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Sample records for nonlinear hyperelastic material

  1. A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials

    Science.gov (United States)

    Li, Chen; Liao, Yufei

    2018-03-01

    Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.

  2. Fundamental Hyperelastic Material Study Project

    Data.gov (United States)

    National Aeronautics and Space Administration — This research is part of an innovative effort to use hyperelastic materials to produce flexible and seamless aircraft structures that reduce drag and...

  3. Isogeometric Analysis of Hyperelastic Materials Using PetIGA

    KAUST Repository

    Bernal, L.M.

    2013-06-01

    In this work different nonlinear hyperelastic models for slightly compressible materials are implemented in an isogeometric finite element model. This is done within the recently developed computational framework called PetIGA, which uses isoge- ometric analysis and modern computational tools to solve systems of equations directly and iteratively. A flexible theoretical background is described to implement other hyperelastic models and possibly transient problems in future work. Results show quadratic convergence of the nonlinear solution consistent with the Newton-Raphson method that was used. Finally, PetIGA proves to be a powerful and versatile tool to solve these types of problems efficiently.

  4. Isogeometric Analysis of Hyperelastic Materials Using PetIGA

    KAUST Repository

    Bernal, L.M.; Calo, Victor M.; Collier, Nathan; Espinosa, G.A.; Fuentes, F.; Mahecha, J.C.

    2013-01-01

    In this work different nonlinear hyperelastic models for slightly compressible materials are implemented in an isogeometric finite element model. This is done within the recently developed computational framework called PetIGA, which uses isoge- ometric analysis and modern computational tools to solve systems of equations directly and iteratively. A flexible theoretical background is described to implement other hyperelastic models and possibly transient problems in future work. Results show quadratic convergence of the nonlinear solution consistent with the Newton-Raphson method that was used. Finally, PetIGA proves to be a powerful and versatile tool to solve these types of problems efficiently.

  5. HYPERELASTIC MODELS FOR GRANULAR MATERIALS

    Energy Technology Data Exchange (ETDEWEB)

    Humrickhouse, Paul W; Corradini, Michael L

    2009-01-29

    A continuum framework for modeling of dust mobilization and transport, and the behavior of granular systems in general, has been reviewed, developed and evaluated for reactor design applications. The large quantities of micron-sized particles expected in the international fusion reactor design, ITER, will accumulate into piles and layers on surfaces, which are large relative to the individual particle size; thus, particle-particle, rather than particle-surface, interactions will determine the behavior of the material in bulk, and a continuum approach is necessary and justified in treating the phenomena of interest; e.g., particle resuspension and transport. The various constitutive relations that characterize these solid particle interactions in dense granular flows have been discussed previously, but prior to mobilization their behavior is not even fluid. Even in the absence of adhesive forces between particles, dust or sand piles can exist in static equilibrium under gravity and other forces, e.g., fluid shear. Their behavior is understood to be elastic, though not linear. The recent “granular elasticity” theory proposes a non-linear elastic model based on “Hertz contacts” between particles; the theory identifies the Coulomb yield condition as a requirement for thermodynamic stability, and has successfully reproduced experimental results for stress distributions in sand piles. The granular elasticity theory is developed and implemented in a stand- alone model and then implemented as part of a finite element model, ABAQUS, to determine the stress distributions in dust piles subjected to shear by a fluid flow. We identify yield with the onset of mobilization, and establish, for a given dust pile and flow geometry, the threshold pressure (force) conditions on the surface due to flow required to initiate it. While the granular elasticity theory applies strictly to cohesionless granular materials, attractive forces are clearly important in the interaction of

  6. Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

    Science.gov (United States)

    Mihai, L. Angela; Woolley, Thomas E.; Goriely, Alain

    2018-03-01

    Biological and synthetic materials often exhibit intrinsic variability in their elastic responses under large strains, owing to microstructural inhomogeneity or when elastic data are extracted from viscoelastic mechanical tests. For these materials, although hyperelastic models calibrated to mean data are useful, stochastic representations accounting also for data dispersion carry extra information about the variability of material properties found in practical applications. We combine finite elasticity and information theories to construct homogeneous isotropic hyperelastic models with random field parameters calibrated to discrete mean values and standard deviations of either the stress-strain function or the nonlinear shear modulus, which is a function of the deformation, estimated from experimental tests. These quantities can take on different values, corresponding to possible outcomes of the experiments. As multiple models can be derived that adequately represent the observed phenomena, we apply Occam's razor by providing an explicit criterion for model selection based on Bayesian statistics. We then employ this criterion to select a model among competing models calibrated to experimental data for rubber and brain tissue under single or multiaxial loads.

  7. Digital Materials - Evaluation of the Possibilities of using Selected Hyperelastic Models to Describe Constitutive Relations

    Science.gov (United States)

    Mańkowski, J.; Lipnicki, J.

    2017-08-01

    The authors tried to identify the parameters of numerical models of digital materials, which are a kind of composite resulting from the manufacture of the product in 3D printers. With the arrangement of several heads of the printer, the new material can result from mixing of materials with radically different properties, during the process of producing single layer of the product. The new material has properties dependent on the base materials properties and their proportions. Digital materials tensile characteristics are often non-linear and qualify to be described by hyperelastic materials models. The identification was conducted based on the results of tensile tests models, its various degrees coefficients of the polynomials to various degrees coefficients of the polynomials. The Drucker's stability criterion was also examined. Fourteen different materials were analyzed.

  8. Digital Materials – Evaluation of the Possibilities of using Selected Hyperelastic Models to Describe Constitutive Relations

    Directory of Open Access Journals (Sweden)

    Mańkowski J.

    2017-08-01

    Full Text Available The authors tried to identify the parameters of numerical models of digital materials, which are a kind of composite resulting from the manufacture of the product in 3D printers. With the arrangement of several heads of the printer, the new material can result from mixing of materials with radically different properties, during the process of producing single layer of the product. The new material has properties dependent on the base materials properties and their proportions. Digital materials tensile characteristics are often non-linear and qualify to be described by hyperelastic materials models. The identification was conducted based on the results of tensile tests models, its various degrees coefficients of the polynomials to various degrees coefficients of the polynomials. The Drucker’s stability criterion was also examined. Fourteen different materials were analyzed.

  9. Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials

    KAUST Repository

    Mihai, L. A.; Goriely, A.

    2011-01-01

    Motivated by recent experiments on biopolymer gels whereby the reverse of the usual (positive) Poynting effect was observed, we investigate the effect of the so-called 'adscititious inequalities' on the behaviour of hyperelastic materials subject

  10. Hyperelastic Material Properties of Mouse Skin under Compression.

    Directory of Open Access Journals (Sweden)

    Yuxiang Wang

    Full Text Available The skin is a dynamic organ whose complex material properties are capable of withstanding continuous mechanical stress while accommodating insults and organism growth. Moreover, synchronized hair cycles, comprising waves of hair growth, regression and rest, are accompanied by dramatic fluctuations in skin thickness in mice. Whether such structural changes alter skin mechanics is unknown. Mouse models are extensively used to study skin biology and pathophysiology, including aging, UV-induced skin damage and somatosensory signaling. As the skin serves a pivotal role in the transfer function from sensory stimuli to neuronal signaling, we sought to define the mechanical properties of mouse skin over a range of normal physiological states. Skin thickness, stiffness and modulus were quantitatively surveyed in adult, female mice (Mus musculus. These measures were analyzed under uniaxial compression, which is relevant for touch reception and compression injuries, rather than tension, which is typically used to analyze skin mechanics. Compression tests were performed with 105 full-thickness, freshly isolated specimens from the hairy skin of the hind limb. Physiological variables included body weight, hair-cycle stage, maturity level, skin site and individual animal differences. Skin thickness and stiffness were dominated by hair-cycle stage at young (6-10 weeks and intermediate (13-19 weeks adult ages but by body weight in mature mice (26-34 weeks. Interestingly, stiffness varied inversely with thickness so that hyperelastic modulus was consistent across hair-cycle stages and body weights. By contrast, the mechanics of hairy skin differs markedly with anatomical location. In particular, skin containing fascial structures such as nerves and blood vessels showed significantly greater modulus than adjacent sites. Collectively, this systematic survey indicates that, although its structure changes dramatically throughout adult life, mouse skin at a given

  11. Hybrid High-Order methods for finite deformations of hyperelastic materials

    Science.gov (United States)

    Abbas, Mickaël; Ern, Alexandre; Pignet, Nicolas

    2018-01-01

    We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order k≥1 on the mesh skeleton, together with cell-based polynomials that can be eliminated locally by static condensation. The discrete problem is written as the minimization of a broken nonlinear elastic energy where a local reconstruction of the displacement gradient is used. Two HHO methods are considered: a stabilized method where the gradient is reconstructed as a tensor-valued polynomial of order k and a stabilization is added to the discrete energy functional, and an unstabilized method which reconstructs a stable higher-order gradient and circumvents the need for stabilization. Both methods satisfy the principle of virtual work locally with equilibrated tractions. We present a numerical study of the two HHO methods on test cases with known solution and on more challenging three-dimensional test cases including finite deformations with strong shear layers and cavitating voids. We assess the computational efficiency of both methods, and we compare our results to those obtained with an industrial software using conforming finite elements and to results from the literature. The two HHO methods exhibit robust behavior in the quasi-incompressible regime.

  12. An iterative hyperelastic parameters reconstruction for breast cancer assessment

    Science.gov (United States)

    Mehrabian, Hatef; Samani, Abbas

    2008-03-01

    In breast elastography, breast tissues usually undergo large compressions resulting in significant geometric and structural changes, and consequently nonlinear mechanical behavior. In this study, an elastography technique is presented where parameters characterizing tissue nonlinear behavior is reconstructed. Such parameters can be used for tumor tissue classification. To model the nonlinear behavior, tissues are treated as hyperelastic materials. The proposed technique uses a constrained iterative inversion method to reconstruct the tissue hyperelastic parameters. The reconstruction technique uses a nonlinear finite element (FE) model for solving the forward problem. In this research, we applied Yeoh and Polynomial models to model the tissue hyperelasticity. To mimic the breast geometry, we used a computational phantom, which comprises of a hemisphere connected to a cylinder. This phantom consists of two types of soft tissue to mimic adipose and fibroglandular tissues and a tumor. Simulation results show the feasibility of the proposed method in reconstructing the hyperelastic parameters of the tumor tissue.

  13. Fundamental Research into Hyperelastic Materials for Flight Applications (FY15)

    Data.gov (United States)

    National Aeronautics and Space Administration — This research project is working to develop methods to characterize elastomer materials for flight applications as well as instrumentation methods to monitor their...

  14. Recovery of material parameters of soft hyperelastic tissue by an inverse spectral technique

    KAUST Repository

    Gou, Kun

    2012-07-01

    An inverse spectral method is developed for recovering a spatially inhomogeneous shear modulus for soft tissue. The study is motivated by a novel use of the intravascular ultrasound technique to image arteries. The arterial wall is idealized as a nonlinear isotropic cylindrical hyperelastic body. A boundary value problem is formulated for the response of the arterial wall within a specific class of quasistatic deformations reflective of the response due to imposed blood pressure. Subsequently, a boundary value problem is developed via an asymptotic construction modeling intravascular ultrasound interrogation which generates small amplitude, high frequency time harmonic vibrations superimposed on the static finite deformation. This leads to a system of second order ordinary Sturm-Liouville boundary value problems that are then employed to reconstruct the shear modulus through a nonlinear inverse spectral technique. Numerical examples are demonstrated to show the viability of the method. © 2012 Elsevier Ltd. All rights reserved.

  15. Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials

    KAUST Repository

    Mihai, L. A.

    2011-08-10

    Motivated by recent experiments on biopolymer gels whereby the reverse of the usual (positive) Poynting effect was observed, we investigate the effect of the so-called \\'adscititious inequalities\\' on the behaviour of hyperelastic materials subject to shear. We first demonstrate that for homogeneous isotropic materials subject to pure shear, the resulting deformation consists of a triaxial stretch combined with a simple shear in the direction of the shear force if and only if the Baker-Ericksen inequalities hold. Then for a cube deformed under pure shear, the positive Poynting effect occurs if the \\'sheared faces spread apart\\', whereas the negative Poynting effect is obtained if the \\'sheared faces draw together\\'. Similarly, under simple shear deformation, the positive Poynting effect is obtained if the \\'sheared faces tend to spread apart\\', whereas the negative Poynting effect occurs if the \\'sheared faces tend to draw together\\'. When the Poynting effect occurs under simple shear, it is reasonable to assume that the same sign Poynting effect is btained also under pure shear. Since the observation of the negative Poynting effect in semiflexible biopolymers implies that the (stronger) empirical inequalities may not hold, we conclude that these inequalities must not be imposed when such materials are described. © 2011 The Royal Society.

  16. Three wave mixing test of hyperelasticity in highly nonlinear solids: sedimentary rocks.

    Science.gov (United States)

    D'Angelo, R M; Winkler, K W; Johnson, D L

    2008-02-01

    Measurements of three-wave mixing amplitudes on solids whose third order elastic constants have also been measured by means of the elasto-acoustic effect are reported. Because attenuation and diffraction are important aspects of the measurement technique results are analyzed using a frequency domain version of the KZK equation, modified to accommodate an arbitrary frequency dependence to the attenuation. It is found that the value of beta so deduced for poly(methylmethacrylate) (PMMA) agrees quite well with that predicted from the stress-dependent sound speed measurements, establishing that PMMA may be considered a hyperelastic solid, in this context. The beta values of sedimentary rocks, though they are typically two orders of magnitude larger than, e.g., PMMA's, are still a factor of 3-10 less than those predicted from the elasto-acoustic effect. Moreover, these samples exhibit significant heterogeneity on a centimeter scale, which heterogeneity is not apparent from a measurement of the position dependent sound speed.

