Modified multiple time scale method for solving strongly nonlinear damped forced vibration systems

Science.gov (United States)

Razzak, M. A.; Alam, M. Z.; Sharif, M. N.

2018-03-01

In this paper, modified multiple time scale (MTS) method is employed to solve strongly nonlinear forced vibration systems. The first-order approximation is only considered in order to avoid complexicity. The formulations and the determination of the solution procedure are very easy and straightforward. The classical multiple time scale (MS) and multiple scales Lindstedt-Poincare method (MSLP) do not give desire result for the strongly damped forced vibration systems with strong damping effects. The main aim of this paper is to remove these limitations. Two examples are considered to illustrate the effectiveness and convenience of the present procedure. The approximate external frequencies and the corresponding approximate solutions are determined by the present method. The results give good coincidence with corresponding numerical solution (considered to be exact) and also provide better result than other existing results. For weak nonlinearities with weak damping effect, the absolute relative error measures (first-order approximate external frequency) in this paper is only 0.07% when amplitude A = 1.5 , while the relative error gives MSLP method is surprisingly 28.81%. Furthermore, for strong nonlinearities with strong damping effect, the absolute relative error found in this article is only 0.02%, whereas the relative error obtained by MSLP method is 24.18%. Therefore, the present method is not only valid for weakly nonlinear damped forced systems, but also gives better result for strongly nonlinear systems with both small and strong damping effect.

Strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections

Energy Technology Data Exchange (ETDEWEB)

Chen, Zhaoting; Wang, Rong Hui; Chen, Li; Dong, Chung Uang [School of Civil Engineering and Transportation, South China University of Technology, Guangzhou (China)

2016-08-15

This article investigated the strongly nonlinear free vibration of four edges simply supported stiffened plates with geometric imperfections. The von Karman nonlinear strain-displacement relationships are applied. The nonlinear vibration of stiffened plate is reduced to a one-degree-of-freedom nonlinear system by assuming mode shapes. The Multiple scales Lindstedt-Poincare method (MSLP) and Modified Lindstedt-Poincare method (MLP) are used to solve the governing equations of vibration. Numerical examples for stiffened plates with different initial geometric imperfections are presented in order to discuss the influences to the strongly nonlinear free vibration of the stiffened plate. The results showed that: the frequency ratio reduced as the initial geometric imperfections of plate increased, which showed that the increase of the initial geometric imperfections of plate can lead to the decrease of nonlinear effect; by comparing the results calculated by MSLP method, using MS method to study strongly nonlinear vibration can lead to serious mistakes.

Relative Nonlinear Electrodynamics Interaction of Charged Particles with Strong and Super Strong Laser Fields

CERN Document Server

Avetissian, Hamlet

2006-01-01

This book covers a large class of fundamental investigations into Relativistic Nonlinear Electrodynamics. It explores the interaction between charged particles and strong laser fields, mainly concentrating on contemporary problems of x-ray lasers, new type small set-up high-energy accelerators of charged particles, as well as electron-positron pair production from super powerful laser fields of relativistic intensities. It will also discuss nonlinear phenomena of threshold nature that eliminate the concurrent inverse processes in the problems of Laser Accelerator and Free Electron Laser, thus creating new opportunities for solving these problems.

A nonlinear efficient layerwise finite element model for smart piezolaminated composites under strong applied electric field

International Nuclear Information System (INIS)

Kapuria, S; Yaqoob Yasin, M

2013-01-01

In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined. (paper)

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles.

Science.gov (United States)

Fonseca, P Z G; Aranas, E B; Millen, J; Monteiro, T S; Barker, P F

2016-10-21

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Nonlinear Dynamics and Strong Cavity Cooling of Levitated Nanoparticles

Science.gov (United States)

Fonseca, P. Z. G.; Aranas, E. B.; Millen, J.; Monteiro, T. S.; Barker, P. F.

2016-10-01

Optomechanical systems explore and exploit the coupling between light and the mechanical motion of macroscopic matter. A nonlinear coupling offers rich new physics, in both quantum and classical regimes. We investigate a dynamic, as opposed to the usually studied static, nonlinear optomechanical system, comprising a nanosphere levitated in a hybrid electro-optical trap. The cavity offers readout of both linear-in-position and quadratic-in-position (nonlinear) light-matter coupling, while simultaneously cooling the nanosphere, for indefinite periods of time and in high vacuum. We observe the cooling dynamics via both linear and nonlinear coupling. As the background gas pressure was lowered, we observed a greater than 1000-fold reduction in temperature before temperatures fell below readout sensitivity in the present setup. This Letter opens the way to strongly coupled quantum dynamics between a cavity and a nanoparticle largely decoupled from its environment.

Blow-Up Analysis for a Quasilinear Degenerate Parabolic Equation with Strongly Nonlinear Source

Directory of Open Access Journals (Sweden)

Pan Zheng

2012-01-01

Full Text Available We investigate the blow-up properties of the positive solution of the Cauchy problem for a quasilinear degenerate parabolic equation with strongly nonlinear source ut=div(|∇um|p−2∇ul+uq,  (x,t∈RN×(0,T, where N≥1, p>2 , and m, l,  q>1, and give a secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and nonexistence of global solutions of the Cauchy problem. Moreover, under some suitable conditions we prove single-point blow-up for a large class of radial decreasing solutions.

Nonlinearities in Behavioral Macroeconomics.

Science.gov (United States)

Gomes, Orlando

2017-07-01

This article undertakes a journey across the literature on behavioral macroeconomics, with attention concentrated on the nonlinearities that the behavioral approach typically suggests or implies. The emphasis is placed on thinking the macro economy as a living organism, composed of many interacting parts, each one having a will of its own, which is in sharp contrast with the mechanism of the orthodox view (well represented by the neoclassical or new Keynesian dynamic stochastic general equilibrium - DSGE - model). The paper advocates that a thorough understanding of individual behavior in collective contexts is the only possible avenue to further explore macroeconomic phenomena and the often observed 'anomalies' that the benchmark DSGE macro framework is unable to explain or justify. After a reflection on the role of behavioral traits as a fundamental component of a new way of thinking the economy, the article proceeds with a debate on some of the most relevant frameworks in the literature that somehow link macro behavior and nonlinearities; covered subjects include macro models with disequilibrium rules, agent-based models that highlight interaction and complexity, evolutionary switching frameworks, and inattention based decision problems. These subjects have, as a fundamental point in common, the use of behavioral elements to transform existing interpretations of the economic reality, making it more evident how irregular fluctuations emerge and unfold on the aggregate.

A method for regulating strong nonlinear vibration energy of the flexible arm

Directory of Open Access Journals (Sweden)

Yushu Bian

2015-07-01

Full Text Available For an oscillating system, large amplitude indicates strong vibration energy. In this article, modal interaction is used as a useful means to regulate strong nonlinear vibration energy of the flexible arm undergoing rigid motion. A method is put forward to migrate and dissipate vibration energy based on modal interaction. By means of multiple-scale perturbation analysis, it is proven that internal resonance can be successfully established between modes of the flexible arm and the vibration absorber. Through examples and analyses, it is verified that this control method is effective in regulating strong vibration energy and can be used to suppress strong nonlinear vibration of the flexible arm undergoing rigid motion.

Strongly nonlinear dynamics of electrolytes in large ac voltages

DEFF Research Database (Denmark)

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

2010-01-01

to suppress the strongly nonlinear regime in the limit of concentrated electrolytes, ionic liquids, and molten salts. Beyond the model problem, our reduced equations for thin double layers, based on uniformly valid matched asymptotic expansions, provide a useful mathematical framework to describe additional...

Dissipative behavior of some fully non-linear KdV-type equations

Science.gov (United States)

Brenier, Yann; Levy, Doron

2000-03-01

The KdV equation can be considered as a special case of the general equation u t+f(u) x-δg(u xx) x=0, δ>0, where f is non-linear and g is linear, namely f( u)= u2/2 and g( v)= v. As the parameter δ tends to 0, the dispersive behavior of the KdV equation has been throughly investigated (see, e.g., [P.G. Drazin, Solitons, London Math. Soc. Lect. Note Ser. 85, Cambridge University Press, Cambridge, 1983; P.D. Lax, C.D. Levermore, The small dispersion limit of the Korteweg-de Vries equation, III, Commun. Pure Appl. Math. 36 (1983) 809-829; G.B. Whitham, Linear and Nonlinear Waves, Wiley/Interscience, New York, 1974] and the references therein). We show through numerical evidence that a completely different, dissipative behavior occurs when g is non-linear, namely when g is an even concave function such as g( v)=-∣ v∣ or g( v)=- v2. In particular, our numerical results hint that as δ→0 the solutions strongly converge to the unique entropy solution of the formal limit equation, in total contrast with the solutions of the KdV equation.

Strongly nonlinear evolution of low-frequency wave packets in a dispersive plasma

Science.gov (United States)

Vasquez, Bernard J.

1993-01-01

The evolution of strongly nonlinear, strongly modulated wave packets is investigated in a dispersive plasma using a hybrid numerical code. These wave packets have amplitudes exceeding the strength of the external magnetic field, along which they propagate. Alfven (left helicity) wave packets show strong steepening for p Schrodinger (DNLS) equation.

Nonlinear hydromagnetic Rayleigh-Taylor instability for strong viscous fluids in porous media

CERN Document Server

El-Dib, Y O

2003-01-01

In the present work a weakly nonlinear stability for magnetic fluid is discussed. The research of an interface between two strong viscous homogeneous incompressible fluids through porous medium is investigated theoretically and graphically. The effect of the vertical magnetic field has been demonstrated in this study. The linear form of equation of motion is solved in the light of the nonlinear boundary conditions. The boundary value problem leads to construct nonlinear characteristic equation having complex coefficients in elevation function. The nonlinearity is kept to third-order expansion. The nonlinear characteristic equation leads to derive the well-known nonlinear Schroedinger equation. This equation having complex coefficients of the disturbance amplitude varies in both space and time. Stability criteria have been performed for nonlinear Chanderasekhar dispersion relation including the porous effects. Stability conditions are discussed through the assumption of equal kinematic viscosity. The calculati...

Nonlinear Finite Strain Consolidation Analysis with Secondary Consolidation Behavior

Directory of Open Access Journals (Sweden)

Jieqing Huang

2014-01-01

Full Text Available This paper aims to analyze nonlinear finite strain consolidation with secondary consolidation behavior. On the basis of some assumptions about the secondary consolidation behavior, the continuity equation of pore water in Gibson’s consolidation theory is modified. Taking the nonlinear compressibility and nonlinear permeability of soils into consideration, the governing equation for finite strain consolidation analysis is derived. Based on the experimental data of Hangzhou soft clay samples, the new governing equation is solved with the finite element method. Afterwards, the calculation results of this new method and other two methods are compared. It can be found that Gibson’s method may underestimate the excess pore water pressure during primary consolidation. The new method which takes the secondary consolidation behavior, the nonlinear compressibility, and nonlinear permeability of soils into consideration can precisely estimate the settlement rate and the final settlement of Hangzhou soft clay sample.

Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment

Energy Technology Data Exchange (ETDEWEB)

Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.; Obayashi, T.

1986-01-01

A rocket-borne experiment called MINIX was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction Experiment and was carried out on August 29, 1983. The objectives of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere such as the Ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no Ohmic heating effects were detected. 4 figures.

Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment

Science.gov (United States)

Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.

A rocket-borne experiment called 'MINIX' was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction eXperiment and was carried out on August 29, 1983. The objective of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere, such as the ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no ohmic heating effects were detected.

Nonlinear interaction of strong microwave beam with the ionosphere MINIX rocket experiment

International Nuclear Information System (INIS)

Kaya, N.; Matsumoto, H.; Miyatake, S.; Kimura, I.; Nagatomo, M.; Obayashi, T.

1986-01-01

A rocket-borne experiment called MINIX was carried out to investigate the nonlinear interaction of a strong microwave energy beam with the ionosphere. The MINIX stands for Microwave-Ionosphere Nonlinear Interaction Experiment and was carried out on August 29, 1983. The objectives of the MINIX is to study possible impacts of the SPS microwave energy beam on the ionosphere such as the Ohmic heating and plasma wave excitation. The experiment showed that the microwave with f = 2.45 GHz nonlinearly excites various electrostatic plasma waves, though no Ohmic heating effects were detected. 4 figures

Nonlinear propagation of strong-field THz pulses in doped semiconductors

DEFF Research Database (Denmark)

Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias C.

2012-01-01

We report on nonlinear propagation of single-cycle THz pulses with peak electric fields reaching 300 kV/cm in n-type semiconductors at room temperature. Dramatic THz saturable absorption effects are observed in GaAs, GaP, and Ge, which are caused by the nonlinear electron transport in THz fields....... The semiconductor conductivity, and hence the THz absorption, is modulated due to the acceleration of carriers in strong THz fields, leading to an increase of the effective mass of the electron population, as the electrons are redistributed from the low-momentum, low-effective-mass states to the high-momentum, high...

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.

Nonlinear phononics and structural control of strongly correlated materials

Energy Technology Data Exchange (ETDEWEB)

Mankowsky, Roman

2016-01-20

Mid-infrared light pulses can be used to resonantly excite infrared-active vibrational modes for the phase control of strongly correlated materials on subpicosecond timescales. As the energy is transferred directly into atomic motions, dissipation into the electronic system is reduced, allowing for the emergence of unusual low energy collective properties. Light-induced superconductivity, insulator-metal transitions and melting of magnetic order demonstrate the potential of this method. An understanding of the mechanism, by which these transitions are driven, is however missing. The aim of this work is to uncover this process by investigating the nonlinear lattice dynamics induced by the excitation and to elucidate their contribution to the modulation of collective properties of strongly correlated materials. The first signature of nonlinear lattice dynamics was reported in the observation of coherent phonon oscillations, resonant with the excitation of an infrared-active phonon mode in a manganite. This nonlinear phononic coupling can be described within a model, which predicts not only oscillatory coherent phonons dynamics but also directional atomic displacements along the coupled modes on average, which could cause the previously observed transitions. We verified this directional response and quantified the anharmonic coupling constant by tracing the atomic motions in a time-resolved hard X-ray diffraction experiment with sub-picometer spatial and femtosecond temporal resolution. In a subsequent study, we investigated the role of nonlinear lattice dynamics in the emergence of superconductivity far above the equilibrium transition temperature, an intriguing effect found to follow lattice excitation of YBa{sub 2}Cu{sub 3}O{sub 6+x}. By combining density functional theory (DFT) calculations of the anharmonic coupling constants with time-resolved X-ray diffraction experiments, we identified a structural rearrangement, which appears and decays with the same temporal

A novel strong tracking finite-difference extended Kalman filter for nonlinear eye tracking

Institute of Scientific and Technical Information of China (English)

ZHANG ZuTao; ZHANG JiaShu

2009-01-01

Non-Intrusive methods for eye tracking are Important for many applications of vision-based human computer interaction. However, due to the high nonlinearity of eye motion, how to ensure the robust-ness of external interference and accuracy of eye tracking poses the primary obstacle to the integration of eye movements into today's interfaces. In this paper, we present a strong tracking finite-difference extended Kalman filter algorithm, aiming to overcome the difficulty In modeling nonlinear eye tracking. In filtering calculation, strong tracking factor is introduced to modify a priori covariance matrix and im-prove the accuracy of the filter. The filter uses finite-difference method to calculate partial derivatives of nonlinear functions for eye tracking. The latest experimental results show the validity of our method for eye tracking under realistic conditions.

Nonlinear damping of drift waves by strong flow curvature

International Nuclear Information System (INIS)

Sidikman, K.L.; Carreras, B.A.; Garcia, L.; Diamond, P.H.

1993-01-01

A single-equation model has been used to study the effect of a fixed poloidal flow (V 0 ) on turbulent drift waves. The electron dynamics come from a laminar kinetic equation in the dissipative trapped-electron regime. In the past, the authors have assumed that the mode frequency is close to the drift-wave frequency. Trapped-electron density fluctuations are then related to potential fluctuations by an open-quotes iδclose quotes term. Flow shear (V 0 ') and curvature (V 0 double-prime) both have a stabilizing effect on linear modes for this open-quotes iδclose quotes model. However, in the nonlinear regime, single-helicity effects inhibit the flow damping. Neither V 0 ' nor V 0 double-prime produces a nonlinear damping effect. The above assumption on the frequency can be relaxed by including the electron time-response in the linear part of the evolution. In this time-dependent model, instability drive due to trapped electrons is reduced when mode frequency is greater than drift-wave frequency. Since V 0 double-prime produces such a frequency shift, its linear effect is enhanced. There is also nonlinear damping, since single-helicity effects do not eliminate the shift. Renormalized theory for this model predicts nonlinear stability for sufficiently large curvature. Single-helicity calculations have already shown nonlinear damping, and this strong V 0 double-prime regime is being explored. In the theory, the Gaussian shape of the nonlinear diffusivity is expanded to obtain a quadratic potential. The implications of this assumption will be tested by solving the full renormalized equation using a shooting method

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.

Nonlinear transport behavior of low dimensional electron systems

Science.gov (United States)

Zhang, Jingqiao

The nonlinear behavior of low-dimensional electron systems attracts a great deal of attention for its fundamental interest as well as for potentially important applications in nanoelectronics. In response to microwave radiation and dc bias, strongly nonlinear electron transport that gives rise to unusual electron states has been reported in two-dimensional systems of electrons in high magnetic fields. There has also been great interest in the nonlinear response of quantum ballistic constrictions, where the effects of quantum interference, spatial dispersion and electron-electron interactions play crucial roles. In this thesis, experimental results of the research of low dimensional electron gas systems are presented. The first nonlinear phenomena were observed in samples of highly mobile two dimensional electrons in GaAs heavily doped quantum wells at different magnitudes of DC and AC (10 KHz to 20 GHz) excitations. We found that in the DC excitation regime the differential resistance oscillates with the DC current and external magnetic field, similar behavior was observed earlier in AlGaAs/GaAs heterostructures [C.L. Yang et al. ]. At external AC excitations the resistance is found to be also oscillating as a function of the magnetic field. However the form of the oscillations is considerably different from the DC case. We show that at frequencies below 100 KHz the difference is a result of a specific average of the DC differential resistance during the period of the external AC excitations. Secondly, in similar samples, strong suppression of the resistance by the electric field is observed in magnetic fields at which the Landau quantization of electron motion occurs. The phenomenon survives at high temperatures at which the Shubnikov de Haas oscillations are absent. The scale of the electric fields essential for the effect, is found to be proportional to temperature in the low temperature limit. We suggest that the strong reduction of the longitudinal resistance

Nonlinear dynamic behaviors of an optically injected vertical-cavity surface-emitting laser

International Nuclear Information System (INIS)

Li Xiaofeng; Pan Wei; Luo Bin; Ma Dong; Wang Yong; Li Nuohan

2006-01-01

Nonlinear dynamics of a vertical-cavity surface-emitting laser (VCSEL) with external optical injection are studied numerically. We consider a master-slave configuration where the dynamic characteristics of the slave are affected by the optical injection from the master, and we also establish the corresponding Simulink model. The period-doubling route as well as the period-halving route is observed, where the regular, double-periodic, and chaotic pulsings are found. By adjusting the injection strength properly, the laser can be controlled to work at a given state. The effects of frequency detuning on the nonlinear behaviors are also investigated in terms of the bifurcation diagrams of photon density with the frequency detuning. For weak injection case, the nonlinear dynamics shown by the laser are quite different when the value of frequency detuning varies contrarily (positive and negative direction). If the optical injection is strong enough, the slave can be locked by the master even though the frequency detuning is relatively large

Sampling strong tracking nonlinear unscented Kalman filter and its application in eye tracking

International Nuclear Information System (INIS)

Zu-Tao, Zhang; Jia-Shu, Zhang

2010-01-01

The unscented Kalman filter is a developed well-known method for nonlinear motion estimation and tracking. However, the standard unscented Kalman filter has the inherent drawbacks, such as numerical instability and much more time spent on calculation in practical applications. In this paper, we present a novel sampling strong tracking nonlinear unscented Kalman filter, aiming to overcome the difficulty in nonlinear eye tracking. In the above proposed filter, the simplified unscented transform sampling strategy with n + 2 sigma points leads to the computational efficiency, and suboptimal fading factor of strong tracking filtering is introduced to improve robustness and accuracy of eye tracking. Compared with the related unscented Kalman filter for eye tracking, the proposed filter has potential advantages in robustness, convergence speed, and tracking accuracy. The final experimental results show the validity of our method for eye tracking under realistic conditions. (classical areas of phenomenology)

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.)

On the Nonlinear Behavior of the Piezoelectric Coupling on Vibration-Based Energy Harvesters

Directory of Open Access Journals (Sweden)

Luciana L. Silva

2015-01-01

Full Text Available Vibration-based energy harvesting with piezoelectric elements has an increasing importance nowadays being related to numerous potential applications. A wide range of nonlinear effects is observed in energy harvesting devices and the analysis of the power generated suggests that they have considerable influence on the results. Linear constitutive models for piezoelectric materials can provide inconsistencies on the prediction of the power output of the energy harvester, mainly close to resonant conditions. This paper investigates the effect of the nonlinear behavior of the piezoelectric coupling. A one-degree of freedom mechanical system is coupled to an electrical circuit by a piezoelectric element and different coupling models are investigated. Experimental tests available in the literature are employed as a reference establishing the best matches of the models. Subsequently, numerical simulations are carried out showing different responses of the system indicating that nonlinear piezoelectric couplings can strongly modify the system dynamics.

Nonlinear electro-mechanobiological behavior of cell membrane during electroporation

KAUST Repository

Deng, Peigang; Lee, Yi-Kuen; Lin, Ran; Zhang, Tong-Yi

2012-01-01

A nonlinear electroporation (EP) model is proposed to study the electro-mechanobiological behavior of cell membrane during EP, by taking the nonlinear large deformation of the membrane into account. The proposed model predicts the critical

Strong phase correlations of solitons of nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Litvak, A.G.; Mironov, V.A.; Protogenov, A.P.

1994-06-01

We discuss the possibility to suppress the collapse in the nonlinear 2+1 D Schroedinger equation by using the gauge theory of strong phase correlations. It is shown that invariance relative to q-deformed Hopf algebra with deformation parameter q being the fourth root of unity makes the values of the Chern-Simons term coefficient, k=2, and of the coupling constant, g=1/2, fixed; no collapsing solutions are present at those values. (author). 21 refs

Strongly nonlinear theory of rapid solidification near absolute stability

Science.gov (United States)

Kowal, Katarzyna N.; Altieri, Anthony L.; Davis, Stephen H.

2017-10-01

We investigate the nonlinear evolution of the morphological deformation of a solid-liquid interface of a binary melt under rapid solidification conditions near two absolute stability limits. The first of these involves the complete stabilization of the system to cellular instabilities as a result of large enough surface energy. We derive nonlinear evolution equations in several limits in this scenario and investigate the effect of interfacial disequilibrium on the nonlinear deformations that arise. In contrast to the morphological stability problem in equilibrium, in which only cellular instabilities appear and only one absolute stability boundary exists, in disequilibrium the system is prone to oscillatory instabilities and a second absolute stability boundary involving attachment kinetics arises. Large enough attachment kinetics stabilize the oscillatory instabilities. We derive a nonlinear evolution equation to describe the nonlinear development of the solid-liquid interface near this oscillatory absolute stability limit. We find that strong asymmetries develop with time. For uniform oscillations, the evolution equation for the interface reduces to the simple form f''+(βf')2+f =0 , where β is the disequilibrium parameter. Lastly, we investigate a distinguished limit near both absolute stability limits in which the system is prone to both cellular and oscillatory instabilities and derive a nonlinear evolution equation that captures the nonlinear deformations in this limit. Common to all these scenarios is the emergence of larger asymmetries in the resulting shapes of the solid-liquid interface with greater departures from equilibrium and larger morphological numbers. The disturbances additionally sharpen near the oscillatory absolute stability boundary, where the interface becomes deep-rooted. The oscillations are time-periodic only for small-enough initial amplitudes and their frequency depends on a single combination of physical parameters, including the

Nonlinear Principal Component Analysis Using Strong Tracking Filter

Institute of Scientific and Technical Information of China (English)

无

2007-01-01

The paper analyzes the problem of blind source separation (BSS) based on the nonlinear principal component analysis (NPCA) criterion. An adaptive strong tracking filter (STF) based algorithm was developed, which is immune to system model mismatches. Simulations demonstrate that the algorithm converges quickly and has satisfactory steady-state accuracy. The Kalman filtering algorithm and the recursive leastsquares type algorithm are shown to be special cases of the STF algorithm. Since the forgetting factor is adaptively updated by adjustment of the Kalman gain, the STF scheme provides more powerful tracking capability than the Kalman filtering algorithm and recursive least-squares algorithm.

Size effects in non-linear heat conduction with flux-limited behaviors

Science.gov (United States)

Li, Shu-Nan; Cao, Bing-Yang

2017-11-01

Size effects are discussed for several non-linear heat conduction models with flux-limited behaviors, including the phonon hydrodynamic, Lagrange multiplier, hierarchy moment, nonlinear phonon hydrodynamic, tempered diffusion, thermon gas and generalized nonlinear models. For the phonon hydrodynamic, Lagrange multiplier and tempered diffusion models, heat flux will not exist in problems with sufficiently small scale. The existence of heat flux needs the sizes of heat conduction larger than their corresponding critical sizes, which are determined by the physical properties and boundary temperatures. The critical sizes can be regarded as the theoretical limits of the applicable ranges for these non-linear heat conduction models with flux-limited behaviors. For sufficiently small scale heat conduction, the phonon hydrodynamic and Lagrange multiplier models can also predict the theoretical possibility of violating the second law and multiplicity. Comparisons are also made between these non-Fourier models and non-linear Fourier heat conduction in the type of fast diffusion, which can also predict flux-limited behaviors.

Nonlinear behavior of the radiative condensation instability

International Nuclear Information System (INIS)

McCarthy, D.; Drake, J.F.

1991-01-01

An investigation of the nonlinear behavior of the radiative condensation instability is presented in a simple one-dimensional magnetized plasma. It is shown that the radiative condensation is typically a nonlinear instability---the growth of the instability is stronger once the disturbance reaches finite amplitude. Moreover, classical parallel thermal conduction is insufficient by itself to saturate the instability. Radiative collapse continues until the temperature in the high density condensation falls sufficiently to reduce the radiation rate

Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation

International Nuclear Information System (INIS)

Bouard, Anne de; Debussche, Arnaud

2006-01-01

In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1

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.

Investigation of nonlinear I–V behavior of CNTs filled polymer composites

International Nuclear Information System (INIS)

Wang, Jian; Yu, Shuhui; Luo, Suibin; Chu, Baojin; Sun, Rong; Wong, Ching-Ping

2016-01-01

Graphical abstract: - Highlights: • Mechanism of nonlinear behavior of the CNT composites was systematically investigated. • There are one linear region (I) and two nonlinear regions (II and III) in the I–V curves. • This phenomenon was analyzed based on hopping, tunneling and Joule heating effects. - Abstract: Nonlinear current–voltage (I–V) behavior is a typical feature of polymeric composites containing conductor or semiconductor fillers, which are desired to handle the transient voltage and electrostatic discharge (ESD) of microelectronic devices. In this paper, the mechanism of nonlinear behavior of carbon nanotubes (CNTs) filled polymer composites in the applied electric field was explored. The I–V curves of the composites exhibited three regions. The variation of current at low voltages (region I) is linear. Under relatively higher voltages (region II), the variation is nonlinear and grows rapidly with voltage. As the voltage is further increased, the I–V curve is still non-linear (region III), but the growth rate is significantly slowed down. The I–V characteristics in the above three regions were analyzed systematically based on the calculation of the electrons hopping from the conduction band of CNTs to epoxy, the induced current under electric field, as well as Joule-heating and tunneling effect.

Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

KAUST Repository

Gottlieb, Sigal

2015-04-10

High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.

A new nonlinear conjugate gradient coefficient under strong Wolfe-Powell line search

Science.gov (United States)

Mohamed, Nur Syarafina; Mamat, Mustafa; Rivaie, Mohd

2017-08-01

A nonlinear conjugate gradient method (CG) plays an important role in solving a large-scale unconstrained optimization problem. This method is widely used due to its simplicity. The method is known to possess sufficient descend condition and global convergence properties. In this paper, a new nonlinear of CG coefficient βk is presented by employing the Strong Wolfe-Powell inexact line search. The new βk performance is tested based on number of iterations and central processing unit (CPU) time by using MATLAB software with Intel Core i7-3470 CPU processor. Numerical experimental results show that the new βk converge rapidly compared to other classical CG method.

Ensemble-based Kalman Filters in Strongly Nonlinear Dynamics

Institute of Scientific and Technical Information of China (English)

Zhaoxia PU; Joshua HACKER

2009-01-01

This study examines the effectiveness of ensemble Kalman filters in data assimilation with the strongly nonlinear dynamics of the Lorenz-63 model, and in particular their use in predicting the regime transition that occurs when the model jumps from one basin of attraction to the other. Four configurations of the ensemble-based Kalman filtering data assimilation techniques, including the ensemble Kalman filter, ensemble adjustment Kalman filter, ensemble square root filter and ensemble transform Kalman filter, are evaluated with their ability in predicting the regime transition (also called phase transition) and also are compared in terms of their sensitivity to both observational and sampling errors. The sensitivity of each ensemble-based filter to the size of the ensemble is also examined.

Nonlinear Physics of Plasmas

CERN Document Server

Kono, Mitsuo

2010-01-01

A nonlinearity is one of the most important notions in modern physics. A plasma is rich in nonlinearities and provides a variety of behaviors inherent to instabilities, coherent wave structures and turbulence. The book covers the basic concepts and mathematical methods, necessary to comprehend nonlinear problems widely encountered in contemporary plasmas, but also in other fields of physics and current research on self-organized structures and magnetized plasma turbulence. The analyses make use of strongly nonlinear models solved by analytical techniques backed by extensive simulations and available experiments. The text is written for senior undergraduates, graduate students, lecturers and researchers in laboratory, space and fusion plasmas.

A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations

International Nuclear Information System (INIS)

Ge, Gen; Li, ZePeng

2016-01-01

A modified stochastic averaging method on single-degree-of-freedom (SDOF) oscillators under white noise excitations with strongly nonlinearity was proposed. Considering the existing approach dealing with strongly nonlinear SDOFs derived by Zhu and Huang [14, 15] is quite time consuming in calculating the drift coefficient and diffusion coefficients and the expressions of them are considerable long, the so-called He's energy balance method was applied to overcome the minor defect of the Zhu and Huang's method. The modified method can offer more concise approximate expressions of the drift and diffusion coefficients without weakening the accuracy of predicting the responses of the systems too much by giving an averaged frequency beforehand. Three examples, a cubic and quadratic nonlinearity coexisting oscillator, a quadratic nonlinear oscillator under external white noise excitations and an externally excited Duffing–Rayleigh oscillator, were given to illustrate the approach we proposed. The three examples were excited by the Gaussian white noise and the Gaussian colored noise separately. The stationary responses of probability density of amplitudes and energy, together with joint probability density of displacement and velocity are studied to verify the presented approach. The reliability of the systems were also investigated to offer further support. Digital simulations were carried out and the output of that are coincide with the theoretical approximations well.

Non-linear Behavior of Curved Sandwich Panels

DEFF Research Database (Denmark)

Berggreen, Carl Christian; Jolma, P.; Karjalainen, J. P.

2003-01-01

In this paper the non-linear behavior of curved sandwich panels is investigated both numerically and experimentally. Focus is on various aspects of finite element modeling and calculation procedures. A simply supported, singly curved, CFRP/PVC sandwich panel is analyzed under uniform pressure loa...

Understanding of flux-limited behaviors of heat transport in nonlinear regime

Energy Technology Data Exchange (ETDEWEB)

Guo, Yangyu, E-mail: yangyuhguo@gmail.com [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China); Jou, David, E-mail: david.jou@uab.es [Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia (Spain); Wang, Moran, E-mail: mrwang@tsinghua.edu [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China)

2016-01-28

The classical Fourier's law of heat transport breaks down in highly nonequilibrium situations as in nanoscale heat transport, where nonlinear effects become important. The present work is aimed at exploring the flux-limited behaviors based on a categorization of existing nonlinear heat transport models in terms of their theoretical foundations. Different saturation heat fluxes are obtained, whereas the same qualitative variation trend of heat flux versus exerted temperature gradient is got in diverse nonlinear models. The phonon hydrodynamic model is proposed to act as a standard to evaluate other heat flux limiters because of its more rigorous physical foundation. A deeper knowledge is thus achieved about the phenomenological generalized heat transport models. The present work provides deeper understanding and accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit. - Highlights: • Exploring flux-limited behaviors based on a categorization of existing nonlinear heat transport models. • Proposing phonon hydrodynamic model as a standard to evaluate heat flux limiters. • Providing accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit.

Explicit and exact solutions for a generalized long-short wave resonance equations with strong nonlinear term

International Nuclear Information System (INIS)

Shang Yadong

2005-01-01

In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions

Analysis of the Nonlinear Static and Dynamic Behavior of Offshore Structures

KAUST Repository

Alfosail, Feras

2015-01-01

Understanding static and dynamic nonlinear behavior of pipes and risers is crucial for the design aspects in offshore engineering fields. In this work, we examine two nonlinear problems in offshore engineering field: vortex Induced vibration

Nonlinear behavior of three-terminal graphene junctions at room temperature

International Nuclear Information System (INIS)

Kim, Wonjae; Riikonen, Juha; Lipsanen, Harri; Pasanen, Pirjo

2012-01-01

We demonstrate nonlinear behavior in three-terminal T-branch graphene devices at room temperature. A rectified nonlinear output at the center branch is observed when the device is biased by a push–pull configuration. Nonlinearity is assumed to arise from a difference in charge transfer through the metal–graphene contact barrier between two contacts. The sign of the rectification can be altered by changing the carrier type using the back-gate voltage. (paper)

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.

Nonlinear DC Conduction Behavior in Graphene Nanoplatelets/Epoxy Resin Composites

Science.gov (United States)

Yuan, Yang; Wang, Qingguo; Qu, Zhaoming

2018-01-01

Graphene nanoplatelets (GNPs)/Epoxy resin (ER) with a low percolation threshold were fabricated. Then the nonlinear DC conduction behavior of GNPs/ER composites was investigated, which indicates that dispersion, exfoliation level and conductivity of GNPs in specimens are closely related to the conduction of composites. Moreover, it could be seen that the modified graphene nanoplatelets made in this paper could be successfully used for increasing the electric conductivity of the epoxy resin, and the GNPs/ER composites with nonlinear conduction behavior have a good application prospects in the field of intelligent electromagnetic protection.

Nonlinear dynamics in human behavior

Energy Technology Data Exchange (ETDEWEB)

Huys, Raoul [Centre National de la Recherche Scientifique (CNRS), 13 - Marseille (France); Marseille Univ. (France). Movement Science Inst.; Jirsa, Viktor K. (eds.) [Centre National de la Recherche Scientifique (CNRS), 13 - Marseille (France); Marseille Univ. (France). Movement Science Inst.; Florida Atlantic Univ., Boca Raton, FL (United States). Center for Complex Systems and Brain Sciences

2010-07-01

Humans engage in a seemingly endless variety of different behaviors, of which some are found across species, while others are conceived of as typically human. Most generally, behavior comes about through the interplay of various constraints - informational, mechanical, neural, metabolic, and so on - operating at multiple scales in space and time. Over the years, consensus has grown in the research community that, rather than investigating behavior only from bottom up, it may be also well understood in terms of concepts and laws on the phenomenological level. Such top down approach is rooted in theories of synergetics and self-organization using tools from nonlinear dynamics. The present compendium brings together scientists from all over the world that have contributed to the development of their respective fields departing from this background. It provides an introduction to deterministic as well as stochastic dynamical systems and contains applications to motor control and coordination, visual perception and illusion, as well as auditory perception in the context of speech and music. (orig.)

Chameleon's behavior of modulable nonlinear electrical transmission line

Science.gov (United States)

Togueu Motcheyo, A. B.; Tchinang Tchameu, J. D.; Fewo, S. I.; Tchawoua, C.; Kofane, T. C.

2017-12-01

We show that modulable discrete nonlinear transmission line can adopt Chameleon's behavior due to the fact that, without changing its appearance structure, it can become alternatively purely right or left handed line which is different to the composite one. Using a quasidiscrete approximation, we derive a nonlinear Schrödinger equation, that predicts accurately the carrier frequency threshold from the linear analysis. It appears that the increasing of the linear capacitor in parallel in the series branch induced the selectivity of the filter in the right-handed region while it increases band pass filter in the left-handed region. Numerical simulations of the nonlinear model confirm the forward wave in the right handed line and the backward wave in the left handed one.

Strong coupling between coherent gratings due to nonlinear spatial frequency mixing in Bi12SiO20

DEFF Research Database (Denmark)

Andersen, Peter E.; Buchhave, P.; Petersen, Paul Michael

1996-01-01

Nonlinear interactions between multiple coherent photorefractive gratings in Bi12SiO20 are investigated. It is demonstrated that the nonlinear mixing, or cross talk, is strongly influenced by the intensity ration kappa between the two object beams. The diffraction efficiency of a specific grating...... may be increased or strongly decreased depending on kappa. In the limit of a weak reference beam intensity compared to the sum of the object beam intencities, we derive an analytical expression for the cross talk valid for all kappa. Furthermore, we find the value of kappa yielding zero cross talk. We...

Modeling of Nonlinear Propagation in Multi-layer Biological Tissues for Strong Focused Ultrasound

International Nuclear Information System (INIS)

Ting-Bo, Fan; Zhen-Bo, Liu; Zhe, Zhang; Dong, Zhang; Xiu-Fen, Gong

2009-01-01

A theoretical model of the nonlinear propagation in multi-layered tissues for strong focused ultrasound is proposed. In this model, the spheroidal beam equation (SBE) is utilized to describe the nonlinear sound propagation in each layer tissue, and generalized oblique incidence theory is used to deal with the sound transmission between two layer tissues. Computer simulation is performed on a fat-muscle-liver tissue model under the irradiation of a 1 MHz focused transducer with a large aperture angle of 35°. The results demonstrate that the tissue layer would change the amplitude of sound pressure at the focal region and cause the increase of side petals. (fundamental areas of phenomenology (including applications))

Nonlinear dynamical phenomena in liquid crystals

International Nuclear Information System (INIS)

Wang, X.Y.; Sun, Z.M.

1988-09-01

Because of the existence of the orientational order and anisotropy in liquid crystals, strong nonlinear phenomena and singular behaviors, such as solitary wave, transient periodic structure, chaos, fractal and viscous fingering, can be excited by a very small disturbance. These phenomena and behaviors are in connection with physics, biology and mathematics. 12 refs, 6 figs

Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity

Science.gov (United States)

Riviere, J.; Guyer, R.; Renaud, G.; TenCate, J. A.; Johnson, P. A.

2012-12-01

In comparison with standard nonlinear ultrasonic methods like frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. This method consists of exciting a sample in Bulk-mode resonance at strains of 10-7 to 10-5 and simultaneously probing with a sequence of high frequency, low amplitude pulses. Time of flight and amplitudes of these pulses, respectively related to nonlinear elastic and dissipative parameters, can be plotted versus vibration strain level. Despite complex nonlinear signatures obtained for most rocks, it can be shown that for low strain amplitude (Pasqualini et al., JGR 2007), but not with the extreme detail of elasticity provided by DAE. Previous quasi-static measurements made in Berea sandstone (Claytor et al, GRL 2009), show that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate (static limit). Therefore, future work will aim at linking quasi-static and dynamic observations, i.e. the frequency or strain-rate dependence, in order to understand underlying physical phenomena.

Nonlinear analysis of a rotor-bearing system using describing functions

Science.gov (United States)

Maraini, Daniel; Nataraj, C.

2018-04-01

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool.

Optimization of hardening/softening behavior of plane frame structures using nonlinear normal modes

DEFF Research Database (Denmark)

Dou, Suguang; Jensen, Jakob Søndergaard

2016-01-01

Devices that exploit essential nonlinear behavior such as hardening/softening and inter-modal coupling effects are increasingly used in engineering and fundamental studies. Based on nonlinear normal modes, we present a gradient-based structural optimization method for tailoring the hardening...... involving plane frame structures where the hardening/softening behavior is qualitatively and quantitatively tuned by simple changes in the geometry of the structures....

Strong asymmetry for surface modes in nonlinear lattices with long-range coupling

International Nuclear Information System (INIS)

Martinez, Alejandro J.; Vicencio, Rodrigo A.; Molina, Mario I.

2010-01-01

We analyze the formation of localized surface modes on a nonlinear cubic waveguide array in the presence of exponentially decreasing long-range interactions. We find that the long-range coupling induces a strong asymmetry between the focusing and defocusing cases for the topology of the surface modes and also for the minimum power needed to generate them. In particular, for the defocusing case, there is an upper power threshold for exciting staggered modes, which depends strongly on the long-range coupling strength. The power threshold for dynamical excitation of surface modes increases (decreases) with the strength of long-range coupling for the focusing (defocusing) cases. These effects seem to be generic for discrete lattices with long-range interactions.

Asymptotic behavior for a quadratic nonlinear Schrodinger equation

Directory of Open Access Journals (Sweden)

Pavel I. Naumkin

2008-02-01

Full Text Available We study the initial-value problem for the quadratic nonlinear Schrodinger equation $$displaylines{ iu_{t}+frac{1}{2}u_{xx}=partial _{x}overline{u}^{2},quad xin mathbb{R},; t>1, cr u(1,x=u_{1}(x,quad xin mathbb{R}. }$$ For small initial data $u_{1}in mathbf{H}^{2,2}$ we prove that there exists a unique global solution $uin mathbf{C}([1,infty ;mathbf{H}^{2,2}$ of this Cauchy problem. Moreover we show that the large time asymptotic behavior of the solution is defined in the region $|x|leq Csqrt{t}$ by the self-similar solution $frac{1}{sqrt{t}}MS(frac{x}{sqrt{t}}$ such that the total mass $$ frac{1}{sqrt{t}}int_{mathbb{R}}MS(frac{x}{sqrt{t}} dx=int_{mathbb{R}}u_{1}(xdx, $$ and in the far region $|x|>sqrt{t}$ the asymptotic behavior of solutions has rapidly oscillating structure similar to that of the cubic nonlinear Schrodinger equations.

