordered nonlinear crystals having homogeneous refractive index and spatially random distribution of ferroelectric domains. This method relies on the analysis of the wave-dependent spatial distribution of the second harmonic, in the plane perpendicular to the optical axis in combination with numerical simulations. We apply this technique to the characterization of two different media, Calcium Barium Niobate and Strontium Barium Niobate, with drastically different statistical distributions of ferroelectric domains.

Graphene-clad tapered fiber: effective nonlinearity and propagation losses.

PubMed

Gorbach, A V; Marini, A; Skryabin, D V

2013-12-15

We derive a pulse propagation equation for a graphene-clad optical fiber, treating the optical response of the graphene and nonlinearity of the dielectric fiber core as perturbations in asymptotic expansion of Maxwell equations. We analyze the effective nonlinear and attenuation coefficients due to the graphene layer. Based on the recent experimental measurements of the nonlinear graphene conductivity, we predict considerable enhancement of the effective nonlinearity for subwavelength fiber core diameters.

Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

NASA Technical Reports Server (NTRS)

Przekop, Adam; Rizzi, Stephen A.

2006-01-01

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.

Nonlinear Reduced Order Random Response Analysis of Structures With Shallow Curvature

NASA Technical Reports Server (NTRS)

Przekop, Adam; Rizzi, Stephen A.

2005-01-01

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Those having symmetric transverse displacements (ST modes) can be designated as transverse dominated (ST-T) modes and in-plane dominated (ST-I) modes. Those having anti-symmetric transverse displacements (AT modes) can similarly be designated as transverse dominated (AT-T) modes and in-plane dominated (AT-I) modes. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of ST-T modes is important for all response regimes, it is found that the ST-I modes become increasingly important in the nonlinear response regime, and that AT-T and AT-I modes are critical in the autoparametric regime.

Characterizing Hypervelocity Impact (HVI)-Induced Pitting Damage Using Active Guided Ultrasonic Waves: From Linear to Nonlinear

PubMed Central

Liu, Menglong; Wang, Kai; Lissenden, Cliff J.; Wang, Qiang; Zhang, Qingming; Long, Renrong; Su, Zhongqing; Cui, Fangsen

2017-01-01

Hypervelocity impact (HVI), ubiquitous in low Earth orbit with an impacting velocity in excess of 1 km/s, poses an immense threat to the safety of orbiting spacecraft. Upon penetration of the outer shielding layer of a typical two-layer shielding system, the shattered projectile, together with the jetted materials of the outer shielding material, subsequently impinge the inner shielding layer, to which pitting damage is introduced. The pitting damage includes numerous craters and cracks disorderedly scattered over a wide region. Targeting the quantitative evaluation of this sort of damage (multitudinous damage within a singular inspection region), a characterization strategy, associating linear with nonlinear features of guided ultrasonic waves, is developed. Linear-wise, changes in the signal features in the time domain (e.g., time-of-flight and energy dissipation) are extracted, for detecting gross damage whose characteristic dimensions are comparable to the wavelength of the probing wave; nonlinear-wise, changes in the signal features in the frequency domain (e.g., second harmonic generation), which are proven to be more sensitive than their linear counterparts to small-scale damage, are explored to characterize HVI-induced pitting damage scattered in the inner layer. A numerical simulation, supplemented with experimental validation, quantitatively reveals the accumulation of nonlinearity of the guided waves when the waves traverse the pitting damage, based on which linear and nonlinear damage indices are proposed. A path-based rapid imaging algorithm, in conjunction with the use of the developed linear and nonlinear indices, is developed, whereby the HVI-induced pitting damage is characterized in images in terms of the probability of occurrence. PMID:28772908

Stochastic Resonance and Safe Basin of Single-Walled Carbon Nanotubes with Strongly Nonlinear Stiffness under Random Magnetic Field.

PubMed

Xu, Jia; Li, Chao; Li, Yiran; Lim, Chee Wah; Zhu, Zhiwen

2018-05-04

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of the microstructure is considered based on Eringen’s differential constitutive model. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.

Evolution of basic equations for nearshore wave field

PubMed Central

ISOBE, Masahiko

2013-01-01

In this paper, a systematic, overall view of theories for periodic waves of permanent form, such as Stokes and cnoidal waves, is described first with their validity ranges. To deal with random waves, a method for estimating directional spectra is given. Then, various wave equations are introduced according to the assumptions included in their derivations. The mild-slope equation is derived for combined refraction and diffraction of linear periodic waves. Various parabolic approximations and time-dependent forms are proposed to include randomness and nonlinearity of waves as well as to simplify numerical calculation. Boussinesq equations are the equations developed for calculating nonlinear wave transformations in shallow water. Nonlinear mild-slope equations are derived as a set of wave equations to predict transformation of nonlinear random waves in the nearshore region. Finally, wave equations are classified systematically for a clear theoretical understanding and appropriate selection for specific applications. PMID:23318680

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 low frequency electrostatic structures in a magnetized two-component auroral plasma

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

Rufai, O. R., E-mail: rajirufai@gmail.com; Scientific Computing, Memorial University of Newfoundland, St John's, Newfoundland and Labrador A1C 5S7; Bharuthram, R., E-mail: rbharuthram@uwc.ac.za

2016-03-15

Finite amplitude nonlinear ion-acoustic solitons, double layers, and supersolitons in a magnetized two-component plasma composed of adiabatic warm ions fluid and energetic nonthermal electrons are studied by employing the Sagdeev pseudopotential technique and assuming the charge neutrality condition at equilibrium. The model generates supersoliton structures at supersonic Mach numbers regime in addition to solitons and double layers, whereas in the unmagnetized two-component plasma case only, soliton and double layer solutions can be obtained. Further investigation revealed that wave obliqueness plays a critical role for the evolution of supersoliton structures in magnetized two-component plasmas. In addition, the effect of ion temperaturemore » and nonthermal energetic electron tends to decrease the speed of oscillation of the nonlinear electrostatic structures. The present theoretical results are compared with Viking satellite observations.« less

Freak waves in random oceanic sea states.

PubMed

Onorato, M; Osborne, A R; Serio, M; Bertone, S

2001-06-18

Freak waves are very large, rare events in a random ocean wave train. Here we study their generation in a random sea state characterized by the Joint North Sea Wave Project spectrum. We assume, to cubic order in nonlinearity, that the wave dynamics are governed by the nonlinear Schrödinger (NLS) equation. We show from extensive numerical simulations of the NLS equation how freak waves in a random sea state are more likely to occur for large values of the Phillips parameter alpha and the enhancement coefficient gamma. Comparison with linear simulations is also reported.

Generation mechanism of nonlinear ultrasonic Lamb waves in thin plates with randomly distributed micro-cracks.

PubMed

Zhao, Youxuan; Li, Feilong; Cao, Peng; Liu, Yaolu; Zhang, Jianyu; Fu, Shaoyun; Zhang, Jun; Hu, Ning

2017-08-01

Since the identification of micro-cracks in engineering materials is very valuable in understanding the initial and slight changes in mechanical properties of materials under complex working environments, numerical simulations on the propagation of the low frequency S 0 Lamb wave in thin plates with randomly distributed micro-cracks were performed to study the behavior of nonlinear Lamb waves. The results showed that while the influence of the randomly distributed micro-cracks on the phase velocity of the low frequency S 0 fundamental waves could be neglected, significant ultrasonic nonlinear effects caused by the randomly distributed micro-cracks was discovered, which mainly presented as a second harmonic generation. By using a Monte Carlo simulation method, we found that the acoustic nonlinear parameter increased linearly with the micro-crack density and the size of micro-crack zone, and it was also related to the excitation frequency and friction coefficient of the micro-crack surfaces. In addition, it was found that the nonlinear effect of waves reflected by the micro-cracks was more noticeable than that of the transmitted waves. This study theoretically reveals that the low frequency S 0 mode of Lamb waves can be used as the fundamental waves to quantitatively identify micro-cracks in thin plates. Copyright © 2017 Elsevier B.V. All rights reserved.

Nonlinear Optics with 2D Layered Materials.

PubMed

Autere, Anton; Jussila, Henri; Dai, Yunyun; Wang, Yadong; Lipsanen, Harri; Sun, Zhipei

2018-06-01

2D layered materials (2DLMs) are a subject of intense research for a wide variety of applications (e.g., electronics, photonics, and optoelectronics) due to their unique physical properties. Most recently, increasing research efforts on 2DLMs are projected toward the nonlinear optical properties of 2DLMs, which are not only fascinating from the fundamental science point of view but also intriguing for various potential applications. Here, the current state of the art in the field of nonlinear optics based on 2DLMs and their hybrid structures (e.g., mixed-dimensional heterostructures, plasmonic structures, and silicon/fiber integrated structures) is reviewed. Several potential perspectives and possible future research directions of these promising nanomaterials for nonlinear optics are also presented. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Growth and wall-transpiration control of nonlinear unsteady Görtler vortices forced by free-stream vortical disturbances

NASA Astrophysics Data System (ADS)

Marensi, Elena; Ricco, Pierre

2017-11-01

The generation, nonlinear evolution, and wall-transpiration control of unsteady Görtler vortices in an incompressible boundary layer over a concave plate is studied theoretically and numerically. Görtler rolls are initiated and driven by free-stream vortical perturbations of which only the low-frequency components are considered because they penetrate the most into the boundary layer. The formation and development of the disturbances are governed by the nonlinear unsteady boundary-region equations with the centrifugal force included. These equations are subject to appropriate initial and outer boundary conditions, which account for the influence of the upstream and free-stream forcing in a rigorous and mutually consistent manner. Numerical solutions show that the stabilizing effect on nonlinearity, which also occurs in flat-plate boundary layers, is significantly enhanced in the presence of centrifugal forces. Sufficiently downstream, the nonlinear vortices excited at different free-stream turbulence intensities Tu saturate at the same level, proving that the initial amplitude of the forcing becomes unimportant. At low Tu, the disturbance exhibits a quasi-exponential growth with the growth rate being intensified for more curved plates and for lower frequencies. At higher Tu, in the typical range of turbomachinery applications, the Görtler vortices do not undergo a modal stage as nonlinearity saturates rapidly, and the wall curvature does not affect the boundary-layer response. Good quantitative agreement with data from direct numerical simulations and experiments is obtained. Steady spanwise-uniform and spanwise-modulated zero-mass-flow-rate wall transpiration is shown to attenuate the growth of the Görtler vortices significantly. A novel modified version of the Fukagata-Iwamoto-Kasagi identity, used for the first time to study a transitional flow, reveals which terms in the streamwise momentum balance are mostly affected by the wall transpiration, thus offering insight into the increased nonlinear growth of the wall-shear stress.

The Effect of Basis Selection on Static and Random Acoustic Response Prediction Using a Nonlinear Modal Simulation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Przekop, Adam

2005-01-01

An investigation of the effect of basis selection on geometric nonlinear response prediction using a reduced-order nonlinear modal simulation is presented. The accuracy is dictated by the selection of the basis used to determine the nonlinear modal stiffness. This study considers a suite of available bases including bending modes only, bending and membrane modes, coupled bending and companion modes, and uncoupled bending and companion modes. The nonlinear modal simulation presented is broadly applicable and is demonstrated for nonlinear quasi-static and random acoustic response of flat beam and plate structures with isotropic material properties. Reduced-order analysis predictions are compared with those made using a numerical simulation in physical degrees-of-freedom to quantify the error associated with the selected modal bases. Bending and membrane responses are separately presented to help differentiate the bases.

A novel method for predicting the power outputs of wave energy converters

NASA Astrophysics Data System (ADS)

Wang, Yingguang

2018-03-01

This paper focuses on realistically predicting the power outputs of wave energy converters operating in shallow water nonlinear waves. A heaving two-body point absorber is utilized as a specific calculation example, and the generated power of the point absorber has been predicted by using a novel method (a nonlinear simulation method) that incorporates a second order random wave model into a nonlinear dynamic filter. It is demonstrated that the second order random wave model in this article can be utilized to generate irregular waves with realistic crest-trough asymmetries, and consequently, more accurate generated power can be predicted by subsequently solving the nonlinear dynamic filter equation with the nonlinearly simulated second order waves as inputs. The research findings demonstrate that the novel nonlinear simulation method in this article can be utilized as a robust tool for ocean engineers in their design, analysis and optimization of wave energy converters.

Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.

1999-01-01

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

Super-Resolution Community Detection for Layer-Aggregated Multilayer Networks

PubMed Central

Taylor, Dane; Caceres, Rajmonda S.; Mucha, Peter J.

2017-01-01

Applied network science often involves preprocessing network data before applying a network-analysis method, and there is typically a theoretical disconnect between these steps. For example, it is common to aggregate time-varying network data into windows prior to analysis, and the trade-offs of this preprocessing are not well understood. Focusing on the problem of detecting small communities in multilayer networks, we study the effects of layer aggregation by developing random-matrix theory for modularity matrices associated with layer-aggregated networks with N nodes and L layers, which are drawn from an ensemble of Erdős–Rényi networks with communities planted in subsets of layers. We study phase transitions in which eigenvectors localize onto communities (allowing their detection) and which occur for a given community provided its size surpasses a detectability limit K*. When layers are aggregated via a summation, we obtain K∗∝O(NL/T), where T is the number of layers across which the community persists. Interestingly, if T is allowed to vary with L, then summation-based layer aggregation enhances small-community detection even if the community persists across a vanishing fraction of layers, provided that T/L decays more slowly than 𝒪(L−1/2). Moreover, we find that thresholding the summation can, in some cases, cause K* to decay exponentially, decreasing by orders of magnitude in a phenomenon we call super-resolution community detection. In other words, layer aggregation with thresholding is a nonlinear data filter enabling detection of communities that are otherwise too small to detect. Importantly, different thresholds generally enhance the detectability of communities having different properties, illustrating that community detection can be obscured if one analyzes network data using a single threshold. PMID:29445565

Super-Resolution Community Detection for Layer-Aggregated Multilayer Networks.

PubMed

Taylor, Dane; Caceres, Rajmonda S; Mucha, Peter J

2017-01-01

Applied network science often involves preprocessing network data before applying a network-analysis method, and there is typically a theoretical disconnect between these steps. For example, it is common to aggregate time-varying network data into windows prior to analysis, and the trade-offs of this preprocessing are not well understood. Focusing on the problem of detecting small communities in multilayer networks, we study the effects of layer aggregation by developing random-matrix theory for modularity matrices associated with layer-aggregated networks with N nodes and L layers, which are drawn from an ensemble of Erdős-Rényi networks with communities planted in subsets of layers. We study phase transitions in which eigenvectors localize onto communities (allowing their detection) and which occur for a given community provided its size surpasses a detectability limit K * . When layers are aggregated via a summation, we obtain [Formula: see text], where T is the number of layers across which the community persists. Interestingly, if T is allowed to vary with L , then summation-based layer aggregation enhances small-community detection even if the community persists across a vanishing fraction of layers, provided that T/L decays more slowly than ( L -1/2 ). Moreover, we find that thresholding the summation can, in some cases, cause K * to decay exponentially, decreasing by orders of magnitude in a phenomenon we call super-resolution community detection. In other words, layer aggregation with thresholding is a nonlinear data filter enabling detection of communities that are otherwise too small to detect. Importantly, different thresholds generally enhance the detectability of communities having different properties, illustrating that community detection can be obscured if one analyzes network data using a single threshold.

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

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.

Cascaded K-means convolutional feature learner and its application to face recognition

NASA Astrophysics Data System (ADS)

Zhou, Daoxiang; Yang, Dan; Zhang, Xiaohong; Huang, Sheng; Feng, Shu

2017-09-01

Currently, considerable efforts have been devoted to devise image representation. However, handcrafted methods need strong domain knowledge and show low generalization ability, and conventional feature learning methods require enormous training data and rich parameters tuning experience. A lightened feature learner is presented to solve these problems with application to face recognition, which shares similar topology architecture as a convolutional neural network. Our model is divided into three components: cascaded convolution filters bank learning layer, nonlinear processing layer, and feature pooling layer. Specifically, in the filters learning layer, we use K-means to learn convolution filters. Features are extracted via convoluting images with the learned filters. Afterward, in the nonlinear processing layer, hyperbolic tangent is employed to capture the nonlinear feature. In the feature pooling layer, to remove the redundancy information and incorporate the spatial layout, we exploit multilevel spatial pyramid second-order pooling technique to pool the features in subregions and concatenate them together as the final representation. Extensive experiments on four representative datasets demonstrate the effectiveness and robustness of our model to various variations, yielding competitive recognition results on extended Yale B and FERET. In addition, our method achieves the best identification performance on AR and labeled faces in the wild datasets among the comparative methods.

Nonlinear development and secondary instability of Gortler vortices in hypersonic flows

NASA Technical Reports Server (NTRS)

Fu, Yibin B.; Hall, Philip

1991-01-01

In a hypersonic boundary layer over a wall of variable curvature, the region most susceptible to Goertler vortices is the temperature adjustment layer over which the basic state temperature decreases monotonically to its free stream value. Except for a special wall curvature distribution, the evolution of Goertler vortices trapped in the temperature adjustment layer will in general be strongly affected by the boundary layer growth through the O(M sup 3/2) curvature of the basic state, where M is the free stream Mach number. Only when the local wavenumber becomes as large as of order M sup 3/8, do nonparallel effects become negligible in the determination of stability properties. In the latter case, Goertler vortices will be trapped in a thin layer of O(epsilon sup 1/2) thickness which is embedded in the temperature adjustment layer; here epsilon is the inverse of the local wavenumber. A weakly nonlinear theory is presented in which the initial nonlinear development of Goertler vortices in the neighborhood of the neutral position is studied and two coupled evolution equations are derived. From these, it can be determined whether the vortices are decaying or growing depending on the sign of a constant which is related to wall curvature and the basic state temperature.

Experimental Design for Hanford Low-Activity Waste Glasses with High Waste Loading

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

Piepel, Gregory F.; Cooley, Scott K.; Vienna, John D.

This report discusses the development of an experimental design for the initial phase of the Hanford low-activity waste (LAW) enhanced glass study. This report is based on a manuscript written for an applied statistics journal. Appendices A, B, and E include additional information relevant to the LAW enhanced glass experimental design that is not included in the journal manuscript. The glass composition experimental region is defined by single-component constraints (SCCs), linear multiple-component constraints (MCCs), and a nonlinear MCC involving 15 LAW glass components. Traditional methods and software for designing constrained mixture experiments with SCCs and linear MCCs are not directlymore » applicable because of the nonlinear MCC. A modification of existing methodology to account for the nonlinear MCC was developed and is described in this report. One of the glass components, SO 3, has a solubility limit in glass that depends on the composition of the balance of the glass. A goal was to design the experiment so that SO 3 would not exceed its predicted solubility limit for any of the experimental glasses. The SO 3 solubility limit had previously been modeled by a partial quadratic mixture model expressed in the relative proportions of the 14 other components. The partial quadratic mixture model was used to construct a nonlinear MCC in terms of all 15 components. In addition, there were SCCs and linear MCCs. This report describes how a layered design was generated to (i) account for the SCCs, linear MCCs, and nonlinear MCC and (ii) meet the goals of the study. A layered design consists of points on an outer layer, and inner layer, and a center point. There were 18 outer-layer glasses chosen using optimal experimental design software to augment 147 existing glass compositions that were within the LAW glass composition experimental region. Then 13 inner-layer glasses were chosen with the software to augment the existing and outer-layer glasses. The experimental design was completed by a center-point glass, a Vitreous State Laboratory glass, and replicates of the center point and Vitreous State Laboratory glasses.« less

Absolute second order nonlinear susceptibility of Pt nanowire arrays on MgO faceted substrates with various cross-sectional shapes

NASA Astrophysics Data System (ADS)

Ogata, Yoichi; Mizutani, Goro

2013-08-01

We have measured optical second harmonic generation (SHG) intensity from three types of Pt nanowires with 7 nm widths of elliptical and boomerang cross-sectional shapes and with 2 nm width elliptical cross-sectional shapes on the MgO faceted templates. From the SHG intensities, we calculated the absolute value of the nonlinear susceptibility χ(2) integrated in the direction of the wire-layer thickness. The tentatively obtained bulk χ(2)B of the wire layer was very large, approaching the value of the well-known nonlinear optical material BaTiO3.

Nonlinear scattering of acoustic waves by natural and artificially generated subsurface bubble layers in sea.

PubMed

Ostrovsky, Lev A; Sutin, Alexander M; Soustova, Irina A; Matveyev, Alexander L; Potapov, Andrey I; Kluzek, Zigmund

2003-02-01

The paper describes nonlinear effects due to a biharmonic acoustic signal scattering from air bubbles in the sea. The results of field experiments in a shallow sea are presented. Two waves radiated at frequencies 30 and 31-37 kHz generated backscattered signals at sum and difference frequencies in a bubble layer. A motorboat propeller was used to generate bubbles with different concentrations at different times, up to the return to the natural subsurface layer. Theoretical consideration is given for these effects. The experimental data are in a reasonably good agreement with theoretical predictions.

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

Relationships between nonlinear normal modes and response to random inputs

DOE PAGES

Schoneman, Joseph D.; Allen, Matthew S.; Kuether, Robert J.

2016-07-25

The ability to model nonlinear structures subject to random excitation is of key importance in designing hypersonic aircraft and other advanced aerospace vehicles. When a structure is linear, superposition can be used to construct its response to a known spectrum in terms of its linear modes. Superposition does not hold for a nonlinear system, but several works have shown that a system's dynamics can still be understood qualitatively in terms of its nonlinear normal modes (NNMs). Here, this work investigates the connection between a structure's undamped nonlinear normal modes and the spectrum of its response to high amplitude random forcing.more » Two examples are investigated: a spring-mass system and a clamped-clamped beam modeled within a geometrically nonlinear finite element package. In both cases, an intimate connection is observed between the smeared peaks in the response spectrum and the frequency-energy dependence of the nonlinear normal modes. In order to understand the role of coupling between the underlying linear modes, reduced order models with and without modal coupling terms are used to separate the effect of each NNM's backbone from the nonlinear couplings that give rise to internal resonances. In the cases shown here, uncoupled, single-degree-of-freedom nonlinear models are found to predict major features in the response with reasonable accuracy; a highly inexpensive approximation such as this could be useful in design and optimization studies. More importantly, the results show that a reduced order model can be expected to give accurate results only if it is also capable of accurately predicting the frequency-energy dependence of the nonlinear modes that are excited.« less

The role of ferroelectric domain structure in second harmonic generation in random quadratic media.

PubMed

Roppo, Vito; Wang, W; Kalinowski, K; Kong, Y; Cojocaru, C; Trull, J; Vilaseca, R; Scalora, M; Krolikowski, W; Kivshar, Yu

2010-03-01

We study theoretically and numerically the second harmonic generation in a nonlinear crystal with random distribution of ferroelectric domains. We show that the specific features of disordered domain structure greatly affect the emission pattern of the generated harmonics. This phenomena can be used to characterize the degree of disorder in nonlinear photonic structures.

Sum-Frequency Generation from a Thin Cylindrical Layer

NASA Astrophysics Data System (ADS)

Shamyna, A. A.; Kapshai, V. N.

2018-01-01

In the Rayleigh-Gans-Debye approximation, we have solved the problem of the sum-frequency generation by two plane elliptically polarized electromagnetic waves from the surface of a dielectric particle of a cylindrical shape that is coated by a thin layer possessing nonlinear optical properties. The formulas that describe the sum-frequency field have been presented in the tensor and vector forms for the second-order nonlinear dielectric susceptibility tensor, which was chosen in the general form, containing chiral components. Expressions describing the sum-frequency field from the cylindrical particle ends have been obtained for the case of a nonlinear layer possessing chiral properties. Three-dimensional directivity patterns of the sum-frequency radiation have been analyzed for different combinations of parameters (angles of incidence, degrees of ellipticity, orientations of polarization ellipses, cylindrical particle dimensions). The mathematical properties of the spatial distribution functions of the sum-frequency field, which characterize the symmetry of directivity patterns, have been revealed.

A nonlinear steady model for moist hydrostatic mountain waves

NASA Technical Reports Server (NTRS)

Barcilon, A.; Fitzjarrald, D.

1985-01-01

The dynamics of hydrostatic gravity waves generated by the passage of a steady, stably stratified, moist flow over a two-dimensional topography is considered. Coriolis effects are neglected. The cloud region is determined by the dynamics, and within that region the Brunt-Vaisala frequency takes on a value smaller than the outside value. In both the dry and cloudy regions the Brunt-Vaisala frequency is constant with height. The moist layer is considered to be either next to the mountain or at midlevels and to be deep enough so that an entire cloud forms in that layer. The nonlinearity in the flow and lower boundary affects the dynamics of these waves and wave drag. The latter is found to depend upon: (1) the location of the moist layer with respect to the ground, (2) the amount of moisture, (3) the degree of nonlinearity and (4) the departure from symmetry in the bottom topography.

Nonlinear Estimation of Discrete-Time Signals Under Random Observation Delay

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

Caballero-Aguila, R.; Jimenez-Lopez, J. D.; Hermoso-Carazo, A.

2008-11-06

This paper presents an approximation to the nonlinear least-squares estimation problem of discrete-time stochastic signals using nonlinear observations with additive white noise which can be randomly delayed by one sampling time. The observation delay is modelled by a sequence of independent Bernoulli random variables whose values, zero or one, indicate that the real observation arrives on time or it is delayed and, hence, the available measurement to estimate the signal is not up-to-date. Assuming that the state-space model generating the signal is unknown and only the covariance functions of the processes involved in the observation equation are ready for use,more » a filtering algorithm based on linear approximations of the real observations is proposed.« less

Nonlinear Ballistic Transport in an Atomically Thin Material.

PubMed

Boland, Mathias J; Sundararajan, Abhishek; Farrokhi, M Javad; Strachan, Douglas R

2016-01-26

Ultrashort devices that incorporate atomically thin components have the potential to be the smallest electronics. Such extremely scaled atomically thin devices are expected to show ballistic nonlinear behavior that could make them tremendously useful for ultrafast applications. While nonlinear diffusive electron transport has been widely reported, clear evidence for intrinsic nonlinear ballistic transport in the growing array of atomically thin conductors has so far been elusive. Here we report nonlinear electron transport of an ultrashort single-layer graphene channel that shows quantitative agreement with intrinsic ballistic transport. This behavior is shown to be distinctly different than that observed in similarly prepared ultrashort devices consisting, instead, of bilayer graphene channels. These results suggest that the addition of only one extra layer of an atomically thin material can make a significant impact on the nonlinear ballistic behavior of ultrashort devices, which is possibly due to the very different chiral tunneling of their charge carriers. The fact that we observe the nonlinear ballistic response at room temperature, with zero applied magnetic field, in non-ultrahigh vacuum conditions and directly on a readily accessible oxide substrate makes the nanogap technology we utilize of great potential for achieving extremely scaled high-speed atomically thin devices.

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer.

PubMed

Sui, Jize; Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

2017-02-01

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized " n -diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter [Formula: see text] introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system.

A novel investigation of a micropolar fluid characterized by nonlinear constitutive diffusion model in boundary layer flow and heat transfer

PubMed Central

Zhao, Peng; Cheng, Zhengdong; Zheng, Liancun; Zhang, Xinxin

2017-01-01

The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized “n-diffusion theory,” which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system. PMID:28344433

Performance analysis of smart laminated composite plate integrated with distributed AFC material undergoing geometrically nonlinear transient vibrations

NASA Astrophysics Data System (ADS)

Shivakumar, J.; Ashok, M. H.; Khadakbhavi, Vishwanath; Pujari, Sanjay; Nandurkar, Santosh

2018-02-01

The present work focuses on geometrically nonlinear transient analysis of laminated smart composite plates integrated with the patches of Active fiber composites (AFC) using Active constrained layer damping (ACLD) as the distributed actuators. The analysis has been carried out using generalised energy based finite element model. The coupled electromechanical finite element model is derived using Von Karman type nonlinear strain displacement relations and a first-order shear deformation theory (FSDT). Eight-node iso-parametric serendipity elements are used for discretization of the overall plate integrated with AFC patch material. The viscoelastic constrained layer is modelled using GHM method. The numerical results shows the improvement in the active damping characteristics of the laminated composite plates over the passive damping for suppressing the geometrically nonlinear transient vibrations of laminated composite plates with AFC as patch material.

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

Nonlinear interaction between a pair of oblique modes in a supersonic mixing layer: Long-wave limit

NASA Technical Reports Server (NTRS)

Balsa, Thomas F.; Gartside, James

1995-01-01

The nonlinear interaction between a pair of symmetric, oblique, and spatial instability modes is studied in the long-wave limit using asymptotic methods. The base flow is taken to be a supersonic mixing layer whose Mach number is such that the corresponding vortex sheet is marginally stable according to Miles' criterion. It is shown that the amplitude of the mode obeys a nonlinear integro-differential equation. Numerical solutions of this equation show that, when the obliqueness angle is less than pi/4, the effect of the nonlinearity is to enhance the growth rate of the instability. The solution terminates in a singularity at a finite streamwise location. This result is reminiscent of that obtained in the vicinity of the neutral point by other authors in several different types of flows. On the other hand, when the obliqueness angle is more than pi/4, the streamwise development of the amplitude is characterized by a series of modulations. This arises from the fact that the nonlinear term in the amplitude equation may be either stabilizing or destabilizing, depending on the value of the streamwise coordinate. However, even in this case the amplitude of the disturbance increases, though not as rapidly as in the case for which the angle is less than pi/4. Quite generally then, the nonlinear interaction between two oblique modes in a supersonic mixing layer enhances the growth of the disturbance.

Theoretical and lidar studies of the density response of the mesospheric sodium layer to gravity wave perturbations

NASA Technical Reports Server (NTRS)

Shelton, J. D.; Gardner, C. S.

1981-01-01

The density response of atmospheric layers to gravity waves is developed in two forms, an exact solution and a perturbation series solution. The degree of nonlinearity in the layer density response is described by the series solution whereas the exact solution gives insight into the nature of the responses. Density perturbation in an atmospheric layer are shown to be substantially greater than the atmospheric density perturbation associated with the propagation of a gravity wave. Because of the density gradients present in atmospheric layers, interesting effects were observed such as a phase reversal in the linear layer response which occurs near the layer peak. Once the layer response is understood, the sodium layer can be used as a tracer of atmospheric wave motions. A two dimensional digital signal processing technique was developed. Both spatial and temporal filtering are utilized to enhance the resolution by decreasing shot noise by more han 10 dB. Many of the features associated with a layer density response to gravity waves were observed in high resolution density profiles of the mesospheric sodium layer. These include nonlinearities as well as the phase reversal in the linear layer response.

Data-driven non-Markovian closure models

NASA Astrophysics Data System (ADS)

Kondrashov, Dmitri; Chekroun, Mickaël D.; Ghil, Michael

2015-03-01

This paper has two interrelated foci: (i) obtaining stable and efficient data-driven closure models by using a multivariate time series of partial observations from a large-dimensional system; and (ii) comparing these closure models with the optimal closures predicted by the Mori-Zwanzig (MZ) formalism of statistical physics. Multilayer stochastic models (MSMs) are introduced as both a generalization and a time-continuous limit of existing multilevel, regression-based approaches to closure in a data-driven setting; these approaches include empirical model reduction (EMR), as well as more recent multi-layer modeling. It is shown that the multilayer structure of MSMs can provide a natural Markov approximation to the generalized Langevin equation (GLE) of the MZ formalism. A simple correlation-based stopping criterion for an EMR-MSM model is derived to assess how well it approximates the GLE solution. Sufficient conditions are derived on the structure of the nonlinear cross-interactions between the constitutive layers of a given MSM to guarantee the existence of a global random attractor. This existence ensures that no blow-up can occur for a broad class of MSM applications, a class that includes non-polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants. The EMR-MSM methodology is first applied to a conceptual, nonlinear, stochastic climate model of coupled slow and fast variables, in which only slow variables are observed. It is shown that the resulting closure model with energy-conserving nonlinearities efficiently captures the main statistical features of the slow variables, even when there is no formal scale separation and the fast variables are quite energetic. Second, an MSM is shown to successfully reproduce the statistics of a partially observed, generalized Lotka-Volterra model of population dynamics in its chaotic regime. The challenges here include the rarity of strange attractors in the model's parameter space and the existence of multiple attractor basins with fractal boundaries. The positivity constraint on the solutions' components replaces here the quadratic-energy-preserving constraint of fluid-flow problems and it successfully prevents blow-up.

Transition Theory and Experimental Comparisons on (I) Amplification into Streets and (II) a Strongly Nonlinear Break-up Criterion

NASA Astrophysics Data System (ADS)

Smith, F. T.; Bowles, R. I.

1992-10-01

The two stages I, II are studied by using recent nonlinear theory and then compared with the experiments of Nishioka et al. (1979) on the transition of plane Poiseuille flow. The first stage I starts at low amplitude from warped input, which is deformed through weakly nonlinear interaction into a blow-up in amplitude and phase accompanied by spanwise focusing into streets. This leads into the strongly nonlinear stage II. It holds for a broad range of interactive boundary layers and related flows, to all of which the nonlinear break-up criterion applies. The experimental comparisons on I, II for channel flow overall show encouraging quantitative agreement, supporting recent comparisons (in the boundary-layer setting) of the description of stage I in Stewart & Smith (1992) with the experiments of Klebanoff & Tidstrom (1959) and of the break-up criterion of Smith (1988a) with the computations of Peridier et al. (1991 a, b).

Nonlinear Dynamics of the Nearshore Boundary Layer of a Large Lake (Lake Geneva)

NASA Astrophysics Data System (ADS)

Cimatoribus, Andrea A.; Lemmin, U.; Bouffard, D.; Barry, D. A.

2018-02-01

We examine nearshore and pelagic current variability in Lake Geneva, a large and deep lake in western Europe, using observations from several measurement locations and a three-dimensional numerical model for the period 2014-2016. Linear internal seiche modes excited by wind forcing clearly appear as peaks in the energy spectra for measurements in offshore locations. In contrast, spectra from the nearshore data, where currents interact with the lake bed, reveal a negligible contribution of internal seiches to the total kinetic energy. A similar contrast is seen in the spectra obtained from the numerical model at the same locations. Comparing the contribution of the different terms in the vertically averaged momentum equation from the modeling results shows that the nonlinear advective term dominates in the nearshore boundary layer. Its contribution decays with distance from shore. The width of this nearshore boundary layer, which may extend for several kilometers, seems to be mainly determined by local topography. Both field measurements and modeling results indicate that nonlinear dynamics are of primary importance in the nearshore boundary layer.

Attofarad resolution capacitance-voltage measurement of nanometer scale field effect transistors utilizing ambient noise.

PubMed

Gokirmak, Ali; Inaltekin, Hazer; Tiwari, Sandip

2009-08-19

A high resolution capacitance-voltage (C-V) characterization technique, enabling direct measurement of electronic properties at the nanoscale in devices such as nanowire field effect transistors (FETs) through the use of random fluctuations, is described. The minimum noise level required for achieving sub-aF (10(-18) F) resolution, the leveraging of stochastic resonance, and the effect of higher levels of noise are illustrated through simulations. The non-linear DeltaC(gate-source/drain)-V(gate) response of FETs is utilized to determine the inversion layer capacitance (C(inv)) and carrier mobility. The technique is demonstrated by extracting the carrier concentration and effective electron mobility in a nanoscale Si FET with C(inv) = 60 aF.

On the Nonlinear Stability of a High-Speed, Axisymmetric Boundary Layer

DTIC Science & Technology

1991-03-01

NASA Contractor Report 187538 IN ICASE Report No. 91-30 ICASE ON THE NONLINEAR STABILITY OF A HIGH-SPEED, AXISYMMETRIC BOUNDARY LAYER C. David Pruett... David Pruett National Research Council Associate Lian L. Ng Analytical Services and Materials Gordon Erlebacher t Senior Scientist, ICASE NASA Langley...Oct. 5, 1989. 29) Fetterman , D. E., Jr., "Preliminary Sizing and Performance of Aircraft", NASA TM-86357, July 1985. 30) Gaster, M., "A Note on the

On the nonlinear development of the most unstable Goertler vortex mode

NASA Technical Reports Server (NTRS)

Denier, James P.; Hall, Philip

1991-01-01

The nonlinear development of the most unstable Gortler vortex mode in boundary layer flows over curved walls is investigated. The most unstable Gortler mode is confined to a viscous wall layer of thickness O(G -1/5) and has spanwise wavelength O(G 11/5); it is, of course, most relevant to flow situations where the Gortler number G is much greater than 1. The nonlinear equations covering the evolution of this mode over an O(G -3/5) streamwise lengthscale are derived and are found to be of a fully nonparallel nature. The solution of these equations is achieved by making use of the numerical scheme used by Hall (1988) for the numerical solution of the nonlinear Gortler equations valid for O(1) Gortler numbers. Thus, the spanwise dependence of the flow is described by a Fourier expansion, whereas the streamwise and normal variations of the flow are dealt with by employing a suitable finite difference discretization of the governing equations. Our calculations demonstrate that, given a suitable initial disturbance, after a brief interval of decay, the energy in all the higher harmonics grows until a singularity is encountered at some downstream position. The structure of the flowfield as this singularity is approached suggests that the singularity is responsible for the vortices, which are initially confined to the thin viscous wall layer, moving away from the wall and into the core of the boundary layer.

Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition

NASA Technical Reports Server (NTRS)

Smith, F. T.

1988-01-01

The nonlinear interactions that evolve between a planar or nearly planar Tollmien-Schlichting (TS) wave and the associated longitudinal vortices are considered theoretically for a boundary layer at high Reynolds number. The vortex flow is either induced by the TS nonlinear forcing or is input upstream, and similarly for the nonlinear wave development. Three major kinds of nonlinear spatial evolution, Types 1-3, are found. Each can start from secondary instability and then become nonlinear, Type 1 proving to be relatively benign but able to act as a pre-cursor to the Types 2, 3 which turn out to be very powerful nonlinear interactions. Type 2 involves faster stream-wise dependence and leads to a finite-distance blow-up in the amplitudes, which then triggers the full nonlinear 3-D triple-deck response, thus entirely altering the mean-flow profile locally. In contrast, Type 3 involves slower streamwise dependence but a faster spanwise response, with a small TS amplitude thereby causing an enhanced vortex effect which, again, is substantial enough to entirely alter the meanflow profile, on a more global scale. Streak-like formations in which there is localized concentration of streamwise vorticity and/or wave amplitude can appear, and certain of the nonlinear features also suggest by-pass processes for transition and significant changes in the flow structure downstream. The powerful nonlinear 3-D interactions 2, 3 are potentially very relevant to experimental findings in transition.

Neural network approximation of nonlinearity in laser nano-metrology system based on TLMI

NASA Astrophysics Data System (ADS)

Olyaee, Saeed; Hamedi, Samaneh

2011-02-01

In this paper, an approach based on neural network (NN) for nonlinearity modeling in a nano-metrology system using three-longitudinal-mode laser heterodyne interferometer (TLMI) for length and displacement measurements is presented. We model nonlinearity errors that arise from elliptically and non-orthogonally polarized laser beams, rotational error in the alignment of laser head with respect to the polarizing beam splitter, rotational error in the alignment of the mixing polarizer, and unequal transmission coefficients in the polarizing beam splitter. Here we use a neural network algorithm based on the multi-layer perceptron (MLP) network. The simulation results show that multi-layer feed forward perceptron network is successfully applicable to real noisy interferometer signals.

Sheared Layers in the Continental Crust: Nonlinear and Linearized inversion for Ps receiver functions

NASA Astrophysics Data System (ADS)

Park, J. J.

2017-12-01

Sheared Layers in the Continental Crust: Nonlinear and Linearized inversion for Ps receiver functions Jeffrey Park, Yale University The interpretation of seismic receiver functions (RFs) in terms of isotropic and anisotropic layered structure can be complex. The relationship between structure and body-wave scattering is nonlinear. The anisotropy can involve more parameters than the observations can readily constrain. Finally, reflectivity-predicted layer reverberations are often not prominent in data, so that nonlinear waveform inversion can search in vain to match ghost signals. Multiple-taper correlation (MTC) receiver functions have uncertainties in the frequency domain that follow Gaussian statistics [Park and Levin, 2016a], so grid-searches for the best-fitting collections of interfaces can be performed rapidly to minimize weighted misfit variance. Tests for layer-reverberations can be performed in the frequency domain without reflectivity calculations, allowing flexible modelling of weak, but nonzero, reverberations. Park and Levin [2016b] linearized the hybridization of P and S body waves in an anisotropic layer to predict first-order Ps conversion amplitudes at crust and mantle interfaces. In an anisotropic layer, the P wave acquires small SV and SH components. To ensure continuity of displacement and traction at the top and bottom boundaries of the layer, shear waves are generated. Assuming hexagonal symmetry with an arbitrary symmetry axis, theory confirms the empirical stacking trick of phase-shifting transverse RFs by 90 degrees in back-azimuth [Shiomi and Park, 2008; Schulte-Pelkum and Mahan, 2014] to enhance 2-lobed and 4-lobed harmonic variation. Ps scattering is generated by sharp interfaces, so that RFs resemble the first derivative of the model. MTC RFs in the frequency domain can be manipulated to obtain a first-order reconstruction of the layered anisotropy, under the above modeling constraints and neglecting reverberations. Examples from long-running continental stations will be discussed. Park, J., and V. Levin, 2016a. doi:10.1093/gji/ggw291. Park, J., and V. Levin, 2016b. doi:10.1093/gji/ggw323. Schulte-Pelkum, V., and Mahan, K. H., 2014. doi:10.1007/s00024-014-0853-4. Shiomi, K., & Park, J., 2008. doi:10.1029/2007JB005535.

Investigation of broadband terahertz generation from metasurface

NASA Astrophysics Data System (ADS)

Fang, Ming; Niu, Kaikun; Huang, Zhiaxiang; Sha, Wei E. I.; Wu, Xianliang; Koschny, Thomas; Soukoulis, Costas M.

2018-05-01

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designing nonlinear plasmonic metamaterials.

Investigation of broadband terahertz generation from metasurface.

PubMed

Fang, Ming; Niu, Kaikun; Huang, Zhiaxiang; Sha, Wei E I; Wu, Xianliang; Koschny, Thomas; Soukoulis, Costas M

2018-05-28

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designing nonlinear plasmonic metamaterials.

