Exact bright and dark spatial soliton solutions in saturable nonlinear media

International Nuclear Information System (INIS)

Calvo, Gabriel F.; Belmonte-Beitia, Juan; Perez-Garcia, Victor M.

2009-01-01

We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schroedinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.

Staggered and short-period solutions of the saturable discrete nonlinear Schrodinger equation

DEFF Research Database (Denmark)

Khare, A.; Rasmussen, K.O.; Samuelsen, Mogens Rugholm

2009-01-01

We point out that the nonlinear Schrodinger lattice with a saturable nonlinearity also admits staggered periodic aswell as localized pulse-like solutions. Further, the same model also admits solutions with a short period. We examine the stability of these solutions and find that the staggered as ...

An Analysis and Design for Nonlinear Quadratic Systems Subject to Nested Saturation

Directory of Open Access Journals (Sweden)

Minsong Zhang

2013-01-01

Full Text Available This paper considers the stability problem for nonlinear quadratic systems with nested saturation input. The interesting treatment method proposed to nested saturation here is put into use a well-established linear differential control tool. And the new conclusions include the existing conclusion on this issue and have less conservatism than before. Simulation example illustrates the effectiveness of the established methodologies.

Toroidal effects on the non-linearly saturated m = 1 island in tokamaks

International Nuclear Information System (INIS)

Avinash, K.; Haas, F.A.; Thyagaraja, A.

1990-01-01

This paper investigates the influence of toroidal effects (due to the coupling of various poloidal harmonics) on the non-linear saturation of the m=1 island. Bounds are obtained relating the aspect ratio, the shear at the q=1 surface and the saturated island width. Provided these bounds are satisfied, then we find that the cylindrical m=1 island theory is valid for toroidal geometry. (author)

Double shock dynamics induced by the saturation of defocusing nonlinearities

KAUST Repository

Crosta, Matteo

2012-01-01

We show that the saturation of defocusing nonlinearities leads to qualitative changes in the onset of wave breaking, determining double shock formation whose regularization occurs in terms of antidark solitons. In a given material, the crossover between different regimes can be controlled by changing the input intensity. © 2012 Optical Society of America.

Nonlinear saturation of the slab ITG instability and zonal flow generation with fully kinetic ions

Science.gov (United States)

Miecnikowski, Matthew T.; Sturdevant, Benjamin J.; Chen, Yang; Parker, Scott E.

2018-05-01

Fully kinetic turbulence models are of interest for their potential to validate or replace gyrokinetic models in plasma regimes where the gyrokinetic expansion parameters are marginal. Here, we demonstrate fully kinetic ion capability by simulating the growth and nonlinear saturation of the ion-temperature-gradient instability in shearless slab geometry assuming adiabatic electrons and including zonal flow dynamics. The ion trajectories are integrated using the Lorentz force, and the cyclotron motion is fully resolved. Linear growth and nonlinear saturation characteristics show excellent agreement with analogous gyrokinetic simulations across a wide range of parameters. The fully kinetic simulation accurately reproduces the nonlinearly generated zonal flow. This work demonstrates nonlinear capability, resolution of weak gradient drive, and zonal flow physics, which are critical aspects of modeling plasma turbulence with full ion dynamics.

Nonlinear saturated states of the magnetic-curvature-driven Rayleigh-Taylor instability in three dimensions

International Nuclear Information System (INIS)

Das, Amita; Sen, Abhijit; Kaw, Predhiman; Benkadda, S.; Beyer, Peter

2005-01-01

Three-dimensional electromagnetic fluid simulations of the magnetic-curvature-driven Rayleigh-Taylor instability are presented. Issues related to the existence of nonlinear saturated states and the nature of the temporal evolution to such states from random initial conditions are addressed. It is found that nonlinear saturated states arising from generation of zonal shear flows continue to exist in certain parametric domains but their spectrum and spatial characteristics have important differences from earlier two-dimensional results reported in Phys. Plasmas 4, 1018 (1997) and Phys. Plasmas 8, 5104 (2001). In particular, the three-dimensional nonlinear states possess a significant power level in short scales and the spatial structures of the potential and density fluctuations appear not to develop any functional correlations. Electromagnetic effects are found to inhibit the formation of zonal flows and thereby to considerably restrict the parametric domain of nonlinear stabilization. The role of finite k parallel and the contribution of the unstable drift wave branch are also discussed and delineated through a number of simulation studies carried out in special simplified limits

Adaptive fuzzy control of a class of nonaffine nonlinear system with input saturation based on passivity theorem.

Science.gov (United States)

Molavi, Ali; Jalali, Aliakbar; Ghasemi Naraghi, Mahdi

2017-07-01

In this paper, based on the passivity theorem, an adaptive fuzzy controller is designed for a class of unknown nonaffine nonlinear systems with arbitrary relative degree and saturation input nonlinearity to track the desired trajectory. The system equations are in normal form and its unforced dynamic may be unstable. As relative degree one is a structural obstacle in system passivation approach, in this paper, backstepping method is used to circumvent this obstacle and passivate the system step by step. Because of the existence of uncertainty and disturbance in the system, exact passivation and reference tracking cannot be tackled, so the approximate passivation or passivation with respect to a set is obtained to hold the tracking error in a neighborhood around zero. Furthermore, in order to overcome the non-smoothness of the saturation input nonlinearity, a parametric smooth nonlinear function with arbitrary approximation error is used to approximate the input saturation. Finally, the simulation results for the theoretical and practical examples are given to validate the proposed controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear crack mechanics

International Nuclear Information System (INIS)

Khoroshun, L.P.

1995-01-01

The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero

Nonlinear saturation of non-resonant internal instabilities in a straight spheromak

International Nuclear Information System (INIS)

Park, W.; Jardin, S.C.

1982-04-01

An initial value numerical solution of the time dependent nonlinear ideal magnetohydrodynamic equations demonstrates that spheromak equilibria which are linearly unstable to nonresonant helical internal perturbations saturate at low amplitude without developing singularities. These instabilities thus represent the transition from an axisymmetric to a non-axisymmetric equilibrium state, caused by a peaking of the current density

Stable one-dimensional periodic waves in Kerr-type saturable and quadratic nonlinear media

International Nuclear Information System (INIS)

Kartashov, Yaroslav V; Egorov, Alexey A; Vysloukh, Victor A; Torner, Lluis

2004-01-01

We review the latest progress and properties of the families of bright and dark one-dimensional periodic waves propagating in saturable Kerr-type and quadratic nonlinear media. We show how saturation of the nonlinear response results in the appearance of stability (instability) bands in a focusing (defocusing) medium, which is in sharp contrast with the properties of periodic waves in Kerr media. One of the key results discovered is the stabilization of multicolour periodic waves in quadratic media. In particular, dark-type waves are shown to be metastable, while bright-type waves are completely stable in a broad range of energy flows and material parameters. This yields the first known example of completely stable periodic wave patterns propagating in conservative uniform media supporting bright solitons. Such results open the way to the experimental observation of the corresponding self-sustained periodic wave patterns

Semiconductor saturable absorbers for ultrafast terahertz signals

DEFF Research Database (Denmark)

Hoffmann, Matthias C.; Turchinovich, Dmitry

2010-01-01

states, due to conduction band onparabolicity and scattering into satellite valleys in strong THz fields. Saturable absorber parameters, such as linear and nonsaturable transmission, and saturation fluence, are extracted by fits to a classic saturable absorber model. Further, we observe THz pulse......We demonstrate saturable absorber behavior of n-type semiconductors GaAs, GaP, and Ge in the terahertz THz frequency range at room temperature using nonlinear THz spectroscopy. The saturation mechanism is based on a decrease in electron conductivity of semiconductors at high electron momentum...

Saturation of a toroidal Alfvén eigenmode due to enhanced damping of nonlinear sidebands

Science.gov (United States)

Todo, Y.; Berk, H. L.; Breizman, B. N.

2012-09-01

This paper examines nonlinear magneto-hydrodynamic effects on the energetic particle driven toroidal Alfvén eigenmode (TAE) for lower dissipation coefficients and with higher numerical resolution than in the previous simulations (Todo et al 2010 Nucl. Fusion 50 084016). The investigation is focused on a TAE mode with toroidal mode number n = 4. It is demonstrated that the mechanism of mode saturation involves generation of zonal (n = 0) and higher-n (n ⩾ 8) sidebands, and that the sidebands effectively increase the mode damping rate via continuum damping. The n = 0 sideband includes the zonal flow peaks at the TAE gap locations. It is also found that the n = 0 poloidal flow represents a balance between the nonlinear driving force from the n = 4 components and the equilibrium plasma response to the n = 0 fluctuations. The spatial profile of the n = 8 sideband peaks at the n = 8 Alfvén continuum, indicating enhanced dissipation due to continuum damping.

Classical Mechanics as Nonlinear Quantum Mechanics

International Nuclear Information System (INIS)

Nikolic, Hrvoje

2007-01-01

All measurable predictions of classical mechanics can be reproduced from a quantum-like interpretation of a nonlinear Schroedinger equation. The key observation leading to classical physics is the fact that a wave function that satisfies a linear equation is real and positive, rather than complex. This has profound implications on the role of the Bohmian classical-like interpretation of linear quantum mechanics, as well as on the possibilities to find a consistent interpretation of arbitrary nonlinear generalizations of quantum mechanics

Comments on ''The non-linear saturation of a magnetic island'' by J. Norris

International Nuclear Information System (INIS)

Thyagaraja, A.

1990-01-01

Recent results derived on non-linear saturation of tearing modes (Norris, J., Plasma Phys. Contr. Fusion, 1989, Vol. 31, 699) are examined in relation to previously published literature. It is explicitly demonstrated that they are at variance in several important respects with those due to previous workers in this area. (author)

Nonlinear saturation of E x B instability in a plasma slab

International Nuclear Information System (INIS)

Alfsen, K.H.; Holter, Oe.

1984-09-01

The saturation of the E bar x B bar instability is investigated in the nonlinear regime. The governing equations are studied analytically and numerically by using a spectral method with mode truncation. The nonlinear stabilization is due to modifications of the background density- and potential profiles. In the time asymptotic limit a stationary solution, which is independent of the initial conditions is obtained. The asymptotic state is characterized by a splitting of the interacting modes into two almost non-interacting groups, where the modes with even mode number sum; i.e. the modes driven by the linearly most unstable mode, is found to dominate the system. For this group fixed point calculations are performed analytically with six interacting modes. Comparison with numerical calculations indicates excellent agreement far into the unstable region. (Auth.)

SATURATION OF MAGNETOROTATIONAL INSTABILITY THROUGH MAGNETIC FIELD GENERATION

International Nuclear Information System (INIS)

Ebrahimi, F.; Prager, S. C.; Schnack, D. D.

2009-01-01

The saturation mechanism of magnetorotational instability (MRI) is examined through analytical quasi-linear theory and through nonlinear computation of a single mode in a rotating disk. We find that large-scale magnetic field is generated through the α-effect (the correlated product of velocity and magnetic field fluctuations) and causes the MRI mode to saturate. If the large-scale plasma flow is allowed to evolve, the mode can also saturate through its flow relaxation. In astrophysical plasmas, for which the flow cannot relax because of gravitational constraints, the mode saturates through field generation only.

Asymptotic stability of discrete-time systems with time-varying delay subject to saturation nonlinearities

International Nuclear Information System (INIS)

Chen, S.-F.

2009-01-01

The asymptotic stability problem for discrete-time systems with time-varying delay subject to saturation nonlinearities is addressed in this paper. In terms of linear matrix inequalities (LMIs), a delay-dependent sufficient condition is derived to ensure the asymptotic stability. A numerical example is given to demonstrate the theoretical results.

Ultrahigh precision nonlinear reflectivity measurement system for saturable absorber mirrors with self-referenced fluence characterization.

Science.gov (United States)

Orsila, Lasse; Härkönen, Antti; Hyyti, Janne; Guina, Mircea; Steinmeyer, Günter

2014-08-01

Measurement of nonlinear optical reflectivity of saturable absorber devices is discussed. A setup is described that enables absolute accuracy of reflectivity measurements better than 0.3%. A repeatability within 0.02% is shown for saturable absorbers with few-percent modulation depth. The setup incorporates an in situ knife-edge characterization of beam diameters, making absolute reflectivity estimations and determination of saturation fluences significantly more reliable. Additionally, several measures are discussed to substantially improve the reliability of the reflectivity measurements. At its core, the scheme exploits the limits of state-of-the-art digital lock-in technology but also greatly benefits from a fiber-based master-oscillator power-amplifier source, the use of an integrating sphere, and simultaneous comparison with a linear reflectivity standard.

Nonlinear hybrid simulation of toroidicity-induced alfven eigenmode

International Nuclear Information System (INIS)

Fu, G.Y.; Park, W.

1994-11-01

Gyrokinetic/Magnetohydrodynamics hybrid simulations have been carried out using MH3D-K code to study the nonlinear saturation of the toroidicity-induced Alfven eigenmode driven by energetic particles in a tokamak plasma. It is shown that the wave particle trapping is the nonlinear saturation mechanism for the parameters considered. The corresponding density profile flattening of hot particles is observed. The saturation amplitude is proportional to the square of linear growth rate. In addition to TAE modes, a new n = 1, m = 0 global Alfven eigenmode is shown to be excited by the energetic particles

The Effects of NaCl Concentration and Confining Pressure on Mechanical and Acoustic Behaviors of Brine-Saturated Sandstone

Directory of Open Access Journals (Sweden)

Yan-Hua Huang

2018-02-01

Full Text Available To better understand the mechanical behavior of rock with brine saturation, conventional triaxial experiments were carried out on sandstone for a range of confining pressures (0–60 MPa and NaCl concentrations (0–30%. As the confining pressure and NaCl concentration increased, the triaxial compressive strength, crack damage threshold, Young’s modulus, cohesion, and internal friction angle all increased. Real-time ultrasonic wave and acoustic emission (AE techniques were used to obtain the relationship between acoustic behavior and stress level during the whole triaxial compression process. During the whole deformation process, the evolution of P-wave velocity and accumulated AE count could be divided into four phases. The microstructural characteristics of brine-saturated sandstone, before and after loading, indicated that the strength enhancement mechanism may be attributed to an increase in inter-particle friction resulting from salt crystallisation around the points of contact. The angle of friction increased by more than 86% at maximum NaCl concentration compared to that for distilled water. The NaCl deposition in the pore space resulted in nonlinear strength increases for the brine-saturated sandstone specimens with increasing salinity. The present study is expected to improve the knowledge of the strength and failure mechanisms of sedimentary rock in deep saline aquifers.

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

International Nuclear Information System (INIS)

Liu Wan-Hai; Jiang Hong-Bin; Ma Wen-Fang; Wang Xiang

2016-01-01

The classical planar Richtmyer–Meshkov instability (RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order, and then according to definition of nonlinear saturation amplitude (NSA) in Rayleigh–Taylor instability (RTI), the NSA in planar RMI is obtained explicitly. It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface, while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength. Without marginal influence of the initial amplitude, the NSA increases linearly with wavelength. The NSA normalized by the wavelength in planar RMI is about 0.11, larger than that corresponding to RTI. (paper)

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...

Effect of desaturation and re-saturation on shale in underground galleries

International Nuclear Information System (INIS)

Pham, Q.T.

2006-03-01

The aim of this thesis is to characterize by experimental and numerical approaches the hydric, mechanical and hydro-mechanical effects due to the desaturation and re-saturation of the Eastern argillite, host rock of the Bure site, future underground radioactive waste disposal facility. Experimental and numerical approaches for the characterization of hydric transfers in argilites are presented. A simple identification method is proposed which uses the determination of the linearized hydric diffusivity from weight measurements performed on samples (thin tubes and plates) submitted to humidity steps according to a desaturation-re-saturation cycle. The hydric transfer is nonlinear. In order to interpret this phenomenon, a non-linear numerical model is established which takes into account the physical phenomena (hydraulic conduction, vapor diffusion, phase change..). The evolution of the physical and mechanical behaviour of the argillaceous rock with respect to the imposed humidity is then analyzed according to a desaturation-re-saturation cycle by successive steps. The hydric deformation, the velocity of ultrasonic waves propagation, the elastic properties, the rupture characteristics and the delayed phenomena depend on the hydric state of the material. The desaturation and re-saturation influence on a scale model of tunnel is analyzed. Thick tubes parallel or perpendicular to the stratification are used to show up the anisotropy of the rock. These tubes are submitted to hydric loads by blowing air with variable hygrometry through their center hole. A nonlinear poro-elastic model is used to interpret the anisotropic hydro-mechanical phenomena observed. It is shown that hydric loads can lead to the rupture of test samples which follow the anisotropic directions of the rock and which can be interpreted by the hydro-mechanical model as a violation of a rupture criterion in total pulling stress. Finally, numerical calculations for the phenomena generated by desaturation

Single-ion nonlinear mechanical oscillator

International Nuclear Information System (INIS)

Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.

2010-01-01

We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

Nonlinear phenomena in collisionless plasmas. Progress report, September 1, 1974--August 31, 1975

International Nuclear Information System (INIS)

Aamodt, R.E.

1975-01-01

The nonlinear evolution of unstable collective modes common to conventional mirror machines is being analyzed in order to evaluate measurable saturation amplitudes, spectrum properties, and concomitant particle loss rates. The nonlinear dispersion relation for the classic drift-cone mode, including nonlinear E x B VECTOR convective cells is presently being evaluated to find its self-saturation properties. Large amplitude rf heating mechanisms, localized mode nonlinearities, and propagation and amplification of transverse modes in collisionless inhomogeneous plasmas have also been partially evaluated. (U.S.)

Suppression of mode-beating in a saturated hole-coupled FEL oscillator

International Nuclear Information System (INIS)

Krishnagopal, S.; Xie, M.; Kim, K.J.

1992-08-01

In a hole-coupled resonator, either empty or loaded with a linear FEL gain medium, the phenomenon of mode-degeneracy and mode-beating have been studied. When the magnitudes of the eigenvalues, derived from a linear analysis, are equal for two or more dominant eigenmodes, the system cannot achieve a stable beam-profile. We investigate this phenomenon when a saturated FEL is present within the cavity, thus introducing non-linearity. We use a three-dimensional FEL oscillator code, based on the amplifier code TDA, and show that mode-beating is completely suppressed in the nonlinear saturated regime. We suggest a simple, qualitative model for the mechanism responsible for this suppression

Vibrational mechanics nonlinear dynamic effects, general approach, applications

CERN Document Server

Blekhman, Iliya I

2000-01-01

This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat

THE SATURATION OF SASI BY PARASITIC INSTABILITIES

International Nuclear Information System (INIS)

Guilet, Jerome; Sato, Jun'ichi; Foglizzo, Thierry

2010-01-01

The standing accretion shock instability (SASI) is commonly believed to be responsible for large amplitude dipolar oscillations of the stalled shock during core collapse, potentially leading to an asymmetric supernovae explosion. The degree of asymmetry depends on the amplitude of SASI, but the nonlinear saturation mechanism has never been elucidated. We investigate the role of parasitic instabilities as a possible cause of nonlinear SASI saturation. As the shock oscillations create both vorticity and entropy gradients, we show that both Kelvin-Helmholtz and Rayleigh-Taylor types of instabilities are able to grow on a SASI mode if its amplitude is large enough. We obtain simple estimates of their growth rates, taking into account the effects of advection and entropy stratification. In the context of the advective-acoustic cycle, we use numerical simulations to demonstrate how the acoustic feedback can be decreased if a parasitic instability distorts the advected structure. The amplitude of the shock deformation is estimated analytically in this scenario. When applied to the set up of Fernandez and Thompson, this saturation mechanism is able to explain the dramatic decrease of the SASI power when both the nuclear dissociation energy and the cooling rate are varied. Our results open new perspectives for anticipating the effect, on the SASI amplitude, of the physical ingredients involved in the modeling of the collapsing star.

Nonlinear optimal filter technique for analyzing energy depositions in TES sensors driven into saturation

Directory of Open Access Journals (Sweden)

B. Shank

2014-11-01

Full Text Available We present a detailed thermal and electrical model of superconducting transition edge sensors (TESs connected to quasiparticle (qp traps, such as the W TESs connected to Al qp traps used for CDMS (Cryogenic Dark Matter Search Ge and Si detectors. We show that this improved model, together with a straightforward time-domain optimal filter, can be used to analyze pulses well into the nonlinear saturation region and reconstruct absorbed energies with optimal energy resolution.

Nonlinear drift tearing mode

International Nuclear Information System (INIS)

Zelenyj, L.M.; Kuznetsova, M.M.

1989-01-01

Nonlinear study of magnetic perturbation development under single-mode conditions in collision-free plasma in configurations with the magnetic field shear is investigated. Results are obtained with regard of transverse component of electrical field and its effect on ion dynamics within wide range of ion Larmor radius value and values of magnetic field shear. Increments of nonlinear drift tearing mode are obtained and it is shown that excitation drastic conditions of even linearly stable modes are possible. Mechanism of instability nonlinear stabilization is considered and the value of magnetic island at the saturation threshold is estimeted. Energy of nonlinear drift tearing mode is discussed

Grey-box state-space identification of nonlinear mechanical vibrations

Science.gov (United States)

Noël, J. P.; Schoukens, J.

2018-05-01

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.

International Conference on Differential Equations and Nonlinear Mechanics

CERN Document Server

2001-01-01

The International Conference on Differential Equations and Nonlinear Mechanics was hosted by the University of Central Florida in Orlando from March 17-19, 1999. One of the conference days was dedicated to Professor V. Lakshmikantham in th honor of his 75 birthday. 50 well established professionals (in differential equations, nonlinear analysis, numerical analysis, and nonlinear mechanics) attended the conference from 13 countries. Twelve of the attendees delivered hour long invited talks and remaining thirty-eight presented invited forty-five minute talks. In each of these talks, the focus was on the recent developments in differential equations and nonlinear mechanics and their applications. This book consists of 29 papers based on the invited lectures, and I believe that it provides a good selection of advanced topics of current interest in differential equations and nonlinear mechanics. I am indebted to the Department of Mathematics, College of Arts and Sciences, Department of Mechanical, Materials and Ae...

Nonlinear amplitude dynamics in flagellar beating.

Science.gov (United States)

Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

2017-03-01

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.

Nonlinear Dynamic Phenomena in Mechanics

CERN Document Server

Warminski, Jerzy; Cartmell, Matthew P

2012-01-01

Nonlinear phenomena should play a crucial role in the design and control of engineering systems and structures as they can drastically change the prevailing dynamical responses. This book covers theoretical and applications-based problems of nonlinear dynamics concerned with both discrete and continuous systems of interest in civil and mechanical engineering. They include pendulum-like systems, slender footbridges, shape memory alloys, sagged elastic cables and non-smooth problems. Pendulums can be used as a dynamic absorber mounted in high buildings, bridges or chimneys. Geometrical nonlinear

Criterion of magnetic saturation and simulation of nonlinear magnetization for a linear multi-core pulse transformer

International Nuclear Information System (INIS)

Zeng Zhengzhong; Kuai Bin; Sun Fengju; Cong Peitian; Qiu Aici

2002-01-01

The linear multi-core pulse transformer is an important primary driving source used in pulsed power apparatus for the production of dense plasm owing to its compact, relatively low-cost and easy-to-handle characteristics. The evaluation of the magnetic saturation of the transformer cores is essential to the transformer design, because the energy transfer efficiency of the transformer will degrade significantly after magnetic saturation. This work proposes analytical formulas of the criterion of magnetic saturation for the cores when the transformer drives practical loads. Furthermore, an electric circuit model based on a dependent source treatment for simulating the electric behavior of the cores related to their nonlinear magnetization is developed using the initial magnetization curve of the cores. The numerical simulation with the model is used to evaluate the validity of the criterion. Both the criterion and the model are found to be in agreement with the experimental data

Nonlinear optomechanical measurement of mechanical motion

DEFF Research Database (Denmark)

Brawley, G.A.; Vanner, M R; Larsen, Peter Emil

2016-01-01

Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with oth......Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing...... with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of nonlinear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator...... by exploiting the intrinsic nonlinearity of the radiation-pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100 pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can...

Evidence for a saturable mechanism of disappearance of standard heparin in rabbits

International Nuclear Information System (INIS)

Boneu, B.; Caranobe, C.; Gabaig, A.M.; Dupouy, D.; Sie, P.; Buchanan, M.R.; Hirsh, J.

1987-01-01

This work demonstrates that after bolus intravenous injection standard heparin (SH) disappearance results from the combination of a saturable and a non saturable mechanism. Pharmacokinetics and pharmacodynamics of SH were studied by measuring the disappearance of increasing doses (5 - 500 anti-factor Xa U/kg) of 125 I-heparin and of its biological effects. CPM curves allowed the determination of the half lives of heparin according to the dose injected. The half lives were clearly dose dependent and reached a plateau over 100 anti-factor Xa U/kg. The complex curve which describes the amount of heparin cleared per time unit after any given dose has been resolved into its two components reflecting a saturable and a non saturable mechanism of disappearance. For the doses less than 100 anti-factor Xa U/kg the saturable mechanism was preeminent and the anti-factor Xa activity disappearance followed an exponential pattern; for the doses less than 100 anti-factor Xa U/kg the contribution of the non saturable mechanism becomes more important and the anti-factor Xa activity disappearance followed a concave-convex pattern. Further experiments showed that the heparin half life shortened as the circulating anti-factor Xa activity decreased; this phenomenon may explain the concave-convex pattern of the curve of the anticoagulant effect observed after injection of large doses of SH

The effect of saturation of the mechanical properties of tuff at Yucca Mountain

International Nuclear Information System (INIS)

Karakouzian, M.; Hudyma, N.

1996-01-01

This study investigates the effect of saturation on the mechanical properties, namely compressive strength and Young's Modulus, of Tiva Canyon welded tuff and Topopah Spring welded tuff from the Nevada Test Site. Unconfined compression tests on air dried and saturated specimens show that saturation lowers both the average compressive strength and the average Young's Modulus of Topopah Spring and Tiva Canyon tuff specimens. Saturation increases the variability of the mechanical properties of Topopah Spring tuff and the variability of the compressive strength of Tiva Canyon tuff

Influence of gradual density transition and nonlinear saturation on Rayleigh-Taylor instability growth

International Nuclear Information System (INIS)

Jacobs, H.

1984-08-01

Linear theory of Rayleigh-Taylor instability growth at a density profile which varies exponentially between regions of constant density is discussed in detail. The exact theory provides an approximate but conservative simple formula for the growth constant and it shows that a hitherto widely used theory erroneously underestimates the growth constant. A simple but effective ''synthetical model'' of nonlinear bubble growth is obtained from a synthesis of linear theory and constant terminal bubble speed. It is applied to pusher shell break-up in an inertial confinement fusion pellet to determine the maximum allowable initial perturbations and the most dangerous wavelength. In a situation typical of heavy ion drivers it is found that the allowable initial perturbations are increased by a few orders of magnitude by the gradual density transition and another order of magnitude by nonlinear saturation of the bubble speed. The gradual density transition also shifts the most dangerous wavelength from about once to about four times the minimum pusher shell thickness. The following topics are treated briefly: Reasons conflicting with use of the synthetical model to decide whether the pusher shell in a certain simulation will be broken up; other nonlinear theories available in the literature; further realistic effects that might aggravate instability growth. (orig.) [de

Saturation mechanism of decaying ion temperature gradient driven turbulence with kinetic electrons

International Nuclear Information System (INIS)

Idomura, Yasuhiro

2016-01-01

We present full-f gyrokinetic simulations of the ion temperature gradient driven (ITG) turbulence including kinetic electrons. By comparing decaying ITG turbulence simulations with adiabatic and kinetic electron models, an impact of kinetic electrons on the ITG turbulence is investigated. It is found that significant electron transport occurs even in the ITG turbulence, and both ion and electron temperature profiles are relaxed. In steady states, both cases show upshifts of nonlinear critical ion temperature gradients from linear ones, while their saturation mechanisms are qualitatively different. In the adiabatic electron case, the ITG mode is stabilized by turbulence driven zonal flows. On the other hand, in the kinetic electron case, passing electrons transport shows fine resonant structures at mode rational surfaces, which generate corrugated density profiles. Such corrugated density profiles lead to fine radial electric fields following the neoclassical force balance relation. The resulting E × B shearing rate greatly exceeds the linear growth rate of the ITG mode. (author)

Ultra-broadband nonlinear saturable absorption of high-yield MoS2 nanosheets

Science.gov (United States)

Wei, Rongfei; Zhang, Hang; Hu, Zhongliang; Qiao, Tian; He, Xin; Guo, Qiangbing; Tian, Xiangling; Chen, Zhi; Qiu, Jianrong

2016-07-01

High-yield MoS2 nanosheets with strong nonlinear optical (NLO) responses in a broad near-infrared range were synthesized by a facile hydrothermal method. The observation of saturable absorption, which was excited by the light with photon energy smaller than the gap energy of MoS2, can be attributed to the enhancement of the hybridization between the Mo d-orbital and S p-orbital by the oxygen incorporation into MoS2. High-yield MoS2 nanosheets with high modulation depth and large saturable intensity generated a stable, passively Q-switched fiber laser pulse at 1.56 μm. The high output power of 1.08 mW can be attained under a very low pump power of 30.87 mW. Compared to recently reported passively Q-switched fiber lasers utilizing exfoliated MoS2 nanosheets, the efficiency of the laser for our passive Q-switching operation is larger and reaches 3.50%. This research may extend the understanding on the NLO properties of MoS2 and indicate the feasibility of the high-yield MoS2 nanosheets to passively Q-switched fiber laser effectively at low pump strengths.

Non-linear finite element analysis in structural mechanics

CERN Document Server

Rust, Wilhelm

2015-01-01

This monograph describes the numerical analysis of non-linearities in structural mechanics, i.e. large rotations, large strain (geometric non-linearities), non-linear material behaviour, in particular elasto-plasticity as well as time-dependent behaviour, and contact. Based on that, the book treats stability problems and limit-load analyses, as well as non-linear equations of a large number of variables. Moreover, the author presents a wide range of problem sets and their solutions. The target audience primarily comprises advanced undergraduate and graduate students of mechanical and civil engineering, but the book may also be beneficial for practising engineers in industry.

Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

KAUST Repository

Yavari, Arash

2012-03-09

We present a geometric theory of nonlinear solids with distributed dislocations. In this theory the material manifold-where the body is stress free-is a Weitzenböck manifold, that is, a manifold with a flat affine connection with torsion but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan\\'s moving frames we construct the material manifold for several examples of bodies with distributed dislocations. We also present non-trivial examples of zero-stress dislocation distributions. More importantly, in this geometric framework we are able to calculate the residual stress fields, assuming that the nonlinear elastic body is incompressible. We derive the governing equations of nonlinear dislocation mechanics covariantly using balance of energy and its covariance. © 2012 Springer-Verlag.

Saturation and postsaturation phenomena of Rayleigh-Taylor instability with adjacent modes

International Nuclear Information System (INIS)

Ikegawa, Tadashi; Nishihara, Katsunobu

2003-01-01

A weakly nonlinear theory has been developed for the classical Rayleigh-Taylor instability with a finite bandwidth taken into account self-consistently. The theory includes up to third order nonlinearity, which results in the saturation of linear growth and determines subsequent weakly nonlinear growth. Analytical results are shown to agree fairly well with two-dimensional hydrodynamic simulations. There are generally many local peaks of a perturbation with a finite bandwidth due to the interference of modes. Since a local amplitude is determined from phases among the modes as well as the bandwidth, we have investigated an onset of the linear growth saturation and the subsequent weakly nonlinear growth for different bandwidths and phases. It is shown that the saturation of the linear growth occurs locally, i.e., each of the local maximum amplitudes (LMAs) grows exponentially until it reaches almost the same saturation amplitude. In the random phase case, the root mean square amplitude thus saturates with almost the same amplitude as the LMA, after most of the LMAs have saturated. The saturation amplitude of the LMA is found to be independent of the bandwidth and depends on the Atwood number. We derive a formula of the saturation amplitude of modes based on the results obtained, and discuss its relation with Haan's formula [Phys. Rev. A 39, 5812 (1989)]. The LMAs grow linearly in time after the saturation and their speeds are approximated by the product of the linear growth rate and the saturation amplitude. We investigate the Atwood number dependence of both the saturation amplitude and the weakly nonlinear growth

Nonlinear State of Sausage-like Instability of Electron Current Channels in Fast Ignition Concept of Inertial Fusion

International Nuclear Information System (INIS)

Jain, Neeraj; Das, Amita; Kaw, Predhiman; Sengupta, Sudip

2003-01-01

This paper deals with a detailed fluid simulation study of linear and nonlinear aspects of the velocity shear modes in electron current channels in a two dimensional geometry. Simulation results clearly show the flattening of flow profile and the development of sausage like structures (kink structures, which are intrinsically three dimensional excitations, are ruled out in the present simulations) which grow linearly and eventually saturate by nonlinear effects. An analytic understanding of the nonlinear saturation mechanism is also provided

Adaptive fuzzy dynamic surface control of nonlinear systems with input saturation and time-varying output constraints

Science.gov (United States)

Edalati, L.; Khaki Sedigh, A.; Aliyari Shooredeli, M.; Moarefianpour, A.

2018-02-01

This paper deals with the design of adaptive fuzzy dynamic surface control for uncertain strict-feedback nonlinear systems with asymmetric time-varying output constraints in the presence of input saturation. To approximate the unknown nonlinear functions and overcome the problem of explosion of complexity, a Fuzzy logic system is combined with the dynamic surface control in the backstepping design technique. To ensure the output constraints satisfaction, an asymmetric time-varying Barrier Lyapunov Function (BLF) is used. Moreover, by applying the minimal learning parameter technique, the number of the online parameters update for each subsystem is reduced to 2. Hence, the semi-globally uniformly ultimately boundedness (SGUUB) of all the closed-loop signals with appropriate tracking error convergence is guaranteed. The effectiveness of the proposed control is demonstrated by two simulation examples.

Semiconductor saturable absorbers for ultrafast THz signals

DEFF Research Database (Denmark)

Hoffmann, Matthias C.; Turchinovich, Dmitry

We demonstrate saturable absorber behavior of n-type semiconductors in the THz frequency range using nonlinear THz spectroscopy. Further, we observe THz pulse shortening and increase of the group refractive index at high field strengths.......We demonstrate saturable absorber behavior of n-type semiconductors in the THz frequency range using nonlinear THz spectroscopy. Further, we observe THz pulse shortening and increase of the group refractive index at high field strengths....

Nonlinear Klein-Gordon soliton mechanics

International Nuclear Information System (INIS)

Reinisch, G.

1992-01-01

Nonlinear Klein-Gordon solitary waves - or solitons in a loose sense - in n+1 dimensions, driven by very general external fields which must only satisfy continuity - together with regularity conditions at the boundaries of the system, obey a quite simple equation of motion. This equation is the exact generalization to this dynamical system of infinite number of degrees of freedom - which may be conservative or not - of the second Newton's law setting the basis of material point mechanics. In the restricted case of conservative nonlinear Klein-Gordon systems, where the external driving force is derivable from a potential energy, we recover the generalized Ehrenfest theorem which was itself the extension to such systems of the well-known Ehrenfest theorem in quantum mechanics. This review paper first displays a few (of one-dimensional sine-Gordon type) typical examples of the basic difficulties related to the trial construction of solitary-waves is proved and the derivation of the previous sine-Gordon examples from this theorem is displayed. Two-dimensional nonlinear solitary-wave patterns are considered, as well as a special emphasis is put on the applications to space-time complexity of 1-dim. sine-Gordon systems

Premature saturation in backpropagation networks: Mechanism and necessary conditions

International Nuclear Information System (INIS)

Vitela, J.E.; Reifman, J.

1997-01-01

The mechanism that gives rise to the phenomenon of premature saturation of the output units of feedforward multilayer neural networks during training with the standard backpropagation algorithm is described. The entire process of premature saturation is characterized by three distinct stages and it is concluded that the momentum term plays the leading role in the occurrence of the phenomenon. The necessary conditions for the occurrence of premature saturation are presented and a new method is proposed, based on these conditions, that eliminates the occurrence of the phenomenon. Validity of the conditions and the proposed method are illustrated through simulation results. Three case studies are presented. The first two came from a training session for classification of three component failures in a nuclear power plant. The last case, comes from a training session for classification of welded fuel elements

Ultrafast THz Saturable Absorption in Doped Semiconductors

DEFF Research Database (Denmark)

Turchinovich, Dmitry; Hoffmann, Matthias C.

2011-01-01

We demonstrate ultrafast THz saturable absorption in n-doped semiconductors by nonlinear THz time-domain spectroscopy. This effect is caused by the semiconductor conductivity modulation due to electron heating and satellite-valley scattering in strong THz fields.......We demonstrate ultrafast THz saturable absorption in n-doped semiconductors by nonlinear THz time-domain spectroscopy. This effect is caused by the semiconductor conductivity modulation due to electron heating and satellite-valley scattering in strong THz fields....

Saturation of drift instabilities by ExB advection of resonant electrons

International Nuclear Information System (INIS)

Dimits, A.M.

1990-01-01

Saturation of the collisionless and weakly collisional drift instabilities by nonlinear ExB advection of resonant electrons is considered. The nonlinear ExB advection of the resonant electrons around the O points and X points of the potential shuts off the linear phase shift between the electron density and the potential, and hence the linear growth, and produces residual oscillations at the ExB-trapping frequency. Two analytical solutions of a three-mode model of Lee et al. [Phys. Fluids 27, 2652 (1984)], which describes the saturation of drift waves by this mechanism, are found. The first is an exact solution in the form of a steadily propagating wave of constant amplitude, and is relevant when electron pitch-angle scattering is present. The second is an approximate time-dependent analytical solution, obtained using the method of O'Neil [Phys. Fluids 8, 2255 (1965)], and is relevant to the collisionless case. The predictions that follow from this solution for the saturation level and for the amplitude oscillation frequency are in excellent agreement with the direct numerical solutions of the three-mode system

Saturation and linear transport equation

International Nuclear Information System (INIS)

Kutak, K.

2009-03-01

We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)

Nonlinearity induced synchronization enhancement in mechanical oscillators

Science.gov (United States)

Czaplewski, David A.; Lopez, Omar; Guest, Jeffrey R.; Antonio, Dario; Arroyo, Sebastian I.; Zanette, Damian H.

2018-05-08

An autonomous oscillator synchronizes to an external harmonic force only when the forcing frequency lies within a certain interval, known as the synchronization range, around the oscillator's natural frequency. Under ordinary conditions, the width of the synchronization range decreases when the oscillation amplitude grows, which constrains synchronized motion of micro- and nano-mechanical resonators to narrow frequency and amplitude bounds. The present invention shows that nonlinearity in the oscillator can be exploited to manifest a regime where the synchronization range increases with an increasing oscillation amplitude. The present invention shows that nonlinearities in specific configurations of oscillator systems, as described herein, are the key determinants of the effect. The present invention presents a new configuration and operation regime that enhances the synchronization of micro- and nano-mechanical oscillators by capitalizing on their intrinsic nonlinear dynamics.

Tearing mode saturation with finite pressure

International Nuclear Information System (INIS)

Lee, J.K.

1988-01-01

With finite pressure, the saturation of the current-driven tearing mode is obtained in three-dimensional nonlinear resistive magnetohydrodynamic simulations for Tokamak plasmas. To effectively focus on the tearing modes, the perturbed pressure effects are excluded while the finite equilibrium pressure effects are retained. With this model, the linear growth rates of the tearing modes are found to be very insensitive to the equilibrium pressure increase. The nonlinear aspects of the tearing modes, however, are found to be very sensitive to the pressure increase in that the saturation level of the nonlinear harmonics of the tearing modes increases monotonically with the pressure rise. The increased level is associated with enhanced tearing island sizes or increased stochastic magnetic field region. (author)

SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

Energy Technology Data Exchange (ETDEWEB)

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

1998-09-01

This report summarizes the key continuum mechanics concepts required for the systematic prescription and numerical solution of finite deformation solid mechanics problems. Topics surveyed include measures of deformation appropriate for media undergoing large deformations, stress measures appropriate for such problems, balance laws and their role in nonlinear continuum mechanics, the role of frame indifference in description of large deformation response, and the extension of these theories to encompass two dimensional idealizations, structural idealizations, and rigid body behavior. There are three companion reports that describe the problem formulation, constitutive modeling, and finite element technology for nonlinear continuum mechanics systems.

Ultrafast nonlinear optical processes in metal-dielectric nanocomposites and nanostructures

Energy Technology Data Exchange (ETDEWEB)

Kim, Kwang-Hyon

2012-04-13

This work reports results of a theoretical study of nonlinear optical processes in metal-dielectric nanocomposites used for the increase of the nonlinear coefficients and for plasmonic field enhancement. The main results include the study of the transient saturable nonlinearity in dielectric composites doped with metal nanoparticles, its physical mechanism as well its applications in nonlinear optics. For the study of the transient response, a time-depending equation for the dielectric function of the nanocomposite using the semi-classical two-temperature model is derived. By using this approach, we study the transient nonlinear characteristics of these materials in comparison with preceding experimental measurements. The results show that these materials behave as efficient saturable absorbers for passive mode-locking of lasers in the spectral range from the visible to near IR. We present results for the modelocked dynamics in short-wavelength solid-state and semiconductor disk lasers; in this spectral range other efficient saturable absorbers do not exist. We suggest a new mechanism for the realization of slow light phenomenon by using glasses doped with metal nanoparticles in a pump-probe regime near the plasmonic resonance. Furthermore, we study femtosecond plasmon generation by mode-locked surface plasmon polariton lasers with Bragg reflectors and metal-gain-absorber layered structures. In the final part of the thesis, we present results for high-order harmonic generation near a metallic fractal rough surface. The results show a possible reduction of the pump intensities by three orders of magnitudes and two orders of magnitudes higher efficiency compared with preceding experimental results by using bow-tie nanostructures.

Optical interrupter based in the internal total reflection of spatial solitons at nonlinear saturable interfaces; Interruptores opticos basados en reflexion interna total de solitones espaciales en interfaces no lineales saturables

Energy Technology Data Exchange (ETDEWEB)

Alvarado-Mendez, E.; Torres-Cisneros, M.; Gutierrez-Hernandez, D. A.; Andrade-Lucio, J. A.; Rojas-Lagunas, R.; Pedraza-Ortega, J. C.; Torres Cisneros, G. E. [Universidad de Guanajuato, Guanajuato (Mexico); Sanchez Mondragon, J. J. [Universidad Autonoma del Estado de Morelos, Morelos (Mexico); Flores-Alvarado, G. [Preparatoria por Cooperacion Domingo Arenas, Tlaxcala (Mexico)

2001-06-01

We study the reflection of one-dimensional spatial soliton at the nonlinear interface between a saturable type medium and linear medium. Our study makes emphasis on determining the physical conditions under which the beam reflected by the interface is still a spatial soliton. Depended the incidence angle we find three critical regions for spatial solitons in the interface. We observed nonlinear Goos- Haechen shift is determined if reflection angle are conserved. Finally, we present preliminary experimental results in SBN61:Ce of the total internal reflection of one dimensional beam. [Spanish] Estudiamos la reflexion de un soliton espacial unidimensional en una interfase formada por un medio no lineal saturable y un medio lineal. Nuestros estudios hacen enfasis en determinar las condiciones fisicas bajo las cuales el haz reflejado por la interfase no lineal sigue siendo soliton. Encontramos tres regiones criticas para un soliton especial en la interfase, dependiendo del valor que tome el angulo de incidencia. Asi mismo observamos corrimiento Goos-Haechen no lineal que es determinante para la conservacion del angulo de reflexion. Finalmente, presentamos resultados preliminares experimentales en SBN61:Ce de la reflexion interna total de un haz unidimensional.

Ultrafast THz Saturable Absorption in Semiconductors

DEFF Research Database (Denmark)

Turchinovich, Dmitry; Hoffmann, Matthias C.

2011-01-01

We demonstrate THz saturable absorption in n-doped semiconductors GaAs, GaP, and Ge in a nonlinear THz time-domain spectroscopy experiment. Saturable absorption is caused by sample conductivity modulation due to electron heating and satellite valley scattering in the field of a strong THz pulse....

The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence

Energy Technology Data Exchange (ETDEWEB)

Staebler, G. M.; Candy, J. [General Atomics, San Diego, California 92186 (United States); Howard, N. T. [Oak Ridge Institute for Science Education (ORISE), Oak Ridge, Tennessee 37831 (United States); Holland, C. [University of California San Diego, San Diego, California 92093 (United States)

2016-06-15

The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. The zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ion-scale gyrokinetic simulations.

Two-beam interaction in saturable media

DEFF Research Database (Denmark)

Schjødt-Eriksen, Jens; Schmidt, Michel R.; Juul Rasmussen, Jens

1998-01-01

The dynamics of two coupled soliton solutions of the nonlinear Schrodinger equation with a saturable nonlinearity is investigated It is shown by means of a variational method and by direct numerical calculations that two well-separated solitons can orbit around each other, if their initial velocity...

On the saturation of astrophysical dynamos

DEFF Research Database (Denmark)

Dorch, Bertil; Archontis, Vasilis

2004-01-01

In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and we study the dynamo's mode of operation during both the linear and non-linear saturation regimes. It turns out that in addition to a high growth rate in the li......In the context of astrophysical dynamos we illustrate that the no-cosines flow, with zero mean helicity, can drive fast dynamo action and we study the dynamo's mode of operation during both the linear and non-linear saturation regimes. It turns out that in addition to a high growth rate...

