Green function formalism for nonlinear acoustic waves in layered media

International Nuclear Information System (INIS)

Lobo, A.; Tsoy, E.; De Sterke, C.M.

2000-01-01

Full text: The applications of acoustic waves in identifying defects in adhesive bonds between metallic plates have received little attention at high intensities where the media respond nonlinearly. However, the effects of reduced bond strength are more distinct in the nonlinear response of the structure. Here we assume a weak nonlinearity acting as a small perturbation, thereby reducing the problem to a linear one. This enables us to develop a specialized Green function formalism for calculating acoustic fields in layered media

Jump phenomena. [large amplitude responses of nonlinear systems

Science.gov (United States)

Reiss, E. L.

1980-01-01

The paper considers jump phenomena composed of large amplitude responses of nonlinear systems caused by small amplitude disturbances. Physical problems where large jumps in the solution amplitude are important features of the response are described, including snap buckling of elastic shells, chemical reactions leading to combustion and explosion, and long-term climatic changes of the earth's atmosphere. A new method of rational functions was then developed which consists of representing the solutions of the jump problems as rational functions of the small disturbance parameter; this method can solve jump problems explicitly.

Structural optimization for nonlinear dynamic response

DEFF Research Database (Denmark)

Dou, Suguang; Strachan, B. Scott; Shaw, Steven W.

2015-01-01

by a single vibrating mode, or by a pair of internally resonant modes. The approach combines techniques from nonlinear dynamics, computational mechanics and optimization, and it allows one to relate the geometric and material properties of structural elements to terms in the normal form for a given resonance......Much is known about the nonlinear resonant response of mechanical systems, but methods for the systematic design of structures that optimize aspects of these responses have received little attention. Progress in this area is particularly important in the area of micro-systems, where nonlinear...... resonant behaviour is being used for a variety of applications in sensing and signal conditioning. In this work, we describe a computational method that provides a systematic means for manipulating and optimizing features of nonlinear resonant responses of mechanical structures that are described...

Spectral theory and nonlinear functional analysis

CERN Document Server

Lopez-Gomez, Julian

2001-01-01

This Research Note addresses several pivotal problems in spectral theory and nonlinear functional analysis in connection with the analysis of the structure of the set of zeroes of a general class of nonlinear operators. It features the construction of an optimal algebraic/analytic invariant for calculating the Leray-Schauder degree, new methods for solving nonlinear equations in Banach spaces, and general properties of components of solutions sets presented with minimal use of topological tools. The author also gives several applications of the abstract theory to reaction diffusion equations and systems.The results presented cover a thirty-year period and include recent, unpublished findings of the author and his coworkers. Appealing to a broad audience, Spectral Theory and Nonlinear Functional Analysis contains many important contributions to linear algebra, linear and nonlinear functional analysis, and topology and opens the door for further advances.

Confidence bounds for nonlinear dose-response relationships

DEFF Research Database (Denmark)

Baayen, C; Hougaard, P

2015-01-01

An important aim of drug trials is to characterize the dose-response relationship of a new compound. Such a relationship can often be described by a parametric (nonlinear) function that is monotone in dose. If such a model is fitted, it is useful to know the uncertainty of the fitted curve...... intervals for the dose-response curve. These confidence bounds have better coverage than Wald intervals and are more precise and generally faster than bootstrap methods. Moreover, if monotonicity is assumed, the profile likelihood approach takes this automatically into account. The approach is illustrated...

Nonlinear optics response of semiconductor quantum wells under high magnetic fields

International Nuclear Information System (INIS)

Chemla, D.S.

1993-07-01

Recent investigations on the nonlinear optical response of semiconductor quantum wells in a strong perpendicular magnetic field, H, are reviewed. After some introductory material the evolution of the linear optical properties of GaAs QW's as a function of H is discussed; an examination is made of how the magneto-excitons (MX) extrapolate continuously between quasi-2D QW excitons (X) when H = 0, and pairs of Landau levels (LL) when H → ∞. Next, femtosecond time resolved investigations of their nonlinear optical response are presented; the evolution of MX-MX interactions with increasing H is stressed. Finally, how, as the dimensionality is reduced by application of H, the number of scattering channels is limited and relaxation of electron-hole pairs is affected. How nonlinear optical spectroscopy can be exploited to access the relaxation of angular momentum within magneto-excitons is also discussed

Nonlinear responses of chiral fluids from kinetic theory

Science.gov (United States)

Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

2018-01-01

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

A non-linear kinematic hardening function

International Nuclear Information System (INIS)

Ottosen, N.S.

1977-05-01

Based on the classical theory of plasticity, and accepting the von Mises criterion as the initial yield criterion, a non-linear kinematic hardening function applicable both to Melan-Prager's and to Ziegler's hardening rule is proposed. This non-linear hardening function is determined by means of the uniaxial stress-strain curve, and any such curve is applicable. The proposed hardening function considers the problem of general reversed loading, and a smooth change in the behaviour from one plastic state to another nearlying plastic state is obtained. A review of both the kinematic hardening theory and the corresponding non-linear hardening assumptions is given, and it is shown that material behaviour is identical whether Melan-Prager's or Ziegler's hardening rule is applied, provided that the von Mises yield criterion is adopted. (author)

Nonlinear optics principles and applications

CERN Document Server

Rottwitt, Karsten

2014-01-01

IntroductionReview of linear opticsInduced polarizationHarmonic oscillator modelLocal field correctionsEstimated nonlinear responseSummaryTime-domain material responseThe polarization time-response functionThe Born-Oppenheimer approximationRaman scattering response function of silicaSummaryMaterial response in the frequency domain, susceptibility tensorsThe susceptibility tensorThe induced polarization in the frequency domainSum of monochromatic fieldsThe prefactor to the induced polarizationThird-order polarization in the Born-Oppenheimer approximation in the frequency domainKramers-Kronig relationsSummarySymmetries in nonlinear opticsSpatial symmetriesSecond-order materialsThird-order nonlinear materialsCyclic coordinate-systemContracted notation for second-order susceptibility tensorsSummaryThe nonlinear wave equationMono and quasi-monochromatic beamsPlane waves - the transverse problemWaveguidesVectorial approachNonlinear birefringenceSummarySecond-order nonlinear effectsGeneral theoryCoupled wave theoryP...

Nonlinear response and avalanche behavior in metallic glasses

Science.gov (United States)

Riechers, B.; Samwer, K.

2017-08-01

The response to different stress amplitudes at temperatures below the glass transition temperature is analyzed by mechanical oscillatory excitation of Pd40Ni40P20 metallic glass samples in single cantilever bending geometry. While low amplitude oscillatory excitations are commonly used in mechanical spectroscopy to probe the relaxation spectrum, in this work the response to comparably high amplitudes is investigated. The strain response of the material is well below the critical yield stress even for highest stress amplitudes, implying the expectation of a linear relation between stress and strain according to Hooke's Law. However, a deviation from the linear behavior is evident, which is analyzed in terms of temperature dependence and influence of the applied stress amplitude by two different approaches of evaluation. The nonlinear approach is based on a nonlinear expansion of the stress-strain-relation, assuming an intrinsic nonlinear character of the shear or elastic modulus. The degree of nonlinearity is extracted by a period-by-period Fourier-analysis and connected to nonlinear coefficients, describing the intensity of nonlinearity at the fundamental and higher harmonic frequencies. The characteristic timescale to adapt to a significant change in stress amplitude in terms of a recovery timescale to a steady state value is connected to the structural relaxation time of the material, suggesting a connection between the observed nonlinearity and primary relaxation processes. The second approach of evaluation is termed the incremental analysis and relates the observed response behavior to avalanches, which occur due to the activation and correlation of local microstructural rearrangements. These rearrangements are connected with shear transformation zones and correspond to localized plastic events, which are superimposed on the linear response behavior of the material.

Non-linear stochastic response of a shallow cable

DEFF Research Database (Denmark)

Larsen, Jesper Winther; Nielsen, Søren R.K.

2004-01-01

The paper considers the stochastic response of geometrical non-linear shallow cables. Large rain-wind induced cable oscillations with non-linear interactions have been observed in many large cable stayed bridges during the last decades. The response of the cable is investigated for a reduced two...

Models of the delayed nonlinear Raman response in diatomic gases

International Nuclear Information System (INIS)

Palastro, J. P.; Antonsen, T. M. Jr.; Pearson, A.

2011-01-01

We examine the delayed response of a diatomic gas to a polarizing laser field with the goal of obtaining computationally efficient methods for use with laser pulse propagation simulations. We demonstrate that for broadband pulses, heavy molecules such as O 2 and N 2 , and typical atmospheric temperatures, the initial delayed response requires only classical physics. The linear kinetic Green's function is derived from the Boltzmann equation and shown to be in excellent agreement with full density-matrix calculations. A straightforward perturbation approach for the fully nonlinear, kinetic impulse response is also presented. With the kinetic theory a reduced fluid model of the diatomic gas' orientation is derived. Transport coefficients are introduced to model the kinetic phase mixing of the delayed response. In addition to computational rapidity, the fluid model provides intuition through the use of familiar macroscopic quantities. Both the kinetic and the fluid descriptions predict a nonlinear steady-state alignment after passage of the laser pulse, which in the fluid model is interpreted as an anisotropic temperature of the diatomic fluid with respect to motion about the polarization axis.

Nonlinear Dielectric Response of Water Treed XLPE Cable Insulation

Energy Technology Data Exchange (ETDEWEB)

Hvidsten, Sverre

1999-07-01

Condition assessment of XLPE power cables is becoming increasingly important for the utilities, due to a large number of old cables in service with high probability of failure caused by water tree degradation. The commercial available techniques are generally based upon measurements of the dielectric response, either by time (polarisation/depolarisation current or return voltage) or frequency domain measurements. Recently it has been found that a high number of water trees in XLPE insulated cables causes the dielectric response to increase more than linearly with increasing test voltage. This nonlinear feature of water tree degraded XLPE insulation has been suggested to be of a great importance, both for diagnostic purposes, and for fundamental understanding of the water tree phenomenon itself. The main purpose of this thesis have been to study the nonlinear feature of the dielectric response measured on watertreed XLPE insulation. This has been performed by dielectric response measurements in both time and frequency domain, numerical calculations of losses of simplified water tree models, and fmally water content and water permeation measurements on single water trees. The dielectric response measurements were performed on service aged cable samples and laboratory aged Rogowski type objects. The main reason for performing laboratory ageing was to facilitate diagnostic testing as a function of ageing time of samples containing mainly vented water trees. A new method, based upon inserting NaC1 particles at the interface between the upper semiconductive screen and the insulation, was found to successfully enhance initiation and growth of vented water trees. AC breakdown strength testing show that it is the vented water trees that reduce the breakdown level of both the laboratory aged test objects and service aged cable samples. Vented water treeing was found to cause the dielectric response to become nonlinear at a relatively low voltage level. However, the measured

Optical polarization based logic functions (XOR or XNOR) with nonlinear Gallium nitride nanoslab.

Science.gov (United States)

Bovino, F A; Larciprete, M C; Giardina, M; Belardini, A; Centini, M; Sibilia, C; Bertolotti, M; Passaseo, A; Tasco, V

2009-10-26

We present a scheme of XOR/XNOR logic gate, based on non phase-matched noncollinear second harmonic generation from a medium of suitable crystalline symmetry, Gallium nitride. The polarization of the noncollinear generated beam is a function of the polarization of both pump beams, thus we experimentally investigated all possible polarization combinations, evidencing that only some of them are allowed and that the nonlinear interaction of optical signals behaves as a polarization based XOR. The experimental results show the peculiarity of the nonlinear optical response associated with noncollinear excitation, and are explained using the expression for the effective second order optical nonlinearity in noncollinear scheme.

Nonlinear mechanical response of the extracellular matrix: learning from articular cartilage

Science.gov (United States)

Kearns, Sarah; Das, Moumita

2015-03-01

We study the mechanical structure-function relations in the extracellular matrix (ECM) with focus on nonlinear shear and compression response. As a model system, our study focuses on the ECM in articular cartilage tissue which has two major mechanobiological components: a network of the biopolymer collagen that acts as a stiff, reinforcing matrix, and a flexible aggrecan network that facilitates deformability. We model this system as a double network hydrogel made of interpenetrating networks of stiff and flexible biopolymers respectively. We study the linear and nonlinear mechanical response of the model ECM to shear and compression forces using a combination of rigidity percolation theory and energy minimization approaches. Our results may provide useful insights into the design principles of the ECM as well as biomimetic hydrogels that are mechanically robust and can, at the same time, easily adapt to cues in their surroundings.

Nonlinear Dynamic Response of Compliant Journal Bearings

Directory of Open Access Journals (Sweden)

Glavatskih S.

2012-07-01

Full Text Available This paper investigates the dynamic response of the compliant tilting pad journal bearings subjected to synchronous excitation. Bearing compliance is affected by the properties of pad liner and pad support geometry. Different unbalance eccentricities are considered. It is shown that bearing dynamic response is non-linear. Journal orbit complexity increases with pad compliance though the orbit amplitudes are marginally affected at low loads. At high loads, the journal is forced to operate outside the bearing clearance. The polymer liner reduces the maximum oil film pressure by a factor of 2 when compared to the white metal liner. The nonlinear dynamic response of compliant tilting pad journal bearings is thoroughly discussed.

Extension of a nonlinear systems theory to general-frequency unsteady transonic aerodynamic responses

Science.gov (United States)

Silva, Walter A.

1993-01-01

A methodology for modeling nonlinear unsteady aerodynamic responses, for subsequent use in aeroservoelastic analysis and design, using the Volterra-Wiener theory of nonlinear systems is presented. The methodology is extended to predict nonlinear unsteady aerodynamic responses of arbitrary frequency. The Volterra-Wiener theory uses multidimensional convolution integrals to predict the response of nonlinear systems to arbitrary inputs. The CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code is used to generate linear and nonlinear unit impulse responses that correspond to each of the integrals for a rectangular wing with a NACA 0012 section with pitch and plunge degrees of freedom. The computed kernels then are used to predict linear and nonlinear unsteady aerodynamic responses via convolution and compared to responses obtained using the CAP-TSD code directly. The results indicate that the approach can be used to predict linear unsteady aerodynamic responses exactly for any input amplitude or frequency at a significant cost savings. Convolution of the nonlinear terms results in nonlinear unsteady aerodynamic responses that compare reasonably well with those computed using the CAP-TSD code directly but at significant computational cost savings.

Nonlinear functional analysis

CERN Document Server

Deimling, Klaus

1985-01-01

topics. However, only a modest preliminary knowledge is needed. In the first chapter, where we introduce an important topological concept, the so-called topological degree for continuous maps from subsets ofRn into Rn, you need not know anything about functional analysis. Starting with Chapter 2, where infinite dimensions first appear, one should be familiar with the essential step of consider­ ing a sequence or a function of some sort as a point in the corresponding vector space of all such sequences or functions, whenever this abstraction is worthwhile. One should also work out the things which are proved in § 7 and accept certain basic principles of linear functional analysis quoted there for easier references, until they are applied in later chapters. In other words, even the 'completely linear' sections which we have included for your convenience serve only as a vehicle for progress in nonlinearity. Another point that makes the text introductory is the use of an essentially uniform mathematical languag...

A Photonic Basis for Deriving Nonlinear Optical Response

Science.gov (United States)

Andrews, David L.; Bradshaw, David S.

2009-01-01

Nonlinear optics is generally first presented as an extension of conventional optics. Typically the subject is introduced with reference to a classical oscillatory electric polarization, accommodating correction terms that become significant at high intensities. The material parameters that quantify the extent of the nonlinear response are cast as…

Modeling and non-linear responses of MEMS capacitive accelerometer

Directory of Open Access Journals (Sweden)

Sri Harsha C.

2014-01-01

Full Text Available A theoretical investigation of an electrically actuated beam has been illustrated when the electrostatic-ally actuated micro-cantilever beam is separated from the electrode by a moderately large gap for two distinct types of geometric configurations of MEMS accelerometer. Higher order nonlinear terms have been taken into account for studying the pull in voltage analysis. A nonlinear model of gas film squeezing damping, another source of nonlinearity in MEMS devices is included in obtaining the dynamic responses. Moreover, in the present work, the possible source of nonlinearities while formulating the mathematical model of a MEMS accelerometer and their influences on the dynamic responses have been investigated. The theoretical results obtained by using MATLAB has been verified with the results obtained in FE software and has been found in good agreement. Criterion towards stable micro size accelerometer for each configuration has been investigated. This investigation clearly provides an understanding of nonlinear static and dynamics characteristics of electrostatically micro cantilever based device in MEMS.

Computational mechanics of nonlinear response of shells

Energy Technology Data Exchange (ETDEWEB)

Kraetzig, W.B. (Bochum Univ. (Germany, F.R.). Inst. fuer Statik und Dynamik); Onate, E. (Universidad Politecnica de Cataluna, Barcelona (Spain). Escuela Tecnica Superior de Ingenieros de Caminos) (eds.)

1990-01-01

Shell structures and their components are utilized in a wide spectrum of engineering fields reaching from space and aircraft structures, pipes and pressure vessels over liquid storage tanks, off-shore installations, cooling towers and domes, to bodyworks of motor vehicles. Of continuously increasing importance is their nonlinear behavior, in which large deformations and large rotations are involved as well as nonlinear material properties. The book starts with a survey about nonlinear shell theories from the rigorous point of view of continuum mechanics, this starting point being unavoidable for modern computational concepts. There follows a series of papers on nonlinear, especially unstable shell responses, which draw computational connections to well established tools in the field of static and dynamic stability of systems. Several papers are then concerned with new finite element derivations for nonlinear shell problems, and finally a series of authors contribute to specific applications opening a small window of the above mentioned wide spectrum. (orig./HP) With 159 figs.

Computational mechanics of nonlinear response of shells

International Nuclear Information System (INIS)

Kraetzig, W.B.; Onate, E.

1990-01-01

Shell structures and their components are utilized in a wide spectrum of engineering fields reaching from space and aircraft structures, pipes and pressure vessels over liquid storage tanks, off-shore installations, cooling towers and domes, to bodyworks of motor vehicles. Of continuously increasing importance is their nonlinear behavior, in which large deformations and large rotations are involved as well as nonlinear material properties. The book starts with a survey about nonlinear shell theories from the rigorous point of view of continuum mechanics, this starting point being unavoidable for modern computational concepts. There follows a series of papers on nonlinear, especially unstable shell responses, which draw computational connections to well established tools in the field of static and dynamic stability of systems. Several papers are then concerned with new finite element derivations for nonlinear shell problems, and finally a series of authors contribute to specific applications opening a small window of the above mentioned wide spectrum. (orig./HP) With 159 figs

Nonlinear generalization of the Kallen-Welton formula

International Nuclear Information System (INIS)

Kargin, A.Yu.

1982-01-01

Nonlinear dissipative-fluctuation relations permitting to find spectral correlation functions of (n+1) order for fluctuations of different electrodynamic values in plasma using the given value of tensor of nonlinear response of n order have been obtained for equilibrium plasma. At n=1 the relations obtained transform to the Kallen-Welton dissipative-fluctuation relation. Transformation of the nonlinear dissipative-fluctuation relation for cubical nonlinearity permitting to find nonlinear electric plasma susceptibility from the Known spectral correlation function of fourth order for charge density fluctUations in the absence of particle interaction is considered as an example. A compact expression for tensor of nonlinear plasma response has been obtained for an arbitrary order of nonlinearity

Measuring localized nonlinear components in a circular accelerator with a nonlinear tune response matrix

Directory of Open Access Journals (Sweden)

G. Franchetti

2008-09-01

Full Text Available In this paper we present a method for measuring the nonlinear errors in a circular accelerator by taking advantage of the feed-down effect of high order multipoles when the closed orbit is globally deformed. We devise a nonlinear tune response matrix in which the response to a closed orbit deformation is obtained in terms of change of machine tune and correlated with the strength of the local multipoles. A numerical example and a proof of principle experiment to validate the theoretical methods are presented and discussed.

Enhancement of nonlinear optical response of weakly confined excitons in GaAs thin films by spectrally rectangle-shape-pulse-excitation

International Nuclear Information System (INIS)

Kojima, O; Isu, T; Ishi-Hayase, J; Sasaki, M; Tsuchiya, M

2007-01-01

We report the enhancement of the nonlinear optical response of the weakly confined excitons with use of spectrally rectangular pulse. The nonlinear optical response was investigated as a function of excitation energy by a degenerate four-wave-mixing (DFWM) technique. In the case that the laser pulse with the controlled spectral shape excites the plural exciton states simultaneously, the DFWM signal intensity is enhanced by a factor of two in comparison with the intensity under the excitation of a single exciton state. This enhancement is caused by the superposition of the nonlinear optical responses from the plural exciton states

Inducing in situ, nonlinear soil response applying an active source

Science.gov (United States)

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

2009-01-01

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

Optimization of nonlinear wave function parameters

International Nuclear Information System (INIS)

Shepard, R.; Minkoff, M.; Chemistry

2006-01-01

An energy-based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed-shell and open-shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy-based optimization is formulated in terms of analytic arc factor gradients and orbital-level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital-level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of > 10 24 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules

On the dimension of complex responses in nonlinear structural vibrations

Science.gov (United States)

Wiebe, R.; Spottswood, S. M.

2016-07-01

The ability to accurately model engineering systems under extreme dynamic loads would prove a major breakthrough in many aspects of aerospace, mechanical, and civil engineering. Extreme loads frequently induce both nonlinearities and coupling which increase the complexity of the response and the computational cost of finite element models. Dimension reduction has recently gained traction and promises the ability to distill dynamic responses down to a minimal dimension without sacrificing accuracy. In this context, the dimensionality of a response is related to the number of modes needed in a reduced order model to accurately simulate the response. Thus, an important step is characterizing the dimensionality of complex nonlinear responses of structures. In this work, the dimensionality of the nonlinear response of a post-buckled beam is investigated. Significant detail is dedicated to carefully introducing the experiment, the verification of a finite element model, and the dimensionality estimation algorithm as it is hoped that this system may help serve as a benchmark test case. It is shown that with minor modifications, the method of false nearest neighbors can quantitatively distinguish between the response dimension of various snap-through, non-snap-through, random, and deterministic loads. The state-space dimension of the nonlinear system in question increased from 2-to-10 as the system response moved from simple, low-level harmonic to chaotic snap-through. Beyond the problem studied herein, the techniques developed will serve as a prescriptive guide in developing fast and accurate dimensionally reduced models of nonlinear systems, and eventually as a tool for adaptive dimension-reduction in numerical modeling. The results are especially relevant in the aerospace industry for the design of thin structures such as beams, panels, and shells, which are all capable of spatio-temporally complex dynamic responses that are difficult and computationally expensive to

A New Nonlinear Unit Root Test with Fourier Function

OpenAIRE

Güriş, Burak

2017-01-01

Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an Exponential Smooth Threshold Autore...

Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions

Science.gov (United States)

Ishizaki, Akihito; Tanimura, Yoshitaka

2008-05-01

Based on the influence functional formalism, we have derived a nonperturbative equation of motion for a reduced system coupled to a harmonic bath with colored noise in which the system-bath coupling operator does not necessarily commute with the system Hamiltonian. The resultant expression coincides with the time-convolutionless quantum master equation derived from the second-order perturbative approximation, which is also equivalent to a generalized Redfield equation. This agreement occurs because, in the nonperturbative case, the relaxation operators arise from the higher-order system-bath interaction that can be incorporated into the reduced density matrix as the influence operator; while the second-order interaction remains as a relaxation operator in the equation of motion. While the equation describes the exact dynamics of the density matrix beyond weak system-bath interactions, it does not have the capability to calculate nonlinear response functions appropriately. This is because the equation cannot describe memory effects which straddle the external system interactions due to the reduced description of the bath. To illustrate this point, we have calculated the third-order two-dimensional (2D) spectra for a two-level system from the present approach and the hierarchically coupled equations approach that can handle quantal system-bath coherence thanks to its hierarchical formalism. The numerical demonstration clearly indicates the lack of the system-bath correlation in the present formalism as fast dephasing profiles of the 2D spectra.

Functional possibilities of nonlinear crystals for frequency conversion: uniaxial crystals

Energy Technology Data Exchange (ETDEWEB)

Andreev, Yu M [Institute of Monitoring of Climatic and Ecological Systems, Siberian Branch of the Russian Academy of Sciences, Tomsk (Russian Federation); Arapov, Yu D; Kasyanov, I V [E.I. Zababakhin All-Russian Scientific-Research Institute of Technical Physics, Russian Federal Nuclear Centre, Snezhinsk, Chelyabinsk region (Russian Federation); Grechin, S G; Nikolaev, P P [N.E. Bauman Moscow State Technical University, Moscow (Russian Federation)

2016-01-31

The method and results of the analysis of phase-matching and nonlinear properties for all point groups of symmetry of uniaxial crystals that determine their functional possibilities for solving various problems of nonlinear frequency conversion of laser radiation are presented. (nonlinear optical phenomena)

Nonlinear correction to the longitudinal structure function at small x

International Nuclear Information System (INIS)

Boroun, G.R.

2010-01-01

We computed the longitudinal proton structure function F L , using the nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation approach at small x. For the gluon distribution, the nonlinear effects are related to the longitudinal structure function. As the very small-x behavior of the gluon distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear shadowing term incorporated, we show that the strong rise that corresponds to the linear QCD evolution equations can be tamed by screening effects. Consequently, the obtained longitudinal structure function shows a tamed growth at small x. We computed the predictions for all details of the nonlinear longitudinal structure function in the kinematic range where it has been measured by the H1 Collaboration and made comparisons with the computation by Moch, Vermaseren and Vogt at the second order with input data from the MRST QCD fit. (orig.)

Distributed nonlinear optical response

DEFF Research Database (Denmark)

Nikolov, Nikola Ivanov

2005-01-01

of bound states of out of phase bright solitons and dark solitons. Also, the newly introduced analogy between the nonlocal cubic nonlinear and the quadratic nonlinear media, presented in paper B and Chapter 3 is discussed. In particular it supplies intuitive physical meaning of the formation of solitons...... in quadratic nonlinear media. In the second part of the report (Chapter 4), the possibility to obtain light with ultrabroad spectrum due to the interplay of many nonlinear effects based on cubic nonlinearity is investigated thoroughly. The contribution of stimulated Raman scattering, a delayed nonlinear...... a modified nonlinear Schroedinger model equation. Chapter 4 and papers D and E are dedicated to this part of the research....

Finite-time generalized function matrix projective lag synchronization of coupled dynamical networks with different dimensions via the double power function nonlinear feedback control method

International Nuclear Information System (INIS)

Dai, Hao; Si, Gangquan; Jia, Lixin; Zhang, Yanbin

2014-01-01

This paper investigates the problem of finite-time generalized function matrix projective lag synchronization between two different coupled dynamical networks with different dimensions of network nodes. The double power function nonlinear feedback control method is proposed in this paper to guarantee that the state trajectories of the response network converge to the state trajectories of the drive network according to a function matrix in a given finite time. Furthermore, in comparison with the traditional nonlinear feedback control method, the new method improves the synchronization efficiency, and shortens the finite synchronization time. Numerical simulation results are presented to illustrate the effectiveness of this method. (papers)

Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators

Science.gov (United States)

Gil', M. I.

2005-08-01

We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.

Identifying the nonlinear mechanical behaviour of micro-speakers from their quasi-linear electrical response

Science.gov (United States)

Zilletti, Michele; Marker, Arthur; Elliott, Stephen John; Holland, Keith

2017-05-01

In this study model identification of the nonlinear dynamics of a micro-speaker is carried out by purely electrical measurements, avoiding any explicit vibration measurements. It is shown that a dynamic model of the micro-speaker, which takes into account the nonlinear damping characteristic of the device, can be identified by measuring the response between the voltage input and the current flowing into the coil. An analytical formulation of the quasi-linear model of the micro-speaker is first derived and an optimisation method is then used to identify a polynomial function which describes the mechanical damping behaviour of the micro-speaker. The analytical results of the quasi-linear model are compared with numerical results. This study potentially opens up the possibility of efficiently implementing nonlinear echo cancellers.

Nonlinear response of the quantum Hall system to a strong electromagnetic radiation

International Nuclear Information System (INIS)

Avetissian, H.K.; Mkrtchian, G.F.

2016-01-01

We study nonlinear response of a quantum Hall system in semiconductor-hetero-structures via third harmonic generation process and nonlinear Faraday effect. We demonstrate that Faraday rotation angle and third harmonic radiation intensity have a characteristic Hall plateaus feature. These nonlinear effects remain robust against the significant broadening of Landau levels. We predict realization of an experiment through the observation of the third harmonic signal and Faraday rotation angle, which are within the experimental feasibility. - Highlights: • Nonlinear optical response of a quantum Hall system has specific plateaus feature. • This effect remains robust against the significant broadening of Landau levels. • It can be observed via the third harmonic signal and the nonlinear Faraday effect.

Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis

Science.gov (United States)

Rahman, M. A.; Ahmed, U.; Uddin, M. S.

2013-08-01

A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement

Structural stability of nonlinear population dynamics.

Science.gov (United States)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Structural stability of nonlinear population dynamics

Science.gov (United States)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Nonlinear optical response of some Graphene oxide and Graphene fluoride derivatives

OpenAIRE

Liaros Nikolaos; Orfanos Ioannis; Papadakis Ioannis; Couris Stelios

2016-01-01

The nonlinear optical properties of two graphene derivatives, graphene oxide and graphene fluoride, are investigated by means of the Z-scan technique employing 35 ps and 4 ns, visible (532 nm) laser excitation. Both derivatives were found to exhibit significant third-order nonlinear optical response at both excitation regimes, with the nonlinear absorption being relatively stronger and concealing the presence of nonlinear refraction under ns excitation, while ps excita...

Exact solutions for nonlinear evolution equations using Exp-function method

International Nuclear Information System (INIS)

Bekir, Ahmet; Boz, Ahmet

2008-01-01

In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations

Nonlinear response and bistability of driven ion acoustic waves

Science.gov (United States)

Akbari-Moghanjoughi, M.

2017-08-01

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

Computer-aided Nonlinear Control System Design Using Describing Function Models

CERN Document Server

Nassirharand, Amir

2012-01-01

A systematic computer-aided approach provides a versatile setting for the control engineer to overcome the complications of controller design for highly nonlinear systems. Computer-aided Nonlinear Control System Design provides such an approach based on the use of describing functions. The text deals with a large class of nonlinear systems without restrictions on the system order, the number of inputs and/or outputs or the number, type or arrangement of nonlinear terms. The strongly software-oriented methods detailed facilitate fulfillment of tight performance requirements and help the designer to think in purely nonlinear terms, avoiding the expedient of linearization which can impose substantial and unrealistic model limitations and drive up the cost of the final product. Design procedures are presented in a step-by-step algorithmic format each step being a functional unit with outputs that drive the other steps. This procedure may be easily implemented on a digital computer with example problems from mecha...

Solving eigenvalue response matrix equations with nonlinear techniques

International Nuclear Information System (INIS)

Roberts, Jeremy A.; Forget, Benoit

2014-01-01

Highlights: • High performance solvers were applied within ERMM for the first time. • Accelerated fixed-point methods were developed that reduce computational times by 2–3. • A nonlinear, Newton-based ERMM led to similar improvement and more robustness. • A 3-D, SN-based ERMM shows how ERMM can apply fine-mesh methods to full-core analysis. - Abstract: This paper presents new algorithms for use in the eigenvalue response matrix method (ERMM) for reactor eigenvalue problems. ERMM spatially decomposes a domain into independent nodes linked via boundary conditions approximated as truncated orthogonal expansions, the coefficients of which are response functions. In its simplest form, ERMM consists of a two-level eigenproblem: an outer Picard iteration updates the k-eigenvalue via balance, while the inner λ-eigenproblem imposes neutron balance between nodes. Efficient methods are developed for solving the inner λ-eigenvalue problem within the outer Picard iteration. Based on results from several diffusion and transport benchmark models, it was found that the Krylov–Schur method applied to the λ-eigenvalue problem reduces Picard solver times (excluding response generation) by a factor of 2–5. Furthermore, alternative methods, including Picard acceleration schemes, Steffensen’s method, and Newton’s method, are developed in this paper. These approaches often yield faster k-convergence and a need for fewer k-dependent response function evaluations, which is important because response generation is often the primary cost for problems using responses computed online (i.e., not from a precomputed database). Accelerated Picard iteration was found to reduce total computational times by 2–3 compared to the unaccelerated case for problems dominated by response generation. In addition, Newton’s method was found to provide nearly the same performance with improved robustness

Effect of Forcing Function on Nonlinear Acoustic Standing Waves

Science.gov (United States)

Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce

2003-01-01

Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.

Nonlinear differential equations with exact solutions expressed via the Weierstrass function

NARCIS (Netherlands)

Kudryashov, NA

2004-01-01

A new problem is studied, that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. A method is discussed to construct nonlinear ordinary differential equations with exact solutions. The main step of our method is the assumption that nonlinear

Nonlinear dynamics of cortical responses to color in the human cVEP.

Science.gov (United States)

Nunez, Valerie; Shapley, Robert M; Gordon, James

2017-09-01

The main finding of this paper is that the human visual cortex responds in a very nonlinear manner to the color contrast of pure color patterns. We examined human cortical responses to color checkerboard patterns at many color contrasts, measuring the chromatic visual evoked potential (cVEP) with a dense electrode array. Cortical topography of the cVEPs showed that they were localized near the posterior electrode at position Oz, indicating that the primary cortex (V1) was the major source of responses. The choice of fine spatial patterns as stimuli caused the cVEP response to be driven by double-opponent neurons in V1. The cVEP waveform revealed nonlinear color signal processing in the V1 cortex. The cVEP time-to-peak decreased and the waveform's shape was markedly narrower with increasing cone contrast. Comparison of the linear dynamics of retinal and lateral geniculate nucleus responses with the nonlinear dynamics of the cortical cVEP indicated that the nonlinear dynamics originated in the V1 cortex. The nature of the nonlinearity is a kind of automatic gain control that adjusts cortical dynamics to be faster when color contrast is greater.

Synthesis, characterization and non-linear optical response of organophilic carbon dots

KAUST Repository

Bourlinos, Athanasios B.

2013-09-01

For the first time ever we report the nonlinear optical (NLO) properties of carbon dots (C-dots). The C-dots for these experiments were synthesized by mild pyrolysis of lauryl gallate. The resulting C-dots bear lauryl chains and, hence, are highly dispersible in polar organic solvents, like chloroform. Dispersions in CHCl3 show significant NLO response. Specifically, the C-dots show negative nonlinear absorption coefficient and negative nonlinear refraction. Using suspensions with different concentrations these parameters are quantified and compared to those of fullerene a well-known carbon molecule with proven NLO response. © 2013 Elsevier Ltd. All rights reserved.

Synthesis, characterization and non-linear optical response of organophilic carbon dots

KAUST Repository

Bourlinos, Athanasios B.; Karakassides, Michael A.; Kouloumpis, Antonios; Gournis, Dimitrios; Bakandritsos, Aristides; Papagiannouli, Irene; Aloukos, Panagiotis; Couris, Stelios; Hola, Katerina; Zboril, Radek; Krysmann, Marta; Giannelis, Emmanuel P.

2013-01-01

For the first time ever we report the nonlinear optical (NLO) properties of carbon dots (C-dots). The C-dots for these experiments were synthesized by mild pyrolysis of lauryl gallate. The resulting C-dots bear lauryl chains and, hence, are highly dispersible in polar organic solvents, like chloroform. Dispersions in CHCl3 show significant NLO response. Specifically, the C-dots show negative nonlinear absorption coefficient and negative nonlinear refraction. Using suspensions with different concentrations these parameters are quantified and compared to those of fullerene a well-known carbon molecule with proven NLO response. © 2013 Elsevier Ltd. All rights reserved.

Stability of Nonlinear Neutral Stochastic Functional Differential Equations

Directory of Open Access Journals (Sweden)

Minggao Xue

2010-01-01

Full Text Available Neutral stochastic functional differential equations (NSFDEs have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper is to remove the linear growth condition and establish a Khasminskii-type test for nonlinear NSFDEs. New criteria not only cover a wide class of highly nonlinear NSFDEs but they can also be verified much more easily than the classical criteria. Finally, several examples are given to illustrate main results.

Modeling exposure–lag–response associations with distributed lag non-linear models

Science.gov (United States)

Gasparrini, Antonio

2014-01-01

In biomedical research, a health effect is frequently associated with protracted exposures of varying intensity sustained in the past. The main complexity of modeling and interpreting such phenomena lies in the additional temporal dimension needed to express the association, as the risk depends on both intensity and timing of past exposures. This type of dependency is defined here as exposure–lag–response association. In this contribution, I illustrate a general statistical framework for such associations, established through the extension of distributed lag non-linear models, originally developed in time series analysis. This modeling class is based on the definition of a cross-basis, obtained by the combination of two functions to flexibly model linear or nonlinear exposure-responses and the lag structure of the relationship, respectively. The methodology is illustrated with an example application to cohort data and validated through a simulation study. This modeling framework generalizes to various study designs and regression models, and can be applied to study the health effects of protracted exposures to environmental factors, drugs or carcinogenic agents, among others. © 2013 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd. PMID:24027094

Detection of Differential Item Functioning with Nonlinear Regression: A Non-IRT Approach Accounting for Guessing

Czech Academy of Sciences Publication Activity Database

Drabinová, Adéla; Martinková, Patrícia

2017-01-01

Roč. 54, č. 4 (2017), s. 498-517 ISSN 0022-0655 R&D Projects: GA ČR GJ15-15856Y Institutional support: RVO:67985807 Keywords : differential item functioning * non-linear regression * logistic regression * item response theory Subject RIV: AM - Education OBOR OECD: Statistics and probability Impact factor: 0.979, year: 2016

Adaptive Neural Control of Nonaffine Nonlinear Systems without Differential Condition for Nonaffine Function

Directory of Open Access Journals (Sweden)

Chaojiao Sun

2016-01-01

Full Text Available An adaptive neural control scheme is proposed for nonaffine nonlinear system without using the implicit function theorem or mean value theorem. The differential conditions on nonaffine nonlinear functions are removed. The control-gain function is modeled with the nonaffine function probably being indifferentiable. Furthermore, only a semibounded condition for nonaffine nonlinear function is required in the proposed method, and the basic idea of invariant set theory is then constructively introduced to cope with the difficulty in the control design for nonaffine nonlinear systems. It is rigorously proved that all the closed-loop signals are bounded and the tracking error converges to a small residual set asymptotically. Finally, simulation examples are provided to demonstrate the effectiveness of the designed method.

Nonlinear response of dense colloidal suspensions under oscillatory shear: mode-coupling theory and Fourier transform rheology experiments.

Science.gov (United States)

Brader, J M; Siebenbürger, M; Ballauff, M; Reinheimer, K; Wilhelm, M; Frey, S J; Weysser, F; Fuchs, M

2010-12-01

Using a combination of theory, experiment, and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently developed schematic mode-coupling-type theory describing colloidal suspensions under externally applied flow. For finite strain amplitudes the theory generates a nonlinear response, characterized by significant higher harmonic contributions. An important feature of the theory is the prediction of an ideal glass transition at sufficiently strong coupling, which is accompanied by the discontinuous appearance of a dynamic yield stress. For the oscillatory shear flow under consideration we find that the yield stress plays an important role in determining the nonlinearity of the time-dependent stress response. Our theoretical findings are strongly supported by both large amplitude oscillatory experiments (with Fourier transform rheology analysis) on suspensions of thermosensitive core-shell particles dispersed in water and Brownian dynamics simulations performed on a two-dimensional binary hard-disk mixture. In particular, theory predicts nontrivial values of the exponents governing the final decay of the storage and loss moduli as a function of strain amplitude which are in good agreement with both simulation and experiment. A consistent set of parameters in the presented schematic model achieves to jointly describe linear moduli, nonlinear flow curves, and large amplitude oscillatory spectroscopy.

Induced dynamic nonlinear ground response at Gamer Valley, California

Science.gov (United States)

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

2008-01-01

We present results from a prototype experiment in which we actively induce, observe, and quantify in situ nonlinear sediment response in the near surface. This experiment was part of a suite of experiments conducted during August 2004 in Garner Valley, California, using a large mobile shaker truck from the Network for Earthquake Engineering Simulation (NEES) facility. We deployed a dense accelerometer array within meters of the mobile shaker truck to replicate a controlled, laboratory-style soil dynamics experiment in order to observe wave-amplitude-dependent sediment properties. Ground motion exceeding 1g acceleration was produced near the shaker truck. The wave field was dominated by Rayleigh surface waves and ground motions were strong enough to produce observable nonlinear changes in wave velocity. We found that as the force load of the shaker increased, the Rayleigh-wave phase velocity decreased by as much as ???30% at the highest frequencies used (up to 30 Hz). Phase velocity dispersion curves were inverted for S-wave velocity as a function of depth using a simple isotropic elastic model to estimate the depth dependence of changes to the velocity structure. The greatest change in velocity occurred nearest the surface, within the upper 4 m. These estimated S-wave velocity values were used with estimates of surface strain to compare with laboratory-based shear modulus reduction measurements from the same site. Our results suggest that it may be possible to characterize nonlinear soil properties in situ using a noninvasive field technique.

Spatial nonlinearities: Cascading effects in the earth system

Science.gov (United States)

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

2006-01-01

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

Detection of Differential Item Functioning with Nonlinear Regression: A Non-IRT Approach Accounting for Guessing

Science.gov (United States)

Drabinová, Adéla; Martinková, Patrícia

2017-01-01

In this article we present a general approach not relying on item response theory models (non-IRT) to detect differential item functioning (DIF) in dichotomous items with presence of guessing. The proposed nonlinear regression (NLR) procedure for DIF detection is an extension of method based on logistic regression. As a non-IRT approach, NLR can…

Nonlinear dynamic response of electro-thermo-mechanically loaded piezoelectric cylindrical shell reinforced with BNNTs

International Nuclear Information System (INIS)

Yang, J H; Yang, J; Kitipornchai, S

2012-01-01

This paper presents an investigation on the nonlinear dynamic response of piezoelectric cylindrical shells reinforced with boron nitride nanotubes (BNNTs) under a combined axisymmetric electro-thermo-mechanical loading. By employing the classical Donnell shell theory, the von Kármán–Donnell kinematic relationship, and a piezo-elastic constitutive law including thermal effects, the nonlinear governing equations of motion of the shell are derived through the Reissner variational principle. The finite difference method and a time-integration scheme are used to obtain the nonlinear dynamic response of the BNNT-reinforced piezoelectric shell. A parametric study is conducted, showing the effects of geometrically nonlinear deformation, applied voltage, temperature change, mechanical load, BNNT volume fraction and boundary conditions on the nonlinear dynamic response. (paper)

Nonlinear ultrafast optical response in organic molecular crystals

Science.gov (United States)

Rahman, Talat S.; Turkowski, Volodymyr; Leuenberger, Michael N.