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.

Photoinduced Nonlinear Mixing of Terahertz Dipole Resonances in Graphene Metadevices.

PubMed

In, Chihun; Kim, Hyeon-Don; Min, Bumki; Choi, Hyunyong

2016-02-17

The first experimental demonstration of nonlinear terahertz difference-frequency generation in a hybrid graphene metadevice is reported. Decades of research have revealed that terahertz-wave generation is impossible in single-layer graphene. This limitation is overcome and nonlinear terahertz generation by ultra-short optical pulse injection is demonstrated. This device is an essential step toward atomically thin, nonlinear terahertz optoelectronic components. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Surface plasmon polariton Akhmediev Breather in a dielectric-metal-dielectric geometry with subwavelength thickness

NASA Astrophysics Data System (ADS)

Devi, Koijam Monika; Porsezian, K.; Sarma, Amarendra K.

2018-05-01

We report Akhmediev Breather solutions in a nonlinear multilayer structure comprising of a metal sandwiched between two semi-infinite dielectric layers with subwavelength thickness. These nonlinear solutions inherit the properties of Surface plasmon polaritons and its dynamics is governed by the Nonlinear Schrodinger equation. The breather evolution is studied for specific values of nonlinear and dispersion parameters. An experimental scheme to observe these breathers is also proposed.

Surface spontaneous parametric down-conversion.

PubMed

Perina, Jan; Luks, Antonín; Haderka, Ondrej; Scalora, Michael

2009-08-07

Surface spontaneous parametric down-conversion is predicted as a consequence of continuity requirements for electric- and magnetic-field amplitudes at a discontinuity of chi;{(2)} nonlinearity. A generalization of the usual two-photon spectral amplitude is suggested to describe this effect. Examples of nonlinear layered structures and periodically poled nonlinear crystals show that surface contributions to spontaneous down-conversion can be important.

Nonlinear subdiffusive fractional equations and the aggregation phenomenon.

PubMed

Fedotov, Sergei

2013-09-01

In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on the mean density of particles. We derive a set of nonlinear subdiffusive fractional master equations and consider their diffusion approximations. We show that these equations describe the transition from an intermediate subdiffusive regime to asymptotically normal advection-diffusion transport regime. This transition is governed by nonlinear tempering parameter that generalizes the standard linear tempering. We illustrate the general results through the use of the examples from cell and population biology. We find that a nonuniform anomalous exponent has a strong influence on the aggregation phenomenon.

Nonlinear Dynamic Characteristics of Oil-in-Water Emulsions

NASA Astrophysics Data System (ADS)

Yin, Zhaoqi; Han, Yunfeng; Ren, Yingyu; Yang, Qiuyi; Jin, Ningde

2016-08-01

In this article, the nonlinear dynamic characteristics of oil-in-water emulsions under the addition of surfactant were experimentally investigated. Firstly, based on the vertical upward oil-water two-phase flow experiment in 20 mm inner diameter (ID) testing pipe, dynamic response signals of oil-in-water emulsions were recorded using vertical multiple electrode array (VMEA) sensor. Afterwards, the recurrence plot (RP) algorithm and multi-scale weighted complexity entropy causality plane (MS-WCECP) were employed to analyse the nonlinear characteristics of the signals. The results show that the certainty is decreasing and the randomness is increasing with the increment of surfactant concentration. This article provides a novel method for revealing the nonlinear dynamic characteristics, complexity, and randomness of oil-in-water emulsions with experimental measurement signals.

Nonlinear Wave Mixing Technique for Nondestructive Assessment of Infrastructure Materials

NASA Astrophysics Data System (ADS)

Ju, Taeho

To operate safely, structures and components need to be inspected or monitored either periodically or in real time for potential failure. For this purpose, ultrasonic nondestructive evaluation (NDE) techniques have been used extensively. Most of these ultrasonic NDE techniques utilize only the linear behavior of the ultrasound. These linear techniques are effective in detecting discontinuities in materials such as cracks, voids, interfaces, inclusions, etc. However, in many engineering materials, it is the accumulation of microdamage that leads to degradation and eventual failure of a component. Unfortunately, it is difficult for linear ultrasonic NDE techniques to characterize or quantify such damage. On the other hand, the acoustic nonlinearity parameter (ANLP) of a material is often positively correlated with such damage in a material. Thus, nonlinear ultrasonic NDE methods have been used in recently years to characterize cumulative damage such as fatigue in metallic materials, aging in polymeric materials, and degradation of cement-based materials due to chemical reactions. In this thesis, we focus on developing a suit of novel nonlinear ultrasonic NDE techniques based on the interactions of nonlinear ultrasonic waves, namely wave mixing. First, a noncollinear wave mixing technique is developed to detect localized damage in a homogeneous material by using a pair of noncollinear a longitudinal wave (L-wave) and a shear wave (S-wave). This pair of incident waves make it possible to conduct NDE from a single side of the component, a condition that is often encountered in practical applications. The proposed noncollinear wave mixing technique is verified experimentally by carrying out measurements on aluminum alloy (AA 6061) samples. Numerical simulations using the Finite Element Method (FEM) are also conducted to further demonstrate the potential of the proposed technique to detect localized damage in structural components. Second, the aforementioned nonlinear mixing technique is adapted to develop an NDE technique for characterizing thermal aging of adhesive joints. To this end, a nonlinear spring model is used to simulate the effect of the adhesive layer. Based on this nonlinear spring model, analytical expressions of the resonant wave generated by the adhesive layers is obtained through an asymptotic analysis when the adhesive layer thickness is much smaller than the pertinent wavelength. The solutions are expressed in terms of the properties of the adhesive layer. The nonlinear spring model shows a good agreement with the finite layer model solutions in the limit of a small thickness to wavelength ratio. Third, to demonstrate the effectiveness of this newly developed technique, measurements are conducted on adhesive joint samples made of two aluminum adherends bonded together by a polymer adhesive tape. The samples are aged in a thermal chamber to induce thermal ageing degradation in the adhesive layer. Using the developed wave-mixing technique in conjunction with the nonlinear spring model, we show that the thermal aging damage of the adhesive layer can be quantified from only one side of the sample. Finally, by mixing two L-waves, we develop a mixing technique to nondestructively evaluate the damage induced by alkali-silica reaction (ASR) in concrete. Experimental measurements are conducted on concrete prism samples that contain reactive aggregates and have been subjected to different ASR conditioning. This new technique takes into consideration of the significant attenuation caused by ASR-induced microcracks and scattering by the aggregates. The measurement results show that the ANLP has a much greater sensitivity to ASR damage than other parameters such as attenuation and wave speed. More remarkably, it is also found that the measured acoustic nonlinearity parameter is well-correlated with the reduction of the compressive strength induced by ASR damage. Thus, ANLP can be used to nondestructively track ASR damage in concrete.

Alternative Modal Basis Selection Procedures for Nonlinear Random Response Simulation

NASA Technical Reports Server (NTRS)

Przekop, Adam; Guo, Xinyun; Rizzi, Stephen A.

2010-01-01

Three procedures to guide selection of an efficient modal basis in a nonlinear random response analysis are examined. One method is based only on proper orthogonal decomposition, while the other two additionally involve smooth orthogonal decomposition. Acoustic random response problems are employed to assess the performance of the three modal basis selection approaches. A thermally post-buckled beam exhibiting snap-through behavior, a shallowly curved arch in the auto-parametric response regime and a plate structure are used as numerical test articles. The results of the three reduced-order analyses are compared with the results of the computationally taxing simulation in the physical degrees of freedom. For the cases considered, all three methods are shown to produce modal bases resulting in accurate and computationally efficient reduced-order nonlinear simulations.

Testing for nonlinearity in non-stationary physiological time series.

PubMed

Guarín, Diego; Delgado, Edilson; Orozco, Álvaro

2011-01-01

Testing for nonlinearity is one of the most important preprocessing steps in nonlinear time series analysis. Typically, this is done by means of the linear surrogate data methods. But it is a known fact that the validity of the results heavily depends on the stationarity of the time series. Since most physiological signals are non-stationary, it is easy to falsely detect nonlinearity using the linear surrogate data methods. In this document, we propose a methodology to extend the procedure for generating constrained surrogate time series in order to assess nonlinearity in non-stationary data. The method is based on the band-phase-randomized surrogates, which consists (contrary to the linear surrogate data methods) in randomizing only a portion of the Fourier phases in the high frequency domain. Analysis of simulated time series showed that in comparison to the linear surrogate data method, our method is able to discriminate between linear stationarity, linear non-stationary and nonlinear time series. Applying our methodology to heart rate variability (HRV) records of five healthy patients, we encountered that nonlinear correlations are present in this non-stationary physiological signals.

Privacy-preserving outlier detection through random nonlinear data distortion.

PubMed

Bhaduri, Kanishka; Stefanski, Mark D; Srivastava, Ashok N

2011-02-01

Consider a scenario in which the data owner has some private or sensitive data and wants a data miner to access them for studying important patterns without revealing the sensitive information. Privacy-preserving data mining aims to solve this problem by randomly transforming the data prior to their release to the data miners. Previous works only considered the case of linear data perturbations--additive, multiplicative, or a combination of both--for studying the usefulness of the perturbed output. In this paper, we discuss nonlinear data distortion using potentially nonlinear random data transformation and show how it can be useful for privacy-preserving anomaly detection from sensitive data sets. We develop bounds on the expected accuracy of the nonlinear distortion and also quantify privacy by using standard definitions. The highlight of this approach is to allow a user to control the amount of privacy by varying the degree of nonlinearity. We show how our general transformation can be used for anomaly detection in practice for two specific problem instances: a linear model and a popular nonlinear model using the sigmoid function. We also analyze the proposed nonlinear transformation in full generality and then show that, for specific cases, it is distance preserving. A main contribution of this paper is the discussion between the invertibility of a transformation and privacy preservation and the application of these techniques to outlier detection. The experiments conducted on real-life data sets demonstrate the effectiveness of the approach.

Nonlinear wave chaos: statistics of second harmonic fields.

PubMed

Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M

2017-10-01

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.

The role of nonlinear viscoelasticity on the functionality of laminating shortenings

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

Macias-Rodriguez, Braulio A.; Peyronel, Fernanda; Marangoni, Alejandro G.

The rheology of fats is essential for the development of homogeneous and continuous layered structures of doughs. Here, we define laminating shortenings in terms of rheological behavior displayed during linear-to-nonlinear shear deformations, investigated by large amplitude oscillatory shear rheology. Likewise, we associate the rheological behavior of the shortenings with structural length scales elucidated by ultra-small angle x-ray scattering and cryo-electron microscopy. Shortenings exhibited solid-like viscoelastic and viscoelastoplastic behaviors in the linear and nonlinear regimes respectively. In the nonlinear region, laminating shortenings dissipated more viscous energy (larger normalized dynamic viscosities) than a cake bakery shortening. The fat solid-like network of laminatingmore » shortening displayed a three-hierarchy structure and layered crystal aggregates, in comparison to two-hierarchy structure and spherical-like crystal aggregates of a cake shortening. We argue that the observed rheology, correlated to the structural network, is crucial for optimal laminating performance of shortenings.« less

Nonlinear electrokinetic phenomena in microfluidic devices

NASA Astrophysics Data System (ADS)

Ben, Yuxing

This thesis addresses nonlinear electrokinetic mechanisms for transporting fluid and particles in microfluidic devices for potential applications in biomedical chips, microelectronic cooling and micro-fuel cells. Nonlinear electrokinetics have many advantages, such as low voltage, low power, high velocity, and no significant gas formation in the electrolyte. However, they involve new and complex charging and flow mechanisms that are still not fully understood or explored. Linear electrokinetic fingering that occurs when a fluid with a lower electrolyte concentration advances into one with a higher concentration is first analyzed. Unlike earlier miscible fingering theories, the linear stability analysis is carried out in the self-similar coordinates of the diffusing front. This new spectral theory is developed for small-amplitude gravity and viscous miscible fingering phenomena in general and applied to electrokinetic miscible fingering specifically. Transient electrokinetic fingering is shown to be insignificant in sub-millimeter micro-devices. Nonlinear electroosmotic flow around an ion-exchange spherical granule is studied next. When an electric field is applied across a conducting and ion-selective porous granule in an electrolyte solution, a polarized surface layer with excess counter-ions is created. The flux-induced polarization produces a nonlinear slip velocity to produce micro-vortices around this sphere. This polarization layer is reduced by convection at high velocity. Two velocity scalings at low and high electric fields are derived and favorably compared with experimental results. A mixing device based on this mechanism is shown to produce mixing efficiency 10-100 times higher than molecular diffusion. Finally, AC nonlinear electrokinetic flow on planar electrodes is studied. Two double layer charging mechanisms are responsible for the flow---one due to capacitive charging of ions from the bulk electrolyte and one due to Faradaic reactions at the electrode that consume or produce ions in the double layer. Faradaic charging is analyzed for specific reactions. From the theory, particular electrokinetic flows above the electrodes are selected for micropumps and bioparticle trapping by specifying the electrode geometry and the applied voltage and frequency.

The rollup of a vortex layer near a wall

NASA Technical Reports Server (NTRS)

Jimenez, Javier; Orlandi, Paolo

1993-01-01

The behavior of an inviscid vortex layer of non-zero thickness near a wall is studied, both through direct numerical simulation of the two-dimensional vorticity equation at high Reynolds numbers, and using an approximate ordinary nonlinear integro-differential equation which is satisfied in the limit of a thin layer under long-wavelength perturbations. For appropriate initial conditions the layer rolls up and breaks into compact vortices which move along the wall at constant speed. Because of the effect of the wall, they correspond to equilibrium counter-rotating vortex dipoles. This breakup can be related to the disintegration of the initial conditions of the approximate nonlinear dispersive equation into solitary waves. The study is motivated by the formation of longitudinal vortices from vortex sheets in the wall region of a turbulent channel.

Comments on How Does the Boundary Layer Contribute to Eyewall Replacement Cycles in Axisymmetric Tropical Cyclones?

DTIC Science & Technology

2014-12-01

broaden, the existing vorticity perturbation.’’ The nonlinear effects are, in the above quoted para- graph, simply contributing to a radially inward...quantitative effects , the nonlinear boundary layer dynamics do not seem to be invoked in K13 to fundamentally alter the feedback pro- cess sketched...the Coriolis parameter, r represents radius, and ›/›r denotes the partial derivative with respect to r. To com- pute w‘ in Fig. 2, the height of 3 km

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary.

PubMed

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.

Analytic Approximate Solutions to the Boundary Layer Flow Equation over a Stretching Wall with Partial Slip at the Boundary

PubMed Central

Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan

2016-01-01

Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations. PMID:27031232

Non-linear behavior of fiber composite laminates

NASA Technical Reports Server (NTRS)

Hashin, Z.; Bagchi, D.; Rosen, B. W.

1974-01-01

The non-linear behavior of fiber composite laminates which results from lamina non-linear characteristics was examined. The analysis uses a Ramberg-Osgood representation of the lamina transverse and shear stress strain curves in conjunction with deformation theory to describe the resultant laminate non-linear behavior. A laminate having an arbitrary number of oriented layers and subjected to a general state of membrane stress was treated. Parametric results and comparison with experimental data and prior theoretical results are presented.

Spatio-temporal instabilities for counterpropagating waves in periodic media.

PubMed

Haus, Joseph; Soon, Boon Yi; Scalora, Michael; Bloemer, Mark; Bowden, Charles; Sibilia, Concita; Zheltikov, Alexei

2002-01-28

Nonlinear evolution of coupled forward and backward fields in a multi-layered film is numerically investigated. We examine the role of longitudinal and transverse modulation instabilities in media of finite length with a homogeneous nonlinear susceptibility c((3)). The numerical solution of the nonlinear equations by a beam-propagation method that handles backward waves is described.

Open-closed-loop iterative learning control for a class of nonlinear systems with random data dropouts

NASA Astrophysics Data System (ADS)

Cheng, X. Y.; Wang, H. B.; Jia, Y. L.; Dong, YH

2018-05-01

In this paper, an open-closed-loop iterative learning control (ILC) algorithm is constructed for a class of nonlinear systems subjecting to random data dropouts. The ILC algorithm is implemented by a networked control system (NCS), where only the off-line data is transmitted by network while the real-time data is delivered in the point-to-point way. Thus, there are two controllers rather than one in the control system, which makes better use of the saved and current information and thereby improves the performance achieved by open-loop control alone. During the transfer of off-line data between the nonlinear plant and the remote controller data dropout occurs randomly and the data dropout rate is modeled as a binary Bernoulli random variable. Both measurement and control data dropouts are taken into consideration simultaneously. The convergence criterion is derived based on rigorous analysis. Finally, the simulation results verify the effectiveness of the proposed method.

Investigation of broadband terahertz generation from metasurface

DOE PAGES

Fang, Ming; Niu, Kaikun; Huang, ZHixiang; ...

2018-01-01

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Investigation of broadband terahertz generation from metasurface

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

Fang, Ming; Niu, Kaikun; Huang, ZHixiang

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Investigation of broadband terahertz generation from metasurface

DOE PAGES

Fang, Ming; Niu, Kaikun; Huang, ZHixiang; ...

2018-05-21

The nonlinear metamaterials have been shown to provide nonlinear properties with high nonlinear conversion efficiency and in a myriad of light manipulation. Here we study terahertz generation from nonlinear metasurface consisting of single layer nanoscale split-ring resonator array. The terahertz generation due to optical rectification by the second-order nonlinearity of the split-ring resonator is investigated by a time-domain implementation of the hydrodynamic model for electron dynamics in metal. The results show that the nonlinear metasurface enables us to generate broadband terahertz radiation and free from quasi-phase-matching conditions. The proposed scheme provides a new concept of broadband THz source and designingmore » nonlinear plasmonic metamaterials.« less

Comparison of Random Forest and Parametric Imputation Models for Imputing Missing Data Using MICE: A CALIBER Study

PubMed Central

Shah, Anoop D.; Bartlett, Jonathan W.; Carpenter, James; Nicholas, Owen; Hemingway, Harry

2014-01-01

Multivariate imputation by chained equations (MICE) is commonly used for imputing missing data in epidemiologic research. The “true” imputation model may contain nonlinearities which are not included in default imputation models. Random forest imputation is a machine learning technique which can accommodate nonlinearities and interactions and does not require a particular regression model to be specified. We compared parametric MICE with a random forest-based MICE algorithm in 2 simulation studies. The first study used 1,000 random samples of 2,000 persons drawn from the 10,128 stable angina patients in the CALIBER database (Cardiovascular Disease Research using Linked Bespoke Studies and Electronic Records; 2001–2010) with complete data on all covariates. Variables were artificially made “missing at random,” and the bias and efficiency of parameter estimates obtained using different imputation methods were compared. Both MICE methods produced unbiased estimates of (log) hazard ratios, but random forest was more efficient and produced narrower confidence intervals. The second study used simulated data in which the partially observed variable depended on the fully observed variables in a nonlinear way. Parameter estimates were less biased using random forest MICE, and confidence interval coverage was better. This suggests that random forest imputation may be useful for imputing complex epidemiologic data sets in which some patients have missing data. PMID:24589914

Comparison of random forest and parametric imputation models for imputing missing data using MICE: a CALIBER study.

PubMed

Shah, Anoop D; Bartlett, Jonathan W; Carpenter, James; Nicholas, Owen; Hemingway, Harry

2014-03-15

Multivariate imputation by chained equations (MICE) is commonly used for imputing missing data in epidemiologic research. The "true" imputation model may contain nonlinearities which are not included in default imputation models. Random forest imputation is a machine learning technique which can accommodate nonlinearities and interactions and does not require a particular regression model to be specified. We compared parametric MICE with a random forest-based MICE algorithm in 2 simulation studies. The first study used 1,000 random samples of 2,000 persons drawn from the 10,128 stable angina patients in the CALIBER database (Cardiovascular Disease Research using Linked Bespoke Studies and Electronic Records; 2001-2010) with complete data on all covariates. Variables were artificially made "missing at random," and the bias and efficiency of parameter estimates obtained using different imputation methods were compared. Both MICE methods produced unbiased estimates of (log) hazard ratios, but random forest was more efficient and produced narrower confidence intervals. The second study used simulated data in which the partially observed variable depended on the fully observed variables in a nonlinear way. Parameter estimates were less biased using random forest MICE, and confidence interval coverage was better. This suggests that random forest imputation may be useful for imputing complex epidemiologic data sets in which some patients have missing data.

Anisotropy in Third-Order Nonlinear Optical Susceptibility of a Squarylium Dye in a Nematic Liquid Crystal

NASA Astrophysics Data System (ADS)

Jin, Zhao-Hui; Li, Zhong-Yu; Kasatani, Kazuo; Okamoto, Hiroaki

2006-03-01

A squarylium dye is dissolved in 4-cyano-4'-pentylbiphenyl (5CB) and oriented by sandwiching mixtures between two pieces of rubbed glass plates. The optical absorption spectra of the oriented squarylium dye-5CB layers exhibit high anisotropy. The third-order nonlinear optical responses and susceptibilities χ(3)e of squarylium dye in 5CB are measured with light polarizations parallel and perpendicular to the orientational direction by the resonant femtosecond degenerate four-wave mixing (DFWM) technique. Temporal profiles of the DFWM signal of the oriented squarylium dye-5CB layers with light polarizations parallel and perpendicular to the orientational direction are measured with a time resolution of 0.3 ps (FWHM), and are found to consist of two components, i.e., the coherent instantaneous nonlinear response and slow response due to the formation of excited molecules. A high anisotropic ratio of χ(3)e, 10.8±1.2, is observed for the oriented layers.

Reliable gain-scheduled control of discrete-time systems and its application to CSTR model

NASA Astrophysics Data System (ADS)

Sakthivel, R.; Selvi, S.; Mathiyalagan, K.; Shi, Y.

2016-10-01

This paper is focused on reliable gain-scheduled controller design for a class of discrete-time systems with randomly occurring nonlinearities and actuator fault. Further, the nonlinearity in the system model is assumed to occur randomly according to a Bernoulli distribution with measurable time-varying probability in real time. The main purpose of this paper is to design a gain-scheduled controller by implementing a probability-dependent Lyapunov function and linear matrix inequality (LMI) approach such that the closed-loop discrete-time system is stochastically stable for all admissible randomly occurring nonlinearities. The existence conditions for the reliable controller is formulated in terms of LMI constraints. Finally, the proposed reliable gain-scheduled control scheme is applied on continuously stirred tank reactor model to demonstrate the effectiveness and applicability of the proposed design technique.

Alternative Modal Basis Selection Procedures For Reduced-Order Nonlinear Random Response Simulation

NASA Technical Reports Server (NTRS)

Przekop, Adam; Guo, Xinyun; Rizi, Stephen A.

2012-01-01

Three procedures to guide selection of an efficient modal basis in a nonlinear random response analysis are examined. One method is based only on proper orthogonal decomposition, while the other two additionally involve smooth orthogonal decomposition. Acoustic random response problems are employed to assess the performance of the three modal basis selection approaches. A thermally post-buckled beam exhibiting snap-through behavior, a shallowly curved arch in the auto-parametric response regime and a plate structure are used as numerical test articles. The results of a computationally taxing full-order analysis in physical degrees of freedom are taken as the benchmark for comparison with the results from the three reduced-order analyses. For the cases considered, all three methods are shown to produce modal bases resulting in accurate and computationally efficient reduced-order nonlinear simulations.

Rosenzweig instability in a thin layer of a magnetic fluid

NASA Astrophysics Data System (ADS)

Korovin, V. M.

2013-12-01

A simple mathematical model of the initial stage of nonlinear evolution of the Rosenzweig instability in a thin layer of a nonlinearly magnetized viscous ferrofluid coating a horizontal nonmagnetizable plate is constructed on the basis of the system of equations and boundary conditions of ferrofluid dynamics. A dispersion relation is derived and analyzed using the linearized equations of this model. The critical magnetization of the initial layer with a flat free surface, the threshold wavenumber, and the characteristic time of evolution of the most rapidly growing mode are determined. The equation for the neutral stability curve, which is applicable for any physically admissible law of magnetization of a ferrofluid, is derived analytically.

Band Structure Simulations of the Photoinduced Changes in the MgB₂:Cr Films.

PubMed

Kityk, Iwan V; Fedorchuk, Anatolii O; Ozga, Katarzyna; AlZayed, Nasser S

2015-04-02

An approach for description of the photoinduced nonlinear optical effects in the superconducting MgB₂:Cr₂O₃ nanocrystalline film is proposed. It includes the molecular dynamics step-by-step optimization of the two separate crystalline phases. The principal role for the photoinduced nonlinear optical properties plays nanointerface between the two phases. The first modified layers possess a form of slightly modified perfect crystalline structure. The next layer is added to the perfect crystalline structure and the iteration procedure is repeated for the next layer. The total energy here is considered as a varied parameter. To avoid potential jumps on the borders we have carried out additional derivative procedure.

Properties of internal solitary waves in a symmetric three-layer fluid

NASA Astrophysics Data System (ADS)

Vladykina, E. A.; Polukhina, O. E.; Kurkin, A. A.

2009-04-01

Though all the natural media have smooth density stratifications (with the exception of special cases such as sea surface, inversion layer in the atmosphere), the scales of density variations can be different, and some of them can be considered as very sharp. Therefore for the description of internal wave propagation and interaction in the ocean and atmosphere the n-layer models are often used. In these models density profile is usually approximated by a piecewise-constant function. The advantage of the layered models is the finite number of parameters and relatively simple solutions of linear and weakly nonlinear problems. Layered models are also very popular in the laboratory experiments with stratified fluid. In this study we consider symmetric, continuously stratified, smoothed three-layer fluid bounded by rigid horizontal surface and bottom. Three-layer stratification is proved to be a proper approximation of sea water density profile in some basins in the World Ocean with specific hydrological conditions. Such a medium is interesting from the point of view of internal gravity wave dynamics, because in the symmetric case it leads to disappearing of quadratic nonlinearity when described in the framework of weakly nonlinear evolutionary models, that are derived through the asymptotic expansion in small parameters of nonlinearity and dispersion. The goal of our study is to determine the properties of localized stationary internal gravity waveforms (solitary waves) in this symmetric three-layer fluid. The investigation is carried out in the framework of improved mathematical model describing the transformation of internal wave fields generated by an initial disturbance. The model is based on the program complex for the numerical simulation of the two-dimensional (vertical plane) fully nonlinear Euler equations for incompressible stratified fluid under the Boussinesq approximation. Initial disturbances of both polarities evolve into stationary, solitary-like waves of corresponding polarity, for which we found the amplitude-width, amplitude-velocity, mass-amplitude, and energy-amplitude relations. Small-amplitude impulses to a good approximation can be described by the modified Korteweg-de Vries equation, but larger waves tend to become wide, and absolute value of their amplitude is bounded by the upper limit. Authors thank prof. K.G. Lamb for the opportunity to use the program code for numerical simulations of Euler equations. The research was supported by RFBR (09-05-00447, 09-05-00204) and by President of RF (MD-3024.2008.5 for young doctors of science).

High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models

NASA Astrophysics Data System (ADS)

Engwirda, Darren; Kelley, Maxwell; Marshall, John

2017-08-01

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

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.

An enstrophy-based linear and nonlinear receptivity theory

NASA Astrophysics Data System (ADS)

Sengupta, Aditi; Suman, V. K.; Sengupta, Tapan K.; Bhaumik, Swagata

2018-05-01

In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.

Geometrically nonlinear transient vibrations of actively damped anti-symmetric angle ply laminated composite shallow shell using active fibre composite (AFC) actuators

NASA Astrophysics Data System (ADS)

Ashok, M. H.; Shivakumar, J.; Nandurkar, Santosh; Khadakbhavi, Vishwanath; Pujari, Sanjay

2018-02-01

In present work, the thin laminated composite shallow shell as smart structure with AFC material’s ACLD treatment is analyzed for geometrically nonlinear transient vibrations. The AFC material is used to make the constraining layer of the ACLD treatment. Golla-Hughes-McTavish (GHM) is used to model the constrained viscoelastic layer of the ACLD treatment in time domain. Along with a simple first-order shear deformation theory the Von Kármán type non-linear strain displacement relations are used for deriving this electromechanical coupled problem. A 3-dimensional finite element model of smart composite panels integrated with the ACLD treated patches has been modelled to reveal the performance of ACLD treated patches on improving the damping properties of slender anti-symmetric angle-ply laminated shallow shell, in controlling the transient vibrations which are geometrically nonlinear. The mathematical results explain that the ACLD treated patches considerably enhance the damping properties of anti-symmetric angle-ply panels undergoing geometrically nonlinear transient vibrations.

New generation of one-dimensional photonic crystal cavities as robust high-efficient frequency converter

NASA Astrophysics Data System (ADS)

Parvini, T. S.; Tehranchi, M. M.; Hamidi, S. M.

2017-07-01

An effective method is proposed to design finite one-dimensional photonic crystal cavities (PhCCs) as robust high-efficient frequency converter. For this purpose, we consider two groups of PhCCs which are constructed by stacking m nonlinear (LiNbO3) and n linear (air) layers with variable thicknesses. In the first group, the number of linear layers is less than the nonlinear layers by one and in the second group by two. The conversion efficiency is calculated as a function of the arrangement and thicknesses of the linear and nonlinear layers by benefiting from nonlinear transfer matrix method. Our numerical simulations show that for each group of PhCCs, there is a structural formula by which the configurations with the highest efficiency can be constructed for any values of m and n (i.e. any number of layers). The efficient configurations are equivalent to Fabry-Pérot cavities that depend on the relationship between m and n and the mirrors in two sides of these cavities can be periodic or nonperiodic. The conversion efficiencies of these designed PhCCs are more than 5 orders of magnitude higher than the perfect ones which satisfy photonic bandgap edge and quasi-phase matching. Moreover, the results reveal that conversion efficiencies of Fabry-Pérot cavities with non-periodic mirrors are one order of magnitude higher than those with periodic mirrors. The major physical mechanisms of the enhancement are quasi-phase matching effect, cavity effect induced by dispersive mirrors, and double resonance for the pump and the harmonic fields in defect state. We believe that this method is very beneficial to the design of high-efficient compact optical frequency converters.

Analysis of the power flow in nonlinear oscillators driven by random excitation using the first Wiener kernel

NASA Astrophysics Data System (ADS)

Hawes, D. H.; Langley, R. S.

2018-01-01

Random excitation of mechanical systems occurs in a wide variety of structures and, in some applications, calculation of the power dissipated by such a system will be of interest. In this paper, using the Wiener series, a general methodology is developed for calculating the power dissipated by a general nonlinear multi-degree-of freedom oscillatory system excited by random Gaussian base motion of any spectrum. The Wiener series method is most commonly applied to systems with white noise inputs, but can be extended to encompass a general non-white input. From the extended series a simple expression for the power dissipated can be derived in terms of the first term, or kernel, of the series and the spectrum of the input. Calculation of the first kernel can be performed either via numerical simulations or from experimental data and a useful property of the kernel, namely that the integral over its frequency domain representation is proportional to the oscillating mass, is derived. The resulting equations offer a simple conceptual analysis of the power flow in nonlinear randomly excited systems and hence assist the design of any system where power dissipation is a consideration. The results are validated both numerically and experimentally using a base-excited cantilever beam with a nonlinear restoring force produced by magnets.

The roll-up and merging of coherent structures in shallow mixing layers

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

Lam, M. Y., E-mail: celmy@connect.ust.hk; Ghidaoui, M. S.; Kolyshkin, A. A.

2016-09-15

The current study seeks a fundamental explanation to the development of two-dimensional coherent structures (2DCSs) in shallow mixing layers. A nonlinear numerical model based on the depth-averaged shallow water equations is used to investigate the temporal evolution of shallow mixing layers, where the mapping from temporal to spatial results is made using the velocity at the center of the mixing layers. The flow is periodic in the streamwise direction. Transmissive boundary conditions are used in the cross-stream boundaries to prevent reflections. Numerical results are compared to linear stability analysis, mean-field theory, and secondary stability analysis. Results suggest that the onsetmore » and development of 2DCS in shallow mixing layers are the result of a sequence of instabilities governed by linear theory, mean-field theory, and secondary stability theory. The linear instability of the shearing velocity gradient gives the onset of 2DCS. When the perturbations reach a certain amplitude, the flow field of the perturbations changes from a wavy shape to a vortical (2DCS) structure because of nonlinearity. The development of the vertical 2DCS does not appear to follow weakly nonlinear theory; instead, it follows mean-field theory. After the formation of 2DCS, separate 2DCSs merge to form larger 2DCS. In this way, 2DCSs grow and shallow mixing layers develop and grow in scale. The merging of 2DCS in shallow mixing layers is shown to be caused by the secondary instability of the 2DCS. Eventually 2DCSs are dissipated by bed friction. The sequence of instabilities can cause the upscaling of the turbulent kinetic energy in shallow mixing layers.« less

Spherical cloaking using nonlinear transformations for improved segmentation into concentric isotropic coatings.

PubMed

Qiu, Cheng-Wei; Hu, Li; Zhang, Baile; Wu, Bae-Ian; Johnson, Steven G; Joannopoulos, John D

2009-08-03

Two novel classes of spherical invisibility cloaks based on nonlinear transformation have been studied. The cloaking characteristics are presented by segmenting the nonlinear transformation based spherical cloak into concentric isotropic homogeneous coatings. Detailed investigations of the optimal discretization (e.g., thickness control of each layer, nonlinear factor, etc.) are presented for both linear and nonlinear spherical cloaks and their effects on invisibility performance are also discussed. The cloaking properties and our choice of optimal segmentation are verified by the numerical simulation of not only near-field electric-field distribution but also the far-field radar cross section (RCS).

Detection of nonlinear transfer functions by the use of Gaussian statistics

NASA Technical Reports Server (NTRS)

Sheppard, J. G.

1972-01-01

The possibility of using on-line signal statistics to detect electronic equipment nonlinearities is discussed. The results of an investigation using Gaussian statistics are presented, and a nonlinearity test that uses ratios of the moments of a Gaussian random variable is developed and discussed. An outline for further investigation is presented.

Broadband gate-tunable terahertz plasmons in graphene heterostructures

NASA Astrophysics Data System (ADS)

Yao, Baicheng; Liu, Yuan; Huang, Shu-Wei; Choi, Chanyeol; Xie, Zhenda; Flor Flores, Jaime; Wu, Yu; Yu, Mingbin; Kwong, Dim-Lee; Huang, Yu; Rao, Yunjiang; Duan, Xiangfeng; Wong, Chee Wei

2018-01-01

Graphene, a unique two-dimensional material comprising carbon in a honeycomb lattice1, has brought breakthroughs across electronics, mechanics and thermal transport, driven by the quasiparticle Dirac fermions obeying a linear dispersion2,3. Here, we demonstrate a counter-pumped all-optical difference frequency process to coherently generate and control terahertz plasmons in atomic-layer graphene with octave-level tunability and high efficiency. We leverage the inherent surface asymmetry of graphene for strong second-order nonlinear polarizability4,5, which, together with tight plasmon field confinement, enables a robust difference frequency signal at terahertz frequencies. The counter-pumped resonant process on graphene uniquely achieves both energy and momentum conservation. Consequently, we demonstrate a dual-layer graphene heterostructure with terahertz charge- and gate-tunability over an octave, from 4.7 THz to 9.4 THz, bounded only by the pump amplifier optical bandwidth. Theoretical modelling supports our single-volt-level gate tuning and optical-bandwidth-bounded 4.7 THz phase-matching measurements through the random phase approximation, with phonon coupling, saturable absorption and below the Landau damping, to predict and understand graphene plasmon physics.

Inverting Monotonic Nonlinearities by Entropy Maximization

PubMed Central

López-de-Ipiña Pena, Karmele; Caiafa, Cesar F.

2016-01-01

This paper proposes a new method for blind inversion of a monotonic nonlinear map applied to a sum of random variables. Such kinds of mixtures of random variables are found in source separation and Wiener system inversion problems, for example. The importance of our proposed method is based on the fact that it permits to decouple the estimation of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source separation matrix or deconvolution filter), which can be solved by applying any convenient linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes the idea of Gaussianization of the observation by maximizing its entropy instead. We developed two versions of our algorithm based either in a polynomial or a neural network parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear function and the probability distribution that gives a guarantee for the MaxEnt method to succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is compared with existing algorithms for blind approximation of nonlinear maps. Experiments show that MaxEnt is able to successfully compensate monotonic distortions outperforming other methods in terms of the obtained Signal to Noise Ratio in many important cases, for example when the number of variables in a mixture is small. Besides its ability for compensating nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results. PMID:27780261

Inverting Monotonic Nonlinearities by Entropy Maximization.

PubMed

Solé-Casals, Jordi; López-de-Ipiña Pena, Karmele; Caiafa, Cesar F

2016-01-01

This paper proposes a new method for blind inversion of a monotonic nonlinear map applied to a sum of random variables. Such kinds of mixtures of random variables are found in source separation and Wiener system inversion problems, for example. The importance of our proposed method is based on the fact that it permits to decouple the estimation of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source separation matrix or deconvolution filter), which can be solved by applying any convenient linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes the idea of Gaussianization of the observation by maximizing its entropy instead. We developed two versions of our algorithm based either in a polynomial or a neural network parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear function and the probability distribution that gives a guarantee for the MaxEnt method to succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is compared with existing algorithms for blind approximation of nonlinear maps. Experiments show that MaxEnt is able to successfully compensate monotonic distortions outperforming other methods in terms of the obtained Signal to Noise Ratio in many important cases, for example when the number of variables in a mixture is small. Besides its ability for compensating nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results.

Fabrication and notable optical nonlinearities of ultrathin composite films derived from water-soluble Keggin-type polyoxometalates and water-insoluble phthalocyanine.

PubMed

Shehzad, Farooq Khurum; Qu, Ningning; Zhou, Yunshan; Zhang, Lijuan; Ji, Huanyao; Shi, Zonghai; Li, Jiaqi; Hassan, Sadaf Ul

2016-11-28

Composite films with the general formula (POM/CuTAPc) n derived from water-soluble Keggin-type polyoxometalates (POMs = H 5 PMo 10 V 2 O 40 , H 4 SiW 12 O 40 , H 3 PMo 12 O 40 and H 3 PW 12 O 40 ) and water-insoluble 4,9,16,23-copper tetraaminophthalocyanine (denoted CuTAPc) are successfully fabricated by a layer-by-layer self-assembly technique and systematically characterized. The structure of the polyoxometalate anions in the multilayers is kept intact; the deposition amounts of POM and CuTAPc remain constant in every adsorption cycle of the composite film assembly process. The nonlinear optical properties of the composite films were studied by a Z-scan technique at a wavelength of 532 nm and a pulse width of 7 ns. The results not only show that the composite films exhibit notable optical nonlinear self-defocusing behavior and a saturated absorption effect with the nonlinear optical absorption co-efficient β, refractive index n 2 , and third-order NLO susceptibility χ (3) of the films increasing with the increase in number of layers of the films, but also reveal importantly that the discrepancy of LUMO levels between CuTAPc and POMs is proportional to their third-order NLO response.

Transient response of an active nonlinear sandwich piezolaminated plate

NASA Astrophysics Data System (ADS)

Oveisi, Atta; Nestorović, Tamara

2017-04-01

In this paper, the dynamic modelling and active vibration control of a piezolaminated plate with geometrical nonlinearities are investigated using a semi-analytical approach. For active vibration control purposes, the core orthotropic elastic layer is assumed to be perfectly bonded with two piezo-layers on its top and bottom surfaces which act as sensor and actuator, respectively. In the modelling procedure, the piezo-layers are assumed to be connected via a proportional derivative (PD) feedback control law. Hamilton's principle is employed to acquire the strong form of the dynamic equation in terms of additional higher order strain expressions by means of von Karman strain-displacement correlation. The obtained nonlinear partial differential equation (NPDE) is converted to a system of nonlinear ordinary differential equations (NODEs) by engaging Galerkin method and using the orthogonality of shape functions for the simply supported boundary conditions. Then, the resulting system of NODEs is solved numerically by employing the built-in Mathematica function, "NDSolve". Next, the vibration attenuation performance is evaluated and sensitivity of the closed-loop system is investigated for several control parameters and the external disturbance parameters. The proposed solution in open loop configuration is validated by finite element (FE) package ABAQUS both in the spatial domain and for the time-/frequency-dependent response.

Transverse thermal depinning and nonlinear sliding friction of an adsorbed monolayer.

PubMed

Granato, E; Ying, S C

2000-12-18

We study the response of an adsorbed monolayer under a driving force as a model of sliding friction phenomena between two crystalline surfaces with a boundary lubrication layer. Using Langevin-dynamics simulation, we determine the nonlinear response in the direction transverse to a high symmetry direction along which the layer is already sliding. We find that below a finite transition temperature there exist a critical depinning force and hysteresis effects in the transverse response in the dynamical state when the adlayer is sliding smoothly along the longitudinal direction.

Solution of the nonlinear Poisson-Boltzmann equation: Application to ionic diffusion in cementitious materials

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

Arnold, J.; Kosson, D.S., E-mail: david.s.kosson@vanderbilt.edu; Garrabrants, A.

2013-02-15

A robust numerical solution of the nonlinear Poisson-Boltzmann equation for asymmetric polyelectrolyte solutions in discrete pore geometries is presented. Comparisons to the linearized approximation of the Poisson-Boltzmann equation reveal that the assumptions leading to linearization may not be appropriate for the electrochemical regime in many cementitious materials. Implications of the electric double layer on both partitioning of species and on diffusive release are discussed. The influence of the electric double layer on anion diffusion relative to cation diffusion is examined.