Saturation of single toroidal number Alfvén modes

International Nuclear Information System (INIS)

Wang, X; Briguglio, S

2016-01-01

The results of numerical simulations are presented to illustrate the saturation mechanism of a single toroidal number Alfvén mode, driven unstable, in a tokamak plasma, by the resonant interaction with energetic ions. The effects of equilibrium geometry non-uniformities and finite mode radial width on the wave-particle nonlinear dynamics are discussed. Saturation occurs as the fast-ion density flattening produced by the radial flux associated to the resonant particles captured in the potential well of the Alfvén wave extends over the whole region where mode-particle power exchange can take place. The occurrence of two different saturation regimes is shown. In the first regime, dubbed resonance detuning, that region is limited by the resonance radial width (that is, the width of the region where the fast-ion resonance frequency matches the mode frequency). In the second regime, called radial decoupling, the power exchange region is limited by the mode radial width. In the former regime, the mode saturation amplitude scales quadratically with the growth rate; in the latter, it scales linearly. The occurrence of one or the other regime can be predicted on the basis of linear dynamics: in particular, the radial profile of the fast-ion resonance frequency and the mode structure. Here, we discuss how such properties can depend on the considered toroidal number and compare simulation results with the predictions obtained from a simplified nonlinear pendulum model. (paper)

Influence of helical external driven current on nonlinear resistive tearing mode evolution and saturation in tokamaks

Science.gov (United States)

Zhang, W.; Wang, S.; Ma, Z. W.

2017-06-01

The influences of helical driven currents on nonlinear resistive tearing mode evolution and saturation are studied by using a three-dimensional toroidal resistive magnetohydrodynamic code (CLT). We carried out three types of helical driven currents: stationary, time-dependent amplitude, and thickness. It is found that the helical driven current is much more efficient than the Gaussian driven current used in our previous study [S. Wang et al., Phys. Plasmas 23(5), 052503 (2016)]. The stationary helical driven current cannot persistently control tearing mode instabilities. For the time-dependent helical driven current with f c d = 0.01 and δ c d < 0.04 , the island size can be reduced to its saturated level that is about one third of the initial island size. However, if the total driven current increases to about 7% of the total plasma current, tearing mode instabilities will rebound again due to the excitation of the triple tearing mode. For the helical driven current with time dependent strength and thickness, the reduction speed of the radial perturbation component of the magnetic field increases with an increase in the driven current and then saturates at a quite low level. The tearing mode is always controlled even for a large driven current.

Modelling suction instabilities in soils at varying degrees of saturation

Directory of Open Access Journals (Sweden)

Buscarnera Giuseppe

2016-01-01

Full Text Available Wetting paths imparted by the natural environment and/or human activities affect the state of soils in the near-surface, promoting transitions across different regimes of saturation. This paper discusses a set of techniques aimed at quantifying the role of hydrologic processes on the hydro-mechanical stability of soil specimens subjected to saturation events. Emphasis is given to the mechanical conditions leading to coupled flow/deformation instabilities. For this purpose, energy balance arguments for three-phase systems are used to derive second-order work expressions applicable to various regimes of saturation. Controllability analyses are then performed to relate such work input with constitutive singularities that reflect the loss of strength under coupled and/or uncoupled hydro-mechanical forcing. A suction-dependent plastic model is finally used to track the evolution of stability conditions in samples subjected to wetting, thus quantifying the growth of the potential for coupled failure modes upon increasing degree of saturation. These findings are eventually linked with the properties of the field equations that govern pore pressure transients, thus disclosing a conceptual link between the onset of coupled hydro-mechanical failures and the evolution of suction with time. Such results point out that mathematical instabilities caused by a non-linear suction dependent behaviour play an important role in the advanced constitutive and/or numerical tools that are commonly used for the analysis of geomechanical problems in the unsaturated zone, and further stress that the relation between suction transients and soil deformations is a key factor for the interpretation of runaway failures caused by intense saturation events.

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

Analytical model and design of spoke-type permanent-magnet machines accounting for saturation and nonlinearity of magnetic bridges

Science.gov (United States)

Liang, Peixin; Chai, Feng; Bi, Yunlong; Pei, Yulong; Cheng, Shukang

2016-11-01

Based on subdomain model, this paper presents an analytical method for predicting the no-load magnetic field distribution, back-EMF and torque in general spoke-type motors with magnetic bridges. Taking into account the saturation and nonlinearity of magnetic material, the magnetic bridges are equivalent to fan-shaped saturation regions. For getting standard boundary conditions, a lumped parameter magnetic circuit model and iterative method are employed to calculate the permeability. The final field domain is divided into five types of simple subdomains. Based on the method of separation of variables, the analytical expression of each subdomain is derived. The analytical results of the magnetic field distribution, Back-EMF and torque are verified by finite element method, which confirms the validity of the proposed model for facilitating the motor design and optimization.

Saturation mechanism and improvement of conversion efficiency of free electron laser

International Nuclear Information System (INIS)

Taguchi, T.; Mima, K.; Mochizuki, T.

1980-01-01

Saturation mechanisms of free electron laser are investigated in the Compton regime. It is found that the saturation occurs due to quasi-linear energy spreading of electron beam in the case of many mode excitation. The energy conversion efficiency remains low even if many modes are taken into account. For improvement of the conversion efficiency, effects of reacceleration by a traveling wave are investigated and turn out to increase the efficiency up to more than 50%. (author)

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

Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

KAUST Repository

Pavarino, L.F.; Scacchi, S.; Zampini, Stefano

2015-01-01

The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics

KAUST Repository

Pavarino, L.F.

2015-07-18

The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

The Human Cochlear Mechanical Nonlinearity Inferred via Psychometric Functions

Directory of Open Access Journals (Sweden)

Nizami Lance

2013-12-01

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

Nitrogen saturation in stream ecosystems.

Science.gov (United States)

Earl, Stevan R; Valett, H Maurice; Webster, Jackson R

2006-12-01

The concept of nitrogen (N) saturation has organized the assessment of N loading in terrestrial ecosystems. Here we extend the concept to lotic ecosystems by coupling Michaelis-Menten kinetics and nutrient spiraling. We propose a series of saturation response types, which may be used to characterize the proximity of streams to N saturation. We conducted a series of short-term N releases using a tracer (15NO3-N) to measure uptake. Experiments were conducted in streams spanning a gradient of background N concentration. Uptake increased in four of six streams as NO3-N was incrementally elevated, indicating that these streams were not saturated. Uptake generally corresponded to Michaelis-Menten kinetics but deviated from the model in two streams where some other growth-critical factor may have been limiting. Proximity to saturation was correlated to background N concentration but was better predicted by the ratio of dissolved inorganic N (DIN) to soluble reactive phosphorus (SRP), suggesting phosphorus limitation in several high-N streams. Uptake velocity, a reflection of uptake efficiency, declined nonlinearly with increasing N amendment in all streams. At the same time, uptake velocity was highest in the low-N streams. Our conceptual model of N transport, uptake, and uptake efficiency suggests that, while streams may be active sites of N uptake on the landscape, N saturation contributes to nonlinear changes in stream N dynamics that correspond to decreased uptake efficiency.

Nonlinear saturation of stimulated Raman scattering in a collisional homogeneous plasma

International Nuclear Information System (INIS)

McKinstrie, C.J.

1985-11-01

Using multiple scale analysis, the nonlinear saturation of the stimulated Raman scattering instability is examined in a collisional homogeneous plasma. The first problem considered is the temporal problem in an infinite plasma, with a ubiquitous driver and arbitrary damping for each wave. The second problem considered is the absolute Raman instability in a finite plasma. The incident wave amplitude exceeds the absolute instability threshold by the fractional amount Δ. In the marginally unstable regime, the complete time dependence and spatial variation of each wave amplitude is obtained. An expression for the reflected light intensity is determined analytically, and is proportional to Δ. The conditions under which the steady-state results can be extended to the moderately unstable regime are discussed. The reflected light intensity is compared to values predicted for the convective instability, for the same incident intensity. In ''short'' plasmas, i.e., ones which extend over only a few linear convective gain lengths, the reflected intensity is found to be much higher when the absolute instability is excited

Distributed Event-Based Set-Membership Filtering for a Class of Nonlinear Systems With Sensor Saturations Over Sensor Networks.

Science.gov (United States)

Ma, Lifeng; Wang, Zidong; Lam, Hak-Keung; Kyriakoulis, Nikos

2017-11-01

In this paper, the distributed set-membership filtering problem is investigated for a class of discrete time-varying system with an event-based communication mechanism over sensor networks. The system under consideration is subject to sector-bounded nonlinearity, unknown but bounded noises and sensor saturations. Each intelligent sensing node transmits the data to its neighbors only when certain triggering condition is violated. By means of a set of recursive matrix inequalities, sufficient conditions are derived for the existence of the desired distributed event-based filter which is capable of confining the system state in certain ellipsoidal regions centered at the estimates. Within the established theoretical framework, two additional optimization problems are formulated: one is to seek the minimal ellipsoids (in the sense of matrix trace) for the best filtering performance, and the other is to maximize the triggering threshold so as to reduce the triggering frequency with satisfactory filtering performance. A numerically attractive chaos algorithm is employed to solve the optimization problems. Finally, an illustrative example is presented to demonstrate the effectiveness and applicability of the proposed algorithm.

Nonlinear features of the electron temperature gradient mode and electron thermal transport in tokamaks

International Nuclear Information System (INIS)

Kaw, P.K.; Singh, R.; Weiland, J.G.

2001-01-01

Analytical investigations of several linear and nonlinear features of ETG turbulence are reported. The linear theory includes effects such as finite beta induced electromagnetic shielding, coupling to electron magnetohydrodynamic modes like whistlers etc. It is argued that nonlinearly, turbulence and transport are dominated by radially extended modes called 'streamers'. A nonlinear mechanism generating streamers based on a modulational instability theory of the ETG turbulence is also presented. The saturation levels of the streamers using a Kelvin Helmholtz secondary instability mechanism are calculated and levels of the electron thermal transport due to streamers are estimated. (author)

Energy dependent saturable and reverse saturable absorption in cube-like polyaniline/polymethyl methacrylate film

Energy Technology Data Exchange (ETDEWEB)

Thekkayil, Remyamol [Department of Chemistry, Indian Institute of Space Science and Technology, Valiamala, Thiruvananthapuram 695 547 (India); Philip, Reji [Light and Matter Physics Group, Raman Research Institute, C.V. Raman Avenue, Bangalore 560 080 (India); Gopinath, Pramod [Department of Physics, Indian Institute of Space Science and Technology, Valiamala, Thiruvananthapuram 695 547 (India); John, Honey, E-mail: honey@iist.ac.in [Department of Chemistry, Indian Institute of Space Science and Technology, Valiamala, Thiruvananthapuram 695 547 (India)

2014-08-01

Solid films of cube-like polyaniline synthesized by inverse microemulsion polymerization method have been fabricated in a transparent PMMA host by an in situ free radical polymerization technique, and are characterized by spectroscopic and microscopic techniques. The nonlinear optical properties are studied by open aperture Z-scan technique employing 5 ns (532 nm) and 100 fs (800 nm) laser pulses. At the relatively lower laser pulse energy of 5 μJ, the film shows saturable absorption both in the nanosecond and femtosecond excitation domains. An interesting switchover from saturable absorption to reverse saturable absorption is observed at 532 nm when the energy of the nanosecond laser pulses is increased. The nonlinear absorption coefficient increases with increase in polyaniline concentration, with low optical limiting threshold, as required for a good optical limiter. - Highlights: • Synthesized cube-like polyaniline nanostructures. • Fabricated polyaniline/PMMA nanocomposite films. • At 5 μJ energy, saturable absorption is observed both at ns and fs regime. • Switchover from SA to RSA is observed as energy of laser beam increases. • Film (0.1 wt % polyaniline) shows high β{sub eff} (230 cm GW{sup −1}) and low limiting threshold at 150 μJ.

Computational mechanics of nonlinear response of shells

Energy Technology Data Exchange (ETDEWEB)

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

1990-01-01

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

Computational mechanics of nonlinear response of shells

International Nuclear Information System (INIS)

Kraetzig, W.B.; Onate, E.

1990-01-01

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

Nonlinear 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 non-linear dynamics of a coupled electro-mechanical system

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2012-01-01

Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one...... excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a......, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steadystate response of the electro-mechanical system exposed to a harmonic close-resonance mechanical...

Non-linear coupling of drift modes in a quadrupole

International Nuclear Information System (INIS)

Elliott, J.A.; Sandeman, J.C.; Tessema, G.Y.

1990-01-01

We report continuing experimental studies of non-linear interactions of drift waves, with direct evidence of a growth saturation mechanism by transfer of energy to lower frequency modes. Wave launching experiments show that the decay rate of drift waves can be strongly amplitude dependent. (author) 9 refs., 5 figs

Nonlinear real index of refraction variations of a gas medium due to a monochromatic radiation near resonance

International Nuclear Information System (INIS)

Vasconcellos, J.I.C.

1982-01-01

The nonlinear real index of refraction variations of a gas medium due to a strong monochromatic radiation causing saturation effects is calculated. The gas is supposed to be composed of two-level molecules with which the external field is nearly resonant. It is assumed homogeneous (hard collisions, spontaneous decay) and inhomogeneous (Doppler effect) broadening mechanisms acting on the real index of refraction of the medium. The nonlinear dispersion of the medium is studied as a function of the detuning frequencies, saturation conditions and for various ratios between the homogeneous and inhomogeneous linewidths. In particular, the modification of the index of refraction due to saturation effects are emphasized. (Author) [pt

A numerical toolkit to understand the mechanics of partially saturated granular materials

OpenAIRE

Roux , Jean-Noël

2015-01-01

``Focus on Fluids'' section; International audience; The mechanisms by which a wetting, non-saturating liquid bestows macroscopic cohesion and strength to a granular material are usually not accessible to micromechanical investigations for saturations exceeding the pendular regime of isolated menisci, easily studied by discrete element models. The " JFM-Rapids " paper (vol. 762, R5, 2015) by Delenne, Richefeu and Radja¨ıRadja¨ı, exploiting a multiphase Lattice Boltzmann approach, pioneers the...

Sector-condition-based results for adaptive control and synchronization of chaotic systems under input saturation

International Nuclear Information System (INIS)

Iqbal, Muhammad; Rehan, Muhammad; Hong, Keum-Shik; Khaliq, Abdul; Saeed-ur-Rehman

2015-01-01

This paper addresses the design of adaptive feedback controllers for two problems (namely, stabilization and synchronization) of chaotic systems with unknown parameters by considering input saturation constraints. A novel generalized sector condition is developed to deal with the saturation nonlinearities for synthesizing the nonlinear and the adaptive controllers for the stabilization and synchronization control objectives. By application of the proposed sector condition and rigorous regional stability analysis, control and adaptation laws are formulated to guarantee local stabilization of a nonlinear system under actuator saturation. Further, simple control and adaptation laws are developed to synchronize two chaotic systems under uncertain parameters and input saturation nonlinearity. Numerical simulation results for Rössler and FitzHugh–Nagumo models are provided to demonstrate the effectiveness of the proposed adaptive stabilization and synchronization control methodologies

Transition-metal dichalcogenides heterostructure saturable absorbers for ultrafast photonics.

Science.gov (United States)

Chen, Hao; Yin, Jinde; Yang, Jingwei; Zhang, Xuejun; Liu, Mengli; Jiang, Zike; Wang, Jinzhang; Sun, Zhipei; Guo, Tuan; Liu, Wenjun; Yan, Peiguang

2017-11-01

In this Letter, high-quality WS 2 film and MoS 2 film were vertically stacked on the tip of a single-mode fiber in turns to form heterostructure (WS 2 -MoS 2 -WS 2 )-based saturable absorbers with all-fiber integrated features. Their nonlinear saturable absorption properties were remarkable, such as a large modulation depth (∼16.99%) and a small saturable intensity (6.23  MW·cm -2 ). Stable pulses at 1.55 μm with duration as short as 296 fs and average power as high as 25 mW were obtained in an erbium-doped fiber laser system. The results demonstrate that the proposed heterostructures own remarkable nonlinear optical properties and offer a platform for adjusting nonlinear optical properties by stacking different transition-metal dichalcogenides or modifying the thickness of each layer, paving the way for engineering functional ultrafast photonics devices with desirable properties.

Shocks, singularities and oscillations in nonlinear optics and fluid mechanics

CERN Document Server

Santo, Daniele; Lannes, David

2017-01-01

The book collects the most relevant results from the INdAM Workshop "Shocks, Singularities and Oscillations in Nonlinear Optics and Fluid Mechanics" held in Rome, September 14-18, 2015. The contributions discuss recent major advances in the study of nonlinear hyperbolic systems, addressing general theoretical issues such as symmetrizability, singularities, low regularity or dispersive perturbations. It also investigates several physical phenomena where such systems are relevant, such as nonlinear optics, shock theory (stability, relaxation) and fluid mechanics (boundary layers, water waves, Euler equations, geophysical flows, etc.). It is a valuable resource for researchers in these fields. .

Riemann–Cartan Geometry of Nonlinear Dislocation Mechanics

KAUST Repository

Yavari, Arash; Goriely, Alain

2012-01-01

but vanishing non-metricity. Torsion of the material manifold is identified with the dislocation density tensor of nonlinear dislocation mechanics. Using Cartan's moving frames we construct the material manifold for several examples of bodies with distributed

Nonlinear mechanics a supplement to theoretical mechanics of particles and continua

CERN Document Server

Fetter, Alexander L

2006-01-01

In their prior Dover book, Theoretical Mechanics of Particles and Continua, Alexander L. Fetter and John Dirk Walecka provided a lucid and self-contained account of classical mechanics, together with appropriate mathematical methods. This supplement-an update of that volume-offers a bridge to contemporary mechanics.The original book's focus on continuum mechanics-with chapters on sound waves in fluids, surface waves on fluids, heat conduction, and viscous fluids-forms the basis for this supplement's discussion of nonlinear continuous systems. Topics include linearized stability analysis; a det

Deep saturated Free Electron Laser oscillators and frozen spikes

Energy Technology Data Exchange (ETDEWEB)

Ottaviani, P.L. [ENEA - Centro Ricerche Bologna, via Martiri di Monte Sole, 4, IT 40129, Bologna (Italy); Pagnutti, S., E-mail: simonetta.pagnutti@enea.it [ENEA - Centro Ricerche Bologna, via Martiri di Monte Sole, 4, IT 40129, Bologna (Italy); Dattoli, G., E-mail: giuseppe.dattoli@enea.it [ENEA - Centro Ricerche Frascati, via E. Fermi, 45, IT 00044, Frascati, Roma (Italy); Sabia, E., E-mail: elio.sabia@enea.it [ENEA - Centro Ricerche Frascati, via E. Fermi, 45, IT 00044, Frascati, Roma (Italy); Petrillo, V., E-mail: vittoria.petrillo@mi.infn.it [Universita' degli Studi di Milano, via Celoria 16, IT 20133, Milano (Italy); INFN - Mi, via Celoria 16, IT 20133, Milano (Italy); Slot, P.J.M. van der, E-mail: p.j.m.vanderslot@utwente.nl [Mesa+ Institute for Nanotechnology, University of Twente, P.O.Box 217, 7500 AE, Enschede (Netherlands); Biedron, S., E-mail: sandra.biedron@colostate.edu [Department of Electrical and Computer Engineering Colorado State University (United States); Milton, S., E-mail: milton@engr.colostate.edu [Department of Electrical and Computer Engineering Colorado State University (United States)

2016-10-21

We analyze the behavior of Free Electron Laser (FEL) oscillators operating in the deep saturated regime and point out the formation of sub-peaks of the optical pulse. These are very stable configurations and the sub-peaks are found to have a duration corresponding to the coherence length. We speculate on the physical mechanisms underlying their growth and attempt an identification with natural mode-locked structures in FEL oscillators. Their impact on the intra-cavity nonlinear harmonic generation is also discussed along with the possibility of exploiting them as cavity out-coupler.

Nonlinear continuum mechanics and large inelastic deformations

CERN Document Server

Dimitrienko, Yuriy I

2010-01-01

This book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead t...

Linear differential equations to solve nonlinear mechanical problems: A novel approach

OpenAIRE

Nair, C. Radhakrishnan

2004-01-01

Often a non-linear mechanical problem is formulated as a non-linear differential equation. A new method is introduced to find out new solutions of non-linear differential equations if one of the solutions of a given non-linear differential equation is known. Using the known solution of the non-linear differential equation, linear differential equations are set up. The solutions of these linear differential equations are found using standard techniques. Then the solutions of the linear differe...

Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities

DEFF Research Database (Denmark)

Khare, A.; Rasmussen, Kim Ø; Salerno, M.

2006-01-01

-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.......A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz...

Acoustic and mechanical response of reservoir rocks under variable saturation and effective pressure.

Science.gov (United States)

Ravazzoli, C L; Santos, J E; Carcione, J M

2003-04-01

We investigate the acoustic and mechanical properties of a reservoir sandstone saturated by two immiscible hydrocarbon fluids, under different saturations and pressure conditions. The modeling of static and dynamic deformation processes in porous rocks saturated by immiscible fluids depends on many parameters such as, for instance, porosity, permeability, pore fluid, fluid saturation, fluid pressures, capillary pressure, and effective stress. We use a formulation based on an extension of Biot's theory, which allows us to compute the coefficients of the stress-strain relations and the equations of motion in terms of the properties of the single phases at the in situ conditions. The dry-rock moduli are obtained from laboratory measurements for variable confining pressures. We obtain the bulk compressibilities, the effective pressure, and the ultrasonic phase velocities and quality factors for different saturations and pore-fluid pressures ranging from normal to abnormally high values. The objective is to relate the seismic and ultrasonic velocity and attenuation to the microstructural properties and pressure conditions of the reservoir. The problem has an application in the field of seismic exploration for predicting pore-fluid pressures and saturation regimes.

A Model to Couple Flow, Thermal and Reactive Chemical Transport, and Geo-mechanics in Variably Saturated Media

Science.gov (United States)

Yeh, G. T.; Tsai, C. H.

2015-12-01

This paper presents the development of a THMC (thermal-hydrology-mechanics-chemistry) process model in variably saturated media. The governing equations for variably saturated flow and reactive chemical transport are obtained based on the mass conservation principle of species transport supplemented with Darcy's law, constraint of species concentration, equation of states, and constitutive law of K-S-P (Conductivity-Degree of Saturation-Capillary Pressure). The thermal transport equation is obtained based on the conservation of energy. The geo-mechanic displacement is obtained based on the assumption of equilibrium. Conventionally, these equations have been implicitly coupled via the calculations of secondary variables based on primary variables. The mechanisms of coupling have not been obvious. In this paper, governing equations are explicitly coupled for all primary variables. The coupling is accomplished via the storage coefficients, transporting velocities, and conduction-dispersion-diffusion coefficient tensor; one set each for every primary variable. With this new system of equations, the coupling mechanisms become clear. Physical interpretations of every term in the coupled equations will be discussed. Examples will be employed to demonstrate the intuition and superiority of these explicit coupling approaches. Keywords: Variably Saturated Flow, Thermal Transport, Geo-mechanics, Reactive Transport.

A novel auto-tuning PID control mechanism for nonlinear systems.

Science.gov (United States)

Cetin, Meric; Iplikci, Serdar

2015-09-01

In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Analytical model and design of spoke-type permanent-magnet machines accounting for saturation and nonlinearity of magnetic bridges

Energy Technology Data Exchange (ETDEWEB)

Liang, Peixin; Chai, Feng [State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001 (China); Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150001 (China); Bi, Yunlong [Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150001 (China); Pei, Yulong, E-mail: peiyulong1@163.com [Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150001 (China); Cheng, Shukang [State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001 (China); Department of Electrical Engineering, Harbin Institute of Technology, Harbin 150001 (China)

2016-11-01

Based on subdomain model, this paper presents an analytical method for predicting the no-load magnetic field distribution, back-EMF and torque in general spoke-type motors with magnetic bridges. Taking into account the saturation and nonlinearity of magnetic material, the magnetic bridges are equivalent to fan-shaped saturation regions. For getting standard boundary conditions, a lumped parameter magnetic circuit model and iterative method are employed to calculate the permeability. The final field domain is divided into five types of simple subdomains. Based on the method of separation of variables, the analytical expression of each subdomain is derived. The analytical results of the magnetic field distribution, Back-EMF and torque are verified by finite element method, which confirms the validity of the proposed model for facilitating the motor design and optimization. - Highlights: • The no-load magnetic field of poke-type motors is firstly calculated by analytical method. • The magnetic circuit model and iterative method are employed to calculate the permeability. • The analytical expression of each subdomain is derived.. • The proposed method can effectively reduce the predesign stages duration.

Analytical model and design of spoke-type permanent-magnet machines accounting for saturation and nonlinearity of magnetic bridges

International Nuclear Information System (INIS)

Liang, Peixin; Chai, Feng; Bi, Yunlong; Pei, Yulong; Cheng, Shukang

2016-01-01

Based on subdomain model, this paper presents an analytical method for predicting the no-load magnetic field distribution, back-EMF and torque in general spoke-type motors with magnetic bridges. Taking into account the saturation and nonlinearity of magnetic material, the magnetic bridges are equivalent to fan-shaped saturation regions. For getting standard boundary conditions, a lumped parameter magnetic circuit model and iterative method are employed to calculate the permeability. The final field domain is divided into five types of simple subdomains. Based on the method of separation of variables, the analytical expression of each subdomain is derived. The analytical results of the magnetic field distribution, Back-EMF and torque are verified by finite element method, which confirms the validity of the proposed model for facilitating the motor design and optimization. - Highlights: • The no-load magnetic field of poke-type motors is firstly calculated by analytical method. • The magnetic circuit model and iterative method are employed to calculate the permeability. • The analytical expression of each subdomain is derived.. • The proposed method can effectively reduce the predesign stages duration.

Terahertz Nonlinear Optics in Semiconductors

DEFF Research Database (Denmark)

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

2013-01-01

We demonstrate the nonlinear optical effects – selfphase modulation and saturable absorption of a single-cycle THz pulse in a semiconductor. Resulting from THz-induced modulation of Drude plasma, these nonlinear optical effects, in particular, lead to self-shortening and nonlinear spectral...... breathing of a single-cycle THz pulse in a semiconductor....

Nonlinear wave mechanics from classical dynamics and scale covariance

International Nuclear Information System (INIS)

Hammad, F.

2007-01-01

Nonlinear Schroedinger equations proposed by Kostin and by Doebner and Goldin are rederived from Nottale's prescription for obtaining quantum mechanics from classical mechanics in nondifferentiable spaces; i.e., from hydrodynamical concepts and scale covariance. Some soliton and plane wave solutions are discussed

Introduction to nonlinear acoustics

Science.gov (United States)

Bjørnø, Leif

2010-01-01

A brief review of the basic principles of fluid mechanics needed for development of linear and nonlinear ultrasonic concepts will be given. The fundamental equations of nonlinear ultrasonics will be derived and their physical properties explained. It will be shown how an originally monochromatic finite-amplitude ultrasonic wave, due to nonlinear effects, will distort during its propagation in time and space to form higher harmonics to its fundamental frequency. The concepts of shock formation will be presented. The material nonlinearity, described by the nonlinearity parameter B/A of the material, and the convective nonlinearity, described by the ultrasonic Mach Number, will be explained. Two procedures for determination of B/A will briefly be described and some B/A-values characterizing biological materials will be presented. Shock formation, described by use of the Goldberg Number,and Ultrasonic Saturation will be discussed.. An introduction to focused ultrasonic fields will be given and it will be shown how the ultrasonic intensity will vary axially and laterally in and near the focal region and how the field parameters of interest to biomedical applications may be described by use of the KZK-Model. Finally, an introduction will be given to the parametric acoustic array formed by mixing and interaction of two monochromatic, finite-amplitude ultrasonic waves in a liquid and the potentials of this mixing process in biomedical ultrasound will briefly be mentioned.

On nonlinear dynamics and control of a robotic arm with chaos

Directory of Open Access Journals (Sweden)

Felix J. L. P.

2014-01-01

Full Text Available In this paper a robotic arm is modelled by a double pendulum excited in its base by a DC motor of limited power via crank mechanism and elastic connector. In the mathematical model, a chaotic motion was identified, for a wide range of parameters. Controlling of the chaotic behaviour of the system, were implemented using, two control techniques, the nonlinear saturation control (NSC and the optimal linear feedback control (OLFC. The actuator and sensor of the device are allowed in the pivot and joints of the double pendulum. The nonlinear saturation control (NSC is based in the order second differential equations and its action in the pivot/joint of the robotic arm is through of quadratic nonlinearities feedback signals. The optimal linear feedback control (OLFC involves the application of two control signals, a nonlinear feedforward control to maintain the controlled system to a desired periodic orbit, and control a feedback control to bring the trajectory of the system to the desired orbit. Simulation results, including of uncertainties show the feasibility of the both methods, for chaos control of the considered system.

Nonlinear operators and nonlinear transformations studied via the differential form of the completeness relation in quantum mechanics

International Nuclear Information System (INIS)

Fan Hongyi; Yu Shenxi

1994-01-01

We show that the differential form of the fundamental completeness relation in quantum mechanics and the technique of differentiation within an ordered product (DWOP) of operators provide a new approach for calculating normal product expansions of some nonlinear operators and study some nonlinear transformations. Their usefulness in perturbative calculations is pointed out. (orig.)

Mathematica for Theoretical Physics Classical Mechanics and Nonlinear Dynamics

CERN Document Server

Baumann, Gerd

2005-01-01

Mathematica for Theoretical Physics: Classical Mechanics and Nonlinear Dynamics This second edition of Baumann's Mathematica® in Theoretical Physics shows readers how to solve physical problems and deal with their underlying theoretical concepts while using Mathematica® to derive numeric and symbolic solutions. Each example and calculation can be evaluated by the reader, and the reader can change the example calculations and adopt the given code to related or similar problems. The second edition has been completely revised and expanded into two volumes: The first volume covers classical mechanics and nonlinear dynamics. Both topics are the basis of a regular mechanics course. The second volume covers electrodynamics, quantum mechanics, relativity, and fractals and fractional calculus. New examples have been added and the representation has been reworked to provide a more interactive problem-solving presentation. This book can be used as a textbook or as a reference work, by students and researchers alike. A...

Low-loss saturable absorbers based on tapered fibers embedded in carbon nanotube/polymer composites

Science.gov (United States)

Martinez, Amos; Al Araimi, Mohammed; Dmitriev, Artemiy; Lutsyk, Petro; Li, Shen; Mou, Chengbo; Rozhin, Alexey; Sumetsky, Misha; Turitsyn, Sergei

2017-12-01

The emergence of low-dimensional materials has opened new opportunities in the fabrication of compact nonlinear photonic devices. Single-walled carbon nanotubes were among the first of those materials to attract the attention of the photonics community owing to their high third order susceptibility, broadband operation, and ultrafast response. Saturable absorption, in particular, has become a widespread application for nanotubes in the mode-locking of a fiber laser where they are used as nonlinear passive amplitude modulators to initiate pulsed operation. Numerous approaches have been proposed for the integration of nanotubes in fiber systems; these can be divided into those that rely on direct interaction (where the nanotubes are sandwiched between fiber connectors) and those that rely on lateral interaction with the evanescence field of the propagating wave. Tapered fibers, in particular, offer excellent flexibility to adjust the nonlinearity of nanotube-based devices but suffer from high losses (typically exceeding 50%) and poor saturable to non-saturable absorption ratios (typically above 1:5). In this paper, we propose a method to fabricate carbon nanotube saturable absorbers with controllable saturation power, low-losses (as low as 15%), and large saturable to non-saturable loss ratios approaching 1:1. This is achieved by optimizing the procedure of embedding tapered fibers in low-refractive index polymers. In addition, this study sheds light in the operation of these devices, highlighting a trade-off between losses and saturation power and providing guidelines for the design of saturable absorbers according to their application.

N=4 supersymmetric mechanics with nonlinear chiral supermultiplet

International Nuclear Information System (INIS)

Bellucci, S.; Beylin, A.; Krivonos, S.; Nersessian, A.; Orazi, E.

2005-01-01

We construct N=4 supersymmetric mechanics using the N=4 nonlinear chiral supermultiplet. The two bosonic degrees of freedom of this supermultiplet parameterize the sphere S 2 and go into the bosonic components of the standard chiral multiplet when the radius of the sphere goes to infinity. We construct the most general action and demonstrate that the nonlinearity of the supermultiplet results in the deformation of the connection, which couples the fermionic degrees of freedom with the background, and of the bosonic potential. Also a non-zero magnetic field could appear in the system

Foundations of the non-linear mechanics of continua

CERN Document Server

Sedov, L I

1966-01-01

International Series of Monographs on Interdisciplinary and Advanced Topics in Science and Engineering, Volume 1: Foundations of the Non-Linear Mechanics of Continua deals with the theoretical apparatus, principal concepts, and principles used in the construction of models of material bodies that fill space continuously. This book consists of three chapters. Chapters 1 and 2 are devoted to the theory of tensors and kinematic applications, focusing on the little-known theory of non-linear tensor functions. The laws of dynamics and thermodynamics are covered in Chapter 3.This volume is suitable

Mechanics of inter-modal tunneling in nonlinear waveguides

Science.gov (United States)

Jiao, Weijian; Gonella, Stefano

2018-02-01

In this article, we investigate the mechanics of nonlinearly induced inter-modal energy tunneling between flexurally-dominated and axially-dominated modes in phononic waveguides. Special attention is devoted to elucidating the role played by the coupling between axial and flexural degrees of freedom in the determination of the available mode hopping conditions and the associated mechanisms of deformation. Waveguides offer an ideal test bed to investigate the mechanics of nonlinear energy tunneling, due to the fact that they naturally feature, even at low frequencies, families of modes (flexural and axial) that are intrinsically characterized by extreme complementarity. Moreover, thanks to their geometric simplicity, their behavior can be explained by resorting to intuitive structural mechanics models that effectively capture the dichotomy and interplay between flexural and axial mechanisms. After having delineated the fundamental mechanics of flexural-to-axial hopping using the benchmark example of a homogeneous structure, we adapt the analysis to the case of periodic waveguides, in which the complex dispersive behavior due to periodicity results in additional richness of mode hopping mechanisms. We finally extend the analysis to periodic waveguides with internal resonators, in which the availability of locally-resonant bandgaps implies the possibility to activate the resonators even at relatively low frequencies, thus increasing the degree of modal complementarity that is available in the acoustic range. In this context, inter-modal tunneling provides an unprecedented mechanism to transfer conspicuous packets of energy to the resonating microstructure.

Effect of desaturation and re-saturation on shale in underground galleries; Effets de la desaturation et de la resaturation sur l'argilite dans les ouvrages souterrains

Energy Technology Data Exchange (ETDEWEB)

Pham, Q.T

2006-03-15

The aim of this thesis is to characterize by experimental and numerical approaches the hydric, mechanical and hydro-mechanical effects due to the desaturation and re-saturation of the Eastern argillite, host rock of the Bure site, future underground radioactive waste disposal facility. Experimental and numerical approaches for the characterization of hydric transfers in argilites are presented. A simple identification method is proposed which uses the determination of the linearized hydric diffusivity from weight measurements performed on samples (thin tubes and plates) submitted to humidity steps according to a desaturation-re-saturation cycle. The hydric transfer is nonlinear. In order to interpret this phenomenon, a non-linear numerical model is established which takes into account the physical phenomena (hydraulic conduction, vapor diffusion, phase change..). The evolution of the physical and mechanical behaviour of the argillaceous rock with respect to the imposed humidity is then analyzed according to a desaturation-re-saturation cycle by successive steps. The hydric deformation, the velocity of ultrasonic waves propagation, the elastic properties, the rupture characteristics and the delayed phenomena depend on the hydric state of the material. The desaturation and re-saturation influence on a scale model of tunnel is analyzed. Thick tubes parallel or perpendicular to the stratification are used to show up the anisotropy of the rock. These tubes are submitted to hydric loads by blowing air with variable hygrometry through their center hole. A nonlinear poro-elastic model is used to interpret the anisotropic hydro-mechanical phenomena observed. It is shown that hydric loads can lead to the rupture of test samples which follow the anisotropic directions of the rock and which can be interpreted by the hydro-mechanical model as a violation of a rupture criterion in total pulling stress. Finally, numerical calculations for the phenomena generated by desaturation

Nonlinear mechanics of non-rigid origami: an efficient computational approach

Science.gov (United States)

Liu, K.; Paulino, G. H.

2017-10-01

Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on `bar-and-hinge' models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.

Output feedback control of linear fractional transformation systems subject to actuator saturation

Science.gov (United States)

Ban, Xiaojun; Wu, Fen

2016-11-01

In this paper, the control problem for a class of linear parameter varying (LPV) plant subject to actuator saturation is investigated. For the saturated LPV plant depending on the scheduling parameters in linear fractional transformation (LFT) fashion, a gain-scheduled output feedback controller in the LFT form is designed to guarantee the stability of the closed-loop LPV system and provide optimised disturbance/error attenuation performance. By using the congruent transformation, the synthesis condition is formulated as a convex optimisation problem in terms of a finite number of LMIs for which efficient optimisation techniques are available. The nonlinear inverted pendulum problem is employed to demonstrate the effectiveness of the proposed approach. Moreover, the comparison between our LPV saturated approach with an existing linear saturated method reveals the advantage of the LPV controller when handling nonlinear plants.

Experimental analysis of nonlinear problems in solid mechanics

International Nuclear Information System (INIS)

1982-01-01

The booklet presents abstracts of papers from the Euromech Colloqium No. 152 held from Sept. 20th to 24th, 1982 in Wuppertal, Federal Republic of Germany. All the papers are dealing with Experimental Analysis of Nonlinear Problems in Solid Mechanics. (RW)

Low-loss saturable absorbers based on tapered fibers embedded in carbon nanotube/polymer composites

Directory of Open Access Journals (Sweden)

Amos Martinez

2017-12-01

Full Text Available The emergence of low-dimensional materials has opened new opportunities in the fabrication of compact nonlinear photonic devices. Single-walled carbon nanotubes were among the first of those materials to attract the attention of the photonics community owing to their high third order susceptibility, broadband operation, and ultrafast response. Saturable absorption, in particular, has become a widespread application for nanotubes in the mode-locking of a fiber laser where they are used as nonlinear passive amplitude modulators to initiate pulsed operation. Numerous approaches have been proposed for the integration of nanotubes in fiber systems; these can be divided into those that rely on direct interaction (where the nanotubes are sandwiched between fiber connectors and those that rely on lateral interaction with the evanescence field of the propagating wave. Tapered fibers, in particular, offer excellent flexibility to adjust the nonlinearity of nanotube-based devices but suffer from high losses (typically exceeding 50% and poor saturable to non-saturable absorption ratios (typically above 1:5. In this paper, we propose a method to fabricate carbon nanotube saturable absorbers with controllable saturation power, low-losses (as low as 15%, and large saturable to non-saturable loss ratios approaching 1:1. This is achieved by optimizing the procedure of embedding tapered fibers in low-refractive index polymers. In addition, this study sheds light in the operation of these devices, highlighting a trade-off between losses and saturation power and providing guidelines for the design of saturable absorbers according to their application.

Surface plasmon enhanced third-order optical nonlinearity of Ag nanocomposite film

International Nuclear Information System (INIS)

Singh, Vijender; Aghamkar, Praveen

2014-01-01

We obtain a large third-order optical nonlinearity (χ (3)  ≈ 10 −10 esu) of silver nanoparticles dispersed in polyvinyl alcohol/tetraethyl orthosilicate matrix using single beam z-scan technique at 532 nm by Q-switched Nd:YAG laser. We have shown that mechanisms responsible for third-order optical nonlinearity of Ag nanocomposite film are reverse saturable absorption (RSA) and self-defocusing in the purlieu of surface plasmon resonance (SPR). Optical band-gap and width of SPR band of Ag nanocomposite film decrease with increasing silver concentration, which leads to enhancement of local electric field and hence third-order optical nonlinearity. Optical limiting, due to RSA has also been demonstrated at 532 nm

Nonlinear theory of the collisional Rayleigh-Taylor instability in equatorial spread F

International Nuclear Information System (INIS)

Chaturvedi, P.K.; Ossakow, S.L.

1977-01-01

The nonlinear behavior of the collisional Rayleigh-Taylor instability is studied in equatorial Spread F by including a dominant two-dimensional nonlinearity. It is found that on account of this nonlinearity the instability saturates by generating damped higher spatial harmonics. The saturated power spectrum for the density fluctuations is discussed. A comparison between experimental observations and theory is presented

Non-linear hydrodynamic instability and turbulence in eccentric astrophysical discs with vertical structure

Science.gov (United States)

Wienkers, A. F.; Ogilvie, G. I.

2018-04-01

Non-linear evolution of the parametric instability of inertial waves inherent to eccentric discs is studied by way of a new local numerical model. Mode coupling of tidal deformation with the disc eccentricity is known to produce exponentially growing eccentricities at certain mean-motion resonances. However, the details of an efficient saturation mechanism balancing this growth still are not fully understood. This paper develops a local numerical model for an eccentric quasi-axisymmetric shearing box which generalises the often-used cartesian shearing box model. The numerical method is an overall second order well-balanced finite volume method which maintains the stratified and oscillatory steady-state solution by construction. This implementation is employed to study the non-linear outcome of the parametric instability in eccentric discs with vertical structure. Stratification is found to constrain the perturbation energy near the mid-plane and localise the effective region of inertial wave breaking that sources turbulence. A saturated marginally sonic turbulent state results from the non-linear breaking of inertial waves and is subsequently unstable to large-scale axisymmetric zonal flow structures. This resulting limit-cycle behaviour reduces access to the eccentric energy source and prevents substantial transport of angular momentum radially through the disc. Still, the saturation of this parametric instability of inertial waves is shown to damp eccentricity on a time-scale of a thousand orbital periods. It may thus be a promising mechanism for intermittently regaining balance with the exponential growth of eccentricity from the eccentric Lindblad resonances and may also help explain the occurrence of "bursty" dynamics such as the superhump phenomenon.

Features and states of microscopic particles in nonlinear quantum-mechanics systems

Institute of Scientific and Technical Information of China (English)

2008-01-01

In this paper,we present the elementary principles of nonlinear quantum mechanics(NLQM),which is based on some problems in quantum mechanics.We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles.Concretely speaking,we study in this paper the wave-particle duality of the solution of the nonlinear Schr6dinger equation,the stability of microscopic particles described by NLQM,invariances and conservation laws of motion of particles,the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations,the classical rule of microscopic particle motion,the mechanism and rules of particle collision,the features of reflection and the transmission of particles at interfaces,and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles,and so on.We obtained the invariance and conservation laws of mass,energy and momentum and angular momenturn for the microscopic particles,which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions.We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics(LQM).They have a lot of new properties;for example,the particles possess the real wave-corpuscle duality,obey the classical rule of motion and conservation laws of energy,momentum and mass,satisfy minimum uncertainty relation,can be localized due to the nonlinear interaction,and its position and momentum can also be determined,etc.From these studies,we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM.Therefore,the NLQM is a new physical theory,and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems,which can

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Science.gov (United States)

Clark, S. E.; Oishi, Jeffrey S.

2017-05-01

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg-Landau equation. We further find that the Ginzburg-Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

The Weakly Nonlinear Magnetorotational Instability in a Local Geometry

Energy Technology Data Exchange (ETDEWEB)

Clark, S. E. [Department of Astronomy, Columbia University, New York, NY 10027 (United States); Oishi, Jeffrey S., E-mail: seclark@astro.columbia.edu [Department of Physics and Astronomy, Bates College, Lewiston, ME 04240 (United States)

2017-05-20

The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple-scales analysis of the non-ideal MRI in the weakly nonlinear regime—that is, when the most unstable MRI mode has a growth rate asymptotically approaching zero from above. Here, we develop our theory in a local, Cartesian channel. Our results confirm the finding by Umurhan et al. that the perturbation amplitude follows a Ginzburg–Landau equation. We further find that the Ginzburg–Landau equation will arise for the local MRI system with shear-periodic boundary conditions, when the effects of ambipolar diffusion are considered. A detailed force balance for the saturated azimuthal velocity and vertical magnetic field demonstrates that, even when diffusive effects are important, the bulk flow saturates via the combined processes of reducing the background shear and rearranging and strengthening the background vertical magnetic field. We directly simulate the Ginzburg–Landau amplitude evolution for our system, and demonstrate the pattern formation our model predicts on long scales of length- and timescales. We compare the weakly nonlinear theory results to a direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.

Saturable absorption in detonation nanodiamond dispersions

Science.gov (United States)

Vanyukov, Viatcheslav; Mikheev, Gennady; Mogileva, Tatyana; Puzyr, Alexey; Bondar, Vladimir; Lyashenko, Dmitry; Chuvilin, Andrey

2017-07-01

We report on a saturable absorption in aqueous dispersions of nanodiamonds with femtosecond laser pulse excitation at a wavelength of 795 nm. The open aperture Z-scan experiments reveal that in a wide range of nanodiamond particle sizes and concentrations, a light-induced increase of transmittance occurs. The transmittance increase originates from the saturation of light absorption and is associated with a light absorption at 1.5 eV by graphite and dimer chains (Pandey dimer chains). The obtained key nonlinear parameters of nanodiamond dispersions are compared with those of graphene and carbon nanotubes, which are widely used for the mode-locking.

The mechanism by which nonlinearity sustains turbulence in plane Couette flow

Science.gov (United States)

Nikolaidis, M.-A.; Farrell, B. F.; Ioannou, P. J.

2018-04-01

Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energy-transferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at R = 600 and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence.