  17. Hyperelastic tension of graphene

    Energy Technology Data Exchange (ETDEWEB)

    Saavedra Flores, E. I., E-mail: erick.saavedra@usach.cl [Departamento de Ingeniería en Obras Civiles, Universidad de Santiago de Chile, Av. Ecuador 3659, Santiago (Chile); Ajaj, R. M. [Aeronautics and Astronautics, University of Southampton, Southampton SO171BJ (United Kingdom); Adhikari, S.; Dayyani, I.; Friswell, M. I. [College of Engineering, Swansea University, Singleton Park, Swansea SA2 8PP (United Kingdom); Castro-Triguero, Rafael [Department of Mechanics, University of Cordoba, Campus de Rabanales, Cordoba CP 14071 (Spain)

    2015-02-09

    In this paper, we investigate the hyperelastic tensile behaviour of single layer graphene sheets (SLGSs). A one-term incompressible Ogden-type hyperelastic model is chosen to describe the mechanical response of C-C bonds. By establishing equality between the Ogden strain-energy and the variation of the Tersoff-Brenner interatomic potential, three different geometries of SLGSs are studied under tensile loading. We compute the Young's modulus, the finite-deformation Poisson's ratio, ultimate strains, total reactions, and the variation of the potential energy per carbon atom for large strains. Numerical simulations are compared with results obtained by molecular mechanics and molecular dynamics simulations, finite elements, continuum mechanics theory, and experiments. Our predictions are validated, revealing the potential predictive capabilities of the present hyperelastic framework for the analysis of graphene in the context of infinitesimal and large deformations. The good agreement found between our calculations and the published data suggests that graphene may be described as a hyperelastic material.

  18. Hyper-elastic modeling and mechanical behavior investigation of porous poly-D-L-lactide/nano-hydroxyapatite scaffold material.

    Science.gov (United States)

    Han, Quan Feng; Wang, Ze Wu; Tang, Chak Yin; Chen, Ling; Tsui, Chi Pong; Law, Wing Cheung

    2017-07-01

    Poly-D-L-lactide/nano-hydroxyapatite (PDLLA/nano-HA) can be used as the biological scaffold material in bone tissue engineering as it can be readily made into a porous composite material with excellent performance. However, constitutive modeling for the mechanical response of porous PDLLA/nano-HA under various stress conditions has been very limited so far. In this work, four types of fundamental compressible hyper-elastic constitutive models were introduced for constitutive modeling and investigation of mechanical behaviors of porous PDLLA/nano-HA. Moreover, the unitary expressions of Cauchy stress tensor have been derived for the PDLLA/nano-HA under uniaxial compression (or stretch), biaxial compression (or stretch), pure shear and simple shear load by using the theory of continuum mechanics. The theoretical results determined from the approach based on the Ogden compressible hyper-elastic constitutive model were in good agreement with the experimental data from the uniaxial compression tests. Furthermore, this approach can also be used to predict the mechanical behaviors of the porous PDLLA/nano-HA material under the biaxial compression (or stretch), pure shear and simple shear. Copyright © 2017 Elsevier Ltd. All rights reserved.

  19. Topology optimization of hyperelastic structures using a level set method

    Science.gov (United States)

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

    2017-12-01

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

  20. Generalization of exponential based hyperelastic to hyper-viscoelastic model for investigation of mechanical behavior of rate dependent materials.

    Science.gov (United States)

    Narooei, K; Arman, M

    2018-03-01

    In this research, the exponential stretched based hyperelastic strain energy was generalized to the hyper-viscoelastic model using the heredity integral of deformation history to take into account the strain rate effects on the mechanical behavior of materials. The heredity integral was approximated by the approach of Goh et al. to determine the model parameters and the same estimation was used for constitutive modeling. To present the ability of the proposed hyper-viscoelastic model, the stress-strain response of the thermoplastic elastomer gel tissue at different strain rates from 0.001 to 100/s was studied. In addition to better agreement between the current model and experimental data in comparison to the extended Mooney-Rivlin hyper-viscoelastic model, a stable material behavior was predicted for pure shear and balance biaxial deformation modes. To present the engineering application of current model, the Kolsky bars impact test of gel tissue was simulated and the effects of specimen size and inertia on the uniform deformation were investigated. As the mechanical response of polyurea was provided over wide strain rates of 0.0016-6500/s, the current model was applied to fit the experimental data. The results were shown more accuracy could be expected from the current research than the extended Ogden hyper-viscoelastic model. In the final verification example, the pig skin experimental data was used to determine parameters of the hyper-viscoelastic model. Subsequently, a specimen of pig skin at different strain rates was loaded to a fixed strain and the change of stress with time (stress relaxation) was obtained. The stress relaxation results were revealed the peak stress increases by applied strain rate until the saturated loading rate and the equilibrium stress with magnitude of 0.281MPa could be reached. Copyright © 2017 Elsevier Ltd. All rights reserved.

  1. Fundamentals of nonlinear optical materials

    Indian Academy of Sciences (India)

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

  2. 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...

  3. A fiber orientation-adapted integration scheme for computing the hyperelastic Tucker average for short fiber reinforced composites

    Science.gov (United States)

    Goldberg, Niels; Ospald, Felix; Schneider, Matti

    2017-10-01

    In this article we introduce a fiber orientation-adapted integration scheme for Tucker's orientation averaging procedure applied to non-linear material laws, based on angular central Gaussian fiber orientation distributions. This method is stable w.r.t. fiber orientations degenerating into planar states and enables the construction of orthotropic hyperelastic energies for truly orthotropic fiber orientation states. We establish a reference scenario for fitting the Tucker average of a transversely isotropic hyperelastic energy, corresponding to a uni-directional fiber orientation, to microstructural simulations, obtained by FFT-based computational homogenization of neo-Hookean constituents. We carefully discuss ideas for accelerating the identification process, leading to a tremendous speed-up compared to a naive approach. The resulting hyperelastic material map turns out to be surprisingly accurate, simple to integrate in commercial finite element codes and fast in its execution. We demonstrate the capabilities of the extracted model by a finite element analysis of a fiber reinforced chain link.

  4. Non-linear optical materials

    CERN Document Server

    Saravanan, R

    2018-01-01

    Non-linear optical materials have widespread and promising applications, but the efforts to understand the local structure, electron density distribution and bonding is still lacking. The present work explores the structural details, the electron density distribution and the local bond length distribution of some non-linear optical materials. It also gives estimation of the optical band gap, the particle size, crystallite size, and the elemental composition from UV-Visible analysis, SEM, XRD and EDS of some non-linear optical materials respectively.

  5. On the inflation of poro-hyperelastic annuli

    Science.gov (United States)

    Selvadurai, A. P. S.; Suvorov, A. P.

    2017-10-01

    The paper presents the radially and spherically symmetric problems associated with the inflation of poro-hyperelastic regions. The theory of poro-hyperelasticity is a convenient framework for modelling the mechanical behaviour of highly deformable materials in which the pore space is saturated with fluids. Including the coupled mechanical responses of both the hyperelastic porous skeleton and the fluid is regarded as an important consideration for the application of the results, particularly to soft tissues encountered in biomechanical applications. The analytical solutions for radially and spherically symmetric problems involving annular domains are used to benchmark the accuracy of a standard computational approach. The paper also generates results applicable to the hyperelastic solutions when coupling is eliminated through the presence of a highly permeable pore structure.

  6. Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

    KAUST Repository

    Angela Mihai, L.; Goriely, Alain

    2013-01-01

    Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects

  7. Variational principles for nonlinear piezoelectric materials

    Energy Technology Data Exchange (ETDEWEB)

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

    2004-12-01

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

  8. Cavity nonlinear optics with layered materials

    Directory of Open Access Journals (Sweden)

    Fryett Taylor

    2017-12-01

    Full Text Available Unprecedented material compatibility and ease of integration, in addition to the unique and diverse optoelectronic properties of layered materials, have generated significant interest in their utilization in nanophotonic devices. While initial nanophotonic experiments with layered materials primarily focused on light sources, modulators, and detectors, recent efforts have included nonlinear optical devices. In this paper, we review the current state of cavity-enhanced nonlinear optics with layered materials. Along with conventional nonlinear optics related to harmonic generation, we report on emerging directions of nonlinear optics, where layered materials can potentially play a significant role.

  9. A visco-hyperelastic constitutive model and its application in bovine tongue tissue.

    Science.gov (United States)

    Yousefi, Ali-Akbar Karkhaneh; Nazari, Mohammad Ali; Perrier, Pascal; Panahi, Masoud Shariat; Payan, Yohan

    2018-04-11

    Material properties of the human tongue tissue have a significant role in understanding its function in speech, respiration, suckling, and swallowing. Tongue as a combination of various muscles is surrounded by the mucous membrane and is a complicated architecture to study. As a first step before the quantitative mechanical characterization of human tongue tissues, the passive biomechanical properties in the superior longitudinal muscle (SLM) and the mucous tissues of a bovine tongue have been measured. Since the rate of loading has a sizeable contribution to the resultant stress of soft tissues, the rate dependent behavior of tongue tissues has been investigated via uniaxial tension tests (UTTs). A method to determine the mechanical properties of transversely isotropic tissues using UTTs and inverse finite element (FE) method has been proposed. Assuming the strain energy as a general nonlinear relationship with respect to the stretch and the rate of stretch, two visco-hyperelastic constitutive laws (CLs) have been proposed for isotropic and transversely isotropic soft tissues to model their stress-stretch behavior. Both of them have been implemented in ABAQUS explicit through coding a user-defined material subroutine called VUMAT and the experimental stress-stretch points have been well tracked by the results of FE analyses. It has been demonstrated that the proposed laws make a good description of the viscous nature of tongue tissues. Reliability of the proposed models has been compared with similar nonlinear visco-hyperelastic CLs. Copyright © 2018 Elsevier Ltd. All rights reserved.

  10. Modeling Non-Linear Material Properties in Composite Materials

    Science.gov (United States)

    2016-06-28

    Technical Report ARWSB-TR-16013 MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS Michael F. Macri Andrew G...REPORT TYPE Technical 3. DATES COVERED (From - To) 4. TITLE AND SUBTITLE MODELING NON-LINEAR MATERIAL PROPERTIES IN COMPOSITE MATERIALS ...systems are increasingly incorporating composite materials into their design. Many of these systems subject the composites to environmental conditions

  11. Probing hysteretic elasticity in weakly nonlinear materials

    Energy Technology Data Exchange (ETDEWEB)

    Johnson, Paul A [Los Alamos National Laboratory; Haupert, Sylvain [UPMC UNIV PARIS; Renaud, Guillaume [UPMC UNIV PARIS; Riviere, Jacques [UPMC UNIV PARIS; Talmant, Maryline [UPMC UNIV PARIS; Laugier, Pascal [UPMC UNIV PARIS

    2010-12-07

    Our work is aimed at assessing the elastic and dissipative hysteretic nonlinear parameters' repeatability (precision) using several classes of materials with weak, intermediate and high nonlinear properties. In this contribution, we describe an optimized Nonlinear Resonant Ultrasound Spectroscopy (NRUS) measuring and data processing protocol applied to small samples. The protocol is used to eliminate the effects of environmental condition changes that take place during an experiment, and that may mask the intrinsic elastic nonlinearity. As an example, in our experiments, we identified external temperature fluctuation as a primary source of material resonance frequency and elastic modulus variation. A variation of 0.1 C produced a frequency variation of 0.01 %, which is similar to the expected nonlinear frequency shift for weakly nonlinear materials. In order to eliminate environmental effects, the variation in f{sub 0} (the elastically linear resonance frequency proportional to modulus) is fit with the appropriate function, and that function is used to correct the NRUS calculation of nonlinear parameters. With our correction procedure, we measured relative resonant frequency shifts of 10{sup -5} , which are below 10{sup -4}, often considered the limit to NRUS sensitivity under common experimental conditions. Our results show that the procedure is an alternative to the stringent control of temperature often applied. Applying the approach, we report nonlinear parameters for several materials, some with very small nonclassical nonlinearity. The approach has broad application to NRUS and other Nonlinear Elastic Wave Spectroscopy approaches.

  12. Micromechanical model of lung parenchyma hyperelasticity

    Science.gov (United States)

    Concha, Felipe; Sarabia-Vallejos, Mauricio; Hurtado, Daniel E.

    2018-03-01

    Mechanics plays a key role in respiratory physiology, as lung tissue cyclically deforms to bring air in and out the lung, a life-long process necessary for respiration. The study of regional mechanisms of deformation in lung parenchyma has received great attention to date due to its clinical relevance, as local overstretching and stress concentration in lung tissue is currently associated to pathological conditions such as lung injury during mechanical ventilation therapy. This mechanical approach to lung physiology has motivated the development of constitutive models to better understand the relation between stress and deformation in the lung. While material models proposed to date have been key in the development of whole-lung simulations, either they do not directly relate microstructural properties of alveolar tissue with coarse-scale behavior, or they require a high computational effort when based on real alveolar geometries. Furthermore, most models proposed to date have not been thoroughly validated for anisotropic deformation states, which are commonly found in normal lungs in-vivo. In this work, we develop a novel micromechanical model of lung parenchyma hyperelasticity using the framework of finite-deformation homogenization. To this end, we consider a tetrakaidecahedron unit cell with incompressible Neo-Hookean structural elements that account for the alveolar wall tissue responsible for the elastic response, and derive expressions for its effective coarse-scale behavior that directly depend on the alveolar wall elasticity, reference porosity, and two other geometrical coefficients. To validate the proposed model, we simulate the non-linear elastic response of twelve representative volume elements (RVEs) of lung parenchyma with micrometric dimensions, whose geometry is obtained from micrometric computed-tomography reconstructions of murine lungs. We show that the proposed micromechanical model accurately captures the RVEs response not only for isotropic

  13. Dynamic nonlinear elasticity in geo materials

    International Nuclear Information System (INIS)

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

    2001-01-01

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

  14. Nonlinear materials for frequency conversion

    International Nuclear Information System (INIS)

    Velsko, S.P.; Eimerl, D.

    1988-01-01

    Two figures of merit, the threshold power (P/sub th/) and the limiting volume (V/sub min/) can be used to compare the relative efficiency and economy of new harmonic generating crystals. The properties of barium metaborate and L-Arginine phosphate are used to illustrate the effect of nonlinearity, birefringence, and damage threshold on these figures of merit

  15. Nonlinear constitutive relations for anisotropic elastic materials

    Science.gov (United States)

    Sokolova, Marina; Khristich, Dmitrii

    2018-03-01

    A general approach to constructing of nonlinear variants of connection between stresses and strains in anisotropic materials with different types of symmetry of properties is considered. This approach is based on the concept of elastic proper subspaces of anisotropic materials introduced in the mechanics of solids by J. Rychlewski and on the particular postulate of isotropy proposed by A. A. Il’yushin. The generalization of the particular postulate on the case of nonlinear anisotropic materials is formulated. Systems of invariants of deformations as lengths of projections of the strain vector into proper subspaces are developed. Some variants of nonlinear constitutive relations for anisotropic materials are offered. The analysis of these relations from the point of view of their satisfaction to general and limit forms of generalization of partial isotropy postulate on anisotropic materials is performed. The relations for particular cases of anisotropy are written.