Tunneling and Origin of Large Access Resistance in Layered-Crystal Organic Transistors

NASA Astrophysics Data System (ADS)

Hamai, Takamasa; Arai, Shunto; Minemawari, Hiromi; Inoue, Satoru; Kumai, Reiji; Hasegawa, Tatsuo

2017-11-01

Layered crystallinity of organic semiconductors is crucial to obtaining high-performance organic thin-film transistors (OTFTs), as it allows both smooth-channel-gate-insulator interface formation and efficient two-dimensional carrier transport along the interface. However, the role of vertical transport across the crystalline molecular layers in device operations has not been a crucial subject so far. Here, we show that the interlayer carrier transport causes unusual nonlinear current-voltage characteristics and enormous access resistance in extremely high-quality single-crystal OTFTs based on 2-decyl-7-phenyl[1]-benzothieno[3 ,2 -b ][1]benzothiophene (Ph -BTBT -C10 ) that involve inherent multiple semiconducting π -conjugated layers interposed, respectively, by electrically inert alkyl-chain layers. The output characteristics present layer-number (n )-dependent nonlinearity that becomes more evident at larger n (1 ≤n ≤15 ), demonstrating tunneling across multiple alkyl-chain layers. The n -dependent device mobility and four-probe measurements reveal that the alkyl-chain layers generate a large access resistance that suppresses the device mobility from the intrinsic value of about 20 cm2 V-1 s-1 . Our findings clarify the reason why device characteristics are distributed in single-crystal OTFTs.

Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm.

PubMed

Chow, Sy-Miin; Lu, Zhaohua; Sherwood, Andrew; Zhu, Hongtu

2016-03-01

The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation-maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.

A simple approach to nonlinear estimation of physical systems

USGS Publications Warehouse

Christakos, G.

1988-01-01

Recursive algorithms for estimating the states of nonlinear physical systems are developed. This requires some key hypotheses regarding the structure of the underlying processes. Members of this class of random processes have several desirable properties for the nonlinear estimation of random signals. An assumption is made about the form of the estimator, which may then take account of a wide range of applications. Under the above assumption, the estimation algorithm is mathematically suboptimal but effective and computationally attractive. It may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. To link theory with practice, some numerical results for a simulated system are presented, in which the responses from the proposed and the extended Kalman algorithms are compared. ?? 1988.

FITTING NONLINEAR ORDINARY DIFFERENTIAL EQUATION MODELS WITH RANDOM EFFECTS AND UNKNOWN INITIAL CONDITIONS USING THE STOCHASTIC APPROXIMATION EXPECTATION–MAXIMIZATION (SAEM) ALGORITHM

PubMed Central

Chow, Sy- Miin; Lu, Zhaohua; Zhu, Hongtu; Sherwood, Andrew

2014-01-01

The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation–maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed. PMID:25416456

A Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer

NASA Astrophysics Data System (ADS)

Parsakhoo, Zahra; Shao, Yaping

2017-04-01

Near-surface turbulent mixing has considerable effect on surface fluxes, cloud formation and convection in the atmospheric boundary layer (ABL). Its quantifications is however a modeling and computational challenge since the small eddies are not fully resolved in Eulerian models directly. We have developed a Lagrangian stochastic model to demonstrate multi-scale interactions between convection and land surface heterogeneity in the atmospheric boundary layer based on the Ito Stochastic Differential Equation (SDE) for air parcels (particles). Due to the complexity of the mixing in the ABL, we find that linear Ito SDE cannot represent convections properly. Three strategies have been tested to solve the problem: 1) to make the deterministic term in the Ito equation non-linear; 2) to change the random term in the Ito equation fractional, and 3) to modify the Ito equation by including Levy flights. We focus on the third strategy and interpret mixing as interaction between at least two stochastic processes with different Lagrangian time scales. The model is in progress to include the collisions among the particles with different characteristic and to apply the 3D model for real cases. One application of the model is emphasized: some land surface patterns are generated and then coupled with the Large Eddy Simulation (LES).

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

NASA Technical Reports Server (NTRS)

Rabinowitz, Matthew (Inventor)

2002-01-01

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.

Advanced Numerical Methods for Computing Statistical Quantities of Interest from Solutions of SPDES

DTIC Science & Technology

2012-01-19

and related optimization problems; developing numerical methods for option pricing problems in the presence of random arbitrage return. 1. Novel...equations (BSDEs) are connected to nonlinear partial differen- tial equations and non-linear semigroups, to the theory of hedging and pricing of contingent...the presence of random arbitrage return [3] We consider option pricing problems when we relax the condition of no arbitrage in the Black- Scholes

Probabilistic analysis of a materially nonlinear structure

NASA Technical Reports Server (NTRS)

Millwater, H. R.; Wu, Y.-T.; Fossum, A. F.

1990-01-01

A probabilistic finite element program is used to perform probabilistic analysis of a materially nonlinear structure. The program used in this study is NESSUS (Numerical Evaluation of Stochastic Structure Under Stress), under development at Southwest Research Institute. The cumulative distribution function (CDF) of the radial stress of a thick-walled cylinder under internal pressure is computed and compared with the analytical solution. In addition, sensitivity factors showing the relative importance of the input random variables are calculated. Significant plasticity is present in this problem and has a pronounced effect on the probabilistic results. The random input variables are the material yield stress and internal pressure with Weibull and normal distributions, respectively. The results verify the ability of NESSUS to compute the CDF and sensitivity factors of a materially nonlinear structure. In addition, the ability of the Advanced Mean Value (AMV) procedure to assess the probabilistic behavior of structures which exhibit a highly nonlinear response is shown. Thus, the AMV procedure can be applied with confidence to other structures which exhibit nonlinear behavior.

Active and passive controls of Jeffrey nanofluid flow over a nonlinear stretching surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

This communication explores magnetohydrodynamic (MHD) boundary-layer flow of Jeffrey nanofluid over a nonlinear stretching surface with active and passive controls of nanoparticles. A nonlinear stretching surface generates the flow. Effects of thermophoresis and Brownian diffusion are considered. Jeffrey fluid is electrically conducted subject to non-uniform magnetic field. Low magnetic Reynolds number and boundary-layer approximations have been considered in mathematical modelling. The phenomena of impulsing the particles away from the surface in combination with non-zero mass flux condition is known as the condition of zero mass flux. Convergent series solutions for the nonlinear governing system are established through optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the temperature and concentration distributions are affected by distinct physical flow parameters. Skin friction coefficient and local Nusselt and Sherwood numbers are also computed and analyzed. Our findings show that the temperature and concentration distributions are increasing functions of Hartman number and thermophoresis parameter.

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

Samanta, C.; Yasasvi Gangavarapu, P. R.; Naik, A. K.

Atomically thin two dimensional (2D) layered materials have emerged as a new class of material for nanoelectromechanical systems (NEMS) due to their extraordinary mechanical properties and ultralow mass density. Among them, graphene has been the material of choice for nanomechanical resonator. However, recent interest in 2D chalcogenide compounds has also spurred research in using materials such as MoS{sub 2} for the NEMS applications. As the dimensions of devices fabricated using these materials shrink down to atomically thin membrane, strain and nonlinear effects have become important. A clear understanding of the nonlinear effects and the ability to manipulate them is essentialmore » for next generation sensors. Here, we report on all electrical actuation and detection of few-layer MoS{sub 2} resonator. The ability to electrically detect multiple modes and actuate the modes deep into the nonlinear regime enables us to probe the nonlinear coupling between various vibrational modes. The modal coupling in our device is strong enough to detect three distinct internal resonances.« less

Thermomagnetic instabilities in a vertical layer of ferrofluid: nonlinear analysis away from a critical point

NASA Astrophysics Data System (ADS)

Dey, Pinkee; Suslov, Sergey A.

2016-12-01

A finite amplitude instability has been analysed to discover the exact mechanism leading to the appearance of stationary magnetoconvection patterns in a vertical layer of a non-conducting ferrofluid heated from the side and placed in an external magnetic field perpendicular to the walls. The physical results have been obtained using a version of a weakly nonlinear analysis that is based on the disturbance amplitude expansion. It enables a low-dimensional reduction of a full nonlinear problem in supercritical regimes away from a bifurcation point. The details of the reduction are given in comparison with traditional small-parameter expansions. It is also demonstrated that Squire’s transformation can be introduced for higher-order nonlinear terms thus reducing the full three-dimensional problem to its equivalent two-dimensional counterpart and enabling significant computational savings. The full three-dimensional instability patterns are subsequently recovered using the inverse transforms The analysed stationary thermomagnetic instability is shown to occur as a result of a supercritical pitchfork bifurcation.

High efficiency all-optical plasmonic diode based on a nonlinear side-coupled waveguide-cavity structure with broken symmetry

NASA Astrophysics Data System (ADS)

Liang, Hong-Qin; Liu, Bin; Hu, Jin-Feng; He, Xing-Dao

2018-05-01

An all-optical plasmonic diode, comprising a metal-insulator-metal waveguide coupled with a stub cavity, is proposed based on a nonlinear Fano structure. The key technique used is to break structural spatial symmetry by a simple reflector layer in the waveguide. The spatial asymmetry of the structure gives rise to the nonreciprocity of coupling efficiencies between the Fano cavity and waveguides on both sides of the reflector layer, leading to a nonreciprocal nonlinear response. Transmission properties and dynamic responses are numerically simulated and investigated by the nonlinear finite-difference time-domain method. In the proposed structure, high-efficiency nonreciprocal transmission can be achieved with a low power threshold and an ultrafast response time (subpicosecond level). A high maximum transmittance of 89.3% and an ultra-high transmission contrast ratio of 99.6% can also be obtained. The device can be flexibly adjusted for working wavebands by altering the stub cavity length.

A nonlinear and fractional derivative viscoelastic model for rail pads in the dynamic analysis of coupled vehicle-slab track systems

NASA Astrophysics Data System (ADS)

Zhu, Shengyang; Cai, Chengbiao; Spanos, Pol D.

2015-01-01

A nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the complex behavior of rail pads. It is implemented into the dynamic analysis of coupled vehicle-slab track (CVST) systems. The vehicle is treated as a multi-body system with 10 degrees of freedom, and the slab track is represented by a three layer Bernoulli-Euler beam model. The model for the rail pads is one dimensional, and the force-displacement relation is based on a superposition of elastic, friction, and FDV forces. This model takes into account the influences of the excitation frequency and of the displacement amplitude through a fractional derivative element, and a nonlinear friction element, respectively. The Grünwald representation of the fractional derivatives is employed to numerically solve the fractional and nonlinear equations of motion of the CVST system by means of an explicit integration algorithm. A dynamic analysis of the CVST system exposed to excitations of rail harmonic irregularities is carried out, pointing out the stiffness and damping dependence on the excitation frequency and the displacement amplitude. The analysis indicates that the dynamic stiffness and damping of the rail pads increase with the excitation frequency while they decrease with the displacement amplitude. Furthermore, comparisons between the proposed model and ordinary Kelvin model adopted for the CVST system, under excitations of welded rail joint irregularities and of random track irregularities, are conducted in the time domain as well as in the frequency domain. The proposed model is shown to possess several modeling advantages over the ordinary Kelvin element which overestimates both the stiffness and damping features at high frequencies.

Black phosphorus quantum dots for femtosecond laser photonics

NASA Astrophysics Data System (ADS)

Liu, Meng; Jiang, Xiao-Fang; Yan, Yu-Rong; Wang, Xu-De; Luo, Ai-Ping; Xu, Wen-Cheng; Luo, Zhi-Chao

2018-01-01

As a rising two-dimensional (2D) nanomaterial, layered black phosphorus (BP) nanosheets have shown promising applications in electronics and photonics. Besides the 2D layered structure, recently black phosphorus quantum dots (BPQDs) exhibiting unique optoelectronic properties had been successfully fabricated. However, the nonlinear optical properties of BPQDs at the telecommunication band have not been investigated. Herein, we synthesized the BPQDs by using a liquid exfoliation method that combined probe sonication and bath sonication. It was found that the evident saturable absorption ability of BPQDs at 1.55 μm waveband could be clearly observed. As for the applications of ultrafast photonics, we fabricated the BPQDs saturable absorber (BPQDs-SA) and applied it to an ultrafast laser. By virtue of the excellent nonlinear optical properties of BPQDs, the fiber laser delivers the stable pulse train with duration as short as 291 fs, whose performance could, to the best of our knowledge, compete with nowadays' commercial optical saturable absorber devices. In addition, due to the highly nonlinear optical effect generated by the fabricated BPQDs-SA, the multi-soliton nonlinear dynamics in the fiber laser were also investigated. The obtained results suggest that the BPQDs could be an attractive nonlinear optical material for applications in the field of nonlinear optics.

Physics and control of wall turbulence for drag reduction.

PubMed

Kim, John

2011-04-13

Turbulence physics responsible for high skin-friction drag in turbulent boundary layers is first reviewed. A self-sustaining process of near-wall turbulence structures is then discussed from the perspective of controlling this process for the purpose of skin-friction drag reduction. After recognizing that key parts of this self-sustaining process are linear, a linear systems approach to boundary-layer control is discussed. It is shown that singular-value decomposition analysis of the linear system allows us to examine different approaches to boundary-layer control without carrying out the expensive nonlinear simulations. Results from the linear analysis are consistent with those observed in full nonlinear simulations, thus demonstrating the validity of the linear analysis. Finally, fundamental performance limit expected of optimal control input is discussed.

Boundary-Layer Receptivity and Integrated Transition Prediction

NASA Technical Reports Server (NTRS)

Chang, Chau-Lyan; Choudhari, Meelan

2005-01-01

The adjoint parabold stability equations (PSE) formulation is used to calculate the boundary layer receptivity to localized surface roughness and suction for compressible boundary layers. Receptivity efficiency functions predicted by the adjoint PSE approach agree well with results based on other nonparallel methods including linearized Navier-Stokes equations for both Tollmien-Schlichting waves and crossflow instability in swept wing boundary layers. The receptivity efficiency function can be regarded as the Green's function to the disturbance amplitude evolution in a nonparallel (growing) boundary layer. Given the Fourier transformed geometry factor distribution along the chordwise direction, the linear disturbance amplitude evolution for a finite size, distributed nonuniformity can be computed by evaluating the integral effects of both disturbance generation and linear amplification. The synergistic approach via the linear adjoint PSE for receptivity and nonlinear PSE for disturbance evolution downstream of the leading edge forms the basis for an integrated transition prediction tool. Eventually, such physics-based, high fidelity prediction methods could simulate the transition process from the disturbance generation through the nonlinear breakdown in a holistic manner.

Direct numerical simulation of a compressible boundary-layer flow past an isolated three-dimensional hump in a high-speed subsonic regime

NASA Astrophysics Data System (ADS)

De Grazia, D.; Moxey, D.; Sherwin, S. J.; Kravtsova, M. A.; Ruban, A. I.

2018-02-01

In this paper we study the boundary-layer separation produced in a high-speed subsonic boundary layer by a small wall roughness. Specifically, we present a direct numerical simulation (DNS) of a two-dimensional boundary-layer flow over a flat plate encountering a three-dimensional Gaussian-shaped hump. This work was motivated by the lack of DNS data of boundary-layer flows past roughness elements in a similar regime which is typical of civil aviation. The Mach and Reynolds numbers are chosen to be relevant for aeronautical applications when considering small imperfections at the leading edge of wings. We analyze different heights of the hump: The smaller heights result in a weakly nonlinear regime, while the larger result in a fully nonlinear regime with an increasing laminar separation bubble arising downstream of the roughness element and the formation of a pair of streamwise counterrotating vortices which appear to support themselves.

Evolution of inviscid Kelvin-Helmholtz instability from a piecewise linear shear layer

NASA Astrophysics Data System (ADS)

Guha, Anirban; Rahmani, Mona; Lawrence, Gregory

2012-11-01

Here we study the evolution of 2D, inviscid Kelvin-Helmholtz instability (KH) ensuing from a piecewise linear shear layer. Although KH pertaining to smooth shear layers (eg. Hyperbolic tangent profile) has been thorough investigated in the past, very little is known about KH resulting from sharp shear layers. Pozrikidis and Higdon (1985) have shown that piecewise shear layer evolves into elliptical vortex patches. This non-linear state is dramatically different from the well known spiral-billow structure of KH. In fact, there is a little acknowledgement that elliptical vortex patches can represent non-linear KH. In this work, we show how such patches evolve through the interaction of vorticity waves. Our work is based on two types of computational methods (i) Contour Dynamics: a boundary-element method which tracks the evolution of the contour of a vortex patch using Lagrangian marker points, and (ii) Direct Numerical Simulation (DNS): an Eulerian pseudo-spectral method heavily used in studying hydrodynamic instability and turbulence.

Numerical study of entropy generation and melting heat transfer on MHD generalised non-Newtonian fluid (GNF): Application to optimal energy

NASA Astrophysics Data System (ADS)

Iqbal, Z.; Mehmood, Zaffar; Ahmad, Bilal

2018-05-01

This paper concerns an application to optimal energy by incorporating thermal equilibrium on MHD-generalised non-Newtonian fluid model with melting heat effect. Highly nonlinear system of partial differential equations is simplified to a nonlinear system using boundary layer approach and similarity transformations. Numerical solutions of velocity and temperature profile are obtained by using shooting method. The contribution of entropy generation is appraised on thermal and fluid velocities. Physical features of relevant parameters have been discussed by plotting graphs and tables. Some noteworthy findings are: Prandtl number, power law index and Weissenberg number contribute in lowering mass boundary layer thickness and entropy effect and enlarging thermal boundary layer thickness. However, an increasing mass boundary layer effect is only due to melting heat parameter. Moreover, thermal boundary layers have same trend for all parameters, i.e., temperature enhances with increase in values of significant parameters. Similarly, Hartman and Weissenberg numbers enhance Bejan number.

Effect of plate permeability on nonlinear stability of the asymptotic suction boundary layer.

PubMed

Wedin, Håkan; Cherubini, Stefania; Bottaro, Alessandro

2015-07-01

The nonlinear stability of the asymptotic suction boundary layer is studied numerically, searching for finite-amplitude solutions that bifurcate from the laminar flow state. By changing the boundary conditions for disturbances at the plate from the classical no-slip condition to more physically sound ones, the stability characteristics of the flow may change radically, both for the linearized as well as the nonlinear problem. The wall boundary condition takes into account the permeability K̂ of the plate; for very low permeability, it is acceptable to impose the classical boundary condition (K̂=0). This leads to a Reynolds number of approximately Re(c)=54400 for the onset of linearly unstable waves, and close to Re(g)=3200 for the emergence of nonlinear solutions [F. A. Milinazzo and P. G. Saffman, J. Fluid Mech. 160, 281 (1985); J. H. M. Fransson, Ph.D. thesis, Royal Institute of Technology, KTH, Sweden, 2003]. However, for larger values of the plate's permeability, the lower limit for the existence of linear and nonlinear solutions shifts to significantly lower Reynolds numbers. For the largest permeability studied here, the limit values of the Reynolds numbers reduce down to Re(c)=796 and Re(g)=294. For all cases studied, the solutions bifurcate subcritically toward lower Re, and this leads to the conjecture that they may be involved in the very first stages of a transition scenario similar to the classical route of the Blasius boundary layer initiated by Tollmien-Schlichting (TS) waves. The stability of these nonlinear solutions is also investigated, showing a low-frequency main unstable mode whose growth rate decreases with increasing permeability and with the Reynolds number, following a power law Re(-ρ), where the value of ρ depends on the permeability coefficient K̂. The nonlinear dynamics of the flow in the vicinity of the computed finite-amplitude solutions is finally investigated by direct numerical simulations, providing a viable scenario for subcritical transition due to TS waves.

Statistical linearization for multi-input/multi-output nonlinearities

NASA Technical Reports Server (NTRS)

Lin, Ching-An; Cheng, Victor H. L.

1991-01-01

Formulas are derived for the computation of the random input-describing functions for MIMO nonlinearities; these straightforward and rigorous derivations are based on the optimal mean square linear approximation. The computations involve evaluations of multiple integrals. It is shown that, for certain classes of nonlinearities, multiple-integral evaluations are obviated and the computations are significantly simplified.

Neonatal Seizure Detection Using Deep Convolutional Neural Networks.

PubMed

Ansari, Amir H; Cherian, Perumpillichira J; Caicedo, Alexander; Naulaers, Gunnar; De Vos, Maarten; Van Huffel, Sabine

2018-04-02

Identifying a core set of features is one of the most important steps in the development of an automated seizure detector. In most of the published studies describing features and seizure classifiers, the features were hand-engineered, which may not be optimal. The main goal of the present paper is using deep convolutional neural networks (CNNs) and random forest to automatically optimize feature selection and classification. The input of the proposed classifier is raw multi-channel EEG and the output is the class label: seizure/nonseizure. By training this network, the required features are optimized, while fitting a nonlinear classifier on the features. After training the network with EEG recordings of 26 neonates, five end layers performing the classification were replaced with a random forest classifier in order to improve the performance. This resulted in a false alarm rate of 0.9 per hour and seizure detection rate of 77% using a test set of EEG recordings of 22 neonates that also included dubious seizures. The newly proposed CNN classifier outperformed three data-driven feature-based approaches and performed similar to a previously developed heuristic method.

Effect of Micro-Bubbles in Water on Beam Patterns of Parametric Array

NASA Astrophysics Data System (ADS)

Hashiba, Kunio; Masuzawa, Hiroshi

2003-05-01

The improvement in efficiency of a parametric array by nonlinear oscillation of micro-bubbles in water is studied in this paper. The micro-bubble oscillation can increase the nonlinear coefficient of the acoustic medium. The amplitude of the difference-frequency wave along the longitudinal axis and its beam patterns in the field including the layer with micro-bubbles were analyzed using a Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. As a result, the largest improvement in efficiency was obtained and a narrow parametric beam was formed by forming a layer with micro-bubbles in front of a parametric sound radiator as thick as about the shock formation distance. If the layer becomes significantly thicker than the distance, the beam of the difference-frequency wave in the far-field will become broader. If the layer is significantly thinner than the distance, the intensity level of the wave in the far-field will be too low.

Chaotic behavior in the locomotion of Amoeba proteus.

PubMed

Miyoshi, H; Kagawa, Y; Tsuchiya, Y

2001-01-01

The locomotion of Amoeba proteus has been investigated by algorithms evaluating correlation dimension and Lyapunov spectrum developed in the field of nonlinear science. It is presumed by these parameters whether the random behavior of the system is stochastic or deterministic. For the analysis of the nonlinear parameters, n-dimensional time-delayed vectors have been reconstructed from a time series of periphery and area of A. proteus images captured with a charge-coupled-device camera, which characterize its random motion. The correlation dimension analyzed has shown the random motion of A. proteus is subjected only to 3-4 macrovariables, though the system is a complex system composed of many degrees of freedom. Furthermore, the analysis of the Lyapunov spectrum has shown its largest exponent takes positive values. These results indicate the random behavior of A. proteus is chaotic and deterministic motion on an attractor with low dimension. It may be important for the elucidation of the cell locomotion to take account of nonlinear interactions among a small number of dynamics such as the sol-gel transformation, the cytoplasmic streaming, and the relating chemical reaction occurring in the cell.

Problems in Nonlinear Acoustics: Pulsed Finite Amplitude Sound Beams, Nonlinear Propagation of Sound in Layered Media, Time Domain Solutions for Focused Sound Beams, Focusing of Sound with an Ellipsoidal Mirror, and Modeling Finite Amplitude Propagation in Waveguides.

DTIC Science & Technology

1991-08-01

performed entirely in the time domain, solves the KZK (Khokhlov-Zabolotskaya-Kuznetsov) nonlinear parabolic wdve equation for pulsed, axisymmetric...finite amplitude sound beams. The KZK equation accounts for the combined effects of nonlinearity, diffraction and thermoviscous absorption on the...those used by Naze Tjotta, Tjotta, and Vefring to produce Fig. 7 of Ref. 4 with a frequency domain numerical solution of the KZK equation. However

Identifying sensitive areas of adaptive observations for prediction of the Kuroshio large meander using a shallow-water model

NASA Astrophysics Data System (ADS)

Zou, Guang'an; Wang, Qiang; Mu, Mu

2016-09-01

Sensitive areas for prediction of the Kuroshio large meander using a 1.5-layer, shallow-water ocean model were investigated using the conditional nonlinear optimal perturbation (CNOP) and first singular vector (FSV) methods. A series of sensitivity experiments were designed to test the sensitivity of sensitive areas within the numerical model. The following results were obtained: (1) the eff ect of initial CNOP and FSV patterns in their sensitive areas is greater than that of the same patterns in randomly selected areas, with the eff ect of the initial CNOP patterns in CNOP sensitive areas being the greatest; (2) both CNOP- and FSV-type initial errors grow more quickly than random errors; (3) the eff ect of random errors superimposed on the sensitive areas is greater than that of random errors introduced into randomly selected areas, and initial errors in the CNOP sensitive areas have greater eff ects on final forecasts. These results reveal that the sensitive areas determined using the CNOP are more sensitive than those of FSV and other randomly selected areas. In addition, ideal hindcasting experiments were conducted to examine the validity of the sensitive areas. The results indicate that reduction (or elimination) of CNOP-type errors in CNOP sensitive areas at the initial time has a greater forecast benefit than the reduction (or elimination) of FSV-type errors in FSV sensitive areas. These results suggest that the CNOP method is suitable for determining sensitive areas in the prediction of the Kuroshio large-meander path.

DC magnetic field sensing based on the nonlinear magnetoelectric effect in magnetic heterostructures

NASA Astrophysics Data System (ADS)

Burdin, Dmitrii; Chashin, Dmitrii; Ekonomov, Nikolai; Fetisov, Leonid; Fetisov, Yuri; Shamonin, Mikhail

2016-09-01

Recently, highly sensitive magnetic field sensors using the magnetoelectric effect in composite ferromagnetic-piezoelectric layered structures have been demonstrated. However, most of the proposed concepts are not useful for measuring dc magnetic fields, because the conductivity of piezoelectric layers results in a strong decline of the sensor’s sensitivity at low frequencies. In this paper, a novel functional principle of magnetoelectric sensors for dc magnetic field measurements is described. The sensor employs the nonlinear effect of voltage harmonic generation in a composite magnetoelectric structure under the simultaneous influence of a strong imposed ac magnetic field and a weak dc magnetic field to be measured. This physical effect arises due to the nonlinear dependence of the magnetostriction in the ferromagnetic layer on the magnetic field. A sensor prototype comprising of a piezoelectric fibre transducer sandwiched between two layers of the amorphous ferromagnetic Metglas® alloy was fabricated. The specifications regarding the magnetic field range, frequency characteristics, and noise level were studied experimentally. The prototype showed the responsivity of 2.5 V mT-1 and permitted the measurement of dc magnetic fields in the range of ~10 nT to about 0.4 mT. Although sensor operation is based on the nonlinear effect, the sensor response can be made linear with respect to the measured magnetic field in a broad dynamic range extending over 5 orders of magnitude. The underlying physics is explained through a simplified theory for the proposed sensor. The functionality, differences and advantages of the magnetoelectric sensor compare well with fluxgate magnetometers. The ways to enhance the sensor performance are considered.

Superconductor-normal-superconductor with distributed Sharvin point contacts

DOEpatents

Holcomb, Matthew J.; Little, William A.

1994-01-01

A non-linear superconducting junction device comprising a layer of high transient temperature superconducting material which is superconducting at an operating temperature, a layer of metal in contact with the layer of high temperature superconducting material and which remains non-superconducting at the operating temperature, and a metal material which is superconducting at the operating temperature and which forms distributed Sharvin point contacts with the metal layer.

On Nonlinear Functionals of Random Spherical Eigenfunctions

NASA Astrophysics Data System (ADS)

Marinucci, Domenico; Wigman, Igor

2014-05-01

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

Learning accurate and interpretable models based on regularized random forests regression

PubMed Central

2014-01-01

Background Many biology related research works combine data from multiple sources in an effort to understand the underlying problems. It is important to find and interpret the most important information from these sources. Thus it will be beneficial to have an effective algorithm that can simultaneously extract decision rules and select critical features for good interpretation while preserving the prediction performance. Methods In this study, we focus on regression problems for biological data where target outcomes are continuous. In general, models constructed from linear regression approaches are relatively easy to interpret. However, many practical biological applications are nonlinear in essence where we can hardly find a direct linear relationship between input and output. Nonlinear regression techniques can reveal nonlinear relationship of data, but are generally hard for human to interpret. We propose a rule based regression algorithm that uses 1-norm regularized random forests. The proposed approach simultaneously extracts a small number of rules from generated random forests and eliminates unimportant features. Results We tested the approach on some biological data sets. The proposed approach is able to construct a significantly smaller set of regression rules using a subset of attributes while achieving prediction performance comparable to that of random forests regression. Conclusion It demonstrates high potential in aiding prediction and interpretation of nonlinear relationships of the subject being studied. PMID:25350120

Ytterbium-doped fiber laser passively mode locked by few-layer Molybdenum Disulfide (MoS2) saturable absorber functioned with evanescent field interaction

PubMed Central

Du, Juan; Wang, Qingkai; Jiang, Guobao; Xu, Changwen; Zhao, Chujun; Xiang, Yuanjiang; Chen, Yu; Wen, Shuangchun; Zhang, Han

2014-01-01

By coupling few-layer Molybdenum Disulfide (MoS2) with fiber-taper evanescent light field, a new type of MoS2 based nonlinear optical modulating element had been successfully fabricated as a two-dimensional layered saturable absorber with strong light-matter interaction. This MoS2-taper-fiber device is not only capable of passively mode-locking an all-normal-dispersion ytterbium-doped fiber laser and enduring high power laser excitation (up to 1 W), but also functions as a polarization sensitive optical modulating component (that is, different polarized light can induce different nonlinear optical response). Thanks to the combined advantages from the strong nonlinear optical response in MoS2 together with the sufficiently-long-range interaction between light and MoS2, this device allows for the generation of high power stable dissipative solitons at 1042.6 nm with pulse duration of 656 ps and a repetition rate of 6.74 MHz at a pump power of 210 mW. Our work may also constitute the first example of MoS2-enabled wave-guiding photonic device, and potentially give some new insights into two-dimensional layered materials related photonics. PMID:25213108

Experimental and Numerical Studies on Wave Breaking Characteristics over a Fringing Reef under Monochromatic Wave Conditions

PubMed Central

2014-01-01

Fringing reefs play an important role in protecting the coastal area by inducing wave breaking and wave energy dissipation. However, modeling of wave transformation and energy dissipation on this topography is still difficult due to the unique structure. In the present study, two-dimensional laboratory experiments were conducted to investigate the cross-shore variations of wave transformation, setup, and breaking phenomena over an idealized fringing reef with the 1/40 reef slope and to verify the Boussinesq model under monochromatic wave conditions. One-layer and two-layer model configurations of the Boussinesq model were used to figure out the model capability. Both models predicted well (r 2 > 0.8) the cross-shore variation of the wave heights, crests, troughs, and setups when the nonlinearity is not too high (A 0/h 0 < 0.07 in this study). However, as the wave nonlinearity and steepness increase, the one-layer model showed problems in prediction and stability due to the error on the vertical profile of fluid velocity. The results in this study revealed that one-layer model is not suitable in the highly nonlinear wave condition over a fringing reef bathymetry. This data set can contribute to the numerical model verification. PMID:25276853

Experimental and numerical studies on wave breaking characteristics over a fringing reef under monochromatic wave conditions.

PubMed

Lee, Jong-In; Shin, Sungwon; Kim, Young-Taek

2014-01-01

Fringing reefs play an important role in protecting the coastal area by inducing wave breaking and wave energy dissipation. However, modeling of wave transformation and energy dissipation on this topography is still difficult due to the unique structure. In the present study, two-dimensional laboratory experiments were conducted to investigate the cross-shore variations of wave transformation, setup, and breaking phenomena over an idealized fringing reef with the 1/40 reef slope and to verify the Boussinesq model under monochromatic wave conditions. One-layer and two-layer model configurations of the Boussinesq model were used to figure out the model capability. Both models predicted well (r (2) > 0.8) the cross-shore variation of the wave heights, crests, troughs, and setups when the nonlinearity is not too high (A 0/h 0 < 0.07 in this study). However, as the wave nonlinearity and steepness increase, the one-layer model showed problems in prediction and stability due to the error on the vertical profile of fluid velocity. The results in this study revealed that one-layer model is not suitable in the highly nonlinear wave condition over a fringing reef bathymetry. This data set can contribute to the numerical model verification.

Transformation of nonlinear behaviors: from bright- to dark-gap soliton in a one-dimensional photonic crystal containing a nonlinear indefinite metamaterial defect.

PubMed

Zhang, Wei; Chen, Yuanyuan; Hou, Peng; Shi, Jielong; Wang, Qi

2010-12-01

Nonlinear propagation characteristics are investigated theoretically in a one-dimensional photonic band-gap structure doped with a nonlinear indefinite metamaterial defect for five distinct frequency intervals. It is found from the electric field distribution that there exists the bright gap solitonlike when the nonlinear indefinite metamaterial defect is a cut-off medium, while the dark gap solitonlike can appear in the nonlinear never cut-off defect layer. It is also found that there exists corresponding bistable lateral shift the properties of which are strongly dependent on the permittivity and permeability of nonlinear indefinite metamaterials. Moreover, in contrast to the switch-down threshold value, the switch-up threshold value is more sensitive to the incident frequency.

Modelling nonlinearity in piezoceramic transducers: From equations to nonlinear equivalent circuits.

PubMed

Parenthoine, D; Tran-Huu-Hue, L-P; Haumesser, L; Vander Meulen, F; Lematre, M; Lethiecq, M

2011-02-01

Quadratic nonlinear equations of a piezoelectric element under the assumptions of 1D vibration and weak nonlinearity are derived by the perturbation theory. It is shown that the nonlinear response can be represented by controlled sources that are added to the classical hexapole used to model piezoelectric ultrasonic transducers. As a consequence, equivalent electrical circuits can be used to predict the nonlinear response of a transducer taking into account the acoustic loads on the rear and front faces. A generalisation of nonlinear equivalent electrical circuits to cases including passive layers and propagation media is then proposed. Experimental results, in terms of second harmonic generation, on a coupled resonator are compared to theoretical calculations from the proposed model. Copyright © 2010 Elsevier B.V. All rights reserved.

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.

Wave kinetics of random fibre lasers

PubMed Central

Churkin, D V.; Kolokolov, I V.; Podivilov, E V.; Vatnik, I D.; Nikulin, M A.; Vergeles, S S.; Terekhov, I S.; Lebedev, V V.; Falkovich, G.; Babin, S A.; Turitsyn, S K.

2015-01-01

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example—random fibre laser—we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics. PMID:25645177

Broadband nonlinear optical response in multi-layer black phosphorus: an emerging infrared and mid-infrared optical material.

PubMed

Lu, S B; Miao, L L; Guo, Z N; Qi, X; Zhao, C J; Zhang, H; Wen, S C; Tang, D Y; Fan, D Y

2015-05-04

Black phosphorous (BP), the most thermodynamically stable allotrope of phosphorus, is a high-mobility layered semiconductor with direct band-gap determined by the number of layers from 0.3 eV (bulk) to 2.0 eV (single layer). Therefore, BP is considered as a natural candidate for broadband optical applications, particularly in the infrared (IR) and mid-IR part of the spectrum. The strong light-matter interaction, narrow direct band-gap, and wide range of tunable optical response make BP as a promising nonlinear optical material, particularly with great potentials for infrared and mid-infrared opto-electronics. Herein, we experimentally verified its broadband and enhanced saturable absorption of multi-layer BP (with a thickness of ~10 nm) by wide-band Z-scan measurement technique, and anticipated that multi-layer BPs could be developed as another new type of two-dimensional saturable absorber with operation bandwidth ranging from the visible (400 nm) towards mid-IR (at least 1930 nm). Our results might suggest that ultra-thin multi-layer BP films could be potentially developed as broadband ultra-fast photonics devices, such as passive Q-switcher, mode-locker, optical switcher etc.

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 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.

Nonlinear optical cryptosystem based on joint Fresnel transform correlator under vector wave illumination

NASA Astrophysics Data System (ADS)

Xueju, Shen; Chao, Lin; Xiao, Zou; Jianjun, Cai

2015-05-01

We present a nonlinear optical cryptosystem with multi-dimensional keys including phase, polarization and diffraction distance. To make full use of the degrees of freedom that optical processing offers, an elaborately designed vector wave with both a space-variant phase and locally linear polarization is generated with a common-path interferometer for illumination. The joint transform correlator in the Fresnel domain, implemented with a double optical wedge, is utilized as the encryption framework which provides an additional key known as the Fresnel diffraction distance. Two nonlinear operations imposed on the recorded joint Fresnel power distribution (JFPD) by a charge coupled device (CCD) are adopted. The first one is the division of power distribution of the reference window random function which is previously proposed by researchers and can improve the quality of the decrypted image. The second one is the recording of a hybrid JFPD using a micro-polarizers array with orthogonal and random transmissive axes attached to the CCD. Then the hybrid JFPD is further scrambled by substituting random noise for partial power distribution. The two nonlinear operations break the linearity of this cryptosystem and provide ultra security. We verify our proposal using a quick response code for noise-free recovery.

Sustainability of transport structures - some aspects of the nonlinear reliability assessment

NASA Astrophysics Data System (ADS)

Pukl, Radomír; Sajdlová, Tereza; Strauss, Alfred; Lehký, David; Novák, Drahomír

2017-09-01

Efficient techniques for both nonlinear numerical analysis of concrete structures and advanced stochastic simulation methods have been combined in order to offer an advanced tool for assessment of realistic behaviour, failure and safety assessment of transport structures. The utilized approach is based on randomization of the non-linear finite element analysis of the structural models. Degradation aspects such as carbonation of concrete can be accounted in order predict durability of the investigated structure and its sustainability. Results can serve as a rational basis for the performance and sustainability assessment based on advanced nonlinear computer analysis of the structures of transport infrastructure such as bridges or tunnels. In the stochastic simulation the input material parameters obtained from material tests including their randomness and uncertainty are represented as random variables or fields. Appropriate identification of material parameters is crucial for the virtual failure modelling of structures and structural elements. Inverse analysis using artificial neural networks and virtual stochastic simulations approach is applied to determine the fracture mechanical parameters of the structural material and its numerical model. Structural response, reliability and sustainability have been investigated on different types of transport structures made from various materials using the above mentioned methodology and tools.

Efficient Numerical Methods for Nonlinear-Facilitated Transport and Exchange in a Blood-Tissue Exchange Unit

PubMed Central

Poulain, Christophe A.; Finlayson, Bruce A.; Bassingthwaighte, James B.

2010-01-01

The analysis of experimental data obtained by the multiple-indicator method requires complex mathematical models for which capillary blood-tissue exchange (BTEX) units are the building blocks. This study presents a new, nonlinear, two-region, axially distributed, single capillary, BTEX model. A facilitated transporter model is used to describe mass transfer between plasma and intracellular spaces. To provide fast and accurate solutions, numerical techniques suited to nonlinear convection-dominated problems are implemented. These techniques are the random choice method, an explicit Euler-Lagrange scheme, and the MacCormack method with and without flux correction. The accuracy of the numerical techniques is demonstrated, and their efficiencies are compared. The random choice, Euler-Lagrange and plain MacCormack method are the best numerical techniques for BTEX modeling. However, the random choice and Euler-Lagrange methods are preferred over the MacCormack method because they allow for the derivation of a heuristic criterion that makes the numerical methods stable without degrading their efficiency. Numerical solutions are also used to illustrate some nonlinear behaviors of the model and to show how the new BTEX model can be used to estimate parameters from experimental data. PMID:9146808

Improved nonlinear plasmonic slot waveguide: a full study

NASA Astrophysics Data System (ADS)

Elsawy, Mahmoud M. R.; Nazabal, Virginie; Chauvet, Mathieu; Renversez, Gilles

2016-04-01

We present a full study of an improved nonlinear plasmonic slot waveguides (NPSWs) in which buffer linear dielectric layers are added between the Kerr type nonlinear dielectric core and the two semi-infinite metal regions. Our approach computes the stationary solutions using the fixed power algorithm, in which for a given structure the wave power is an input parameter and the outputs are the propagation constant and the corresponding field components. For TM polarized waves, the inclusion of these supplementary layers have two consequences. First, they reduced the overall losses. Secondly, they modify the types of solutions that propagate in the NPSWs adding new profiles enlarging the possibilities offered by these nonlinear waveguides. In addition to the symmetric linear plasmonic profile obtained in the simple plasmonic structure with linear core such that its effective index is above the linear core refractive index, we obtained a new field profile which is more localized in the core with an effective index below the core linear refractive index. In the nonlinear case, if the effective index of the symmetric linear mode is above the core linear refractive index, the mode field profiles now exhibit a spatial transition from a plasmonic type profile to a solitonic type one. Our structure also provides longer propagation length due to the decrease of the losses compared to the simple nonlinear slot waveguide and exhibits, for well-chosen refractive index or thickness of the buffer layer, a spatial transition of its main modes that can be controlled by the power. We provide a full phase diagram of the TM wave operating regimes of these improved NPSWs. The stability of the main TM modes is then demonstrated numerically using the FDTD. We also demonstrate the existence of TE waves for both linear and nonlinear cases (for some configurations) in which the maximum intensity is located in the middle of the waveguide. We indicate the bifurcation of the nonlinear asymmetric TE mode from the symmetric nonlinear one through the Hopf bifurcation. This kind of bifurcation is similar to the ones already obtained in TM case for our improved structure, and also for the simple NPSWs. At high power, above the bifurcation threshold, the fundamental symmetric nonlinear TE mode moves gradually to new nonlinear mode in which the soliton peak displays two peaks in the core. The losses of the TE modes decrease with the power for all the cases. This kind of structures could be fabricated and characterized experimentally due to the realistic parameters chosen to model them.

Nonlinear Bubble Dynamics And The Effects On Propagation Through Near-Surface Bubble Layers

NASA Astrophysics Data System (ADS)

Leighton, Timothy G.

2004-11-01

Nonlinear bubble dynamics are often viewed as the unfortunate consequence of having to use high acoustic pressure amplitudes when the void fraction in the near-surface oceanic bubble layer is great enough to cause severe attenuation (e.g. >50 dB/m). This is seen as unfortunate since existing models for acoustic propagation in bubbly liquids are based on linear bubble dynamics. However, the development of nonlinear models does more than just allow quantification of the errors associated with the use of linear models. It also offers the possibility of propagation modeling and acoustic inversions which appropriately incorporate the bubble nonlinearity. Furthermore, it allows exploration and quantification of possible nonlinear effects which may be exploited. As a result, high acoustic pressure amplitudes may be desirable even in low void fractions, because they offer opportunities to gain information about the bubble cloud from the nonlinearities, and options to exploit the nonlinearities to enhance communication and sonar in bubbly waters. This paper presents a method for calculating the nonlinear acoustic cross-sections, scatter, attenuations and sound speeds from bubble clouds which may be inhomogeneous. The method allows prediction of the time dependency of these quantities, both because the cloud may vary and because the incident acoustic pulse may have finite and arbitrary time history. The method can be readily adapted for bubbles in other environments (e.g. clouds of interacting bubbles, sediments, structures, in vivo, reverberant conditions etc.). The possible exploitation of bubble acoustics by marine mammals, and for sonar enhancement, is explored.