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

International Nuclear Information System (INIS)

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

2012-01-01

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

Effects of initial radius of the interface and Atwood number on nonlinear saturation amplitudes in cylindrical Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Liu, Wanhai; Yu, Changping; Li, Xinliang

2014-01-01

Nonlinear saturation amplitudes (NSAs) of the first two harmonics in classical Rayleigh-Taylor instability (RTI) in cylindrical geometry for arbitrary Atwood numbers have been analytically investigated considering nonlinear corrections up to the fourth-order. The NSA of the fundamental mode is defined as the linear (purely exponential) growth amplitude of the fundamental mode at the saturation time when the growth of the fundamental mode (first harmonic) is reduced by 10% in comparison to its corresponding linear growth, and the NSA of the second harmonic can be obtained in the same way. The analytic results indicate that the effects of the initial radius of the interface (r 0 ) and the Atwood number (A) play an important role in the NSAs of the first two harmonics in cylindrical RTI. On the one hand, the NSA of the fundamental mode first increases slightly and then decreases quickly with increasing A. For given A, the smaller the r 0 /λ (with λ perturbation wavelength) is, the larger the NSA of the fundamental mode is. When r 0 /λ is large enough (r 0 ≫λ), the NSA of the fundamental mode is reduced to the prediction of previous literatures within the framework of third-order perturbation theory [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988); S. W. Haan, Phys. Fluids B 3, 2349 (1991)]. On the other hand, the NSA of the second harmonic first decreases quickly with increasing A, reaching a minimum, and then increases slowly. Furthermore, the r 0 can reduce the NSA of the second harmonic for arbitrary A at r 0 ≲2λ while increase it for A ≲ 0.6 at r 0 ≳2λ. Thus, it should be included in applications where the NSA has a role, such as inertial confinement fusion ignition target design

MECHANISM OF OPTICAL NONLINEARITY IN “LYOTROPIC LIQUID CRYSTAL — VIOLOGEN” SYSTEM

Directory of Open Access Journals (Sweden)

Hanna Bordyuh

2014-06-01

Full Text Available In the present work we analyze the characteristics of holographic grating recording and consider a mechanism of optical nonlinearity in the lyotropic liquid crystal (LLC — viologen samples. Taking into account structural and electrooptical properties of the admixture molecules it is possible to suggest that the recording is realized due to the change of polarizability of π-electron system of coloured viologen derivatives under the action of laser radiation. The main nonlinear optical parameters such as nonlinear refraction coefficient n2, cubic nonlinear susceptibility χ(3, and hyperpolarizability γ were calculated.

Nonlinear feedback control of chaotic pendulum in presence of saturation effect

Energy Technology Data Exchange (ETDEWEB)

Alasty, Aria [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 1458889694 (Iran, Islamic Republic of)]. E-mail: aalasti@sharif.edu; Salarieh, Hassan [Center of Excellence in Design, Robotics, and Automation (CEDRA), Department of Mechanical Engineering, Sharif University of Technology, Azadi Avenue, Tehran 1458889694 (Iran, Islamic Republic of)]. E-mail: salarieh@mehr.sharif.edu

2007-01-15

In present paper, a feedback linearization control is applied to control a chaotic pendulum system. Tracking the desired periodic orbits such as period-one, period-two, and period-four orbits is efficiently achieved. Due to the presence of saturation in real world control signals, the stability of controller is investigated in presence of saturation and sufficient stability conditions are obtained. At first feedback linearization control law is designed, then to avoid the singularity condition, a saturating constraint is applied to the control signal. The stability conditions are obtained analytically. These conditions must be investigated for each specific case numerically. Simulation results show the effectiveness and robustness of proposed controller. A major advantage of this method is its shorter chaotic transient time in compare to other methods such as OGY and Pyragas controllers.

Technical report on micro-mechanical versus conventional modelling in non-linear fracture mechanics

International Nuclear Information System (INIS)

2001-07-01

While conventional fracture mechanics is capable of predicting crack growth behaviour if sufficient experimental observations are available, micro-mechanical modelling can both increase the accuracy of these predictions and model phenomena that are inaccessible by the conventional theory such as the ductile-cleavage temperature transition. A common argument against micro-mechanical modelling is that it is too complicated for use in routine engineering applications. This is both a computational and an educational problem. That micro-mechanical modelling is unnecessarily complicated is certainly true in many situations. The on-going development of micro-mechanical models, computational algorithms and computer speed will however most probably diminish the computational problem rather rapidly. Compare for instance the rate of development of computational methods for structural analysis. Meanwhile micro-mechanical modelling may serve as a tool by which more simplified engineering methods can be validated. The process of receiving a wide acceptance of the new methods is probably much slower. This involves many steps. First the research community must be in reasonable agreement on the methods and their use. Then the methods have to be implemented into computer software and into code procedures. The development and acceptance of conventional fracture mechanics may serve as an historical example of the time required before a new methodology has received a wide usage. The CSNI Working Group on Integrity and Ageing (IAGE) decided to carry out a report on micro-mechanical modeling to promote this promising and valuable technique. The report presents a comparison with non-linear fracture mechanics and highlights key aspects that could lead to a better knowledge and accurate predictions. Content: - 1. Introduction; - 2. Concepts of non-linear fracture mechanics with point crack tip modelling; - 3. Micro-mechanical models for cleavage fracture; - 4, Micro-mechanical modelling of

Surface plasmon enhanced third-order optical nonlinearity of Ag nanocomposite film

Energy Technology Data Exchange (ETDEWEB)

Singh, Vijender [Department of Applied Science, N.C. College of Engineering, Israna, Panipat 132107, Haryana (India); Aghamkar, Praveen, E-mail: p-aghamkar@yahoo.in [Department of Physics, Chaudhary Devi Lal University, Sirsa 125055, Haryana (India)

2014-03-17

We obtain a large third-order optical nonlinearity (χ{sup (3)} ≈ 10{sup −10}esu) of silver nanoparticles dispersed in polyvinyl alcohol/tetraethyl orthosilicate matrix using single beam z-scan technique at 532 nm by Q-switched Nd:YAG laser. We have shown that mechanisms responsible for third-order optical nonlinearity of Ag nanocomposite film are reverse saturable absorption (RSA) and self-defocusing in the purlieu of surface plasmon resonance (SPR). Optical band-gap and width of SPR band of Ag nanocomposite film decrease with increasing silver concentration, which leads to enhancement of local electric field and hence third-order optical nonlinearity. Optical limiting, due to RSA has also been demonstrated at 532 nm.

Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schrödinger equation

KAUST Repository

Crosta, M.; Fratalocchi, Andrea; Trillo, S.

2011-01-01

We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.

Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schrödinger equation

KAUST Repository

Crosta, M.

2011-12-05

We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.

Analysis of the interplay of quantum phases and nonlinearity applied to dimers with anharmonic interactions

International Nuclear Information System (INIS)

Raghavan, S.

1997-06-01

We extend our analysis of the effects of the interplay of quantum phases and nonlinearity to address saturation effects in small quantum systems. We find that initial phases dramatically control the dependence of self-trapping on initial asymmetry of quasiparticle population and can compete or act with nonlinearity as well as saturation effects. We find that there is a minimum finite saturation value in order to obtain self-trapping that crucially depends on the initial quasiparticle phases and present a detailed phase-diagram in terms of the control parameters of the system: nonlinearity and saturation. (author). 14 refs, 3 figs

A Galerkin discretisation-based identification for parameters in nonlinear mechanical systems

Science.gov (United States)

Liu, Zuolin; Xu, Jian

2018-04-01

In the paper, a new parameter identification method is proposed for mechanical systems. Based on the idea of Galerkin finite-element method, the displacement over time history is approximated by piecewise linear functions, and the second-order terms in model equation are eliminated by integrating by parts. In this way, the lost function of integration form is derived. Being different with the existing methods, the lost function actually is a quadratic sum of integration over the whole time history. Then for linear or nonlinear systems, the optimisation of the lost function can be applied with traditional least-squares algorithm or the iterative one, respectively. Such method could be used to effectively identify parameters in linear and arbitrary nonlinear mechanical systems. Simulation results show that even under the condition of sparse data or low sampling frequency, this method could still guarantee high accuracy in identifying linear and nonlinear parameters.

Nonlinear Viscoelastic Mechanism for Aftershock Triggering and Decay

Science.gov (United States)

Shcherbakov, R.; Zhang, X.

2016-12-01

Aftershocks are ubiquitous in nature. They are the manifestation of relaxation phenomena observed in various physical systems. In one prominent example, they typically occur after large earthquakes. They also occur in other natural or experimental systems, for example, in solar flares, in fracture experiments on porous materials and acoustic emissions, after stock market crashes, in the volatility of stock prices returns, in internet traffic variability and e-mail spamming, to mention a few. The observed aftershock sequences usually obey several well defined non-trivial empirical laws in magnitude, temporal, and spatial domains. In many cases their characteristics follow scale-invariant distributions. The occurrence of aftershocks displays a prominent temporal behavior due to time-dependent mechanisms of stress and/or energy transfer. In this work, we consider a slider-block model to mimic the behavior of a seismogenic fault. In the model, we introduce a nonlinear viscoelastic coupling mechanism to capture the essential characteristics of crustal rheology and stress interaction between the blocks and the medium. For this purpose we employ nonlinear Kelvin-Voigt elements consisting of an elastic spring and a dashpot assembled in parallel to introduce viscoelastic coupling between the blocks and the driving plate. By mapping the model into a cellular automaton we derive the functional form of the stress transfer mechanism in the model. We show that the nonlinear viscoelasticity plays a critical role in triggering of aftershocks. It explains the functional form of the Omori-Utsu law and gives physical interpretation of its parameters. The proposed model also suggests that the power-law rheology of the fault gauge and underlying lower crust and upper mantle control the decay rate of aftershocks. To verify this, we analyze several prominent aftershock sequences to estimate their decay rates and correlate with the rheological properties of the underlying lower crust and

Non-linearity in radiocaesium soil to plant transfer: fact or fiction?

International Nuclear Information System (INIS)

Beresford, N.A.; Scott, W.A.; Wright, S.M.

2004-01-01

The basis premise of many radiological assessments is the assumption that the transfer of many radionuclides from soil to herbage and hence animal derived food products is a positive linear relationship for a given set of ecological conditions. However, a number of authors have published results which they conclude demonstrate non-linear transfer of radiocaesium to plants and animals with transfer being highest when soil concentrations are lowest. Whilst we may expect non-linear transfer of radionuclides under homeostatic control or present in comparatively large chemical quantities there appears no credible hypothesis to support such an observation for radiocaesium. In this paper we review those articles which have reported non-linear radiocaesium transfer and also analyse novel data. Mechanisms for the observation as presented in the original works are critically assessed. For instance, some authors have speculated that radiocaesium root uptake is saturated. We suggest that this is unlikely as whilst saturation of root uptake of radiocaesium has been observed above 1.37 mg Cs + L -1 in growth solutions, concentrations of Cs + in soil solutions are typically -1 , and 1 MBq m -2 of 137 Cs will add only 0.3 mg Cs + m -2 . We discuss alternative hypotheses to explain the reported observations and suggest that sampling bias, countermeasure application and statistical chance all contribute to the reported non-linearity in radiocaesium transfer. (author)

Positive Nonlinear Dynamical Group Uniting Quantum Mechanics and Thermodynamics

OpenAIRE

Beretta, Gian Paolo

2006-01-01

We discuss and motivate the form of the generator of a nonlinear quantum dynamical group 'designed' so as to accomplish a unification of quantum mechanics (QM) and thermodynamics. We call this nonrelativistic theory Quantum Thermodynamics (QT). Its conceptual foundations differ from those of (von Neumann) quantum statistical mechanics (QSM) and (Jaynes) quantum information theory (QIT), but for thermodynamic equilibrium (TE) states it reduces to the same mathematics, and for zero entropy stat...

Molecular mechanisms underlying the protective effects of hydrogen-saturated saline on noise-induced hearing loss.

Science.gov (United States)

Chen, Liwei; Han, Mingkun; Lu, Yan; Chen, Daishi; Sun, Xuejun; Yang, Shiming; Sun, Wei; Yu, Ning; Zhai, Suoqiang

2017-10-01

This study aimed to explore the molecular mechanism of the protective effects of hydrogen-saturated saline on NIHL. Guinea pigs were divided into three groups: hydrogen-saturated saline; normal saline; and control. For saline administration, the guinea pigs were given daily abdominal injections 3 d before and 1 h before noise exposure. ABR were tested to examine cochlear physiology changes. The changes of 8-hydroxy-desoxyguanosine (8-HOdG), interleukin-1 (IL-1), interleukin-6 (IL-6), interleukin-10 (IL-10), tumor necrosis factor-α (TNF-α), intercellular cell adhesion molecule-1 (ICAM-1) and high mobility group box-1 protein (HMGB1) in the cochlea were also examined. The results showed that pre-treatment with hydrogen-saturated saline could significantly attenuate noise-induced hearing loss. The concentration of 8-HOdG was also significantly decreased in the hydrogen-saturated saline group compared with the normal saline group. After noise exposure, the concentrations of IL-1, IL-6, TNF-α, and ICAM-1 in the cochlea of guinea pigs in the hydrogen-saturated saline group were dramatically reduced compared to those in the normal saline group. The concentrations of HMGB-1 and IL-10 in the hydrogen-saturated saline group were significantly higher than in those in the normal saline group immediately and at 7 d after noise exposure. This study revealed for the first time the protective effects of hydrogen-saturated saline on noise-induced hearing loss (NIHL) are related to both the anti-oxidative activity and anti-inflammatory activity.

Non color-saturated cross-sections of non-linear tomography and seismicity

International Nuclear Information System (INIS)

Panza, G.F.; Raykova, R.B.

2007-11-01

We define the structure and the rheology of the lithosphere in Italy and surrounding, combining the cellular velocity model, derived from the non-linear tomographic inversion, with the distribution versus depth of the hypocenters to assess the brittle properties of the fragile Earth. The mechanical properties, and their uncertainties, of the uppermost 60 km of the Earth crust/mantle and the seismicity, grouping hypocenter's depth with a step of 4 km, are averaged over cells of 1 deg. by 1 deg. For most of the cells the earthquake energy released has a maximum in the depth range, from 5 to 15 km, i.e. mainly in the upper crust. For some regions, where orogenic processes are in progress, the release of seismic energy is shallower and is concentrated in the uppermost 10 km of the crust. (author)

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

Science.gov (United States)

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

2010-06-01

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

Nonlinear dynamics of a driven mode near marginal stability

International Nuclear Information System (INIS)

Berk, H.L.; Breizman, B.N.; Pekker, M.

1995-09-01

The nonlinear dynamics of a linearly unstable mode in a driven kinetic system is investigated to determine scaling of the saturated fields near the instability threshold. To leading order, this problem reduces to solving an integral equation with a temporally nonlocal cubic term. This equation can exhibit a self-similar solution that blows up in a finite time. When the blow-up occurs, higher nonlinearities become important and the mode saturates due to plateau formation arising from particle trapping in the wave. Otherwise, the simplified equation gives a regular solution that leads to a different saturation scaling reflecting the closeness to the instability threshold

Lectures in nonlinear mechanics and chaos theory

CERN Document Server

Stetz, Albert W

2016-01-01

This elegant book presents a rigorous introduction to the theory of nonlinear mechanics and chaos. It turns out that many simple mechanical systems suffer from a peculiar malady. They are deterministic in the sense that their motion can be described with partial differential equations, but these equations have no proper solutions and the behavior they describe can be wildly unpredictable. This is implicit in Newtonian physics, and although it was analyzed in the pioneering work of Poincaré in the 19th century, its full significance has only been realized since the advent of modern computing. This book follows this development in the context of classical mechanics as it is usually taught in most graduate programs in physics. It starts with the seminal work of Laplace, Hamilton, and Liouville in the early 19th century and shows how their formulation of mechanics inevitably leads to systems that cannot be 'solved' in the usual sense of the word. It then discusses perturbation theory which, rather than providing...

4th International Conference on Nonlinear Mechanics

CERN Document Server

Maugin, G

2003-01-01

The mechanics of electromagnetic materials and structures has been developing rapidly with extensive applications in, e. g. , electronics industry, nuclear engineering, and smart materials and structures. Researchers in this interdisciplinary field are with diverse background and motivation. The Symposium on the Mechanics of Electromagnetic Materials and Structures of the Fourth International Conference on Nonlinear Mechanics in Shanghai, China in August 13-16, 2002 provided an opportunity for an intimate gathering of researchers and exchange of ideas. This volume contains papers based on most of the presentations at the symposium, and articles from a few invited contributors. These papers reflect some of the recent activities in the mechanics of electromagnetic materials and structures. The first twelve papers are in the order in which they were listed in the program of the conference. These are followed by six invited papers in alphabetical order of the last names of the first authors. We would like to exte...

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

Science.gov (United States)

Kearns, Sarah; Das, Moumita

2015-03-01

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

Nonlinear development of the two-plasmon decay instability in three dimensions

Energy Technology Data Exchange (ETDEWEB)

Vu, H. X. [University of California, San Diego, La Jolla, California 92093 (United States); DuBois, D. F.; Russell, D. A. [Lodestar Research Corporation, Boulder, Colorado 80301 (United States); Myatt, J. F.; Zhang, J. [Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623 (United States); Department of Mechanical Engineering, University of Rochester, Rochester, New York 14627 (United States)

2014-04-15

Most recent experiments on the excitation of the two plasmon-decay (TPD) instability involve a three-dimensional (3D) array of overlapping laser beams. Our recent two dimensional (2D) simulations suggested that Langmuir cavitation and collapse are important nonlinear saturation mechanisms for TPD. There are important quantitative differences in the Langmuir collapse process in 2D and 3D. To address these and other issues, we have developed a 3D Zakharov code. It has been applied to study the evolution of TPD from absolute instabilities (arising from 3D laser geometries) to the nonlinear state (J. Zhang et al., Phys. Rev. Lett. (submitted)). The present paper concentrates on the nonlinear saturated state excited by the collective action of two crossed laser beams with arbitrary polarizations. Remarkable agreement between 3D and 2D simulations is found for several averaged physical quantities when the beams are polarized in their common plane. As in the previous 2D simulations, we find: (a) the collective, initially convectively unstable triad modes dominate after a sub-picosecond burst, (b) Langmuir cavitation and collapse are important nonlinearities, and (c) that the statistics of intense cavitons are characteristic of a Gaussian random process. The 3D steady-state saturated Langmuir energy level is about 30% higher than in 2D. The auto-correlation functions of the Langmuir envelope field and of the low-frequency electron density field yield the spatial shape of the strongest collapsing cavitons which are 3D ellipsoids whose orientation depends on the laser polarizations. This tilting of the caviton's strongest electric field direction away from the normal to the target surface is a major new 3D result. This tilting may deflect the hot electron flux and thereby mitigate target preheat.

Identification of Nonlinear Micron-Level Mechanics for a Precision Deployable Joint

Science.gov (United States)

Bullock, S. J.; Peterson, L. D.

1994-01-01

The experimental identification of micron-level nonlinear joint mechanics and dynamics for a pin-clevis joint used in a precision, adaptive, deployable space structure are investigated. The force-state mapping method is used to identify the behavior of the joint under a preload. The results of applying a single tension-compression cycle to the joint under a tensile preload are presented. The observed micron-level behavior is highly nonlinear and involves all six rigid body motion degrees-of-freedom of the joint. it is also suggests that at micron levels of motion modelling of the joint mechanics and dynamics must include the interactions between all internal components, such as the pin, bushings, and the joint node.

Experimental and numerical study on thermal conductivity of partially saturated unconsolidated sands

Science.gov (United States)

Lee, Youngmin; Keehm, Youngseuk; Kim, Seong-Kyun; Shin, Sang Ho

2016-04-01

A class of problems in heat flow applications requires an understanding of how water saturation affects thermal conductivity in the shallow subsurface. We conducted a series of experiments using a sand box to evaluate thermal conductivity (TC) of partially saturated unconsolidated sands under varying water saturation (Sw). We first saturated sands fully with water and varied water saturation by drainage through the bottom of the sand box. Five water-content sensors were integrated vertically into the sand box to monitor water saturation changes and a needle probe was embedded to measure thermal conductivity of partially saturated sands. The experimental result showed that thermal conductivity decreases from 2.5 W/mK for fully saturated sands to 0.7 W/mK when water saturation is 5%. We found that the decreasing trend is quite non-linear: highly sensitive at very high and low water saturations. However, the boundary effects on the top and the bottom of the sand box seemed to be responsible for this high nonlinearity. We also found that the determination of water saturation is quite important: the saturation by averaging values from all five sensors and that from the sensor at the center position, showed quite different trends in the TC-Sw domain. In parallel, we conducted a pore-scale numerical modeling, which consists of the steady-state two-phase Lattice-Boltzmann simulator and FEM thermal conduction simulator on digital pore geometry of sand aggregation. The simulation results showed a monotonous decreasing trend, and are reasonably well matched with experimental data when using average water saturations. We concluded that thermal conductivity would decrease smoothly as water saturation decreases if we can exclude boundary effects. However, in dynamic conditions, i.e. imbibition or drainage, the thermal conductivity might show hysteresis, which can be investigated with pore-scale numerical modeling with unsteady-state two-phase flow simulators in our future work.

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

Modeling of Nonlinear Mechanical Response in CFRP Angle-Ply Laminates

Science.gov (United States)

Ogihara, Shinji

2014-03-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

1999-03-01

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

Nonlinear Thermo-mechanical Finite Element Analysis of Polymer Foam Cored Sandwich Structures including Geometrical and Material Nonlinearity

DEFF Research Database (Denmark)

Palleti, Hara Naga Krishna Teja; Thomsen, Ole Thybo; Taher, Siavash Talebi

In this paper, polymer foam cored sandwich structures with fibre reinforced composite face sheets subjected to combined mechanical and thermal loads will be analysed using the commercial FE code ABAQUS® incorporating both material and geometrical nonlinearity. Large displacements and rotations...

A non-linear state space approach to model groundwater fluctuations

NARCIS (Netherlands)

Berendrecht, W.L.; Heemink, A.W.; Geer, F.C. van; Gehrels, J.C.

2006-01-01

A non-linear state space model is developed for describing groundwater fluctuations. Non-linearity is introduced by modeling the (unobserved) degree of water saturation of the root zone. The non-linear relations are based on physical concepts describing the dependence of both the actual

Single-nary philosophy for non-linear study of mechanics of materials

International Nuclear Information System (INIS)

Tran, C.

2005-01-01

Non-linear study of mechanics of materials is formulated in this paper as a problem of meta-intelligent system analysis. Non-linearity will be singled out as an important concept for understanding of high-order complex systems. Through single-nary thinking, which will be represented in this work, we introduce a modification of Aristotelian philosophy using modal logic and multi-valued logic (these logics we call 'high-order' logic). Next, non-linear cause - effect relations are expressed through non-additive measures and multiple-information aggregation principles based on fuzzy integration. The study of real time behaviors, required experiences and intuition, will be realized using truth measures (non-additive measures) and a procedure for information processing in intelligence levels. (author)

Spectral dependence of third-order nonlinear optical properties in InN

International Nuclear Information System (INIS)

Ahn, H.; Lee, M.-T.; Chang, Y.-M.

2014-01-01

We report on the nonlinear optical properties of InN measured in a wide near-infrared spectral range with the femtosecond Z-scan technique. The above-bandgap nonlinear absorption in InN is found to originate from the saturation of absorption by the band-state-filling and its cross-section increases drastically near the bandgap energy. With below-bandgap excitation, the nonlinear absorption undergoes a transition from saturation absorption (SA) to reverse-SA (RSA), attributed to the competition between SA of band-tail states and two-photon-related RSA. The measured large nonlinear refractive index of the order of 10 −10 cm 2 /W indicates InN as a potential material for all-optical switching and related applications

Third order nonlinear optical properties and optical limiting behavior of alkali metal complexes of p-nitrophenol

Science.gov (United States)

Thangaraj, M.; Vinitha, G.; Sabari Girisun, T. C.; Anandan, P.; Ravi, G.

2015-10-01

Optical nonlinearity of metal complexes of p-nitrophenolate (M=Li, Na and K) in ethanol is studied by using a continuous wave (cw) diode pumped Nd:YAG laser (532 nm, 50 mW). The predominant mechanism of observed nonlinearity is thermal in origin. The nonlinear refractive index and the nonlinear absorption coefficient of the samples were found to be in the order of 10-8 cm2/W and 10-3 cm/W respectively. Magnitude of third-order optical parameters varies according to the choice of alkali metal chosen for metal complex formation of p-nitrophenolate. The third-order nonlinear susceptibility was found to be in the order of 10-6 esu. The observed saturable absorption and the self-defocusing effect were used to demonstrate the optical limiting action at 532 nm by using the same cw laser beam.

Spread F bubbles - Nonlinear Rayleigh-Taylor mode in two dimensions

Science.gov (United States)

Hudson, M. K.

1978-01-01

The paper discusses long-wavelength developed bottomside spread F which has been attributed to the Rayleigh-Taylor instability. The nonlinear saturation amplitude and the k spectrum of the inertia-dominated Rayleigh-Taylor instability is found in two directions: east-west and vertical. As in the collisional case (Chaturvedi and Ossakow, 1977), the dominant nonlinearity is found to be two-dimensional. It is found that the linearly most unstable modes, which are primarily horizontal, saturate by the nonlinear generation of vertical spatial harmonics. The harmonics are damped by diffusion or recombination. The resulting amplitude spectrum indicates that bubbles are vertically elongated in both inertial and collisional regimes.

The role of dendritic non-linearities in single neuron computation

Directory of Open Access Journals (Sweden)

Boris Gutkin

2014-05-01

Full Text Available Experiment has demonstrated that summation of excitatory post-synaptic protientials (EPSPs in dendrites is non-linear. The sum of multiple EPSPs can be larger than their arithmetic sum, a superlinear summation due to the opening of voltage-gated channels and similar to somatic spiking. The so-called dendritic spike. The sum of multiple of EPSPs can also be smaller than their arithmetic sum, because the synaptic current necessarily saturates at some point. While these observations are well-explained by biophysical models the impact of dendritic spikes on computation remains a matter of debate. One reason is that dendritic spikes may fail to make the neuron spike; similarly, dendritic saturations are sometime presented as a glitch which should be corrected by dendritic spikes. We will provide solid arguments against this claim and show that dendritic saturations as well as dendritic spikes enhance single neuron computation, even when they cannot directly make the neuron fire. To explore the computational impact of dendritic spikes and saturations, we are using a binary neuron model in conjunction with Boolean algebra. We demonstrate using these tools that a single dendritic non-linearity, either spiking or saturating, combined with somatic non-linearity, enables a neuron to compute linearly non-separable Boolean functions (lnBfs. These functions are impossible to compute when summation is linear and the exclusive OR is a famous example of lnBfs. Importantly, the implementation of these functions does not require the dendritic non-linearity to make the neuron spike. Next, We show that reduced and realistic biophysical models of the neuron are capable of computing lnBfs. Within these models and contrary to the binary model, the dendritic and somatic non-linearity are tightly coupled. Yet we show that these neuron models are capable of linearly non-separable computations.

Hidden Area and Mechanical Nonlinearities in Freestanding Graphene

Science.gov (United States)

Nicholl, Ryan J. T.; Lavrik, Nickolay V.; Vlassiouk, Ivan; Srijanto, Bernadeta R.; Bolotin, Kirill I.

2017-06-01

We investigated the effect of out-of-plane crumpling on the mechanical response of graphene membranes. In our experiments, stress was applied to graphene membranes using pressurized gas while the strain state was monitored through two complementary techniques: interferometric profilometry and Raman spectroscopy. By comparing the data obtained through these two techniques, we determined the geometric hidden area which quantifies the crumpling strength. While the devices with hidden area ˜0 % obeyed linear mechanics with biaxial stiffness 428 ±10 N /m , specimens with hidden area in the range 0.5%-1.0% were found to obey an anomalous nonlinear Hooke's law with an exponent ˜0.1 .

Traveling wave fronts and the transition to saturation

International Nuclear Information System (INIS)

Munier, S.; Peschanski, R.

2004-01-01

We propose a general method to study the solutions to nonlinear QCD evolution equations, based on a deep analogy with the physics of traveling waves. In particular, we show that the transition to the saturation regime of high energy QCD is identical to the formation of the front of a traveling wave. Within this physical picture, we provide the expressions for the saturation scale and the gluon density profile as a function of the total rapidity and the transverse momentum. The application to the Balitskii-Kovchegov equation for both fixed and running coupling constants confirms the effectiveness of this method

Control mechanisms for a nonlinear model of international relations

Energy Technology Data Exchange (ETDEWEB)

Pentek, A.; Kadtke, J. [Univ. of California, San Diego, La Jolla, CA (United States). Inst. for Pure and Applied Physical Sciences; Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.

1997-07-15

Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.

Occurrence of two-photon absorption saturation in Ag nanocolloids, prepared by chemical reduction method

Energy Technology Data Exchange (ETDEWEB)

Rahulan, K. Mani, E-mail: krahul.au@gmail.com [Department of Physics, Anna University, Chennai (India); Ganesan, S. [Department of Physics, Anna University, Chennai (India); Aruna, P., E-mail: aruna@annauniv.edu [Department of Physics, Anna University, Chennai (India)

2012-09-01

Highlights: Black-Right-Pointing-Pointer Ag nanocolloids were synthesized via chemical reduction method. Black-Right-Pointing-Pointer The molecules of PVP play an important role in growth and agglomeration of silver nanocolloids. Black-Right-Pointing-Pointer Saturation behaviour followed by two photon absorption was responsible for good optical limiting characteristics in these nanocolloids. Black-Right-Pointing-Pointer The nonlinear optical parameters calculated from the data showed that these materials could be used as efficient optical limiters. - Abstract: Silver nanocolloids stabilized with polyvinyl pyrrolidone (PVP) have been prepared from (AgNO{sub 3}) by a chemical reduction method, involving the intermediate preparation of (Ag{sub 2}O) colloidal dispersions in the presence of sodium dodecycle sulfate as a surfactant and formaldehyde as reducing agent. The molecules of PVP play an important role in growth and agglomeration of silver nanocolloids. The formation of Ag nanocolloids was studied from the UV-vis absorption characteristics. An energy dispersive X-ray (EDX) spectrum and X-ray diffraction peak of the nanoparticles showed the highly crystalline nature of silver structure. The particle size was found to be 40 nm as analyzed from Field emission scanning electron microscopy (FESEM). The nonlinear optical and optical limiting properties of these nanoparticle dispersions were studied by using the Z-scan technique at 532 nm. Experimental results show that the Ag nanocolloids possess strong optical limiting effect, originated from absorption saturation followed by two-photon mechanism. The data show that Ag nanocolloids have great potential for nonlinear optical devices.

Is there a relativistic nonlinear generalization of quantum mechanics?

Energy Technology Data Exchange (ETDEWEB)

Elze, Hans-Thomas [Dipartimento di Fisica ' Enrico Fermi' , Largo Pontecorvo 3, I-56127 Pisa (Italy)

2007-05-15

Yes, there is. - A new kind of gauge theory is introduced, where the minimal coupling and corresponding covariant derivatives are defined in the space of functions pertaining to the functional Schroedinger picture of a given field theory. While, for simplicity, we study the example of a U(1) symmetry, this kind of gauge theory can accommodate other symmetries as well. We consider the resulting relativistic nonlinear extension of quantum mechanics and show that it incorporates gravity in the (0+1)-dimensional limit, where it leads to the Schroedinger-Newton equations. Gravity is encoded here into a universal nonlinear extension of quantum theory. The probabilistic interpretation, i.e. Born's rule, holds provided the underlying model has only dimensionless parameters.

TAE Saturation of Alpha Particle Driven Instability in TFTR

International Nuclear Information System (INIS)

Berk, H.L.; Chen, Y.; Gorelenkov, N.N.; White, R.B.

1998-01-01

A nonlinear theory of kinetic instabilities near threshold [H.L. Berk, et al., Plasma Phys. Rep. 23, (1997) 842] is applied to calculate the saturation level of Toroidicity-induced Alfvn Eigenmodes (TAE) and be compared with the predictions of (delta)f method calculations [Y. Chen, Ph.D. Thesis, Princeton University, 1998]. Good agreement is observed between the predictions of both methods and the predicted saturation levels are comparable with experimentally measured amplitudes of the TAE oscillations in TFTR [D.J. Grove and D.M. Meade, Nucl. Fusion 25, (1985) 1167

Improved dq-Axes Model of PMSM Considering Airgap Flux Harmonics and Saturation

DEFF Research Database (Denmark)

Fasil, Muhammed; Antaloae, Ciprian; Mijatovic, Nenad

2016-01-01

In this work, the classical linear model of a permanent magnet synchronous motor (PMSM) is modified by adding d and q-axes harmonic inductances so that the modified model can consider non-linearities present in an interior permanent magnet (IPM) motor. Further, a method has been presented to assess...... the effect of saturation and cross-saturation on constant torque curves of PMSM. Two IPM motors with two different rotor topologies and different specifications are designed to evaluate the effect of saturation on synchronous and harmonic inductances, and on operating points of the machines...

Phosphorene quantum dot saturable absorbers for ultrafast fiber lasers

Science.gov (United States)

Du, J.; Zhang, M.; Guo, Z.; Chen, J.; Zhu, X.; Hu, G.; Peng, P.; Zheng, Z.; Zhang, H.

2017-01-01

We fabricate ultrasmall phosphorene quantum dots (PQDs) with an average size of 2.6 ± 0.9 nm using a liquid exfoliation method involving ultrasound probe sonication followed by bath sonication. By coupling the as-prepared PQDs with microfiber evanescent light field, the PQD-based saturable absorber (SA) device exhibits ultrafast nonlinear saturable absorption property, with an optical modulation depth of 8.1% at the telecommunication band. With the integration of the all-fiber PQD-based SA, a continuous-wave passively mode-locked erbium-doped (Er-doped) laser cavity delivers stable, self-starting pulses with a pulse duration of 0.88 ps and at the cavity repetition rate of 5.47 MHz. Our results contribute to the growing body of work studying the nonlinear optical properties of ultrasmall PQDs that present new opportunities of this two-dimensional (2D) nanomaterial for future ultrafast photonic technologies. PMID:28211471

Numerical study of bandwidth effect on stimulated Raman backscattering in nonlinear regime

Science.gov (United States)

Zhou, H. Y.; Xiao, C. Z.; Zou, D. B.; Li, X. Z.; Yin, Y.; Shao, F. Q.; Zhuo, H. B.

2018-06-01

Nonlinear behaviors of stimulated Raman scattering driven by finite bandwidth pumps are studied by one dimensional particle-in-cell simulations. The broad spectral feature of plasma waves and backscattered light reveals the different coupling and growth mechanisms, which lead to the suppression effect before the deep nonlinear stage. It causes nonperiodic plasma wave packets and reduces packet and etching velocities. Based on the negative frequency shift and electron energy distribution, the long-time evolution of instability can be divided into two stages by the relaxation time. It is a critical time after which the alleviation effects of nonlinear frequency shift and hot electrons are replaced by enhancement. Thus, the broadband pump suppresses instability at early time. However, it aggravates in the deep nonlinear stage by lifting the saturation level due to the coupling of the incident pump with each frequency shifted plasma wave. Our simulation results show that the nonlinear effects are valid in a bandwidth range from 2.25% to 3.0%, and the physics are similar within a nearby parameter space.

Active disturbance rejection attitude control for a hypersonic reentry vehicle with actuator saturation

Directory of Open Access Journals (Sweden)

Hongjiu Yang

2017-05-01

Full Text Available In this article, nonlinear uncertainty has been investigated for a hypersonic reentry vehicle subject to actuator saturation via active disturbance rejection control technology. A nonlinear extended state observer is designed to estimate “total disturbances,” which is compensated with a linear controller. Both convergence of the nonlinear extended state observer and stabilization of the closed-loop system are studied in this article. Some simulation results are given to illustrate the effectiveness of the proposed method.

Nonlinear Mirror and Weibel modes: peculiarities of quasi-linear dynamics

Directory of Open Access Journals (Sweden)

O. A. Pokhotelov

2010-12-01

Full Text Available A theory for nonlinear evolution of the mirror modes near the instability threshold is developed. It is shown that during initial stage the major instability saturation is provided by the flattening of the velocity distribution function in the vicinity of small parallel ion velocities. The relaxation scenario in this case is accompanied by rapid attenuation of resonant particle interaction which is replaced by a weaker adiabatic interaction with mirror modes. The saturated plasma state can be considered as a magnetic counterpart to electrostatic BGK modes. After quasi-linear saturation a further nonlinear scenario is controlled by the mode coupling effects and nonlinear variation of the ion Larmor radius. Our analytical model is verified by relevant numerical simulations. Test particle and PIC simulations indeed show that it is a modification of distribution function at small parallel velocities that results in fading away of free energy driving the mirror mode. The similarity with resonant Weibel instability is discussed.

Micro-macro-discrepancies in nonlinear microrheology: I. Quantifying mechanisms in a suspension of Brownian ellipsoids

International Nuclear Information System (INIS)

DePuit, Ryan J; Squires, Todd M

2012-01-01

Active and nonlinear microrheology experiments involve a colloidal probe that is forced to move within a material, with the goal of recovering the nonlinear rheological response properties of the material. Various mechanisms cause discrepancies between the nonlinear rheology measured microrheologically and macroscopically, including direct probe-bath collisions, the Lagrangian unsteadiness experienced by the material elements, and the spatially inhomogeneous and rheologically mixed strain field set up around the probe. Here, we perform computational nonlinear microrheology experiments, in which a colloidal probe translates through a dilute suspension of Brownian ellipsoids, whose results we compare against analogous computational experiments on the macroscopic shear rheology of the same model material. The quantitative impact of each of the mechanisms for micro-macro-discrepancy can thus be computed directly, with additional computational experiments performed where the processes in question are ‘turned off’. We show that all three discrepancy mechanisms impact the microrheological measurement quantitatively, and that none can be neglected. This motivates a search for microrheological probes whose geometry or forcing is optimized to minimize these impacts, which we present in a companion article.

Nonlinear dynamic mechanism of vocal tremor from voice analysis and model simulations

Science.gov (United States)

Zhang, Yu; Jiang, Jack J.

2008-09-01

Nonlinear dynamic analysis and model simulations are used to study the nonlinear dynamic characteristics of vocal folds with vocal tremor, which can typically be characterized by low-frequency modulation and aperiodicity. Tremor voices from patients with disorders such as paresis, Parkinson's disease, hyperfunction, and adductor spasmodic dysphonia show low-dimensional characteristics, differing from random noise. Correlation dimension analysis statistically distinguishes tremor voices from normal voices. Furthermore, a nonlinear tremor model is proposed to study the vibrations of the vocal folds with vocal tremor. Fractal dimensions and positive Lyapunov exponents demonstrate the evidence of chaos in the tremor model, where amplitude and frequency play important roles in governing vocal fold dynamics. Nonlinear dynamic voice analysis and vocal fold modeling may provide a useful set of tools for understanding the dynamic mechanism of vocal tremor in patients with laryngeal diseases.

Study of Al-Si Alloy Oxygen Saturation on Its Microstructure and Mechanical Properties.

Science.gov (United States)

Finkelstein, Arkady; Schaefer, Arseny; Chikova, Оlga; Borodianskiy, Konstantin

2017-07-11

One of the main goals of modern materials research is obtaining different microstructures and studying their influence on the mechanical properties of metals; aluminum alloys are particularly of interest due to their advanced performance. Traditionally, their required properties are obtained by alloying process, modification, or physical influence during solidification. The present work describes a saturation of the overheated AlSi₇Fe₁ casting alloy by oxides using oxygen blowing approach in overheated alloy. Changes in metals' microstructural and mechanical properties are also described in the work. An Al 10 SiFe intermetallic complex compound was obtained as a preferable component to Al₂O₃ precipitation on it, and its morphology was investigated by scanning electron microscopy. The mechanical properties of the alloy after the oxygen blowing treatment are discussed in this work.

Visual aftereffects and sensory nonlinearities from a single statistical framework

Science.gov (United States)

Laparra, Valero; Malo, Jesús

2015-01-01

When adapted to a particular scenery our senses may fool us: colors are misinterpreted, certain spatial patterns seem to fade out, and static objects appear to move in reverse. A mere empirical description of the mechanisms tuned to color, texture, and motion may tell us where these visual illusions come from. However, such empirical models of gain control do not explain why these mechanisms work in this apparently dysfunctional manner. Current normative explanations of aftereffects based on scene statistics derive gain changes by (1) invoking decorrelation and linear manifold matching/equalization, or (2) using nonlinear divisive normalization obtained from parametric scene models. These principled approaches have different drawbacks: the first is not compatible with the known saturation nonlinearities in the sensors and it cannot fully accomplish information maximization due to its linear nature. In the second, gain change is almost determined a priori by the assumed parametric image model linked to divisive normalization. In this study we show that both the response changes that lead to aftereffects and the nonlinear behavior can be simultaneously derived from a single statistical framework: the Sequential Principal Curves Analysis (SPCA). As opposed to mechanistic models, SPCA is not intended to describe how physiological sensors work, but it is focused on explaining why they behave as they do. Nonparametric SPCA has two key advantages as a normative model of adaptation: (i) it is better than linear techniques as it is a flexible equalization that can be tuned for more sensible criteria other than plain decorrelation (either full information maximization or error minimization); and (ii) it makes no a priori functional assumption regarding the nonlinearity, so the saturations emerge directly from the scene data and the goal (and not from the assumed function). It turns out that the optimal responses derived from these more sensible criteria and SPCA are

Using saturation water percentage data to predict mechanical composition of soils

International Nuclear Information System (INIS)

Mbagwu, J.S.C.; Okafor, D.O.

1995-04-01

One hundred and sixty-six soil samples representing eleven textural classes and having wide variations in organic matter (OM) contents and other physico-chemical properties were collected from different locations in southeastern Nigeria to study the relationship between mechanical composition and saturation water percentage (SP). The objective was to develop a prediction model for silt + clay (SC) and clay (C) contents of these soils using the SP values. The magnitude of the correlation coefficients (r) between SC or C and SP was dependent on the amount of organic matter (OM) present in the soils. For soils with ≤ 1.00% OM, the correlation (r) between SC and SP was 0.9659 (p ≤ 0.001) and that between C and SP was 0.9539 (p ≤ 0.001). For soils with ≥ 2.00% OM, the 'r' values were generally low, varying between 0.5320 and 0.2665 for SC and 0.6008 and 0.3000 for C. The best-fit regression models for predicting SC and C were developed with soils having ≤ 1.00% OM. An independent data set from 25 soil samples collected from other parts of the study area was used to test the predictive ability of the best-fit models. These models predicted SC and C accurately in soils having between 0.28 and 1.10% OM, but poorly in soils having between 1.31 and 3.91% OM. These results show that the use of saturation water percentage to predict the mechanical composition of soils is most reliable for soils with low (≤ 1.00%) OM contents. (author). 18 refs, 2 figs, 5 tabs

Effective Hydro-Mechanical Properties of Fluid-Saturated Fracture Networks

Science.gov (United States)

Pollmann, N.; Vinci, C.; Renner, J.; Steeb, H.

2015-12-01

Consideration of hydro-mechanical processes is essential for the characterization of liquid-resources as well as for many engineering applications. Furthermore, the modeling of seismic waves in fractured porous media finds application not only in geophysical exploration but also reservoir management. Fractures exhibit high-aspect-ratio geometries, i.e. they constitute thin and long hydraulic conduits. Motivated by this peculiar geometry, the investigation of the hydro-mechanically coupled processes is performed by means of a hybrid-dimensional modeling approach. The effective material behavior of domains including complex fracture patterns in a porous rock is assessed by investigating the fluid pressure and the solid displacement of the skeleton saturated by compressible fluids. Classical balance equations are combined with a Poiseuille-type flow in the dimensionally reduced fracture. In the porous surrounding rock, the classical Biot-theory is applied. For simple geometries, our findings show that two main fluid-flow processes occur, leak-off from fractures to the surrounding rock and fracture flow within and between the connected fractures. The separation of critical frequencies of the two flow processes is not straightforward, in particular for systems containing a large number of fractures. Our aim is to model three dimensional hydro-mechanically coupled processes within complex fracture patterns and in particular determine the frequency-dependent attenuation characteristics. Furthermore, the effect of asperities of the fracture surfaces on the fracture stiffness and on the hydraulic conductivity will be added to the approach.