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.

Nonlinear Dynamical Analysis for a Plain Bearing

Directory of Open Access Journals (Sweden)

Ali Belhamra

2014-03-01

Full Text Available This paper investigates the nonlinear dynamic behavior for a plain classic bearing (fluid bearing lubricated by a non-Newtonian fluid of a turbo machine rotating with high speed; this type of fluid contains additives viscosity (couple-stress fluid film. The solution of the nonlinear dynamic problem of this type of bearing is determined with a spatial discretisation of the modified Reynolds' equation written in dynamic mode by using the optimized short bearing theory and a temporal discretisation for equations of rotor motion by the help of Euler's explicit diagram. This study analyzes the dynamic behavior of a rotor supported by two couple-stress fluid film journal lubricant enhances the dynamic stability of the rotor-bearing system considerably compared to that obtained when using a traditional Newtonian lubricant. The analysis shows that the dynamic behavior of a shaft which turns with high velocities is strongly nonlinear even for poor eccentricities of unbalance; the presence of parameters of couple stress allows strongly attenuating the will synchrony (unbalance and asynchrony (whipping amplitudes of vibrations of the shaft which supports more severe conditions (large unbalances.

Nonlinear interaction of charged particles with strong laser pulses in a gaseous media

Directory of Open Access Journals (Sweden)

H. K. Avetissian

2007-07-01

Full Text Available The charged particles nonlinear dynamics in the field of a strong electromagnetic wave pulse of finite duration and certain form of the envelope, in the refractive medium with a constant and variable refraction indexes, is investigated by means of numerical integration of the classical relativistic equations of motion. The particle energy dependence on the pulse intensity manifests the nonlinear threshold phenomenon of a particle reflection and capture by actual laser pulses in dielectric-gaseous media that takes place for a plane electromagnetic wave in the induced Cherenkov process. Laser acceleration of the particles in the result of the reflection from the pulse envelope and in the capture regime with the variable refraction index along the pulse propagation direction is investigated.

Strongly nonlinear electronic transport in Cr-Si composite films

International Nuclear Information System (INIS)

Burkov, A.T.; Vinzelberg, H.; Schumann, J.; Nakama, T.; Yagasaki, K.

2004-01-01

The phase formation, the resistivity and the thermopower of amorphous Cr 0.15 Si 0.85 , and nanocrystalline CrSi 2 -Si thin film composites have been studied. The films were produced by a magnetron sputtering of a composite target onto unheated substrates with subsequent crystallization of the film at high temperatures. As the film composite develops under the heat treatment from the initial amorphous state into the final polycrystalline material, two percolation thresholds were found. At first, the percolating cluster of nanocrystalline CrSi 2 is formed. However, this cluster is destroyed with further annealing due to crystallization and redistribution of Si. The composite films which are close to this insulating threshold reveal a strongly nonlinear conductivity. The conductivity increases with the current by two orders of magnitude

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

Mathematical Systems Theory : from Behaviors to Nonlinear Control

CERN Document Server

Julius, A; Pasumarthy, Ramkrishna; Rapisarda, Paolo; Scherpen, Jacquelien

2015-01-01

This treatment of modern topics related to mathematical systems theory forms the proceedings of a workshop, Mathematical Systems Theory: From Behaviors to Nonlinear Control, held at the University of Groningen in July 2015. The workshop celebrated the work of Professors Arjan van der Schaft and Harry Trentelman, honouring their 60th Birthdays. The first volume of this two-volume work covers a variety of topics related to nonlinear and hybrid control systems. After giving a detailed account of the state of the art in the related topic, each chapter presents new results and discusses new directions. As such, this volume provides a broad picture of the theory of nonlinear and hybrid control systems for scientists and engineers with an interest in the interdisciplinary field of systems and control theory. The reader will benefit from the expert participants’ ideas on exciting new approaches to control and system theory and their predictions of future directions for the subject that were discussed at the worksho...

Variational Boussinesq model for strongly nonlinear dispersive waves

NARCIS (Netherlands)

Lawrence, C.; Adytia, D.; van Groesen, E.

2018-01-01

For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be

The thermomechanics of nonlinear irreversible behaviors an introduction

CERN Document Server

Maugin, Gérard A

1999-01-01

In this invaluable book, macroscopic irreversible thermodynamics is presented in its realm and its splendor by appealing to the notion of internal variables of state. This applies to both fluids and solids with or without microstructures of mechanical or electromagnetic origin. This unmatched richness of essentially nonlinear behaviors is the result of the use of modern mathematical techniques such as convex analysis in a clear-cut framework which allows one to put under the umbrella of "irreversible thermodynamics" behaviors which until now have been commonly considered either not easily cove

Analysis of nonlinear elastic behavior in miniature pneumatic artificial muscles

Science.gov (United States)

Hocking, Erica G.; Wereley, Norman M.

2013-01-01

Pneumatic artificial muscles (PAMs) are well known for their excellent actuator characteristics, including high specific work, specific power, and power density. Recent research has focused on miniaturizing this pneumatic actuator technology in order to develop PAMs for use in small-scale mechanical systems, such as those found in robotic or aerospace applications. The first step in implementing these miniature PAMs was to design and characterize the actuator. To that end, this study presents the manufacturing process, experimental characterization, and analytical modeling of PAMs with millimeter-scale diameters. A fabrication method was developed to consistently produce low-cost, high performance, miniature PAMs using commercially available materials. The quasi-static behavior of these PAMs was determined through experimentation on a single actuator with an active length of 39.16 mm (1.54 in) and a diameter of 4.13 mm (0.1625 in). Testing revealed the PAM’s full evolution of force with displacement for operating pressures ranging from 207 to 552 kPa (30-80 psi in 10 psi increments), as well as the blocked force and free contraction at each pressure. Three key nonlinear phenomena were observed: nonlinear PAM stiffness, hysteresis of the force versus displacement response for a given pressure, and a pressure deadband. To address the analysis of the nonlinear response of these miniature PAMs, a nonlinear stress versus strain model, a hysteresis model, and a pressure bias are introduced into a previously developed force balance analysis. Parameters of these nonlinear model refinements are identified from the measured force versus displacement data. This improved nonlinear force balance model is shown to capture the full actuation behavior of the miniature PAMs at each operating pressure and reconstruct miniature PAM response with much more accuracy than previously possible.

Analysis of nonlinear elastic behavior in miniature pneumatic artificial muscles

International Nuclear Information System (INIS)

Hocking, Erica G; Wereley, Norman M

2013-01-01

Pneumatic artificial muscles (PAMs) are well known for their excellent actuator characteristics, including high specific work, specific power, and power density. Recent research has focused on miniaturizing this pneumatic actuator technology in order to develop PAMs for use in small-scale mechanical systems, such as those found in robotic or aerospace applications. The first step in implementing these miniature PAMs was to design and characterize the actuator. To that end, this study presents the manufacturing process, experimental characterization, and analytical modeling of PAMs with millimeter-scale diameters. A fabrication method was developed to consistently produce low-cost, high performance, miniature PAMs using commercially available materials. The quasi-static behavior of these PAMs was determined through experimentation on a single actuator with an active length of 39.16 mm (1.54 in) and a diameter of 4.13 mm (0.1625 in). Testing revealed the PAM’s full evolution of force with displacement for operating pressures ranging from 207 to 552 kPa (30–80 psi in 10 psi increments), as well as the blocked force and free contraction at each pressure. Three key nonlinear phenomena were observed: nonlinear PAM stiffness, hysteresis of the force versus displacement response for a given pressure, and a pressure deadband. To address the analysis of the nonlinear response of these miniature PAMs, a nonlinear stress versus strain model, a hysteresis model, and a pressure bias are introduced into a previously developed force balance analysis. Parameters of these nonlinear model refinements are identified from the measured force versus displacement data. This improved nonlinear force balance model is shown to capture the full actuation behavior of the miniature PAMs at each operating pressure and reconstruct miniature PAM response with much more accuracy than previously possible. (paper)

Nonlinear Dynamic Behavior of a Bi-Axial Torsional MEMS Mirror with Sidewall Electrodes

Directory of Open Access Journals (Sweden)

Mehmet Ozdogan

2016-03-01

Full Text Available Nonlinear dynamic responses of a Micro-Electro-Mechanical Systems (MEMS mirror with sidewall electrodes are presented that are in close agreement with previously-reported experimental data. An analysis of frequency responses reveals softening behavior, and secondary resonances originated from the dominant quadratic nonlinearity. The quadratic nonlinearity is an electromechanical coupling effect caused by the electrostatic force. This effect is reflected in our mathematical model used to simulate the dynamic response of the micro-mirror. The effects of increased forcing and decreased damping on the frequency response are investigated as the mirrors are mostly used in vacuum packages. The results can predict MEMS mirror behaviors in optical devices better than previously-reported models.

Nonlinear electro-mechanobiological behavior of cell membrane during electroporation

KAUST Repository

Deng, Peigang

2012-01-01

A nonlinear electroporation (EP) model is proposed to study the electro-mechanobiological behavior of cell membrane during EP, by taking the nonlinear large deformation of the membrane into account. The proposed model predicts the critical transmembrane potential and the activation energy for EP, the equilibrium pore size, and the resealing process of the pore. Single-cell EP experiments using a micro EP chip were conducted on chicken red blood cells at different temperatures to determine the activation energy and the critical transmembrane potential for EP. The experimental results are in good agreement with the theoretical predictions. © 2012 American Institute of Physics.

Complex behavior in chains of nonlinear oscillators.

Science.gov (United States)

Alonso, Leandro M

2017-06-01

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions is sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.

Modal representation of geometrically nonlinear behavior by the finite element method

International Nuclear Information System (INIS)

Nagy, D.A.

1977-01-01

A method is presented for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of linear elastic and linear (bifurcation) buckling analysis results for structural loading or geometry situations which violate the idealized restrictive (perfect) interpretation of linear behavior up to bifurcation. (Auth.)

Strong saturable absorption of black titanium oxide nanoparticle films

Science.gov (United States)

Zhang, Rong-Fang; Guo, Deng-Zhu; Zhang, Geng-Min

2017-12-01

Nonlinear optical materials with strong saturable absorption (SA) properties play an essential role in passive mode-locking generation of ultrafast lasers. Here we report black TiO2-x nanoparticles are promising candidate for such an application. Black TiO2-x nanoparticles are synthesized by using cathodic plasma electrolysis, and nanoparticle films are deposited on optical glass plates via natural sedimentation and post annealing. Characterization of the samples with TEM, SEM, XRD and XPS reveal that nanoparticles have diameters of 8-70 nm, and are in polycrystalline structure and co-existence of anatase, rutile and abundant oxygen-deficient phases. Optical transmittance and reflectance measurements with a UV/VIS/NIR spectrophotometer evidence an excellent wide-spectral optical absorption property. The nonlinear optical properties of the samples were measured by using open-aperture Z-scan technique with picosecond 532-nm laser, and verified by direct transmission measurements using nanosecond 1064-nm laser. Strong SA behavior was detected, and the nonlinear absorption coefficient is as high as β = - 4.9 × 10-8 m/W, at least two orders larger than most previous reports on ordinary TiO2. The strong SA behaviors are ascribed to the existence of plenty surface states and defect states within bandgap, and the relaxation rates of electrons from upper energy levels to lower ones are much slower than excitation rates.

Using strong nonlinearity and high-frequency vibrations to control effective mechanical stiffness

DEFF Research Database (Denmark)

Thomsen, Jon Juel

2008-01-01

the method of direct separation of motions with results of a modified multiple scales ap-proach, valid also for strong nonlinearity, the stiffening ef-fect is predicted for a generic 1-dof system, and results are tested against numerical simulation and ((it is planned)) laboratory experiments.......High-frequency excitation (HFE) can be used to change the effective stiffness of an elastic structure, and related quanti-ties such as resonance frequencies, wave speed, buckling loads, and equilibrium states. There are basically two ways to do this: By using parametrical HFE (with or without non...

Nonlinear Stress-Strain Behavior of Plasma Sprayed Ceramic Coatings

Czech Academy of Sciences Publication Activity Database

Nohava, Jiří; Kroupa, František

2005-01-01

Roč. 50, č. 3 (2005), s. 251-262 ISSN 0001-7043 R&D Projects: GA AV ČR KSK1010104 Institutional research plan: CEZ:AV0Z20430508 Keywords : plasma spraying * ceramic coatings * Young’s modulus * nonlinear behavior * microcracks Subject RIV: JH - Ceramics, Fire-Resistant Materials and Glass

Nonlinear dynamics of trions under strong optical excitation in monolayer MoSe2.

Science.gov (United States)

Ye, Jialiang; Yan, Tengfei; Niu, Binghui; Li, Ying; Zhang, Xinhui

2018-02-05

By employing ultrafast transient reflection measurements based on two-color pump-probe spectroscopy, the population and valley polarization dynamics of trions in monolayer MoSe 2 were investigated at relatively high excitation densities under near-resonant excitation. Both the nonlinear dynamic photobleaching of the trion resonance and the redshift of the exciton resonance were found to be responsible for the excitation-energy- and density-dependent transient reflection change as a result of many-body interactions. Furthermore, from the polarization-resolved measurements, it was revealed that the initial fast population and polarization decay process upon strong photoexcitation observed for trions was determined by trion formation, transient phase-space filling and the short valley lifetime of excitons. The results provide a basic understanding of the nonlinear dynamics of population and valley depolarization of trions, as well as exciton-trion correlation in atomically thin MoSe 2 and other transition metal dichalcogenide materials.

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

Science.gov (United States)

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

2018-02-01

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

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.

Theoretical and Experimental Investigation of the Nonlinear Behavior of an Electrostatically Actuated In-Plane MEMS Arch

KAUST Repository

Ramini, Abdallah

2016-05-02

We present theoretical and experimental investigation of the nonlinear behavior of a clamped-clamped in-plane MEMS arch when excited by a DC electrostatic load superimposed to an AC harmonic load. Experimentally, a case study of in-plane silicon micromachined arch is examined and its mechanical behavior is measured using optical techniques. An algorithm is developed to extract the various parameters, such as the induced axial force and the initial rise, needed to model the behavior of the arch. A softening spring behavior is observed when the excitation is close to the first resonance frequency due to the quadratic nonlinearity coming from the arch geometry and the electrostatic force. Also, a hardening spring behavior is observed when the excitation is close to the third (second symmetric) resonance frequency due to the cubic nonlinearity coming from mid-plane stretching. Dynamic snap-through behavior is also reported for larger range of electric loads. Theoretically, a multi-mode Galerkin reduced order model is utilized to simulate the arch behavior. General agreement is reported among the theoretical and experimental data.

Nonlinear dynamics of semiconductors in strong THz electric fields

DEFF Research Database (Denmark)

Tarekegne, Abebe Tilahun

In this thesis, we investigate nonlinear interactions of an intense terahertz (THz) field with semiconductors, in particular the technologically relevant materials silicon and silicon carbide. We reveal the time-resolved dynamics of the nonlinear processes by pump-probe experiments that involve...

Nonlinear behavior of micro bubbles under ultrasound due to heat transfer

International Nuclear Information System (INIS)

Lim, Chan Soo; Kwak, Ho Young; Kim, Jeong Eun; Lee, Jae Young

2009-01-01

We investigated the nonlinear behavior of a microbubble under ultrasound, taking into account the heat transfer inside the bubble and through the bubble wall. The polytropic relation, which has been used for the process of pressure change depending on the volume variation of ideal gases, cannot properly treat heat transfer involving the oscillating bubble under ultrasound. In this study, a set of solutions of the Navier-Stokes equations for the gas inside the bubble along with an analytical treatment of the Navier-Stokes equations for the liquid adjacent to the bubble wall was used to treat properly the heat transfer process for the oscillating bubble under ultrasound. Entropy generation due to finite heat transfer, which induces the lost work during bubble evolution, reduces the collapsing process and considerably affects the nonlinear behavior of the bubble

Nonlinear dynamic behavior of an assembly of tubes under transverse fluid flow

International Nuclear Information System (INIS)

Beaufils, B.; Axisa, F.; Antunes, J.

1989-01-01

The mechanical vibrations induced by a transverse fluid flow passing through an assembly of cylindrical tubes is investigated. Studies on the numerical modeling of such phenomena are presented. The purpose of the work is to allow the evaluation of the risks induced by the vibrations in industrial heat exchangers. The methods for the analysis of nonlinear problems and numerical calculations of the nonlinear dynamic behavior are performed [fr

Nonlinear behavior in the time domain in argon atmospheric dielectric-barrier discharges

International Nuclear Information System (INIS)

Shi Hong; Wang Yanhui; Wang Dezhen

2008-01-01

A vast majority of nonlinear behavior in atmospheric pressure discharges has so far been studied in the space domain, and their time-domain characters are often believed to exact the periodicity of the externally applied voltage. In this paper, based on one-dimensional fluid mode, we study complex nonlinear behavior in the time domain in argon atmospheric dielectric-barrier discharges at very broad frequency range from kilohertz to megahertz. Under certain conditions, the discharge not only can be driven to chaos from time-periodic state through period-doubling bifurcation, but also can return stable periodic motion from chaotic state through an inverse period-doubling bifurcation sequence. Upon changing the parameter the discharge undergoes alternatively chaotic and periodic behavior. Some periodic windows embedded in chaos, as well as the secondary bifurcation occurring in the periodic windows can also be observed. The corresponding discharge characteristics are investigated.

Universal behavior of strongly correlated Fermi systems

Energy Technology Data Exchange (ETDEWEB)

Shaginyan, Vasilii R [B.P. Konstantinov St. Petersburg Institute of Nuclear Physics, Russian Academy of Sciences, Gatchina, Leningrad region, Rusian Federation (Russian Federation); Amusia, M Ya [A.F. Ioffe Physico-Technical Institute, Russian Academy of Sciences, St. Petersburg (Russian Federation); Popov, Konstantin G [Komi Scientific Center, Ural Branch of the Russian Academy of Sciences, Syktyvkar (Russian Federation)

2007-06-30

This review discusses the construction of a theory and the analysis of phenomena occurring in strongly correlated Fermi systems such as high-T{sub c} superconductors, heavy-fermion metals, and quasi-two-dimensional Fermi systems. It is shown that the basic properties and the universal behavior of strongly correlated Fermi systems can be described in the framework of the Fermi-condensate quantum phase transition and the well-known Landau paradigm of quasiparticles and the order parameter. The concept of fermion condensation may be fruitful in studying neutron stars, finite Fermi systems, ultra-cold gases in traps, and quark plasma. (reviews of topical problems)

Universal behavior of strongly correlated Fermi systems

International Nuclear Information System (INIS)

Shaginyan, Vasilii R; Amusia, M Ya; Popov, Konstantin G

2007-01-01

This review discusses the construction of a theory and the analysis of phenomena occurring in strongly correlated Fermi systems such as high-T c superconductors, heavy-fermion metals, and quasi-two-dimensional Fermi systems. It is shown that the basic properties and the universal behavior of strongly correlated Fermi systems can be described in the framework of the Fermi-condensate quantum phase transition and the well-known Landau paradigm of quasiparticles and the order parameter. The concept of fermion condensation may be fruitful in studying neutron stars, finite Fermi systems, ultra-cold gases in traps, and quark plasma. (reviews of topical problems)

Modal representation of geometrically nonlinear behavior by the finite element method

International Nuclear Information System (INIS)

Nagy, D.A.

1977-01-01

A method is presented for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of linear elastic and linear (bifurcation) buckling analysis results for structural loading or geometry situations which violate the idealized restrictive (perfect) interpretation of linear behavior up to bifurcation. Formulation of the finite element displacement method for material linearity but retaining the full, nonlinear strain-displacement relations (geometric nonlinearity) leads to highly nonlinear equations relating the unknown nodal generalized displacements r to the applied loading R. Restriction to small strains alone does not linearize these equations for thin-type structural configurations; only explicitly requiring that all products of displacement gadients be much smaller than the gadients themselves reduces the equations to the familiar linear form Ksub(e)r=R, where Ksub(e) is the elastic stiffness. Assuming then that the solutions r of the linear equations also satisfies the full nonlinear equations (i.e., that the above explicit requirement is satisfied), a second solution to the full equations can be sought for a one-parameter loading path lambdaR, leading to the well-known linear (bifurcation) buckling eigenvalue problem Ksub(e)X=-Ksub(g)XΛ where Ksub(g) is the geometric stiffness, X the matrix whose columns are the eigenvectors (so-called buckling mode shapes) and Λ is a diagonal matrix of eigenvalues lambda(i) (so-called load scale factors). From the viewpoint of the practising structural analyst using finite element software, the method presented here gives broader and deeper significance to an existing linear (bifurcation) buckling analysis capability, in that the additional computations are minimal beyond those already required for a linear static and buckling analysis, and should be easily performable within any well-designed general purpose finite element system

Nonlinear photocurrent-intensity behavior of amorphous InZnO thin film transistors

Science.gov (United States)

Lu, Huiling; Zhou, Xiaoliang; Liang, Ting; Zhang, Letao; Zhang, Shengdong

2018-01-01

The photocurrent (IPH) of amorphous InZnO thin film transistors in the off-state is investigated as a function of incident optical power (P). The results show that IPH exhibits a nonlinear dependence on P. Additionally, the dependence of IPH on P exhibits a strong photon energy (hυ)-dependent feature. When P is relatively low, IPH is shown to be proportional to Pγ, where γ is greater than 1. The γ > 1 behavior may be ascribed to the source-barrier-lowering effect due to the accumulation of photo-induced positive charges at the source side. When P is relatively high, while IPH remains proportional to Pγ under the incident light with hυ larger than the optical bandgap (Eg) of a-IZO, it turns to increase at an exponential rate with P if hυ of the incident light is smaller than the Eg. The exponential increase in IPH is attributed to the source-barrier-thinning effect, which leads to a significantly enhanced tunneling current.

A study of the cavity polariton under strong excitation:dynamics and nonlinearities in II-VI micro-cavities

International Nuclear Information System (INIS)

Muller, Markus

2000-01-01

This work contains an experimental study of the photoluminescence dynamics of cavity polaritons in strong coupling micro-cavities based on II-VI semiconductor compounds. The small exciton size and the strong exciton binding energy in these materials allowed us to study the strong coupling regime between photon and exciton up to high excitation densities, exploring the linear and non-linear emission regimes. Our main experimental techniques are picosecond time-resolved and angular photoluminescence spectroscopy. In the linear regime and for a negative photon-exciton detuning, we observe a suppression of the polariton relaxation by the emission of acoustic phonons leading to a non-equilibrium polariton distribution on the lower branch. This 'bottleneck' effect, which has already been described for polaritons in bulk semiconductors, results from the pronounced photon like character of the polaritons near k(parallel) = 0 in this configuration. At high excitation densities, non-linear relaxation processes, namely final state stimulation of the relaxation and polariton-polariton scattering, bypass this bottleneck giving rise to a very rapid relaxation down to the bottom of the band. We show that this dramatic change in the relaxation dynamics is finally responsible of the super-linear increase of the polariton emission from these states. (author) [fr

Nonlinear electromechanical modelling and dynamical behavior analysis of a satellite reaction wheel

Science.gov (United States)

Aghalari, Alireza; Shahravi, Morteza

2017-12-01

The present research addresses the satellite reaction wheel (RW) nonlinear electromechanical coupling dynamics including dynamic eccentricity of brushless dc (BLDC) motor and gyroscopic effects, as well as dry friction of shaft-bearing joints (relative small slip) and bearing friction. In contrast to other studies, the rotational velocity of the flywheel is considered to be controllable, so it is possible to study the reaction wheel dynamical behavior in acceleration stages. The RW is modeled as a three-phases BLDC motor as well as flywheel with unbalances on a rigid shaft and flexible bearings. Improved Lagrangian dynamics for electromechanical systems is used to obtain the mathematical model of the system. The developed model can properly describe electromechanical nonlinear coupled dynamical behavior of the satellite RW. Numerical simulations show the effectiveness of the presented approach.

Effect of Nonlinear Hardening of Lead Rubber Bearing on Long Term Behavior of Base Isolated Containment Building

International Nuclear Information System (INIS)

Park, Junhee; Choun, Young-Sun; Kim, Min-Kyu

2015-01-01

The rubber material used in laminated rubber bearings is the hyper elastic material whose stress-strain relationship can be defined as nonlinearly elastic. From the previous research, it was presented that the rubber hardness and stiffness was increased by the aging of LRB. The mechanical properties of LRB changed by aging can directly affect a nonlinear hardening behavior. Therefore it is needed to consider the nonlinear hardening effect for exactly evaluating the seismic safety of base isolated structure during the life time. In this study, the seismic response analysis of base isolated containment building was performed by using the bilinear model and the hardening model to identify the effect of structural response on the nonlinear hardening behavior of isolator. Moreover the floor response spectrum of base isolated structure considering the aging was analyzed by according to the analysis model of LRB.. The hardening behavior of lead rubber bearing occurs at high strain. Therefore it is reasonable to assume that the hysteretic model of LRB is the nonlinear hardening model for exactly evaluating the seismic response of base isolated structure. The nonlinear analysis of base isolated containment was performed by using the nonlinear hardening variables which was resulted from the test results and finite element analysis. From the analysis results, it was represented that the FRS was higher about 40% with nonlinear hardening model than with the bilinear model. Therefore the seismic response of base isolated structure with bilinear model can be underestimated than the real response. It is desired that the nonlinear hardening model of LRB is applied for the seismic risk evaluation requiring the ultimate state of LRB

Nonlinear behavior of multiple-helicity resistive interchange modes near marginally stable states

International Nuclear Information System (INIS)

Sugama, Hideo; Nakajima, Noriyoshi; Wakatani, Masahiro.

1991-05-01

Nonlinear behavior of resistive interchange modes near marginally stable states is theoretically studied under the multiple-helicity condition. Reduced fluid equations in the sheared slab configuration are used in order to treat a local transport problem. With the use of the invariance property of local reduced fluid model equations under a transformation between the modes with different rational surfaces, weakly nonlinear theories for single-helicity modes by Hamaguchi and Nakajima are extended to the multiple-helicity case and applied to the resistive interchange modes. We derive the nonlinear amplitude equations of the multiple-helicity modes, from which the convective transport in the saturated state is obtained. It is shown how the convective transport is enhanced by nonlinear interaction between modes with different rational surfaces compared with the single-helicity case. We confirm that theoretical results are in good agreement with direct numerical simulations. (author)

A new algebraic growth of nonlinear tearing mode

International Nuclear Information System (INIS)

Li, D.

1995-01-01

It is found that the quasilinear modification of magnetic field produces a nonlinear Lorentz force opposing the linear driving force and slowing down the vortex flow. A new algebraic growth appears due to this damping mechanism to oppose the linear growth of the tearing mode. This effect was eliminated in Rutherford's model [Phys. Fluids 16, 1903 (1973)] under the flux average operation and the assumption ∂/∂t much-lt η/δ 2 (here η is the resistivity, δ is the resistive layer width). A unified analytical model is developed by using standard perturbation theory for the linear and nonlinear growth of the tearing mode. The inertia effect and quasilinear effects of both the current density and the magnetic field have been included. A nonlinear evolution equation is analytically derived for the tearing mode to describe the linear growth, Rutherford's behavior, and the new behavior. The classical linear result is exactly recovered as the quasilinear effects are negligible. It is shown that a more slowly algebraic growth like Ψ 1 ∝t can become dominant in the nonlinear phase instead of Rutherford behavior like Ψ 1 ∝t 2 , provided the tearing mode in the linear phase is strongly unstable. Here Ψ 1 is the magnetic flux perturbation. copyright 1995 American Institute of Physics

Nonlinear shear behavior of rock joints using a linearized implementation of the Barton–Bandis model

Directory of Open Access Journals (Sweden)

Simon Heru Prassetyo

2017-08-01

Full Text Available Experiments on rock joint behaviors have shown that joint surface roughness is mobilized under shearing, inducing dilation and resulting in nonlinear joint shear strength and shear stress vs. shear displacement behaviors. The Barton–Bandis (BB joint model provides the most realistic prediction for the nonlinear shear behavior of rock joints. The BB model accounts for asperity roughness and strength through the joint roughness coefficient (JRC and joint wall compressive strength (JCS parameters. Nevertheless, many computer codes for rock engineering analysis still use the constant shear strength parameters from the linear Mohr–Coulomb (M−C model, which is only appropriate for smooth and non-dilatant joints. This limitation prevents fractured rock models from capturing the nonlinearity of joint shear behavior. To bridge the BB and the M−C models, this paper aims to provide a linearized implementation of the BB model using a tangential technique to obtain the equivalent M−C parameters that can satisfy the nonlinear shear behavior of rock joints. These equivalent parameters, namely the equivalent peak cohesion, friction angle, and dilation angle, are then converted into their mobilized forms to account for the mobilization and degradation of JRC under shearing. The conversion is done by expressing JRC in the equivalent peak parameters as functions of joint shear displacement using proposed hyperbolic and logarithmic functions at the pre- and post-peak regions of shear displacement, respectively. Likewise, the pre- and post-peak joint shear stiffnesses are derived so that a complete shear stress-shear displacement relationship can be established. Verifications of the linearized implementation of the BB model show that the shear stress-shear displacement curves, the dilation behavior, and the shear strength envelopes of rock joints are consistent with available experimental and numerical results.

Reduction of Photodiode Nonlinearities by Adaptive Biasing

Science.gov (United States)

2016-10-14

designers. In characterizing the nonlinear behavior of the output current, the most obvious method would be to Taylor expand the output current in...2This is reminiscent of a quote by Damon Runyon: “The race is not always to the swift , nor victory to the strong, but that’s the way you bet.” 3By

Optical rogue waves generation in a nonlinear metamaterial

Science.gov (United States)

Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin

2014-11-01

We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.

Transition from weak to strong measurements by nonlinear quantum feedback control

International Nuclear Information System (INIS)

Zhang Jing; Liu Yuxi; Wu Rebing; Li Chunwen; Tarn, Tzyh-Jong

2010-01-01

We find that feedback control may induce 'pseudo'-nonlinear dynamics in a damped harmonic oscillator, whose centroid trajectory in the phase space behaves like a classical nonlinear system. Thus, similar to nonlinear amplifiers (e.g., rf-driven Josephson junctions), feedback control on the harmonic oscillator can induce nonlinear bifurcation, which can be used to amplify small signals and further to measure quantum states of qubits. Using the cavity QED and the circuit QED systems as examples, we show how to apply our method to measuring the states of two-level atoms and superconducting charge qubits.

Investigation of the nonlinear static and dynamic behaviour of rectangular microplates under electrostatic actuation

KAUST Repository

Saghir, Shahid; Younis, Mohammad I.

2016-01-01

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary resonance. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased.

Investigation of the nonlinear static and dynamic behaviour of rectangular microplates under electrostatic actuation

KAUST Repository

Saghir, Shahid

2016-11-16

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary resonance. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased.

Assessment of Effects of a Delay Block and a Nonlinear Block in Systems with Chaotic Behavior Using Lyapunov Exponents

Directory of Open Access Journals (Sweden)

Pablo César Rodríguez Gómez

2017-05-01

Full Text Available Context: Because feedback systems are very common and widely used, studies of the structural characteristics under which chaotic behavior is generated have been developed. These can be separated into a nonlinear system and a linear system at least of the third order. Methods such as the descriptive function have been used for analysis. Method: A feedback system is proposed comprising a linear system, a nonlinear system and a delay block, in order to assess his behavior using Lyapunov exponents. It is evaluated with three different linear systems, different delay values and different values for parameters of nonlinear characteristic, aiming to reach chaotic behavior. Results: One hundred experiments were carried out for each of the three linear systems, by changing the value of some parameters, assessing their influence on the dynamics of the system. Contour plots that relate these parameters to the Largest Lyapunov exponent were obtained and analyzed. Conclusions: In spite non-linearity is a condition for the existence of chaos, this does not imply that any nonlinear characteristic generates a chaotic system, it is reflected by the contour plots showing the transitions between chaotic and no chaotic behavior of the feedback system. Language: English

Numerical simulation of non-linear phenomena in geotechnical engineering

DEFF Research Database (Denmark)

Sørensen, Emil Smed

Geotechnical problems are often characterized by the non-linear behavior of soils and rock which are strongly linked to the inherent properties of the porous structure of the material as well as the presence and possible flow of any surrounding fluids. Dynamic problems involving such soil-fluid i...

Hidden regularity for a strongly nonlinear wave equation

International Nuclear Information System (INIS)

Rivera, J.E.M.

1988-08-01

The nonlinear wave equation u''-Δu+f(u)=v in Q=Ωx]0,T[;u(0)=u 0 ,u'(0)=u 1 in Ω; u(x,t)=0 on Σ= Γx]0,T[ where f is a continuous function satisfying, lim |s| sup →+∞ f(s)/s>-∞, and Ω is a bounded domain of R n with smooth boundary Γ, is analysed. It is shown that there exist a solution for the presented nonlinear wave equation that satisfies the regularity condition: |∂u/∂ η|ε L 2 (Σ). Moreover, it is shown that there exist a constant C>0 such that, |∂u/∂ η|≤c{ E(0)+|v| 2 Q }. (author) [pt

Localized Effects in the Nonlinear Behavior of Sandwich Panels with a Transversely Flexible Core

DEFF Research Database (Denmark)

Frostig, Y.; Thomsen, Ole Thybo

2005-01-01

This paper presents the results of an investigation of the role of localized effects within the geometrically nonlinear domain on structural sandwich panels with a "compliant" core. Special emphasis is focused on the nonlinear response near concentrated loads and stiffened core regions. The adopted...... nonlinear analysis approach incorporates the effects of the vertical flexibility of the core, and it is based on the approach of the High-order Sandwich Panel Theory (HSAPT). The results demonstrate that the effects of localized loads, when taken into the geometrically nonlinear domain, change the response...... of the panel from a strength problem controlled by stress constraints into a stability problem with unstable limit point behavior when force-controlled loads are applied. The stability problem emerge as the nonlinear response develops with the formation of a small number of buckling waves in the compressed...

Nonlinear vibration behaviors of suspended cables under two-frequency excitation with temperature effects

Science.gov (United States)

Zhao, Yaobing; Huang, Chaohui; Chen, Lincong; Peng, Jian

2018-03-01

The aim of this paper is to investigate temperature effects on the nonlinear vibration behaviors of suspended cables under two-frequency excitation. For this purpose, two combination and simultaneous resonances are chosen and studied in detail. First of all, based on the assumptions of the temperature effects, the partial differential equations of the in-plane and out-of-plane motions with thermal effects under multi-frequency excitations are obtained. The Galerkin method is adopted to discretize the nonlinear dynamic equations, and the single-mode planar discretization is considered. Then, in the absence of the primary and internal resonances, the frequency response equations are obtained by using the multiple scales method. The stability analyses are conducted via investigating the nature of the singular points of equations. After that, temperature effects on nonlinear vibration characteristics of the first symmetric mode are studied. Parametric investigations of temperature effects on corresponding non-dimensional factors and coefficients of linear and nonlinear terms are performed. Numerical results are presented to show the temperature effects via the frequency-response curves and detuning-phase curves of four different sag-to-span ratios. It is found out that effects of temperature variations would lead to significant quantitative and/or qualitative changes of the nonlinear vibration properties, and these effects are closely related to the sag-to-span ratio and the degree of the temperature variation. Specifically, the softening/hardening-type spring behaviors, the response amplitude, the range of the resonance, the intersection and number of branches, the number and phase of the steady-state solutions are all affected by the temperature changes.

Probing the interatomic potential of solids with strong-field nonlinear phononics

Science.gov (United States)

von Hoegen, A.; Mankowsky, R.; Fechner, M.; Först, M.; Cavalleri, A.

2018-03-01

Nonlinear optical techniques at visible frequencies have long been applied to condensed matter spectroscopy. However, because many important excitations of solids are found at low energies, much can be gained from the extension of nonlinear optics to mid-infrared and terahertz frequencies. For example, the nonlinear excitation of lattice vibrations has enabled the dynamic control of material functions. So far it has only been possible to exploit second-order phonon nonlinearities at terahertz field strengths near one million volts per centimetre. Here we achieve an order-of-magnitude increase in field strength and explore higher-order phonon nonlinearities. We excite up to five harmonics of the A1 (transverse optical) phonon mode in the ferroelectric material lithium niobate. By using ultrashort mid-infrared laser pulses to drive the atoms far from their equilibrium positions, and measuring the large-amplitude atomic trajectories, we can sample the interatomic potential of lithium niobate, providing a benchmark for ab initio calculations for the material. Tomography of the energy surface by high-order nonlinear phononics could benefit many aspects of materials research, including the study of classical and quantum phase transitions.

Local interaction simulation approach to modelling nonclassical, nonlinear elastic behavior in solids.

Science.gov (United States)

Scalerandi, Marco; Agostini, Valentina; Delsanto, Pier Paolo; Van Den Abeele, Koen; Johnson, Paul A

2003-06-01

Recent studies show that a broad category of materials share "nonclassical" nonlinear elastic behavior much different from "classical" (Landau-type) nonlinearity. Manifestations of "nonclassical" nonlinearity include stress-strain hysteresis and discrete memory in quasistatic experiments, and specific dependencies of the harmonic amplitudes with respect to the drive amplitude in dynamic wave experiments, which are remarkably different from those predicted by the classical theory. These materials have in common soft "bond" elements, where the elastic nonlinearity originates, contained in hard matter (e.g., a rock sample). The bond system normally comprises a small fraction of the total material volume, and can be localized (e.g., a crack in a solid) or distributed, as in a rock. In this paper a model is presented in which the soft elements are treated as hysteretic or reversible elastic units connected in a one-dimensional lattice to elastic elements (grains), which make up the hard matrix. Calculations are performed in the framework of the local interaction simulation approach (LISA). Experimental observations are well predicted by the model, which is now ready both for basic investigations about the physical origins of nonlinear elasticity and for applications to material damage diagnostics.

Order and chaos in the nonlinear response of driven nuclear spin systems

Energy Technology Data Exchange (ETDEWEB)

Brun, E; Derighetti, B; Holzner, R; Ravani, M [Zurich Univ. (Switzerland). Inst. fuer Physik

1984-01-01

The authors report on observations of ordered and chaotic behavior of a nonlinear system of strongly polarized nuclear spins inside the tuning coil of an NMR detector. The combined system: spins plus LC-circuit, may act as a nonlinear bistable absorber or a spin-flip laser, depending on the sign of the nuclear spin polarization. For the NMR laser experimental evidence is presented for limit-cycle behavior, sequences of bifurcations which lead to chaos, intermittency, multistability, and pronounced hysteresis effects. The experimental facts are compared with computer solutions of appropriate Bloch equations for the macroscopic order parameters.

Nonlinear Approaches in Engineering Applications

CERN Document Server

Jazar, Reza

2012-01-01

Nonlinear Approaches in Engineering Applications focuses on nonlinear phenomena that are common in the engineering field. The nonlinear approaches described in this book provide a sound theoretical base and practical tools to design and analyze engineering systems with high efficiency and accuracy and with less energy and downtime. Presented here are nonlinear approaches in areas such as dynamic systems, optimal control and approaches in nonlinear dynamics and acoustics. Coverage encompasses a wide range of applications and fields including mathematical modeling and nonlinear behavior as applied to microresonators, nanotechnologies, nonlinear behavior in soil erosion,nonlinear population dynamics, and optimization in reducing vibration and noise as well as vibration in triple-walled carbon nanotubes. This book also: Provides a complete introduction to nonlinear behavior of systems and the advantages of nonlinearity as a tool for solving engineering problems Includes applications and examples drawn from the el...

Nonlinear Thomson scattering of a relativistically strong tightly focused ultrashort laser pulse

Energy Technology Data Exchange (ETDEWEB)

Vais, O. E.; Bochkarev, S. G., E-mail: bochkar@sci.lebedev.ru; Bychenkov, V. Yu. [Russian Academy of Sciences, Lebedev Physical Institute (Russian Federation)

2016-09-15

The problem of nonlinear Thomson scattering of a relativistically strong linearly polarized ultrashort laser pulse tightly focused into a spot with a diameter of D{sub F} ≳ λ (where λ is the laser wavelength) is solved. The energy, spectral, and angular distributions of radiation generated due to Thomson scattering from test electrons located in the focal region are found. The characteristics of scattered radiation are studied as functions of the tightness of laser focusing and the initial position of test particles relative to the center of the focal region for a given laser pulse energy. It is demonstrated that the ultratight focusing is not optimal for obtaining the brightest and hardest source of secondary electromagnetic radiation. The hardest and shortest radiation pulse is generated when the beam waist diameter is ≃10λ.

Inducing Strong Non-Linearities in a Phonon Trapping Quartz Bulk Acoustic Wave Resonator Coupled to a Superconducting Quantum Interference Device

Directory of Open Access Journals (Sweden)

Maxim Goryachev

2018-04-01

Full Text Available A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10 18 Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structure of the spectrum in both incident power and frequency. The result gives an insight into the open loop behaviour of a future Cryogenic Quartz Oscillator in the strong signal regime.

Generation of Caustics and Rogue Waves from Nonlinear Instability.

Science.gov (United States)

Safari, Akbar; Fickler, Robert; Padgett, Miles J; Boyd, Robert W

2017-11-17

Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.

Strong convergence of modified Ishikawa iterations for nonlinear ...

Indian Academy of Sciences (India)

interval [0, 1]. The second iteration process is referred to as Ishikawa's iteration process [11] which is .... Let E be a smooth Banach space with dual E∗ ..... and applications, in: Theory and Applications of Nonlinear Operators of Accretive and.