2012-02-01

We analyze possible nonlinear excitonic effects in the organic molecule crystals by using a combined time-dependent DFT and many-body approach. In particular, we analyze possible effects of the time-dependent (retarded)interaction between different types of excitations, Frenkel excitons, charge transfer excitons and excimers, on the electric and the optical response of the system. We pay special attention to the case of constant electric field and ultrafast pulses, including that of four-wave mixing experiments. As a specific application we examine the optical excitations of pentacene nanocrystals and compare the results with available experimental data.[1] Our results demostrate that the nonlinear effects can play an important role in the optical response of these systems. [1] A. Kabakchiev, ``Scanning Tunneling Luminescence of Pentacene Nanocrystals'', PhD Thesis (EPFL, Lausanne, 2010).

Quark fragmentation function and the nonlinear chiral quark model

International Nuclear Information System (INIS)

Zhu, Z.K.

1993-01-01

The scaling law of the fragmentation function has been proved in this paper. With that, we show that low-P T quark fragmentation function can be studied as a low energy physocs in the light-cone coordinate frame. We therefore use the nonlinear chiral quark model which is able to study the low energy physics under scale Λ CSB to study such a function. Meanwhile the formalism for studying the quark fragmentation function has been established. The nonlinear chiral quark model is quantized on the light-front. We then use old-fashioned perturbation theory to study the quark fragmentation function. Our first order result for such a function shows in agreement with the phenomenological model study of e + e - jet. The probability for u,d pair formation in the e + e - jet from our calculation is also in agreement with the phenomenological model results

Time domain simulation of the response of geometrically nonlinear panels subjected to random loading

Science.gov (United States)

Moyer, E. Thomas, Jr.

1988-01-01

The response of composite panels subjected to random pressure loads large enough to cause geometrically nonlinear responses is studied. A time domain simulation is employed to solve the equations of motion. An adaptive time stepping algorithm is employed to minimize intermittent transients. A modified algorithm for the prediction of response spectral density is presented which predicts smooth spectral peaks for discrete time histories. Results are presented for a number of input pressure levels and damping coefficients. Response distributions are calculated and compared with the analytical solution of the Fokker-Planck equations. RMS response is reported as a function of input pressure level and damping coefficient. Spectral densities are calculated for a number of examples.

Geometrically Nonlinear Static Analysis of Edge Cracked Timoshenko Beams Composed of Functionally Graded Material

Directory of Open Access Journals (Sweden)

Şeref Doğuşcan Akbaş

2013-01-01

Full Text Available Geometrically nonlinear static analysis of edge cracked cantilever Timoshenko beams composed of functionally graded material (FGM subjected to a nonfollower transversal point load at the free end of the beam is studied with large displacements and large rotations. Material properties of the beam change in the height direction according to exponential distributions. The cracked beam is modeled as an assembly of two subbeams connected through a massless elastic rotational spring. In the study, the finite element of the beam is constructed by using the total Lagrangian Timoshenko beam element approximation. The nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. The convergence study is performed for various numbers of finite elements. In the study, the effects of the location of crack, the depth of the crack, and various material distributions on the nonlinear static response of the FGM beam are investigated in detail. Also, the difference between the geometrically linear and nonlinear analysis of edge cracked FGM beam is investigated in detail.

Non-linear dynamic response of reactor containment

International Nuclear Information System (INIS)

Takemori, T.; Sotomura, K.; Yamada, M.

1975-01-01

A computer program was developed to investigate the elasto-plastic behavior of structures. This program is outlined and the problems of non-linear response of structures are discussed. Since the mode superposition method is only valid in an elastic analysis, the direct integration method was adopted here. As the sample model, an actual reactor containment (reactor building) of PWR plant was adopted. This building consists of three components, that is, a concrete internal structure, a steel containment vessel and a concrete outer shield wall. These components are resting on a rigid foundation mat. Therefore they were modeled with a lumped mass model respectively and coupled on the foundation. The following assumptions were employed to establish the properties of dynamic model: rocking and swaying springs of soil can be obtained from an elastic half-space solution, and the hysteretic characteristic of springs is bi-linear; springs connecting each mass are dealt with shear beams so that both bending and shear deflections can be included (Hysteretic characteristics of springs are linear, bi-linear and tri-linear for the internal structure, the containment vessel and the outer shield wall, respectively); generally, each damping coefficient is given for each mode in modal superposition (However, a damping matrix must be made directly in a non-linear response). Therefore the damping matrix of the model was made by combining the damping matrices [C] of each component obtained by Caughy's method and a damping value of the rocking and swaying by the half-space solution. On the basis of above conditions, the non-linear response of the structure was obtained and the difference between elastic and elasto-plastic analysis is presented

Another Class of Perfect Nonlinear Polynomial Functions

Directory of Open Access Journals (Sweden)

Menglong Su

2013-01-01

Full Text Available Perfect nonlinear (PN functions have been an interesting subject of study for a long time and have applications in coding theory, cryptography, combinatorial designs, and so on. In this paper, the planarity of the trinomials xpk+1+ux2+vx2pk over GF(p2k are presented. This class of PN functions are all EA-equivalent to x2.

Control-focused, nonlinear and time-varying modelling of dielectric elastomer actuators with frequency response analysis

International Nuclear Information System (INIS)

Jacobs, William R; Dodd, Tony J; Anderson, Sean R; Wilson, Emma D; Porrill, John; Assaf, Tareq; Rossiter, Jonathan

2015-01-01

Current models of dielectric elastomer actuators (DEAs) are mostly constrained to first principal descriptions that are not well suited to the application of control design due to their computational complexity. In this work we describe an integrated framework for the identification of control focused, data driven and time-varying DEA models that allow advanced analysis of nonlinear system dynamics in the frequency-domain. Experimentally generated input–output data (voltage-displacement) was used to identify control-focused, nonlinear and time-varying dynamic models of a set of film-type DEAs. The model description used was the nonlinear autoregressive with exogenous input structure. Frequency response analysis of the DEA dynamics was performed using generalized frequency response functions, providing insight and a comparison into the time-varying dynamics across a set of DEA actuators. The results demonstrated that models identified within the presented framework provide a compact and accurate description of the system dynamics. The frequency response analysis revealed variation in the time-varying dynamic behaviour of DEAs fabricated to the same specifications. These results suggest that the modelling and analysis framework presented here is a potentially useful tool for future work in guiding DEA actuator design and fabrication for application domains such as soft robotics. (paper)

Tracing the transition of a macro electron shuttle into nonlinear response

Energy Technology Data Exchange (ETDEWEB)

Kim, Chulki [Sensor System Research Center, Korea Institute of Science and Technology, Seoul 136791 (Korea, Republic of); Prada, Marta [I. Institut für Theoretische Physik, Universität Hamburg, Jungiusstr. 9, Hamburg 20355 (Germany); Qin, Hua [Key Laboratory of Nanodevices, Suzhou Institute of Nano-Tech and Nano-Bionics, Chinese Academy of Sciences, 398 Ruoshui Road, Industrial Park, Suzhou City, Jiangsu 215123 (China); Kim, Hyun-Seok [Division of Electronics and Electrical Engineering, Dongguk University-Seoul, 100715 Seoul (Korea, Republic of); Blick, Robert H., E-mail: rblick@physnet.uni-hamburg.de [Department of Physics, University of Wisconsin-Madison, 1150 University Avenue, Madison, Wisconsin-53706 (United States); Center for Hybrid Nanostructures, Universität Hamburg, Jungiusstr. 11c, Hamburg 20355 (Germany); Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 1415 Engineering Dr. Madison, Wisconsin-53706 (United States)

2015-02-09

We present a study on a macroscopic electron shuttle in the transition from linear to nonlinear response. The shuttle consists of a classical mechanical pendulum situated between two capacitor plates. The metallic pendulum enables mechanical transfer of electrons between the plates, hence allowing to directly trace electron shuttling in the time domain. By applying a high voltage to the plates, we drive the system into a controlled nonlinear response, where we observe period doubling.

Artificial Neural Networks for Nonlinear Dynamic Response Simulation in Mechanical Systems

DEFF Research Database (Denmark)

Christiansen, Niels Hørbye; Høgsberg, Jan Becker; Winther, Ole

2011-01-01

It is shown how artificial neural networks can be trained to predict dynamic response of a simple nonlinear structure. Data generated using a nonlinear finite element model of a simplified wind turbine is used to train a one layer artificial neural network. When trained properly the network is ab...... to perform accurate response prediction much faster than the corresponding finite element model. Initial result indicate a reduction in cpu time by two orders of magnitude....

Study of horizontal-vertical interactive Sway Rocking (SR) model for basemat uplift. Part 2: non-linear response analysis and validation

International Nuclear Information System (INIS)

Momma, T.; Shirahama, K.; Suzuki, K.; Ogihara, M.

1995-01-01

Non-linear earthquake response analyses of a BWR MARK-II type nuclear reactor building are conducted by using a Sway Rocking model (SR model) proposed in Part 1 considering the interaction between horizontal and vertical motion. The results are compared with those of accurate mathematical model using the Green Function method. Horizontal response of the SR model agrees very well with that of the Green Function model. The floor response spectra of induced vertical motions by both methods are also corresponding well in periodic characteristics as well as peak-levels. From these results, it is confirmed that the horizontal-vertical interactive SR model is applicable to non-linear response analyses considering basemat uplift. Based on the comparison of the induced vertical motions due to basemat uplift by both methods, an application limit of the horizontal-vertical interactive SR model is set up at the ground contact ratio of about 50%. (author). 4 refs., 8 figs., 1 tab

Superradiance Effects in the Linear and Nonlinear Optical Response of Quantum Dot Molecules

Science.gov (United States)

Sitek, A.; Machnikowski, P.

2008-11-01

We calculate the linear optical response from a single quantum dot molecule and the nonlinear, four-wave-mixing response from an inhomogeneously broadened ensemble of such molecules. We show that both optical signals are affected by the coupling-dependent superradiance effect and by optical interference between the two polarizations. As a result, the linear and nonlinear responses are not identical.

Nonlinear Response of the Stratosphere and the North Atlantic-European Climate to Global Warming

Science.gov (United States)

Manzini, E.; Karpechko, A. Yu.; Kornblueh, L.

2018-05-01

The response of the northern winter atmospheric circulation for two consecutive global warming periods of 2 K is examined in a grand ensemble (68 members) of idealized CO2 increase experiments performed with the same climate model. The comparison of the atmospheric responses for the two periods shows remarkable differences, indicating the nonlinearity of the response. The nonlinear signature of the atmospheric and surface responses is reminiscent of the positive phase of the annular mode of variability. The stratospheric vortex response shifts from an easterly wind change for the first 2 K to a westerly wind change for the second 2 K. The North Atlantic storm track shifts poleward only in the second period. A weaker November Arctic amplification during the second period suggests that differences in Arctic sea ice changes can act to trigger the atmospheric nonlinear response. Stratosphere-troposphere coupling thereafter can provide for the persistence of this nonlinearity throughout the winter.

Nonlinear response of the anterior cingulate and prefrontal cortex in schizophrenia as a function of variable attentional control.

Science.gov (United States)

Blasi, Giuseppe; Taurisano, Paolo; Papazacharias, Apostolos; Caforio, Grazia; Romano, Raffaella; Lobianco, Luciana; Fazio, Leonardo; Di Giorgio, Annabella; Latorre, Valeria; Sambataro, Fabio; Popolizio, Teresa; Nardini, Marcello; Mattay, Venkata S; Weinberger, Daniel R; Bertolino, Alessandro

2010-04-01

Previous studies have reported abnormal prefrontal and cingulate activity during attentional control processing in schizophrenia. However, it is not clear how variation in attentional control load modulates activity within these brain regions in this brain disorder. The aim of this study in schizophrenia is to investigate the impact of increasing levels of attentional control processing on prefrontal and cingulate activity. Blood oxygen level-dependent (BOLD) responses of 16 outpatients with schizophrenia were compared with those of 21 healthy subjects while performing a task eliciting increasing levels of attentional control during event-related functional magnetic resonance imaging at 3 T. Results showed reduced behavioral performance in patients at greater attentional control levels. Imaging data indicated greater prefrontal activity at intermediate attentional control levels in patients but greater prefrontal and cingulate responses at high attentional control demands in controls. The BOLD activity profile of these regions in controls increased linearly with increasing cognitive loads, whereas in patients, it was nonlinear. Correlation analysis consistently showed differential region and load-specific relationships between brain activity and behavior in the 2 groups. These results indicate that varying attentional control load is associated in schizophrenia with load- and region-specific modification of the relationship between behavior and brain activity, possibly suggesting earlier saturation of cognitive capacity.

Nonlinear Response of Cantilever Beams to Combination and Subcombination Resonances

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Ali H. Nayfeh

1998-01-01

Full Text Available The nonlinear planar response of cantilever metallic beams to combination parametric and external subcombination resonances is investigated, taking into account the effects of cubic geometric and inertia nonlinearities. The beams considered here are assumed to have large length-to-width aspect ratios and thin rectangular cross sections. Hence, the effects of shear deformations and rotatory inertia are neglected. For the case of combination parametric resonance, a two-mode Galerkin discretization along with Hamilton’s extended principle is used to obtain two second-order nonlinear ordinary-differential equations of motion and associated boundary conditions. Then, the method of multiple scales is applied to obtain a set of four first-order nonlinear ordinary-differential equations governing the modulation of the amplitudes and phases of the two excited modes. For the case of subcombination resonance, the method of multiple scales is applied directly to the Lagrangian and virtual-work term. Then using Hamilton’s extended principle, we obtain a set of four first-order nonlinear ordinary-differential equations governing the amplitudes and phases of the two excited modes. In both cases, the modulation equations are used to generate frequency- and force-response curves. We found that the trivial solution exhibits a jump as it undergoes a subcritical pitchfork bifurcation. Similarly, the nontrivial solutions also exhibit jumps as they undergo saddle-node bifurcations.

Modeling Nonlinear Site Response Uncertainty in Broadband Ground Motion Simulations for the Los Angeles Basin

Science.gov (United States)

Assimaki, D.; Li, W.; Steidl, J. M.; Schmedes, J.

2007-12-01

source parameters for the ensemble of site conditions. Elastic, equivalent linear and nonlinear simulations are implemented for the deterministic description of the base-model velocity and attenuation structures and nonlinear soil properties, to examine the variability in ground motion predictions as a function of ground motion amplitude and frequency content, and nonlinear site response methodology. The modeling site response uncertainty introduced in the broadband ground motion predictions is reported by means of the COV of site amplification, defined as the ratio of the predicted peak ground acceleration (PGA) and spectral acceleration (SA) at short and long periods to the corresponding intensity measure on the ground surface of a typical NEHRP BC boundary profile (Vs30=760m/s), for the ensemble of approximate and incremental nonlinear models implemented. A frequency index is developed to describe the frequency content of incident ground motion. In conjunction with the rock-outcrop acceleration level, this index is used to identify the site and ground motion conditions where incremental nonlinear analyses should be employed in lieu of approximate methodologies. Finally, the effects of modeling uncertainty in ground response analysis is evaluated in the estimation of site amplification factors, which are successively compared to recently published factors of the New Generation Attenuation Relations (NGA) and the currently employed Seismic Code Provisions (NEHRP).

Nonlinear Local Bending Response and Bulging Factors for Longitudinal and Circumferential Cracks in Pressurized Cylindrical Shells

Science.gov (United States)

Young, Richard D.; Rose, Cheryl A.; Starnes, James H., Jr.

2000-01-01

Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased stresses due to curvature for longitudinal and circumferential cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in the form of contour plots of the bulging factor as a function of two nondimensional parameters: the shell curvature parameter, lambda, which is a function of the shell geometry, Poisson's ratio, and the crack length; and a loading parameter, eta, which is a function of the shell geometry, material properties, and the applied internal pressure. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant. Simple empirical expressions for the bulging factor are then derived from the numerical results and shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks. The numerical results are also compared with analytical solutions based on linear shallow shell theory for thin shells, and with some other semi-empirical solutions from the literature, and limitations on the use of these other expressions are suggested.

Existence Results for Some Nonlinear Functional-Integral Equations in Banach Algebra with Applications

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Lakshmi Narayan Mishra

2016-04-01

Full Text Available In the present manuscript, we prove some results concerning the existence of solutions for some nonlinear functional-integral equations which contains various integral and functional equations that considered in nonlinear analysis and its applications. By utilizing the techniques of noncompactness measures, we operate the fixed point theorems such as Darbo's theorem in Banach algebra concerning the estimate on the solutions. The results obtained in this paper extend and improve essentially some known results in the recent literature. We also provide an example of nonlinear functional-integral equation to show the ability of our main result.

Hash function based on piecewise nonlinear chaotic map

International Nuclear Information System (INIS)

Akhavan, A.; Samsudin, A.; Akhshani, A.

2009-01-01

Chaos-based cryptography appeared recently in the early 1990s as an original application of nonlinear dynamics in the chaotic regime. In this paper, an algorithm for one-way hash function construction based on piecewise nonlinear chaotic map with a variant probability parameter is proposed. Also the proposed algorithm is an attempt to present a new chaotic hash function based on multithreaded programming. In this chaotic scheme, the message is connected to the chaotic map using probability parameter and other parameters of chaotic map such as control parameter and initial condition, so that the generated hash value is highly sensitive to the message. Simulation results indicate that the proposed algorithm presented several interesting features, such as high flexibility, good statistical properties, high key sensitivity and message sensitivity. These properties make the scheme a suitable choice for practical applications.

Ultra-fast dynamics in the nonlinear optical response of silver nanoprism ordered arrays.

Science.gov (United States)

Sánchez-Esquivel, Héctor; Raygoza-Sanchez, Karen Y; Rangel-Rojo, Raúl; Kalinic, Boris; Michieli, Niccolò; Cesca, Tiziana; Mattei, Giovanni

2018-03-15

In this work we present the study of the ultra-fast dynamics of the nonlinear optical response of a honeycomb array of silver triangular nanoprisms, performed using a femtosecond pulsed laser tuned with the dipolar surface plasmon resonance of the nanoarray. Nonlinear absorption and refraction, and their time-dependence, were explored using the z-scan and time-resolved excite-probe techniques. Nonlinear absorption is shown to change sign with the input irradiance and the behavior was explained on the basis of a three-level model. The response time was determined to be in the picosecond regime. A technique based on a variable frequency chopper was also used in order to discriminate the thermal and electronic contributions to the nonlinearity, which were found to have opposite signs. All these findings propel the investigated nanoprism arrays as good candidates for applications in advanced ultra-fast nonlinear nanophotonic devices.

The application of He's exp-function method to a nonlinear differential-difference equation

International Nuclear Information System (INIS)

Dai Chaoqing; Cen Xu; Wu Shengsheng

2009-01-01

This paper applies He's exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear partial differential equations (NPDEs) or coupled nonlinear partial differential equations (CNPDEs), to a nonlinear differential-difference equation, and some new travelling wave solutions are obtained.

ON-LINE NONLINEAR CHROMATICITY CORRECTION USING OFF-MOMENTUM TUNE RESPONSE MATRIX

International Nuclear Information System (INIS)

LUO, Y.; FISCHER, W.; MALISKY, N.; TEPIKIAN, S.; TROBJEVIC, D.

2007-01-01

In this article, we propose a method for the online nonlinear chromaticity correction at store in the Relativistic Heavy Ion Collider (RHIC). With 8 arc sextupole families in each RHIC ring, the nonlinear chromaticities can be minimized online by matching the off-momentum tunes onto the wanted tunes given by the linear chromaticities. The Newton method is used for this multi-dimensional nonlinear optimization, where the off-momentum tune response matrix with respect to sextupole strength changes is adopted. The off-momentum tune response matrix can be calculated with the online accelerator optics model or directly measured with the real beam. In this article, the correction algorithm for the RHIC is presented. Simulations are also carried out to verify the method. The preliminary results from the beam experiments taken place in the RHIC 2007 Au run are reviewed

Nonlinear response matrix methods for radiative transfer

International Nuclear Information System (INIS)

Miller, W.F. Jr.; Lewis, E.E.

1987-01-01

A nonlinear response matrix formalism is presented for the solution of time-dependent radiative transfer problems. The essential feature of the method is that within each computational cell the temperature is calculated in response to the incoming photons from all frequency groups. Thus the updating of the temperature distribution is placed within the iterative solution of the spaceangle transport problem, instead of being placed outside of it. The method is formulated for both grey and multifrequency problems and applied in slab geometry. The method is compared to the more conventional source iteration technique. 7 refs., 1 fig., 4 tabs

Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

Directory of Open Access Journals (Sweden)

Taher S. Hassan

2016-01-01

Full Text Available We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t≔ri(tϕαixi-1Δ(t,  i=1,…,n-1,   with  x0=x,  ϕβ(u≔uβsgn⁡u, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.

Nonlinear dynamics in ecosystem response to climatic change: Case studies and policy implications

Science.gov (United States)

Burkett, Virginia R.; Wilcox, Douglas A.; Stottlemyer, Robert; Barrow, Wylie; Fagre, Dan; Baron, Jill S.; Price, Jeff; Nielsen, Jennifer L.; Allen, Craig D.; Peterson, David L.; Ruggerone, Greg; Doyle, Thomas

2005-01-01

Many biological, hydrological, and geological processes are interactively linked in ecosystems. These ecological phenomena normally vary within bounded ranges, but rapid, nonlinear changes to markedly different conditions can be triggered by even small differences if threshold values are exceeded. Intrinsic and extrinsic ecological thresholds can lead to effects that cascade among systems, precluding accurate modeling and prediction of system response to climate change. Ten case studies from North America illustrate how changes in climate can lead to rapid, threshold-type responses within ecological communities; the case studies also highlight the role of human activities that alter the rate or direction of system response to climate change. Understanding and anticipating nonlinear dynamics are important aspects of adaptation planning since responses of biological resources to changes in the physical climate system are not necessarily proportional and sometimes, as in the case of complex ecological systems, inherently nonlinear.

Modulational instability in nonlocal nonlinear Kerr media

DEFF Research Database (Denmark)

Krolikowski, Wieslaw; Bang, Ole; Juul Rasmussen, Jens

2001-01-01

We study modulational instability (MI) of plane waves in nonlocal nonlinear Kerr media. For a focusing nonlinearity we show that, although the nonlocality tends to suppress MI, it can never remove it completely, irrespective of the particular profile of the nonlocal response function. For a defoc...

Nonlinear Site Response Validation Studies Using KIK-net Strong Motion Data

Science.gov (United States)

Asimaki, D.; Shi, J.

2014-12-01

Earthquake simulations are nowadays producing realistic ground motion time-series in the range of engineering design applications. Of particular significance to engineers are simulations of near-field motions and large magnitude events, for which observations are scarce. With the engineering community slowly adopting the use of simulated ground motions, site response models need to be re-evaluated in terms of their capabilities and limitations to 'translate' the simulated time-series from rock surface output to structural analyses input. In this talk, we evaluate three one-dimensional site response models: linear viscoelastic, equivalent linear and nonlinear. We evaluate the performance of the models by comparing predictions to observations at 30 downhole stations of the Japanese network KIK-Net that have recorded several strong events, including the 2011 Tohoku earthquake. Velocity profiles are used as the only input to all models, while additional parameters such as quality factor, density and nonlinear dynamic soil properties are estimated from empirical correlations. We quantify the differences of ground surface predictions and observations in terms of both seismological and engineering intensity measures, including bias ratios of peak ground response and visual comparisons of elastic spectra, and inelastic to elastic deformation ratio for multiple ductility ratios. We observe that PGV/Vs,30 — as measure of strain— is a better predictor of site nonlinearity than PGA, and that incremental nonlinear analyses are necessary to produce reliable estimates of high-frequency ground motion components at soft sites. We finally discuss the implications of our findings on the parameterization of nonlinear amplification factors in GMPEs, and on the extensive use of equivalent linear analyses in probabilistic seismic hazard procedures.

Computation of Value Functions in Nonlinear Differential Games with State Constraints

KAUST Repository

Botkin, Nikolai; Hoffmann, Karl-Heinz; Mayer, Natalie; Turova, Varvara

2013-01-01

Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a

Time-domain Green's Function Method for three-dimensional nonlinear subsonic flows

Science.gov (United States)

Tseng, K.; Morino, L.

1978-01-01

The Green's Function Method for linearized 3D unsteady potential flow (embedded in the computer code SOUSSA P) is extended to include the time-domain analysis as well as the nonlinear term retained in the transonic small disturbance equation. The differential-delay equations in time, as obtained by applying the Green's Function Method (in a generalized sense) and the finite-element technique to the transonic equation, are solved directly in the time domain. Comparisons are made with both linearized frequency-domain calculations and existing nonlinear results.

Application of Exp-function method for (2 + 1)-dimensional nonlinear evolution equations

International Nuclear Information System (INIS)

Bekir, Ahmet; Boz, Ahmet

2009-01-01

In this paper, the Exp-function method is used to construct solitary and soliton solutions of (2 + 1)-dimensional nonlinear evolution equations. (2 + 1)-dimensional breaking soliton (Calogero) equation, modified Zakharov-Kuznetsov and Konopelchenko-Dubrovsky equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations.

Functionally unidimensional item response models for multivariate binary data

DEFF Research Database (Denmark)

Ip, Edward; Molenberghs, Geert; Chen, Shyh-Huei

2013-01-01

The problem of fitting unidimensional item response models to potentially multidimensional data has been extensively studied. The focus of this article is on response data that have a strong dimension but also contain minor nuisance dimensions. Fitting a unidimensional model to such multidimensio......The problem of fitting unidimensional item response models to potentially multidimensional data has been extensively studied. The focus of this article is on response data that have a strong dimension but also contain minor nuisance dimensions. Fitting a unidimensional model...... to such multidimensional data is believed to result in ability estimates that represent a combination of the major and minor dimensions. We conjecture that the underlying dimension for the fitted unidimensional model, which we call the functional dimension, represents a nonlinear projection. In this article we investigate...... tool. An example regarding a construct of desire for physical competency is used to illustrate the functional unidimensional approach....

Non-linear variation of the beta function with momentum

International Nuclear Information System (INIS)

Parzen, G.

1983-07-01

A theory is presented for computing the non-linear dependence of the β-functions on momentum. Results are found for the quadratic term. The results of the theory are compared with computed results. A procedure is proposed for computing the strengths of the sextupole correctors to correct the dependence of the β-function on momentum

Response statistics of rotating shaft with non-linear elastic restoring forces by path integration

Science.gov (United States)

Gaidai, Oleg; Naess, Arvid; Dimentberg, Michael

2017-07-01

Extreme statistics of random vibrations is studied for a Jeffcott rotor under uniaxial white noise excitation. Restoring force is modelled as elastic non-linear; comparison is done with linearized restoring force to see the force non-linearity effect on the response statistics. While for the linear model analytical solutions and stability conditions are available, it is not generally the case for non-linear system except for some special cases. The statistics of non-linear case is studied by applying path integration (PI) method, which is based on the Markov property of the coupled dynamic system. The Jeffcott rotor response statistics can be obtained by solving the Fokker-Planck (FP) equation of the 4D dynamic system. An efficient implementation of PI algorithm is applied, namely fast Fourier transform (FFT) is used to simulate dynamic system additive noise. The latter allows significantly reduce computational time, compared to the classical PI. Excitation is modelled as Gaussian white noise, however any kind distributed white noise can be implemented with the same PI technique. Also multidirectional Markov noise can be modelled with PI in the same way as unidirectional. PI is accelerated by using Monte Carlo (MC) estimated joint probability density function (PDF) as initial input. Symmetry of dynamic system was utilized to afford higher mesh resolution. Both internal (rotating) and external damping are included in mechanical model of the rotor. The main advantage of using PI rather than MC is that PI offers high accuracy in the probability distribution tail. The latter is of critical importance for e.g. extreme value statistics, system reliability, and first passage probability.

Nonlinear Optics: Principles and Applications

DEFF Research Database (Denmark)

Rottwitt, Karsten; Tidemand-Lichtenberg, Peter

of applications, Nonlinear Optics: Principles and Applications effectively bridges physics and mathematics with relevant applied material for real-world use. The book progresses naturally from fundamental aspects to illustrative examples, and presents a strong theoretical foundation that equips the reader...... and matter, this text focuses on the physical understanding of nonlinear optics, and explores optical material response functions in the time and frequency domain....

Robust Predictive Functional Control for Flight Vehicles Based on Nonlinear Disturbance Observer

Directory of Open Access Journals (Sweden)

Yinhui Zhang

2015-01-01

Full Text Available A novel robust predictive functional control based on nonlinear disturbance observer is investigated in order to address the control system design for flight vehicles with significant uncertainties, external disturbances, and measurement noise. Firstly, the nonlinear longitudinal dynamics of the flight vehicle are transformed into linear-like state-space equations with state-dependent coefficient matrices. And then the lumped disturbances are considered in the linear structure predictive model of the predictive functional control to increase the precision of the predictive output and resolve the intractable mismatched disturbance problem. As the lumped disturbances cannot be derived or measured directly, the nonlinear disturbance observer is applied to estimate the lumped disturbances, which are then introduced to the predictive functional control to replace the unknown actual lumped disturbances. Consequently, the robust predictive functional control for the flight vehicle is proposed. Compared with the existing designs, the effectiveness and robustness of the proposed flight control are illustrated and validated in various simulation conditions.

Evaluation of time integration methods for transient response analysis of nonlinear structures

International Nuclear Information System (INIS)

Park, K.C.

1975-01-01

Recent developments in the evaluation of direct time integration methods for the transient response analysis of nonlinear structures are presented. These developments, which are based on local stability considerations of an integrator, show that the interaction between temporal step size and nonlinearities of structural systems has a pronounced effect on both accuracy and stability of a given time integration method. The resulting evaluation technique is applied to a model nonlinear problem, in order to: 1) demonstrate that it eliminates the present costly process of evaluating time integrator for nonlinear structural systems via extensive numerical experiments; 2) identify the desirable characteristics of time integration methods for nonlinear structural problems; 3) develop improved stiffly-stable methods for application to nonlinear structures. Extension of the methodology for examination of the interaction between a time integrator and the approximate treatment of nonlinearities (such as due to pseudo-force or incremental solution procedures) is also discussed. (Auth.)

Nonlinear optical interactions in silicon waveguides

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Kuyken B.

2017-03-01

Full Text Available The strong nonlinear response of silicon photonic nanowire waveguides allows for the integration of nonlinear optical functions on a chip. However, the detrimental nonlinear optical absorption in silicon at telecom wavelengths limits the efficiency of many such experiments. In this review, several approaches are proposed and demonstrated to overcome this fundamental issue. By using the proposed methods, we demonstrate amongst others supercontinuum generation, frequency comb generation, a parametric optical amplifier, and a parametric optical oscillator.

Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review

Science.gov (United States)

Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.

2017-03-01

Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.

Elastic Nonlinear Response in Granular Media Under Resonance Conditions

Science.gov (United States)

Jia, X.; Johnson, P. A.

2004-12-01

We are studying the elastic linear and nonlinear behavior of granular media using dynamic wave methods. In the work presented here, our goal is to quantify the elastic nonlinear response by applying wave resonance. Resonance studies are desirable because they provide the means to easily study amplitude dependencies of elastic nonlinear behavior and thus to characterize the physical nature of the elastic nonlinearity. This work has implications for a variety of topics, in particular, the in situ nonlinear response of surface sediments. For this work we constructed an experimental cell in which high sensitivity dynamic resonance studies were conducted using granular media under controlled effective pressure. We limit our studies here to bulk modes but have the capability to employ shear waves as well. The granular media are composed of glass beads held under pressure by a piston, while applying resonance waves from transducers as both the excitation and the material probe. The container is closed with two fitted pistons and a normal load is applied to the granular sample across the top piston. Force and displacement are measured directly. Resonant frequency sweeps with frequencies corresponding to the fundamental bulk mode are applied to the longitudinal source transducer. The pore pressure in the system is 1 atm. The glass beads used in our experiments are of diameter 0.5 mm, randomly deposited in a duralumin cylinder of diameter 30 mm and height of 15 mm. This corresponds to a granular skeleton acoustic wave velocity of v ª 750m/s under 50 N of force [0.07 Mpa]. The loaded system gives fundamental mode resonances in the audio frequency band at half a wavelength where resonance frequency is effective-pressure dependent. The volume fraction of glass beads thus obtained is found to be 0.63 ± 0.01. Plane-wave generating and detecting transducers of diameter 30 mm are placed on axis at the top and bottom of the cylindrical container in direct contact with the glass

Unsteady Solution of Non-Linear Differential Equations Using Walsh Function Series

Science.gov (United States)

Gnoffo, Peter A.

2015-01-01

Walsh functions form an orthonormal basis set consisting of square waves. The discontinuous nature of square waves make the system well suited for representing functions with discontinuities. The product of any two Walsh functions is another Walsh function - a feature that can radically change an algorithm for solving non-linear partial differential equations (PDEs). The solution algorithm of non-linear differential equations using Walsh function series is unique in that integrals and derivatives may be computed using simple matrix multiplication of series representations of functions. Solutions to PDEs are derived as functions of wave component amplitude. Three sample problems are presented to illustrate the Walsh function series approach to solving unsteady PDEs. These include an advection equation, a Burgers equation, and a Riemann problem. The sample problems demonstrate the use of the Walsh function solution algorithms, exploiting Fast Walsh Transforms in multi-dimensions (O(Nlog(N))). Details of a Fast Walsh Reciprocal, defined here for the first time, enable inversion of aWalsh Symmetric Matrix in O(Nlog(N)) operations. Walsh functions have been derived using a fractal recursion algorithm and these fractal patterns are observed in the progression of pairs of wave number amplitudes in the solutions. These patterns are most easily observed in a remapping defined as a fractal fingerprint (FFP). A prolongation of existing solutions to the next highest order exploits these patterns. The algorithms presented here are considered a work in progress that provide new alternatives and new insights into the solution of non-linear PDEs.

Nonlinear Plasma Response to Resonant Magnetic Perturbation in Rutherford Regime

Science.gov (United States)

Zhu, Ping; Yan, Xingting; Huang, Wenlong

2017-10-01

Recently a common analytic relation for both the locked mode and the nonlinear plasma response in the Rutherford regime has been developed based on the steady-state solution to the coupled dynamic system of magnetic island evolution and torque balance equations. The analytic relation predicts the threshold and the island size for the full penetration of resonant magnetic perturbation (RMP). It also rigorously proves a screening effect of the equilibrium toroidal flow. In this work, we test the theory by solving for the nonlinear plasma response to a single-helicity RMP of a circular-shaped limiter tokamak equilibrium with a constant toroidal flow, using the initial-value, full MHD simulation code NIMROD. Time evolution of the parallel flow or ``slip frequency'' profile and its asymptotic approach to steady state obtained from the NIMROD simulations qualitatively agree with the theory predictions. Further comparisons are carried out for the saturated island size, the threshold for full mode penetration, as well as the screening effects of equilibrium toroidal flow in order to understand the physics of nonlinear plasma response in the Rutherford regime. Supported by National Magnetic Confinement Fusion Science Program of China Grants 2014GB124002 and 2015GB101004, the 100 Talent Program of the Chinese Academy of Sciences, and U.S. Department of Energy Grants DE-FG02-86ER53218 and DE-FC02-08ER54975.

On the effects of nonlinearities in room impulse response measurements with exponential sweeps

DEFF Research Database (Denmark)

Ciric, Dejan; Markovic, Milos; Mijic, Miomir

2013-01-01

In room impulse response measurements, there are some common disturbances that affect the measured results. These disturbances include nonlinearity, noise and time variance. In this paper, the effects of nonlinearities in the measurements with exponential sweep-sine signals are analyzed from diff...

Third-order nonlinear optical response of colloidal gold nanoparticles prepared by sputtering deposition

Energy Technology Data Exchange (ETDEWEB)

Castro, Hemerson P. S.; Alencar, Márcio A. R. C.; Hickmann, Jandir M. [Optics and Materials Group–OPTMA, Universidade Federal de Alagoas, CAIXA POSTAL 2051, 57061-970 Maceió (Brazil); Wender, Heberton [Brazilian Synchrotron National Laboratory (LNLS), CNPEM, Rua Giuseppe Máximo Scolfaro 10.000, 13083-970 Campinas (Brazil); Department of Physics, Universidade Federal do Mato Grosso do Sul, 79070-900, Campo Grande (Brazil); Teixeira, Sergio R. [Institute of Physics, Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre (Brazil); Dupont, Jairton [Laboratory of Molecular Catalysis, Institute of Chemistry, Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre (Brazil)

2013-11-14

The nonlinear optical responses of gold nanoparticles dispersed in castor oil produced by sputtering deposition were investigated, using the thermally managed Z-scan technique. Particles with spherical shape and 2.6 nm of average diameter were obtained and characterized by transmission electron microscopy and small angle X-ray scattering. This colloid was highly stable, without the presence of chemical impurities, neither stabilizers. It was observed that this system presents a large refractive third-order nonlinear response and a negligible nonlinear absorption. Moreover, the evaluation of the all-optical switching figures of merit demonstrated that the colloidal nanoparticles prepared by sputtering deposition have a good potential for the development of ultrafast photonic devices.

A non-linear association between self-reported negative emotional response to stress and subsequent allostatic load

DEFF Research Database (Denmark)

Dich, Nadya; Doan, Stacey N; Kivimäki, Mika

2014-01-01

dysregulation. Allostatic load also increased with age, but the association between negative emotional response and allostatic load remained stable over time. These results provide evidence for a more nuanced understanding of the role of negative emotions in long-term physical health....... response to major life events and allostatic load, a multisystem indicator of physiological dysregulation. Study sample was 6764 British civil service workers from the Whitehall II cohort. Negative emotional response was assessed by self-report at baseline. Allostatic load was calculated using...... cardiovascular, metabolic and immune function biomarkers at three clinical follow-up examinations. A non-linear association between negative emotional response and allostatic load was observed: being at either extreme end of the distribution of negative emotional response increased the risk of physiological...

Jacobian elliptic function expansion solutions of nonlinear stochastic equations

International Nuclear Information System (INIS)

Wei Caimin; Xia Zunquan; Tian Naishuo

2005-01-01

Jacobian elliptic function expansion method is extended and applied to construct the exact solutions of the nonlinear Wick-type stochastic partial differential equations (SPDEs) and some new exact solutions are obtained via this method and Hermite transformation

Designing Hybrids of Graphene Oxide and Gold Nanoparticles for Nonlinear Optical Response

Science.gov (United States)

Yadav, Rajesh Kumar; Aneesh, J.; Sharma, Rituraj; Abhiramnath, P.; Maji, Tuhin Kumar; Omar, Ganesh Ji; Mishra, A. K.; Karmakar, Debjani; Adarsh, K. V.

2018-04-01

Nonlinear optical absorption of light by materials is weak due to its perturbative nature, although a strong nonlinear response is of crucial importance to applications in optical limiting and switching. Here we demonstrate experimentally and theoretically an extremely efficient scheme of excited-state absorption by charge transfer between donor and acceptor materials as a method to enhance the nonlinear absorption by orders of magnitude. With this idea, we demonstrate a strong excited-state absorption (ESA) in reduced graphene oxide that otherwise shows an increased transparency at high fluence and enhancement of ESA by one order of magnitude in graphene oxide by attaching gold nanoparticles (Au NP) in the tandem configuration that acts as an efficient charge-transfer pair when excited at the plasmonic wavelength. To explain the unprecedented enhancement, we develop a five-level rate-equation model based on the charge transfer between the two materials and numerically simulate the results. To understand the correlation of interfacial charge transfer with the concentration and type of the functional ligands attached to the graphene oxide sheet, we investigate the Au-NP—graphene oxide interface with various possible ligand configurations from first-principles calculations. By using the strong ESA of our hybrid materials, we fabricate liquid cell-based high-performance optical limiters with important device parameters better than that of the benchmark optical limiters.

Ecological prediction with nonlinear multivariate time-frequency functional data models

Science.gov (United States)

Yang, Wen-Hsi; Wikle, Christopher K.; Holan, Scott H.; Wildhaber, Mark L.

2013-01-01

Time-frequency analysis has become a fundamental component of many scientific inquiries. Due to improvements in technology, the amount of high-frequency signals that are collected for ecological and other scientific processes is increasing at a dramatic rate. In order to facilitate the use of these data in ecological prediction, we introduce a class of nonlinear multivariate time-frequency functional models that can identify important features of each signal as well as the interaction of signals corresponding to the response variable of interest. Our methodology is of independent interest and utilizes stochastic search variable selection to improve model selection and performs model averaging to enhance prediction. We illustrate the effectiveness of our approach through simulation and by application to predicting spawning success of shovelnose sturgeon in the Lower Missouri River.

The Impact of Dam-Reservoir-Foundation Interaction on Nonlinear Response of Concrete Gravity Dams

International Nuclear Information System (INIS)

Amini, Ali Reza; Motamedi, Mohammad Hossein; Ghaemian, Mohsen

2008-01-01

To study the impact of dam-reservoir-foundation interaction on nonlinear response of concrete gravity dams, a two-dimensional finite element model of a concrete gravity dam including the dam body, a part of its foundation and a part of the reservoir was made. In addition, the proper boundary conditions were used in both reservoir and foundation in order to absorb the energy of outgoing waves at the far end boundaries. Using the finite element method and smeared crack approach, some different seismic nonlinear analyses were done and finally, we came to a conclusion that the consideration of dam-reservoir-foundation interaction in nonlinear analysis of concrete dams is of great importance, because from the performance point of view, this interaction significantly improves the nonlinear response of concrete dams

A Generalized Halanay Inequality for Stability of Nonlinear Neutral Functional Differential Equations

Directory of Open Access Journals (Sweden)

Wansheng Wang

2010-01-01

Full Text Available This paper is devoted to generalize Halanay's inequality which plays an important rule in study of stability of differential equations. By applying the generalized Halanay inequality, the stability results of nonlinear neutral functional differential equations (NFDEs and nonlinear neutral delay integrodifferential equations (NDIDEs are obtained.