Nonlinear Dynamical Modes as a Basis for Short-Term Forecast of Climate Variability

NASA Astrophysics Data System (ADS)

Feigin, A. M.; Mukhin, D.; Gavrilov, A.; Seleznev, A.; Loskutov, E.

2017-12-01

We study abilities of data-driven stochastic models constructed by nonlinear dynamical decomposition of spatially distributed data to quantitative (short-term) forecast of climate characteristics. We compare two data processing techniques: (i) widely used empirical orthogonal function approach, and (ii) nonlinear dynamical modes (NDMs) framework [1,2]. We also make comparison of two kinds of the prognostic models: (i) traditional autoregression (linear) model and (ii) model in the form of random ("stochastic") nonlinear dynamical system [3]. We apply all combinations of the above-mentioned data mining techniques and kinds of models to short-term forecasts of climate indices based on sea surface temperature (SST) data. We use NOAA_ERSST_V4 dataset (monthly SST with space resolution 20 × 20) covering the tropical belt and starting from the year 1960. We demonstrate that NDM-based nonlinear model shows better prediction skill versus EOF-based linear and nonlinear models. Finally we discuss capability of NDM-based nonlinear model for long-term (decadal) prediction of climate variability. [1] D. Mukhin, A. Gavrilov, E. Loskutov , A.Feigin, J.Kurths, 2015: Principal nonlinear dynamical modes of climate variability, Scientific Reports, rep. 5, 15510; doi: 10.1038/srep15510. [2] Gavrilov, A., Mukhin, D., Loskutov, E., Volodin, E., Feigin, A., & Kurths, J., 2016: Method for reconstructing nonlinear modes with adaptive structure from multidimensional data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 26(12), 123101. [3] Ya. Molkov, D. Mukhin, E. Loskutov, A. Feigin, 2012: Random dynamical models from time series. Phys. Rev. E, Vol. 85, n.3.

Nonlinear dual-axis biodynamic response of the semi-supine human body during longitudinal horizontal whole-body vibration

NASA Astrophysics Data System (ADS)

Huang, Ya; Griffin, Michael J.

2008-04-01

The resonance frequencies in frequency response functions of the human body (e.g. apparent mass and transmissibility) decrease with increasing vibration magnitude. This nonlinear biodynamic response is found with various sitting and standing postures requiring postural control. The present study measured the apparent mass of the body in a relaxed semi-supine posture with two types of longitudinal horizontal vibration (in the z-axis of the semi-supine body): (i) continuous random excitation (0.25-20 Hz) at five magnitudes (0.125, 0.25, 0.5, 0.75 and 1.0 ms -2 rms); (ii) intermittent random excitation (0.25-20 Hz) alternately at 0.25 and 1.0 ms -2 rms. With continuous random vibration, the dominant primary resonance frequency in the median normalised apparent mass decreased from 3.7 to 2.4 Hz as the vibration magnitude increased from 0.125 to 1.0 ms -2 rms. A nonlinear response was apparent in both the horizontal ( z-axis) apparent mass and the vertical ( x-axis) cross-axis apparent mass. With intermittent random vibration, as the vibration magnitude increased from 0.25 to 1.0 ms -2 rms, the median resonance frequency of the apparent mass decreased from 3.2 to 2.5 Hz whereas, with continuous random vibration over the same range of magnitudes, the resonance frequency decreased from 3.4 to 2.4 Hz. The median change in the resonance frequency (between 0.25 and 1.0 ms -2 rms) was 0.6 Hz with the intermittent random vibration and 0.9 Hz with the continuous random vibration. With intermittent vibration, the resonance frequency was higher at the high magnitude and lower at the low magnitude than with continuous vibration at the same magnitudes. The responses were consistent with passive thixotropy being a primary cause of nonlinear biodynamic responses to whole-body vibration, although reflex activity of the muscles may also have an influence.

Nonlinear dual-axis biodynamic response of the semi-supine human body during vertical whole-body vibration

NASA Astrophysics Data System (ADS)

Huang, Ya; Griffin, Michael J.

2008-04-01

Nonlinear biodynamic responses are evident in many studies of the apparent masses of sitting and standing subjects in static postures that require muscle activity for postural control. In the present study, 12 male subjects adopted a relaxed semi-supine posture assumed to involve less muscle activity than during static sitting and standing. The supine subjects were exposed to two types of vertical vibration (in the x-axis of the semi-supine body): (i) continuous random vibration (0.25-20 Hz) at five magnitudes (0.125, 0.25, 0.5, 0.75, and 1.0 m s -2 rms); (ii) intermittent random vibration (0.25-20 Hz) alternately at 0.25 and 1.0 m s -2 rms. With continuous random vibration, the dominant primary resonance frequency in the median normalised apparent mass decreased from 10.35 to 7.32 Hz as the vibration magnitude increased from 0.125 to 1.0 m s -2 rms. This nonlinear response was apparent in both the vertical ( x-axis) apparent mass and in the horizontal ( z-axis) cross-axis apparent mass. As the vibration magnitude increased from 0.25 to 1.0 m s -2 rms, the median resonance frequency of the apparent mass with intermittent random vibration decreased from 9.28 to 8.06 Hz whereas, over the same range of magnitudes with continuous random vibration, the resonance frequency decreased from 9.62 to 7.81 Hz. The median change in the resonance frequency (between 0.25 and 1.0 m s -2 rms) was 1.37 Hz with the intermittent random vibration and 1.71 with the continuous random vibration. With the intermittent vibration, the resonance frequency was higher at the high magnitude and lower at the low magnitude than with continuous vibration of the same magnitudes. The response was typical of thixotropy that may be a primary cause of the nonlinear biodynamic responses to whole-body vibration.

Third-order nonlinear electro-optic measurements in the smectic-? phase

NASA Astrophysics Data System (ADS)

Nowicka, Kamila; Bielejewska, Natalia

2018-02-01

The chiral smectic subphase with three-layer structure, ?, is now of great interest from the point of view of device technologies such as multistate or symmetric switching. We report that the unique nonlinear electro-optic response can serve as precise mark of the phase transition into three-layer structure. The problem is illustrated with the first and third harmonic electro-optic spectra. Furthermore, the characteristic response of the helical liquid crystal phases correlated with particular collective modes using the Debye-type relaxation method for the well-known prototype liquid crystal material (MHPOBC) are presented.

Refined Models for an Analysis of Internal and External Buckling Modes of a Monolayer in a Layered Composite

NASA Astrophysics Data System (ADS)

Paimushin, V. N.

2017-11-01

For an analysis of internal and external buckling modes of a monolayer inside or at the periphery of a layered composite, refined geometrically nonlinear equations are constructed. They are based on modeling the monolayer as a thin plate interacting with binder layers at the points of boundary surfaces. The binder layer is modeled as a transversely soft foundation. It is assumed the foundations, previously compressed in the transverse direction (the first loading stage), have zero displacements of its external boundary surfaces at the second loading stage, but the contact interaction of the plate with foundations occurs without slippage or delamination. The deformation of the plate at a medium flexure is described by geometrically nonlinear relations of the classical plate theory based on the Kirchhoff-Love hypothesis (the first variant) or the refined Timoshenko model with account of the transverse shear and compression (the second variant). The foundation is described by linearized 3D equations of elasticity theory, which are simplified within the framework of the model of a transversely soft layer. Integrating the linearized equations along the transverse coordinate and satisfying the kinematic joining conditions of the plate with foundations, with account of their initial compression in the thickness direction, a system of 2D geometrically nonlinear equations and appropriate boundary conditions are derived. These equations describe the contact interaction between elements of the deformable system. The relations obtained are simplified for the case of a symmetric stacking sequence.

Aberrated surface soliton formation in a nonlinear 1D and 2D photonic crystal

PubMed Central

Lysak, Tatiana M.; Trykin, Evgenii M.

2018-01-01

We discuss a novel type of surface soliton—aberrated surface soliton—appearance in a nonlinear one dimensional photonic crystal and a possibility of this surface soliton formation in two dimensional photonic crystal. An aberrated surface soliton possesses a nonlinear distribution of the wavefront. We show that, in one dimensional photonic crystal, the surface soliton is formed at the photonic crystal boundary with the ambient medium. Essentially, that it occupies several layers at the photonic crystal boundary and penetrates into the ambient medium at a distance also equal to several layers, so that one can infer about light energy localization at the lateral surface of the photonic crystal. In the one dimensional case, the surface soliton is formed from an earlier formed soliton that falls along the photonic crystal layers at an angle which differs slightly from the normal to the photonic crystal face. In the two dimensional case, the soliton can appear if an incident Gaussian beam falls on the photonic crystal face. The influence of laser radiation parameters, optical properties of photonic crystal layers and ambient medium on the one dimensional surface soliton formation is investigated. We also discuss the influence of two dimensional photonic crystal configuration on light energy localization near the photonic crystal surface. It is important that aberrated surface solitons can be created at relatively low laser pulse intensity and for close values of alternating layers dielectric permittivity which allows their experimental observation. PMID:29558497

Comparison of Nonlinear Random Response Using Equivalent Linearization and Numerical Simulation

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2000-01-01

A recently developed finite-element-based equivalent linearization approach for the analysis of random vibrations of geometrically nonlinear multiple degree-of-freedom structures is validated. The validation is based on comparisons with results from a finite element based numerical simulation analysis using a numerical integration technique in physical coordinates. In particular, results for the case of a clamped-clamped beam are considered for an extensive load range to establish the limits of validity of the equivalent linearization approach.

The development of a mixing layer under the action of weak streamwise vortices

NASA Technical Reports Server (NTRS)

Goldstein, Marvin E.; Mathew, Joseph

1993-01-01

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds-number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon(sup -1)), where epsilon is much less than 1 is the cross flow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by the appearance of a singularity. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the singular location.

The development of a mixing layer under the action of weak streamwise vortices

NASA Technical Reports Server (NTRS)

Goldstein, M. E.; Mathew, Joseph

1993-01-01

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon sup -1), where (epsilon much less than 1) is the crossflow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by a breakdown in the numerical procedure. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the terminal location.

Interferometric pump-probe characterization of the nonlocal response of optically transparent ion implanted polymers

NASA Astrophysics Data System (ADS)

Stefanov, Ivan L.; Hadjichristov, Georgi B.

2012-03-01

Optical interferometric technique is applied to characterize the nonlocal response of optically transparent ion implanted polymers. The thermal nonlinearity of the ion-modified material in the near-surface region is induced by continuous wave (cw) laser irradiation at a relatively low intensity. The interferometry approach is demonstrated for a subsurface layer of a thickness of about 100 nm formed in bulk polymethylmethacrylate (PMMA) by implantation with silicon ions at an energy of 50 keV and fluence in the range 1014-1017 cm-2. The laser-induced thermooptic effect in this layer is finely probed by interferometric imaging. The interference phase distribution in the plane of the ion implanted layer is indicative for the thermal nonlinearity of the near-surface region of ion implanted optically transparent polymeric materials.

Optimal control of singularly perturbed nonlinear systems with state-variable inequality constraints

NASA Technical Reports Server (NTRS)

Calise, A. J.; Corban, J. E.

1990-01-01

The established necessary conditions for optimality in nonlinear control problems that involve state-variable inequality constraints are applied to a class of singularly perturbed systems. The distinguishing feature of this class of two-time-scale systems is a transformation of the state-variable inequality constraint, present in the full order problem, to a constraint involving states and controls in the reduced problem. It is shown that, when a state constraint is active in the reduced problem, the boundary layer problem can be of finite time in the stretched time variable. Thus, the usual requirement for asymptotic stability of the boundary layer system is not applicable, and cannot be used to construct approximate boundary layer solutions. Several alternative solution methods are explored and illustrated with simple examples.

Unstable flow structures in the Blasius boundary layer.

PubMed

Wedin, H; Bottaro, A; Hanifi, A; Zampogna, G

2014-04-01

Finite amplitude coherent structures with a reflection symmetry in the spanwise direction of a parallel boundary layer flow are reported together with a preliminary analysis of their stability. The search for the solutions is based on the self-sustaining process originally described by Waleffe (Phys. Fluids 9, 883 (1997)). This requires adding a body force to the Navier-Stokes equations; to locate a relevant nonlinear solution it is necessary to perform a continuation in the nonlinear regime and parameter space in order to render the body force of vanishing amplitude. Some states computed display a spanwise spacing between streaks of the same length scale as turbulence flow structures observed in experiments (S.K. Robinson, Ann. Rev. Fluid Mech. 23, 601 (1991)), and are found to be situated within the buffer layer. The exact coherent structures are unstable to small amplitude perturbations and thus may be part of a set of unstable nonlinear states of possible use to describe the turbulent transition. The nonlinear solutions survive down to a displacement thickness Reynolds number Re * = 496 , displaying a 4-vortex structure and an amplitude of the streamwise root-mean-square velocity of 6% scaled with the free-stream velocity. At this Re* the exact coherent structure bifurcates supercritically and this is the point where the laminar Blasius flow starts to cohabit the phase space with alternative simple exact solutions of the Navier-Stokes equations.

Optical Random Riemann Waves in Integrable Turbulence

NASA Astrophysics Data System (ADS)

Randoux, Stéphane; Gustave, François; Suret, Pierre; El, Gennady

2017-06-01

We examine integrable turbulence (IT) in the framework of the defocusing cubic one-dimensional nonlinear Schrödinger equation. This is done theoretically and experimentally, by realizing an optical fiber experiment in which the defocusing Kerr nonlinearity strongly dominates linear dispersive effects. Using a dispersive-hydrodynamic approach, we show that the development of IT can be divided into two distinct stages, the initial, prebreaking stage being described by a system of interacting random Riemann waves. We explain the low-tailed statistics of the wave intensity in IT and show that the Riemann invariants of the asymptotic nonlinear geometric optics system represent the observable quantities that provide new insight into statistical features of the initial stage of the IT development by exhibiting stationary probability density functions.

Generalized Nonlinear Yule Models

NASA Astrophysics Data System (ADS)

Lansky, Petr; Polito, Federico; Sacerdote, Laura

2016-11-01

With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

Nonlinear ring resonator: spatial pattern generation

NASA Astrophysics Data System (ADS)

Ivanov, Vladimir Y.; Lachinova, Svetlana L.; Irochnikov, Nikita G.

2000-03-01

We consider theoretically spatial pattern formation processes in a unidirectional ring cavity with thin layer of Kerr-type nonlinear medium. Our method is based on studying of two coupled equations. The first is a partial differential equation for temporal dynamics of phase modulation of light wave in the medium. It describes nonlinear interaction in the Kerr-type lice. The second is a free propagation equation for the intracavity field complex amplitude. It involves diffraction effects of light wave in the cavity.

Moderately nonlinear diffuse-charge dynamics under an ac voltage.

PubMed

Stout, Robert F; Khair, Aditya S

2015-09-01

The response of a symmetric binary electrolyte between two parallel, blocking electrodes to a moderate amplitude ac voltage is quantified. The diffuse charge dynamics are modeled via the Poisson-Nernst-Planck equations for a dilute solution of point-like ions. The solution to these equations is expressed as a Fourier series with a voltage perturbation expansion for arbitrary Debye layer thickness and ac frequency. Here, the perturbation expansion in voltage proceeds in powers of V_{o}/(k_{B}T/e), where V_{o} is the amplitude of the driving voltage and k_{B}T/e is the thermal voltage with k_{B} as Boltzmann's constant, T as the temperature, and e as the fundamental charge. We show that the response of the electrolyte remains essentially linear in voltage amplitude at frequencies greater than the RC frequency of Debye layer charging, D/λ_{D}L, where D is the ion diffusivity, λ_{D} is the Debye layer thickness, and L is half the cell width. In contrast, nonlinear response is predicted at frequencies below the RC frequency. We find that the ion densities exhibit symmetric deviations from the (uniform) equilibrium density at even orders of the voltage amplitude. This leads to the voltage dependence of the current in the external circuit arising from the odd orders of voltage. For instance, the first nonlinear contribution to the current is O(V_{o}^{3}) which contains the expected third harmonic but also a component oscillating at the applied frequency. We use this to compute a generalized impedance for moderate voltages, the first nonlinear contribution to which is quadratic in V_{o}. This contribution predicts a decrease in the imaginary part of the impedance at low frequency, which is due to the increase in Debye layer capacitance with increasing V_{o}. In contrast, the real part of the impedance increases at low frequency, due to adsorption of neutral salt from the bulk to the Debye layer.

Bottom boundary layer forced by finite amplitude long and short surface waves motions

NASA Astrophysics Data System (ADS)

Elsafty, H.; Lynett, P.

2018-04-01

A multiple-scale perturbation approach is implemented to solve the Navier-Stokes equations while including bottom boundary layer effects under a single wave and under two interacting waves. In this approach, fluid velocities and the pressure field are decomposed into two components: a potential component and a rotational component. In this study, the two components are exist throughout the entire water column and each is scaled with appropriate length and time scales. A one-way coupling between the two components is implemented. The potential component is assumed to be known analytically or numerically a prior, and the rotational component is forced by the potential component. Through order of magnitude analysis, it is found that the leading-order coupling between the two components occurs through the vertical convective acceleration. It is shown that this coupling plays an important role in the bottom boundary layer behavior. Its effect on the results is discussed for different wave-forcing conditions: purely harmonic forcing and impurely harmonic forcing. The approach is then applied to derive the governing equations for the bottom boundary layer developed under two interacting wave motions. Both motions-the shorter and the longer wave-are decomposed into two components, potential and rotational, as it is done in the single wave. Test cases are presented wherein two different wave forcings are simulated: (1) two periodic oscillatory motions and (2) short waves interacting with a solitary wave. The analysis of the two periodic motions indicates that nonlinear effects in the rotational solution may be significant even though nonlinear effects are negligible in the potential forcing. The local differences in the rotational velocity due to the nonlinear vertical convection coupling term are found to be on the order of 30% of the maximum boundary layer velocity for the cases simulated in this paper. This difference is expected to increase with the increase in wave nonlinearity.

Model-based damage evaluation of layered CFRP structures

NASA Astrophysics Data System (ADS)

Munoz, Rafael; Bochud, Nicolas; Rus, Guillermo; Peralta, Laura; Melchor, Juan; Chiachío, Juan; Chiachío, Manuel; Bond, Leonard J.

2015-03-01

An ultrasonic evaluation technique for damage identification of layered CFRP structures is presented. This approach relies on a model-based estimation procedure that combines experimental data and simulation of ultrasonic damage-propagation interactions. The CFPR structure, a [0/90]4s lay-up, has been tested in an immersion through transmission experiment, where a scan has been performed on a damaged specimen. Most ultrasonic techniques in industrial practice consider only a few features of the received signals, namely, time of flight, amplitude, attenuation, frequency contents, and so forth. In this case, once signals are captured, an algorithm is used to reconstruct the complete signal waveform and extract the unknown damage parameters by means of modeling procedures. A linear version of the data processing has been performed, where only Young modulus has been monitored and, in a second nonlinear version, the first order nonlinear coefficient β was incorporated to test the possibility of detection of early damage. The aforementioned physical simulation models are solved by the Transfer Matrix formalism, which has been extended from linear to nonlinear harmonic generation technique. The damage parameter search strategy is based on minimizing the mismatch between the captured and simulated signals in the time domain in an automated way using Genetic Algorithms. Processing all scanned locations, a C-scan of the parameter of each layer can be reconstructed, obtaining the information describing the state of each layer and each interface. Damage can be located and quantified in terms of changes in the selected parameter with a measurable extension. In the case of the nonlinear coefficient of first order, evidence of higher sensitivity to damage than imaging the linearly estimated Young Modulus is provided.

Nonlinear control of absorption in one-dimensional photonic crystal with graphene-based defect.

PubMed

Vincenti, M A; de Ceglia, D; Grande, M; D'Orazio, A; Scalora, M

2013-09-15

Perfect, narrow-band absorption is achieved in an asymmetric 1D photonic crystal with a monolayer graphene defect. Thanks to the large third-order nonlinearity of graphene and field localization in the defect layer we demonstrate the possibility to achieve controllable, saturable absorption for the pump frequency.

Non-random species loss in a forest herbaceous layer following nitrogen addition

Treesearch

Christopher A. ​Walter; Mary Beth Adams; Frank S. Gilliam; William T. Peterjohn

2017-01-01

Nitrogen (N) additions have decreased species richness (S) in hardwood forest herbaceous layers, yet the functional mechanisms for these decreases have not been explicitly evaluated.We tested two hypothesized mechanisms, random species loss (RSL) and non-random species loss (NRSL), in the hardwood forest herbaceous layer of a long-term, plot-scale...

Layer-Dependent Third-Harmonic Generation in Graphene

NASA Astrophysics Data System (ADS)

Yang, Hao; Guan, Honghua; Dadap, Jerry; Osgood, Richard; Richard Osgood Team

Graphene has become a subject of intense interest and study because of its remarkable 2D electronic properties. Multilayer graphene also offers an array of properties that are also of interest for optical physics and devices. Despite its second-order-nonlinear optical response is intrinsically weak, third-order nonlinear optical effects in graphene are symmetry-allowed thus leading to studies of several third-order process in few-layer graphene. In this work, we report third-harmonic generation in multilayer graphene mounted on fused silica and with thicknesses which approach the bulk continuum. THG signals show cubic power dependence with respect to the intensity of fundamental beam. Third-harmonic generation spectroscopy enables a good fit using linear optical detection, which shows strong contrast for different layer number graphene. The maximum THG efficiency appears at layer number around 30. Two models are used for describing this layer dependent phenomenon and shows absorption plays a key role in THG of multilayer graphene. This work also provides a new imaging technology for graphene detection and identification with better contrast and resolution. U.S. Department of Energy under Contract No. DE-FG 02-04-ER-46157.

Strong guided mode resonant local field enhanced visible harmonic generation in an azo-polymer resonant waveguide grating.

PubMed

Lin, Jian Hung; Tseng, Chun-Yen; Lee, Ching-Ting; Young, Jeff F; Kan, Hung-Chih; Hsu, Chia Chen

2014-02-10

Guided mode resonance (GMR) enhanced second- and third-harmonic generation (SHG and THG) is demonstrated in an azo-polymer resonant waveguide grating (RWG), comprised of a poled azo-polymer layer on top of a textured SU8 substrate with a thin intervening layer of TiO2. Strong SHG and THG outputs are observed by matching either in-coming fundamental- or out-going harmonic-wavelength to the GMR wavelengths of the azo-polymer RWG. Without the azo-polymer coating, pure TiO2 RWGs, do not generate any detectable SHG using a fundamental beam peak intensity of 2 MW/cm(2). Without the textured TiO2 layer, a planar poled azo-polymer layer results in 3650 times less SHG than the full nonlinear RWG structure under identical excitation conditions. Rigorous coupled-wave analysis calculations confirm that this enhancement of the nonlinear conversion is due to strong local electric fields that are generated at the interfaces of the TiO2 and azo-polymer layers when the RWG is excited at resonant wavelengths associated with both SHG and THG conversion processes.

Adaptive nonlinear polynomial neural networks for control of boundary layer/structural interaction

NASA Technical Reports Server (NTRS)

Parker, B. Eugene, Jr.; Cellucci, Richard L.; Abbott, Dean W.; Barron, Roger L.; Jordan, Paul R., III; Poor, H. Vincent

1993-01-01

The acoustic pressures developed in a boundary layer can interact with an aircraft panel to induce significant vibration in the panel. Such vibration is undesirable due to the aerodynamic drag and structure-borne cabin noises that result. The overall objective of this work is to develop effective and practical feedback control strategies for actively reducing this flow-induced structural vibration. This report describes the results of initial evaluations using polynomial, neural network-based, feedback control to reduce flow induced vibration in aircraft panels due to turbulent boundary layer/structural interaction. Computer simulations are used to develop and analyze feedback control strategies to reduce vibration in a beam as a first step. The key differences between this work and that going on elsewhere are as follows: that turbulent and transitional boundary layers represent broadband excitation and thus present a more complex stochastic control scenario than that of narrow band (e.g., laminar boundary layer) excitation; and secondly, that the proposed controller structures are adaptive nonlinear infinite impulse response (IIR) polynomial neural network, as opposed to the traditional adaptive linear finite impulse response (FIR) filters used in most studies to date. The controllers implemented in this study achieved vibration attenuation of 27 to 60 dB depending on the type of boundary layer established by laminar, turbulent, and intermittent laminar-to-turbulent transitional flows. Application of multi-input, multi-output, adaptive, nonlinear feedback control of vibration in aircraft panels based on polynomial neural networks appears to be feasible today. Plans are outlined for Phase 2 of this study, which will include extending the theoretical investigation conducted in Phase 2 and verifying the results in a series of laboratory experiments involving both bum and plate models.

Nonlinear dead water resistance at subcritical speed

NASA Astrophysics Data System (ADS)

Grue, John

2015-08-01

The dead water resistance F 1 = /1 2 C d w ρ S U 2 (ρ fluid density, U ship speed, S wetted body surface, Cdw resistance coefficient) on a ship moving at subcritical speed along the upper layer of a two-layer fluid is calculated by a strongly nonlinear method assuming potential flow in each layer. The ship dimensions correspond to those of the Polar ship Fram. The ship draught, b0, is varied in the range 0.25h0-0.9h0 (h0 the upper layer depth). The calculations show that Cdw/(b0/h0)2 depends on the Froude number only, in the range close to critical speed, Fr = U/c0 ˜ 0.875-1.125 (c0 the linear internal long wave speed), irrespective of the ship draught. The function Cdw/(b0/h0)2 attains a maximum at subcritical Froude number depending on the draught. Maximum Cdw/(b0/h0)2 becomes 0.15 for Fr = 0.76, b0/h0 = 0.9, and 0.16 for Fr = 0.74, b0/h0 = 1, where the latter extrapolated value of the dead water resistance coefficient is about 60 times higher than the frictional drag coefficient and relevant for the historical dead water observations. The nonlinear Cdw significantly exceeds linear theory (Fr < 0.85). The ship generated waves have a wave height comparable to the upper layer depth. Calculations of three-dimensional wave patterns at critical speed compare well to available laboratory experiments. Upstream solitary waves are generated in a wave tank of finite width, when the layer depths differ, causing an oscillation of the force. In a wide ocean, a very wide wave system develops at critical speed. The force approaches a constant value for increasing time.

Analytical and Numerical Modeling of Tsunami Wave Propagation for double layer state in Bore

NASA Astrophysics Data System (ADS)

Yuvaraj, V.; Rajasekaran, S.; Nagarajan, D.

2018-04-01

Tsunami wave enters into the river bore in the landslide. Tsunami wave propagation are described in two-layer states. The velocity and amplitude of the tsunami wave propagation are calculated using the double layer. The numerical and analytical solutions are given for the nonlinear equation of motion of the wave propagation in a bore.

Temporal and Spatial Evolution Characteristics of Disturbance Wave in a Hypersonic Boundary Layer due to Single-Frequency Entropy Disturbance

PubMed Central

Lv, Hongqing; Shi, Jianqiang

2014-01-01

By using a high-order accurate finite difference scheme, direct numerical simulation of hypersonic flow over an 8° half-wedge-angle blunt wedge under freestream single-frequency entropy disturbance is conducted; the generation and the temporal and spatial nonlinear evolution of boundary layer disturbance waves are investigated. Results show that, under the freestream single-frequency entropy disturbance, the entropy state of boundary layer is changed sharply and the disturbance waves within a certain frequency range are induced in the boundary layer. Furthermore, the amplitudes of disturbance waves in the period phase are larger than that in the response phase and ablation phase and the frequency range in the boundary layer in the period phase is narrower than that in these two phases. In addition, the mode competition, dominant mode transformation, and disturbance energy transfer exist among different modes both in temporal and in spatial evolution. The mode competition changes the characteristics of nonlinear evolution of the unstable waves in the boundary layer. The development of the most unstable mode along streamwise relies more on the motivation of disturbance waves in the upstream than that of other modes on this motivation. PMID:25143983

Temporal and spatial evolution characteristics of disturbance wave in a hypersonic boundary layer due to single-frequency entropy disturbance.

PubMed

Wang, Zhenqing; Tang, Xiaojun; Lv, Hongqing; Shi, Jianqiang

2014-01-01

By using a high-order accurate finite difference scheme, direct numerical simulation of hypersonic flow over an 8° half-wedge-angle blunt wedge under freestream single-frequency entropy disturbance is conducted; the generation and the temporal and spatial nonlinear evolution of boundary layer disturbance waves are investigated. Results show that, under the freestream single-frequency entropy disturbance, the entropy state of boundary layer is changed sharply and the disturbance waves within a certain frequency range are induced in the boundary layer. Furthermore, the amplitudes of disturbance waves in the period phase are larger than that in the response phase and ablation phase and the frequency range in the boundary layer in the period phase is narrower than that in these two phases. In addition, the mode competition, dominant mode transformation, and disturbance energy transfer exist among different modes both in temporal and in spatial evolution. The mode competition changes the characteristics of nonlinear evolution of the unstable waves in the boundary layer. The development of the most unstable mode along streamwise relies more on the motivation of disturbance waves in the upstream than that of other modes on this motivation.

Aspect ratio effects on limited scrape-off layer plasma turbulence

NASA Astrophysics Data System (ADS)

Jolliet, Sébastien; Halpern, Federico D.; Loizu, Joaquim; Mosetto, Annamaria; Ricci, Paolo

2014-02-01

The drift-reduced Braginskii model describing turbulence in the tokamak scrape-off layer is written for a general magnetic configuration with a limiter. The equilibrium is then specified for a circular concentric magnetic geometry retaining aspect ratio effects. Simulations are then carried out with the help of the global, flux-driven fluid three-dimensional code GBS [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. Linearly, both simulations and simplified analytical models reveal a stabilization of ballooning modes. Nonlinearly, flux-driven nonlinear simulations give a pressure characteristic length whose trends are correctly captured by the gradient removal theory [Ricci and Rogers, Phys. Plasmas 20, 010702 (2013)], that assumes the profile flattening from the linear modes as the saturation mechanism. More specifically, the linear stabilization of ballooning modes is reflected by a 15% increase in the steady-state pressure gradient obtained from GBS nonlinear simulations when going from an infinite to a realistic aspect ratio.

Learning in the Machine: Random Backpropagation and the Deep Learning Channel.

PubMed

Baldi, Pierre; Sadowski, Peter; Lu, Zhiqin

2018-07-01

Random backpropagation (RBP) is a variant of the backpropagation algorithm for training neural networks, where the transpose of the forward matrices are replaced by fixed random matrices in the calculation of the weight updates. It is remarkable both because of its effectiveness, in spite of using random matrices to communicate error information, and because it completely removes the taxing requirement of maintaining symmetric weights in a physical neural system. To better understand random backpropagation, we first connect it to the notions of local learning and learning channels. Through this connection, we derive several alternatives to RBP, including skipped RBP (SRPB), adaptive RBP (ARBP), sparse RBP, and their combinations (e.g. ASRBP) and analyze their computational complexity. We then study their behavior through simulations using the MNIST and CIFAR-10 bechnmark datasets. These simulations show that most of these variants work robustly, almost as well as backpropagation, and that multiplication by the derivatives of the activation functions is important. As a follow-up, we study also the low-end of the number of bits required to communicate error information over the learning channel. We then provide partial intuitive explanations for some of the remarkable properties of RBP and its variations. Finally, we prove several mathematical results, including the convergence to fixed points of linear chains of arbitrary length, the convergence to fixed points of linear autoencoders with decorrelated data, the long-term existence of solutions for linear systems with a single hidden layer and convergence in special cases, and the convergence to fixed points of non-linear chains, when the derivative of the activation functions is included.

Explosive magnetic reconnection caused by an X-shaped current-vortex layer in a collisionless plasma

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

Hirota, M.; Hattori, Y.; Morrison, P. J.

2015-05-15

A mechanism for explosive magnetic reconnection is investigated by analyzing the nonlinear evolution of a collisionless tearing mode in a two-fluid model that includes the effects of electron inertia and temperature. These effects cooperatively enable a fast reconnection by forming an X-shaped current-vortex layer centered at the reconnection point. A high-resolution simulation of this model for an unprecedentedly small electron skin depth d{sub e} and ion-sound gyroradius ρ{sub s}, satisfying d{sub e}=ρ{sub s}, shows an explosive tendency for nonlinear growth of the tearing mode, where it is newly found that the explosive widening of the X-shaped layer occurs locally aroundmore » the reconnection point with the length of the X shape being shorter than the domain length and the wavelength of the linear tearing mode. The reason for the onset of this locally enhanced reconnection is explained theoretically by developing a novel nonlinear and nonequilibrium inner solution that models the local X-shaped layer, and then matching it to an outer solution that is approximated by a linear tearing eigenmode with a shorter wavelength than the domain length. This theoretical model proves that the local reconnection can release the magnetic energy more efficiently than the global one and the estimated scaling of the explosive growth rate agrees well with the simulation results.« less

Effects of discrete-electrode arrangement on traveling-wave electroosmotic pumping

NASA Astrophysics Data System (ADS)

Liu, Weiyu; Shao, Jinyou; Ren, Yukun; Wu, Yupan; Wang, Chunhui; Ding, Haitao; Jiang, Hongyuan; Ding, Yucheng

2016-09-01

Traveling-wave electroosmotic (TWEO) pumping arises from the action of an imposed traveling-wave (TW) electric field on its own induced charge in the diffuse double layer, which is formed on top of an electrode array immersed in electrolyte solutions. Such a traveling field can be merely realized in practice by a discrete electrode array upon which the corresponding voltages of correct phase are imposed. By employing the theory of linear and weakly nonlinear double-layer charging dynamics, a physical model incorporating both the nonlinear surface capacitance of diffuse layer and Faradaic current injection is developed herein in order to quantify the changes in TWEO pumping performance from a single-mode TW to discrete electrode configuration. Benefiting from the linear analysis, we investigate the influence of using discrete electrode array to create the TW signal on the resulting fluid motion, and several approaches are suggested to improve the pumping performance. In the nonlinear regime, our full numerical analysis considering the intervening isolation spacing indicates that a practical four-phase discrete electrode configuration of equal electrode and gap width exhibits stronger nonlinearity than expected from the idealized pump applied with a single-mode TW in terms of voltage-dependence of the ideal pumping frequency and peak flow rate, though it has a much lower pumping performance. For model validation, pumping of electrolytes by TWEO is achieved over a confocal spiral four-phase electrode array covered by an insulating microchannel; measurement of flow velocity indicates the modified nonlinear theory considering moderate Faradaic conductance is indeed a more accurate physical description of TWEO. These results offer useful guidelines for designing high-performance TWEO microfluidic pumps with discrete electrode array.

Nonlinear Wave Process Hierarchies and the Cyclic Development of Quasi-Ordered Structures in Turbulent Shear Flows.

DTIC Science & Technology

1979-11-01

can be evaluated semi- analitically in both the strongly nonlinear inner (critical layer) region and the weakly nonlinear outer region, reproduce the...experimental evidence of Ref. 8 (Figure 3, stage 3). Whereas the exact s~lutions of the Schridinger equation (Ref. 13) predict that an arbitrary smooth...peaks and valleys, different from the comon rate predicted by linear theory) arise suddenly and at surpris- ingly low disturbance levels [(u’/U 10-2] as

Influence of a density increase on the evolution of the Kelvin-Helmholtz instability and vortices

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

Amerstorfer, U. V.; Erkaev, N. V.; Institute of Computational Modelling, 660036 Krasnoyarsk

2010-07-15

Results of two-dimensional nonlinear numerical simulations of the magnetohydrodynamic Kelvin-Helmholtz instability are presented. A boundary layer of a certain width is assumed, which separates the plasma in the upper layer from the plasma in the lower layer. A special focus is given on the influence of a density increase toward the lower layer. The evolution of the Kelvin-Helmholtz instability can be divided into three different phases, namely, a linear growth phase at the beginning, followed by a nonlinear phase with regular structures of the vortices, and finally, a turbulent phase with nonregular structures. The spatial scales of the vortices aremore » about five times the initial width of the boundary layer. The considered configuration is similar to the situation around unmagnetized planets, where the solar wind (upper plasma layer) streams past the ionosphere (lower plasma layer), and thus the plasma density increases toward the planet. The evolving vortices might detach around the terminator of the planet and eventually so-called plasma clouds might be formed, through which ionospheric material can be lost. For the special case of a Venus-like planet, loss rates are estimated, which are of the order of estimated loss rates from observations at Venus.« less

Anomalous transport in discrete arcs and simulation of double layers in a model auroral circuit

NASA Technical Reports Server (NTRS)

Smith, Robert A.

1987-01-01

The evolution and long-time stability of a double layer (DL) in a discrete auroral arc requires that the parallel current in the arc, which may be considered uniform at the source, be diverted within the arc to charge the flanks of the U-shaped double layer potential structure. A simple model is presented in which this current redistribution is effected by anomalous transport based on electrostatic lower hybrid waves driven by the flank structure itself. This process provides the limiting constraint on the double layer potential. The flank charging may be represented as that of a nonlinear transmission line. A simplified model circuit, in which the transmission line is represented by a nonlinear impedance in parallel with a variable resistor, is incorporated in a one-dimensional simulation model to give the current density at the DL boundaries. Results are presented for the scaling of the DL potential as a function of the width of the arc and the saturation efficiency of the lower hybrid instability mechanism.

Anomalous transport in discrete arcs and simulation of double layers in a model auroral circuit

NASA Technical Reports Server (NTRS)

Smith, Robert A.

1987-01-01

The evolution and long-time stability of a double layer in a discrete auroral arc requires that the parallel current in the arc, which may be considered uniform at the source, be diverted within the arc to charge the flanks of the U-shaped double-layer potential structure. A simple model is presented in which this current re-distribution is effected by anomalous transport based on electrostatic lower hybrid waves driven by the flank structure itself. This process provides the limiting constraint on the double-layer potential. The flank charging may be represented as that of a nonlinear transmission. A simplified model circuit, in which the transmission line is represented by a nonlinear impedance in parallel with a variable resistor, is incorporated in a 1-d simulation model to give the current density at the DL boundaries. Results are presented for the scaling of the DL potential as a function of the width of the arc and the saturation efficiency of the lower hybrid instability mechanism.

APPLICATION OF NEURAL NETWORK ALGORITHMS FOR BPM LINEARIZATION

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

Musson, John C.; Seaton, Chad; Spata, Mike F.

2012-11-01

Stripline BPM sensors contain inherent non-linearities, as a result of field distortions from the pickup elements. Many methods have been devised to facilitate corrections, often employing polynomial fitting. The cost of computation makes real-time correction difficult, particulalry when integer math is utilized. The application of neural-network technology, particularly the multi-layer perceptron algorithm, is proposed as an efficient alternative for electrode linearization. A process of supervised learning is initially used to determine the weighting coefficients, which are subsequently applied to the incoming electrode data. A non-linear layer, known as an activation layer, is responsible for the removal of saturation effects. Implementationmore » of a perceptron in an FPGA-based software-defined radio (SDR) is presented, along with performance comparisons. In addition, efficient calculation of the sigmoidal activation function via the CORDIC algorithm is presented.« less

Effect of temperature degeneracy and Landau quantization on drift solitary waves and double layers

NASA Astrophysics Data System (ADS)

Shan, Shaukat Ali; Haque, Q.

2018-01-01

The linear and nonlinear drift ion acoustic waves have been investigated in an inhomogeneous, magnetized, dense degenerate, and quantized magnetic field plasma. The linear drift ion acoustic wave propagation along with the nonlinear structures like double layers and solitary waves has been found to be strongly dependent on the drift speed, magnetic field quantization parameter β, and the temperature degeneracy. The graphical illustrations show that the frequency of linear waves and the amplitude of the solitary waves increase with the increase in temperature degeneracy and Landau quantization effect, while the amplitude of the double layers decreases with the increase in η and T. The relevance of the present study is pointed out in the plasma environment of fast ignition inertial confinement fusion, the white dwarf stars, and short pulsed petawatt laser technology.

Accessible solitons of fractional dimension

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

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A&M University at Qatar, P.O. Box 23874, Doha; Belić, Milivoj

We demonstrate that accessible solitons described by an extended Schrödinger equation with the Laplacian of fractional dimension can exist in strongly nonlocal nonlinear media. The soliton solutions of the model are constructed by two special functions, the associated Legendre polynomials and the Laguerre polynomials in the fraction-dimensional space. Our results show that these fractional accessible solitons form a soliton family which includes crescent solitons, and asymmetric single-layer and multi-layer necklace solitons. -- Highlights: •Analytic solutions of a fractional Schrödinger equation are obtained. •The solutions are produced by means of self-similar method applied to the fractional Schrödinger equation with parabolic potential.more » •The fractional accessible solitons form crescent, asymmetric single-layer and multilayer necklace profiles. •The model applies to the propagation of optical pulses in strongly nonlocal nonlinear media.« less

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].

A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

PubMed

Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

2016-01-01

This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

On a generalized laminate theory with application to bending, vibration, and delamination buckling in composite laminates

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

Barbero, E.J.