Nonlinear beam mechanics

NARCIS (Netherlands)

Westra, H.J.R.

2012-01-01

In this Thesis, nonlinear dynamics and nonlinear interactions are studied from a micromechanical point of view. Single and doubly clamped beams are used as model systems where nonlinearity plays an important role. The nonlinearity also gives rise to rich dynamic behavior with phenomena like

Emergence of Complex Spatio-Temporal Behavior in Nonlinear Field Theories

International Nuclear Information System (INIS)

Gleiser, Marcelo; Howell, Rafael C.

2006-01-01

We investigate the emergence of time-dependent nonperturbative configurations during the evolution of nonlinear scalar field models with symmetric and asymmetric double-well potentials. Complex spatio-temporal behavior emerges as the system seeks to establish equipartition after a fast quench. We show that fast quenches may dramatically modify the decay rate of metastable states in first order phase transitions. We discuss possible applications in condensed matter systems and early universe cosmology

Study of the critical behavior of the O(N) linear and nonlinear sigma models

International Nuclear Information System (INIS)

Graziani, F.R.

1983-01-01

A study of the large N behavior of both the O(N) linear and nonlinear sigma models is presented. The purpose is to investigate the relationship between the disordered (ordered) phase of the linear and nonlinear sigma models. Utilizing operator product expansions and stability analyses, it is shown that for 2 - (lambda/sub R/(M) is the dimensionless renormalized quartic coupling and lambda* is the IR fixed point) limit of the linear sigma model which yields the nonlinear sigma model. It is also shown that stable large N linear sigma models with lambda 0) and nonlinear models are trivial. This result (i.e., triviality) is well known but only for one and two component models. Interestingly enough, the lambda< d = 4 linear sigma model remains nontrivial and tachyonic free

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.

Current structure of strongly nonlinear interfacial solitary waves

Science.gov (United States)

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

2015-04-01

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

Reproducing the nonlinear dynamic behavior of a structured beam with a generalized continuum model

Science.gov (United States)

Vila, J.; Fernández-Sáez, J.; Zaera, R.

2018-04-01

In this paper we study the coupled axial-transverse nonlinear vibrations of a kind of one dimensional structured solids by application of the so called Inertia Gradient Nonlinear continuum model. To show the accuracy of this axiomatic model, previously proposed by the authors, its predictions are compared with numeric results from a previously defined finite discrete chain of lumped masses and springs, for several number of particles. A continualization of the discrete model equations based on Taylor series allowed us to set equivalent values of the mechanical properties in both discrete and axiomatic continuum models. Contrary to the classical continuum model, the inertia gradient nonlinear continuum model used herein is able to capture scale effects, which arise for modes in which the wavelength is comparable to the characteristic distance of the structured solid. The main conclusion of the work is that the proposed generalized continuum model captures the scale effects in both linear and nonlinear regimes, reproducing the behavior of the 1D nonlinear discrete model adequately.

Optical nonlinearity and bistability in the bound exciton energy range of CdS

International Nuclear Information System (INIS)

Hoenig, T.; Gutowski, J.

1988-01-01

Under high excitation conditions thick CdS samples show pronounced broad-band nonlinear transmission in the bound exciton region and up to a wavelength of about 515 nm at cryo-temperatures. This behavior is only explainable in a model based on impurity neutralization and bound exciton creation. The suitability of these nonlinearities to yield optical bistability will be shown. Bistable operation is investigated in dependence of crystal thickness, impurity concentration, excitation density, wavelength, and temperature. A strong correlation to acceptor-bound exciton generation is obtained, and the explanation of this bistable operation fits well with that of the above mentioned transmission behavior. (author)

A non-linear theory of strong interactions

International Nuclear Information System (INIS)

Skyrme, T.H.R.

1994-01-01

A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a φ 4 term; this destroys the continuous rotation group in the iso-space, leaving a 'cubic' symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to 'strangeness'; one consequences is that, at least in elementary interactions, charge is only conserved module 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone. (author). 7 refs

Nonlinear behavior: One degree of freedom

International Nuclear Information System (INIS)

Greene, J.M.

1987-01-01

There has been very considerable progress in the past few years on the theory of two conservative, coupled, nonlinear oscillators. This is a very general theory, and applies to many equivalent systems including approximate models of particle accelerators. A typical problem of this class has a solution that is so complicated that it is impossible to find an expression for the state of the system that is valid for all time. However, recent results are making it possible to determine the next most useful type of information. This is the asymptotic behavior of individual orbits in the limit of very long times. It is just the information that is desired in many situations. For example, it determines the stability of the motion. They key to our present understanding is renormalization. The present state of the art has been described in Robert MacKay's thesis, for which this is an advertisement

Nonlinear quantum electrodynamic and electroweak processes in strong laser fields

Energy Technology Data Exchange (ETDEWEB)

Meuren, Sebastian

2015-06-24

Various nonlinear electrodynamic and electroweak processes in strong plane-wave laser fields are considered with an emphasis on short-pulse effects. In particular, the momentum distribution of photoproduced electron-positron pairs is calculated numerically and a semiclassical interpretation of its characteristic features is established. By proving the optical theorem, compact double-integral expressions for the total pair-creation probability are obtained and numerically evaluated. The exponential decay of the photon wave function in a plane wave is included by solving the Schwinger-Dyson equations to leading-order in the quasistatic approximation. In this respect, the polarization operator in a plane wave is investigated and its Ward-Takahashi identity verified. A classical analysis indicates that a photoproduced electron-positron pair recollides for certain initial conditions. The contributions of such recollision processes to the polarization operator are identified and calculated both analytically and numerically. Furthermore, the existence of nontrivial electron-spin dynamics induced by quantum fluctuations is verified for ultra-short laser pulses. Finally, the exchange of weak gauge bosons is considered, which is essential for neutrino-photon interactions. In particular, the axial-vector-vector coupling tensor is calculated and the so-called Adler-Bell-Jackiw (ABJ) anomaly investigated.

Effects of non-linearity of material properties on the coupled mechanical-hydraulic-thermal behavior in rock mass

International Nuclear Information System (INIS)

Kobayashi, Akira; Ohnishi, Yuzo

1986-01-01

The nonlinearity of material properties used in the coupled mechanical-hydraulic-thermal analysis is investigated from the past literatures. Some nonlinearity that is respectively effective for the system is introduced into our computer code for analysis such a coupling problem by using finite element method. And the effects of nonlinearity of each material property on the coupled behavior in rock mass are examined for simple model and Stripa project model with the computer code. (author)

Bubble nonlinear dynamics and stimulated scattering process

Science.gov (United States)

Jie, Shi; De-Sen, Yang; Sheng-Guo, Shi; Bo, Hu; Hao-Yang, Zhang; Shi-Yong, Hu

2016-02-01

A complete understanding of the bubble dynamics is deemed necessary in order to achieve their full potential applications in industry and medicine. For this purpose it is first needed to expand our knowledge of a single bubble behavior under different possible conditions including the frequency and pressure variations of the sound field. In addition, stimulated scattering of sound on a bubble is a special effect in sound field, and its characteristics are associated with bubble oscillation mode. A bubble in liquid can be considered as a representative example of nonlinear dynamical system theory with its resonance, and its dynamics characteristics can be described by the Keller-Miksis equation. The nonlinear dynamics of an acoustically excited gas bubble in water is investigated by using theoretical and numerical analysis methods. Our results show its strongly nonlinear behavior with respect to the pressure amplitude and excitation frequency as the control parameters, and give an intuitive insight into stimulated sound scattering on a bubble. It is seen that the stimulated sound scattering is different from common dynamical behaviors, such as bifurcation and chaos, which is the result of the nonlinear resonance of a bubble under the excitation of a high amplitude acoustic sound wave essentially. The numerical analysis results show that the threshold of stimulated sound scattering is smaller than those of bifurcation and chaos in the common condition. Project supported by the Program for Changjiang Scholars and Innovative Research Team in University, China (Grant No. IRT1228) and the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 11204050 and 11204049).

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

Science.gov (United States)

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

2018-04-01

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

An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

KAUST Repository

Xu, Tiantian

2014-08-17

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

Nonlinear growth of strongly unstable tearing modes

International Nuclear Information System (INIS)

Waelbroeck, F.L.

1993-11-01

Rutherford's theory of the tearing instability is extended to cases where current nonlinearities are important, such as long wavelength modes in current slabs and the m = 1 instability in tokamaks with moderately large aspect-ratios. Of particular interest is the possibility that the associated magnetic islands, as a result of secondary instabilities, have a singular response to the Ohmic diffusion of the current. A family of islands is used to test this possibility; it is found that the response remains bounded

Selected Problems in Nonlinear Dynamics and Sociophysics

Science.gov (United States)

Westley, Alexandra Renee

This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.

Introduction to nonlinear science

CERN Document Server

Nicolis, G

1995-01-01

One of the most unexpected results in science in recent years is that quite ordinary systems obeying simple laws can give rise to complex, nonlinear or chaotic, behavior. In this book, the author presents a unified treatment of the concepts and tools needed to analyze nonlinear phenomena and to outline some representative applications drawn from the physical, engineering, and biological sciences. Some of the interesting topics covered include: dynamical systems with a finite number of degrees of freedom, linear stability analysis of fixed points, nonlinear behavior of fixed points, bifurcation analysis, spatially distributed systems, broken symmetries, pattern formation, and chaotic dynamics. The author makes a special effort to provide a logical connection between ordinary dynamical systems and spatially extended systems, and to balance the emphasis on chaotic behavior and more classical nonlinear behavior. He also develops a statistical approach to complex systems and compares it to traditional deterministi...

Nonlinear Brillouin amplification of finite-duration seeds in the strong coupling regime

International Nuclear Information System (INIS)

Lehmann, G.; Spatschek, K. H.

2013-01-01

Parametric plasma processes received renewed interest in the context of generating ultra-intense and ultra-short laser pulses up to the exawatt-zetawatt regime. Both Raman as well as Brillouin amplifications of seed pulses were proposed. Here, we investigate Brillouin processes in the one-dimensional (1D) backscattering geometry with the help of numerical simulations. For optimal seed amplification, Brillouin scattering is considered in the so called strong coupling (sc) regime. Special emphasis lies on the dependence of the amplification process on the finite duration of the initial seed pulses. First, the standard plane-wave instability predictions are generalized to pulse models, and the changes of initial seed pulse forms due to parametric instabilities are investigated. Three-wave-interaction results are compared to predictions by a new (kinetic) Vlasov code. The calculations are then extended to the nonlinear region with pump depletion. Generation of different seed layers is interpreted by self-similar solutions of the three-wave interaction model. Similar to Raman amplification, shadowing of the rear layers by the leading layers of the seed occurs. The shadowing is more pronounced for initially broad seed pulses. The effect is quantified for Brillouin amplification. Kinetic Vlasov simulations agree with the three-wave interaction predictions and thereby affirm the universal validity of self-similar layer formation during Brillouin seed amplification in the strong coupling regime

Nonlinear acoustic/seismic waves in earthquake processes

International Nuclear Information System (INIS)

Johnson, Paul A.

2012-01-01

Nonlinear dynamics induced by seismic sources and seismic waves are common in Earth. Observations range from seismic strong ground motion (the most damaging aspect of earthquakes), intense near-source effects, and distant nonlinear effects from the source that have important consequences. The distant effects include dynamic earthquake triggering—one of the most fascinating topics in seismology today—which may be elastically nonlinearly driven. Dynamic earthquake triggering is the phenomenon whereby seismic waves generated from one earthquake trigger slip events on a nearby or distant fault. Dynamic triggering may take place at distances thousands of kilometers from the triggering earthquake, and includes triggering of the entire spectrum of slip behaviors currently identified. These include triggered earthquakes and triggered slow, silent-slip during which little seismic energy is radiated. It appears that the elasticity of the fault gouge—the granular material located between the fault blocks—is key to the triggering phenomenon.

A high-precision instrument for analyzing nonlinear dynamic behavior of bearing cage

Energy Technology Data Exchange (ETDEWEB)

Yang, Z., E-mail: zhaohui@nwpu.edu.cn; Yu, T. [School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072 (China); Chen, H. [Xi’an Aerospace Propulsion Institute, Xi’an 710100 (China); Li, B. [State Key Laboratory for Manufacturing and Systems Engineering, Xi’an Jiaotong University, Xi’an 710054 (China)

2016-08-15

The high-precision ball bearing is fundamental to the performance of complex mechanical systems. As the speed increases, the cage behavior becomes a key factor in influencing the bearing performance, especially life and reliability. This paper develops a high-precision instrument for analyzing nonlinear dynamic behavior of the bearing cage. The trajectory of the rotational center and non-repetitive run-out (NRRO) of the cage are used to evaluate the instability of cage motion. This instrument applied an aerostatic spindle to support and spin test the bearing to decrease the influence of system error. Then, a high-speed camera is used to capture images when the bearing works at high speeds. A 3D trajectory tracking software TEMA Motion is used to track the spot which marked the cage surface. Finally, by developing the MATLAB program, a Lissajous’ figure was used to evaluate the nonlinear dynamic behavior of the cage with different speeds. The trajectory of rotational center and NRRO of the cage with various speeds are analyzed. The results can be used to predict the initial failure and optimize cage structural parameters. In addition, the repeatability precision of instrument is also validated. In the future, the motorized spindle will be applied to increase testing speed and image processing algorithms will be developed to analyze the trajectory of the cage.

A high-precision instrument for analyzing nonlinear dynamic behavior of bearing cage

International Nuclear Information System (INIS)

Yang, Z.; Yu, T.; Chen, H.; Li, B.

2016-01-01

The high-precision ball bearing is fundamental to the performance of complex mechanical systems. As the speed increases, the cage behavior becomes a key factor in influencing the bearing performance, especially life and reliability. This paper develops a high-precision instrument for analyzing nonlinear dynamic behavior of the bearing cage. The trajectory of the rotational center and non-repetitive run-out (NRRO) of the cage are used to evaluate the instability of cage motion. This instrument applied an aerostatic spindle to support and spin test the bearing to decrease the influence of system error. Then, a high-speed camera is used to capture images when the bearing works at high speeds. A 3D trajectory tracking software TEMA Motion is used to track the spot which marked the cage surface. Finally, by developing the MATLAB program, a Lissajous’ figure was used to evaluate the nonlinear dynamic behavior of the cage with different speeds. The trajectory of rotational center and NRRO of the cage with various speeds are analyzed. The results can be used to predict the initial failure and optimize cage structural parameters. In addition, the repeatability precision of instrument is also validated. In the future, the motorized spindle will be applied to increase testing speed and image processing algorithms will be developed to analyze the trajectory of the cage.

Inflation and acceleration of the universe by nonlinear magnetic monopole fields

Energy Technology Data Exchange (ETDEWEB)

Oevguen, A. [Eastern Mediterranean Univ., Famagusta (Country Unknown). Dept. of Physics

2017-02-15

Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields. (orig.)

Inflation and acceleration of the universe by nonlinear magnetic monopole fields

Science.gov (United States)

Övgün, A.

2017-02-01

Despite impressive phenomenological success, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Maxwell electrodynamics, considered as a source of the classical Einstein field equations, leads to the singular isotropic Friedmann solutions. In the context of Friedmann-Robertson-Walker (FRW) spacetime, we show that singular behavior does not occur for a class of nonlinear generalizations of the electromagnetic theory for strong fields. A new mathematical model is proposed for which the analytical nonsingular extension of FRW solutions is obtained by using the nonlinear magnetic monopole fields.

Advanced data assimilation in strongly nonlinear dynamical systems

Science.gov (United States)

Miller, Robert N.; Ghil, Michael; Gauthiez, Francois

1994-01-01

Advanced data assimilation methods are applied to simple but highly nonlinear problems. The dynamical systems studied here are the stochastically forced double well and the Lorenz model. In both systems, linear approximation of the dynamics about the critical points near which regime transitions occur is not always sufficient to track their occurrence or nonoccurrence. Straightforward application of the extended Kalman filter yields mixed results. The ability of the extended Kalman filter to track transitions of the double-well system from one stable critical point to the other depends on the frequency and accuracy of the observations relative to the mean-square amplitude of the stochastic forcing. The ability of the filter to track the chaotic trajectories of the Lorenz model is limited to short times, as is the ability of strong-constraint variational methods. Examples are given to illustrate the difficulties involved, and qualitative explanations for these difficulties are provided. Three generalizations of the extended Kalman filter are described. The first is based on inspection of the innovation sequence, that is, the successive differences between observations and forecasts; it works very well for the double-well problem. The second, an extension to fourth-order moments, yields excellent results for the Lorenz model but will be unwieldy when applied to models with high-dimensional state spaces. A third, more practical method--based on an empirical statistical model derived from a Monte Carlo simulation--is formulated, and shown to work very well. Weak-constraint methods can be made to perform satisfactorily in the context of these simple models, but such methods do not seem to generalize easily to practical models of the atmosphere and ocean. In particular, it is shown that the equations derived in the weak variational formulation are difficult to solve conveniently for large systems.

Nonlinear drift tearing mode. Strong mode of excitation and stabilization mechanisms

International Nuclear Information System (INIS)

Galeev, A.A.; Zelenyj, L.M.; Kuznetsova, M.M.

1985-01-01

A nonlinear theory of magnetic disturbance development in collisionless configurations with magnetic field shear is considered. The instability evolution is investigated with account for the dynamics of ions and potential electric fields which determine the mode stabilization. It has been found that the drift tearing mode possesses metastable properties: in a nonlinear mode even the growth of linearly stable disturbances of the finite amplitude is possible

Study nonlinear dynamics of stratospheric ozone concentration at Pakistan Terrestrial region

Science.gov (United States)

Jan, Bulbul; Zai, Muhammad Ayub Khan Yousuf; Afradi, Faisal Khan; Aziz, Zohaib

2018-03-01

This study investigates the nonlinear dynamics of the stratospheric ozone layer at Pakistan atmospheric region. Ozone considered now the most important issue in the world because of its diverse effects on earth biosphere, including human health, ecosystem, marine life, agriculture yield and climate change. Therefore, this paper deals with total monthly time series data of stratospheric ozone over the Pakistan atmospheric region from 1970 to 2013. Two approaches, basic statistical analysis and Fractal dimension (D) have adapted to study the nature of nonlinear dynamics of stratospheric ozone level. Results obtained from this research have shown that the Hurst exponent values of both methods of fractal dimension revealed an anti-persistent behavior (negatively correlated), i.e. decreasing trend for all lags and Rescaled range analysis is more appropriate as compared to Detrended fluctuation analysis. For seasonal time series all month follows an anti-persistent behavior except in the month of November which shown persistence behavior i.e. time series is an independent and increasing trend. The normality test statistics also confirmed the nonlinear behavior of ozone and the rejection of hypothesis indicates the strong evidence of the complexity of data. This study will be useful to the researchers working in the same field in the future to verify the complex nature of stratospheric ozone.

Nonlinear Mechanics of MEMS Rectangular Microplates under Electrostatic Actuation

KAUST Repository

Saghir, Shahid

2016-12-01

The first objective of the dissertation is to develop a suitable reduced order model capable of investigating the nonlinear mechanical behavior of von-Karman plates under electrostatic actuation. The second objective is to investigate the nonlinear static and dynamic behavior of rectangular microplates under small and large actuating forces. In the first part, we present and compare various approaches to develop reduced order models for the nonlinear von-Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. In the second part, we present an investigation of the static and dynamic behavior of a fully clamped microplate. We investigate the effect of different non-dimensional design parameters on the static response. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of midplane stretching. However, the behavior switches to softening as the DC load is increased. Next, near-square plates are studied to understand the effect of geometric imperfections of microplates. In the final part of the dissertation, we investigate the mechanical behavior of

Nonlinear parity readout with a microwave photodetector

Science.gov (United States)

Schöndorf, M.; Wilhelm, F. K.

2018-04-01

Robust high-fidelity parity measurement is an important operation in many applications of quantum computing. In this work we show how in a circuit QED architecture, one can measure parity in a single shot at very high contrast by taking advantage of the nonlinear behavior of a strongly driven microwave cavity coupled to one or multiple qubits. We work in a nonlinear dispersive regime treated in an exact dispersive transformation. We show that appropriate tuning of experimental parameters leads to very high contrast in the cavity and therefore to a high-efficiency parity readout with a microwave photon counter or another amplitude detector. These tuning conditions are based on nonlinearity and are hence more robust than previously described linear tuning schemes. In the first part of the paper we show in detail how to achieve this for two-qubit parity measurements and extend this to N qubits in the second part of the paper. We also study the quantum nondemolition character of the protocol.

Strongly interacting photons and atoms

International Nuclear Information System (INIS)

Alge, W.

1999-05-01

This thesis contains the main results of the research topics I have pursued during the my PhD studies at the University of Innsbruck and partly in collaboration with the Institut d' Optique in Orsay, France. It is divided into three parts. The first and largest part discusses the possibility of using strong standing waves as a tool to cool and trap neutral atoms in optical cavities. This is very important in the field of nonlinear optics where several successful experiments with cold atoms in cavities have been performed recently. A discussion of the optical parametric oscillator in a regime where the nonlinearity dominates the evolution is the topic of the second part. We investigated mainly the statistical properties of the cavity output of the three interactive cavity modes. Very recently a system has been proposed which promises fantastic properties. It should exhibit a giant Kerr nonlinearity with negligible absorption thus leading to a photonic turnstile device based on cold atoms in cavity. We have shown that this model suffers from overly simplistic assumptions and developed several more comprehensive approaches to study the behavior of this system. Apart from the division into three parts of different contents the thesis is divided into publications, supplements and invisible stuff. The intention of the supplements is to reach researchers which work in related areas and provide them with more detailed information about the concepts and the numerical tools we used. It is written especially for diploma and PhD students to give them a chance to use the third part of our work which is actually the largest one. They consist of a large number of computer programs we wrote to investigate the behavior of the systems in parameter regions where no hope exists to solve the equations analytically. (author)

Chaotic behavior of earthquakes induced by a nonlinear magma up flow

International Nuclear Information System (INIS)

Pelap, F.B.; Kagho, L.Y.; Fogang, C.F.

2016-01-01

This paper considers the dynamics of a modified 1D nonlinear spring-block model for earthquake subjected to the strengths induced by the motion of the tectonic plates and the up flow of magma during volcanism. Based on the multiple time scales method, we establish that after the slip, the fault remains active and the frictions increase with the power of the earthquake. We also obtain in the non-resonance case that the appearing probability of an event decreases with these frictions. In the resonance case, the dynamics of harmonic oscillations show that the rocks constituting the block will fracture or resist to the effects induced by the magma motion. Our analytical investigations are complemented by numerical simulations from which it appears that, for given values of the magma thrust strength magnitude, the friction coefficient, the quadratic and cubic nonlinear parameters, the system exhibits chaotic behavior.

Analysis of the Nonlinear Static and Dynamic Behavior of Offshore Structures

KAUST Repository

Alfosail, Feras

2015-07-01

Understanding static and dynamic nonlinear behavior of pipes and risers is crucial for the design aspects in offshore engineering fields. In this work, we examine two nonlinear problems in offshore engineering field: vortex Induced vibration of straight horizontal pipes, and boundary layer static solution of inclined risers. In the first study, we analyze the effect of the internal velocity of straight horizontal pipe and obtain the vortex induced vibration forces via coupling the pipe equation of motion with the recently modified Van Der Pol oscillator governing the lift coefficient. Our numerical results are obtained for two different pipe configurations: hinged-hinged, and clamped- clamped. The results show that the internal velocity reduces the vibration and the oscillation amplitudes. Also, it is shown that the clamped-clamped pipe configuration offers a wider range of internal velocities before buckling instability occurs. The results also demonstrate the effect of the end condition on the amplitudes of vibration. In the second study, we develop a boundary layer perturbation static solution to govern and simulate the static behavior of inclined risers. In the boundary layer analysis, we take in consideration the effects of the axial stretch, applied tension, and internal velocity. Our numerical simulation results show good agreement with the exact solutions for special cases. In addition, our developed method overcomes the mathematical and numerical limitations of the previous methods used before.

Fundamentals of nonlinear optical materials

Indian Academy of Sciences (India)

Nonlinear optics; nonlinear polarization; optical fiber communication; optical switch- ing. PACS Nos 42.65Tg; ... The importance of nonlinear optics is to understand the nonlinear behavior in the induced polarization and to ..... but much work in material development and characterization remains to be done. 16. Conclusion.

Nonlinear behavior of photoluminescence from silicon particles under two-photon excitation

International Nuclear Information System (INIS)

Xu Xingsheng; Yokoyama, Shiyoshi

2011-01-01

Two-photon excited fluorescence (TPEF) under continuous-wave excitation from silicon particles produced by a pulsed laser is investigated. Spectra and images of TPEF from silicon particles are studied under different excitation intensities and operation modes (continuous wave or pulse). It is found that the photoluminescence depends superlinearly on the excitation intensity and that the spectral shape and peaks vary with different silicon particles. The above phenomena show the nonlinear behavior of TPEF from silicon particles, and stimulated emission is a possible process.

Nonlinear Cross-Diffusion with Size Exclusion

KAUST Repository

Burger, Martin

2010-01-01

The aim of this paper is to investigate the mathematical properties of a continuum model for diffusion of multiple species incorporating size exclusion effects. The system for two species leads to nonlinear cross-diffusion terms with double degeneracy, which creates significant novel challenges in the analysis of the system. We prove global existence of weak solutions and well-posedness of strong solutions close to equilibrium. We further study some asymptotics of the model, and in particular we characterize the large-time behavior of solutions. 2010 © Society for Industrial and Applied Mathematics.

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).

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

Science.gov (United States)

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

2017-12-01

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

Study of critical behavior in concrete during curing by application of dynamic linear and nonlinear means.

Science.gov (United States)

Lacouture, Jean-Christoph; Johnson, Paul A; Cohen-Tenoudji, Frederic

2003-03-01

The monitoring of both linear and nonlinear elastic properties of a high performance concrete during curing is presented by application of compressional and shear waves. To follow the linear elastic behavior, both compressional and shear waves are used in wide band pulse echo mode. Through the value of the complex reflection coefficient between the cell material (Lucite) and the concrete within the cell, the elastic moduli are calculated. Simultaneously, the transmission of a continuous compressional sine wave at progressively increasing drive levels permits us to calculate the nonlinear properties by extracting the harmonics amplitudes of the signal. Information regarding the chemical evolution of the concrete based upon the reaction of hydration of cement is obtained by monitoring the temperature inside the sample. These different types of measurements are linked together to interpret the critical behavior.

Strong anticipation: Multifractal cascade dynamics modulate scaling in synchronization behaviors

International Nuclear Information System (INIS)

Stephen, Damian G.; Dixon, James A.

2011-01-01

Research highlights: → We investigated anticipatory behaviors in response to chaotic metronomes. → We assessed multifractal structure in tap intervals and onset intervals. → Strength of multifractality in tap intervals appears to match that in onset intervals. - Abstract: Previous research on anticipatory behaviors has found that the fractal scaling of human behavior may attune to the fractal scaling of an unpredictable signal [Stephen DG, Stepp N, Dixon JA, Turvey MT. Strong anticipation: Sensitivity to long-range correlations in synchronization behavior. Physica A 2008;387:5271-8]. We propose to explain this attunement as a case of multifractal cascade dynamics [Schertzer D, Lovejoy S. Generalised scale invariance in turbulent phenomena. Physico-Chem Hydrodyn J 1985;6:623-5] in which perceptual-motor fluctuations are coordinated across multiple time scales. This account will serve to sharpen the contrast between strong and weak anticipation: whereas the former entails a sensitivity to the intermittent temporal structure of an unpredictable signal, the latter simply predicts sensitivity to an aggregate description of an unpredictable signal irrespective of actual sequence. We pursue this distinction through a reanalysis of Stephen et al.'s data by examining the relationship between the widths of singularity spectra for intertap interval time series and for each corresponding interonset interval time series. We find that the attunement of fractal scaling reported by Stephen et al. was not the trivial result of sensitivity to temporal structure in aggregate but reflected a subtle sensitivity to the coordination across multiple time scales of fluctuation in the unpredictable signal.

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.)

Robust energy harvesting from walking vibrations by means of nonlinear cantilever beams

Science.gov (United States)

Kluger, Jocelyn M.; Sapsis, Themistoklis P.; Slocum, Alexander H.

2015-04-01

In the present work we examine how mechanical nonlinearity can be appropriately utilized to achieve strong robustness of performance in an energy harvesting setting. More specifically, for energy harvesting applications, a great challenge is the uncertain character of the excitation. The combination of this uncertainty with the narrow range of good performance for linear oscillators creates the need for more robust designs that adapt to a wider range of excitation signals. A typical application of this kind is energy harvesting from walking vibrations. Depending on the particular characteristics of the person that walks as well as on the pace of walking, the excitation signal obtains completely different forms. In the present work we study a nonlinear spring mechanism that is composed of a cantilever wrapping around a curved surface as it deflects. While for the free cantilever, the force acting on the free tip depends linearly on the tip displacement, the utilization of a contact surface with the appropriate distribution of curvature leads to essentially nonlinear dependence between the tip displacement and the acting force. The studied nonlinear mechanism has favorable mechanical properties such as low frictional losses, minimal moving parts, and a rugged design that can withstand excessive loads. Through numerical simulations we illustrate that by utilizing this essentially nonlinear element in a 2 degrees-of-freedom (DOF) system, we obtain strongly nonlinear energy transfers between the modes of the system. We illustrate that this nonlinear behavior is associated with strong robustness over three radically different excitation signals that correspond to different walking paces. To validate the strong robustness properties of the 2DOF nonlinear system, we perform a direct parameter optimization for 1DOF and 2DOF linear systems as well as for a class of 1DOF and 2DOF systems with nonlinear springs similar to that of the cubic spring that are physically realized

Dynamical soil-structure interactions: influence of soil behaviour nonlinearities

International Nuclear Information System (INIS)

Gandomzadeh, Ali

2011-01-01

The interaction of the soil with the structure has been largely explored the assumption of material and geometrical linearity of the soil. Nevertheless, for moderate or strong seismic events, the maximum shear strain can easily reach the elastic limit of the soil behavior. Considering soil-structure interaction, the nonlinear effects may change the soil stiffness at the base of the structure and therefore energy dissipation into the soil. Consequently, ignoring the nonlinear characteristics of the dynamic soil-structure interaction (DSSI) this phenomenon could lead to erroneous predictions of structural response. The goal of this work is to implement a fully nonlinear constitutive model for soils into a numerical code in order to investigate the effect of soil nonlinearity on dynamic soil structure interaction. Moreover, different issues are taken into account such as the effect of confining stress on the shear modulus of the soil, initial static condition, contact elements in the soil-structure interface, etc. During this work, a simple absorbing layer method based on a Rayleigh/Caughey damping formulation, which is often already available in existing Finite Element softwares, is also presented. The stability conditions of the wave propagation problems are studied and it is shown that the linear and nonlinear behavior are very different when dealing with numerical dispersion. It is shown that the 10 points per wavelength rule, recommended in the literature for the elastic media is not sufficient for the nonlinear case. The implemented model is first numerically verified by comparing the results with other known numerical codes. Afterward, a parametric study is carried out for different types of structures and various soil profiles to characterize nonlinear effects. Different features of the DSSI are compared to the linear case: modification of the amplitude and frequency content of the waves propagated into the soil, fundamental frequency, energy dissipation in

BRIEF COMMUNICATIONS: Strong reflection of a series of pulses from a four-wave mirror with thermal nonlinearity under parametric feedback conditions

Science.gov (United States)

Barashkov, M. S.; Bel'dyugin, Igor'M.; Zolotarev, M. V.; Kruzhilin, Yu I.; Krymskiĭ, M. I.; Oshkin, S. P.; Starkov, G. S.; Umnov, A. F.; Kharchenko, M. A.

1989-04-01

A four-wave mirror exhibiting a thermal nonlinearity was used in a study of the interaction of concurrent waves under parametric feedback conditions in the presence of a nonreciprocal element. Strong reflection of a series of pulses of ~ 300 ns duration from a neodymium glass laser was demonstrated: the maximum reflection coefficient was in excess of 30. An analysis was made of the quality of the radiation reflected from this four-mirror parametric feedback system. A considerable reduction was observed in the steady-state threshold for the operation of this mirror with a thermal nonlinearity when the angles of convergence of the interacting beams were small compared with the case of head-on collision of the waves.

Electromagnetic pulses at the boundary of a nonlinear plasma

International Nuclear Information System (INIS)

Satorius, E.H.

1975-01-01

An investigation was made of the behavior of strong electromagnetic pulses at the boundary of a nonlinear, cold, collisionless, and uniform plasma. The nonlinearity considered here is due to the nonlinear terms in the fluid equation which is used to describe the plasma. Two cases are studied. First, the case where there is a voltage pulse applied across the plane boundary of a semi-infinite, nonlinear plasma. Two different voltage pulses are considered, i.e., a delta function pulse and a suddenly turned-on sinusoidal pulse. The resulting electromagnetic fields propagating in the nonlinear plasma are found in this case. In the second case, the reflection of incident E-polarized and H-polarized, electromagnetic pulses at various angles of incidence from a nonlinear, semi-infinite plasma are considered. Again, two forms of incident pulses are considered: a delta function pulse and a suddenly turned-on sinusoidal pulse. In case two, the reflected electromagnetic fields are found. In both cases, the method used for finding the fields is to first solve the fluid equation (which describes the plasma) for the nonlinear conduction current in terms of the electric field using a perturbation method (since the nonlinear effects are assumed to be small). Next, this current is substituted into Maxwell's equations, and finally the electromagnetic fields which satisfy the boundary conditions are found. (U.S.)

The propagation of nonlinear rayleigh waves in layered elastic half-space

International Nuclear Information System (INIS)

Ahmetolan, S.

2004-01-01

In this work, the propagation of small but finite amplitude generalized Rayleigh waves in an elastic half-space covered by a different elastic layer of uniform and finite thickness is considered. The constituent materials are assumed to be homogeneous, isotropic, compressible hyperelastic. Excluding the harmonic resonance phenomena, it is shown that the nonlinear self modulation of generalized Rayleigh waves is governed asymptotically by a nonlinear Schrodinger (NLS) equation. The stability of the solutions and the existence of solitary wave-type solutions a NLS are strongly depend on the sign of the product of the coefficients of the nonlinear and dipersion terms of the equation.Therefore the analysis continues with the examination of dependence of these coefficients on the nonlinear material parameters. Three different models have been considered which are nonlinear layer-nonlinear half space, linear layer-nonlinear half space and nonlinear layer-linear half space. The behavior of the coefficients of the NLS equation was also analyzed the limit as h(thickness of the layer) goes to zero and k(the wave number) is constant. Then conclusions are drawn about the effect of nonlinear material parameters on the wave modulation. In the numerical investigations both hypothetical and real material models are used

Nonlinear and quantum optics near nanoparticles

Science.gov (United States)

Dhayal, Suman

We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. We have also studied the modifications of the electromagnetic fields in a collection of nanoparticles due to strong near field nonlinear interactions using the generalized Mie theory for the case of many particles applicable in photovoltaics (PV). We also consider quantum coherence phenomena such as modification of dark states, stimulated Raman adiabatic passage (STIRAP), optical pumping in 4-level atoms near nanoparticles by using rotating wave approximation to describe the Hamiltonian of the atomic system. We also considered the behavior of atomic and the averaged atomic polarization in 7-level atoms near nanoparticles. This could be used as a prototype to study

Nonlinear dynamics of structures

CERN Document Server

Oller, Sergio

2014-01-01

This book lays the foundation of knowledge that will allow a better understanding of nonlinear phenomena that occur in structural dynamics.   This work is intended for graduate engineering students who want to expand their knowledge on the dynamic behavior of structures, specifically in the nonlinear field, by presenting the basis of dynamic balance in non‐linear behavior structures due to the material and kinematics mechanical effects.   Particularly, this publication shows the solution of the equation of dynamic equilibrium for structure with nonlinear time‐independent materials (plasticity, damage and frequencies evolution), as well as those time dependent non‐linear behavior materials (viscoelasticity and viscoplasticity). The convergence conditions for the non‐linear dynamic structure solution  are studied, and the theoretical concepts and its programming algorithms are presented.  

A study on nonlinear behavior of reactor containment structures during ultimate accident condition(I)

Energy Technology Data Exchange (ETDEWEB)

Kim, Sun Hoon; Kim, Young Jin; Park, Joo Yeon [Youngdong Univ., Yeongdong (Korea, Republic of)] (and others)

2003-03-15

In this study, the following scope and contents are established for first year's study of determining ultimate pressure capacity of CANDU-type reactor containment. State-of-arts on the prediction of the ultimate pressure capacity of prestressed concrete reactor containment. Comparative study on structural characteristics and analysis model of CANDU-type reactor containment. State-of-arts on evaluation method of the ultimate pressure capacity of prestressed concrete reactor containment. Enhancement of evaluation method of the ultimate pressure capacity for PWR containment structure. In order to determine a realistic lower bound of a typical reactor containment structural capacity for internal pressure, modelling techniques and analytical investigation to predict its non-linear behavior up to ultimate capacity are required. Especially, the in-depth evaluation of modeling technique and analysis procedure for determining ultimate pressure capacity of CANDU-type reactor containment is required. Therefore, modelling techniques and analytical investigation to predict its non-linear behavior up to ultimate pressure capacity of CANDU-type reactor containment for internal pressure will be suggested in this study.

A study on nonlinear behavior of reactor containment structures during ultimate accident condition(I)

International Nuclear Information System (INIS)

Kim, Sun Hoon; Kim, Young Jin; Park, Joo Yeon

2003-03-01

In this study, the following scope and contents are established for first year's study of determining ultimate pressure capacity of CANDU-type reactor containment. State-of-arts on the prediction of the ultimate pressure capacity of prestressed concrete reactor containment. Comparative study on structural characteristics and analysis model of CANDU-type reactor containment. State-of-arts on evaluation method of the ultimate pressure capacity of prestressed concrete reactor containment. Enhancement of evaluation method of the ultimate pressure capacity for PWR containment structure. In order to determine a realistic lower bound of a typical reactor containment structural capacity for internal pressure, modelling techniques and analytical investigation to predict its non-linear behavior up to ultimate capacity are required. Especially, the in-depth evaluation of modeling technique and analysis procedure for determining ultimate pressure capacity of CANDU-type reactor containment is required. Therefore, modelling techniques and analytical investigation to predict its non-linear behavior up to ultimate pressure capacity of CANDU-type reactor containment for internal pressure will be suggested in this study

On Poisson Nonlinear Transformations

Directory of Open Access Journals (Sweden)

Nasir Ganikhodjaev

2014-01-01

Full Text Available We construct the family of Poisson nonlinear transformations defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. We have proved that these nonlinear transformations are regular.

Elucidating and tuning the strain-induced non-linear behavior of polymer nanocomposites: a detailed molecular dynamics simulation study.

Science.gov (United States)

Shen, Jianxiang; Liu, Jun; Gao, Yangyang; Li, Xiaolin; Zhang, Liqun

2014-07-28

By setting up a coarse-grained model of polymer nanocomposites, we monitored the change in the elastic modulus as a function of the strain, derived from the stress-strain behavior by determining uniaxial tension and simple shear of two typical spatial distribution states (aggregation and dispersion) of nanoparticles (NPs). In both these cases, we observed that the elastic modulus decreases non-linearly with the increase of strain and reaches a low plateau at larger strains. This phenomenon is similar to the so-called "Payne effect" for elastomer nanocomposites. Particularly, the modulus of the aggregation case is more sensitive to the imposed strain. By examining the structural parameters, such as the number of neighboring NPs, coordination number of NPs, root-mean-squared average force exerted on the NPs, local strain, chain conformations (bridge, dangle, loop, interface bead and connection bead), and the total interaction energy of NP-polymer and NP-NP, we inferred that the underlying mechanism of the aggregation case is the disintegration of the NP network or clusters formed through direct contact; however, for the dispersion case, the non-linear behavior is attributed to the destruction of the NP network or clusters formed through the bridging of adsorbed polymer segments among the NPs. The former physical network is influenced by NP-NP interaction and NP volume fraction, while the latter is influenced by NP-polymer interaction and NP volume fraction. Lastly, we found that for the dispersion case, further increasing the inter-particle distance or grafting NPs with polymer chains can effectively reduce the non-linear behavior due to the decrease of the physical network density. In general, this simulation work, for the first time, establishes the correlation between the micro-structural evolution and the strain-induced non-linear behavior of polymer nanocomposites, and sheds some light on how to reduce the "Payne effect".

Theoretical and Experimental Investigation of the Nonlinear Behavior of an Electrostatically Actuated In-Plane MEMS Arch

KAUST Repository

Ramini, Abdallah; Al Hennawi, Qais M.; Younis, Mohammad I.

2016-01-01

We present theoretical and experimental investigation of the nonlinear behavior of a clamped-clamped in-plane MEMS arch when excited by a DC electrostatic load superimposed to an AC harmonic load. Experimentally, a case study of in-plane silicon

Electrodynamic soil plate oscillator: Modeling nonlinear mesoscopic elastic behavior and hysteresis in nonlinear acoustic landmine detection

Science.gov (United States)

Korman, M. S.; Duong, D. V.; Kalsbeck, A. E.