Supersymmetric quantum mechanics approach to a nonlinear lattice

International Nuclear Information System (INIS)

Ricotta, Regina Maria; Drigo Filho, Elso

2011-01-01

Full text: DNA is one of the most important macromolecules of all biological system. New discoveries about it have open a vast new field of research, the physics of nonlinear DNA. A particular feature that has attracted a lot of attention is the thermal denaturation, i.e., the spontaneous separation of the two strands upon heating. In 1989 a simple lattice model for the denaturation of the DNA was proposed, the Peyrard-Bishop model, PB. The bio molecule is described by two chains of particles coupled by nonlinear springs, simulating the hydrogen bonds that connect the two basis in a pair. The potential for the hydrogen bonds is usually approximated by a Morse potential. The Hamiltonian system generates a partition function which allows the evaluation of the thermodynamical quantities such as mean strength of the basis pairs. As a byproduct the Hamiltonian system was shown to be a NLSE (nonlinear Schroedinger equation) having soliton solutions. On the other hand, a reflectionless potential with one bound state, constructed using supersymmetric quantum mechanics, SQM, can be shown to be identical to a soliton solution of the KdV equation. Thus, motivated by this Hamiltonian problem and inspired by the PB model, we consider the Hamiltonian of a reflectionless potential through SQM, in order to evaluate thermodynamical quantities of a unidimensional lattice with possible biological applications. (author)

Nonlinearity Mechanism and Correction of Sapphire Fiber Temperature Sensor on Blackbody Cavity

Directory of Open Access Journals (Sweden)

Tiejun Cao

2014-06-01

Full Text Available Based on the principle of blackbody radiation, sapphire optic fiber temperature sensor has been more widely used in recent years, and its temperature range is between 800 ~ 2000 oC, and the response time is in 10-2 magnitude, and transient temperature measurement can be high precision in harsh environments. Nonlinear constraints on sapphire fiber temperature sensor affect the accuracy and stability of the sensor. In order to solve the nonlinear problems which exist in the measurement, at first, the sapphire fiber optic temperature sensor temperature measurement principle and nonlinear generation mechanism are studied; secondly piecewise linear interpolation and spline interpolation linearization algorithm is designed with combining the nonlinear characteristics of sapphire optical fiber temperature sensor, and the program is designed on its linear and associated signal processing. Experimental results show that a good linearization of sapphire fiber optic temperature sensor can been achieved in this method.

Nonlinear theory of the free-electron laser

International Nuclear Information System (INIS)

Chian, A.C.-L.; Padua Brito Serbeto, A. de.

1984-01-01

A theory of Raman free-electron laser using a circularly polarized electromagnetic pump is investigated. Coupled wave equations that describe both linear and nonlinear evolution of stimulated Raman scattering are derived. The dispersion relation and the growth rate for the parametric instability are obtained. Nonlinear processes that may lead to saturation of the free-electron laser are discussed. (Author) [pt

Elastoplastic model for unsaturated, quasi-saturated and fully saturated fine soils

Directory of Open Access Journals (Sweden)

Lai Ba Tien

2016-01-01

Full Text Available In unsaturated soils, the gaseous phase is commonly assumed to be continuous. This assumption is no more valid at high saturation ratio. In that case, air bubbles and pockets can be trapped in the porous network by the liquid phase and the gas phase becomes discontinuous. This trapped air reduces the apparent compressibility of the pore fluid and affect the mechanical behavior of the soil. Although it is trapped in the pores, its dissolution can take place. Dissolved air can migrate through the pore space, either by following the flow of the fluid or by diffusion. In this context, this paper present a hydro mechanical model that separately considers the kinematics and the mechanical behavior of each fluid species (eg liquid water, dissolved air, gaseous air and the solid matrix. This new model was implemented in a C++ code. Some numerical simulations are performed to demonstrate the ability of this model to reproduce a continuous transition of unsaturated to saturated states.

Study of Al-Si Alloy Oxygen Saturation on Its Microstructure and Mechanical Properties

Directory of Open Access Journals (Sweden)

Arkady Finkelstein

2017-07-01

Full Text Available One of the main goals of modern materials research is obtaining different microstructures and studying their influence on the mechanical properties of metals; aluminum alloys are particularly of interest due to their advanced performance. Traditionally, their required properties are obtained by alloying process, modification, or physical influence during solidification. The present work describes a saturation of the overheated AlSi7Fe1 casting alloy by oxides using oxygen blowing approach in overheated alloy. Changes in metals’ microstructural and mechanical properties are also described in the work. An Al10SiFe intermetallic complex compound was obtained as a preferable component to Al2O3 precipitation on it, and its morphology was investigated by scanning electron microscopy. The mechanical properties of the alloy after the oxygen blowing treatment are discussed in this work.

On the asymptotic stability of nonlinear mechanical switched systems

Science.gov (United States)

Platonov, A. V.

2018-05-01

Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

Reconstructing a nonlinear dynamical framework for testing quantum mechanics

International Nuclear Information System (INIS)

Jordan, T.F.

1993-01-01

The nonlinear generalization of quantum dynamics constructed by Weinberg as a basis for experimental tests is reconstructed in terms of density-matrix elements to allow independent dynamics for subsystems. Dynamics is generated with a Lie bracket and a nonlinear Hamiltonian function. It takes density matrices to density matrices and pure states to pure states. Each density matrix has a Hamiltonian operator that makes its evolution for an infinitesimal time, but the Hamiltonian operator may be different for different density matrices and may change in time as the density matrix changes. A Hamiltonian function for a subsystem serves also for the entire system. Independence of separate subsystems is confirmed by seeing that brackets are zero for functions from different subsystems and by looking at the Hamiltonian operator for each density matrix. Scaling properties of Hamiltonian functions are found to be important in connection with locality. An example of all this is obtained from every one of the local nonlinear Schroedinger equations described by Bialynicki-Birula and Mycielski. Examples are worked out for spins coupled together or to fields, demonstrating Hamiltonian functions and equations of motion written directly in terms of physical mean values. Observables and states are taken to be the same as in ordinary quantum mechanics. An attempt to find nonlinear representations of observables by characterizing propositions as functions equal to their squares yields a negative result. Sharper interpretation of mixed states is proposed. In a mixture of parts that are prepared separately, time dependence must be calculated separately for each part so different mixtures that yield the same density matrix can be distinguished. No criticism has shown that a consistent interpretation cannot be made this way. Thus, nonlinearity remains a viable hypothesis for experimental tests. 16 refs

Investigation of nonlinear optical properties of various organic materials by the Z-scan method

Science.gov (United States)

Ganeev, R. A.; Boltaev, G. S.; Tugushev, R. I.; Usmanov, T.

2012-06-01

We have studied the nonlinear optical properties of various organic materials (vegetable oil, juice, wine, cognac, Coca-Cola and Fanta drinks, Nescafé coffee, tea, gasoline, clock oil, glycerol, and polyphenyl ether) that are used in everyday life. Their nonlinearities have been studied by the Z-scan method in the near-IR and visible spectral ranges. We have shown that the majority of samples possess a nonlinear absorption; however, some of the studied materials show a strong saturated absorption and nonlinear refraction. Red wine and glycerol proved to be the most interesting materials. For these samples, we have observed a change in the sign of the nonlinear absorption with increasing laser intensity, which was attributed to the competition between two-photon absorption and saturated absorption.

Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Directory of Open Access Journals (Sweden)

Khaled A. Gepreel

2013-01-01

Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.

Twistacene contained molecule for optical nonlinearity: Excited-state based negative refraction and optical limiting

Science.gov (United States)

Wu, Xingzhi; Xiao, Jinchong; Sun, Ru; Jia, Jidong; Yang, Junyi; Ao, Guanghong; Shi, Guang; Wang, Yuxiao; Zhang, Xueru; Song, Yinglin

2018-06-01

Spindle-type molecules containing twisted acenes (PyBTA-1 &PyBTA-2) are designed, synthesized characterized. Picosecond Z-scan experiments under 532 nm show reverse saturable absorption and negative nonlinear refraction, indicating large third-order optical nonlinearity in PyBTA-1. The mechanism of the optical nonlinearity is investigated and the results show that the nonlinear absorption and refraction in PyBTA-1 originates from a charge transfer (CT) state. Furthermore, relatively long lifetime and absorptive cross section of the CT state are measured. Based on the excited state absorption in PyBTA-1, strong optical limiting with ∼0.3 J/cm2 thresholds are obtained when excited by picoseconds and nanoseconds pulses. The findings on nonlinear optics suggest PyBTA-1 a promising material of all optical modulation and laser protection, which enrich the potential applications of these spindle-type molecules. Comparing to the previously reported spindle-type molecules with analogous structures, the introduction of ICT in PyBTA-1 &PyBTA-2 dramatically decreases the two-photon absorption while enhances the nonlinear refraction. The results could be used to selectively tailor the optical nonlinearity in such kind of compounds.

Electrospun microcrimped fibers with nonlinear mechanical properties enhance ligament fibroblast phenotype

International Nuclear Information System (INIS)

Grace Chao, Pen-hsiu; Hsu, Hsiang-Yi; Tseng, Hsiao-Yun

2014-01-01

Fiber structure and order greatly impact the mechanical behavior of fibrous materials. In biological tissues, the nonlinear mechanics of fibrous scaffolds contribute to the functionality of the material. The nonlinear mechanical properties of the wavy structure (crimp) in collagen allow tissue flexibility while preventing over-extension. A number of approaches have tried to recreate this complex mechanical functionality. We generated microcrimped fibers by briefly heating electrospun parallel fibers over the glass transition temperature or by ethanol treatment. The crimp structure is similar to those of collagen fibers found in native aorta, intestines, or ligaments. Using poly-L-lactic acid fibers, we demonstrated that the bulk materials exhibit changed stress–strain behaviors with a significant increase in the toe region in correlation to the degree of crimp, similar to those observed in collagenous tissues. In addition to mimicking the stress–strain behavior of biological tissues, the microcrimped fibers are instructive in cell morphology and promote ligament phenotypic gene expression. This effect can be further enhanced by dynamic tensile loading, a physiological perturbation in vivo. This rapid and economical approach for microcrimped fiber production provides an accessible platform to study structure–function relationships and a novel functional scaffold for tissue engineering and cell mechanobiology studies. (papers)

Electrospun microcrimped fibers with nonlinear mechanical properties enhance ligament fibroblast phenotype.

Science.gov (United States)

Grace Chao, Pen-hsiu; Hsu, Hsiang-Yi; Tseng, Hsiao-Yun

2014-09-01

Fiber structure and order greatly impact the mechanical behavior of fibrous materials. In biological tissues, the nonlinear mechanics of fibrous scaffolds contribute to the functionality of the material. The nonlinear mechanical properties of the wavy structure (crimp) in collagen allow tissue flexibility while preventing over-extension. A number of approaches have tried to recreate this complex mechanical functionality. We generated microcrimped fibers by briefly heating electrospun parallel fibers over the glass transition temperature or by ethanol treatment. The crimp structure is similar to those of collagen fibers found in native aorta, intestines, or ligaments. Using poly-L-lactic acid fibers, we demonstrated that the bulk materials exhibit changed stress-strain behaviors with a significant increase in the toe region in correlation to the degree of crimp, similar to those observed in collagenous tissues. In addition to mimicking the stress-strain behavior of biological tissues, the microcrimped fibers are instructive in cell morphology and promote ligament phenotypic gene expression. This effect can be further enhanced by dynamic tensile loading, a physiological perturbation in vivo. This rapid and economical approach for microcrimped fiber production provides an accessible platform to study structure-function relationships and a novel functional scaffold for tissue engineering and cell mechanobiology studies.

Fluid mechanics and heat transfer advances in nonlinear dynamics modeling

CERN Document Server

Asli, Kaveh Hariri

2015-01-01

This valuable new book focuses on new methods and techniques in fluid mechanics and heat transfer in mechanical engineering. The book includes the research of the authors on the development of optimal mathematical models and also uses modern computer technology and mathematical methods for the analysis of nonlinear dynamic processes. It covers technologies applicable to both fluid mechanics and heat transfer problems, which include a combination of physical, mechanical, and thermal techniques. The authors develop a new method for the calculation of mathematical models by computer technology, using parametric modeling techniques and multiple analyses for mechanical system. The information in this book is intended to help reduce the risk of system damage or failure. Included are sidebar discussions, which contain information and facts about each subject area that help to emphasize important points to remember.

Input-output linearizing tracking control of induction machine with the included magnetic saturation

DEFF Research Database (Denmark)

Dolinar, Drago; Ljusev, Petar; Stumberger, Gorazd

2003-01-01

The tracking control design of an induction motor, based on input-output linearisation with magnetic saturation included is addressed. The magnetic saturation is represented by a nonlinear magnetising curve for the iron core and is used in the control, the observer of the state variables......, and in the load torque estimator. An input-output linearising control is used to achieve better tracking performances. It is based on the mixed 'stator current - rotor flux linkage' induction motor model with magnetic saturation considered in the stationary reference frame. Experimental results show...... that the proposed input-output linearising tracking control with saturation included behaves considerably better than the one without saturation, and that it introduces smaller position and speed errors, and better motor stiffness on account of the increased computational complexity....

Piecewise nonlinear dynamic characteristics study of the control rod drive mechanism

International Nuclear Information System (INIS)

Shen Xiaoyao; Wang Feng

2011-01-01

Piecewise nonlinear dynamics of the control rod mechanism (CRDM), one of the critical components in PWR nuclear power plants, are studied for its lifting process in this paper. Firstly, equations of the electric circuit and the magnetic circuit are set up. Then based on the dynamic lifting process analysis of CRDM, its motion procedure is divided into three stages, and the coupled magnetic-electric-mechanical equation for each stage is derived. By combining the analytical solution method and the numerical simulation method, the piecewise nonlinear governing equations are solved. Finally, parameters which can illustrate the dynamic characteristics of CRDM, such as the magnetic force, the coil current, the armature displacement, the armature velocity and the acceleration are obtained and corresponding curves with the time are drawn and analyzed. The analysis results are confirmed by the test which proves the validity of our method. Work in this paper can be used for design and analysis as well as the site fault diagnosis of CRDM. (author)

Quantum-mechanical Green's functions and nonlinear superposition law

International Nuclear Information System (INIS)

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

1986-01-01

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

Quantum-mechanical Green's function and nonlinear superposition law

International Nuclear Information System (INIS)

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

1986-01-01

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

Dynamical study of a laser with a saturable absorber

Energy Technology Data Exchange (ETDEWEB)

Dignowity, D; RamIrez, R [Centro de Investigaciones en Optica, Loma del Bosque 115, Col. Lomas del Campestre, 37150, Leon, Guanajuato (Mexico)

2005-01-01

The study of a laser including a saturable absorber is presented. The non-linear system describing the complex dynamics of the laser is presented. The laser is shown to operate in several regimes depending on the parameters used. It is also shown how the control of the laser is possible depending on the operating regime parameters.

On the propagation of a coupled saturation and pressure front

Energy Technology Data Exchange (ETDEWEB)

Vasco, D. W.

2010-12-01

Using an asymptotic technique, valid for a medium with smoothly varying heterogeneity, I derive an expression for the velocity of a propagating, coupled saturation and pressure front. Due to the nonlinearity of the governing equations, the velocity of the propagating front depends upon the magnitude of the saturation and pressure changes across the front in addition to the properties of the medium. Thus, the expression must be evaluated in conjunction with numerical reservoir simulation. The propagation of the two-phase front is governed by the background saturation distribution, the saturation-dependent component of the fluid mobility, the porosity, the permeability, the capillary pressure function, the medium compressibility, and the ratio of the slopes of the relative permeability curves. Numerical simulation of water injection into a porous layer saturated with a nonaqueous phase liquid indicates that two modes of propagation are important. The fastest mode of propagation is a pressure-dominated disturbance that travels through the saturated layer. This is followed, much later, by a coupled mode with a large saturation change. These two modes are also observed in a simulation using a heterogeneous porous layer. A comparison between the propagation times estimated from the results of the numerical simulation and predictions from the asymptotic expression indicates overall agreement.

Weinberg's nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox

Science.gov (United States)

Polchinski, Joseph

1991-01-01

The constraints imposed on observables by the requirement that transmission not occur in the Einstein-Podolsky-Rosen (EPR) experiment are determined, leading to a different treatment of separated systems from that originally proposed by Weinberg (1989). It is found that forbidding EPR communication in nonlinear quantum mechanics necessarily leads to another sort of unusual communication: that between different branches of the wave function.

Tuning the nonlinear optical absorption of reduced graphene oxide by chemical reduction.

Science.gov (United States)

Shi, Hongfei; Wang, Can; Sun, Zhipei; Zhou, Yueliang; Jin, Kuijuan; Redfern, Simon A T; Yang, Guozhen

2014-08-11

Reduced graphene oxides with varying degrees of reduction have been produced by hydrazine reduction of graphene oxide. The linear and nonlinear optical properties of both graphene oxide as well as the reduced graphene oxides have been measured by single beam Z-scan measurement in the picosecond region. The results reveal both saturable absorption and two-photon absorption, strongly dependent on the intensity of the pump pulse: saturable absorption occurs at lower pump pulse intensity (~1.5 GW/cm2 saturation intensity) whereas two-photon absorption dominates at higher intensities (≥5.7 GW/cm2). Intriguingly, we find that the two-photon absorption coefficient (from 1.5 cm/GW to 4.5cm/GW) and the saturation intensity (from 1 GW/cm2 to 2 GW/cm2) vary with chemical reduction, which is ascribed to the varying concentrations of sp2 domains and sp2 clusters in the reduced graphene oxides. Our results not only provide an insight into the evolution of the nonlinear optical coefficient in reduced graphene oxide, but also suggest that chemical engineering techniques may usefully be applied to tune the nonlinear optical properties of various nano-materials, including atomically thick graphene sheets.

Large nonlinear absorption and refraction coefficients of carbon nanotubes estimated from femtosecond z-scan measurements

Science.gov (United States)

Kamaraju, N.; Kumar, Sunil; Sood, A. K.; Guha, Shekhar; Krishnamurthy, Srinivasan; Rao, C. N. R.

2007-12-01

Nonlinear transmission of 80 and 140fs pulsed light with 0.79μm wavelength through single walled carbon nanotubes suspended in water containing sodium dodecyl sulfate is studied. Pulse-width independent saturation absorption and negative cubic nonlinearity are observed, respectively, in open and closed aperture z-scan experiments. The theoretical expressions derived to analyze the z-dependent transmission in the saturable limit require two photon absorption coefficient β0˜1.4cm/MW and a nonlinear index γ ˜-5.5×10-11cm2/W to fit the data.

Scaling of saturation amplitudes in baroclinic instability

International Nuclear Information System (INIS)

Shepherd, T.G.

1994-01-01

By using finite-amplitude conservation laws for pseudomomentum and pseudoenergy, rigorous upper bounds have been derived on the saturation amplitudes in baroclinic instability for layered and continuously-stratified quasi-geostrophic models. Bounds have been obtained for both the eddy energy and the eddy potential enstrophy. The bounds apply to conservative (inviscid, unforced) flow, as well as to forced-dissipative flow when the dissipation is proportional to the potential vorticity. This approach provides an efficient way of extracting an analytical estimate of the dynamical scalings of the saturation amplitudes in terms of crucial non-dimensional parameters. A possible use is in constructing eddy parameterization schemes for zonally-averaged climate models. The scaling dependences are summarized, and compared with those derived from weakly-nonlinear theory and from baroclinic-adjustment estimates

Heisenberg saturation of the Froissart bound from AdS-CFT

International Nuclear Information System (INIS)

Kang, Kyungsik; Nastase, Horatiu

2005-01-01

In a previous paper, we have analyzed high energy QCD from AdS-CFT and proved the saturation of the Froissart bound (a purely QCD proof of which is still lacking). In this Letter we describe the calculation in more physical terms and map it to QCD language. We find a remarkable agreement with the 1952 Heisenberg description of the saturation (pre-QCD!) in terms of shockwave collisions of pion field distributions. It provides a direct map between gauge theory physics and the gravitational physics on the IR brane of the Randall-Sundrum model. Saturation occurs through black hole production on the IR brane, which is in QCD production of a nonlinear pion field soliton of a Born-Infeld action in the hadron collision, that decays into free pions

Statistical approach of weakly nonlinear ablative Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Garnier, J.; Masse, L.

2005-01-01

A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in presence of ablation and thermal transport. The nonlinear effects for a single-mode disturbance are computed, included the nonlinear correction to the exponential growth of the fundamental modulation. Mode coupling in the spectrum of a multimode disturbance is thoroughly analyzed by a statistical approach. The exponential growth of the linear regime is shown to be reduced by the nonlinear mode coupling. The saturation amplitude is around 0.1λ for long wavelengths, but higher for short instable wavelengths in the ablative regime

Sticky traps saturate with navel orangeworm in a non-linear fashion

Science.gov (United States)

In order to evaluate saturation thresholds as well as differences among wing-trap types, we used unmated female navel orangeworm (NOW) as sex pheromone baits in wing-traps that varied by color and glue/trapping surface. These results were compared to male capture in red delta and simple water cup tr...

Nonlinear finite element analysis of the plantar fascia due to the windlass mechanism.

Science.gov (United States)

Cheng, Hsin-Yi Kathy; Lin, Chun-Li; Chou, Shih-Wei; Wang, Hsien-Wen

2008-08-01

Tightening of plantar fascia by passively dorsiflexing the toes during walking has functional importance. The purpose of this research was to evaluate the influence of big toe dorsiflexion angles upon plantar fascia tension (the windlass effect) with a nonlinear finite element approach. A two-dimensional finite element model of the first ray was constructed for biomechanical analysis. In order to imitate the windlass effect and to evaluate the mechanical responses of the plantar fascia under various conditions, 12 model simulations--three dorsiflexion angles of the big toe (45 degrees, 30 degrees, and 15 degrees), two plantar fascia properties (linear, nonlinear), and two weightbearing conditions (with body weight, without body weight)--were designed and analyzed. Our results demonstrated that nonlinear modeling of the plantar fascia provides a more sophisticated representation of experimental data than the linear one. Nonlinear plantar fascia setting also predicted a higher stress distribution along the fiber directions especially with larger toe dorsiflexion angles (45 degrees>30 degrees>15 degrees). The plantar fascia stress was found higher near the metatarsal insertion and faded as it moved toward the calcaneal insertion. Passively dorsiflexing the big toe imposes tension onto the plantar fascia. Windlass mechanism also occurs during stance phase of walking while the toes begin to dorsiflex. From a biomechanical standpoint, the plantar fascia tension may help propel the body upon its release at the point of push off. A controlled stretch via dorsiflexing the big toe may have a positive effect on treating plantar fasciitis by providing proper guidance for collagen regeneration. The windlass mechanism is also active during the stance phase of walking when the toes begin to dorsiflex.

Computational contact and impact mechanics fundamentals of modeling interfacial phenomena in nonlinear finite element analysis

CERN Document Server

Laursen, Tod A

2003-01-01

This book comprehensively treats the formulation and finite element approximation of contact and impact problems in nonlinear mechanics. Intended for students, researchers and practitioners interested in numerical solid and structural analysis, as well as for engineers and scientists dealing with technologies in which tribological response must be characterized, the book includes an introductory but detailed overview of nonlinear finite element formulations before dealing with contact and impact specifically. Topics encompassed include the continuum mechanics, mathematical structure, variational framework, and finite element implementations associated with contact/impact interaction. Additionally, important and currently emerging research topics in computational contact mechanics are introduced, encompassing such topics as tribological complexity, conservative treatment of inelastic impact interaction, and novel spatial discretization strategies.

Simulation of the saturation process of a radwaste storage cell

International Nuclear Information System (INIS)

Robbe, M.F.; Clouard, A.

2001-01-01

This paper presents a simulation of the saturation of the barrier and the plug of a storage cell by the surrounding host rock. Generally speaking, the unsaturated barrier and plug start saturating immediately in the vicinity of the quasi-saturated host rock. Then the saturation front propagates towards the canisters and the symmetry axis. Apart from the part in contact with the plug, the barrier is saturated at about 30 years. The part of the barrier near the plug is saturated around 80 years. If the top of the plug is saturated very soon, the part in the corner near the gallery and the symmetry axis is not completely saturated after 100 years. In the site, we observe a small desaturation during the first month, at the limit with the plug and the barrier, and especially in the corner limited by both FoCa clay pieces. This transient phenomenon may be assigned to the time difference between the immediate suction of water by the unsaturated materials and the delayed water flows coming from the saturated host rock to compensate the water suction. The purpose of this computation was at once to estimate the time necessary for the saturation of the clay layers surrounding the radwaste canisters and to evaluate the hydro-mechanical behaviour of the storage cell during the saturation process. Therefore a mechanical simulation was performed using the present hydraulic results to initiate the mechanical computation. (authors)

Theoretical analysis of saturation and limit cycles in short pulse FEL oscillators

Energy Technology Data Exchange (ETDEWEB)

Piovella, N.; Chaix, P.; Jaroszynski, D. [Commissariat a l`Energie Atomique, Bruyeres-le-Chatel (France)] [and others

1995-12-31

We derive a model for the non linear evolution of a short pulse oscillator from low signal up to saturation in the small gain regime. This system is controlled by only two independent parameters: cavity detuning and losses. Using a closure relation, this model reduces to a closed set of 5 non linear partial differential equations for the EM field and moments of the electron distribution. An analysis of the linearised system allows to define and calculate the eigenmodes characterising the small signal regime. An arbitrary solution of the complete nonlinear system can then be expanded in terms of these eigenmodes. This allows interpreting various observed nonlinear behaviours, including steady state saturation, limit cycles, and transition to chaos. The single mode approximation reduces to a Landau-Ginzburg equation. It allows to obtain gain, nonlinear frequency shift, and efficiency as functions of cavity detuning and cavity losses. A generalisation to two modes allows to obtain a simple description of the limit cycle behaviour, as a competition between these two modes. An analysis of the transitions to more complex dynamics is also given. Finally, the analytical results are compared to the experimental data from the FELIX experiment.

Outline of a nonlinear, relativistic quantum mechanics of extended particles

International Nuclear Information System (INIS)

Mielke, E.W.

1981-01-01

A quantum theory of intrinsically extended particles similar to de Broglie's theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton-type solutions of nonlinear, relativistic wave equations. These droplet-type waves have a quasi-objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum-mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle-wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum-theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self-interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle. (author)

Outline of a nonlinear, relativistic quantum mechanics of extended particles

International Nuclear Information System (INIS)

Mielke, E.W.

1981-01-01

A quantum theory of intrinsically extended particles similar to de Broglie's Theory of the Double Solution is proposed. A rational notion of the particle's extension is enthroned by realizing its internal structure via soliton-type solutions of nonlinear, relativistic wave equations. These droplet-type waves have a quasi-objective character except for certain boundary conditions which may be subject to stochastic fluctuations. More precisely, this assumption amounts to a probabilistic description of the center of a soliton such that it would follow the conventional quantum-mechanical formalism in the limit of zero particle radius. At short interaction distances, however, a promising nonlinear and nonlocal theory emerges. This model is not only capable of achieving a conceptually satisfying synthesis of the particle-wave dualism, but may also lead to a rational resolution of epistemological problems in the quantum-theoretical measurement process. Within experimental errors the results for, e.g., the hydrogen atom can be reproduced by appropriately specifying the nature of the nonlinear self-interaction. It is speculated that field theoretical issues raised by such notions as identical particles, field quantization and renormalization are already incorporated or resolved by this nonlocal theory, at least in principle. (author)

Jacobi Elliptic Solutions for Nonlinear Differential Difference Equations in Mathematical Physics

Directory of Open Access Journals (Sweden)

Khaled A. Gepreel

2012-01-01

Full Text Available We put a direct new method to construct the rational Jacobi elliptic solutions for nonlinear differential difference equations which may be called the rational Jacobi elliptic functions method. We use the rational Jacobi elliptic function method to construct many new exact solutions for some nonlinear differential difference equations in mathematical physics via the lattice equation and the discrete nonlinear Schrodinger equation with a saturable nonlinearity. The proposed method is more effective and powerful to obtain the exact solutions for nonlinear differential difference equations.

Experimental investigations of nonlinearities and destruction mechanisms of an experimental phospholipid-based ultrasound contrast agent.

Science.gov (United States)

Casciaro, Sergio; Palmizio Errico, Rosa; Errico, Rosa Palmizio; Conversano, Francesco; Demitri, Christian; Distante, Alessandro

2007-02-01

We sought to characterize the acoustical behavior of the experimental ultrasound contrast agent BR14 by determining the acoustic pressure threshold above which nonlinear oscillation becomes significant and investigating microbubble destruction mechanisms. We used a custom-designed in vitro setup to conduct broadband attenuation measurements at 3.5 MHz varying acoustic pressure (range, 50-190 kPa). We also performed granulometric analyses on contrast agent solutions to accurately measure microbubble size distribution and to evaluate insonification effects. Attenuation did not depend on acoustic pressure less than 100 kPa, indicating this pressure as the threshold for the appearance of microbubble nonlinear behavior. At the lowest excitation amplitude, attenuation increased during insonification, while, at higher excitation levels, the attenuation decreased over time, indicating microbubble destruction. The destruction rate changed with pressure amplitude suggesting different destruction mechanisms, as it was confirmed by granulometric analysis. Microbubbles showed a linear behavior until 100 kPa, whereas beyond this value significant nonlinearities occurred. Observed destruction phenomena seem to be mainly due to gas diffusion and bubble fragmentation mechanisms.

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

KAUST Repository

Yang, Haijian

2016-07-26

Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.

Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media

KAUST Repository

Yang, Haijian; Yang, Chao; Sun, Shuyu

2016-01-01

Fully implicit methods are drawing more attention in scientific and engineering applications due to the allowance of large time steps in extreme-scale simulations. When using a fully implicit method to solve two-phase flow problems in porous media, one major challenge is the solution of the resultant nonlinear system at each time step. To solve such nonlinear systems, traditional nonlinear iterative methods, such as the class of the Newton methods, often fail to achieve the desired convergent rate due to the high nonlinearity of the system and/or the violation of the boundedness requirement of the saturation. In the paper, we reformulate the two-phase model as a variational inequality that naturally ensures the physical feasibility of the saturation variable. The variational inequality is then solved by an active-set reduced-space method with a nonlinear elimination preconditioner to remove the high nonlinear components that often causes the failure of the nonlinear iteration for convergence. To validate the effectiveness of the proposed method, we compare it with the classical implicit pressure-explicit saturation method for two-phase flow problems with strong heterogeneity. The numerical results show that our nonlinear solver overcomes the often severe limits on the time step associated with existing methods, results in superior convergence performance, and achieves reduction in the total computing time by more than one order of magnitude.

Simplified Model of Nonlinear Landau Damping

International Nuclear Information System (INIS)

Yampolsky, N.A.; Fisch, N.J.

2009-01-01

The nonlinear interaction of a plasma wave with resonant electrons results in a plateau in the electron distribution function close to the phase velocity of the plasma wave. As a result, Landau damping of the plasma wave vanishes and the resonant frequency of the plasma wave downshifts. However, this simple picture is invalid when the external driving force changes the plasma wave fast enough so that the plateau cannot be fully developed. A new model to describe amplification of the plasma wave including the saturation of Landau damping and the nonlinear frequency shift is proposed. The proposed model takes into account the change of the plasma wave amplitude and describes saturation of the Landau damping rate in terms of a single fluid equation, which simplifies the description of the inherently kinetic nature of Landau damping. A proposed fluid model, incorporating these simplifications, is verified numerically using a kinetic Vlasov code.

Nonlinear hybrid simulation of internal kink with beam ion effects in DIII-D

Energy Technology Data Exchange (ETDEWEB)

Shen, Wei; Sheng, Zheng-Mao [Department of Physics, Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 310027 (China); Fu, G. Y.; Tobias, Benjamin [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Zeeland, Michael Van [General Atomics, San Diego, California 92186-5608 (United States); Wang, Feng [School of Physics and Optoelectronic Engineering, Dalian University of Technology, Dalian 116024 (China)

2015-04-15

In DIII-D sawteething plasmas, long-lived (1,1) kink modes are often observed between sawtooth crashes. The saturated kink modes have two distinct frequencies. The mode with higher frequency transits to a fishbone-like mode with sufficient on-axis neutral beam power. In this work, hybrid simulations with the global kinetic-magnetohydrodynamic (MHD) hybrid code M3D-K have been carried out to investigate the linear stability and nonlinear dynamics of the n = 1 mode with effects of energetic beam ions for a typical DIII-D discharge where both saturated kink mode and fishbone were observed. Linear simulation results show that the n = 1 internal kink mode is unstable in MHD limit. However, with kinetic effects of beam ions, a fishbone-like mode is excited with mode frequency about a few kHz depending on beam pressure profile. The mode frequency is higher at higher beam power and/or narrower radial profile consistent with the experimental observation. Nonlinear simulations have been performed to investigate mode saturation as well as energetic particle transport. The nonlinear MHD simulations show that the unstable kink mode becomes a saturated kink mode after a sawtooth crash. With beam ion effects, the fishbone-like mode can also transit to a saturated kink mode with a small but finite mode frequency. These results are consistent with the experimental observation of saturated kink mode between sawtooth crashes.

Efficient control of ultrafast optical nonlinearity of reduced graphene oxide by infrared reduction

Energy Technology Data Exchange (ETDEWEB)

Bhattachraya, S.; Maiti, R.; Das, A. C.; Saha, S.; Mondal, S.; Ray, S. K.; Bhaktha, S. N. B.; Datta, P. K., E-mail: pkdatta.iitkgp@gmail.com [Department of Physics, Indian Institute of Technology Kharagpur, Kharagpur 721302 (India)

2016-07-07

Simultaneous occurrence of saturable absorption nonlinearity and two-photon absorption nonlinearity in the same medium is well sought for the devices like optical limiter and laser mode-locker. Pristine graphene sheet consisting entirely of sp{sup 2}-hybridized carbon atoms has already been identified having large optical nonlinearity. However, graphene oxide (GO), a precursor of graphene having both sp{sup 2} and sp{sup 3}-hybridized carbon atom, is increasingly attracting cross-discipline researchers for its controllable properties by reduction of oxygen containing groups. In this work, GO has been prepared by modified Hummers method, and it has been further reduced by infrared (IR) radiation. Characterization of reduced graphene oxide (RGO) by means of Raman spectroscopy, X-ray photoelectron spectroscopy, and UV-Visible absorption measurements confirms an efficient reduction with infrared radiation. Here, we report precise control of non-linear optical properties of RGO in femtosecond regime with increased degrees of IR reduction measured by open aperture z-scan technique. Depending on the intensity, both saturable absorption and two-photon absorption effects are found to contribute to the non-linearity of all the samples. Saturation dominates at low intensity (∼127 GW/cm{sup 2}) while two-photon absorption becomes prominent at higher intensities (from 217 GW/cm{sup 2} to 302 GW/cm{sup 2}). The values of two-photon absorption co-efficient (∼0.0022–0.0037 cm/GW for GO, and ∼0.0128–0.0143 cm/GW for RGO) and the saturation intensity (∼57 GW/cm{sup 2} for GO, and ∼194 GW/cm{sup 2} for RGO) increase with increasing reduction, indicating GO and RGO as novel tunable photonic devices. We have also explained the reason of tunable nonlinear optical properties by using amorphous carbon model.

Efficient control of ultrafast optical nonlinearity of reduced graphene oxide by infrared reduction

International Nuclear Information System (INIS)

Bhattachraya, S.; Maiti, R.; Das, A. C.; Saha, S.; Mondal, S.; Ray, S. K.; Bhaktha, S. N. B.; Datta, P. K.

2016-01-01

Simultaneous occurrence of saturable absorption nonlinearity and two-photon absorption nonlinearity in the same medium is well sought for the devices like optical limiter and laser mode-locker. Pristine graphene sheet consisting entirely of sp"2-hybridized carbon atoms has already been identified having large optical nonlinearity. However, graphene oxide (GO), a precursor of graphene having both sp"2 and sp"3-hybridized carbon atom, is increasingly attracting cross-discipline researchers for its controllable properties by reduction of oxygen containing groups. In this work, GO has been prepared by modified Hummers method, and it has been further reduced by infrared (IR) radiation. Characterization of reduced graphene oxide (RGO) by means of Raman spectroscopy, X-ray photoelectron spectroscopy, and UV-Visible absorption measurements confirms an efficient reduction with infrared radiation. Here, we report precise control of non-linear optical properties of RGO in femtosecond regime with increased degrees of IR reduction measured by open aperture z-scan technique. Depending on the intensity, both saturable absorption and two-photon absorption effects are found to contribute to the non-linearity of all the samples. Saturation dominates at low intensity (∼127 GW/cm"2) while two-photon absorption becomes prominent at higher intensities (from 217 GW/cm"2 to 302 GW/cm"2). The values of two-photon absorption co-efficient (∼0.0022–0.0037 cm/GW for GO, and ∼0.0128–0.0143 cm/GW for RGO) and the saturation intensity (∼57 GW/cm"2 for GO, and ∼194 GW/cm"2 for RGO) increase with increasing reduction, indicating GO and RGO as novel tunable photonic devices. We have also explained the reason of tunable nonlinear optical properties by using amorphous carbon model.

Dynamical heterogeneities and mechanical non-linearities: Modeling the onset of plasticity in polymer in the glass transition.

Science.gov (United States)

Masurel, R J; Gelineau, P; Lequeux, F; Cantournet, S; Montes, H

2017-12-27

In this paper we focus on the role of dynamical heterogeneities on the non-linear response of polymers in the glass transition domain. We start from a simple coarse-grained model that assumes a random distribution of the initial local relaxation times and that quantitatively describes the linear viscoelasticity of a polymer in the glass transition regime. We extend this model to non-linear mechanics assuming a local Eyring stress dependence of the relaxation times. Implementing the model in a finite element mechanics code, we derive the mechanical properties and the local mechanical fields at the beginning of the non-linear regime. The model predicts a narrowing of distribution of relaxation times and the storage of a part of the mechanical energy --internal stress-- transferred to the material during stretching in this temperature range. We show that the stress field is not spatially correlated under and after loading and follows a Gaussian distribution. In addition the strain field exhibits shear bands, but the strain distribution is narrow. Hence, most of the mechanical quantities can be calculated analytically, in a very good approximation, with the simple assumption that the strain rate is constant.

Nonlinear photoacoustic spectroscopy of hemoglobin

Energy Technology Data Exchange (ETDEWEB)

Danielli, Amos; Maslov, Konstantin; Favazza, Christopher P.; Xia, Jun; Wang, Lihong V., E-mail: LHWANG@WUSTL.EDU [Optical Imaging Laboratory, Department of Biomedical Engineering, Washington University in St. Louis, One Brookings Drive, St. Louis, Missouri 63130 (United States)

2015-05-18

As light intensity increases in photoacoustic imaging, the saturation of optical absorption and the temperature dependence of the thermal expansion coefficient result in a measurable nonlinear dependence of the photoacoustic (PA) signal on the excitation pulse fluence. Here, under controlled conditions, we investigate the intensity-dependent photoacoustic signals from oxygenated and deoxygenated hemoglobin at varied optical wavelengths and molecular concentrations. The wavelength and concentration dependencies of the nonlinear PA spectrum are found to be significantly greater in oxygenated hemoglobin than in deoxygenated hemoglobin. These effects are further influenced by the hemoglobin concentration. These nonlinear phenomena provide insights into applications of photoacoustics, such as measurements of average inter-molecular distances on a nm scale or with a tuned selection of wavelengths, a more accurate quantitative PA tomography.

Nonlinear photoacoustic spectroscopy of hemoglobin.

Science.gov (United States)

Danielli, Amos; Maslov, Konstantin; Favazza, Christopher P; Xia, Jun; Wang, Lihong V

2015-05-18

As light intensity increases in photoacoustic imaging, the saturation of optical absorption and the temperature dependence of the thermal expansion coefficient result in a measurable nonlinear dependence of the photoacoustic (PA) signal on the excitation pulse fluence. Here, under controlled conditions, we investigate the intensity-dependent photoacoustic signals from oxygenated and deoxygenated hemoglobin at varied optical wavelengths and molecular concentrations. The wavelength and concentration dependencies of the nonlinear PA spectrum are found to be significantly greater in oxygenated hemoglobin than in deoxygenated hemoglobin. These effects are further influenced by the hemoglobin concentration. These nonlinear phenomena provide insights into applications of photoacoustics, such as measurements of average inter-molecular distances on a nm scale or with a tuned selection of wavelengths, a more accurate quantitative PA tomography.

Nonlinear photoacoustic spectroscopy of hemoglobin

International Nuclear Information System (INIS)

Danielli, Amos; Maslov, Konstantin; Favazza, Christopher P.; Xia, Jun; Wang, Lihong V.

2015-01-01

As light intensity increases in photoacoustic imaging, the saturation of optical absorption and the temperature dependence of the thermal expansion coefficient result in a measurable nonlinear dependence of the photoacoustic (PA) signal on the excitation pulse fluence. Here, under controlled conditions, we investigate the intensity-dependent photoacoustic signals from oxygenated and deoxygenated hemoglobin at varied optical wavelengths and molecular concentrations. The wavelength and concentration dependencies of the nonlinear PA spectrum are found to be significantly greater in oxygenated hemoglobin than in deoxygenated hemoglobin. These effects are further influenced by the hemoglobin concentration. These nonlinear phenomena provide insights into applications of photoacoustics, such as measurements of average inter-molecular distances on a nm scale or with a tuned selection of wavelengths, a more accurate quantitative PA tomography

H∞ Loop Shaping Control of Input Saturated Systems with Norm-Bounded Parametric Uncertainty

Directory of Open Access Journals (Sweden)

Renan Lima Pereira

2015-01-01

Full Text Available This paper proposes a gain-scheduling control design strategy for a class of linear systems with the presence of both input saturation constraints and norm-bounded parametric uncertainty. LMI conditions are derived in order to obtain a gain-scheduled controller that ensures the robust stability and performance of the closed loop system. The main steps to obtain such a controller are given. Differently from other gain-scheduled approaches in the literature, this one focuses on the problem of H∞ loop shaping control design with input saturation nonlinearity and norm-bounded uncertainty to reduce the effect of the disturbance input on the controlled outputs. Here, the design problem has been formulated in the four-block H∞ synthesis framework, in which it is possible to describe the parametric uncertainty and the input saturation nonlinearity as perturbations to normalized coprime factors of the shaped plant. As a result, the shaped plant is represented as a linear parameter-varying (LPV system while the norm-bounded uncertainty and input saturation are incorporated. This procedure yields a linear parameter-varying structure for the controller that ensures the stability of the polytopic LPV shaped plant from the vertex property. Finally, the effectiveness of the method is illustrated through application to a physical system: a VTOL “vertical taking-off landing” helicopter.

On stabilization of linear systems with stochastic disturbances and input saturation

NARCIS (Netherlands)

Stoorvogel, A.A.; Weiland, S.; Saberi, A.

2004-01-01

It is well-known that for linear systems internal asymptotic stability implies external stability in the sense that when the external input is in Lp then also the state will be in Lp. However, for the control of linear systems with saturation where the controlled system is nonlinear this implication

Multifractal spectrum analysis of nonlinear dynamical mechanisms in China’s agricultural futures markets

Science.gov (United States)

Chen, Shu-Peng; He, Ling-Yun

2010-04-01

Based on Partition Function and Multifractal Spectrum Analysis, we investigated the nonlinear dynamical mechanisms in China’s agricultural futures markets, namely, Dalian Commodity Exchange (DCE for short) and Zhengzhou Commodity Exchange (ZCE for short), where nearly all agricultural futures contracts are traded in the two markets. Firstly, we found nontrivial multifractal spectra, which are the empirical evidence of the existence of multifractal features, in 4 representative futures markets in China, that is, Hard Winter wheat (HW for short) and Strong Gluten wheat (SG for short) futures markets from ZCE and Soy Meal (SM for short) futures and Soy Bean No.1 (SB for short) futures markets from DCE. Secondly, by shuffling the original time series, we destroyed the underlying nonlinear temporal correlation; thus, we identified that long-range correlation mechanism constitutes major contributions in the formation in the multifractals of the markets. Thirdly, by tracking the evolution of left- and right-half spectra, we found that there exist critical points, between which there are different behaviors, in the left-half spectra for large price fluctuations; but for the right-hand spectra for small price fluctuations, the width of those increases slowly as the delay t increases in the long run. Finally, the dynamics of large fluctuations is significantly different from that of the small ones, which implies that there exist different underlying mechanisms in the formation of multifractality in the markets. Our main contributions focus on that we not only provided empirical evidence of the existence of multifractal features in China agricultural commodity futures markets; but also we pioneered in investigating the sources of the multifractality in China’s agricultural futures markets in current literature; furthermore, we investigated the nonlinear dynamical mechanisms based on spectrum analysis, which offers us insights into the underlying dynamical mechanisms in

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

Science.gov (United States)

Mamatsashvili, G.; Stefani, F.; Guseva, A.; Avila, M.

2018-01-01

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)—a relative of the standard MRI—in a magnetized Taylor-Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

Third-order nonlinear optical properties of the poly(methyl methacrylate)-phenothiazinium dye hybrid thin films

International Nuclear Information System (INIS)

Sun, Ru; Lu, Yue-Ting; Yan, Bao-Long; Lu, Jian-Mei; Wu, Xing-Zhi; Song, Ying-Lin; Ge, Jian-Feng

2014-01-01

The third-order nonlinear optical properties of poly(methyl methacrylate) films doped with charge flowable 3,7-di(piperidinyl)phenothiazin-5-ium chloride, which tested by Z-scan method with nanosecond laser beam at 532 nm, are reported. Large third-order nonlinear optical susceptibilities (up to 10 −7 esu) and high second hyperpolarizabilities (up to 10 −27 esu) are found. The third-order nonlinear absorptions change from reverse saturated absorptions to saturated absorptions with different percentage of the phenothiazinium dye in the poly(methyl methacrylate) films, which can be explained by the accumulation phenomenon of the phenothiazinium. The results suggest that the phenothiazinium salt is a promising material for third order non-linear applications. - Highlights: • Phenothiazinium containing optical films • Strong third-order nonlinear optical (NLO) absorption • Large third-order NLO susceptibilities

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

Trapping effects and acoustoelectric current saturation in ZnO single crystals

DEFF Research Database (Denmark)

Mosekilde, Erik

1970-01-01

Measurements of current-voltage characteristics for ZnO single crystals at temperatures between 77 and 640 °K are reported. Because of the buildup of an intense acoustic flux, a strong current saturation sets in when the trap-controlled electron drift velocity is equal to the velocity of sound....... The temperature dependence of the saturated current is discussed in terms of a trapping model which includes nonlinear trapping effects. Our results indicate the presence of a shallow-donor level with an ionization energy of 50 meV and a deep-donor level approximately 230 meV below the conduction-band edge...