  16. Nonlinear ultrasonics for material state awareness

    Science.gov (United States)

    Jacobs, L. J.

    2014-02-01

    Predictive health monitoring of structural components will require the development of advanced sensing techniques capable of providing quantitative information on the damage state of structural materials. By focusing on nonlinear acoustic techniques, it is possible to measure absolute, strength based material parameters that can then be coupled with uncertainty models to enable accurate and quantitative life prediction. Starting at the material level, this review will present current research that involves a combination of sensing techniques and physics-based models to characterize damage in metallic materials. In metals, these nonlinear ultrasonic measurements can sense material state, before the formation of micro- and macro-cracks. Typically, cracks of a measurable size appear quite late in a component's total life, while the material's integrity in terms of toughness and strength gradually decreases due to the microplasticity (dislocations) and associated change in the material's microstructure. This review focuses on second harmonic generation techniques. Since these nonlinear acoustic techniques are acoustic wave based, component interrogation can be performed with bulk, surface and guided waves using the same underlying material physics; these nonlinear ultrasonic techniques provide results which are independent of the wave type used. Recent physics-based models consider the evolution of damage due to dislocations, slip bands, interstitials, and precipitates in the lattice structure, which can lead to localized damage.

  17. Nonlinear optics of liquid crystalline materials

    International Nuclear Information System (INIS)

    Khoo, Iam Choon

    2009-01-01

    Liquid crystals occupy an important niche in nonlinear optics as a result of their unique physical and optical properties. Besides their broadband birefringence and transparency, abilities to self-assemble into various crystalline phases and to conform to various flexible forms and shapes, liquid crystals are compatible with almost all other optoelectronic materials and technology platforms. In both isotropic and ordered phases, liquid crystals possess extraordinarily large optical nonlinearities that stretch over multiple time scales. To date, almost all conceivable nonlinear optical phenomena have been observed in a very broad spectrum spanning the entire visible to infrared and beyond. In this review, we present a self-contained complete discussion of the optical nonlinearities of liquid crystals, and a thorough review of a wide range of nonlinear optical processes and phenomena enabled by these unique properties. Starting with a brief historical account of the development of nonlinear optical studies of the mesophases of liquid crystals, we then review various liquid crystalline materials and structures, and their nonlinear optical properties. Emphasis is placed on the nematic phase, which best exemplifies the dual nature of liquid crystals, although frequent references to other phases are also made. We also delve into recent work on novel structures such as photonic crystals, metamaterials and nanostructures and their special characteristics and emergent properties. The mechanisms and complex nonlocal dynamics of optical nonlinearities associated with laser induced director axis reorientation, thermal, density, and order parameter fluctuations, space charge field formation and photorefractivity are critically reviewed as a foundation for the discussions of various nonlinear optical processes detailed in this paper

  18. Stochastic hyperelastic constitutive laws and identification procedure for soft biological tissues with intrinsic variability.

    Science.gov (United States)

    Staber, B; Guilleminot, J

    2017-01-01

    In this work, we address the constitutive modeling, in a probabilistic framework, of the hyperelastic response of soft biological tissues. The aim is on the one hand to mimic the mean behavior and variability that are typically encountered in the experimental characterization of such materials, and on the other hand to derive mathematical models that are almost surely consistent with the theory of nonlinear elasticity. Towards this goal, we invoke information theory and discuss a stochastic model relying on a low-dimensional parametrization. We subsequently propose a two-step methodology allowing for the calibration of the model using standard data, such as mean and standard deviation values along a given loading path. The framework is finally applied and benchmarked on three experimental databases proposed elsewhere in the literature. It is shown that the stochastic model allows experiments to be accurately reproduced, regardless of the tissue under consideration. Copyright © 2016 Elsevier Ltd. All rights reserved.

  19. Nonlinearity in structural and electronic materials

    International Nuclear Information System (INIS)

    Bishop, A.R.; Beardmore, K.M.; Ben-Naim, E.

    1997-01-01

    This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project strengthens a nonlinear technology base relevant to a variety of problems arising in condensed matter and materials science, and applies this technology to those problems. In this way the controlled synthesis of, and experiments on, novel electronic and structural materials provide an important focus for nonlinear science, while nonlinear techniques help advance the understanding of the scientific principles underlying the control of microstructure and dynamics in complex materials. This research is primarily focused on four topics: (1) materials microstructure: growth and evolution, and porous media; (2) textures in elastic/martensitic materials; (3) electro- and photo-active polymers; and (4) ultrafast photophysics in complex electronic materials. Accomplishments included the following: organization of a ''Nonlinear Materials'' seminar series and international conferences including ''Fracture, Friction and Deformation,'' ''Nonequilibrium Phase Transitions,'' and ''Landscape Paradigms in Physics and Biology''; invited talks at international conference on ''Synthetic Metals,'' ''Quantum Phase Transitions,'' ''1996 CECAM Euroconference,'' and the 1995 Fall Meeting of the Materials Research Society; large-scale simulations and microscopic modeling of nonlinear coherent energy storage at crack tips and sliding interfaces; large-scale simulation and microscopic elasticity theory for precursor microstructure and dynamics at solid-solid diffusionless phase transformations; large-scale simulation of self-assembling organic thin films on inorganic substrates; analysis and simulation of smoothing of rough atomic surfaces; and modeling and analysis of flux pattern formation in equilibrium and nonequilibrium Josephson junction arrays and layered superconductors

  20. Elastomeric Structural Attachment Concepts for Aircraft Flap Noise Reduction - Challenges and Approaches to Hyperelastic Structural Modeling and Analysis

    Science.gov (United States)

    Sreekantamurthy, Thammaiah; Turner, Travis L.; Moore, James B.; Su, Ji

    2014-01-01

    Airframe noise is a significant part of the overall noise of transport aircraft during the approach and landing phases of flight. Airframe noise reduction is currently emphasized under the Environmentally Responsible Aviation (ERA) and Fixed Wing (FW) Project goals of NASA. A promising concept for trailing-edge-flap noise reduction is a flexible structural element or link that connects the side edges of the deployable flap to the adjacent main-wing structure. The proposed solution is distinguished by minimization of the span-wise extent of the structural link, thereby minimizing the aerodynamic load on the link structure at the expense of increased deformation requirement. Development of such a flexible structural link necessitated application of hyperelastic materials, atypical structural configurations and novel interface hardware. The resulting highly-deformable structural concept was termed the FLEXible Side Edge Link (FLEXSEL) concept. Prediction of atypical elastomeric deformation responses from detailed structural analysis was essential for evaluating feasible concepts that met the design constraints. The focus of this paper is to describe the many challenges encountered with hyperelastic finite element modeling and the nonlinear structural analysis of evolving FLEXSEL concepts. Detailed herein is the nonlinear analysis of FLEXSEL concepts that emerged during the project which include solid-section, foamcore, hollow, extended-span and pre-stressed concepts. Coupon-level analysis performed on elastomeric interface joints, which form a part of the FLEXSEL topology development, are also presented.

  1. A constrained reconstruction technique of hyperelasticity parameters for breast cancer assessment

    Energy Technology Data Exchange (ETDEWEB)

    Mehrabian, Hatef; Samani, Abbas [Department of Electrical and Computer Engineering, University of Western Ontario, London, ON (Canada); Campbell, Gordon, E-mail: asamani@uwo.c [Department of Medical Biophysics, University of Western Ontario, London, ON (Canada)

    2010-12-21

    In breast elastography, breast tissue usually undergoes large compression resulting in significant geometric and structural changes. This implies that breast elastography is associated with tissue nonlinear behavior. In this study, an elastography technique is presented and an inverse problem formulation is proposed to reconstruct parameters characterizing tissue hyperelasticity. Such parameters can potentially be used for tumor classification. This technique can also have other important clinical applications such as measuring normal tissue hyperelastic parameters in vivo. Such parameters are essential in planning and conducting computer-aided interventional procedures. The proposed parameter reconstruction technique uses a constrained iterative inversion; it can be viewed as an inverse problem. To solve this problem, we used a nonlinear finite element model corresponding to its forward problem. In this research, we applied Veronda-Westmann, Yeoh and polynomial models to model tissue hyperelasticity. To validate the proposed technique, we conducted studies involving numerical and tissue-mimicking phantoms. The numerical phantom consisted of a hemisphere connected to a cylinder, while we constructed the tissue-mimicking phantom from polyvinyl alcohol with freeze-thaw cycles that exhibits nonlinear mechanical behavior. Both phantoms consisted of three types of soft tissues which mimic adipose, fibroglandular tissue and a tumor. The results of the simulations and experiments show feasibility of accurate reconstruction of tumor tissue hyperelastic parameters using the proposed method. In the numerical phantom, all hyperelastic parameters corresponding to the three models were reconstructed with less than 2% error. With the tissue-mimicking phantom, we were able to reconstruct the ratio of the hyperelastic parameters reasonably accurately. Compared to the uniaxial test results, the average error of the ratios of the parameters reconstructed for inclusion to the middle

  2. A constrained reconstruction technique of hyperelasticity parameters for breast cancer assessment

    Science.gov (United States)

    Mehrabian, Hatef; Campbell, Gordon; Samani, Abbas

    2010-12-01

    In breast elastography, breast tissue usually undergoes large compression resulting in significant geometric and structural changes. This implies that breast elastography is associated with tissue nonlinear behavior. In this study, an elastography technique is presented and an inverse problem formulation is proposed to reconstruct parameters characterizing tissue hyperelasticity. Such parameters can potentially be used for tumor classification. This technique can also have other important clinical applications such as measuring normal tissue hyperelastic parameters in vivo. Such parameters are essential in planning and conducting computer-aided interventional procedures. The proposed parameter reconstruction technique uses a constrained iterative inversion; it can be viewed as an inverse problem. To solve this problem, we used a nonlinear finite element model corresponding to its forward problem. In this research, we applied Veronda-Westmann, Yeoh and polynomial models to model tissue hyperelasticity. To validate the proposed technique, we conducted studies involving numerical and tissue-mimicking phantoms. The numerical phantom consisted of a hemisphere connected to a cylinder, while we constructed the tissue-mimicking phantom from polyvinyl alcohol with freeze-thaw cycles that exhibits nonlinear mechanical behavior. Both phantoms consisted of three types of soft tissues which mimic adipose, fibroglandular tissue and a tumor. The results of the simulations and experiments show feasibility of accurate reconstruction of tumor tissue hyperelastic parameters using the proposed method. In the numerical phantom, all hyperelastic parameters corresponding to the three models were reconstructed with less than 2% error. With the tissue-mimicking phantom, we were able to reconstruct the ratio of the hyperelastic parameters reasonably accurately. Compared to the uniaxial test results, the average error of the ratios of the parameters reconstructed for inclusion to the middle

  3. Probabilistic analysis of a materially nonlinear structure

    Science.gov (United States)

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

    1990-01-01

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

  4. Nonlinear Optics with 2D Layered Materials.

    Science.gov (United States)

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

    2018-03-25

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

  5. Predicting the mixed-mode I/II spatial damage propagation along 3D-printed soft interfacial layer via a hyperelastic softening model

    Science.gov (United States)

    Liu, Lei; Li, Yaning

    2018-07-01

    A methodology was developed to use a hyperelastic softening model to predict the constitutive behavior and the spatial damage propagation of nonlinear materials with damage-induced softening under mixed-mode loading. A user subroutine (ABAQUS/VUMAT) was developed for numerical implementation of the model. 3D-printed wavy soft rubbery interfacial layer was used as a material system to verify and validate the methodology. The Arruda - Boyce hyperelastic model is incorporated with the softening model to capture the nonlinear pre-and post- damage behavior of the interfacial layer under mixed Mode I/II loads. To characterize model parameters of the 3D-printed rubbery interfacial layer, a series of scarf-joint specimens were designed, which enabled systematic variation of stress triaxiality via a single geometric parameter, the slant angle. It was found that the important model parameter m is exponentially related to the stress triaxiality. Compact tension specimens of the sinusoidal wavy interfacial layer with different waviness were designed and fabricated via multi-material 3D printing. Finite element (FE) simulations were conducted to predict the spatial damage propagation of the material within the wavy interfacial layer. Compact tension experiments were performed to verify the model prediction. The results show that the model developed is able to accurately predict the damage propagation of the 3D-printed rubbery interfacial layer under complicated stress-state without pre-defined failure criteria.

  6. A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements

    KAUST Repository

    Duddu, Ravindra

    2011-10-05

    We present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient. When modeling a nearly incompressible solid, the transport of the deformation gradient is decomposed into its isochoric part and the Jacobian determinant as independent fields. A homogeneous isotropic hyperelastic solid is assumed and B-splines-based finite elements are used for the spatial discretization. A variational multiscale residual-based approach is employed to stabilize the transport equations. The performance of the scheme is explored for both compressible and nearly incompressible applications. The numerical results are in good agreement with theory illustrating the viability of the computational scheme. © 2011 John Wiley & Sons, Ltd.

  7. The Quest for the Ultimate Nonlinear Optical Material

    Science.gov (United States)

    Dagenais, M.

    1990-10-01

    The following sections are included: * Introduction * From Infancy to the Real World * Highly Efficient Nonlinear Optical Materials for Switching and Processing * The Era of Pragmatism * Conclusion * References

  8. Design of advanced materials for linear and nonlinear dynamics

    DEFF Research Database (Denmark)

    Frandsen, Niels Morten Marslev

    to reveal the fundamental dynamic characteristics and thus the relevant design parameters.The thesis is built around the characterization of two one-dimensional, periodic material systems. The first is a nonlinear mass-spring chain with periodically varying material properties, representing a simple......The primary catalyst of this PhD project has been an ambition to design advanced materials and structural systems including, and possibly even exploiting, nonlinear phenomena such as nonlinear modal interaction leading to energy conversion between modes. An important prerequisite for efficient...... but general model of inhomogeneous structural materials with nonlinear material characteristics. The second material system is an “engineered” material in the sense that a classical structural element, a linear elastic and homogeneous rod, is “enhanced” by applying a mechanism on its surface, amplifying...

  9. Power laws and elastic nonlinearity in materials with complex microstructure

    Energy Technology Data Exchange (ETDEWEB)

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

    2016-01-28

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

  10. Nonlinear dynamic characterization of two-dimensional materials

    NARCIS (Netherlands)

    Davidovikj, D.; Alijani, F.; Cartamil Bueno, S.J.; van der Zant, H.S.J.; Amabili, M.; Steeneken, P.G.