1989-01-01

In this study, a computational model for accurate analysis of composite laminates and laminates with including delaminated interfaces is developed. An accurate prediction of stress distributions, including interlaminar stresses, is obtained by using the Generalized Laminate Plate Theory of Reddy in which layer-wise linear approximation of the displacements through the thickness is used. Analytical as well as finite-element solutions of the theory are developed for bending and vibrations of laminated composite plates for the linear theory. Geometrical nonlinearity, including buckling and postbuckling are included and used to perform stress analysis of laminated plates. A general two dimensional theory of laminatedmore » cylindrical shells is also developed in this study. Geometrical nonlinearity and transverse compressibility are included. Delaminations between layers of composite plates are modelled by jump discontinuity conditions at the interfaces. The theory includes multiple delaminations through the thickness. Geometric nonlinearity is included to capture layer buckling. The strain energy release rate distribution along the boundary of delaminations is computed by a novel algorithm. The computational models presented herein are accurate for global behavior and particularly appropriate for the study of local effects.« less

Nonlinear Wave Chaos and the Random Coupling Model

NASA Astrophysics Data System (ADS)

Zhou, Min; Ott, Edward; Antonsen, Thomas M.; Anlage, Steven

The Random Coupling Model (RCM) has been shown to successfully predict the statistical properties of linear wave chaotic cavities in the highly over-moded regime. It is of interest to extend the RCM to strongly nonlinear systems. To introduce nonlinearity, an active nonlinear circuit is connected to two ports of the wave chaotic 1/4-bowtie cavity. The active nonlinear circuit consists of a frequency multiplier, an amplifier and several passive filters. It acts to double the input frequency in the range from 3.5 GHz to 5 GHz, and operates for microwaves going in only one direction. Measurements are taken between two additional ports of the cavity and we measure the statistics of the second harmonic voltage over an ensemble of realizations of the scattering system. We developed an RCM-based model of this system as two chaotic cavities coupled by means of a nonlinear transfer function. The harmonics received at the output are predicted to be the product of three statistical quantities that describe the three elements correspondingly. Statistical results from simulation, RCM-based modeling, and direct experimental measurements will be compared. ONR under Grant No. N000141512134, AFOSR under COE Grant FA9550-15-1-0171,0 and the Maryland Center for Nanophysics and Advanced Materials.

Shoaling of nonlinear internal waves in Massachusetts Bay

USGS Publications Warehouse

Scotti, A.; Beardsley, R.C.; Butman, B.; Pineda, J.

2008-01-01

The shoaling of the nonlinear internal tide in Massachusetts Bay is studied with a fully nonlinear and nonhydrostatic model. The results are compared with current and temperature observations obtained during the August 1998 Massachusetts Bay Internal Wave Experiment and observations from a shorter experiment which took place in September 2001. The model shows how the approaching nonlinear undular bore interacts strongly with a shoaling bottom, offshore of where KdV theory predicts polarity switching should occur. It is shown that the shoaling process is dominated by nonlinearity, and the model results are interpreted with the aid of a two-layer nonlinear but hydrostatic model. After interacting with the shoaling bottom, the undular bore emerges on the shallow shelf inshore of the 30-m isobath as a nonlinear internal tide with a range of possible shapes, all of which are found in the available observational record. Copyright 2008 by the American Geophysical Union.

Self-excitation of a nonlinear scalar field in a random medium

PubMed Central

Zeldovich, Ya. B.; Molchanov, S. A.; Ruzmaikin, A. A.; Sokoloff, D. D.

1987-01-01

We discuss the evolution in time of a scalar field under the influence of a random potential and diffusion. The cases of a short-correlation in time and of stationary potentials are considered. In a linear approximation and for sufficiently weak diffusion, the statistical moments of the field grow exponentially in time at growth rates that progressively increase with the order of the moment; this indicates the intermittent nature of the field. Nonlinearity halts this growth and in some cases can destroy the intermittency. However, in many nonlinear situations the intermittency is preserved: high, persistent peaks of the field exist against the background of a smooth field distribution. These widely spaced peaks may make a major contribution to the average characteristics of the field. PMID:16593872

The effect of reactive ion etch (RIE) process conditions on ReRAM device performance

NASA Astrophysics Data System (ADS)

Beckmann, K.; Holt, J.; Olin-Ammentorp, W.; Alamgir, Z.; Van Nostrand, J.; Cady, N. C.

2017-09-01

The recent surge of research on resistive random access memory (ReRAM) devices has resulted in a wealth of different materials and fabrication approaches. In this work, we describe the performance implications of utilizing a reactive ion etch (RIE) based process to fabricate HfO2 based ReRAM devices, versus a more unconventional shadow mask fabrication approach. The work is the result of an effort to increase device yield and reduce individual device size. Our results show that choice of RIE etch gas (SF6 versus CF4) is critical for defining the post-etch device profile (cross-section), and for tuning the removal of metal layers used as bottom electrodes in the ReRAM device stack. We have shown that etch conditions leading to a tapered profile for the device stack cause poor electrical performance, likely due to metal re-deposition during etching, and damage to the switching layer. These devices exhibit nonlinear I-V during the low resistive state, but this could be improved to linear behavior once a near-vertical etch profile was achieved. Device stacks with vertical etch profiles also showed an increase in forming voltage, reduced switching variability and increased endurance.

3-DOF Force-Sensing Motorized Micro-Forceps for Robot-Assisted Vitreoretinal Surgery

PubMed Central

Gonenc, Berk; Chamani, Alireza; Handa, James; Gehlbach, Peter; Taylor, Russell H.; Iordachita, Iulian

2017-01-01

In vitreoretinal surgery, membrane peeling is a prototypical task where a layer of fibrous tissue is delaminated off the retina with a micro-forceps by applying very fine forces that are mostly imperceptible to the surgeon. Previously we developed sensitized ophthalmic surgery tools based on fiber Bragg grating (FBG) strain sensors, which were shown to precisely detect forces at the instrument’s tip in two degrees of freedom perpendicular to the tool axis. This paper presents a new design that employs an additional sensor to capture also the tensile force along the tool axis. The grasping functionality is provided via a compact motorized unit. To compute forces, we investigate two distinct fitting methods: a linear regression and a nonlinear fitting based on second-order Bernstein polynomials. We carry out experiments to test the repeatability of sensor outputs, calibrate the sensor and validate its performance. Results demonstrate sensor wavelength repeatability within 2 pm. Although the linear method provides sufficient accuracy in measuring transverse forces, in the axial direction it produces a root mean square (rms) error over 3 mN even for a confined magnitude and direction of forces. On the other hand, the nonlinear method provides a more consistent and accurate measurement of both the transverse and axial forces for the entire force range (0–25 mN). Validation including random samples shows that our tool with the nonlinear force computation method can predict 3-D forces with an rms error under 0.15 mN in the transverse plane and within 2 mN accuracy in the axial direction. PMID:28736508

Statistically accurate low-order models for uncertainty quantification in turbulent dynamical systems.

PubMed

Sapsis, Themistoklis P; Majda, Andrew J

2013-08-20

A framework for low-order predictive statistical modeling and uncertainty quantification in turbulent dynamical systems is developed here. These reduced-order, modified quasilinear Gaussian (ROMQG) algorithms apply to turbulent dynamical systems in which there is significant linear instability or linear nonnormal dynamics in the unperturbed system and energy-conserving nonlinear interactions that transfer energy from the unstable modes to the stable modes where dissipation occurs, resulting in a statistical steady state; such turbulent dynamical systems are ubiquitous in geophysical and engineering turbulence. The ROMQG method involves constructing a low-order, nonlinear, dynamical system for the mean and covariance statistics in the reduced subspace that has the unperturbed statistics as a stable fixed point and optimally incorporates the indirect effect of non-Gaussian third-order statistics for the unperturbed system in a systematic calibration stage. This calibration procedure is achieved through information involving only the mean and covariance statistics for the unperturbed equilibrium. The performance of the ROMQG algorithm is assessed on two stringent test cases: the 40-mode Lorenz 96 model mimicking midlatitude atmospheric turbulence and two-layer baroclinic models for high-latitude ocean turbulence with over 125,000 degrees of freedom. In the Lorenz 96 model, the ROMQG algorithm with just a single mode captures the transient response to random or deterministic forcing. For the baroclinic ocean turbulence models, the inexpensive ROMQG algorithm with 252 modes, less than 0.2% of the total, captures the nonlinear response of the energy, the heat flux, and even the one-dimensional energy and heat flux spectra.

Nonlinear evolution of Mack modes in a hypersonic boundary layer

NASA Astrophysics Data System (ADS)

Chokani, Ndaona

2005-01-01

In hypersonic boundary layer flows the nonlinear disturbance evolution occurs relatively slowly over a very long length scale and has a profound effect on boundary layer transition. In the case of low-level freestream disturbances and negligible surface roughness, the transition is due to the modal growth of exponentially growing Mack modes that are destabilized by wall cooling. Cross-bicoherence measurements, derived from hot-wire data acquired in a quiet hypersonic tunnel, are used to identify and quantify phase-locked, quadratic sum and difference interactions involving the Mack modes. In the early stages of the nonlinear disturbance evolution, cross-bicoherence measurements indicate that the energy exchange between the Mack mode and the mean flow first occurs to broaden the sidebands; this is immediately followed by a sum interaction of the Mack mode to generate the first harmonic. In the next stages of the nonlinear disturbance evolution, there is a difference interaction of the first harmonic, which is also thought to contribute to the mean flow distortion. This difference interaction, in the latter stages, is also accompanied by a difference interaction between Mack mode and first harmonic, and a sum interaction, which forces the second harmonic. Analysis using the digital complex demodulation technique, shows that the low-frequency, phase-locked interaction that is identified in the cross bicoherence when the Mack mode and first harmonic have large amplitudes, arises due to the amplitude modulation of Mack mode and first harmonic.

Stochastic theory of polarized light in nonlinear birefringent media: An application to optical rotation

NASA Astrophysics Data System (ADS)

Tsuchida, Satoshi; Kuratsuji, Hiroshi

2018-05-01

A stochastic theory is developed for the light transmitting the optical media exhibiting linear and nonlinear birefringence. The starting point is the two-component nonlinear Schrödinger equation (NLSE). On the basis of the ansatz of “soliton” solution for the NLSE, the evolution equation for the Stokes parameters is derived, which turns out to be the Langevin equation by taking account of randomness and dissipation inherent in the birefringent media. The Langevin equation is converted to the Fokker-Planck (FP) equation for the probability distribution by employing the technique of functional integral on the assumption of the Gaussian white noise for the random fluctuation. The specific application is considered for the optical rotation, which is described by the ellipticity (third component of the Stokes parameters) alone: (i) The asymptotic analysis is given for the functional integral, which leads to the transition rate on the Poincaré sphere. (ii) The FP equation is analyzed in the strong coupling approximation, by which the diffusive behavior is obtained for the linear and nonlinear birefringence. These would provide with a basis of statistical analysis for the polarization phenomena in nonlinear birefringent media.

Nonlinear acoustics in cicada mating calls enhance sound propagation.

PubMed

Hughes, Derke R; Nuttall, Albert H; Katz, Richard A; Carter, G Clifford

2009-02-01

An analysis of cicada mating calls, measured in field experiments, indicates that the very high levels of acoustic energy radiated by this relatively small insect are mainly attributed to the nonlinear characteristics of the signal. The cicada emits one of the loudest sounds in all of the insect population with a sound production system occupying a physical space typically less than 3 cc. The sounds made by tymbals are amplified by the hollow abdomen, functioning as a tuned resonator, but models of the signal based solely on linear techniques do not fully account for a sound radiation capability that is so disproportionate to the insect's size. The nonlinear behavior of the cicada signal is demonstrated by combining the mutual information and surrogate data techniques; the results obtained indicate decorrelation when the phase-randomized and non-phase-randomized data separate. The Volterra expansion technique is used to fit the nonlinearity in the insect's call. The second-order Volterra estimate provides further evidence that the cicada mating calls are dominated by nonlinear characteristics and also suggests that the medium contributes to the cicada's efficient sound propagation. Application of the same principles has the potential to improve radiated sound levels for sonar applications.

Optical wave turbulence and the condensation of light

NASA Astrophysics Data System (ADS)

Bortolozzo, Umberto; Laurie, Jason; Nazarenko, Sergey; Residori, Stefania

2009-11-01

In an optical experiment, we report a wave turbulence regime that, starting with weakly nonlinear waves with randomized phases, shows an inverse cascade of photons towards the lowest wavenumbers. We show that the cascade is induced by a six-wave resonant interaction process and is characterized by increasing nonlinearity. At low wavenumbers the nonlinearity becomes strong and leads to modulational instability developing into solitons, whose number is decreasing further along the beam.

Incorporation of nonlinear thermorheological complexity into the phenomenologies of structural relaxation.

PubMed

Hodge, Ian M

2005-09-22

A distribution of activation energies is introduced into the nonlinear Adam-Gibbs ("Hodge-Scherer") phenomenology for structural relaxation. The resulting dependencies of the stretched exponential beta parameter on thermodynamic temperature and fictive temperature (nonlinear thermorheological complexity) are derived. No additional adjustable parameters are introduced, and contact is made with the predictions of the random first-order transition theory of aging of Lubchenko and Wolynes [J. Chem. Physics121, 2852 (2004)].

Detuned resonances of Tollmien-Schlichting waves in an airfoil boundary layer: Experiment, theory, and direct numerical simulation

NASA Astrophysics Data System (ADS)

Würz, W.; Sartorius, D.; Kloker, M.; Borodulin, V. I.; Kachanov, Y. S.; Smorodsky, B. V.

2012-09-01

Transition prediction in two-dimensional laminar boundary layers developing on airfoil sections at subsonic speeds and very low turbulence levels is still a challenge. The commonly used semi-empirical prediction tools are mainly based on linear stability theory and do not account for nonlinear effects present unavoidably starting with certain stages of transition. One reason is the lack of systematic investigations of the weakly nonlinear stages of transition, especially of the strongest interactions of the instability modes predominant in non-self-similar boundary layers. The present paper is devoted to the detailed experimental, numerical, and theoretical study of weakly nonlinear subharmonic resonances of Tollmien-Schlichting waves in an airfoil boundary layer, representing main candidates for the strongest mechanism of these initial nonlinear stages. The experimental approach is based on phase-locked hot-wire measurements under controlled disturbance conditions using a new disturbance source being capable to produce well-defined, complex wave compositions in a wide range of streamwise and spanwise wave numbers. The tests were performed in a low-turbulence wind tunnel at a chord Reynolds number of Re = 0.7 × 106. Direct numerical simulations (DNS) were utilized to provide a detailed comparison for the test cases. The results of weakly nonlinear theory (WNT) enabled a profound understanding of the underlying physical mechanisms observed in the experiments and DNS. The data obtained in experiment, DNS and WNT agree basically and provide a high degree of reliability of the results. Interactions occurring between components of various initial frequency-wavenumber spectra of instability waves are investigated by systematic variation of parameters. It is shown that frequency-detuned and spanwise-wavenumber-detuned subharmonic-type resonant interactions have an extremely large spectral width. Similar to results obtained for self-similar base flows it is found that the amplification factors in the frequency-detuned resonances can be even higher than in tuned cases, in spite of the strong base-flow non-self-similarity. An explanation of this unusual phenomenon is found based on the theoretical analysis and comparison of experimental, theoretical, and DNS data.

Contributions to the simulation of turbulence

NASA Technical Reports Server (NTRS)

Dutton, J. A.; Kerman, B. R.; Petersen, E. L.

1976-01-01

The simulation modeling of turbulence in the boundary layer in consolidated in terms of boundary layer similarity principles and empirical results. The modeling is extended for some aspects of the nonlinear and non-Gaussian structure of the turbulence. Properties of the discrete gust form structure of the modeled turbulence are identified.

Multi-Layered Feedforward Neural Networks for Image Segmentation

DTIC Science & Technology

1991-12-01

the Gram-Schmidt Network ...................... 80 xi Preface WILLIAM SHAKESPEARE 1564-1616 Is this a dagger which I see before me, The handle toward...any input-output mapping with a single hidden layer of non-linear nodes, the result may be like proving that a monkey could write Hamlet . Certainly it

Super-Joule heating in graphene and silver nanowire network

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

Maize, Kerry; Das, Suprem R.; Sadeque, Sajia

Transistors, sensors, and transparent conductors based on randomly assembled nanowire networks rely on multi-component percolation for unique and distinctive applications in flexible electronics, biochemical sensing, and solar cells. While conduction models for 1-D and 1-D/2-D networks have been developed, typically assuming linear electronic transport and self-heating, the model has not been validated by direct high-resolution characterization of coupled electronic pathways and thermal response. In this letter, we show the occurrence of nonlinear “super-Joule” self-heating at the transport bottlenecks in networks of silver nanowires and silver nanowire/single layer graphene hybrid using high resolution thermoreflectance (TR) imaging. TR images at the microscopicmore » self-heating hotspots within nanowire network and nanowire/graphene hybrid network devices with submicron spatial resolution are used to infer electrical current pathways. The results encourage a fundamental reevaluation of transport models for network-based percolating conductors.« less

A Novel Extreme Learning Control Framework of Unmanned Surface Vehicles.

PubMed

Wang, Ning; Sun, Jing-Chao; Er, Meng Joo; Liu, Yan-Cheng

2016-05-01

In this paper, an extreme learning control (ELC) framework using the single-hidden-layer feedforward network (SLFN) with random hidden nodes for tracking an unmanned surface vehicle suffering from unknown dynamics and external disturbances is proposed. By combining tracking errors with derivatives, an error surface and transformed states are defined to encapsulate unknown dynamics and disturbances into a lumped vector field of transformed states. The lumped nonlinearity is further identified accurately by an extreme-learning-machine-based SLFN approximator which does not require a priori system knowledge nor tuning input weights. Only output weights of the SLFN need to be updated by adaptive projection-based laws derived from the Lyapunov approach. Moreover, an error compensator is incorporated to suppress approximation residuals, and thereby contributing to the robustness and global asymptotic stability of the closed-loop ELC system. Simulation studies and comprehensive comparisons demonstrate that the ELC framework achieves high accuracy in both tracking and approximation.

The Soft Rock Socketed Monopile with Creep Effects - A Reliability Approach based on Wavelet Neural Networks

NASA Astrophysics Data System (ADS)

Kozubal, Janusz; Tomanovic, Zvonko; Zivaljevic, Slobodan

2016-09-01

In the present study the numerical model of the pile embedded in marl described by a time dependent model, based on laboratory tests, is proposed. The solutions complement the state of knowledge of the monopile loaded by horizontal force in its head with respect to its random variability values in time function. The investigated reliability problem is defined by the union of failure events defined by the excessive horizontal maximal displacement of the pile head in each periods of loads. Abaqus has been used for modeling of the presented task with a two layered viscoplastic model for marl. The mechanical parameters for both parts of model: plastic and rheological were calibrated based on the creep laboratory test results. The important aspect of the problem is reliability analysis of a monopile in complex environment under random sequences of loads which help understanding the role of viscosity in nature of rock basis constructions. Due to the lack of analytical solutions the computations were done by the method of response surface in conjunction with wavelet neural network as a method recommended for time sequences process and description of nonlinear phenomenon.

Double-Diffusive Convection at Low Prandtl Number

NASA Astrophysics Data System (ADS)

Garaud, Pascale

2018-01-01

This work reviews present knowledge of double-diffusive convection at low Prandtl number obtained using direct numerical simulations, in both the fingering regime and the oscillatory regime. Particular emphasis is given to modeling the induced turbulent mixing and its impact in various astrophysical applications. The nonlinear saturation of fingering convection at low Prandtl number usually drives small-scale turbulent motions whose transport properties can be predicted reasonably accurately using a simple semi-analytical model. In some instances, large-scale internal gravity waves can be excited by a collective instability and eventually cause layering. The nonlinear saturation of oscillatory double-diffusive convection exhibits much more complex behavior. Weakly stratified systems always spontaneously transition into layered convection associated with very efficient mixing. More strongly stratified systems remain dominated by weak wave turbulence unless they are initialized into a layered state. The effects of rotation, shear, lateral gradients, and magnetic fields are briefly discussed.

Nonlinear interaction of an intense radio wave with ionospheric D/E layer plasma

NASA Astrophysics Data System (ADS)

Sodha, Mahendra Singh; Agarwal, Sujeet Kumar

2018-05-01

This paper considers the nonlinear interaction of an intense electromagnetic wave with the D/E layer plasma in the ionosphere. A simultaneous solution of the electromagnetic wave equation and the equations describing the kinetics of D/E layer plasma is obtained; the phenomenon of ohmic heating of electrons by the electric field of the wave causes enhanced collision frequency and ionization of neutral species. Electron temperature dependent recombination of electrons with ions, electron attachment to O 2 molecules, and detachment of electrons from O2 - ions has also been taken into account. The dependence of the plasma parameters on the square of the electric vector of the wave E0 2 has been evaluated for three ionospheric heights (viz., 90, 100, and 110 km) corresponding to the mid-latitude mid-day ionosphere and discussed; these results are used to investigate the horizontal propagation of an intense radio wave at these heights.

Multi-layer holographic bifurcative neural network system for real-time adaptive EOS data analysis

NASA Technical Reports Server (NTRS)

Liu, Hua-Kuang; Huang, K. S.; Diep, J.

1993-01-01

Optical data processing techniques have the inherent advantage of high data throughout, low weight and low power requirements. These features are particularly desirable for onboard spacecraft in-situ real-time data analysis and data compression applications. the proposed multi-layer optical holographic neural net pattern recognition technique will utilize the nonlinear photorefractive devices for real-time adaptive learning to classify input data content and recognize unexpected features. Information can be stored either in analog or digital form in a nonlinear photofractive device. The recording can be accomplished in time scales ranging from milliseconds to microseconds. When a system consisting of these devices is organized in a multi-layer structure, a feedforward neural net with bifurcating data classification capability is formed. The interdisciplinary research will involve the collaboration with top digital computer architecture experts at the University of Southern California.

Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence

PubMed Central

2017-01-01

Phase relations between specific scales in a turbulent boundary layer are studied here by highlighting the associated nonlinear scale interactions in the flow. This is achieved through an experimental technique that allows for targeted forcing of the flow through the use of a dynamic wall perturbation. Two distinct large-scale modes with well-defined spatial and temporal wavenumbers were simultaneously forced in the boundary layer, and the resulting nonlinear response from their direct interactions was isolated from the turbulence signal for the study. This approach advances the traditional studies of large- and small-scale interactions in wall turbulence by focusing on the direct interactions between scales with triadic wavenumber consistency. The results are discussed in the context of modelling high Reynolds number wall turbulence. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’. PMID:28167576

Nonlinear Autoregressive Exogenous modeling of a large anaerobic digester producing biogas from cattle waste.

PubMed

Dhussa, Anil K; Sambi, Surinder S; Kumar, Shashi; Kumar, Sandeep; Kumar, Surendra

2014-10-01

In waste-to-energy plants, there is every likelihood of variations in the quantity and characteristics of the feed. Although intermediate storage tanks are used, but many times these are of inadequate capacity to dampen the variations. In such situations an anaerobic digester treating waste slurry operates under dynamic conditions. In this work a special type of dynamic Artificial Neural Network model, called Nonlinear Autoregressive Exogenous model, is used to model the dynamics of anaerobic digesters by using about one year data collected on the operating digesters. The developed model consists of two hidden layers each having 10 neurons, and uses 18days delay. There are five neurons in input layer and one neuron in output layer for a day. Model predictions of biogas production rate are close to plant performance within ±8% deviation. Copyright © 2014 Elsevier Ltd. All rights reserved.

A nonlinear investigation of the stationary modes of instability of the three-dimensional compressible boundary layer due to a rotating disc

NASA Technical Reports Server (NTRS)

Seddougui, Sharon O.

1989-01-01

The effects of compressibility on a stationary mode of instability of the 3-D boundary layer due to a rotating disc are investigated. The aim is to determine whether this mode will be important in the finite amplitude destabilization of the boundary layer. This stationary mode is characterized by the effective velocity profile having zero shear stress at the wall. Triple-deck solutions are presented for an adiabatic wall and an isothermal wall. It is found that this stationary mode is only possible over a finite range of Mach numbers. Asymptotic solutions are obtained which describe the structure of the wavenumber and the orientation of these modes as functions of the local Mach number. The effects of nonlinearity are investigated allowing the finite amplitude growth of a disturbance close to the neutral location to be described.

A Nonlinear Viscoelastic Model for Ceramics at High Temperatures

NASA Technical Reports Server (NTRS)

Powers, Lynn M.; Panoskaltsis, Vassilis P.; Gasparini, Dario A.; Choi, Sung R.

2002-01-01

High-temperature creep behavior of ceramics is characterized by nonlinear time-dependent responses, asymmetric behavior in tension and compression, and nucleation and coalescence of voids leading to creep rupture. Moreover, creep rupture experiments show considerable scatter or randomness in fatigue lives of nominally equal specimens. To capture the nonlinear, asymmetric time-dependent behavior, the standard linear viscoelastic solid model is modified. Nonlinearity and asymmetry are introduced in the volumetric components by using a nonlinear function similar to a hyperbolic sine function but modified to model asymmetry. The nonlinear viscoelastic model is implemented in an ABAQUS user material subroutine. To model the random formation and coalescence of voids, each element is assigned a failure strain sampled from a lognormal distribution. An element is deleted when its volumetric strain exceeds its failure strain. Element deletion has been implemented within ABAQUS. Temporal increases in strains produce a sequential loss of elements (a model for void nucleation and growth), which in turn leads to failure. Nonlinear viscoelastic model parameters are determined from uniaxial tensile and compressive creep experiments on silicon nitride. The model is then used to predict the deformation of four-point bending and ball-on-ring specimens. Simulation is used to predict statistical moments of creep rupture lives. Numerical simulation results compare well with results of experiments of four-point bending specimens. The analytical model is intended to be used to predict the creep rupture lives of ceramic parts in arbitrary stress conditions.

A nonlinear q-voter model with deadlocks on the Watts-Strogatz graph

NASA Astrophysics Data System (ADS)

Sznajd-Weron, Katarzyna; Michal Suszczynski, Karol

2014-07-01

We study the nonlinear $q$-voter model with deadlocks on a Watts-Strogats graph. Using Monte Carlo simulations, we obtain so called exit probability and exit time. We determine how network properties, such as randomness or density of links influence exit properties of a model.

An Examination of the Utility of Non-Linear Dynamics Techniques for Analyzing Human Information Behaviors.

ERIC Educational Resources Information Center

Snyder, Herbert; Kurtze, Douglas

1992-01-01

Discusses the use of chaos, or nonlinear dynamics, for investigating computer-mediated communication. A comparison between real, human-generated data from a computer network and similarly constructed random-generated data is made, and mathematical procedures for determining chaos are described. (seven references) (LRW)

Local Influence Analysis of Nonlinear Structural Equation Models

ERIC Educational Resources Information Center

Lee, Sik-Yum; Tang, Nian-Sheng

2004-01-01

By regarding the latent random vectors as hypothetical missing data and based on the conditional expectation of the complete-data log-likelihood function in the EM algorithm, we investigate assessment of local influence of various perturbation schemes in a nonlinear structural equation model. The basic building blocks of local influence analysis…

The development of the deterministic nonlinear PDEs in particle physics to stochastic case

NASA Astrophysics Data System (ADS)

Abdelrahman, Mahmoud A. E.; Sohaly, M. A.

2018-06-01

In the present work, accuracy method called, Riccati-Bernoulli Sub-ODE technique is used for solving the deterministic and stochastic case of the Phi-4 equation and the nonlinear Foam Drainage equation. Also, the control on the randomness input is studied for stability stochastic process solution.

Fiber-Type Random Laser Based on a Cylindrical Waveguide with a Disordered Cladding Layer.

PubMed

Zhang, Wei Li; Zheng, Meng Ya; Ma, Rui; Gong, Chao Yang; Yang, Zhao Ji; Peng, Gang Ding; Rao, Yun Jiang

2016-05-25

This letter reports a fiber-type random laser (RL) which is made from a capillary coated with a disordered layer at its internal surface and filled with a gain (laser dye) solution in the core region. This fiber-type optical structure, with the disordered layer providing randomly scattered light into the gain region and the cylindrical waveguide providing confinement of light, assists the formation of random lasing modes and enables a flexible and efficient way of making random lasers. We found that the RL is sensitive to laser dye concentration in the core region and there exists a fine exponential relationship between the lasing intensity and particle concentration in the gain solution. The proposed structure could be a fine platform of realizing random lasing and random lasing based sensing.

Random attractor of non-autonomous stochastic Boussinesq lattice system

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

Zhao, Min, E-mail: zhaomin1223@126.com; Zhou, Shengfan, E-mail: zhoushengfan@yahoo.com

2015-09-15

In this paper, we first consider the existence of tempered random attractor for second-order non-autonomous stochastic lattice dynamical system of nonlinear Boussinesq equations effected by time-dependent coupled coefficients and deterministic forces and multiplicative white noise. Then, we establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.

Wave phenomena in a high Reynolds number compressible boundary layer

NASA Technical Reports Server (NTRS)

Bayliss, A.; Maestrello, L.; Parikh, P.; Turkel, E.

1985-01-01

Growth of unstable disturbances in a high Reynolds number compressible boundary layer is numerically simulated. Localized periodic surface heating and cooling as a means of active control of these disturbances is studied. It is shown that compressibility in itself stabilizes the flow but at a lower Mach number, significant nonlinear distortions are produced. Phase cancellation is shown to be an effective mechanism for active boundary layer control.

Elastic solitons in delaminated bars: splitting leads to fission

NASA Astrophysics Data System (ADS)

Samsonov, A. M.; Dreiden, G. V.; Khusnutdinova, K. R.; Semenova, I. V.

2008-06-01

Recent theoretical and successful experimental studies confirmed existence and demonstrated main properties of bulk strain solitary waves in nonlinearly elastic solid wave guides. Our current research is devoted to nonlinear wave processes in layered elastic wave guides with inhomogeneities modelling delamination. We present first theoretical and experimental results showing the influence of delamination on the parameters of the longitudinal strain solitary wave.

Improving accuracy of electrochemical capacitance and solvation energetics in first-principles calculations

NASA Astrophysics Data System (ADS)

Sundararaman, Ravishankar; Letchworth-Weaver, Kendra; Schwarz, Kathleen A.

2018-04-01

Reliable first-principles calculations of electrochemical processes require accurate prediction of the interfacial capacitance, a challenge for current computationally efficient continuum solvation methodologies. We develop a model for the double layer of a metallic electrode that reproduces the features of the experimental capacitance of Ag(100) in a non-adsorbing, aqueous electrolyte, including a broad hump in the capacitance near the potential of zero charge and a dip in the capacitance under conditions of low ionic strength. Using this model, we identify the necessary characteristics of a solvation model suitable for first-principles electrochemistry of metal surfaces in non-adsorbing, aqueous electrolytes: dielectric and ionic nonlinearity, and a dielectric-only region at the interface. The dielectric nonlinearity, caused by the saturation of dipole rotational response in water, creates the capacitance hump, while ionic nonlinearity, caused by the compactness of the diffuse layer, generates the capacitance dip seen at low ionic strength. We show that none of the previously developed solvation models simultaneously meet all these criteria. We design the nonlinear electrochemical soft-sphere solvation model which both captures the capacitance features observed experimentally and serves as a general-purpose continuum solvation model.

Clinical Nonlinear Laser Imaging of Human Skin: A Review

PubMed Central

Pavone, Francesco Saverio

2014-01-01

Nonlinear optical microscopy has the potential of being used in vivo as a noninvasive imaging modality for both epidermal and dermal imaging. This paper reviews the capabilities of nonlinear microscopy as a noninvasive high-resolution tool for clinical skin inspection. In particular, we show that two-photon fluorescence microscopy can be used as a diagnostic tool for characterizing epidermal layers by means of a morphological examination. Additional functional information on the metabolic state of cells can be provided by measuring the fluorescence decay of NADH. This approach allows differentiating epidermal layers having different structural and cytological features and has the potential of diagnosing pathologies in a very early stage. Regarding therapy follow-up, we demonstrate that nonlinear microscopy could be successfully used for monitoring the effect of a treatment. In particular, combined two-photon fluorescence and second-harmonic generation microscopy were used in vivo for monitoring collagen remodeling after microablative fractional laser resurfacing and for quantitatively monitoring psoriasis on the basis of the morphology of epidermal cells and dermal papillae. We believe that the described microscopic modalities could find in the near future a stable place in a clinical dermatological setting for quantitative diagnostic purposes and as a monitoring method for various treatments. PMID:25250337

Numerical Study of Nonlinear Structures of Locally Excited Marangoni Convection in the Long-Wave Approximation

NASA Astrophysics Data System (ADS)

Wertgeim, Igor I.

2018-02-01

We investigate stationary and non-stationary solutions of nonlinear equations of the long-wave approximation for the Marangoni convection caused by a localized source of heat or a surface active impurity (surfactant) in a thin horizontal layer of a viscous incompressible fluid with a free surface. The distribution of heat or concentration flux is determined by the uniform vertical gradient of temperature or impurity concentration, distorted by the imposition of a slightly inhomogeneous heating or of surfactant, localized in the horizontal plane. The lower boundary of the layer is considered thermally insulated or impermeable, whereas the upper boundary is free and deformable. The equations obtained in the long-wave approximation are formulated in terms of the amplitudes of the temperature distribution or impurity concentration, deformation of the surface, and vorticity. For a simplification of the problem, a sequence of nonlinear equations is obtained, which in the simplest form leads to a nonlinear Schrödinger equation with a localized potential. The basic state of the system, its dependence on the parameters and stability are investigated. For stationary solutions localized in the region of the surface tension inhomogeneity, domains of parameters corresponding to different spatial patterns are delineated.

Influence of heating rate on the condensational instability. [in outer layers of solar atmosphere

NASA Technical Reports Server (NTRS)

Dahlburg, R. B.; Mariska, J. T.

1988-01-01

Analysis and numerical simulation are used to determine the effect that various heating rates have on the linear and nonlinear evolution of a typical plasma within a solar magnetic flux tube subject to the condensational instability. It is found that linear stability depends strongly on the heating rate. The results of numerical simulations of the nonlinear evolution of the condensational instability in a solar magnetic flux tube are presented. Different heating rates lead to quite different nonlinear evolutions, as evidenced by the behavior of the global internal energy.

Optical nonlinearity in gelatin layer film containing Au nanoparticles

NASA Astrophysics Data System (ADS)

Hirose, Tomohiro; Arisawa, Michiko; Omatsu, Takashige; Kuge, Ken'ichi; Hasegawa, Akira; Tateda, Mitsuhiro

2002-09-01

We demonstrate a novel technique to fabricate a gelatin film containing Au-nano-particles. The technique is based on silver halide photographic development. We investigated third-order non-linearity of the film by forward-four-wave-mixing technique. Peak absorption appeared at the wavelength of 560nm. Self-diffraction by the use of third order nonlinear grating formed by intense pico-second pulses was observed. Experimental diffraction efficiency was proportional to the square of the pump intensity. Third-order susceptibility c(3) of the film was estimated to be 1.8?~10^-7esu.

Simulation of nonlinear convective thixotropic liquid with Cattaneo-Christov heat flux

NASA Astrophysics Data System (ADS)

Zubair, M.; Waqas, M.; Hayat, T.; Ayub, M.; Alsaedi, A.

2018-03-01

In this communication we utilized a modified Fourier approach featuring thermal relaxation effect in nonlinear convective flow by a vertical exponentially stretchable surface. Temperature-dependent thermal conductivity describes the heat transfer process. Thixotropic liquid is modeled. Convergent local similar solutions by homotopic approach are obtained. Graphical results for emerging parameters of interest are analyzed. Skin friction is calculated and interpreted. Consideration of larger local buoyancy and nonlinear convection parameters yields an enhancement in velocity distribution. Temperature and thermal layer thickness are reduced for larger thermal relaxation factor.

Ionically Paired Layer-by-Layer Hydrogels: Water and Polyelectrolyte Uptake Controlled by Deposition Time

DOE PAGES

Selin, Victor; Ankner, John Francis; Sukhishvili, Svetlana

2018-01-11

Despite intense recent interest in weakly bound nonlinear (“exponential”) multilayers, the underlying structure-property relationships of these films are still poorly understood. This study explores the effect of time used for deposition of individual layers of nonlinearly growing layer-by-layer (LbL) films composed of poly(methacrylic acid) (PMAA) and quaternized poly-2-(dimethylamino)ethyl methacrylate (QPC) on film internal structure, swelling, and stability in salt solution, as well as the rate of penetration of invading polyelectrolyte chains. Thicknesses of dry and swollen films were measured by spectroscopic ellipsometry, film internal structure—by neutron reflectometry (NR), and degree of PMAA ionization—by Fourier-transform infrared spectroscopy (FTIR). The results suggestmore » that longer deposition times resulted in thicker films with higher degrees of swelling (up to swelling ratio as high as 4 compared to dry film thickness) and stronger film intermixing. The stronger intermixed films were more swollen in water, exhibited lower stability in salt solutions, and supported a faster penetration rate of invading polyelectrolyte chains. These results can be useful in designing polyelectrolyte nanoassemblies for biomedical applications, such as drug delivery coatings for medical implants or tissue engineering matrices.« less

Ionically Paired Layer-by-Layer Hydrogels: Water and Polyelectrolyte Uptake Controlled by Deposition Time

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

Selin, Victor; Ankner, John Francis; Sukhishvili, Svetlana

Despite intense recent interest in weakly bound nonlinear (“exponential”) multilayers, the underlying structure-property relationships of these films are still poorly understood. This study explores the effect of time used for deposition of individual layers of nonlinearly growing layer-by-layer (LbL) films composed of poly(methacrylic acid) (PMAA) and quaternized poly-2-(dimethylamino)ethyl methacrylate (QPC) on film internal structure, swelling, and stability in salt solution, as well as the rate of penetration of invading polyelectrolyte chains. Thicknesses of dry and swollen films were measured by spectroscopic ellipsometry, film internal structure—by neutron reflectometry (NR), and degree of PMAA ionization—by Fourier-transform infrared spectroscopy (FTIR). The results suggestmore » that longer deposition times resulted in thicker films with higher degrees of swelling (up to swelling ratio as high as 4 compared to dry film thickness) and stronger film intermixing. The stronger intermixed films were more swollen in water, exhibited lower stability in salt solutions, and supported a faster penetration rate of invading polyelectrolyte chains. These results can be useful in designing polyelectrolyte nanoassemblies for biomedical applications, such as drug delivery coatings for medical implants or tissue engineering matrices.« less

Local carrier distribution imaging on few-layer MoS2 exfoliated on SiO2 by scanning nonlinear dielectric microscopy

NASA Astrophysics Data System (ADS)

Yamasue, Kohei; Cho, Yasuo

2018-06-01

We demonstrate that scanning nonlinear dielectric microscopy (SNDM) can be used for the nanoscale characterization of dominant carrier distribution on atomically thin MoS2 mechanically exfoliated on SiO2. For stable imaging without damaging microscopy tips and samples, SNDM was combined with peak-force tapping mode atomic force microscopy. The identification of dominant carriers and their spatial distribution becomes possible even for single and few-layer MoS2 on SiO2 using the proposed method allowing differential capacitance (dC/dV) imaging. We can expect that SNDM can also be applied to the evaluation of other two-dimensional semiconductors and devices.

Theoretical Investigation of Light Transmission in a Slab Cavity via Kerr Nonlinearity of Carbon Nanotube Quantum Dot Nanostructure

NASA Astrophysics Data System (ADS)

Solookinejad, Gh.; Jabbari, M.; Sangachin, E. Ahmadi; Asadpour, S. H.

2018-01-01

In this paper, we discuss the transmission properties of weak probe laser field propagate through slab cavity with defect layer of carbon-nanotube quantum dot (CNT-QD) nanostructure. We show that due to spin-orbit coupling, the double electromagnetically induced transparency (EIT) windows appear and the giant Kerr nonlinearity of the intracavity medium can lead to manipulating of transmission coefficient of weak probe light. The thickness effect of defect layer medium has also been analyzed on transmission properties of probe laser field. Our proposed model may be useful for integrated photonics devices based on CNT-QD for applications in all-optical systems which require multiple EIT effect.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

PubMed

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

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.

Chemical reaction and heat generation/absorption aspects in MHD nonlinear convective flow of third grade nanofluid over a nonlinear stretching sheet with variable thickness

NASA Astrophysics Data System (ADS)

Qayyum, Sajid; Hayat, Tasawar; Alsaedi, Ahmed

Nonlinear thermal radiation and chemical reaction in magnetohydrodynamic (MHD) flow of third grade nanofluid over a stretching sheet with variable thickness are addressed. Heat generation/absorption and nonlinear convection are considered. The sheet moves with nonlinear velocity. Sheet is convectively heated. In addition zero mass flux condition for nanoparticle concentration is imposed. Results for velocity, temperature, concentration, skin friction and local Nusselt number are presented and examined. It is found that velocity and boundary layer thickness are increasing for Reynolds number. Temperature is a increasing function of the heat generation/absorption parameter while it causes a decrease in the heat transfer rate. Moreover effect of Brownian motion and chemical reaction on the concentration are quite reverse.

EVOLUTION OF FAST MAGNETOACOUSTIC PULSES IN RANDOMLY STRUCTURED CORONAL PLASMAS

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

Yuan, D.; Li, B.; Pascoe, D. J.

2015-02-01

We investigate the evolution of fast magnetoacoustic pulses in randomly structured plasmas, in the context of large-scale propagating waves in the solar atmosphere. We perform one-dimensional numerical simulations of fast wave pulses propagating perpendicular to a constant magnetic field in a low-β plasma with a random density profile across the field. Both linear and nonlinear regimes are considered. We study how the evolution of the pulse amplitude and width depends on their initial values and the parameters of the random structuring. Acting as a dispersive medium, a randomly structured plasma causes amplitude attenuation and width broadening of the fast wavemore » pulses. After the passage of the main pulse, secondary propagating and standing fast waves appear. Width evolution of both linear and nonlinear pulses can be well approximated by linear functions; however, narrow pulses may have zero or negative broadening. This arises because narrow pulses are prone to splitting, while broad pulses usually deviate less from their initial Gaussian shape and form ripple structures on top of the main pulse. Linear pulses decay at an almost constant rate, while nonlinear pulses decay exponentially. A pulse interacts most efficiently with a random medium with a correlation length of about half of the initial pulse width. This detailed model of fast wave pulses propagating in highly structured media substantiates the interpretation of EIT waves as fast magnetoacoustic waves. Evolution of a fast pulse provides us with a novel method to diagnose the sub-resolution filamentation of the solar atmosphere.« less

Multi-disease analysis of maternal antibody decay using non-linear mixed models accounting for censoring.