2015-10-01

An apparatus (SPO), designed to study flexural vibrations of a soil loaded plate, consists of a thin circular elastic clamped plate (and cylindrical wall) supporting a vertical soil column. A small magnet attached to the center of the plate is driven by a rigid AC coil (located coaxially below the plate) to complete the electrodynamic soil plate oscillator SPO design. The frequency dependent mechanical impedance Zmech (force / particle velocity, at the plate's center) is inversely proportional to the electrical motional impedance Zmot. Measurements of Zmot are made using the complex output to input response of a Wheatstone bridge that has an identical coil element in one of its legs. Near resonance, measurements of Zmot (with no soil) before and after a slight point mass loading at the center help determine effective mass, spring, damping and coupling constant parameters of the system. "Tuning curve" behavior of real{ Zmot } and imaginary{ Zmot } at successively higher vibration amplitudes of dry sifted masonry sand are measured. They exhibit a decrease "softening" in resonance frequency along with a decrease in the quality Q factor. In soil surface vibration measurements a bilinear hysteresis model predicts the tuning curve shape for this nonlinear mesoscopic elastic SPO behavior - which also models the soil vibration over an actual plastic "inert" VS 1.6 buried landmine. Experiments are performed where a buried 1m cube concrete block supports a 12 inch deep by 30 inch by 30 inch concrete soil box for burying a VS 1.6 in dry sifted masonry sand for on-the-mine and off-the-mine soil vibration experiments. The backbone curve (a plot of the peak amplitude vs. corresponding resonant frequency from a family of tuning curves) exhibits mostly linear behavior for "on target" soil surface vibration measurements of the buried VS 1.6 or drum-like mine simulants for relatively low particle velocities of the soil. Backbone curves for "on target" measurements exhibit

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

Science.gov (United States)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Nonlinear single-spin spectrum analyzer.

Science.gov (United States)

Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

2013-03-15

Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.

Nonlinear dynamics of resistive electrostatic drift waves

DEFF Research Database (Denmark)

Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.

1999-01-01

The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... polarity, i.e. a pair of electrostatic convective cells....

Improving stability and strength characteristics of framed structures with nonlinear behavior

Science.gov (United States)

Pezeshk, Shahram

1990-01-01

In this paper an optimal design procedure is introduced to improve the overall performance of nonlinear framed structures. The design methodology presented here is a multiple-objective optimization procedure whose objective functions involve the buckling eigenvalues and eigenvectors of the structure. A constant volume with bounds on the design variables is used in conjunction with an optimality criterion approach. The method provides a general tool for solving complex design problems and generally leads to structures with better limit strength and stability. Many algorithms have been developed to improve the limit strength of structures. In most applications geometrically linear analysis is employed with the consequence that overall strength of the design is overestimated. Directly optimizing the limit load of the structure would require a full nonlinear analysis at each iteration which would be prohibitively expensive. The objective of this paper is to develop an algorithm that can improve the limit-load of geometrically nonlinear framed structures while avoiding the nonlinear analysis. One of the novelties of the new design methodology is its ability to efficiently model and design structures under multiple loading conditions. These loading conditions can be different factored loads or any kind of loads that can be applied to the structure simultaneously or independently. Attention is focused on optimal design of space framed structures. Three-dimensional design problems are more complicated to carry out, but they yield insight into real behavior of the structure and can help avoiding some of the problems that might appear in planar design procedure such as the need for out-of-plane buckling constraint. Although researchers in the field of structural engineering generally agree that optimum design of three-dimension building frames especially in the seismic regions would be beneficial, methods have been slow to emerge. Most of the research in this area has dealt

High-precision 2MASS JHK{sub s} light curves and other data for RR Lyrae star SDSS J015450 + 001501: Strong constraints for nonlinear pulsation models

Energy Technology Data Exchange (ETDEWEB)

Szabó, Róbert; Ivezić, Željko; Kiss, László L.; Kolláth, Zoltán [Konkoly Observatory, MTA CSFK, Konkoly Thege Miklós út 15-17, H-1121 Budapest (Hungary); Jones, Lynne; Becker, Andrew C.; Davenport, James R. A. [Astronomy Department, University of Washington, Box 351580, Seattle, WA 98195-1580 (United States); Sesar, Branimir [Division of Physics, Mathematics and Astronomy, Caltech, Pasadena, CA 91125 (United States); Cutri, Roc M., E-mail: rszabo@konkoly.hu [Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125 (United States)

2014-01-01

We present and discuss an extensive data set for the non-Blazhko ab-type RR Lyrae star SDSS J015450+001501, including optical Sloan Digital Sky Survey ugriz light curves and spectroscopic data, LINEAR and Catalina Sky Survey unfiltered optical light curves, and infrared Two Micron All Sky Survey (2MASS) JHK{sub s} and Wide-field Infrared Survey Explorer W1 and W2 light curves. Most notable is that light curves obtained by 2MASS include close to 9000 photometric measures collected over 3.3 yr and provide an exceedingly precise view of near-infrared variability. These data demonstrate that static atmosphere models are insufficient to explain multiband photometric light-curve behavior and present strong constraints for nonlinear pulsation models for RR Lyrae stars. It is a challenge to modelers to produce theoretical light curves that can explain data presented here, which we make publicly available.

Nonlinear stochastic heat equations with cubic nonlinearities and additive Q-regular noise in R^1

Directory of Open Access Journals (Sweden)

Henri Schurz

2010-09-01

Full Text Available Semilinear stochastic heat equations perturbed by cubic-type nonlinearities and additive space-time noise with homogeneous boundary conditions are discussed in R^1. The space-time noise is supposed to be Gaussian in time and possesses a Fourier expansion in space along the eigenfunctions of underlying Lapace operators. We follow the concept of approximate strong (classical Fourier solutions. The existence of unique continuous L^2-bounded solutions is proved. Furthermore, we present a procedure for its numerical approximation based on nonstandard methods (linear-implicit and justify their stability and consistency. The behavior of related total energy functional turns out to be crucial in the presented analysis.

Nonlinear dynamics and numerical uncertainties in CFD

Science.gov (United States)

Yee, H. C.; Sweby, P. K.

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.

Effect of Various Excitation Conditions on Vibrational Energy in a Multi-Degree-of-Freedom Torsional System with Piecewise-Type Nonlinearities

Directory of Open Access Journals (Sweden)

Jong-Yun Yoon

2015-09-01

Full Text Available Dynamic behaviors in practical driveline systems for wind turbines or vehicles are inherently affected by multiple nonlinearities such as piecewise-type torsional springs. However, various excitation conditions with different levels of magnitudes also show strong relationships to the dynamic behaviors when system responses are examined in both frequency and time domains. This study investigated the nonlinear responses of torsional systems under various excitations by using the harmonic balance method and numerical analysis. In order to understand the effect of piecewise-type nonlinearities on vibrational energy with different excitations, the nonlinear responses were investigated with various comparisons. First, two different jumping phenomena with frequency up- and down-sweeping conditions were determined under severe excitation levels. Second, practical system analysis using the phase plane and Poincaré map was conducted in various ways. When the system responses were composed of quasi-periodic components, Poincaré map analysis clearly revealed the nonlinear dynamic characteristics and thus it is suggested to investigate complicated nonlinear dynamic responses in practical driveline systems.

Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers

International Nuclear Information System (INIS)

Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.

2005-01-01

The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized πelectrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized π electrons along an extended group of atoms in such molecules

Some Aspects of Nonlinear Dynamics and CFD

Science.gov (United States)

Yee, Helen C.; Merriam, Marshal (Technical Monitor)

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with examples of spurious behavior observed in CFD computations.

Strongly increasing solutions of cyclic systems of second order differential equations with power-type nonlinearities

Directory of Open Access Journals (Sweden)

Jaroslav Jaroš

2015-01-01

Full Text Available We consider \\(n\\-dimensional cyclic systems of second order differential equations \\[(p_i(t|x_{i}'|^{\\alpha_i -1}x_{i}'' = q_{i}(t|x_{i+1}|^{\\beta_i-1}x_{i+1},\\] \\[\\quad i = 1,\\ldots,n, \\quad (x_{n+1} = x_1 \\tag{\\(\\ast\\}\\] under the assumption that the positive constants \\(\\alpha_i\\ and \\(\\beta_i\\ satisfy \\(\\alpha_1{\\ldots}\\alpha_n \\gt \\beta_1{\\ldots}\\beta_n\\ and \\(p_i(t\\ and \\(q_i(t\\ are regularly varying functions, and analyze positive strongly increasing solutions of system (\\(\\ast\\ in the framework of regular variation. We show that the situation for the existence of regularly varying solutions of positive indices for (\\(\\ast\\ can be characterized completely, and moreover that the asymptotic behavior of such solutions is governed by the unique formula describing their order of growth precisely. We give examples demonstrating that the main results for (\\(\\ast\\ can be applied to some classes of partial differential equations with radial symmetry to acquire accurate information about the existence and the asymptotic behavior of their radial positive strongly increasing solutions.

Ideal gas behavior of a strongly coupled complex (dusty) plasma.

Science.gov (United States)

Oxtoby, Neil P; Griffith, Elias J; Durniak, Céline; Ralph, Jason F; Samsonov, Dmitry

2013-07-05

In a laboratory, a two-dimensional complex (dusty) plasma consists of a low-density ionized gas containing a confined suspension of Yukawa-coupled plastic microspheres. For an initial crystal-like form, we report ideal gas behavior in this strongly coupled system during shock-wave experiments. This evidence supports the use of the ideal gas law as the equation of state for soft crystals such as those formed by dusty plasmas.

Ideal gas behavior of a strongly-coupled complex (dusty) plasma

OpenAIRE

Oxtoby, Neil P.; Griffith, Elias J.; Durniak, Céline; Ralph, Jason F.; Samsonov, Dmitry

2012-01-01

In a laboratory, a two-dimensional complex (dusty) plasma consists of a low-density ionized gas containing a confined suspension of Yukawa-coupled plastic microspheres. For an initial crystal-like form, we report ideal gas behavior in this strongly-coupled system during shock-wave experiments. This evidence supports the use of the ideal gas law as the equation of state for soft crystals such as those formed by dusty plasmas.

Modeling, numerical simulation, and nonlinear dynamic behavior analysis of PV microgrid-connected inverter with capacitance catastrophe

Science.gov (United States)

Li, Sichen; Liao, Zhixian; Luo, Xiaoshu; Wei, Duqu; Jiang, Pinqun; Jiang, Qinghong

2018-02-01

The value of the output capacitance (C) should be carefully considered when designing a photovoltaic (PV) inverter since it can cause distortion in the working state of the circuit, and the circuit produces nonlinear dynamic behavior. According to Kirchhoff’s laws and the characteristics of an ideal operational amplifier for a strict piecewise linear state equation, a circuit simulation model is constructed to study the system parameters (time, C) for the current passing through an inductor with an inductance of L and the voltage across the capacitor with a capacitance of C. The developed simulation model uses Runge-Kutta methods to solve the state equations. This study focuses on predicting the fault of the circuit from the two aspects of the harmonic distortion and simulation results. Moreover, the presented model is also used to research the working state of the system in the case of a load capacitance catastrophe. The nonlinear dynamic behaviors in the inverter are simulated and verified.

The nonlinear unloading behavior of a typical Ni-based superalloy during hot deformation. A new elasto-viscoplastic constitutive model

Energy Technology Data Exchange (ETDEWEB)

Chen, Ming-Song; Li, Kuo-Kuo [Central South University, School of Mechanical and Electrical Engineering, Changsha (China); State Key Laboratory of High Performance Complex Manufacturing, Changsha (China); Lin, Y.C. [Central South University, School of Mechanical and Electrical Engineering, Changsha (China); State Key Laboratory of High Performance Complex Manufacturing, Changsha (China); Central South University, Light Alloy Research Institute, Changsha (China); Chen, Jian [Changsha University of Science and Technology, School of Energy and Power Engineering, Key Laboratory of Efficient and Clean Energy Utilization, Changsha (China)

2016-09-15

The nonlinear unloading behavior of a typical Ni-based superalloy is investigated by hot compressive experiments with intermediate unloading-reloading cycles. The experimental results show that there are at least four types of unloading curves. However, it is found that there is no essential difference among four types of unloading curves. The variation curves of instantaneous Young's modulus with stress for all types of unloading curves include four segments, i.e., three linear elastic segments (segments I, II, and III) and one subsequent nonlinear elastic segment (segment IV). The instantaneous Young's modulus of segments I and III is approximately equal to that of reloading process, while smaller than that of segment II. In the nonlinear elastic segment, the instantaneous Young's modulus linearly decreases with the decrease in stress. In addition, the relationship between stress and strain rate can be accurately expressed by the hyperbolic sine function. This study includes two parts. In the present part, the characters of unloading curves are discussed in detail, and a new elasto-viscoplastic constitutive model is proposed to describe the nonlinear unloading behavior based on the experimental findings. While in the latter part (Chen et al. in Appl Phys A. doi:10.1007/s00339-016-0385-0, 2016), the effects of deformation temperature, strain rate, and pre-strain on the parameters of this new constitutive model are analyzed, and a unified elasto-viscoplastic constitutive model is proposed to predict the unloading behavior at arbitrary deformation temperature, strain rate, and pre-strain. (orig.)

The nonlinear unloading behavior of a typical Ni-based superalloy during hot deformation. A new elasto-viscoplastic constitutive model

International Nuclear Information System (INIS)

Chen, Ming-Song; Li, Kuo-Kuo; Lin, Y.C.; Chen, Jian

2016-01-01

The nonlinear unloading behavior of a typical Ni-based superalloy is investigated by hot compressive experiments with intermediate unloading-reloading cycles. The experimental results show that there are at least four types of unloading curves. However, it is found that there is no essential difference among four types of unloading curves. The variation curves of instantaneous Young's modulus with stress for all types of unloading curves include four segments, i.e., three linear elastic segments (segments I, II, and III) and one subsequent nonlinear elastic segment (segment IV). The instantaneous Young's modulus of segments I and III is approximately equal to that of reloading process, while smaller than that of segment II. In the nonlinear elastic segment, the instantaneous Young's modulus linearly decreases with the decrease in stress. In addition, the relationship between stress and strain rate can be accurately expressed by the hyperbolic sine function. This study includes two parts. In the present part, the characters of unloading curves are discussed in detail, and a new elasto-viscoplastic constitutive model is proposed to describe the nonlinear unloading behavior based on the experimental findings. While in the latter part (Chen et al. in Appl Phys A. doi:10.1007/s00339-016-0385-0, 2016), the effects of deformation temperature, strain rate, and pre-strain on the parameters of this new constitutive model are analyzed, and a unified elasto-viscoplastic constitutive model is proposed to predict the unloading behavior at arbitrary deformation temperature, strain rate, and pre-strain. (orig.)

A nonlinear equation for ionic diffusion in a strong binary electrolyte

Science.gov (United States)

Ghosal, Sandip; Chen, Zhen

2010-01-01

The problem of the one-dimensional electro-diffusion of ions in a strong binary electrolyte is considered. The mathematical description, known as the Poisson–Nernst–Planck (PNP) system, consists of a diffusion equation for each species augmented by transport owing to a self-consistent electrostatic field determined by the Poisson equation. This description is also relevant to other important problems in physics, such as electron and hole diffusion across semiconductor junctions and the diffusion of ions in plasmas. If concentrations do not vary appreciably over distances of the order of the Debye length, the Poisson equation can be replaced by the condition of local charge neutrality first introduced by Planck. It can then be shown that both species diffuse at the same rate with a common diffusivity that is intermediate between that of the slow and fast species (ambipolar diffusion). Here, we derive a more general theory by exploiting the ratio of the Debye length to a characteristic length scale as a small asymptotic parameter. It is shown that the concentration of either species may be described by a nonlinear partial differential equation that provides a better approximation than the classical linear equation for ambipolar diffusion, but reduces to it in the appropriate limit. PMID:21818176

Linear instability and nonlinear motion of rotating plasma

International Nuclear Information System (INIS)

Liu, J.

1985-01-01

Two coupled nonlinear equations describing the flute dynamics of the magnetically confined low-β collisionless rotating plasma are derived. The linear instability and nonlinear dynamics of the rotating column are analyzed theoretically. In the linear stability analysis, a new sufficient condition of stability is obtained. From the exact solution of eigenvalue equation for Gaussian density profile and uniform rotation of the plasma, the stability of the system strongly depends on the direction of plasma rotation, FLR effect and the location of the conducting wall. An analytic expression showing the finite wall effect on different normal modes is obtained and it explains the different behavior of (1,0) normal mode from other modes. The sheared rotation driven instability is investigated by using three model equilibrium profiles, and the analytic expressions of eigenvalues which includes the wall effect are obtained. The analogy between shear rotation driven instability and the instability driven by sheared plane parallel flow in the inviscid fluid is analyzed. Applying the linear analysis to the central cell of tandem mirror system, the trapped particle instability with only passing electronics is analyzed. For uniform rotation and Gaussian density profile, an analytic expression that determines the stability boundary is found. The nonlinear analysis shows that the nonlinear equations have a solitary vortex solution which is very similar to the vortex solution of nonlinear Rossby wave equation

Nonlinear approaches in engineering applications 2

CERN Document Server

Jazar, Reza N

2013-01-01

Provides updated principles and applications of the nonlinear approaches in solving engineering and physics problems Demonstrates how nonlinear approaches may open avenues to better, safer, cheaper systems with less energy consumption Has a strong emphasis on the application, physical meaning, and methodologies of nonlinear approaches in different engineering and science problems

Nonlinear complexity behaviors of agent-based 3D Potts financial dynamics with random environments

Science.gov (United States)

Xing, Yani; Wang, Jun

2018-02-01

A new microscopic 3D Potts interaction financial price model is established in this work, to investigate the nonlinear complexity behaviors of stock markets. 3D Potts model, which extends the 2D Potts model to three-dimensional, is a cubic lattice model to explain the interaction behavior among the agents. In order to explore the complexity of real financial markets and the 3D Potts financial model, a new random coarse-grained Lempel-Ziv complexity is proposed to certain series, such as the price returns, the price volatilities, and the random time d-returns. Then the composite multiscale entropy (CMSE) method is applied to the intrinsic mode functions (IMFs) and the corresponding shuffled data to study the complexity behaviors. The empirical results indicate that the 3D financial model is feasible.

On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations

International Nuclear Information System (INIS)

An Hengbin; Mo Zeyao; Xu Xiaowen; Liu Xu

2009-01-01

The 2-D 3-T heat conduction equations can be used to approximately describe the energy broadcast in materials and the energy swapping between electron and photon or ion. To solve the equations, a fully implicit finite volume scheme is often used as the discretization method. Because the energy diffusion and swapping coefficients have a strongly nonlinear dependence on the temperature, and some physical parameters are discontinuous across the interfaces between the materials, it is a challenge to solve the discretized nonlinear algebraic equations. Particularly, as time advances, the temperature varies so greatly in the front of energy that it is difficult to choose an effective initial iterate when the nonlinear algebraic equations are solved by an iterative method. In this paper, a method of choosing a nonlinear initial iterate is proposed for iterative solving this kind of nonlinear algebraic equations. Numerical results show the proposed initial iterate can improve the computational efficiency, and also the convergence behavior of the nonlinear iteration.

Nonlinear aeroelastic behavior of compliant airfoils

International Nuclear Information System (INIS)

Thwapiah, G; Campanile, L F

2010-01-01

Since the beginning of aviation and up to the present time, airfoils have always been built as rigid structures. They are designed to fly under their divergence speed in order to avoid static aeroelastic instabilities and the resulting large deformations, which are not compatible with the typically low compliance of such airfoils. In recent years, research on airfoil morphing has generated interest in innovative ideas like the use of compliant systems, i.e. systems built to allow for large deformations without failure, in airfoil construction. Such systems can operate in the neighborhood of divergence and take advantage of large aeroelastic servo-effects. This, in turn, allows compact, advanced actuators to control the airfoil's deformation and loads, and hence complement or even replace conventional flaps. In order to analyze and design such compliant, active aeroelastic structures a nonlinear approach to static aeroelasticity is needed, which takes into account the effect of large deformations on aerodynamics and structure. Such an analytical approach is presented in this paper and applied to a compliant passive airfoil as the preliminary step in the realization of a piezoelectrically driven, active aeroelastic airfoil. Wind tunnel test results are also presented and compared with the analytic prediction. The good agreement and the observed behavior in the wind tunnel give confidence in the potential of this innovative idea

Nonlinear aeroelastic behavior of compliant airfoils

Science.gov (United States)

Thwapiah, G.; Campanile, L. F.

2010-03-01

Since the beginning of aviation and up to the present time, airfoils have always been built as rigid structures. They are designed to fly under their divergence speed in order to avoid static aeroelastic instabilities and the resulting large deformations, which are not compatible with the typically low compliance of such airfoils. In recent years, research on airfoil morphing has generated interest in innovative ideas like the use of compliant systems, i.e. systems built to allow for large deformations without failure, in airfoil construction. Such systems can operate in the neighborhood of divergence and take advantage of large aeroelastic servo-effects. This, in turn, allows compact, advanced actuators to control the airfoil's deformation and loads, and hence complement or even replace conventional flaps. In order to analyze and design such compliant, active aeroelastic structures a nonlinear approach to static aeroelasticity is needed, which takes into account the effect of large deformations on aerodynamics and structure. Such an analytical approach is presented in this paper and applied to a compliant passive airfoil as the preliminary step in the realization of a piezoelectrically driven, active aeroelastic airfoil. Wind tunnel test results are also presented and compared with the analytic prediction. The good agreement and the observed behavior in the wind tunnel give confidence in the potential of this innovative idea.

Joule-Thomson Coefficient for Strongly Interacting Unitary Fermi Gas

International Nuclear Information System (INIS)

Liao Kai; Chen Jisheng; Li Chao

2010-01-01

The Joule-Thomson effect reflects the interaction among constituent particles of macroscopic system. For classical ideal gas, the corresponding Joule-Thomson coefficient is vanishing while it is non-zero for ideal quantum gas due to the quantum degeneracy. In recent years, much attention is paid to the unitary Fermi gas with infinite two-body scattering length. According to universal analysis, the thermodynamical law of unitary Fermi gas is similar to that of non-interacting ideal gas, which can be explored by the virial theorem P = 2E/3V. Based on previous works, we further study the unitary Fermi gas properties. The effective chemical potential is introduced to characterize the nonlinear levels crossing effects in a strongly interacting medium. The changing behavior of the rescaled Joule-Thomson coefficient according to temperature manifests a quite different behavior from that for ideal Fermi gas. (general)

Superior optical nonlinearity of an exceptional fluorescent stilbene dye

Energy Technology Data Exchange (ETDEWEB)

He, Tingchao [College of Physics Science and Technology, Shenzhen University, Shenzhen 518060 (China); Division of Physics and Applied Physics, Centre for Disruptive Photonic Technologies (CDPT), School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371 (Singapore); Sreejith, Sivaramapanicker; Zhao, Yanli [Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371 (Singapore); Gao, Yang; Grimsdale, Andrew C. [School of Materials Science and Engineering, Nanyang Technological University, Singapore, Singapore 639798 (Singapore); Lin, Xiaodong, E-mail: linxd@szu.edu.cn, E-mail: hdsun@ntu.edu.sg [College of Physics Science and Technology, Shenzhen University, Shenzhen 518060 (China); Sun, Handong, E-mail: linxd@szu.edu.cn, E-mail: hdsun@ntu.edu.sg [Division of Physics and Applied Physics, Centre for Disruptive Photonic Technologies (CDPT), School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371 (Singapore)

2015-03-16

Strong multiphoton absorption and harmonic generation in organic fluorescent chromophores are, respectively, significant in many fields of research. However, most of fluorescent chromophores fall short of the full potential due to the absence of the combination of such different nonlinear upconversion behaviors. Here, we demonstrate that an exceptional fluorescent stilbene dye could exhibit efficient two- and three-photon absorption under the excitation of femtosecond pulses in solution phase. Benefiting from its biocompatibility and strong excited state absorption behavior, in vitro two-photon bioimaging and superior optical limiting have been exploited, respectively. Simultaneously, the chromophore could generate efficient three-photon excited fluorescence and third-harmonic generation (THG) when dispersed into PMMA film, circumventing the limitations of classical fluorescent chromophores. Such chromophore may find application in the production of coherent light sources of higher photon energy. Moreover, the combination of three-photon excited fluorescence and THG can be used in tandem to provide complementary information in biomedical studies.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

Science.gov (United States)

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

2015-05-21

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

Model-on-Demand Predictive Control for Nonlinear Hybrid Systems With Application to Adaptive Behavioral Interventions

Science.gov (United States)

Nandola, Naresh N.; Rivera, Daniel E.

2011-01-01

This paper presents a data-centric modeling and predictive control approach for nonlinear hybrid systems. System identification of hybrid systems represents a challenging problem because model parameters depend on the mode or operating point of the system. The proposed algorithm applies Model-on-Demand (MoD) estimation to generate a local linear approximation of the nonlinear hybrid system at each time step, using a small subset of data selected by an adaptive bandwidth selector. The appeal of the MoD approach lies in the fact that model parameters are estimated based on a current operating point; hence estimation of locations or modes governed by autonomous discrete events is achieved automatically. The local MoD model is then converted into a mixed logical dynamical (MLD) system representation which can be used directly in a model predictive control (MPC) law for hybrid systems using multiple-degree-of-freedom tuning. The effectiveness of the proposed MoD predictive control algorithm for nonlinear hybrid systems is demonstrated on a hypothetical adaptive behavioral intervention problem inspired by Fast Track, a real-life preventive intervention for improving parental function and reducing conduct disorder in at-risk children. Simulation results demonstrate that the proposed algorithm can be useful for adaptive intervention problems exhibiting both nonlinear and hybrid character. PMID:21874087

Controller Design of Complex System Based on Nonlinear Strength

Directory of Open Access Journals (Sweden)

Rongjun Mu

2015-01-01

Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

Reliability analysis of reinforced concrete grids with nonlinear material behavior

Energy Technology Data Exchange (ETDEWEB)

Neves, Rodrigo A [EESC-USP, Av. Trabalhador Sao Carlense, 400, 13566-590 Sao Carlos (Brazil); Chateauneuf, Alaa [LaMI-UBP and IFMA, Campus de Clermont-Fd, Les Cezeaux, BP 265, 63175 Aubiere cedex (France)]. E-mail: alaa.chateauneuf@ifma.fr; Venturini, Wilson S [EESC-USP, Av. Trabalhador Sao Carlense, 400, 13566-590 Sao Carlos (Brazil)]. E-mail: venturin@sc.usp.br; Lemaire, Maurice [LaMI-UBP and IFMA, Campus de Clermont-Fd, Les Cezeaux, BP 265, 63175 Aubiere cedex (France)

2006-06-15

Reinforced concrete grids are usually used to support large floor slabs. These grids are characterized by a great number of critical cross-sections, where the overall failure is usually sudden. However, nonlinear behavior of concrete leads to the redistribution of internal forces and accurate reliability assessment becomes mandatory. This paper presents a reliability study on reinforced concrete (RC) grids based on coupling Monte Carlo simulations with the response surface techniques. This approach allows us to analyze real RC grids with large number of failure components. The response surface is used to evaluate the structural safety by using first order reliability methods. The application to simple grids shows the interest of the proposed method and the role of moment redistribution in the reliability assessment.

Strong Tracking Filter for Nonlinear Systems with Randomly Delayed Measurements and Correlated Noises

Directory of Open Access Journals (Sweden)

Hongtao Yang

2018-01-01

Full Text Available This paper proposes a novel strong tracking filter (STF, which is suitable for dealing with the filtering problem of nonlinear systems when the following cases occur: that is, the constructed model does not match the actual system, the measurements have the one-step random delay, and the process and measurement noises are correlated at the same epoch. Firstly, a framework of decoupling filter (DF based on equivalent model transformation is derived. Further, according to the framework of DF, a new extended Kalman filtering (EKF algorithm via using first-order linearization approximation is developed. Secondly, the computational process of the suboptimal fading factor is derived on the basis of the extended orthogonality principle (EOP. Thirdly, the ultimate form of the proposed STF is obtained by introducing the suboptimal fading factor into the above EKF algorithm. The proposed STF can automatically tune the suboptimal fading factor on the basis of the residuals between available and predicted measurements and further the gain matrices of the proposed STF tune online to improve the filtering performance. Finally, the effectiveness of the proposed STF has been proved through numerical simulation experiments.

Unidirectional reflection and invisibility in nonlinear media with an incoherent nonlinearity

Science.gov (United States)

Mostafazadeh, Ali; Oflaz, Neslihan

2017-11-01

We give explicit criteria for the reflectionlessness, transparency, and invisibility of a finite-range potential in the presence of an incoherent (intensity-dependent) nonlinearity that is confined to the range of the potential. This allows us to conduct a systematic study of the effects of such a nonlinearity on a locally periodic class of finite-range potentials that display perturbative unidirectional invisibility. We use our general results to examine the effects of a weak Kerr nonlinearity on the behavior of these potentials and show that the presence of nonlinearity destroys the unidirectional invisibility of these potentials. If the strength of the Kerr nonlinearity is so weak that the first-order perturbation theory is reliable, the presence of nonlinearity does not affect the unidirectional reflectionlessness and transmission reciprocity of the potential. We show that the expected violation of the latter is a second order perturbative effect.

Spin quenching assisted by a strongly anisotropic compression behavior in MnP

Energy Technology Data Exchange (ETDEWEB)

Han, Fei; Wang, Di; Wang, Yonggang; Li, Nana; Bao, Jin-Ke; Li, Bing; Botana, Antia S.; Xiao, Yuming; Chow, Paul; Chung, Duck Young; Chen, Jiuhua; Wan, Xiangang; Kanatzidis, Mercouri G.; Yang, Wenge; Mao, Ho-Kwang

2018-02-01

We studied the crystal structure and spin state of MnP under high pressure with synchrotron X-ray diffraction and X-ray emission spectroscopy. MnP has an exceedingly strong anisotropy in compressibility, with the primary compressible direction along the b axis of the Pnma structure. X-ray emission spectroscopy reveals a pressure-driven quenching of the spin state in MnP. First-principles calculations suggest that the strongly anisotropic compression behavior significantly enhances the dispersion of the Mn d-orbitals and the splitting of the d-orbital levels compared to the hypothetical isotropic compression behavior. Thus, we propose spin quenching results mainly from the significant enhancement of the itinerancy of d electrons and partly from spin rearrangement occurring in the split d-orbital levels near the Fermi level. This explains the fast suppression of magnetic ordering in MnP under high pressure. The spin quenching lags behind the occurrence of superconductivity at ~8 GPa implying that spin fluctuations govern the electron pairing for superconductivity.

The nonlinear unloading behavior of a typical Ni-based superalloy during hot deformation. A unified elasto-viscoplastic constitutive model

International Nuclear Information System (INIS)

Chen, Ming-Song; Lin, Y.C.; Li, Kuo-Kuo; Chen, Jian

2016-01-01

In authors' previous work (Chen et al. in Appl Phys A. doi:10.1007/s00339-016-0371-6, 2016), the nonlinear unloading behavior of a typical Ni-based superalloy was investigated by hot compressive experiments with intermediate unloading-reloading cycles. The characters of unloading curves were discussed in detail, and a new elasto-viscoplastic constitutive model was proposed to describe the nonlinear unloading behavior of the studied Ni-based superalloy. Still, the functional relationships between the deformation temperature, strain rate, pre-strain and the parameters of the proposed constitutive model need to be established. In this study, the effects of deformation temperature, strain rate and pre-strain on the parameters of the new constitutive model proposed in authors' previous work (Chen et al. 2016) are analyzed, and a unified elasto-viscoplastic constitutive model is proposed to predict the unloading behavior at arbitrary deformation temperature, strain rate and pre-strain. (orig.)

Nonlinearity management in higher dimensions

International Nuclear Information System (INIS)

Kevrekidis, P G; Pelinovsky, D E; Stefanov, A

2006-01-01

In the present paper, we revisit nonlinearity management of the time-periodic nonlinear Schroedinger equation and the related averaging procedure. By means of rigorous estimates, we show that the averaged nonlinear Schroedinger equation does not blow up in the higher dimensional case so long as the corresponding solution remains smooth. In particular, we show that the H 1 norm remains bounded, in contrast with the usual blow-up mechanism for the focusing Schroedinger equation. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management

Collapse of nonlinear Langmuir waves

International Nuclear Information System (INIS)

Malkin, V.M.

1986-01-01

The dispersion of sufficiently intensive Langmuir waves is determined by intrinsic (electron) nonlinearity. During Langmuir collapse the wave energy density required for the appearance of electron nonlinearity is attained, generally speaking, prior to the development of dissipative processes. Up to now, the effect of electron nonlinearity on the collapse dynamics and spectrum of strong Langmuir turbulence ( which may be very appreciable ) has not been studied extensively because of the difficulty of describing nonlinear Langmuir waves. In the present paper the positive determinacy of the electron nonlinear hamiltonian is proven, the increment of modulation instability of a nonlinear Langmuir wave cluster localized in a cavity is calculated, and the universal law of their collapse is found

Wave propagation in a strongly nonlinear locally resonant granular crystal

Science.gov (United States)

Vorotnikov, K.; Starosvetsky, Y.; Theocharis, G.; Kevrekidis, P. G.

2018-02-01

In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.

Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion

Science.gov (United States)

Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin

2014-09-01

We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

Extreme nonlinear energy exchanges in a geometrically nonlinear lattice oscillating in the plane

Science.gov (United States)

Zhang, Zhen; Manevitch, Leonid I.; Smirnov, Valeri; Bergman, Lawrence A.; Vakakis, Alexander F.

2018-01-01

We study the in-plane damped oscillations of a finite lattice of particles coupled by linear springs under distributed harmonic excitation. Strong nonlinearity in this system is generated by geometric effects due to the in-plane stretching of the coupling spring elements. The lattice has a finite number of nonlinear transverse standing waves (termed nonlinear normal modes - NNMs), and an equal number of axial linear modes which are nonlinearly coupled to the transverse ones. Nonlinear interactions between the transverse and axial modes under harmonic excitation give rise to unexpected and extreme nonlinear energy exchanges in the lattice. In particular, we directly excite a transverse NNM by harmonic forcing (causing simulataneous indirect excitation of a corresponding axial linear mode due to nonlinear coupling), and identify three energy transfer mechanisms in the lattice. First, we detect the stable response of the directly excited transverse NNM (despite its instability in the absence of forcing), with simultaneous stability of the indirectly excited axial linear mode. Second, by changing the system and forcing parameters we report extreme nonlinear "energy explosions," whereby, after an initial regime of stability, the directly excited transverse NNM loses stability, leading to abrupt excitation of all transverse and axial modes of the lattice, at all possible wave numbers. This strong instability is triggered by the parametric instability of an indirectly excited axial mode which builds energy until the explosion. This is proved through theoretical analysis. Finally, in other parameter ranges we report intermittent, intense energy transfers from the directly excited transverse NNM to a small set of transverse NNMs with smaller wavelengths, and from the indirectly excited axial mode to a small set of axial modes, but with larger wavelengths. These intermittent energy transfers resemble energy cascades occurring in turbulent flows. Our results show that

The behavior of steady quasisolitons near the limit cases of third-order nonlinear Schrödinger equation

DEFF Research Database (Denmark)

Karpman, V.I.; Shagalov, A.G.; Juul Rasmussen, J.

2002-01-01

The behavior of steady quasisoliton solutions to the extended third-order nonlinear Schrodinger (NLS) equation is studied in two cases: (i) when the coefficients in the equation approach the Hirota conditions, and (ii) near the limit of the regular NLS equation. (C) 2002 Published by Elsevier...

Nonlinear silicon photonics

Science.gov (United States)

Borghi, M.; Castellan, C.; Signorini, S.; Trenti, A.; Pavesi, L.

2017-09-01

Silicon photonics is a technology based on fabricating integrated optical circuits by using the same paradigms as the dominant electronics industry. After twenty years of fervid development, silicon photonics is entering the market with low cost, high performance and mass-manufacturable optical devices. Until now, most silicon photonic devices have been based on linear optical effects, despite the many phenomenologies associated with nonlinear optics in both bulk materials and integrated waveguides. Silicon and silicon-based materials have strong optical nonlinearities which are enhanced in integrated devices by the small cross-section of the high-index contrast silicon waveguides or photonic crystals. Here the photons are made to strongly interact with the medium where they propagate. This is the central argument of nonlinear silicon photonics. It is the aim of this review to describe the state-of-the-art in the field. Starting from the basic nonlinearities in a silicon waveguide or in optical resonator geometries, many phenomena and applications are described—including frequency generation, frequency conversion, frequency-comb generation, supercontinuum generation, soliton formation, temporal imaging and time lensing, Raman lasing, and comb spectroscopy. Emerging quantum photonics applications, such as entangled photon sources, heralded single-photon sources and integrated quantum photonic circuits are also addressed at the end of this review.

Effects of nonlinearity in the materials used for the semi-rigid pedicle screw systems on biomechanical behaviors of the lumbar spine after surgery

International Nuclear Information System (INIS)

Kim, Hyun; Lee, Sung-Jae; Lim, Do-Hyung; Oh, Hyun-Ju; Lee, Kwon-Yong

2011-01-01

Recently, various types of semi-rigid pedicle screw fixation systems have been developed for the surgical treatment of the lumbar spine. They were introduced to address the adverse issues commonly found in traditional rigid spinal fusion--abnormally large motion at the adjacent level and subsequent degeneration. The semi-rigid system uses more compliant materials (nitinol or polymers) and/or changes in rod design (coiled or twisted rods) as compared to the conventional rigid straight rods made of Ti alloys (E = 114 GPa, υ = 0.32). However, biomechanical studies on the semi-rigid pedicle screw systems were usually limited to linear modeling of the implant and anatomic elements, which may not be capable of reflecting realistic post-operative motions of the spine. In this study, we evaluated the effects of nonlinearity in materials used for semi-rigid pedicle screw fixation systems to evaluate the changes in biomechanical behaviors using finite element analysis. Changes in range of motion (ROM) and center of rotation (COR) were assessed at the operated and adjacent levels. Actual load-displacement results of the semi-rigid rod from mechanical test were carried out to reflect the nonlinearity of the implant. In addition, nonlinear material properties of various spinal ligaments studies were used for the finite element modeling. The post-operative models were constructed by modifying the previously validated intact model of the L1-S1 spine. Eight different post-operative models were made to address the effects of nonlinearity-with a traditional stiffness modulus rod (with linear ligaments, case 1; with nonlinear ligaments, case 5), with a rigid rod (with linear ligaments, case 2; with nonlinear ligaments, case 6), with a soft rod (with linear ligaments, case 3; with nonlinear ligaments, case 7), and with a nonlinear rod (with linear ligaments, case 4; with nonlinear ligaments, case 8). To simulate the load on the lumbar spine in a neutral posture, follower load (400 N

Strong gravity and supersymmetry

International Nuclear Information System (INIS)

Chamseddine, Ali H.; Salam, A.; Strathdee, J.

1977-11-01

A supersymmetric theory is constructed for a strong f plus a weak g graviton, together with their accompanying massive gravitinos, by gaugin the gradel 0Sp(2,2,1)x 0Sp(2,2,1) structure. The mixing term between f and g fields, which makes the strong graviton massive, can be introduced through a spontaneous symmetry-breaking mechanism implemented in this note by constructing a non-linear realization of the symmetry group

Geometrically Nonlinear Transient Response of Laminated Plates with Nonlinear Elastic Restraints

Directory of Open Access Journals (Sweden)

Shaochong Yang

2017-01-01

Full Text Available To investigate the dynamic behavior of laminated plates with nonlinear elastic restraints, a varied constraint force model and a systematic numerical procedure are presented in this work. Several kinds of typical relationships of force-displacement for spring are established to simulate the nonlinear elastic restraints. In addition, considering the restraining moments of flexible pads, the pads are modeled by translational and rotational springs. The displacement- dependent constraint forces are added to the right-hand side of equations of motion and treated as additional applied loads. These loads can be explicitly defined, via an independent set of nonlinear load functions. The time histories of transverse displacements at typical points of the laminated plate are obtained through the transient analysis. Numerical examples show that the present method can effectively treat the geometrically nonlinear transient response of plates with nonlinear elastic restraints.

Analysis of nonlinear behavior of loudspeakers using the instantaneous frequency

DEFF Research Database (Denmark)

Huang, Hai; Jacobsen, Finn

2003-01-01

on the Fourier transform. In this work, a new method using the instantaneous frequency is introduced for describing and characterizing loudspeaker nonlinearities. First, numerical integration is applied to simulate the nonlinearities of loudspeakers caused by two nonlinear parameters, force factor and stiffness...

Octave-Spanning Mid-IR Supercontinuum Generation with Ultrafast Cascaded Nonlinearities

DEFF Research Database (Denmark)

Zhou, Binbin; Guo, Hairun; Liu, Xing

2014-01-01

An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation.......An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation....

Tokamak m = 1 magnetohydrodynamic calculations in toroidal geometry using a full set of nonlinear resistive magnetohydrodynamic equations

International Nuclear Information System (INIS)

Charlton, L.A.; Carreras, B.A.; Holmes, J.A.; Lynch, V.E.

1988-01-01

The linear stability and nonlinear evolution of the resistive m = 1 mode in tokamaks is studied using a full set of resistive magnetohydrodynamic (MHD) equations in toroidal geometry. The modification of the linear and nonlinear properties of the mode by a combination of strong toroidal effects and low resistivity is the focus of this work. Linearly there is a transition from resistive kink to resistive tearing behavior as the aspect ratio and resistivity are reduced, and there is a corresponding modification of the nonlinear behavior, including a slowing of the island growth and development of a Rutherford regime, as the tearing regime is approached. In order to study the sensitivity of the stability and evolution to assumptions concerning the equation of state, two sets of full nonlinear resistive MHD equations (a pressure convection set and an incompressible set) are used. Both sets give more stable nonlinear behavior as the aspect ratio is reduced. The pressure convection set shows a transition from a Kadomtsev reconnection at large aspect ratio to a saturation at small aspect ratio. The incompressible set yields Kadomtsev reconnection for all aspect ratios, but with a significant lengthening of the reconnection time and development of a Rutherford regime at an aspect ratio approaching the transition from a resistive kink mode to a tearing mode. The pressure convection set gives an incomplete reconnection similar to that sometimes seen experimentally. The pressure convection set is, however, strictly justified only at high beta

Dynamic behavior of a nonlinear rational difference equation and generalization

Directory of Open Access Journals (Sweden)

Shi Qihong

2011-01-01

Full Text Available Abstract This paper is concerned about the dynamic behavior for the following high order nonlinear difference equation x n = (x n-k + x n-m + x n-l /(x n-k x n-m + x n-m x n-l +1 with the initial data { x - l , x - l + 1 , … , x - 1 } ∈ ℝ + l and 1 ≤ k ≤ m ≤ l. The convergence of solution to this equation is investigated by introducing a new sequence, which extends and includes corresponding results obtained in the references (Li in J Math Anal Appl 312:103-111, 2005; Berenhaut et al. Appl. Math. Lett. 20:54-58, 2007; Papaschinopoulos and Schinas J Math Anal Appl 294:614-620, 2004 to a large extent. In addition, some propositions for generalized equations are reported.