Saturation of alpha particle driven instability in Tokamak Fusion Test Reactor

International Nuclear Information System (INIS)

Gorelenkov, N.N.; Chen, Y.; White, R.B.; Berk, H.L.

1999-01-01

A nonlinear theory of kinetic instabilities near threshold [Berk et al., Plasma Phys. Rep. 23, 842 (1997)] is applied to calculate the saturation level of toroidicity-induced Alfven eigenmodes (TAE), and to be compared with the predictions of δf method calculations (Y. Chen, Ph.D. thesis, Princeton University, 1998). Good agreement is observed between the predictions of both methods and the predicted saturation levels are comparable to experimentally measured amplitudes of the TAE oscillations in Tokamak Fusion Test Reactor [D. J. Grove and D. M. Meade, Nucl. Fusion 25, 1167 (1985)]. copyright 1999 American Institute of Physics

Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?

KAUST Repository

Gadelha, H.

2010-05-12

Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape-no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems.

Dynamic Mechanical Behavior of Dry and Water Saturated Igneous Rock with Acoustic Emission Monitoring

Directory of Open Access Journals (Sweden)

Jun Guo

2018-01-01

Full Text Available The uniaxial cyclic loading tests have been conducted to study the mechanical behavior of dry and water saturated igneous rock with acoustic emission (AE monitoring. The igneous rock samples are dried, naturally immersed, and boiled to get specimens with different water contents for the testing. The mineral compositions and the microstructures of the dry and water saturated igneous rock are also presented. The dry specimens present higher strength, fewer strains, and rapid increase of AE count subjected to the cyclic loading, which reflects the hard and brittle behavior and strong burst proneness of igneous rock. The water saturated specimens have lower peak strength, more accumulated strains, and increase of AE count during the cyclic loading. The damage of the igneous rocks with different water contents has been identified by the Felicity Ratio Analysis. The cyclic loading and unloading increase the dislocation between the mineral aggregates and the water-rock interactions further break the adhesion of the clay minerals, which jointly promote the inner damage of the igneous rock. The results suggest that the groundwater can reduce the burst proneness of the igneous rock but increase the potential support failure of the surrounding rock in igneous invading area. In addition, the results inspire the fact that the water injection method is feasible for softening the igneous rock and for preventing the dynamic disasters within the roadways and working faces located in the igneous intrusion area.

Experimental and numerical study on frost heave of saturated rock under uniform freezing conditions

Science.gov (United States)

Lv, Zhitao; Xia, Caichu; Li, Qiang

2018-04-01

A series of freezing experiments are conducted on saturated sandstone and mortar specimens to investigate the frost heave of saturated rock under uniform freezing conditions. The experimental results show that the frost heave of saturated rock is isotropic under uniform freezing conditions. During the freezing process, three stages are observed in the curves of variation of total frost heaving strain versus time: the thermal contraction stage, the frost heaving stage and the steady stage. Moreover, the amount of final stable frost heave first increases and then decreases with decrease in freezing temperature, and the maximum final stable frost heave occurs at different freezing temperature in saturated sandstone and mortar. Furthermore, a coupled thermal-mechanical (TM) model of frost heave of saturated rock is proposed in which a constraint coefficient \\zeta is used to consider the susceptibility of the internal rock grain structure to the expansion of pore ice. Then, numerical simulations are implemented with COMSOL to solve the governing equations of the TM model. Comparisons of the numerical results with the experimental results are performed to demonstrate the reliability of the model. The influences of elastic modulus and porosity on frost heave are also investigated, and the results show that the total frost heaving strain decreases non-linearly with increasing elastic modulus, and the decrease is significant when the elastic modulus is less than 3000 MPa, or approximately five times the elastic modulus of ice. In addition, the total frost heaving strain increases linearly with increasing porosity. Finally, an empirical equation between total frost heaving strain and freezing temperature is proposed and the equation well describes the variation of total frost heaving strain with freezing temperature.

Inverse operator theory method mathematics-mechanization for the solutions of nonlinear equations and some typical applications in nonlinear physics

International Nuclear Information System (INIS)

Fang Jinqing; Yao Weiguang

1992-12-01

Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science

CsPbBr3 nanocrystal saturable absorber for mode-locking ytterbium fiber laser

Science.gov (United States)

Zhou, Yan; Hu, Zhiping; Li, Yue; Xu, Jianqiu; Tang, Xiaosheng; Tang, Yulong

2016-06-01

Cesium lead halide perovskite nanocrystals (CsPbX3, X = Cl, Br, I) have been reported as efficient light-harvesting and light-emitting semiconductor materials, but their nonlinear optical properties have been seldom touched upon. In this paper, we prepare layered CsPbBr3 nanocrystal films and characterize their physical properties. Broadband linear absorption from ˜0.8 to over 2.2 μm and nonlinear optical absorption at the 1-μm wavelength region are measured. The CsPbBr3 saturable absorber (SA), manufactured by drop-casting of colloidal CsPbBr3 liquid solution on a gold mirror, shows modulation depth and saturation intensity of 13.1% and 10.7 MW/cm2, respectively. With this SA, mode-locking operation of a polarization-maintained ytterbium fiber laser produces single pulses with duration of ˜216 ps, maximum average output power of 10.5 mW, and the laser spectrum is centered at ˜1076 nm. This work shows that CsPbBr3 films can be efficient SA candidates for fiber lasers and also have great potential to become broadband linear and nonlinear optical materials for photonics and optoelectronics.

Impact of magnetic saturation on the input-output linearising tracking control of an induction motor

DEFF Research Database (Denmark)

Dolinar, Drago; Ljusev, Petar; Stumberger, Gorazd

2004-01-01

This paper deals with the tracking control design of an induction motor, based on input-output linearization with magnetic saturation included. Magnetic saturation is represented by the nonlinear magnetizing curve of the iron core and is used in the control design, the observer of state variables......, and in the load torque estimator. An input-output linearising control is used to achieve better tracking performances of the drive. It is based on the mixed ”stator current - rotor flux linkage” induction motor model with magnetic saturation considered in the stationary reference frame. Experimental results show...... that the proposed input-output linearising tracking control with the included saturation behaves considerably better than the one without saturation, and that it introduces smaller position and speed errors, and better motor stiffness on account of the increased computational complexity....

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.

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)

Ablation and optical third-order nonlinearities in Ag nanoparticles

Directory of Open Access Journals (Sweden)

Carlos Torres-Torres

2010-11-01

Full Text Available Carlos Torres-Torres1, Néstor Peréa-López2, Jorge Alejandro Reyes-Esqueda3, Luis Rodríguez-Fernández3, Alejandro Crespo-Sosa3, Juan Carlos Cheang-Wong3, Alicia Oliver31Section of Graduate Studies and Research, School of Mechanical and Electrical Engineering, National Polytechnic Institute, Zacatenco, Distrito Federal, Mexico; 2Laboratory for Nanoscience and Nanotechnology Research and Advanced Materials Department, IPICYT, Camino a la Presa San Jose, San Luis Potosi, Mexico; 3Instituto de Física, Universidad Nacional Autónoma de México, A.P. 20-364, México, D.F. 01000, MéxicoAbstract: The optical damage associated with high intensity laser excitation of silver nanoparticles (NPs was studied. In order to investigate the mechanisms of optical nonlinearity of a nanocomposite and their relation with its ablation threshold, a high-purity silica sample implanted with Ag ions was exposed to different nanosecond and picosecond laser irradiations. The magnitude and sign of picosecond refractive and absorptive nonlinearities were measured near and far from the surface plasmon resonance (SPR of the Ag NPs with a self-diffraction technique. Saturable optical absorption and electronic polarization related to self-focusing were identified. Linear absorption is the main process involved in nanosecond laser ablation, but nonlinearities are important for ultrashort picosecond pulses when the absorptive process become significantly dependent on the irradiance. We estimated that near the resonance, picosecond intraband transitions allow an expanded distribution of energy among the NPs, in comparison to the energy distribution resulting in a case of far from resonance, when the most important absorption takes place in silica. We measured important differences in the ablation threshold and we estimated that the high selectiveness of the SPR of Ag NPs as well as their corresponding optical nonlinearities can be strongly significant for laser

Incorporating damage mechanics into explosion simulation models

International Nuclear Information System (INIS)

Sammis, C.G.

1993-01-01

The source region of an underground explosion is commonly modeled as a nested series of shells. In the innermost open-quotes hydrodynamic regimeclose quotes pressures and temperatures are sufficiently high that the rock deforms as a fluid and may be described using a PVT equation of state. Just beyond the hydrodynamic regime, is the open-quotes non-linear regimeclose quotes in which the rock has shear strength but the deformation is nonlinear. This regime extends out to the open-quotes elastic radiusclose quotes beyond which the deformation is linear. In this paper, we develop a model for the non-linear regime in crystalline source rock where the nonlinearity is mostly due to fractures. We divide the non-linear regime into a open-quotes damage regimeclose quotes in which the stresses are sufficiently high to nucleate new fractures from preexisting ones and a open-quotes crack-slidingclose quotes regime where motion on preexisting cracks produces amplitude dependent attenuation and other non-linear effects, but no new cracks are nucleated. The boundary between these two regimes is called the open-quotes damage radius.close quotes The micromechanical damage mechanics recently developed by Ashby and Sammis (1990) is used to write an analytic expression for the damage radius in terms of the initial fracture spectrum of the source rock, and to develop an algorithm which may be used to incorporate damage mechanics into computer source models for the damage regime. Effects of water saturation and loading rate are also discussed

Nonlinear interaction of fast particles with Alfven waves in toroidal plasmas

International Nuclear Information System (INIS)

Candy, J.; Borba, D.; Huysmans, G.T.A.; Kerner, W.; Berk, H.L.

1996-01-01

A numerical algorithm to study the nonlinear, resonant interaction of fast particles with Alfven waves in tokamak geometry has been developed. The scope of the formalism is wide enough to describe the nonlinear evolution of fishbone modes, toroidicity-induced Alfven eigenmodes and ellipticity-induced Alfven eigenmodes, driven by both passing and trapped fast ions. When the instability is sufficiently weak, it is known that the wave-particle trapping nonlinearity will lead to mode saturation before wave-wave nonlinearities are appreciable. The spectrum of linear modes can thus be calculated using a magnetohydrodynamic normal-mode code, then nonlinearly evolved in time in an efficient way according to a two-time-scale Lagrangian dynamical wave model. The fast particle kinetic equation, including the effect of orbit nonlinearity arising from the mode perturbation, is simultaneously solved of the deviation, δf = f - f 0 , from an initial analytic distribution f 0 . High statistical resolution allows linear growth rates, frequency shifts, resonance broadening effects, and nonlinear saturation to be calculated quickly and precisely. The results have been applied to an ITER instability scenario. Results show that weakly-damped core-localized modes alone cause negligible alpha transport in ITER-like plasmas--even with growth rates one order of magnitude higher than expected values. However, the possibility of significant transport in reactor-type plasmas due to weakly unstable global modes remains an open question

Memory in Nonlinear Ionization of Transparent Solids

International Nuclear Information System (INIS)

Rajeev, P. P.; Simova, E.; Hnatovsky, C.; Taylor, R. S.; Rayner, D. M.; Corkum, P. B.; Gertsvolf, M.; Bhardwaj, V. R.

2006-01-01

We demonstrate a shot-to-shot reduction in the threshold laser intensity for ionization of bulk glasses illuminated by intense femtosecond pulses. For SiO 2 the threshold change serves as positive feedback reenforcing the process that produced it. This constitutes a memory in nonlinear ionization of the material. The threshold change saturates with the number of pulses incident at a given spot. Irrespective of the pulse energy, the magnitude of the saturated threshold change is constant (∼20%). However, the number of shots required to reach saturation does depend on the pulse energy. Recognition of a memory in ionization is vital to understand multishot optical or electrical breakdown phenomena in dielectrics

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

Science.gov (United States)

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

2018-04-01

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

Single-mode saturation of the bump-on-tail instability

International Nuclear Information System (INIS)

Simon, A.; Rosenbluth, M.N.

1976-01-01

A slightly unstable plasma with only one or a few linear modes unstable is considered. Nonlinear saturation at small amplitudes has been treated by time-asymptotic analysis which is a generalization of the methods of Bogolyubov and co-workers. In this paper the method is applied to instability in a collisionless plasma governed by the vlasov equation. The bump-on-tail instability is considered for a one-dimensional plasma

Magnetic flux pumping in 3D nonlinear magnetohydrodynamic simulations

Science.gov (United States)

Krebs, I.; Jardin, S. C.; Günter, S.; Lackner, K.; Hoelzl, M.; Strumberger, E.; Ferraro, N.

2017-10-01

A self-regulating magnetic flux pumping mechanism in tokamaks that maintains the core safety factor at q ≈1 , thus preventing sawteeth, is analyzed in nonlinear 3D magnetohydrodynamic simulations using the M3D-C1 code. In these simulations, the most important mechanism responsible for the flux pumping is that a saturated (m =1 ,n =1 ) quasi-interchange instability generates an effective negative loop voltage in the plasma center via a dynamo effect. It is shown that sawtoothing is prevented in the simulations if β is sufficiently high to provide the necessary drive for the (m =1 ,n =1 ) instability that generates the dynamo loop voltage. The necessary amount of dynamo loop voltage is determined by the tendency of the current density profile to centrally peak which, in our simulations, is controlled by the peakedness of the applied heat source profile.

Non-linear mixing in coupled photonic crystal nanobeam cavities due to cross-coupling opto-mechanical mechanisms

Energy Technology Data Exchange (ETDEWEB)

Ramos, Daniel, E-mail: daniel.ramos@csic.es; Frank, Ian W.; Deotare, Parag B.; Bulu, Irfan; Lončar, Marko [School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138 (United States)

2014-11-03

We investigate the coupling between mechanical and optical modes supported by coupled, freestanding, photonic crystal nanobeam cavities. We show that localized cavity modes for a given gap between the nanobeams provide weak optomechanical coupling with out-of-plane mechanical modes. However, we show that the coupling can be significantly increased, more than an order of magnitude for the symmetric mechanical mode, due to optical resonances that arise from the interaction of the localized cavity modes with standing waves formed by the reflection from thesubstrate. Finally, amplification of motion for the symmetric mode has been observed and attributed to the strong optomechanical interaction of our hybrid system. The amplitude of these self-sustained oscillations is large enough to put the system into a non-linear oscillation regime where a mixing between the mechanical modes is experimentally observed and theoretically explained.

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...

Nonlinear time reversal signal processing techniques applied to acousto-mechanical imaging of complex materials

Czech Academy of Sciences Publication Activity Database

Dos Santos, S.; Dvořáková, Zuzana; Caliez, M.; Převorovský, Zdeněk

2015-01-01

Roč. 138, č. 3 (2015) ISSN 0001-4966 Institutional support: RVO:61388998 Keywords : acousto-mechanical characterization of skin aging * nonlinear elastic wave spectroscopy (NEWS) * PM-space statistical approach Subject RIV: BI - Acoustics

Characterization of site-specific biomechanical properties of human meniscus-Importance of collagen and fluid on mechanical nonlinearities.

Science.gov (United States)

Danso, E K; Mäkelä, J T A; Tanska, P; Mononen, M E; Honkanen, J T J; Jurvelin, J S; Töyräs, J; Julkunen, P; Korhonen, R K

2015-06-01

Meniscus adapts to joint loads by depth- and site-specific variations in its composition and structure. However, site-specific mechanical characteristics of intact meniscus under compression are poorly known. In particular, mechanical nonlinearities caused by different meniscal constituents (collagen and fluid) are not known. In the current study, in situ indentation testing was conducted to determine site-specific elastic, viscoelastic and poroelastic properties of intact human menisci. Lateral and medial menisci (n=26) were harvested from the left knee joint of 13 human cadavers. Indentation tests, using stress-relaxation and dynamic (sinusoidal) loading protocols, were conducted for menisci at different sites (anterior, middle, posterior, n=78). Sample- and site-specific axisymmetric finite element models with fibril-reinforced poroelastic properties were fitted to the corresponding stress-relaxation curves to determine the mechanical parameters. Elastic moduli, especially the instantaneous and dynamic moduli, showed site-specific variation only in the medial meniscus (pmeniscus. The phase angle showed no statistically significant variation between the sites (p>0.05). The values for the strain-dependent fibril network modulus (nonlinear behaviour of collagen) were significantly different (pmeniscus only between the middle and posterior sites. For the strain-dependent permeability coefficient, only anterior and middle sites showed a significant difference (pmeniscus. This parameter demonstrated a significant difference (pmeniscus shows more site-dependent variation in the mechanical properties as compared to lateral meniscus. In particular, anterior horn of medial meniscus was the stiffest and showed the most nonlinear mechanical behaviour. The nonlinearity was related to both collagen fibrils and fluid. Copyright © 2015 Elsevier Ltd. All rights reserved.

Modal model for the nonlinear multimode Rayleigh endash Taylor instability

International Nuclear Information System (INIS)

Ofer, D.; Alon, U.; Shvarts, D.; McCrory, R.L.; Verdon, C.P.

1996-01-01

A modal model for the Rayleigh endash Taylor (RT) instability, applicable at all stages of the flow, is introduced. The model includes a description of nonlinear low-order mode coupling, mode growth saturation, and post-saturation mode coupling. It is shown to significantly extend the range of applicability of a previous model proposed by Haan, to cases where nonlinear mode generation is important. Using the new modal model, we study the relative importance of mode coupling at late nonlinear stages and resolve the difference between cases in which mode generation assumes a dominant role, leading to the late time inverse cascade of modes and loss of memory of initial conditions, and cases where mode generation is not important and memory of initial conditions is retained. Effects of finite density ratios (Atwood number A<1) are also included in the model and the difference between various measures of the mixing zone penetration depth for A<1 is discussed. copyright 1996 American Institute of Physics

Development and validation of mechanical model for saturated/unsaturated bentonite buffer

International Nuclear Information System (INIS)

Yamamoto, S.; Komine, H.; Kato, S.

2010-01-01

Document available in extended abstract form only. Development and validation of mechanical models for bentonite buffer and backfill materials are one of important subjects to appropriately evaluate long term behaviour or condition of the EBS in radioactive waste disposal. The Barcelona Basic Model (BBM), which is one of extensions of the modified Cam-Clay model for unsaturated and expansive soil, has been developed and widely applied to several problems by using the coupled THM code, Code B right. Advantage of the model is that mechanical characteristics of buffer and backfill materials under not only saturated condition but also unsaturated one are taken account as well as swelling characteristics due to wetting. In this study the BBM is compared with already existing experimental data and already developed another model in terms of swelling characteristics of Japanese bentonite Kunigel-V1, and is validated in terms of consolidation characteristics based on newly performed controlled-suction oedometer tests for the Kunigel-V1 bentonite. Komine et al. (2003) have proposed a model (set of equations) for predicting swelling characteristics based on the diffuse double layer concept and the van der Waals force concept etc. They performed a lot of swelling deformation tests of bentonite and sand-bentonite mixture to confirm the applicability of the model. The BBM well agrees with the model proposed by Komine et al. and the experimental data in terms of swelling characteristics. Compression index and swelling index depending on suction are introduced in the BBM. Controlled-suction consolidation tests (oedometer tests) were performed to confirm the applicability of the suction dependent indexes to unsaturated bentonite. Compacted bentonite with initial dry density of 1.0 Mg/m 3 was tested. Constant suction, 80 kPa, 280 kPa and 480 kPa was applied and kept during the consolidation tests. Applicability of the BBM to consolidation and swelling behaviour of saturated and

All-optical reservoir computer based on saturation of absorption.

Science.gov (United States)

Dejonckheere, Antoine; Duport, François; Smerieri, Anteo; Fang, Li; Oudar, Jean-Louis; Haelterman, Marc; Massar, Serge

2014-05-05

Reservoir computing is a new bio-inspired computation paradigm. It exploits a dynamical system driven by a time-dependent input to carry out computation. For efficient information processing, only a few parameters of the reservoir needs to be tuned, which makes it a promising framework for hardware implementation. Recently, electronic, opto-electronic and all-optical experimental reservoir computers were reported. In those implementations, the nonlinear response of the reservoir is provided by active devices such as optoelectronic modulators or optical amplifiers. By contrast, we propose here the first reservoir computer based on a fully passive nonlinearity, namely the saturable absorption of a semiconductor mirror. Our experimental setup constitutes an important step towards the development of ultrafast low-consumption analog computers.

Studies of the underlying mechanisms for optical nonlinearities of blue phase liquid crystals (Presentation Recording)

Science.gov (United States)

Chen, Chun-Wei; Khoo, Iam Choon; Zhao, Shuo; Lin, Tsung-Hsien; Ho, Tsung-Jui

2015-10-01

We have investigated the mechanisms responsible for nonlinear optical processes occurring in azobenzene-doped blue phase liquid crystals (BPLC), which exhibit two thermodynamically stable BPs: BPI and BPII. In coherent two wave-mixing experiments, a slow (minutes) and a fast (few milliseconds) side diffractions are observed. The underlying mechanisms were disclosed by monitoring the dynamics of grating formation and relaxation as well as by some supplementary experiments. We found the photothermal indexing and dye/LC intermolecular torque leading to lattice distortion to be the dominant mechanisms for the observed nonlinear response in BPLC. Moreover, the response time of the nonlinear optical process varied with operating phase. The rise time of the thermal indexing process was in good agreement with our findings on the temperature dependence of BP refractive index: τ(ISO) > τ(BPI) > τ(BPII). The relaxation time of the torque-induced lattice distortion was analogue to its electrostriction counterpart: τ'(BPI) > τ'(BPII). In a separate experiment, lattice swelling with selective reflection of direction changed from green to red was also observed. This was attributable to the isomerization-induced change in cholesteric pitch, which directly affects the lattice spacing. The phenomenon was confirmed by measuring the optical rotatory power of the BPLC.

The nonlinear interaction of convection modes in a box of a saturated porous medium

Science.gov (United States)

Florio, Brendan J.; Bassom, Andrew P.; Fowkes, Neville; Judd, Kevin; Stemler, Thomas

2015-05-01

A plethora of convection modes may occur within a confined box of porous medium when the associated dimensionless Rayleigh number R is above some critical value dependent on the geometry. In many cases the crucial Rayleigh number Rc for onset is different for each mode, and in practice the mode with the lowest associated Rc is likely to be the dominant one. For particular sizes of box, however, it is possible for multiple modes (typically three) to share a common Rc. For box shapes close to these special geometries the modes interact and compete nonlinearly near the onset of convection. Here this mechanism is explored and it is shown that generically the dynamics of the competition takes on one of two possible structures. A specific example of each is described, while the general properties of the system enables us to compare our results with some previous calculations for particular box dimensions.

Local-field enhancement effect on the nonlinear optical response of gold-silver nanoplanets.

Science.gov (United States)

Cesca, T; Calvelli, P; Battaglin, G; Mazzoldi, P; Mattei, G

2012-02-13

We report on the nonlinear optical properties of Au-Ag nanoplanets produced by ion implantation and irradiation in silica, experimentally investigated by means of the single beam z-scan technique. The measurements provided experimental evidence of the intense local-field enhancement effect theoretically demonstrated for these plasmonic nanosystems. In particular, this has a dramatic impact on their nonlinear absorption behavior and results in a tunable changeover from reverse saturable absorption to saturable absorption by slightly varying the pump intensity and in the possibility to activate and observe nonlinear phenomena of the electron dynamics otherwise unaccessible in the intensity range that can be employed to study these materials. Finally, for the nanoplanet configuration we found a dramatic decrease of the intensity-dependent absorption coefficient, which could be very promising for obtaining optical gain materials.

To Apply Microdosing or Not? Recommendations to Single Out Compounds with Non-Linear Pharmacokinetics

NARCIS (Netherlands)

Bosgra, S.; Vlaming, M.L.H.; Vaes, W.H.J.

2015-01-01

Non-linearities occur no more frequently between microdose and therapeutic dose studies than in therapeutic range ascending-dose studies. Most non-linearities are due to known saturable processes, and can be foreseen by integrating commonly available preclinical data. The guidance presented here may

Effective stress principle for partially saturated media

International Nuclear Information System (INIS)

McTigue, D.F.; Wilson, R.K.; Nunziato, J.W.

1984-04-01

In support of the Nevada Nuclear Waste Storage Investigation (NNWSI) Project, we have undertaken a fundamental study of water migration in partially saturated media. One aspect of that study, on which we report here, has been to use the continuum theory of mixtures to extend the classical notion of effective stress to partially saturated media. Our analysis recovers previously proposed phenomenological representations for the effective stress in terms of the capillary pressure. The theory is illustrated by specializing to the case of linear poroelasticity, for which we calculate the deformation due to the fluid pressure in a static capillary fringe. We then examine the transient consolidation associated with liquid flow induced by an applied surface load. Settlement accompanies this flow as the liquid is redistributed by a nonlinear diffusion process. For material properties characteristic of tuff from the Nevada Test Site, these effects are found to be vanishingly small. 14 references, 7 figures, 1 table

Assessing species saturation: conceptual and methodological challenges.

Science.gov (United States)

Olivares, Ingrid; Karger, Dirk N; Kessler, Michael

2018-05-07

Is there a maximum number of species that can coexist? Intuitively, we assume an upper limit to the number of species in a given assemblage, or that a lineage can produce, but defining and testing this limit has proven problematic. Herein, we first outline seven general challenges of studies on species saturation, most of which are independent of the actual method used to assess saturation. Among these are the challenge of defining saturation conceptually and operationally, the importance of setting an appropriate referential system, and the need to discriminate among patterns, processes and mechanisms. Second, we list and discuss the methodological approaches that have been used to study species saturation. These approaches vary in time and spatial scales, and in the variables and assumptions needed to assess saturation. We argue that assessing species saturation is possible, but that many studies conducted to date have conceptual and methodological flaws that prevent us from currently attaining a good idea of the occurrence of species saturation. © 2018 Cambridge Philosophical Society.

Metamaterial-Enhanced Nonlinear Terahertz Spectroscopy

Directory of Open Access Journals (Sweden)

Zhang X.

2013-03-01

Full Text Available We demonstrate large nonlinear terahertz responses in the gaps of metamaterial split ring resonators in several materials and use nonlinear THz transmission and THz-pump/THz-probe spectroscopy to study the nonlinear responses and dynamics. We use the field enhancement in the SRR gaps to initiate high-field phenomena at lower incident fields. In vanadium dioxide, we drive the insulator-to-metal phase transition with high-field THz radiation. The film conductivity increases by over two orders of magnitude and the phase transition occurs on a several picosecond timescale. In gallium arsenide, we observe high-field transport phenomena, including mobility saturation and impact ionization. The carrier density increases by up to ten orders of magnitude at high fields. At the highest fields, we demonstrate THz-induced damage in both vanadium dioxide and gallium arsenide.

Effect of surface loading on the hydro-mechanical response of a tunnel in saturated ground

Directory of Open Access Journals (Sweden)

Simon Heru Prassetyo

2016-09-01

Full Text Available The design of underground spaces in urban areas must account not only for the current overburden load but also for future surface loads, such as from construction of high-rise buildings above underground structures. In saturated ground, the surface load will generate an additional mechanical response through stress changes and ground displacement, as well as a hydraulic response through pore pressure changes. These hydro-mechanical (H-M changes can severely influence tunnel stability. This paper examines the effect of surface loading on the H-M response of a typical horseshoe-shaped tunnel in saturated ground. Two tunnel models were created in the computer code Fast Lagrangian Analysis of Continua (FLAC. One model represented weak and low permeability ground (stiff clay, and the other represented strong and high permeability ground (weathered granite. Each of the models was run under two liner permeabilities: permeable and impermeable. Two main cases were compared. In Case 1, the surface load was applied 10 years after tunnel construction. In Case 2, the surface load was applied after the steady state pore pressure condition was achieved. The simulation results show that tunnels with impermeable liners experienced the most severe influence from the surface loading, with high pore pressures, large inward displacement around the tunnels, and high bending moments in the liner. In addition, the severity of the response increased toward steady state. This induced H-M response was worse for tunnels in clay than for those in granite. Furthermore, the long-term liner stabilities in Case 1 and Case 2 were similar, indicating that the influence of the length of time between when the tunnel was completed and when the surface load was applied was negligible. These findings suggest that under surface loading, in addition to the ground strength, tunnel stability in saturated ground is largely influenced by liner permeability and the long-term H-M response of

Spectral dependence of nonlinear optical absorption of silica glass with copper nanoparticles

International Nuclear Information System (INIS)

Golubev, A N; Nikitin, S I; Smirnov, M A; Stepanov, A L

2011-01-01

The nonlinear optical properties of silica glass with copper nanoparticles synthesized by ion implantation were investigated by z-scan method in nanosecond time scale. The reverse saturation absorption (RSA) at the wavelength range of 450–540 nm and saturation absorption (SA) at 550–585 nm were observed. It was supposed that the two-photon electron absorption from bound of d-states determined the RSA effect and the SA is due to saturation of plasmon excitation.

Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

KAUST Repository

Eleiwi, Fadi; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model

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

Science.gov (United States)

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

2017-05-01

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

Nonlinear analysis of collapse mechanism in superstructure vehicle

Science.gov (United States)

Nor, M. K. Mohd; Ho, C. S.; Ma'at, N.

2017-04-01

The EU directive 2001/85/EC is an official European text which describes the specifications for "single deck class II and III vehicles" required to be approved by the regulation UN/ECE no.66 (R66). To prevent the catastrophic consequences by occupant during an accident, the Malaysian government has reinforced the same regulation upon superstructure construction. This paper discusses collapse mechanism analysis of a superstructure vehicle using a Crash D nonlinear analysis computer program based on this regulation. The analysis starts by hand calculation to define the required energy absorption by the chosen structure. Simple calculations were then performed to define the weakest collapse mechanism after undesirable collapse modes are eliminated. There are few factors highlighted in this work to pass the regulation. Using the selected cross section, Crash D simulation showed a good result. Generally, the deformation is linearly correlates to the energy absorption for the structure with low stiffness. Failure of critical members such as vertical lower side wall must be avoided to sustain safety of the passenger compartment and prevent from severe and fatal injuries to the trapped occupant.

Influences of the Control on the Nonlinear Vibrations of a Variable Compression Ratio Mechanism

Directory of Open Access Journals (Sweden)

Mănescu Bogdan

2018-01-01

Full Text Available For the mechanism described in references the study of the nonlinear vibrations is performed considering a multibody approach for the elements of the mechanism and different laws of motion for the control element. A great attention is paid to the equilibrium of the motion. The influence of different parameters of control is highlighted in the paper. The results are numerically validated.

Rapid determination of oxygen saturation and vascularity for cancer detection.

Directory of Open Access Journals (Sweden)

Fangyao Hu

Full Text Available A rapid heuristic ratiometric analysis for estimating tissue hemoglobin concentration and oxygen saturation from measured tissue diffuse reflectance spectra is presented. The analysis was validated in tissue-mimicking phantoms and applied to clinical measurements in head and neck, cervical and breast tissues. The analysis works in two steps. First, a linear equation that translates the ratio of the diffuse reflectance at 584 nm and 545 nm to estimate the tissue hemoglobin concentration using a Monte Carlo-based lookup table was developed. This equation is independent of tissue scattering and oxygen saturation. Second, the oxygen saturation was estimated using non-linear logistic equations that translate the ratio of the diffuse reflectance spectra at 539 nm to 545 nm into the tissue oxygen saturation. Correlations coefficients of 0.89 (0.86, 0.77 (0.71 and 0.69 (0.43 were obtained for the tissue hemoglobin concentration (oxygen saturation values extracted using the full spectral Monte Carlo and the ratiometric analysis, for clinical measurements in head and neck, breast and cervical tissues, respectively. The ratiometric analysis was more than 4000 times faster than the inverse Monte Carlo analysis for estimating tissue hemoglobin concentration and oxygen saturation in simulated phantom experiments. In addition, the discriminatory power of the two analyses was similar. These results show the potential of such empirical tools to rapidly estimate tissue hemoglobin in real-time spectral imaging applications.

Nonlinearity and disorder: Classification and stability of nonlinear impurity modes

DEFF Research Database (Denmark)

Sukhorukov, Andrey A.; Kivshar, Yuri S.; Bang, Ole

2001-01-01

We study the effects produced by competition of two physical mechanisms of energy localization in inhomogeneous nonlinear systems. As an example, we analyze spatially localized modes supported by a nonlinear impurity in the generalized nonlinear Schrödinger equation and describe three types of no...... the case of a power-law nonlinearity in detail. We discuss several scenarios of the instability-induced dynamics of the nonlinear impurity modes, including the mode decay or switching to a new stable state, and collapse at the impurity site....

Nonlinear photoresponse of field effect transistors terahertz detectors at high irradiation intensities

International Nuclear Information System (INIS)

But, D. B.; Drexler, C.; Ganichev, S. D.; Sakhno, M. V.; Sizov, F. F.; Dyakonova, N.; Drachenko, O.; Gutin, A.; Knap, W.

2014-01-01

Terahertz power dependence of the photoresponse of field effect transistors, operating at frequencies from 0.1 to 3 THz for incident radiation power density up to 100 kW/cm 2 was studied for Si metal–oxide–semiconductor field-effect transistors and InGaAs high electron mobility transistors. The photoresponse increased linearly with increasing radiation intensity up to the kW/cm 2 range. Nonlinearity followed by saturation of the photoresponse was observed for all investigated field effect transistors for intensities above several kW/cm 2 . The observed photoresponse nonlinearity is explained by nonlinearity and saturation of the transistor channel current. A theoretical model of terahertz field effect transistor photoresponse at high intensity was developed. The model explains quantitative experimental data both in linear and nonlinear regions. Our results show that dynamic range of field effect transistors is very high and can extend over more than six orders of magnitudes of power densities (from ∼0.5 mW/cm 2 to ∼5 kW/cm 2 )

Gradient-based optimization in nonlinear structural dynamics

DEFF Research Database (Denmark)

Dou, Suguang

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

Generalized Nonlinear Yule Models

Science.gov (United States)

Lansky, Petr; Polito, Federico; Sacerdote, Laura

2016-11-01

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

Amplitude saturation of MEMS resonators explained by autoparametric resonance

International Nuclear Information System (INIS)

Van der Avoort, C; Bontemps, J J M; Steeneken, P G; Le Phan, K; Van Beek, J T M; Van der Hout, R; Hulshof, J; Fey, R H B

2010-01-01

This paper describes a phenomenon that limits the power handling of MEMS resonators. It is observed that above a certain driving level, the resonance amplitude becomes independent of the driving level. In contrast to previous studies of power handling of MEMS resonators, it is found that this amplitude saturation cannot be explained by nonlinear terms in the spring constant or electrostatic force. Instead we show that the amplitude in our experiments is limited by nonlinear terms in the equation of motion which couple the in-plane length-extensional resonance mode to one or more out-of-plane (OOP) bending modes. We present experimental evidence for the autoparametric excitation of these OOP modes using a vibrometer. The measurements are compared to a model that can be used to predict a power-handling limit for MEMS resonators

Amplitude saturation of MEMS resonators explained by autoparametric resonance

Energy Technology Data Exchange (ETDEWEB)

Van der Avoort, C; Bontemps, J J M; Steeneken, P G; Le Phan, K; Van Beek, J T M [NXP Research, Eindhoven (Netherlands); Van der Hout, R; Hulshof, J [Department of Mathematics, VU University—Faculty of Sciences, De Boelelaan 1081a, 1081 HV Amsterdam (Netherlands); Fey, R H B, E-mail: cas.van.der.avoort@nxp.com [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB, Eindhoven (Netherlands)

2010-10-15

This paper describes a phenomenon that limits the power handling of MEMS resonators. It is observed that above a certain driving level, the resonance amplitude becomes independent of the driving level. In contrast to previous studies of power handling of MEMS resonators, it is found that this amplitude saturation cannot be explained by nonlinear terms in the spring constant or electrostatic force. Instead we show that the amplitude in our experiments is limited by nonlinear terms in the equation of motion which couple the in-plane length-extensional resonance mode to one or more out-of-plane (OOP) bending modes. We present experimental evidence for the autoparametric excitation of these OOP modes using a vibrometer. The measurements are compared to a model that can be used to predict a power-handling limit for MEMS resonators.

Magnetic field saturation in the Riga dynamo experiment.

Science.gov (United States)

Gailitis, A; Lielausis, O; Platacis, E; Dement'ev, S; Cifersons, A; Gerbeth, G; Gundrum, T; Stefani, F; Christen, M; Will, G

2001-04-02

After the dynamo experiment in November 1999 [A. Gailitis et al., Phys. Rev. Lett. 84, 4365 (2000)] had shown magnetic field self-excitation in a spiraling liquid metal flow, in a second series of experiments emphasis was placed on the magnetic field saturation regime as the next principal step in the dynamo process. The dependence of the strength of the magnetic field on the rotation rate is studied. Various features of the saturated magnetic field are outlined and possible saturation mechanisms are discussed.

Nonlinear mechanism for the suppression of error field magnetic islands by plasma flow

International Nuclear Information System (INIS)

Parker, R.D.

1992-01-01

Non-axisymmetric magnetic field perturbations generated, for example, by errors in the alignment of the field coils are known to lead to reduced confinement in a tokamak. By inducing the formation of small, stationary, magnetic islands on all rational surfaces they can enhance radial transport and under certain circumstances interact with MHD instabilities to trigger the onset of locked modes leading, in some cases, to disruption of the plasma discharge. Given the stationary nature of the error field islands it is natural to consider whether they can be reduced significantly by the viscous drag of a sheared flow resulting from a bulk rotation of the plasma. In this paper, we examine this interaction by modelling the nonlinear growth and saturation of force-reconnected magnetic islands driven by a corrugated boundary in a slab plasma with an initially uniform flow. A systematic parameter study is made of the time asymptotic steady state. (author) 3 figs., 5 refs

Fault Diagnosis for Nonlinear Hydraulic-Mechanical Drilling Pipe Handling System

DEFF Research Database (Denmark)

Choux, Martin; Blanke, Mogens

2011-01-01

Leakage and increased friction are common faults in hydraulic cylinders that can have serious consequences if they are not detected at early stage. In this paper, the design of a fault detector for a nonlinear hydraulic mechanical system is presented. By considering the system in steady state, two...... residual signals are generated and analysed with a composite hypothesis test which accommodates for unknown parameters. The resulting detector is able to detect abrupt changes in leakage or friction given the noisy pressure and position measurements. Test rig measurements validate the properties...

Nonlinearity from quantum mechanics: Dynamically unstable Bose-Einstein condensate in a double-well trap

International Nuclear Information System (INIS)

Javanainen, Juha

2010-01-01

We study theoretically an atomic Bose-Einstein condensate in a double-well trap, both quantum-mechanically and classically, under conditions such that in the classical model an unstable equilibrium dissolves into large-scale oscillations of the atoms between the potential wells. Quantum mechanics alone does not exhibit such nonlinear dynamics, but measurements of the atom numbers in the potential wells may nevertheless cause the condensate to behave essentially classically.

Structural, Linear, and Nonlinear Optical and Mechanical Properties of New Organic L-Serine Crystal

Directory of Open Access Journals (Sweden)

K. Rajesh

2014-01-01

Full Text Available Nonlinear optical single crystal of organic amino acid L-Serine (LS was grown by slow evaporation technique. Solubility study of the compound was measured and metastable zone width was found. Single crystal X-ray diffraction study was carried out for the grown crystal. The linear and nonlinear optical properties of the crystal were confirmed by UV-Vis analysis and powder SHG tester. FT-IR spectrum was recorded and functional groups were analyzed. Vickers’ microhardness studies showed the mechanical strength of the grown crystal. Laser damage threshold value of the crystal was calculated. Photoconductivity studies reveal the conductivity of the crystal.

Nonlinear oscillations

CERN Document Server

Nayfeh, Ali Hasan

1995-01-01

Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim

Improving tokamak vertical position control in the presence of power supply voltage saturation

International Nuclear Information System (INIS)

Favez, J-Y; Lister, J B; Muellhaupt, Ph; Srinivasan, B

2005-01-01

The control of the current, position and shape of an elongated cross-section tokamak plasma is complicated by the so-called instability of the current vertical position. Linearized models all share the feature of a single unstable eigenmode, attributable to this vertical instability of the plasma equilibrium movement, and a large number of stable or marginally stable eigenmodes, attributable to zero or positive resistance in all other model circuit equations. Due to the size and therefore cost of the ITER tokamak, there will naturally be smaller margins in the poloidal field coil power supplies, implying that the feedback control will experience actuator saturation during large transients due to a variety of plasma disturbances. Current saturation is relatively benign, due to the integrating nature of the tokamak, resulting in a reasonable time horizon for strategically handling the approach to saturation which leads to the loss of one degree of freedom in the feedback control for each saturated coil. On the other hand, voltage saturation is produced by the feedback controller itself, with no intrinsic delay. This paper presents a feedback controller design approach which explicitly takes saturation of the power supply voltage into account when producing the power supply demand signals. We consider the vertically stabilizing part of the ITER controller (fast controller) with one power supply and therefore a single saturated input. We consider an existing ITER controller and enlarge its region of attraction to the full null controllable region by adding a continuous nonlinearity into the control. In a system with a single unstable eigenmode and a single stable eigenmode we have already provided a proof of the asymptotical stability of the closed loop system, and we have examined the performance of this new continuous nonlinear controller. We have subsequently extended this analysis to a system with a single eigenmode and multiple stable eigenmodes. The method

Estimating intratidal nonlinearity of respiratory system mechanics: a model study using the enhanced gliding-SLICE method

International Nuclear Information System (INIS)

Schumann, Stefan; Burcza, Boris; Guttmann, Josef; Haberthür, Christoph; Lichtwarck-Aschoff, Michael

2009-01-01

In the clinical situation and in most research work, the analysis of respiratory system mechanics is limited to the estimation of single-value compliances during static or quasi-static conditions. In contrast, our SLICE method analyses intratidal nonlinearity under the dynamic conditions of mechanical ventilation by calculating compliance and resistance for six conjoined volume portions (slices) of the pressure–volume loop by multiple linear regression analysis. With the gliding-SLICE method we present a new approach to determine continuous intratidal nonlinear compliance. The performance of the gliding-SLICE method was tested both in computer simulations and in a physical model of the lung, both simulating different intratidal compliance profiles. Compared to the original SLICE method, the gliding-SLICE method resulted in smaller errors when calculating the compliance or pressure course (all p 2 O s L −1 to 0.8 ± 0.3 cmH 2 O s L −1 (mathematical model) and from 7.2 ± 3.9 cmH 2 O s L −1 to 0.4 ± 0.2 cmH 2 O s L −1 (physical model) (all p < 0.001). We conclude that the new gliding-SLICE method allows detailed assessment of intratidal nonlinear respiratory system mechanics without discontinuity error

CsPbBr{sub 3} nanocrystal saturable absorber for mode-locking ytterbium fiber laser

Energy Technology Data Exchange (ETDEWEB)

Zhou, Yan; Li, Yue; Xu, Jianqiu; Tang, Yulong, E-mail: yulong@sjtu.edu.cn [Key Laboratory for Laser Plasmas (MOE), Department of Physics and Astronomy, Collaborative Innovation Center of IFSA, Shanghai Jiao Tong University, Shanghai 200240 (China); Hu, Zhiping; Tang, Xiaosheng [Key Laboratory of Optoelectronic Technology and Systems of the Education Ministry of China, College of Optoelectronic Engineering, Chongqing University, Chongqing 400044 (China)

2016-06-27

Cesium lead halide perovskite nanocrystals (CsPbX{sub 3}, X = Cl, Br, I) have been reported as efficient light-harvesting and light-emitting semiconductor materials, but their nonlinear optical properties have been seldom touched upon. In this paper, we prepare layered CsPbBr{sub 3} nanocrystal films and characterize their physical properties. Broadband linear absorption from ∼0.8 to over 2.2 μm and nonlinear optical absorption at the 1-μm wavelength region are measured. The CsPbBr{sub 3} saturable absorber (SA), manufactured by drop-casting of colloidal CsPbBr{sub 3} liquid solution on a gold mirror, shows modulation depth and saturation intensity of 13.1% and 10.7 MW/cm{sup 2}, respectively. With this SA, mode-locking operation of a polarization-maintained ytterbium fiber laser produces single pulses with duration of ∼216 ps, maximum average output power of 10.5 mW, and the laser spectrum is centered at ∼1076 nm. This work shows that CsPbBr{sub 3} films can be efficient SA candidates for fiber lasers and also have great potential to become broadband linear and nonlinear optical materials for photonics and optoelectronics.

Computing with networks of nonlinear mechanical oscillators.

Directory of Open Access Journals (Sweden)

Jean C Coulombe

Full Text Available As it is getting increasingly difficult to achieve gains in the density and power efficiency of microelectronic computing devices because of lithographic techniques reaching fundamental physical limits, new approaches are required to maximize the benefits of distributed sensors, micro-robots or smart materials. Biologically-inspired devices, such as artificial neural networks, can process information with a high level of parallelism to efficiently solve difficult problems, even when implemented using conventional microelectronic technologies. We describe a mechanical device, which operates in a manner similar to artificial neural networks, to solve efficiently two difficult benchmark problems (computing the parity of a bit stream, and classifying spoken words. The device consists in a network of masses coupled by linear springs and attached to a substrate by non-linear springs, thus forming a network of anharmonic oscillators. As the masses can directly couple to forces applied on the device, this approach combines sensing and computing functions in a single power-efficient device with compact dimensions.