PubMed

Goeyvaerts, Nele; Leuridan, Elke; Faes, Christel; Van Damme, Pierre; Hens, Niel

2015-09-10

Biomedical studies often generate repeated measures of multiple outcomes on a set of subjects. It may be of interest to develop a biologically intuitive model for the joint evolution of these outcomes while assessing inter-subject heterogeneity. Even though it is common for biological processes to entail non-linear relationships, examples of multivariate non-linear mixed models (MNMMs) are still fairly rare. We contribute to this area by jointly analyzing the maternal antibody decay for measles, mumps, rubella, and varicella, allowing for a different non-linear decay model for each infectious disease. We present a general modeling framework to analyze multivariate non-linear longitudinal profiles subject to censoring, by combining multivariate random effects, non-linear growth and Tobit regression. We explore the hypothesis of a common infant-specific mechanism underlying maternal immunity using a pairwise correlated random-effects approach and evaluating different correlation matrix structures. The implied marginal correlation between maternal antibody levels is estimated using simulations. The mean duration of passive immunity was less than 4 months for all diseases with substantial heterogeneity between infants. The maternal antibody levels against rubella and varicella were found to be positively correlated, while little to no correlation could be inferred for the other disease pairs. For some pairs, computational issues occurred with increasing correlation matrix complexity, which underlines the importance of further developing estimation methods for MNMMs. Copyright © 2015 John Wiley & Sons, Ltd.

Randomized trial of four-layer and two-layer bandage systems in the management of chronic venous ulceration.

PubMed

Moffatt, Christine J; McCullagh, Lynn; O'Connor, Theresa; Doherty, Debra C; Hourican, Catherine; Stevens, Julie; Mole, Trevor; Franks, Peter J

2003-01-01

To compare a four-layer bandage system with a two-layer system in the management of chronic venous leg ulceration, a prospective randomized open parallel groups trial was undertaken. In total, 112 patients newly presenting to leg ulcer services with chronic leg ulceration, screened to exclude the presence of arterial disease (ankle brachial pressure index <0.8) and causes of ulceration other than venous disease, were entered into the trial. Patients were randomized to receive either four-layer (Profore) or two-layer (Surepress) high-compression elastic bandage systems. In all, 109 out of 112 patients had at least one follow-up. After 24 weeks, 50 out of 57 (88%) patients randomized to the four-layer bandage system with follow-up had ulcer closure (full epithelialization) compared with 40 out of 52 (77%) on the two-layer bandage, hazard ratio = 1.18 (95% confidence interval 0.69-2.02), p = 0.55. After 12 weeks, 40 out of 57 (70%) patients randomized to the four-layer bandage system with follow-up had ulcer closure compared with 30 out of 52 (58%) on the two-layer bandage, odds ratio = 4.23 (95% confidence interval 1.29-13.86), p = 0.02. Withdrawal rates were significantly greater on the two-layer bandage (30 out of 54; 56%) compared with the four-layer bandage system (8 out of 58; 14%), p < 0.001, and the number of patients with at least one device-related adverse incident was significantly greater on the two-layer bandaging system (15 out of 54; 28%) compared with four-layer bandaging (5 out of 54; 9%), p = 0.01. The higher mean cost of treatment in the two-layer bandaging system arm over 24 weeks ($1374 [ pound 916] vs. $1314 [ pound 876]) was explained by the increased mean number of bandage changes (1.5 vs. 1.1 per week) with the two-layer system. In conclusion, the four-layer bandage offers advantages over the two-layer bandage in terms of reduced withdrawal from treatment, fewer adverse incidents, and lower treatment cost.

Nonlinear analyses of composite aerospace structures in sonic fatigue

NASA Technical Reports Server (NTRS)

Mei, Chuh

1993-01-01

This report summarizes the semiannual research progress, accomplishments, and future plans performed under the NASA Langley Research Center Grant No. NAG-1-1358. The primary research effort of this project is the development of analytical methods for the prediction of nonlinear random response of composite aerospace structures subjected to combined acoustic and thermal loads. The progress, accomplishments, and future plates on four sonic fatigue research topics are described. The sonic fatigue design and passive control of random response of shape memory alloy hybrid composites presented in section 4, which is suited especially for HSCT, is a new initiative.

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

NASA Astrophysics Data System (ADS)

Zverev, V. V.; Rubinstein, B. Ya.

1991-04-01

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.

Fluid limit of nonintegrable continuous-time random walks in terms of fractional differential equations.

PubMed

Sánchez, R; Carreras, B A; van Milligen, B Ph

2005-01-01

The fluid limit of a recently introduced family of nonintegrable (nonlinear) continuous-time random walks is derived in terms of fractional differential equations. In this limit, it is shown that the formalism allows for the modeling of the interaction between multiple transport mechanisms with not only disparate spatial scales but also different temporal scales. For this reason, the resulting fluid equations may find application in the study of a large number of nonlinear multiscale transport problems, ranging from the study of self-organized criticality to the modeling of turbulent transport in fluids and plasmas.

Nonlinear analyses of composite aerospace structures in sonic fatigue

NASA Astrophysics Data System (ADS)

Mei, Chuh

1993-06-01

This report summarizes the semiannual research progress, accomplishments, and future plans performed under the NASA Langley Research Center Grant No. NAG-1-1358. The primary research effort of this project is the development of analytical methods for the prediction of nonlinear random response of composite aerospace structures subjected to combined acoustic and thermal loads. The progress, accomplishments, and future plates on four sonic fatigue research topics are described. The sonic fatigue design and passive control of random response of shape memory alloy hybrid composites presented in section 4, which is suited especially for HSCT, is a new initiative.

On MHD nonlinear stretching flow of Powell-Eyring nanomaterial

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Sajjad, Rai; Muhammad, Taseer; Alsaedi, Ahmed; Ellahi, Rahmat

This communication addresses the magnetohydrodynamic (MHD) flow of Powell-Eyring nanomaterial bounded by a nonlinear stretching sheet. Novel features regarding thermophoresis and Brownian motion are taken into consideration. Powell-Eyring fluid is electrically conducted subject to non-uniform applied magnetic field. Assumptions of small magnetic Reynolds number and boundary layer approximation are employed in the mathematical development. Zero nanoparticles mass flux condition at the sheet is selected. Adequate transformation yield nonlinear ordinary differential systems. The developed nonlinear systems have been computed through the homotopic approach. Effects of different pertinent parameters on velocity, temperature and concentration fields are studied and analyzed. Further numerical data of skin friction and heat transfer rate is also tabulated and interpreted.

The Characteristics of Vibration Isolation System with Damping and Stiffness Geometrically Nonlinear

NASA Astrophysics Data System (ADS)

Lu, Ze-Qi; Chen, Li-Qun; Brennan, Michael J.; Li, Jue-Ming; Ding, Hu

2016-09-01

The paper concerns an investigation into the use of both stiffness and damping nonlinearity in the vibration isolator to improve its effectiveness. The nonlinear damping and nonlinear stiffness are both achieved by horizontal damping and stiffness as the way of the geometrical nonlinearity. The harmonic balance method is used to analyze the force transmissibility of such vibration isolation system. It is found that as the horizontal damping increasing, the height of the force transmissibility peak is decreased and the high-frequency force transmissibility is almost the same. The results are also validated by some numerical method. Then the RMS of transmissibility under Gaussian white noise is calculated numerically, the results demonstrate that the beneficial effects of the damping nonlinearity can be achieved under random excitation.

On the secondary instability of the most dangerous Goertler vortex

NASA Technical Reports Server (NTRS)

Otto, S. R.; Denier, James P.

1993-01-01

Recent studies have demonstrated the most unstable Goertler vortex mode is found in flows, both two and three-dimensional, with regions of (moderately) large body curvature and these modes reside within a thin layer situated at the base of the conventional boundary layer. Further work concerning the nonlinear development of the most dangerous mode demonstrates that the flow results in a self induced flow reversal. However, prior to the point at which flow reversal is encountered, the total streamwise velocity profile is found to be highly inflectional in nature. Previous work then suggests that the nonlinear vortex state will become unstable to secondary, inviscid, Rayleigh wave instabilities prior to the point of flow reversal. Our concern is with the secondary instability of the nonlinear vortex states, which result from the streamwise evolution of the most unstable Goertler vortex mode, with the aim of determining whether such modes can induce a transition to a fully turbulent state before separation is encountered.

The simulation of electromagnetically driven strong Langmuir turbulence effect on the backscatter radiation from ionosphere

NASA Astrophysics Data System (ADS)

Kochetov, Andrey

2016-07-01

Numerical simulations of the dynamics of electromagnetic fields in a smoothly inhomogeneous nonlinear plasma layer in frameworks of the nonlinear Schrödinger equation with boundary conditions responsible for the pumping of the field in the layer by an incident wave and the inverse radiation losses supplemented the volume field dissipation due to the electromagnetic excitation of Langmuir turbulence are carried out. The effects of the threshold of non-linearity and it's evolution, of the threshold and saturation levels of dissipation in the vicinity of the wave reflection point on the features of the dynamics of reflection and absorption indexes are investigated. We consider the hard drive damping depending on the local field amplitude and hysteresis losses with different in several times "on" and "off" absorption thresholds as well. The dependence of the thresholds of the steady-state, periodic and chaotic regimes of plasma-wave interaction on the scenario of turbulence evolution is demonstrated. The results are compared with the experimental observations of Langmuir stage ionospheric modification.

A numerical study of nonlinear waves in a transcritical flow of stratified fluid past an obstacle

NASA Astrophysics Data System (ADS)

Hanazaki, Hideshi

1992-10-01

A numerical study of the flow of stratified fluid past an obstacle in a horizontal channel is described. Upstream advancing of waves near critically (resonance) appears in the case of ordinary two-layer flow, in which case the flow is described well by the solution of the forced extended Korteweg-de Vries (KdV) equation which has a cubic nonlinear term. It is shown theoretically that the upstream waves in the general two-layer flow cannot be well described by the forced KdV equation except when the wave amplitude is very small. The critical-level flow is also governed by the forced extended KdV equation. However, because of the smallness of the coefficient of the quadratic nonlinear term, the bore cannot propagate upstream at exact resonance. The results for the linearly stratified Boussinesq flow show good agreement with the solution of the Grimshaw and Yi (1991) equation, at least for exact resonance.

Magnetohydrodynamic three-dimensional flow of viscoelastic nanofluid in the presence of nonlinear thermal radiation

NASA Astrophysics Data System (ADS)

Hayat, T.; Muhammad, Taseer; Alsaedi, A.; Alhuthali, M. S.

2015-07-01

Magnetohydrodynamic (MHD) three-dimensional flow of couple stress nanofluid in the presence of thermophoresis and Brownian motion effects is analyzed. Energy equation subject to nonlinear thermal radiation is taken into account. The flow is generated by a bidirectional stretching surface. Fluid is electrically conducting in the presence of a constant applied magnetic field. The induced magnetic field is neglected for a small magnetic Reynolds number. Mathematical formulation is performed using boundary layer analysis. Newly proposed boundary condition requiring zero nanoparticle mass flux is employed. The governing nonlinear mathematical problems are first converted into dimensionless expressions and then solved for the series solutions of velocities, temperature and nanoparticles concentration. Convergence of the constructed solutions is verified. Effects of emerging parameters on the temperature and nanoparticles concentration are plotted and discussed. Skin friction coefficients and Nusselt number are also computed and analyzed. It is found that the thermal boundary layer thickness is an increasing function of radiative effect.

Nonlinear and Nonequilibrium Spin Injection in Magnetic Tunneling Junctions

NASA Astrophysics Data System (ADS)

Guo, Hong

2007-03-01

Quantitative analysis of charge and spin quantum transport in spintronic devices requires an atomistic first principles approach that can handle nonlinear and nonequilibrium transport conditions. We have developed an approach for this purpose based on real space density functional theory (DFT) carried out within the Keldysh nonequilibrium Green's function formalism (NEGF). We report theoretical analysis of nonlinear and nonequilibrium spin injection and quantum transport in Fe/MgO/Fe trilayer structures as a function of external bias voltage. Devices with well relaxed atomic structures and with FeO oxidization layers are investigated as a function of external bias voltage. We also report calculations of nonequilibrium spin injection into molecular layers and graphene. Comparisons to experimental data will be presented. Work in collaborations with: Derek Waldron, Vladimir Timochevski (McGill University); Ke Xia (Institute of Physics, Chinese Academy of Science, Beijing, China); Eric Zhu, Jian Wang (University of Hong Kong); Paul Haney, and Allan MacDonald (University of Texas at Austin).

Study of non-linear deformation of vocal folds in simulations of human phonation

NASA Astrophysics Data System (ADS)

Saurabh, Shakti; Bodony, Daniel

2014-11-01

Direct numerical simulation is performed on a two-dimensional compressible, viscous fluid interacting with a non-linear, viscoelastic solid as a model for the generation of the human voice. The vocal fold (VF) tissues are modeled as multi-layered with varying stiffness in each layer and using a finite-strain Standard Linear Solid (SLS) constitutive model implemented in a quadratic finite element code and coupled to a high-order compressible Navier-Stokes solver through a boundary-fitted fluid-solid interface. The large non-linear mesh deformation is handled using an elliptic/poisson smoothening technique. Supra-glottal flow shows asymmetry in the flow, which in turn has a coupling effect on the motion of the VF. The fully compressible simulations gives direct insight into the sound produced as pressure distributions and the vocal fold deformation helps study the unsteady vortical flow resulting from the fluid-structure interaction along the full phonation cycle. Supported by the National Science Foundation (CAREER Award Number 1150439).

On nonlinear Tollmien-Schlichting/vortex interaction in three-dimensional boundary layers

NASA Technical Reports Server (NTRS)

Davis, Dominic A. R.; Smith, Frank T.

1993-01-01

The instability of an incompressible three-dimensional boundary layer (that is, one with cross-flow) is considered theoretically and computationally in the context of vortex/wave interactions. Specifically the work centers on two low amplitude, lower-branch Tollmien-Schlichting waves which mutually interact to induce a weak longitudinal vortex flow; the vortex motion, in turn, gives rise to significant wave-modulation via wall-shear forcing. The characteristic Reynolds number is taken as a large parameter and, as a consequence, the waves' and the vortex motion are governed primarily by triple-deck theory. The nonlinear interaction is captured by a viscous partial-differential system for the vortex coupled with a pair of amplitude equations for each wave pressure. Three distinct possibilities were found to emerge for the nonlinear behavior of the flow solution downstream - an algebraic finite-distance singularity, far downstream saturation or far-downstream wave-decay (leaving pure vortex flow) - depending on the input conditions, the wave angles, and the size of the cross-flow.

Novel Composites for Wing and Fuselage Applications: Speedy Nonlinear Analysis of Postbuckled Panels in Shear (SNAPPS)

NASA Technical Reports Server (NTRS)

Sharp, Dave; Sobel, Larry

1997-01-01

A simple and rapid analysis method, consisting of a number of modular, 'strength-of-materials-type' models, is presented for predicting the nonlinear response and stiffener separation of postbuckled, flat, composite, shear panels. The analysis determines the maximum principal tensile stress in the skin surface layer under to toe. Failure is said to occur when this stress reaches the mean transverse tensile strength of the layer. The analysis methodology consists of a number of closed-form equations that can easily be used in a 'hand analysis. For expediency, they have been programmed into a preliminary design code called SNAPPS (Speedy Nonlinear Analysis of Postbuckled Panels in Shear), which rapidly predicts postbuckling response of the panel for each value of the applied shear load. SNAPPS response and failure predictions were found to agree well with test results for three panels with widely different geometries, laminates and stiffnesses. Design guidelines are given for increasing the load-carrying capacity of stiffened, composite shear panels.

Utilization of the computational technique to improve the thermophysical performance in the transportation of an electrically conducting Al2O3 - Ag/H2O hybrid nanofluid

NASA Astrophysics Data System (ADS)

Iqbal, Z.; Azhar, Ehtsham; Maraj, E. N.

2017-12-01

In this study, we analyzed the induced magnetic field effect on stagnation-point flow of a Al2O3-Ag/water hybrid nanofluid over a stretching sheet. Hybrid nanofluid, a new type of conventional fluid has been used for enhancement of heat transfer within boundary layer flow. It is notable here that only 1% to 5% contribution of nanoparticles enhance thermal conductivity of water. Nonlinear governing equations are simplified into boundary layer equations under boundary layer approximation assumption. A coupled system of nonlinear partial differential equation is transformed into a nonlinear system of ordinary differential equation by implementing suitable similarity conversions. Numerical analysis is performed by means of Keller box scheme. Effects of different non-dimensional governing parameters on velocity, induced magnetic field and temperature profiles, along with skinfriction coefficient and local Nusselt number, are discussed and presented through graphs and tables. Hybrid nanofluid is considered by keeping the 0.1% volumetric fraction of silver. From this study it is observed that the heat transfer rate of hybrid nanofluid (Al2O3-Ag/water) is higher than nanofluid (Ag/water). Novel results computed are useful in academic studies of hybrid nanofluids in engineering and industry.

A multi-scale and multi-field coupling nonlinear constitutive theory for the layered magnetoelectric composites

NASA Astrophysics Data System (ADS)

Xu, Hao; Pei, Yongmao; Li, Faxin; Fang, Daining

2018-05-01

The magnetic, electric and mechanical behaviors are strongly coupled in magnetoelectric (ME) materials, making them great promising in the application of functional devices. In this paper, the magneto-electro-mechanical fully coupled constitutive behaviors of ME laminates are systematically studied both theoretically and experimentally. A new probabilistic domain switching function considering the surface ferromagnetic anisotropy and the interface charge-mediated effect is proposed. Then a multi-scale multi-field coupling nonlinear constitutive model for layered ME composites is developed with physical measureable parameters. The experiments were performed to compare the theoretical predictions with the experimental data. The theoretical predictions have a good agreement with experimental results. The proposed constitutive relation can be used to describe the nonlinear multi-field coupling properties of both ME laminates and thin films. Several novel coupling experimental phenomena such as the electric-field control of magnetization, and the magnetic-field tuning of polarization are observed and analyzed. Furthermore, the size-effect of the electric tuning behavior of magnetization is predicted, which demonstrates a competition mechanism between the interface strain-mediated effect and the charge-driven effect. Our study offers deep insight into the coupling microscopic mechanism and macroscopic properties of ME layered composites, which is benefit for the design of electromagnetic functional devices.

Incorporation of Keplerate-type Mo-O based macroanions into Zn2Al-LDH results in the formation of all-inorganic composite films with remarkable third-order optical nonlinearity.

PubMed

Ren, Haizhou; Shehzad, Farooq Khurum; Zhou, Yunshan; Zhang, Lijuan; Iqbal, Arshad; Long, Yi

2018-05-01

Herein, new all-inorganic transparent composite films with the formula (Zn2Al-LDH/{Mo132-Ac})n have been fabricated by a layer-by-layer method using the exfoliated Zn2Al-LDH monolayer nanosheets and Keplerate-type macroanion {Mo132-Ac}. They were characterized by UV-vis absorption spectroscopy, SEM, AFM, and XPS techniques. The Z-scan measurements, which were conducted under laser irradiation at a wavelength of 532 nm, a pulse width of 6 ns, a repetition rate of 10 Hz, and the light intensity at a focus E0 of 10 μJ, revealed that all the films had notable saturated absorption and self-defocusing effect with a large third-order optical nonlinear susceptibility χ(3). With an increase in the number of layers (i.e., n) corresponding to the increase in the thickness of the films, the third-order nonlinear absorption β and refractive effects of the films were improved (i.e., the χ(3) value was up to 1.99 × 10-11 esu when n = 24); this implied that the NLO responses could be modified by fine-tuning the thickness of the composite films to meet the demands of different devices.

Kolakoski sequence as an element to radiate giant forward and backward second harmonic signals

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

Parvini, T. S.; Tehranchi, M. M., E-mail: m-hamidi@sbu.ac.ir, E-mail: teranchi@sbu.ac.ir; Laser and Plasma Research Institute, Shahid Beheshti University, Tehran

2015-11-14

We propose a novel type of aperiodic one-dimensional photonic crystal structures which can be used for generating giant forward and backward second harmonic signals. The studied structure is formed by stacking together the air and nonlinear layers according to the Kolakoski self-generation scheme in which each nonlinear layer contains a pair of antiparallel 180° poled LiNbO{sub 3} crystal layers. For different generation stages of the structure, conversion efficiencies of forward and backward second harmonic waves have been calculated by nonlinear transfer matrix method. Numerical simulations show that conversion efficiencies in the Kolakoski-based multilayer are larger than the perfect ones formore » at least one order of magnitude. Especially for 33rd and 39th generation stages, forward second harmonic wave are 42 and 19 times larger, respectively. In this paper, we validate the strong fundamental field enhancement and localization within Kolakoski-based multilayer due to periodicity breaking which consequently leads to very strong radiation of backward and forward second harmonic signals. Following the applications of analogous aperiodic structures, we expect that Kolakosi-based multilayer can play a role in optical parametric devices such as multicolor second harmonic generators with high efficiency.« less

Multi-Target Regression via Robust Low-Rank Learning.

PubMed

Zhen, Xiantong; Yu, Mengyang; He, Xiaofei; Li, Shuo

2018-02-01

Multi-target regression has recently regained great popularity due to its capability of simultaneously learning multiple relevant regression tasks and its wide applications in data mining, computer vision and medical image analysis, while great challenges arise from jointly handling inter-target correlations and input-output relationships. In this paper, we propose Multi-layer Multi-target Regression (MMR) which enables simultaneously modeling intrinsic inter-target correlations and nonlinear input-output relationships in a general framework via robust low-rank learning. Specifically, the MMR can explicitly encode inter-target correlations in a structure matrix by matrix elastic nets (MEN); the MMR can work in conjunction with the kernel trick to effectively disentangle highly complex nonlinear input-output relationships; the MMR can be efficiently solved by a new alternating optimization algorithm with guaranteed convergence. The MMR leverages the strength of kernel methods for nonlinear feature learning and the structural advantage of multi-layer learning architectures for inter-target correlation modeling. More importantly, it offers a new multi-layer learning paradigm for multi-target regression which is endowed with high generality, flexibility and expressive ability. Extensive experimental evaluation on 18 diverse real-world datasets demonstrates that our MMR can achieve consistently high performance and outperforms representative state-of-the-art algorithms, which shows its great effectiveness and generality for multivariate prediction.

Nanoindentation of the surface layer of Hadfield's steel after sliding friction

NASA Astrophysics Data System (ADS)

Kolubaev, A. V.; Kolubaev, E. A.; Sizova, O. V.

2007-12-01

We have measured the nanohardness of a deformed near-surface layer of Hadfield’s steel upon friction testing. The phenomenon of shape recovery upon indentation has been observed, which is retained for several days after tribological tests. It s suggested that the strained material exhibits behavior analogous to nonlinear elasticity.

Numerical analysis of finite Debye-length effects in induced-charge electro-osmosis.

PubMed

Gregersen, Misha Marie; Andersen, Mathias Baekbo; Soni, Gaurav; Meinhart, Carl; Bruus, Henrik

2009-06-01

For a microchamber filled with a binary electrolyte and containing a flat unbiased center electrode at one wall, we employ three numerical models to study the strength of the resulting induced-charge electro-osmotic (ICEO) flow rolls: (i) a full nonlinear continuum model resolving the double layer, (ii) a linear slip-velocity model not resolving the double layer and without tangential charge transport inside this layer, and (iii) a nonlinear slip-velocity model extending the linear model by including the tangential charge transport inside the double layer. We show that, compared to the full model, the slip-velocity models significantly overestimate the ICEO flow. This provides a partial explanation of the quantitative discrepancy between observed and calculated ICEO velocities reported in the literature. The discrepancy increases significantly for increasing Debye length relative to the electrode size, i.e., for nanofluidic systems. However, even for electrode dimensions in the micrometer range, the discrepancies in velocity due to the finite Debye length can be more than 10% for an electrode of zero height and more than 100% for electrode heights comparable to the Debye length.

Sound absorption of a porous material with a perforated facing at high sound pressure levels

NASA Astrophysics Data System (ADS)

Peng, Feng

2018-07-01

A semi-empirical model is proposed to predict the sound absorption of an acoustical unit consisting of a rigid-porous material layer with a perforated facing under the normal incidence at high sound pressure levels (SPLs) of pure tones. The nonlinearity of the perforated facing and the porous material, and the interference between them are considered in the model. The sound absorptive performance of the acoustical unit is tested at different incident SPLs and in three typical configurations: 1) when the perforated panel (PP) directly contacts with the porous layer, 2) when the PP is separated from the porous layer by an air gap and 3) when an air cavity is set between the porous material and the hard backing wall. The test results agree well with the corresponding theoretical predictions. Moreover, the results show that the interference effect is correlated to the width of the air gap between the PP and the porous layer, which alters not only the linear acoustic impedance but also the nonlinear acoustic impedance of the unit and hence its sound absorptive properties.

Postbuckling analysis of multi-layered graphene sheets under non-uniform biaxial compression

NASA Astrophysics Data System (ADS)

Farajpour, Ali; Arab Solghar, Alireza; Shahidi, Alireza

2013-01-01

In this article, the nonlinear buckling characteristics of multi-layered graphene sheets are investigated. The graphene sheet is modeled as an orthotropic nanoplate with size-dependent material properties. The graphene film is subjected by non-uniformly distributed in-plane load through its thickness. To include the small scale and the geometrical nonlinearity effects, the governing differential equations are derived based on the nonlocal elasticity theory in conjunction with the von Karman geometrical model. Explicit expressions for the postbuckling loads of single- and double-layered graphene sheets with simply supported edges under biaxial compression are obtained. For numerical results, six types of armchair and zigzag graphene sheets with different aspect ratio are considered. The present formulation and method of solution are validated by comparing the results, in the limit cases, with those available in the open literature. Excellent agreement between the obtained and available results is observed. Finally, the effects of nonlocal parameter, buckling mode number, compression ratio and non-uniform parameter on the postbuckling behavior of multi-layered graphene sheets are studied.

Second-harmonic generation from a thin spherical layer and No-generation conditions

NASA Astrophysics Data System (ADS)

Kapshai, V. N.; Shamyna, A. A.

2017-09-01

In the Rayleigh-Gans-Debye approximation, we solve the problem of second-harmonic generation by an elliptically polarized electromagnetic wave incident on the surface of a spherical particle that is coated by an optically nonlinear layer and is placed in a dielectric. The formulas obtained characterize the spatial distribution of the electric field of the second harmonic in the far-field zone. The most general form of the second-order dielectric susceptibility tensor is considered, which contains four independent components, with three of them being nonchiral and one, chiral. Consistency and inconsistencies between the obtained solution and formulas from works of other authors are found. We analyze the directivity patterns that characterize the spatial distribution of the generated radiation for the nonchiral layer and their dependences on the anisotropy and ellipticity coefficients of the incident wave. It is found that, with increasing radius of the nonlinear layer, the generated radiation becomes more directional. Combinations of parameters for which no radiation is generated are revealed. Based on this, we propose methods for experimental determination of the anisotropy coefficients.

Nonlinear Coherent Structures, Microbursts and Turbulence

NASA Astrophysics Data System (ADS)

Lakhina, G. S.

2015-12-01

Nonlinear waves are found everywhere, in fluids, atmosphere, laboratory, space and astrophysical plasmas. The interplay of nonlinear effects, dispersion and dissipation in the medium can lead to a variety of nonlinear waves and turbulence. Two cases of coherent nonlinear waves: chorus and electrostatic solitary waves (ESWs) and their impact on modifying the plasma medium are discussed. Chorus is a right-hand, circularly-polarized electromagnetic plane wave. Dayside chorus is a bursty emission composed of rising frequency "elements" with duration of ~0.1 to 1.0 s. Each element is composed of coherent subelements with durations of ~1 to 100 ms or more. The cyclotron resonant interaction between energetic electrons and the coherent chorus waves is studied. An expression for the pitch angle transport due to this interaction is derived considering a Gaussian distribution for the time duration of the chorus elements. The rapid pitch scattering can provide an explanation for the ionospheric microbursts of ~0.1 to 0.5 s in bremsstrahlung x-rays formed by ~10-100 keV precipitating electrons. On the other hand, the ESWs are observed in the electric field component parallel to the background magnetic field, and are usually bipolar or tripolar. Generation of coherent ESWs has been explained in terms of nonlinear fluid models of ion- and electron-acoustic solitons and double layers (DLs) based on Sagdeev pseudopotential technique. Fast Fourier transform of electron- and ion-acoustic solitons/DLs produces broadband wave spectra which can explain the properties of the electrostatic turbulence observed in the magnetosheath and plasma sheet boundary layer, and in the solar wind, respectively.

Time domain reflectometry measurements of solute transport across a soil layer boundary

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

Nissen, H.H.; Moldrup, P.; Kachanoski, R.G.

2000-02-01

The mechanisms governing solute transport through layered soil are not fully understood. Solute transport at, above, and beyond the interface between two soil layers during quasi-steady-state soil water movement was investigated using time domain reflectometry (TDR). A 0.26-m sandy loam layer was packed on top of a 1.35-m fine sand layer in a soil column. Soil water content ({theta}) and bulk soil electrical conductivity (EC{sub b}) were measured by 50 horizontal and 2 vertical TDR probes. A new TDR calibration method that gives a detailed relationship between apparent relative dielectric permittivity (K{sub s}) and {theta} was applied. Two replicate solutemore » transport experiments were conducted adding a conservative tracer (CCl) to the surface as a short pulse. The convective lognormal transfer function model (CLT) was fitted to the TDR-measured time integral-normalized resident concentration breakthrough curves (BTCs). The BTCs and the average solute-transport velocities showed preferential flow occurred across the layer boundary. A nonlinear decrease in TDR-measured {theta} in the upper soil toward the soil layer boundary suggests the existence of a 0.10-m zone where water is confined towards fingered flow, creating lateral variations in the area-averaged water flux above the layer boundary. A comparison of the time integral-normalized flux concentration measured by vertical and horizontal TDR probes at the layer boundary also indicates a nonuniform solute transport. The solute dispersivity remained constant in the upper soil layer, but increased nonlinearly (and further down, linearly) with depth in the lower layer, implying convective-dispersive solute transport in the upper soil, a transition zone just below the boundary, and stochastic-convective solute transport in the remaining part of the lower soil.« less

Inter-layer synchronization in multiplex networks of identical layers

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

Sevilla-Escoboza, R.; Sendiña-Nadal, I.; Leyva, I.

2016-06-15

Inter-layer synchronization is a distinctive process of multiplex networks whereby each node in a given layer evolves synchronously with all its replicas in other layers, irrespective of whether or not it is synchronized with the other units of the same layer. We analytically derive the necessary conditions for the existence and stability of such a state, and verify numerically the analytical predictions in several cases where such a state emerges. We further inspect its robustness against a progressive de-multiplexing of the network, and provide experimental evidence by means of multiplexes of nonlinear electronic circuits affected by intrinsic noise and parametermore » mismatch.« less

Nonlinear modeling of chaotic time series: Theory and applications

NASA Astrophysics Data System (ADS)

Casdagli, M.; Eubank, S.; Farmer, J. D.; Gibson, J.; Desjardins, D.; Hunter, N.; Theiler, J.

We review recent developments in the modeling and prediction of nonlinear time series. In some cases, apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases, it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifying and quantifying low-dimensional chaotic behavior. During the past few years, methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics, and human speech.

Optimized Wavelength-Tuned Nonlinear Frequency Conversion Using a Liquid Crystal Clad Waveguide

NASA Technical Reports Server (NTRS)

Stephen, Mark A. (Inventor)

2018-01-01

An optimized wavelength-tuned nonlinear frequency conversion process using a liquid crystal clad waveguide. The process includes implanting ions on a top surface of a lithium niobate crystal to form an ion implanted lithium niobate layer. The process also includes utilizing a tunable refractive index of a liquid crystal to rapidly change an effective index of the lithium niobate crystal.

Response of corrugated fiberboard to moisture flow : a 3-D finite element transient nonlinear analysis

Treesearch

Adeeb A. Rahman; Thomas J. Urbanik; Mustafa Mahamid

2003-01-01

Collapse of fiberboard packaging boxes, in the shipping industry, due to rise in humidity conditions is common and very costly. A 3D FE nonlinear model is developed to predict the moisture flow throughout a corrugated packaging fiberboard sandwich structure. The model predicts how the moisture diffusion will permeate through the layers of a fiberboard (medium and...

Monotonic entropy growth for a nonlinear model of random exchanges.

PubMed

Apenko, S M

2013-02-01

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific "coarse graining" of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.

Probabilistic finite elements for transient analysis in nonlinear continua

NASA Technical Reports Server (NTRS)

Liu, W. K.; Belytschko, T.; Mani, A.

1985-01-01

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Monotonic entropy growth for a nonlinear model of random exchanges

NASA Astrophysics Data System (ADS)

Apenko, S. M.

2013-02-01

We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We represent each step of this dynamics as a combination of two processes. The first one is a linear energy-conserving evolution of the two-particle distribution, for which the entropy growth can be easily verified. The original nonlinear process is actually a result of a specific “coarse graining” of this linear evolution, when after the collision one variable is integrated away. This coarse graining is of the same type as the real space renormalization group transformation and leads to an additional entropy growth. The combination of these two factors produces the required result which is obtained only by means of information theory inequalities.

Probabilistic DHP adaptive critic for nonlinear stochastic control systems.

PubMed

Herzallah, Randa

2013-06-01

Following the recently developed algorithms for fully probabilistic control design for general dynamic stochastic systems (Herzallah & Káarnáy, 2011; Kárný, 1996), this paper presents the solution to the probabilistic dual heuristic programming (DHP) adaptive critic method (Herzallah & Káarnáy, 2011) and randomized control algorithm for stochastic nonlinear dynamical systems. The purpose of the randomized control input design is to make the joint probability density function of the closed loop system as close as possible to a predetermined ideal joint probability density function. This paper completes the previous work (Herzallah & Káarnáy, 2011; Kárný, 1996) by formulating and solving the fully probabilistic control design problem on the more general case of nonlinear stochastic discrete time systems. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained. Copyright © 2013 Elsevier Ltd. All rights reserved.

Multiscale volatility duration characteristics on financial multi-continuum percolation dynamics

NASA Astrophysics Data System (ADS)

Wang, Min; Wang, Jun

A random stock price model based on the multi-continuum percolation system is developed to investigate the nonlinear dynamics of stock price volatility duration, in an attempt to explain various statistical facts found in financial data, and have a deeper understanding of mechanisms in the financial market. The continuum percolation system is usually referred to be a random coverage process or a Boolean model, it is a member of a class of statistical physics systems. In this paper, the multi-continuum percolation (with different values of radius) is employed to model and reproduce the dispersal of information among the investors. To testify the rationality of the proposed model, the nonlinear analyses of return volatility duration series are preformed by multifractal detrending moving average analysis and Zipf analysis. The comparison empirical results indicate the similar nonlinear behaviors for the proposed model and the actual Chinese stock market.

Effects of intermode nonlinearity and intramode nonlinearity on modulation instability in randomly birefringent two-mode optical fibers

NASA Astrophysics Data System (ADS)

Li, Jin Hua; Xu, Hui; Sun, Ting Ting; Pei, Shi Xin; Ren, Hai Dong

2018-05-01

We analyze in detail the effects of the intermode nonlinearity (IEMN) and intramode nonlinearity (IRMN) on modulation instability (MI) in randomly birefringent two-mode optical fibers (RB-TMFs). In the anomalous dispersion regime, the MI gain enhances significantly as the IEMN and IRMN coefficients increases. In the normal dispersion regime, MI can be generated without the differential mode group delay (DMGD) effect, as long as the IEMN coefficient between two distinct modes is above a critical value, or the IRMN coefficient inside a mode is below a critical value. This critical IEMN (IRMN) coefficient depends strongly on the given IRMN (IEMN) coefficient and DMGD for a given nonlinear RB-TMF structure, and is independent on the input total power, the power ratio distribution and the group velocity dispersion (GVD) ratio between the two modes. On the other hand, in contrast to the MI band arising from the pure effect of DMGD in the normal dispersion regime, where MI vanishes after a critical total power, the generated MI band under the combined effects of IEMN and IRMN without DMGD exists for any total power and enhances with the total power. The MI analysis is verified numerically by launching perturbed continuous waves (CWs) with wave propagation method.

Random forests in non-invasive sensorimotor rhythm brain-computer interfaces: a practical and convenient non-linear classifier.

PubMed

Steyrl, David; Scherer, Reinhold; Faller, Josef; Müller-Putz, Gernot R

2016-02-01

There is general agreement in the brain-computer interface (BCI) community that although non-linear classifiers can provide better results in some cases, linear classifiers are preferable. Particularly, as non-linear classifiers often involve a number of parameters that must be carefully chosen. However, new non-linear classifiers were developed over the last decade. One of them is the random forest (RF) classifier. Although popular in other fields of science, RFs are not common in BCI research. In this work, we address three open questions regarding RFs in sensorimotor rhythm (SMR) BCIs: parametrization, online applicability, and performance compared to regularized linear discriminant analysis (LDA). We found that the performance of RF is constant over a large range of parameter values. We demonstrate - for the first time - that RFs are applicable online in SMR-BCIs. Further, we show in an offline BCI simulation that RFs statistically significantly outperform regularized LDA by about 3%. These results confirm that RFs are practical and convenient non-linear classifiers for SMR-BCIs. Taking into account further properties of RFs, such as independence from feature distributions, maximum margin behavior, multiclass and advanced data mining capabilities, we argue that RFs should be taken into consideration for future BCIs.

Probabilistic design of fibre concrete structures

NASA Astrophysics Data System (ADS)

Pukl, R.; Novák, D.; Sajdlová, T.; Lehký, D.; Červenka, J.; Červenka, V.

2017-09-01

Advanced computer simulation is recently well-established methodology for evaluation of resistance of concrete engineering structures. The nonlinear finite element analysis enables to realistically predict structural damage, peak load, failure, post-peak response, development of cracks in concrete, yielding of reinforcement, concrete crushing or shear failure. The nonlinear material models can cover various types of concrete and reinforced concrete: ordinary concrete, plain or reinforced, without or with prestressing, fibre concrete, (ultra) high performance concrete, lightweight concrete, etc. Advanced material models taking into account fibre concrete properties such as shape of tensile softening branch, high toughness and ductility are described in the paper. Since the variability of the fibre concrete material properties is rather high, the probabilistic analysis seems to be the most appropriate format for structural design and evaluation of structural performance, reliability and safety. The presented combination of the nonlinear analysis with advanced probabilistic methods allows evaluation of structural safety characterized by failure probability or by reliability index respectively. Authors offer a methodology and computer tools for realistic safety assessment of concrete structures; the utilized approach is based on randomization of the nonlinear finite element analysis of the structural model. Uncertainty of the material properties or their randomness obtained from material tests are accounted in the random distribution. Furthermore, degradation of the reinforced concrete materials such as carbonation of concrete, corrosion of reinforcement, etc. can be accounted in order to analyze life-cycle structural performance and to enable prediction of the structural reliability and safety in time development. The results can serve as a rational basis for design of fibre concrete engineering structures based on advanced nonlinear computer analysis. The presented methodology is illustrated on results from two probabilistic studies with different types of concrete structures related to practical applications and made from various materials (with the parameters obtained from real material tests).

Model Equation for Acoustic Nonlinear Measurement of Dispersive Specimens at High Frequency

NASA Astrophysics Data System (ADS)

Zhang, Dong; Kushibiki, Junichi; Zou, Wei

2006-10-01

We present a theoretical model for acoustic nonlinearity measurement of dispersive specimens at high frequency. The nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation governs the nonlinear propagation in the SiO2/specimen/SiO2 multi-layer medium. The dispersion effect is considered in a special manner by introducing the frequency-dependant sound velocity in the KZK equation. Simple analytic solutions are derived by applying the superposition technique of Gaussian beams. The solutions are used to correct the diffraction and dispersion effects in the measurement of acoustic nonlinearity of cottonseed oil in the frequency range of 33-96 MHz. Regarding two different ultrasonic devices, the accuracies of the measurements are improved to ±2.0% and ±1.3% in comparison with ±9.8% and ±2.9% obtained from the previous plane wave model.

A numerical study on flexoelectric bistable energy harvester

NASA Astrophysics Data System (ADS)

Kumar, Anuruddh; Sharma, Anshul; Vaish, Rahul; Kumar, Rajeev; Jain, Satish Chandra

2018-07-01

A flexoelectric energy harvesting can be a viable solution of energy source for low power devices and sensors due to its higher performance at nano/micro domain size. Numerical study has been performed on energy harvester based on flexoelectric phenomenon of dielectric materials. Cantilever type structure was opted here as it induces the polarization due to the breaking of lattice symmetry upon bending. Host layer of cantilever is made of barium strontium titanate (BST) as it has high flexoelectric coefficient, and electrodes are attached with the host layer to collect the charges. In this study, nonlinearity has been introduced using pair of magnets at the free end of the cantilever. Characteristics of the harvester performance (linear-non-linear) changes by varying the distance between magnets. Results revealed that the bistable energy harvester gives more operating frequency range when excitation is random as compared to the linear energy harvester. For the given dimension of the harvester, when magnets distance d = 6 mm, effective harvesting frequency ranges are 5-17.3 and 17.6-26 Hz as compared to linear harvester. Further, role of load resistance was investigated to understand the impact on the performance. Hysteresis loop between voltage and displacement significantly varies with the resistance. This hysteresis loop confirmed the backward coupling of flexoelectric layer, in which voltage affects the displacement due to actuation. Area under the hysteresis loop is maximum for optimum resistance value (20.4 kΩ) which confirms the maximum extraction of power during vibration.

Separation of variables solution for non-linear radiative cooling

NASA Technical Reports Server (NTRS)

Siegel, Robert

1987-01-01

A separation of variables solution has been obtained for transient radiative cooling of an absorbing-scattering plane layer. The solution applies after an initial transient period required for adjustment of the temperature and scattering source function distributions. The layer emittance, equal to the instantaneous heat loss divided by the fourth power of the instantaneous mean temperature, becomes constant. This emittance is a function of only the optical thickness of the layer and the scattering albedo; its behavior as a function of these quantities is considerably different than for a layer at constant temperature.

Comparison of the Predictive Performance and Interpretability of Random Forest and Linear Models on Benchmark Data Sets.