Topology optimization of nonlinear optical devices

DEFF Research Database (Denmark)

Jensen, Jakob Søndergaard

2011-01-01

This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation and an incremen......This paper considers the design of nonlinear photonic devices. The nonlinearity stems from a nonlinear material model with a permittivity that depends on the local time-averaged intensity of the electric field. A finite element model is developed for time-harmonic wave propagation...... limiter. Here, air, a linear and a nonlinear material are distributed so that the wave transmission displays a strong sensitivity to the amplitude of the incoming wave....

Rogue waves generation in a left-handed nonlinear transmission line with series varactor diodes

Science.gov (United States)

Onana Essama, B. G.; Atangana, J.; Biya Motto, F.; Mokhtari, B.; Cherkaoui Eddeqaqi, N.; Kofane, Timoleon C.

2014-07-01

We investigate the electromagnetic wave behavior and its characterization using collective variables technique. Second-order dispersion, first- and second-order nonlinearities, which strongly act in a left-handed nonlinear transmission line with series varactor diodes, are taken into account. Four frequency ranges have been found. The first one gives the so-called energetic soliton due to a perfect combination of second-order dispersion and first-order nonlinearity. The second frequency range presents a dispersive soliton leading to the collapse of the electromagnetic wave at the third frequency range. But the fourth one shows physical conditions which are able to provoke the appearance of wave trains generation with some particular waves, the rogue waves. Moreover, we demonstrate that the number of rogue waves increases with frequency. The soliton, thereafter, gains a relative stability when second-order nonlinearity comes into play with some specific values in the fourth frequency range. Furthermore, the stability conditions of the electromagnetic wave at high frequencies have been also discussed.

An investigation of the static and dynamic behavior of electrically actuated rectangular microplates

KAUST Repository

Saghir, S.

2016-06-16

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the effect of different non-dimensional design parameters. The static results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased. Finally, near-square plates are studied to understand the effect of geometric imperfections of microplates.

An investigation of the static and dynamic behavior of electrically actuated rectangular microplates

KAUST Repository

Saghir, Shahid; Younis, Mohammad I.

2016-01-01

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the effect of different non-dimensional design parameters. The static results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased. Finally, near-square plates are studied to understand the effect of geometric imperfections of microplates.

NONLINEAR DYNAMICS OF ORGANIZATION DEVELOPMENT

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Денис Антонович БУШУЕВ

2016-02-01

Full Text Available The nonlinear behavior of organizations in development projects is considered. The nonlinear behavior is initiated in the growth of organizations and requires a restructuring of governance in identifying dysfunctions. Such a restructuring is needed in the area of soft components, determining the organizational levels of competence in the management of projects, programs, portfolios and heads of the Project Management Office. An important component of the strategic development of the organization is the proposed concept for formation and management of development programs in the context according to their life cycle. It should take into account the non-linear behavior of the soft components of the system and violation of functional processes of the organization. The specific management syndromes of projects and programs are considered. Such as syndromes time management project linked to the singular points of the project. These syndromes are "shift to the right", "point of no return", "braking at the end of the project" and others.

Variational principles for nonlinear piezoelectric materials

Energy Technology Data Exchange (ETDEWEB)

Rodriguez-Ramos, R.; Guinovart-Diaz, R. [Universidad de la Habana, Facultad de Matematica y Computacion, Vedado, Habana (Cuba); Pobedria, B.E. [Moscow State University M. V. Lomonosov, Composites Department, Moscow (Russian Federation); Padilla, P. [Universidad Nacional Autonoma de Mexico, Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas (IIMAS), Cd. Universitaria, Mexico D.F. (Mexico); Bravo-Castillero, J. [Universidad de la Habana, Facultad de Matematica y Computacion, Vedado, Habana (Cuba); Campus Estado de Mexico. Division de Arquitectura e Ingenieria, Instituto Tecnologico de Estudios Superiores de Monterrey, Atizapan de Zaragoza, Estado de Mexico (Mexico); Maugin, G.A. [Universite Pierre et Marie Curie. Case 162, UMR 7607 CNRS, Laboratoire de Modelisation en Mecanique, Paris Cedex 05 (France)

2004-12-01

In the present paper, we consider the behavior of nonlinear piezoelectric materials by generalization for this case of the Hashin-Shtrikman variational principles. The new general formulation used here differs from others, because, it gives the possibility to evaluate the upper and lower Hashin-Shtrikman bounds for specific physical nonlinearities of piezoelectric materials. Geometrical nonlinearities are not considered. (orig.)

NONLINEAR DYNAMICS OF CARBON NANOTUBES UNDER LARGE ELECTROSTATIC FORCE

KAUST Repository

Xu, Tiantian

2015-06-01

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

KAUST Repository

Xu, Tiantian

2015-06-01

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems undergoing large motion, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler-Bernoulli beam model to study for the first time the dynamic behavior of CNTs when excited by large electrostatic force. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effects of the DC and AC voltage loads on the behavior have been studied. The impacts of the initial slack level and CNT diameter are also demonstrated.

Nonlinear temporal modulation of pulsar radioemission

International Nuclear Information System (INIS)

Chian, A.C.-L.

1984-01-01

A nonlinear theory is discussed for self-modulation of pulsar radio pulses. A nonlinear Schroedinger equation is derived for strong electromagnetic waves propagating in an electron-positron plasma. The nonlinearities arising from wave intensity induced relativistic particle mass variation may excite the modulational instability of circularly and linearly polarized pulsar radiation. The resulting wave envelopes can take the form of periodic wave trains or solitons. These nonlinear stationary wave forms may account for the formation of pulsar microstructures. (Author) [pt

On the dynamics of Airy beams in nonlinear media with nonlinear losses.

Science.gov (United States)

Ruiz-Jiménez, Carlos; Nóbrega, K Z; Porras, Miguel A

2015-04-06

We investigate on the nonlinear dynamics of Airy beams in a regime where nonlinear losses due to multi-photon absorption are significant. We identify the nonlinear Airy beam (NAB) that preserves the amplitude of the inward Hänkel component as an attractor of the dynamics. This attractor governs also the dynamics of finite-power (apodized) Airy beams, irrespective of the location of the entrance plane in the medium with respect to the Airy waist plane. A soft (linear) input long before the waist, however, strongly speeds up NAB formation and its persistence as a quasi-stationary beam in comparison to an abrupt input at the Airy waist plane, and promotes the formation of a new type of highly dissipative, fully nonlinear Airy beam not described so far.

Experimental and Model Studies on Loading Path-Dependent and Nonlinear Gas Flow Behavior in Shale Fractures

Science.gov (United States)

Li, Honglian; Lu, Yiyu; Zhou, Lei; Tang, Jiren; Han, Shuaibin; Ao, Xiang

2018-01-01

Interest in shale gas as an energy source is growing worldwide. Because the rock's natural fracture system can contribute to gas production, it is important to understand the flow behavior of natural fractures in shale. Previous studies on the flow characteristics in shale fractures were limited and did not consider the effect of nonlinearity. To understand the basic mechanics of the gas flow behavior in shale fractures, laboratory investigations with consideration of the fluid pressure gradient, the confining stress, the loading history and the fracture geometry were conducted in this paper. Izbash's equation was used to analyze the nonlinearity of the flow. The results show that the behavior of the friction factors is similar to that shown in flow tests in smooth and rough pipes. The increase of the confining stress and the irreversible damage to the shale decreased the hydraulic aperture and increased the relative roughness. Thus, turbulent flow could appear at a low Reynolds number, resulting in a significant pressure loss. The limits of the cubic law and the existing correction factor for transmissivity are discussed. It is found that the previous friction models overestimate the friction factor in the laminar regime and underestimate the friction factor in the turbulent regime. For this reason, a new friction model based on a linear combination of the Reynolds number and the relative roughness was developed.

Analytical evaluation of nonlinear distortion effects on multicarrier signals

CERN Document Server

Araújo, Theresa

2015-01-01

Due to their ability to support reliable high quality of service as well as spectral and power efficiency, multicarrier modulation systems have found increasing use in modern communications services. However, one of the main drawbacks of these systems is their vulnerability to nonlinear distortion effects. Analytical Evaluation of Nonlinear Distortion Effects on Multicarrier Signals details a unified approach to well-known analytical results on memoryless nonlinearities that takes advantage of the Gaussian behavior of multicarrier signals.Sharing new insights into the behavior of nonlinearly d

Nonlinear Seismic Behavior of Different Boundary Conditions of Transmission Line Systems under Earthquake Loading

Directory of Open Access Journals (Sweden)

Li Tian

2016-01-01

Full Text Available Nonlinear seismic behaviors of different boundary conditions of transmission line system under earthquake loading are investigated in this paper. The transmission lines are modeled by cable element accounting for the nonlinearity of the cable. For the suspension type, three towers and two span lines with spring model (Model 1 and three towers and four span lines’ model (Model 2 are established, respectively. For the tension type, three towers and two span lines’ model (Model 3 and three towers and four span lines’ model (Model 4 are created, respectively. The frequencies of the transmission towers and transmission lines of the suspension type and tension type are calculated, respectively. The responses of the suspension type and tension type are investigated using nonlinear time history analysis method, respectively. The results show that the responses of the transmission tower and transmission line of the two models of the suspension type are slightly different. However, the responses of transmission tower and transmission line of the two models of the tension type are significantly different. Therefore, in order to obtain accurate results, a reasonable model should be considered. The results could provide a reference for the seismic analysis of the transmission tower-line system.

Strong nonlinearity-induced correlations for counterpropagating photons scattering on a two-level emitter

DEFF Research Database (Denmark)

Nysteen, Anders; McCutcheon, Dara; Mørk, Jesper

2015-01-01

We analytically treat the scattering of two counterpropagating photons on a two-level emitter embedded in an optical waveguide. We find that the nonlinearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could be quanti......We analytically treat the scattering of two counterpropagating photons on a two-level emitter embedded in an optical waveguide. We find that the nonlinearity of the emitter can give rise to significant pulse-dependent directional correlations in the scattered photonic state, which could...

Linear and non-linear simulation of joints contact surface using ...

African Journals Online (AJOL)

The joint modelling including non-linear effects needs accurate and precise study of their behaviors. When joints are under the dynamic loading, micro, macro- slip happens in contact surface which is non-linear reason of the joint contact surface. The non-linear effects of joint contact surface on total behavior of structure are ...

Nonlinear evolution of MHD instabilities

International Nuclear Information System (INIS)

Bateman, G.; Hicks, H.R.; Wooten, J.W.; Dory, R.A.

1975-01-01

A 3-D nonlinear MHD computer code was used to study the time evolution of internal instabilities. Velocity vortex cells are observed to persist into the nonlinear evolution. Pressure and density profiles convect around these cells for a weak localized instability, or convect into the wall for a strong instability. (U.S.)

Non-linear behavior of public opinion on the issues regarding inhabitants' polls

International Nuclear Information System (INIS)

Ohnishi, Teruaki; Suganuma, Jyun-ichi

2003-01-01

The observed change of public attitude around the time of inhabitants' poll in Japan was compared with model calculation to investigate its non-linear behavior. Two inhabitants' polls regarding nuclear issues, the approval and disapproval of the construction of Maki nuclear station, and of the MOX fuel use at Kashiwazaki-Kariwa nuclear station, were considered together with the poll on the reconstruction of the tenth weir in Yoshino river carried out in Tokushima. By using a mathematical model such that the individual attitude is mainly subject to two factors of the information environment and the mutual communication between the public, it was found that the change and the unification of public attitude around the time of inhabitants' poll can be interpreted as a manifestation of self-organization resulted from the cooperative phenomenon of those two factors. Moreover, it was also found that the abrupt change of public attitude just before the poll can be interpreted as a result of positive feedback of the information environment formed by the various types of propaganda activities to the attitude change, though the extent of such non-linear effects differs from case to case. (author)

Nonlinear Single Spin Spectrum Analayzer

Science.gov (United States)

Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

2014-05-01

Qubits are excellent probes of their environment. When operating in the linear regime, they can be used as linear spectrum analyzers of the noise processes surrounding them. These methods fail for strong non-Gaussian noise where the qubit response is no longer linear. Here we solve the problem of nonlinear spectral analysis, required for strongly coupled environments. Our non-perturbative analytic model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We developed a noise characterization scheme adapted to this non-linearity. We then applied it using a single trapped 88Sr+ ion as the a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. With this method, we attained a ten fold improvement over the standard Fourier limit. Finally, we experimentally compared the performance of equidistant vs. Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013), Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: National Institute of Standards and Tehcnology, Boulder, CO.

A nonlinear dynamics approach for incorporating wind-speed patterns into wind-power project evaluation.

Science.gov (United States)

Huffaker, Ray; Bittelli, Marco

2015-01-01

Wind-energy production may be expanded beyond regions with high-average wind speeds (such as the Midwest U.S.A.) to sites with lower-average speeds (such as the Southeast U.S.A.) by locating favorable regional matches between natural wind-speed and energy-demand patterns. A critical component of wind-power evaluation is to incorporate wind-speed dynamics reflecting documented diurnal and seasonal behavioral patterns. Conventional probabilistic approaches remove patterns from wind-speed data. These patterns must be restored synthetically before they can be matched with energy-demand patterns. How to accurately restore wind-speed patterns is a vexing problem spurring an expanding line of papers. We propose a paradigm shift in wind power evaluation that employs signal-detection and nonlinear-dynamics techniques to empirically diagnose whether synthetic pattern restoration can be avoided altogether. If the complex behavior of observed wind-speed records is due to nonlinear, low-dimensional, and deterministic system dynamics, then nonlinear dynamics techniques can reconstruct wind-speed dynamics from observed wind-speed data without recourse to conventional probabilistic approaches. In the first study of its kind, we test a nonlinear dynamics approach in an application to Sugarland Wind-the first utility-scale wind project proposed in Florida, USA. We find empirical evidence of a low-dimensional and nonlinear wind-speed attractor characterized by strong temporal patterns that match up well with regular daily and seasonal electricity demand patterns.

Nonlinear Weibel Instability and Turbulence in Strong Collisionless Shocks

International Nuclear Information System (INIS)

Medvedev, Mikhail M.

2008-01-01

This research project was devoted to studies of collisionless shocks, their properties, microphysics and plasma physics of underlying phenomena, such as Weibel instability and generation of small-scale fields at shocks, particle acceleration and transport in the generated random fields, radiation mechanisms from these fields in application to astrophysical phenomena and laboratory experiments (e.g., laser-plasma and beam-plasma interactions, the fast ignition and inertial confinement, etc.). Thus, this study is highly relevant to astrophysical sciences, the inertial confinement program and, in particular, the Fast Ignition concept, etc. It makes valuable contributions to the shock physics, nonlinear plasma theory, as well as to the basic plasma science, in general

Nonlinear dynamics between linear and impact limits

CERN Document Server

Pilipchuk, Valery N; Wriggers, Peter

2010-01-01

This book examines nonlinear dynamic analyses based on the existence of strongly nonlinear but simple counterparts to the linear models and tools. Discusses possible application to periodic elastic structures with non-smooth or discontinuous characteristics.

Numerical simulation of the nonlinear dynamics of packets of spiral density waves

International Nuclear Information System (INIS)

Korchagin, V.I.

1987-01-01

In a numerical experiment, the behavior of nonlinear packets of spiral density waves in a gas disk has been investigated for different initial wave amplitudes. If the amplitude of the density perturbations is small (<5%), the wave packet is drawn toward the center or toward the periphery of the disk in accordance with the linear theory. The behavior of linear packets of waves with wavelength comparable to the disk radius (R/sub d//lambda = 4) exhibits good agreement with the conclusions of the linear theory of tightly wound spiral waves. The dynamics of wave packets with initial density amplitudes 16, 30, 50% demonstrates the nonlinear nature of the behavior. THe behavior is governed by whether or not the nonlinear effects of higher than third order in the wave amplitude play a part. If the wave packet dynamics is determined by the cubic nonlinearity, the results of the numerical experiment are in qualitative and quantitative agreement with the nonlinear theory of short waves, although the characteristic scale of the packet and the wavelength are of the order of the disk radius. In the cases when the nonlinear effects of higher orders in the amplitude play an important part, the behavior of a packet does not differ qualitatively from the behavior predicted by the theory of cubic nonlinearity, but the nonlinear spreading of the packet takes place more rapidly

Generic strong coupling behavior of Cooper pairs in the surface of superfluid nuclei

International Nuclear Information System (INIS)

Pillet, N.; Sandulescu, N.; Schuck, P.

2007-01-01

With realistic HFB calculations, using the D1S Gogny force, we reveal a generic behavior of concentration of small sized Cooper pairs (2-3 fm) in the surface of superfluid nuclei. This study confirms and extends previous results given in the literature that use more schematic approaches. It is shown that the strong concentration of pair probability of small Cooper pairs in the nuclear surface is a quite general and generic feature and that nuclear pairing is much closer to the strong coupling regime than previously assumed

Generic strong coupling behavior of Cooper pairs in the surface of superfluid nuclei

Energy Technology Data Exchange (ETDEWEB)

Pillet, N. [DPTA/Service de Physique nucleaire, CEA/DAM Ile de France, BP12, F-91680 Bruyeres-le-Chatel (France); Sandulescu, N. [DPTA/Service de Physique nucleaire, CEA/DAM Ile de France, BP12, F-91680 Bruyeres-le-Chatel (France)]|[Institute of Physics and Nuclear Engineering, 76900 Bucharest (Romania)]|[Institut de Physique Nucleaire, CNRS, UMR 8608, Orsay, F-91406 (France); Schuck, P. [Institut de Physique Nucleaire, CNRS, UMR 8608, Orsay, F-91406 (France)]|[Universite Paris-Sud, Orsay, F-91505 (France)

2007-01-15

With realistic HFB calculations, using the D1S Gogny force, we reveal a generic behavior of concentration of small sized Cooper pairs (2-3 fm) in the surface of superfluid nuclei. This study confirms and extends previous results given in the literature that use more schematic approaches. It is shown that the strong concentration of pair probability of small Cooper pairs in the nuclear surface is a quite general and generic feature and that nuclear pairing is much closer to the strong coupling regime than previously assumed.

Numerical analysis of the asymptotic behavior of solutions of a boundary problem for a nonlinear parabolic equation

International Nuclear Information System (INIS)

Vasileva, D.P.

1993-01-01

Blow-up and global time self-similar solutions of a boundary problem for a nonlinear equation u t = Δ u σ+1 + u β are found in the case β = σ + 1. It is shown that they describe the asymptotic behavior of a wide class of initial perturbations. A numerical investigation of the solutions in the case β>σ + 1 is also made. A hypothesis is done that the behavior for large times of global time solutions is described by the self-similar solutions of the equation without source.(author). 20 refs.; 9 figs

Photoconductivity, photoluminescence and optical Kerr nonlinear effects in zinc oxide films containing chromium nanoclusters

International Nuclear Information System (INIS)

Torres-Torres, C.; García-Cruz, M.L.; Castañeda, L.; Rangel Rojo, R.; Tamayo-Rivera, L.; Maldonado, A.; Avendaño-Alejo, M.

2012-01-01

Chromium doped zinc oxide thin solid films were deposited on soda–lime glass substrates. The photoconductivity of the material and its influence on the optical behavior was evaluated. A non-alkoxide sol–gel synthesis approach was used for the preparation of the samples. An enhancement of the photoluminescence response exhibited by the resulting photoconductive films with embedded chromium nanoclusters is presented. The modification in the photoconduction induced by a 445 nm wavelength was measured and then associated with the participation of the optical absorptive response. In order to investigate the third order optical nonlinearities of the samples, a standard time-resolved Optical Kerr Gate configuration with 80 fs pulses at 830 nm was used and a quasi-instantaneous pure electronic nonlinearity without the contribution of nonlinear optical absorption was observed. We estimate that from the inclusion of Cr nanoclusters into the sample results a strong optical Kerr effect originated by quantum confinement. The large photoluminescence response and the important refractive nonlinearity of the photoconductive samples seem to promise potential applications for the development of multifunctional all-optical nanodevices. - Highlights: ► Enhancement in photoluminescence for chromium doped zinc oxide films is presented. ► A strong and ultrafast optical Kerr effect seems to result from quantum confinement. ► Photoconductive properties for optical and optoelectronic functions were observed.

Photoconductivity, photoluminescence and optical Kerr nonlinear effects in zinc oxide films containing chromium nanoclusters

Energy Technology Data Exchange (ETDEWEB)

Torres-Torres, C., E-mail: crstorres@yahoo.com.mx [Seccion de Estudios de Posgrado e Investigacion, ESIME-Z, Instituto Politecnico Nacional, Mexico, DF 07738 (Mexico); Garcia-Cruz, M.L. [Centro de Investigacion en Dispositivos Semiconductores, Benemerita Universidad Autonoma de Puebla, A. P. J-48, Puebla 72570, Mexico (Mexico); Castaneda, L., E-mail: luisca@sirio.ifuap.buap.mx [Instituto de Fisica, Benemerita Universidad Autonoma de Puebla, A. P. J-48, Puebla 72570, Mexico (Mexico); Rangel Rojo, R. [CICESE/Depto. de Optica, A. P. 360, Ensenada, BC 22860 (Mexico); Tamayo-Rivera, L. [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico, DF 01000 (Mexico); Maldonado, A. [Depto. de Ing. Electrica, CINVESTAV IPN-SEES, A. P. 14740, Mexico DF 07000 (Mexico); Avendano-Alejo, M., E-mail: imax_aa@yahoo.com.mx [Centro de Ciencias Aplicadas y Desarrollo Tecnologico, Universidad Nacional Autonoma de Mexico, A. P. 70-186, 04510, DF (Mexico); and others

2012-04-15

Chromium doped zinc oxide thin solid films were deposited on soda-lime glass substrates. The photoconductivity of the material and its influence on the optical behavior was evaluated. A non-alkoxide sol-gel synthesis approach was used for the preparation of the samples. An enhancement of the photoluminescence response exhibited by the resulting photoconductive films with embedded chromium nanoclusters is presented. The modification in the photoconduction induced by a 445 nm wavelength was measured and then associated with the participation of the optical absorptive response. In order to investigate the third order optical nonlinearities of the samples, a standard time-resolved Optical Kerr Gate configuration with 80 fs pulses at 830 nm was used and a quasi-instantaneous pure electronic nonlinearity without the contribution of nonlinear optical absorption was observed. We estimate that from the inclusion of Cr nanoclusters into the sample results a strong optical Kerr effect originated by quantum confinement. The large photoluminescence response and the important refractive nonlinearity of the photoconductive samples seem to promise potential applications for the development of multifunctional all-optical nanodevices. - Highlights: Black-Right-Pointing-Pointer Enhancement in photoluminescence for chromium doped zinc oxide films is presented. Black-Right-Pointing-Pointer A strong and ultrafast optical Kerr effect seems to result from quantum confinement. Black-Right-Pointing-Pointer Photoconductive properties for optical and optoelectronic functions were observed.

The Effect of Foreign Direct Investment in Economic Growth from the Perspective of Nonlinear Dynamics

Directory of Open Access Journals (Sweden)

Ch. K. Volos

2015-09-01

Full Text Available In today’s globalized economy one of the most crucial factors for the economic growth of a country, especially of a developing country, is the foreign direct investment, not only because of the transfer of capital but also of technology. In this work, the effect of foreign direct investments in a county’s economic growth by using tools of nonlinear dynamics is studied. As a model of the economic growth of a country, a well-known nonlinear discrete-time dynamical system, the Logistic map, is used. The system under study consists of two countries with a strong economic relationship. The source country of foreign direct investments is an industrialized, economically powerful and technologically advanced country that makes significant investments in the host country, which is a developing country and strong dependent from the source country. Simulation results of system’s behavior and especially the bifurcation diagrams reveal the strong connection between the countries of the proposed system and the effect of foreign direct investments in the economic growth of the host country.

Non-linear radial spinwave modes in thin magnetic disks

International Nuclear Information System (INIS)

Helsen, M.; De Clercq, J.; Vansteenkiste, A.; Van Waeyenberge, B.; Gangwar, A.; Back, C. H.; Weigand, M.

2015-01-01

We present an experimental investigation of radial spin-wave modes in magnetic nano-disks with a vortex ground state. The spin-wave amplitude was measured using a frequency-resolved magneto-optical spectrum analyzer, allowing for high-resolution resonance curves to be recorded. It was found that with increasing excitation amplitude up to about 10 mT, the lowest-order mode behaves strongly non-linearly as the mode frequency redshifts and the resonance peak strongly deforms. This behavior was quantitatively reproduced by micromagnetic simulations. Micromagnetic simulations showed that at higher excitation amplitudes, the spinwaves are transformed into a soliton by self-focusing, and collapse onto the vortex core, dispersing the energy in short-wavelength spinwaves. Additionally, this process can lead to switching of the vortex polarization through the injection of a Bloch point

Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

Energy Technology Data Exchange (ETDEWEB)

Tahara, Masaki [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Kim, Hee Young, E-mail: heeykim@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Inamura, Tomonari; Hosoda, Hideki [Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503 (Japan); Miyazaki, Shuichi, E-mail: miyazaki@ims.tsukuba.ac.jp [Division of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573 (Japan); Center of Excellence for Advanced Materials Research, King Abdulaziz University, P.O. Box 80203, Jeddah 21589 (Saudi Arabia); School of Materials Science and Engineering and ERI, Gyeongsang National University, 900 Gazwadong, Jinju, Gyeongnam 660-701 (Korea, Republic of)

2013-11-15

Highlights: ► {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉{sub β}* rel rods and {1 1 1}{sub β}* rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110}{sub β}〈11{sup ¯}0〉{sub β} transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation.

Role of interstitial atoms in the microstructure and non-linear elastic deformation behavior of Ti–Nb alloy

International Nuclear Information System (INIS)

Tahara, Masaki; Kim, Hee Young; Inamura, Tomonari; Hosoda, Hideki; Miyazaki, Shuichi

2013-01-01

Highlights: ► {110} β 〈11 ¯ 0〉 β transverse type lattice modulation is confirmed in β phase. ► Nanosized modulated region (nanodomain) distributes homogeneously and randomly. ► Nanodomains act as obstacles against the long-ranged martensitic transformation. ► The origin of non-linear elastic deformation behavior is the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation. -- Abstract: In order to clarify the effect of interstitial atoms on the non-linear elastic deformation behavior of the Ti–Nb alloy, the microstructure of (Ti–26Nb)–1.0O alloy was closely investigated by transmission electron microscope (TEM) and in situ X-ray diffraction (XRD) measurements. The 〈1 1 0〉 β * rel rods and {1 1 1} β * rel planes were observed in a reciprocal space for the (Ti–26Nb)–1.0O alloy. Their origin was {110} β 〈11 ¯ 0〉 β transverse type lattice modulation generated by oxygen atoms. Nanosized modulated domain structure (nanodomain) distributed homogeneously and randomly in the β phase and acted as obstacles for the long-ranged martensitic transformation in the (Ti–26Nb)–1.0O alloy. The non-linear elastic strain of the (Ti–26Nb)–1.0O alloy was generated by the continuous increase in lattice distortion strain of the favorable nanodomain variant during tensile deformation

Nonlinear viscoelastic behavior of shells of revolution under arbitrary loading

International Nuclear Information System (INIS)

Leonard, J.W.; Arbaki-Kanjoori, F.

1975-01-01

The requirement of some structural components such as propulsion systems and gas turbines to operate at high temperatures and pressures make the accurate evaluation of the creep phenomenon exigent (in fast breeder reactor for example). For the expected increases in operating temperatures and pressures, it becomes necessary to perform a thorough analysis of integral structural components of nuclear power plants throughout their life span. Since a large class of structures operating at elevated temperatures are composed of rotationally symmetric shells, a solution technique can be developed which involves the numerical integration of the governing shell equations. This method has been successfully applied to the static and dynamic analysis of thin elastic shells of revolution and for some cases of inelastic material behavior. It has been shown to render solutions efficiently and accurately, usually with only a fraction of computer time and storage requirements and data manipulation that is required for other numerical schemes such as the finite element method. Furthermore, the numerical integration method allows more flexibility for varying the integration step lengths than does the finite difference method and can provide uniform accuracy throughout the analysis. For nonlinear viscoelastic behavior the numerical integration technique is expected to provide similar efficiency to that obtained for the elastic problems. The computer program developed can accept time variation of material properties. Since a single form for the material constitutive law cannot encompass all materials, provisions are made so that the analysis of a very large class of material behavior can be accomplished

A nonlinear dynamics of trunk kinematics during manual lifting tasks.

Science.gov (United States)

Khalaf, Tamer; Karwowski, Waldemar; Sapkota, Nabin

2015-01-01

Human responses at work may exhibit nonlinear properties where small changes in the initial task conditions can lead to large changes in system behavior. Therefore, it is important to study such nonlinearity to gain a better understanding of human performance under a variety of physical, perceptual, and cognitive tasks conditions. The main objective of this study was to investigate whether the human trunk kinematics data during a manual lifting task exhibits nonlinear behavior in terms of determinist chaos. Data related to kinematics of the trunk with respect to the pelvis were collected using Industrial Lumbar Motion Monitor (ILMM), and analyzed applying the nonlinear dynamical systems methodology. Nonlinear dynamics quantifiers of Lyapunov exponents and Kaplan-Yorke dimensions were calculated and analyzed under different task conditions. The study showed that human trunk kinematics during manual lifting exhibits chaotic behavior in terms of trunk sagittal angular displacement, velocity and acceleration. The findings support the importance of accounting for nonlinear dynamical properties of biomechanical responses to lifting tasks.

Topological approximation of the nonlinear Anderson model

Science.gov (United States)

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t →+∞. The second moment of the associated probability distribution grows with time as a power law ∝ tα, with the exponent α =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the

Strongly nonlinear nonhomogeneous elliptic unilateral problems with L^1 data and no sign conditions

Directory of Open Access Journals (Sweden)

Elhoussine Azroul

2012-05-01

Full Text Available In this article, we prove the existence of solutions to unilateral problems involving nonlinear operators of the form: $$ Au+H(x,u,abla u=f $$ where $A$ is a Leray Lions operator from $W_0^{1,p(x}(Omega$ into its dual $W^{-1,p'(x}(Omega$ and $H(x,s,xi$ is the nonlinear term satisfying some growth condition but no sign condition. The right hand side $f$ belong to $L^1(Omega$.

Effect of spatial variability of ground motion on non-linear dynamic behavior of cable stayed bridges

Directory of Open Access Journals (Sweden)

Ouanani Mouloud

2018-01-01

Full Text Available This present paper summarizes the main results of incoherence of Spatial Variability of Ground Motion (SVGM component on the non-linear dynamic behavior of a Mila cable stayed bridge. The Hindy and Novack coherence model is developed for the present study in order to examine the SVGM on bridge responses, Nonlinear bridge responses are investigated in terms of transverse displacements and bending moments along the superstructure and substructure of the study bridge, as well as temporal variations of rotational ductility demands at the bridge piers ends under the incoherence SVGM component. The results are systematically compared with those obtained assuming uniform ground motion. As a general trend, it may be concluded that incoherence component of SVGM should be considered for the earthquake response assessments of cable-stayed bridges.

Nanoscale nonlinear effects in Erbium-implanted Yttrium Orthosilicate

Energy Technology Data Exchange (ETDEWEB)

Kukharchyk, Nadezhda, E-mail: nadezhda.kukharchyk@physik.uni-saarland.de [Experimentalphysik, Universität des Saarlandes, D-66123 Saarbrücken (Germany); Angewandte Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Shvarkov, Stepan [Optoelektronische Materialien und Bauelemente, Universität Paderborn, D-33098 Padeborn (Germany); Probst, Sebastian [Quantronics group, Service de Physique de l' Etat Condense, DSM/IRAMIS/SPEC, CNRS UMR 3680, CEA-Saclay, 91191 Gif-sur-Yvette cedex (France); Xia, Kangwei [3. Physikalisches Institut, Universität Stuttgart, D-70569 Stuttgart (Germany); Becker, Hans-Werner [RUBION, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Pal, Shovon [Angewandte Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany); AG THz Spectroscopie und Technologie, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Markmann, Sergej [AG THz Spectroscopie und Technologie, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Kolesov, Roman; Siyushev, Petr; Wrachtrup, Jörg [3. Physikalisches Institut, Universität Stuttgart, D-70569 Stuttgart (Germany); Ludwig, Arne [Angewandte Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany); Ustinov, Alexey V. [Physikalisches Institut, Karlsruhe Institute of Technology, D-76128 Karlsruhe (Germany); Wieck, Andreas D. [Angewandte Festkörperphysik, Ruhr-Universität Bochum, D-44780 Bochum (Germany); and others

2016-09-15

Doping of substrates at desired locations is a key technology for spin-based quantum memory devices. Focused ion beam implantation is well-suited for this task due to its high spacial resolution. In this work, we investigate ion-beam implanted Erbium ensembles in Yttrium Orthosilicate crystals by means of confocal photoluminescence spectroscopy. The sample temperature and the post-implantation annealing step strongly reverberate in the properties of the implanted ions. We find that hot implantation leads to a higher activation rate of the ions. At high enough fluences, the relation between the fluence and final concentration of ions becomes non-linear. Two models are developed explaining the observed behavior.

Structure dynamics with regard to non-linear support behavior; Dynamische Strukturberechnung unter Beruecksichtigung nichtlinearen Lagerverhaltens

Energy Technology Data Exchange (ETDEWEB)

Driessen, W. [Technischer Ueberwachungs-Verein Nord e.V., Hamburg (Germany)

2000-07-01

Because of modifications to a feed-water line of a power plant structural calculations of the pipework were performed. As a result of a linear (modal) analysis very high restraint forces on the supports were calculated. In order to reduce conservatisms in the calculation the model was optimized with regard to the support stiffnesses and nonlinear behavior of slide bearings, guides and shock absorbers were taken into account. The main result of the non-linear analysis, which was performed by methods of direct-integration, was that nonlinearity yields evident differences in structural frequencies and in energy dissipation (damping) in comparison to the linear analysis. The high restraint forces on the supports became smaller for most of the supports but at some points the forces of the non-linear analysis were even higher. So the conservatism of the linear analysis is not fully valid for the whole structure. The relevance of the non-linear effects in dynamic piping calculations is shown by comparing the calculation result with measurements which were performed on structures in the plant. (orig.) [German] Im Rahmen der Aenderung der Speisewasserleitung einer Kraftwerksanlage wurde die Struktur neu berechnet. Die Analysen mit einem linearen Modell (modal), das ueblicherweise verwendet wird, ergaben hohe Lasten an Halterungen. Zum Abbau von Konservativitaeten wurde eine realistischere Modellierung durch die Beruecksichtigung des nichtlinearen Verhaltens der in der Anlage befindlichen Gleitlager, Fuehrungen und Stossbremsen in der Berechnung vorgenommen. Die Untersuchungen haben ergeben, dass durch die Nichtlinearitaet das Frequenzverhalten der Struktur und die Dissipation von Energie durch Reibvorgaenge wesentlich beeinflusst werden. Des Weiteren ist festzustellen, dass aus linearen Analysen nicht uneingeschraenkt konservative Ergebnisse gewonnen werden. Die Relevanz der Beruecksichtigung des nichtlinearen Lagerverhaltens bei einer dynamischen Strukturberechnung wird

Journal Afrika Statistika ISSN 0852-0305 Nonlinear wavelet ...

African Journals Online (AJOL)

mator; Nonparametric regression; Strong mixing condition. ... In this paper we consider the right censorship model and we introduce a new nonlinear ... provide excellent selective review article on nonlinear wavelet methods in nonparametric.

Shaking table testing of a HTGR reactor core, comparison with the results obtained using a nonlinear mathematical model

International Nuclear Information System (INIS)

Berriaud, C.; Cebe, E.; Livolant, M.; Buland, P.

1975-01-01

Two series of horizontal tests have been performed at Saclay on the shaking table VESUVE: sinusoidal test and time history response. Sinusoidal tests have shown the strongly nonlinear dynamic behavior of the core. The resonant frequency of the core is dependent on the level of the excitation. These phenomena have been explained by a computer code, which is a lumped mass nonlinear model. El Centro time history displacement at the level of PCRV was reproduced on the shaking table. The analytical model was applied to this excitation and good comparison was obtained for forces and velocities [fr

Supercritical Nonlinear Vibration of a Fluid-Conveying Pipe Subjected to a Strong External Excitation

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Yan-Lei Zhang

2016-01-01

Full Text Available Nonlinear vibration of a fluid-conveying pipe subjected to a transverse external harmonic excitation is investigated in the case with two-to-one internal resonance. The excitation amplitude is in the same magnitude of the transverse displacement. The fluid in the pipes flows in the speed larger than the critical speed so that the straight configuration becomes an unstable equilibrium and two curved configurations bifurcate as stable equilibriums. The motion measured from each of curved equilibrium configurations is governed by a nonlinear integro-partial-differential equation with variable coefficients. The Galerkin method is employed to discretize the governing equation into a gyroscopic system consisting of a set of coupled nonlinear ordinary differential equations. The method of multiple scales is applied to analyze approximately the gyroscopic system. A set of first-order ordinary differential equations governing the modulations of the amplitude and the phase are derived via the method. In the supercritical regime, the subharmonic, superharmonic, and combination resonances are examined in the presence of the 2 : 1 internal resonance. The steady-state responses and their stabilities are determined. The various jump phenomena in the amplitude-frequency response curves are demonstrated. The effects of the viscosity, the excitation amplitude, the nonlinearity, and the flow speed are observed. The analytical results are supported by the numerical integration.

Nonlinear Ballistic Transport in an Atomically Thin Material.

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

2016-01-26

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

Terahertz semiconductor nonlinear optics

DEFF Research Database (Denmark)

Turchinovich, Dmitry; Hvam, Jørn Märcher; Hoffmann, Matthias

2013-01-01

In this proceedings we describe our recent results on semiconductor nonlinear optics, investigated using single-cycle THz pulses. We demonstrate the nonlinear absorption and self-phase modulation of strong-field THz pulses in doped semiconductors, using n-GaAs as a model system. The THz...... nonlinearity in doped semiconductors originates from the near-instantaneous heating of free electrons in the ponderomotive potential created by electric field of the THz pulse, leading to ultrafast increase of electron effective mass by intervalley scattering. Modification of effective mass in turn leads...... to a decrease of plasma frequency in semiconductor and produces a substantial modification of THz-range material dielectric function, described by the Drude model. As a result, the nonlinearity of both absorption coefficient and refractive index of the semiconductor is observed. In particular we demonstrate...

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)

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.

Existence and asymptotic behavior of solutions for nonlinear Schrödinger-Poisson systems with steep potential well.

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Du, Miao; Tian, Lixin; Wang, Jun; Zhang, Fubao

2016-03-01

In this paper, we are concerned with a class of Schrödinger-Poisson systems with the asymptotically linear or asymptotically 3-linear nonlinearity. Under some suitable assumptions on V , K , a , and f , we prove the existence, nonexistence, and asymptotic behavior of solutions via variational methods. In particular, the potential V is allowed to be sign-changing for the asymptotically linear case.

Heterogeneous Effects of a Nonlinear Price Schedule for Outpatient Care.

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Farbmacher, Helmut; Ihle, Peter; Schubert, Ingrid; Winter, Joachim; Wuppermann, Amelie

2017-10-01

Nonlinear price schedules generally have heterogeneous effects on health-care demand. We develop and apply a finite mixture bivariate probit model to analyze whether there are heterogeneous reactions to the introduction of a nonlinear price schedule in the German statutory health insurance system. In administrative insurance claims data from the largest German health insurance plan, we find that some individuals strongly react to the new price schedule while a second group of individuals does not react. Post-estimation analyses reveal that the group of the individuals who do not react to the reform includes the relatively sick. These results are in line with forward-looking behavior: Individuals who are already sick expect that they will hit the kink in the price schedule and thus are less sensitive to the co-payment. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Nonlinear theory for axisymmetric self-similar two-dimensional oscillations of electrons in cold plasma with constant proton background

Science.gov (United States)

Osherovich, V. A.; Fainberg, J.

2018-01-01

We consider simultaneous oscillations of electrons moving both along the axis of symmetry and also in the direction perpendicular to the axis. We derive a system of three nonlinear ordinary differential equations which describe self-similar oscillations of cold electrons in a constant proton density background (np = n0 = constant). These three equations represent an exact class of solutions. For weak nonlinear conditions, the frequency spectra of electric field oscillations exhibit split frequency behavior at the Langmuir frequency ωp0 and its harmonics, as well as presence of difference frequencies at low spectral values. For strong nonlinear conditions, the spectra contain peaks at frequencies with values ωp0(n +m √{2 }) , where n and m are integer numbers (positive and negative). We predict that both spectral types (weak and strong) should be observed in plasmas where axial symmetry may exist. To illustrate possible applications of our theory, we present a spectrum of electric field oscillations observed in situ in the solar wind by the WAVES experiment on the Wind spacecraft during the passage of a type III solar radio burst.

Numerical Analysis of Strongly Nonlinear Oscillation Systems using He's Max-Min Method

DEFF Research Database (Denmark)

Babazadeh, H; Domairry, G; Barari, Amin

2011-01-01

Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method...

Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators

International Nuclear Information System (INIS)

Belendez, A.; Gimeno, E.; Alvarez, M.L.; Mendez, D.I.; Hernandez, A.

2008-01-01

An analytical approximate technique for conservative nonlinear oscillators is proposed. This method is a modification of the rational harmonic balance method in which analytical approximate solutions have rational form. This approach gives us the frequency of the motion as a function of the amplitude of oscillation. We find that this method works very well for the whole range of parameters, and excellent agreement of the approximate frequencies with the exact one has been demonstrated and discussed. The most significant features of this method are its simplicity and its excellent accuracy for the whole range of oscillation amplitude values and the results reveal that this technique is very effective and convenient for solving conservative truly nonlinear oscillatory systems with complex nonlinearities

Nonlinearity in nanomechanical cantilevers

DEFF Research Database (Denmark)

Villanueva Torrijo, Luis Guillermo; Karabalin, R. B.; Matheny, M. H.

2013-01-01

Euler-Bernoulli beam theory is widely used to successfully predict the linear dynamics of micro-and nanocantilever beams. However, its capacity to characterize the nonlinear dynamics of these devices has not yet been rigorously assessed, despite its use in nanoelectromechanical systems developmen....... These findings underscore the delicate balance between inertial and geometric nonlinear effects in the fundamental mode, and strongly motivate further work to develop theories beyond the Euler-Bernoulli approximation. DOI: 10.1103/PhysRevB.87.024304...

Power laws and elastic nonlinearity in materials with complex microstructure

Energy Technology Data Exchange (ETDEWEB)

Scalerandi, M., E-mail: marco.scalerandi@infm.polito.it

2016-01-28

Nonlinear ultrasonic methods have been widely used to characterize the microstructure of damaged solids and consolidated granular media. Besides distinguishing between materials exhibiting classical nonlinear behaviors from those exhibiting hysteresis, it could be of importance the discrimination between ultrasonic indications from different physical sources (scatterers). Elastic hysteresis could indeed be due to dislocations, grain boundaries, stick-slip at interfaces, etc. Analyzing data obtained on various concrete samples, we show that the power law behavior of the nonlinear indicator vs. the energy of excitation could be used to classify different microscopic features. In particular, the power law exponent ranges between 1 and 3, depending on the nature of nonlinearity. We also provide a theoretical interpretation of the collected data using models for clapping and hysteretic nonlinearities. - Highlights: • Several materials exhibit a nontrivial nonlinear elastic behavior which can be ascribed to different physical sources. • The quantitative nonlinear response is dependent on the type of microstructure present in the material. • A nonlinear indicator could be defined which depends on the excitation energy of the sample. • Assuming a power law dependence, the exponent depends on the microstructure of the material and could evolve in time. • Experimental results on concrete are discussed and a theoretical description is proposed.

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....

Ishikawa iteration process for nonlinear Lipschitz strongly accretive mappings

International Nuclear Information System (INIS)

Chidume, C.E.; Osilike, M.O.

1994-05-01

Let E=L p , p≥2 and let T:E→ E be a Lipschitzian and strongly accretive mapping. Let S:E → E be defined by Sx=f-Tx+x. It is proved that under suitable conditions on the real sequences {α n } ∞ n=0 and {β n } ∞ n=0 , the iteration process, x 0 is an element of E, x n+1 =(1-α n ) x n +α n S[(1-β n ) x n +β n Sx n ], n≥0, converges strongly to the unique solution of Tx=f. A related result deals with the iterative approximation of fixed points for Lipschitz strongly pseudocontractive mappings in E. A consequence of our results gives an affirmative answer to a problem posed by one of the authors in 1990. (J. Math. Anal. Appl. 151, 2 (1990) p. 460). (author). 36 refs

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

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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.

Numerical study on the discharge characteristics and nonlinear behaviors of atmospheric pressure coaxial electrode dielectric barrier discharges

International Nuclear Information System (INIS)

Zhang Ding-Zong; Wang Yan-Hui; Wang De-Zhen

2017-01-01

The discharge characteristics and temporal nonlinear behaviors of the atmospheric pressure coaxial electrode dielectric barrier discharges are studied by using a one-dimensional fluid model. It is shown that the discharge is always asymmetrical between the positive pulses and negative pulses. The gas gap severely affects this asymmetry. But it is hard to acquire a symmetrical discharge by changing the gas gap. This asymmetry is proportional to the asymmetric extent of electrode structure, namely the ratio of the outer electrode radius to the inner electrode radius. When this ratio is close to unity, a symmetrical discharge can be obtained. With the increase of frequency, the discharge can exhibit a series of nonlinear behaviors such as period-doubling bifurcation, secondary bifurcation and chaotic phenomena. In the period-doubling bifurcation sequence the period- n discharge becomes more and more unstable with the increase of n . The period-doubling bifurcation can also be obtained by altering the discharge gas gap. The mechanisms of two bifurcations are further studied. It is found that the residual quasineutral plasma from the previous discharges and corresponding electric field distribution can weaken the subsequent discharge, and leads to the occurrence of bifurcation. (paper)

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.

Retrieval of high-order susceptibilities of nonlinear metamaterials

International Nuclear Information System (INIS)

Wang Zhi-Yu; Qiu Jin-Peng; Chen Hua; Mo Jiong-Jiong; Yu Fa-Xin

2017-01-01

Active metamaterials embedded with nonlinear elements are able to exhibit strong nonlinearity in microwave regime. However, existing S -parameter based parameter retrieval approaches developed for linear metamaterials do not apply in nonlinear cases. In this paper, a retrieval algorithm of high-order susceptibilities for nonlinear metamaterials is derived. Experimental demonstration shows that, by measuring the power level of each harmonic while sweeping the incident power, high-order susceptibilities of a thin-layer nonlinear metamaterial can be effectively retrieved. The proposedapproach can be widely used in the research of active metamaterials. (paper)

The Power of Unit Root Tests Against Nonlinear Local Alternatives

DEFF Research Database (Denmark)

Demetrescu, Matei; Kruse, Robinson

of Econometrics 112, 359-379) in comparison to the linear Dickey-Fuller test. To this end, we consider different adjustment schemes for deterministic terms. We provide asymptotic results which imply that the error variance has a severe impact on the behavior of the tests in the nonlinear case; the reason...... for such behavior is the interplay of nonstationarity and nonlinearity. In particular, we show that nonlinearity of the data generating process can be asymptotically negligible when the error variance is moderate or large (compared to the "amount of nonlinearity"), rendering the linear test more powerful than...

Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks

Science.gov (United States)

Sebastian, Resmi; Sitharam, T. G.

2018-01-01

Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.

Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations

International Nuclear Information System (INIS)

Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.

2003-01-01

We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations

Nonlinear dynamical modeling and prediction of the terrestrial magnetospheric activity

International Nuclear Information System (INIS)

Vassiliadis, D.

1992-01-01

The irregular activity of the magnetosphere results from its complex internal dynamics as well as the external influence of the solar wind. The dominating self-organization of the magnetospheric plasma gives rise to repetitive, large-scale coherent behavior manifested in phenomena such as the magnetic substorm. Based on the nonlinearity of the global dynamics this dissertation examines the magnetosphere as a nonlinear dynamical system using time series analysis techniques. Initially the magnetospheric activity is modeled in terms of an autonomous system. A dimension study shows that its observed time series is self-similar, but the correlation dimension is high. The implication of a large number of degrees of freedom is confirmed by other state space techniques such as Poincare sections and search for unstable periodic orbits. At the same time a stability study of the time series in terms of Lyapunov exponents suggests that the series is not chaotic. The absence of deterministic chaos is supported by the low predictive capability of the autonomous model. Rather than chaos, it is an external input which is largely responsible for the irregularity of the magnetospheric activity. In fact, the external driving is so strong that the above state space techniques give results for magnetospheric and solar wind time series that are at least qualitatively similar. Therefore the solar wind input has to be included in a low-dimensional nonautonomous model. Indeed it is shown that such a model can reproduce the observed magnetospheric behavior up to 80-90 percent. The characteristic coefficients of the model show little variation depending on the external disturbance. The impulse response is consistent with earlier results of linear prediction filters. The model can be easily extended to contain nonlinear features of the magnetospheric activity and in particular the loading-unloading behavior of substorms

Numerical insight into the seismic behavior of eight masonry towers in Northern Italy: FE pushover vs non-linear dynamic analyses

International Nuclear Information System (INIS)

Milani, Gabriele; Valente, Marco

2015-01-01

This study presents some FE results regarding the behavior under horizontal loads of eight existing masonry towers located in the North-East of Italy. The towers, albeit unique for geometric and architectural features, show some affinities which justify a comparative analysis, as for instance the location and the similar masonry material. Their structural behavior under horizontal loads is therefore influenced by geometrical issues, such as slenderness, walls thickness, perforations, irregularities, presence of internal vaults, etc., all features which may be responsible for a peculiar output. The geometry of the towers is deduced from both existing available documentation and in-situ surveys. On the basis of such geometrical data, a detailed 3D realistic mesh is conceived, with a point by point characterization of each single geometric element. The FE models are analysed under seismic loads acting along geometric axes of the plan section, both under non-linear static (pushover) and non-linear dynamic excitation assumptions. A damage-plasticity material model exhibiting softening in both tension and compression, already available in the commercial code Abaqus, is used for masonry. Pushover analyses are performed with both G1 and G2 horizontal loads distribution, according to Italian code requirements, along X+/− and Y+/− directions. Non-linear dynamic analyses are performed along both X and Y directions with a real accelerogram scaled to different peak ground accelerations. Some few results are presented in this paper. It is found that the results obtained with pushover analyses reasonably well fit expensive non-linear dynamic simulations, with a slightly less conservative trend

Numerical insight into the seismic behavior of eight masonry towers in Northern Italy: FE pushover vs non-linear dynamic analyses

Energy Technology Data Exchange (ETDEWEB)

Milani, Gabriele, E-mail: milani@stru.polimi.it, E-mail: gabriele.milani@polimi.it; Valente, Marco [Department of Architecture, Built Environment and Construction Engineering (ABC), Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milan (Italy)

2015-12-31

This study presents some FE results regarding the behavior under horizontal loads of eight existing masonry towers located in the North-East of Italy. The towers, albeit unique for geometric and architectural features, show some affinities which justify a comparative analysis, as for instance the location and the similar masonry material. Their structural behavior under horizontal loads is therefore influenced by geometrical issues, such as slenderness, walls thickness, perforations, irregularities, presence of internal vaults, etc., all features which may be responsible for a peculiar output. The geometry of the towers is deduced from both existing available documentation and in-situ surveys. On the basis of such geometrical data, a detailed 3D realistic mesh is conceived, with a point by point characterization of each single geometric element. The FE models are analysed under seismic loads acting along geometric axes of the plan section, both under non-linear static (pushover) and non-linear dynamic excitation assumptions. A damage-plasticity material model exhibiting softening in both tension and compression, already available in the commercial code Abaqus, is used for masonry. Pushover analyses are performed with both G1 and G2 horizontal loads distribution, according to Italian code requirements, along X+/− and Y+/− directions. Non-linear dynamic analyses are performed along both X and Y directions with a real accelerogram scaled to different peak ground accelerations. Some few results are presented in this paper. It is found that the results obtained with pushover analyses reasonably well fit expensive non-linear dynamic simulations, with a slightly less conservative trend.

Correlation potential of a test ion near a strongly charged plate.

Science.gov (United States)

Lu, Bing-Sui; Xing, Xiangjun

2014-03-01

We analytically calculate the correlation potential of a test ion near a strongly charged plate inside a dilute m:-n electrolyte. We do this by calculating the electrostatic Green's function in the presence of a nonlinear background potential, the latter having been obtained using the nonlinear Poisson-Boltzmann theory. We consider the general case where the dielectric constants of the plate and the electrolyte are distinct. The following generic results emerge from our analyses: (1) If the distance to the plate Δz is much larger than a Gouy-Chapman length, the plate surface will behave effectively as an infinitely charged surface, and the dielectric constant of the plate effectively plays no role. (2) If Δz is larger than a Gouy-Chapman length but shorter than a Debye length, the correlation potential can be interpreted in terms of an image charge that is three times larger than the source charge. This behavior is independent of the valences of the ions. (3) The Green's function vanishes inside the plate if the surface charge density is infinitely large; hence the electrostatic potential is constant there. In this respect, a strongly charged plate behaves like a conductor plate. (4) If Δz is smaller than a Gouy-Chapman length, the correlation potential is dominated by the conventional image charge due to the dielectric discontinuity at the interface. (5) If Δz is larger than a Debye length, the leading order behavior of the correlation potential will depend on the valences of the ions in the electrolyte. Furthermore, inside an asymmetric electrolyte, the correlation potential is singly screened, i.e., it undergoes exponential decay with a decay width equal to the Debye length.

FRF decoupling of nonlinear systems

Science.gov (United States)

Kalaycıoğlu, Taner; Özgüven, H. Nevzat

2018-03-01

Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.

Nonlinear Electromagnetic Stabilization of Plasma Microturbulence

Science.gov (United States)

Whelan, G. G.; Pueschel, M. J.; Terry, P. W.

2018-04-01

The physical causes for the strong stabilizing effect of finite plasma β on ion-temperature-gradient-driven turbulence, which far exceeds quasilinear estimates, are identified from nonlinear gyrokinetic simulations. The primary contribution stems from a resonance of frequencies in the dominant nonlinear interaction between the unstable mode, the stable mode, and zonal flows, which maximizes the triplet correlation time and therefore the energy transfer efficiency. A modification to mixing-length transport estimates is constructed, which reproduces nonlinear heat fluxes throughout the examined β range.

Nonlinear oscillation system of mass with serial linear and nonlinear springs

DEFF Research Database (Denmark)

Seyedalizadeh Ganji,, S.R; Barari, Amin; Karimpour, S

2013-01-01

In this paper, two powerful methods called Max–Min and parameter expansion have been applied for the determination of the periodic solutions of the nonlinear free vibration of a conservative oscillator with inertia and static type cubic nonlinearities. It is found that these methods introduce two...... alternatives to overcome the difficulty of capturing the periodic behavior of the solution, as the most evident characteristic of oscillators. It can be clearly observed that approximate frequencies and periodic solutions are in excellent agreement with the exact ones. First approximation leads to high...

Nonlinear Pricing in Energy and Environmental Markets

Science.gov (United States)

Ito, Koichiro

This dissertation consists of three empirical studies on nonlinear pricing in energy and environmental markets. The first investigates how consumers respond to multi-tier nonlinear price schedules for residential electricity. Chapter 2 asks a similar research question for residential water pricing. Finally, I examine the effect of nonlinear financial rewards for energy conservation by applying a regression discontinuity design to a large-scale electricity rebate program that was implemented in California. Economic theory generally assumes that consumers respond to marginal prices when making economic decisions, but this assumption may not hold for complex price schedules. The chapter "Do Consumers Respond to Marginal or Average Price? Evidence from Nonlinear Electricity Pricing" provides empirical evidence that consumers respond to average price rather than marginal price when faced with nonlinear electricity price schedules. Nonlinear price schedules, such as progressive income tax rates and multi-tier electricity prices, complicate economic decisions by creating multiple marginal prices for the same good. Evidence from laboratory experiments suggests that consumers facing such price schedules may respond to average price as a heuristic. I empirically test this prediction using field data by exploiting price variation across a spatial discontinuity in electric utility service areas. The territory border of two electric utilities lies within several city boundaries in southern California. As a result, nearly identical households experience substantially different nonlinear electricity price schedules. Using monthly household-level panel data from 1999 to 2008, I find strong evidence that consumers respond to average price rather than marginal or expected marginal price. I show that even though this sub-optimizing behavior has a minimal impact on individual welfare, it can critically alter the policy implications of nonlinear pricing. The second chapter " How Do

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.)

Electrophoresis in strong electric fields.

Science.gov (United States)

Barany, Sandor

2009-01-01

Two kinds of non-linear electrophoresis (ef) that can be detected in strong electric fields (several hundred V/cm) are considered. The first ("classical" non-linear ef) is due to the interaction of the outer field with field-induced ionic charges in the electric double layer (EDL) under conditions, when field-induced variations of electrolyte concentration remain to be small comparatively to its equilibrium value. According to the Shilov theory, the non-linear component of the electrophoretic velocity for dielectric particles is proportional to the cubic power of the applied field strength (cubic electrophoresis) and to the second power of the particles radius; it is independent of the zeta-potential but is determined by the surface conductivity of particles. The second one, the so-called "superfast electrophoresis" is connected with the interaction of a strong outer field with a secondary diffuse layer of counterions (space charge) that is induced outside the primary (classical) diffuse EDL by the external field itself because of concentration polarization. The Dukhin-Mishchuk theory of "superfast electrophoresis" predicts quadratic dependence of the electrophoretic velocity of unipolar (ionically or electronically) conducting particles on the external field gradient and linear dependence on the particle's size in strong electric fields. These are in sharp contrast to the laws of classical electrophoresis (no dependence of V(ef) on the particle's size and linear dependence on the electric field gradient). A new method to measure the ef velocity of particles in strong electric fields is developed that is based on separation of the effects of sedimentation and electrophoresis using videoimaging and a new flowcell and use of short electric pulses. To test the "classical" non-linear electrophoresis, we have measured the ef velocity of non-conducting polystyrene, aluminium-oxide and (semiconductor) graphite particles as well as Saccharomice cerevisiae yeast cells as a

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

Science.gov (United States)

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

2018-01-01

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

Nonlinear Squeeze Film Dampers without Centralized Springs

Directory of Open Access Journals (Sweden)

Zhu Changsheng

2000-01-01

Full Text Available In this paper, the bifurcation behavior of a flexible rotor supported on nonlinear squeeze film dampers without centralized springs is analyzed numerically by means of rotor trajectories, Poincar maps, bifurcation diagrams and power spectra, based on the short bearing and cavitated film assumptions. It is shown that there also exist two different operations (i.e., socalled bistable operations in some speed regions in the rotor system supported on the nonlinear squeeze film dampers without centralized springs. In the bistable operation speed regions, the rotor system exhibits synchronous, sub-synchronous, sub-super-synchronous and almost-periodic as well as nonperiodic motions. The periodic bifurcation behaviors of the rotor system supported on nonlinear squeeze film dampers without centralized springs are very complex and require further investigations.

Nonlinear Dynamic Models in Advanced Life Support

Science.gov (United States)

Jones, Harry

2002-01-01

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Nonlinear dynamic analysis of hydrodynamically-coupled stainless steel structures

International Nuclear Information System (INIS)

Zhao, Y.

1996-01-01

Spent nuclear fuel is usually stored temporarily on the site of nuclear power plants. The spent fuel storage racks are nuclear-safety-related stainless steel structures required to be analyzed for seismic loads. When the storage pool is subjected to three-dimensional (3-D) floor seismic excitations, rack modules, stored fuel bundles, adjacent racks and pool walls, and surrounding water are hydrodynamically coupled. Hydrodynamic coupling (HC) significantly affects the dynamic responses of the racks that are free-standing and submerged in water within the pool. A nonlinear time-history dynamic analysis is usually needed to describe the motion behavior of the racks that are both geometrically nonlinear and material nonlinear in nature. The nonlinearities include the friction resistance between the rack supporting legs and the pool floor, and various potential impacts of fuel-rack, rack-rack, and rack-pool wall. The HC induced should be included in the nonlinear dynamic analysis using the added-hydrodynamic-mass concept based on potential theory per the US Nuclear Regulatory Commission (USNRC) acceptance criteria. To this end, a finite element analysis constitutes a feasible and effective tool. However, most people perform somewhat simplified 1-D, or 2-D, or 3-D single rack and 2-D multiple rack analyses. These analyses are incomplete because a 3-D single rack model behaves quite differently from a 2-D mode. Furthermore, a 3-D whole pool multi-rack model behaves differently than a 3-D single rack model, especially when the strong HC effects are unsymmetrical. In this paper 3-D nonlinear dynamic time-history analyses were performed in a more quantitative manner using sophisticated finite element models developed for a single rack as well as all twelve racks in the whole-pool. Typical response results due to different HC effects are determined and discussed

Device Applications of Nonlinear Dynamics

CERN Document Server

Baglio, Salvatore

2006-01-01

This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.

Dynamic nonlinear elasticity in geo materials

International Nuclear Information System (INIS)

Ostrovsky, L.A.; Johnson, P.A.

2001-01-01

The nonlinear elastic behaviour of earth materials is an extremely rich topic, one that has broad implications to earth and materials sciences, including strong ground motion, rock physics, nondestructive evaluation and materials science. The mechanical properties of rock appear to place it in a broader class of materials, it can be named the Structural nonlinear elasticity class (also Mesoscopic/nano scale elasticity, or MS/NSE class). These terms are in contrast to materials that display classical, Atomic Elasticity, such as most fluids and monocrystalline solids. The difference between these two categories of materials is both in intensity and origin of their nonlinear response. The nonlinearity of atomic elastic materials is due to the atomic/molecular lattice anharmonicity. The latter is relatively small because the intermolecular forces are extremely strong. In contrast, the materials considered below contain small soft features that it is called the bond system (cracks, grain contacts, dislocations, etc.) within a hard matrix and relaxation (slow dynamical effects) are characteristic, non of which appear in atomic elastic materials. The research begins with a brief historical background from nonlinear acoustics to the recent developments in rock nonlinearity. This is followed by an overview of some representative laboratory measurements which serve as primary indicators of nonlinear behaviour, followed by theoretical development, and finally, mention a variety of observations of nonlinearity under field conditions and applications to nondestructive testing of materials. The goal is not to survey all papers published in the are but to demonstrate some experimental and theoretical results and ideas that will the reader to become oriented in this broad and rapidly growing area bridging macro-, meso- and microscale (nano scale) phenomena in physics, materials science, and geophysics

Ceramic coatings: A phenomenological modeling for damping behavior related to microstructural features

International Nuclear Information System (INIS)

Tassini, N.; Patsias, S.; Lambrinou, K.

2006-01-01

Recent research has shown that both stiffness and damping of ceramic coatings exhibit different non-linearities. These properties strongly depend on the microstructure, which is characterized by heterogeneous sets of elastic elements with mesoscopic sizes and shapes, as in non-linear mesoscopic elastic materials. To predict the damping properties of this class of materials, we have implemented a phenomenological model that characterizes their elastic properties. The model is capable of reproducing the basic features of the observed damping behavior for zirconia coatings prepared by air plasma spraying and electron-beam physical-vapor-deposition

Nonlinear electrodynamics and cosmology

International Nuclear Information System (INIS)

Breton, Nora

2010-01-01

Nonlinear electrodynamics (NLED) generalizes Maxwell's theory for strong fields. When coupled to general relativity NLED presents interesting features like the non-vanishing of the trace of the energy-momentum tensor that leads to the possibility of violation of some energy conditions and of acting as a repulsive contribution in the Raychaudhuri equation. This theory is worth to study in cosmological and astrophysical situations characterized by strong electromagnetic and gravitational fields.

Non-linear electromagnetic interactions in thermal QED

International Nuclear Information System (INIS)

Brandt, F.T.; Frenkel, J.

1994-08-01

The behavior of the non-linear interactions between electromagnetic fields at high temperature is examined. It is shown that, in general, the log(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero-temperature. It is argued that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T -> ∞. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action. (author). 12 refs, 1 fig

Observation of Self-Similar Behavior of the 3D, Nonlinear Rayleigh-Taylor Instability

International Nuclear Information System (INIS)

Sadot, O.; Smalyuk, V.A.; Delettrez, J.A.; Sangster, T.C.; Goncharov, V.N.; Meyerhofer, D.D.; Betti, R.; Shvarts, D.

2005-01-01

The Rayleigh-Taylor unstable growth of laser-seeded, 3D broadband perturbations was experimentally measured in the laser-accelerated, planar plastic foils. The first experimental observation showing the self-similar behavior of the bubble size and amplitude distributions under ablative conditions is presented. In the nonlinear regime, the modulation σ rms grows as α σ gt 2 , where g is the foil acceleration, t is the time, and α σ is constant. The number of bubbles evolves as N(t)∝(ωt√(g)+C) -4 and the average size evolves as (t)∝ω 2 gt 2 , where C is a constant and ω=0.83±0.1 is the measured scaled bubble-merging rate

Linear and nonlinear market correlations: Characterizing financial crises and portfolio optimization

Science.gov (United States)

Haluszczynski, Alexander; Laut, Ingo; Modest, Heike; Räth, Christoph

2017-12-01

Pearson correlation and mutual information-based complex networks of the day-to-day returns of U.S. S&P500 stocks between 1985 and 2015 have been constructed to investigate the mutual dependencies of the stocks and their nature. We show that both networks detect qualitative differences especially during (recent) turbulent market periods, thus indicating strongly fluctuating interconnections between the stocks of different companies in changing economic environments. A measure for the strength of nonlinear dependencies is derived using surrogate data and leads to interesting observations during periods of financial market crises. In contrast to the expectation that dependencies reduce mainly to linear correlations during crises, we show that (at least in the 2008 crisis) nonlinear effects are significantly increasing. It turns out that the concept of centrality within a network could potentially be used as some kind of an early warning indicator for abnormal market behavior as we demonstrate with the example of the 2008 subprime mortgage crisis. Finally, we apply a Markowitz mean variance portfolio optimization and integrate the measure of nonlinear dependencies to scale the investment exposure. This leads to significant outperformance as compared to a fully invested portfolio.

Chaos control of third-order phase-locked loops using backstepping nonlinear controller

International Nuclear Information System (INIS)

Harb, Ahmad M.; Harb, Bassam A.

2004-01-01

Previous study showed that a third-order phase-locked loop (PLL) with sinusoidal phase detector characteristics experienced a Hopf bifurcation point as well as chaotic behavior. As a result, this behavior drives the PLL to the out-of-lock (unstable) state. The analysis was based on a modern nonlinear theory such as bifurcation and chaos. The main goal of this paper is to control this chaotic behavior. A nonlinear controller based on the theory of backstepping is designed. The study showed the effectiveness of the designed nonlinear controller in controlling the undesirable unstable behavior and pulling the PLL back to the in-lock state

A nonlinear model for AC induced corrosion

Directory of Open Access Journals (Sweden)

N. Ida

2012-09-01

Full Text Available The modeling of corrosion poses particular difficulties. The understanding of corrosion as an electrochemical process has led to simple capacitive-resistive models that take into account the resistance of the electrolytic cell and the capacitive effect of the surface potential at the interface between conductors and the electrolyte. In some models nonlinear conduction effects have been added to account for more complex observed behavior. While these models are sufficient to describe the behavior in systems with cathodic protection, the behavior in the presence of induced AC currents from power lines and from RF sources cannot be accounted for and are insufficient to describe the effects observed in the field. Field observations have shown that a rectifying effect exists that affects the cathodic protection potential and this effect is responsible for corrosion in the presence of AC currents. The rectifying effects of the metal-corrosion interface are totally missing from current models. This work proposes a nonlinear model based on finite element analysis that takes into account the nonlinear behavior of the metal-oxide interface and promises to improve modeling by including the rectification effects at the interface.

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

Science.gov (United States)

Tsuchida, Satoshi; Kuratsuji, Hiroshi

2018-05-01

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

Nonlinear ionic transport through microstructured solid electrolytes: homogenization estimates

Science.gov (United States)

Curto Sillamoni, Ignacio J.; Idiart, Martín I.

2016-10-01

We consider the transport of multiple ionic species by diffusion and migration through microstructured solid electrolytes in the presence of strong electric fields. The assumed constitutive relations for the constituent phases follow from convex energy and dissipation potentials which guarantee thermodynamic consistency. The effective response is heuristically deduced from a multi-scale convergence analysis of the relevant field equations. The resulting homogenized response involves an effective dissipation potential per species. Each potential is mathematically akin to that of a standard nonlinear heterogeneous conductor. A ‘linear-comparison’ homogenization technique is then used to generate estimates for these nonlinear potentials in terms of available estimates for corresponding linear conductors. By way of example, use is made of the Maxwell-Garnett and effective-medium linear approximations to generate estimates for two-phase systems with power-law dissipation. Explicit formulas are given for some limiting cases. In the case of threshold-type behavior, the estimates exhibit non-analytical dilute limits and seem to be consistent with fields localized in low energy paths.

Multi-frequency Defect Selective Imaging via Nonlinear Ultrasound

Science.gov (United States)

Solodov, Igor; Busse, Gerd

The concept of defect-selective ultrasonic nonlinear imaging is based on visualization of strongly nonlinear inclusions in the form of localized cracked defects. For intense excitation, the ultrasonic response of defects is affected by mechanical constraint between their fragments that makes their vibrations extremely nonlinear. The cracked flaws, therefore, efficiently generate multiple new frequencies, which can be used as a nonlinear "tag" to detect and image them. In this paper, the methodologies of nonlinear scanning laser vibrometry (NSLV) and nonlinear air-coupled emission (NACE) are applied for nonlinear imaging of various defects in hi-tech and constructional materials. A broad database obtained demonstrates evident advantages of the nonlinear approach over its linear counterpart. The higher-order nonlinear frequencies provide increase in signal-to-noise ratio and enhance the contrast of imaging. Unlike conventional ultrasonic instruments, the nonlinear approach yields abundant multi-frequency information on defect location. The application of image recognition and processing algorithms is described and shown to improve reliability and quality of ultrasonic imaging.

Examining the Islamic stock market efficiency: Evidence from nonlinear ESTAR unit root tests

Directory of Open Access Journals (Sweden)

Rahmat Heru Setianto

2015-04-01

Full Text Available This paper empirically examines the efficient market hypothesis (EMH in the Islamic stock market namely Jakarta Islamic Index by emphasizing on the random walk behavior and nonlinearity. In the first step, we employ Brock et al. (1996 test to examine the presence of nonlinear behavior in Jakarta Islamic Index. The evidence of nonlinear behavior in the indices, motivate us to use nonlinear ESTAR unit root test procedure recently developed by Kapetanios et al. (2003 and Kruse (2011. The nonlinear unit root test procedure fail to rejects the null hypothesis of unit root for the indices, suggesting that Jakarta Islamic Index characterized by random walk process supporting the theory of efficient market hypothesis. In addition, Lumsdaine and Papel (LP test identified significant structural breaks in the index series.

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.

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

A strongly coupled open system with a non-linear bath: fluctuation-dissipation and Langevin dynamics

Science.gov (United States)

Bhadra, Chitrak

2018-03-01

The study of Langevin dynamics and fluctuation-dissipation relation (FDR) for a generic probe system (represented by a mass M ), bilinearly coupled to a bath of harmonic oscillators, has been a standard paradigm for the microscopic theory of stochastic processes for several decades. The question that we probe in this paper is, how robust the structure of the classical FDR is, when one replaces the harmonic bath by an anharmonic one in the limit of strong system-bath coupling? Such a picture carries the signature of the probe system in the zeroth order through a nonlocal time kernel. We observe that the two-time noise correlations hold a rich structure from which the usual FDR emerges only in the leading order of perturbation. Beyond this order, multiple time scales and nontrivial dependence on the temperature starts to manifest. These new aspects conspire to break the time-translational invariance of the noise-correlations. Several other interesting features show up and we discuss them methodically through rigorous calculations order-by-order in perturbation. This formalistic derivation along with a specific example of non-linearity can be easily applied to a huge range of processes and statistical observables that fall under the purview of a system-reservoir theory.

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

Five parameters for the evaluation of the soil nonlinearity during the Ms8.0 Wenchuan Earthquake using the HVSR method

Science.gov (United States)

Ren, Yefei; Wen, Ruizhi; Yao, Xinxin; Ji, Kun

2017-08-01

The consideration of soil nonlinearity is important for the accurate estimation of the site response. To evaluate the soil nonlinearity during the 2008 Ms8.0 Wenchuan Earthquake, 33 strong-motion records obtained from the main shock and 890 records from 157 aftershocks were collected for this study. The horizontal-to-vertical spectral ratio (HVSR) method was used to calculate five parameters: the ratio of predominant frequency (RFp), degree of nonlinearity (DNL), absolute degree of nonlinearity (ADNL), frequency of nonlinearity (fNL), and percentage of nonlinearity (PNL). The purpose of this study was to evaluate the soil nonlinearity level of 33 strong-motion stations and to investigate the characteristics, performance, and effective usage of these five parameters. Their correlations with the peak ground acceleration (PGA), peak ground velocity (PGV), average uppermost 30-m shear-wave velocity ( V S30), and maximum amplitude of HVSR ( A max) were investigated. The results showed that all five parameters correlate well with PGA and PGV. The DNL, ADNL, and PNL also show a good correlation with A max, which means that the degree of soil nonlinearity not only depends on the ground-motion amplitude (e.g., PGA and PGV) but also on the site condition. The fNL correlates with PGA and PGV but shows no correlation with either A max or V S30, implying that the frequency width affected by the soil nonlinearity predominantly depends on the ground-motion amplitude rather than the site condition. At 16 of the 33 stations analyzed in this study, the site response showed evident (i.e., strong and medium) nonlinearity during the main shock of the Wenchuan Earthquake, where the ground-motion level was almost beyond the threshold of PGA > 200 cm/s2 or PGV > 15 cm/s. The site response showed weak and no nonlinearity at the other 14 and 3 stations. These results also confirm that RFp, DNL, ADNL, and PNL are effective in identifying the soil nonlinearity behavior. The identification

Small systems of Duffing oscillators and the Fermi-Pasta-Ulam-Tsingou system An examination of the possible reasons for the unusual stability of localized nonlinear excitations in these systems

Science.gov (United States)

Kashyap, Rahul; Westley, Alexandra; Sen, Surajit

The Duffing oscillator, a nonlinear oscillator with a potential energy with both quadratic and cubic terms, is known to show highly chaotic solutions in certain regions of its parameter space. Here, we examine the behaviors of small chains of harmonically and anharmonically coupled Duffing oscillators and show that these chains exhibit localized nonlinear excitations (LNEs) similar to the ones seen in the Fermi-Pasta-Ulam-Tsingou (FPUT) system. These LNEs demonstrate properties such as long-time energy localization, high periodicity, and slow energy leaking which rapidly accelerates upon frequency matching with the adjacent particles all of which have been observed in the FPUT system. Furthermore, by examining bifurcation diagrams, we will show that many qualitative properties of this system during the transition from weakly to strongly nonlinear behavior depend directly upon the frequencies associated with the individual Duffing oscillators.

Nonlinear rock behavior and its implications on deeper-level platinum mining

CSIR Research Space (South Africa)

Watson, BP

2008-10-01

Full Text Available Uniaxial tests performed on core from instrumented sites at Amandelbult 1 shaft, Impala 10 shaft and Union Section Spud-shaft showed a nonlinear elastic relationship between applied load and induced deformation. This nonlinear behaviour does...

Nonlinear behaviors in a pulsed dielectric barrier discharge at atmospheric pressure

Energy Technology Data Exchange (ETDEWEB)

Zhang Jiao; Wang Yanhui, E-mail: wangyh@dlut.edu.cn; Wang Dezhen

2011-08-01

In this paper, the temporal nonlinear behaviors of pulsed dielectric barrier discharge in atmospheric helium are studied numerically by a one-dimensional fluid model. The results show that the common single-period pulsed discharge with two current pulses per single voltage pulse can take place over a broad parameter range. The rising and falling times of the voltage pulse can affect the discharge characteristics greatly. When the discharge is ignited by a pulse voltage with long rising and falling times, a single-period pulsed discharge with multiple current peaks can be observed. Under appropriate rising and falling times of the voltage pulse, a stable period-two discharge can occur over wide frequency and voltage ranges. Also this period-two discharge can exhibit different current and voltage characteristics with changing the duty cycle. With other parameters fixed, the pulsed DBD could be driven to chaos through period-doubling route by increasing either the falling time or the frequency of voltage pulse.

Nonlinear Mechanics of MEMS Rectangular Microplates under Electrostatic Actuation

KAUST Repository

Saghir, Shahid

2016-01-01

The first objective of the dissertation is to develop a suitable reduced order model capable of investigating the nonlinear mechanical behavior of von-Karman plates under electrostatic actuation. The second objective is to investigate the nonlinear

On a parabolic strongly nonlinear problem on manifolds

Directory of Open Access Journals (Sweden)

A. O. Marinho

2008-03-01

Full Text Available In this work we will prove the existence uniqueness and asymptotic behavior of weak solutions for the system (* involving the pseudo Laplacian operator and the condition $\\displaystyle\\frac{\\partial u}{\\partial t} + \\sum_{i=1}^n \\big|\\frac{\\partial u}{\\partial x_i}\\big|^{p-2}\\frac{\\partial u}{\\partial x_i}\

Iterative solution of nonlinear equations with strongly accretive operators

International Nuclear Information System (INIS)

Chidume, C.E.

1991-10-01

Let E be a real Banach space with a uniformly convex dual, and let K be a nonempty closed convex and bounded subset of E. Suppose T:K→K is a strongly accretive map such that for each f is an element of K the equation Tx=f has a solution in K. It is proved that each of the two well known fixed point iteration methods (the Mann and Ishikawa iteration methods) converges strongly to a solution of the equation Tx=f. Furthermore, our method shows that such a solution is necessarily unique. Explicit error estimates are given. Our results resolve in the affirmative two open problems (J. Math. Anal. Appl. Vol 151(2) (1990), p. 460) and generalize important known results. (author). 32 refs

Phase-space topography characterization of nonlinear ultrasound waveforms.

Science.gov (United States)

Dehghan-Niri, Ehsan; Al-Beer, Helem

2018-03-01

Fundamental understanding of ultrasound interaction with material discontinuities having closed interfaces has many engineering applications such as nondestructive evaluation of defects like kissing bonds and cracks in critical structural and mechanical components. In this paper, to analyze the acoustic field nonlinearities due to defects with closed interfaces, the use of a common technique in nonlinear physics, based on a phase-space topography construction of ultrasound waveform, is proposed. The central idea is to complement the "time" and "frequency" domain analyses with the "phase-space" domain analysis of nonlinear ultrasound waveforms. A nonlinear time series method known as pseudo phase-space topography construction is used to construct equivalent phase-space portrait of measured ultrasound waveforms. Several nonlinear models are considered to numerically simulate nonlinear ultrasound waveforms. The phase-space response of the simulated waveforms is shown to provide different topographic information, while the frequency domain shows similar spectral behavior. Thus, model classification can be substantially enhanced in the phase-space domain. Experimental results on high strength aluminum samples show that the phase-space transformation provides a unique detection and classification capabilities. The Poincaré map of the phase-space domain is also used to better understand the nonlinear behavior of ultrasound waveforms. It is shown that the analysis of ultrasound nonlinearities is more convenient and informative in the phase-space domain than in the frequency domain. Copyright © 2017 Elsevier B.V. All rights reserved.

Analysis, Synthesis, and Classification of Nonlinear Systems Using Synchronized Swept-Sine Method for Audio Effects

Directory of Open Access Journals (Sweden)

Novak Antonin

2010-01-01

Full Text Available A new method of identification, based on an input synchronized exponential swept-sine signal, is used to analyze and synthesize nonlinear audio systems like overdrive pedals for guitar. Two different pedals are studied; the first one exhibiting a strong influence of the input signal level on its input/output law and the second one exhibiting a weak influence of this input signal level. The Synchronized Swept Sine method leads to a Generalized Polynomial Hammerstein model equivalent to the pedals under test. The behaviors of both pedals are illustrated through model-based resynthesized signals. Moreover, it is also shown that this method leads to a criterion allowing the classification of the nonlinear systems under test, according to the influence of the input signal levels on their input/output law.

Strong photonic crystal behavior in regular arrays of core-shell and quantum disc InGaN/GaN nanorod light-emitting diodes

Energy Technology Data Exchange (ETDEWEB)

Lewins, C. J., E-mail: c.j.lewins@bath.ac.uk; Le Boulbar, E. D.; Lis, S. M.; Shields, P. A.; Allsopp, D. W. E., E-mail: d.allsopp@bath.ac.uk [Department of Electronic and Electrical Engineering, University of Bath, Claverton Down, Bath BA2 7AY (United Kingdom); Edwards, P. R.; Martin, R. W. [Department of Physics, SUPA, University of Strathclyde, Glasgow G4 0NG (United Kingdom)

2014-07-28

We show that arrays of emissive nanorod structures can exhibit strong photonic crystal behavior, via observations of the far-field luminescence from core-shell and quantum disc InGaN/GaN nanorods. The conditions needed for the formation of directional Bloch modes characteristic of strong photonic behavior are found to depend critically upon the vertical shape of the nanorod sidewalls. Index guiding by a region of lower volume-averaged refractive index near the base of the nanorods creates a quasi-suspended photonic crystal slab at the top of the nanorods which supports Bloch modes. Only diffractive behavior could be observed without this region. Slab waveguide modelling of the vertical structure shows that the behavioral regime of the emissive nanorod arrays depends strongly upon the optical coupling between the nanorod region and the planar layers below. The controlled crossover between the two regimes of photonic crystal operation enables the design of photonic nanorod structures formed on planar substrates that exploit either behavior depending on device requirements.

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

Science.gov (United States)

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

2018-03-01

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

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.

Flexible polyelectrolyte chain in a strong electrolyte solution: Insight into equilibrium properties and force-extension behavior from mesoscale simulation

Science.gov (United States)

Malekzadeh Moghani, Mahdy; Khomami, Bamin

2016-01-01

Macromolecules with ionizable groups are ubiquitous in biological and synthetic systems. Due to the complex interaction between chain and electrostatic decorrelation lengths, both equilibrium properties and micro-mechanical response of dilute solutions of polyelectrolytes (PEs) are more complex than their neutral counterparts. In this work, the bead-rod micromechanical description of a chain is used to perform hi-fidelity Brownian dynamics simulation of dilute PE solutions to ascertain the self-similar equilibrium behavior of PE chains with various linear charge densities, scaling of the Kuhn step length (lE) with salt concentration cs and the force-extension behavior of the PE chain. In accord with earlier theoretical predictions, our results indicate that for a chain with n Kuhn segments, lE ˜ cs-0.5 as linear charge density approaches 1/n. Moreover, the constant force ensemble simulation results accurately predict the initial non-linear force-extension region of PE chain recently measured via single chain experiments. Finally, inspired by Cohen's extraction of Warner's force law from the inverse Langevin force law, a novel numerical scheme is developed to extract a new elastic force law for real chains from our discrete set of force-extension data similar to Padè expansion, which accurately depicts the initial non-linear region where the total Kuhn length is less than the thermal screening length.