Another look at zonal flows: Resonance, shearing, and frictionless saturation

Science.gov (United States)

Li, J. C.; Diamond, P. H.

2018-04-01

We show that shear is not the exclusive parameter that represents all aspects of flow structure effects on turbulence. Rather, wave-flow resonance enters turbulence regulation, both linearly and nonlinearly. Resonance suppresses the linear instability by wave absorption. Flow shear can weaken the resonance, and thus destabilize drift waves, in contrast to the near-universal conventional shear suppression paradigm. Furthermore, consideration of wave-flow resonance resolves the long-standing problem of how zonal flows (ZFs) saturate in the limit of weak or zero frictional drag, and also determines the ZF scale. We show that resonant vorticity mixing, which conserves potential enstrophy, enables ZF saturation in the absence of drag, and so is effective at regulating the Dimits up-shift regime. Vorticity mixing is incorporated as a nonlinear, self-regulation effect in an extended 0D predator-prey model of drift-ZF turbulence. This analysis determines the saturated ZF shear and shows that the mesoscopic ZF width scales as LZ F˜f3 /16(1-f ) 1 /8ρs5/8l03 /8 in the (relevant) adiabatic limit (i.e., τckk‖2D‖≫1 ). f is the fraction of turbulence energy coupled to ZF and l0 is the base state mixing length, absent ZF shears. We calculate and compare the stationary flow and turbulence level in frictionless, weakly frictional, and strongly frictional regimes. In the frictionless limit, the results differ significantly from conventionally quoted scalings derived for frictional regimes. To leading order, the flow is independent of turbulence intensity. The turbulence level scales as E ˜(γL/εc) 2 , which indicates the extent of the "near-marginal" regime to be γLcase of avalanche-induced profile variability. Here, εc is the rate of dissipation of potential enstrophy and γL is the characteristic linear growth rate of fluctuations. The implications for dynamics near marginality of the strong scaling of saturated E with γL are discussed.

Investigations of the role of nonlinear couplings in structure formation and transport regulation in plasma turbulence

Science.gov (United States)

Holland, Christopher George

Studies of nonlinear couplings and dynamics in plasma turbulence are presented. Particular areas of focus are analytic studies of coherent structure formation in electron temperature gradient turbulence, measurement of nonlinear energy transfer in simulations of plasma turbulence, and bispectral analysis of experimental and computational data. The motivation for these works has been to develop and expand the existing theories of plasma transport, and verify the nonlinear predictions of those theories in simulation and experiment. In Chapter II, we study electromagnetic secondary instabilities of electron temperature gradient turbulence. The growth rate for zonal flow generation via modulational instability of electromagnetic ETG turbulence is calculated, as well as that for zonal (magnetic) field generation. In Chapter III, the stability and saturation of streamers in ETG turbulence is considered, and shown to depend sensitively upon geometry and the damping rates of the Kelvin-Helmholtz mode. Requirements for a credible theory of streamer transport are presented. In addition, a self-consistent model for interactions between ETG and ITG (ion temperature gradient) turbulence is presented. In Chapter IV, the nonlinear transfer of kinetic and internal energy is measured in simulations of plasma turbulence. The regulation of turbulence by radial decorrelation due to zonal flows and generation of zonal flows via the Reynolds stress are explicitly demonstrated, and shown to be symmetric facets of a single nonlinear process. Novel nonlinear saturation mechanisms for zonal flows are discussed. In Chapter V, measurements of fluctuation bicoherence in the edge of the DIII-D tokamak are presented. It is shown that the bicoherence increases transiently before a L-H transition, and decays to its initial value after the barrier has formed. The increase in bicoherence is localized to the region where the transport barrier forms, and shows strong coupling between well

Nonlinear MHD analysis for LHD plasmas

International Nuclear Information System (INIS)

Ichiguchi, K.; Nakajima, N.; Wakatani, M.; Carreras, B.A.

2003-01-01

The nonlinear behavior of the interchange modes with multi-helicity in the Large Helical Device is analyzed based on the reduced MHD equations. In the equilibrium at sufficiently low beta value, the saturation of a single mode and the following excitation of other single mode whose resonant surface is close to that of the saturated mode are slowly repeated. This sequence leads to the local deformation of the pressure profile. Increasing the beta value with the pressure profile fixed, a bursting phenomenon due to the overlap of multiple modes is observed in the kinetic energy, which results in the global reduction of the pressure profile. Increasing the beta value using the pressure profile saturated at the lower beta value suppresses the bursting behavior. This result indicates the possibility that the pressure profile is self-organized so that the LHD plasma should attain the high beta regime through a stable path. (author)

Experimental investigations of optical nonlinearities in semiconductor-doped glass waveguides

International Nuclear Information System (INIS)

Dannberg, P.; Possner, T.; Braeuer, A.; Bartuch, U.

1988-01-01

Both, thermal and electronic optical nonlinearities are studied in semiconductor-doped glass (SDG) waveguides which are fabricated in commercially available sharp-cut filters by Cs + -K + ion exchange. The relaxation time in photodarkened substrates is measured to be 30 ps. By means of a prism coupling set-up the saturation value of the nonlinear index change is determined. Furthermore, a high stability dual-beam interferometer is presented for the measurement of both, thermal and electronic nonlinear refractive index n 2 in planar waveguides. Conclusions about the application of SDG to opto-optical switching are given. (author)

Amplification mechanism of ion-ripple lasers and its possible application

International Nuclear Information System (INIS)

Chen, K.R.; Dawson, J.M.

1992-05-01

The IRL is an advanced scheme for generating coherent high-power radiation, in which a relativistic electron beam propagates obliquely through an ion ripple in a plasma. Its amplification mechanism is described by a low gain theory while the linear growth rate is given by the dispersion relation. The efficiency of the lasing is determined by the nonlinear saturation mechanism discussed. By proper choice of device parameters, sources of microwaves, optical, and perhaps even x-rays can be made. The availability of tunable sources for wide wavelength regimes, coherence and high-power, as well as lower cost and simplicity of equipment are emphasized

Nonlinear magnetoelectric effect and magnetostriction in piezoelectric CsCuCl{sub 3} in paramagnetic and antiferromagnetic states

Energy Technology Data Exchange (ETDEWEB)

Kharkovskiy, A. I., E-mail: akharkovskiy@inbox.ru [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland); L.F. Vereshchagin Institute for High Pressure Physics RAS, 142190 Troitsk, Moscow (Russian Federation); Shaldin, Yu. V. [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland); Institute for Crystallography RAS, Lenin' s Avenue 59, 119333 Moscow (Russian Federation); Nizhankovskii, V. I. [International Laboratory of High Magnetic Fields and Low Temperatures, Gajowicka 95, 53-421 Wrocław (Poland)

2016-01-07

The direct nonlinear magnetoelectric (ME) effect and the magnetostriction of piezoelectric CsCuCl{sub 3} single crystals were comprehensively studied over a wide temperature range in stationary magnetic fields of up to 14 T. The direct nonlinear ME effect measurements were also performed in pulsed magnetic fields up to 31 T, at liquid helium temperature in the antiferromagnetic (AF) state for the crystallographic direction in which effect has the maximum value. The nonlinear ME effect was quadratic in the paramagnetic state for the whole range of magnetic fields. In the AF state the phase transition between different configurations of spins manifested itself as plateau-like peculiarity on the nonlinear ME effect. The nonlinear ME effect was saturated by the phase transition to the spin-saturated paramagnetic state. Two contributions to the nonlinear ME effects in CsCuCl{sub 3} were extracted from the experimental data: the intrinsic ME effect originated from the magnetoelectric interactions, and the extrinsic one, which resulted from a magnetostriction-induced piezoelectric effect.

Thermal effects on tearing mode saturation

International Nuclear Information System (INIS)

Kim, J.S.; Chu, M.S.; Greene, J.M.

1988-01-01

The effect of geometry on tearing modes, saturated states of tearing modes, and the thermal effect on tearing modes are presented. The configuration of current and magnetic fields are quite different in slabs and in Tokamaks. However, for any magnetic island regardless of geometry and heating conditions, at island saturation the product of resistivity and current is the same at magnetic O and X lines. The temperature perturbation effect on the nonlinear development of tearing modes is investigated. Thermal conduction along the field lines is much faster than that in the perpendicular direction, and thus the temperature profile follows the island structure. Utilizing Spitzer's conductivity relation, the temperature perturbation is modelled as helical components of resistivity. For a usual tearing mode unstable Tokamak, where shear is positive, the islands continue to grow to a larger size when the islands are cooled. When they are heated, the island sizes are reduced. The temperature perturbation can induce islands even for equilibria stable with respect to tearing modes. Again, the islands appear when cooling takes place. The equilibria with the cooled islands show enhanced field line stochasticity, thus enhanced heat transport. Therefore, thermal instability can be directly related to pressure disruptions. (author)

Nonlinear stochastic systems with network-induced phenomena recursive filtering and sliding-mode design

CERN Document Server

Hu, Jun; Gao, Huijun

2014-01-01

This monograph introduces methods for handling filtering and control problems in nonlinear stochastic systems arising from network-induced phenomena consequent on limited communication capacity. Such phenomena include communication delay, packet dropout, signal quantization or saturation, randomly occurring nonlinearities and randomly occurring uncertainties.The text is self-contained, beginning with an introduction to nonlinear stochastic systems, network-induced phenomena and filtering and control, moving through a collection of the latest research results which focuses on the three aspects

All-optical signal processing in quadratic nonlinear materials

DEFF Research Database (Denmark)

Johansen, Steffen Kjær

2002-01-01

of materials with a second order nonlinearity, the so-called X(2) materials, is faster and stronger than that of more conventional materials with a cubic nonlinearity. The X(2) materials support spatial solitons consisting of two coupled components, the fundamental wave (FW) and its second harmonic (SH......). During this project the interaction between such spatial solitons has been investigated theoretically through perturbation theory and experimentally via numerical simulations. The outcome of this research isnew theoretical tools for quantitatively predicting the escape angle, i.e. the angle of incidence...... are dedicated to this part of the research. In chapter 4 the generality of the theoretical approach is emphasised with the derivation and verification of equivalent tools for media with a saturable nonlinearity. The strength of the X(2) nonlinearity strongly depends on the phase mismatch between the FW...

Development of Nonlinear Flight Mechanical Model of High Aspect Ratio Light Utility Aircraft

Science.gov (United States)

Bahri, S.; Sasongko, R. A.

2018-04-01

The implementation of Flight Control Law (FCL) for Aircraft Electronic Flight Control System (EFCS) aims to reduce pilot workload, while can also enhance the control performance during missions that require long endurance flight and high accuracy maneuver. In the development of FCL, a quantitative representation of the aircraft dynamics is needed for describing the aircraft dynamics characteristic and for becoming the basis of the FCL design. Hence, a 6 Degree of Freedom nonlinear model of a light utility aircraft dynamics, also called the nonlinear Flight Mechanical Model (FMM), is constructed. This paper shows the construction of FMM from mathematical formulation, the architecture design of FMM, the trimming process and simulations. The verification of FMM is done by analysis of aircraft behaviour in selected trimmed conditions.

Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

Science.gov (United States)

Avdyushev, Victor A.

2017-12-01

Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the

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...

Synchronization of multiple 3-DOF helicopters under actuator faults and saturations with prescribed performance.

Science.gov (United States)

Yang, Huiliao; Jiang, Bin; Yang, Hao; Liu, Hugh H T

2018-04-01

The distributed cooperative control strategy is proposed to make the networked nonlinear 3-DOF helicopters achieve the attitude synchronization in the presence of actuator faults and saturations. Based on robust adaptive control, the proposed control method can both compensate the uncertain partial loss of control effectiveness and deal with the system uncertainties. To address actuator saturation problem, the control scheme is designed to ensure that the saturation constraint on the actuation will not be violated during the operation in spite of the actuator faults. It is shown that with the proposed control strategy, both the tracking errors of the leading helicopter and the attitude synchronization errors of each following helicopter are bounded in the existence of faulty actuators and actuator saturations. Moreover, the state responses of the entire group would not exceed the predesigned performance functions which are totally independent from the underlaying interaction topology. Simulation results illustrate the effectiveness of the proposed control scheme. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Collector modulation in high-voltage bipolar transistor in the saturation mode: Analytical approach

Science.gov (United States)

Dmitriev, A. P.; Gert, A. V.; Levinshtein, M. E.; Yuferev, V. S.

2018-04-01

A simple analytical model is developed, capable of replacing the numerical solution of a system of nonlinear partial differential equations by solving a simple algebraic equation when analyzing the collector resistance modulation of a bipolar transistor in the saturation mode. In this approach, the leakage of the base current into the emitter and the recombination of non-equilibrium carriers in the base are taken into account. The data obtained are in good agreement with the results of numerical calculations and make it possible to describe both the motion of the front of the minority carriers and the steady state distribution of minority carriers across the collector in the saturation mode.

TRUST: A Computer Program for Variably Saturated Flow in Multidimensional, Deformable Media

Energy Technology Data Exchange (ETDEWEB)

Reisenauer, A. E.; Key, K. T.; Narasimhan, T. N.; Nelson, R. W.

1982-01-01

The computer code, TRUST. provides a versatile tool to solve a wide spectrum of fluid flow problems arising in variably saturated deformable porous media. The governing equations express the conservation of fluid mass in an elemental volume that has a constant volume of solid. Deformation of the skeleton may be nonelastic. Permeability and compressibility coefficients may be nonlinearly related to effective stress. Relationships between permeability and saturation with pore water pressure in the unsaturated zone may include hysteresis. The code developed by T. N. Narasimhan grew out of the original TRUNP code written by A. L. Edwards. The code uses an integrated finite difference algorithm for numerically solving the governing equation. Narching in time is performed by a mixed explicit-implicit numerical procedure in which the time step is internally controlled. The time step control and related feature in the TRUST code provide an effective control of the potential numerical instabilities that can arise in the course of solving this difficult class of nonlinear boundary value problem. This document brings together the equations, theory, and users manual for the code as well as a sample case with input and output.

WHATIF-AQ, Geochem Speciation and Saturation of Aqueous Solution

International Nuclear Information System (INIS)

Nielsen, Ole John; Jensen, Bror Skytte

1988-01-01

1 - Description of program or function: WHATIF-AQ is part of a family of programs for calculations of geochemistry in the near-field of radioactive waste with temperature gradients. The program calculates speciation and saturation indices for an aqueous solution at temperatures in the range 0 - 125 degrees C. The chemical equilibrium is determined by solving a set of nonlinear equations consisting of the equilibrium constant and mass balance constraints. 2 - Method of solution: The set of equations is solved using a generalized Newton-Raphson technique

The use of the J* integral for non-linear fracture mechanics

International Nuclear Information System (INIS)

Hellen, T.K.

1976-09-01

The Griffith energy balance criterion, first postulated over 50 years ago, is still the basis of linear elastic fracture mechanics. From this, accurate numerical methods for establishing stress intensity factors and energy release rates have been developed. One such method involves path independent contour integrals about the crack tip. An improved contour integral, designated J* is discussed, and shown to have distinct advantages over others in non-linear strain situations. A number of examples are shown including fractures in thermo-plastic and creep situations. (author)

A family of nonlinear PID-like regulators for a class of torque-driven robot manipulators equipped with torque-constrained actuators

Directory of Open Access Journals (Sweden)

Adriana Salinas

2016-02-01

Full Text Available This article addresses the joint position control of torque-driven robot manipulators under actuators subject to torque saturation. Robots having viscous friction, but without gravity vector, are considered. By assuming a static model for the torque actuator (specifically, a model of nonlinear and non-differentiable hard saturation function, a family of nonlinear proportional–integral–derivative-like controllers is proposed. Lyapunov stability theory is used to establish conditions for local asymptotic stability of the closed-loop system. A notable feature of the proposed controller is that stability conditions do not depend on the saturation levels of the actuators. In addition, an experimental study complements the proposed theory.

A Configurable Event-Driven Convolutional Node with Rate Saturation Mechanism for Modular ConvNet Systems Implementation

Science.gov (United States)

Camuñas-Mesa, Luis A.; Domínguez-Cordero, Yaisel L.; Linares-Barranco, Alejandro; Serrano-Gotarredona, Teresa; Linares-Barranco, Bernabé

2018-01-01

Convolutional Neural Networks (ConvNets) are a particular type of neural network often used for many applications like image recognition, video analysis or natural language processing. They are inspired by the human brain, following a specific organization of the connectivity pattern between layers of neurons known as receptive field. These networks have been traditionally implemented in software, but they are becoming more computationally expensive as they scale up, having limitations for real-time processing of high-speed stimuli. On the other hand, hardware implementations show difficulties to be used for different applications, due to their reduced flexibility. In this paper, we propose a fully configurable event-driven convolutional node with rate saturation mechanism that can be used to implement arbitrary ConvNets on FPGAs. This node includes a convolutional processing unit and a routing element which allows to build large 2D arrays where any multilayer structure can be implemented. The rate saturation mechanism emulates the refractory behavior in biological neurons, guaranteeing a minimum separation in time between consecutive events. A 4-layer ConvNet with 22 convolutional nodes trained for poker card symbol recognition has been implemented in a Spartan6 FPGA. This network has been tested with a stimulus where 40 poker cards were observed by a Dynamic Vision Sensor (DVS) in 1 s time. Different slow-down factors were applied to characterize the behavior of the system for high speed processing. For slow stimulus play-back, a 96% recognition rate is obtained with a power consumption of 0.85 mW. At maximum play-back speed, a traffic control mechanism downsamples the input stimulus, obtaining a recognition rate above 63% when less than 20% of the input events are processed, demonstrating the robustness of the network. PMID:29515349

A Configurable Event-Driven Convolutional Node with Rate Saturation Mechanism for Modular ConvNet Systems Implementation

Directory of Open Access Journals (Sweden)

Luis A. Camuñas-Mesa

2018-02-01

Full Text Available Convolutional Neural Networks (ConvNets are a particular type of neural network often used for many applications like image recognition, video analysis or natural language processing. They are inspired by the human brain, following a specific organization of the connectivity pattern between layers of neurons known as receptive field. These networks have been traditionally implemented in software, but they are becoming more computationally expensive as they scale up, having limitations for real-time processing of high-speed stimuli. On the other hand, hardware implementations show difficulties to be used for different applications, due to their reduced flexibility. In this paper, we propose a fully configurable event-driven convolutional node with rate saturation mechanism that can be used to implement arbitrary ConvNets on FPGAs. This node includes a convolutional processing unit and a routing element which allows to build large 2D arrays where any multilayer structure can be implemented. The rate saturation mechanism emulates the refractory behavior in biological neurons, guaranteeing a minimum separation in time between consecutive events. A 4-layer ConvNet with 22 convolutional nodes trained for poker card symbol recognition has been implemented in a Spartan6 FPGA. This network has been tested with a stimulus where 40 poker cards were observed by a Dynamic Vision Sensor (DVS in 1 s time. Different slow-down factors were applied to characterize the behavior of the system for high speed processing. For slow stimulus play-back, a 96% recognition rate is obtained with a power consumption of 0.85 mW. At maximum play-back speed, a traffic control mechanism downsamples the input stimulus, obtaining a recognition rate above 63% when less than 20% of the input events are processed, demonstrating the robustness of the network.

A Configurable Event-Driven Convolutional Node with Rate Saturation Mechanism for Modular ConvNet Systems Implementation.

Science.gov (United States)

Camuñas-Mesa, Luis A; Domínguez-Cordero, Yaisel L; Linares-Barranco, Alejandro; Serrano-Gotarredona, Teresa; Linares-Barranco, Bernabé

2018-01-01

Convolutional Neural Networks (ConvNets) are a particular type of neural network often used for many applications like image recognition, video analysis or natural language processing. They are inspired by the human brain, following a specific organization of the connectivity pattern between layers of neurons known as receptive field. These networks have been traditionally implemented in software, but they are becoming more computationally expensive as they scale up, having limitations for real-time processing of high-speed stimuli. On the other hand, hardware implementations show difficulties to be used for different applications, due to their reduced flexibility. In this paper, we propose a fully configurable event-driven convolutional node with rate saturation mechanism that can be used to implement arbitrary ConvNets on FPGAs. This node includes a convolutional processing unit and a routing element which allows to build large 2D arrays where any multilayer structure can be implemented. The rate saturation mechanism emulates the refractory behavior in biological neurons, guaranteeing a minimum separation in time between consecutive events. A 4-layer ConvNet with 22 convolutional nodes trained for poker card symbol recognition has been implemented in a Spartan6 FPGA. This network has been tested with a stimulus where 40 poker cards were observed by a Dynamic Vision Sensor (DVS) in 1 s time. Different slow-down factors were applied to characterize the behavior of the system for high speed processing. For slow stimulus play-back, a 96% recognition rate is obtained with a power consumption of 0.85 mW. At maximum play-back speed, a traffic control mechanism downsamples the input stimulus, obtaining a recognition rate above 63% when less than 20% of the input events are processed, demonstrating the robustness of the network.

A Perturbation Analysis of Harmonics Generation from Saturated Elements in Power Systems

Science.gov (United States)

Kumano, Teruhisa

Nonlinear phenomena such as saturation in magnetic flux give considerable effects in power system analysis. It is reported that a failure in a real 500kV system triggered islanding operation, where resultant even harmonics caused malfunctions in protective relays. It is also reported that the major origin of this wave distortion is nothing but unidirectional magnetization of the transformer iron core. Time simulation is widely used today to analyze this type of phenomena, but it has basically two shortcomings. One is that the time simulation takes two much computing time in the vicinity of inflection points in the saturation characteristic curve because certain iterative procedure such as N-R (Newton-Raphson) should be used and such methods tend to be caught in an ill conditioned numerical hunting. The other is that such simulation methods sometimes do not help intuitive understanding of the studied phenomenon because the whole nonlinear equations are treated in a matrix form and not properly divided into understandable parts as done in linear systems. This paper proposes a new computation scheme which is based on so called perturbation method. Magnetic saturation in iron cores in a generator and a transformer are taken into account. The proposed method has a special feature against the first shortcoming of the N-R based time simulation method stated above. In the proposed method no iterative process is used to reduce the equation residue but uses perturbation series, which means free from the ill condition problem. Users have only to calculate each perturbation terms one by one until he reaches necessary accuracy. In a numerical example treated in the present paper the first order perturbation can make reasonably high accuracy, which means very fast computing. In numerical study three nonlinear elements are considered. Calculated results are almost identical to the conventional Newton-Raphson based time simulation, which shows the validity of the method. The

Nonlinear stochastic systems with incomplete information filtering and control

CERN Document Server

Shen, Bo; Shu, Huisheng

2013-01-01

Nonlinear Stochastic Processes addresses the frequently-encountered problem of incomplete information. The causes of this problem considered here include: missing measurements; sensor delays and saturation; quantization effects; and signal sampling. Divided into three parts, the text begins with a focus on H∞ filtering and control problems associated with general classes of nonlinear stochastic discrete-time systems. Filtering problems are considered in the second part, and in the third the theory and techniques previously developed are applied to the solution of issues arising in complex networks with the design of sampled-data-based controllers and filters. Among its highlights, the text provides: ·         a unified framework for handling filtering and control problems in complex communication networks with limited bandwidth; ·         new concepts such as random sensor and signal saturations for more realistic modeling; and ·         demonstration of the use of techniques such...

Mechanical characterization and non-linear elastic modeling of poly(glycerol sebacate) for soft tissue engineering.

Science.gov (United States)

Mitsak, Anna G; Dunn, Andrew M; Hollister, Scott J

2012-07-01

Scaffold tissue engineering strategies for repairing and replacing soft tissue aim to improve reconstructive and corrective surgical techniques whose limitations include suboptimal mechanical properties, fibrous capsule formation and volume loss due to graft resorption. An effective tissue engineering strategy requires a scaffolding material with low elastic modulus that behaves similarly to soft tissue, which has been characterized as a nonlinear elastic material. The material must also have the ability to be manufactured into specifically designed architectures. Poly(glycerol sebacate) (PGS) is a thermoset elastomer that meets these criteria. We hypothesize that the mechanical properties of PGS can be modulated through curing condition and architecture to produce materials with a range of stiffnesses. To evaluate this hypothesis, we manufactured PGS constructs cured under various conditions and having one of two architectures (solid or porous). Specimens were then tensile tested according to ASTM standards and the data were modeled using a nonlinear elastic Neo-Hookean model. Architecture and testing conditions, including elongation rate and wet versus dry conditions, affected the mechanical properties. Increasing curing time and temperature led to increased tangent modulus and decreased maximum strain for solid constructs. Porous constructs had lower nonlinear elastic properties, as did constructs of both architectures tested under simulated physiological conditions (wetted at 37 °C). Both solid and porous PGS specimens could be modeled well with the Neo-Hookean model. Future studies include comparing PGS properties to other biological tissue types and designing and characterizing PGS scaffolds for regenerating these tissues. Copyright © 2012 Elsevier Ltd. All rights reserved.

Nonlinear dynamics and complexity

CERN Document Server

Luo, Albert; Fu, Xilin

2014-01-01

This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

Fluctuating Nonlinear Spring Model of Mechanical Deformation of Biological Particles.

Directory of Open Access Journals (Sweden)

Olga Kononova

2016-01-01

Full Text Available The mechanical properties of virus capsids correlate with local conformational dynamics in the capsid structure. They also reflect the required stability needed to withstand high internal pressures generated upon genome loading and contribute to the success of important events in viral infectivity, such as capsid maturation, genome uncoating and receptor binding. The mechanical properties of biological nanoparticles are often determined from monitoring their dynamic deformations in Atomic Force Microscopy nanoindentation experiments; but a comprehensive theory describing the full range of observed deformation behaviors has not previously been described. We present a new theory for modeling dynamic deformations of biological nanoparticles, which considers the non-linear Hertzian deformation, resulting from an indenter-particle physical contact, and the bending of curved elements (beams modeling the particle structure. The beams' deformation beyond the critical point triggers a dynamic transition of the particle to the collapsed state. This extreme event is accompanied by a catastrophic force drop as observed in the experimental or simulated force (F-deformation (X spectra. The theory interprets fine features of the spectra, including the nonlinear components of the FX-curves, in terms of the Young's moduli for Hertzian and bending deformations, and the structural damage dependent beams' survival probability, in terms of the maximum strength and the cooperativity parameter. The theory is exemplified by successfully describing the deformation dynamics of natural nanoparticles through comparing theoretical curves with experimental force-deformation spectra for several virus particles. This approach provides a comprehensive description of the dynamic structural transitions in biological and artificial nanoparticles, which is essential for their optimal use in nanotechnology and nanomedicine applications.

The algebra of non-local charges in non-linear sigma models

International Nuclear Information System (INIS)

Abdalla, E.; Abdalla, M.C.B.; Brunelli, J.C.; Zadra, A.

1994-01-01

It is derived the complete Dirac algebra satisfied by non-local charges conserved in non-linear sigma models. Some examples of calculation are given for the O(N) symmetry group. The resulting algebra corresponds to a saturated cubic deformation (with only maximum order terms) of the Kac-Moody algebra. The results are generalized for when a Wess-Zumino term be present. In that case the algebra contains a minor order correction (sub-saturation). (author). 1 ref

Noise-Immune Cavity-Enhanced Optical Heterodyne Molecular Spectrometry Modelling Under Saturated Absorption

Science.gov (United States)

Dupré, Patrick

2015-06-01

The Noise-Immune Cavity-Enhanced Optical Heterodyne Molecular Spectrometry (NICE-OHMS) is a modern technique renowned for its ultimate sensitivity, because it combines long equivalent absorption length provided by a high finesse cavity, and a detection theoretically limited by the sole photon-shot-noise. One fallout of the high finesse is the possibility to accumulating strong intracavity electromagnetic fields (EMF). Under this condition, molecular transitions can be easy saturated giving rise to the usual Lamb dips (or hole burning). However, the unusual shape of the basically trichromatic EMF (due to the RF lateral sidebands) induces nonlinear couplings, i.e., new crossover transitions. An analytical methodology will be presented to calculate spectra provided by NICE-OHMS experiments. It is based on the solutions of the equations of motion of an open two-blocked-level system performed in the frequency-domain (optically thin medium). Knowing the transition dipole moment, the NICE-OHMS signals (``absorption-like'' and ``dispersion-like'') can be simulated by integration over the Doppler shifts and by paying attention to the molecular Zeeman sublevels and to the EMF polarization The approach has been validated by discussion experimental data obtained on two transitions of {C2H2} in the near-infrared under moderated saturation. One of the applications of the saturated absorption is to be able to simultaneously determine the transition intensity and the density number while only one these 2 quantities can only be assessed in nonlinear absorption. J. Opt. Soc. Am. B 32, 838 (2015) Optics Express 16, 14689 (2008)

On non-linear dynamics of coupled 1+1DOF versus 1+1/2DOF Electro-Mechanical System

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2014-01-01

The electro-mechanical systems (EMS) are used from nano-/micro-scale (NEMS/MEMS) up to macro-scale applications. From mathematical view point, they are modelled with the second order differential equation (or a set of equations) for mechanical system, which is nonlinearly coupled with the second...... or the first order differential equation (or a set of equations) for electrical system, depending on properties of the electrical circuit. For the sake of brevity, we assume a 1DOF mechanical system, coupled to 1 or 1/2DOF electrical system (depending whether the capacitance is, or is not considered......). In the paper, authors perform a parametric study to identify operation regimes, where the capacitance term contributes to the non-linear behaviour of the coupled system. To accomplish this task, the classical method of multiple scales is used. The parametric study allows us to assess for which applications...

Picosecond optical nonlinearities in symmetrical and unsymmetrical ...

Indian Academy of Sciences (India)

It is evident that the saturable absorption (SA) behaviour changed to reverse sat- urable absorption (RSA) and the nonlinear coefficients were obtained using the equation α = α0I/[1 + (I/Is)]. The open-aperture scans were fitted by solving the propagation equation for homogeneous medium dI/dz = {−α0I/[1+(I/Is)]}−βI2.

Dispersion and Nonlinearity Characterization of a Mode-Locked Erbium-Doped Fiber Laser

National Research Council Canada - National Science Library

Louthain, James

2001-01-01

.... These chirped Bragg gratings served as one of the mirrors in the linear fiber laser cavity. Finally, we measured the nonlinearity of five different muhiple quantum well saturable absorbers using a z-scan technique...

A net normal dispersion all-fiber laser using a hybrid mode-locking mechanism

International Nuclear Information System (INIS)

Xu, Bo; Martinez, Amos; Yamashita, Shinji; Set, Sze Yun; Goh, Chee Seong

2014-01-01

We propose and demonstrate an all-fiber, dispersion-mapped, erbium-doped fiber laser with net normal dispersion generating dissipative solitons. The laser is mode-locked by a hybrid mode-locking mechanism consisting of a nonlinear amplifying loop mirror and a carbon nanotube saturable absorber. We achieve self-starting, mode-locked operation generating 2.75 nJ pulses at a fundamental repetition rate of 10.22 MHz with remarkable long term stability. (letter)

Spacecraft reorientation control in presence of attitude constraint considering input saturation and stochastic disturbance

Science.gov (United States)

Cheng, Yu; Ye, Dong; Sun, Zhaowei; Zhang, Shijie

2018-03-01

This paper proposes a novel feedback control law for spacecraft to deal with attitude constraint, input saturation, and stochastic disturbance during the attitude reorientation maneuver process. Applying the parameter selection method to improving the existence conditions for the repulsive potential function, the universality of the potential-function-based algorithm is enhanced. Moreover, utilizing the auxiliary system driven by the difference between saturated torque and command torque, a backstepping control law, which satisfies the input saturation constraint and guarantees the spacecraft stability, is presented. Unlike some methods that passively rely on the inherent characteristic of the existing controller to stabilize the adverse effects of external stochastic disturbance, this paper puts forward a nonlinear disturbance observer to compensate the disturbance in real-time, which achieves a better performance of robustness. The simulation results validate the effectiveness, reliability, and universality of the proposed control law.

The Design of Feedback Control Systems Containing a Saturation Type Nonlinearity

Science.gov (United States)

Schmidt, Stanley F.; Harper, Eleanor V.

1960-01-01

A derivation of the optimum response for a step input for plant transfer functions which have an unstable pole and further data on plants with a single zero in the left half of the s plane. The calculated data are presented tabulated in normalized form. Optimum control systems are considered. The optimum system is defined as one which keeps the error as small as possible regardless of the input, under the constraint that the input to the plant (or controlled system) is limited. Intuitive arguments show that in the case where only the error can be sensed directly, the optimum system is obtained from the optimum relay or on-off solution. References to known solutions are presented. For the case when the system is of the sampled-data type, arguments are presented which indicate the optimum sampled-data system may be extremely difficult if not impossible to realize practically except for very simple plant transfer functions. Two examples of aircraft attitude autopilots are presented, one for a statically stable and the other for a statically unstable airframe. The rate of change of elevator motion is assumed limited for these examples. It is shown that by use of nonlinear design techniques described in NASA TN D-20 one can obtain near optimum response for step inputs and reason- able response to sine wave inputs for either case. Also, the nonlinear design prevents inputs from driving the system unstable for either case.

The effect of temperature and concentration on the corrosion inhibition mechanism of an amphiphilic amido-amine in CO2 saturated solution

OpenAIRE

Desimone, Paula Mariela; Gordillo, Gabriel Jorge; Simison, Silvia Noemi

2017-01-01

The corrosion inhibition mechanism of the N-[2-[(2-aminoethyl)amino]ethyl]-9-octadecenamide on mild steel surface in CO2-saturated 5% NaCl solution has been studied. The inhibition efficiency decreases with increasing temperature. Adsorption of the inhibitor studied is found to follow the Frumkin adsorption isotherm. EIS results show that the mechanism of its corrosion inhibition at concentrations higher than critical micelle concentration is by forming a protective porous bi-layer. The a...

On the nonlinear shaping mechanism for gravity wave spectrum in the atmosphere

Directory of Open Access Journals (Sweden)

I. P. Chunchuzov

2009-11-01

Full Text Available The nonlinear mechanism of shaping of a high vertical wave number spectral tail in the field of a few discrete internal gravity waves in the atmosphere is studied in this paper. The effects of advection of fluid parcels by interacting gravity waves are taken strictly into account by calculating wave field in Lagrangian variables, and performing a variable transformation from Lagrangian to Eulerian frame. The vertical profiles and vertical wave number spectra of the Eulerian displacement field are obtained for both the case of resonant and non-resonant wave-wave interactions. The evolution of these spectra with growing parameter of nonlinearity of the internal wave field is studied and compared to that of a broad band spectrum of gravity waves with randomly independent amplitudes and phases. The calculated vertical wave number spectra of the vertical displacements or relative temperature fluctuations are found to be consistent with the observed spectra in the middle atmosphere.

Experimental study on poro-mechanical behavior of saturated Meuse-Haute/Marne argillite subjected to triaxial compression

International Nuclear Information System (INIS)

Hu, Dawei; Zhang, Fan; Xie, Shouyi; Shao, Jianfu

2012-01-01

Document available in extended abstract form only. Due to its low permeability (10 -18 to 10 -20 m 2 ), the Meuse-Haute/Marne argillite is chosen as the candidate host rock for the geological disposal of high-level radioactive waste by 'Agence Nationale de gestion des Dechets Radioactifs' (ANDRA). During the excavation of the underground tunnel in argillite formation, the Excavation Damaged Zone (EDZ) is expected to develop due to the stress redistribution during excavation and subsequent rock convergence. The nucleation and propagation of microcracks in EDZ can consequently affect the poro-mechanical behavior of the host rock. Therefore, it is of crucial importance to study the poro-mechanical behavior of Meuse-Haute/Marne argillite under the influence of stress induced microcracks. For this purpose, this paper presents the original experimental results of drained and undrained triaxial compression tests as well as evolution of Biot's coefficient during hydrostatic and deviatoric loading of saturated Meuse-Haute/Marne argillite. The size of samples used in the present work is 20x20 mm in order to reduce the saturating time. The axis of the cylindrical sample is perpendicular to the bedding planes. The test system is placed in an insulated room and a temperature control system is used to maintain a constant temperature of 20 ±0.2 C. The saturation condition is an important factor for the determination of the mechanical and poro-elastic properties of saturated argillite. Thus, for each sample, after putting into the triaxial cell, the confining pressure is loaded to 2 MPa and we inject distilled water both at the injection and outlet faces in order to insure the pore pressure at the two faces hold at 1 MPa. This procedure will be keep to 72 hours. Then, the pore pressure at the injection face is increased to 1.5 MPa, and we record the pore pressure at the outlet face. Once the pore pressure at the outlet face reaches the same value at injection face, the sample is

Searching saturation effects in inclusive and exclusive eA processes

International Nuclear Information System (INIS)

Goncalves, V.P.

2016-01-01

In this contribution we have discussed the search of saturation effects in inclusive and exclusive eA processes. In particular, we present a comparison between the linear and non-linear predictions for the nuclear structure functions as well as for the Deep Virtual Compton Scattering (DVCS) and vector meson production in future eA colliders. These results demonstrated that although the inclusive observables are sensitive to saturation effects, it is not yet possible to draw any firm conclusion concerning the QCD dynamics from inclusive quantities due to the large uncertainty present in the collinear predictions. In contrast, exclusive processes are promising observables to search saturation effects, due to the quadratic dependence on the forward scattering amplitude. In particular, the analysis of the nuclear DVCS and vector meson production demonstrated that the energy dependence of the differential cross sections are strongly modified with the increasing of the atomic mass number and that coherent cross section dominates at small t and the incoherent one at large t. Moreover, the number of dips at small t increases with the atomic number, with the position of the dips being almost independent of the model used to treat the dipole - proton interaction

Nonlinear Optical Characteristics of Crystal VioletDye Doped Polystyrene Films by Using Z-Scan Technique

Directory of Open Access Journals (Sweden)

Mahasin F. Hadi

2017-07-01

Full Text Available Z-scan technique was employed to study the nonlinear optical properties (nonlinear refractive index and nonlinear absorption coefficient for crystal violet doped polystyrene films as a function of doping ratio in chloroform solvent. Samples exhibits in closed aperture Z-scan positive nonlinear refraction (self-focusing. While in the open aperture Z-scan gives reverse saturation absorption (RSA (positive absorption for all film with different doping ratio making samples candidates for optical limiting devices for protection of sensors and eyes from energetic laser light pulses under the experimental conditions.

Analysis of saturation effects on the operation of magnetic-controlled switcher type FCL

Directory of Open Access Journals (Sweden)

Faramarz Faghihi

2009-12-01

Full Text Available With the extensive application of electrical power system, suppression of fault current limiter is an important subject that guarantees system security. The superconducting fault current limiters (SFCL have been expected as a possible type of power apparatus to reduce the fault current in the power system. The results shown that under normal state, the FCL has no obvious effect on the power system; under fault state, the current limiting inductance connected in the bias current will be inserted into the fault circuit to limit the fault current. By regulating the bias current, the FCL voltage loss under normal state and the fault current can be adjusted to prescribed level. This kind of SFCL used the nonlinear permeability of the magnetic core for create a sufficient impedance and The transient performance considering the magnetic saturation is analyzed by Preisach model. Preisach model that intrinsically satisfies nonlinear properties is used as the numerical method for analysis of saturation effects. It is able to identification isotropic and no isotropic behaviour. The main idea is to compute the magnetization vector in two steps independently, amplitude and phase. The described model yield results in qualitative agreement with the experimental results.

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

Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

KAUST Repository

Eleiwi, Fadi

2015-07-01

This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model is semi-descretized in space, and a nonlinear state-space representation is provided. The control is designed to force the temperature difference along the membrane sides to track a desired reference asymptotically, and hence a desired flux would be generated. Certain constraints are put on the control law inputs to be within an economic range of energy supplies. The effect of the controller gain is discussed. Simulations with real process parameters for the model, and the controller are provided. © 2015 American Automatic Control Council.

A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic

International Nuclear Information System (INIS)

Singh, Vimal

2007-01-01

In [Singh V. Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic. IEEE Trans Circ Syst 1990;37(6):814-8], a frequency-domain criterion for the suppression of limit cycles in fixed-point state-space digital filters using saturation overflow arithmetic was presented. The passivity property owing to the presence of multiple saturation nonlinearities was exploited therein. In the present paper, a new notion of passivity, namely, that involving the state variables is considered, thereby arriving at an entirely new frequency-domain criterion for the suppression of limit cycles in such filters

Data driven discrete-time parsimonious identification of a nonlinear state-space model for a weakly nonlinear system with short data record

Science.gov (United States)

Relan, Rishi; Tiels, Koen; Marconato, Anna; Dreesen, Philippe; Schoukens, Johan

2018-05-01

Many real world systems exhibit a quasi linear or weakly nonlinear behavior during normal operation, and a hard saturation effect for high peaks of the input signal. In this paper, a methodology to identify a parsimonious discrete-time nonlinear state space model (NLSS) for the nonlinear dynamical system with relatively short data record is proposed. The capability of the NLSS model structure is demonstrated by introducing two different initialisation schemes, one of them using multivariate polynomials. In addition, a method using first-order information of the multivariate polynomials and tensor decomposition is employed to obtain the parsimonious decoupled representation of the set of multivariate real polynomials estimated during the identification of NLSS model. Finally, the experimental verification of the model structure is done on the cascaded water-benchmark identification problem.

Theory of resistivity-gradient-driven turbulence

International Nuclear Information System (INIS)

Garcia, L.; Carreras, B.A.; Diamond, P.H.; Callen, J.D.

1984-10-01

A theory of the nonlinear evolution and saturation of resistivity-driven turbulence, which evolves from linear rippling instabilities, is presented. The nonlinear saturation mechanism is identified both analytically and numerically. Saturation occurs when the turbulent diffusion of the resistivity is large enough so that dissipation due to parallel electron thermal conduction balances the nonlinearly modified resistivity gradient driving term. The levels of potential, resistivity, and density fluctuations at saturation are calculated. A combination of computational modeling and analytic treatment is used in this investigation

Hydrologic mechanisms governing fluid flow in partially saturated, fractured, porous tuff at Yucca Mountain

International Nuclear Information System (INIS)

Wang, J.S.Y.; Narasimhan, T.N.

1984-10-01

In contrast to the saturated zone where fluid moves rapidly along fractures, the fractures (with apertures large relative to the size of matrix pores) will desaturate first during drainage process and the bulk of fluid flow would be through interconnected pores in the matrix. Within a partially drained fracture, the presence of a relatively continuous air phase will produce practically an infinite resistance to liquid flow in the direction parallel to the fracture. The residual liquid will be held by capillary force in regions around fracture contact areas where the apertures are small. Normal to the fracture surfaces, the drained portion of the fractures will reduce the effective area for liquid flow from one matrix block to another matrix block. A general statistical theory is constructed for flow along the fracture and for flow between the matrix blocks to the fractures under partially saturated conditions. Results are obtained from an aperture distribution model for fracture saturation, hydraulic conductivity, and effective matrix-fracture flow areas as functions of pressure. Drainage from a fractured tuff column is simulated. The parameters for the simulations are deduced from fracture surface characteristics, spacings and orientations based on core analyses, and from matrix characteristics curve based on laboratory measurements. From the cases simulated for the fractured, porous column with discrete vertical and horizontal fractures and porous matrix blocks explicitly taken into account, it is observed that the highly transient changes from fully saturated conditions to partially saturated conditions are extremely sensitive to the fracture properties. However, the quasi-steady changes of the fluid flow of a partially saturated, fractured, porous system could be approximately simulated without taking the fractures into account. 22 references, 16 figures

Gas migration mechanism of saturated dense bentonite and its modeling

International Nuclear Information System (INIS)

Tanaka, Yukihisa; Hironaga, Michihiko; Kudo, Koji

2007-01-01

In the current concept of repository for nuclear waste disposal, compacted bentonite will be used as an engineered barrier mainly for inhibiting migration of radioactive nuclides. Hydrogen gas can be generated inside the engineered barrier by anaerobic corrosion of metals used for containers, etc. If the gas generation rate exceeds the diffusion rate of gas molecules inside of the engineered barrier, gas will accumulate in the void space inside of the engineered barrier until its pressure becomes large enough for it to enter the bentonite as a discrete gaseous phase. It is expected to be not easy for gas to entering into the bentonite as a discrete gaseous phase because the pore of compacted bentonite is so minute. Therefore it is necessary to investigate the following subjects: a) Effect of the accumulated gas pressure on surrounding objects such as concrete lining, rock mass. b) Effect of gas breakthrough on the barrier function of bentonite. c) Revealing and modeling gas migration mechanism for overcoming the scale effects in laboratory specimen test. Therefore in this study, gas migration tests for compacted and saturated bentonite to investigate and to model the mechanism of gas migration phenomenon. Firstly, the following conclusions were obtained through by the results of the gas migration tests which are conducted in this study: 1) Bubbles appear in the semitransparent drainage tube at first when the total gas is equal to the initial total axial stress or somewhat smaller. By increasing the gas pressure more, breakthrough of gas migration, which is defined as a sudden increase of amount of emission gas, occurred. When the total gas pressure exceeds the initial total axial stress, the total axial stress is always equal to the total gas pressure because specimens shrink in the axial direction with causing the clearance between the end of the specimen and porous metal. 2) Effective gas conductivity after breakthrough of gas migration is times larger than that

Apparent embrittlement saturation and radiation mechanisms of reactor pressure vessel steels

International Nuclear Information System (INIS)

Pachur, D.