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

Science.gov (United States)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Combined effects of traveling seismic waves and soil nonlinearity on nuclear power plant response

International Nuclear Information System (INIS)

Lee, T.H.; Charman, C.M.

1981-01-01

The effects of ground motion nonuniformity on the seismic input have been actively studied in recent years by considering the passage of traveling seismic waves. These studies gave rise to a new class of soil-structure interaction problems in which the seismic input is modified as a result of the spatial variations of ground motion. The phenomena were usually studied by using the elastic half-space simulation or discrete spring-models for modeling the soil medium. Finite element methods were also used recently on a limited scope. Results obtained from these investigations are often manifested by an attenuation of translational excitation along with an addition of rotational ground motion input. The decrease in structural response resulting from the input loss in the translational component was often insignificant since the response reduction tends to be offset by the effects from rotational input. The traveling wave effects have, so far, been investigated within the framework of linear theory with soil nonlinearity ignored. Conversely, the incorporation of soil nonlinearity in soil-structure interaction analyses has been done without including wave effect. Seismic analyses considering the hysteretic behavior of soil have been performed using highly idealized models for steady-state solution. More elaborate nonlinear seismic models deal with only the strain-dependent soil modulus rather than the transient unloading-reloading type of hysteretic characteristics of soil under a time-function input of earthquake trace. Apparently, the traveling wave effect and soil nonlinearity have been separately treated in the past. The purpose of this paper is to demonstrate that these two major effects can be combined in one model such that the influence of wave passage is reflected through the hysteretic behavior of soil particles, and thereby achieving significant reduction in seismic loads. (orig./RW)

Effective response of nonlinear cylindrical coated composites under external AC and DC electric field

International Nuclear Information System (INIS)

Yu-Yan, Shen; Xiao-Gang, Chen; Wei, Cui; Yan-Hua, Hao; Qian-Qian, Li

2009-01-01

This paper uses the perturbation method to study effective response of nonlinear cylindrical coated composites. Under the external AC and DC electric field E a (1 + sin ωt), the local potentials of composites at all harmonic frequencies are induced. An effective nonlinear response to composite is given for the cylindrical coated inclusions in the dilute limit. (condensed matter: electronic structure, electrical, magnetic, and optical properties)

Filtering Non-Linear Transfer Functions on Surfaces.

Science.gov (United States)

Heitz, Eric; Nowrouzezahrai, Derek; Poulin, Pierre; Neyret, Fabrice

2014-07-01

Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view- and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few

The nonlinear response of the complex structural system in nuclear reactors using dynamic substructure method

International Nuclear Information System (INIS)

Zheng, Z.C.; Xie, G.; Du, Q.H.

1987-01-01

Because of the existence of nonlinear characteristics in practical engineering structures, such as large steam turbine-foundation system and offshore platform, it is necessary to predict nonlinear dynamic responses for these very large and complex structural systems subjected extreme load. Due to the limited storage and high executing cost of computers, there are still some difficulties in the analysis for such systems although the traditional finite element methods provide basic available methods to the problems. The dynamic substructure methods, which were developed as a branch of general structural dynamics in the past more than 20 years and have been widely used from aircraft, space vehicles to other mechanical and civil engineering structures, present a powerful method to the analysis of very large structural systems. The key to success is due to the considerable reduction in the number of degrees of freedom while not changing the physical essence of the problems investigated. The dynamic substructure method has been extended to nonlinear system and applicated to the analysis of nonlinear dynamic response of an offshore platform by Z.C. Zheng, et al. (1983, 1985a, b, c). In this paper, the method is presented to analyze dynamic responses of the systems contained intrinsic nonlinearities and with nonlinear attachments and nonlinear supports of nuclear structural systems. The efficiency of the method becomes more clear for nonlinear dynamic problems due to the adoption of iterating processes. For simplicity, the analysis procedure is demonstrated briefly. The generalized substructure method of nonlinear systems is similar to linear systems, only the nonlinear terms are treated as pseudo-forces. Interface coordinates are classified into two categories, the connecting interface coordinates which connect with each other directly in the global system and the linking interface coordinates which link to each other through attachments. (orig./GL)

Accuracy of three-dimensional seismic ground response analysis in time domain using nonlinear numerical simulations

Science.gov (United States)

Liang, Fayun; Chen, Haibing; Huang, Maosong

2017-07-01

To provide appropriate uses of nonlinear ground response analysis for engineering practice, a three-dimensional soil column with a distributed mass system and a time domain numerical analysis were implemented on the OpenSees simulation platform. The standard mesh of a three-dimensional soil column was suggested to be satisfied with the specified maximum frequency. The layered soil column was divided into multiple sub-soils with a different viscous damping matrix according to the shear velocities as the soil properties were significantly different. It was necessary to use a combination of other one-dimensional or three-dimensional nonlinear seismic ground analysis programs to confirm the applicability of nonlinear seismic ground motion response analysis procedures in soft soil or for strong earthquakes. The accuracy of the three-dimensional soil column finite element method was verified by dynamic centrifuge model testing under different peak accelerations of the earthquake. As a result, nonlinear seismic ground motion response analysis procedures were improved in this study. The accuracy and efficiency of the three-dimensional seismic ground response analysis can be adapted to the requirements of engineering practice.

New Exact Penalty Functions for Nonlinear Constrained Optimization Problems

Directory of Open Access Journals (Sweden)

Bingzhuang Liu

2014-01-01

Full Text Available For two kinds of nonlinear constrained optimization problems, we propose two simple penalty functions, respectively, by augmenting the dimension of the primal problem with a variable that controls the weight of the penalty terms. Both of the penalty functions enjoy improved smoothness. Under mild conditions, it can be proved that our penalty functions are both exact in the sense that local minimizers of the associated penalty problem are precisely the local minimizers of the original constrained problem.

Nonlinear optical and optical limiting properties of fullerene, multi-walled carbon nanotubes, graphene and their derivatives with oxygen-containing functional groups

International Nuclear Information System (INIS)

Zhang, Xiao-Liang; Li, Xiao-Chun; Liu, Zhi-Bo; Yan, Xiao-Qing; Tian, Jian-Guo; Chen, Yong-Sheng

2015-01-01

Nonlinear optical properties (NLO) and optical limiting effect of fullerene (C 60 ), multi-walled carbon nanotubes (MWNTs), reduced graphene oxide (RGO) and their oxygenated derivatives were investigated by open-aperture Z-scan technique with nanosecond pulses at 532 nm. C 60 functionalized by oxygen-containing functional groups exhibits weaker NLO properties than that of pristine C 60 . Graphene oxide (GO) with many oxygen-containing functional groups also shows weaker NLO properties than that of RGO. That can be attributed to the disruption of conjugative structures of C 60 and graphene by oxygen-containing functional groups. However, MWNTs and their oxygenated derivatives exhibit comparable NLO properties due to the small weight ratio of these oxygen-containing groups. To investigate the correlation between structures and NLO response for these carbon nanomaterials with different dimensions, nonlinear scattered signal spectra versus input fluence were also measured. (paper)

Non-linear frequency response of non-isothermal adsorption controlled by micropore diffusion with variable diffusivity

Directory of Open Access Journals (Sweden)

MENKA PETKOVSKA

2000-12-01

Full Text Available The concept of higher order frequency response functions (FRFs is used for the analysis of non-linear adsorption kinetics on a particle scale, for the case of non-isothermal micropore diffusion with variable diffusivity. Six series of FRFs are defined for the general non-isothermal case. A non-linerar mathematical model is postulated and the first and second order FRFs derived and simulated. A variable diffusivity influences the shapes of the second order FRFs relating the sorbate concentration in the solid phase and t he gas pressure significantly, but they still keep their characteristics which can be used for discrimination of this from other kinetic mechanisms. It is also shown that first and second order particle FRFs offter sufficient information for an easy and fast estimation of all model parameters, including those defining the system non-linearity.

Strong nonlinear photonic responses from microbiologically synthesized tellurium nanocomposites

Science.gov (United States)

Liao, K.-S.; Wang, Jingyuan; Dias, S.; Dewald, J.; Alley, N.J.; Baesman, S.M.; Oremland, R.S.; Blau, W.J.; Curran, S.A.

2010-01-01

A new class of nanomaterials, namely microbiologically-formed nanorods composed of elemental tellurium [Te(0)] that forms unusual nanocomposites when combined with poly(m-phenylenevinylene-co-2,5-dioctoxy-phenylenevinylene) (PmPV) is described. These bio-nanocomposites exhibit excellent broadband optical limiting at 532 and 1064 nm. Nonlinear scattering, originating from the laser induced solvent bubbles and microplasmas, is responsible for this nonlinear behavior. The use of bacterially-formed Te(0) when combined with an organic chemical host (e.g., PmPV) is a new green method of nanoparticle syntheses. This opens the possibilities of using unique, biologically synthesized materials to advance future nanoelectronic and nanophotonic applications. ?? 2009 Elsevier B.V. All rights reserved.

Optical measurement of the weak non-linearity in the eardrum vibration response to auditory stimuli

Science.gov (United States)

Aerts, Johan

The mammalian hearing organ consists of the external ear (auricle and ear canal) followed by the middle ear (eardrum and ossicles) and the inner ear (cochlea). Its function is to convert the incoming sound waves and convert them into nerve pulses which are processed in the final stage by the brain. The main task of the external and middle ear is to concentrate the incoming sound waves on a smaller surface to reduce the loss that would normally occur in transmission from air to inner ear fluid. In the past it has been shown that this is a linear process, thus without serious distortions, for sound waves going up to pressures of 130 dB SPL (˜90 Pa). However, at large pressure changes up to several kPa, the middle ear movement clearly shows non-linear behaviour. Thus, it is possible that some small non-linear distortions are also present in the middle ear vibration at lower sound pressures. In this thesis a sensitive measurement set-up is presented to detect this weak non-linear behaviour. Essentially, this set-up consists of a loud-speaker which excites the middle ear, and the resulting vibration is measured with an heterodyne vibrometer. The use of specially designed acoustic excitation signals (odd random phase multisines) enables the separation of the linear and non-linear response. The application of this technique on the middle ear demonstrates that there are already non-linear distortions present in the vibration of the middle ear at a sound pressure of 93 dB SPL. This non-linear component also grows strongly with increasing sound pressure. Knowledge of this non-linear component can contribute to the improvement of modern hearing aids, which operate at higher sound pressures where the non-linearities could distort the signal considerably. It is also important to know the contribution of middle ear non-linearity to otoacoustic emissions. This are non-linearities caused by the active feedback amplifier in the inner ear, and can be detected in the external and

Nonlinear robust hierarchical control for nonlinear uncertain systems

Directory of Open Access Journals (Sweden)

Leonessa Alexander

1999-01-01

Full Text Available A nonlinear robust control-system design framework predicated on a hierarchical switching controller architecture parameterized over a set of moving nominal system equilibria is developed. Specifically, using equilibria-dependent Lyapunov functions, a hierarchical nonlinear robust control strategy is developed that robustly stabilizes a given nonlinear system over a prescribed range of system uncertainty by robustly stabilizing a collection of nonlinear controlled uncertain subsystems. The robust switching nonlinear controller architecture is designed based on a generalized (lower semicontinuous Lyapunov function obtained by minimizing a potential function over a given switching set induced by the parameterized nominal system equilibria. The proposed framework robustly stabilizes a compact positively invariant set of a given nonlinear uncertain dynamical system with structured parametric uncertainty. Finally, the efficacy of the proposed approach is demonstrated on a jet engine propulsion control problem with uncertain pressure-flow map data.

Fast evaluation of nonlinear functionals of tensor product wavelet expansions

NARCIS (Netherlands)

Schwab, C.; Stevenson, R.

2011-01-01

Abstract For a nonlinear functional f, and a function u from the span of a set of tensor product interpolets, it is shown how to compute the interpolant of f (u) from the span of this set of tensor product interpolets in linear complexity, assuming that the index set has a certain multiple tree

Modeling of nonlinear responses for reciprocal transducers involving polarization switching

DEFF Research Database (Denmark)

Willatzen, Morten; Wang, Linxiang

2007-01-01

Nonlinearities and hysteresis effects in a reciprocal PZT transducer are examined by use of a dynamical mathematical model on the basis of phase-transition theory. In particular, we consider the perovskite piezoelectric ceramic in which the polarization process in the material can be modeled...... by Landau theory for the first-order phase transformation, in which each polarization state is associated with a minimum of the Landau free-energy function. Nonlinear constitutive laws are obtained by using thermodynamical equilibrium conditions, and hysteretic behavior of the material can be modeled...... intrinsically. The time-dependent Ginzburg-Landau theory is used in the parameter identification involving hysteresis effects. We use the Chebyshev collocation method in the numerical simulations. The elastic field is assumed to be coupled linearly with other fields, and the nonlinearity is in the E-D coupling...

Effects of structural nonlinearity and foundation sliding on probabilistic response of a nuclear structure

International Nuclear Information System (INIS)

Hashemi, Alidad; Elkhoraibi, Tarek; Ostadan, Farhang

2015-01-01

Highlights: • Probabilistic SSI analysis including structural nonlinearity and sliding are shown. • Analysis is done for a soil and a rock site and probabilistic demands are obtained. • Structural drift ratios and In-structure response spectra are evaluated. • Structural nonlinearity significantly impacts local demands in the structure. • Sliding generally reduces seismic demands and can be accommodated in design. - Abstract: This paper examines the effects of structural nonlinearity and foundation sliding on the results of probabilistic structural analysis of a typical nuclear structure where structural nonlinearity, foundation sliding and soil-structure interaction (SSI) are explicitly included. The evaluation is carried out for a soil and a rock site at 10"4, 10"5, and 10"6 year return periods (1E − 4, 1E − 5, and 1E − 6 hazard levels, respectively). The input motions at each considered hazard level are deaggregated into low frequency (LF) and high frequency (HF) motions and a sample size of 30 is used for uncertainty propagation. The statistical distribution of structural responses including story drifts, and in-structure response spectra (ISRS) as well as foundation sliding displacements are examined. The probabilistic implementation of explicit structural nonlinearity and foundation sliding in combination with the SSI effects are demonstrated using nonlinear response history analysis (RHA) of the structure with the foundation motions obtained from elastic SSI analyses, which are applied as input to fixed-base inelastic analyses. This approach quantifies the expected structural nonlinearity and sliding for the particular structural configuration and provides a robust analytical basis for the estimation of the probabilistic distribution of selected demands parameters both at the design level and beyond design level seismic input. For the subject structure, the inclusion of foundation sliding in the analysis is found to have reduced both

Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model

International Nuclear Information System (INIS)

Ngai, K. L.

2015-01-01

Nonlinear dielectric measurements at high electric fields of glass-forming glycerol and propylene carbonate initially were carried out to elucidate the dynamic heterogeneous nature of the structural α-relaxation. Recently, the measurements were extended to sufficiently high frequencies to investigate the nonlinear dielectric response of faster processes including the so-called excess wing (EW), appearing as a second power law at high frequencies in the loss spectra of many glass formers without a resolved secondary relaxation. While a strong increase of dielectric constant and loss is found in the nonlinear dielectric response of the α-relaxation, there is a lack of significant change in the EW. A surprise to the experimentalists finding it, this difference in the nonlinear dielectric properties between the EW and the α-relaxation is explained in the framework of the coupling model by identifying the EW investigated with the nearly constant loss (NCL) of caged molecules, originating from the anharmonicity of the intermolecular potential. The NCL is terminated at longer times (lower frequencies) by the onset of the primitive relaxation, which is followed sequentially by relaxation processes involving increasing number of molecules until the terminal Kohlrausch α-relaxation is reached. These intermediate faster relaxations, combined to form the so-called Johari-Goldstein (JG) β-relaxation, are spatially and dynamically heterogeneous, and hence exhibit nonlinear dielectric effects, as found in glycerol and propylene carbonate, where the JG β-relaxation is not resolved and in D-sorbitol where it is resolved. Like the linear susceptibility, χ 1 (f), the frequency dispersion of the third-order dielectric susceptibility, χ 3 (f), was found to depend primarily on the α-relaxation time, and independent of temperature T and pressure P. I show this property of the frequency dispersions of χ 1 (f) and χ 3 (f) is the characteristic of the many-body relaxation

Microscopic investigations of the terahertz and the extreme nonlinear optical response of semiconductors

Energy Technology Data Exchange (ETDEWEB)

Golde, Daniel

2010-06-22

In the major part of this Thesis, we discuss the linear THz response of semiconductor nanostructures based on a microscopic theory. Here, two different problems are investigated: intersubband transitions in optically excited quantum wells and the THz plasma response of two-dimensional systems. In the latter case, we analyze the response of correlated electron and electron-hole plasmas. Extracting the plasma frequency from the linear response, we find significant deviations from the commonly accepted two-dimensional plasma frequency. Besides analyzing the pure plasma response, we also consider an intermediate regime where the response of the electron-hole plasma consists of a mixture of plasma contributions and excitonic transitions. A quantitative experiment-theory comparison provides novel insights into the behavior of the system at the transition from one regime to the other. The discussion of the intersubband transitions mainly focuses on the coherent superposition of the responses from true THz transitions and the ponderomotively accelerated carriers. We present a simple method to directly identify ponderomotive effects in the linear THz response. Apart from that, the excitonic contributions to intersubband transitions are investigated. The last part of the present Thesis deals with a completely different regime. Here, the extreme nonlinear optical response of low-dimensional semiconductor structures is discussed. Formally, extreme nonlinear optics describes the regime of light-matter interaction where the exciting field is strong enough such that the Rabi frequency is comparable to or larger than the characteristic transition frequency of the investigated system. Here, the Rabi frequency is given by the product of the electrical field strength and the dipole-matrix element of the respective transition. Theoretical investigations have predicted a large number of novel nonlinear effects arising for such strong excitations. Some of them have been observed in

Non-Linear Back-propagation: Doing Back-Propagation withoutDerivatives of the Activation Function

DEFF Research Database (Denmark)

Hertz, John; Krogh, Anders Stærmose; Lautrup, Benny

1997-01-01

The conventional linear back-propagation algorithm is replaced by a non-linear version, which avoids the necessity for calculating the derivative of the activation function. This may be exploited in hardware realizations of neural processors. In this paper we derive the non-linear back...

Alkali-Responsive Absorption Spectra and Third-Order Optical Nonlinearities of Imino Squaramides

International Nuclear Information System (INIS)

Li Zhong-Yu; Xu Song; Zhou Xin-Yu; Zhang Fu-Shi

2012-01-01

Third-order optical nonlinearities and dynamic responses of two imino squaramides under neutral and base conditions were studied using the femtosecond degenerate four-wave mixing technique at 800 nm. Ultrafast optical responses have been observed and the magnitude of the second-order hyperpolarizabilities of the squaramides has been measured to be as large as 10 −31 esu. The absorption spectra, color of solution, and third-order optical nonlinearities of two imino squaramides change with the addition of sodium hydroxide. The γ value under the base condition for each dye is approximately 1.25 times larger than that under neutral conditions. (fundamental areas of phenomenology(including applications))

Quantum-mechanical Green's functions and nonlinear superposition law

International Nuclear Information System (INIS)

Nassar, A.B.; Bassalo, J.M.F.; Antunes Neto, H.S.; Alencar, P. de T.S.

1986-01-01

The quantum-mechanical Green's function is derived for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field. (Author) [pt

Quantum-mechanical Green's function and nonlinear superposition law

International Nuclear Information System (INIS)

Nassar, A.B.; Bassalo, J.M.F.; Antunes Neto, H.S.; Alencar, P.T.S.

1986-01-01

It is derived the quantum-mechanical Green's function for the problem of a time-dependent variable mass particle subject to a time-dependent forced harmonic-oscillator potential by taking direct recourse of the corresponding Schroedinger equation. Through the usage of the nonlinear superposition law of Ray and Reid, it is shown that such a Green's function can be obtained from that for the problem of a particle with unit (constant) mass subject to either a forced harmonic potential with constant frequency or only to a time-dependent linear field

Unbalance Response Prediction for Rotors on Ball Bearings Using Speed and Load Dependent Nonlinear Bearing Stiffness

Science.gov (United States)

Fleming, David P.; Poplawski, J. V.

2003-01-01

Rolling-element bearing forces vary nonlinearly with bearing deflection. Thus an accurate rotordynamic analysis requires that bearing forces corresponding to the actual bearing deflection be utilized. For this work bearing forces were calculated by COBRA-AHS, a recently developed rolling-element bearing analysis code. Bearing stiffness was found to be a strong function of bearing deflection, with higher deflection producing markedly higher stiffness. Curves fitted to the bearing data for a range of speeds and loads were supplied to a flexible rotor unbalance response analysis. The rotordynamic analysis showed that vibration response varied nonlinearly with the amount of rotor imbalance. Moreover, the increase in stiffness as critical speeds were approached caused a large increase in rotor and bearing vibration amplitude over part of the speed range compared to the case of constant bearing stiffness. Regions of bistable operation were possible, in which the amplitude at a given speed was much larger during rotor acceleration than during deceleration. A moderate amount of damping will eliminate the bistable region, but this damping is not inherent in ball bearings.

A Two-Step Hybrid Approach for Modeling the Nonlinear Dynamic Response of Piezoelectric Energy Harvesters

Directory of Open Access Journals (Sweden)

Claudio Maruccio

2018-01-01

Full Text Available An effective hybrid computational framework is described here in order to assess the nonlinear dynamic response of piezoelectric energy harvesting devices. The proposed strategy basically consists of two steps. First, fully coupled multiphysics finite element (FE analyses are performed to evaluate the nonlinear static response of the device. An enhanced reduced-order model is then derived, where the global dynamic response is formulated in the state-space using lumped coefficients enriched with the information derived from the FE simulations. The electromechanical response of piezoelectric beams under forced vibrations is studied by means of the proposed approach, which is also validated by comparing numerical predictions with some experimental results. Such numerical and experimental investigations have been carried out with the main aim of studying the influence of material and geometrical parameters on the global nonlinear response. The advantage of the presented approach is that the overall computational and experimental efforts are significantly reduced while preserving a satisfactory accuracy in the assessment of the global behavior.

Microstructural Origins of Nonlinear Response in Associating Polymers under Oscillatory Shear

Directory of Open Access Journals (Sweden)

Mark A. Wilson

2017-10-01

Full Text Available The response of associating polymers with oscillatory shear is studied through large-scale simulations. A hybrid molecular dynamics (MD, Monte Carlo (MC algorithm is employed. Polymer chains are modeled as a coarse-grained bead-spring system. Functionalized end groups, at both ends of the polymer chains, can form reversible bonds according to MC rules. Stress-strain curves show nonlinearities indicated by a non-ellipsoidal shape. We consider two types of nonlinearities. Type I occurs at a strain amplitude much larger than one, type II at a frequency at which the elastic storage modulus dominates the viscous loss modulus. In this last case, the network topology resembles that of the system at rest. The reversible bonds are broken and chains stretch when the system moves away from the zero-strain position. For type I, the chains relax and the number of reversible bonds peaks when the system is near an extreme of the motion. During the movement to the other extreme of the cycle, first a stress overshoot occurs, then a yield accompanied by shear-banding. Finally, the network restructures. Interestingly, the system periodically restores bonds between the same associating groups. Even though major restructuring occurs, the system remembers previous network topologies.

A nonlinear bounce kinetic equation for trapped electrons

International Nuclear Information System (INIS)

Gang, F.Y.

1990-03-01

A nonlinear bounce averaged drift kinetic equation for trapped electrons is derived. This equation enables one to compute the nonlinear response of the trapped electron distribution function in terms of the field-line projection of a potential fluctuation left-angle e -inqθ φ n right-angle b . It is useful for both analytical and computational studies of the nonlinear evolution of short wavelength (n much-gt 1) trapped electron mode-driven turbulence. 7 refs

Time-dependent density functional theory for nonlinear properties of open-shell systems.

Science.gov (United States)

Rinkevicius, Zilvinas; Jha, Prakash Chandra; Oprea, Corneliu I; Vahtras, Olav; Agren, Hans

2007-09-21

This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.

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

International Nuclear Information System (INIS)

Khare, Avinash; Saxena, Avadh

2014-01-01

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

Analysis and Implementation of Nonlinear Transducer Response over a Wider Response Range

Directory of Open Access Journals (Sweden)

Sheroz Khan

2008-03-01

Full Text Available In today’s automation systems transducers are making core elements in the instruments and the circuits used for measurement, control and industrial applications. The task of a transducer is to reproduce a physical quantity as an electrical signal which with the help of conditioning circuits, is transformed into a form that suits a corresponding ADC requirement before a digital equivalent output of the required physical quantity is produced. In the most ideal cases a digital quantity is a true replica of the physical quantity when the transducer has got a linear response. However, in most of the cases the transducers characteristics are nonlinear, and hence at very points along the whole range of the transducer characteristics, the corresponding digital output is an exact replica of the concerned physical parameter. This work is about how a physical read more accurately in the case of nonlinear sensor characteristics, and then a microcontroller is programmed with the same technique while reading from an input over the entire range. The data of the microcontroller reading shows very closely matched with the actual sensors response. Further, the reading error is considerably reduced to within 10 % of the actual physical which shows the utility of the technique in very sensitive applications.

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

Energy Technology Data Exchange (ETDEWEB)

Johnson, P.A.; McCall, K.R.; Meegan, G.D. Jr. [Los Alamos National Lab., NM (United States)

1993-11-01

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

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

International Nuclear Information System (INIS)

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

1993-01-01

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

TS Fuzzy Model-Based Controller Design for a Class of Nonlinear Systems Including Nonsmooth Functions

DEFF Research Database (Denmark)

Vafamand, Navid; Asemani, Mohammad Hassan; Khayatiyan, Alireza

2018-01-01

This paper proposes a novel robust controller design for a class of nonlinear systems including hard nonlinearity functions. The proposed approach is based on Takagi-Sugeno (TS) fuzzy modeling, nonquadratic Lyapunov function, and nonparallel distributed compensation scheme. In this paper, a novel...... criterion, new robust controller design conditions in terms of linear matrix inequalities are derived. Three practical case studies, electric power steering system, a helicopter model and servo-mechanical system, are presented to demonstrate the importance of such class of nonlinear systems comprising...

Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion

Directory of Open Access Journals (Sweden)

Jun Wang

2013-01-01

Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.

Nonlinear H∞ Optimal Control Scheme for an Underwater Vehicle with Regional Function Formulation

Directory of Open Access Journals (Sweden)

Zool H. Ismail

2013-01-01

Full Text Available A conventional region control technique cannot meet the demands for an accurate tracking performance in view of its inability to accommodate highly nonlinear system dynamics, imprecise hydrodynamic coefficients, and external disturbances. In this paper, a robust technique is presented for an Autonomous Underwater Vehicle (AUV with region tracking function. Within this control scheme, nonlinear H∞ and region based control schemes are used. A Lyapunov-like function is presented for stability analysis of the proposed control law. Numerical simulations are presented to demonstrate the performance of the proposed tracking control of the AUV. It is shown that the proposed control law is robust against parameter uncertainties, external disturbances, and nonlinearities and it leads to uniform ultimate boundedness of the region tracking error.

Equivalent circuit simulation of HPEM-induced transient responses at nonlinear loads

Directory of Open Access Journals (Sweden)

M. Kotzev

2017-09-01

Full Text Available In this paper the equivalent circuit modeling of a nonlinearly loaded loop antenna and its transient responses to HPEM field excitations are investigated. For the circuit modeling the general strategy to characterize the nonlinearly loaded antenna by a linear and a nonlinear circuit part is pursued. The linear circuit part can be determined by standard methods of antenna theory and numerical field computation. The modeling of the nonlinear circuit part requires realistic circuit models of the nonlinear loads that are given by Schottky diodes. Combining both parts, appropriate circuit models are obtained and analyzed by means of a standard SPICE circuit simulator. It is the main result that in this way full-wave simulation results can be reproduced. Furthermore it is clearly seen that the equivalent circuit modeling offers considerable advantages with respect to computation speed and also leads to improved physical insights regarding the coupling between HPEM field excitation and nonlinearly loaded loop antenna.

Soliton solution for nonlinear partial differential equations by cosine-function method

International Nuclear Information System (INIS)

Ali, A.H.A.; Soliman, A.A.; Raslan, K.R.

2007-01-01

In this Letter, we established a traveling wave solution by using Cosine-function algorithm for nonlinear partial differential equations. The method is used to obtain the exact solutions for five different types of nonlinear partial differential equations such as, general equal width wave equation (GEWE), general regularized long wave equation (GRLW), general Korteweg-de Vries equation (GKdV), general improved Korteweg-de Vries equation (GIKdV), and Coupled equal width wave equations (CEWE), which are the important soliton equations

Mutual Connectivity Analysis (MCA) Using Generalized Radial Basis Function Neural Networks for Nonlinear Functional Connectivity Network Recovery in Resting-State Functional MRI.

Science.gov (United States)

DSouza, Adora M; Abidin, Anas Zainul; Nagarajan, Mahesh B; Wismüller, Axel

2016-03-29

We investigate the applicability of a computational framework, called mutual connectivity analysis (MCA), for directed functional connectivity analysis in both synthetic and resting-state functional MRI data. This framework comprises of first evaluating non-linear cross-predictability between every pair of time series prior to recovering the underlying network structure using community detection algorithms. We obtain the non-linear cross-prediction score between time series using Generalized Radial Basis Functions (GRBF) neural networks. These cross-prediction scores characterize the underlying functionally connected networks within the resting brain, which can be extracted using non-metric clustering approaches, such as the Louvain method. We first test our approach on synthetic models with known directional influence and network structure. Our method is able to capture the directional relationships between time series (with an area under the ROC curve = 0.92 ± 0.037) as well as the underlying network structure (Rand index = 0.87 ± 0.063) with high accuracy. Furthermore, we test this method for network recovery on resting-state fMRI data, where results are compared to the motor cortex network recovered from a motor stimulation sequence, resulting in a strong agreement between the two (Dice coefficient = 0.45). We conclude that our MCA approach is effective in analyzing non-linear directed functional connectivity and in revealing underlying functional network structure in complex systems.

Differential quadrature method of nonlinear bending of functionally graded beam

Science.gov (United States)

Gangnian, Xu; Liansheng, Ma; Wang, Youzhi; Quan, Yuan; Weijie, You

2018-02-01

Using the third-order shear deflection beam theory (TBT), nonlinear bending of functionally graded (FG) beams composed with various amounts of ceramic and metal is analyzed utilizing the differential quadrature method (DQM). The properties of beam material are supposed to accord with the power law index along to thickness. First, according to the principle of stationary potential energy, the partial differential control formulae of the FG beams subjected to a distributed lateral force are derived. To obtain numerical results of the nonlinear bending, non-dimensional boundary conditions and control formulae are dispersed by applying the DQM. To verify the present solution, several examples are analyzed for nonlinear bending of homogeneous beams with various edges. A minute parametric research is in progress about the effect of the law index, transverse shear deformation, distributed lateral force and boundary conditions.

Experiments in nonlinear dynamics using control-based continuation: Tracking stable and unstable response curves

DEFF Research Database (Denmark)

Bureau, Emil; Schilder, Frank; Santos, Ilmar

2014-01-01

We show how to implement control-based continuation in a nonlinear experiment using existing and freely available software. We demonstrate that it is possible to track the complete frequency response, including the unstable branches, for a harmonically forced impact oscillator.......We show how to implement control-based continuation in a nonlinear experiment using existing and freely available software. We demonstrate that it is possible to track the complete frequency response, including the unstable branches, for a harmonically forced impact oscillator....

Testing the Granger noncausality hypothesis in stationary nonlinear models of unknown functional form

DEFF Research Database (Denmark)

Péguin-Feissolle, Anne; Strikholm, Birgit; Teräsvirta, Timo

In this paper we propose a general method for testing the Granger noncausality hypothesis in stationary nonlinear models of unknown functional form. These tests are based on a Taylor expansion of the nonlinear model around a given point in the sample space. We study the performance of our tests b...

Contractivity and Exponential Stability of Solutions to Nonlinear Neutral Functional Differential Equations in Banach Spaces

Institute of Scientific and Technical Information of China (English)

Wan-sheng WANG; Shou-fu LI; Run-sheng YANG

2012-01-01

A series of contractivity and exponential stability results for the solutions to nonlinear neutral functional differential equations (NFDEs) in Banach spaces are obtained,which provide unified theoretical foundation for the contractivity analysis of solutions to nonlinear problems in functional differential equations (FDEs),neutral delay differential equations (NDDEs) and NFDEs of other types which appear in practice.

Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis.

Science.gov (United States)

Bornkamp, Björn; Ickstadt, Katja

2009-03-01

In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose-response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose-response analysis.

A nonlinear theory of generalized functions

CERN Document Server

1990-01-01

This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applicati...

Nonlinear dynamics of the human lumbar intervertebral disc.

Science.gov (United States)

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J

2015-02-05

Systems with a quasi-static response similar to the axial response of the intervertebral disc (i.e. progressive stiffening) often present complex dynamics, characterized by peculiar nonlinearities in the frequency response. However, such characteristics have not been reported for the dynamic response of the disc. The accurate understanding of disc dynamics is essential to investigate the unclear correlation between whole body vibration and low back pain. The present study investigated the dynamic response of the disc, including its potential nonlinear response, over a range of loading conditions. Human lumbar discs were tested by applying a static preload to the top and a sinusoidal displacement at the bottom of the disc. The frequency of the stimuli was set to increase linearly from a low frequency to a high frequency limit and back down. In general, the response showed nonlinear and asymmetric characteristics. For each test, the disc had different response in the frequency-increasing compared to the frequency-decreasing sweep. In particular, the system presented abrupt changes of the oscillation amplitude at specific frequencies, which differed between the two sweeps. This behaviour indicates that the system oscillation has a different equilibrium condition depending on the path followed by the stimuli. Preload and amplitude of the oscillation directly influenced the disc response by changing the nonlinear dynamics and frequency of the jump-phenomenon. These results show that the characterization of the dynamic response of physiological systems should be readdressed to determine potential nonlinearities. Their direct effect on the system function should be further investigated. Copyright © 2014 Elsevier Ltd. All rights reserved.

Estimation of Nonlinear Functions of State Vector for Linear Systems with Time-Delays and Uncertainties

Directory of Open Access Journals (Sweden)

Il Young Song

2015-01-01

Full Text Available This paper focuses on estimation of a nonlinear function of state vector (NFS in discrete-time linear systems with time-delays and model uncertainties. The NFS represents a multivariate nonlinear function of state variables, which can indicate useful information of a target system for control. The optimal nonlinear estimator of an NFS (in mean square sense represents a function of the receding horizon estimate and its error covariance. The proposed receding horizon filter represents the standard Kalman filter with time-delays and special initial horizon conditions described by the Lyapunov-like equations. In general case to calculate an optimal estimator of an NFS we propose using the unscented transformation. Important class of polynomial NFS is considered in detail. In the case of polynomial NFS an optimal estimator has a closed-form computational procedure. The subsequent application of the proposed receding horizon filter and nonlinear estimator to a linear stochastic system with time-delays and uncertainties demonstrates their effectiveness.

Parametric Identification of Nonlinear Dynamical Systems

Science.gov (United States)

Feeny, Brian

2002-01-01

In this project, we looked at the application of harmonic balancing as a tool for identifying parameters (HBID) in a nonlinear dynamical systems with chaotic responses. The main idea is to balance the harmonics of periodic orbits extracted from measurements of each coordinate during a chaotic response. The periodic orbits are taken to be approximate solutions to the differential equations that model the system, the form of the differential equations being known, but with unknown parameters to be identified. Below we summarize the main points addressed in this work. The details of the work are attached as drafts of papers, and a thesis, in the appendix. Our study involved the following three parts: (1) Application of the harmonic balance to a simulation case in which the differential equation model has known form for its nonlinear terms, in contrast to a differential equation model which has either power series or interpolating functions to represent the nonlinear terms. We chose a pendulum, which has sinusoidal nonlinearities; (2) Application of the harmonic balance to an experimental system with known nonlinear forms. We chose a double pendulum, for which chaotic response were easily generated. Thus we confronted a two-degree-of-freedom system, which brought forth challenging issues; (3) A study of alternative reconstruction methods. The reconstruction of the phase space is necessary for the extraction of periodic orbits from the chaotic responses, which is needed in this work. Also, characterization of a nonlinear system is done in the reconstructed phase space. Such characterizations are needed to compare models with experiments. Finally, some nonlinear prediction methods can be applied in the reconstructed phase space. We developed two reconstruction methods that may be considered if the common method (method of delays) is not applicable.

Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions

KAUST Repository

Alkhalifah, Tariq Ali

2012-09-25

Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.

Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions

KAUST Repository

Alkhalifah, Tariq Ali; Choi, Yun Seok

2012-01-01

Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.

Interpreting the nonlinear dielectric response of glass-formers in terms of the coupling model

Energy Technology Data Exchange (ETDEWEB)

Ngai, K. L. [CNR-IPCF, Largo Bruno Pontecorvo 3, I-56127 Pisa, Italy and Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa (Italy)

2015-03-21

Nonlinear dielectric measurements at high electric fields of glass-forming glycerol and propylene carbonate initially were carried out to elucidate the dynamic heterogeneous nature of the structural α-relaxation. Recently, the measurements were extended to sufficiently high frequencies to investigate the nonlinear dielectric response of faster processes including the so-called excess wing (EW), appearing as a second power law at high frequencies in the loss spectra of many glass formers without a resolved secondary relaxation. While a strong increase of dielectric constant and loss is found in the nonlinear dielectric response of the α-relaxation, there is a lack of significant change in the EW. A surprise to the experimentalists finding it, this difference in the nonlinear dielectric properties between the EW and the α-relaxation is explained in the framework of the coupling model by identifying the EW investigated with the nearly constant loss (NCL) of caged molecules, originating from the anharmonicity of the intermolecular potential. The NCL is terminated at longer times (lower frequencies) by the onset of the primitive relaxation, which is followed sequentially by relaxation processes involving increasing number of molecules until the terminal Kohlrausch α-relaxation is reached. These intermediate faster relaxations, combined to form the so-called Johari-Goldstein (JG) β-relaxation, are spatially and dynamically heterogeneous, and hence exhibit nonlinear dielectric effects, as found in glycerol and propylene carbonate, where the JG β-relaxation is not resolved and in D-sorbitol where it is resolved. Like the linear susceptibility, χ{sub 1}(f), the frequency dispersion of the third-order dielectric susceptibility, χ{sub 3}(f), was found to depend primarily on the α-relaxation time, and independent of temperature T and pressure P. I show this property of the frequency dispersions of χ{sub 1}(f) and χ{sub 3}(f) is the characteristic of the many

Stochastic Parameter Estimation of Non-Linear Systems Using Only Higher Order Spectra of the Measured Response

Science.gov (United States)

Vasta, M.; Roberts, J. B.

1998-06-01

Methods for using fourth order spectral quantities to estimate the unknown parameters in non-linear, randomly excited dynamic systems are developed. Attention is focused on the case where only the response is measurable and the excitation is unmeasurable and known only in terms of a stochastic process model. The approach is illustrated through application to a non-linear oscillator with both non-linear damping and stiffness and with excitation modelled as a stationary Gaussian white noise process. The methods have applications in studies of the response of structures to random environmental loads, such as wind and ocean wave forces.

Mean-state SST Response to global warming caused by the ENSO Nonlinearity

Science.gov (United States)

Kohyama, T.; Hartmann, D. L.

2017-12-01

The majority of the models that participated in the Coupled Model Intercomparison Project phase 5 (CMIP5) exhibit El Niño-like trends under global warming. GFDL-ESM2M, however, is an exception that exhibits a La Niña-like response with strengthened trade winds. Our previous studies have shown that this La Niña-like trend could be a physically consistent warming response, and we proposed the Nonlinear ENSO Warming Suppression (NEWS) mechanism to explain this La Niña-like response to global warming. The most important necessary condition of NEWS is the ENSO skewness (El Niños are stronger than La Niñas). Most CMIP5 models do not reproduce the observed ENSO skewness, while GFDL-ESM2M exhibits the realistic ENSO skewness, which suggests that, despite being in the minority, the La Niña-like trend of GFDL-ESM2M could be a plausible equatorial Pacific response to warming. In this study, we introduce another interesting outlier, MIROC5, which reproduces the observed skewness, yet exhibits an El Niño-like response. By decomposing the source of the ENSO nonlinearity into the following three components: "SST anomalies modulate winds", "winds excite oceanic waves", and "oceanic waves modulate the subsurface temperature", we show that the large inter-model spread of the third component appears to explain the most important cause of the poor reproducibility of the ENSO nonlinearity in CMIP5 models. It is concluded that the change in the response of subsurface temperature to oceanic waves is the primary explanation for the different warming response of GFDL-ESM2M and MIROC5. Our analyses suggest that the difference of the warming response are caused by difference in the climatological thermal stratification. This study may shed new light on the fundamental question of why observed ENSO has a strong skewness and on the implications of this skewed ENSO for the mean-state sea surface temperature response to global warming.

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

Science.gov (United States)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

A novel method for non-parametric identification of nonlinear restoring forces in nonlinear vibrations from noisy response data: A conservative system

International Nuclear Information System (INIS)

Jang, T. S.; Kwon, S. H.; Han, S. L.