    2017-01-01

    Owing to their atomic-scale thickness, the resonances of two-dimensional (2D) material membranes show signatures of nonlinearities at forces of only a few picoNewtons. Although the linear dynamics of membranes is well understood, the exact relation between the nonlinear response and the resonator's

  11. 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...

  12. Optimum shape design of incompressible hyperelastic structures with analytical sensitivity analysis

    International Nuclear Information System (INIS)

    Jarraya, A.; Wali, M.; Dammark, F.

    2014-01-01

    This paper is focused on the structural shape optimization of incompressible hyperelastic structures. An analytical sensitivity is developed for the rubber like materials. The whole shape optimization process is carried out by coupling a closed geometric shape in R 2 with boundaries, defined by B-splines curves, exact sensitivity analysis and mathematical programming method (S.Q.P: sequential quadratic programming). Design variables are the control points coordinate. The objective function is to minimize Von-Mises stress, constrained to the total material volume of the structure remains constant. In order to validate the exact Jacobian method, the sensitivity calculation is performed: numerically by an efficient finite difference scheme and by the exact Jacobian method. Numerical optimization examples are presented for elastic and hyperelastic materials using the proposed method.

  13. New organic materials for optics: optical storage and nonlinear optics

    International Nuclear Information System (INIS)

    Gan, F.

    1996-01-01

    New organic materials have received considerable attention recently, due to their easy preparation and different variety. The most application fields in optics are optical storage and nonlinear optics. In optical storage the organic dyes have been used for example, in record able and erasable compact disks (CD-R, CD-E) nonlinear optical effects, such as nonlinear optical absorption, second and third order optical absorption, second and third order optical nonlinearities, can be applied for making optical limiters, optical modulators, as well as laser second and third harmonic generations. Due to high value of optical absorption and optical nonlinearity organic materials are always used as thin films in optical integration. In this paper the new experimental results have been presented, and future development has been also discussed. (author)

  14. Energy nonlinearity in radiation detection materials: Causes and consequences

    International Nuclear Information System (INIS)

    Jaffe, J.E.; Jordan, D.V.; Peurrung, A.J.

    2007-01-01

    The phenomenology and present theoretical understanding of energy nonlinearity (nonproportionality) in radiation detection materials is reviewed, with emphasis on gamma-ray spectroscopy. Scintillators display varying degrees and patterns of nonlinearity, while semiconductor detectors are extremely linear, and gas detectors show a characteristic form of nonproportionality associated with core levels. The relation between nonlinear response (to both primary particles and secondary electrons) and spectrometer resolution is also discussed. We review the qualitative ideas about the origin of nonlinearity in scintillators that have been proposed to date, with emphasis on transport and recombination of electronic excitations. Recent computational and experimental work on the basic physics of scintillators is leading towards a better understanding of energy nonlinearity and should result in new, more linear scintillator materials in the near future

  15. Time history nonlinear earthquake response analysis considering materials and geometrical nonlinearity

    International Nuclear Information System (INIS)

    Kobayashi, T.; Yoshikawa, K.; Takaoka, E.; Nakazawa, M.; Shikama, Y.

    2002-01-01

    A time history nonlinear earthquake response analysis method was proposed and applied to earthquake response prediction analysis for a Large Scale Seismic Test (LSST) Program in Hualien, Taiwan, in which a 1/4 scale model of a nuclear reactor containment structure was constructed on sandy gravel layer. In the analysis both of strain-dependent material nonlinearity, and geometrical nonlinearity by base mat uplift, were considered. The 'Lattice Model' for the soil-structure interaction model was employed. An earthquake record on soil surface at the site was used as control motion, and deconvoluted to the input motion of the analysis model at GL-52 m with 300 Gal of maximum acceleration. The following two analyses were considered: (A) time history nonlinear, (B) equivalent linear, and the advantage of time history nonlinear earthquake response analysis method is discussed

  16. Measurement of the hyperelastic properties of 44 pathological ex vivo breast tissue samples

    International Nuclear Information System (INIS)

    O'Hagan, Joseph J; Samani, Abbas

    2009-01-01

    The elastic and hyperelastic properties of biological soft tissues have been of interest to the medical community. There are several biomedical applications where parameters characterizing such properties are critical for a reliable clinical outcome. These applications include surgery planning, needle biopsy and brachtherapy where tissue biomechanical modeling is involved. Another important application is interpreting nonlinear elastography images. While there has been considerable research on the measurement of the linear elastic modulus of small tissue samples, little research has been conducted for measuring parameters that characterize the nonlinear elasticity of tissues included in tissue slice specimens. This work presents hyperelastic measurement results of 44 pathological ex vivo breast tissue samples. For each sample, five hyperelastic models have been used, including the Yeoh, N = 2 polynomial, N = 1 Ogden, Arruda-Boyce, and Veronda-Westmann models. Results show that the Yeoh, polynomial and Ogden models are the most accurate in terms of fitting experimental data. The results indicate that almost all of the parameters corresponding to the pathological tissues are between two times to over two orders of magnitude larger than those of normal tissues, with C 11 showing the most significant difference. Furthermore, statistical analysis indicates that C 02 of the Yeoh model, and C 11 and C 20 of the polynomial model have very good potential for cancer classification as they show statistically significant differences for various cancer types, especially for invasive lobular carcinoma. In addition to the potential for use in cancer classification, the presented data are very important for applications such as surgery planning and virtual reality based clinician training systems where accurate nonlinear tissue response modeling is required.

  17. Measurement of the hyperelastic properties of 44 pathological ex vivo breast tissue samples

    Energy Technology Data Exchange (ETDEWEB)

    O' Hagan, Joseph J; Samani, Abbas [Department of Electrical and Computer Engineering, University of Western Ontario, London, ON (Canada)], E-mail: asamani@uwo.ca

    2009-04-21

    The elastic and hyperelastic properties of biological soft tissues have been of interest to the medical community. There are several biomedical applications where parameters characterizing such properties are critical for a reliable clinical outcome. These applications include surgery planning, needle biopsy and brachtherapy where tissue biomechanical modeling is involved. Another important application is interpreting nonlinear elastography images. While there has been considerable research on the measurement of the linear elastic modulus of small tissue samples, little research has been conducted for measuring parameters that characterize the nonlinear elasticity of tissues included in tissue slice specimens. This work presents hyperelastic measurement results of 44 pathological ex vivo breast tissue samples. For each sample, five hyperelastic models have been used, including the Yeoh, N = 2 polynomial, N = 1 Ogden, Arruda-Boyce, and Veronda-Westmann models. Results show that the Yeoh, polynomial and Ogden models are the most accurate in terms of fitting experimental data. The results indicate that almost all of the parameters corresponding to the pathological tissues are between two times to over two orders of magnitude larger than those of normal tissues, with C{sub 11} showing the most significant difference. Furthermore, statistical analysis indicates that C{sub 02} of the Yeoh model, and C{sub 11} and C{sub 20} of the polynomial model have very good potential for cancer classification as they show statistically significant differences for various cancer types, especially for invasive lobular carcinoma. In addition to the potential for use in cancer classification, the presented data are very important for applications such as surgery planning and virtual reality based clinician training systems where accurate nonlinear tissue response modeling is required.

  18. Measurement of the hyperelastic properties of 44 pathological ex vivo breast tissue samples

    Science.gov (United States)

    O'Hagan, Joseph J.; Samani, Abbas

    2009-04-01

    The elastic and hyperelastic properties of biological soft tissues have been of interest to the medical community. There are several biomedical applications where parameters characterizing such properties are critical for a reliable clinical outcome. These applications include surgery planning, needle biopsy and brachtherapy where tissue biomechanical modeling is involved. Another important application is interpreting nonlinear elastography images. While there has been considerable research on the measurement of the linear elastic modulus of small tissue samples, little research has been conducted for measuring parameters that characterize the nonlinear elasticity of tissues included in tissue slice specimens. This work presents hyperelastic measurement results of 44 pathological ex vivo breast tissue samples. For each sample, five hyperelastic models have been used, including the Yeoh, N = 2 polynomial, N = 1 Ogden, Arruda-Boyce, and Veronda-Westmann models. Results show that the Yeoh, polynomial and Ogden models are the most accurate in terms of fitting experimental data. The results indicate that almost all of the parameters corresponding to the pathological tissues are between two times to over two orders of magnitude larger than those of normal tissues, with C11 showing the most significant difference. Furthermore, statistical analysis indicates that C02 of the Yeoh model, and C11 and C20 of the polynomial model have very good potential for cancer classification as they show statistically significant differences for various cancer types, especially for invasive lobular carcinoma. In addition to the potential for use in cancer classification, the presented data are very important for applications such as surgery planning and virtual reality based clinician training systems where accurate nonlinear tissue response modeling is required.

  19. Waves in nonlinear pre-stressed materials

    CERN Document Server

    Schneider, Wilhelm; Saccomandi, G

    2007-01-01

    The papers in this book provide a unique state-of-the-art multidisciplinary overview on the subject of waves in pre-stressed materials through the interaction of several topics, ranging from the mathematical modelling of incremental material response (elastic and inelastic), to the analysis of the governing differential equations and boundary-value problems, and to computational methods for the solution to these problems, with particular reference to industrial, geophysical, and biomechanical applications. A complete view on the title subject is proposed, including: The basic and fundamental theoretical issues (mechanical modelling, exact solutions, asymptotic methods, numerical treatment); A unified introduction to wave propagation (small on large and large on large); A look toward classical (such as geophysics and the mechanics of rubber-like solids) and emergent (such as biomechanics) applications.

  20. Materials for Nonlinear Optics Chemical Perspectives

    Science.gov (United States)

    1991-01-01

    potassium iodide for 15 h at reflux. The benzaldehyde product was then allowed to react with diethyl(4-nitrobenzyl)phosphonate in the presence of ...photocrosslinking of NLO-inactive polyacrylate monomers. Recent advances in optical technology have created great interest in the construction of second-order...might be potassium niobate.) Because of this, the value of finding an "improved" material can be accurately gauged in a relative sense, and compared to

  1. Detection of electromagnetic radiation using nonlinear materials

    Science.gov (United States)

    Hwang, Harold Y.; Liu, Mengkun; Averitt, Richard D.; Nelson, Keith A.; Sternbach, Aaron; Fan, Kebin

    2016-06-14

    An apparatus for detecting electromagnetic radiation within a target frequency range is provided. The apparatus includes a substrate and one or more resonator structures disposed on the substrate. The substrate can be a dielectric or semiconductor material. Each of the one or more resonator structures has at least one dimension that is less than the wavelength of target electromagnetic radiation within the target frequency range, and each of the resonator structures includes at least two conductive structures separated by a spacing. Charge carriers are induced in the substrate near the spacing when the resonator structures are exposed to the target electromagnetic radiation. A measure of the change in conductivity of the substrate due to the induced charge carriers provides an indication of the presence of the target electromagnetic radiation.

  2. Nonlinear Ballistic Transport in an Atomically Thin Material.

    Science.gov (United States)

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

    2016-01-26

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

  3. Linearity and Non-linearity of Photorefractive effect in Materials ...

    African Journals Online (AJOL)

    Linearity and Non-linearity of Photorefractive effect in Materials using the Band transport ... For low light beam intensities the change in the refractive index is ... field is spatially phase shifted by /2 relative to the interference fringe pattern, which ...

  4. Linearity and Non-linearity of Photorefractive effect in Materials ...

    African Journals Online (AJOL)

    In this paper we have studied the Linearity and Non-linearity of Photorefractive effect in materials using the band transport model. For low light beam intensities the change in the refractive index is proportional to the electric field for linear optics while for non- linear optics the change in refractive index is directly proportional ...

  5. Eddy current modeling in linear and nonlinear multifilamentary composite materials

    Science.gov (United States)

    Menana, Hocine; Farhat, Mohamad; Hinaje, Melika; Berger, Kevin; Douine, Bruno; Lévêque, Jean

    2018-04-01

    In this work, a numerical model is developed for a rapid computation of eddy currents in composite materials, adaptable for both carbon fiber reinforced polymers (CFRPs) for NDT applications and multifilamentary high temperature superconductive (HTS) tapes for AC loss evaluation. The proposed model is based on an integro-differential formulation in terms of the electric vector potential in the frequency domain. The high anisotropy and the nonlinearity of the considered materials are easily handled in the frequency domain.

  6. Composite Beam Theory with Material Nonlinearities and Progressive Damage

    Science.gov (United States)

    Jiang, Fang

    Beam has historically found its broad applications. Nowadays, many engineering constructions still rely on this type of structure which could be made of anisotropic and heterogeneous materials. These applications motivate the development of beam theory in which the impact of material nonlinearities and damage on the global constitutive behavior has been a focus in recent years. Reliable predictions of these nonlinear beam responses depend on not only the quality of the material description but also a comprehensively generalized multiscale methodology which fills the theoretical gaps between the scales in an efficient yet high-fidelity manner. The conventional beam modeling methodologies which are built upon ad hoc assumptions are in lack of such reliability in need. Therefore, the focus of this dissertation is to create a reliable yet efficient method and the corresponding tool for composite beam modeling. A nonlinear beam theory is developed based on the Mechanics of Structure Genome (MSG) using the variational asymptotic method (VAM). The three-dimensional (3D) nonlinear continuum problem is rigorously reduced to a one-dimensional (1D) beam model and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities by exploiting the small geometric parameter which is an inherent geometric characteristic of the beam. The 2D nonlinear cross-sectional analysis utilizes the 3D material models to homogenize the beam cross-sectional constitutive responses considering the nonlinear elasticity and progressive damage. The results from such a homogenization are inputs as constitutive laws into the global nonlinear 1D beam analysis. The theoretical foundation is formulated without unnecessary kinematic assumptions. Curvilinear coordinates and vector calculus are utilized to build the 3D deformation gradient tensor, of which the components are formulated in terms of cross-sectional coordinates, generalized beam strains, unknown warping

  7. The chemistry and physics of nonlinear optical materials

    International Nuclear Information System (INIS)

    Velsko, S.P.; Eimerl, D.