Observation of an octave-spanning supercontinuum in the mid-infrared using ultrafast cascaded nonlinearities

DEFF Research Database (Denmark)

Bache, Morten; Liu, Xing; Zhou, Binbin

2014-01-01

An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation. ©OSA 2014.......An octave-spanning mid-IR supercontinuum is observed experimentally using ultrafast cascaded nonlinearities in an LiInS2 quadratic nonlinear crystal pumped with 70 fs energetic mid-IR pulses and cut for strongly phase-mismatched second-harmonic generation. ©OSA 2014....

Methods of stability analysis in nonlinear mechanics

International Nuclear Information System (INIS)

Warnock, R.L.; Ruth, R.D.; Gabella, W.; Ecklund, K.

1989-01-01

We review our recent work on methods to study stability in nonlinear mechanics, especially for the problems of particle accelerators, and compare our ideals to those of other authors. We emphasize methods that (1) show promise as practical design tools, (2) are effective when the nonlinearity is large, and (3) have a strong theoretical basis. 24 refs., 2 figs., 2 tabs

Boundary-layer theory, strong-coupling series, and large-order behavior

International Nuclear Information System (INIS)

Bender, Carl M.; Pelster, Axel; Weissbach, Florian

2002-01-01

The introduction of a lattice converts a singular boundary-layer problem in the continuum into a regular perturbation problem. However, the continuum limit of the discrete problem is extremely nontrivial and is not completely understood. This article examines two singular boundary-layer problems taken from mathematical physics, the instanton problem and the Blasius equation, and in each case examines two strategies, Pade resummation and variational perturbation theory, to recover the solution to the continuum problem from the solution to the associated discrete problem. Both resummation procedures produce good and interesting results for the two cases, but the results still deviate from the exact solutions. To understand the discrepancy a comprehensive large-order behavior analysis of the strong-coupling lattice expansions for each of the two problems is done

Model of anisotropic nonlinearity in self-defocusing photorefractive media.

Science.gov (United States)

Barsi, C; Fleischer, J W

2015-09-21

We develop a phenomenological model of anisotropy in self-defocusing photorefractive crystals. In addition to an independent term due to nonlinear susceptibility, we introduce a nonlinear, non-separable correction to the spectral diffraction operator. The model successfully describes the crossover between photovoltaic and photorefractive responses and the spatially dispersive shock wave behavior of a nonlinearly spreading Gaussian input beam. It should prove useful for characterizing internal charge dynamics in complex materials and for accurate image reconstruction through nonlinear media.

Percolation-enhanced nonlinear scattering from semicontinuous metal films

Science.gov (United States)

Breit, M.; von Plessen, G.; Feldmann, J.; Podolskiy, V. A.; Sarychev, A. K.; Shalaev, V. M.; Gresillon, S.; Rivoal, J. C.; Gadenne, P.

2001-03-01

Strongly enhanced second-harmonic generation (SHG), which is characterized by nearly isotropic distribution, is observed for gold-glass films near the percolation threshold. The diffuse-like SHG scattering, which can be thought of as nonlinear critical opalescence, is in sharp contrast with highly collimated linear reflection and transmission from these nanostructured semicontinuous metal films. Our observations, which can be explained by giant fluctuations of local nonlinear sources for SHG, verify recent predictions of percolation-enhanced nonlinear scattering.

Analytical Solutions to Non-linear Mechanical Oscillation Problems

DEFF Research Database (Denmark)

Kaliji, H. D.; Ghadimi, M.; Barari, Amin

2011-01-01

In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...

Nonlinear structural mechanics theory, dynamical phenomena and modeling

CERN Document Server

Lacarbonara, Walter

2013-01-01

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

Science.gov (United States)

Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

Interaction of strong electromagnetic fields with atoms

International Nuclear Information System (INIS)

Brandi, H.S.; Davidovich, L.; Zagury, N.

1982-06-01

Several non-linear processes involvoing the interaction of atoms with strong laser fields are discussed, with particular emphasis on the ionization problem. Non-perturbative methods which have been proposed to tackle this problem are analysed, and shown to correspond to an expansion in the intra-atomic potential. The relation between tunneling and multiphoton absorption as ionization mechanisms, and the generalization of Einstein's photoelectric equation to the strong-field case are discussed. (Author) [pt

Beam Stability and Nonlinear Dynamics. Proceedings

International Nuclear Information System (INIS)

Parsa, Z.

1997-01-01

These proceedings represent papers presented at the Beam Stability and Nonlinear Dynamics symposium held in Santa Barbara in December 1996. The symposium was sponsored by the National Science Foundation as part of the United States long term accelerator research. The focus of this symposium was on nonlinear dynamics and beam stability. The topics included single-particle and many-particle dynamics, and stability in large circular accelerators such as the Large Hadron Collider(LHC). Other subjects covered were spin dynamics, nonlinear aberration correction, collective effects in the LHC, sawtooth instability and Landau damping in the presence of strong nonlinearity. There were presentations concerning plasma physics including the effect of beam echo. There are 17 papers altogether in these proceedings and 8 of them have been abstracted for the Energy Science and Technology database

SPP propagation in nonlinear glass-metal interface

KAUST Repository

Sagor, Rakibul Hasan

2011-12-01

The non-linear propagation of Surface-Plasmon-Polaritons (SPP) in single interface of metal and chalcogenide glass (ChG) is considered. A time domain simulation algorithm is developed using the Finite Difference Time Domain (FDTD) method. The general polarization algorithm incorporated in the auxiliary differential equation (ADE) is used to model frequency-dependent dispersion relation and third-order nonlinearity of ChG. The main objective is to observe the nonlinear behavior of SPP propagation and study the dynamics of the whole structure. © 2011 IEEE.

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

Science.gov (United States)

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

2018-05-01

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

Density gradient effects in weakly nonlinear ablative Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Wang, L. F.; Ye, W. H.; He, X. T.

2012-01-01

In this research, density gradient effects (i.e., finite thickness of ablation front effects) in ablative Rayleigh-Taylor instability (ARTI), in the presence of preheating within the weakly nonlinear regime, are investigated numerically. We analyze the weak, medium, and strong ablation surfaces which have different isodensity contours, respectively, to study the influences of finite thickness of ablation front on the weakly nonlinear behaviors of ARTI. Linear growth rates, generation coefficients of the second and the third harmonics, and coefficients of the third-order feedback to the fundamental mode are obtained. It is found that the linear growth rate which has a remarkable maximum, is reduced, especially when the perturbation wavelength λ is short and a cut-off perturbation wavelength λ c appears when the perturbation wavelength λ is sufficiently short, where no higher harmonics exists when λ c . The phenomenon of third-order positive feedback to the fundamental mode near the λ c [J. Sanz et al., Phys. Rev. Lett. 89, 195002 (2002); J. Garnier et al., Phys. Rev. Lett. 90, 185003 (2003); J. Garnier and L. Masse, Phys. Plasmas 12, 062707 (2005)] is confirmed in numerical simulations, and the physical mechanism of the third-order positive feedback is qualitatively discussed. Moreover, it is found that generations and growths of the second and the third harmonics are stabilized (suppressed and reduced) by the ablation effect. Meanwhile, the third-order negative feedback to the fundamental mode is also reduced by the ablation effect, and hence, the linear saturation amplitude (typically ∼0.2λ in our simulations) is increased significantly and therefore exceeds the classical prediction 0.1λ, especially for the strong ablation surface with a small perturbation wavelength. Overall, the ablation effect stabilizes the ARTI in the weakly nonlinear regime. Numerical results obtained are in general agreement with the recent weakly nonlinear theories and simulations

Strongly correlated Fermi-systems: Non-Fermi liquid behavior, quasiparticle effective mass and their interplay

Energy Technology Data Exchange (ETDEWEB)

Shaginyan, V.R. [Petersburg Nuclear Physics Institute, RAS, Gatchina 188300 (Russian Federation); Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)], E-mail: vrshag@thd.pnpi.spb.ru; Amusia, M.Ya. [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel); Popov, K.G. [Komi Science Center, Ural Division, RAS, Syktyvkar 167982 (Russian Federation)

2009-06-15

Basing on the density functional theory of fermion condensation, we analyze the non-Fermi liquid behavior of strongly correlated Fermi-systems such as heavy-fermion metals. When deriving equations for the effective mass of quasiparticles, we consider solids with a lattice and homogeneous systems. We show that the low-temperature thermodynamic and transport properties are formed by quasiparticles, while the dependence of the effective mass on temperature, number density, magnetic fields, etc., gives rise to the non-Fermi liquid behavior. Our theoretical study of the heat capacity, magnetization, energy scales, the longitudinal magnetoresistance and magnetic entropy are in good agreement with the remarkable recent facts collected on the heavy-fermion metal YbRh{sub 2}Si{sub 2}.

Strongly correlated Fermi-systems: Non-Fermi liquid behavior, quasiparticle effective mass and their interplay

International Nuclear Information System (INIS)

Shaginyan, V.R.; Amusia, M.Ya.; Popov, K.G.

2009-01-01

Basing on the density functional theory of fermion condensation, we analyze the non-Fermi liquid behavior of strongly correlated Fermi-systems such as heavy-fermion metals. When deriving equations for the effective mass of quasiparticles, we consider solids with a lattice and homogeneous systems. We show that the low-temperature thermodynamic and transport properties are formed by quasiparticles, while the dependence of the effective mass on temperature, number density, magnetic fields, etc., gives rise to the non-Fermi liquid behavior. Our theoretical study of the heat capacity, magnetization, energy scales, the longitudinal magnetoresistance and magnetic entropy are in good agreement with the remarkable recent facts collected on the heavy-fermion metal YbRh 2 Si 2 .

Computer simulations on the nonlinear frequency shift and nonlinear modulation of ion-acoustic waves

International Nuclear Information System (INIS)

Ohsawa, Yukiharu; Kamimura, Tetsuo.

1976-11-01

The nonlinear behavior of ion-acoustic waves with rather short wave-length, k lambda sub(De) asymptotically equals 1, is investigated by computer sumulations. It is observed that the nonlinear frequency shift is negative and is proportional to square root of the initial wave amplitude when the amplitude is not too large. This proportionality breaks down and the frequency shift can become positive (for large Te/Ti), when (n tilde sub(i)/n 0 )sup(1/2)>0.25, where n tilde sub(i) is the ion density perturbation and n 0 the average plasma density. Nonlinear modulation of the wave-packet is clearly seen; however, modulational instability was not observed. The importance of the effects of trapped ions to these phenomena is emphasized. (auth.)

Phase transitions, nonequilibrium dynamics, and critical behavior of strongly interacting systems

International Nuclear Information System (INIS)

Mottola, E.; Bhattacharya, T.; Cooper, F.

1998-01-01

This is the final report of a three-year, Laboratory Directed Research and Development project at Los Alamos National Laboratory. In this effort, large-scale simulations of strongly interacting systems were performed and a variety of approaches to the nonequilibrium dynamics of phase transitions and critical behavior were investigated. Focus areas included (1) the finite-temperature quantum chromodynamics phase transition and nonequilibrium dynamics of a new phase of matter (the quark-gluon plasma) above the critical temperature, (2) nonequilibrium dynamics of a quantum fields using mean field theory, and (3) stochastic classical field theoretic models with applications to spinodal decomposition and structural phase transitions in a variety of systems, such as spin chains and shape memory alloys

Phase transitions, nonequilibrium dynamics, and critical behavior of strongly interacting systems

Energy Technology Data Exchange (ETDEWEB)

Mottola, E.; Bhattacharya, T.; Cooper, F. [and others

1998-12-31

This is the final report of a three-year, Laboratory Directed Research and Development project at Los Alamos National Laboratory. In this effort, large-scale simulations of strongly interacting systems were performed and a variety of approaches to the nonequilibrium dynamics of phase transitions and critical behavior were investigated. Focus areas included (1) the finite-temperature quantum chromodynamics phase transition and nonequilibrium dynamics of a new phase of matter (the quark-gluon plasma) above the critical temperature, (2) nonequilibrium dynamics of a quantum fields using mean field theory, and (3) stochastic classical field theoretic models with applications to spinodal decomposition and structural phase transitions in a variety of systems, such as spin chains and shape memory alloys.

Non-linearities in Holocene floodplain sediment storage

Science.gov (United States)

Notebaert, Bastiaan; Nils, Broothaerts; Jean-François, Berger; Gert, Verstraeten

2013-04-01

that a strong multifractality is present in the scaling relationship between sediment storage and catchment area, depending on geomorphic landscape properties. Extrapolation of data from one spatial scale to another inevitably leads to large errors: when only the data of the upper floodplains are considered, a regression analysis results in an overestimation of total floodplain deposition for the entire catchment of circa 115%. This example demonstrates multifractality and related non-linearity in scaling relationships, which influences extrapolations beyond the initial range of measurements. These different examples indicate how traditional extrapolation techniques and assumptions in sediment budget studies can be challenged by field data, further complicating our understanding of these systems. Although simplifications are often necessary when working on large spatial scale, such non-linearities may form challenges for a better understanding of system behavior.

Nonlinear Analysis of the Space Shuttle Superlightweight External Fuel Tank

Science.gov (United States)

Nemeth, Michael P.; Britt, Vicki O.; Collins, Timothy J.; Starnes, James H., Jr.

1996-01-01

Results of buckling and nonlinear analyses of the Space Shuttle external tank superlightweight liquid-oxygen (LO2) tank are presented. Modeling details and results are presented for two prelaunch loading conditions and for two full-scale structural tests that were conducted on the original external tank. The results illustrate three distinctly different types of nonlinear response for thin-walled shells subjected to combined mechanical and thermal loads. The nonlinear response phenomena consist of bifurcation-type buckling, short-wavelength nonlinear bending, and nonlinear collapse associated with a limit point. For each case, the results show that accurate predictions of non- linear behavior generally require a large-scale, high-fidelity finite-element model. Results are also presented that show that a fluid-filled launch-vehicle shell can be highly sensitive to initial geometric imperfections. In addition, results presented for two full-scale structural tests of the original standard-weight external tank suggest that the finite-element modeling approach used in the present study is sufficient for representing the nonlinear behavior of the superlightweight LO2 tank.

Some nonlinear problems in the manipulation of beams

International Nuclear Information System (INIS)

Sessler, A.M.

1990-01-01

An overview is given of nonlinear problems that arise in the manipulation of beams. Beams can be made of material particles or photons, can be intense or dilute, can be energetic or not, and they can be propagating in vacuum or in a medium. The nonlinear aspects of the motion are different in each case, and this diversity of behavior is categorized. Many examples are given, which serves to illustrate the categorization and, furthermore, display the richness of behavior encountered in the physics of beams. 25 refs., 5 figs

Engineering high-order nonlinear dissipation for quantum superconducting circuits

Science.gov (United States)

Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.

Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.

Nonlinear Analysis of the Space Shuttle Super-Lightweight External Fuel Tank

Science.gov (United States)

Nemeth, Michael P.; Britt, Vicki O.; Collins, Timothy J.; Starnes, James H., Jr.

1996-01-01

The results of buckling and nonlinear analyses of the Space Shuttle External Tank super-lightweight liquid oxygen (LOX) tank are presented. Modeling details and results are presented for two prelaunch loading conditions and for two full-scale structural tests conducted on the original external tank. These results illustrate three distinctly different types of nonlinear responses for thin-walled shells subjected to combined mechanical and thermal loads. These nonlinear response phenomena consist of bifurcation-type buckling, short-wavelength nonlinear bending, and nonlinear collapse associated with a limit point. For each case, the results show that accurate predictions of nonlinear behavior generally require a large scale high-fidelity finite element model. Results are also presented that show that a fluid filled launch vehicle shell can be highly sensitive to initial geometric imperfections. In addition, results presented for two full scale structural tests of the original standard weight external tank suggest that the finite element modeling approach used in the present study is sufficient for representing the nonlinear behavior of the super lightweight LOX tank.

Mathematical models for suspension bridges nonlinear structural instability

CERN Document Server

Gazzola, Filippo

2015-01-01

This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.

Nonlinear dynamic analysis of flexible multibody systems

Science.gov (United States)

Bauchau, Olivier A.; Kang, Nam Kook

1991-01-01

Two approaches are developed to analyze the dynamic behavior of flexible multibody systems. In the first approach each body is modeled with a modal methodology in a local non-inertial frame of reference, whereas in the second approach, each body is modeled with a finite element methodology in the inertial frame. In both cases, the interaction among the various elastic bodies is represented by constraint equations. The two approaches were compared for accuracy and efficiency: the first approach is preferable when the nonlinearities are not too strong but it becomes cumbersome and expensive to use when many modes must be used. The second approach is more general and easier to implement but could result in high computation costs for a large system. The constraints should be enforced in a time derivative fashion for better accuracy and stability.

Nonlinear Dynamic Behavior of a Flexible Structure to Combined External Acoustic and Parametric Excitation

Directory of Open Access Journals (Sweden)

Paulo S. Varoto

2006-01-01

Full Text Available Flexible structures are frequently subjected to multiple inputs when in the field environment. The accurate determination of the system dynamic response to multiple inputs depends on how much information is available from the excitation sources that act on the system under study. Detailed information include, but are not restricted to appropriate characterization of the excitation sources in terms of their variation in time and in space for the case of distributed loads. Another important aspect related to the excitation sources is how inputs of different nature contribute to the measured dynamic response. A particular and important driving mechanism that can occur in practical situations is the parametric resonance. Another important input that occurs frequently in practice is related to acoustic pressure distributions that is a distributed type of loading. In this paper, detailed theoretical and experimental investigations on the dynamic response of a flexible cantilever beam carrying a tip mass to simultaneously applied external acoustic and parametric excitation signals have been performed. A mathematical model for transverse nonlinear vibration is obtained by employing Lagrange’s equations where important nonlinear effects such as the beam’s curvature and quadratic viscous damping are accounted for in the equation of motion. The beam is driven by two excitation sources, a sinusoidal motion applied to the beam’s fixed end and parallel to its longitudinal axis and a distributed sinusoidal acoustic load applied orthogonally to the beam’s longitudinal axis. The major goal here is to investigate theoretically as well as experimentally the dynamic behavior of the beam-lumped mass system under the action of these two excitation sources. Results from an extensive experimental work show how these two excitation sources interacts for various testing conditions. These experimental results are validated through numerically simulated results

Simulation and modeling of the crushing behavior of structural members

International Nuclear Information System (INIS)

Toi, Yutaka

1986-01-01

The analysis of the crushing behavior (the behavior of compressive breakdown accompanied by super large deformation) of structural members is an important subject which becomes the base of the ultimate strength design of the structures which may cause collision accident such as automobiles, ships and aircrafts, and of those which are feared to be collided such as offshore structures, bridge piers and nuclear power plants. However, since it is a phenomenon of very strong nonlinearity, its analysis is accompanied by large difficulty. In this report, three kinds of the approach for this problem, that is, rigid-plastic theoretical analysis, the simulation using a rigid body and spring model and nonlinear finite element analysis, are explained, referring to the example of calculation by the authors on the non-axisymmetric crushing problem of cylindrical shells. In crushing problem, the matters of concern are the amount of collision energy which can be absorbed by the plastic deformation of structures and the amount of deformation. It can be said that the increase of calculation cost brings about the heightening of calculation accuracy. The nonlinear finite element analysis is promising because its calculation cost is expected to lower in future. (Kako, I.)

Nonlinearities in reservoir engineering: Enhancing quantum correlations

Science.gov (United States)

Hu, Xiangming; Hu, Qingping; Li, Lingchao; Huang, Chen; Rao, Shi

2017-12-01

There are two decisive factors for quantum correlations in reservoir engineering, but they are strongly reversely dependent on the atom-field nonlinearities. One is the squeezing parameter for the Bogoliubov modes-mediated collective interactions, while the other is the dissipative rates for the engineered collective dissipations. Exemplifying two-level atomic ensembles, we show that the moderate nonlinearities can compromise these two factors and thus enhance remarkably two-mode squeezing and entanglement of different spin atomic ensembles or different optical fields. This suggests that the moderate nonlinearities of the two-level systems are more advantageous for applications in quantum networks associated with reservoir engineering.

Nonlinear and Nonequilibrium Dynamics in Geomaterials

OpenAIRE

TenCate, James A.; Pasqualini, Donatella; Habib, Salman; Heitmann, Katrin; Higdon, David; Johnson, Paul A.

2004-01-01

The transition from linear to nonlinear dynamical elasticity in rocks is of considerable interest in seismic wave propagation as well as in understanding the basic dynamical processes in consolidated granular materials. We have carried out a careful experimental investigation of this transition for Berea and Fontainebleau sandstones. Below a well-characterized strain, the materials behave linearly, transitioning beyond that point to a nonlinear behavior which can be accurately captured by a s...

Nonlinear excitation of electron cyclotron waves by a monochromatic strong microwave: computer simulation analysis of the MINIX results

Energy Technology Data Exchange (ETDEWEB)

Matsumoto, H.; Kimura, T.

1986-01-01

Triggered by the experimental results of the MINIX, a computer simulation study was initiated on the nonlinear excitation of electrostatic electron cyclotron waves by a monochromatic electromagnetic wave such as the transmitted microwave in the MINIX. The model used assumes that both of the excited waves and exciting (pumping) electromagnetic wave as well as the idler electromagnetic wave propagate in the direction perpendicular to the external magnetic field. The simulation code used for this study was the one-and-two-half dimensional electromagnetic particle code named KEMPO. The simulation result shows the high power electromagnetic wave produces both the backscattered electromagnetic wave and electrostatic electron cyclotron waves as a result of nonlinear parametric instability. Detailed nonlinear microphysics related to the wave excitation is discussed in terms of the nonlinear wave-wave couplings and associated ponderomotive force produced by the high power electromagnetic waves. 2 references, 4 figures.

Nonlinear excitation of electron cyclotron waves by a monochromatic strong microwave: computer simulation analysis of the MINIX results

International Nuclear Information System (INIS)

Matsumoto, H.; Kimura, T.

1986-01-01

Triggered by the experimental results of the MINIX, a computer simulation study was initiated on the nonlinear excitation of electrostatic electron cyclotron waves by a monochromatic electromagnetic wave such as the transmitted microwave in the MINIX. The model used assumes that both of the excited waves and exciting (pumping) electromagnetic wave as well as the idler electromagnetic wave propagate in the direction perpendicular to the external magnetic field. The simulation code used for this study was the one-and-two-half dimensional electromagnetic particle code named KEMPO. The simulation result shows the high power electromagnetic wave produces both the backscattered electromagnetic wave and electrostatic electron cyclotron waves as a result of nonlinear parametric instability. Detailed nonlinear microphysics related to the wave excitation is discussed in terms of the nonlinear wave-wave couplings and associated ponderomotive force produced by the high power electromagnetic waves. 2 references, 4 figures

Measurement of nonlinear mode coupling of tearing fluctuations

International Nuclear Information System (INIS)

Assadi, S.; Prager, S.C.; Sidikman, K.L.

1992-03-01

Three-wave nonlinear coupling of spatial Fourier modes is measured in the MST reversed field pinch by applying bi-spectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 polodial modes and 32 toroidal modes. Comparison to bi-spectra predicted by MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomittant with a broadened (presumably nonlinearly generated) k-spectrum

A constitutive model for developing blood clots with various compositions and their nonlinear viscoelastic behavior.

Science.gov (United States)

van Kempen, Thomas H S; Donders, Wouter P; van de Vosse, Frans N; Peters, Gerrit W M

2016-04-01

The mechanical properties determine to a large extent the functioning of a blood clot. These properties depend on the composition of the clot and have been related to many diseases. However, the various involved components and their complex interactions make it difficult at this stage to fully understand and predict properties as a function of the components. Therefore, in this study, a constitutive model is developed that describes the viscoelastic behavior of blood clots with various compositions. Hereto, clots are formed from whole blood, platelet-rich plasma and platelet-poor plasma to study the influence of red blood cells, platelets and fibrin, respectively. Rheological experiments are performed to probe the mechanical behavior of the clots during their formation. The nonlinear viscoelastic behavior of the mature clots is characterized using a large amplitude oscillatory shear deformation. The model is based on a generalized Maxwell model that accurately describes the results for the different rheological experiments by making the moduli and viscosities a function of time and the past and current deformation. Using the same model with different parameter values enables a description of clots with different compositions. A sensitivity analysis is applied to study the influence of parameter variations on the model output. The relative simplicity and flexibility make the model suitable for numerical simulations of blood clots and other materials showing similar behavior.

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

Science.gov (United States)

Harvey, Gerald; Gachagan, Anthony

2011-04-01

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

Nonlinear Dynamics and Bifurcation Behavior of a 2-DOF Spring Resonator with End Stopper for Energy Harvesting

Directory of Open Access Journals (Sweden)

El Aroudi A.

2014-01-01

Full Text Available In this paper, the model of a two-degree-of-freedom (2-DOF spring resonator with end stopper for an energy harvesting application is presented. Then we characterize its nonlinear dynamical behavior by numerical simulations when some suitable parameters are varied. The system is formed by two resonators subject to external vibrational excitation and with an end stopper. We present the continuous time dynamical model of the system in the form of a switched fourth order differential equation. Harmonic vibrations are considered as the main ambient energy source for the system and its frequency response representing the RMS value of the displacement is first computed. The dynamical behavior is unveiled by computing state-space trajectories, timedomain series and FFT spectra and frequency response as the excitation amplitude is varied.

Nonlinear behavior of stimulated scatter in large underdense plasmas

International Nuclear Information System (INIS)

Kruer, W.L.; Estabrook, K.G.

1979-01-01

Several nonlinear effects which limit Brillouin and Raman scatter of intense light in large underdense plasmas are examined. After briefly considering ion trapping and harmonic generation, we focus on the self-consistent ion heating which occurs as an integral part of the Brillouin scattering process. In the long-term nonlinear state, the ion wave amplitude is determined by damping on the heated ion tail which self-consistently forms. A simple model of the scatter is presented and compared with particle simulations. A similar model is also applied to Raman scatter and compared with simulations. Our calculations emphasize that modest tails on the electron distribution function can significantly limit instabilities involving electron plasma waves

Pressure tunable cascaded third order nonlinearity and temporal pulse switching

DEFF Research Database (Denmark)

Eilenberger, Falk; Bache, Morten; Minardi, Stefano

2013-01-01

Effects based on the χ(3)-nonlinearity are arguably the most commonly discussed nonlinear interactions in photonics. In the description of pulse propagation, however, the generation of the third harmonic (TH) is commonly neglected, because it is strongly phase mismatched in most materials...

Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators.

Science.gov (United States)

Sun, Xuan; Liang, Hanxiao; Luo, Rui; Jiang, Wei C; Zhang, Xi-Cheng; Lin, Qiang

2017-06-12

Recent advance of lithium niobate microphotonic devices enables the exploration of intriguing nonlinear optical effects. We show complex nonlinear oscillation dynamics in high-Q lithium niobate microresonators that results from unique competition between the thermo-optic nonlinearity and the photorefractive effect, distinctive to other device systems and mechanisms ever reported. The observed phenomena are well described by our theory. This exploration helps understand the nonlinear optical behavior of high-Q lithium niobate microphotonic devices which would be crucial for future application of on-chip nonlinear lithium niobate photonics.

Bound-Electron Nonlinearity Beyond the Ionization Threshold

Science.gov (United States)

Wahlstrand, J. K.; Zahedpour, S.; Bahl, A.; Kolesik, M.; Milchberg, H. M.

2018-05-01

We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

Study of nonlinear optical absorption properties of V{sub 2}O{sub 5} nanoparticles in the femtosecond excitation regime

Energy Technology Data Exchange (ETDEWEB)

Molli, Muralikrishna; Bhat Kademane, Abhijit; Pradhan, Prabin; Sai Muthukumar, V. [Sri Sathya Sai Institute of Higher Learning, Department of Physics, Puttaparthi, Andhra Pradesh (India)

2016-08-15

In this work, we report for the first time, the nonlinear optical absorption properties of vanadium pentoxide (V{sub 2}O{sub 5}) nanoparticles in the femtosecond excitation regime. V{sub 2}O{sub 5} nanoparticles were synthesized through solution combustion technique. The as-synthesized samples were further characterized using XRD, FESEM, EDAX, TEM and UV-visible spectroscopy. X-ray diffraction results revealed the crystalline nature of the nanoparticles. Electron microscopy studies showed the size of the nanoparticles to be ∝200 nm. Open-aperture z-scan technique was employed to study the nonlinear optical absorption behavior of the synthesized samples using a 100-fs laser pulses at 800 nm from a regeneratively amplified Ti: sapphire laser. The mechanism of nonlinear absorption was found to be a three-photon absorption process which was explained using the density of states of V{sub 2}O{sub 5} obtained using density functional theory. These nanoparticles exhibit strong intensity-dependent nonlinear optical absorption and hence could be considered for optical-power-limiting applications. (orig.)

Spectral analysis of noisy nonlinear maps

International Nuclear Information System (INIS)

Hirshman, S.P.; Whitson, J.C.

1982-01-01

A path integral equation formalism is developed to obtain the frequency spectrum of nonlinear mappings exhibiting chaotic behavior. The one-dimensional map, x/sub n+1/ = f(x/sub n/), where f is nonlinear and n is a discrete time variable, is analyzed in detail. This map is introduced as a paradigm of systems whose exact behavior is exceedingly complex, and therefore irretrievable, but which nevertheless possess smooth, well-behaved solutions in the presence of small sources of external noise. A Boltzmann integral equation is derived for the probability distribution function p(x,n). This equation is linear and is therefore amenable to spectral analysis. The nonlinear dynamics in f(x) appear as transition probability matrix elements, and the presence of noise appears simply as an overall multiplicative scattering amplitude. This formalism is used to investigate the band structure of the logistic equation and to analyze the effects of external noise on both the invariant measure and the frequency spectrum of x/sub n/ for several values of lambda epsilon [0,1

Nonlinear optical studies of curcumin metal derivatives with cw laser

Energy Technology Data Exchange (ETDEWEB)

Henari, F. Z., E-mail: fzhenari@rcsi-mub.com; Cassidy, S. [Department of Basic Medical Sciences, Royal College of Surgeons in Ireland, Medical University of Bahrain (Bahrain)

2015-03-30

We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10{sup −7} cm{sup 2}/W and negative nonlinear absorption of the order of 10{sup −6} cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition model with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated.

Nonlinear optical studies of curcumin metal derivatives with cw laser

International Nuclear Information System (INIS)

Henari, F. Z.; Cassidy, S.

2015-01-01

We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10 −7 cm 2 /W and negative nonlinear absorption of the order of 10 −6 cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition model with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated

Simulation of the Nonlinear Dose Dependence of Stabilized Point Defects

International Nuclear Information System (INIS)

Chen, R; Pagonis, V; Lawless, J L

2010-01-01

The dose dependence of the concentration of point defects in alkali-halides as well as other crystals, as exhibited by the dependence of the thermoluminescence (TL), optical absorption and ESR on the dose of non-ionizing UV excitation is studied using numerical simulation. The relevant set of coupled rate equations are first written and plausible sets of trapping parameters are chosen. Instead of using simplifying assumptions previously used for reaching conclusions concerning this dose behavior, exact numerical solutions have now been reached. Depending on the parameters chosen, different dose dependencies are seen. In some cases, linear dose dependence is reached in a broad range. Sublinear dose dependence, close to a D 1/2 dependence when D is the dose of excitation can be reached when retrapping is stronger than trapping in other traps stabilizing the defects. When strong competition between stabilizing traps takes place, an initial linear range is observed followed by strong superlinearity and an approach to saturation. All these behaviors have been observed experimentally in TL measurements as well as ESR and optical absorption in different materials. Similarities and dissimilarities to linear and non-linear dose dependencies obtained experimentally and by simulations when ionizing irradiation is used for excitation are discussed.

Nonlinear ordinary differential equations analytical approximation and numerical methods

CERN Document Server

Hermann, Martin

2016-01-01

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march...

Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

KAUST Repository

Xu, Tiantian; Younis, Mohammad I.

2015-01-01

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction

Nonlinear instability and convection in a vertically vibrated granular bed

NARCIS (Netherlands)

Shukla, P.; Ansari, I.H.; van der Meer, Roger M.; Lohse, Detlef; Alam, M.

2014-01-01

The nonlinear instability of the density-inverted granular Leidenfrost state and the resulting convective motion in strongly shaken granular matter are analysed via a weakly nonlinear analysis of the hydrodynamic equations. The base state is assumed to be quasi-steady and the effect of harmonic

Spatiotemporal light-beam compression from nonlinear mode coupling

Science.gov (United States)

Krupa, Katarzyna; Tonello, Alessandro; Couderc, Vincent; Barthélémy, Alain; Millot, Guy; Modotto, Daniele; Wabnitz, Stefan

2018-04-01

We experimentally demonstrate simultaneous spatial and temporal compression in the propagation of light pulses in multimode nonlinear optical fibers. We reveal that the spatial beam self-cleaning recently discovered in graded-index multimode fibers is accompanied by significant temporal reshaping and up to fourfold shortening of the injected subnanosecond laser pulses. Since the nonlinear coupling among the modes strongly depends on the instantaneous power, we explore the entire range of the nonlinear dynamics with a single optical pulse, where the optical power is continuously varied across the pulse profile.

Instability and dynamics of two nonlinearly coupled intense laser beams in a quantum plasma

International Nuclear Information System (INIS)

Wang Yunliang; Shukla, P. K.; Eliasson, B.

2013-01-01

We consider nonlinear interactions between two relativistically strong laser beams and a quantum plasma composed of degenerate electron fluids and immobile ions. The collective behavior of degenerate electrons is modeled by quantum hydrodynamic equations composed of the electron continuity, quantum electron momentum (QEM) equation, as well as the Poisson and Maxwell equations. The QEM equation accounts the quantum statistical electron pressure, the quantum electron recoil due to electron tunneling through the quantum Bohm potential, electron-exchange, and electron-correlation effects caused by electron spin, and relativistic ponderomotive forces (RPFs) of two circularly polarized electromagnetic (CPEM) beams. The dynamics of the latter are governed by nonlinear wave equations that include nonlinear currents arising from the relativistic electron mass increase in the CPEM wave fields, as well as from the beating of the electron quiver velocity and electron density variations reinforced by the RPFs of the two CPEM waves. Furthermore, nonlinear electron density variations associated with the driven (by the RPFs) quantum electron plasma oscillations obey a coupled nonlinear Schrödinger and Poisson equations. The nonlinearly coupled equations for our purposes are then used to obtain a general dispersion relation (GDR) for studying the parametric instabilities and the localization of CPEM wave packets in a quantum plasma. Numerical analyses of the GDR reveal that the growth rate of a fastest growing parametrically unstable mode is in agreement with the result that has been deduced from numerical simulations of the governing nonlinear equations. Explicit numerical results for two-dimensional (2D) localized CPEM wave packets at nanoscales are also presented. Possible applications of our investigation to intense laser-solid density compressed plasma experiments are highlighted.

The benefits of noise and nonlinearity: Extracting energy from random vibrations

Energy Technology Data Exchange (ETDEWEB)

Gammaitoni, Luca, E-mail: luca.gammaitoni@pg.infn.it [NiPS Laboratory, Universita di Perugia, I-06100 Perugia (Italy); Neri, Igor; Vocca, Helios [NiPS Laboratory, Universita di Perugia, I-06100 Perugia (Italy)

2010-10-05

Nonlinear behavior is the ordinary feature of the vast majority of dynamical systems and noise is commonly present in any finite temperature physical and chemical system. In this article we briefly review the potentially beneficial outcome of the interplay of noise and nonlinearity by addressing the novel field of vibration energy harvesting. The role of nonlinearity in a piezoelectric harvester oscillator dynamics is modeled with nonlinear stochastic differential equation.

Impurity solitons with quadratic nonlinearities

DEFF Research Database (Denmark)

Clausen, Carl A. Balslev; Torres, Juan P-; Torner, Lluis

1998-01-01

We fmd families of solitary waves mediated by parametric mixing in quadratic nonlinear media that are localized at point-defect impurities. Solitons localized at attractive impurities are found to be dynamically stable. It is shown that localization at the impurity modifies strongly the soliton...

Nonlinear switching dynamics in a photonic-crystal nanocavity

International Nuclear Information System (INIS)

Yu, Yi; Palushani, Evarist; Heuck, Mikkel; Vukovic, Dragana; Peucheret, Christophe; Yvind, Kresten; Mork, Jesper

2014-01-01

We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching contrast.

Nonlinear switching dynamics in a photonic-crystal nanocavity

DEFF Research Database (Denmark)

Yu, Yi; Palushani, Evarist; Heuck, Mikkel

2014-01-01

We report the experimental observation of nonlinear switching dynamics in an InP photonic crystal nanocavity. Usually, the regime of relatively small cavity perturbations is explored, where the signal transmitted through the cavity follows the temporal variation of the cavity resonance. When...... of large dynamical variations of the cavity resonance in combination with nonlinear losses. The results provide insight into the nonlinear optical processes that govern the dynamics of nanocavities and are important for applications in optical signal processing, where one wants to optimize the switching...... the cavity is perturbed by strong pulses, we observe several nonlinear effects, i.e., saturation of the switching contrast, broadening of the switching window, and even initial reduction of the transmission. The effects are analyzed by comparison with nonlinear coupled mode theory and explained in terms...

Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction

Directory of Open Access Journals (Sweden)

Geoff Boeing

2016-11-01

Full Text Available Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be very simple, yet they produce completely unpredictable and divergent behavior. Systems of nonlinear equations are difficult to solve analytically, and scientists have relied heavily on visual and qualitative approaches to discover and analyze the dynamics of nonlinearity. Indeed, few fields have drawn as heavily from visualization methods for their seminal innovations: from strange attractors, to bifurcation diagrams, to cobweb plots, to phase diagrams and embedding. Although the social sciences are increasingly studying these types of systems, seminal concepts remain murky or loosely adopted. This article has three aims. First, it argues for several visualization methods to critically analyze and understand the behavior of nonlinear dynamical systems. Second, it uses these visualizations to introduce the foundations of nonlinear dynamics, chaos, fractals, self-similarity and the limits of prediction. Finally, it presents Pynamical, an open-source Python package to easily visualize and explore nonlinear dynamical systems’ behavior.

Chaotic dynamics with high complexity in a simplified new nonautonomous nonlinear electronic circuit

International Nuclear Information System (INIS)

Arulgnanam, A.; Thamilmaran, K.; Daniel, M.

2009-01-01

A two dimensional nonautonomous dissipative forced series LCR circuit with a simple nonlinear element exhibiting an immense variety of dynamical features is proposed for the first time. Unlike the usual cases of nonlinear element, the nonlinear element used here possesses three segment piecewise linear character with one positive and one negative slope. This nonlinearity is verified to be sufficient to produce chaos with high complexity in many established nonautonomous nonlinear circuits, such as MLC, MLCV, driven Chua, etc., thus indicating an universal behavior similar to the familiar Chua's diode. The dynamics of the proposed circuit is studied experimentally, confirmed numerically, simulated through PSPICE and proved mathematically. An important feature of the circuit is its ability to show dual chaotic behavior.

Nonparametric inference in nonlinear principal components analysis : exploration and beyond

NARCIS (Netherlands)

Linting, Mariëlle

2007-01-01

In the social and behavioral sciences, data sets often do not meet the assumptions of traditional analysis methods. Therefore, nonlinear alternatives to traditional methods have been developed. This thesis starts with a didactic discussion of nonlinear principal components analysis (NLPCA),

Controllable nonlinearity in a dual-coupling optomechanical system under a weak-coupling regime

Science.gov (United States)

Zhu, Gui-Lei; Lü, Xin-You; Wan, Liang-Liang; Yin, Tai-Shuang; Bin, Qian; Wu, Ying

2018-03-01

Strong quantum nonlinearity gives rise to many interesting quantum effects and has wide applications in quantum physics. Here we investigate the quantum nonlinear effect of an optomechanical system (OMS) consisting of both linear and quadratic coupling. Interestingly, a controllable optomechanical nonlinearity is obtained by applying a driving laser into the cavity. This controllable optomechanical nonlinearity can be enhanced into a strong coupling regime, even if the system is initially in the weak-coupling regime. Moreover, the system dissipation can be suppressed effectively, which allows the appearance of phonon sideband and photon blockade effects in the weak-coupling regime. This work may inspire the exploration of a dual-coupling optomechanical system as well as its applications in modern quantum science.

Structural predictor for nonlinear sheared dynamics in simple glass-forming liquids.

Science.gov (United States)

Ingebrigtsen, Trond S; Tanaka, Hajime

2018-01-02

Glass-forming liquids subjected to sufficiently strong shear universally exhibit striking nonlinear behavior; for example, a power-law decrease of the viscosity with increasing shear rate. This phenomenon has attracted considerable attention over the years from both fundamental and applicational viewpoints. However, the out-of-equilibrium and nonlinear nature of sheared fluids have made theoretical understanding of this phenomenon very challenging and thus slower to progress. We find here that the structural relaxation time as a function of the two-body excess entropy, calculated for the extensional axis of the shear flow, collapses onto the corresponding equilibrium curve for a wide range of pair potentials ranging from harsh repulsive to soft and finite. This two-body excess entropy collapse provides a powerful approach to predicting the dynamics of nonequilibrium liquids from their equilibrium counterparts. Furthermore, the two-body excess entropy scaling suggests that sheared dynamics is controlled purely by the liquid structure captured in the form of the two-body excess entropy along the extensional direction, shedding light on the perplexing mechanism behind shear thinning.