2009-01-01

A novel procedure is proposed to identify the functional form of nonlinear restoring forces in the nonlinear oscillatory motion of a conservative system. Although the problem of identification has a unique solution, formulation results in a Volterra-type of integral equation of the 'first' kind: the solution lacks stability because the integral equation is the 'first' kind. Thus, the new problem at hand is ill-posed. Inevitable small errors during the identification procedure can make the prediction of nonlinear restoring forces useless. We overcome the difficulty by using a stabilization technique of Landweber's regularization in this study. The capability of the proposed procedure is investigated through numerical examples

Comparisons of linear and nonlinear plasma response models for non-axisymmetric perturbations

Energy Technology Data Exchange (ETDEWEB)

Turnbull, A. D.; Ferraro, N. M.; Lao, L. L.; Lanctot, M. J. [General Atomics, P.O. Box 85608, San Diego, California 92186-5608 (United States); Izzo, V. A. [University of California-San Diego, 9500 Gilman Dr., La Jolla, California 92093-0417 (United States); Lazarus, E. A.; Hirshman, S. P. [Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831 (United States); Park, J.-K.; Lazerson, S.; Reiman, A. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States); Cooper, W. A. [Association Euratom-Confederation Suisse, Centre de Recherches en Physique des Plasmas, Ecole Polytechnique Federale de Lausanne, Lausanne (Switzerland); Liu, Y. Q. [Culham Centre for Fusion Energy, Culham Science Centre, Abingdon, Oxfordshire, OX14 3DB (United Kingdom); Turco, F. [Columbia University, 116th St and Broadway, New York, New York 10027 (United States)

2013-05-15

With the installation of non-axisymmetric coil systems on major tokamaks for the purpose of studying the prospects of ELM-free operation, understanding the plasma response to the applied fields is a crucial issue. Application of different response models, using standard tools, to DIII-D discharges with applied non-axisymmetric fields from internal coils, is shown to yield qualitatively different results. The plasma response can be treated as an initial value problem, following the system dynamically from an initial unperturbed state, or from a nearby perturbed equilibrium approach, and using both linear and nonlinear models [A. D. Turnbull, Nucl. Fusion 52, 054016 (2012)]. Criteria are discussed under which each of the approaches can yield a valid response. In the DIII-D cases studied, these criteria show a breakdown in the linear theory despite the small 10{sup −3} relative magnitude of the applied magnetic field perturbations in this case. For nonlinear dynamical evolution simulations to reach a saturated nonlinear steady state, appropriate damping mechanisms need to be provided for each normal mode comprising the response. Other issues arise in the technical construction of perturbed flux surfaces from a displacement and from the presence of near nullspace normal modes. For the nearby equilibrium approach, in the absence of a full 3D equilibrium reconstruction with a controlled comparison, constraints relating the 2D system profiles to the final profiles in the 3D system also need to be imposed to assure accessibility. The magnetic helicity profile has been proposed as an appropriate input to a 3D equilibrium calculation and tests of this show the anticipated qualitative behavior.

Complex motor task associated with non-linear BOLD responses in cerebro-cortical areas and cerebellum.

Science.gov (United States)

Alahmadi, Adnan A S; Samson, Rebecca S; Gasston, David; Pardini, Matteo; Friston, Karl J; D'Angelo, Egidio; Toosy, Ahmed T; Wheeler-Kingshott, Claudia A M

2016-06-01

Previous studies have used fMRI to address the relationship between grip force (GF) applied to an object and BOLD response. However, whilst the majority of these studies showed a linear relationship between GF and neural activity in the contralateral M1 and ipsilateral cerebellum, animal studies have suggested the presence of non-linear components in the GF-neural activity relationship. Here, we present a methodology for assessing non-linearities in the BOLD response to different GF levels, within primary motor as well as sensory and cognitive areas and the cerebellum. To be sensitive to complex forms, we designed a feasible grip task with five GF targets using an event-related visually guided paradigm and studied a cohort of 13 healthy volunteers. Polynomial functions of increasing order were fitted to the data. (1) activated motor areas irrespective of GF; (2) positive higher-order responses in and outside M1, involving premotor, sensory and visual areas and cerebellum; (3) negative correlations with GF, predominantly involving the visual domain. Overall, our results suggest that there are physiologically consistent behaviour patterns in cerebral and cerebellar cortices; for example, we observed the presence of a second-order effect in sensorimotor areas, consistent with an optimum metabolic response at intermediate GF levels, while higher-order behaviour was found in associative and cognitive areas. At higher GF levels, sensory-related cortical areas showed reduced activation, interpretable as a redistribution of the neural activity for more demanding tasks. These results have the potential of opening new avenues for investigating pathological mechanisms of neurological diseases.

Spiraling solitons and multipole localized modes in nonlocal nonlinear media

International Nuclear Information System (INIS)

Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan; Desyatnikov, Anton S.; Bang, Ole; Krolikowski, Wieslaw; Kivshar, Yuri S.

2007-01-01

We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two different models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form

Spiralling solitons and multipole localized modes in nonlocal nonlinear media

DEFF Research Database (Denmark)

Buccoliero, Daniel; Lopez-Aguayo, Servando; Skupin, Stefan

2007-01-01

We analyze the propagation of rotating multi-soliton localized structures in optical media with spatially nonlocal nonlinearity. We demonstrate that nonlocality stabilizes the azimuthal breakup of rotating dipole as well as multipole localized soliton modes. We compare the results for two differe...... models of nonlocal nonlinearity and suggest that the stabilization mechanism is a generic property of a spatial nonlocal nonlinear response independent of its particular functional form....

Nonlinear flowering responses to climate: are species approaching their limits of phenological change?

Science.gov (United States)

Iler, Amy M.; Høye, Toke T.; Inouye, David W.; Schmidt, Niels M.

2013-01-01

Many alpine and subalpine plant species exhibit phenological advancements in association with earlier snowmelt. While the phenology of some plant species does not advance beyond a threshold snowmelt date, the prevalence of such threshold phenological responses within plant communities is largely unknown. We therefore examined the shape of flowering phenology responses (linear versus nonlinear) to climate using two long-term datasets from plant communities in snow-dominated environments: Gothic, CO, USA (1974–2011) and Zackenberg, Greenland (1996–2011). For a total of 64 species, we determined whether a linear or nonlinear regression model best explained interannual variation in flowering phenology in response to increasing temperatures and advancing snowmelt dates. The most common nonlinear trend was for species to flower earlier as snowmelt advanced, with either no change or a slower rate of change when snowmelt was early (average 20% of cases). By contrast, some species advanced their flowering at a faster rate over the warmest temperatures relative to cooler temperatures (average 5% of cases). Thus, some species seem to be approaching their limits of phenological change in response to snowmelt but not temperature. Such phenological thresholds could either be a result of minimum springtime photoperiod cues for flowering or a slower rate of adaptive change in flowering time relative to changing climatic conditions. PMID:23836793

Polythiophene derivative functionalized with disperse red 1 chromophore: Its third-order nonlinear optical properties through Z-scan technique under continuous and femtosecond irradiation

Science.gov (United States)

de la Garza-Rubí, R. M. A.; Güizado-Rodríguez, M.; Mayorga-Cruz, D.; Basurto-Pensado, M. A.; Guerrero-Álvarez, J. A.; Ramos-Ortiz, G.; Rodríguez, M.; Maldonado, J. L.

2015-08-01

A copolymer of 3-hexylthiophene and thiophene functionalized with disperse red 1, poly(3-HT-co-TDR1), was synthesized. Chemical structure, molecular weight distribution, optical and thermal properties of this copolymer were characterized by NMR, FT-IR, UV-vis, GPC and DSC-TGA. An optical nonlinear analysis by Z-scan method was also performed for both continuous wave (CW) and pulsed laser pumping. In the CW regime the nonlinearities were evaluated in solid films, and a negative nonlinear refractive index in the range 2.7-4.1 × 10-4 cm2/W was obtained. These values are notoriously high and allowed to observe self-defocusing effects at very low laser intensities: below 1 mW. Further, nonlinear self-phase modulation patterns, during laser irradiation, were also observed. In the pulsed excitation the nonlinear response was evaluated in solution resulting in large two-photon absorption cross section of 5725 GM for the whole copolymer chain and with a value of 232 GM per repeated monomeric unit.

Non-Linear Dose Response Relationships in Biology, Toxicology, and Medicine (June 8-10, 2004). Final Report

International Nuclear Information System (INIS)

Calabrese, Edward J.

2004-01-01

The conference attracts approximately 500 scientists researching in the area of non-linear low dose effects. These scientists represent a wide range of biological/medical fields and technical disciplines. Observations that biphasic dose responses are frequently reported in each of these areas but that the recognition of similar dose response relationships across disciplines is very rarely appreciated and exploited. By bringing scientist of such diverse backgrounds together who are working on the common area of non-linear dose response relationships this will enhance our understanding of the occurrence, origin, mechanism, significance and practical applications of such dose response relationships

Dryland responses to global change suggest the potential for rapid non-linear responses to some changes but resilience to others

Science.gov (United States)

Reed, S.; Ferrenberg, S.; Tucker, C.; Rutherford, W. A.; Wertin, T. M.; McHugh, T. A.; Morrissey, E.; Kuske, C.; Belnap, J.

2017-12-01

Drylands represent our planet's largest terrestrial biome, making up over 35% of Earth's land surface. In the context of this vast areal extent, it is no surprise that recent research suggests dryland inter-annual variability and responses to change have the potential to drive biogeochemical cycles and climate at the global-scale. Further, the data we do have suggest drylands can respond rapidly and non-linearly to change. Nevertheless, our understanding of the cross-system consistency of and mechanisms behind dryland responses to a changed environment remains relatively poor. This poor understanding hinders not only our larger understanding of terrestrial ecosystem function, but also our capacity to forecast future global biogeochemical cycles and climate. Here we present data from a series of Colorado Plateau manipulation experiments - including climate, land use, and nitrogen deposition manipulations - to explore how vascular plants, microbial communities, and biological soil crusts (a community of mosses, lichens, and/or cyanobacteria living in the interspace among vascular plants in arid and semiarid ecosystems worldwide) respond to a host of environmental changes. These responses include not only assessments of community composition, but of their function as well. We will explore photosynthesis, net soil CO2 exchange, soil carbon stocks and chemistry, albedo, and nutrient cycling. The experiments were begun with independent questions and cover a range of environmental change drivers and scientific approaches, but together offer a relatively holistic picture of how some drylands can change their structure and function in response to change. In particular, the data show very high ecosystem vulnerability to particular drivers, but surprising resilience to others, suggesting a multi-faceted response of these diverse systems.

Trial function method and exact solutions to the generalized nonlinear Schrödinger equation with time-dependent coefficient

International Nuclear Information System (INIS)

Cao Rui; Zhang Jian

2013-01-01

In this paper, the trial function method is extended to study the generalized nonlinear Schrödinger equation with time-dependent coefficients. On the basis of a generalized traveling wave transformation and a trial function, we investigate the exact envelope traveling wave solutions of the generalized nonlinear Schrödinger equation with time-dependent coefficients. Taking advantage of solutions to trial function, we successfully obtain exact solutions for the generalized nonlinear Schrödinger equation with time-dependent coefficients under constraint conditions. (general)

A phenomenological constitutive model for the nonlinear viscoelastic responses of biodegradable polymers

KAUST Repository

Khan, Kamran; El Sayed, Tamer S.

2012-01-01

We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer

Fast response of the optical nonlinearity in a GaAs/AlGaAs asymmetric triple quantum well structure

CERN Document Server

Ahn, S H; Sawaki, N

1999-01-01

The time response of the optical nonlinear behavior in a GaAs/AlGaAs asymmetric triple quantum well structure is estimated by using a picosecond pump-probe method at 77 K. From the results of the transmission of the probe pulse as a function of the delay time at the excitation wavelengths, a rise time of 5 approx 10 ps and a fall time of 8 approx 16 ps are obtained. The nonlinear behavior is attributed to the triple resonance of the electronic states due to the build-up of the internal field induced by the separation of photo-excited electrons and holes. It is found that the rise time is determined by the tunneling transfer time of the electrons in the narrowest well to an adjacent well separated by a thin potential barrier.

Quantum Nonlinear Optics

CERN Document Server

Hanamura, Eiichi; Yamanaka, Akio

2007-01-01

This graduate-level textbook gives an introductory overview of the fundamentals of quantum nonlinear optics. Based on the quantum theory of radiation, Quantum Nonlinear Optics incorporates the exciting developments in novel nonlinear responses of materials (plus laser oscillation and superradiance) developed over the past decade. It deals with the organization of radiation field, interaction between electronic system and radiation field, statistics of light, mutual manipulation of light and matter, laser oscillation, dynamics of light, nonlinear optical response, and nonlinear spectroscopy, as well as ultrashort and ultrastrong laser pulse. Also considered are Q-switching, mode locking and pulse compression. Experimental and theoretical aspects are intertwined throughout.

Nonlinear optical effects in pure and N-doped semiconductors

International Nuclear Information System (INIS)

Donlagic, N.S.

2000-01-01

Over the last decades, the nonlinear optical properties of condensed matter systems have been an attractive and fruitful field of research. While the linear response functions of solids provide information about the elementary excitations of the systems, nonlinear optical experiments give insight into the dynamics of the fundamental many-body processes which are initiated by the external excitations. Stimulated by the experimental results, new theoretical concepts and methods have been developed in order to relate the observed phenomena to the microscopic properties of the investigated materials. The present work deals with the study of the nonlinear dynamics of the optical interband polarization in pure and n-doped semiconductors.In the first part of the thesis, the relaxation behavior of optically excited electron-hole pairs in a one-dimensional semiconductor, which are coupled to longitudinal optical phonons with an initial lattice temperature T>0, is studied with the help of quantum kinetic equations. Apart from Hartree-Fock-like Coulomb contributions, these equations contain additional Coulomb terms, the so-called vertex corrections, by which the influence of the electron-electron interaction on the electron-phonon scattering processes is taken into account. The numerical studies indicate that the vertex corrections are essential for a correct description of the excitonic dynamics.In the second part of the thesis, the attention is shifted to the characteristics of the optical response of a one-dimensional n-doped two-band semiconductor whose conduction band has been linearized with respect to the two Fermi points. Due to the linearization it is possible to calculate the linear and nonlinear response functions of the interacting electron system exactly. These response functions are then used in order to determine the linear absorption spectrum and the time-integrated signal of a degenerated four-wave-mixing experiment. It is shown that the well-known features

OCOPTR, Minimization of Nonlinear Function, Variable Metric Method, Derivative Calculation. DRVOCR, Minimization of Nonlinear Function, Variable Metric Method, Derivative Calculation

International Nuclear Information System (INIS)

Nazareth, J. L.

1979-01-01

1 - Description of problem or function: OCOPTR and DRVOCR are computer programs designed to find minima of non-linear differentiable functions f: R n →R with n dimensional domains. OCOPTR requires that the user only provide function values (i.e. it is a derivative-free routine). DRVOCR requires the user to supply both function and gradient information. 2 - Method of solution: OCOPTR and DRVOCR use the variable metric (or quasi-Newton) method of Davidon (1975). For OCOPTR, the derivatives are estimated by finite differences along a suitable set of linearly independent directions. For DRVOCR, the derivatives are user- supplied. Some features of the codes are the storage of the approximation to the inverse Hessian matrix in lower trapezoidal factored form and the use of an optimally-conditioned updating method. Linear equality constraints are permitted subject to the initial Hessian factor being chosen correctly. 3 - Restrictions on the complexity of the problem: The functions to which the routine is applied are assumed to be differentiable. The routine also requires (n 2 /2) + 0(n) storage locations where n is the problem dimension

On the Boundary between Nonlinear Jump Phenomenon and Linear Response of Hypoid Gear Dynamics

Directory of Open Access Journals (Sweden)

Jun Wang

2011-01-01

Full Text Available A nonlinear time-varying (NLTV dynamic model of a hypoid gear pair system with time-dependent mesh point, line-of-action vector, mesh stiffness, mesh damping, and backlash nonlinearity is formulated to analyze the transitional phase between nonlinear jump phenomenon and linear response. It is found that the classical jump discontinuity will occur if the dynamic mesh force exceeds the mean value of tooth mesh force. On the other hand, the propensity for the gear response to jump disappears when the dynamic mesh force is lower than the mean mesh force. Furthermore, the dynamic analysis is able to distinguish the specific tooth impact types from analyzing the behaviors of the dynamic mesh force. The proposed theory is general and also applicable to high-speed spur, helical and spiral bevel gears even though those types of gears are not the primary focus of this paper.

Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function

International Nuclear Information System (INIS)

Ge Zhengming; Chang Chingming

2009-01-01

By applying pure error dynamics and elaborate nondiagonal Lyapunov function, the nonlinear generalized synchronization is studied in this paper. Instead of current mixed error dynamics in which master state variables and slave state variables are presented, the nonlinear generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation. The elaborate nondiagonal Lyapunov function is applied rather than current monotonous square sum Lyapunov function deeply weakening the powerfulness of Lyapunov direct method. Both autonomous and nonautonomous double Mathieu systems are used as examples with numerical simulations.

Seismic response analysis of a nuclear reactor structure considering nonlinear soil-structure interaction

International Nuclear Information System (INIS)

Bhaumik, Lopamudra; Raychowdhury, Prishati

2013-01-01

Highlights: • Seismic response analysis of an internal shearwall of a reactor is done. • Incremental dynamic analysis is performed with 30 recorded ground motions. • Equivalent viscous damping increases up to twice when nonlinear SSI is considered. • Roof drift demand increases up to 25% upon consideration of foundation nonlinearity. • Base shear, base moment and ductility reduce up to 62%, 40%, and 35%, respectively. - Abstract: This study focuses on the seismic response analysis of an internal shearwall of a typical Indian reactor resting on a medium dense sandy silty soil, incorporating the nonlinear behavior of the soil-foundation interface. The modeling is done in an open-source finite element framework, OpenSees, where the soil-structure interaction (SSI) is modeled using a Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach. Static pushover analysis and cyclic analysis are performed followed by an incremental dynamic analysis (IDA) with 30 recorded ground motions. For performing IDA, the spectral acceleration of each motion corresponding to the fundamental period, S a (T 1 )is incremented from 0.1 g to 1.0 g with an increment step of 0.1 g. It is observed from the cyclic analysis that the equivalent viscous damping of the system increases upto twice upon incorporation of inelastic SSI. The IDA results demonstrate that the average peak base shear, base moment and displacement ductility demand reduces as much as 62%, 40%, and 35%, respectively, whereas the roof drift demand increases up to 25% upon consideration of foundation nonlinearity for the highest intensity motion. These observations indicate the need of critical consideration of nonlinear soil-structure interaction as any deficient modeling of the same may lead to an inaccurate estimation of the seismic demands of the structure

Seismic response analysis of a nuclear reactor structure considering nonlinear soil-structure interaction

Energy Technology Data Exchange (ETDEWEB)

Bhaumik, Lopamudra, E-mail: lbhaumi2@illinois.edu [University of Illinois at Urbana-Champaign (United States); Raychowdhury, Prishati, E-mail: prishati@iitk.ac.in [Indian Institute of Technology Kanpur (India)

2013-12-15

Highlights: • Seismic response analysis of an internal shearwall of a reactor is done. • Incremental dynamic analysis is performed with 30 recorded ground motions. • Equivalent viscous damping increases up to twice when nonlinear SSI is considered. • Roof drift demand increases up to 25% upon consideration of foundation nonlinearity. • Base shear, base moment and ductility reduce up to 62%, 40%, and 35%, respectively. - Abstract: This study focuses on the seismic response analysis of an internal shearwall of a typical Indian reactor resting on a medium dense sandy silty soil, incorporating the nonlinear behavior of the soil-foundation interface. The modeling is done in an open-source finite element framework, OpenSees, where the soil-structure interaction (SSI) is modeled using a Beam-on-Nonlinear-Winkler-Foundation (BNWF) approach. Static pushover analysis and cyclic analysis are performed followed by an incremental dynamic analysis (IDA) with 30 recorded ground motions. For performing IDA, the spectral acceleration of each motion corresponding to the fundamental period, S{sub a}(T{sub 1})is incremented from 0.1 g to 1.0 g with an increment step of 0.1 g. It is observed from the cyclic analysis that the equivalent viscous damping of the system increases upto twice upon incorporation of inelastic SSI. The IDA results demonstrate that the average peak base shear, base moment and displacement ductility demand reduces as much as 62%, 40%, and 35%, respectively, whereas the roof drift demand increases up to 25% upon consideration of foundation nonlinearity for the highest intensity motion. These observations indicate the need of critical consideration of nonlinear soil-structure interaction as any deficient modeling of the same may lead to an inaccurate estimation of the seismic demands of the structure.

Rationale for nonlinear dose response functions of power greater or less than one

International Nuclear Information System (INIS)

Baum, J.W.

1977-08-01

Risk estimates and radiation protection standards are generally made using a nonthreshold premise and linear extrapolations from existing data to estimate biological radiation effects at lower doses and at lower dose rates. This seems reasonable in light of the variety of shapes of dose-effect relations which have been observed both in animal studies and in human epidemiological studies. An unexplained observation in several studies was a response which followed a power function of dose with exponent less than one. One explanation offered for this type of response in humans was a postulated population of heterogeneous sensitivity. An alternate, though related, way of considering this question is in terms of multiple-stresses, and this postulate is discussed

Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading

Science.gov (United States)

Gholami, Raheb; Ansari, Reza

2018-02-01

This article presents an attempt to study the nonlinear resonance of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) annular sector plates excited by a uniformly distributed harmonic transverse load. To this purpose, first, the extended rule of mixture including the efficiency parameters is employed to approximately obtain the effective material properties of FG-CNTRC annular sector plates. Then, the focus is on presenting the weak form of discretized mathematical formulation of governing equations based on the variational differential quadrature (VDQ) method and Hamilton's principle. The geometric nonlinearity and shear deformation effects are considered based on the von Kármán assumptions and Reddy's third-order shear deformation plate theory, respectively. The discretization process is performed via the generalized differential quadrature (GDQ) method together with numerical differential and integral operators. Then, an efficient multi-step numerical scheme is used to obtain the nonlinear dynamic behavior of the FG-CNTRC annular sector plates near their primary resonance as the frequency-response curve. The accuracy of the present results is first verified and then a parametric study is presented to show the impacts of CNT volume fraction, CNT distribution pattern, geometry of annular sector plate and sector angle on the nonlinear frequency-response curve of FG-CNTRC annular sector plates with different edge supports.

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

Science.gov (United States)

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

2010-04-12

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

Effect of window function for measurement of ultrasonic nonlinear parameter using fast fourier transform of tone-burst signal

Energy Technology Data Exchange (ETDEWEB)

Lee, Kyoung Jun; Kim, Jong Beom; Song, Dong Gil; Jhang, Kyung Young [Dept. of Mechanical Engineering, Hanyang University, Seoul (Korea, Republic of)

2015-08-15

In ultrasonic nonlinear parameter measurement using the fast Fourier transform(FFT) of tone-burst signals, the side lobe and leakage on spectrum because of finite time and non-periodicity of signals makes it difficult to measure the harmonic magnitudes accurately. The window function made it possible to resolve this problem. In this study, the effect of the Hanning and Turkey window functions on the experimental measurement of nonlinear parameters was analyzed. In addition, the effect of changes in tone burst signal number with changes in the window function on the experimental measurement was analyzed. The result for both window functions were similar and showed that they enabled reliable nonlinear parameter measurement. However, in order to restore original signal amplitude, the amplitude compensation coefficient should be considered for each window function. On a separate note, the larger number of tone bursts was advantageous for stable nonlinear parameter measurement, but this effect was more advantageous in the case of the Hanning window than the Tukey window.

Frequency response areas in the inferior colliculus: nonlinearity and binaural interaction

Directory of Open Access Journals (Sweden)

Jane J Yu

2013-05-01

Full Text Available The tuning, binaural properties, and encoding characteristics of neurons in the central nucleus of the inferior colliculus (CNIC were investigated to shed light on nonlinearities in the responses of these neurons. Results were analyzed for three types of neurons (I, O, and V in the CNIC of decerebrate cats. Rate responses to binaural stimuli were characterized using a 1st- plus 2nd-order spectral integration model. Parameters of the model were derived using broadband stimuli with random spectral shapes (RSS. This method revealed four characteristics of CNIC neurons: (1 Tuning curves derived from broadband stimuli have fixed (i. e., level tolerant bandwidths across a 50-60 dB range of sound levels; (2 1st-order contralateral weights (particularly for type I and O neurons were usually larger in magnitude than corresponding ipsilateral weights; (3 contralateral weights were more important than ipsilateral weights when using the model to predict responses to untrained noise stimuli; and (4 2nd-order weight functions demonstrate frequency selectivity different from that of 1st-order weight functions. Furthermore, while the inclusion of 2nd-order terms in the model usually improved response predictions related to untrained RSS stimuli, they had limited impact on predictions related to other forms of filtered broadband noise (e. g., virtual space stimuli. The accuracy of the predictions varied considerably by response type. Predictions were most accurate for I neurons, and less accurate for O and V neurons, except at the lowest stimulus levels. These differences in prediction performance support the idea that type I, O, and V neurons encode different aspects of the stimulus: while type I neurons are most capable of producing linear representations of spectral shape, type O and V neurons may encode spectral features or temporal stimulus properties in a manner not easily explained with the low-order model. Supported by NIH grant DC00115.

Oracle Inequalities for Convex Loss Functions with Non-Linear Targets

DEFF Research Database (Denmark)

Caner, Mehmet; Kock, Anders Bredahl

This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target...... of the same order as that of the oracle. If the target is linear we give sufficient conditions for consistency of the estimated parameter vector. Next, we briefly discuss how a thresholded version of our estimator can be used to perform consistent variable selection. We give two examples of loss functions...

Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method

Science.gov (United States)

Arafa, A. A. M.; Rida, S. Z.; Mohammadein, A. A.; Ali, H. M.

2013-06-01

In this paper, we use Mittag—Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided.

Nonlinear Optical Functions in Crystalline and Amorphous Silicon-on-Insulator Nanowires

DEFF Research Database (Denmark)

Baets, R.; Kuyken, B.; Liu, X.

2012-01-01

Silicon-on-Insulator nanowires provide an excellent platform for nonlinear optical functions in spite of the two-photon absorption at telecom wavelengths. Work on both crystalline and amorphous silicon nanowires is reviewed, in the wavelength range of 1.5 to 2.5 µm....

Response to a pure tone in a nonlinear mechanical-electrical-acoustical model of the cochlea.

Science.gov (United States)

Meaud, Julien; Grosh, Karl

2012-03-21

In this article, a nonlinear mathematical model is developed based on the physiology of the cochlea of the guinea pig. The three-dimensional intracochlear fluid dynamics are coupled to a micromechanical model of the organ of Corti and to electrical potentials in the cochlear ducts and outer hair cells (OHC). OHC somatic electromotility is modeled by linearized piezoelectric relations whereas the OHC hair-bundle mechanoelectrical transduction current is modeled as a nonlinear function of the hair-bundle deflection. The steady-state response of the cochlea to a single tone is simulated in the frequency domain using an alternating frequency time scheme. Compressive nonlinearity, harmonic distortion, and DC shift on the basilar membrane (BM), tectorial membrane (TM), and OHC potentials are predicted using a single set of parameters. The predictions of the model are verified by comparing simulations to available in vivo experimental data for basal cochlear mechanics. In particular, the model predicts more amplification on the reticular lamina (RL) side of the cochlear partition than on the BM, which replicates recent measurements. Moreover, small harmonic distortion and DC shifts are predicted on the BM, whereas more significant harmonic distortion and DC shifts are predicted in the RL and TM displacements and in the OHC potentials. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

A Study on the Analysis and Optimal Control of Nonlinear Systems via Walsh Function

Energy Technology Data Exchange (ETDEWEB)

Kim, Jin Tae; Kim, Tai Hoon; Ahn, Doo Soo [Sungkyunkwan University (Korea); Lee, Myung Kyu [Kyungsung University (Korea)

2000-07-01

This paper presents the new adaptive optimal scheme for the nonlinear systems, which is based on the Picard's iterative approximation and fast Walsh transform. It is well known that the Walsh function approach method is very difficult to apply for the analysis and optimal control of nonlinear systems. However, these problems can be easily solved by the improvement of the previous adaptive optimal scheme. The proposes method is easily applicable to the analysis and optimal control of nonlinear systems. (author). 15 refs., 6 figs., 1 tab.

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

Science.gov (United States)

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

Nonlinear 2D arm dynamics in response to continuous and pulse-shaped force perturbations.

Science.gov (United States)

Happee, Riender; de Vlugt, Erwin; van Vliet, Bart

2015-01-01

Ample evidence exists regarding the nonlinearity of the neuromuscular system but linear models are widely applied to capture postural dynamics. This study quantifies the nonlinearity of human arm postural dynamics applying 2D continuous force perturbations (0.2-40 Hz) inducing three levels of hand displacement (5, 15, 45 mm RMS) followed by force-pulse perturbations inducing large hand displacements (up to 250 mm) in a position task (PT) and a relax task (RT) recording activity of eight shoulder and elbow muscles. The continuous perturbation data were used to analyze the 2D endpoint dynamics in the frequency domain and to identify reflexive and intrinsic parameters of a linear neuromuscular shoulder-elbow model. Subsequently, it was assessed to what extent the large displacements in response to force pulses could be predicted from the 'small amplitude' linear neuromuscular model. Continuous and pulse perturbation responses with varying amplitudes disclosed highly nonlinear effects. In PT, a larger continuous perturbation induced stiffening with a factor of 1.5 attributed to task adaptation evidenced by increased co-contraction and reflexive activity. This task adaptation was even more profound in the pulse responses where reflexes and displacements were strongly affected by the presence and amplitude of preceding continuous perturbations. In RT, a larger continuous perturbation resulted in yielding with a factor of 3.8 attributed to nonlinear mechanical properties as no significant reflexive activity was found. Pulse perturbations always resulted in yielding where a model fitted to the preceding 5-mm continuous perturbations predicted only 37% of the recorded peak displacements in RT and 79% in PT. This demonstrates that linear neuromuscular models, identified using continuous perturbations with small amplitudes, strongly underestimate displacements in pulse-shaped (e.g., impact) loading conditions. The data will be used to validate neuromuscular models including

Nonlinear elasticity in resonance experiments

Science.gov (United States)

Li, Xun; Sens-Schönfelder, Christoph; Snieder, Roel

2018-04-01

Resonant bar experiments have revealed that dynamic deformation induces nonlinearity in rocks. These experiments produce resonance curves that represent the response amplitude as a function of the driving frequency. We propose a model to reproduce the resonance curves with observed features that include (a) the log-time recovery of the resonant frequency after the deformation ends (slow dynamics), (b) the asymmetry in the direction of the driving frequency, (c) the difference between resonance curves with the driving frequency that is swept upward and downward, and (d) the presence of a "cliff" segment to the left of the resonant peak under the condition of strong nonlinearity. The model is based on a feedback cycle where the effect of softening (nonlinearity) feeds back to the deformation. This model provides a unified interpretation of both the nonlinearity and slow dynamics in resonance experiments. We further show that the asymmetry of the resonance curve is caused by the softening, which is documented by the decrease of the resonant frequency during the deformation; the cliff segment of the resonance curve is linked to a bifurcation that involves a steep change of the response amplitude when the driving frequency is changed. With weak nonlinearity, the difference between the upward- and downward-sweeping curves depends on slow dynamics; a sufficiently slow frequency sweep eliminates this up-down difference. With strong nonlinearity, the up-down difference results from both the slow dynamics and bifurcation; however, the presence of the bifurcation maintains the respective part of the up-down difference, regardless of the sweep rate.

Unusual nonlinear absorption response of graphene oxide in the presence of a reduction process

International Nuclear Information System (INIS)

Karimzadeh, Rouhollah; Arandian, Alireza

2015-01-01

The nonlinear absorption responses of graphene, graphene oxide and reduced graphene oxide are investigated using the Z-scan technique and laser beams at 405, 532 and 635 nm in a continuous wave regime. Results show that graphene, graphene oxide and reduced graphene oxide do not show any open Z-scan signals at wavelengths of 532 and 635 nm. At the same time, fresh graphene oxide suspension is found to exhibit a nonlinear absorption process in the case of a laser light at 405 nm. Moreover, it can be observed that the reduction of graphene oxide by 405 nm laser irradiation decreases its nonlinear absorption value significantly. These findings highlight the important role of the reduction process on the nonlinear absorption performance of graphene oxide. (letter)

A non-linear association between self-reported negative emotional response to stress and subsequent allostatic load: prospective results from the Whitehall II cohort study.

Science.gov (United States)

Dich, Nadya; Doan, Stacey N; Kivimäki, Mika; Kumari, Meena; Rod, Naja Hulvej

2014-11-01

Previous research suggests that high levels of negative emotions may affect health. However, it is likely that the absence of an emotional response following stressful events may also be problematic. Accordingly, we investigated whether a non-linear association exists between negative emotional response to major life events and allostatic load, a multisystem indicator of physiological dysregulation. Study sample was 6764 British civil service workers from the Whitehall II cohort. Negative emotional response was assessed by self-report at baseline. Allostatic load was calculated using cardiovascular, metabolic and immune function biomarkers at three clinical follow-up examinations. A non-linear association between negative emotional response and allostatic load was observed: being at either extreme end of the distribution of negative emotional response increased the risk of physiological dysregulation. Allostatic load also increased with age, but the association between negative emotional response and allostatic load remained stable over time. These results provide evidence for a more nuanced understanding of the role of negative emotions in long-term physical health. Copyright © 2014 Elsevier Ltd. All rights reserved.

Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations

Science.gov (United States)

Zhang, Linghai

2017-10-01

The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 traveling wave front as well as the existence and instability of a standing pulse solution if 0 traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.

Interaction of few-cycle laser pulses in an isotropic nonlinear medium

International Nuclear Information System (INIS)

Oganesyan, D L; Vardanyan, A O

2007-01-01

The interaction of few-cycle laser pulses propagating in an isotropic nonlinear medium is studied theoretically. A system of nonlinear Maxwell's equations is integrated numerically with respect to time by the finite difference method. The interaction of mutually orthogonal linearly polarised 0.81-μm, 10-fs pulses is considered. Both the instant Kerr polarisation response and Raman inertial response of the medium in the nonlinear part of the medium are taken into account. The spectral shift of the probe pulse caused by the cross-action of the reference pulse is studied. The spectra of the interacting pulses are studied for different time delays between them and the shifts of these spectra are obtained as a function of the time delay. (nonlinear optical phenomena)

Exposure-lag-response in Longitudinal Studies: Application of Distributed Lag Non-linear Models in an Occupational Cohort.

Science.gov (United States)

Neophytou, Andreas M; Picciotto, Sally; Brown, Daniel M; Gallagher, Lisa E; Checkoway, Harvey; Eisen, Ellen A; Costello, Sadie

2018-02-13

Prolonged exposures can have complex relationships with health outcomes, as timing, duration, and intensity of exposure are all potentially relevant. Summary measures such as cumulative exposure or average intensity of exposure may not fully capture these relationships. We applied penalized and unpenalized distributed lag non-linear models (DLNMs) with flexible exposure-response and lag-response functions in order to examine the association between crystalline silica exposure and mortality from lung cancer and non-malignant respiratory disease in a cohort study of 2,342 California diatomaceous earth workers, followed 1942-2011. We also assessed associations using simple measures of cumulative exposure assuming linear exposure-response and constant lag-response. Measures of association from DLNMs were generally higher than from simpler models. Rate ratios from penalized DLNMs corresponding to average daily exposures of 0.4 mg/m3 during lag years 31-50 prior to the age of observed cases were 1.47 (95% confidence interval (CI) 0.92, 2.35) for lung cancer and 1.80 (95% CI: 1.14, 2.85) for non-malignant respiratory disease. Rate ratios from the simpler models for the same exposure scenario were 1.15 (95% CI: 0.89-1.48) and 1.23 (95% CI: 1.03-1.46) respectively. Longitudinal cohort studies of prolonged exposures and chronic health outcomes should explore methods allowing for flexibility and non-linearities in the exposure-lag-response. © The Author(s) 2018. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health.

Estimation of nonlinearities from pseudodynamic and dynamic responses of bridge structures using the Delay Vector Variance method

Science.gov (United States)

Jaksic, Vesna; Mandic, Danilo P.; Karoumi, Raid; Basu, Bidroha; Pakrashi, Vikram

2016-01-01

Analysis of the variability in the responses of large structural systems and quantification of their linearity or nonlinearity as a potential non-invasive means of structural system assessment from output-only condition remains a challenging problem. In this study, the Delay Vector Variance (DVV) method is used for full scale testing of both pseudo-dynamic and dynamic responses of two bridges, in order to study the degree of nonlinearity of their measured response signals. The DVV detects the presence of determinism and nonlinearity in a time series and is based upon the examination of local predictability of a signal. The pseudo-dynamic data is obtained from a concrete bridge during repair while the dynamic data is obtained from a steel railway bridge traversed by a train. We show that DVV is promising as a marker in establishing the degree to which a change in the signal nonlinearity reflects the change in the real behaviour of a structure. It is also useful in establishing the sensitivity of instruments or sensors deployed to monitor such changes.

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

Science.gov (United States)

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

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

Nonlinear Stochastic Analysis of Subharmonic Response of a Shallow Cable

DEFF Research Database (Denmark)

Zhou, Q.; Stærdahl, Jesper Winther; Nielsen, Søren R.K.

2007-01-01

and stochastic subharmonic response is demonstrated upon comparison with a more involved model based on a spatial finite difference discretization of the full nonlinear partial differential equations of the cable. Since the stochastic response quantities are obtained by Monte Carlo simulation, which is extremely...... time-consuming for the finite difference model, most of the results are next based on the reduced model. Under harmonical varying support point motions the stable subharmonic motion consists of a harmonically varying component in the equilibrium plane and a large subharmonic out-of-plane component...... subharmonic response component is also present in the static equilibrium plane. Further, the time variation of the envelope process of the narrow-banded chordwise elongation process tends to enhance chaotic behaviour of the subharmonic response, which is detectable via extreme sensitivity on the initial...

Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces

Institute of Scientific and Technical Information of China (English)

LI Shoufu

2005-01-01

A series of stability, contractivity and asymptotic stability results of the solutions to nonlinear stiff Volterra functional differential equations (VFDEs) in Banach spaces is obtained, which provides the unified theoretical foundation for the stability analysis of solutions to nonlinear stiff problems in ordinary differential equations(ODEs), delay differential equations(DDEs), integro-differential equations(IDEs) and VFDEs of other type which appear in practice.

The reliability of nonlinear least-squares algorithm for data analysis of neural response activity during sinusoidal rotational stimulation in semicircular canal neurons.

Science.gov (United States)

Ren, Pengyu; Li, Bowen; Dong, Shiyao; Chen, Lin; Zhang, Yuelin

2018-01-01

Although many mathematical methods were used to analyze the neural activity under sinusoidal stimulation within linear response range in vestibular system, the reliabilities of these methods are still not reported, especially in nonlinear response range. Here we chose nonlinear least-squares algorithm (NLSA) with sinusoidal model to analyze the neural response of semicircular canal neurons (SCNs) during sinusoidal rotational stimulation (SRS) over a nonlinear response range. Our aim was to acquire a reliable mathematical method for data analysis under SRS in vestibular system. Our data indicated that the reliability of this method in an entire SCNs population was quite satisfactory. However, the reliability was strongly negatively depended on the neural discharge regularity. In addition, stimulation parameters were the vital impact factors influencing the reliability. The frequency had a significant negative effect but the amplitude had a conspicuous positive effect on the reliability. Thus, NLSA with sinusoidal model resulted a reliable mathematical tool for data analysis of neural response activity under SRS in vestibular system and more suitable for those under the stimulation with low frequency but high amplitude, suggesting that this method can be used in nonlinear response range. This method broke out of the restriction of neural activity analysis under nonlinear response range and provided a solid foundation for future study in nonlinear response range in vestibular system.

Modeling the Non-Linear Response of Fiber-Reinforced Laminates Using a Combined Damage/Plasticity Model

Science.gov (United States)

Schuecker, Clara; Davila, Carlos G.; Pettermann, Heinz E.

2008-01-01

The present work is concerned with modeling the non-linear response of fiber reinforced polymer laminates. Recent experimental data suggests that the non-linearity is not only caused by matrix cracking but also by matrix plasticity due to shear stresses. To capture the effects of those two mechanisms, a model combining a plasticity formulation with continuum damage has been developed to simulate the non-linear response of laminates under plane stress states. The model is used to compare the predicted behavior of various laminate lay-ups to experimental data from the literature by looking at the degradation of axial modulus and Poisson s ratio of the laminates. The influence of residual curing stresses and in-situ effect on the predicted response is also investigated. It is shown that predictions of the combined damage/plasticity model, in general, correlate well with the experimental data. The test data shows that there are two different mechanisms that can have opposite effects on the degradation of the laminate Poisson s ratio which is captured correctly by the damage/plasticity model. Residual curing stresses are found to have a minor influence on the predicted response for the cases considered here. Some open questions remain regarding the prediction of damage onset.

On the geometrically nonlinear elastic response of class θ = 1 tensegrity prisms

Science.gov (United States)

Mascolo, Ida; Amendola, Ada; Zuccaro, Giulio; Feo, Luciano; Fraternali, Fernando

2018-03-01

The present work studies the geometrically nonlinear response of class ϑ=1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables) or compression (bars), under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either 'standard' or 'expanded' configurations. An experimental validation of the predicted constitutive response is conducted with reference to a 'thick' and a 'slender' model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.

Robust approximation-free prescribed performance control for nonlinear systems and its application

Science.gov (United States)

Sun, Ruisheng; Na, Jing; Zhu, Bin

2018-02-01

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.

Nonlinear System Identification via Basis Functions Based Time Domain Volterra Model

Directory of Open Access Journals (Sweden)

Yazid Edwar

2014-07-01

Full Text Available This paper proposes basis functions based time domain Volterra model for nonlinear system identification. The Volterra kernels are expanded by using complex exponential basis functions and estimated via genetic algorithm (GA. The accuracy and practicability of the proposed method are then assessed experimentally from a scaled 1:100 model of a prototype truss spar platform. Identification results in time and frequency domain are presented and coherent functions are performed to check the quality of the identification results. It is shown that results between experimental data and proposed method are in good agreement.