    1989-01-01

    Recent efforts to engineer new nonlinear optical materials with specific desired characteristics has engendered a need for a theoretical description of optical properties which is readily accessible to chemists, yet correctly treats the essential physics of dielectric response. This paper describes a simple empirical molecular orbital model which gives useful insights into the relationship between chemical composition, crystalline structure, and optical susceptibilities. The authors compare the probabilities of finding new harmonic generators in various chemical classes. Rigorous bounds on the magnitudes of linear and nonlinear optical coefficients and their anisotropies are also discussed

  8. Nonlinear Wave Mixing Technique for Nondestructive Assessment of Infrastructure Materials

    Science.gov (United States)

    Ju, Taeho

    To operate safely, structures and components need to be inspected or monitored either periodically or in real time for potential failure. For this purpose, ultrasonic nondestructive evaluation (NDE) techniques have been used extensively. Most of these ultrasonic NDE techniques utilize only the linear behavior of the ultrasound. These linear techniques are effective in detecting discontinuities in materials such as cracks, voids, interfaces, inclusions, etc. However, in many engineering materials, it is the accumulation of microdamage that leads to degradation and eventual failure of a component. Unfortunately, it is difficult for linear ultrasonic NDE techniques to characterize or quantify such damage. On the other hand, the acoustic nonlinearity parameter (ANLP) of a material is often positively correlated with such damage in a material. Thus, nonlinear ultrasonic NDE methods have been used in recently years to characterize cumulative damage such as fatigue in metallic materials, aging in polymeric materials, and degradation of cement-based materials due to chemical reactions. In this thesis, we focus on developing a suit of novel nonlinear ultrasonic NDE techniques based on the interactions of nonlinear ultrasonic waves, namely wave mixing. First, a noncollinear wave mixing technique is developed to detect localized damage in a homogeneous material by using a pair of noncollinear a longitudinal wave (L-wave) and a shear wave (S-wave). This pair of incident waves make it possible to conduct NDE from a single side of the component, a condition that is often encountered in practical applications. The proposed noncollinear wave mixing technique is verified experimentally by carrying out measurements on aluminum alloy (AA 6061) samples. Numerical simulations using the Finite Element Method (FEM) are also conducted to further demonstrate the potential of the proposed technique to detect localized damage in structural components. Second, the aforementioned nonlinear

  9. Error estimation and adaptivity for incompressible hyperelasticity

    KAUST Repository

    Whiteley, J.P.; Tavener, S.J.

    2014-01-01

    SUMMARY: A Galerkin FEM is developed for nonlinear, incompressible (hyper) elasticity that takes account of nonlinearities in both the strain tensor and the relationship between the strain tensor and the stress tensor. By using suitably defined

  10. Studies of nonlinear femtosecond pulse propagation in bulk materials

    Science.gov (United States)

    Eaton, Hilary Kaye

    2000-10-01

    Femtosecond pulse lasers are finding widespread application in a variety of fields including medical research, optical switching and communications, plasma formation, high harmonic generation, and wavepacket formation and control. As the number of applications for femtosecond pulses increases, so does the need to fully understand the linear and nonlinear processes involved in propagating these pulses through materials under various conditions. Recent advances in pulse measurement techniques, such as frequency-resolved optical gating (FROG), allow measurement of the full electric field of the pulse and have made detailed investigations of short- pulse propagation effects feasible. In this thesis, I present detailed experimental studies of my work involving nonlinear propagation of femtosecond pulses in bulk media. Studies of plane-wave propagation in fused silica extend the SHG form of FROG from a simple pulse diagnostic to a useful method of interrogating the nonlinear response of a material. Studies of nonlinear propagation are also performed in a regime where temporal pulse splitting occurs. Experimental results are compared with a three- dimensional nonlinear Schrödinger equation. This comparison fuels the development of a more complete model for pulse splitting. Experiments are also performed at peak input powers above those at which pulse splitting is observed. At these higher intensities, a broadband continuum is generated. This work presents a detailed study of continuum behavior and power loss as well as the first near-field spatial- spectral measurements of the generated continuum light. Nonlinear plane-wave propagation of short pulses in liquids is also investigated, and a non-instantaneous nonlinearity with a surprisingly short response time of 10 fs is observed in methanol. Experiments in water confirm that this effect in methanol is indeed real. Possible explanations for the observed effect are discussed and several are experimentally rejected. This

  11. Nonlinear Optics: Materials, Fundamentals, and Applications. Postdeadline papers

    Science.gov (United States)

    1992-08-01

    The Nonlinear Optics: Materials, Fundamentals, and Applications conference was held on 17-21 Aug. 1992. The following topics were addressed: subpicosecond time resolved four-wave mixing spectroscopy in heteroepitaxial ZnSe thin layers; anisotropic two-photon transition in GaAs/AlGaAs multiple quantum well waveguides; two picosecond, narrow-band, tunable, optical parametric systems using BBO and LBO; second generation in an optically active liquid: experimental observation of a fourth-order optical nonlinearity due to molecular chirality; optical image recognition system implemented with a 3-D memory disk; phase-matched second-harmonic generation in waveguides of polymeric Langmuir-Blodgett films; fluence dependent dynamics observed in the resonant third-order optical response of C60 and C70 films; temporal modulation of spatial optical solitons: a variational approach; measurements of light-scattering noise during two-wave mixing in a Kerr medium; excess noise introduced by beam propagation through an atomic vapor; an approach to all-optical switching based on second-order nonlinearities; multilayer, nonlinear ARROW waveguides for surface emitted sum-frequency mixing; energy scaling of SBS phase conjugate mirrors to 4J; vector versus scalar theory for the double phase conjugate mirror; cross-talk and error probability in counter-beam lambda-multiplexed digital holograms; and modal growth of SHG in doped silica thin film waveguides.

  12. Modal analysis of graphene-based structures for large deformations, contact and material nonlinearities

    Science.gov (United States)

    Ghaffari, Reza; Sauer, Roger A.

    2018-06-01

    The nonlinear frequencies of pre-stressed graphene-based structures, such as flat graphene sheets and carbon nanotubes, are calculated. These structures are modeled with a nonlinear hyperelastic shell model. The model is calibrated with quantum mechanics data and is valid for high strains. Analytical solutions of the natural frequencies of various plates are obtained for the Canham bending model by assuming infinitesimal strains. These solutions are used for the verification of the numerical results. The performance of the model is illustrated by means of several examples. Modal analysis is performed for square plates under pure dilatation or uniaxial stretch, circular plates under pure dilatation or under the effects of an adhesive substrate, and carbon nanotubes under uniaxial compression or stretch. The adhesive substrate is modeled with van der Waals interaction (based on the Lennard-Jones potential) and a coarse grained contact model. It is shown that the analytical natural frequencies underestimate the real ones, and this should be considered in the design of devices based on graphene structures.

  13. Frequency Response of Synthetic Vocal Fold Models with Linear and Nonlinear Material Properties

    Science.gov (United States)

    Shaw, Stephanie M.; Thomson, Scott L.; Dromey, Christopher; Smith, Simeon

    2012-01-01

    Purpose: The purpose of this study was to create synthetic vocal fold models with nonlinear stress-strain properties and to investigate the effect of linear versus nonlinear material properties on fundamental frequency (F[subscript 0]) during anterior-posterior stretching. Method: Three materially linear and 3 materially nonlinear models were…

  14. Nonlinear analysis of the GFRP material wheel hub

    Directory of Open Access Journals (Sweden)

    Dong Yun-Feng

    2015-01-01

    Full Text Available In this paper, the current bicycle wheel was replaced by the ones which composed by the wheel hub with Glassfiber Reinforced Plastic (alkali free thin-walled cylinder material, hereinafter referred to as GFRP material and the protective components made up of rubber outer pneumatic pad. With the help of the basic theory of elastic-plastic mechanics, the finite element “Nonlinear buckling” analysis of the wheel was carried out. The results show that the maximum elastic deformation of the wheel hub and the critical value of buckling failure load were restricted by the elasticity under the condition of external loads. Considering with the tensile strength and elastic modulus of the GFRP value of the material, it is demonstrated that the material is feasible to be used for wheel hub.

  15. Nonlinear phononics and structural control of strongly correlated materials

    Energy Technology Data Exchange (ETDEWEB)

    Mankowsky, Roman

    2016-01-20

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

  16. Design and optimization of carbon-nanotube-material/dielectric hybrid nonlinear optical waveguides

    International Nuclear Information System (INIS)

    Zhao, Xin; Zheng, Zheng; Lu, Zhiting; Zhu, Jinsong; Zhou, Tao

    2011-01-01

    The nonlinear optical characteristics of highly nonlinear waveguides utilizing carbon nanotube composite materials are investigated theoretically. The extremely high nonlinearity and relatively high loss of the carbon nanotube materials are shown to greatly affect the performance of such waveguides for nonlinear optical applications, in contrast to waveguides using conventional nonlinear materials. Different configurations based on applying the carbon nanotube materials to the popular ridge and buried waveguides are thoroughly studied, and the optimal geometries are derived through simulations. It is shown that, though the nonlinear coefficient is often huge for these waveguides, the loss characteristics can significantly limit the maximum achievable accumulated nonlinearity, e.g. the maximum nonlinear phase shift. Our results suggest that SOI-based high-index-contrast, carbon nanotube cladding waveguides, rather than the currently demonstrated low-contrast waveguides, could hold the promise of achieving significantly higher accumulated nonlinearity

  17. Closed form solution for the finite anti-plane shear field for a class of hyperelastic incompressible brittle solids

    Science.gov (United States)

    Stolz, Claude

    2010-12-01

    The equilibrium solution of a damaged zone in finite elasticity is given for a class of hyperelastic materials which does not suffer tension when a critical stretching value is reached. The study is made for a crack in anti-plane shear loading condition. The prescribed loading is that of linearized elastostatics conditions at infinity. The geometry of the damaged zone is found and the stationary propagation is discussed when the inertia terms can be neglected.

  18. Structure/property relationships in non-linear optical materials

    Energy Technology Data Exchange (ETDEWEB)

    Cole, J M [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France); [Durham Univ. (United Kingdom); Howard, J A.K. [Durham Univ. (United Kingdom); McIntyre, G J [Institut Max von Laue - Paul Langevin (ILL), 38 - Grenoble (France)

    1997-04-01

    The application of neutrons to the study of structure/property relationships in organic non-linear optical materials (NLOs) is described. In particular, charge-transfer effects and intermolecular interactions are investigated. Charge-transfer effects are studied by charge-density analysis and an example of one such investigation is given. The study of intermolecular interactions concentrates on the effects of hydrogen-bonding and an example is given of two structurally similar molecules with very disparate NLO properties, as a result of different types of hydrogen-bonding. (author). 3 refs.

  19. 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...

  20. Error estimation and adaptivity for incompressible hyperelasticity

    KAUST Repository

    Whiteley, J.P.

    2014-04-30

    SUMMARY: A Galerkin FEM is developed for nonlinear, incompressible (hyper) elasticity that takes account of nonlinearities in both the strain tensor and the relationship between the strain tensor and the stress tensor. By using suitably defined linearised dual problems with appropriate boundary conditions, a posteriori error estimates are then derived for both linear functionals of the solution and linear functionals of the stress on a boundary, where Dirichlet boundary conditions are applied. A second, higher order method for calculating a linear functional of the stress on a Dirichlet boundary is also presented together with an a posteriori error estimator for this approach. An implementation for a 2D model problem with known solution, where the entries of the strain tensor exhibit large, rapid variations, demonstrates the accuracy and sharpness of the error estimators. Finally, using a selection of model problems, the a posteriori error estimate is shown to provide a basis for effective mesh adaptivity. © 2014 John Wiley & Sons, Ltd.

  1. Heteroepitaxy of orientation-patterned nonlinear optical materials

    Science.gov (United States)

    Tassev, Vladimir L.; Vangala, Shivashankar R.; Peterson, Rita D.; Snure, Michael

    2018-03-01

    We report some recent results on thick heteroepitaxial growth of GaP on GaAs substrates and on orientation-patterned (OP) GaAs templates conducted in a hot-wall horizontal quartz reactor for Hydride Vapor Phase Epitaxy. The growths on the plain substrates resulted in up to 500 μm thick GaP with smooth surface morphology (RMS following stages of growth, as well on the mechanisms of the strain relaxation from the lattice and thermal mismatch between layer and substrate. The efforts to accommodate the growing film to the foreign substrate by engineering an intermediate buffer layer were extended to thick growths of GaAsxP1-x ternary with the idea to combine in one material the best of the nonlinear properties of GaP and GaAs that are strictly relevant to the pursued applications.

  2. Nonlinear electroelasticity: material properties, continuum theory and applications.

    Science.gov (United States)

    Dorfmann, Luis; Ogden, Ray W

    2017-08-01

    In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

  3. Nonlinear electroelasticity: material properties, continuum theory and applications

    Science.gov (United States)

    Dorfmann, Luis; Ogden, Ray W.

    2017-08-01

    In the last few years, it has been recognized that the large deformation capacity of elastomeric materials that are sensitive to electric fields can be harnessed for use in transducer devices such as actuators and sensors. This has led to the reassessment of the mathematical theory that is needed for the description of the electromechanical (in particular, electroelastic) interactions for purposes of material characterization and prediction. After a review of the key experiments concerned with determining the nature of the electromechanical interactions and a discussion of the range of applications to devices, we provide a short account of the history of developments in the nonlinear theory. This is followed by a succinct modern treatment of electroelastic theory, including the governing equations and constitutive laws needed for both material characterization and the analysis of general electroelastic coupling problems. For illustration, the theory is then applied to two simple representative boundary-value problems that are relevant to the geometries of activation devices; in particular, (a) a rectangular plate and (b) a circular cylindrical tube, in each case with compliant electrodes on the major surfaces and a potential difference between them. In (a), an electric field is generated normal to the major surfaces and in (b), a radial electric field is present. This is followed by a short section in which other problems addressed on the basis of the general theory are described briefly.

  4. Nonlinear machine learning in soft materials engineering and design

    Science.gov (United States)

    Ferguson, Andrew

    The inherently many-body nature of molecular folding and colloidal self-assembly makes it challenging to identify the underlying collective mechanisms and pathways governing system behavior, and has hindered rational design of soft materials with desired structure and function. Fundamentally, there exists a predictive gulf between the architecture and chemistry of individual molecules or colloids and the collective many-body thermodynamics and kinetics. Integrating machine learning techniques with statistical thermodynamics provides a means to bridge this divide and identify emergent folding pathways and self-assembly mechanisms from computer simulations or experimental particle tracking data. We will survey a few of our applications of this framework that illustrate the value of nonlinear machine learning in understanding and engineering soft materials: the non-equilibrium self-assembly of Janus colloids into pinwheels, clusters, and archipelagos; engineering reconfigurable ''digital colloids'' as a novel high-density information storage substrate; probing hierarchically self-assembling onjugated asphaltenes in crude oil; and determining macromolecular folding funnels from measurements of single experimental observables. We close with an outlook on the future of machine learning in soft materials engineering, and share some personal perspectives on working at this disciplinary intersection. We acknowledge support for this work from a National Science Foundation CAREER Award (Grant No. DMR-1350008) and the Donors of the American Chemical Society Petroleum Research Fund (ACS PRF #54240-DNI6).