PubMed

Marchese Robinson, Richard L; Palczewska, Anna; Palczewski, Jan; Kidley, Nathan

2017-08-28

The ability to interpret the predictions made by quantitative structure-activity relationships (QSARs) offers a number of advantages. While QSARs built using nonlinear modeling approaches, such as the popular Random Forest algorithm, might sometimes be more predictive than those built using linear modeling approaches, their predictions have been perceived as difficult to interpret. However, a growing number of approaches have been proposed for interpreting nonlinear QSAR models in general and Random Forest in particular. In the current work, we compare the performance of Random Forest to those of two widely used linear modeling approaches: linear Support Vector Machines (SVMs) (or Support Vector Regression (SVR)) and partial least-squares (PLS). We compare their performance in terms of their predictivity as well as the chemical interpretability of the predictions using novel scoring schemes for assessing heat map images of substructural contributions. We critically assess different approaches for interpreting Random Forest models as well as for obtaining predictions from the forest. We assess the models on a large number of widely employed public-domain benchmark data sets corresponding to regression and binary classification problems of relevance to hit identification and toxicology. We conclude that Random Forest typically yields comparable or possibly better predictive performance than the linear modeling approaches and that its predictions may also be interpreted in a chemically and biologically meaningful way. In contrast to earlier work looking at interpretation of nonlinear QSAR models, we directly compare two methodologically distinct approaches for interpreting Random Forest models. The approaches for interpreting Random Forest assessed in our article were implemented using open-source programs that we have made available to the community. These programs are the rfFC package ( https://r-forge.r-project.org/R/?group_id=1725 ) for the R statistical programming language and the Python program HeatMapWrapper [ https://doi.org/10.5281/zenodo.495163 ] for heat map generation.

Force-controlled absorption in a fully-nonlinear numerical wave tank

NASA Astrophysics Data System (ADS)

Spinneken, Johannes; Christou, Marios; Swan, Chris

2014-09-01

An active control methodology for the absorption of water waves in a numerical wave tank is introduced. This methodology is based upon a force-feedback technique which has previously been shown to be very effective in physical wave tanks. Unlike other methods, an a-priori knowledge of the wave conditions in the tank is not required; the absorption controller being designed to automatically respond to a wide range of wave conditions. In comparison to numerical sponge layers, effective wave absorption is achieved on the boundary, thereby minimising the spatial extent of the numerical wave tank. In contrast to the imposition of radiation conditions, the scheme is inherently capable of absorbing irregular waves. Most importantly, simultaneous generation and absorption can be achieved. This is an important advance when considering inclusion of reflective bodies within the numerical wave tank. In designing the absorption controller, an infinite impulse response filter is adopted, thereby eliminating the problem of non-causality in the controller optimisation. Two alternative controllers are considered, both implemented in a fully-nonlinear wave tank based on a multiple-flux boundary element scheme. To simplify the problem under consideration, the present analysis is limited to water waves propagating in a two-dimensional domain. The paper presents an extensive numerical validation which demonstrates the success of the method for a wide range of wave conditions including regular, focused and random waves. The numerical investigation also highlights some of the limitations of the method, particularly in simultaneously generating and absorbing large amplitude or highly-nonlinear waves. The findings of the present numerical study are directly applicable to related fields where optimum absorption is sought; these include physical wavemaking, wave power absorption and a wide range of numerical wave tank schemes.

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Phase Conjugated and Transparent Wavelength Conversions of Nyquist 16-QAM Signals Employing a Single-Layer Graphene Coated Fiber Device

PubMed Central

Hu, Xiao; Zeng, Mengqi; Long, Yun; Liu, Jun; Zhu, Yixiao; Zou, Kaiheng; Zhang, Fan; Fu, Lei; Wang, Jian

2016-01-01

We fabricate a nonlinear optical device based on a fiber pigtail cross-section coated with a single-layer graphene grown by chemical vapor deposition (CVD) method. Using the fabricated graphene-assisted nonlinear optical device and employing Nyquist 16-ary quadrature amplitude modulation (16-QAM) signal, we experimentally demonstrate phase conjugated wavelength conversion by degenerate four-wave mixing (FWM) and transparent wavelength conversion by non-degenerate FWM in graphene. We study the conversion efficiency as functions of the pump power and pump wavelength and evaluate the bit-error rate (BER) performance. We also compare the time-varying symbol sequence for graphene-assisted phase conjugated and transparent wavelength conversions of Nyquist 16-QAM signal. PMID:26932470

Numerical modeling of the atmosphere with an isentropic vertical coordinate

NASA Technical Reports Server (NTRS)

Hsu, Yueh-Jiuan G.; Arakawa, Akio

1990-01-01

A theta-coordinate model simulating the nonlinear evolution of a baroclinic wave is presented. In the model, vertical discretization maintains important integral constraints such as conservation of the angular momentum and total energy. A massless-layer approach is used in the treatment of the intersections of coordinate surfaces with the lower boundary. This formally eliminates the intersection problem, but raises other computational problems. Horizontal discretization of the continuity and momentum equations in the model are designed to overcome these problems. Selected results from a 10-day integration with the 25-layer, beta-plane version of the model are presented. It is concluded that the model can simulate the nonlinear evolution of a baroclinic wave and associated dynamical processes without major computational difficulties.

Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators

NASA Technical Reports Server (NTRS)

Taleghani, Barmac K.; Campbell, Joel F.

1999-01-01

A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.

Propagation of finite amplitude sound through turbulence: Modeling with geometrical acoustics and the parabolic approximation

NASA Astrophysics Data System (ADS)

Blanc-Benon, Philippe; Lipkens, Bart; Dallois, Laurent; Hamilton, Mark F.; Blackstock, David T.

2002-01-01

Sonic boom propagation can be affected by atmospheric turbulence. It has been shown that turbulence affects the perceived loudness of sonic booms, mainly by changing its peak pressure and rise time. The models reported here describe the nonlinear propagation of sound through turbulence. Turbulence is modeled as a set of individual realizations of a random temperature or velocity field. In the first model, linear geometrical acoustics is used to trace rays through each realization of the turbulent field. A nonlinear transport equation is then derived along each eigenray connecting the source and receiver. The transport equation is solved by a Pestorius algorithm. In the second model, the KZK equation is modified to account for the effect of a random temperature field and it is then solved numerically. Results from numerical experiments that simulate the propagation of spark-produced N waves through turbulence are presented. It is observed that turbulence decreases, on average, the peak pressure of the N waves and increases the rise time. Nonlinear distortion is less when turbulence is present than without it. The effects of random vector fields are stronger than those of random temperature fields. The location of the caustics and the deformation of the wave front are also presented. These observations confirm the results from the model experiment in which spark-produced N waves are used to simulate sonic boom propagation through a turbulent atmosphere.

Propagation of finite amplitude sound through turbulence: modeling with geometrical acoustics and the parabolic approximation.

PubMed

Blanc-Benon, Philippe; Lipkens, Bart; Dallois, Laurent; Hamilton, Mark F; Blackstock, David T

2002-01-01

Sonic boom propagation can be affected by atmospheric turbulence. It has been shown that turbulence affects the perceived loudness of sonic booms, mainly by changing its peak pressure and rise time. The models reported here describe the nonlinear propagation of sound through turbulence. Turbulence is modeled as a set of individual realizations of a random temperature or velocity field. In the first model, linear geometrical acoustics is used to trace rays through each realization of the turbulent field. A nonlinear transport equation is then derived along each eigenray connecting the source and receiver. The transport equation is solved by a Pestorius algorithm. In the second model, the KZK equation is modified to account for the effect of a random temperature field and it is then solved numerically. Results from numerical experiments that simulate the propagation of spark-produced N waves through turbulence are presented. It is observed that turbulence decreases, on average, the peak pressure of the N waves and increases the rise time. Nonlinear distortion is less when turbulence is present than without it. The effects of random vector fields are stronger than those of random temperature fields. The location of the caustics and the deformation of the wave front are also presented. These observations confirm the results from the model experiment in which spark-produced N waves are used to simulate sonic boom propagation through a turbulent atmosphere.

Nonlinear consolidation in randomly heterogeneous highly compressible aquitards

NASA Astrophysics Data System (ADS)

Zapata-Norberto, Berenice; Morales-Casique, Eric; Herrera, Graciela S.

2018-05-01

Severe land subsidence due to groundwater extraction may occur in multiaquifer systems where highly compressible aquitards are present. The highly compressible nature of the aquitards leads to nonlinear consolidation where the groundwater flow parameters are stress-dependent. The case is further complicated by the heterogeneity of the hydrogeologic and geotechnical properties of the aquitards. The effect of realistic vertical heterogeneity of hydrogeologic and geotechnical parameters on the consolidation of highly compressible aquitards is investigated by means of one-dimensional Monte Carlo numerical simulations where the lower boundary represents the effect of an instant drop in hydraulic head due to groundwater pumping. Two thousand realizations are generated for each of the following parameters: hydraulic conductivity ( K), compression index ( C c), void ratio ( e) and m (an empirical parameter relating hydraulic conductivity and void ratio). The correlation structure, the mean and the variance for each parameter were obtained from a literature review about field studies in the lacustrine sediments of Mexico City. The results indicate that among the parameters considered, random K has the largest effect on the ensemble average behavior of the system when compared to a nonlinear consolidation model with deterministic initial parameters. The deterministic solution underestimates the ensemble average of total settlement when initial K is random. In addition, random K leads to the largest variance (and therefore largest uncertainty) of total settlement, groundwater flux and time to reach steady-state conditions.

Broadband terahertz generation of metamaterials

DOEpatents

Luo, Liang; Wang, Jigang; Koschny, Thomas; Wegener, Martin; Soukoulis, Costas M.

2017-06-20

Provided are systems and methods to generate single-cycle THz pulses from a few tens of nanometers thin layer of split ring resonators (SRRs) via optical rectification of femtosecond laser pulses. The emitted THz radiation, with a spectrum ranging from about 0.1 to 4 THz, arises exclusively from pumping the magnetic-dipole resonance of SRRs around 200 THz. This resonant enhancement, together with pump polarization dependence and power scaling of the THz emission, underpins the nonlinearity from optically induced circulating currents in SRRs, with a huge effective nonlinear susceptibility of 0.8.times.10.sup.-16 m.sup.2/V that far exceeds surface nonlinearities of both thin films and bulk organic/inorganic crystals and sheet nonlinearities of non-centrosymmetric materials such as ZnTe.

Thermally induced nonlinear optical absorption in metamaterial perfect absorbers

NASA Astrophysics Data System (ADS)

Guddala, Sriram; Kumar, Raghwendra; Ramakrishna, S. Anantha

2015-03-01

A metamaterial perfect absorber consisting of a tri-layer (Al/ZnS/Al) metal-dielectric-metal system with top aluminium nano-disks was fabricated by laser-interference lithography and lift-off processing. The metamaterial absorber had peak resonant absorbance at 1090 nm and showed nonlinear absorption for 600ps laser pulses at 1064 nm wavelength. A nonlinear saturation of reflectance was measured to be dependent on the average laser power incident and not the peak laser intensity. The nonlinear behaviour is shown to arise from the heating due to the absorbed radiation and photo-thermal changes in the dielectric properties of aluminium. The metamaterial absorber is seen to be damage resistant at large laser intensities of 25 MW/cm2.

Teaching and Learning the Interplay between Chance and Determinism in Nonlinear Systems

ERIC Educational Resources Information Center

Stavrou, Dimitrios; Duit, Reinders

2014-01-01

That the interplay of random and deterministic processes may result in both the limited predictability of nonlinear systems and the formation of structures seems to be a most valuable general insight into the nature of science. This study investigates the possibility of teaching and learning the interplay of chance and determinism in nonlinear…

Nonlinear Image Denoising Methodologies

DTIC Science & Technology

2002-05-01

53 5.3 A Multiscale Approach to Scale-Space Analysis . . . . . . . . . . . . . . . . 53 5.4...etc. In this thesis, Our approach to denoising is first based on a controlled nonlinear stochastic random walk to achieve a scale space analysis ( as in... stochastic treatment or interpretation of the diffusion. In addition, unless a specific stopping time is known to be adequate, the resulting evolution

Nonlinear Fatigue Damage Model Based on the Residual Strength Degradation Law

NASA Astrophysics Data System (ADS)

Yongyi, Gao; Zhixiao, Su

In this paper, a logarithmic expression to describe the residual strength degradation process is developed in order to fatigue test results for normalized carbon steel. The definition and expression of fatigue damage due to symmetrical stress with a constant amplitude are also given. The expression of fatigue damage can also explain the nonlinear properties of fatigue damage. Furthermore, the fatigue damage of structures under random stress is analyzed, and an iterative formula to describe the fatigue damage process is deduced. Finally, an approximate method for evaluating the fatigue life of structures under repeated random stress blocking is presented through various calculation examples.

Variational Solutions and Random Dynamical Systems to SPDEs Perturbed by Fractional Gaussian Noise

PubMed Central

Zeng, Caibin; Yang, Qigui; Cao, Junfei

2014-01-01

This paper deals with the following type of stochastic partial differential equations (SPDEs) perturbed by an infinite dimensional fractional Brownian motion with a suitable volatility coefficient Φ: dX(t) = A(X(t))dt+Φ(t)dB H(t), where A is a nonlinear operator satisfying some monotonicity conditions. Using the variational approach, we prove the existence and uniqueness of variational solutions to such system. Moreover, we prove that this variational solution generates a random dynamical system. The main results are applied to a general type of nonlinear SPDEs and the stochastic generalized p-Laplacian equation. PMID:24574903

Nonlinear system controller design based on domain of attaction: An application to CELSS analysis and control

NASA Technical Reports Server (NTRS)

Babcock, P. S., IV

1986-01-01

Nonlinear system controller design based on the domain of attraction is presented. This is particularly suited to investigating Closed Ecological Life Support Systems (CELSS) models. In particular, the dynamic consequences of changes in the waste storage capacity and system mass, and how information is used for control in CELSS models are examined. The models' high dimensionality and nonlinear state equations make them difficult to analyze by any other technique. The domain of attraction is the region in initial conditions that tend toward an attractor and it is delineated by randomly selecting initial conditions from the region of state space being investigated. Error analysis is done by repeating the domain simulations with independent samples. A refinement of this region is the domain of performance which is the region of initial conditions meeting a performance criteria. In nonlinear systems, local stability does not insure stability over a larger region. The domain of attraction marks out this stability region; hence, it can be considered a measure of a nonlinear system's ability to recovery from state perturbations. Considering random perturbations, the minimum radius of the domain is a measure of the magnitude of perturbations for which recovery is guaranteed. Design of both linear and nonlinear controllers are shown. Three CELSS models, with 9 to 30 state variable, are presented. Measures of the domain of attraction are used to show the global behavior of these models under a variety of design and controller scenarios.

Very thick mixture oxide ion beam sputtering films for investigation of nonlinear material properties

NASA Astrophysics Data System (ADS)

Steinecke, Morten; Kiedrowski, Kevin; Jupé, Marco; Ristau, Detlev

2017-11-01

Currently, optical coating technology is facing a multitude of new challenges. Some of the new requirements are addressed to the spectral behavior of complex coatings, but in addition, the power handling capabilities gain in importance. Often, both demands are combined in the same component, for example in chirped mirrors for ultra-short pulse applications. The consequent demands on the accuracy of the layer thicknesses and the stability of the refractive indices require a deposition by sputtering processes. For high end components, Ion Beam Sputtering (IBS) is often the method of choice. Utilizing the Co-sputtering technique, IBS additionally allows a higher flexibility in the possible coating materials by mixing two pure oxides into one ternary composite material. These composite materials are also advantageous for researching third order nonlinear effects, which can limit the functionality of optics at high powers. The layer thicknesses required for this fundamental research often exceed 100 µm, which therefore makes low stress and absorption in the layer materials mandatory. A reduction of these decisive properties can be achieved by a thermal treatment of the sample. Usually, this is performed by a post-deposition annealing. Alternatively, the coating temperature can be increased. This is rarely done for IBS processes, but it can be assumed, that the effect is comparable to that of ex-situ annealing. In this work, different ternary mixtures of Al2O3/SiO2, HfO2/Al2O3 as well as Nb2O5/Al2O3 were investigated for their layer stress and absorption, applying both, in-situ temperature treatment as well as post manufacturing annealing. It is observed that suitable thermal treatment as well as material composition can significantly reduce layer stress and absorption in the deposited layer. This enabled the manufacturing of layers with thicknesses of over 180 µm as well as the measurement of nonlinear properties of the deposited materials. Contribution to the topical issue "Plasma Sources and Plasma Processes (PSPP)", edited by Luis Lemos Alves, Thierry Belmonte and Tiberiu Minea

Predicting the mixed-mode I/II spatial damage propagation along 3D-printed soft interfacial layer via a hyperelastic softening model

NASA Astrophysics Data System (ADS)

Liu, Lei; Li, Yaning

2018-07-01

A methodology was developed to use a hyperelastic softening model to predict the constitutive behavior and the spatial damage propagation of nonlinear materials with damage-induced softening under mixed-mode loading. A user subroutine (ABAQUS/VUMAT) was developed for numerical implementation of the model. 3D-printed wavy soft rubbery interfacial layer was used as a material system to verify and validate the methodology. The Arruda - Boyce hyperelastic model is incorporated with the softening model to capture the nonlinear pre-and post- damage behavior of the interfacial layer under mixed Mode I/II loads. To characterize model parameters of the 3D-printed rubbery interfacial layer, a series of scarf-joint specimens were designed, which enabled systematic variation of stress triaxiality via a single geometric parameter, the slant angle. It was found that the important model parameter m is exponentially related to the stress triaxiality. Compact tension specimens of the sinusoidal wavy interfacial layer with different waviness were designed and fabricated via multi-material 3D printing. Finite element (FE) simulations were conducted to predict the spatial damage propagation of the material within the wavy interfacial layer. Compact tension experiments were performed to verify the model prediction. The results show that the model developed is able to accurately predict the damage propagation of the 3D-printed rubbery interfacial layer under complicated stress-state without pre-defined failure criteria.

Multidimensional density shaping by sigmoids.

PubMed

Roth, Z; Baram, Y

1996-01-01

An estimate of the probability density function of a random vector is obtained by maximizing the output entropy of a feedforward network of sigmoidal units with respect to the input weights. Classification problems can be solved by selecting the class associated with the maximal estimated density. Newton's optimization method, applied to the estimated density, yields a recursive estimator for a random variable or a random sequence. A constrained connectivity structure yields a linear estimator, which is particularly suitable for "real time" prediction. A Gaussian nonlinearity yields a closed-form solution for the network's parameters, which may also be used for initializing the optimization algorithm when other nonlinearities are employed. A triangular connectivity between the neurons and the input, which is naturally suggested by the statistical setting, reduces the number of parameters. Applications to classification and forecasting problems are demonstrated.

Improved decryption quality and security of a joint transform correlator-based encryption system

NASA Astrophysics Data System (ADS)

Vilardy, Juan M.; Millán, María S.; Pérez-Cabré, Elisabet

2013-02-01

Some image encryption systems based on modified double random phase encoding and joint transform correlator architecture produce low quality decrypted images and are vulnerable to a variety of attacks. In this work, we analyse the algorithm of some reported methods that optically implement the double random phase encryption in a joint transform correlator. We show that it is possible to significantly improve the quality of the decrypted image by introducing a simple nonlinear operation in the encrypted function that contains the joint power spectrum. This nonlinearity also makes the system more resistant to chosen-plaintext attacks. We additionally explore the system resistance against this type of attack when a variety of probability density functions are used to generate the two random phase masks of the encryption-decryption process. Numerical results are presented and discussed.

Nonlinear complexity behaviors of agent-based 3D Potts financial dynamics with random environments

NASA Astrophysics Data System (ADS)

Xing, Yani; Wang, Jun

2018-02-01

A new microscopic 3D Potts interaction financial price model is established in this work, to investigate the nonlinear complexity behaviors of stock markets. 3D Potts model, which extends the 2D Potts model to three-dimensional, is a cubic lattice model to explain the interaction behavior among the agents. In order to explore the complexity of real financial markets and the 3D Potts financial model, a new random coarse-grained Lempel-Ziv complexity is proposed to certain series, such as the price returns, the price volatilities, and the random time d-returns. Then the composite multiscale entropy (CMSE) method is applied to the intrinsic mode functions (IMFs) and the corresponding shuffled data to study the complexity behaviors. The empirical results indicate that the 3D financial model is feasible.

Nonlinear Analytical Modeling of Interfacial Phenomenon and Nano-Size Microstructural Features to Better Correlate Nde Electronic Property Measurements to Material State

NASA Astrophysics Data System (ADS)

Roubidoux, J. A.; Jackson, J. E.; Lasseigne, A. N.; Mishra, B.; Olson, D. L.

2010-02-01

This paper correlates nonlinear material properties to nondestructive electronic measurements by using wave analysis techniques (e.g. Perturbation Methods) and incorporating higher-order phenomena. The correlations suggest that nondestructive electronic property measurements and practices can be used to assess thin films, surface layers, and other advanced materials that exhibit modified behaviors based on their space-charged interfacial behavior.

Active control of panel vibrations induced by a boundary layer flow

NASA Technical Reports Server (NTRS)

Chow, Pao-Liu

1995-01-01

The problems of active and passive control of sound and vibration has been investigated by many researchers for a number of years. However, few of the articles are concerned with the sound and vibration with flow-structure interaction. Experimental and numerical studies on the coupling between panel vibration and acoustic radiation due to flow excitation have been done by Maestrello and his associates at NASA/Langley Research Center. Since the coupled system of nonlinear partial differential equations is formidable, an analytical solution to the full problem seems impossible. For this reason, we have to simplify the problem to that of the nonlinear panel vibration induced by a uniform flow or a boundary-layer flow with a given wall pressure distribution. Based on this simplified model, we have been able to consider the control and stabilization of the nonlinear panel vibration, which have not been treated satisfactorily by other authors. Although the sound radiation has not been included, the vibration suppression will clearly reduce the sound radiation power from the panel. The major research findings are presented in three sections. In section two we describe results on the boundary control of nonlinear panel vibration, with or without flow excitation. Sections three and four are concerned with some analytical and numerical results in the optimal control of the linear and nonlinear panel vibrations, respectively, excited by the flow pressure fluctuations. Finally, in section five, we draw some conclusions from research findings.

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

PubMed Central

Allagui, Anis; Freeborn, Todd J.; Elwakil, Ahmed S.; Maundy, Brent J.

2016-01-01

The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal SsC behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance Rs in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (Rs, Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical RsC model. We validate our formulae with the experimental measurements of different EDLCs. PMID:27934904

Coherent Structures in Magnetic Confinement Systems

NASA Astrophysics Data System (ADS)

Horton, W.

2006-04-01

Coherent structures are long-lived, nonlinear localized solutions of the selfconsistient plasma-electromagnetic field equations. They contain appreciable energy density and control various transport and magnetic reconnection processes in plasmas. These structures are self-binding from the nonlinearity balancing, or overcoming, the wave dispersion of energy in smaller amplitude structures. The structures evolve out of the nonlinear interactions in various instabilities or external driving fields. The theoretical basis for these structures are reviewed giving examples from various plasma instabilities and their reduced descriptions from the appropriate partial differential equations. A classic example from drift waves is the formation of monopole, dipole and tripolar vortex structures which have been created in both laboratory and simulation experiments. For vortices, the long life-time and nonlinear interactions of the structures can be understood with conservation laws of angular momentum given by the vorticity field associated with dynamics. Other morphologies include mushrooms, Kelvin-Helmholtz vorticity roll-up, streamers and blobs. We show simulation movies of various examples drawn from ETG modes in NSTX, H-mode like shear flow layers in LAPD and the vortices measured with soft x-ray tomography in the GAMMA 10 tandem mirror. Coherent current-sheet structures form in driven magnetic reconnection layers and control the rate of transformation of magnetic energy to flow and thermal energy.

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

NASA Astrophysics Data System (ADS)

Allagui, Anis; Freeborn, Todd J.; Elwakil, Ahmed S.; Maundy, Brent J.

2016-12-01

The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal SsC behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance Rs in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (Rs, Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical RsC model. We validate our formulae with the experimental measurements of different EDLCs.

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.

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry.

PubMed

Allagui, Anis; Freeborn, Todd J; Elwakil, Ahmed S; Maundy, Brent J

2016-12-09

The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal R s C behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics [corrected]. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance R s in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (R s , Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical R s C model. We validate our formulae with the experimental measurements of different EDLCs.

Versatile soliton emission from a WS2 mode-locked fiber laser

NASA Astrophysics Data System (ADS)

Guo, Bo; Li, Shi; Fan, Ya-xian; Wang, Pengfei

2018-01-01

Recently, few-layer tungsten disulfide (WS2), as a shining 2D material, has been discovered to possess both the saturable absorption ability and large nonlinear refractive index. Here, we demonstrate versatile soliton pulses in a passively mode-locked fiber laser with a WS2-deposited microfiber. The few-layer WS2 is prepared by the liquid-phase exfoliation method and transferred onto a microfiber by the optical deposition method. Study found, the WS2-deposited microfiber can operate simultaneously as a mode-locker and a high-nonlinear device. In experiment, by further inserting the WS2 device into the fiber laser, besides the dual-wavelength soliton, noise-like soliton pulse, conventional soliton and its harmonic form are obtained by properly adjusting the pump strength and the polarization states. For the dual-wavelength soliton pulses and noise-like pulse, the maximum output power of 14.2 mW and pulse energy of 4.74 nJ is obtained, respectively. In addition, we also achieve the maximum harmonic number (135) of conventional soliton, corresponding to a repetition rate of ∼ 497 . 5 MHz. Our study shows clearly that WS2-deposited microfiber can be as a high-nonlinear photonic device for studying a plenty of nonlinear soliton phenomena.

Controlling the stability of nonlinear optical modes via electromagnetically induced transparency

NASA Astrophysics Data System (ADS)

Zhang, Kun; Liang, Yi-zeng; Lin, Ji; Li, Hui-jun

2018-02-01

We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having Λ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schrödinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.

Small-scale plasma turbulence and intermittency in the high latitude F region based on the ICI-2 sounding rocket experiment

NASA Astrophysics Data System (ADS)

Spicher, A.; Miloch, W.; Moen, J. I.; Clausen, L. B. N.

2015-12-01

Small-scale plasma irregularities and turbulence are common phenomena in the F layer of the ionosphere, both in the equatorial and polar regions. A common approach in analyzing data from experiments on space and ionospheric plasma irregularities are power spectra. Power spectra give no information about the phases of the waveforms, and thus do not allow to determine whether some of the phases are correlated or whether they exhibit a random character. The former case would imply the presence of nonlinear wave-wave interactions, while the latter suggests a more turbulent-like process. Discerning between these mechanisms is crucial for understanding high latitude plasma irregularities and can be addressed with bispectral analysis and higher order statistics. In this study, we use higher order spectra and statistics to analyze electron density data observed with the ICI-2 sounding rocket experiment at a meter-scale resolution. The main objective of ICI-2 was to investigate plasma irregularities in the cusp in the F layer ionosphere. We study in detail two regions intersected during the rocket flight and which are characterized by large density fluctuations: a trailing edge of a cold polar cap patch, and a density enhancement subject to cusp auroral particle precipitation. While these two regions exhibit similar power spectra, our analysis reveals that their internal structure is different. The structures on the edge of the polar cap patch are characterized by significant coherent mode coupling and intermittency, while the plasma enhancement associated with precipitation exhibits stronger random characteristics. This indicates that particle precipitation may play a fundamental role in ionospheric plasma structuring by creating turbulent-like structures.

Egg production forecasting: Determining efficient modeling approaches.

PubMed

Ahmad, H A

2011-12-01

Several mathematical or statistical and artificial intelligence models were developed to compare egg production forecasts in commercial layers. Initial data for these models were collected from a comparative layer trial on commercial strains conducted at the Poultry Research Farms, Auburn University. Simulated data were produced to represent new scenarios by using means and SD of egg production of the 22 commercial strains. From the simulated data, random examples were generated for neural network training and testing for the weekly egg production prediction from wk 22 to 36. Three neural network architectures-back-propagation-3, Ward-5, and the general regression neural network-were compared for their efficiency to forecast egg production, along with other traditional models. The general regression neural network gave the best-fitting line, which almost overlapped with the commercial egg production data, with an R(2) of 0.71. The general regression neural network-predicted curve was compared with original egg production data, the average curves of white-shelled and brown-shelled strains, linear regression predictions, and the Gompertz nonlinear model. The general regression neural network was superior in all these comparisons and may be the model of choice if the initial overprediction is managed efficiently. In general, neural network models are efficient, are easy to use, require fewer data, and are practical under farm management conditions to forecast egg production.

Sensitivity Analysis of Mechanical Parameters of Different Rock Layers to the Stability of Coal Roadway in Soft Rock Strata

PubMed Central

Zhao, Zeng-hui; Wang, Wei-ming; Gao, Xin; Yan, Ji-xing

2013-01-01

According to the geological characteristics of Xinjiang Ili mine in western area of China, a physical model of interstratified strata composed of soft rock and hard coal seam was established. Selecting the tunnel position, deformation modulus, and strength parameters of each layer as influencing factors, the sensitivity coefficient of roadway deformation to each parameter was firstly analyzed based on a Mohr-Columb strain softening model and nonlinear elastic-plastic finite element analysis. Then the effect laws of influencing factors which showed high sensitivity were further discussed. Finally, a regression model for the relationship between roadway displacements and multifactors was obtained by equivalent linear regression under multiple factors. The results show that the roadway deformation is highly sensitive to the depth of coal seam under the floor which should be considered in the layout of coal roadway; deformation modulus and strength of coal seam and floor have a great influence on the global stability of tunnel; on the contrary, roadway deformation is not sensitive to the mechanical parameters of soft roof; roadway deformation under random combinations of multi-factors can be deduced by the regression model. These conclusions provide theoretical significance to the arrangement and stability maintenance of coal roadway. PMID:24459447

Bias magnetic field and test period dependences of direct and converse magnetoelectric hysteresis of tri-layered magnetoelectric composite

NASA Astrophysics Data System (ADS)

Zhou, Yun; Li, Xiao-Hong; Wang, Jian-Feng; Zhou, Hao-Miao; Cao, Dan; Jiao, Zhi-Wei; Xu, Long; Li, Qi-Hao

2018-04-01

The direct and converse magnetoelectric hysteresis behavior for a tri-layered composite has been comparatively investigated and significant similarities have been observed. The results show that both the direct and converse magnetoelectric hysteresis is deeply affected by the bias magnetic field and test period. The test time hysteresis caused by a fast varying bias magnetic field can be reduced by prolonging the test period. The observed coercive field, remanence, and ratio of remanence of the direct and converse magnetoelectric effects with the test period obey an exponential decay law. A hysteretic nonlinear magnetoelectric theoretical model for the symmetrical tri-layered structure has been proposed based on a nonlinear constitutive model and pinning effect. The numerical calculation shows that the theoretical results are in good agreement with the experimental results. These findings not only provide insight into the examination and practical applications of magnetoelectric materials, but also propose a theoretical frame for studying the hysteretic characteristics of the magnetoelectric effect.

Phase relations in a forced turbulent boundary layer: implications for modelling of high Reynolds number wall turbulence.

PubMed

Duvvuri, Subrahmanyam; McKeon, Beverley

2017-03-13

Phase relations between specific scales in a turbulent boundary layer are studied here by highlighting the associated nonlinear scale interactions in the flow. This is achieved through an experimental technique that allows for targeted forcing of the flow through the use of a dynamic wall perturbation. Two distinct large-scale modes with well-defined spatial and temporal wavenumbers were simultaneously forced in the boundary layer, and the resulting nonlinear response from their direct interactions was isolated from the turbulence signal for the study. This approach advances the traditional studies of large- and small-scale interactions in wall turbulence by focusing on the direct interactions between scales with triadic wavenumber consistency. The results are discussed in the context of modelling high Reynolds number wall turbulence.This article is part of the themed issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number'. © 2017 The Author(s).

Deoxyribonucleic acid (DNA) cladding layers for nonlinear-optic-polymer-based electro-optic devices

NASA Astrophysics Data System (ADS)

Grote, James G.; Ogata, Naoya; Diggs, Darnell E.; Hopkins, Frank K.

2003-07-01

Nonlinear optic (NLO) polymer based electro-optic devices have been achieving world record low half wave voltages and high frequencies over the last 2-3 years. Part of the advancement is through the use of relatively more conductive polymers for the cladding layers. Based on the current materials available for these cladding materials, however, the desired optical and electromagnetic properites are being balanced for materials processability. One does not want the solvent present in one layer to dissovle the one deposited underneath, or be dissolved by the one being deposited on top. Optimized polymer cladding materials, to further enhance device performance, are continuing to be investigated. Thin films of deoxyribonucleic acid (DNA), derived from salmon sperm, show promise in providing both the desired optical and magnetic properties, as well as the desired resistance to various solvents used for NLO polymer device fabrication. Thin films of DNA were deposited on glass and silicon substrates and the film quality, optical and electromagnetic properties and resistance to various solvents were characterized.

A Sliding Mode Controller Using Nonlinear Sliding Surface Improved With Fuzzy Logic: Application to the Coupled Tanks System

NASA Astrophysics Data System (ADS)

Boubakir, A.; Boudjema, F.; Boubakir, C.

2008-06-01

This paper proposes an approach of hybrid control that is based on the concept of combining fuzzy logic and the methodology of sliding mode control (SMC). In the present works, a first-order nonlinear sliding surface is presented, on which the developed control law is based. Mathematical proof for the stability and convergence of the system is presented. In order to reduce the chattering in sliding mode control, a fixed boundary layer around the switch surface is used. Within the boundary layer, since the fuzzy logic control is applied, the chattering phenomenon, which is inherent in a sliding mode control, is avoided by smoothing the switch signal. Outside the boundary, the sliding mode control is applied to driving the system states into the boundary layer. Experimental studies carried out on a coupled Tanks system indicate that the proposed fuzzy sliding mode control (FSMC) is a good candidate for control applications.

Instabilities in a staircase stratified shear flow

NASA Astrophysics Data System (ADS)

Ponetti, G.; Balmforth, N. J.; Eaves, T. S.

2018-01-01

We study stratified shear flow instability where the density profile takes the form of a staircase of interfaces separating uniform layers. Internal gravity waves riding on density interfaces can resonantly interact due to a background shear flow, resulting in the Taylor-Caulfield instability. The many steps of the density profile permit a multitude of interactions between different interfaces, and a rich variety of Taylor-Caulfield instabilities. We analyse the linear instability of a staircase with piecewise-constant density profile embedded in a background linear shear flow, locating all the unstable modes and identifying the strongest. The interaction between nearest-neighbour interfaces leads to the most unstable modes. The nonlinear dynamics of the instabilities are explored in the long-wavelength, weakly stratified limit (the defect approximation). Unstable modes on adjacent interfaces saturate by rolling up the intervening layer into a distinctive billow. These nonlinear structures coexist when stacked vertically and are bordered by the sharp density gradients that are the remnants of the steps of the original staircase. Horizontal averages remain layer-like.

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

NASA Astrophysics Data System (ADS)

Bache, Morten; Lavrinenko, Andrei V.

2017-09-01

Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.

Effect of aspect ratio on sidewall boundary-layer influence in two-dimensional airfoil testing

NASA Technical Reports Server (NTRS)

Murthy, A. V.

1986-01-01

The effect of sidewall boundary layers in airfoil testing in two-dimensional wind tunnels is investigated. The non-linear crossflow velocity variation induced because of the changes in the sidewall boundary-layer thickness is represented by the flow between a wavy wall and a straight wall. Using this flow model, a correction for the sidewall boundary-layer effects is derived in terms of the undisturbed sidewall boundary-layer properties, the test Mach number and the airfoil aspect ratio. Application of the proposed correction to available experimental data showed good correlation for the shock location and pressure distribution on airfoils.

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 channel equalization for QAM signal constellation using artificial neural networks.

PubMed

Patra, J C; Pal, R N; Baliarsingh, R; Panda, G

1999-01-01

Application of artificial neural networks (ANN's) to adaptive channel equalization in a digital communication system with 4-QAM signal constellation is reported in this paper. A novel computationally efficient single layer functional link ANN (FLANN) is proposed for this purpose. This network has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric polynomials. Because of input pattern enhancement, the FLANN is capable of forming arbitrarily nonlinear decision boundaries and can perform complex pattern classification tasks. Considering channel equalization as a nonlinear classification problem, the FLANN has been utilized for nonlinear channel equalization. The performance of the FLANN is compared with two other ANN structures [a multilayer perceptron (MLP) and a polynomial perceptron network (PPN)] along with a conventional linear LMS-based equalizer for different linear and nonlinear channel models. The effect of eigenvalue ratio (EVR) of input correlation matrix on the equalizer performance has been studied. The comparison of computational complexity involved for the three ANN structures is also provided.

Adaptively combined FIR and functional link artificial neural network equalizer for nonlinear communication channel.

PubMed

Zhao, Haiquan; Zhang, Jiashu

2009-04-01

This paper proposes a novel computational efficient adaptive nonlinear equalizer based on combination of finite impulse response (FIR) filter and functional link artificial neural network (CFFLANN) to compensate linear and nonlinear distortions in nonlinear communication channel. This convex nonlinear combination results in improving the speed while retaining the lower steady-state error. In addition, since the CFFLANN needs not the hidden layers, which exist in conventional neural-network-based equalizers, it exhibits a simpler structure than the traditional neural networks (NNs) and can require less computational burden during the training mode. Moreover, appropriate adaptation algorithm for the proposed equalizer is derived by the modified least mean square (MLMS). Results obtained from the simulations clearly show that the proposed equalizer using the MLMS algorithm can availably eliminate various intensity linear and nonlinear distortions, and be provided with better anti-jamming performance. Furthermore, comparisons of the mean squared error (MSE), the bit error rate (BER), and the effect of eigenvalue ratio (EVR) of input correlation matrix are presented.

Decoupled ARX and RBF Neural Network Modeling Using PCA and GA Optimization for Nonlinear Distributed Parameter Systems.

PubMed

Zhang, Ridong; Tao, Jili; Lu, Renquan; Jin, Qibing

2018-02-01

Modeling of distributed parameter systems is difficult because of their nonlinearity and infinite-dimensional characteristics. Based on principal component analysis (PCA), a hybrid modeling strategy that consists of a decoupled linear autoregressive exogenous (ARX) model and a nonlinear radial basis function (RBF) neural network model are proposed. The spatial-temporal output is first divided into a few dominant spatial basis functions and finite-dimensional temporal series by PCA. Then, a decoupled ARX model is designed to model the linear dynamics of the dominant modes of the time series. The nonlinear residual part is subsequently parameterized by RBFs, where genetic algorithm is utilized to optimize their hidden layer structure and the parameters. Finally, the nonlinear spatial-temporal dynamic system is obtained after the time/space reconstruction. Simulation results of a catalytic rod and a heat conduction equation demonstrate the effectiveness of the proposed strategy compared to several other methods.

Low power continuous-wave nonlinear optical effects in MoS2 nanosheets synthesized by simple bath ultrasonication

NASA Astrophysics Data System (ADS)

Karmakar, S.; Biswas, S.; Kumbhakar, P.

2017-11-01

Here, we have unveiled low power continuous-wave nonlinear optical properties of a few layer (4-12L) Molybdenum disulfide (MoS2) dispersion in N, N-dimethylformamide (DMF) by using spatial self-phase modulation technique. The effective third-order nonlinear susceptibility of the monolayer has been estimated to be as high as ∼10-8 esu. Also a low power technique of syntheses of stable and a few-layer (4-12L) MoS2 dispersion in DMF has been demonstrated here by utilizing ultrasonication bath treatment combined with the natural gravitation sedimentation effect starting from the bulk MoS2 powder. The synthesized samples are exhibiting interesting linear optical absorption and photoluminescence (PL) after exfoliation to a few layer nanosheets (NSs) and the exciton binding energies have been determined from PL emission data in association with 2D hydrogenic Bohr-exciton model. The specific capacitances (Csp) of the electrode prepared with MoS2 NSs have been measured by electrochemical measurement and the highest value of Csp is 382 Fg-1 for 4L sample. The reported intensity driven change of Csp in the presence of light emitted from light emitting diodes of various colours is unprecedented. The demonstrated technique can be scaled up for large scale and easy synthesis of other 2D materials having applications in optoelectronics and energy devices.

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 fractional waves at elastic interfaces

NASA Astrophysics Data System (ADS)

Kappler, Julian; Shrivastava, Shamit; Schneider, Matthias F.; Netz, Roland R.

2017-11-01

We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface.

The Creative Chaos: Speculations on the Connection Between Non-Linear Dynamics and the Creative Process

NASA Astrophysics Data System (ADS)

Zausner, Tobi

Chaos theory may provide models for creativity and for the personality of the artist. A collection of speculative hypotheses examines the connection between art and such fundamentals of non-linear dynamics as iteration, dissipative processes, open systems, entropy, sensitivity to stimuli, autocatalysis, subsystems, bifurcations, randomness, unpredictability, irreversibility, increasing levels of organization, far-from-equilibrium conditions, strange attractors, period doubling, intermittency and self-similar fractal organization. Non-linear dynamics may also explain why certain individuals suffer mental disorders while others remain intact during a lifetime of sustained creative output.

A numerical evaluation of the dynamical systems approach to wall layer turbulence

NASA Technical Reports Server (NTRS)

Berkooz, Gal

1990-01-01

This work attempts to test predictions based on the Dynamical Systems approach to Wall Layer Turbulence. We analyze the Dynamical Systems model for the nonlinear interaction mechanisms between the coherent structures and deduce qualitative behavior as expected. We then test for this behavior in data sets from D.N.S. The agreement is good, given the suboptimal conditions for the test. We discuss implications of this test and work to be done to deepen the understanding of control of turbulent boundary layers.

Passive microwave remote sensing of an anisotropic random-medium layer

NASA Technical Reports Server (NTRS)

Lee, J. K.; Kong, J. A.