Nonlinear Dynamic Response of an Unbalanced Flexible Rotor Supported by Elastic Bearings Lubricated with Piezo-Viscous Polar Fluids

Directory of Open Access Journals (Sweden)

Mustapha Lahmar

2015-04-01

Full Text Available On the basis of the V. K. Stokes micro-continuum theory, the effects of couple stresses on the nonlinear dynamic response of the unbalanced Jeffcott’s flexible rotor supported by layered hydrodynamic journal bearings is presented in this paper. A nonlinear transient modified Reynolds’ equation is derived and discretized by the finite element method to obtain the fluid-film pressure field as well as the film thickness by means of the implicit Euler method. The nonlinear orbits of the rotor center are determined by solving the nonlinear differential equations of motion with the explicit Euler’s scheme taking into account the flexibility of rotor. According to the obtained results, the combined effects of couple stresses due to the presence of polymer additives in lubricant and the pressure dependent viscosity on the nonlinear dynamic response of the rotor-bearing system are significant and cannot be ignored or overlooked. As expected, these effects are more noticeable for polymers characterized by higher length molecular chains.

Dynamic Response of Non-Linear Inelsatic Systems to Poisson-Driven Stochastic Excitations

DEFF Research Database (Denmark)

Nielsen, Søren R. K.; Iwankiewicz, R.

of an equivalent linearization techni que and substituting the non-analytical non-linearity in the original system by the cubic form in the pertinent state variables. The response moments are evaluated for the equivalent systems with the help of a generalized Ito's differential rule. The analytical results...

Fabrication and characterization of THUNDER actuators—pre-stress-induced nonlinearity in the actuation response

International Nuclear Information System (INIS)

Kim, Younghoon; Jiang, Qing; Cai, Ling; Usher, Timothy

2009-01-01

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

Ultrafast nonlinear dynamics of thin gold films due to an intrinsic delayed nonlinearity

Science.gov (United States)

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.

Analysis on Forced Vibration of Thin-Wall Cylindrical Shell with Nonlinear Boundary Condition

Directory of Open Access Journals (Sweden)

Qiansheng Tang

2016-01-01

Full Text Available Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance under external loads, the Newmark method is used to obtain time history, frequency spectrum plot, phase portraits, Poincare section, bifurcation diagrams, and three-dimensional spectrum plot with different parameters. The effects of external loads, supported clearance, and support stiffness on nonlinear dynamics behaviors of cylindrical shell with nonlinear boundary condition were discussed.

Influence of earthquake strong motion duration on nonlinear structural response

International Nuclear Information System (INIS)

Meskouris, K.

1983-01-01

The effects of motion duration on nonlinear structural response of high-rise, moment resisting frames are studied by subjecting shear beam models of a 10- and a 5-story frame to a series of synthetic accelerograms, all matching the same NEWMARK/HALL design spectrum. Two different hysteretic laws are used for the story springs, and calculations are carried out for target ductility values of 2 and 4. Maximum ductilities reached and energy-based damage indicators (maximum seismically input energy, hysteretically dissipated energy) are evaluated and correlated with the motion characteristics. A reasonable extrapolative determination of structural response characteristics based on these indicators seems possible. (orig.)

Non-linear Membrane Properties in Entorhinal Cortical Stellate Cells Reduce Modulation of Input-Output Responses by Voltage Fluctuations

Science.gov (United States)

Fernandez, Fernando R.; Malerba, Paola; White, John A.

2015-01-01

The presence of voltage fluctuations arising from synaptic activity is a critical component in models of gain control, neuronal output gating, and spike rate coding. The degree to which individual neuronal input-output functions are modulated by voltage fluctuations, however, is not well established across different cortical areas. Additionally, the extent and mechanisms of input-output modulation through fluctuations have been explored largely in simplified models of spike generation, and with limited consideration for the role of non-linear and voltage-dependent membrane properties. To address these issues, we studied fluctuation-based modulation of input-output responses in medial entorhinal cortical (MEC) stellate cells of rats, which express strong sub-threshold non-linear membrane properties. Using in vitro recordings, dynamic clamp and modeling, we show that the modulation of input-output responses by random voltage fluctuations in stellate cells is significantly limited. In stellate cells, a voltage-dependent increase in membrane resistance at sub-threshold voltages mediated by Na+ conductance activation limits the ability of fluctuations to elicit spikes. Similarly, in exponential leaky integrate-and-fire models using a shallow voltage-dependence for the exponential term that matches stellate cell membrane properties, a low degree of fluctuation-based modulation of input-output responses can be attained. These results demonstrate that fluctuation-based modulation of input-output responses is not a universal feature of neurons and can be significantly limited by subthreshold voltage-gated conductances. PMID:25909971

Nonlinear seismic response analysis of an embedded reactor building based on the substructure approach

International Nuclear Information System (INIS)

Hasegawa, M.; Ichikawa, T.; Nakai, S.; Watanabe, T.

1987-01-01

A practical method to calculate the elasto-plastic seismic response of structures considering the dynamic soil-structure interaction is presented. The substructure technique in the time domain is utilized in the proposed method. A simple soil spring system with the coupling effects which are usually evaluated by the impedance matrix is introduced to consider the soil-structure interaction for embedded structures. As a numerical example, the response of a BWR-MARK II type reactor building embedded in the layered soil is calculated. The accuracy of the present method is verified by comparing its numerical results with exact solutions. The nonlinear behaivor and the soil-structure interaction effects on the response of the reactor building are also discussed in detail. It is concluded that the present method is effective for the aseismic design considering both the material nonlinearity of the nuclear reactor building and the dynamic soil-structure interaction. (orig.)

Three-dimensional computer code for the nonlinear dynamic response of an HTGR core

International Nuclear Information System (INIS)

Subudhi, M.; Lasker, L.; Koplik, B.; Curreri, J.; Goradia, H.

1979-01-01

A three-dimensional dynamic code has been developed to determine the nonlinear response of an HTGR core. The HTGR core consists of several thousands of hexagonal core blocks. These are arranged inlayers stacked together. Each layer contains many core blocks surrounded on their outer periphery by reflector blocks. The entire assembly is contained within a prestressed concrete reactor vessel. Gaps exist between adjacent blocks in any horizontal plane. Each core block in a given layer is connected to the blocks directly above and below it via three dowell pins. The present analystical study is directed towards an invesstigation of the nonlinear response of the reactor core blocks in the event of a seismic occurrence. The computer code is developed for a specific mathemtical model which represents a vertical arrangement of layers of blocks. This comprises a block module of core elements which would be obtained by cutting a cylindrical portion consisting of seven fuel blocks per layer. It is anticipated that a number of such modules properly arranged could represent the entire core. Hence, the predicted response of this module would exhibit the response characteristics of the core

Photonic surfaces for designable nonlinear power shaping

Energy Technology Data Exchange (ETDEWEB)

Biswas, Roshni, E-mail: rbiswas@usc.edu; Povinelli, Michelle L. [Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089 (United States)

2015-02-09

We propose a method for designing nonlinear input-output power response based on absorptive resonances of nanostructured surfaces. We show that various power transmission trends can be obtained by placing a photonic resonance mode at the appropriate detuning from the laser wavelength. We demonstrate our results in a silicon photonic crystal slab at a laser wavelength of 808 nm. We quantify the overall spectral red shift as a function of laser power. The shift results from absorptive heating and the thermo-optic effect. We then demonstrate devices with increasing, decreasing, and non-monotonic transmission as a function of laser power. The transmission changes are up to 7.5 times larger than in unpatterned silicon. The strong nonlinear transmission is due to a combination of resonantly enhanced absorption, reduced thermal conductivity, and the resonant transmission lineshape. Our results illustrate the possibility of designing different nonlinear power trends within a single materials platform at a given wavelength of interest.

Photonic surfaces for designable nonlinear power shaping

International Nuclear Information System (INIS)

Biswas, Roshni; Povinelli, Michelle L.

2015-01-01

We propose a method for designing nonlinear input-output power response based on absorptive resonances of nanostructured surfaces. We show that various power transmission trends can be obtained by placing a photonic resonance mode at the appropriate detuning from the laser wavelength. We demonstrate our results in a silicon photonic crystal slab at a laser wavelength of 808 nm. We quantify the overall spectral red shift as a function of laser power. The shift results from absorptive heating and the thermo-optic effect. We then demonstrate devices with increasing, decreasing, and non-monotonic transmission as a function of laser power. The transmission changes are up to 7.5 times larger than in unpatterned silicon. The strong nonlinear transmission is due to a combination of resonantly enhanced absorption, reduced thermal conductivity, and the resonant transmission lineshape. Our results illustrate the possibility of designing different nonlinear power trends within a single materials platform at a given wavelength of interest

A nonlinear plate control without linearization

Directory of Open Access Journals (Sweden)

Yildirim Kenan

2017-03-01

Full Text Available In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

Directory of Open Access Journals (Sweden)

Y. N. Pavlov

2015-01-01

Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

Science.gov (United States)

Periaux, J.

1979-01-01

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Simulations of the Ocean Response to a Hurricane: Nonlinear Processes

KAUST Repository

Zedler, Sarah E.

2009-10-01

Superinertial internal waves generated by a tropical cyclone can propagate vertically and laterally away from their local generation site and break, contributing to turbulent vertical mixing in the deep ocean and maintenance of the stratification of the main thermocline. In this paper, the results of a modeling study are reported to investigate the mechanism by which superinertial fluctuations are generated in the deep ocean. The general properties of the superinertial wave wake were also characterized as a function of storm speed and central latitude. The Massachusetts Institute of Technology (MIT) Ocean General Circulation Model (OGCM) was used to simulate the open ocean response to realistic westward-tracking hurricane-type surface wind stress and heat and net freshwater buoyancy forcing for regions representative of midlatitudes in the Atlantic, the Caribbean, and low latitudes in the eastern Pacific. The model had high horizontal [Δ(x, y) = 1/6°] and vertical (Δz = 5 m in top 100 m) resolution and employed a parameterization for vertical mixing induced by shear instability. In the horizontal momentum equation, the relative size of the nonlinear advection terms, which had a dominant frequency near twice the inertial, was large only in the upper 200 m of water. Below 200 m, the linear momentum equations obeyed a linear balance to 2%. Fluctuations at nearly twice the inertial frequency (2f) were prevalent throughout the depth of the water column, indicating that these nonlinear advection terms in the upper 200 m forced a linear mode below at nearly twice the inertial frequency via vorticity conservation. Maximum variance at 2f in horizontal velocity occurred on the south side of the track. This was in response to vertical advection of northward momentum, which in the north momentum equation is an oscillatory positive definite term that constituted a net force to the south at a frequency near 2f. The ratio of this term to the Coriolis force was larger on the

Some nonlinear challenges in biology

International Nuclear Information System (INIS)

Mosconi, Francesco; Julou, Thomas; Desprat, Nicolas; Sinha, Deepak Kumar; Allemand, Jean-François; Croquette, Vincent; Bensimon, David

2008-01-01

Driven by a deluge of data, biology is undergoing a transition to a more quantitative science. Making sense of the data, building new models, asking the right questions and designing smart experiments to answer them are becoming ever more relevant. In this endeavour, nonlinear approaches can play a fundamental role. The biochemical reactions that underlie life are very often nonlinear. The functional features exhibited by biological systems at all levels (from the activity of an enzyme to the organization of a colony of ants, via the development of an organism or a functional module like the one responsible for chemotaxis in bacteria) are dynamically robust. They are often unaffected by order of magnitude variations in the dynamical parameters, in the number or concentrations of actors (molecules, cells, organisms) or external inputs (food, temperature, pH, etc). This type of structural robustness is also a common feature of nonlinear systems, exemplified by the fundamental role played by dynamical fixed points and attractors and by the use of generic equations (logistic map, Fisher–Kolmogorov equation, the Stefan problem, etc.) in the study of a plethora of nonlinear phenomena. However, biological systems differ from these examples in two important ways: the intrinsic stochasticity arising from the often very small number of actors and the role played by evolution. On an evolutionary time scale, nothing in biology is frozen. The systems observed today have evolved from solutions adopted in the past and they will have to adapt in response to future conditions. The evolvability of biological system uniquely characterizes them and is central to biology. As the great biologist T Dobzhansky once wrote: 'nothing in biology makes sense except in the light of evolution'. (open problem)

Application of Nonlinear Elastic Resonance Spectroscopy For Damage Detection In Concrete: An Interesting Story

Energy Technology Data Exchange (ETDEWEB)

Byers, Loren W. [Los Alamos National Laboratory; Ten Cate, James A. [Los Alamos National Laboratory; Johnson, Paul A. [Los Alamos National Laboratory

2012-06-28

Nonlinear resonance ultrasound spectroscopy experiments conducted on concrete cores, one chemically and mechanically damaged by alkali-silica reactivity, and one undamaged, show that this material displays highly nonlinear wave behavior, similar to many other damaged materials. They find that the damaged sample responds more nonlinearly, manifested by a larger resonant peak and modulus shift as a function of strain amplitude. The nonlinear response indicates that there is a hysteretic influence in the stress-strain equation of state. Further, as in some other materials, slow dynamics are present. The nonlinear response they observe in concrete is an extremely sensitive indicator of damage. Ultimately, nonlinear wave methods applied to concrete may be used to guide mixing, curing, or other production techniques, in order to develop materials with particular desired qualities such as enhanced strength or chemical resistance, and to be used for damage inspection.

A variational constitutive framework for the nonlinear viscoelastic response of a dielectric elastomer

KAUST Repository

Khan, Kamran

2012-11-10

We formulate a variational constitutive framework that accounts for nonlinear viscous behavior of electrically sensitive polymers, specifically Dielectric Elastomers (DEs), under large deformation. DEs are highly viscoelastic and their actuation response is greatly affected in dynamic applications. We used the generalized Maxwell model to represent the viscoelastic response of DE allowing the material to relax with multiple mechanisms. The constitutive updates at each load increment are obtained by minimizing an objective function formulated using the free energy and electrostatic energy of the elastomer, in addition to the viscous dissipation potential of the dashpots in each Maxwell branch. The model is then used to predict the electromechanical instability (EMI) of DE. The electro-elastic response of the DE is verified with available analytical solutions in the literature and then the material parameters are calibrated using experimental data. The model is integrated with finite element software to perform a variety of simulations on different types of electrically driven actuators under various electromechanical loadings. The electromechanical response of the DE and the critical conditions at which EMI occurs were found to be greatly affected by the viscoelasticity. Our model predicts that under a dead load EMI can be avoided if the DE operates at a high voltage rate. Subjected to constant, ramp and cyclic voltage, our model qualitatively predicts responses similar to the ones obtained from the analytical solutions and experimental data available in the literature. © 2012 Springer-Verlag Berlin Heidelberg.

Nonlinear optical response in condensed phases : A microscopic theory using the multipolar Hamiltonian

NARCIS (Netherlands)

Knoester, Jasper; Mukamel, Shaul

1990-01-01

A general scheme is presented for calculating the nonlinear optical response in condensed phases that provides a unified picture of excitons, polaritons, retardation, and local-field effects in crystals and in disordered systems. A fully microscopic starting point is taken by considering the

The time-walk of analog constant fraction discriminators using very fast scintillator detectors with linear and non-linear energy response

Energy Technology Data Exchange (ETDEWEB)

Regis, J.-M., E-mail: regis@ikp.uni-koeln.de [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany); Rudigier, M.; Jolie, J.; Blazhev, A.; Fransen, C.; Pascovici, G.; Warr, N. [Institut fuer Kernphysik der Universitaet zu Koeln, Zuelpicher Str. 77, 50937 Koeln (Germany)

2012-08-21

The electronic {gamma}-{gamma} fast timing technique allows for direct nuclear lifetime determination down to the few picoseconds region by measuring the time difference between two coincident {gamma}-ray transitions. Using high resolution ultra-fast LaBr{sub 3}(Ce) scintillator detectors in combination with the recently developed mirror symmetric centroid difference method, nuclear lifetimes are measured with a time resolving power of around 5 ps. The essence of the method is to calibrate the energy dependent position (centroid) of the prompt response function of the setup which is obtained for simultaneously occurring events. This time-walk of the prompt response function induced by the analog constant fraction discriminator has been determined by systematic measurements using different photomultiplier tubes and timing adjustments of the constant fraction discriminator. We propose a universal calibration function which describes the time-walk or the combined {gamma}-{gamma} time-walk characteristics, respectively, for either a linear or a non-linear amplitude versus energy dependency of the scintillator detector output pulses.

Equivalent linear and nonlinear site response analysis for design and risk assessment of safety-related nuclear structures

International Nuclear Information System (INIS)

Bolisetti, Chandrakanth; Whittaker, Andrew S.; Mason, H. Benjamin; Almufti, Ibrahim; Willford, Michael

2014-01-01

Highlights: • Performed equivalent linear and nonlinear site response analyses using industry-standard numerical programs. • Considered a wide range of sites and input ground motions. • Noted the practical issues encountered while using these programs. • Examined differences between the responses calculated from different programs. • Results of biaxial and uniaxial analyses are compared. - Abstract: Site response analysis is a precursor to soil-structure interaction analysis, which is an essential component in the seismic analysis of safety-related nuclear structures. Output from site response analysis provides input to soil-structure interaction analysis. Current practice in calculating site response for safety-related nuclear applications mainly involves the equivalent linear method in the frequency-domain. Nonlinear time-domain methods are used by some for the assessment of buildings, bridges and petrochemical facilities. Several commercial programs have been developed for site response analysis but none of them have been formally validated for large strains and high frequencies, which are crucial for the performance assessment of safety-related nuclear structures. This study sheds light on the applicability of some industry-standard equivalent linear (SHAKE) and nonlinear (DEEPSOIL and LS-DYNA) programs across a broad range of frequencies, earthquake shaking intensities, and sites ranging from stiff sand to hard rock, all with a focus on application to safety-related nuclear structures. Results show that the equivalent linear method is unable to reproduce the high frequency acceleration response, resulting in almost constant spectral accelerations in the short period range. Analysis using LS-DYNA occasionally results in some unrealistic high frequency acceleration ‘noise’, which can be removed by smoothing the piece-wise linear backbone curve. Analysis using DEEPSOIL results in abrupt variations in the peak strains of consecutive soil layers

Generalized hyperbolic functions to find soliton-like solutions for a system of coupled nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, we demonstrate that the known method which is based on the new generalized hyperbolic functions and the new kinds of generalized hyperbolic function transformations, generates classes of exact solutions to a system of coupled nonlinear Schroedinger equations. This system includes the modified Hubbard model and the system of coupled nonlinear Schroedinger derived by Lazarides and Tsironis. Four types of solutions for this system are given explicitly, namely: new bright-bright, new dark-dark, new bright-dark and new dark-bright solitons

Conceptual DFT: the chemical relevance of higher response functions.

Science.gov (United States)

Geerlings, P; De Proft, F

2008-06-07

In recent years conceptual density functional theory offered a perspective for the interpretation/prediction of experimental/theoretical reactivity data on the basis of a series of response functions to perturbations in the number of electrons and/or external potential. This approach has enabled the sharp definition and computation, from first principles, of a series of well-known but sometimes vaguely defined chemical concepts such as electronegativity and hardness. In this contribution, a short overview of the shortcomings of the simplest, first order response functions is illustrated leading to a description of chemical bonding in a covalent interaction in terms of interacting atoms or groups, governed by electrostatics with the tendency to polarize bonds on the basis of electronegativity differences. The second order approach, well known until now, introduces the hardness/softness and Fukui function concepts related to polarizability and frontier MO theory, respectively. The introduction of polarizability/softness is also considered in a historical perspective in which polarizability was, with some exceptions, mainly put forward in non covalent interactions. A particular series of response functions, arising when the changes in the external potential are solely provoked by changes in nuclear configurations (the "R-analogues") are also systematically considered. The main part of the contribution is devoted to third order response functions which, at first sight, may be expected not to yield chemically significant information, as turns out to be for the hyperhardness. A counterexample is the dual descriptor and its R analogue, the initial hardness response, which turns out to yield a firm basis to regain the Woodward-Hoffmann rules for pericyclic reactions based on a density-only basis, i.e. without involving the phase, sign, symmetry of the wavefunction. Even the second order nonlinear response functions are shown possibly to bear interesting information, e

Computation of Value Functions in Nonlinear Differential Games with State Constraints

KAUST Repository

Botkin, Nikolai

2013-01-01

Finite-difference schemes for the computation of value functions of nonlinear differential games with non-terminal payoff functional and state constraints are proposed. The solution method is based on the fact that the value function is a generalized viscosity solution of the corresponding Hamilton-Jacobi-Bellman-Isaacs equation. Such a viscosity solution is defined as a function satisfying differential inequalities introduced by M. G. Crandall and P. L. Lions. The difference with the classical case is that these inequalities hold on an unknown in advance subset of the state space. The convergence rate of the numerical schemes is given. Numerical solution to a non-trivial three-dimensional example is presented. © 2013 IFIP International Federation for Information Processing.

ONIOM Investigation of the Second-Order Nonlinear Optical Responses of Fluorescent Proteins.

Science.gov (United States)

de Wergifosse, Marc; Botek, Edith; De Meulenaere, Evelien; Clays, Koen; Champagne, Benoît

2018-05-17

The first hyperpolarizability (β) of six fluorescent proteins (FPs), namely, enhanced green fluorescent protein, enhanced yellow fluorescent protein, SHardonnay, ZsYellow, DsRed, and mCherry, has been calculated to unravel the structure-property relationships on their second-order nonlinear optical properties, owing to their potential for multidimensional biomedical imaging. The ONIOM scheme has been employed and several of its refinements have been addressed to incorporate efficiently the effects of the microenvironment on the nonlinear optical responses of the FP chromophore that is embedded in a protective β-barrel protein cage. In the ONIOM scheme, the system is decomposed into several layers (here two) treated at different levels of approximation (method1/method2), from the most elaborated method (method1) for its core (called the high layer) to the most approximate one (method2) for the outer surrounding (called the low layer). We observe that a small high layer can already account for the variations of β as a function of the nature of the FP, provided the low layer is treated at an ab initio level to describe properly the effects of key H-bonds. Then, for semiquantitative reproduction of the experimental values obtained from hyper-Rayleigh scattering experiments, it is necessary to incorporate electron correlation as described at the second-order Møller-Plesset perturbation theory (MP2) level as well as implicit solvent effects accounted for using the polarizable continuum model (PCM). This led us to define the MP2/6-31+G(d):HF/6-31+G(d)/IEFPCM scheme as an efficient ONIOM approach and the MP2/6-31+G(d):HF/6-31G(d)/IEFPCM as a better compromise between accuracy and computational needs. Using these methods, we demonstrate that many parameters play a role on the β response of FPs, including the length of the π-conjugated segment, the variation of the bond length alternation, and the presence of π-stacking interactions. Then, noticing the small diversity

Non-linear wave loads and ship responses by a time-domain strip theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hydroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented as a Timoshenko beam. Numerical calculations are presented for the S175 Containership...

Non-Linear Wave Loads and Ship responses by a time-domain Strip Theory

DEFF Research Database (Denmark)

Xia, Jinzhu; Wang, Zhaohui; Jensen, Jørgen Juncher

1998-01-01

. Based on this time-domain strip theory, an efficient non-linear hyroelastic method of wave- and slamming-induced vertical motions and structural responses of ships is developed, where the structure is represented by the Timoshenko beam theory. Numerical calculations are presented for the S175...

Nonlinear modulation of interacting between COMT and depression on brain function.

Science.gov (United States)

Gong, L; He, C; Yin, Y; Ye, Q; Bai, F; Yuan, Y; Zhang, H; Lv, L; Zhang, H; Zhang, Z; Xie, C

2017-09-01

The catechol-O-methyltransferase (COMT) gene is related to dopamine degradation and has been suggested to be involved in the pathogenesis of major depressive disorder (MDD). However, how this gene affects brain function properties in MDD is still unclear. Fifty patients with MDD and 35 cognitively normal participants underwent a resting-state functional magnetic resonance imaging scan. A voxelwise and data-drive global functional connectivity density (gFCD) analysis was used to investigate the main effects and the interactions of disease states and COMT rs4680 gene polymorphism on brain function. We found significant group differences of the gFCD in bilateral fusiform area (FFA), post-central and pre-central cortex, left superior temporal gyrus (STG), rectal and superior temporal gyrus and right ventrolateral prefrontal cortex (vlPFC); abnormal gFCDs in left STG were positively correlated with severity of depression in MDD group. Significant disease×COMT interaction effects were found in the bilateral calcarine gyrus, right vlPFC, hippocampus and thalamus, and left SFG and FFA. Further post-hoc tests showed a nonlinear modulation effect of COMT on gFCD in the development of MDD. Interestingly, an inverted U-shaped modulation was found in the prefrontal cortex (control system) but U-shaped modulations were found in the hippocampus, thalamus and occipital cortex (processing system). Our study demonstrated nonlinear modulation of the interaction between COMT and depression on brain function. These findings expand our understanding of the COMT effect underlying the pathophysiology of MDD. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

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

Science.gov (United States)

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.

Dynamic buckling and nonlinear response of FBR main vessels under earthquake loading

International Nuclear Information System (INIS)

Hagiwara, Yutaka; Kawamoto, Yoji; Nakagawa, Masaki; Akiyama, Hiroshi.

1991-01-01

Pseudo-dynamic tests of cylindrical shells under high temperature were performed in order to study elasto-plastic shear-bending buckling and the nonlinear response of FBR main vessels under earthquake loading. The test results showed a response reduction effect due to pre-buckling plasticity, and a large seismic margin due to post-buckling energy absorption of the cylinders. A simple expression of the response reduction effect was proposed, as a contribution to the safe and effective seismic design of FBRs. Two methods for seismic margin evaluation were also proposed, and it was shown that appropriate seismic margins can be ensured, when the response reduction effect is incorporated into the seismic design. (author)

Iterative method of the parameter variation for solution of nonlinear functional equations

International Nuclear Information System (INIS)

Davidenko, D.F.

1975-01-01

The iteration method of parameter variation is used for solving nonlinear functional equations in Banach spaces. The authors consider some methods for numerical integration of ordinary first-order differential equations and construct the relevant iteration methods of parameter variation, both one- and multifactor. They also discuss problems of mathematical substantiation of the method, study the conditions and rate of convergence, estimate the error. The paper considers the application of the method to specific functional equations

H∞ Balancing for Nonlinear Systems

NARCIS (Netherlands)

Scherpen, Jacquelien M.A.

1996-01-01

In previously obtained balancing methods for nonlinear systems a past and a future energy function are used to bring the nonlinear system in balanced form. By considering a different pair of past and future energy functions that are related to the H∞ control problem for nonlinear systems we define

Non-linear shape functions over time in the space-time finite element method

Directory of Open Access Journals (Sweden)

Kacprzyk Zbigniew

2017-01-01

Full Text Available This work presents a generalisation of the space-time finite element method proposed by Kączkowski in his seminal of 1970’s and early 1980’s works. Kączkowski used linear shape functions in time. The recurrence formula obtained by Kączkowski was conditionally stable. In this paper, non-linear shape functions in time are proposed.

High-order nonlinear susceptibilities of He

International Nuclear Information System (INIS)

Liu, W.C.; Clark, C.W.

1996-01-01

High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. The authors have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s, within the framework of Rayleigh=Schroedinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Ponte and Shakeshaft, and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used; the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals

Linear and nonlinear response matrix and its application to the SIS18 synchrotron

International Nuclear Information System (INIS)

Parfenova, Angelina

2008-01-01

This Thesis is dedicated to the numerical as well as the experimental study of beam dynamics in circular accelerators. The experimental part was undertaken in the SIS18 synchrotron. The detailed description of the experiments contained in this work can be considered as a starting point for future experiments and machine development. The work has the following structure. In Chapter 2 an overview of the GSI and FAIR accelerator facilities, and a general description of the SIS18 instrumentation related to the study of this work are given. The expected SIS18 performance in view of the upgrade program for FAIR project are outlined. The main beam dynamics issues connected with the purpose of this work are discussed. Chapter 3 is devoted to the study of linear beam dynamics in the SIS18. The resonance beam loss measurements were carried out with residual gas profile monitor in the SIS18 (Chapter 4). In the frame of this work a novel technique 'nonlinear tune response matrix method' to identify strengths, polarities and locations of nonlinear errors in circular accelerators is developed (Chapter 5). In the method the feed down effect of the nonlinear components at level of linear tune response to the closed-orbit change is explored. The closed-orbit change is introduced by varying correction steerers. The tune values are retrieved from the spectrum of coherent betatron oscillations excited by a fast kick. The theoretical background, the robustness of the method and numerical examples for the SIS18 using numerical library MICROMAP are presented. The technique to measure lattice nonlinearities was experimentally validated in the SIS18 where two normal as well as two skew sextupolar errors of the order of natural errors were reconstructed with a tolerant precision. It was shown how this technique can be applied to reconstruct sextupolar nonlinear errors in the complete machine. In Chapter 6 the main results and the conclusions of this work are outlined. (orig.)

Non-parametric system identification from non-linear stochastic response

DEFF Research Database (Denmark)

Rüdinger, Finn; Krenk, Steen

2001-01-01

An estimation method is proposed for identification of non-linear stiffness and damping of single-degree-of-freedom systems under stationary white noise excitation. Non-parametric estimates of the stiffness and damping along with an estimate of the white noise intensity are obtained by suitable...... of the energy at mean-level crossings, which yields the damping relative to white noise intensity. Finally, an estimate of the noise intensity is extracted by estimating the absolute damping from the autocovariance functions of a set of modified phase plane variables at different energy levels. The method...

A sampling approach to constructing Lyapunov functions for nonlinear continuous–time systems

NARCIS (Netherlands)

Bobiti, R.V.; Lazar, M.

2016-01-01

The problem of constructing a Lyapunov function for continuous-time nonlinear dynamical systems is tackled in this paper via a sampling-based approach. The main idea of the sampling-based method is to verify a Lyapunov-type inequality for a finite number of points (known state vectors) in the

Sparse non-linear denoising: Generalization performance and pattern reproducibility in functional MRI

DEFF Research Database (Denmark)

Abrahamsen, Trine Julie; Hansen, Lars Kai

2011-01-01

We investigate sparse non-linear denoising of functional brain images by kernel Principal Component Analysis (kernel PCA). The main challenge is the mapping of denoised feature space points back into input space, also referred to as ”the pre-image problem”. Since the feature space mapping is typi...

A nonlinear mixed-effects model for simultaneous smoothing and registration of functional data

DEFF Research Database (Denmark)

Raket, Lars Lau; Sommer, Stefan Horst; Markussen, Bo

2014-01-01

We consider misaligned functional data, where data registration is necessary for proper statistical analysis. This paper proposes to treat misalignment as a nonlinear random effect, which makes simultaneous likelihood inference for horizontal and vertical effects possible. By simultaneously fitti...

Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method

International Nuclear Information System (INIS)

Ebaid, A.

2007-01-01

Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV-mKdV equation are chosen to illustrate the effectiveness of the method

Existence of Solutions of Abstract Nonlinear Mixed Functional Integrodifferential equation with nonlocal conditions

Directory of Open Access Journals (Sweden)

Dhakne Machindra B.

2017-04-01

Full Text Available In this paper we discuss the existence of mild and strong solutions of abstract nonlinear mixed functional integrodifferential equation with nonlocal condition by using Sadovskii’s fixed point theorem and theory of fractional power of operators.

A three-dimensional computer code for the nonlinear dynamic response of an HTGR core

International Nuclear Information System (INIS)

Subudhi, M.; Lasker, L.; Koplik, B.; Curreri, J.; Goradia, H.

1979-01-01

A three-dimensional dynamic code has been developed to determine the nonlinear response of an HTGR core. The HTGR core consists of several thousands of hexagonal core blocks. These are arranged in layers stacked together. Each layer contains many core blocks surrounded on their outer periphery by reflector blocks. The entire assembly is contained within a prestressed concrete reactor vessel. Gaps exist between adjacent blocks in any horizontal plane. Each core block in a given layer is connected to the blocks directly above and below it via three dowell pins. The present analytical study is directed towards an investigation of the nonlinear response of the reactor core blocks in the event of a seismic occurrence. The computer code is developed for a specific mathematical model which represents a vertical arrangement of layers of blocks. This comprises a 'block module' of core elements which would be obtained by cutting a cylindrical portion consisting of seven fuel blocks per layer. It is anticipated that a number of such modules properly arranged could represent the entire core. Hence, the predicted response of this module would exhibit the response characteristics of the core. (orig.)

Isomorphism and the #betta#-function of the non-linear sigma model in symmetric spaces

International Nuclear Information System (INIS)

Hikami, S.

1983-01-01

The renormalization group #betta#-function of the non-linear sigma model in symmetric spaces is discussed via the isomorphic relation and the reciprocal relation about a parameter α. The four-loop term is investigated and the symmetric properties of the #betta#-function are studied. The four-loop term in the #betta#-function is shown to be vanishing for the orthogonal Anderson localization problem. (orig.)

Identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform

Science.gov (United States)

Ta, Minh-Nghi; Lardiès, Joseph

2006-05-01

We consider the free response of a nonlinear vibrating system. Using the ridges and skeletons of the continuous wavelet transform, we identify weak nonlinearities on damping and stiffness and estimate their physical parameters. The crucial choice of the son wavelet function is obtained using an optimization technique based on the entropy of the continuous wavelet transform. The method is applied to simulated single-degree-of-freedom systems and multi-degree-of-freedom systems with nonlinearities on damping and stiffness. Experimental validation of the nonlinear identification and parameter estimation method is presented. The experimental system is a clamped beam with nonlinearities on damping and stiffness and these nonlinearities are identified and quantified from a displacement sensor.

Dopamine reward prediction error responses reflect marginal utility.

Science.gov (United States)

Stauffer, William R; Lak, Armin; Schultz, Wolfram

2014-11-03

Optimal choices require an accurate neuronal representation of economic value. In economics, utility functions are mathematical representations of subjective value that can be constructed from choices under risk. Utility usually exhibits a nonlinear relationship to physical reward value that corresponds to risk attitudes and reflects the increasing or decreasing marginal utility obtained with each additional unit of reward. Accordingly, neuronal reward responses coding utility should robustly reflect this nonlinearity. In two monkeys, we measured utility as a function of physical reward value from meaningful choices under risk (that adhered to first- and second-order stochastic dominance). The resulting nonlinear utility functions predicted the certainty equivalents for new gambles, indicating that the functions' shapes were meaningful. The monkeys were risk seeking (convex utility function) for low reward and risk avoiding (concave utility function) with higher amounts. Critically, the dopamine prediction error responses at the time of reward itself reflected the nonlinear utility functions measured at the time of choices. In particular, the reward response magnitude depended on the first derivative of the utility function and thus reflected the marginal utility. Furthermore, dopamine responses recorded outside of the task reflected the marginal utility of unpredicted reward. Accordingly, these responses were sufficient to train reinforcement learning models to predict the behaviorally defined expected utility of gambles. These data suggest a neuronal manifestation of marginal utility in dopamine neurons and indicate a common neuronal basis for fundamental explanatory constructs in animal learning theory (prediction error) and economic decision theory (marginal utility). Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.

Predominant nonlinear atmospheric response to meridional shift of the Gulf Stream path from the WRF atmospheric model simulations

Science.gov (United States)

Seo, H.; Kwon, Y. O.; Joyce, T. M.

2016-02-01

A remarkably strong nonlinear behavior of the atmospheric circulation response to North Atlantic SST anomalies (SSTA) is revealed from a set of large-ensemble, high-resolution, and hemispheric-scale Weather Research and Forecasting (WRF) model simulations. The model is forced with the SSTA associated with meridional shift of the Gulf Stream (GS) path, constructed from a lag regression of the winter SST on a GS Index from observation. Analysis of the systematic set of experiments with SSTAs of varied amplitudes and switched signs representing various GS-shift scenarios provides unique insights into mechanism for emergence and evolution of transient and equilibrium response of atmospheric circulation to extratropical SSTA. Results show that, independent of sign of the SSTA, the equilibrium response is characterized by an anomalous trough over the North Atlantic Ocean and the Western Europe concurrent with enhanced storm track, increased rainfall, and reduced blocking days. To the north of the anomalous low, an anomalous ridge emerges over the Greenland, Iceland, and Norwegian Seas accompanied by weakened storm track, reduced rainfall and increased blocking days. This nonlinear component of the total response dominates the weak and oppositely signed linear response that is directly forced by the SSTA, yielding an anomalous ridge (trough) downstream of the warm (cold) SSTA. The amplitude of the linear response is proportional to that of the SSTA, but this is masked by the overwhelmingly strong nonlinear behavior showing no clear correspondence to the SSTA amplitude. The nonlinear pattern emerges 3-4 weeks after the model initialization in November and reaches its first peak amplitude in December/January. It appears that altered baroclinic wave activity due to the GS SSTA in November lead to low-frequency height responses in December/January through transient eddy vorticity flux convergence.

Dynamic response analysis of block foundations with nonlinear dry friction mounting system to impact loads

International Nuclear Information System (INIS)

Zheng, Enlai; Zhu, Sihong; Zhou, Xinlong

2014-01-01

It is essential to establish a dynamic model to predict and evaluate the dynamic performance of a nonlinear dry friction mounting system during design procedure, when it is impossible to carry out the test of prototype. Unlike the conventional ideal dry friction model where the direction of dry friction force is always considered to be opposite to that of relative velocity, a new equivalent resistance model of dry friction force is proposed based on the bilinear hysteretic model by introducing a parameter g in this work. The equivalent resistance contains spring force and damping force, whose direction is not opposite to that of relative velocity. Then, a dynamic model of the block foundation with nonlinear dry friction mounting system is established. When the equivalent resistance is applied to the dynamic model, its dynamic responses are obtained under common practical forms of press loads: rectangular pulse, half-sine pulse, and triangular pulse. Compared to experimental results, the dynamic responses based on the equivalent resistance model are more consistent with the simulation results based on the ideal dry friction model and the validity of the equivalent resistance model for the bilinear hysteretic model in this work is verified. Furthermore, the effect of the pulse shape and pulse duration on the dynamic responses of the block foundation with nonlinear dry friction mounting system is investigated.

Nonlinear associations between plasma cholesterol levels and neuropsychological function.

Science.gov (United States)

Wendell, Carrington R; Zonderman, Alan B; Katzel, Leslie I; Rosenberger, William F; Plamadeala, Victoria V; Hosey, Megan M; Waldstein, Shari R

2016-11-01

Although both high and low levels of total and low-density lipoprotein (LDL) cholesterol have been associated with poor neuropsychological function, little research has examined nonlinear effects. We examined quadratic relations of cholesterol to performance on a comprehensive neuropsychological battery. Participants were 190 older adults (53% men, ages 54-83) free of major medical, neurologic, and psychiatric disease. Measures of fasting plasma total and high-density lipoprotein (HDL) cholesterol were assayed, and LDL cholesterol was calculated. Participants completed neuropsychological measures of attention, executive function, memory, visuospatial judgment, and manual speed and dexterity. Multiple regression analyses examined cholesterol levels as quadratic predictors of each measure of cognitive performance, with age (dichotomized as Reproduction II ( b = -.0020, p = .026) and log of the Trail Making Test, Part B (b = .0001, p = .044). Quadratic associations between HDL cholesterol and cognitive performance were nonsignificant. Results indicate differential associations between cholesterol and neuropsychological function across different ages and domains of function. High and low total and LDL cholesterol may confer both risk and benefit for suboptimal cognitive function at different ages. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Toward a unified description of nonlinearity and frequency dispersion of piezoelectric and dielectric responses in Pb(Zr,Ti)O3

International Nuclear Information System (INIS)

Damjanovic, D.; Bharadwaja, S.S.N.; Setter, N.

2005-01-01

A phenomenological approach is proposed describing both nonlinearity and frequency dispersion in dielectric and piezoelectric properties of lead zirconate titanate, Pb(Zr,Ti)O 3 (PZT), thin films and ceramics. The approach couples the frequency dependent response in form of the power law, 1/ω β , with the rate-independent nonlinear response described by the Rayleigh law. The main experimental trends are well described by the model

KEELE, Minimization of Nonlinear Function with Linear Constraints, Variable Metric Method

International Nuclear Information System (INIS)

Westley, G.W.

1975-01-01

1 - Description of problem or function: KEELE is a linearly constrained nonlinear programming algorithm for locating a local minimum of a function of n variables with the variables subject to linear equality and/or inequality constraints. 2 - Method of solution: A variable metric procedure is used where the direction of search at each iteration is obtained by multiplying the negative of the gradient vector by a positive definite matrix which approximates the inverse of the matrix of second partial derivatives associated with the function. 3 - Restrictions on the complexity of the problem: Array dimensions limit the number of variables to 20 and the number of constraints to 50. These can be changed by the user

Estimation of bone Calcium-to-Phosphorous mass ratio using dual-energy nonlinear polynomial functions

International Nuclear Information System (INIS)

Sotiropoulou, P; Koukou, V; Martini, N; Nikiforidis, G; Michail, C; Kandarakis, I; Fountos, G; Kounadi, E

2015-01-01

In this study an analytical approximation of dual-energy inverse functions is presented for the estimation of the calcium-to-phosphorous (Ca/P) mass ratio, which is a crucial parameter in bone health. Bone quality could be examined by the X-ray dual-energy method (XDEM), in terms of bone tissue material properties. Low- and high-energy, log- intensity measurements were combined by using a nonlinear function, to cancel out the soft tissue structures and generate the dual energy bone Ca/P mass ratio. The dual-energy simulated data were obtained using variable Ca and PO 4 thicknesses on a fixed total tissue thickness. The XDEM simulations were based on a bone phantom. Inverse fitting functions with least-squares estimation were used to obtain the fitting coefficients and to calculate the thickness of each material. The examined inverse mapping functions were linear, quadratic, and cubic. For every thickness, the nonlinear quadratic function provided the optimal fitting accuracy while requiring relative few terms. The dual-energy method, simulated in this work could be used to quantify bone Ca/P mass ratio with photon-counting detectors. (paper)

Finite Element Modeling and Analysis of Nonlinear Impact and Frictional Motion Responses Including Fluid—Structure Coupling Effects

Directory of Open Access Journals (Sweden)

Yong Zhao

1997-01-01

Full Text Available A nonlinear three dimensional (3D single rack model and a nonlinear 3D whole pool multi-rack model are developed for the spent fuel storage racks of a nuclear power plant (NPP to determine impacts and frictional motion responses when subjected to 3D excitations from the supporting building floor. The submerged free standing rack system and surrounding water are coupled due to hydrodynamic fluid-structure interaction (FSI using potential theory. The models developed have features that allow consideration of geometric and material nonlinearities including (1 the impacts of fuel assemblies to rack cells, a rack to adjacent racks or pool walls, and rack support legs to the pool floor; (2 the hydrodynamic coupling of fuel assemblies with their storing racks, and of a rack with adjacent racks, pool walls, and the pool floor; and (3 the dynamic motion behavior of rocking, twisting, and frictional sliding of rack modules. Using these models 3D nonlinear time history dynamic analyses are performed per the U.S. Nuclear Regulatory Commission (USNRC criteria. Since few such modeling, analyses, and results using both the 3D single and whole pool multiple rack models are available in the literature, this paper emphasizes description of modeling and analysis techniques using the SOLVIA general purpose nonlinear finite element code. Typical response results with different Coulomb friction coefficients are presented and discussed.