Structural predictor for nonlinear sheared dynamics in simple glass-forming liquids

Science.gov (United States)

Ingebrigtsen, Trond S.; Tanaka, Hajime

2018-01-01

Glass-forming liquids subjected to sufficiently strong shear universally exhibit striking nonlinear behavior; for example, a power-law decrease of the viscosity with increasing shear rate. This phenomenon has attracted considerable attention over the years from both fundamental and applicational viewpoints. However, the out-of-equilibrium and nonlinear nature of sheared fluids have made theoretical understanding of this phenomenon very challenging and thus slower to progress. We find here that the structural relaxation time as a function of the two-body excess entropy, calculated for the extensional axis of the shear flow, collapses onto the corresponding equilibrium curve for a wide range of pair potentials ranging from harsh repulsive to soft and finite. This two-body excess entropy collapse provides a powerful approach to predicting the dynamics of nonequilibrium liquids from their equilibrium counterparts. Furthermore, the two-body excess entropy scaling suggests that sheared dynamics is controlled purely by the liquid structure captured in the form of the two-body excess entropy along the extensional direction, shedding light on the perplexing mechanism behind shear thinning.

Effect of Dislocation Density on Deformation Behavior of Super Strong Bainitic Steel

Directory of Open Access Journals (Sweden)

B. Avishan

2017-02-01

Full Text Available Presence of nanoscale bainitic ferrites and high carbon retained austenites that are stable at ambient temperature within the microstructures of super strong bainitic steels makes it possible to achieve exceptional strengths and ductility properties in these groups of nanostructured steels. This article aims to study the effect of the dislocation density variations during tensile testing in ambient temperature on deformation behavior of nanostructured low temperature bainitic steels. Results indicate that dislocation absorption from bainitic ferrite subunits by surrounding retained austenite reduces the work hardening and therefore increases the formability of bainitic ferrite during deformation, which in turn results in a suitable combination of strength and ductility.

Nonlinear Raman scattering behavior with Langmuir and sound waves coupling in a homogeneous plasma

International Nuclear Information System (INIS)

Bonnaud, G.; Pesme, D.; Pellat, R.

1990-01-01

By means of wave-coupling simulations, the typical nonlinear evolution of stimulated Raman scattering (SRS) is investigated in a homogeneous sub-quarter-critical plasma for present-day low laser irradiances and kilo-electron-volt electron temperatures. The decrease of the Langmuir energy observed after the SRS growth is found to be basically the result of the electrostatic decay instability (EDI) onset, which generates a high-amplitude ion-acoustic wave. The resulting strong modulation of the plasma density causes a conversion process that transforms the initial one-wave-vector Langmuir wave driven by SRS into a Bloch wave and induces SRS detuning and larger damping. The conditions involved herein have allowed isolation of these processes from the modulational instability; in addition, the Langmuir collapse is found not to occur owing to the high electron temperature

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.

Nonlinear Characterization of Half and Full Wavelength Power Ultrasonic Devices

Science.gov (United States)

Mathieson, Andrew; Cerisola, Niccolò; Cardoni, Andrea

It is well known that power ultrasonic devices whilst driven under elevated excitation levels exhibit nonlinear behaviors. If no attempt is made to understand and subsequently control these behaviors, these devices can exhibit poor performance or even suffer premature failure. This paper presents an experimental method for the dynamic characterization of a commercial ultrasonic transducer for bone cutting applications (Piezosurgery® Device) operated together with a variety of rod horns that are tuned to operate in a longitudinal mode of vibration. Near resonance responses, excited via a burst sine sweep method were used to identify nonlinear responses exhibited by the devices, while experimental modal analysis was performed to identify the modal parameters of the longitudinal modes of vibration of the assemblies between 0-80 kHz. This study tries to provide an understanding of the effects that geometry and material choices may have on the nonlinear behavior of a tuned device.

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

Science.gov (United States)

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

2016-12-02

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

Three religious rules of nonlinear physics

International Nuclear Information System (INIS)

Yankov, V.V.

1993-01-01

The theory of strong turbulence is a part of nonlinear physics. The three open-quotes religious rulesclose quotes of nonlinear physics present a heuristic viewpoint that can be used to qualitatively predict the evolution of nonlinear systems. These rules are as follows. (1) The basic results can be obtained from the conservation laws. If some kind of process is not forbidden by these laws, it generally occurs. If it doesn't this means that another conserved quantity imposing the constraint is being missed. (2) The universal law of open-quotes 20/80close quotes takes place: 20% of people drink 80% of beer. In other words, interesting processes usually take place in localized structures occupying a small share of volume. The localized structures interact weakly and therefore maintain their identity. For this reason they are universal and can be investigated. (3) The open-quotes general situationclose quotes is nonintegrable. The special case of exact solutions in integrable models represent a degenerate (nontypical) behavior. Particular exact solutions cannot be taken as representative solutions unless they are attractors. The presence of attractors simplifies the analysis and clarifies the situation. In plasma physics one deals with infinite-dimensional (PDE) systems distributed in space. The application of the religious rules 1 and 2 then leads to the following. If the conservation laws do not prohibit the development of singularities they do occur. If the singularities are prohibited, then stable localized structures take place. Solitons (or solitary waves) and vortices are examples of such stable structures. Wave collapse, wave-breaking, shock waves, magnetic reconnection and singularities in ideal Euler liquid are the examples of singularities. According to rule 3, exact solutions are very essential if they are attractors in some sense. Analysis of this problem is presented for solitons in nonintegrable wave systems and 2D vortices

Experimental verification of transient nonlinear acoustical holography.

Science.gov (United States)

Jing, Yun; Cannata, Jonathan; Wang, Tianren

2013-05-01

This paper presents an experimental study on nonlinear transient acoustical holography. The validity and effectiveness of a recently proposed nonlinear transient acoustical holography algorithm is evaluated in the presence of noise. The acoustic field measured on a post-focal plane of a high-intensity focused transducer is backward projected to reconstruct the pressure distributions on the focal and a pre-focal plane, which are shown to be in good agreement with the measurement. In contrast, the conventional linear holography produces erroneous results in this case where the nonlinearity involved is strong. Forward acoustic field projection was also carried out to further verify the algorithm.

Single nano-hole as a new effective nonlinear element for third-harmonic generation

Science.gov (United States)

Melentiev, P. N.; Konstantinova, T. V.; Afanasiev, A. E.; Kuzin, A. A.; Baturin, A. S.; Tausenev, A. V.; Konyaschenko, A. V.; Balykin, V. I.

2013-07-01

In this letter, we report on a particularly strong optical nonlinearity at the nanometer scale in aluminum. A strong optical nonlinearity of the third order was demonstrated on a single nanoslit. Single nanoslits of different aspect ratio were excited by a laser pulse (120 fs) at the wavelength 1.5 μm, leading predominantly to third-harmonic generation (THG). It has been shown that strong surface plasmon resonance in a nanoslit allows the realization of an effective nanolocalized source of third-harmonic radiation. We show also that a nanoslit in a metal film has a significant advantage in nonlinear processes over its Babinet complementary nanostructure (nanorod): the effective abstraction of heat in a film with a slit makes it possible to use much higher laser radiation intensities.

Acoustic characterization of a nonlinear vibroacoustic absorber at low frequencies and high sound levels

Science.gov (United States)

Chauvin, A.; Monteil, M.; Bellizzi, S.; Côte, R.; Herzog, Ph.; Pachebat, M.

2018-03-01

A nonlinear vibroacoustic absorber (Nonlinear Energy Sink: NES), involving a clamped thin membrane made in Latex, is assessed in the acoustic domain. This NES is here considered as an one-port acoustic system, analyzed at low frequencies and for increasing excitation levels. This dynamic and frequency range requires a suitable experimental technique, which is presented first. It involves a specific impedance tube able to deal with samples of sufficient size, and reaching high sound levels with a guaranteed linear response thank's to a specific acoustic source. The identification method presented here requires a single pressure measurement, and is calibrated from a set of known acoustic loads. The NES reflection coefficient is then estimated at increasing source levels, showing its strong level dependency. This is presented as a mean to understand energy dissipation. The results of the experimental tests are first compared to a nonlinear viscoelastic model of the membrane absorber. In a second step, a family of one degree of freedom models, treated as equivalent Helmholtz resonators is identified from the measurements, allowing a parametric description of the NES behavior over a wide range of levels.

Nonlinear interaction of waves in an inhomogeneous plasma

International Nuclear Information System (INIS)

Istomin, Ya.N.

1988-01-01

Nonlinear wave processes in a weakly inhomogeneous plasma are considered. A quasilinear equation is derived which takes into account the effect of the waves on resonance particles, provided that the inhomogeneity appreciably affects the nature of the resonance interaction. Three-wave interaction is investigated under the same conditions. As an example, the nonlinear interaction in a relativistic plasma moving along a strong curvilinear magnetic field is considered

Nonlinear instabilities induced by the F coil power amplifier at FTU: Modeling and control

International Nuclear Information System (INIS)

Zaccarian, L.; Boncagni, L.; Cascone, D.; Centioli, C.; Cerino, S.; Gravanti, F.; Iannone, F.; Mecocci, F.; Pangione, L.; Podda, S.; Vitale, V.; Vitelli, R.

2009-01-01

In this paper we focus on the instabilities caused by the nonlinear behavior of the F coil current amplifier at FTU. This behavior induces closed-loop instability of the horizontal position stabilizing loop whenever the requested current is below the circulating current level. In the paper we first illustrate a modeling phase where nonlinear dynamics are derived and identified to reproduce the open-loop responses measured by the F coil current amplifier. The derived model is shown to successfully reproduce the experimental behavior by direct comparison with experimental data. Based on this dynamic model, we then reproduce the closed-loop scenario of the experiment and show that the proposed nonlinear model successfully reproduces the nonlinear instabilities experienced in the experimental sessions. Given the simulation setup, we next propose a nonlinear control solution to this instability problem. The proposed solution is shown to recover stability in closed-loop simulations. Experimental tests are scheduled for the next experimental campaign after the FTU restart.

A Novel Rational Design Method for Laminated Composite Structures Exhibiting Complex Geometrically Nonlinear Buckling Behaviour

DEFF Research Database (Denmark)

Lindgaard, Esben; Lund, Erik

2012-01-01

This paper presents a novel FEM-based approach for fiber angle optimal design of laminated composite structures exhibiting complicated nonlinear buckling behavior, thus enabling design of lighter and more cost-effective structures. The approach accounts for the geometrically nonlinear behavior of...

Nonlinear surge motions of a ship in bi-chromatic following waves

Science.gov (United States)

Spyrou, Kostas J.; Themelis, Nikos; Kontolefas, Ioannis

2018-03-01

Unintended motions of a ship operating in steep and long following waves are investigated. A well-known such case is ;surf-riding; where a ship is carried forward by a single wave, an event invoking sometimes lateral instability and even capsize. The dynamics underlying this behavior has been clarified earlier for monochromatic waves. However, the unsteadiness of the phase space associated with ship behavior in a multichromatic sea, combined with the intrinsically strong system nonlinearity, pose new challenges. Here, current theory is extended to cover surging and surf-riding behavior in unidirectional bi-chromatic waves encountering a ship from the stern. Excitation is provided by two unidirectional harmonic wave components having their lengths comparable to the ship length and their frequencies in rational ratio. The techniques applied include (a) continuation analysis; (b) tracking of Lagrangian coherent structures in phase space, approximated through a finite-time Lyapunov exponents' calculation; and (c) large scale simulation. A profound feature of surf-riding in bi-chromatic waves is that it is turned oscillatory. Initially it appears as a frequency-locked motion, ruled by the harmonic wave component dominating the excitation. Transformations of oscillatory surf-riding are realized as the waves become steeper. In particular, heteroclinic tanglings are identified, governing abrupt transitions between qualitatively different motions. Chaotic transients, as well as long-term chaotic motions, exist near to these events. Some extraordinary patterns of ship motion are discovered. These include a counterintuitive low speed motion at very high wave excitation level; and a hybrid motion characterized by a wildly fluctuating velocity. Due to the quite generic nature of the core mathematical model of our investigation, the current results are believed to offer clues about the behavior of a class of nonlinear dynamical systems having in their modeling some analogy with

Algorithms For Integrating Nonlinear Differential Equations

Science.gov (United States)

Freed, A. D.; Walker, K. P.

1994-01-01

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

Nonlinear Cyclotron absorption of a hole doppleron in cadmium

Energy Technology Data Exchange (ETDEWEB)

Voloshin, I.F.; Bugal' ter, G.A.; Demikhovskii, V.Y.; Fisher, L.M.; Yudin, V.A.

1977-10-01

We investigated experimentally the nonlinear behavior of the impedance of a cadmium plate in the region of existence of the hole doppleron. It is shown theoretically that this phenomenon can be attributed to nonlinear cyclotron absorption of the wave in the metal. A theory of nonlinear cyclotron absorption of a hole doppleron in cadmium is constructed. The nonlinearity is due to the influence of the wave magnetic field H that alters the trajectories of the resonant electrons responsible for the cyclotron asorption. The Lorentz force connected with the field H modulates the particle velocity along the magnetic field at a characteristic frequency ..omega../sub 0/ proportional to the square root of the wave amplitude. The modulation of the longitudinal particle velocity leads to violation of the condition of their resonant interaction with the wave, as a result of which the absorption coefficient decreases. The nonlinearity is significant when the frequency ..omega../sub 0/ is large compared with the electron-collision frequency. A decrease of the cyclotron absorption changes radically the picture of the surface-impedance oscillations of the plate in the magnetic field. We studied in the experiment the influence of the temperature, of the angle of inclination of the magnetic field, and of the frequency on the nonlinear-effect threshold field that separates the regions of linear and nonlinear behavior of the sample impedance. The measurement results are in qualitative agreement with the conclusions of the theory.

Numerical study of propagation properties of surface plasmon polaritons in nonlinear media

KAUST Repository

Sagor, Rakibul Hasan; Ghulam Saber, Md.; Alsunaidi, Mohammad

2016-01-01

We present a time-domain algorithm for simulating nonlinear propagation of surface plasmon polaritons (SPPs) in chalcogenide glass. Due to the high non-linearity property and strong dispersion and confinement chalcogenide glasses are widely known

Propagation of flexural waves in inhomogeneous plates exhibiting hysteretic nonlinearity: Nonlinear acoustic black holes.

Science.gov (United States)

Gusev, Vitalyi E; Ni, Chenyin; Lomonosov, Alexey; Shen, Zhonghua

2015-08-01

Theory accounting for the influence of hysteretic nonlinearity of micro-inhomogeneous material on flexural wave in the plates of continuously varying thickness is developed. For the wedges with thickness increasing as a power law of distance from its edge strong modifications of the wave dynamics with propagation distance are predicted. It is found that nonlinear absorption progressively disappearing with diminishing wave amplitude leads to complete attenuation of acoustic waves in most of the wedges exhibiting black hole phenomenon. It is also demonstrated that black holes exist beyond the geometrical acoustic approximation. Applications include nondestructive evaluation of micro-inhomogeneous materials and vibrations damping. Copyright © 2015 Elsevier B.V. All rights reserved.

Pattern formation due to non-linear vortex diffusion

Science.gov (United States)

Wijngaarden, Rinke J.; Surdeanu, R.; Huijbregtse, J. M.; Rector, J. H.; Dam, B.; Einfeld, J.; Wördenweber, R.; Griessen, R.

Penetration of magnetic flux in YBa 2Cu 3O 7 superconducting thin films in an external magnetic field is visualized using a magneto-optic technique. A variety of flux patterns due to non-linear vortex diffusion is observed: (1) Roughening of the flux front with scaling exponents identical to those observed in burning paper including two distinct regimes where respectively spatial disorder and temporal disorder dominate. In the latter regime Kardar-Parisi-Zhang behavior is found. (2) Fractal penetration of flux with Hausdorff dimension depending on the critical current anisotropy. (3) Penetration as ‘flux-rivers’. (4) The occurrence of commensurate and incommensurate channels in films with anti-dots as predicted in numerical simulations by Reichhardt, Olson and Nori. It is shown that most of the observed behavior is related to the non-linear diffusion of vortices by comparison with simulations of the non-linear diffusion equation appropriate for vortices.

Nonlinear Optical Magnetism Revealed by Second-Harmonic Generation in Nanoantennas.

Science.gov (United States)

Kruk, Sergey S; Camacho-Morales, Rocio; Xu, Lei; Rahmani, Mohsen; Smirnova, Daria A; Wang, Lei; Tan, Hark Hoe; Jagadish, Chennupati; Neshev, Dragomir N; Kivshar, Yuri S

2017-06-14

Nonlinear effects at the nanoscale are usually associated with the enhancement of electric fields in plasmonic structures. Recently emerged new platform for nanophotonics based on high-index dielectric nanoparticles utilizes optically induced magnetic response via multipolar Mie resonances and provides novel opportunities for nanoscale nonlinear optics. Here, we observe strong second-harmonic generation from AlGaAs nanoantennas driven by both electric and magnetic resonances. We distinguish experimentally the contribution of electric and magnetic nonlinear response by analyzing the structure of polarization states of vector beams in the second-harmonic radiation. We control continuously the transition between electric and magnetic nonlinearities by tuning polarization of the optical pump. Our results provide a direct observation of nonlinear optical magnetism through selective excitation of multipolar nonlinear modes in nanoantennas.

Nonlinearity of the forward-backward correlation function in the model with string fusion

Science.gov (United States)

Vechernin, Vladimir

2017-12-01

The behavior of the forward-backward correlation functions and the corresponding correlation coefficients between multiplicities and transverse momenta of particles produced in high energy hadronic interactions is analyzed by analytical and MC calculations in the models with and without string fusion. The string fusion is taking into account in simplified form by introducing the lattice in the transverse plane. The results obtained with two alternative definitions of the forward-backward correlation coefficient are compared. It is shown that the nonlinearity of correlation functions increases with the width of observation windows, leading at small string density to a strong dependence of correlation coefficient value on the definition. The results of the modeling enable qualitatively to explain the experimentally observed features in the behavior of the correlation functions between multiplicities and mean transverse momenta at small and large multiplicities.

Analysis of nonlinear systems using ARMA [autoregressive moving average] models

International Nuclear Information System (INIS)

Hunter, N.F. Jr.

1990-01-01

While many vibration systems exhibit primarily linear behavior, a significant percentage of the systems encountered in vibration and model testing are mildly to severely nonlinear. Analysis methods for such nonlinear systems are not yet well developed and the response of such systems is not accurately predicted by linear models. Nonlinear ARMA (autoregressive moving average) models are one method for the analysis and response prediction of nonlinear vibratory systems. In this paper we review the background of linear and nonlinear ARMA models, and illustrate the application of these models to nonlinear vibration systems. We conclude by summarizing the advantages and disadvantages of ARMA models and emphasizing prospects for future development. 14 refs., 11 figs

Some non-linear physics in crystallographic structures

International Nuclear Information System (INIS)

Aubry, S.

1977-10-01

A summary of studies on simple but strongly nonlinear crystallographic models that make use of some methods in stochasticity is presented. Two one-dimensional models are described; one has been studied to understand some aspects of the nonlinear dynamics in crystals when close to the transition temperature, the other is for commensurability and incommensurability problems. Periodic orbits and the dynamics of a one-dimensional coupled double-well chain are considered, along with lattice locking and stochasticity

Image processing with a cellular nonlinear network

International Nuclear Information System (INIS)

Morfu, S.

2005-01-01

A cellular nonlinear network (CNN) based on uncoupled nonlinear oscillators is proposed for image processing purposes. It is shown theoretically and numerically that the contrast of an image loaded at the nodes of the CNN is strongly enhanced, even if this one is initially weak. An image inversion can be also obtained without reconfiguration of the network whereas a gray levels extraction can be performed with an additional threshold filtering. Lastly, an electronic implementation of this CNN is presented

Moderately nonlinear ultrasound propagation in blood-mimicking fluid.

Science.gov (United States)

Kharin, Nikolay A; Vince, D Geoffrey

2004-04-01

In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading.

Modern aspects of nonlinear convection and magnetic field in flow of thixotropic nanofluid over a nonlinear stretching sheet with variable thickness

Science.gov (United States)

Hayat, Tasawar; Qayyum, Sajid; Alsaedi, Ahmed; Ahmad, Bashir

2018-05-01

Main objective of present analysis is to study the magnetohydrodynamic (MHD) nonlinear convective flow of thixotropic nanofluid. Flow is due to nonlinear stretching surface with variable thickness. Nonlinear thermal radiation and heat generation/absorption are utilized in the energy expression. Convective conditions and zero mass flux at sheet are considered. Intention in present analysis is to develop a model for nanomaterial comprising Brownian motion and thermophoresis phenomena. Appropriate transformations are implemented for the conversion of partial differential systems into a sets of ordinary differential equations. The transformed expressions have been scrutinized through homotopic algorithm. Behavior of various sundry variables on velocity, temperature, nanoparticle concentration, skin friction coefficient and local Nusselt number are displayed through graphs. It is concluded that qualitative behaviors of temperature and thermal layer thickness are similar for radiation and temperature ratio variables. Moreover an enhancement in heat generation/absorption show rise to thermal field.

Roles of genes and Alu repeats in nonlinear correlations of HUMHBB DNA sequence

International Nuclear Information System (INIS)

Xiao Yi; Huang Yanzhao

2004-01-01

DNA sequences of different species and different portion of the DNA of the same species may have completely different correlation properties, but the origin of these correlations is still not very clear and is currently being investigated, especially in different particular cases. We report here a study of the DNA sequence of human beta globin region (HUMHBB) which has strong linear and nonlinear correlations. We studied the roles of two of the typical elements of DNA sequence, genes and Alu repeats, in the nonlinear correlations of HUMHBB. We find that there exist strong nonlinear correlations between the exons or introns in different genes and between the Alu repeats. They may be one of the major sources of the nonlinear correlations in HUMBHB

Introduction to Nonlinear and Global Optimization

NARCIS (Netherlands)

Hendrix, E.M.T.; Tóth, B.

2010-01-01

This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization

Rotating black string with nonlinear source

International Nuclear Information System (INIS)

Hendi, S. H.

2010-01-01

In this paper, we derive rotating black string solutions in the presence of two kinds of nonlinear electromagnetic fields, so-called Born-Infeld and power Maxwell invariant. Investigation of the solutions show that for the Born-Infeld black string the singularity is timelike and the asymptotic behavior of the solutions is anti-de Sitter, but for power Maxwell invariant solutions, depending on the values of nonlinearity parameter, the singularity may be timelike as well as spacelike and the solutions are not asymptotically anti-de Sitter for all values of the nonlinearity parameter. Next, we calculate the conserved quantities of the solutions by using the counterterm method, and find that these quantities do not depend on the nonlinearity parameter. We also compute the entropy, temperature, the angular velocity, the electric charge, and the electric potential of the solutions, in which the conserved and thermodynamics quantities satisfy the first law of thermodynamics.

Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schroedinger model

Energy Technology Data Exchange (ETDEWEB)

Kozlowski, K.K.

2010-12-15

Starting from the form factor expansion in finite volume, we derive the multidimensional generalization of the so-called Natte series for the zero-temperature, time and distance dependent reduced density matrix in the non-linear Schroedinger model. This representation allows one to read-off straightforwardly the long-time/large-distance asymptotic behavior of this correlator. Our method of analysis reduces the complexity of the computation of the asymptotic behavior of correlation functions in the so-called interacting integrable models, to the one appearing in free fermion equivalent models. We compute explicitly the first few terms appearing in the asymptotic expansion. Part of these terms stems from excitations lying away from the Fermi boundary, and hence go beyond what can be obtained by using the CFT/Luttinger liquid based predictions. (orig.)

Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices

International Nuclear Information System (INIS)

Testa, J.; Perez, J.; Jeffries, C.

1982-01-01

Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos

Critical behavior and phase transition of dilaton black holes with nonlinear electrodynamics

Energy Technology Data Exchange (ETDEWEB)

Dayyani, Z.; Dehghani, M.H.; Hajkhalili, S. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Sheykhi, A. [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of)

2018-02-15

In this paper, we take into account the dilaton black hole solutions of Einstein gravity in the presence of logarithmic and exponential forms of nonlinear electrodynamics. First of all, we consider the cosmological constant and nonlinear parameter as thermodynamic quantities which can vary. We obtain thermodynamic quantities of the system such as pressure, temperature and Gibbs free energy in an extended phase space. We complete the analogy of the nonlinear dilaton black holes with the Van der Waals liquid-gas system. We work in the canonical ensemble and hence we treat the charge of the black hole as an external fixed parameter. Moreover, we calculate the critical values of temperature, volume and pressure and show that they depend on the dilaton coupling constant as well as on the nonlinear parameter. We also investigate the critical exponents and find that they are universal and independent of the dilaton and nonlinear parameters, which is an expected result. Finally, we explore the phase transition of nonlinear dilaton black holes by studying the Gibbs free energy of the system. We find that in the case of T > T{sub c}, we have no phase transition. When T = T{sub c}, the system admits a second-order phase transition, while for T = T{sub f} < T{sub c} the system experiences a first-order transition. Interestingly, for T{sub f} < T < T{sub c} we observe a zeroth-order phase transition in the presence of a dilaton field. This novel zeroth-order phase transition occurs due to a finite jump in the Gibbs free energy which is generated by the dilaton-electromagnetic coupling constant, α, for a certain range of pressure. (orig.)

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

Science.gov (United States)

Andres, Jeanne Therese H; Cardoso, Silvana S S

2012-09-01

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

Correlations and discreteness in nonlinear QCD evolution

International Nuclear Information System (INIS)

Armesto, N.; Milhano, J.

2006-01-01

We consider modifications of the standard nonlinear QCD evolution in an attempt to account for some of the missing ingredients discussed recently, such as correlations, discreteness in gluon emission and Pomeron loops. The evolution is numerically performed using the Balitsky-Kovchegov equation on individual configurations defined by a given initial value of the saturation scale, for reduced rapidities y=(α s N c /π)Y<10. We consider the effects of averaging over configurations as a way to implement correlations, using three types of Gaussian averaging around a mean saturation scale. Further, we heuristically mimic discreteness in gluon emission by considering a modified evolution in which the tails of the gluon distributions are cut off. The approach to scaling and the behavior of the saturation scale with rapidity in these modified evolutions are studied and compared with the standard mean-field results. For the large but finite values of rapidity explored, no strong quantitative difference in scaling for transverse momenta around the saturation scale is observed. At larger transverse momenta, the influence of the modifications in the evolution seems most noticeable in the first steps of the evolution. No influence on the rapidity behavior of the saturation scale due to the averaging procedure is found. In the cutoff evolution the rapidity evolution of the saturation scale is slowed down and strongly depends on the value of the cutoff. Our results stress the need to go beyond simple modifications of evolution by developing proper theoretical tools that implement such recently discussed ingredients

Time series with tailored nonlinearities

Science.gov (United States)

Räth, C.; Laut, I.

2015-10-01

It is demonstrated how to generate time series with tailored nonlinearities by inducing well-defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncorrelated Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for, e.g., turbulence and financial data can thus be explained in terms of phase correlations.

Long-Term Aging Diagnosis of Rotor Steel Using Acoustic Nonlinearity

Energy Technology Data Exchange (ETDEWEB)

Kim, Chung Seok; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of); Park, Ik Keun; Hyun, Chang Yong [Seoul National University of Science and Tecnology, Seoul (Korea, Republic of)

2011-12-15

The long-term aging of ferritic 2.25CrMo steel was characterized using the acoustic nonlinear effect in order to apply to diagnose the degradation behavior of structural materials. We measured the acoustic nonlinearity parameter for each thermally aged specimen by the higher harmonic-generation technique. The acoustic nonlinearity parameter increased with aging time due to equilibrium M6C carbide precipitation, and has a favorable linear relation with Rockwell hardness. This study suggests that acoustic nonlinearity testing may be applicable to diagnostics on strength degradation in rotor steels.

Effects of Analog-to-Digital Converter Nonlinearities on Radar Range-Doppler Maps

Energy Technology Data Exchange (ETDEWEB)

Doerry, Armin Walter [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Dubbert, Dale F. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Tise, Bertice L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2014-07-01

Radar operation, particularly Ground Moving Target Indicator (GMTI) radar modes, are very sensitive to anomalous effects of system nonlinearities. These throw off harmonic spurs that are sometimes detected as false alarms. One significant source of nonlinear behavior is the Analog to Digital Converter (ADC). One measure of its undesired nonlinearity is its Integral Nonlinearity (INL) specification. We examine in this report the relationship of INL to GMTI performance.

Single nano-hole as a new effective nonlinear element for third-harmonic generation

International Nuclear Information System (INIS)

Melentiev, P N; Konstantinova, T V; Afanasiev, A E; Balykin, V I; Kuzin, A A; Baturin, A S; Tausenev, A V; Konyaschenko, A V

2013-01-01

In this letter, we report on a particularly strong optical nonlinearity at the nanometer scale in aluminum. A strong optical nonlinearity of the third order was demonstrated on a single nanoslit. Single nanoslits of different aspect ratio were excited by a laser pulse (120 fs) at the wavelength 1.5 μm, leading predominantly to third-harmonic generation (THG). It has been shown that strong surface plasmon resonance in a nanoslit allows the realization of an effective nanolocalized source of third-harmonic radiation. We show also that a nanoslit in a metal film has a significant advantage in nonlinear processes over its Babinet complementary nanostructure (nanorod): the effective abstraction of heat in a film with a slit makes it possible to use much higher laser radiation intensities. (letter)

Efficient excitation of nonlinear phonons via chirped pulses: Induced structural phase transitions

Science.gov (United States)

Itin, A. P.; Katsnelson, M. I.

2018-05-01

Nonlinear phononics play important role in strong laser-solid interactions. We discuss a dynamical protocol for efficient phonon excitation, considering recent inspiring proposals: inducing ferroelectricity in paraelectric perovskites, and inducing structural deformations in cuprates [Subedi et al., Phys. Rev. B 89, 220301(R) (2014), 10.1103/PhysRevB.89.220301; Phys. Rev. B 95, 134113 (2017), 10.1103/PhysRevB.95.134113]. High-frequency phonon modes are driven by midinfrared pulses, and coupled to lower-frequency modes those indirect excitations cause structural deformations. We study in more detail the case of KTaO3 without strain, where it was not possible to excite the needed low-frequency phonon mode by resonant driving of the higher frequency one. Behavior of the system is explained using a reduced model of coupled driven nonlinear oscillators. We find a dynamical mechanism which prevents effective excitation at resonance driving. To induce ferroelectricity, we employ driving with sweeping frequency, realizing so-called capture into resonance. The method can be applied to many other related systems.

Elevated nonlinearity as an indicator of shifts in the dynamics of populations under stress.

Science.gov (United States)

Dakos, Vasilis; Glaser, Sarah M; Hsieh, Chih-Hao; Sugihara, George

2017-03-01

Populations occasionally experience abrupt changes, such as local extinctions, strong declines in abundance or transitions from stable dynamics to strongly irregular fluctuations. Although most of these changes have important ecological and at times economic implications, they remain notoriously difficult to detect in advance. Here, we study changes in the stability of populations under stress across a variety of transitions. Using a Ricker-type model, we simulate shifts from stable point equilibrium dynamics to cyclic and irregular boom-bust oscillations as well as abrupt shifts between alternative attractors. Our aim is to infer the loss of population stability before such shifts based on changes in nonlinearity of population dynamics. We measure nonlinearity by comparing forecast performance between linear and nonlinear models fitted on reconstructed attractors directly from observed time series. We compare nonlinearity to other suggested leading indicators of instability (variance and autocorrelation). We find that nonlinearity and variance increase in a similar way prior to the shifts. By contrast, autocorrelation is strongly affected by oscillations. Finally, we test these theoretical patterns in datasets of fisheries populations. Our results suggest that elevated nonlinearity could be used as an additional indicator to infer changes in the dynamics of populations under stress. © 2017 The Author(s).

Report of workshop on X-ray and nonlinear optics

International Nuclear Information System (INIS)

Nasu, Keiichiro; Namikawa, Kazumichi

1994-07-01

As synchrotron radiation has advanced to high luminance, the possibility of realizing coherent light has heightened, and the nonlinear optical phenomena in soft and hard X-ray regions have become the object of the concern of X-ray researchers, and also the researchers in the fields of quantum electronics and optical properties. This workshop was held on September 21 and 22, 1993 at National Laboratory for High energy Physics. Lectures were given on the generation of second harmonic of X-ray by utilizing dynamic diffraction, X-ray parametric scattering induced by strong laser beam, the resonance enhancement of X-ray inelastic scattering induced by strong visible light, Raman scattering in soft X-ray region, the control of nonlinear optical processes by strong external field; the experiments, though they are fundamental, they have not been carried out; undulator radiation X-ray and X-ray free electron laser, the improvement of the coherence of X-ray laser, superradiance of Frenkel excitor system and the measurement of superhigh speed pulses in X-ray region. The comment from the standpoint of the research on nonlinear optics was given. In this document, the gists of these lectures are collected. (K.I.)

Report of workshop on X-ray and nonlinear optics

Energy Technology Data Exchange (ETDEWEB)

Nasu, Keiichiro; Namikawa, Kazumichi [eds.

1994-07-01

As synchrotron radiation has advanced to high luminance, the possibility of realizing coherent light has heightened, and the nonlinear optical phenomena in soft and hard X-ray regions have become the object of the concern of X-ray researchers, and also the researchers in the fields of quantum electronics and optical properties. This workshop was held on September 21 and 22, 1993 at National Laboratory for High energy Physics. Lectures were given on the generation of second harmonic of X-ray by utilizing dynamic diffraction, X-ray parametric scattering induced by strong laser beam, the resonance enhancement of X-ray inelastic scattering induced by strong visible light, Raman scattering in soft X-ray region, the control of nonlinear optical processes by strong external field; the experiments, though they are fundamental, they have not been carried out; undulator radiation X-ray and X-ray free electron laser, the improvement of the coherence of X-ray laser, superradiance of Frenkel excitor system and the measurement of superhigh speed pulses in X-ray region. The comment from the standpoint of the research on nonlinear optics was given. In this document, the gists of these lectures are collected. (K.I.).

On the Nonlinear Dynamics of a Doubly Clamped Microbeam near Primary Resonance

KAUST Repository

Jaber, Nizar; Masri, Karim M.; Younis, Mohammad I.

2017-01-01

This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency-response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of DC bias revealing hardening, mixed, and softening behavior of the microbeam. A multi-mode Galerkin model combined with a shooting technique are implemented to generate the frequency response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show good agreement with the experimental data.

On the Nonlinear Dynamics of a Doubly Clamped Microbeam near Primary Resonance

KAUST Repository

Jaber, Nizar

2017-04-07

This work aims to investigate theoretically and experimentally various nonlinear dynamic behaviors of a doubly clamped microbeam near its primary resonance. Mainly, we investigate the transition behavior from hardening, mixed, and then softening behavior. We show in a single frequency-response curve, under a constant voltage load, the transition from hardening to softening behavior demonstrating the dominance of the quadratic electrostatic nonlinearity over the cubic geometric nonlinearity of the beam as the motion amplitudes becomes large, which may lead eventually to dynamic pull-in. The microbeam is fabricated using polyimide as a structural layer coated with nickel from top and chromium and gold layers from the bottom. Frequency sweep tests are conducted for different values of DC bias revealing hardening, mixed, and softening behavior of the microbeam. A multi-mode Galerkin model combined with a shooting technique are implemented to generate the frequency response curves and to analyze the stability of the periodic motions using the Floquet theory. The simulated curves show good agreement with the experimental data.

Nonlinear Modeling by Assembling Piecewise Linear Models

Science.gov (United States)

Yao, Weigang; Liou, Meng-Sing

2013-01-01

To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.

Computational mechanics of nonlinear response of shells

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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

Non-linear extension of FFT-based methods accelerated by conjugate gradients to evaluate the mechanical behavior of composite materials

International Nuclear Information System (INIS)

Gelebart, Lionel; Mondon-Cancel, Romain

2013-01-01

FFT-based methods are used to solve the problem of a heterogeneous unit-cell submitted to periodic boundary conditions, which is of a great interest in the context of numerical homogenization. Recently (in 2010), Brisard and Zeman proposed simultaneously to use Conjugate Gradient based solvers in order to improve the convergence properties (when compared to the basic scheme, proposed initially in 1994). The purpose of the paper is to extend this idea to the case of non-linear behaviors. The proposed method is based on a Newton-Raphson algorithm and can be applied to various kinds of behaviors (time dependant or independent, with or without internal variables) through a conventional integration procedure as used in finite element codes. It must be pointed out that this approach is fundamentally different from the traditional FFT-based approaches which rely on a fixed-point algorithm (e.g. basic scheme, Eyre and Milton accelerated scheme, Augmented Lagrangian scheme, etc.). The method is compared to the basic scheme on the basis of a simple application (a linear elastic spherical inclusion within a non-linear elastic matrix): a low sensitivity to the reference material and an improved efficiency, for a soft or a stiff inclusion, are observed. At first proposed for a prescribed macroscopic strain, the method is then extended to mixed loadings. (authors)

Nonlinear Vibration and Mode Shapes of FG Cylindrical Shells

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Saeed Mahmoudkhani

Full Text Available Abstract The nonlinear vibration and normal mode shapes of FG cylindrical shells are investigated using an efficient analytical method. The equations of motion of the shell are based on the Donnell’s non-linear shallow-shell, and the material is assumed to be gradually changed across the thickness according to the simple power law. The solution is provided by first discretizing the equations of motion using the multi-mode Galerkin’s method. The nonlinear normal mode of the system is then extracted using the invariant manifold approach and employed to decouple the discretized equations. The homotopy analysis method is finally used to determine the nonlinear frequency. Numerical results are presented for the backbone curves of FG cylindrical shells, nonlinear mode shapes and also the nonlinear invariant modal surfaces. The volume fraction index and the geometric properties of the shell are found to be effective on the type of nonlinear behavior and also the nonlinear mode shapes of the shell. The circumferential half-wave numbers of the nonlinear mode shapes are found to change with time especially in a thinner cylinder.

Nonlinear dynamic model for skidding behavior of angular contact ball bearings

Science.gov (United States)

Han, Qinkai; Chu, Fulei

2015-10-01

A three-dimensional nonlinear dynamic model is proposed to predict the skidding behavior of angular contact ball bearings under combined load condition. The centrifugal and gyroscopic effects induced by ball rotation and revolution, Hertz contact between the ball and inner/outer races, discontinuous contact between the ball and cage and elastohydrodynamic lubrication are considered in the model. Through comparisons with the tested results of the reference, the dynamic model is verified. Based upon these, variations of ball slipping speed with time and space are discussed for the bearing under combined load condition. It is shown that radial load leads to the fluctuations in the slipping velocity of the ball contacting with inner/outer races, especially for the ball in load-decreasing regions. Adding the radial load would significantly increase the amplitude and range of slipping velocity, indicating that the skidding becomes more serious. As the ball still withstands contact load in the load-decreasing region, large slipping velocity would increase the temperature of both bearing and lubricant oil, intensify the wear and then might shorten the bearing service life. Therefore, the radial load should be considered carefully in the design and monitoring of rotating machinery.

Nonlinear dynamics of the relativistic standard map

International Nuclear Information System (INIS)

Nomura, Y.; Ichikawa, Y.H.; Horton, W.

1991-01-01

Heating and acceleration of charged particles by RF fields have been extensively investigated by the standard map (ST). Thus, it is natural to pose the question asking how the relativistic effects change the nonlinear dynamical behavior described by the classical ST map. The authors show that the speed of light limits the rate of advance of the phase in the relativistic standard map (RST) and introduces KAM surfaces persisting in the high momentum region. The RST map is a two parameter (k, β = ω/kc) family of dynamics reducing to the ST map when β → 0. For β ≠ 0 the relativity suppresses the onset of stochasticity. Chernikov et al. has also reported this effect. They have carried out extensive studies of nonlinear dynamics of the RST map and found very intricate structure of mixing of the higher order periodic orbits and chaotic orbits. They have shown that no matter how its gets chaotic the symmetry properties of the RST map determines its nonlinear dynamical behavior. 1 ref

The numerical dynamic for highly nonlinear partial differential equations

Science.gov (United States)

Lafon, A.; Yee, H. C.

1992-01-01

Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

Transverse effects in nonlinear optics: Toward the photon superfluid

Science.gov (United States)

McCormick, Colin Fraser

Nonlinear optics displays a wealth of transverse effects. These effects are particularly rich in the presence of an optical cavity. Many considerations suggest that in a Kerr nonlinear cavity a new state of light known as a "photon superfluid" can form, with strong analogies to atomic superfluids. The conditions for the formation of the photon superfluid include requirements on the cavity, input light fields and the nonlinear medium as well as various timescales. The most favorable candidate nonlinear medium for observing the photon super-fluid is an atomic vapor. With a strong and fast Kerr effect, atomic vapors also have the advantage of a Kerr coefficient that is tunable in both magnitude and sign. A series of z-scan experiments in far-detuned atomic rubidium vapor is reported, measuring the Kerr coefficient and determining its functional dependence on detuning to be that of a Doppler-broadened two-level model with adiabatic following of the electric field by the atom pseudomoment. Saturation effects are found to be important. Z-scan measurements for detunings within the Doppler profile are shown to agree well with numerical simulations based on the Doppler-broadened model. Agreement between absorptive and refractive non-linear coefficients is evidence of the Kramers-Kronig relations at work, even in this nonlinear system. The formation of the photon superfluid is discussed and the calculation of a new process, nearly collinear four-wave mixing, is presented. This process is essentially an inverse beam filamentation that is likely to be the underlying physical mechanism for transverse cooling and condensation of photons in a nonlinear optical cavity. Nearly collinear four-wave mixing may also be related to phenomena in general nonlinear physics, including modulation instability and Fermi-Pasta-Ulam recurrence.