  5. On the dual variable of the Cauchy stress tensor in isotropic finite hyperelasticity

    Science.gov (United States)

    Vallée, Claude; Fortuné, Danielle; Lerintiu, Camelia

    2008-11-01

    Elastic materials are governed by a constitutive law relating the second Piola-Kirchhoff stress tensor Σ and the right Cauchy-Green strain tensor C=FF. Isotropic elastic materials are the special cases for which the Cauchy stress tensor σ depends solely on the left Cauchy-Green strain tensor B=FF. In this Note we revisit the following property of isotropic hyperelastic materials: if the constitutive law relating Σ and C is derivable from a potential ϕ, then σ and lnB are related by a constitutive law derived from the compound potential ϕ○exp. We give a new and concise proof which is based on an explicit integral formula expressing the derivative of the exponential of a tensor. To cite this article: C. Vallée et al., C. R. Mecanique 336 (2008).

  6. A nonlinear CDM based damage growth law for ductile materials

    Science.gov (United States)

    Gautam, Abhinav; Priya Ajit, K.; Sarkar, Prabir Kumar

    2018-02-01

    A nonlinear ductile damage growth criterion is proposed based on continuum damage mechanics (CDM) approach. The model is derived in the framework of thermodynamically consistent CDM assuming damage to be isotropic. In this study, the damage dissipation potential is also derived to be a function of varying strain hardening exponent in addition to damage strain energy release rate density. Uniaxial tensile tests and load-unload-cyclic tensile tests for AISI 1020 steel, AISI 1030 steel and Al 2024 aluminum alloy are considered for the determination of their respective damage variable D and other parameters required for the model(s). The experimental results are very closely predicted, with a deviation of 0%-3%, by the proposed model for each of the materials. The model is also tested with predictabilities of damage growth by other models in the literature. Present model detects the state of damage quantitatively at any level of plastic strain and uses simpler material tests to find the parameters of the model. So, it should be useful in metal forming industries to assess the damage growth for the desired deformation level a priori. The superiority of the new model is clarified by the deviations in the predictability of test results by other models.

  7. Research of carbon composite material for nonlinear finite element method

    Science.gov (United States)

    Kim, Jung Ho; Garg, Mohit; Kim, Ji Hoon

    2012-04-01

    Works on the absorption of collision energy in the structural members are carried out widely with various material and cross-sections. And, with ever increasing safety concerns, they are presently applied in various fields including railroad trains, air crafts and automobiles. In addition to this, problem of lighting structural members became important subject by control of exhaust gas emission, fuel economy and energy efficiency. CFRP(Carbon Fiber Reinforced Plastics) usually is applying the two primary structural members because of different result each design parameter as like stacking thickness, stacking angle, moisture absorption ect. We have to secure the data for applying primary structural members. But it always happens to test design parameters each for securing the data. So, it has much more money and time. We can reduce the money and the time, if can ensure the CFRP material properties each design parameters. In this study, we experiment the coupon test each tension, compression and shear using CFRP prepreg sheet and simulate non-linear analyze at the sources - test result, Caron longitudinal modulus and matrix poisson's ratio using GENOAMQC is specialized at Composite analysis. And then we predict the result that specimen manufacture changing stacking angle and experiment in such a way of test method using GENOA-MCQ.

  8. The application of nonlinear dynamics in the study of ferroelectric materials

    International Nuclear Information System (INIS)

    Blochwitz, S.; Habel, R.; Diestelhorst, M.; Beige, H.

    1996-01-01

    It is well known that the structural phase transitions in ferroelectric materials are connected with strong nonlinear properties. So we can expect all features of nonlinear dynamical systems such as period-doubling cascades and chaos in a dynamical system that contains ferroelectric materials. Therefore we can apply nonlinear dynamics to these ferroelectric materials and we are doing it in two directions: (i) We study the structural phase transitions by analyzing the large signal behaviour with means of nonlinear dynamics. (ii) We control the chaotic behaviour of the system with the method proposed by Ott, Grebogi and Yorke. (authors)

  9. Thermally Stable Heterocyclic Imines as New Potential Nonlinear Optical Materials

    Science.gov (United States)

    Nesterov, Volodymyr V.; Antipin, Mikhail Y.; Nesterov, Vladimir N.; Moore, Craig E.; Cardelino, Beatriz H.; Timofeeva, Tatiana V.

    2004-01-01

    In the course of a search for new thermostable acentric nonlinear optical crystalline materials, several heterocyclic imine derivatives were designed, with the general structure D-pi-A(D'). Introduction of a donor amino group (D') into the acceptor moiety was expected to bring H-bonds into their crystal structures, and so to elevate their melting points and assist in an acentric molecular packing. Six heterocycle-containing compounds of this type were prepared, single crystals were grown for five of them, and these crystals were characterized by X-ray analysis. A significant melting temperature elevation was found for all of the synthesized compounds. Three of the compounds were also found to crystallize in acentric space groups. One of the acentric compounds is built as a three-dimensional H-bonded molecular network. In the other two compounds, with very similar molecular structure, the molecules form one-dimensional H-bonded head-to-head associates (chains). These chains are parallel in two different crystallographic directions and form very unusual interpenetrating chain patterns in an acentric crystal. Two of the compounds crystallized with centrosymmetric molecular packing.

  10. Computational Modeling of Ultrafast Pulse Propagation in Nonlinear Optical Materials

    Science.gov (United States)

    Goorjian, Peter M.; Agrawal, Govind P.; Kwak, Dochan (Technical Monitor)

    1996-01-01

    There is an emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. rib build such devices and subsystems, one needs to model the entire chip. Accurate computer modeling of electromagnetic wave propagation in semiconductors is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Here, the computer simulations are made by solving the full vector, nonlinear, Maxwell's equations, coupled with the semiconductor Bloch equations, without any approximations. The carrier is retained in the description of the optical pulse, (i.e. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. These coupled equations are solved to simulate the propagation of femtosecond optical pulses in semiconductor materials. The simulations describe the dynamics of the optical pulses, as well as the interband and intraband.

  11. Analysis of nonlinear optical properties in donor–acceptor materials

    Energy Technology Data Exchange (ETDEWEB)

    Day, Paul N. [Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433 (United States); General Dynamics Information Technology, Inc., Dayton, Ohio 45431 (United States); Pachter, Ruth [Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433 (United States); Nguyen, Kiet A. [Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433 (United States); UES, Inc., Dayton, Ohio 45432 (United States)

    2014-05-14

    Time-dependent density functional theory has been used to calculate nonlinear optical (NLO) properties, including the first and second hyperpolarizabilities as well as the two-photon absorption cross-section, for the donor-acceptor molecules p-nitroaniline and dimethylamino nitrostilbene, and for respective materials attached to a gold dimer. The CAMB3LYP, B3LYP, PBE0, and PBE exchange-correlation functionals all had fair but variable performance when compared to higher-level theory and to experiment. The CAMB3LYP functional had the best performance on these compounds of the functionals tested. However, our comprehensive analysis has shown that quantitative prediction of hyperpolarizabilities is still a challenge, hampered by inadequate functionals, basis sets, and solvation models, requiring further experimental characterization. Attachment of the Au{sub 2}S group to molecules already known for their relatively large NLO properties was found to further enhance the response. While our calculations show a modest enhancement for the first hyperpolarizability, the enhancement of the second hyperpolarizability is predicted to be more than an order of magnitude.

  12. Integration of Geometrical and Material Nonlinear Energy Sink with Piezoelectric Material Energy Harvester

    Directory of Open Access Journals (Sweden)

    Ye-Wei Zhang

    2017-01-01

    Full Text Available This paper presents a novel design by integrating geometrical and material nonlinear energy sink (NES with a piezoelectric-based vibration energy harvester under shock excitation, which can realize vibration control and energy harvesting. The nonlinear spring and hysteresis behavior of the NES could reflect geometrical and material nonlinearity, respectively. Two configurations of the piezoelectric device, including the piezoelectric element embedded between the NES mass and the single-degree-of-freedom system or ground, are utilised to examine the energy dissipated by damper and hysteresis behavior of NES and the energy harvested by the piezoelectric element. Similar numerical research methods of Runge-Kutta algorithm are used to investigate the two configurations. The energy transaction measure (ETM is adopted to examine the instantaneous energy transaction between the primary and the NES-piezoelectricity system. And it demonstrates that the dissipated and harvested energy transaction is transferred from the primary system to the NES-piezoelectricity system and the instantaneous transaction of mechanical energy occupies a major part of the energy of transaction. Both figurations could realize vibration control efficiently.

  13. Measurement and fitting techniques for the assessment of material nonlinearity using nonlinear Rayleigh waves

    Energy Technology Data Exchange (ETDEWEB)

    Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)

    2015-03-31

    This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.

  14. Nonlocal description of X waves in quadratic nonlinear materials

    DEFF Research Database (Denmark)

    Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole

    2006-01-01

    We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...

  15. Use of a hyperelastic constitutive law for dry woven forming simulations

    International Nuclear Information System (INIS)

    Vidal-Salle, Emmanuelle; Boisse, Philippe; Aimene, Yamina

    2011-01-01

    The increasing use of composite materials in industry implies an increasing use of automatic processes between which LCM processes take a large place. The improvement of such processes needs an extensive use of numerical simulations for all the stages of the process. In particular, it is necessary to know how the dry reinforcement is shaped. This paper presents a hyperelastic constitutive model for textile composite reinforcement at large strain based on an additive potential representative to tension and in-plane shearing. The proposed potential is a function of the right Cauchy Green and structural tensor invariants whose choice corresponds to textile composite reinforcement mechanical behaviour. The model is implemented in a user subroutine of ABAQUS/Explicit. The accuracy of the model has been checked and some simulations are performed on deep drawing with hemispheric punch. A good agreement is obtained with experimental forming experiments.

  16. Finite amplitude, horizontal motion of a load symmetrically supported between isotropic hyperelastic springs.

    Science.gov (United States)

    Beatty, Millard F; Young, Todd R

    2012-03-01

    The undamped, finite amplitude horizontal motion of a load supported symmetrically between identical incompressible, isotropic hyperelastic springs, each subjected to an initial finite uniaxial static stretch, is formulated in general terms. The small amplitude motion of the load about the deformed static state is discussed; and the periodicity of the arbitrary finite amplitude motion is established for all such elastic materials for which certain conditions on the engineering stress and the strain energy function hold. The exact solution for the finite vibration of the load is then derived for the classical neo-Hookean model. The vibrational period is obtained in terms of the complete Heuman lambda-function whose properties are well-known. Dependence of the period and hence the frequency on the physical parameters of the system is investigated and the results are displayed graphically.

  17. Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

    Science.gov (United States)

    Pepi, John W.

    2017-08-01

    Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

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

    International Nuclear Information System (INIS)

    Ahmetolan, S.

    2004-01-01

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

  19. 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.

  20. Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

    Science.gov (United States)

    Singh, Sandeep; Patel, B. P.

    2018-06-01

    Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

  1. A Multiscale, Nonlinear, Modeling Framework Enabling the Design and Analysis of Composite Materials and Structures

    Science.gov (United States)

    Bednarcyk, Brett A.; Arnold, Steven M.

    2012-01-01

    A framework for the multiscale design and analysis of composite materials and structures is presented. The ImMAC software suite, developed at NASA Glenn Research Center, embeds efficient, nonlinear micromechanics capabilities within higher scale structural analysis methods such as finite element analysis. The result is an integrated, multiscale tool that relates global loading to the constituent scale, captures nonlinearities at this scale, and homogenizes local nonlinearities to predict their effects at the structural scale. Example applications of the multiscale framework are presented for the stochastic progressive failure of a SiC/Ti composite tensile specimen and the effects of microstructural variations on the nonlinear response of woven polymer matrix composites.

  2. Nonlinear signal processing for ultrasonic imaging of material complexity

    Czech Academy of Sciences Publication Activity Database

    Dos Santos, S.; Vejvodová, Šárka; Převorovský, Zdeněk

    2010-01-01

    Roč. 59, č. 2 (2010), s. 108-117 ISSN 1736-6046 Institutional research plan: CEZ:AV0Z20760514 Keywords : nonlinear signal processing * TR-NEWS * symmetry analysis * DORT Subject RIV: BI - Acoustics Impact factor: 0.464, year: 2010 www.eap.ee/proceedings

  3. Self-Assembly of Nanocomposite Nonlinear Optical Materials for Photonic Devices, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — This program targets the development of new highly anisotropic nonlinear optical nanocomposite materials for NASA and non-NASA applications in advanced photonic and...

  4. Design considerations for multi component molecular-polymeric nonlinear optical materials

    Energy Technology Data Exchange (ETDEWEB)

    Singer, K.D. (Case Western Reserve Univ., Cleveland, OH (USA). Dept. of Physics); Kuzyk, M.G. (Washington State Univ., Pullman, WA (USA). Dept. of Physics); Fang, T.; Holland, W.R. (AT and T Bell Labs., Princeton, NJ (USA)); Cahill, P.A. (Sandia National Labs., Albuquerque, NM (USA))

    1990-01-01

    We review our work on multi component polymeric nonlinear optical materials. These materials consist of nonlinear optical molecules incorporated in a polymeric host. A cross-linked triazine polymer incorporating a dicyanovinyl terminated azo dye was found to be relatively stable at 85{degree} and posses an electro-optic coefficient of 11pm/V. We have also observed the zero dispersion condition in a new anomalous dispersion dye for phase matched second harmonic generation, and expect efficient conversion to the blue. A squarylium dye, ISQ, has been found to posses a large third order nonlinearity, and may display two-level behavior. 24 refs., 11 figs.

  5. Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

    Science.gov (United States)

    Kourakis, I; Shukla, P K

    2005-07-01

    We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

  6. Analysis of the elastic behaviour of nonclassical nonlinear mesoscopic materials in quasi-static experiments

    International Nuclear Information System (INIS)

    Ruffino, E.; Scalerandi, M.