Study on statistical analysis of nonlinear and nonstationary reactor noises

International Nuclear Information System (INIS)

Hayashi, Koji

1993-03-01

For the purpose of identification of nonlinear mechanism and diagnosis of nuclear reactor systems, analysis methods for nonlinear reactor noise have been studied. By adding newly developed approximate response function to GMDH, a conventional nonlinear identification method, a useful method for nonlinear spectral analysis and identification of nonlinear mechanism has been established. Measurement experiment and analysis were performed on the reactor power oscillation observed in the NSRR installed at the JAERI and the cause of the instability was clarified. Furthermore, the analysis and data recording methods for nonstationary noise have been studied. By improving the time resolution of instantaneous autoregressive spectrum, a method for monitoring and diagnosis of operational status of nuclear reactor has been established. A preprocessing system for recording of nonstationary reactor noise was developed and its usability was demonstrated through a measurement experiment. (author) 139 refs

Nonlinear seismic response analysis of embedded reactor buildings based on the substructure approach in time domain

International Nuclear Information System (INIS)

Hasegawa, M.; Nakai, S.; Watanabe, T.

1985-01-01

A practical method for elasto-plastic seismic response analysis is described under considerations of nonlinear material law of a structure and dynamic soil-structure interaction. The method is essentially based on the substructure approach of time domain analysis. Verification of the present method is carried out for typical BWR-MARK II type reactor building which is embedded in a soil, and the results are compared with those of the frequency response analysis which gives good accuracy for linear system. As a result, the present method exhibits sufficient accuracy. Furthermore, elasto-plastic analyses considering the soil-structure interaction are made as an application of the present method, and nonlinear behaviors of the structure and embedment effects are discussed. (orig.)

On the evaluation of scalarproducts of nonlinear spinorfield state functionals

International Nuclear Information System (INIS)

Stumpf, H.

1981-01-01

The metrical structure of the linear state space of a quantized nonlinear field cannot be given a priori. Rather it is determined by the dynamics of the field itself. For the evaluation of state norms and scalarproducts this metric must be known. In functional quantum theory the metrical structure is expressed by the metric tensor G(j) in functional space. Equivalent to the knowledge of G(j) is the knowledge of the set of dual state functionals ( vertical stroke S(j,a)>) together with the corresponding original state functionals ( vertical stroke F(j,a)>). In preceding papers attempts were made to calculate G(j). In this paper an approach is made to determine the dual state functionals directly. Equations are derived which have to be satisfied by the dual functionals. The method works in those state sectors which are characterized by real (monopole) particles or monopole ghosts, while it does not work for multipole ghost states. Norm calculations are performed for local monopole fermion states and local monopole boson states of the lepton- quark model derived in a preceding paper. (orig.)

Traveling waves in a diffusive predator-prey model with holling type-III functional response

International Nuclear Information System (INIS)

Li Wantong; Wu Shiliang

2008-01-01

We establish the existence of traveling wave solutions and small amplitude traveling wave train solutions for a reaction-diffusion system based on a predator-prey model with Holling type-III functional response. The analysis is in the three-dimensional phase space of the nonlinear ordinary differential equation system given by the diffusive predator-prey system in the traveling wave variable. The methods used to prove the results are the shooting argument, invariant manifold theory and the Hopf bifurcation theorem

A Simplification for Exp-Function Method When the Balanced Nonlinear Term Is a Certain Product

Directory of Open Access Journals (Sweden)

Hong-Zhun Liu

2013-01-01

Full Text Available The Exp-function method plays an important role in searching for analytic solutions of many nonlinear differential equations. In this paper, we prove that the balancing procedure in the method is unnecessary when the balanced nonlinear term is a product of the dependent variable under consideration and its derivatives. And in this case, the ansatz of the method can be simplified to be with less parameters so as to be easy to calculate.

Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity

International Nuclear Information System (INIS)

Granovsky, Alexander B.; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru

2003-01-01

We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D i =ε i (0) E i +χ i (3) |E i | 2 E i . We assume that linear ε i (0) and cubic nonlinear χ i (3) dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function χ eff (3) can be significantly greater (up to 10 3 times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity

Unique solvability of a non-linear non-local boundary-value problem for systems of non-linear functional differential equations

Czech Academy of Sciences Publication Activity Database

Dilna, N.; Rontó, András

2010-01-01

Roč. 60, č. 3 (2010), s. 327-338 ISSN 0139-9918 R&D Projects: GA ČR(CZ) GA201/06/0254 Institutional research plan: CEZ:AV0Z10190503 Keywords : non-linear boundary value-problem * functional differential equation * non-local condition * unique solvability * differential inequality Subject RIV: BA - General Mathematics Impact factor: 0.316, year: 2010 http://link.springer.com/article/10.2478%2Fs12175-010-0015-9

On the Geometrically Nonlinear Elastic Response of Class θ = 1 Tensegrity Prisms

Directory of Open Access Journals (Sweden)

Ida Mascolo

2018-03-01

Full Text Available The present work studies the geometrically nonlinear response of class θ = 1 tensegrity prisms modeled as a collection of elastic springs reacting in tension (strings or cables or compression (bars, under uniform uniaxial loading. The incremental equilibrium equations of the structure are numerically solved through a path-following procedure, with the aim of modeling the mechanical behavior of the structure in the large displacement regime. Several numerical results are presented with reference to a variety of physical models, which use two different materials for the cables and the bars, and show different aspect ratios associated with either “standard” or “expanded” configurations. An experimental validation of the predicted constitutive response is conducted with reference to a “thick” and a “slender” model, observing rather good theory vs. experiment matching. The given numerical and experimental results highlight that the elastic response of the examined structures may switch from stiffening to softening, depending on the geometry of the system, the magnitude of the external load, and the applied prestress. The outcomes of the current study confirm previous literature results on the elastic response of minimal tensegrity prisms, and pave the way to the use of tensegrity systems as nonlinear spring units forming tunable mechanical metamaterials.

On the physical contributions to the third-order nonlinear optical response in plasmonic nanocomposites

International Nuclear Information System (INIS)

Fernández-Hernández, Roberto Carlos; Gleason-Villagran, Roberto; Rodríguez-Fernández, Luis; Crespo-Sosa, Alejandro; Cheang-Wong, Juan Carlos; López-Suárez, Alejandra; Oliver, Alicia; Reyes-Esqueda, Jorge Alejandro; Torres-Torres, Carlos; Rangel-Rojo, Raúl

2012-01-01

Au and Ag isotropic and anisotropic nanocomposites were prepared using the ion implantation technique. Their optical properties were studied at several wavelengths in the optical range 300–800 nm, across their plasmon resonances. The linear regime was characterized by measuring the absorption spectrum and the third-order nonlinear regime by means of the Z-scan technique using a tunable picosecond pulsed laser system (26 ps). Open-aperture Z-scan traces show a superposition of different optical nonlinear absorption (NLA) processes in the whole range studied. We associate these phenomena with the excitation of inter- and intra-band electronic transitions, which contribute with a positive sign to NLA, and to the formation of hot-electrons, which contribute with opposite sign to NLA. Closed-aperture traces for measuring nonlinear refraction (NLR) show different signs for Au and Ag samples, and a change of sign in Au is found when purely inter-band transitions are excited. In this work, for the appropriate wavelength, it is worth remarking on the free-electron response to the exciting light and its strong contribution to the nonlinear optical properties for low (intra-band) and high (hot-electrons) irradiances. (paper)

Reflections on the nature of non-linear responses of the climate to forcing

Science.gov (United States)

Ditlevsen, Peter

2017-04-01

On centennial to multi-millennial time scales the paleoclimatic record shows that climate responds in a very non-linear way to the external forcing. Perhaps most puzzling is the change in glacial period duration at the Middle Pleistocene Transition. From a dynamical systems perspective, this could be a change in frequency locking between the orbital forcing and the climatic response or it could be a non-linear resonance phenomenon. In both cases the climate system shows a non-trivial oscillatory behaviour. From the records it seems that this behaviour can be described by an effective dynamics on a low-dimensional slow manifold. These different possible dynamical behaviours will be discussed. References: Arianna Marchionne, Peter Ditlevsen, and Sebastian Wieczorek, "Three types of nonlinear resonances", arXiv:1605.00858 Peter Ashwin and Peter Ditlevsen, "The middle Pleistocene transition as a generic bifurcation on a slow manifold", Climate Dynamics, 45, 2683, 2015. Peter D. Ditlevsen, "The bifurcation structure and noise assisted transitions in the Pleistocene glacial cycles", Paleoceanography, 24, PA3204, 2009

Homogenized description and retrieval method of nonlinear metasurfaces

Science.gov (United States)

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

Noise in nonlinear nanoelectromechanical resonators

Science.gov (United States)

Guerra Vidal, Diego N.

Nano-Electro-Mechanical Systems (NEMS), due to their nanometer scale size, possess a number of desirable attributes: high sensitivity to applied forces, fast response times, high resonance frequencies and low power consumption. However, ultra small size and low power handling result in unwanted consequences: smaller signal size and higher dissipation, making the NEMS devices more susceptible to external and intrinsic noise. The simplest version of a NEMS, a suspended nanomechanical structure with two distinct excitation states, can be used as an archetypal two state system to study a plethora of fundamental phenomena such as Duffing nonlinearity, stochastic resonance, and macroscopic quantum tunneling at low temperatures. From a technical perspective, there are numerous applications such nanomechanical memory elements, microwave switches and nanomechanical computation. The control and manipulation of the mechanical response of these two state systems can be realized by exploiting a (seemingly) counterintuitive physical phenomenon, Stochastic Resonance: in a noisy nonlinear mechanical system, the presence of noise can enhance the system response to an external stimulus. This Thesis is mainly dedicated to study possible applications of Stochastic Resonance in two-state nanomechanical systems. First, on chip signal amplification by 1/falpha is observed. The effectiveness of the noise assisted amplification is observed to decrease with increasing a. Experimental evidence shows an increase in asymmetry between the two states with increasing noise color. Considering the prevalence of 1/f alpha noise in the materials in integrated circuits, the signal enhancement demonstrated here, suggests beneficial use of the otherwise detrimental noise. Finally, a nanomechanical device, operating as a reprogrammable logic gate, and performing fundamental logic functions such as AND/OR and NAND/NOR is presented. The logic function can be programmed (from AND to OR) dynamically, by

Nonlinear-Based MEMS Sensors and Active Switches for Gas Detection

KAUST Repository

Bouchaala, Adam M.; Jaber, Nizar; Yassine, Omar; Shekhah, Osama; Chernikova, Valeriya; Eddaoudi, Mohamed; Younis, Mohammad I.

2016-01-01

The objective of this paper is to demonstrate the integration of a MOF thin film on electrostatically actuated microstructures to realize a switch triggered by gas and a sensing algorithm based on amplitude tracking. The devices are based on the nonlinear response of micromachined clamped-clamped beams. The microbeams are coated with a metal-organic framework (MOF), namely HKUST-1, to achieve high sensitivity. The softening and hardening nonlinear behaviors of the microbeams are exploited to demonstrate the ideas. For gas sensing, an amplitude-based tracking algorithm is developed to quantify the captured quantity of gas. Then, a MEMS switch triggered by gas using the nonlinear response of the microbeam is demonstrated. Noise analysis is conducted, which shows that the switch has high stability against thermal noise. The proposed switch is promising for delivering binary sensing information, and also can be used directly to activate useful functionalities, such as alarming.

Nonlinear-Based MEMS Sensors and Active Switches for Gas Detection

KAUST Repository

Bouchaala, Adam M.

2016-05-25

The objective of this paper is to demonstrate the integration of a MOF thin film on electrostatically actuated microstructures to realize a switch triggered by gas and a sensing algorithm based on amplitude tracking. The devices are based on the nonlinear response of micromachined clamped-clamped beams. The microbeams are coated with a metal-organic framework (MOF), namely HKUST-1, to achieve high sensitivity. The softening and hardening nonlinear behaviors of the microbeams are exploited to demonstrate the ideas. For gas sensing, an amplitude-based tracking algorithm is developed to quantify the captured quantity of gas. Then, a MEMS switch triggered by gas using the nonlinear response of the microbeam is demonstrated. Noise analysis is conducted, which shows that the switch has high stability against thermal noise. The proposed switch is promising for delivering binary sensing information, and also can be used directly to activate useful functionalities, such as alarming.

Nonlinear-Based MEMS Sensors and Active Switches for Gas Detection.

Science.gov (United States)

Bouchaala, Adam; Jaber, Nizar; Yassine, Omar; Shekhah, Osama; Chernikova, Valeriya; Eddaoudi, Mohamed; Younis, Mohammad I

2016-05-25

The objective of this paper is to demonstrate the integration of a MOF thin film on electrostatically actuated microstructures to realize a switch triggered by gas and a sensing algorithm based on amplitude tracking. The devices are based on the nonlinear response of micromachined clamped-clamped beams. The microbeams are coated with a metal-organic framework (MOF), namely HKUST-1, to achieve high sensitivity. The softening and hardening nonlinear behaviors of the microbeams are exploited to demonstrate the ideas. For gas sensing, an amplitude-based tracking algorithm is developed to quantify the captured quantity of gas. Then, a MEMS switch triggered by gas using the nonlinear response of the microbeam is demonstrated. Noise analysis is conducted, which shows that the switch has high stability against thermal noise. The proposed switch is promising for delivering binary sensing information, and also can be used directly to activate useful functionalities, such as alarming.

Nonlinear optical response of the collagen triple helix and second harmonic microscopy of collagen liquid crystals

Science.gov (United States)

Deniset-Besseau, A.; De Sa Peixoto, P.; Duboisset, J.; Loison, C.; Hache, F.; Benichou, E.; Brevet, P.-F.; Mosser, G.; Schanne-Klein, M.-C.

2010-02-01

Collagen is characterized by triple helical domains and plays a central role in the formation of fibrillar and microfibrillar networks, basement membranes, as well as other structures of the connective tissue. Remarkably, fibrillar collagen exhibits efficient Second Harmonic Generation (SHG) and SHG microscopy proved to be a sensitive tool to score fibrotic pathologies. However, the nonlinear optical response of fibrillar collagen is not fully characterized yet and quantitative data are required to further process SHG images. We therefore performed Hyper-Rayleigh Scattering (HRS) experiments and measured a second order hyperpolarisability of 1.25 10-27 esu for rat-tail type I collagen. This value is surprisingly large considering that collagen presents no strong harmonophore in its amino-acid sequence. In order to get insight into the physical origin of this nonlinear process, we performed HRS measurements after denaturation of the collagen triple helix and for a collagen-like short model peptide [(Pro-Pro-Gly)10]3. It showed that the collagen large nonlinear response originates in the tight alignment of a large number of weakly efficient harmonophores, presumably the peptide bonds, resulting in a coherent amplification of the nonlinear signal along the triple helix. To illustrate this mechanism, we successfully recorded SHG images in collagen liquid solutions by achieving liquid crystalline ordering of the collagen triple helices.

Seismic response of the 'Cut-and Cover' type reactor containment considering nonlinear soil behavior

International Nuclear Information System (INIS)

El-Tahan, H.; Reddy, D.V.

1979-01-01

This paper describes some parametric studies of dynamic soil-structure interaction for the 'cut-and-cover' reactor concept. The dynamic loading considered is a horizontal earthquake motion. The high frequency ranges, which must be considered in the study of soil-structure interaction for nuclear power plants, and the nonlinearity of soil behavior during strong earthquakes are adequately taken into account. Soil nonlinearity is accounted for in an approximate manner using a combination of the 'equivalent linear method' and the method of complex response with complex moduli. The structure considered is a reinforced concrete containment for a 1100 - MWe power plant, buried in a dense sand medium. (orig.)

Nonlinear soil-structure interaction due to base slab uplift on the seismic response of an HTGR plant

International Nuclear Information System (INIS)

Kennedy, R.P.; Short, S.A.; Wesley, D.A.; Lee, T.H.

1975-01-01

The importance of the nonlinear soil-structure interaction effects resulting from substantial base slab uplift occurring during a seismic excitation are evaluated. The structure considered consisted of the containment building and prestressed concrete reactor vessel for a typical HTGR plant. A simplified dynamic mathematical model was utilized consisting of a conventional lumped mass structure with soil-structure interaction accounted for by translational and rotational springs whose properties are determined by elastic half space theory. Three different site soil conditions (a rock site, a moderately stiff soil and a soft soil site) and two levels of horizontal ground motion (0.3g and 0.5g earthquakes) were considered. It may be concluded that linear analysis can be used to conservatively estimate the important behavior of the base slab, even under conditions of substantial base slab uplift. For all cases investigated, linear analysis resulted in higher base overturning moments, greater toe pressures, and greater heel uplift distances than nonlinear analyses. It may also be concluded that the nonlinear effect of uplift does not result in any significant lengthening of the fundamental period of the structure. Also, except in the short period region only negligible differences exist between instructure response spectra based on linear analysis and those based on nonlinear analysis. Finally, for sites in which soil-structure interaction is not significant, as for the rock site, the peak structural response at all locations above the base mat are not significantly influenced by the nonlinear effects of base slab uplift. However, for the two soil sites, the peak shears and moments are, in a few instances, significantly different between linear and nonlinear analyses

New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

Science.gov (United States)

Hosseini, K.; Ayati, Z.; Ansari, R.

2018-04-01

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd-Bullough-Mikhailov and Tzitzéica-Dodd-Bullough equations, are obtained using the expa function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.

A reliable treatment for nonlinear Schroedinger equations

International Nuclear Information System (INIS)

Khani, F.; Hamedi-Nezhad, S.; Molabahrami, A.

2007-01-01

Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation

A lattice Boltzmann model with an amending function for simulating nonlinear partial differential equations

International Nuclear Information System (INIS)

Lin-Jie, Chen; Chang-Feng, Ma

2010-01-01

This paper proposes a lattice Boltzmann model with an amending function for one-dimensional nonlinear partial differential equations (NPDEs) in the form u t + αuu x + βu n u x + γu xx + δu xxx + ζu xxxx = 0. This model is different from existing models because it lets the time step be equivalent to the square of the space step and derives higher accuracy and nonlinear terms in NPDEs. With the Chapman–Enskog expansion, the governing evolution equation is recovered correctly from the continuous Boltzmann equation. The numerical results agree well with the analytical solutions. (general)

A simple non-linear model of immune response

International Nuclear Information System (INIS)

Gutnikov, Sergei; Melnikov, Yuri

2003-01-01

It is still unknown why the adaptive immune response in the natural immune system based on clonal proliferation of lymphocytes requires interaction of at least two different cell types with the same antigen. We present a simple mathematical model illustrating that the system with separate types of cells for antigen recognition and patogen destruction provides more robust adaptive immunity than the system where just one cell type is responsible for both recognition and destruction. The model is over-simplified as we did not have an intention of describing the natural immune system. However, our model provides a tool for testing the proposed approach through qualitative analysis of the immune system dynamics in order to construct more sophisticated models of the immune systems that exist in the living nature. It also opens a possibility to explore specific features of highly non-linear dynamics in nature-inspired computational paradigms like artificial immune systems and immunocomputing . We expect this paper to be of interest not only for mathematicians but also for biologists; therefore we made effort to explain mathematics in sufficient detail for readers without professional mathematical background

Nonlinearly driven harmonics of Alfvén modes

Science.gov (United States)

Zhang, B.; Breizman, B. N.; Zheng, L. J.; Berk, H. L.

2014-01-01

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.

Nonlinearly driven harmonics of Alfvén modes

Energy Technology Data Exchange (ETDEWEB)

Zhang, B., E-mail: bozhang@austin.utexas.edu; Breizman, B. N.; Zheng, L. J.; Berk, H. L. [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)

2014-01-15

In order to study the leading order nonlinear magneto-hydrodynamic (MHD) harmonic response of a plasma in realistic geometry, the AEGIS code has been generalized to account for inhomogeneous source terms. These source terms are expressed in terms of the quadratic corrections that depend on the functional form of a linear MHD eigenmode, such as the Toroidal Alfvén Eigenmode. The solution of the resultant equation gives the second order harmonic response. Preliminary results are presented here.

Modeling of Nonlinear Mechanical Response in CFRP Angle-Ply Laminates

Science.gov (United States)

Ogihara, Shinji

2014-03-01

It is known that the failure process in angle-ply laminate involves matrix cracking and delamination and that they exhibit nonlinear stress-strain relation. There may be a significant effect of the constituent blocked ply thickness on the mechanical behavior of angle-ply laminates. These days, thin prepregs whose thickness is, for example 50 micron, are developed and commercially available. Therefore, we can design wide variety of laminates with various constituent ply thicknesses. In this study, effects of constituent ply thickness on the nonlinear mechanical behavior and the damage behavior of CFRP angle-ply laminates are investigated experimentally. Based on the experimental results, the mechanical response in CFRP angle-ply laminates is modeled by using the finite strain viscoplasticity model. We evaluated the mechanical behavior and damage behavior in CFRP angle-ply laminates with different constituent ply thickness under tensile loading experimentally. It was found that as the constituent ply thickness decreases, the strength and failure strain increases. We also observed difference in damage behavior. The preliminary results of finite strain viscoplasticity model considering the damage effect for laminated composites are shown. A qualitative agreement is obtained.

Nonlinear Optical Response of Polar Semiconductors in the Terahertz Range

Science.gov (United States)

Roman, Eric; Yates, Jonathan; Veithen, Marek; Vanderbilt, David; Souza, Ivo

2006-03-01

Using the Berry-phase finite-field method, we compute from first-principles the recently measured infrared (IR) dispersion of the nonlinear susceptibility (2)circ in III-V zincblende semiconductors. At far-IR (terahertz) frequencies, in addition to the purely electronic response (2)circ∞, the total (2)circ depends on three other parameters, C1, C2, and C3, describing the contributions from ionic motion. They relate to the TO Raman polarizability and the second-order displacement-induced dielectric polarization and forces, respectively. Contrary to a widely-accepted model, but in agreement with the recent experiments on GaAs, ^1 we find that the contribution from mechanical anharmonicity dominates over electrical anharmonicity. By using Richardson extrapolation to evaluate the Berry's phase in k-space by finite differences, we are able to improve the convergence of the nonlinear susceptibility from the usual O[(δk)^2] to O[(δk)^4], dramatically reducing the computational cost. T. Dekorsy, V. A. Yakovlev, W. Seidel, M. Helm, and F. Keilmann, Phys. Rev. Lett. 90, 055508 (2003). C. Flytzanis, Phys. Rev. B 6, 1264 (1972). R. Umari and A. Pasquarello, Phys. Rev. B 68, 085114 (2003).

Effective-medium theory for nonlinear magneto-optics in magnetic granular alloys: cubic nonlinearity

Energy Technology Data Exchange (ETDEWEB)

Granovsky, Alexander B. E-mail: granov@magn.ru; Kuzmichov, Michail V.; Clerc, J.-P.; Inoue, Mitsuteru

2003-03-01

We propose a simple effective-medium approach for calculating the effective dielectric function of a magnetic metal-insulator granular alloy in which there is a weakly nonlinear relation between electric displacement D and electric field E for both constituent materials of the form D{sub i}={epsilon}{sub i}{sup (0)}E{sub i} +{chi}{sub i}{sup (3)}|E{sub i}|{sup 2}E{sub i}. We assume that linear {epsilon}{sub i}{sup (0)} and cubic nonlinear {chi}{sub i}{sup (3)} dielectric functions are diagonal and linear with magnetization non-diagonal components. For such metal-insulator composite magneto-optical effects depend on a light intensity and the effective cubic dielectric function {chi}{sub eff}{sup (3)} can be significantly greater (up to 10{sup 3} times) than that for constituent materials. The calculation scheme is based on the Bergman and Stroud-Hui theory of nonlinear optical properties of granular matter. The giant cubic magneto-optical nonlinearity is found for composites with metallic volume fraction close to the percolation threshold and at a resonance of optical conductivity. It is shown that a composite may exhibit nonlinear magneto-optics even when both constituent materials have no cubic magneto-optical nonlinearity.

Parallel processors and nonlinear structural dynamics algorithms and software

Science.gov (United States)

Belytschko, Ted

1989-01-01

A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

Probabilistic analysis of a materially nonlinear structure

Science.gov (United States)

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.

Arsenite Effects on Mitochondrial Bioenergetics in Human and Mouse Primary Hepatocytes Follow a Nonlinear Dose Response

Directory of Open Access Journals (Sweden)

Hemantkumar Chavan

2017-01-01

Full Text Available Arsenite is a known carcinogen and its exposure has been implicated in a variety of noncarcinogenic health concerns. Increased oxidative stress is thought to be the primary cause of arsenite toxicity and the toxic effect is thought to be linear with detrimental effects reported at all concentrations of arsenite. But the paradigm of linear dose response in arsenite toxicity is shifting. In the present study we demonstrate that arsenite effects on mitochondrial respiration in primary hepatocytes follow a nonlinear dose response. In vitro exposure of primary hepatocytes to an environmentally relevant, moderate level of arsenite results in increased oxidant production that appears to arise from changes in the expression and activity of respiratory Complex I of the mitochondrial proton circuit. In primary hepatocytes the excess oxidant production appears to elicit adaptive responses that promote resistance to oxidative stress and a propensity to increased proliferation. Taken together, these results suggest a nonlinear dose-response characteristic of arsenite with low-dose arsenite promoting adaptive responses in a process known as mitohormesis, with transient increase in ROS levels acting as transducers of arsenite-induced mitohormesis.

Multi-cracks identification based on the nonlinear vibration response of beams subjected to moving harmonic load

Directory of Open Access Journals (Sweden)

Chouiyakh H.

2016-01-01

Full Text Available The aim of this work is to investigate the nonlinear forced vibration of beams containing an arbitrary number of cracks and to perform a multi-crack identification procedure based on the obtained signals. Cracks are assumed to be open and modelled trough rotational springs linking two adjacent sub-beams. Forced vibration analysis is performed by a developed time differential quadrature method. The obtained nonlinear vibration responses are analyzed by Huang Hilbert Transform. The instantaneous frequency is used as damage index tool for cracks detection.

Under which climate and soil conditions the plant productivity-precipitation relationship is linear or nonlinear?

Science.gov (United States)

Ye, Jian-Sheng; Pei, Jiu-Ying; Fang, Chao

2018-03-01

Understanding under which climate and soil conditions the plant productivity-precipitation relationship is linear or nonlinear is useful for accurately predicting the response of ecosystem function to global environmental change. Using long-term (2000-2016) net primary productivity (NPP)-precipitation datasets derived from satellite observations, we identify >5600pixels in the North Hemisphere landmass that fit either linear or nonlinear temporal NPP-precipitation relationships. Differences in climate (precipitation, radiation, ratio of actual to potential evapotranspiration, temperature) and soil factors (nitrogen, phosphorous, organic carbon, field capacity) between the linear and nonlinear types are evaluated. Our analysis shows that both linear and nonlinear types exhibit similar interannual precipitation variabilities and occurrences of extreme precipitation. Permutational multivariate analysis of variance suggests that linear and nonlinear types differ significantly regarding to radiation, ratio of actual to potential evapotranspiration, and soil factors. The nonlinear type possesses lower radiation and/or less soil nutrients than the linear type, thereby suggesting that nonlinear type features higher degree of limitation from resources other than precipitation. This study suggests several factors limiting the responses of plant productivity to changes in precipitation, thus causing nonlinear NPP-precipitation pattern. Precipitation manipulation and modeling experiments should combine with changes in other climate and soil factors to better predict the response of plant productivity under future climate. Copyright © 2017 Elsevier B.V. All rights reserved.

The Human Cochlear Mechanical Nonlinearity Inferred via Psychometric Functions

Directory of Open Access Journals (Sweden)

Nizami Lance

2013-12-01

Extension of the model of Schairer and colleagues results in credible cochlear nonlinearities in man, suggesting that forward-masking provides a non-invasive way to infer the human mechanical cochlear nonlinearity.

Investigation of Nonlinear Site Response and Seismic Compression from Case History Analysis and Laboratory Testing

Science.gov (United States)

Yee, Eric

In this thesis I address a series of issues related to ground failure and ground motions during earthquakes. A major component is the evaluation of cyclic volumetric strain behavior of unsaturated soils, more commonly known as seismic compression, from advanced laboratory testing. Another major component is the application of nonlinear and equivalent linear ground response analyses to large-strain problems involving highly nonlinear dynamic soil behavior. These two components are merged in the analysis of a truly unique and crucial field case history of nonlinear site response and seismic compression. My first topic concerns dynamic soil testing for relatively small strain dynamic soil properties such as threshold strains, gammatv. Such testing is often conducted using specialized devices such as dual-specimen simple-shear, as devices configured for large strain testing produce noisy signals in the small strain range. Working with a simple shear device originally developed for large-strain testing, I extend its low-strain capabilities by characterizing noisy signals and utilizing several statistical methods to extract meaningful responses in the small strain range. I utilize linear regression of a transformed variable to estimate the cyclic shear strain from a noisy signal and the confidence interval on its amplitude. I utilize Kernel regression with the Nadaraya-Watson estimator and a Gaussian kernel to evaluate vertical strain response. A practical utilization of these techniques is illustrated by evaluating threshold shear strains for volume change with a procedure that takes into account uncertainties in the measured shear and vertical strains. My second topic concerns the seismic compression characteristics of non-plastic and low-plasticity silty sands with varying fines content (10 ≤ FC ≤ 60%). Simple shear testing was performed on various sand-fines mixtures at a range of modified Proctor relative compaction levels ( RC) and degrees-of-saturation (S

High Tc superconducting nonlinear inductance and quick response magnetic sensor devices

International Nuclear Information System (INIS)

Uchiyama, T.; Mohri, K.; Ozeki, A.; Shibata, T.

1990-01-01

A flux penetration model considering the demagnetizing effect is presented in order to analyze the nonlinear inductance characteristics for HTcSC. Various quick response magnetic devices such as modulators, magnetic switches and magnetic sensors were constructed. The magnetizing frequency can be set up more than 10 MHz which is difficult to achieve with the conventional ferromagnetic bulk cores. The cut-off frequency of 1.6 MHz was obtained for the sensors using the HTcSC cores at a magnetizing frequency of 11.5 MHz

Green's function-stochastic methods framework for probing nonlinear evolution problems: Burger's equation, the nonlinear Schroedinger's equation, and hydrodynamic organization of near-molecular-scale vorticity

International Nuclear Information System (INIS)

Keanini, R.G.

2011-01-01

Research highlights: → Systematic approach for physically probing nonlinear and random evolution problems. → Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. → Organization of near-molecular scale vorticity mediated by hydrodynamic modes. → Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the

Nonlinear-Based MEMS Sensors and Active Switches for Gas Detection

Directory of Open Access Journals (Sweden)

Adam Bouchaala

2016-05-01

Full Text Available The objective of this paper is to demonstrate the integration of a MOF thin film on electrostatically actuated microstructures to realize a switch triggered by gas and a sensing algorithm based on amplitude tracking. The devices are based on the nonlinear response of micromachined clamped-clamped beams. The microbeams are coated with a metal-organic framework (MOF, namely HKUST-1, to achieve high sensitivity. The softening and hardening nonlinear behaviors of the microbeams are exploited to demonstrate the ideas. For gas sensing, an amplitude-based tracking algorithm is developed to quantify the captured quantity of gas. Then, a MEMS switch triggered by gas using the nonlinear response of the microbeam is demonstrated. Noise analysis is conducted, which shows that the switch has high stability against thermal noise. The proposed switch is promising for delivering binary sensing information, and also can be used directly to activate useful functionalities, such as alarming.

Nonlinear-Based MEMS Sensors and Active Switches for Gas Detection

Science.gov (United States)

Bouchaala, Adam; Jaber, Nizar; Yassine, Omar; Shekhah, Osama; Chernikova, Valeriya; Eddaoudi, Mohamed; Younis, Mohammad I.

2016-01-01

The objective of this paper is to demonstrate the integration of a MOF thin film on electrostatically actuated microstructures to realize a switch triggered by gas and a sensing algorithm based on amplitude tracking. The devices are based on the nonlinear response of micromachined clamped-clamped beams. The microbeams are coated with a metal-organic framework (MOF), namely HKUST-1, to achieve high sensitivity. The softening and hardening nonlinear behaviors of the microbeams are exploited to demonstrate the ideas. For gas sensing, an amplitude-based tracking algorithm is developed to quantify the captured quantity of gas. Then, a MEMS switch triggered by gas using the nonlinear response of the microbeam is demonstrated. Noise analysis is conducted, which shows that the switch has high stability against thermal noise. The proposed switch is promising for delivering binary sensing information, and also can be used directly to activate useful functionalities, such as alarming. PMID:27231914

Nonlinear stability of source defects in the complex Ginzburg–Landau equation

International Nuclear Information System (INIS)

Beck, Margaret; Nguyen, Toan T; Sandstede, Björn; Zumbrun, Kevin

2014-01-01

In an appropriate moving coordinate frame, source defects are time-periodic solutions to reaction–diffusion equations that are spatially asymptotic to spatially periodic wave trains whose group velocities point away from the core of the defect. In this paper, we rigorously establish nonlinear stability of spectrally stable source defects in the complex Ginzburg–Landau equation. Due to the outward transport at the far field, localized perturbations may lead to a highly non-localized response even on the linear level. To overcome this, we first investigate in detail the dynamics of the solution to the linearized equation. This allows us to determine an approximate solution that satisfies the full equation up to and including quadratic terms in the nonlinearity. This approximation utilizes the fact that the non-localized phase response, resulting from the embedded zero eigenvalues, can be captured, to leading order, by the nonlinear Burgers equation. The analysis is completed by obtaining detailed estimates for the resolvent kernel and pointwise estimates for Green's function, which allow one to close a nonlinear iteration scheme. (paper)

Nonlinear dynamic response of an electrically actuated imperfect microbeam resonator

KAUST Repository

Ruzziconi, Laura

2013-08-04

We present a study of the dynamic behavior of a MEMS device constituted of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. The nonlinear behavior is highlighted, which includes ranges of multistability, where the non-resonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is capable also to capture the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach. Copyright © 2013 by ASME.

Examination of the foreign body response to biomaterials by nonlinear intravital microscopy

OpenAIRE

Dondossola, Eleonora; Holzapfel, Boris M.; Alexander, Stephanie; Filippini, Stefano; Hutmacher, Dietmar W.; Friedl, Peter

2016-01-01

Implanted biomaterials often fail because they elicit a foreign body response (FBR) and concomitant fibrotic encapsulation. To design clinically relevant interference approaches, it is crucial to first examine the FBR mechanisms. Here, we report the development and validation of infrared-excited nonlinear microscopy to resolve the three-dimensional (3D) organization and fate of 3D-electrospun scaffolds implanted deep into the skin of mice, and the following step-wise FBR process. We observed ...

Broken space-time symmetries and mechanisms of rectification of ac fields by nonlinear (non)adiabatic response

DEFF Research Database (Denmark)

Denisov, S.; Flach, S.; Ovchinnikov, A. A.

2002-01-01

We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries, which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is em...... is employed to explain the effect. We consider a case of a particle in a periodic potential as an example and discuss the relevant symmetry breakings and the mechanisms of rectification of the current in such a system.......We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries, which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response...

Nonlinear normal vibration modes in the dynamics of nonlinear elastic systems

International Nuclear Information System (INIS)

Mikhlin, Yu V; Perepelkin, N V; Klimenko, A A; Harutyunyan, E

2012-01-01

Nonlinear normal modes (NNMs) are a generalization of the linear normal vibrations. By the Kauderer-Rosenberg concept in the regime of the NNM all position coordinates are single-values functions of some selected position coordinate. By the Shaw-Pierre concept, the NNM is such a regime when all generalized coordinates and velocities are univalent functions of a couple of dominant (active) phase variables. The NNMs approach is used in some applied problems. In particular, the Kauderer-Rosenberg NNMs are analyzed in the dynamics of some pendulum systems. The NNMs of forced vibrations are investigated in a rotor system with an isotropic-elastic shaft. A combination of the Shaw-Pierre NNMs and the Rauscher method is used to construct the forced NNMs and the frequency responses in the rotor dynamics.

The relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations

International Nuclear Information System (INIS)

Liu Chunping; Liu Xiaoping

2004-01-01

First, we investigate the solitary wave solutions of the Burgers equation and the KdV equation, which are obtained by using the hyperbolic function method. Then we present a theorem which will not only give us a clear relation among the hyperbolic-function-type exact solutions of nonlinear evolution equations, but also provide us an approach to construct new exact solutions in complex scalar field. Finally, we apply the theorem to the KdV-Burgers equation and obtain its new exact solutions

Nonlinear systems

CERN Document Server

Palmero, Faustino; Lemos, M; Sánchez-Rey, Bernardo; Casado-Pascual, Jesús

2018-01-01

This book presents an overview of the most recent advances in nonlinear science. It provides a unified view of nonlinear properties in many different systems and highlights many  new developments. While volume 1 concentrates on mathematical theory and computational techniques and challenges, which are essential for the study of nonlinear science, this second volume deals with nonlinear excitations in several fields. These excitations can be localized and transport energy and matter in the form of breathers, solitons, kinks or quodons with very different characteristics, which are discussed in the book. They can also transport electric charge, in which case they are known as polarobreathers or solectrons. Nonlinear excitations can influence function and structure in biology, as for example, protein folding. In crystals and other condensed matter, they can modify transport properties, reaction kinetics and interact with defects. There are also engineering applications in electric lattices, Josephson junction a...

Finite element-implementation of creep of concrete for thin-shell analysis using nonlinear constitutive relations and creep compliance functions

International Nuclear Information System (INIS)

Walter, H.; Mang, H.A.

1991-01-01

A procedure for combining nonlinear short-time behavior of concrete with nonlinear creep compliance functions is presented. It is an important ingredient of a computer code for nonlinear finite element (FE) analysis of prestressed concrete shells, considering creep, shrinkage and ageing of concrete, and relaxation of the prestressing steel. The program was developed at the Institute for Strength of Materials of Technical University of Vienna, Austria. The procedure has resulted from efforts to extend the range of application of a Finite Element program, abbreviated as FESIA, which originally was capable of modeling reinforeced concrete in the context of thin-shell analysis, using nonlinear constitutive relations for both, conrete and steel. The extension encompasses the time-dependent behavior of concrete: Creep, shrinkage and ageing. Creep is modeled with the help of creep compliance functions which may be nonlinear to conform with the short-time constitutive relations. Ageing causes an interdependence between long-time and short-time deformations. The paper contains a description of the physical background of the procedure and hints on the implementation of the algorithm. The focus is on general aspects. Details of the aforementioned computer program are considered only where this is inevitable. (orig.)

A thermodynamic approach to nonlinear ultrasonics for material state awareness and prognosis

Science.gov (United States)

Chillara, Vamshi Krishna

2017-11-01

We develop a thermodynamic framework for modeling nonlinear ultrasonic damage sensing and prognosis in materials undergoing progressive damage. The framework is based on the internal variable approach and relies on the construction of a pseudo-elastic strain energy function that captures the energetics associated with the damage progression. The pseudo-elastic strain energy function is composed of two energy functions—one that describes how a material stores energy in an elastic fashion and the other describes how material dissipates energy or stores it in an inelastic fashion. Experimental motivation for the choice of the above two functionals is discussed and some specific choices pertaining to damage progression during fatigue and creep are presented. The thermodynamic framework is employed to model the nonlinear response of material undergoing stress relaxation and creep-like degradation. For each of the above cases, evolution of the nonlinearity parameter with damage as well as with macroscopic measurables like accumulated plastic strain is obtained.

Forced phase-locked response of a nonlinear system with time delay after Hopf bifurcation

International Nuclear Information System (INIS)

Ji, J.C.; Hansen, Colin H.

2005-01-01

The trivial equilibrium of a nonlinear autonomous system with time delay may become unstable via a Hopf bifurcation of multiplicity two, as the time delay reaches a critical value. This loss of stability of the equilibrium is associated with two coincident pairs of complex conjugate eigenvalues crossing the imaginary axis. The resultant dynamic behaviour of the corresponding nonlinear non-autonomous system in the neighbourhood of the Hopf bifurcation is investigated based on the reduction of the infinite-dimensional problem to a four-dimensional centre manifold. As a result of the interaction between the Hopf bifurcating periodic solutions and the external periodic excitation, a primary resonance can occur in the forced response of the system when the forcing frequency is close to the Hopf bifurcating periodic frequency. The method of multiple scales is used to obtain four first-order ordinary differential equations that determine the amplitudes and phases of the phase-locked periodic solutions. The first-order approximations of the periodic solutions are found to be in excellent agreement with those obtained by direct numerical integration of the delay-differential equation. It is also found that the steady state solutions of the nonlinear non-autonomous system may lose their stability via either a pitchfork or Hopf bifurcation. It is shown that the primary resonance response may exhibit symmetric and asymmetric phase-locked periodic motions, quasi-periodic motions, chaotic motions, and coexistence of two stable motions

Theory of heart biomechanics, biophysics, and nonlinear dynamics of cardiac function

CERN Document Server

Hunter, Peter; McCulloch, Andrew

1991-01-01

In recent years there has been a growth in interest in studying the heart from the perspective of the physical sciences: mechanics, fluid flow, electromechanics. This volume is the result of a workshop held in July 1989 at the Institute for Nonlinear Sciences at the University of California at San Diego that brought together scientists and clinicians with graduate students and postdoctoral fellows who shared an interest in the heart. The chapters were prepared by the invited speakers as didactic reviews of their subjects but also include the structure, mechanical properties, and function of the heart and the myocardium, electrical activity of the heart and myocardium, and mathematical models of heart function.