1985-01-01

The principle of reciprocity is invoked to calculate the brightness temperatures for passive microwave remote sensing of a two-layer anisotropic random medium. The bistatic scattering coefficients are first computed with the Born approximation and then integrated over the upper hemisphere to be subtracted from unity, in order to obtain the emissivity for the random-medium layer. The theoretical results are illustrated by plotting the emissivities as functions of viewing angles and polarizations. They are used to interpret remote sgnsing data obtained from vegetation canopy where the anisotropic random-medium model applies. Field measurements with corn stalks arranged in various configurations with preferred azimuthal directions are successfully interpreted with this model.

Near-Bottom Turbulence and Sediment Resuspension Induced by Nonlinear Internal Waves

DTIC Science & Technology

2011-09-30

boundary layer (BBL) turbulence and particulate resuspension leading to benthic nepheloid layer ( BNL ) formation. OBJECTIVES The specific...identify mechanisms for the capturing of nearbed particles by the BBL-turbulence and their transport/deposition into BNLs . • Analyze field...resuspended particle distributions under NLIWs, a reliable proxy of BNLs , can be used to quantify the transmission or backscatter of optical/acoustic

NH4 Be2 BO3 F2 and γ-Be2 BO3 F: Overcoming the Layering Habit in KBe2 BO3 F2 for the Next-Generation Deep-Ultraviolet Nonlinear Optical Materials.

PubMed

Peng, Guang; Ye, Ning; Lin, Zheshuai; Kang, Lei; Pan, Shilie; Zhang, Min; Lin, Chensheng; Long, Xifa; Luo, Min; Chen, Yu; Tang, Yu-Huan; Xu, Feng; Yan, Tao

2018-05-12

KBe 2 BO 3 F 2 (KBBF) is still the only practically usable crystal that can generate deep-ultraviolet (DUV) coherent light by direct second harmonic generation (SHG). However, applications are hindered by layering, leading to difficulty in the growth of thick crystals and compromised mechanical integrity. Despite efforts, it is still a great challenge to discover new nonlinear optical (NLO) materials that overcome the layering while keeping the DUV SHG available. Now, two new DUV NLO beryllium borates have been successfully designed and synthesized, NH 4 Be 2 BO 3 F 2 (ABBF) and γ-Be 2 BO 3 F (γ-BBF), which not only overcome the layering but also can be used as next-generation DUV NLO materials with the shortest type I phase-matching second-harmonic wavelength down to 173.9 nm and 146 nm, respectively. Significantly, γ-BBF is superior to KBBF in all metrics and would be the most outstanding DUV NLO crystal. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Self-synchronization in an ensemble of nonlinear oscillators

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

Ostrovsky, L. A., E-mail: lev.ostrovsky@gmail.com; Galperin, Y. V.; Skirta, E. A.

2016-06-15

The paper describes the results of study of a system of coupled nonlinear, Duffing-type oscillators, from the viewpoint of their self-synchronization, i.e., generation of a coherent field (order parameter) via instability of an incoherent (random-phase) initial state. We consider both the cases of dissipative coupling (e.g., via the joint radiation) and reactive coupling in a Hamiltonian system.

Acoustic fatigue life prediction for nonlinear structures with multiple resonant modes

NASA Technical Reports Server (NTRS)

Miles, R. N.

1992-01-01

This report documents an effort to develop practical and accurate methods for estimating the fatigue lives of complex aerospace structures subjected to intense random excitations. The emphasis of the current program is to construct analytical schemes for performing fatigue life estimates for structures that exhibit nonlinear vibration behavior and that have numerous resonant modes contributing to the response.

Numerical modeling of nonlinear modulation of coda wave interferometry in a multiple scattering medium with the presence of a localized micro-cracked zone

NASA Astrophysics Data System (ADS)

Chen, Guangzhi; Pageot, Damien; Legland, Jean-Baptiste; Abraham, Odile; Chekroun, Mathieu; Tournat, Vincent

2018-04-01

The spectral element method is used to perform a parametric sensitivity study of the nonlinear coda wave interferometry (NCWI) method in a homogeneous sample with localized damage [1]. The influence of a strong pump wave on a localized nonlinear damage zone is modeled as modifications to the elastic properties of an effective damage zone (EDZ), depending on the pump wave amplitude. The local change of the elastic modulus and the attenuation coefficient have been shown to vary linearly with respect to the excitation amplitude of the pump wave as in previous experimental studies of Zhang et al. [2]. In this study, the boundary conditions of the cracks, i.e. clapping effects is taken into account in the modeling of the damaged zone. The EDZ is then modeled with random cracks of random orientations, new parametric studies are established to model the pump wave influence with two new parameters: the change of the crack length and the crack density. The numerical results reported constitute another step towards quantification and forecasting of the nonlinear acoustic response of a cracked material, which proves to be necessary for quantitative non-destructive evaluation.

Error sensitivity analysis in 10-30-day extended range forecasting by using a nonlinear cross-prediction error model

NASA Astrophysics Data System (ADS)

Xia, Zhiye; Xu, Lisheng; Chen, Hongbin; Wang, Yongqian; Liu, Jinbao; Feng, Wenlan

2017-06-01

Extended range forecasting of 10-30 days, which lies between medium-term and climate prediction in terms of timescale, plays a significant role in decision-making processes for the prevention and mitigation of disastrous meteorological events. The sensitivity of initial error, model parameter error, and random error in a nonlinear crossprediction error (NCPE) model, and their stability in the prediction validity period in 10-30-day extended range forecasting, are analyzed quantitatively. The associated sensitivity of precipitable water, temperature, and geopotential height during cases of heavy rain and hurricane is also discussed. The results are summarized as follows. First, the initial error and random error interact. When the ratio of random error to initial error is small (10-6-10-2), minor variation in random error cannot significantly change the dynamic features of a chaotic system, and therefore random error has minimal effect on the prediction. When the ratio is in the range of 10-1-2 (i.e., random error dominates), attention should be paid to the random error instead of only the initial error. When the ratio is around 10-2-10-1, both influences must be considered. Their mutual effects may bring considerable uncertainty to extended range forecasting, and de-noising is therefore necessary. Second, in terms of model parameter error, the embedding dimension m should be determined by the factual nonlinear time series. The dynamic features of a chaotic system cannot be depicted because of the incomplete structure of the attractor when m is small. When m is large, prediction indicators can vanish because of the scarcity of phase points in phase space. A method for overcoming the cut-off effect ( m > 4) is proposed. Third, for heavy rains, precipitable water is more sensitive to the prediction validity period than temperature or geopotential height; however, for hurricanes, geopotential height is most sensitive, followed by precipitable water.

The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Goertler vortices in curved channel flows

NASA Technical Reports Server (NTRS)

Hall, P.; Smith, F. T.

1987-01-01

It is known that a viscous fluid flow with curved streamlines can support both Tollmien-Schlichting and Taylor-Goertler instabilities. In a situation where both modes are possible on the basis of linear theory a nonlinear theory must be used to determine the effect of the interaction of the instabilities. The details of this interaction are of practical importance because of its possible catastrophic effects on mechanisms used for laminar flow control. This interaction is studied in the context of fully developed flows in curved channels. A part form technical differences associated with boundary layer growth the structures of the instabilities in this flow are very similar to those in the practically more important external boundary layer situation. The interaction is shown to have two distinct phases depending on the size of the disturbances. At very low amplitudes two oblique Tollmein-Schlichting waves interact with a Goertler vortex in such a manner that the amplitudes become infinite at a finite time. This type of interaction is described by ordinary differential amplitude equations with quadratic nonlinearities.

Direct Simulation of Evolution and Control of Nonlinear Instabilities in Attachment-Line Boundary Layers

NASA Technical Reports Server (NTRS)

Joslin, Ronald D.

2004-01-01

The unsteady, incompressible Navier-Stokes equations are used for the direct numerical simulation (DNS) of spatially evolving disturbances in a three-dimensional (3-D) attachment-line boundary layer. Two-dimensional (2-D) disturbances are introduced either by forcing at the in ow or by harmonic-source generators at the wall; 3-D disturbances are introduced by harmonic-source generators at the wall. The DNS results are in good agreement with both 2-D non-parallel theory (for small-amplitude disturbances) and weakly nonlinear theory (for finite-amplitude disturbances), which validates the two theories. The 2-D DNS results indicate that nonlinear disturbance growth occurs near branch II of the neutral stability curve; however, steady suction can be used to stabilize this disturbance growth. For 3-D instabilities that are generated o the attachment line, spreading both toward and away from the attachment line causes energy transfer to the attachment-line and downstream instabilities; suction stabilizes these instabilities. Furthermore, 3-D instabilities are more stable than 2-D or quasi-2-D instabilities.

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.

Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion.

PubMed

Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P

2017-03-01

In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Coherent current-carrying filaments during nonlinear reconnecting ELMs and VDEs

NASA Astrophysics Data System (ADS)

Ebrahimi, Fatima

2017-10-01

We have examined plasmoid-mediated reconnection in a spherical tokamak using global nonlinear three-dimensional resistive MHD simulations with NIMROD. We have shown that physical current sheets/layers develop near the edge as a peeling component of ELMs or during vertical displacement events (associated with the scrape-off layer currents - halo currents), can become unstable to nonaxisymmetric 3-D current-sheet instabilities (peeling- or tearing-like) and nonlinearly form edge coherent current-carrying filaments. Time-evolving edge current sheets with reconnecting nature in NSTX and NSTX-U configurations are identified. In the case of peeling-like edge localized modes, the longstanding problem of quasiperiodic ELMs cycles is explained through the relaxation of edge current via direct numerical calculations of reconnecting emf terms. For the VDEs during disruption, we show that as the plasma is vertically displaced, edge halo current sheet becomes MHD unstable and forms coherent edge current filament structures, which would eventually bleed into the walls. Our model explains some essential asymmetric physics relevant to the experimental observations. Supported by DOE Grants DE-SC0010565, DE-AC02-09CH11466.

Nonlinear modeling of chaotic time series: Theory and applications

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

Casdagli, M.; Eubank, S.; Farmer, J.D.

1990-01-01

We review recent developments in the modeling and prediction of nonlinear time series. In some cases apparent randomness in time series may be due to chaotic behavior of a nonlinear but deterministic system. In such cases it is possible to exploit the determinism to make short term forecasts that are much more accurate than one could make from a linear stochastic model. This is done by first reconstructing a state space, and then using nonlinear function approximation methods to create a dynamical model. Nonlinear models are valuable not only as short term forecasters, but also as diagnostic tools for identifyingmore » and quantifying low-dimensional chaotic behavior. During the past few years methods for nonlinear modeling have developed rapidly, and have already led to several applications where nonlinear models motivated by chaotic dynamics provide superior predictions to linear models. These applications include prediction of fluid flows, sunspots, mechanical vibrations, ice ages, measles epidemics and human speech. 162 refs., 13 figs.« less

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

NASA Astrophysics Data System (ADS)

Fontanela, F.; Grolet, A.; Salles, L.; Chabchoub, A.; Hoffmann, N.

2018-01-01

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

Exact and Approximate Statistical Inference for Nonlinear Regression and the Estimating Equation Approach.

PubMed

Demidenko, Eugene

2017-09-01

The exact density distribution of the nonlinear least squares estimator in the one-parameter regression model is derived in closed form and expressed through the cumulative distribution function of the standard normal variable. Several proposals to generalize this result are discussed. The exact density is extended to the estimating equation (EE) approach and the nonlinear regression with an arbitrary number of linear parameters and one intrinsically nonlinear parameter. For a very special nonlinear regression model, the derived density coincides with the distribution of the ratio of two normally distributed random variables previously obtained by Fieller (1932), unlike other approximations previously suggested by other authors. Approximations to the density of the EE estimators are discussed in the multivariate case. Numerical complications associated with the nonlinear least squares are illustrated, such as nonexistence and/or multiple solutions, as major factors contributing to poor density approximation. The nonlinear Markov-Gauss theorem is formulated based on the near exact EE density approximation.

Bright-dark and dark-dark solitons in coupled nonlinear Schrödinger equation with P T -symmetric potentials

NASA Astrophysics Data System (ADS)

Nath, Debraj; Gao, Yali; Babu Mareeswaran, R.; Kanna, T.; Roy, Barnana

2017-12-01

We explore different nonlinear coherent structures, namely, bright-dark (BD) and dark-dark (DD) solitons in a coupled nonlinear Schrödinger/Gross-Pitaevskii equation with defocusing/repulsive nonlinearity coefficients featuring parity-time ( P T )-symmetric potentials. Especially, for two choices of P T -symmetric potentials, we obtain the exact solutions for BD and DD solitons. We perform the linear stability analysis of the obtained coherent structures. The results of this linear stability analysis are well corroborated by direct numerical simulation incorporating small random noise. It has been found that there exists a parameter regime which can support stable BD and DD solitons.

Computational design of the basic dynamical processes of the UCLA general circulation model

NASA Technical Reports Server (NTRS)

Arakawa, A.; Lamb, V. R.

1977-01-01

The 12-layer UCLA general circulation model encompassing troposphere and stratosphere (and superjacent 'sponge layer') is described. Prognostic variables are: surface pressure, horizontal velocity, temperature, water vapor and ozone in each layer, planetary boundary layer (PBL) depth, temperature, moisture and momentum discontinuities at PBL top, ground temperature and water storage, and mass of snow on ground. Selection of space finite-difference schemes for homogeneous incompressible flow, with/without a free surface, nonlinear two-dimensional nondivergent flow, enstrophy conserving schemes, momentum advection schemes, vertical and horizontal difference schemes, and time differencing schemes are discussed.

Exact modelling of the optical bistability in ferroelectics via two-wave mixing: A system with full nonlinearity

NASA Astrophysics Data System (ADS)

Khushaini, Muhammad Asif A.; Ibrahim, Abdel-Baset M. A.; Choudhury, P. K.

2018-05-01

In this paper, we provide a complete mathematical model of the phenomenon of optical bistability (OB) resulting from the degenerate two-wave mixing (TWM) process of laser beams interacting with a single nonlinear layer of ferroelectric material. Starting with the electromagnetic wave equation for optical wave propagating in nonlinear media, a nonlinear coupled wave (CW) system with both self-phase modulation (SPM) and cross-phase modulation (XPM) sources of nonlinearity are derived. The complete CW system with full nonlinearity is solved numerically and a comparison between both the cases of with and without SPM at various combinations of design parameters is given. Furthermore, to provide a reliable theoretical model for the OB via TWM process, the results obtained theoretically are compared with the available experimental data. We found that the nonlinear system without SPM fails to predict the bistable response at lower combinations of the input parameters. However, at relatively higher values, the solution without SPM shows a reduction in the switching contrast and period in the OB response. A comparison with the experimental results shows better agreement with the system with full nonlinearity.

A novel method to produce nonlinear empirical physical formulas for experimental nonlinear electro-optical responses of doped nematic liquid crystals: Feedforward neural network approach

NASA Astrophysics Data System (ADS)

Yildiz, Nihat; San, Sait Eren; Okutan, Mustafa; Kaya, Hüseyin

2010-04-01

Among other significant obstacles, inherent nonlinearity in experimental physical response data poses severe difficulty in empirical physical formula (EPF) construction. In this paper, we applied a novel method (namely layered feedforward neural network (LFNN) approach) to produce explicit nonlinear EPFs for experimental nonlinear electro-optical responses of doped nematic liquid crystals (NLCs). Our motivation was that, as we showed in a previous theoretical work, an appropriate LFNN, due to its exceptional nonlinear function approximation capabilities, is highly relevant to EPF construction. Therefore, in this paper, we obtained excellently produced LFNN approximation functions as our desired EPFs for above-mentioned highly nonlinear response data of NLCs. In other words, by using suitable LFNNs, we successfully fitted the experimentally measured response and predicted the new (yet-to-be measured) response data. The experimental data (response versus input) were diffraction and dielectric properties versus bias voltage; and they were all taken from our previous experimental work. We conclude that in general, LFNN can be applied to construct various types of EPFs for the corresponding various nonlinear physical perturbation (thermal, electronic, molecular, electric, optical, etc.) data of doped NLCs.

A revised model for Jeffrey nanofluid subject to convective condition and heat generation/absorption

PubMed Central

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-01-01

Here magnetohydrodynamic (MHD) boundary layer flow of Jeffrey nanofluid by a nonlinear stretching surface is addressed. Heat generation/absorption and convective surface condition effects are considered. Novel features of Brownian motion and thermophoresis are present. A non-uniform applied magnetic field is employed. Boundary layer and small magnetic Reynolds number assumptions are employed in the formulation. A newly developed condition with zero nanoparticles mass flux is imposed. The resulting nonlinear systems are solved. Convergence domains are explicitly identified. Graphs are analyzed for the outcome of sundry variables. Further local Nusselt number is computed and discussed. It is observed that the effects of Hartman number on the temperature and concentration distributions are qualitatively similar. Both temperature and concentration distributions are enhanced for larger Hartman number. PMID:28231298

Magnetic current sensor

NASA Technical Reports Server (NTRS)

Black, Jr., William C. (Inventor); Hermann, Theodore M. (Inventor)

1998-01-01

A current determiner having an output at which representations of input currents are provided having an input conductor for the input current and a current sensor supported on a substrate electrically isolated from one another but with the sensor positioned in the magnetic fields arising about the input conductor due to any input currents. The sensor extends along the substrate in a direction primarily perpendicular to the extent of the input conductor and is formed of at least a pair of thin-film ferromagnetic layers separated by a non-magnetic conductive layer. The sensor can be electrically connected to a electronic circuitry formed in the substrate including a nonlinearity adaptation circuit to provide representations of the input currents of increased accuracy despite nonlinearities in the current sensor, and can include further current sensors in bridge circuits.

Flutter Sensitivity to Boundary Layer Thickness, Structural Damping, and Static Pressure Differential for a Shuttle Tile Overlay Repair Concept

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Bartels, Robert E.

2009-01-01

This paper examines the aeroelastic stability of an on-orbit installable Space Shuttle patch panel. CFD flutter solutions were obtained for thick and thin boundary layers at a free stream Mach number of 2.0 and several Mach numbers near sonic speed. The effect of structural damping on these flutter solutions was also examined, and the effect of structural nonlinearities associated with in-plane forces in the panel was considered on the worst case linear flutter solution. The results of the study indicated that adequate flutter margins exist for the panel at the Mach numbers examined. The addition of structural damping improved flutter margins as did the inclusion of nonlinear effects associated with a static pressure difference across the panel.

Global stability and optimal control of epidemic spreading on multiplex networks with nonlinear mutual interaction

NASA Astrophysics Data System (ADS)

Jia, Nan; Ding, Li; Liu, Yu-Jing; Hu, Ping

2018-07-01

In this paper, we consider two interacting pathogens spreading on multiplex networks. Each pathogen spreads only on its single layer, and different layers have the same individuals but different network topology. A state-dependent infectious rate is proposed to describe the nonlinear mutual interaction during the propagation of two pathogens. Then a novel epidemic spreading model incorporating treatment control strategy is established. We investigate the global asymptotic stability of the equilibrium points by using Dulac's criterion, Poincaré-Bendixson theorem and Lyapunov method. Furthermore, we discuss an optimal strategy to minimize the total number of the infected individuals and the cost associated with treatment control for both spreading of two pathogens. Finally, numerical simulations are presented to show the validity and efficiency of our results.

Two-dimensional nonlinear finite element analysis of well damage due to reservoir compaction, well-to-well interactions, and localization on weak layers

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

Hilbert, L.B. Jr.; Fredrich, J.T.; Bruno, M.S.

1996-05-01

In this paper the authors present the results of a coupled nonlinear finite element geomechanics model for reservoir compaction and well-to-well interactions for the high-porosity, low strength diatomite reservoirs of the Belridge field near Bakersfield, California. They show that well damage and failures can occur under the action of two distinct mechanisms: shear deformations induced by pore compaction, and subsidence, and shear deformations due to well-to-well interactions during production or water injection. They show such casting damage or failure can be localized to weak layers that slide or slip under shear due to subsidence. The magnitude of shear displacements andmore » surface subsidence agree with field observations.« less

16-channel DWDM based on 1D defect mode nonlinear photonic crystal

NASA Astrophysics Data System (ADS)

Kalhan, Abhishek; Sharma, Sanjeev; Kumar, Arun

2018-05-01

We propose a sixteen-channel Dense Wavelength Division Multiplexer (DWDM), using the 1-D defect mode nonlinear photonic crystal which is a function of intensity as well as wavelength. Here, we consider an alternate layer of two semiconductor materials in which we found the bandgap of materials when defect layer is introduced then 16-channel dense wavelength division multiplexer is obtained within bandgap. From the theoretical analysis, we can achieve average quality factor of 7800.4, the uniform spectral line-width of 0.2 nm, crosstalk of -31.4 dB, central wavelength changes 0.07 nm/(1GW/cm2) and 100% transmission efficiency. Thus, Sixteen-channel DWDM has very high quality factor, low crosstalk, near 100% power transmission efficiency and small channel spacing (1.44 nm).

Darcy-Forchheimer Three-Dimensional Flow of Williamson Nanofluid over a Convectively Heated Nonlinear Stretching Surface

NASA Astrophysics Data System (ADS)

Hayat, Tasawar; Aziz, Arsalan; Muhammad, Taseer; Alsaedi, Ahmed

2017-09-01

The present study elaborates three-dimensional flow of Williamson nanoliquid over a nonlinear stretchable surface. Fluid flow obeys Darcy-Forchheimer porous medium. A bidirectional nonlinear stretching surface generates the flow. Convective surface condition of heat transfer is taken into consideration. Further the zero nanoparticles mass flux condition is imposed at the boundary. Effects of thermophoresis and Brownian diffusion are considered. Assumption of boundary layer has been employed in the problem formulation. Convergent series solutions for the nonlinear governing system are established through the optimal homotopy analysis method (OHAM). Graphs have been sketched in order to analyze that how the velocity, temperature and concentration distributions are affected by distinct emerging flow parameters. Skin friction coefficients and local Nusselt number are also computed and discussed.

Integrated, nonvolatile, high-speed analog random access memory

NASA Technical Reports Server (NTRS)

Katti, Romney R. (Inventor); Wu, Jiin-Chuan (Inventor); Stadler, Henry L. (Inventor)

1994-01-01

This invention provides an integrated, non-volatile, high-speed random access memory. A magnetically switchable ferromagnetic or ferrimagnetic layer is sandwiched between an electrical conductor which provides the ability to magnetize the magnetically switchable layer and a magneto resistive or Hall effect material which allows sensing the magnetic field which emanates from the magnetization of the magnetically switchable layer. By using this integrated three-layer form, the writing process, which is controlled by the conductor, is separated from the storage medium in the magnetic layer and from the readback process which is controlled by the magnetoresistive layer. A circuit for implementing the memory in CMOS or the like is disclosed.

Mapping the nonlinear optical susceptibility by noncollinear second-harmonic generation.

PubMed

Larciprete, M C; Bovino, F A; Giardina, M; Belardini, A; Centini, M; Sibilia, C; Bertolotti, M; Passaseo, A; Tasco, V

2009-07-15

We present a method, based on noncollinear second-harmonic generation, to evaluate the nonzero elements of the nonlinear optical susceptibility. At a fixed incidence angle, the generated signal is investigated by varying the polarization state of both fundamental beams. The resulting polarization charts allows us to verify if Kleinman's symmetry rules can be applied to a given material or to retrieve the absolute value of the nonlinear optical tensor terms, from a reference measurement. Experimental measurements obtained from gallium nitride layers are reported. The proposed method does not require an angular scan and thus is useful when the generated signal is strongly affected by sample rotation.

Neuro-evolutionary computing paradigm for Painlevé equation-II in nonlinear optics

NASA Astrophysics Data System (ADS)

Ahmad, Iftikhar; Ahmad, Sufyan; Awais, Muhammad; Ul Islam Ahmad, Siraj; Asif Zahoor Raja, Muhammad

2018-05-01

The aim of this study is to investigate the numerical treatment of the Painlevé equation-II arising in physical models of nonlinear optics through artificial intelligence procedures by incorporating a single layer structure of neural networks optimized with genetic algorithms, sequential quadratic programming and active set techniques. We constructed a mathematical model for the nonlinear Painlevé equation-II with the help of networks by defining an error-based cost function in mean square sense. The performance of the proposed technique is validated through statistical analyses by means of the one-way ANOVA test conducted on a dataset generated by a large number of independent runs.

The estimation of branching curves in the presence of subject-specific random effects.

PubMed

Elmi, Angelo; Ratcliffe, Sarah J; Guo, Wensheng

2014-12-20

Branching curves are a technique for modeling curves that change trajectory at a change (branching) point. Currently, the estimation framework is limited to independent data, and smoothing splines are used for estimation. This article aims to extend the branching curve framework to the longitudinal data setting where the branching point varies by subject. If the branching point is modeled as a random effect, then the longitudinal branching curve framework is a semiparametric nonlinear mixed effects model. Given existing issues with using random effects within a smoothing spline, we express the model as a B-spline based semiparametric nonlinear mixed effects model. Simple, clever smoothness constraints are enforced on the B-splines at the change point. The method is applied to Women's Health data where we model the shape of the labor curve (cervical dilation measured longitudinally) before and after treatment with oxytocin (a labor stimulant). Copyright © 2014 John Wiley & Sons, Ltd.

Asymptotics of the evolution semigroup associated with a scalar field in the presence of a non-linear electromagnetic field

NASA Astrophysics Data System (ADS)

Albeverio, Sergio; Tamura, Hiroshi

2018-04-01

We consider a model describing the coupling of a vector-valued and a scalar homogeneous Markovian random field over R4, interpreted as expressing the interaction between a charged scalar quantum field coupled with a nonlinear quantized electromagnetic field. Expectations of functionals of the random fields are expressed by Brownian bridges. Using this, together with Feynman-Kac-Itô type formulae and estimates on the small time and large time behaviour of Brownian functionals, we prove asymptotic upper and lower bounds on the kernel of the transition semigroup for our model. The upper bound gives faster than exponential decay for large distances of the corresponding resolvent (propagator).

Random Photon Absorption Model Elucidates How Early Gain Control in Fly Photoreceptors Arises from Quantal Sampling

PubMed Central

Song, Zhuoyi; Zhou, Yu; Juusola, Mikko

2016-01-01

Many diurnal photoreceptors encode vast real-world light changes effectively, but how this performance originates from photon sampling is unclear. A 4-module biophysically-realistic fly photoreceptor model, in which information capture is limited by the number of its sampling units (microvilli) and their photon-hit recovery time (refractoriness), can accurately simulate real recordings and their information content. However, sublinear summation in quantum bump production (quantum-gain-nonlinearity) may also cause adaptation by reducing the bump/photon gain when multiple photons hit the same microvillus simultaneously. Here, we use a Random Photon Absorption Model (RandPAM), which is the 1st module of the 4-module fly photoreceptor model, to quantify the contribution of quantum-gain-nonlinearity in light adaptation. We show how quantum-gain-nonlinearity already results from photon sampling alone. In the extreme case, when two or more simultaneous photon-hits reduce to a single sublinear value, quantum-gain-nonlinearity is preset before the phototransduction reactions adapt the quantum bump waveform. However, the contribution of quantum-gain-nonlinearity in light adaptation depends upon the likelihood of multi-photon-hits, which is strictly determined by the number of microvilli and light intensity. Specifically, its contribution to light-adaptation is marginal (≤ 1%) in fly photoreceptors with many thousands of microvilli, because the probability of simultaneous multi-photon-hits on any one microvillus is low even during daylight conditions. However, in cells with fewer sampling units, the impact of quantum-gain-nonlinearity increases with brightening light. PMID:27445779

Diffuse-charge dynamics of ionic liquids in electrochemical systems.

PubMed

Zhao, Hui

2011-11-01

We employ a continuum theory of solvent-free ionic liquids accounting for both short-range electrostatic correlations and steric effects (finite ion size) [Bazant et al., Phys. Rev. Lett. 106, 046102 (2011)] to study the response of a model microelectrochemical cell to a step voltage. The model problem consists of a 1-1 symmetric ionic liquid between two parallel blocking electrodes, neglecting any transverse transport phenomena. Matched asymptotic expansions in the limit of thin double layers are applied to analyze the resulting one-dimensional equations and study the overall charge-time relation in the weakly nonlinear regime. One important conclusion is that our simple scaling analysis suggests that the length scale √(λ*(D)l*(c)) accurately characterizes the double-layer structure of ionic liquids with strong electrostatic correlations where l*(c) is the electrostatic correlation length (in contrast, the Debye screening length λ*(D) is the primary double-layer length for electrolytes) and the response time of λ(D)(*3/2)L*/(D*l(c)(1/2)) (not λ*(D)L*/D* that is the primary charging time of electrolytes) is the correct charging time scale of ionic liquids with strong electrostatic correlations where D* is the diffusivity and L* is the separation length of the cell. With these two new scales, data of both electric potential versus distance from the electrode and the total diffuse charge versus time collapse onto each individual master curve in the presence of strong electrostatic correlations. In addition, the dependance of the total diffuse charge on steric effects, short-range correlations, and driving voltages is thoroughly examined. The results from the asymptotic analysis are compared favorably with those from full numerical simulations. Finally, the absorption of excess salt by the double layer creates a depletion region outside the double layer. Such salt depletion may bring a correction to the leading order terms and break down the weakly nonlinear analysis. A criterion which justifies the weakly nonlinear analysis is verified with numerical simulations.

Three dimensional rotating flow of Powell-Eyring nanofluid with non-Fourier's heat flux and non-Fick's mass flux theory

NASA Astrophysics Data System (ADS)

Ibrahim, Wubshet

2018-03-01

This article numerically examines three dimensional boundary layer flow of a rotating Powell-Eyring nanofluid. In modeling heat transfer processes, non-Fourier heat flux theory and for mass transfer non-Fick's mass flux theory are employed. This theory is recently re-initiated and it becomes the active research area to resolves some drawback associated with the famous Fourier heat flux and mass flux theory. The mathematical model of the flow problem is a system of non-linear partial differential equations which are obtained using the boundary layer analysis. The non-linear partial differential equations have been transformed into non-linear high order ordinary differential equations using similarity transformation. Employing bvp4c algorithm from matlab software routine, the numerical solution of the transformed ordinary differential equations is obtained. The governing equations are constrained by parameters such as rotation parameter λ , the non-Newtonian parameter N, dimensionless thermal relaxation and concentration relaxation parameters δt and δc . The impacts of these parameters have been discussed thoroughly and illustrated using graphs and tables. The findings show that thermal relaxation time δt reduces the thermal and concentration boundary layer thickness. Further, the results reveal that the rotational parameter λ has the effect of decreasing the velocity boundary layer thickness in both x and y directions. Further examination pinpoints that the skin friction coefficient along x-axis is an increasing and skin friction coefficient along y-axis is a decreasing function of rotation parameter λ . Furthermore, the non-Newtonian fluid parameter N has the characteristic of reducing the amount of local Nusselt numbers -f″ (0) and -g″ (0) both in x and y -directions.

Single-shot observation of optical rogue waves in integrable turbulence using time microscopy

PubMed Central

Suret, Pierre; Koussaifi, Rebecca El; Tikan, Alexey; Evain, Clément; Randoux, Stéphane; Szwaj, Christophe; Bielawski, Serge

2016-01-01

Optical fibres are favourable tabletop laboratories to investigate both coherent and incoherent nonlinear waves. In particular, exact solutions of the one-dimensional nonlinear Schrödinger equation such as fundamental solitons or solitons on finite background can be generated by launching periodic, specifically designed coherent waves in optical fibres. It is an open fundamental question to know whether these coherent structures can emerge from the nonlinear propagation of random waves. However the typical sub-picosecond timescale prevented—up to now—time-resolved observations of the awaited dynamics. Here, we report temporal ‘snapshots' of random light using a specially designed ‘time-microscope'. Ultrafast structures having peak powers much larger than the average optical power are generated from the propagation of partially coherent waves in optical fibre and are recorded with 250 femtoseconds resolution. Our experiment demonstrates the central role played by ‘breather-like' structures such as the Peregrine soliton in the emergence of heavy-tailed statistics in integrable turbulence. PMID:27713416

Application of multivariable search techniques to the optimization of airfoils in a low speed nonlinear inviscid flow field

NASA Technical Reports Server (NTRS)

Hague, D. S.; Merz, A. W.

1975-01-01

Multivariable search techniques are applied to a particular class of airfoil optimization problems. These are the maximization of lift and the minimization of disturbance pressure magnitude in an inviscid nonlinear flow field. A variety of multivariable search techniques contained in an existing nonlinear optimization code, AESOP, are applied to this design problem. These techniques include elementary single parameter perturbation methods, organized search such as steepest-descent, quadratic, and Davidon methods, randomized procedures, and a generalized search acceleration technique. Airfoil design variables are seven in number and define perturbations to the profile of an existing NACA airfoil. The relative efficiency of the techniques are compared. It is shown that elementary one parameter at a time and random techniques compare favorably with organized searches in the class of problems considered. It is also shown that significant reductions in disturbance pressure magnitude can be made while retaining reasonable lift coefficient values at low free stream Mach numbers.

Nonlinear dynamics of mushy layers induced by external stochastic fluctuations.

PubMed

Alexandrov, Dmitri V; Bashkirtseva, Irina A; Ryashko, Lev B

2018-02-28

The time-dependent process of directional crystallization in the presence of a mushy layer is considered with allowance for arbitrary fluctuations in the atmospheric temperature and friction velocity. A nonlinear set of mushy layer equations and boundary conditions is solved analytically when the heat and mass fluxes at the boundary between the mushy layer and liquid phase are induced by turbulent motion in the liquid and, as a result, have the corresponding convective form. Namely, the 'solid phase-mushy layer' and 'mushy layer-liquid phase' phase transition boundaries as well as the solid fraction, temperature and concentration (salinity) distributions are found. If the atmospheric temperature and friction velocity are constant, the analytical solution takes a parametric form. In the more common case when they represent arbitrary functions of time, the analytical solution is given by means of the standard Cauchy problem. The deterministic and stochastic behaviour of the phase transition process is analysed on the basis of the obtained analytical solutions. In the case of stochastic fluctuations in the atmospheric temperature and friction velocity, the phase transition interfaces (mushy layer boundaries) move faster than in the deterministic case. A cumulative effect of these noise contributions is revealed as well. In other words, when the atmospheric temperature and friction velocity fluctuate simultaneously due to the influence of different external processes and phenomena, the phase transition boundaries move even faster. This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'. © 2018 The Author(s).

Critical Layers and Protoplanetary Disk Turbulence

NASA Astrophysics Data System (ADS)

Umurhan, Orkan M.; Shariff, Karim; Cuzzi, Jeffrey N.

2016-10-01

A linear analysis of the zombie vortex instability (ZVI) is performed in a stratified shearing sheet setting for three model barotropic shear flows. The linear analysis is done by utilizing a Green’s function formulation to resolve the critical layers of the associated normal-mode problem. The instability is the result of a resonant interaction between a Rossby wave and a gravity wave that we refer to as Z-modes. The associated critical layer is the location where the Doppler-shifted frequency of a distant Rossby wave equals the local Brunt-Väisälä frequency. The minimum required Rossby number for instability, {\\mathtt{Ro}}=0.2, is confirmed for parameter values reported in the literature. It is also found that the shear layer supports the instability in the limit where stratification vanishes. The ZVI is examined in a jet model, finding that the instability can occur for {\\mathtt{Ro}}=0.05. Nonlinear vorticity forcing due to unstable Z-modes is shown to result in the creation of a jet flow at the critical layer emerging as the result of the competition between the vertical lifting of perturbation radial vorticity and the radial transport of perturbation vertical vorticity. We find that the picture of this instability leading to a form of nonlinearly driven self-replicating pattern of creation and destruction is warranted: a parent jet spawns a growing child jet at associated critical layers. A mature child jet creates a next generation of child jets at associated critical layers of the former while simultaneously contributing to its own destruction via the Rossby wave instability.

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

NASA Astrophysics Data System (ADS)

Zhang, Yu; Jiang, Jack J.

2008-09-01

Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.

From non-linear magnetoacoustics and spin reorientation transition to magnetoelectric micro/nano-systems

NASA Astrophysics Data System (ADS)

Tiercelin, Nicolas; Preobrazhensky, Vladimir; BouMatar, Olivier; Talbi, Abdelkrim; Giordano, Stefano; Dusch, Yannick; Klimov, Alexey; Mathurin, Théo.; Elmazria, Omar; Hehn, Michel; Pernod, Philippe

2017-09-01

The interaction of a strongly nonlinear spin system with a crystalline lattice through magnetoelastic coupling results in significant modifications of the acoustic properties of magnetic materials, especially in the vicinity of magnetic instabilities associated with the spin-reorientation transition (SRT). The magnetoelastic coupling transfers the critical properties of the magnetic subsystem to the elastic one, which leads to a strong decrease of the sound velocity in the vicinity of the SRT, and allows a large control over acoustic nonlinearities. The general principles of the non-linear magneto-acoustics (NMA) will be introduced and illustrated in `bulk' applications such as acoustic wave phase conjugation, multi-phonon coupling, explosive instability of magneto-elastic vibrations, etc. The concept of the SRT coupled to magnetoelastic interaction has been transferred into nanostructured magnetoelastic multilayers with uni-axial anisotropy. The high sensitivity and the non-linear properties have been demonstrated in cantilever type actuators, and phenomena such as magneto-mechanical RF demodulation have been observed. The combination of the magnetic layers with piezoelectric materials also led to stress-mediated magnetoelectric (ME) composites with high ME coefficients, thanks to the SRT. The magnetoacoustic effects of the SRT have also been studied for surface acoustic waves propagating in the magnetoelastic layers and found to be promising for highly sensitive magnetic field sensors working at room temperature. On the other hand, mechanical stress is a very efficient way to control the magnetic subsystem. The principle of a very energy efficient stress-mediated magnetoelectric writing and reading in a magnetic memory is described.

Wave propagation in ordered, disordered, and nonlinear photonic band gap materials

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

Lidorikis, Elefterios

Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model inmore » which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.« less

Spectral element modelling of seismic wave propagation in visco-elastoplastic media including excess-pore pressure development

NASA Astrophysics Data System (ADS)

Oral, Elif; Gélis, Céline; Bonilla, Luis Fabián; Delavaud, Elise

2017-12-01

Numerical modelling of seismic wave propagation, considering soil nonlinearity, has become a major topic in seismic hazard studies when strong shaking is involved under particular soil conditions. Indeed, when strong ground motion propagates in saturated soils, pore pressure is another important parameter to take into account when successive phases of contractive and dilatant soil behaviour are expected. Here, we model 1-D seismic wave propagation in linear and nonlinear media using the spectral element numerical method. The study uses a three-component (3C) nonlinear rheology and includes pore-pressure excess. The 1-D-3C model is used to study the 1987 Superstition Hills earthquake (ML 6.6), which was recorded at the Wildlife Refuge Liquefaction Array, USA. The data of this event present strong soil nonlinearity involving pore-pressure effects. The ground motion is numerically modelled for different assumptions on soil rheology and input motion (1C versus 3C), using the recorded borehole signals as input motion. The computed acceleration-time histories show low-frequency amplification and strong high-frequency damping due to the development of pore pressure in one of the soil layers. Furthermore, the soil is found to be more nonlinear and more dilatant under triaxial loading compared to the classical 1C analysis, and significant differences in surface displacements are observed between the 1C and 3C approaches. This study contributes to identify and understand the dominant phenomena occurring in superficial layers, depending on local soil properties and input motions, conditions relevant for site-specific studies.

Assessment of computational prediction of tail buffeting

NASA Technical Reports Server (NTRS)

Edwards, John W.

1990-01-01

Assessments of the viability of computational methods and the computer resource requirements for the prediction of tail buffeting are made. Issues involved in the use of Euler and Navier-Stokes equations in modeling vortex-dominated and buffet flows are discussed and the requirement for sufficient grid density to allow accurate, converged calculations is stressed. Areas in need of basic fluid dynamics research are highlighted: vorticity convection, vortex breakdown, dynamic turbulence modeling for free shear layers, unsteady flow separation for moderately swept, rounded leading-edge wings, vortex flows about wings at high subsonic speeds. An estimate of the computer run time for a buffeting response calculation for a full span F-15 aircraft indicates that an improvement in computer and/or algorithm efficiency of three orders of magnitude is needed to enable routine use of such methods. Attention is also drawn to significant uncertainties in the estimates, in particular with regard to nonlinearities contained within the modeling and the question of the repeatability or randomness of buffeting response.

Comparison of anastomotic leakage and stricture formation following layered and stapler oesophagogastric anastomosis for cancer: a prospective randomized controlled trial.

PubMed

Zhang, Y S; Gao, B R; Wang, H J; Su, Y F; Yang, Y Z; Zhang, J H; Wang, C

2010-01-01

The objective of this prospective, randomized, controlled trial, conducted from May 2002 to December 2007, was to compare post-operative anastomotic leakage and stricture formation following layered manual versus stapler oesophagogastric anastomosis in patients who underwent resection of oesophageal or gastric cardia carcinoma. Patients (n = 516) were randomized to receive either layered manual or circular stapled oesophagogastric anastomosis. Mean follow-up time was > 12 months. Anastomotic leakage occurred in one (0.4%) patient in the layered group and six (2.2%) in the stapler group; no statistically significant between-group difference. After operation, two (0.8%) patients in the layered group and 13 (5.0%) in the stapler group developed a benign oesophageal stricture; the difference between the groups was statistically significant. Compared with stapler anastomosis, layered manual anastomosis may significantly reduce the incidence of anastomotic strictures. This method is easy to apply and could be used as an alternative procedure for oesophagogastric anastomosis after resection for oesophageal or cardia carcinoma.

Optimized hardware framework of MLP with random hidden layers for classification applications

NASA Astrophysics Data System (ADS)

Zyarah, Abdullah M.; Ramesh, Abhishek; Merkel, Cory; Kudithipudi, Dhireesha

2016-05-01

Multilayer Perceptron Networks with random hidden layers are very efficient at automatic feature extraction and offer significant performance improvements in the training process. They essentially employ large collection of fixed, random features, and are expedient for form-factor constrained embedded platforms. In this work, a reconfigurable and scalable architecture is proposed for the MLPs with random hidden layers with a customized building block based on CORDIC algorithm. The proposed architecture also exploits fixed point operations for area efficiency. The design is validated for classification on two different datasets. An accuracy of ~ 90% for MNIST dataset and 75% for gender classification on LFW dataset was observed. The hardware has 299 speed-up over the corresponding software realization.

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.