    2000-01-01

    As discovered by recent quasi-static and dynamic resonance experiments, the classical nonlinear theory fails in describing the hysteretic behaviour of nonlinear mesoscopic materials like rocks, concrete, etc. The paper applies the local interaction simulation approach (LISA) for studying such kind of nonclassical nonlinearity. To this purpose, in the LISA treatment of ultrasonic wave propagation has been included a phenomenological model, based on the PM space approach, of the local mesoscopic features of rocks and other materials with localized damages. A quantitative comparison of simulation and experimental results in quasi-static experiments is also presented

  7. Nonlinear Magnetic Phenomena in Highly Polarized Target Materials

    CERN Document Server

    Kiselev, Yu F

    2007-01-01

    The report introduces and surveys nonlinear magnetic phenomena which have been observed at high nuclear polarizations in polarized targets of the SMC and of the COMPASS collaborations at CERN. Some of these phenomena, namely the frequency modulation eect and the distortion of the NMR line shape, promote the development of the polarized target technique. Others, as the spin-spin cross-relaxation between spin subsystems can be used for the development of quantum statistical physics. New findings bear on an electromagnetic noise and the spectrally resolved radiation from LiD with negatively polarized nuclei detected by low temperature bolometers. These nonlinear phenomena need to be taken into account for achieving the ultimate polarizations.

  8. Nonlinear processes of magnons in insulating ferromagnetic materials

    International Nuclear Information System (INIS)

    Araujo, C.B. de.

    1975-04-01

    The representation of coherent states is used to investigate the excitation of magnons by 'parallel pumping', 'perpendicular pumping' and 'phonon pumping'. The stationary regime of the processes is studied with respect to the magnon population and the statistic behavior of the system below and just above the threshold. Particular attention is given to the thermodynamic and the coherence properties of the parametric states. The results show that just above the threshold the generated states become coherent. Also, it is shown that the non-linear processes have characteristics of a second-order phase transition with the pumping power as the 'reservoir variable' and the transverse dynamical magnetization as the 'order parameter'. Finally, the possibilities to extend the theory, its experimental check, and its convenience to study the other nonlinear processes of magnons and phonons in magnetic insulators are discussed. (author) [pt

  9. Hyperelastic pressure sensing with a liquid-embedded elastomer

    International Nuclear Information System (INIS)

    Park, Yong-Lae; Wood, Robert J; Majidi, Carmel; Kramer, Rebecca; Bérard, Phillipe

    2010-01-01

    A hyperelastic pressure transducer is fabricated by embedding silicone rubber with microchannels of conductive liquid eutectic gallium–indium. Pressing the surface of the elastomer with pressures in the range of 0–100 kPa will deform the cross-section of underlying channels and change their electric resistance by as much as 50%. Microchannels with dimensions as small as 25 µm are obtained with a maskless, soft lithography process that utilizes direct laser exposure. Change in electrical resistance is measured as a function of the magnitude and area of the surface pressure as well as the cross-sectional geometry, depth and relative lateral position of the embedded channel. These experimentally measured values closely match closed-form theoretical predictions derived from plane strain elasticity and contact mechanics

  10. A constructive nonlinear array (CNA) method for barely visible impact detection in composite materials

    Science.gov (United States)

    Malfense Fierro, Gian Piero; Meo, Michele

    2017-04-01

    Currently there are numerous phased array techniques such as Full Matrix Capture (FMC) and Total Focusing Method (TFM) that provide good damage assessment for composite materials. Although, linear methods struggle to evaluate and assess low levels of damage, while nonlinear methods have shown great promise in early damage detection. A sweep and subtraction evaluation method coupled with a constructive nonlinear array method (CNA) is proposed in order to assess damage specific nonlinearities, address issues with frequency selection when using nonlinear ultrasound imaging techniques and reduce equipment generated nonlinearities. These methods were evaluated using multiple excitation locations on an impacted composite panel with a complex damage (barely visible impact damage). According to various recent works, damage excitation can be accentuated by exciting at local defect resonance (LDR) frequencies; although these frequencies are not always easily determinable. The sweep methodology uses broadband excitation to determine both local defect and material resonances, by assessing local defect generated nonlinearities using a laser vibrometer it is possible to assess which frequencies excite the complex geometry of the crack. The dual effect of accurately determining local defect resonances, the use of an image subtraction method and the reduction of equipment based nonlinearities using CNA result in greater repeatability and clearer nonlinear imaging (NIM).

  11. Stress evaluation of metallic material under steady state based on nonlinear critically refracted longitudinal wave

    Science.gov (United States)

    Mao, Hanling; Zhang, Yuhua; Mao, Hanying; Li, Xinxin; Huang, Zhenfeng

    2018-06-01

    This paper presents the study of applying the nonlinear ultrasonic wave to evaluate the stress state of metallic materials under steady state. The pre-stress loading method is applied to guarantee components with steady stress. Three kinds of nonlinear ultrasonic experiments based on critically refracted longitudinal wave are conducted on components which the critically refracted longitudinal wave propagates along x, x1 and x2 direction. Experimental results indicate the second and third order relative nonlinear coefficients monotonically increase with stress, and the normalized relationship is consistent with simplified dislocation models, which indicates the experimental result is logical. The combined ultrasonic nonlinear parameter is proposed, and three stress evaluation models at x direction are established based on three ultrasonic nonlinear parameters, which the estimation error is below 5%. Then two stress detection models at x1 and x2 direction are built based on combined ultrasonic nonlinear parameter, the stress synthesis method is applied to calculate the magnitude and direction of principal stress. The results show the prediction error is within 5% and the angle deviation is within 1.5°. Therefore the nonlinear ultrasonic technique based on LCR wave could be applied to nondestructively evaluate the stress of metallic materials under steady state which the magnitude and direction are included.

  12. Cumulative Second Harmonic Generation in Lamb Waves for the Detection of Material Nonlinearities

    International Nuclear Information System (INIS)

    Bermes, Christian; Jacobs, Laurence J.; Kim, Jin-Yeon; Qu, Jianmin

    2007-01-01

    An understanding of the generation of higher harmonics in Lamb waves is of critical importance for applications such as remaining life prediction of plate-like structural components. The objective of this work is to use nonlinear Lamb waves to experimentally investigate inherent material nonlinearities in aluminum plates. These nonlinearities, e.g. lattice anharmonicities, precipitates or vacancies, cause higher harmonics to form in propagating Lamb waves. The amplitudes of the higher harmonics increase with increasing propagation distance due to the accumulation of nonlinearity while the Lamb wave travels along its path. Special focus is laid on the second harmonic, and a relative nonlinearity parameter is defined as a function of the fundamental and second harmonic amplitude. The experimental setup uses an ultrasonic transducer and a wedge for the Lamb wave generation, and laser interferometry for detection. The experimentally measured Lamb wave signals are processed with a short-time Fourier transformation (STFT), which yields the amplitudes at different frequencies as functions of time, allowing the observation of the nonlinear behavior of the material. The increase of the relative nonlinearity parameter with propagation distance as an indicator of cumulative second harmonic generation is shown in the results for the alloy aluminum 1100-H14

  13. Reliability analysis of reinforced concrete grids with nonlinear material behavior

    Energy Technology Data Exchange (ETDEWEB)

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

    2006-06-15

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

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

    Science.gov (United States)

    Chillara, Vamshi Krishna

    2017-11-01

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

  15. Femtosecond laser damage threshold and nonlinear characterization in bulk transparent SiC materials

    International Nuclear Information System (INIS)

    DesAutels, G. Logan; Finet, Marc; Ristich, Scott; Whitaker, Matt; Brewer, Chris; Juhl, Shane; Walker, Mark; Powers, Peter

    2008-01-01

    Semi-insulating and conducting SiC crystalline transparent substrates were studied after being processed by femtosecond (fs) laser radiation (780 nm at 160 fs). Z-scan and damage threshold experiments were performed on both SiC bulk materials to determine each sample's nonlinear and threshold parameters. 'Damage' in this text refers to an index of refraction modification as observed visually under an optical microscope. In addition, a study was performed to understand the damage threshold as a function of numerical aperture. Presented here for the first time, to the best of our knowledge, are the damage threshold, nonlinear index of refraction, and nonlinear absorption measured values

  16. Spatial frequency mixing by nonlinear charge transport in photorefractive materials

    DEFF Research Database (Denmark)

    Limeres, J.; Carrascosa, M.; Arizmendi, L.

    2002-01-01

    in the material. The physical origin of the new gratings is extensively discussed. The formalism is applied to investigate multiple recording in LiNbO3 as a material relevant for applications. The influence of the multiple-recording method (either sequential or simultaneous) on the generation of second...

  17. Material model for non-linear finite element analyses of large concrete structures

    NARCIS (Netherlands)

    Engen, Morten; Hendriks, M.A.N.; Øverli, Jan Arve; Åldstedt, Erik; Beushausen, H.

    2016-01-01

    A fully triaxial material model for concrete was implemented in a commercial finite element code. The only required input parameter was the cylinder compressive strength. The material model was suitable for non-linear finite element analyses of large concrete structures. The importance of including

  18. Analytical Modeling of Hard-Coating Cantilever Composite Plate considering the Material Nonlinearity of Hard Coating

    Directory of Open Access Journals (Sweden)

    Wei Sun

    2015-01-01

    Full Text Available Due to the material nonlinearity of hard coating, the coated structure produces the nonlinear dynamical behaviors of variable stiffness and damping, which make the modeling of hard-coating composite structure become a challenging task. In this study, the polynomial was adopted to characterize this material nonlinearity and an analytical modeling method was developed for the hard-coating composite plate. Firstly, to relate the hard-coating material parameters obtained by test and the analytical model, the expression of equivalent strain of composite plate was derived. Then, the analytical model of hard-coating composite plate was created by energy method considering the material nonlinearity of hard coating. Next, using the Newton-Raphson method to solve the vibration response and resonant frequencies of composite plate and a specific calculation procedure was also proposed. Finally, a cantilever plate coated with MgO + Al2O3 hard coating was chosen as study case; the vibration response and resonant frequencies of composite plate were calculated using the proposed method. The calculation results were compared with the experiment and general linear calculation, and the correctness of the created model was verified. The study shows the proposed method can still maintain an acceptable precision when the material nonlinearity of hard coating is stronger.

  19. Hyperelastic "bone": A highly versatile, growth factor-free, osteoregenerative, scalable, and surgically friendly biomaterial.

    Science.gov (United States)

    Jakus, Adam E; Rutz, Alexandra L; Jordan, Sumanas W; Kannan, Abhishek; Mitchell, Sean M; Yun, Chawon; Koube, Katie D; Yoo, Sung C; Whiteley, Herbert E; Richter, Claus-Peter; Galiano, Robert D; Hsu, Wellington K; Stock, Stuart R; Hsu, Erin L; Shah, Ramille N

    2016-09-28

    Despite substantial attention given to the development of osteoregenerative biomaterials, severe deficiencies remain in current products. These limitations include an inability to adequately, rapidly, and reproducibly regenerate new bone; high costs and limited manufacturing capacity; and lack of surgical ease of handling. To address these shortcomings, we generated a new, synthetic osteoregenerative biomaterial, hyperelastic "bone" (HB). HB, which is composed of 90 weight % (wt %) hydroxyapatite and 10 wt % polycaprolactone or poly(lactic-co-glycolic acid), could be rapidly three-dimensionally (3D) printed (up to 275 cm(3)/hour) from room temperature extruded liquid inks. The resulting 3D-printed HB exhibited elastic mechanical properties (~32 to 67% strain to failure, ~4 to 11 MPa elastic modulus), was highly absorbent (50% material porosity), supported cell viability and proliferation, and induced osteogenic differentiation of bone marrow-derived human mesenchymal stem cells cultured in vitro over 4 weeks without any osteo-inducing factors in the medium. We evaluated HB in vivo in a mouse subcutaneous implant model for material biocompatibility (7 and 35 days), in a rat posterolateral spinal fusion model for new bone formation (8 weeks), and in a large, non-human primate calvarial defect case study (4 weeks). HB did not elicit a negative immune response, became vascularized, quickly integrated with surrounding tissues, and rapidly ossified and supported new bone growth without the need for added biological factors. Copyright © 2016, American Association for the Advancement of Science.

  20. Estimation of non-linear effective permeability of magnetic materials with fine structure

    International Nuclear Information System (INIS)

    Waki, H.; Igarashi, H.; Honma, T.

    2006-01-01

    This paper describes a homogenization method for magnetic materials with fine structure. In this method, the structures of the magnetic materials are assumed to be periodic, and the unit cell is defined. The effective permeability is determined on the basis of magnetic energy balance in the unit cell. This method can be applied not only for linear problems but also for non-linear ones. In this paper, estimation of the effective permeability of non-linear magnetic materials by using the homogenization method is described in detail, and then the validity for the non-liner problems is tested for two-dimensional problems. It is shown that this homogenization method gives accurate non-linear effective permeability

  1. Photon energy conversion by near-zero permittivity nonlinear materials

    Science.gov (United States)

    Luk, Ting S.; Sinclair, Michael B.; Campione, Salvatore

    2017-12-19

    Efficient harmonic light generation can be achieved with ultrathin films by coupling an incident pump wave to an epsilon-near-zero (ENZ) mode of the thin film. As an example, efficient third harmonic generation from an indium tin oxide nanofilm (.lamda./42 thick) on a glass substrate for a pump wavelength of 1.4 .mu.m was demonstrated. A conversion efficiency of 3.3.times.10.sup.-6 was achieved by exploiting the field enhancement properties of the ENZ mode with an enhancement factor of 200. This nanoscale frequency conversion method is applicable to other plasmonic materials and reststrahlen materials in proximity of the longitudinal optical phonon frequencies.

  2. Simultaneous spatial and temporal focusing: a route towards confined nonlinear materials processing

    Science.gov (United States)

    Kammel, Robert; Bergner, Klaus; Thomas, Jens; Ackermann, Roland; Skupin, Stefan; Nolte, Stefan

    2016-03-01

    Ultrashort pulse lasers enable reliable and versatile high precision ablation and surface processing of various materials such as metals, polymers and semiconductors. However, when modifications deep inside the bulk of transparent media are required, nonlinear pulse material interactions can decrease the precision, since weak focusing and the long propagation of the intense pulses within the nonlinear media may induce Kerr self-focusing, filamentation and white light generation. In order to improve the precision of those modifications, simultaneous spatial and temporal focusing (SSTF) allows to reduce detrimental nonlinear interactions, because the ultrashort pulse duration is only obtained at the focus, while outside of the focal region the continuously increasing pulse duration strongly reduces the pulse intensity. In this paper, we review the fundamental concepts of this technology and provide an overview of its applications for purposes of multiphoton microscopy and laser materials processing. Moreover, numerical simulations on the nonlinear pulse propagation within transparent media illustrate the linear and nonlinear pulse propagation, highlighting the differences between conventional focusing and SSTF. Finally, fs-laser induced modifications in gelatine are presented to compare nonlinear side-effects caused by conventional focusing and SSTF. With conventional focusing the complex interplay of self-focusing and filamentation induces strongly inhomogeneous, elongated disruptions. In contrast, disruptions induced by SSTF are homogeneously located at the focal plane and reduced in length by a factor >2, which is in excellent agreement with the numerical simulations of the nonlinear pulse propagation and might favor SSTF for demanding applications such as intraocular fs-laser surgery.