Via generalized function projective synchronization in nonlinear Schrödinger equation for secure communication

Science.gov (United States)

Zhao, L. W.; Du, J. G.; Yin, J. L.

2018-05-01

This paper proposes a novel secured communication scheme in a chaotic system by applying generalized function projective synchronization of the nonlinear Schrödinger equation. This phenomenal approach guarantees a secured and convenient communication. Our study applied the Melnikov theorem with an active control strategy to suppress chaos in the system. The transmitted information signal is modulated into the parameter of the nonlinear Schrödinger equation in the transmitter and it is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory and the adaptive control technique, the controllers are designed to make two identical nonlinear Schrödinger equation with the unknown parameter asymptotically synchronized. The numerical simulation results of our study confirmed the validity, effectiveness and the feasibility of the proposed novel synchronization method and error estimate for a secure communication. The Chaos masking signals of the information communication scheme, further guaranteed a safer and secured information communicated via this approach.

Development of a simple detector response function generation program: The CEARDRFs code

International Nuclear Information System (INIS)

Wang Jiaxin; Wang Zhijian; Peeples, Johanna; Yu Huawei; Gardner, Robin P.

2012-01-01

A simple Monte Carlo program named CEARDRFs has been developed to generate very accurate detector response functions (DRFs) for scintillation detectors. It utilizes relatively rigorous gamma-ray transport with simple electron transport, and accounts for two phenomena that have rarely been treated: scintillator non-linearity and the variable flat continuum part of the DRF. It has been proven that these physics and treatments work well for 3×3″ and 6×6″ cylindrical NaI detector in CEAR's previous work. Now this approach has been expanded to cover more scintillation detectors with various common shapes and sizes. Benchmark experiments of 2×2″ cylindrical BGO detector and 2×4×16″ rectangular NaI detector have been carried out at CEAR with various radiactive sources. The simulation results of CEARDRFs have also been compared with MCNP5 calculations. The benchmark and comparison show that CEARDRFs can generate very accurate DRFs (more accurate than MCNP5) at a very fast speed (hundred times faster than MCNP5). The use of this program can significantly increase the accuracy of applications relying on detector spectroscopy like prompt gamma-ray neutron activation analysis, X-ray fluorescence analysis, oil well logging and homeland security. - Highlights: ► CEARDRF has been developed to generate detector response functions (DRFs) for scintillation detectors a. ► Generated DRFs are very accurate. ► Simulation speed is hundreds of times faster than MCNP5. ► It utilizes rigorous gamma-ray transport with simple electron transport. ► It also accounts for scintillator non-linearity and the variable flat continuum part.

Robust Optimization Using Supremum of the Objective Function for Nonlinear Programming Problems

International Nuclear Information System (INIS)

Lee, Se Jung; Park, Gyung Jin

2014-01-01

In the robust optimization field, the robustness of the objective function emphasizes an insensitive design. In general, the robustness of the objective function can be achieved by reducing the change of the objective function with respect to the variation of the design variables and parameters. However, in conventional methods, when an insensitive design is emphasized, the performance of the objective function can be deteriorated. Besides, if the numbers of the design variables are increased, the numerical cost is quite high in robust optimization for nonlinear programming problems. In this research, the robustness index for the objective function and a process of robust optimization are proposed. Moreover, a method using the supremum of linearized functions is also proposed to reduce the computational cost. Mathematical examples are solved for the verification of the proposed method and the results are compared with those from the conventional methods. The proposed approach improves the performance of the objective function and its efficiency

Response of MDOF strongly nonlinear systems to fractional Gaussian noises

Energy Technology Data Exchange (ETDEWEB)

Deng, Mao-Lin; Zhu, Wei-Qiu, E-mail: wqzhu@zju.edu.cn [Department of Mechanics, State Key Laboratory of Fluid Power and Mechatronic Systems, Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou 310027 (China)

2016-08-15

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises.

Science.gov (United States)

Deng, Mao-Lin; Zhu, Wei-Qiu

2016-08-01

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Response of MDOF strongly nonlinear systems to fractional Gaussian noises

International Nuclear Information System (INIS)

Deng, Mao-Lin; Zhu, Wei-Qiu

2016-01-01

In the present paper, multi-degree-of-freedom strongly nonlinear systems are modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems (including quasi-non-integrable, completely integrable and non-resonant, completely integrable and resonant, partially integrable and non-resonant, and partially integrable and resonant Hamiltonian systems) driven by fractional Gaussian noise is introduced. The averaged fractional stochastic differential equations (SDEs) are derived. The simulation results for some examples show that the averaged SDEs can be used to predict the response of the original systems and the simulation time for the averaged SDEs is less than that for the original systems.

Quantitative theory of driven nonlinear brain dynamics.

Science.gov (United States)

Roberts, J A; Robinson, P A

2012-09-01

Strong periodic stimuli such as bright flashing lights evoke nonlinear responses in the brain and interact nonlinearly with ongoing cortical activity, but the underlying mechanisms for these phenomena are poorly understood at present. The dominant features of these experimentally observed dynamics are reproduced by the dynamics of a quantitative neural field model subject to periodic drive. Model power spectra over a range of drive frequencies show agreement with multiple features of experimental measurements, exhibiting nonlinear effects including entrainment over a range of frequencies around the natural alpha frequency f(α), subharmonic entrainment near 2f(α), and harmonic generation. Further analysis of the driven dynamics as a function of the drive parameters reveals rich nonlinear dynamics that is predicted to be observable in future experiments at high drive amplitude, including period doubling, bistable phase-locking, hysteresis, wave mixing, and chaos indicated by positive Lyapunov exponents. Moreover, photosensitive seizures are predicted for physiologically realistic model parameters yielding bistability between healthy and seizure dynamics. These results demonstrate the applicability of neural field models to the new regime of periodically driven nonlinear dynamics, enabling interpretation of experimental data in terms of specific generating mechanisms and providing new tests of the theory. Copyright © 2012 Elsevier Inc. All rights reserved.

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

Science.gov (United States)

Donges, Jonathan; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik; Marwan, Norbert; Dijkstra, Henk; Kurths, Jürgen

2016-04-01

We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. pyunicorn is available online at https://github.com/pik-copan/pyunicorn. Reference: J.F. Donges, J. Heitzig, B. Beronov, M. Wiedermann, J. Runge, Q.-Y. Feng, L. Tupikina, V. Stolbova, R.V. Donner, N. Marwan, H.A. Dijkstra, and J. Kurths, Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package, Chaos 25, 113101 (2015), DOI: 10.1063/1.4934554, Preprint: arxiv.org:1507.01571 [physics.data-an].

Comparison of Damage Models for Predicting the Non-Linear Response of Laminates Under Matrix Dominated Loading Conditions

Science.gov (United States)

Schuecker, Clara; Davila, Carlos G.; Rose, Cheryl A.

2010-01-01

Five models for matrix damage in fiber reinforced laminates are evaluated for matrix-dominated loading conditions under plane stress and are compared both qualitatively and quantitatively. The emphasis of this study is on a comparison of the response of embedded plies subjected to a homogeneous stress state. Three of the models are specifically designed for modeling the non-linear response due to distributed matrix cracking under homogeneous loading, and also account for non-linear (shear) behavior prior to the onset of cracking. The remaining two models are localized damage models intended for predicting local failure at stress concentrations. The modeling approaches of distributed vs. localized cracking as well as the different formulations of damage initiation and damage progression are compared and discussed.

A class of non-linear exposure-response models suitable for health impact assessment applicable to large cohort studies of ambient air pollution.

Science.gov (United States)

Nasari, Masoud M; Szyszkowicz, Mieczysław; Chen, Hong; Crouse, Daniel; Turner, Michelle C; Jerrett, Michael; Pope, C Arden; Hubbell, Bryan; Fann, Neal; Cohen, Aaron; Gapstur, Susan M; Diver, W Ryan; Stieb, David; Forouzanfar, Mohammad H; Kim, Sun-Young; Olives, Casey; Krewski, Daniel; Burnett, Richard T

2016-01-01

The effectiveness of regulatory actions designed to improve air quality is often assessed by predicting changes in public health resulting from their implementation. Risk of premature mortality from long-term exposure to ambient air pollution is the single most important contributor to such assessments and is estimated from observational studies generally assuming a log-linear, no-threshold association between ambient concentrations and death. There has been only limited assessment of this assumption in part because of a lack of methods to estimate the shape of the exposure-response function in very large study populations. In this paper, we propose a new class of variable coefficient risk functions capable of capturing a variety of potentially non-linear associations which are suitable for health impact assessment. We construct the class by defining transformations of concentration as the product of either a linear or log-linear function of concentration multiplied by a logistic weighting function. These risk functions can be estimated using hazard regression survival models with currently available computer software and can accommodate large population-based cohorts which are increasingly being used for this purpose. We illustrate our modeling approach with two large cohort studies of long-term concentrations of ambient air pollution and mortality: the American Cancer Society Cancer Prevention Study II (CPS II) cohort and the Canadian Census Health and Environment Cohort (CanCHEC). We then estimate the number of deaths attributable to changes in fine particulate matter concentrations over the 2000 to 2010 time period in both Canada and the USA using both linear and non-linear hazard function models.

Position Control of Pneumatic Actuator Using Self-Regulation Nonlinear PID

Directory of Open Access Journals (Sweden)

Syed Najib Syed Salim

2014-01-01

Full Text Available The enhancement of nonlinear PID (N-PID controller for a pneumatic positioning system is proposed to improve the performance of this controller. This is executed by utilizing the characteristic of rate variation of the nonlinear gain that is readily available in N-PID controller. The proposed equation, namely, self-regulation nonlinear function (SNF, is used to reprocess the error signal with the purpose of generating the value of the rate variation, continuously. With the addition of this function, a new self-regulation nonlinear PID (SN-PID controller is proposed. The proposed controller is then implemented to a variably loaded pneumatic actuator. Simulation and experimental tests are conducted with different inputs, namely, step, multistep, and random waveforms, to evaluate the performance of the proposed technique. The results obtained have been proven as a novel initiative at examining and identifying the characteristic based on a new proposal controller resulting from N-PID controller. The transient response is improved by a factor of 2.2 times greater than previous N-PID technique. Moreover, the performance of pneumatic positioning system is remarkably good under various loads.

A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions

Influence of Gaussian white noise on the frequency-dependent first nonlinear polarizability of doped quantum dot

Energy Technology Data Exchange (ETDEWEB)

Ganguly, Jayanta [Department of Chemistry, Brahmankhanda Basapara High School, Basapara, Birbhum 731215, West Bengal (India); Ghosh, Manas, E-mail: pcmg77@rediffmail.com [Department of Chemistry, Physical Chemistry Section, Visva Bharati University, Santiniketan, Birbhum 731 235, West Bengal (India)

2014-05-07

We investigate the profiles of diagonal components of frequency-dependent first nonlinear (β{sub xxx} and β{sub yyy}) optical response of repulsive impurity doped quantum dots. We have assumed a Gaussian function to represent the dopant impurity potential. This study primarily addresses the role of noise on the polarizability components. We have invoked Gaussian white noise consisting of additive and multiplicative characteristics (in Stratonovich sense). The doped system has been subjected to an oscillating electric field of given intensity, and the frequency-dependent first nonlinear polarizabilities are computed. The noise characteristics are manifested in an interesting way in the nonlinear polarizability components. In case of additive noise, the noise strength remains practically ineffective in influencing the optical responses. The situation completely changes with the replacement of additive noise by its multiplicative analog. The replacement enhances the nonlinear optical response dramatically and also causes their maximization at some typical value of noise strength that depends on oscillation frequency.

Assessment of modal-pushover-based scaling procedure for nonlinear response history analysis of ordinary standard bridges

Science.gov (United States)

Kalkan, E.; Kwong, N.

2012-01-01

The earthquake engineering profession is increasingly utilizing nonlinear response history analyses (RHA) to evaluate seismic performance of existing structures and proposed designs of new structures. One of the main ingredients of nonlinear RHA is a set of ground motion records representing the expected hazard environment for the structure. When recorded motions do not exist (as is the case in the central United States) or when high-intensity records are needed (as is the case in San Francisco and Los Angeles), ground motions from other tectonically similar regions need to be selected and scaled. The modal-pushover-based scaling (MPS) procedure was recently developed to determine scale factors for a small number of records such that the scaled records provide accurate and efficient estimates of “true” median structural responses. The adjective “accurate” refers to the discrepancy between the benchmark responses and those computed from the MPS procedure. The adjective “efficient” refers to the record-to-record variability of responses. In this paper, the accuracy and efficiency of the MPS procedure are evaluated by applying it to four types of existing Ordinary Standard bridges typical of reinforced concrete bridge construction in California. These bridges are the single-bent overpass, multi-span bridge, curved bridge, and skew bridge. As compared with benchmark analyses of unscaled records using a larger catalog of ground motions, it is demonstrated that the MPS procedure provided an accurate estimate of the engineering demand parameters (EDPs) accompanied by significantly reduced record-to-record variability of the EDPs. Thus, it is a useful tool for scaling ground motions as input to nonlinear RHAs of Ordinary Standard bridges.

Dynamical soil-structure interactions: influence of soil behaviour nonlinearities

International Nuclear Information System (INIS)

Gandomzadeh, Ali

2011-01-01

the soil and the response of the soil-structure system. Through these parametric studies we show that depending on the soil properties, frequency content of the soil response could change significantly due to the soil nonlinearity. The peaks of the transfer function between free field and outcropping responses shift to lower frequencies and amplification happens at this frequency range. Amplification reduction for the high frequencies and even de-amplification may happen for high level input motions. These changes influence the structural response. We show that depending on the combination of the fundamental frequency of the structure and the the natural frequency of the soil, the effect of soil-structure interaction could be significant or negligible. However, the effect of structure weight and rocking of the superstructure could change the results. Finally, the basin of Nice is used as an example of wave propagation on a heterogeneous nonlinear media and dynamic soil-structure interaction. The basin response is strongly dependent on the combination of soil nonlinearity, topographic effects and impedance contrast between soil layers. For the selected structures and soil profiles of this work, the performed numerical simulations show that the shift of the fundamental frequency is not a good index to discriminate linear from nonlinear soil behavior. (author)

Nonlinear resonant ultrasound spectroscopy (NRUS) applied to damage assessment in bone

Science.gov (United States)

Muller, Marie; Sutin, Alexander; Guyer, Robert; Talmant, Maryline; Laugier, Pascal; Johnson, Paul A.

2005-12-01

Nonlinear resonant ultrasound spectroscopy (NRUS) is a resonance-based technique exploiting the significant nonlinear behavior of damaged materials. In NRUS, the resonant frequency(ies) of an object is studied as a function of the excitation level. As the excitation level increases, the elastic nonlinearity is manifest by a shift in the resonance frequency. This study shows the feasibility of this technique for application to damage assessment in bone. Two samples of bovine cortical bone were subjected to progressive damage induced by application of mechanical cycling. Before cycling commenced, and at each step in the cycling process, NRUS was applied for damage assessment. For independent assessment of damage, high-energy x-ray computed tomography imaging was performed but was only useful in identifying the prominent cracks. As the integral quantity of damage increased, NRUS revealed a corresponding increase in the nonlinear response. The measured change in nonlinear response is much more sensitive than the change in linear modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work must be carried out for a better understanding of the physical nature of damaged bone and for the ultimate goal of the challenging in vivo implementation of the technique.

Orientation phenomena in chromophore DR1-containing polymer films and their non-linear optical response

International Nuclear Information System (INIS)

Moencke, Doris; Mountrichas, Grigoris; Pispas, Stergios; Kamitsos, Efstratios I.

2011-01-01

The effectiveness of chromophore alignment in polymer films following corona poling can be assessed by the generated second harmonic signal. Optimization of the stability and strength of this nonlinear optical response may improve with a better understanding of the underlying principal order phenomena. Structural analysis by vibrational, optical, and 1 H NMR spectroscopy reveals side chain tacticity, aggregation effects, and changes in orientation as a function of temperature. Co-polymers with the functionalized chromophore Disperse Red 1 methacrylate (MDR1) were prepared for three different methacrylate types. High side chain polarity and short side chain length increase generally chromophore aggregation in films, whereas the very long poly-ether side chains in PMEO based co-polymers are wrapped separately around the DR1 entities. Side chain tacticity depends on space requirements, but also on the capacity of side groups to form OH-bridges. Side chain tacticity might present an additional parameter for the assessment of chromophore aggregation and poling induced alignments. Stepwise heating of co-polymer films causes an increase in the number of random over ordered side chain arrangements. Cross-linking by anhydride formation is observed after heating the methacrylic acid based co-polymer.

Linking structure and activity in nonlinear spiking networks.

Directory of Open Access Journals (Sweden)

Gabriel Koch Ocker

2017-06-01

Full Text Available Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities-including those of different cell types-combine with connectivity to shape population activity and function.

Linking structure and activity in nonlinear spiking networks.

Science.gov (United States)

Ocker, Gabriel Koch; Josić, Krešimir; Shea-Brown, Eric; Buice, Michael A

2017-06-01

Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural activity arises from the structure of neural connectivity and intrinsic neural dynamics. This problem of structure-driven activity has drawn major interest in computational neuroscience. Existing methods for relating activity and architecture in spiking networks rely on linearizing activity around a central operating point and thus fail to capture the nonlinear responses of individual neurons that are the hallmark of neural information processing. Here, we overcome this limitation and present a new relationship between connectivity and activity in networks of nonlinear spiking neurons by developing a diagrammatic fluctuation expansion based on statistical field theory. We explicitly show how recurrent network structure produces pairwise and higher-order correlated activity, and how nonlinearities impact the networks' spiking activity. Our findings open new avenues to investigating how single-neuron nonlinearities-including those of different cell types-combine with connectivity to shape population activity and function.

Studies of biaxial mechanical properties and nonlinear finite element modeling of skin.

Science.gov (United States)

Shang, Xituan; Yen, Michael R T; Gaber, M Waleed

2010-06-01

The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.

Chaotic synchronization of two complex nonlinear oscillators

International Nuclear Information System (INIS)

Mahmoud, Gamal M.; Mahmoud, Emad E.; Farghaly, Ahmed A.; Aly, Shaban A.

2009-01-01

Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing's oscillators. Physica A 2001;292:193-206], a system of periodically forced complex Duffing's oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schroedinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

A Stream Function Theory Based Calculation of Wave Kinematics for Very Steep Waves Using a Novel Non-linear Stretching Technique

DEFF Research Database (Denmark)

Stroescu, Ionut Emanuel; Sørensen, Lasse; Frigaard, Peter Bak

2016-01-01

A non-linear stretching method was implemented for stream function theory to solve wave kinematics for physical conditions close to breaking waves in shallow waters, with wave heights limited by the water depth. The non-linear stretching method proves itself robust, efficient and fast, showing good...

Non-linear dielectric monitoring of biological suspensions

International Nuclear Information System (INIS)

Treo, E F; Felice, C J

2007-01-01

Non-linear dielectric spectroscopy as a tool for in situ monitoring of enzyme assumes a non-linear behavior of the sample when a sinusoidal voltage is applied to it. Even many attempts have been made to improve the original experiments, all of them had limited success. In this paper we present upgrades made to a non-linear dielectric spectrometer developed and the results obtained when using different cells. We emphasized on the electrode surface, characterizing the grinding and polishing procedure. We found that the biological medium does not behave as expected, and the non-linear response is generated in the electrode-electrolyte interface. The electrochemistry of this interface can bias unpredictably the measured non-linear response

Multiscale numerical study on ferroelectric nonlinear response of PZT thin films (Conference Presentation)

Science.gov (United States)

Wakabayashi, Hiroki; Uetsuji, Yasutomo; Tsuchiya, Kazuyoshi

2017-06-01

PZT thin films have excellent performance in deformation precision and response speed, so it is used widely for actuators and sensors of Micro Electro Mechanical System (MEMS). Although PZT thin films outputs large piezoelectricity at morphotropic phase bounfary (MPB), it shows a complicated hysteresis behavior caused by domain switching and structural phase transition between tetragonal and rhombohedral. In general, PZT thin films have some characteristic crystal morphologies. Additionally mechanical strains occur by lattice mismatch with substrate. Therefore it is important for fabrication and performance improvement of PZT thin films to understand the relation between macroscopic hysteresis response and microstructural changes. In this study, a multiscale nonlinear finite element simulation was proposed for PZT thin films at morphotropic phase boundary (MPB) on the substrate. The homogenization theory was employed for scale-bridging between macrostructure and microstructure. Figure 1 shows the proposed multiscale nonlinear simulation [1-3] based on the homogenization theory. Macrostructure is a homogeneous structure to catch the whole behaviors of actuators and sensors. And microstructure is a periodic inhomogeneous structure consisting of domains and grains. Macrostructure and microstructure are connected perfectly by homogenization theory and are analyzed by finite element method. We utilized an incremental form of fundamental constitutive law in consideration with physical property change caused by domain switching and structural phase transition. The developed multiscale finite element method was applied to PZT thin films with lattice mismatch strain on the substrate, and the relation between the macroscopic hysteresis response and microscopic domain switching and structural phase transition were investigated. Especially, we discuss about the effect of crystal morphologies and lattice mismatch strain on hysteresis response.

New Generalized Hyperbolic Functions to Find New Exact Solutions of the Nonlinear Partial Differential Equations

Directory of Open Access Journals (Sweden)

Yusuf Pandir

2013-01-01

Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.

Nonlinear photonic metasurfaces

Science.gov (United States)

Li, Guixin; Zhang, Shuang; Zentgraf, Thomas

2017-03-01

Compared with conventional optical elements, 2D photonic metasurfaces, consisting of arrays of antennas with subwavelength thickness (the 'meta-atoms'), enable the manipulation of light-matter interactions on more compact platforms. The use of metasurfaces with spatially varying arrangements of meta-atoms that have subwavelength lateral resolution allows control of the polarization, phase and amplitude of light. Many exotic phenomena have been successfully demonstrated in linear optics; however, to meet the growing demand for the integration of more functionalities into a single optoelectronic circuit, the tailorable nonlinear optical properties of metasurfaces will also need to be exploited. In this Review, we discuss the design of nonlinear photonic metasurfaces — in particular, the criteria for choosing the materials and symmetries of the meta-atoms — for the realization of nonlinear optical chirality, nonlinear geometric Berry phase and nonlinear wavefront engineering. Finally, we survey the application of nonlinear photonic metasurfaces in optical switching and modulation, and we conclude with an outlook on their use for terahertz nonlinear optics and quantum information processing.

Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

Science.gov (United States)

Chiang, C. K.; Xue, David Y.; Mei, Chuh

1993-04-01

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

Composite Beam Theory with Material Nonlinearities and Progressive Damage

Science.gov (United States)

Jiang, Fang

functions, and the 3D spatial gradients of these warping functions. Asymptotic analysis of the extended Hamiltonian's principle suggests dropping the terms of axial gradients of the warping functions. As a result, the solid mechanics problem resolved into a 3D continuum is dimensionally reduced to a problem of solving the warping functions on a 2D cross-sectional field by minimizing the information loss. The present theory is implemented using the finite element method (FEM) in Variational Asymptotic Beam Sectional Analysis (VABS), a general-purpose cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model in the form of the Euler-Bernoulli beam theory. The deformation gradient tensor is directly used to enable the capability of dealing with finite deformation, various strain definitions, and several types of material constitutive laws regarding the nonlinear elasticity and progressive damage. Analytical and numerical examples are given for various problems including the trapeze effect, Poynting effect, Brazier effect, extension-bending coupling effect, and free edge damage. By comparison with the predictions from 3D finite element analyses (FEA), 2D FEA based on plane stress assumptions, and experimental data, the structural and material responses are proven to be rigorously captured by the present theory and the computational cost is significantly reduced. Due to the semi-analytical feature of the code developed, the unrealistic numerical issues widely seen in the conventional FEA with strain softening material behaviors are prevented by VABS. In light of these intrinsic features, the nonlinear elastic and inelastic 3D material models can be economically calibrated by data-matching the VABS predictions directly with the experimental measurements from slender coupons. Furthermore, the global behavior of slender composite structures in meters can also be effectively characterized by VABS without unnecessary

Modeling human auditory evoked brainstem responses based on nonlinear cochlear processing

DEFF Research Database (Denmark)

Harte, James; Rønne, Filip Munch; Dau, Torsten

2010-01-01

. To generate AEPs recorded at remote locations, a convolution was made on an empirically obtained elementary unit waveform with the instantaneous discharge rate function for the corresponding AN unit. AEPs to click-trains, as well as to tone pulses at various frequencies, were both modelled and recorded...... at different stimulation levels and repetition rates. The observed nonlinearities in the recorded potential patterns, with respect to ABR wave V latencies and amplitudes, could be largely accounted for by level-dependent BM processing as well as effects of short-term neural adaptation. The present study...

Nonlinear optical response and its theoretical modelling of Sb2S3 nanorod

Science.gov (United States)

Yadav, Rajesh Kumar; Barik, A. R.; Das, Amlan; Adarsh, K. V.

2018-05-01

Light-matter interaction in nanoscale regime have unprecedented and accelerating demand in optoelectronics, valley electronics and device applications. Such interaction in 1-dimention (1D) metal chalcogenides has emerged as an important research topic because of its possibility to custom design optical properties, implying enormous application including optical computers, communications, bioimaging, and so on. However, understanding of nonlinear optical response of these nanostructures is still lacking, although it constitutes an interesting problem on the light-matter interaction. Here, we have presented the nonlinear optical response in Sb2S3 nanorod using Z-scan technique. Our experimental findings show a strong saturable absorption (SA). In this context, we have numerically simulated the experimental result using two level rate equation. The solutions of these two-level rate equation for a Gaussian shaped pulse exactly replicated the experimental data. From the best numerical fit, we found excited state decay time (τ ≈ 0.15ns) and saturation intensity (IS ≈ 0.01 GW/cm2). Additionally, we have calculated number of career density (N ≈ 5.31 × 10-17 cm-3), ground state absorption cross section (σ1 ≈ 1.63 × 10-17 cm2). Our experimental finding indicates that they can be employed as saturable absorbers.

Nonlinear rheology of complex fluid-fluid interfaces

NARCIS (Netherlands)

Sagis, L.M.C.; Fischer, P.

2014-01-01

Fluid–fluid interfaces stabilized by proteins, protein aggregates, polymers, or colloidal particles, tend to have a complex microstructure. Their response to an applied deformation is often highly nonlinear, even at small deformation (rates). The nonlinearity of the response is a result of changes

Nonlinear laser pulse response in a crystalline lens.

Science.gov (United States)

Sharma, R P; Gupta, Pradeep Kumar; Singh, Ram Kishor; Strickland, D

2016-04-01

The propagation characteristics of a spatial Gaussian laser pulse have been studied inside a gradient-index structured crystalline lens with constant-density plasma generated by the laser-tissue interaction. The propagation of the laser pulse is affected by the nonlinearities introduced by the generated plasma inside the crystalline lens. Owing to the movement of plasma species from a higher- to a lower-temperature region, an increase in the refractive index occurs that causes the focusing of the laser pulse. In this study, extended paraxial approximation has been applied to take into account the evolution of the radial profile of the Gaussian laser pulse. To examine the propagation characteristics, variation of the beam width parameter has been observed as a function of the laser power and initial beam radius. The cavitation bubble formation, which plays an important role in the restoration of the elasticity of the crystalline lens, has been investigated.

Free-vibration acoustic resonance of a nonlinear elastic bar

Science.gov (United States)

Tarumi, Ryuichi; Oshita, Yoshihito

2011-02-01

Free-vibration acoustic resonance of a one-dimensional nonlinear elastic bar was investigated by direct analysis in the calculus of variations. The Lagrangian density of the bar includes a cubic term of the deformation gradient, which is responsible for both geometric and constitutive nonlinearities. By expanding the deformation function into a complex Fourier series, we derived the action integral in an analytic form and evaluated its stationary conditions numerically with the Ritz method for the first three resonant vibration modes. This revealed that the bar shows the following prominent nonlinear features: (i) amplitude dependence of the resonance frequency; (ii) symmetry breaking in the vibration pattern; and (iii) excitation of the high-frequency mode around nodal-like points. Stability of the resonant vibrations was also addressed in terms of a convex condition on the strain energy density.

Numerical study of surface plasmon enhanced nonlinear absorption and refraction.

Science.gov (United States)

Kohlgraf-Owens, Dana C; Kik, Pieter G

2008-07-07

Maxwell Garnett effective medium theory is used to study the influence of silver nanoparticle induced field enhancement on the nonlinear response of a Kerr-type nonlinear host. We show that the composite nonlinear absorption coefficient, beta(c), can be enhanced relative to the host nonlinear absorption coefficient near the surface plasmon resonance of silver nanoparticles. This enhancement is not due to a resonant enhancement of the host nonlinear absorption, but rather due to a phase shifted enhancement of the host nonlinear refractive response. The enhancement occurs at the expense of introducing linear absorption, alpha(c), which leads to an overall reduced figure of merit beta(c)/alpha(c) for nonlinear absorption. For thin (< 1 microm) composites, the use of surface plasmons is found to result in an increased nonlinear absorption response compared to that of the host material.

Development of a simple detector response function generation program: The CEARDRFs code

Energy Technology Data Exchange (ETDEWEB)

Wang Jiaxin, E-mail: jwang3@ncsu.edu [Center for Engineering Applications of Radioisotopes (CEAR), Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695 (United States); Wang Zhijian; Peeples, Johanna [Center for Engineering Applications of Radioisotopes (CEAR), Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695 (United States); Yu Huawei [Center for Engineering Applications of Radioisotopes (CEAR), Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695 (United States); College of Geo-Resources and Information, China University of Petroleum, Qingdao, Shandong 266555 (China); Gardner, Robin P. [Center for Engineering Applications of Radioisotopes (CEAR), Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695 (United States)

2012-07-15

A simple Monte Carlo program named CEARDRFs has been developed to generate very accurate detector response functions (DRFs) for scintillation detectors. It utilizes relatively rigorous gamma-ray transport with simple electron transport, and accounts for two phenomena that have rarely been treated: scintillator non-linearity and the variable flat continuum part of the DRF. It has been proven that these physics and treatments work well for 3 Multiplication-Sign 3 Double-Prime and 6 Multiplication-Sign 6 Double-Prime cylindrical NaI detector in CEAR's previous work. Now this approach has been expanded to cover more scintillation detectors with various common shapes and sizes. Benchmark experiments of 2 Multiplication-Sign 2 Double-Prime cylindrical BGO detector and 2 Multiplication-Sign 4 Multiplication-Sign 16 Double-Prime rectangular NaI detector have been carried out at CEAR with various radiactive sources. The simulation results of CEARDRFs have also been compared with MCNP5 calculations. The benchmark and comparison show that CEARDRFs can generate very accurate DRFs (more accurate than MCNP5) at a very fast speed (hundred times faster than MCNP5). The use of this program can significantly increase the accuracy of applications relying on detector spectroscopy like prompt gamma-ray neutron activation analysis, X-ray fluorescence analysis, oil well logging and homeland security. - Highlights: Black-Right-Pointing-Pointer CEARDRF has been developed to generate detector response functions (DRFs) for scintillation detectors a. Black-Right-Pointing-Pointer Generated DRFs are very accurate. Black-Right-Pointing-Pointer Simulation speed is hundreds of times faster than MCNP5. Black-Right-Pointing-Pointer It utilizes rigorous gamma-ray transport with simple electron transport. Black-Right-Pointing-Pointer It also accounts for scintillator non-linearity and the variable flat continuum part.

Impurity-related linear and nonlinear optical response in quantum-well wires with triangular cross section

Energy Technology Data Exchange (ETDEWEB)

Duque, C.A., E-mail: cduque@fisica.udea.edu.co [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia); Mora-Ramos, M.E. [Instituto de Física, Universidad de Antioquia, AA 1226, Medellín (Colombia); Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, CP 62209, Cuernavaca, Morelos, México (Mexico); Kasapoglu, E.; Ungan, F.; Yesilgul, U. [Cumhuriyet University, Physics Department, 58140 Sivas (Turkey); Sakiroglu, S. [Dokuz Eylül University, Physics Department, 35160 Buca, İzmir (Turkey); Sari, H. [Cumhuriyet University, Physics Department, 58140 Sivas (Turkey); Sökmen, I. [Dokuz Eylül University, Physics Department, 35160 Buca, İzmir (Turkey)

2013-11-15

The 1s-like and 2p-like donor impurity energy states are studied in a semiconductor quantum wire of equilateral triangular cross section as functions of the impurity position and the geometrical size of the structure. Linear and nonlinear coefficients for the optical absorption and relative refractive index change associated with 1s→2p transitions are calculated for both the x-polarization and y-polarization of the incident light. The results show a mixed effect of redshift and blueshift depending on the location of the donor atom. Also, strong nonlinear contributions to the optical absorption coefficient are obtained for both polarizations in the on-center impurity case. -- Highlights: • The 1s- and 2p-like impurity states in triangular quantum-well wires. • Optical absorption and relative refractive index changes are calculated. • Redshift and blueshift in the optical structures depend on the donor position. • Strong nonlinear contributions to the absorption coefficient have been obtained.

Nucleon-nucleon scattering in the functional quantum theory of the nonlinear spinor field

International Nuclear Information System (INIS)

Haegele, G.

1979-01-01

The author calculates the S matrix for the elastic nucleon-nucleon scattering in the lowest approximation using the quantum theory of nonlinear spinor fields with special emphasis to the ghost configuration of this theory. Introducing a general scalar product a new functional channel calculus is considered. From the results the R and T matrix elements and the differential and integral cross sections are derived. (HSI)

The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

Czech Academy of Sciences Publication Activity Database

Mukhigulashvili, Sulkhan; Půža, B.

2015-01-01

Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

Input signal shaping based on harmonic frequency response function for suppressing nonlinear optical frequency in frequency-scanning interferometry

Science.gov (United States)

Zhu, Yu; Liu, Zhigang; Deng, Wen; Deng, Zhongwen

2018-05-01

Frequency-scanning interferometry (FSI) using an external cavity diode laser (ECDL) is essential for many applications of the absolute distance measurement. However, owing to the hysteresis and creep of the piezoelectric actuator inherent in the ECDL, the optical frequency scanning exhibits a nonlinearity that seriously affects the phase extraction accuracy of the interference signal and results in the reduction of the measurement accuracy. To suppress the optical frequency nonlinearity, a harmonic frequency synthesis method for shaping the desired input signal instead of the original triangular wave is presented. The effectiveness of the presented shaping method is demonstrated through the comparison of the experimental results. Compared with an incremental Renishaw interferometer, the standard deviation of the displacement measurement of the FSI system is less than 2.4 μm when driven by the shaped signal.

Cascaded nonlinearities for ultrafast nonlinear optical science and applications

DEFF Research Database (Denmark)

Bache, Morten

the cascading nonlinearity is investigated in detail, especially with focus on femtosecond energetic laser pulses being subjected to this nonlinear response. Analytical, numerical and experimental results are used to understand the cascading interaction and applications are demonstrated. The defocusing soliton...... observations with analogies in fiber optics are observed numerically and experimentally, including soliton self-compression, soliton-induced resonant radiation, supercontinuum generation, optical wavebreaking and shock-front formation. All this happens despite no waveguide being present, thanks...... is of particular interest here, since it is quite unique and provides the solution to a number of standing challenges in the ultrafast nonlinear optics community. It solves the problem of catastrophic focusing and formation of a filaments in bulk glasses, which even under controlled circumstances is limited...

Nonlinear seismic analysis of a large sodium pump

International Nuclear Information System (INIS)

Huang, S.N.

1985-01-01

The bearings and seismic bumpers used in a large sodium pump of a typical breeder reactor plant may need to be characterized by nonlinear springs and gaps. Then, nonlinear seismic analysis utilizing the time-history method is an effective way to predict the pump behaviors during seismic events, especially at those bearing and seismic bumper areas. In this study, synthesized time histories were developed based on specified seismic response spectra. A nonlinear seismic analysis was then conducted and results were compared with those obtained by linear seismic analysis using the response spectrum method. In contrast to some previous nonlinear analysis trends, the bearing impact forces predicted by nonlinear analysis were higher than those obtained by the response spectrum method. This might be due to the larger gaps and stiffer bearing supports used in this specific pump. However, at locations distant from the impact source, the nonlinear seismic analysis has predicted slightly less responses than those obtained by linear seismic analysis. The seismically induced bearing impact forces were used to study the friction induced thermal stresses on the hydrostatic bearing and to predict the coastdown time of the pump. Results and discussions are presented

Nonlinear seismic analysis of a large sodium pump

International Nuclear Information System (INIS)

Huang, S.N.

1985-01-01

The bearings and seismic bumpers used in a large sodium pump of a typical breeder reactor plant may need to be characterized by nonlinear springs and gaps. Then, nonlinear seismic analysis utilizing the time-history method is an effective way to predict the pump behaviors during seismic events - especially at those bearing and seismic bumper areas. In this study, synthesized time histories were developed based on specified seismic response spectra. A nonlinear seismic analysis was then conducted and results were compared with those obtained by linear seismic analysis using the response spectrum method. In contrast to some previous nonlinear analysis trends, the bearing impact forces predicted by nonlinear analysis were higher than those obtained by the response spectrum method. This might be due to the larger gaps and stiffer bearing supports used in this specific pump. However, at locations distant from the impact source, the nonlinear seismic analysis has predicted slightly less responses than those obtained by linear seismic analysis. The seismically induced bearing impact forces were used to study the friction induced thermal stresses on the hydrostatic bearing and to predict the coastdown time of the pump. Results and discussions are presented

Non-linear seismic response of base-isolated liquid storage tanks to bi-directional excitation

International Nuclear Information System (INIS)

Shrimali, M.K.; Jangid, R.S.

2002-01-01

Seismic response of the liquid storage tanks isolated by lead-rubber bearings is investigated for bi-directional earthquake excitation (i.e. two horizontal components). The biaxial force-deformation behaviour of the bearings is considered as bi-linear modelled by coupled non-linear differential equations. The continuous liquid mass of the tank is modelled as lumped masses known as convective mass, impulsive mass and rigid mass. The corresponding stiffness associated with these lumped masses has been worked out depending upon the properties of the tank wall and liquid mass. Since the force-deformation behaviour of the bearings is non-linear, as a result, the seismic response is obtained by the Newmark's step-by-step method. The seismic responses of two types of the isolated tanks (i.e. slender and broad) are investigated under several recorded earthquake ground to study the effects of bi-directional interaction. Further, a parametric study is also carried out to study the effects of important system parameters on the effectiveness of seismic isolation for liquid storage tanks. The various important parameters considered are: (i) the period of isolation, (ii) the damping of isolation bearings and (iii) the yield strength level of the bearings. It has been observed that the seismic response of isolated tank is found to be insensitive to interaction effect of the bearing forces. Further, there exists an optimum value of isolation damping for which the base shear in the tank attains the minimum value. Therefore, increasing the bearing damping beyond a certain value may decrease the bearing and sloshing displacements but it may increase the base shear

Insight into the effect of screw dislocations and oxygen vacancy defects on the optical nonlinear refraction response in chemically grown ZnO/Al2O3 films

Science.gov (United States)

Agrawal, Arpana; Saroj, Rajendra K.; Dar, Tanveer A.; Baraskar, Priyanka; Sen, Pratima; Dhar, Subhabrata

2017-11-01

We report the effect of screw dislocations and oxygen vacancy defects on the optical nonlinear refraction response of ZnO films grown on a sapphire substrate at various oxygen flow rates using the chemical vapor deposition technique. The nonlinear refraction response was investigated in the off-resonant regime using a CW He-Ne laser source to examine the role of the intermediate bandgap states. It has been observed that the structural defects strongly influence the optical nonlinearity in the off-resonant regime. Nonlinearity has been found to improve as the oxygen flow rate is lowered from 2 sccm to 0.3 sccm. From photoluminescence studies, we observe that the enhanced defect density of the electronic defect levels due to the increased concentration of structural defects (with the decrease in the oxygen flow rate) is responsible for this improved optical nonlinearity along with the thermal effect. This suggests that defect engineering is an effective way to tailor the nonlinearity of ZnO films and their utility for optoelectronic device applications.

Microwave second-harmonic response of ceramic MgB2 samples

International Nuclear Information System (INIS)

Agliolo Gallitto, A.; Bonsignore, G.; Li Vigni, M.

2005-01-01

Nonlinear microwave response of different ceramic MgB 2 samples has been investigated by the technique of second-harmonic emission. The second-harmonic signal has been investigated as a function of temperature, DC magnetic field and input microwave power. The attention has mainly been devoted to the response at low magnetic fields, where nonlinear processes arising from motion of Abrikosov fluxons are ineffective. The results show that different mechanisms are responsible for the nonlinear response in the different ranges of temperature. At low temperatures, the nonlinear response is due to processes involving weak links. At temperatures close to T c , a further contribution to the harmonic emission is present; it can be ascribed to modulation of the order parameter by the microwave field and gives rise to a peak in the temperature dependence of the harmonic signal

Coupled large earthquakes in the Baikal rift system: Response to bifurcations in nonlinear resonance hysteresis

Directory of Open Access Journals (Sweden)

Anatoly V. Klyuchevskii

2013-11-01

Full Text Available The current lithospheric geodynamics and tectonophysics in the Baikal rift are discussed in terms of a nonlinear oscillator with dissipation. The nonlinear oscillator model is applicable to the area because stress change shows up as quasi-periodic inharmonic oscillations at rifting attractor structures (RAS. The model is consistent with the space-time patterns of regional seismicity in which coupled large earthquakes, proximal in time but distant in space, may be a response to bifurcations in nonlinear resonance hysteresis in a system of three oscillators corresponding to the rifting attractors. The space-time distribution of coupled MLH > 5.5 events has been stable for the period of instrumental seismicity, with the largest events occurring in pairs, one shortly after another, on two ends of the rift system and with couples of smaller events in the central part of the rift. The event couples appear as peaks of earthquake ‘migration’ rate with an approximately decadal periodicity. Thus the energy accumulated at RAS is released in coupled large events by the mechanism of nonlinear oscillators with dissipation. The new knowledge, with special focus on space-time rifting attractors and bifurcations in a system of nonlinear resonance hysteresis, may be of theoretical and practical value for earthquake prediction issues. Extrapolation of the results into the nearest future indicates the probability of such a bifurcation in the region, i.e., there is growing risk of a pending M ≈ 7 coupled event to happen within a few years.