1981-01-01

The irradiation and annealing results of three different reactor pressure vessel steels are reported. Steel A, a basic material according to ASTM A-533 B having 0.15 percent vanadium; and Steel C contained 3.2 percent nickel. The steels were irradiated at 150, 300, and 400 degree C with neutron fluxes of 6 multiplied by 10 11 and 3 multiplied by 10 13 neutrons (n)/cm 2 /s. An apparent saturation-in-irradiation effect was found within certain neutron fluence ranges. During the annealing, various recovery processes occur in different temperature ranges. These are characterized by various activation energies. The individual processes were determined by the different time dependencies at various temperatures. Two causes for the apparent saturation were discovered from the behavior of the annealing curves

Fitness Effects of Network Non-Linearity Induced by Gene Expression Noise

Science.gov (United States)

Ray, Christian; Cooper, Tim; Balazsi, Gabor

2012-02-01

In the non-equilibrium dynamics of growing microbial cells, metabolic enzymes can create non-linearities in metabolite concentration because of non-linear degradation (utilization): an enzyme can saturate in the process of metabolite utilization. Increasing metabolite production past the saturation point then results in an ultrasensitive metabolite response. If the production rate of a metabolite depends on a second enzyme or other protein-mediated process, uncorrelated gene expression noise can thus cause transient metabolite concentration bursts. Such bursts are physiologically unnecessary and may represent a source of selection against the ultrasensitive switch, especially if the fluctuating metabolic intermediate is toxic. Selection may therefore favor correlated gene expression fluctuations for enzymes in the same pathway, such as by same-operon membership in bacteria. Using a modified experimental lac operon system, we are undertaking a combined theoretical-experimental approach to demonstrate that (i) the lac operon has an implicit ultrasensitive switch that we predict is avoided by gene expression correlations induced by same-operon membership; (ii) bacterial growth rates are sensitive to crossing the ultrasensitive threshold. Our results suggest that correlations in intrinsic gene expression noise are exploited by evolution to ameliorate the detrimental effects of nonlinearities in metabolite concentrations.

Nonlinearity and nonclassicality in a nanomechanical resonator

Energy Technology Data Exchange (ETDEWEB)

Teklu, Berihu [Clermont Universite, Blaise Pascal University, CNRS, PHOTON-N2, Institut Pascal, Aubiere Cedex (France); Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy); Ferraro, Alessandro; Paternostro, Mauro [Queen' s University, Centre for Theoretical Atomic, Molecular, and Optical Physics, School of Mathematics and Physics, Belfast (United Kingdom); Paris, Matteo G.A. [Universita degli Studi di Milano, Dipartimento di Fisica, Milano (Italy)

2015-12-15

We address quantitatively the relationship between the nonlinearity of a mechanical resonator and the nonclassicality of its ground state. In particular, we analyze the nonclassical properties of the nonlinear Duffing oscillator (being driven or not) as a paradigmatic example of a nonlinear nanomechanical resonator. We first discuss how to quantify the nonlinearity of this system and then show that the nonclassicality of the ground state, as measured by the volume occupied by the negative part of the Wigner function, monotonically increases with the nonlinearity in all the working regimes addressed in our study. Our results show quantitatively that nonlinearity is a resource to create nonclassical states in mechanical systems. (orig.)

Nonlinear damping for vibration isolation of microsystems using shear thickening fluid

Science.gov (United States)

Iyer, S. S.; Vedad-Ghavami, R.; Lee, H.; Liger, M.; Kavehpour, H. P.; Candler, R. N.

2013-06-01

This work reports the measurement and analysis of nonlinear damping of micro-scale actuators immersed in shear thickening fluids (STFs). A power-law damping term is added to the linear second-order model to account for the shear-dependent viscosity of the fluid. This nonlinear model is substantiated by measurements of oscillatory motion of a torsional microactuator. At high actuation forces, the vibration velocity amplitude saturates. The model accurately predicts the nonlinear damping characteristics of the STF using a power-law index extracted from independent rheology experiments. This result reveals the potential to use STFs as adaptive, passive dampers for vibration isolation of microelectromechanical systems.

Output power PDF of a saturated semiconductor optical amplifier: Second-order noise contributions by path integral method

DEFF Research Database (Denmark)

Öhman, Filip; Mørk, Jesper; Tromborg, Bjarne

2007-01-01

We have developed a second-order small-signal model for describing the nonlinear redistribution of noise in a saturated semiconductor optical amplifier. In this paper, the details of the model are presented. A numerical example is used to compare the model to statistical simulations. We show that...

LDRD report nonlinear model reduction

Energy Technology Data Exchange (ETDEWEB)

Segalman, D.; Heinstein, M.

1997-09-01

The very general problem of model reduction of nonlinear systems was made tractable by focusing on the very large subclass consisting of linear subsystems connected by nonlinear interfaces. Such problems constitute a large part of the nonlinear structural problems encountered in addressing the Sandia missions. A synthesis approach to this class of problems was developed consisting of: detailed modeling of the interface mechanics; collapsing the interface simulation results into simple nonlinear interface models; constructing system models by assembling model approximations of the linear subsystems and the nonlinear interface models. These system models, though nonlinear, would have very few degrees of freedom. A paradigm problem, that of machine tool vibration, was selected for application of the reduction approach outlined above. Research results achieved along the way as well as the overall modeling of a specific machine tool have been very encouraging. In order to confirm the interface models resulting from simulation, it was necessary to develop techniques to deduce interface mechanics from experimental data collected from the overall nonlinear structure. A program to develop such techniques was also pursued with good success.

Development of finite element code for the analysis of coupled thermo-hydro-mechanical behaviors of saturated-unsaturated medium

International Nuclear Information System (INIS)

Ohnishi, Y.; Shibata, H.; Kobayashi, A.

1985-01-01

A model is presented which describes fully coupled thermo-hydro-mechanical behavior of porous geologic medium. The mathematical formulation for the model utilizes the Biot theory for the consolidation and the energy balance equation. The medium is in the condition of saturated-unsaturated flow, then the free surfaces are taken into consideration in the model. The model, incorporated in a finite element numerical procedure, was implemented in a two-dimensional computer code. The code was developed under the assumptions that the medium is poro-elastic and in plane strain condition; water in the ground does not change its phase; heat is transferred by conductive and convective flow. Analytical solutions pertaining to consolidation theory for soils and rocks, thermoelasticity for solids and hydrothermal convection theory provided verification of stress and fluid flow couplings, respectively in the coupled model. Several types of problems are analyzed. The one is a study of some of the effects of completely coupled thermo-hydro-mechanical behavior on the response of a saturated-unsaturated porous rock containing a buried heat source. Excavation of an underground opening which has radioactive wastes at elevated temperatures is modeled and analyzed. The results shows that the coupling phenomena can be estimated at some degree by the numerical procedure. The computer code has a powerful ability to analyze of the repository the complex nature of the repository

Adaptive near-optimal neuro controller for continuous-time nonaffine nonlinear systems with constrained input.

Science.gov (United States)

Esfandiari, Kasra; Abdollahi, Farzaneh; Talebi, Heidar Ali

2017-09-01

In this paper, an identifier-critic structure is introduced to find an online near-optimal controller for continuous-time nonaffine nonlinear systems having saturated control signal. By employing two Neural Networks (NNs), the solution of Hamilton-Jacobi-Bellman (HJB) equation associated with the cost function is derived without requiring a priori knowledge about system dynamics. Weights of the identifier and critic NNs are tuned online and simultaneously such that unknown terms are approximated accurately and the control signal is kept between the saturation bounds. The convergence of NNs' weights, identification error, and system states is guaranteed using Lyapunov's direct method. Finally, simulation results are performed on two nonlinear systems to confirm the effectiveness of the proposed control strategy. Copyright © 2017 Elsevier Ltd. All rights reserved.

Reverse saturable absorption (RSA) in fluorinated iridium derivatives

Science.gov (United States)

Ferry, Michael J.; O'Donnell, Ryan M.; Bambha, Neal; Ensley, Trenton R.; Shensky, William M.; Shi, Jianmin

2017-08-01

The photophysical properties of cyclometallated iridium compounds are beneficial for nonlinear optical (NLO) applications, such as the design of reverse saturable absorption (RSA) materials. We report on the NLO characterization of a family of compounds of the form [Ir(pbt)2(LX)], where pbt is 2-phenylbenzothiazole and LX is a beta-diketonate ligand. In particular, we investigate the effects of trifluoromethylation on compound solubility and photophysics compared to the parent acetylacetonate (acac) version. The NLO properties, such as the singlet and triplet excited-state cross sections, of these compounds were measured using the Z-scan technique. The excited-state lifetimes were determined from visible transient absorption spectroscopy.

Block backstepping design of nonlinear state feedback control law for underactuated mechanical systems

CERN Document Server

Rudra, Shubhobrata; Maitra, Madhubanti

2017-01-01

This book presents a novel, generalized approach to the design of nonlinear state feedback control laws for a large class of underactuated mechanical systems based on application of the block backstepping method. The control law proposed here is robust against the effects of model uncertainty in dynamic and steady-state performance and addresses the issue of asymptotic stabilization for the class of underactuated mechanical systems. An underactuated system is defined as one for which the dimension of space spanned by the configuration vector is greater than that of the space spanned by the control variables. Control problems concerning underactuated systems currently represent an active field of research due to their broad range of applications in robotics, aerospace, and marine contexts. The book derives a generalized theory of block backstepping control design for underactuated mechanical systems, and examines several case studies that cover interesting examples of underactuated mechanical systems. The math...

Experimental and numerical approaches of the hydro-mechanical behaviour of a quasi-saturated compacted clayey soil

Directory of Open Access Journals (Sweden)

Li Zhong-Sen

2016-01-01

Full Text Available The present research is funded by the French National Project « TerreDurable », which is dedicated to the study of soils in quasi-saturated conditions (close to saturation for the analysis of stability and settlement of earth structures such as embankment, dams. A global presentation of the drying-wetting test shows the volume change, air entry and soil-water characteristics of the soil at slurry and oven-dried conditions. Unsaturated undrained triaxial test was carried out in order to investigate the variation of pore-water pressure from quasi-saturated domain to saturation. The experimental results of the triaxial test are then modeled using a two-dimensional explicit finite difference program (Flac 2D. A constitutive law developed in the TerreDurable project allows better understanding the behaviour of quasi-saturated soils using the water retention curve of quasi-saturated domain proposed by Boutonnier (2007, 2010. A simple effective stress model is used (Cam Clay by taking into account both the suction and the compressibility of equivalent fluid (water + air. The results from numerical calculation and experimental measurements are compared.

Lie-Nambu and Lie-Poisson structures in linear and nonlinear quantum mechanics

International Nuclear Information System (INIS)

Czachor, M.

1996-01-01

Space of density matrices in quantum mechanics can be regarded as a Poisson manifold with the dynamics given by certain Lie-Poisson bracket corresponding to an infinite dimensional Lie algebra. The metric structure associated with this Lie algebra is given by a metric tensor which is not equivalent to the Cartan-Killing metric. The Lie-Poisson bracket can be written in a form involving a generalized (Lie-)Nambu bracket. This bracket can be used to generate a generalized, nonlinear and completely integrable dynamics of density matrices. (author)

Pressure-anisotropy-induced nonlinearities in the kinetic magnetorotational instability

Science.gov (United States)

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

2017-12-01

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

THE SEARCH FOR SUPER-SATURATION IN CHROMOSPHERIC EMISSION

International Nuclear Information System (INIS)

Christian, Damian J.; Arias, Tersi; Mathioudakis, Mihalis; Jess, David B.; Jardine, Moira

2011-01-01

We investigate if the super-saturation phenomenon observed at X-ray wavelengths for the corona exists in the chromosphere for rapidly rotating late-type stars. Moderate resolution optical spectra of fast-rotating EUV- and X-ray-selected late-type stars were obtained. Stars in α Per were observed in the northern hemisphere with the Isaac Newton 2.5 m telescope and Intermediate Dispersion Spectrograph. Selected objects from IC 2391 and IC 2602 were observed in the southern hemisphere with the Blanco 4 m telescope and R-C spectrograph at CTIO. Ca II H and K fluxes were measured for all stars in our sample. We find the saturation level for Ca II K at log (L CaK /L bol ) = -4.08. The Ca II K flux does not show a decrease as a function of increased rotational velocity or smaller Rossby number as observed in the X-ray. This lack of 'super-saturation' supports the idea of coronal stripping as the cause of saturation and super-saturation in stellar chromospheres and coronae, but the detailed underlying mechanism is still under investigation.

Linear and nonlinear kinetic-stability studies in tokamaks

International Nuclear Information System (INIS)

Tang, W.M.; Chance, M.S.; Chen, L.; Krommes, J.A.; Lee, W.W.; Rewoldt, G.

1982-09-01

This paper presents results of theoretical investigations on important linear kinetic properties of low frequency instabilities in toroidal systems and on nonlinear processes which could significantly influence their impact on anomalous transport. Analytical and numerical methods and also particle simulations have been employed to carry out these studies. In particular, the following subjects are considered: (1) linear stability analysis of kinetic instabilities for realistic tokamak equilibria and the application of such calculations to the PDX and PLT tokamak experiments including the influence of a hot beam-ion component; (2) determination of nonlinearly saturated, statistically steady states of three interacting drift modes; and (3) gyrokinetic particle simulation of drift instabilities

Nonlinear Whistler Wave Physics in the Radiation Belts

Science.gov (United States)

Crabtree, Chris

2016-10-01

Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data

Poromechanical approach describing the moisture influence on the non-linear quasi-static and dynamic behaviour of porous building materials

NARCIS (Netherlands)

Carmeliet, J.; Abeele, van den K.E.A.

2004-01-01

The non-linear quasi-static and dynamic elastic behaviour of Berea sandstone has been experimentally analysed showing hysteresis and a strong influence of moisture especially in the lower saturation range. It is shown that non-linear hysteretic response originates within the "bond system" of the

Gain dynamics and saturation in semiconductor quantum dot amplifiers

DEFF Research Database (Denmark)

Berg, Tommy Winther; Mørk, Jesper; Hvam, Jørn Märcher

2004-01-01

Quantum dot (QD)-based semiconductor optical amplifiers offer unique properties compared with conventional devices based on bulk or quantum well material. Due to the bandfilling properties of QDs and the existence of a nearby reservoir of carriers in the form of a wetting layer, QD semiconductor...... optical amplifiers may be operated in regimes of high linearity, i.e. with a high saturation power, but can also show strong and fast nonlinearities by breaking the equilibrium between discrete dot states and the continuum of wetting layer states. In this paper, we analyse the interplay of these two...

Nonlinear dynamics of single-helicity neoclassical MHD tearing instabilities

International Nuclear Information System (INIS)

Spong, D.A.; Shaing, K.C.; Carreras, B.A.; Callen, J.D.; Garcia, L.

1988-10-01

Neoclassical magnetohydrodynamic (MHD) effects can significantly alter the nonlinear evolution of resistive tearing instabilities. This is studied numerically by using a flux-surface-averaged set of evolution equations that includes the lowest-order neoclassical MHD effects. The new terms in the equations are fluctuating bootstrap current, neoclassical modification of the resistivity, and neoclassical damping of the vorticity. Single-helicity tearing modes are studied in a cylindrical model over a range of neoclassical viscosities (μ/sub e//ν/sup e/) and values of the Δ' parameter of tearing mode theory. Increasing the neoclassical viscosity leads to increased growth rate and saturated island width as predicted analytically. The larger island width is caused by the fluctuating bootstrap current contribution in Ohm's law. The Δ' parameter no longer solely determines the island width, and finite-width saturated islands may be obtained even when Δ' is negative. The importance of the bootstrap current (/approximately/∂/rho///partial derivative/psi/) in the nonlinear dynamics leads us to examine the sensitivity of the results with respect to different models for the density evolution. 11 refs., 8 figs

Structural optimization for nonlinear dynamic response

DEFF Research Database (Denmark)

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

2015-01-01

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

Regional Quasi-Three-Dimensional Unsaturated-Saturated Water Flow Model Based on a Vertical-Horizontal Splitting Concept

Directory of Open Access Journals (Sweden)

Yan Zhu

2016-05-01

Full Text Available Due to the high nonlinearity of the three-dimensional (3-D unsaturated-saturated water flow equation, using a fully 3-D numerical model is computationally expensive for large scale applications. A new unsaturated-saturated water flow model is developed in this paper based on the vertical/horizontal splitting (VHS concept to split the 3-D unsaturated-saturated Richards’ equation into a two-dimensional (2-D horizontal equation and a one-dimensional (1-D vertical equation. The horizontal plane of average head gradient in the triangular prism element is derived to split the 3-D equation into the 2-D equation. The lateral flow in the horizontal plane of average head gradient represented by the 2-D equation is then calculated by the water balance method. The 1-D vertical equation is discretized by the finite difference method. The two equations are solved simultaneously by coupling them into a unified nonlinear system with a single matrix. Three synthetic cases are used to evaluate the developed model code by comparing the modeling results with those of Hydrus1D, SWMS2D and FEFLOW. We further apply the model to regional-scale modeling to simulate groundwater table fluctuations for assessing the model applicability in complex conditions. The proposed modeling method is found to be accurate with respect to measurements.

Seismic response analysis of the deep saturated soil deposits in Shanghai

Science.gov (United States)

Huang, Yu; Ye, Weimin; Chen, Zhuchang

2009-01-01

The quaternary deposits in Shanghai are horizontal soil layers of thickness up to about 280 m in the urban area with an annual groundwater table between 0.5 and 0.7 m from the surface. The characteristics of deep saturated deposits may have important influences upon seismic response of the ground in Shanghai. Based on the Biot theory for porous media, the water-saturated soil deposits are modeled as a two-phase porous system consisting of solid and fluid phases, in this paper. A nonlinear constitutive model for predicting the seismic response of the ground is developed to describe the dynamic characters of the deep-saturated soil deposits in Shanghai. Subsequently, the seismic response of a typical site with 280 m deep soil layers, which is subjected to four base excitations (El Centro, Taft, Sunan, and Tangshan earthquakes), is analyzed in terms of an effective stress-based finite element method with the proposed constitutive model. Special emphasis is given to the computed results of accelerations, excess pore-water pressures, and settlements during the seismic excitations. It has been found that the analysis can capture fundamental aspects of the ground response and produce preliminary results for seismic assessment.

Nonlinear Dynamic Analysis of Telescopic Mechanism for Truss Structure Bridge Inspection Vehicle Under Pedestrian Excitation

Directory of Open Access Journals (Sweden)

Wenwen Sui

Full Text Available Abstract Nonlinear dynamic analysis of an axially moving telescopic mechanism for truss structure bridge inspection vehicle under pedestrian excitation is carried out. A biomechanically inspired inverted-pendulum model is utilized to simplify the pedestrian. The nonlinear equations of motion for the beam-pedestrian system are derived using the Hamilton's principle. The equations are transformed into two ordinary differential equations by applying the Galerkin's method at the first two orders. The solutions to the equations are acquired by using the Newmark-β method associated with the Newton-Raphson method. The time-dependent feature of the eigenfunctions for the two beams are taken into consideration in the solutions. Accordingly, the equations of motion for a simplified system, in which the pedestrian is regarded as moving cart, are given. In the numerical examples, dynamic responses of the telescopic mechanism in eight conditions of different beam-telescoping and pedestrian-moving directions are simulated. Comparisons between the vibrations of the beams under pedestrian excitation and corresponding moving cart are carried out to investigate the influence of the pedestrian excitation on the telescopic mechanism. The results show that the displacement of the telescopic mechanism under pedestrian excitation is smaller than that under moving cart especially when the pedestrian approaches the beams end. Additionally, compared with moving cart, the pedestrian excitation can effectively strengthen the vibration when the beam extension is small or when the pedestrian is close to the beams end.

Nonlinear streak computation using boundary region equations

Energy Technology Data Exchange (ETDEWEB)

Martin, J A; Martel, C, E-mail: juanangel.martin@upm.es, E-mail: carlos.martel@upm.es [Depto. de Fundamentos Matematicos, E.T.S.I Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid (Spain)

2012-08-01

The boundary region equations (BREs) are applied for the simulation of the nonlinear evolution of a spanwise periodic array of streaks in a flat plate boundary layer. The well-known BRE formulation is obtained from the complete Navier-Stokes equations in the high Reynolds number limit, and provides the correct asymptotic description of three-dimensional boundary layer streaks. In this paper, a fast and robust streamwise marching scheme is introduced to perform their numerical integration. Typical streak computations present in the literature correspond to linear streaks or to small-amplitude nonlinear streaks computed using direct numerical simulation (DNS) or the nonlinear parabolized stability equations (PSEs). We use the BREs to numerically compute high-amplitude streaks, a method which requires much lower computational effort than DNS and does not have the consistency and convergence problems of the PSE. It is found that the flow configuration changes substantially as the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, which end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results. (paper)

Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

Science.gov (United States)

Sozio, Fabio; Yavari, Arash

2017-01-01

In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.

Selective nonspecific solvation under dielectric saturation and fluorescence spectra of dye solutions in binary solvents.

Science.gov (United States)

Bakhshiev, N G; Kiselev, M B

1991-09-01

The influence of selective nonspecific solvation on the fluorescence spectra of three substitutedN-methylphthalimides in a binary solvent system consisting of a nonpolar (n-heptane) and a polar (pyridine) component has been studied under conditions close to dielectric saturation. The substantially nonlinearity of the effect is confirmation that the spectral shifts of fluorescence bands depend on the number of polar solvent molecules involved in solvating the dye molecule. The measured fluorescence spectral shifts determined by substituting one nonpolar solvent molecula with a polar one in the proximity of the dye molecule agree quantitatively with the forecasts of the previously proposed semiempirical theory which describes this nonlinear solvation phenomenon.

An enhanced nonlinear damping approach accounting for system constraints in active mass dampers

Science.gov (United States)

Venanzi, Ilaria; Ierimonti, Laura; Ubertini, Filippo

2015-11-01

Active mass dampers are a viable solution for mitigating wind-induced vibrations in high-rise buildings and improve occupants' comfort. Such devices suffer particularly when they reach force saturation of the actuators and maximum extension of their stroke, which may occur in case of severe loading conditions (e.g. wind gust and earthquake). Exceeding actuators' physical limits can impair the control performance of the system or even lead to devices damage, with consequent need for repair or substitution of part of the control system. Controllers for active mass dampers should account for their technological limits. Prior work of the authors was devoted to stroke issues and led to the definition of a nonlinear damping approach, very easy to implement in practice. It consisted of a modified skyhook algorithm complemented with a nonlinear braking force to reverse the direction of the mass before reaching the stroke limit. This paper presents an enhanced version of this approach, also accounting for force saturation of the actuator and keeping the simplicity of implementation. This is achieved by modulating the control force by a nonlinear smooth function depending on the ratio between actuator's force and saturation limit. Results of a numerical investigation show that the proposed approach provides similar results to the method of the State Dependent Riccati Equation, a well-established technique for designing optimal controllers for constrained systems, yet very difficult to apply in practice.

Contributions of non-intrusive coupling in nonlinear structural mechanics

International Nuclear Information System (INIS)

Duval, Mickael

2016-01-01

This PhD thesis, part of the ANR ICARE project, aims at developing methods for complex analysis of large scale structures. The scientific challenge is to investigate very localised areas, but potentially critical as of mechanical systems resilience. Classically, representation models, discretizations, mechanical behaviour models and numerical tools are used at both global and local scales for simulation needs of graduated complexity. Global problem is handled by a generic code with topology (plate formulation, geometric approximation...) and behaviour (homogenization) simplifications while local analysis needs implementation of specialized tools (routines, dedicated codes) for an accurate representation of the geometry and behaviour. The main goal of this thesis is to develop an efficient non-intrusive coupling tool for multi-scale and multi-model structural analysis. Constraints of non-intrusiveness result in the non-modification of the stiffness operator, connectivity and the global model solver, allowing to work in a closed source software environment. First, we provide a detailed study of global/local non-intrusive coupling algorithm. Making use of several relevant examples (cracking, elastic-plastic behaviour, contact...), we show the efficiency and the flexibility of such coupling method. A comparative analysis of several optimisation tools is also carried on, and the interacting multiple patches situation is handled. Then, non-intrusive coupling is extended to globally non-linear cases, and a domain decomposition method with non-linear re-localization is proposed. Such methods allowed us to run a parallel computation using only sequential software, on a high performance computing cluster. Finally, we apply the coupling algorithm to mesh refinement with patches of finite elements. We develop an explicit residual based error estimator suitable for multi-scale solutions arising from the non-intrusive coupling, and apply it inside an error driven local mesh

Nonlinear mechanisms of two-dimensional wave-wave transformations in the initially coupled acoustic structure

Science.gov (United States)

Vorotnikov, K.; Starosvetsky, Y.

2018-01-01

The present study concerns two-dimensional nonlinear mechanisms of bidirectional and unidirectional channeling of longitudinal and shear waves emerging in the locally resonant acoustic structure. The system under consideration comprises an oscillatory chain of the axially coupled masses. Each mass of the chain is subject to the local linear potential along the lateral direction and incorporates the lightweight internal rotator. In the present work, we demonstrate the emergence of special resonant regimes of complete bi- and unidirectional transitions between the longitudinal and the shear waves of the locally resonant chain. These regimes are manifested by the two-dimensional energy channeling between the longitudinal and the shear traveling waves in the recurrent as well as the irreversible fashion. We show that the spatial control of the two dimensional energy flow between the longitudinal and the shear waves is solely governed by the motion of the internal rotators. Nonlinear analysis of the regimes of a bidirectional wave channeling unveils their global bifurcation structure and predicts the zones of their spontaneous transitions from a complete bi-directional wave channeling to the one-directional entrapment. An additional regime of a complete irreversible resonant transformation of the longitudinal wave into a shear wave is analyzed in the study. The intrinsic mechanism governing the unidirectional wave reorientation is described analytically. The results of the analysis of both mechanisms are substantiated by the numerical simulations of the full model and are found to be in a good agreement.

Nonlinear bleaching, absorption, and scattering of 532-nm-irradiated plasmonic nanoparticles

International Nuclear Information System (INIS)

Liberman, V.; Sworin, M.; Kingsborough, R. P.; Geurtsen, G. P.; Rothschild, M.

2013-01-01

Single-pulse irradiation of Au and Ag suspensions of nanospheres and nanodisks with 532-nm 4-ns pulses has identified complex optical nonlinearities while minimizing material damage. For all materials tested, we observe competition between saturable absorption (SA) and reverse SA (RSA), with RSA behavior dominating for intensities above ∼50 MW/cm 2 . Due to reduced laser damage in single-pulse experiments, the observed intrinsic nonlinear absorption coefficients are the highest reported to date for Au nanoparticles. We find size dependence to the nonlinear absorption enhancement for Au nanoparticles, peaking in magnitude for 80-nm nanospheres and falling off at larger sizes. The nonlinear absorption coefficients for Au and Ag spheres are comparable in magnitude. On the other hand, the nonlinear absorption for Ag disks, when corrected for volume fraction, is several times higher. These trends in nonlinear absorption are correlated to local electric field enhancement through quasi-static mean-field theory. Through variable size aperture measurements, we also separate nonlinear scattering from nonlinear absorption. For all materials tested, we find that nonlinear scattering is highly directional and that its magnitude is comparable to that of nonlinear absorption. These results indicate methods to improve the efficacy of plasmonic nanoparticles as optical limiters in pulsed laser systems.

Nonlinear effects in varactor-tuned resonators.

Science.gov (United States)

Everard, Jeremy; Zhou, Liang

2006-05-01

This paper describes the effects of RF power level on the performance of varactor-tuned resonator circuits. A variety of topologies are considered, including series and parallel resonators operating in both unbalanced and balanced modes. As these resonators were designed to produce oscillators with minimum phase noise, the initial small signal insertion loss was set to 6 dB and, hence, QL/Q0 = 1/2. To enable accurate analysis and simulation, S parameter and PSPICE models for the varactors were optimized and developed. It is shown that these resonators start to demonstrate nonlinear operation at very low power levels demonstrating saturation and lowering of the resonant frequency. On occasion squegging is observed for modified bias conditions. The nonlinear effects are dependent on the unloaded Q (Q0), the ratio of loaded to unloaded Q (QL/Q0), the bias voltage, and circuit configurations with typical nonlinear effects occurring at -8 dBm in a circuit with a loaded Q of 63 and a varactor bias voltage of 3 V. Analysis, simulation, and measurements that show close correlation are presented.

Angular Momentum Transport in Protoplanetary and Black Hole Accretion Disks: The Role of Parasitic Modes in the Saturation of MHD Turbulence

DEFF Research Database (Denmark)

Pessah, Martin Elias

2010-01-01

The magnetorotational instability (MRI) is considered a key process for driving efficient angular momentum transport in astrophysical disks. Understanding its nonlinear saturation constitutes a fundamental problem in modern accretion disk theory. The large dynamical range in physical conditions...

Spatial optical (2+1)-dimensional scalar- and vector-solitons in saturable nonlinear media

Energy Technology Data Exchange (ETDEWEB)

Weilnau, C.; Traeger, D.; Schroeder, J.; Denz, C. [Institute of Applied Physics, Westfaelische Wilhelms-Universitaet Muenster, Corrensstr. 2/4, 48149 Muenster (Germany); Ahles, M.; Petter, J. [Institute of Applied Physics, Technische Universitaet Darmstadt, Hochschulstr. 6, 64289 Darmstadt (Germany)

2002-10-01

(2+1)-dimensional optical spatial solitons have become a major field of research in nonlinear physics throughout the last decade due to their potential in adaptive optical communication technologies. With the help of photorefractive crystals that supply the required type of nonlinearity for soliton generation, we are able to demonstrate experimentally the formation, the dynamic properties, and especially the interaction of solitary waves, which were so far only known from general soliton theory. Among the complex interaction scenarios of scalar solitons, we reveal a distinct behavior denoted as anomalous interaction, which is unique in soliton-supporting systems. Further on, we realize highly parallel, light-induced waveguide configurations based on photorefractive screening solitons that give rise to technical applications towards waveguide couplers and dividers as well as all-optical information processing devices where light is controlled by light itself. Finally, we demonstrate the generation, stability and propagation dynamics of multi-component or vector solitons, multipole transverse optical structures bearing a complex geometry. In analogy to the particle-light dualism of scalar solitons, various types of vector solitons can - in a broader sense - be interpreted as molecules of light. (Abstract Copyright [2002], Wiley Periodicals, Inc.)

Spatial optical (2+1)-dimensional scalar- and vector-solitons in saturable nonlinear media

International Nuclear Information System (INIS)

Weilnau, C.; Traeger, D.; Schroeder, J.; Denz, C.; Ahles, M.; Petter, J.

2002-01-01

(2+1)-dimensional optical spatial solitons have become a major field of research in nonlinear physics throughout the last decade due to their potential in adaptive optical communication technologies. With the help of photorefractive crystals that supply the required type of nonlinearity for soliton generation, we are able to demonstrate experimentally the formation, the dynamic properties, and especially the interaction of solitary waves, which were so far only known from general soliton theory. Among the complex interaction scenarios of scalar solitons, we reveal a distinct behavior denoted as anomalous interaction, which is unique in soliton-supporting systems. Further on, we realize highly parallel, light-induced waveguide configurations based on photorefractive screening solitons that give rise to technical applications towards waveguide couplers and dividers as well as all-optical information processing devices where light is controlled by light itself. Finally, we demonstrate the generation, stability and propagation dynamics of multi-component or vector solitons, multipole transverse optical structures bearing a complex geometry. In analogy to the particle-light dualism of scalar solitons, various types of vector solitons can - in a broader sense - be interpreted as molecules of light. (Abstract Copyright [2002], Wiley Periodicals, Inc.)

Waves and Structures in Nonlinear Nondispersive Media General Theory and Applications to Nonlinear Acoustics

CERN Document Server

Gurbatov, S N; Saichev, A I

2012-01-01

"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...

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...

Onset and saturation of backward stimulated Raman scattering of laser in trapping regime in three spatial dimensions

International Nuclear Information System (INIS)

Yin, L.; Albright, B. J.; Rose, H. A.; Bowers, K. J.; Bergen, B.; Montgomery, D. S.; Kline, J. L.; Fernandez, J. C.

2009-01-01

A suite of three-dimensional (3D) VPIC[K. J. Bowers et al., Phys. Plasmas 15, 055703 (2008)] particle-in-cell simulations of backward stimulated Raman scattering (SRS) in inertial confinement fusion hohlraum plasma has been performed on the heterogeneous multicore supercomputer, Roadrunner, presently the world's most powerful supercomputer. These calculations reveal the complex nonlinear behavior of SRS and point to a new era of 'at scale' 3D modeling of SRS in solitary and multiple laser speckles. The physics governing nonlinear saturation of SRS in a laser speckle in 3D is consistent with that of prior two-dimensional (2D) studies [L. Yin et al., Phys. Rev. Lett. 99, 265004 (2007)], but with important differences arising from enhanced diffraction and side loss in 3D compared with 2D. In addition to wave front bowing of electron plasma waves (EPWs) due to trapped electron nonlinear frequency shift and amplitude-dependent damping, we find for the first time that EPW self-focusing, which evolved from trapped particle modulational instability [H. A. Rose and L. Yin, Phys. Plasmas 15, 042311 (2008)], also exhibits loss of angular coherence by formation of a filament necklace, a process not available in 2D. These processes in 2D and 3D increase the side-loss rate of trapped electrons, increase wave damping, decrease source coherence for backscattered light, and fundamentally limit how much backscatter can occur from a laser speckle. For both SRS onset and saturation, the nonlinear trapping induced physics is not captured in linear gain modeling of SRS. A simple metric is described for using single-speckle reflectivities obtained from VPIC simulations to infer the total reflectivity from the population of laser speckles of amplitude sufficient for significant trapping-induced nonlinearity to arise.

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

Saturated Switching Systems

CERN Document Server

Benzaouia, Abdellah

2012-01-01

Saturated Switching Systems treats the problem of actuator saturation, inherent in all dynamical systems by using two approaches: positive invariance in which the controller is designed to work within a region of non-saturating linear behaviour; and saturation technique which allows saturation but guarantees asymptotic stability. The results obtained are extended from the linear systems in which they were first developed to switching systems with uncertainties, 2D switching systems, switching systems with Markovian jumping and switching systems of the Takagi-Sugeno type. The text represents a thoroughly referenced distillation of results obtained in this field during the last decade. The selected tool for analysis and design of stabilizing controllers is based on multiple Lyapunov functions and linear matrix inequalities. All the results are illustrated with numerical examples and figures many of them being modelled using MATLAB®. Saturated Switching Systems will be of interest to academic researchers in con...

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.

Migration of Gas in Water Saturated Clays by Coupled Hydraulic-Mechanical Model

Directory of Open Access Journals (Sweden)

Aliaksei Pazdniakou

2018-01-01

Full Text Available Understanding the gas migration in highly water saturated sedimentary rock formations is of great importance for safety of radioactive waste repositories which may use these host rocks as barrier. Recent experiments on drainage in argillite samples have demonstrated that they cannot be represented in terms of standard two-phase flow Darcy model. It has been suggested that gas flows along highly localized dilatant pathways. Due to very small pore size and the opacity of the material, it is not possible to observe this two-phase flow directly. In order to better understand the gas transport, a numerical coupled hydraulic-mechanical model at the pore scale is proposed. The model is formulated in terms of Smoothed Particle Hydrodynamics (SPH and is applied to simulate drainage within a sample reconstructed from the Focused Ion Beam (FIB images of Callovo-Oxfordian claystone. A damage model is incorporated to take into account the degradation of elastic solid properties due to local conditions, which may lead to formation of new pathways and thus to modifications of fluid transport. The influence of the damage model as well as the possible importance of rigid inclusions is demonstrated and discussed.

Nonlinear Hamiltonian mechanics applied to molecular dynamics theory and computational methods for understanding molecular spectroscopy and chemical reactions

CERN Document Server

Farantos, Stavros C

2014-01-01

This brief presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied. Vibrationally excited and reacting molecules are nonlinear dynamical systems, and thus, nonlinear mechanics is the proper theory to elucidate molecular dynamics by investigating invariant structures in phase space. Intramolecular energy transfer, and the breaking and forming of a chemical bond have now found a rigorous explanation by studying phase space structures.

Differential saturation study of radial and angular modulation mechanisms of electron spin--lattice relaxation for trapped hydrogen atoms in sulfuric acid glasses. [X radiation

Energy Technology Data Exchange (ETDEWEB)

Plonka, A; Kevan, L

1976-11-01

A differential ESR saturation study of allowed transitions and forbidden proton spin-flip satellite transitions for trapped hydrogen atoms in sulfuric acid glasses indicates that angular modulation dominates the spin-lattice relaxation mechanisms and suggests that the modulation arises from motion of the H atom.

Nonlinear Distortion Mechanisms and Efficiency of Balanced-Armature Loudspeakers

DEFF Research Database (Denmark)

Jensen, Joe

are inherently nonlinear devices, since any displacement of the loudspeaker diaphragm in- evitably changes the magnetic and electrical characteristics of the loudspeaker. Additionally, for the balanced-armature loudspeaker the signal has to be transmitted through the magnetic domain (as a magnetic B -field...... and to validate simpler equivalent circuit models. A large scale model of a balanced-armature loudspeaker has been developed and its inherent nonlinear parameters have been measured and compared to the theoretically predicted values. A measurement setup for determining the magnetic properties of soft magnetic...... materials has also been developed, since it is of great importance to understand what kind of linear and nonlinear transformations the magnetic materials impose on the signal. In hearing aid applications the power efficiency of the loudspeaker is important because every reduction in power consumption...

Riemann-Cartan geometry of nonlinear disclination mechanics

KAUST Repository

Yavari, A.; Goriely, A.

2012-01-01

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining

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.

Field guide to nonlinear optics

CERN Document Server

Powers, Peter E

2013-01-01

Optomechanics is a field of mechanics that addresses the specific design challenges associated with optical systems. This [i]Field Guide [/i]describes how to mount optical components, as well as how to analyze a given design. It is intended for practicing optical and mechanical engineers whose work requires knowledge in both optics and mechanics. This Field Guide is designed for those looking for a condensed and concise source of key concepts, equations, and techniques for nonlinear optics. Topics covered include technologically important effects, recent developments in nonlinear optics

Studies of non-isothermal flow in saturated and partially saturated porous media

International Nuclear Information System (INIS)

Ho, C.K.; Maki, K.S.; Glass, R.J.

1993-01-01

Physical and numerical experiments have been performed to investigate the behavior of nonisothermal flow in two-dimensional saturated and partially saturated porous media. The physical experiments were performed to identify non-isothermal flow fields and temperature distributions in fully saturated, half-saturated, and residually saturated two-dimensional porous media with bottom heating and top cooling. Two counter-rotating liquid-phase convective cells were observed to develop in the saturated regions of all three cases. Gas-phase convection was also evidenced in the unsaturated regions of the partially saturated experiments. TOUGH2 numerical simulations of the saturated case were found to be strongly dependent on the assumed boundary conditions of the physical system. Models including heat losses through the boundaries of the test cell produced temperature and flow fields that were in better agreement with the observed temperature and flow fields than models that assumed insulated boundary conditions. A sensitivity analysis also showed that a reduction of the bulk permeability of the porous media in the numerical simulations depressed the effects of convection, flattening the temperature profiles across the test cell

Stability of orbits in nonlinear mechanics for finite but very long times

International Nuclear Information System (INIS)

Warnock, R.L.; Ruth, R.D.

1990-07-01

In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, Ψ), such that action J is nearly constant while the angle Ψ advances almost linearly with the time. By examining the change in J during a time T 0 from many initial conditions in the open domain Ω of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain Ω 0 contained-in Ω. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10 8 turns). 10 refs., 6 figs., 1 tab

Stability of orbits in nonlinear mechanics for finite but very long times

Energy Technology Data Exchange (ETDEWEB)

Warnock, R.L.; Ruth, R.D.

1990-07-01

In various applications of nonlinear mechanics, especially in accelerator design, it would be useful to set bounds on the motion for finite but very long times. Such bounds can be sought with the help of a canonical transformation to new action-angle variables (J, {Psi}), such that action J is nearly constant while the angle {Psi} advances almost linearly with the time. By examining the change in J during a time T{sub 0} from many initial conditions in the open domain {Omega} of phase space, one can estimate the change in J during a much larger time T, on any orbit starting in a smaller open domain {Omega}{sub 0} {contained in} {Omega}. A numerical realization of this idea is described. The canonical transformations, equivalent to close approximations to invariant tori, are constructed by an effective new method in which surfaces are fitted to orbit data. In a first application to a model sextupole lattice in a region of strong nonlinearity, we predict stability of betatron motion in two degrees of freedom for a time comparable to the storage time in a proton storage ring (10{sup 8} turns). 10 refs., 6 figs., 1 tab.

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

International Nuclear Information System (INIS)

Khare, Avinash; Saxena, Avadh

2014-01-01

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

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

Nonlinear elastic waves in materials

CERN Document Server

Rushchitsky, Jeremiah J

2014-01-01

The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...

Saturation mechanism of the heat release response of a premixed swirl flame using LES

NARCIS (Netherlands)

Krediet, H.J.; Beck, C. H.; Krebs, W.; Kok, J. B.W.

2013-01-01

The nonlinear heat release response of a premixed swirl flame to velocity perturbations is investigated using Large Eddy Simulation. The nonlinear heat release response is required for the prediction of thermoacoustic limit cycle pressure amplitudes and is represented here by the Flame Describing

Geometric scaling in ultrahigh energy neutrinos and nonlinear perturbative QCD

International Nuclear Information System (INIS)

Machado, Magno V.T.

2011-01-01

The ultrahigh energy neutrino cross section is a crucial ingredient in the calculation of the event rate in high energy neutrino telescopes. Currently there are several approaches which predict different behaviors for its magnitude for ultrahigh energies. In this contribution is presented a summary of current predictions based on the non-linear QCD evolution equations, the so-called perturbative saturation physics. In particular, predictions are shown based on the parton saturation approaches and the consequences of geometric scaling property at high energies are discussed. The scaling property allows an analytical computation of the neutrino scattering on nucleon/nucleus at high energies, providing a theoretical parameterization. (author)

Magnetically nonlinear dynamic model of synchronous motor with permanent magnets

International Nuclear Information System (INIS)

Hadziselimovic, Miralem; Stumberger, Gorazd; Stumberger, Bojan; Zagradisnik, Ivan

2007-01-01

This paper deals with a magnetically nonlinear two-axis dynamic model of a permanent magnet synchronous motor (PMSM). The geometrical and material properties of iron core and permanent magnets, the effects of winding distribution, saturation, cross-saturation and slotting effects are, for the first time, simultaneously accounted for in a single two-axis dynamic model of a three-phase PMSM. They are accounted for by current- and position-dependent characteristics of flux linkages. These characteristics can be determined either experimentally or by the finite element (FE) computations. The results obtained by the proposed dynamic model show a very good agreement with the measured ones and those obtained by the FE computation

Modeling of water and solute transport under variably saturated conditions: state of the art

International Nuclear Information System (INIS)

Lappala, E.G.

1980-01-01

This paper reviews the equations used in deterministic models of mass and energy transport in variably saturated porous media. Analytic, quasi-analytic, and numerical solution methods to the nonlinear forms of transport equations are discussed with respect to their advantages and limitations. The factors that influence the selection of a modeling method are discussed in this paper; they include the following: (1) the degree of coupling required among the equations describing the transport of liquids, gases, solutes, and energy; (2) the inclusion of an advection term in the equations; (3) the existence of sharp fronts; (4) the degree of nonlinearity and hysteresis in the transport coefficients and boundary conditions; (5) the existence of complex boundaries; and (6) the availability and reliability of data required by the models

Riemann-Cartan geometry of nonlinear disclination mechanics

KAUST Repository

Yavari, A.

2012-03-23

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan\\'s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).

Ultrahigh energy neutrinos and nonlinear QCD dynamics

International Nuclear Information System (INIS)

Machado, Magno V.T.

2004-01-01

The ultrahigh energy neutrino-nucleon cross sections are computed taking into account different phenomenological implementations of the nonlinear QCD dynamics. Based on the color dipole framework, the results for the saturation model supplemented by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution as well as for the Balitskii-Fadin-Kuraev-Lipatov (BFKL) formalism in the geometric scaling regime are presented. They are contrasted with recent calculations using next-to-leading order DGLAP and unified BFKL-DGLAP formalisms

Nonlinear particle-wave kinetics in weakly unstable plasmas

International Nuclear Information System (INIS)

Breizman, B.N.; Berk, H.L.; Pekker, M.S.

1996-01-01

With the motivation to address the behavior of the fusion produced alpha particles in a thermonuclear reactor, a theory is developed for predicting the wave saturation levels and particle transport in weakly unstable systems with a discrete number of modes in the presence of energetic particle sources and sinks. Conditions are established for either steady state or bursting nonlinear scenarios when several modes are excited for cases where there is and there is not resonance overlap. Depending on parameters, the particles can undergo benign relaxation, with only a small fraction of the available free energy released to waves and with no global transport, or the particles can experience rapid global transport caused by a substantial conversion of their free energy into wave energy. When the resonance condition of the particle-wave interaction is varied adiabatically, the particles trapped in a wave are found to form phase space holes or clumps that enhance the particle-wave energy exchange. This mechanism, which has been experimentally observed when there is frequency chirping, causes increased saturation levels of instabilities. If resonance sweeping is imposed externally, the particle free energy can even be tapped in stable systems where background dissipation suppresses linear instability. Externally applied resonance sweeping can be important for alpha particle energy channeling, as well as for understanding fishbone and some Alfven wave instability experiments. Near instability threshold, that is when the destabilizing drive just exceeds the background dissipation, a more sophisticated analysis is developed to predict the correct saturation. To leading order, this problem reduces to an integral equation for the wave amplitude with a temporally non local cubic term. This equation has a self-similar solution that blows-up in a finite time

Nonlinear dynamics and anisotropic structure of rotating sheared turbulence.