Documentation for assessment of modal pushover-based scaling procedure for nonlinear response history analysis of "ordinary standard" bridges

Science.gov (United States)

Kalkan, Erol; Kwong, Neal S.

2010-01-01

The earthquake engineering profession is increasingly utilizing nonlinear response history analyses (RHA) to evaluate seismic performance of existing structures and proposed designs of new structures. One of the main ingredients of nonlinear RHA is a set of ground-motion records representing the expected hazard environment for the structure. When recorded motions do not exist (as is the case for the central United States), or when high-intensity records are needed (as is the case for San Francisco and Los Angeles), ground motions from other tectonically similar regions need to be selected and scaled. The modal-pushover-based scaling (MPS) procedure recently was developed to determine scale factors for a small number of records, such that the scaled records provide accurate and efficient estimates of 'true' median structural responses. The adjective 'accurate' refers to the discrepancy between the benchmark responses and those computed from the MPS procedure. The adjective 'efficient' refers to the record-to-record variability of responses. Herein, the accuracy and efficiency of the MPS procedure are evaluated by applying it to four types of existing 'ordinary standard' bridges typical of reinforced-concrete bridge construction in California. These bridges are the single-bent overpass, multi span bridge, curved-bridge, and skew-bridge. As compared to benchmark analyses of unscaled records using a larger catalog of ground motions, it is demonstrated that the MPS procedure provided an accurate estimate of the engineering demand parameters (EDPs) accompanied by significantly reduced record-to-record variability of the responses. Thus, the MPS procedure is a useful tool for scaling ground motions as input to nonlinear RHAs of 'ordinary standard' bridges.

Distributed synchronization of networked drive-response systems: A nonlinear fixed-time protocol.

Science.gov (United States)

Zhao, Wen; Liu, Gang; Ma, Xi; He, Bing; Dong, Yunfeng

2017-11-01

The distributed synchronization of networked drive-response systems is investigated in this paper. A novel nonlinear protocol is proposed to ensure that the tracking errors converge to zeros in a fixed-time. By comparison with previous synchronization methods, the present method considers more practical conditions and the synchronization time is not dependent of arbitrary initial conditions but can be offline pre-assign according to the task assignment. Finally, the feasibility and validity of the presented protocol have been illustrated by a numerical simulation. Copyright © 2017. Published by Elsevier Ltd.

Seismic analysis of equipment system with non-linearities such as gap and friction using equivalent linearization method

International Nuclear Information System (INIS)

Murakami, H.; Hirai, T.; Nakata, M.; Kobori, T.; Mizukoshi, K.; Takenaka, Y.; Miyagawa, N.

1989-01-01

Many of the equipment systems of nuclear power plants contain a number of non-linearities, such as gap and friction, due to their mechanical functions. It is desirable to take such non-linearities into account appropriately for the evaluation of the aseismic soundness. However, in usual design works, linear analysis method with rough assumptions is applied from engineering point of view. An equivalent linearization method is considered to be one of the effective analytical techniques to evaluate non-linear responses, provided that errors to a certain extent are tolerated, because it has greater simplicity in analysis and economization in computing time than non-linear analysis. The objective of this paper is to investigate the applicability of the equivalent linearization method to evaluate the maximum earthquake response of equipment systems such as the CANDU Fuelling Machine which has multiple non- linearities

Solution of continuous nonlinear PDEs through order completion

CERN Document Server

Oberguggenberger, MB

1994-01-01

This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.

Response analysis and energy transmissibility of a vibration isolation system with real-power nonlinearities under a NMPPF controller

International Nuclear Information System (INIS)

Huang, Dongmei; Xu, Wei; Shi, Lingling

2016-01-01

Highlights: • The nonlinear modified positive position feedback (NMPPF) scheme and the real-power form of restoring and damping forces are combined to improve the response performance of a vibration isolation system. • The primary resonance, dynamical stability and energy transmissibility of the real-power vibration isolation system are studied. • The sensitivity of the controller parameters on the responses has been analyzed. • In order to suppress the amplitude peak, the feedback parameters have been determined by the frequency response. • The energy transmissibility is investigated. - Abstract: In this paper, the nonlinear modified positive position feedback (NMPPF) scheme and the real-power form of restoring and damping forces are combined to improve the response performance of a vibration isolation system. Based on the method of multiple scales, the frequency response, the stability and the energy transmissibility of the real-power vibration isolation system are studied. It is found that the controlled isolation system exhibits a softening behavior for sub-linear restoring force, while it exhibits the two peak response characteristic rather than a hardening behavior for over-linear restoring force. Further, the sensitivity of the feedback parameters on the responses is discussed. The results, compared to the conventional PPF and IRC methods, show that the proposed method is significantly more effective in controlling the steady-state response, and slightly advantageous for the steady-state dynamics control. The effectiveness of this method is also verified by time domain analysis. Then, the suitable feedback and controller parameters are derived by simulation results in which the amplitude peak is suppressed and the resonance stability is maintained. Finally, the energy transmissibility of the vibration isolation system is investigated. The results show that the feedback gain can reduce the whole transmissibility level and greatly suppress vibration

On Stabilization of Nonautonomous Nonlinear Systems

International Nuclear Information System (INIS)

Bogdanov, A. Yu.

2008-01-01

The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.

New exact travelling wave solutions of nonlinear physical models

International Nuclear Information System (INIS)

Bekir, Ahmet; Cevikel, Adem C.

2009-01-01

In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.

Nonlinear feedback drives homeostatic plasticity in H2O2 stress response

Science.gov (United States)

Goulev, Youlian; Morlot, Sandrine; Matifas, Audrey; Huang, Bo; Molin, Mikael; Toledano, Michel B; Charvin, Gilles

2017-01-01

Homeostatic systems that rely on genetic regulatory networks are intrinsically limited by the transcriptional response time, which may restrict a cell’s ability to adapt to unanticipated environmental challenges. To bypass this limitation, cells have evolved mechanisms whereby exposure to mild stress increases their resistance to subsequent threats. However, the mechanisms responsible for such adaptive homeostasis remain largely unknown. Here, we used live-cell imaging and microfluidics to investigate the adaptive response of budding yeast to temporally controlled H2O2 stress patterns. We demonstrate that acquisition of tolerance is a systems-level property resulting from nonlinearity of H2O2 scavenging by peroxiredoxins and our study reveals that this regulatory scheme induces a striking hormetic effect of extracellular H2O2 stress on replicative longevity. Our study thus provides a novel quantitative framework bridging the molecular architecture of a cellular homeostatic system to the emergence of nonintuitive adaptive properties. DOI: http://dx.doi.org/10.7554/eLife.23971.001 PMID:28418333

Experimental investigation of alternative transmission functions: Quantitative evidence for the importance of nonlinear transmission dynamics in host-parasite systems.

Science.gov (United States)

Orlofske, Sarah A; Flaxman, Samuel M; Joseph, Maxwell B; Fenton, Andy; Melbourne, Brett A; Johnson, Pieter T J

2018-05-01

Understanding pathogen transmission is crucial for predicting and managing disease. Nonetheless, experimental comparisons of alternative functional forms of transmission remain rare, and those experiments that are conducted are often not designed to test the full range of possible forms. To differentiate among 10 candidate transmission functions, we used a novel experimental design in which we independently varied four factors-duration of exposure, numbers of parasites, numbers of hosts and parasite density-in laboratory infection experiments. We used interactions between amphibian hosts and trematode parasites as a model system and all candidate models incorporated parasite depletion. An additional manipulation involving anaesthesia addressed the effects of host behaviour on transmission form. Across all experiments, nonlinear transmission forms involving either a power law or a negative binomial function were the best-fitting models and consistently outperformed the linear density-dependent and density-independent functions. By testing previously published data for two other host-macroparasite systems, we also found support for the same nonlinear transmission forms. Although manipulations of parasite density are common in transmission studies, the comprehensive set of variables tested in our experiments revealed that variation in density alone was least likely to differentiate among competing transmission functions. Across host-pathogen systems, nonlinear functions may often more accurately represent transmission dynamics and thus provide more realistic predictions for infection. © 2017 The Authors. Journal of Animal Ecology published by John Wiley & Sons Ltd on behalf of British Ecological Society.

Wave propagation in ordered, disordered, and nonlinear photonic band gap materials

Energy Technology Data Exchange (ETDEWEB)

Lidorikis, Elefterios [Iowa State Univ., Ames, IA (United States)

1999-12-10

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 in 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.

Symbolic computation of exact solutions expressible in rational formal hyperbolic and elliptic functions for nonlinear partial differential equations

International Nuclear Information System (INIS)

Wang Qi; Chen Yong

2007-01-01

With the aid of symbolic computation, some algorithms are presented for the rational expansion methods, which lead to closed-form solutions of nonlinear partial differential equations (PDEs). The new algorithms are given to find exact rational formal polynomial solutions of PDEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symbolic computation system Maple. As applications of the methods, we choose some nonlinear PDEs to illustrate the methods. As a result, we not only can successfully obtain the solutions found by most existing Jacobi elliptic function methods and Tanh-methods, but also find other new and more general solutions at the same time

Variance gradients and uncertainty budgets for nonlinear measurement functions with independent inputs

International Nuclear Information System (INIS)

Campanelli, Mark; Kacker, Raghu; Kessel, Rüdiger

2013-01-01

A novel variance-based measure for global sensitivity analysis, termed a variance gradient (VG), is presented for constructing uncertainty budgets under the Guide to the Expression of Uncertainty in Measurement (GUM) framework for nonlinear measurement functions with independent inputs. The motivation behind VGs is the desire of metrologists to understand which inputs' variance reductions would most effectively reduce the variance of the measurand. VGs are particularly useful when the application of the first supplement to the GUM is indicated because of the inadequacy of measurement function linearization. However, VGs reduce to a commonly understood variance decomposition in the case of a linear(ized) measurement function with independent inputs for which the original GUM readily applies. The usefulness of VGs is illustrated by application to an example from the first supplement to the GUM, as well as to the benchmark Ishigami function. A comparison of VGs to other available sensitivity measures is made. (paper)

Multiscale empirical interpolation for solving nonlinear PDEs

KAUST Repository

Calo, Victor M.

2014-12-01

In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM). To solve nonlinear equations, the GMsFEM is used to represent the solution on a coarse grid with multiscale basis functions computed offline. Computing the GMsFEM solution involves calculating the system residuals and Jacobians on the fine grid. We use empirical interpolation concepts to evaluate these residuals and Jacobians of the multiscale system with a computational cost which is proportional to the size of the coarse-scale problem rather than the fully-resolved fine scale one. The empirical interpolation method uses basis functions which are built by sampling the nonlinear function we want to approximate a limited number of times. The coefficients needed for this approximation are computed in the offline stage by inverting an inexpensive linear system. The proposed multiscale empirical interpolation techniques: (1) divide computing the nonlinear function into coarse regions; (2) evaluate contributions of nonlinear functions in each coarse region taking advantage of a reduced-order representation of the solution; and (3) introduce multiscale proper-orthogonal-decomposition techniques to find appropriate interpolation vectors. We demonstrate the effectiveness of the proposed methods on several nonlinear multiscale PDEs that are solved with Newton\\'s methods and fully-implicit time marching schemes. Our numerical results show that the proposed methods provide a robust framework for solving nonlinear multiscale PDEs on a coarse grid with bounded error and significant computational cost reduction.

THE ANISOTROPIC TWO-POINT CORRELATION FUNCTIONS OF THE NONLINEAR TRACELESS TIDAL FIELD IN THE PRINCIPAL-AXIS FRAME

International Nuclear Information System (INIS)

Lee, Jounghun; Hahn, Oliver; Porciani, Cristiano

2009-01-01

Galaxies on the largest scales of the universe are observed to be embedded in the filamentary cosmic web, which is shaped by the nonlinear tidal field. As an efficient tool to quantitatively describe the statistics of this cosmic web, we present the anisotropic two-point correlation functions of the nonlinear traceless tidal field in the principal-axis frame, which are measured using numerical data from an N-body simulation. We show that both the nonlinear density and traceless tidal fields are more strongly correlated along the directions perpendicular to the eigenvectors associated with the largest eigenvalues of the local tidal field. The correlation length scale of the traceless tidal field is found to be ∼20 h -1 Mpc, which is much larger than that of the density field ∼5 h -1 Mpc. We also provide analytic fitting formulae for the anisotropic correlation functions of the traceless tidal field, which turn out to be in excellent agreement with the numerical results. We expect that our numerical results and analytical formula are useful to disentangle cosmological information from the filamentary network of the large-scale structures.

Covalent functionalization of reduced graphene oxide with porphyrin by means of diazonium chemistry for nonlinear optical performance

Science.gov (United States)

Wang, Aijian; Yu, Wang; Huang, Zhipeng; Zhou, Feng; Song, Jingbao; Song, Yinglin; Long, Lingliang; Cifuentes, Marie P.; Humphrey, Mark G.; Zhang, Long; Shao, Jianda; Zhang, Chi

2016-03-01

Reduced graphene oxide (RGO)-porphyrin (TPP) nanohybrids (RGO-TPP 1 and RGO-TPP 2) were prepared by two synthetic routes that involve functionalization of the RGO using diazonium salts. The microscopic structures, morphology, photophysical properties and nonlinear optical performance of the resultant RGO-TPP nanohybrids were investigated. The covalent bonding of the porphyrin-functionalized-RGO nanohybrid materials was confirmed by Fourier transform infrared spectroscopy, Raman spectroscopy, X-ray photoelectron spectroscopy, transmission electron microscopy, and thermogravimetric analysis. Attachment of the porphyrin units to the surface of the RGO by diazotization significantly improves the solubility and ease of processing of these RGO-based nanohybrid materials. Ultraviolet/visible absorption and steady-state fluorescence studies indicate considerable π-π interactions and effective photo-induced electron and/or energy transfer between the porphyrin moieties and the extended π-system of RGO. The nonlinear optical properties of RGO-TPP 1 and RGO-TPP 2 were investigated by open-aperture Z-scan measurements at 532 nm with both 4 ns and 21 ps laser pulses, the results showing that the chemical nanohybrids exhibit improved nonlinear optical properties compared to those of the benchmark material C60, and the constituent RGO or porphyrins.

Nonlinear Modeling and Simulation of Thermal Effects in Microcantilever Resonators Dynamic

International Nuclear Information System (INIS)

Tadayon, M A; Sayyaadi, H; Jazar, G Nakhaie

2006-01-01

Thermal dependency of material characteristics in micro electromechanical systems strongly affects their performance, design, and control. Hence, it is essential to understand and model that in MEMS devices to optimize their designs. A thermal phenomenon introduces two main effects: damping due to internal friction, and softening due to Young modulus temperature relation. Based on some reported theoretical and experimental results, we model the thermal phenomena and use two Lorentzian functions to describe the restoring and damping forces caused by thermal phenomena. In order to emphasize the thermal effects, a nonlinear model of the MEMS, by considering capacitor nonlinearity, have been used. The response of the system is developed by employing multiple time scales perturbation method on nondimensionalized form of equations. Frequency response, resonant frequency and peak amplitude are examined for variation of dynamic parameters involved

Exact solutions for oscillators with quadratic damping and mixed-parity nonlinearity

International Nuclear Information System (INIS)

Lai, S K; Chow, K W

2012-01-01

Exact vibration modes of a nonlinear oscillator, which contains both quadratic friction and a mixed-parity restoring force, are derived analytically. Two families of exact solutions are obtained in terms of rational expressions for classical Jacobi elliptic functions. The present solutions allow the investigation of the dynamical behaviour of the system in response to changes in physical parameters that concern nonlinearity. The physical significance of the signs (i.e. attractive or repulsive nature) of the linear, quadratic and cubic restoring forces is discussed. A qualitative analysis is also conducted to provide valuable physical insight into the nature of the system. (paper)

PRESS-based EFOR algorithm for the dynamic parametrical modeling of nonlinear MDOF systems

Science.gov (United States)

Liu, Haopeng; Zhu, Yunpeng; Luo, Zhong; Han, Qingkai

2017-09-01

In response to the identification problem concerning multi-degree of freedom (MDOF) nonlinear systems, this study presents the extended forward orthogonal regression (EFOR) based on predicted residual sums of squares (PRESS) to construct a nonlinear dynamic parametrical model. The proposed parametrical model is based on the non-linear autoregressive with exogenous inputs (NARX) model and aims to explicitly reveal the physical design parameters of the system. The PRESS-based EFOR algorithm is proposed to identify such a model for MDOF systems. By using the algorithm, we built a common-structured model based on the fundamental concept of evaluating its generalization capability through cross-validation. The resulting model aims to prevent over-fitting with poor generalization performance caused by the average error reduction ratio (AERR)-based EFOR algorithm. Then, a functional relationship is established between the coefficients of the terms and the design parameters of the unified model. Moreover, a 5-DOF nonlinear system is taken as a case to illustrate the modeling of the proposed algorithm. Finally, a dynamic parametrical model of a cantilever beam is constructed from experimental data. Results indicate that the dynamic parametrical model of nonlinear systems, which depends on the PRESS-based EFOR, can accurately predict the output response, thus providing a theoretical basis for the optimal design of modeling methods for MDOF nonlinear systems.

Solitons supported by localized nonlinearities in periodic media

International Nuclear Information System (INIS)

Dror, Nir; Malomed, Boris A.

2011-01-01

Nonlinear periodic systems, such as photonic crystals and Bose-Einstein condensates (BEC's) loaded into optical lattices, are often described by the nonlinear Schroedinger or Gross-Pitaevskii equation with a sinusoidal potential. Here, we consider a model based on such a periodic potential, with the nonlinearity (attractive or repulsive) concentrated either at a single point or at a symmetric set of two points, which are represented, respectively, by a single δ function or a combination of two δ functions. With the attractive or repulsive sign of the nonlinearity, this model gives rise to ordinary solitons or gap solitons (GS's), which reside, respectively, in the semi-infinite or finite gaps of the system's linear spectrum, being pinned to the δ functions. Physical realizations of these systems are possible in optics and BEC's, using diverse variants of the nonlinearity management. First, we demonstrate that the single δ function multiplying the nonlinear term supports families of stableregular solitons in the self-attractive case, while a family of solitons supported by the attractive δ function in the absence of the periodic potential is completely unstable. In addition, we show that the δ function can support stable GS's in the first finite band gap in both the self-attractive and repulsive models. The stability analysis for the GS's in the second finite band gap is reported too, for both signs of the nonlinearity. Alongside the numerical analysis, analytical approximations are developed for the solitons in the semi-infinite and first two finite gaps, with the single δ function positioned at a minimum or maximum of the periodic potential. In the model with the symmetric set of two δ functions, we study the effect of the spontaneous symmetry breaking of the pinned solitons. Two configurations are considered, with the δ functions set symmetrically with respect to the minimum or maximum of the underlying potential.

A study of discrete nonlinear systems

International Nuclear Information System (INIS)

Dhillon, H.S.

2001-04-01

An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

Useful tools for non-linear systems: Several non-linear integral inequalities

Czech Academy of Sciences Publication Activity Database

Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.

2013-01-01

Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf

An update on modeling dose-response relationships: Accounting for correlated data structure and heterogeneous error variance in linear and nonlinear mixed models.

Science.gov (United States)

Gonçalves, M A D; Bello, N M; Dritz, S S; Tokach, M D; DeRouchey, J M; Woodworth, J C; Goodband, R D

2016-05-01

Advanced methods for dose-response assessments are used to estimate the minimum concentrations of a nutrient that maximizes a given outcome of interest, thereby determining nutritional requirements for optimal performance. Contrary to standard modeling assumptions, experimental data often present a design structure that includes correlations between observations (i.e., blocking, nesting, etc.) as well as heterogeneity of error variances; either can mislead inference if disregarded. Our objective is to demonstrate practical implementation of linear and nonlinear mixed models for dose-response relationships accounting for correlated data structure and heterogeneous error variances. To illustrate, we modeled data from a randomized complete block design study to evaluate the standardized ileal digestible (SID) Trp:Lys ratio dose-response on G:F of nursery pigs. A base linear mixed model was fitted to explore the functional form of G:F relative to Trp:Lys ratios and assess model assumptions. Next, we fitted 3 competing dose-response mixed models to G:F, namely a quadratic polynomial (QP) model, a broken-line linear (BLL) ascending model, and a broken-line quadratic (BLQ) ascending model, all of which included heteroskedastic specifications, as dictated by the base model. The GLIMMIX procedure of SAS (version 9.4) was used to fit the base and QP models and the NLMIXED procedure was used to fit the BLL and BLQ models. We further illustrated the use of a grid search of initial parameter values to facilitate convergence and parameter estimation in nonlinear mixed models. Fit between competing dose-response models was compared using a maximum likelihood-based Bayesian information criterion (BIC). The QP, BLL, and BLQ models fitted on G:F of nursery pigs yielded BIC values of 353.7, 343.4, and 345.2, respectively, thus indicating a better fit of the BLL model. The BLL breakpoint estimate of the SID Trp:Lys ratio was 16.5% (95% confidence interval [16.1, 17.0]). Problems with

Nonlinear plasma waves excited near resonance

International Nuclear Information System (INIS)

Cohen, B.I.; Kaufman, A.N.

1977-01-01

The nonlinear resonant response of a uniform plasma to an external plane-wave field is formulated in terms of the mismatch Δ/sub n l/ between the driving frequency and the time-dependent, complex, nonlinear normal mode frequency at the driving wavenumber. This formalism is applied to computer simulations of this process, yielding a deduced nonlinear frequency shift. The time dependence of the nonlinear phenomena, at frequency Δ/sub n l/ and at the bounce frequency of the resonant particles, is analyzed. The interdependence of the nonlinear features is described by means of energy and momentum relations

Noise Reduction for Nonlinear Nonstationary Time Series Data using Averaging Intrinsic Mode Function

Directory of Open Access Journals (Sweden)

Christofer Toumazou

2013-07-01

Full Text Available A novel noise filtering algorithm based on averaging Intrinsic Mode Function (aIMF, which is a derivation of Empirical Mode Decomposition (EMD, is proposed to remove white-Gaussian noise of foreign currency exchange rates that are nonlinear nonstationary times series signals. Noise patterns with different amplitudes and frequencies were randomly mixed into the five exchange rates. A number of filters, namely; Extended Kalman Filter (EKF, Wavelet Transform (WT, Particle Filter (PF and the averaging Intrinsic Mode Function (aIMF algorithm were used to compare filtering and smoothing performance. The aIMF algorithm demonstrated high noise reduction among the performance of these filters.

Nonlinear VLF Wave Physics in the Radiation Belts

Science.gov (United States)

Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Mithaiwala, M.; Rudakov, L.; Hospodarsky, G. B.; Kletzing, C.

2014-12-01

Electromagnetic VLF waves, such as whistler mode waves, both control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering and are responsible for the energization of electrons during storms. Traditional approaches to understanding the influence of waves on trapped electrons have assumed that the wave characteristics (frequency spectrum, wave-normal angle distribution, etc.) were both stationary in time and amplitude independent from event to event. In situ data from modern satellite missions, such as the Van Allen probes, are showing that this assumption may not be justified. In addition, recent theoretical results [Crabtree et al. 2012] show that the threshold for nonlinear wave scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear wave scattering (Nonlinear Landau Damping) is an amplitude dependent mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Nonlinear scattering can alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al., 2012]. Such nonlinear wave effects can dramatically reduce electron lifetimes. Nonlinear wave dynamics such as these occur when there are more than one wave present, such a condition necessarily violates the assumption of traditional wave-normal analysis [Santolik et al., 2003] which rely on the plane wave assumption. To investigate nonlinear wave dynamics using modern in situ data we apply the maximum entropy method [Skilling and Bryan, 1984] to solve for the wave distribution function

Dynamics of a photorefractive response and competition of nonlinear processes in self-pumping double phase-conjugate mirrors

International Nuclear Information System (INIS)

Mogaddam, Mehran Wahdani; Shuvalov, Vladimir V

2005-01-01

The dynamics of formation of a nonlinear response of a double phase-conjugate (PC) BaTiO 3 mirror is calculated. It is shown that because of competition between processes of different types (related to the presence of several PC channels, the local and nonlocal components of the photorefractive nonlinearity), the transient and dynamic lasing regimes for this mirror can be substantially different. It is found that the development of lasing begins with the successive formation and phasing of dynamic holograms of two different types (two PC channels). It is shown that even under optimal conditions, the lasing regime is not stationary due to competition between processes of different types, and the parameters of output fields fluctuate in time in a nontrivial way (due to the presence of the in-phase and out-of-phase components). Several scenarios of transition to the dynamic chaos are described. (nonlinear optical phenomena)

Rail vehicle dynamic response to a nonlinear physical 'in-service' model of its secondary suspension hydraulic dampers

Science.gov (United States)

Wang, W. L.; Zhou, Z. R.; Yu, D. S.; Qin, Q. H.; Iwnicki, S.

2017-10-01

A full nonlinear physical 'in-service' model was built for a rail vehicle secondary suspension hydraulic damper with shim-pack-type valves. In the modelling process, a shim pack deflection theory with an equivalent-pressure correction factor was proposed, and a Finite Element Analysis (FEA) approach was applied. Bench test results validated the damper model over its full velocity range and thus also proved that the proposed shim pack deflection theory and the FEA-based parameter identification approach are effective. The validated full damper model was subsequently incorporated into a detailed vehicle dynamics simulation to study how its key in-service parameter variations influence the secondary-suspension-related vehicle system dynamics. The obtained nonlinear physical in-service damper model and the vehicle dynamic response characteristics in this study could be used in the product design optimization and nonlinear optimal specifications of high-speed rail hydraulic dampers.

Gradient-based optimization in nonlinear structural dynamics

DEFF Research Database (Denmark)

Dou, Suguang

The intrinsic nonlinearity of mechanical structures can give rise to rich nonlinear dynamics. Recently, nonlinear dynamics of micro-mechanical structures have contributed to developing new Micro-Electro-Mechanical Systems (MEMS), for example, atomic force microscope, passive frequency divider......, frequency stabilization, and disk resonator gyroscope. For advanced design of these structures, it is of considerable value to extend current optimization in linear structural dynamics into nonlinear structural dynamics. In this thesis, we present a framework for modelling, analysis, characterization......, and optimization of nonlinear structural dynamics. In the modelling, nonlinear finite elements are used. In the analysis, nonlinear frequency response and nonlinear normal modes are calculated based on a harmonic balance method with higher-order harmonics. In the characterization, nonlinear modal coupling...

Earthquake response analysis of embedded reactor building considering soil-structure separation and nonlinearity of soil

International Nuclear Information System (INIS)

Ichikawa, T.; Hayashi, Y.; Nakai, S.

1987-01-01

In the earthquake response analysis for a rigid and massive structure as a nuclear reactor building, it is important to estimate the effect of soil-structure interaction (SSI) appropriately. In case of strong earthquakes, the nonlinearity, such as the wall-ground separation, the base mat uplift of sliding, makes the behavior of the soil-structure system complex. But, if the nuclear reactor building is embedded in a relatively soft ground with surface layer, the wall-ground separation plays the most important role in the response of soil-structure system. Because, it is expected that the base uplift and slide would be less significant due to the effect of the embedment, and the wall-ground friction is usually neglected in design. But, the nonlinearity of ground may have some effect on the wall-ground separation and the response of the structure. These problems have been studied by use of FEM. Others used joint elements between the ground and the structure which does not resist tensile force. Others studied the effect of wall-ground separation with non-tension springs. But the relationship between the ground condition and the effect of the separation has not been clarified yet. To clarify the effect the analyses by FE model and lumped mass model (sway-rocking model) are performed and compared. The key parameter is the ground profile, namely the stiffness of the side soil

Periodic precursors of nonlinear dynamical transitions

International Nuclear Information System (INIS)

Jiang Yu; Dong Shihai; Lozada-Cassou, M.

2004-01-01

We study the resonant response of a nonlinear system to external periodic perturbations. We show by numerical simulation that the periodic resonance curve may anticipate the dynamical instability of the unperturbed nonlinear periodic system, at parameter values far away from the bifurcation points. In the presence of noise, the buried intrinsic periodic dynamics can be picked out by analyzing the system's response to periodic modulation of appropriate intensity

Dendritic nonlinearities are tuned for efficient spike-based computations in cortical circuits.

Science.gov (United States)

Ujfalussy, Balázs B; Makara, Judit K; Branco, Tiago; Lengyel, Máté

2015-12-24

Cortical neurons integrate thousands of synaptic inputs in their dendrites in highly nonlinear ways. It is unknown how these dendritic nonlinearities in individual cells contribute to computations at the level of neural circuits. Here, we show that dendritic nonlinearities are critical for the efficient integration of synaptic inputs in circuits performing analog computations with spiking neurons. We developed a theory that formalizes how a neuron's dendritic nonlinearity that is optimal for integrating synaptic inputs depends on the statistics of its presynaptic activity patterns. Based on their in vivo preynaptic population statistics (firing rates, membrane potential fluctuations, and correlations due to ensemble dynamics), our theory accurately predicted the responses of two different types of cortical pyramidal cells to patterned stimulation by two-photon glutamate uncaging. These results reveal a new computational principle underlying dendritic integration in cortical neurons by suggesting a functional link between cellular and systems--level properties of cortical circuits.

Mode coupling in the nonlinear response of black holes

International Nuclear Information System (INIS)

Zlochower, Yosef; Gomez, Roberto; Husa, Sascha; Lehner, Luis; Winicour, Jeffrey

2003-01-01

We study the properties of the outgoing gravitational wave produced when a nonspinning black hole is excited by an ingoing gravitational wave. Simulations using a numerical code for solving Einstein's equations allow the study to be extended from the linearized approximation, where the system is treated as a perturbed Schwarzschild black hole, to the fully nonlinear regime. Several nonlinear features are found which bear importance to the data analysis of gravitational waves. When compared to the results obtained in the linearized approximation, we observe large phase shifts, a stronger than linear generation of gravitational wave output and considerable generation of radiation in polarization states which are not found in the linearized approximation. In terms of a spherical harmonic decomposition, the nonlinear properties of the harmonic amplitudes have simple scaling properties which offer an economical way to catalog the details of the waves produced in such black hole processes

Cumulants of heat transfer across nonlinear quantum systems

Science.gov (United States)

Li, Huanan; Agarwalla, Bijay Kumar; Li, Baowen; Wang, Jian-Sheng

2013-12-01

We consider thermal conduction across a general nonlinear phononic junction. Based on two-time observation protocol and the nonequilibrium Green's function method, heat transfer in steady-state regimes is studied, and practical formulas for the calculation of the cumulant generating function are obtained. As an application, the general formalism is used to study anharmonic effects on fluctuation of steady-state heat transfer across a single-site junction with a quartic nonlinear on-site pinning potential. An explicit nonlinear modification to the cumulant generating function exact up to the first order is given, in which the Gallavotti-Cohen fluctuation symmetry is found still valid. Numerically a self-consistent procedure is introduced, which works well for strong nonlinearity.

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

Science.gov (United States)

Scott, M

2012-08-01

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

Small-χ singlet structure functions from the nonlinear GLR equation

International Nuclear Information System (INIS)

Kim, V.T.; Ryskin, M.G.

1991-06-01

The effect of absorptive corrections in the nonlinear GLR evolution equation is considered. A simple method how to estimate the corrections numerically is described. In the case of the parametrization based on semihard hadron phenomenology developed earlier a visible difference between linear and nonlinear evolution is expected at HERA energies. (orig.)

Pescara benchmarks: nonlinear identification

Science.gov (United States)

Gandino, E.; Garibaldi, L.; Marchesiello, S.

2011-07-01

Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled "Monitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing", financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.

Pescara benchmarks: nonlinear identification

International Nuclear Information System (INIS)

Gandino, E; Garibaldi, L; Marchesiello, S

2011-01-01

Recent nonlinear methods are suitable for identifying large systems with lumped nonlinearities, but in practice most structural nonlinearities are distributed and an ideal nonlinear identification method should cater for them as well. In order to extend the current NSI method to be applied also on realistic large engineering structures, a modal counterpart of the method is proposed in this paper. The modal NSI technique is applied on one of the reinforced concrete beams that have been tested in Pescara, under the project titled M onitoring and diagnostics of railway bridges by means of the analysis of the dynamic response due to train crossing , financed by Italian Ministry of Research. The beam showed a softening nonlinear behaviour, so that the nonlinearity concerning the first mode is characterized and its force contribution is quantified. Moreover, estimates for the modal parameters are obtained and the model is validated by comparing the measured and the reconstructed output. The identified estimates are also used to accurately predict the behaviour of the same beam, when subject to different initial conditions.

Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation

Science.gov (United States)

Peter, Simon; Leine, Remco I.

2017-11-01

Phase resonance testing is one method for the experimental extraction of nonlinear normal modes. This paper proposes a novel method for nonlinear phase resonance testing. Firstly, the issue of appropriate excitation is approached on the basis of excitation power considerations. Therefore, power quantities known from nonlinear systems theory in electrical engineering are transferred to nonlinear structural dynamics applications. A new power-based nonlinear mode indicator function is derived, which is generally applicable, reliable and easy to implement in experiments. Secondly, the tuning of the excitation phase is automated by the use of a Phase-Locked-Loop controller. This method provides a very user-friendly and fast way for obtaining the backbone curve. Furthermore, the method allows to exploit specific advantages of phase control such as the robustness for lightly damped systems and the stabilization of unstable branches of the frequency response. The reduced tuning time for the excitation makes the commonly used free-decay measurements for the extraction of backbone curves unnecessary. Instead, steady-state measurements for every point of the curve are obtained. In conjunction with the new mode indicator function, the correlation of every measured point with the associated nonlinear normal mode of the underlying conservative system can be evaluated. Moreover, it is shown that the analysis of the excitation power helps to locate sources of inaccuracies in the force appropriation process. The method is illustrated by a numerical example and its functionality in experiments is demonstrated on a benchmark beam structure.

The non-linear relationship between body size and function in parrotfishes

Science.gov (United States)

Lokrantz, J.; Nyström, M.; Thyresson, M.; Johansson, C.

2008-12-01

Parrotfishes are a group of herbivores that play an important functional role in structuring benthic communities on coral reefs. Increasingly, these fish are being targeted by fishermen, and resultant declines in biomass and abundance may have severe consequences for the dynamics and regeneration of coral reefs. However, the impact of overfishing extends beyond declining fish stocks. It can also lead to demographic changes within species populations where mean body size is reduced. The effect of reduced mean body size on population dynamics is well described in literature but virtually no information exists on how this may influence important ecological functions. The study investigated how one important function, scraping (i.e., the capacity to remove algae and open up bare substratum for coral larval settlement), by three common species of parrotfishes ( Scarus niger, Chlorurus sordidus, and Chlorurus strongylocephalus) on coral reefs at Zanzibar (Tanzania) was influenced by the size of individual fishes. There was a non-linear relationship between body size and scraping function for all species examined, and impact through scraping was also found to increase markedly when fish reached a size of 15 20 cm. Thus, coral reefs which have a high abundance and biomass of parrotfish may nonetheless be functionally impaired if dominated by small-sized individuals. Reductions in mean body size within parrotfish populations could, therefore, have functional impacts on coral reefs that previously have been overlooked.

Optical nonlinearity of D-A-π-D and D-A-π-A type of new chalcones for potential applications in optical limiting and density functional theory studies

Science.gov (United States)

Chandra Shekhara Shetty, T.; Chidan Kumar, C. S.; Gagan Patel, K. N.; Chia, Tze Shyang; Dharmaprakash, S. M.; Ramasami, Ponnadurai; Umar, Yunusa; Chandraju, Siddegowda; Quah, Ching Kheng

2017-09-01

Two new chalcones namely, (2E)-1-(3-fluoro-4-methoxyphenyl)-3-(4-methoxyphenyl) prop-2-en-1-one and (2E)-3-(4-chlorophenyl)-1-(3-fluoro-4-methoxyphenyl)prop-2-en-1-one were synthesized and grown as single crystals by slow evaporation technique in methanol. The FTIR spectrum recorded confirms the presence of functional groups in these materials. The molecular conformation of the compounds was achieved by single crystal X-ray diffraction studies. The thermal stability of the crystals was determined from TGA/DSC curve. The third order optical nonlinearity of the chalcone compounds in DMF solution has been carried out using an Nd:YAG laser at 532 nm as the source of excitation. The nonlinear optical response was characterized by measuring the intensity dependent refractive index n2 of the medium using Z-scan technique. It is seen that the molecules exhibit a negative (defocusing) nonlinearity and large nonlinear refractive index of the order of -1.8 × 10-11 esu. The third-order nonlinearity of the studied chalcones is dominated by nonlinear refraction, which leads to strong optical limiting of laser. The result reveals that these two new chalcone molecules would be a promising material for optical limiting applications. In addition, the optimized molecular geometry, vibrational frequencies in gas, and the Molecular Electrostatic Potential (MEP) surface parameters of the two molecules were calculated using DFT/B3LYP method with 6-311++G(d,p) basis set in ground state. All the theoretical calculations were found in good agreement with experimental data.

Transient response of nonlinear polymer networks: A kinetic theory

Science.gov (United States)

Vernerey, Franck J.

2018-06-01

Dynamic networks are found in a majority of natural materials, but also in engineering materials, such as entangled polymers and physically cross-linked gels. Owing to their transient bond dynamics, these networks display a rich class of behaviors, from elasticity, rheology, self-healing, or growth. Although classical theories in rheology and mechanics have enabled us to characterize these materials, there is still a gap in our understanding on how individuals (i.e., the mechanics of each building blocks and its connection with others) affect the emerging response of the network. In this work, we introduce an alternative way to think about these networks from a statistical point of view. More specifically, a network is seen as a collection of individual polymer chains connected by weak bonds that can associate and dissociate over time. From the knowledge of these individual chains (elasticity, transient attachment, and detachment events), we construct a statistical description of the population and derive an evolution equation of their distribution based on applied deformation and their local interactions. We specifically concentrate on nonlinear elastic response that follows from the strain stiffening response of individual chains of finite size. Upon appropriate averaging operations and using a mean field approximation, we show that the distribution can be replaced by a so-called chain distribution tensor that is used to determine important macroscopic measures such as stress, energy storage and dissipation in the network. Prediction of the kinetic theory are then explored against known experimental measurement of polymer responses under uniaxial loading. It is found that even under the simplest assumptions of force-independent chain kinetics, the model is able to reproduce complex time-dependent behaviors of rubber and self-healing supramolecular polymers.

New Traveling Wave Solutions of the Higher Dimensional Nonlinear Partial Differential Equation by the Exp-Function Method

Directory of Open Access Journals (Sweden)

Hasibun Naher

2012-01-01

Full Text Available We construct new analytical solutions of the (3+1-dimensional modified KdV-Zakharov-Kuznetsev equation by the Exp-function method. Plentiful exact traveling wave solutions with arbitrary parameters are effectively obtained by the method. The obtained results show that the Exp-function method is effective and straightforward mathematical tool for searching analytical solutions with arbitrary parameters of higher-dimensional nonlinear partial differential equation.

Nonlinear Poisson equation for heterogeneous media.

Science.gov (United States)

Hu, Langhua; Wei, Guo-Wei

2012-08-22

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Balancing for Unstable Nonlinear Systems

NARCIS (Netherlands)

Scherpen, J.M.A.

1993-01-01

A previously obtained method of balancing for stable nonlinear systems is extended to unstable nonlinear systems. The similarity invariants obtained by the concept of LQG balancing for an unstable linear system can also be obtained by considering a past and future energy function of the system. By

Linear and nonlinear Biot waves in a noncohesive granular medium slab: transfer function, self-action, second harmonic generation.

Science.gov (United States)

Legland, J-B; Tournat, V; Dazel, O; Novak, A; Gusev, V

2012-06-01

Experimental results are reported on second harmonic generation and self-action in a noncohesive granular medium supporting wave energy propagation both in the solid frame and in the saturating fluid. The acoustic transfer function of the probed granular slab can be separated into two main frequency regions: a low frequency region where the wave propagation is controlled by the solid skeleton elastic properties, and a higher frequency region where the behavior is dominantly due to the air saturating the beads. Experimental results agree well with a recently developed nonlinear Biot wave model applied to granular media. The linear transfer function, second harmonic generation, and self-action effect are studied as a function of bead diameter, compaction step, excitation amplitude, and frequency. This parametric study allows one to isolate different propagation regimes involving a range of described and interpreted linear and nonlinear processes that are encountered in granular media experiments. In particular, a theoretical interpretation is proposed for the observed strong self-action effect.

Nonlinear Dynamic Phenomena in Mechanics

CERN Document Server

Warminski, Jerzy; Cartmell, Matthew P

2012-01-01

Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear

The anisotropic Kerr nonlinear refractive index of the beta-barium borate (β-BaB₂O₄) nonlinear crystal

DEFF Research Database (Denmark)

Bache, Morten; Guo, Hairun; Zhou, Binbin

2013-01-01

We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (β-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant χ(3) cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments in the literat...... a complete list that we propose as reference of the four major cubic tensor components in BBO. We finally discuss the impact of using the cubic anisotropic response in ultrafast cascading experiments in BBO.......We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (β-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant χ(3) cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments...... in the literature are analyzed and we correct the data from some of the experiments for contributions from cascading as well as for updated material parameters. We also perform an additional experimental measurement of the Kerr nonlinear tensor component responsible for self-phase modulation in cascading, and we...