Science.gov (United States)

Salhi, A; Jacobitz, F G; Schneider, K; Cambon, C

2014-01-01

Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations.

Steady-state mechanical squeezing and ground-state cooling of a Duffing anharmonic oscillator in an optomechanical cavity assisted by a nonlinear medium

Science.gov (United States)

Momeni, F.; Naderi, M. H.

2018-05-01

In this paper, we study theoretically a hybrid optomechanical system consisting of a degenerate optical parametric amplifier inside a driven optical cavity with a moving end mirror which is modeled as a stiffening Duffing-like anharmonic quantum mechanical oscillator. By providing analytical expressions for the critical values of the system parameters corresponding to the emergence of the multistability behavior in the steady-state response of the system, we show that the stiffening mechanical Duffing anharmonicity reduces the width of the multistability region while the optical parametric nonlinearity can be exploited to drive the system toward the multistability region. We also show that for appropriate values of the mechanical anharmonicity strength the steady-state mechanical squeezing and the ground-state cooling of the mechanical resonator can be achieved. Moreover, we find that the presence of the nonlinear gain medium can lead to the improvement of the mechanical anharmonicity-induced cooling of the mechanical motion, as well as to the mechanical squeezing beyond the standard quantum limit of 3 dB.

Non-linear finite element modeling

DEFF Research Database (Denmark)

Mikkelsen, Lars Pilgaard

The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...

Simulation of coupled flow and mechanical deformation using IMplicit Pressure-Displacement Explicit Saturation (IMPDES) scheme

KAUST Repository

El-Amin, Mohamed

2012-01-01

The problem of coupled structural deformation with two-phase flow in porous media is solved numerically using cellcentered finite difference (CCFD) method. In order to solve the system of governed partial differential equations, the implicit pressure explicit saturation (IMPES) scheme that governs flow equations is combined with the the implicit displacement scheme. The combined scheme may be called IMplicit Pressure-Displacement Explicit Saturation (IMPDES). The pressure distribution for each cell along the entire domain is given by the implicit difference equation. Also, the deformation equations are discretized implicitly. Using the obtained pressure, velocity is evaluated explicitly, while, using the upwind scheme, the saturation is obtained explicitly. Moreover, the stability analysis of the present scheme has been introduced and the stability condition is determined.

Studies on third-order optical nonlinearity and power limiting of conducting polymers using the z-scan technique for nonlinear optical applications

International Nuclear Information System (INIS)

Pramodini, S; Poornesh, P; Sudhakar, Y N; SelvaKumar, M

2014-01-01

We present the synthesis and characterization of third-order optical nonlinearity and optical limiting of the conducting polymers poly (aniline-co-o-anisidine) and poly (aniline-co-pyrrole). Nonlinear optical studies were carried out by employing the z-scan technique using a He–Ne laser operating in continuous wave mode at 633 nm. The copolymers exhibited a reverse saturable absorption process and self-defocusing properties under the experimental conditions. The estimated values of β eff , n 2 and χ (3) were found to be of the order of 10 −2  cm W −1 , 10 -5  esu and 10 −7  esu respectively. Self-diffraction rings were observed due to refractive index change when exposed to the laser beam. The copolymers possess a lower limiting threshold and clamping level, which is essential to a great extent for power limiting devices. Therefore, copolymers of aniline emerge as a potential candidate for nonlinear optical device applications. (paper)

Studies on third-order optical nonlinearity and power limiting of conducting polymers using the z-scan technique for nonlinear optical applications

Science.gov (United States)

Pramodini, S.; Sudhakar, Y. N.; SelvaKumar, M.; Poornesh, P.

2014-04-01

We present the synthesis and characterization of third-order optical nonlinearity and optical limiting of the conducting polymers poly (aniline-co-o-anisidine) and poly (aniline-co-pyrrole). Nonlinear optical studies were carried out by employing the z-scan technique using a He-Ne laser operating in continuous wave mode at 633 nm. The copolymers exhibited a reverse saturable absorption process and self-defocusing properties under the experimental conditions. The estimated values of βeff, n2 and χ(3) were found to be of the order of 10-2 cm W-1, 10-5 esu and 10-7 esu respectively. Self-diffraction rings were observed due to refractive index change when exposed to the laser beam. The copolymers possess a lower limiting threshold and clamping level, which is essential to a great extent for power limiting devices. Therefore, copolymers of aniline emerge as a potential candidate for nonlinear optical device applications.

Nuclear matter saturation in a U(1) circle-times chiral model

International Nuclear Information System (INIS)

Lin, Wei

1989-01-01

The mean-field approximation in the U(1) circle-times chiral model for nuclear matter maturation is reviewed. Results show that it cannot be the correct saturation mechanism. It is argued that in this chiral model, other than the fact the ω mass can depend on the density of nuclear matter, saturation is still quite like the Walecka picture. 16 refs., 3 figs

Longitudinal Absolute Stability of a BWB Aircraft-Pilot System with Saturated Actuator Model

Directory of Open Access Journals (Sweden)

Claudia Alice STATE

2013-09-01

Full Text Available This paper deals with the analysis of the P(ilot I(n-the-Loop O(scillations of the second category (with rate and position liming in the closed loop pilot-vehicle system, caused by the dynamic coupling between the human pilot and the aircraft. The analysis is made in the context of the longitudinal motion and the theoretical model of the airplane presented in this article is a (Blended(Wing (Body tailless configuration. In what concerns the human operator, this is expressed by the Synchronous Pilot Model, which is represented by a simple gain, without a specific delay. The Routh-Hurwitz criterion is used in order to analyze the longitudinal stability of the low-order pilot-airplane system without the influence of actuator nonlinearity (this means that the unsaturated actuator model is employed for the mentioned algebraic criterion. Most emphasis is put on the frequency Popov criterion, which is used to investigate the absolute stability property of the short-period model in the presence of the actuator rate saturation, in the condition of the Lurie problem. The transfer function of the longitudinal BWB model, obtained from open-loop analysis, has a double pole at the origin and, for the absolute stability feedback structure that contains the nonlinearity of the saturation type, the Popov frequency-domain inequalities are applied to the PIO II problem in this critical case.

Saturated Adaptive Output-Feedback Power-Level Control for Modular High Temperature Gas-Cooled Reactors

Directory of Open Access Journals (Sweden)

Zhe Dong

2014-11-01

Full Text Available Small modular reactors (SMRs are those nuclear fission reactors with electrical output powers of less than 300 MWe. Due to its inherent safety features, the modular high temperature gas-cooled reactor (MHTGR has been seen as one of the best candidates for building SMR-based nuclear plants with high safety-level and economical competitive power. Power-level control is crucial in providing grid-appropriation for all types of SMRs. Usually, there exists nonlinearity, parameter uncertainty and control input saturation in the SMR-based plant dynamics. Motivated by this, a novel saturated adaptive output-feedback power-level control of the MHTGR is proposed in this paper. This newly-built control law has the virtues of having relatively neat form, of being strong adaptive to parameter uncertainty and of being able to compensate control input saturation, which are given by constructing Lyapunov functions based upon the shifted-ectropies of neutron kinetics and reactor thermal-hydraulics, giving an online tuning algorithm for the controller parameters and proposing a control input saturation compensator respectively. It is proved theoretically that input-to-state stability (ISS can be guaranteed for the corresponding closed-loop system. In order to verify the theoretical results, this new control strategy is then applied to the large-range power maneuvering control for the MHTGR of the HTR-PM plant. Numerical simulation results show not only the relationship between regulating performance and control input saturation bound but also the feasibility of applying this saturated adaptive control law practically.

Unsaturated and Saturated Permeabilities of Fiber Reinforcement: Critics and Suggestions

Directory of Open Access Journals (Sweden)

Chung Hae ePARK

2015-04-01

Full Text Available In general, permeability measurement results show a strong scattering according to the measurement method, the type of test fluid and the fluid injection condition, even though permeability is regarded as a unique property of porous medium. In particular, the discrepancy between the unsaturated and saturated permeabilities for the same fabric has been widely reported. In the literature, relative permeability has been adopted to model the unsaturated flow. This approach has some limits in the modeling of double-scale porosity medium. We address this issue of permeability measurement by rigorously examining the mass conservation condition. Finally, we identify that the pressure gradient is non-linear with positive curvature in the unsaturated flow and a misinterpretation of pressure gradient is the main reason for the difference between the saturated and unsaturated permeabilities of the same fiber reinforcement. We propose to use a fixed value of permeability and to modify the mass conservation equation if there are air voids which are entrapped inside the fiber tow. Finally, we also suggest some guidelines and future perspectives to obtain more consistent permeability measurement results.

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

KAUST Repository

Yang, Haijian

2016-12-10

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

KAUST Repository

Yang, Haijian; Sun, Shuyu; Yang, Chao

2016-01-01

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

Overview of nonlinear kinetic instabilities

Science.gov (United States)

Berk, H. L.

2012-09-01

The saturation of shear Alfvén-like waves by alpha particles is presented from the general viewpoint of determining the saturation mechanisms of basic waves in a plasma destabilized by a perturbing source of free energy. The formalism is reviewed and then followed by analyses of isolated mode saturation far from and close to marginal stability. The effect of multiple waves that are isolated or are overlapping is then discussed. The presentation is concluded with a discussion of a non-conventional quasilinear theory that covers both extreme cases as well as the intermediate regime between the extremes.

An analytical study of non-linear behaviour of coupled 2+2x0.5 DOF electro-magneto-mechanical system by a method of multiple scales

DEFF Research Database (Denmark)

Darula, Radoslav; Sorokin, Sergey

2013-01-01

An electro-magneto-mechanical system combines three physical domains - a mechanical structure, a magnetic field and an electric circuit. The interaction between these domains is analysed for a structure with two degrees of freedom (translational and rotational) and two electrical circuits. Each...... electrical circuit is described by a differential equation of the 1st order, which is considered to contribute to the coupled system by 0.5 DOF. The electrical and mechanical systems are coupled via a magnetic circuit, which is inherently non-linear, due to a non-linear nature of the electro-magnetic force...

Dynamic Output Feedback Robust MPC with Input Saturation Based on Zonotopic Set-Membership Estimation

Directory of Open Access Journals (Sweden)

Xubin Ping

2016-01-01

Full Text Available For quasi-linear parameter varying (quasi-LPV systems with bounded disturbance, a synthesis approach of dynamic output feedback robust model predictive control (OFRMPC with the consideration of input saturation is investigated. The saturated dynamic output feedback controller is represented by a convex hull involving the actual dynamic output controller and an introduced auxiliary controller. By taking both the actual output feedback controller and the auxiliary controller with a parameter-dependent form, the main optimization problem can be formulated as convex optimization. The consideration of input saturation in the main optimization problem reduces the conservatism of dynamic output feedback controller design. The estimation error set and bounded disturbance are represented by zonotopes and refreshed by zonotopic set-membership estimation. Compared with the previous results, the proposed algorithm can not only guarantee the recursive feasibility of the optimization problem, but also improve the control performance at the cost of higher computational burden. A nonlinear continuous stirred tank reactor (CSTR example is given to illustrate the effectiveness of the approach.

An investigation of the mechanical and hydrologic behavior of tuff fractures under saturated conditions

International Nuclear Information System (INIS)

Voss, C.F.; Shotwell, L.R.

1990-04-01

The mechanical and hydrologic behavior of natural fractures in a partially welded tuff rock were investigated. Tuff cores, each containing part of the same natural fracture oriented subparallel to the core axis, were subjected a range of stress and hydraulic gradients while simultaneously monitoring changes in the fracture aperture and volumetric flow rate. The fractures were tested in three configurations: intact, mated, and offset. Fracture deformation was nonlinear over the stress range tested with permanent deformation and hysteresis occurring with each loading cycle. The offset samples had larger permanent deformation and significantly reduced normal stiffness at lower stress levels. The cubic flow law appears to be valid for the relatively undisturbed tuff fractures at the scale tested. The cubic law did not explain the observed hydraulic behavior of the offset fractures. 6 refs., 10 figs., 2 tabs

Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

International Nuclear Information System (INIS)

Minati, Ludovico; Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge; D'Incerti, Ludovico

2015-01-01

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D 2 ), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes

Synchronization, non-linear dynamics and low-frequency fluctuations: Analogy between spontaneous brain activity and networked single-transistor chaotic oscillators

Energy Technology Data Exchange (ETDEWEB)

Minati, Ludovico, E-mail: lminati@ieee.org, E-mail: ludovico.minati@unitn.it, E-mail: lminati@istituto-besta.it [Scientific Department, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy); Center for Mind/Brain Sciences, University of Trento, Trento (Italy); Chiesa, Pietro; Tabarelli, Davide; Jovicich, Jorge [Center for Mind/Brain Sciences, University of Trento, Trento (Italy); D' Incerti, Ludovico [Neuroradiology Unit, Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan (Italy)

2015-03-15

In this paper, the topographical relationship between functional connectivity (intended as inter-regional synchronization), spectral and non-linear dynamical properties across cortical areas of the healthy human brain is considered. Based upon functional MRI acquisitions of spontaneous activity during wakeful idleness, node degree maps are determined by thresholding the temporal correlation coefficient among all voxel pairs. In addition, for individual voxel time-series, the relative amplitude of low-frequency fluctuations and the correlation dimension (D{sub 2}), determined with respect to Fourier amplitude and value distribution matched surrogate data, are measured. Across cortical areas, high node degree is associated with a shift towards lower frequency activity and, compared to surrogate data, clearer saturation to a lower correlation dimension, suggesting presence of non-linear structure. An attempt to recapitulate this relationship in a network of single-transistor oscillators is made, based on a diffusive ring (n = 90) with added long-distance links defining four extended hub regions. Similarly to the brain data, it is found that oscillators in the hub regions generate signals with larger low-frequency cycle amplitude fluctuations and clearer saturation to a lower correlation dimension compared to surrogates. The effect emerges more markedly close to criticality. The homology observed between the two systems despite profound differences in scale, coupling mechanism and dynamics appears noteworthy. These experimental results motivate further investigation into the heterogeneity of cortical non-linear dynamics in relation to connectivity and underline the ability for small networks of single-transistor oscillators to recreate collective phenomena arising in much more complex biological systems, potentially representing a future platform for modelling disease-related changes.

Nonlinear absorbing cationic iridium(III) complexes bearing benzothiazolylfluorene motif on the bipyridine (N∧N) ligand: synthesis, photophysics and reverse saturable absorption.

Science.gov (United States)

Li, Yuhao; Dandu, Naveen; Liu, Rui; Hu, Lei; Kilina, Svetlana; Sun, Wenfang

2013-07-24

reverse saturable absorbers at 532 nm and could potentially be used as broadband nonlinear absorbing materials.

The effect of CO{sub 2} saturation on mechanical properties of Australian black coal using acoustic emission

Energy Technology Data Exchange (ETDEWEB)

P.G. Ranjit; D. Jasinge; S.K. Choi; M. Mehic; B. Shannon [Monash University (Australia). Department of Civil Engineering

2010-08-15

Acoustic emission (AE) methods are now widely used for damage evaluation. For a better understanding of the damage mechanics of materials such as rocks, AE has been used to monitor stresses which induce crack closure, crack initiation and crack damage. In the present study, an AE system was used to study the damage behaviour of some Australian black coal samples subjected to uniaxial compression. Several samples were left in a container filled with 100% carbon dioxide (CO{sub 2}) at a certain pressure for 72 h prior to testing. The results were compared with samples which had only been exposed to the atmosphere to see if CO{sub 2} had any adverse effect on the strength of coal. Strain gauges were installed on the samples and the measured axial and volumetric strains were studied in conjunction with the AE counts. The AE method was successfully used for detecting the onset of crack initiation and the crack damage stress threshold of the black coal samples. Of the coal samples examined, crack initiation and crack closure of the samples subjected to saturation with CO{sub 2} occurred at stress corresponding to a higher percentage of the peak strength when compared to the samples which had only been exposed to atmospheric conditions. However, crack damage occurred at a higher percentage of peak strength and the average peak strength showed a higher value for samples in atmospheric condition when compared to CO{sub 2} saturated samples. The results show that sorption of CO{sub 2} can cause a reduction in strength of the black coal samples when tested under uniaxial compression. As the coal samples were highly inhomogeneous more tests are required in order to be able to confirm whether the adsorption of CO{sub 2} will cause strength reduction in coal and to identify the actual underlying mechanisms. 36 refs., 8 figs., 2 tabs.

Fault creep and stress drops in saturated silt-clay gouge

International Nuclear Information System (INIS)

Bombolakis, E.G.; Hepburn, J.C.; Roy, D.C.

1978-01-01

An analysis of physicochemical processes in saturated silt-clay gouge indicates that this type of fault zone material can account for for the following phenomena: (1) the nonlinear mechanical behavior indicated by certain geophysical measurements along the San Andreas fault zone, (2) the low stress drops associated with earthquakes to several kilometers' depth, and (3) the recurrence of creep-induced instabilities at shallow depths along fault zones. A rheological model is described for a gouge consisting of colloidal size clay platelets with absorbed water, brittle silt size particles, and 'free' pore water. Recurrence of shallow earthquakes or accelerated creep is explained in the model by thixotropic hardening of the colloidal phase following shear deformation, i.e., by electrochemical reorientation of clay platelets from a dispersed structure to a face-to-edge type of structure during a quiescent period. The silt phase must support part of the effective mean stress for thixotropic hardening to occur at several kilometers' depth. The peak shear strength of the gouge in this case is expressed in functional form by S/sub p/=f[kappaP/sub e/+sigma-bar/sub c/ tan psi/sub e/; sigma-bar/sub s/ tan psi/sub s/], where kappa, P/sub e/, and psi/sub e/ are Hvorslev parameters; sigma-bar/sub c/ is the effective stress in the colloidal phase, acting normal to the shear zone; sigma-bar/sub s/ is the effective stress in the silt phase, acting normal to the shear zone; and psi/sub s/ is the 'friction angle' of the silt phase. The peak shear strength is time dependent owing to viscous type contacts between absorbed water layers surrounding the colloidal platelets. The time-dependent nature of S/sub p/ may be responsible for certain nonlinear behavior noted in fault zones and for the small stress drops associated with earthquakes occurring at several kilometers' depth

Cage-rotor induction motor inter-turn short circuit fault detection with and without saturation effect by MEC model.

Science.gov (United States)

Naderi, Peyman

2016-09-01

The inter-turn short fault for the Cage-Rotor-Induction-Machine (CRIM) is studied in this paper and its local saturation is taken into account. However, in order to observe the exact behavior of machine, the Magnetic-Equivalent-Circuit (MEC) and nonlinear B-H curve are proposed to provide an insight into the machine model and saturation effect respectively. The electrical machines are generally operated near to their saturation zone due to some design necessities. Hence, when the machine is exposed to a fault such as short circuit or eccentricities, it is operated within its saturation zone and thus, time and space harmonics are integrated and as a result, current and torque harmonics are generated which the phenomenon cannot be explored when saturation is dismissed. Nonetheless, inter-turn short circuit may lead to local saturation and this occurrence is studied in this paper using MEC model. In order to achieve the mentioned objectives, two and also four-pole machines are modeled as two samples and the machines performances are analyzed in healthy and faulty cases with and without saturation effect. A novel strategy is proposed to precisely detect inter-turn short circuit fault according to the stator׳s lines current signatures and the accuracy of the proposed method is verified by experimental results. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Surface wave propagation in a fluid-saturated incompressible ...

Indian Academy of Sciences (India)

dilatational and one rotational elastic waves in fluid-saturated porous solids. Biot theory ..... If the pore liquid is absent or gas is filled in the pores, then ρF ..... Biot M A (1962) Mechanics of deformation and acoustic propagation in porous media.

Microscopic analysis of saturable absorbers: Semiconductor saturable absorber mirrors versus graphene

Energy Technology Data Exchange (ETDEWEB)

Hader, J.; Moloney, J. V. [Nonlinear Control Strategies, Inc., 3542 N. Geronimo Ave., Tucson, Arizona 85705 (United States); College of Optical Sciences, University of Arizona, Tucson, Arizona 85721 (United States); Yang, H.-J.; Scheller, M. [College of Optical Sciences, University of Arizona, Tucson, Arizona 85721 (United States); Koch, S. W. [Department of Physics and Materials Sciences Center, Philipps Universität Marburg, Renthof 5, 35032 Marburg (Germany)

2016-02-07

Fully microscopic many-body calculations are used to study the influence of strong sub-picosecond pulses on the carrier distributions and corresponding optical response in saturable absorbers used for mode-locking—semiconductor (quantum well) saturable absorber mirrors (SESAMs) and single layer graphene based saturable absorber mirrors (GSAMs). Unlike in GSAMs, the saturation fluence and recovery time in SESAMs show a strong spectral dependence. While the saturation fluence in the SESAM is minimal at the excitonic bandgap, the optimal recovery time and least pulse distortion due to group delay dispersion are found for excitation higher in the first subband. For excitation near the SESAM bandgap, the saturation fluence is about one tenth of that in the GSAM. At energies above the bandgap, the fluences in both systems become similar. A strong dependence of the saturation fluence on the pulse width in both systems is caused by carrier relaxation during the pulse. The recovery time in graphene is found to be about two to four times faster than that in the SESAMs. The occurrence of negative differential transmission in graphene is shown to be caused by dopant related carriers. In SESAMs, a negative differential transmission is found when exciting below the excitonic resonance where excitation induced dephasing leads to an enhancement of the absorption. Comparisons of the simulation data to the experiment show a very good quantitative agreement.

Non-linear effects in transition edge sensors for X-ray detection

International Nuclear Information System (INIS)

Bandler, S.R.; Figueroa-Feliciano, E.; Iyomoto, N.; Kelley, R.L.; Kilbourne, C.A.; Murphy, K.D.; Porter, F.S.; Saab, T.; Sadleir, J.

2006-01-01

In a microcalorimeter that uses a transition-edge sensor to detect energy depositions, the small signal energy resolution improves with decreasing heat capacity. This improvement remains true up to the point where non-linear and saturation effects become significant. This happens when the energy deposition causes a significant change in the sensor resistance. Not only does the signal size become a non-linear function of the energy deposited, but also the noise becomes non-stationary over the duration of the pulse. Algorithms have been developed that can calculate the optimal performance given this non-linear behavior that typically requires significant processing and calibration work-both of which are impractical for space missions. We have investigated the relative importance of the various non-linear effects, with the hope that a computationally simple transformation can overcome the largest of the non-linear and non-stationary effects, producing a highly linear 'gain' for pulse-height versus energy, and close to the best energy resolution at all energies when using a Wiener filter

Nonlinear approaches in engineering applications applied mechanics, vibration control, and numerical analysis

CERN Document Server

Jazar, Reza

2015-01-01

This book focuses on the latest applications of nonlinear approaches in different disciplines of engineering. For each selected topic, detailed concept development, derivations, and relevant knowledge are provided for the convenience of the readers. The topics range from dynamic systems and control to optimal approaches in nonlinear dynamics. The volume includes invited chapters from world class experts in the field. The selected topics are of great interest in the fields of engineering and physics and this book is ideal for engineers and researchers working in a broad range of practical topics and approaches. This book also: ·         Explores the most up-to-date applications and underlying principles of nonlinear approaches to problems in engineering and physics, including sections on analytic nonlinearity and practical nonlinearity ·         Enlightens readers to the conceptual significance of nonlinear approaches with examples of applications in scientific and engineering problems from v...

Determining the magnetically nonlinear characteristics of a three phase core-type power transformer

International Nuclear Information System (INIS)

Dolinar, Matjaz; Stumberger, Gorazd; Polajzer, Bostjan; Dolinar, Drago

2006-01-01

This paper presents nonlinear iron core model of a three-phase, three-limb power transformer which is given by the current-dependant characteristics of flux linkages. The magnetically nonlinear characteristics are determined by controlled magnetic excitation of all three limbs which allows to take into account the variable magnetic-cross couplings between different coils placed on limbs, caused by saturation. The corresponding partial derivatives of measured flux linkage characteristics are used in the transformer circuit model as a magnetically nonlinear iron core model in order to analyze the behaviour of a nonsymmetrically excited transformer. Numerical results using transformer model with the determined iron core model agree very well with the measured results

Nonlinear optical response and its theoretical modelling of Sb2S3 nanorod

Science.gov (United States)

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

2018-05-01

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

Third harmonic current injection into highly saturated multi-phase machines

Directory of Open Access Journals (Sweden)

Klute Felix

2017-03-01

Full Text Available One advantage of multi-phase machines is the possibility to use the third harmonic of the rotor flux for additional torque generation. This effect can be maximised for Permanent Magnet Synchronous Machines (PMSM with a high third harmonic content in the magnet flux. This paper discusses the effects of third harmonic current injection (THCI on a five-phase PMSM with a conventional magnet shape depending on saturation. The effects of THCI in five-phase machines are shown in a 2D FEM model in Ansys Maxwell verified by measurement results. The results of the FEM model are analytically analysed using the Park model. It is shown in simulation and measurement that the torque improvement by THCI increases significantly with the saturation level, as the amplitude of the third harmonic flux linkage increases with the saturation level but the phase shift of the rotor flux linkage has to be considered. This paper gives a detailed analysis of saturation mechanisms of PMSM, which can be used for optimizing the efficiency in operating points of high saturations, without using special magnet shapes.

Nonlinear optical activity in Bridgman growth layered compounds

Energy Technology Data Exchange (ETDEWEB)

Miah, M.I., E-mail: m.miah@griffith.edu.au [Queensland Micro- and Nanotechnology Centre, Griffith University, Nathan, Brisbane, QLD 4111 (Australia); Biomolecular and Physical Sciences, Griffith University, Nathan, Brisbane, QLD 4111 (Australia); Department of Physics, University of Chittagong, Chittagong 4331 (Bangladesh)

2010-02-15

Layered semiconductor compound CdI{sub 2} has been grown with the Bridgman technique and studied by nonlinear transmittance spectroscopy. The optical absorption in CdI{sub 2} shows a nonlinear transmission of the incident laser power (P{sub 0}) within a lower power limit. The transmission, however, is found to saturate at high powers, giving a clamped output. The value of the incident power (P{sub 0C}) at which clamping starts is also found to depend on the crystal temperature (T{sub L}). The values of P{sub OC} ranges from 55 to 65 MW cm{sup -2} for T{sub L} = 4.2-180 K. The dynamic range (D{sub R}) as a function of T{sub L} is calculated and the values are found to range from D{sub R} = 2 to 1.6. The optical limiting mechanisms are discussed. The two-photon absorption (TPA) coefficient ({beta}) of the optical nonlinear process in CdI{sub 2} is estimated. The values are found to be within a range from {beta} = 47 to 25 cm GW{sup -1} and be decreasing with increasing T{sub L}. As expected for the TPA process, the experimental data within a certain range follows the linear relation: log (P{sub 0}/P{sub T}) = A{sub G} + {Omega}(P{sub 0} - P{sub T}), where P{sub T} is the transmitted power, A{sub G} is the absorbance of the ground state and {Omega} is a constant depending on the absorption cross-section and the relaxation time. The values of A{sub G} and {Omega} estimated from the fits to the measured data vary with T{sub L}. The findings resulting from this investigation might have potential applications in optical sensors protection.

A new differential equations-based model for nonlinear history-dependent magnetic behaviour

International Nuclear Information System (INIS)

Aktaa, J.; Weth, A. von der

2000-01-01

The paper presents a new kind of numerical model describing nonlinear magnetic behaviour. The model is formulated as a set of differential equations taking into account history dependence phenomena like the magnetisation hysteresis as well as saturation effects. The capability of the model is demonstrated carrying out comparisons between measurements and calculations

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

DEFF Research Database (Denmark)

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

2002-01-01

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

Nonlinear evolution of the mode structure of ELMs in realistic ASDEX Upgrade geometry

Energy Technology Data Exchange (ETDEWEB)

Krebs, Isabel; Hoelzl, Matthias; Lackner, Karl; Guenter, Sibylle [Max-Planck-Institut fuer Plasmaphysik, EURATOM Association, Boltzmannstr. 2, Garching (Germany); Collaboration: The ASDEX Upgrade Team

2013-07-01

Edge-localized modes (ELMs) are edge instabilities in H-mode plasmas, which eject particles and energy. The suitability of the H-mode for future fusion reactors depends crucially on the exact ELM dynamics as they can damage plasma facing components if too large. We have simulated ELMs in ASDEX Upgrade geometry using the nonlinear MHD code JOREK. Emphasis was put on the mode structure evolution in the early ELM phase which is characterized by the exponential growth of the unstable toroidal Fourier harmonics followed by a phase of saturation. In the linear phase, toroidal harmonics grow independently, whereas at larger amplitudes, the nonlinear interaction between the toroidal harmonics influences their growth and structure. Prior to mode saturation, the evolution of the mode structure can be reproduced well by a simple quadratic mode-interaction model, which yields a possible explanation for the strong n=1 component of type-I ELMs observed in ASDEX Upgrade. In the linear phase of the simulations, intermediate toroidal mode numbers (n 6-14) are most unstable as predicted by the peeling-ballooning model. But non-linearly, the n=1 component becomes important due to an energy transfer from pairs of linearly dominant toroidal harmonics with neighboring mode numbers to the n=1. The latter thereby changes its spatial structure.

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)

Q-switched Yb3+:YAG laser using plasmonic Cu2-xSe quantum dots as saturable absorbers

Science.gov (United States)

Wang, Yimeng; Zhan, Yi; Lee, Sooho; Wang, Li; Zhang, Xinping

2018-04-01

Cu2-xSe quantum dots (QDs) were synthesized by organometallic synthesis methods. Due to heavy self-doping, the Cu2-xSe QDs exhibit particle plasmon resonance in the near-infrared. Transient absorption spectroscopic investigation revealed strong nonlinear optical absorption and bleaching performance of the QDs under femtosecond pulse excitation, which enabled the Cu2-xSe QDs to be excellent saturable absorbers and applied in Q-switched or mode-locked lasers. A passively Q-switched Yb3+:YAG solid-state laser at 1.03 μm was achieved by coating Cu2-xSe QDs as saturable absorbers onto one of the output coupler of the V-shaped linear cavity.

Classical Yang-Mills mechanics. Nonlinear colour oscillations

International Nuclear Information System (INIS)

Matinyan, S.G.; Savvidi, G.K.; Ter-Arutyunyan-Savvidi, N.G.

1981-01-01

A novel class of solutions of the classical Yang-Mills equations in the Minkowsky space which leads to nonlinear colour oscillations is studied. The system discribing these oscillations is apparently stochastic. Periodic trajectories corresponding to the solutions are found and studied and it is demonstrated that they constitute at least an enumerable set [ru

Effect of Forcing Function on Nonlinear Acoustic Standing Waves

Science.gov (United States)

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

2003-01-01

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

Mode-locked Er-doped fiber laser based on PbS/CdS core/shell quantum dots as saturable absorber.

Science.gov (United States)

Ming, Na; Tao, Shina; Yang, Wenqing; Chen, Qingyun; Sun, Ruyi; Wang, Chang; Wang, Shuyun; Man, Baoyuan; Zhang, Huanian

2018-04-02

Previously, PbS/CdS core/shell quantum dots with excellent optical properties have been widely used as light-harvesting materials in solar cell and biomarkers in bio-medicine. However, the nonlinear absorption characteristics of PbS/CdS core/shell quantum dots have been rarely investigated. In this work, PbS/CdS core/shell quantum dots were successfully employed as nonlinear saturable absorber (SA) for demonstrating a mode-locked Er-doped fiber laser. Based on a film-type SA, which was prepared by incorporating the quantum dots with the polyvinyl alcohol (PVA), mode-locked Er-doped operation with a pulse width of 54 ps and a maximum average output power of 2.71 mW at the repetition rate of 3.302 MHz was obtained. Our long-time stable results indicate that the CdS shell can effectively protect the PbS core from the effect of photo-oxidation and PbS/CdS core/shell quantum dots were efficient SA candidates for demonstrating pulse fiber lasers due to its tunable absorption peak and excellent saturable absorption properties.

Saturable Absorption in 2D Ti3 C2 MXene Thin Films for Passive Photonic Diodes.

Science.gov (United States)

Dong, Yongchang; Chertopalov, Sergii; Maleski, Kathleen; Anasori, Babak; Hu, Longyu; Bhattacharya, Sriparna; Rao, Apparao M; Gogotsi, Yury; Mochalin, Vadym N; Podila, Ramakrishna

2018-03-01

MXenes comprise a new class of 2D transition metal carbides, nitrides, and carbonitrides that exhibit unique light-matter interactions. Recently, 2D Ti 3 CNT x (T x represents functional groups such as OH and F) was found to exhibit nonlinear saturable absorption (SA) or increased transmittance at higher light fluences, which is useful for mode locking in fiber-based femtosecond lasers. However, the fundamental origin and thickness dependence of SA behavior in MXenes remain to be understood. 2D Ti 3 C 2 T x thin films of different thicknesses are fabricated using an interfacial film formation technique to systematically study their nonlinear optical properties. Using the open aperture Z-scan method, it is found that the SA behavior in Ti 3 C 2 T x MXene arises from plasmon-induced increase in the ground state absorption at photon energies above the threshold for free carrier oscillations. The saturation fluence and modulation depth of Ti 3 C 2 T x MXene is observed to be dependent on the film thickness. Unlike other 2D materials, Ti 3 C 2 T x is found to show higher threshold for light-induced damage with up to 50% increase in nonlinear transmittance. Lastly, building on the SA behavior of Ti 3 C 2 T x MXenes, a Ti 3 C 2 T x MXene-based photonic diode that breaks time-reversal symmetry to achieve nonreciprocal transmission of nanosecond laser pulses is demonstrated. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Numerical simulation of seismic performance of the underground structure buried in the dense saturated sand

International Nuclear Information System (INIS)

Kawai, Tadashi

2006-01-01

The applicability of the advanced earthquake resistant performance verification method on reinforced concrete underground structures developed by CRIEPI was investigated for the structures which buried in the dry sand. For the advancement of the method in practical use, the applicability to the structures buried in the saturated ground is expected to be verified. In this study the applicability of the effective stress based soil modeling method in numerical analysis, which was proposed through the modification of the formerly developed model by CRIEPI, was verified through the non-linear dynamic numerical simulations of the large centrifuge tests conducted by using a model comprised of fully saturated sand and a aluminium duct type structure specially prepared for the measurement of the load acting on the structure surface with the soil-structure interaction. The magnitudes of the simulated loads and the resultant deformations of the structure were almost same as those of experiments. As a result it is confirmed that the performance verification method is useful for the structures buried in the saturated ground with using the proposed effective stress based ground modeling method. (author)

Acoustic-gravity nonlinear structures

Directory of Open Access Journals (Sweden)

D. Jovanović

2002-01-01

Full Text Available A catalogue of nonlinear vortex structures associated with acoustic-gravity perturbations in the Earth's atmosphere is presented. Besides the previously known Kelvin-Stewart cat's eyes, dipolar and tripolar structures, new solutions having the form of a row of counter-rotating vortices, and several weakly two-dimensional vortex chains are given. The existence conditions for these nonlinear structures are discussed with respect to the presence of inhomogeneities of the shear flows. The mode-coupling mechanism for the nonlinear generation of shear flows in the presence of linearly unstable acoustic-gravity waves, possibly also leading to intermittency and chaos, is presented.

Landau damping: the mechanics model and its ultimate entropy gain

International Nuclear Information System (INIS)

Hannay, J H; Kluge, Michel

2011-01-01

Classical mechanics has only been invoked to account for Landau damping in a rather half-hearted way, alongside plasma perturbation theory. In particular this invocation is essential for the study of the saturation, or post-linear (or 'nonlinear') regime of the damping initiated by Dawson and O'Neill. By embracing mechanics wholeheartedly here, with its attendant phase space, one can access results, old and new, cleanly and directly, and with one fewer numerical integration for the post-linear regime. By using a summation technique familiar in semiclassical quantum mechanics (Poisson summation), the one remaining numerical integration can be much improved in accuracy. Also accessible from mechanics is the ultimate entropy gain. Though zero for any finite time (in the absence of coarse graining), the entropy gain is ultimately non-zero (at infinite time the required coarse graining is zero). It is calculated analytically by using the appropriate asymptotics, hitherto not fully exploited.

The algebra of non-local charges in non-linear sigma models

International Nuclear Information System (INIS)

Abdalla, E.; Abdalla, M.C.B.; Brunelli, J.C.; Zadra, A.

1993-07-01

We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower. (author). 22 refs, 5 figs

Thickness-dependent nonlinear optical properties of CsPbBr3 perovskite nanosheets.

Science.gov (United States)

Zhang, Jun; Jiang, Tian; Zheng, Xin; Shen, Chao; Cheng, Xiang'ai

2017-09-01

Halide perovskite has attracted significant attention because of excellent optical properties. Here, we study the optical properties of CsPbBr 3 perovskite nanosheets and observe that the nonlinear optical properties can be tuned by the thickness. The photoluminescence (PL) properties and nonlinear absorption effects induced by saturation absorption (SA) and two-photon absorption (TPA) in CsPbBr 3 nanosheets with different thicknesses (from 104.6 to 195.4 nm) have been studied. The PL intensity increases nearly three times with changing from the thinnest one to the thinnest under the same excitation condition. Moreover, the same phenomenon takes place no matter when SA or TPA effects happen. The PL lifetime (τ) varies inversely with the thickness. When SA happens, τ decreases from 11.54 to 9.43 ns while when TPA happens new decay channels emerge with the increase of the thickness. Besides, both saturation intensity (I sat ) and the modulation depth are proportional to the thickness (I sat rises from 3.12 to 4.79  GW/cm 2 , the modulation depth increases from 18.6% to 32.3%), while the TPA coefficient (β) is inversely proportional with the thickness (decreases from 10.94 to 4.73  cm/GW). In addition, quantum yields and thicknesses are in the direct ratio. This Letter advocates great promise for nonlinear optical property related photonics devices.

Gluon saturation in a saturated environment

International Nuclear Information System (INIS)

Kopeliovich, B. Z.; Potashnikova, I. K.; Schmidt, Ivan

2011-01-01

A bootstrap equation for self-quenched gluon shadowing leads to a reduced magnitude of broadening for partons propagating through a nucleus. Saturation of small-x gluons in a nucleus, which has the form of transverse momentum broadening of projectile gluons in pA collisions in the nuclear rest frame, leads to a modification of the parton distribution functions in the beam compared with pp collisions. In nucleus-nucleus collisions all participating nucleons acquire enhanced gluon density at small x, which boosts further the saturation scale. Solution of the reciprocity equations for central collisions of two heavy nuclei demonstrate a significant, up to several times, enhancement of Q sA 2 , in AA compared with pA collisions.

Ion cyclotron instability saturation and turbulent plasma heating in the presence of ions moving across the magnetic field

International Nuclear Information System (INIS)

Mikhajlenko, V.S.; Stepanov, K.N.

1981-01-01

Ion cyclotron instability saturation is considered in terms of the turbulence theory when there is a beam of heavy ions with large thermal longitudinal velocity spread. The instability excitation is due to a cyclotron interaction with ions of the beam under the anomalous Doppler effect. The instability is shown to be saturated due to an induced plasma ion scattering of ion cyclotron waves when the beam ion charge number Zsub(b) is approximately 1. Decay processes, wave scattering by virtual wave polarization clouds and resonance broadening due to random walk of plasma ions in turbulent instability fields appear to be unimportant. For Zsub(b)>>1 the induced wave scattering by the beam ions is the main process determining the nonlinear stage of the instability. Estimates are given for the oscillation energy density in the instability saturation state and for the turbulent heating rate of plasma and beam ions [ru

Generation of “gigantic” ultra-short microwave pulses based on passive mode-locking effect in electron oscillators with saturable absorber in the feedback loop

International Nuclear Information System (INIS)

Ginzburg, N. S.; Denisov, G. G.; Vilkov, M. N.; Zotova, I. V.; Sergeev, A. S.

2016-01-01

A periodic train of powerful ultrashort microwave pulses can be generated in electron oscillators with a non-linear saturable absorber installed in the feedback loop. This method of pulse formation resembles the passive mode-locking widely used in laser physics. Nevertheless, there is a specific feature in the mechanism of pulse amplification when consecutive energy extraction from different fractions of a stationary electron beam takes place due to pulse slippage over the beam caused by the difference between the wave group velocity and the electron axial velocity. As a result, the peak power of generated “gigantic” pulses can exceed not only the level of steady-state generation but also, in the optimal case, the power of the driving electron beam.

A model for predicting pellet-cladding interaction induced fuel rod failure, based on nonlinear fracture mechanics

International Nuclear Information System (INIS)

Jernkvist, L.O.

1993-01-01

A model for predicting pellet-cladding mechanical interaction induced fuel rod failure, suitable for implementation in finite element fuel-performance codes, is presented. Cladding failure is predicted by explicitly modelling the propagation of radial cracks under varying load conditions. Propagation is assumed to be due to either iodine induced stress corrosion cracking or ductile fracture. Nonlinear fracture mechanics concepts are utilized in modelling these two mechanisms of crack growth. The novelty of this approach is that the development of cracks, which may ultimately lead to fuel rod failure, can be treated as a dynamic and time-dependent process. The influence of cyclic loading, ramp rates and material creep on the failure mechanism can thereby be investigated. Results of numerical calculations, in which the failure model has been used to study the dependence of cladding creep rate on crack propagation velocity, are presented. (author)

Lipid order, saturation and surface property relationships: a study of human meibum saturation.

Science.gov (United States)

Mudgil, Poonam; Borchman, Douglas; Yappert, Marta C; Duran, Diana; Cox, Gregory W; Smith, Ryan J; Bhola, Rahul; Dennis, Gary R; Whitehall, John S

2013-11-01

Tear film stability decreases with age however the cause(s) of the instability are speculative. Perhaps the more saturated meibum from infants may contribute to tear film stability. The meibum lipid phase transition temperature and lipid hydrocarbon chain order at physiological temperature (33 °C) decrease with increasing age. It is reasonable that stronger lipid-lipid interactions could stabilize the tear film since these interactions must be broken for tear break up to occur. In this study, meibum from a pool of adult donors was saturated catalytically. The influence of saturation on meibum hydrocarbon chain order was determined by infrared spectroscopy. Meibum is in an anhydrous state in the meibomian glands and on the surface of the eyelid. The influence of saturation on the surface properties of meibum was determined using Langmuir trough technology. Saturation of native human meibum did not change the minimum or maximum values of hydrocarbon chain order so at temperatures far above or below the phase transition of human meibum, saturation does not play a role in ordering or disordering the lipid hydrocarbon chains. Saturation did increase the phase transition temperature in human meibum by over 20 °C, a relatively high amount. Surface pressure-area studies showing the late take off and higher maximum surface pressure of saturated meibum compared to native meibum suggest that the saturated meibum film is quite molecularly ordered (stiff molecular arrangement) and elastic (molecules are able to rearrange during compression and expansion) compared with native meibum films which are more fluid agreeing with the infrared spectroscopic results of this study. In saturated meibum, the formation of compacted ordered islands of lipids above the surfactant layer would be expected to decrease the rate of evaporation compared to fluid and more loosely packed native meibum. Higher surface pressure observed with films of saturated meibum compared to native meibum

Nonlinear observer-based Lyapunov boundary control of distributed heat transfer mechanisms for membrane distillation plant

KAUST Repository

Eleiwi, Fadi

2016-09-19

This paper presents a nonlinear observer-based Lyapunov control for a membrane distillation (MD) process. The control considers the inlet temperatures of the feed and the permeate solutions as inputs, transforming it to boundary control process, and seeks to maintain the temperature difference along the membrane boundaries around a sufficient level to promote water production. MD process is modeled with advection diffusion equation model in two dimensions, where the diffusion and convection heat transfer mechanisms are best described. Model analysis, effective order reduction and parameters physical interpretation, are provided. Moreover, a nonlinear observer has been designed to provide the control with estimates of the temperature evolution at each time instant. In addition, physical constraints are imposed on the control to have an acceptable range of feasible inputs, and consequently, better energy consumption. Numerical simulations for the complete process with real membrane parameter values are provided, in addition to detailed explanations for the role of the controller and the observer. (C) 2016 Elsevier Ltd. All rights reserved.

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

Science.gov (United States)

Asadi, Reza; Ouyang, Zhengbiao

2018-03-01

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

Multipactor saturation in parallel-plate waveguides

International Nuclear Information System (INIS)

Sorolla, E.; Mattes, M.

2012-01-01

The saturation stage of a multipactor discharge is considered of interest, since it can guide towards a criterion to assess the multipactor onset. The electron cloud under multipactor regime within a parallel-plate waveguide is modeled by a thin continuous distribution of charge and the equations of motion are calculated taking into account the space charge effects. The saturation is identified by the interaction of the electron cloud with its image charge. The stability of the electron population growth is analyzed and two mechanisms of saturation to explain the steady-state multipactor for voltages near above the threshold onset are identified. The impact energy in the collision against the metal plates decreases during the electron population growth due to the attraction of the electron sheet on the image through the initial plate. When this growth remains stable till the impact energy reaches the first cross-over point, the electron surface density tends to a constant value. When the stability is broken before reaching the first cross-over point the surface charge density oscillates chaotically bounded within a certain range. In this case, an expression to calculate the maximum electron surface charge density is found whose predictions agree with the simulations when the voltage is not too high.