  3. Non-linear modeling of active biohybrid materials

    KAUST Repository

    Paetsch, C.

    2013-11-01

    Recent advances in engineered muscle tissue attached to a synthetic substrate motivate the development of appropriate constitutive and numerical models. Applications of active materials can be expanded by using robust, non-mammalian muscle cells, such as those of Manduca sexta. In this study, we propose a model to assist in the analysis of biohybrid constructs by generalizing a recently proposed constitutive law for Manduca muscle tissue. The continuum model accounts (i) for the stimulation of muscle fibers by introducing multiple stress-free reference configurations for the active and passive states and (ii) for the hysteretic response by specifying a pseudo-elastic energy function. A simple example representing uniaxial loading-unloading is used to validate and verify the characteristics of the model. Then, based on experimental data of muscular thin films, a more complex case shows the qualitative potential of Manduca muscle tissue in active biohybrid constructs. © 2013 Elsevier Ltd. All rights reserved.

  4. Existence of solutions for quasistatic problems of unilateral contact with nonlocal friction for nonlinear elastic materials

    Directory of Open Access Journals (Sweden)

    Alain Mignot

    2005-09-01

    Full Text Available This paper shows the existence of a solution of the quasi-static unilateral contact problem with nonlocal friction law for nonlinear elastic materials. We set up a variational incremental problem which admits a solution, when the friction coefficient is small enough, and then by passing to the limit with respect to time we obtain a solution.

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

    Science.gov (United States)

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

    2018-04-01

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

  6. Mesomorphic glass nanocomposites made of metal alkanoates and nanoparticles as emerging nonlinear-optical materials

    Science.gov (United States)

    Garbovskiy, Y.; Klimusheva, G.; Mirnaya, T.

    2016-09-01

    Mesomorphic metal alkanoates is very promising yet overlooked class of nonlinear-optical materials. Metal alkanoates can exhibit a broad variety of condensed states of matter including solid crystals, plastic crystals, lyotropic and thermotropic ionic liquid crystals, liquids, mesomorphic glasses, and Langmuir-Blodgett films. Glass-forming properties of metal alkanoates combined with their use as nano-reactors and anisotropic host open up simple and efficient way to design various photonic nanomaterials. Despite very interesting physics, the experimental data on optical and nonlinearoptical properties of such materials are scarce. The goal of the present paper is to fill the gap by discussing recent advances in the field of photonic materials made of metal alkanoates, organic dyes, and nanoparticles. Optical and nonlinear-optical properties of the following materials are reviewed: (i) mesomorphic glass doped with organic dyes; (ii) smectic glass composed of cobalt alkanoates; (iii) semiconductor nanoparticles embedded in a glassy host; (iv) metal nanoparticles - glass (the cobalt octanoate) nanocomposites.

  7. 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)

  8. A general one-dimension nonlinear magneto-elastic coupled constitutive model for magnetostrictive materials

    International Nuclear Information System (INIS)

    Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao

    2015-01-01

    For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications

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

    Directory of Open Access Journals (Sweden)

    Şeref Doğuşcan Akbaş

    2013-01-01

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

  10. Sensitivity of acoustic nonlinearity parameter to the microstructural changes in cement-based materials

    Science.gov (United States)

    Kim, Gun; Kim, Jin-Yeon; Kurtis, Kimberly E.; Jacobs, Laurence J.

    2015-03-01

    This research experimentally investigates the sensitivity of the acoustic nonlinearity parameter to microcracks in cement-based materials. Based on the second harmonic generation (SHG) technique, an experimental setup using non-contact, air-coupled detection is used to receive the consistent Rayleigh surface waves. To induce variations in the extent of microscale cracking in two types of specimens (concrete and mortar), shrinkage reducing admixture (SRA), is used in one set, while a companion specimen is prepared without SRA. A 50 kHz wedge transducer and a 100 kHz air-coupled transducer are implemented for the generation and detection of nonlinear Rayleigh waves. It is shown that the air-coupled detection method provides more repeatable fundamental and second harmonic amplitudes of the propagating Rayleigh waves. The obtained amplitudes are then used to calculate the relative nonlinearity parameter βre, the ratio of the second harmonic amplitude to the square of the fundamental amplitude. The experimental results clearly demonstrate that the nonlinearity parameter (βre) is highly sensitive to the microstructural changes in cement-based materials than the Rayleigh phase velocity and attenuation and that SRA has great potential to avoid shrinkage cracking in cement-based materials.

  11. POD for Real-Time Simulation of Hyperelastic Soft Biological Tissue Using the Point Collocation Method of Finite Spheres

    Directory of Open Access Journals (Sweden)

    Suleiman Banihani

    2013-01-01

    Full Text Available The point collocation method of finite spheres (PCMFS is used to model the hyperelastic response of soft biological tissue in real time within the framework of virtual surgery simulation. The proper orthogonal decomposition (POD model order reduction (MOR technique was used to achieve reduced-order model of the problem, minimizing computational cost. The PCMFS is a physics-based meshfree numerical technique for real-time simulation of surgical procedures where the approximation functions are applied directly on the strong form of the boundary value problem without the need for integration, increasing computational efficiency. Since computational speed has a significant role in simulation of surgical procedures, the proposed technique was able to model realistic nonlinear behavior of organs in real time. Numerical results are shown to demonstrate the effectiveness of the new methodology through a comparison between full and reduced analyses for several nonlinear problems. It is shown that the proposed technique was able to achieve good agreement with the full model; moreover, the computational and data storage costs were significantly reduced.

  12. Nonlinear Microstructured Material to Reduce Noise and Vibrations at Low Frequencies

    International Nuclear Information System (INIS)

    Lavazec, Deborah; Cumunel, Gwendal; Duhamel, Denis; Soize, Christian; Batou, Anas

    2016-01-01

    At low frequencies, for which the wavelengths are wide, the acoustic waves and the mechanical vibrations cannot easily be reduced in the structures at macroscale by using dissipative materials, contrarily to the middle- and high-frequency ranges. The final objective of this work is to reduce the vibrations and the induced noise on a broad low-frequency band by using a microstructured material by inclusions that are randomly arranged in the material matrix. The dynamical regimes of the inclusions will be imposed in the nonlinear domain in order that the energy be effectively pumped over a broad frequency band around the resonance frequency, due to the nonlinearity. The first step of this work is to design and to analyze the efficiency of an inclusion, which is made up of a hollow frame including a point mass centered on a beam. This inclusion is designed in order to exhibit nonlinear geometric effects in the low-frequency band that is observed. For this first step, the objective is to develop the simplest mechanical model that has the capability to roughly predict the experimental results that are measured. The second step, which is not presented in the paper, will consist in developing a more sophisticated nonlinear dynamical model of the inclusion. In this paper, devoted to the first step, it is proved that the nonlinearity induces an attenuation on a broad frequency band around the resonance, contrarily to its linear behavior for which the attenuation is only active in a narrow frequency band around the resonance. We will present the design in terms of geometry, dimension and materials for the inclusion, the experimental manufacturing of this system realized with a 3D printing system, and the experimental measures that have been performed. We compare the prevision given by the stochastic computational model with the measurements. The results obtained exhibit the physical attenuation over a broad low-frequency band, which were expected. (paper)

  13. Synthesis of polymeric micro- and nanostructural materials for application in non-linear optics

    International Nuclear Information System (INIS)

    Kravets, Lyubov; Palistrant, Natalia; Bivol, Valerii; Robu, Stepan; Barba, Nikolai; Orelovitch, Oleg

    2007-01-01

    The present paper describes a new approach developed for the preparation of micro- and nanostructural materials on the basis of polymeric compositions used as a matrix in non-linear optics. This approach consists in filling the pores of poly(ethylene terephthalate) track membranes (PET TM) from polymeric compositions using an impregnation method. It is shown that depending on the concentration of polymeric compositions in the solution it is possible to form a variety of micro- and nanostructural materials (tubules and wires as well as composite membranes) with a wide spectrum of characteristics. The developed method of producing micro- and nanostructural materials provides a possible way for creating polymeric objects with non-linear optic properties which can be used to design electronic micro- and nanodevices and to obtain chemical and optical sensors

  14. Potential for efficient frequency conversion at high average power using solid state nonlinear optical materials

    International Nuclear Information System (INIS)

    Eimerl, D.

    1985-01-01

    High-average-power frequency conversion using solid state nonlinear materials is discussed. Recent laboratory experience and new developments in design concepts show that current technology, a few tens of watts, may be extended by several orders of magnitude. For example, using KD*P, efficient doubling (>70%) of Nd:YAG at average powers approaching 100 KW is possible; and for doubling to the blue or ultraviolet regions, the average power may approach 1 MW. Configurations using segmented apertures permit essentially unlimited scaling of average power. High average power is achieved by configuring the nonlinear material as a set of thin plates with a large ratio of surface area to volume and by cooling the exposed surfaces with a flowing gas. The design and material fabrication of such a harmonic generator are well within current technology

  15. 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)

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

    Energy Technology Data Exchange (ETDEWEB)

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

    1999-12-10

    Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model in which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.

  17. Solutions to the equations describing materials with competing quadratic and cubic nonlinearities

    International Nuclear Information System (INIS)

    Li-Na, Zhao; Ji, Lin; Zi-Shuang, Tong

    2009-01-01

    The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations share some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation

  18. A general 3-D nonlinear magnetostrictive constitutive model for soft ferromagnetic materials

    International Nuclear Information System (INIS)

    Zhou Haomiao; Zhou Youhe; Zheng Xiaojing; Ye Qiang; Wei Jing

    2009-01-01

    In this paper, a new general nonlinear magnetostrictive constitutive model is proposed for soft ferromagnetic materials, and it can predict magnetostrictive strain and magnetization curves under various pre-stresses. From the viewpoint of magnetic domain, it is based on the important physical fact that a nonlinear part of the elastic strain produced by magnetic domain wall motion under a pre-stress is responsible for the change of the maximum magnetostrictive strain in accordance with the pre-stress. Then the reduction of magnetostrictive strain from the maximum is caused by the domain rotation. Meanwhile, the magnetization under various pre-stresses in this model is introduced by magnetostrictive effect under the same pre-stress. A simplified 3-D model is put forward by means of linearizing the nonlinear function, i.e. the nonlinear part of the elastic strain produced by domain wall motion, and by using the quartic of magnetization to describe domain rotation. Besides, for the convenience of engineering applications, two-dimensional (plate or film) and one-dimensional (rod) models are also given for isotropic materials and their application ranges are discussed too. In comparison with the experimental data of Kuruzar and Jiles, it is found that this model can predict magnetostrictive strain and magnetization curves under various pre-stresses. The numerical simulation further illustrates that the new model can effectively describe the effects of the pre-stress or residual stress on the magnetization and magnetostrictive strain curves. Additionally, this model can be degenerated to the existing magnetostrictive constitutive model for giant magnetostrictive materials (GMM), i.e. a special soft ferromagnetic material

  19. Detecting Damage in Composite Material Using Nonlinear Elastic Wave Spectroscopy Methods

    Science.gov (United States)

    Meo, Michele; Polimeno, Umberto; Zumpano, Giuseppe

    2008-05-01

    Modern aerospace structures make increasing use of fibre reinforced plastic composites, due to their high specific mechanical properties. However, due to their brittleness, low velocity impact can cause delaminations beneath the surface, while the surface may appear to be undamaged upon visual inspection. Such damage is called barely visible impact damage (BVID). Such internal damages lead to significant reduction in local strengths and ultimately could lead to catastrophic failures. It is therefore important to detect and monitor damages in high loaded composite components to receive an early warning for a well timed maintenance of the aircraft. Non-linear ultrasonic spectroscopy methods are promising damage detection and material characterization tools. In this paper, two different non-linear elastic wave spectroscopy (NEWS) methods are presented: single mode nonlinear resonance ultrasound (NRUS) and nonlinear wave modulation technique (NWMS). The NEWS methods were applied to detect delamination damage due to low velocity impact (<12 J) on various composite plates. The results showed that the proposed methodology appear to be highly sensitive to the presence of damage with very promising future NDT and structural health monitoring applications.

  20. Emerging Low-Dimensional Materials for Nonlinear Optics and Ultrafast Photonics.

    Science.gov (United States)

    Liu, Xiaofeng; Guo, Qiangbing; Qiu, Jianrong

    2017-04-01

    Low-dimensional (LD) materials demonstrate intriguing optical properties, which lead to applications in diverse fields, such as photonics, biomedicine and energy. Due to modulation of electronic structure by the reduced structural dimensionality, LD versions of metal, semiconductor and topological insulators (TIs) at the same time bear distinct nonlinear optical (NLO) properties as compared with their bulk counterparts. Their interaction with short pulse laser excitation exhibits a strong nonlinear character manifested by NLO absorption, giving rise to optical limiting or saturated absorption associated with excited state absorption and Pauli blocking in different materials. In particular, the saturable absorption of these emerging LD materials including two-dimensional semiconductors as well as colloidal TI nanoparticles has recently been utilized for Q-switching and mode-locking ultra-short pulse generation across the visible, near infrared and middle infrared wavelength regions. Beside the large operation bandwidth, these ultrafast photonics applications are especially benefit from the high recovery rate as well as the facile processibility of these LD materials. The prominent NLO response of these LD materials have also provided new avenues for the development of novel NLO and photonics devices for all-optical control as well as optical circuits beyond ultrafast lasers. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  1. Strongly nonlinear optical glass fibers from noncentrosymmetric phase-change chalcogenide materials.

    Science.gov (United States)

    Chung, In; Jang, Joon I; Malliakas, Christos D; Ketterson, John B; Kanatzidis, Mercouri G

    2010-01-13

    We report that the one-dimensional polar selenophosphate compounds APSe(6) (A = K, Rb), which show crystal-glass phase-change behavior, exhibit strong second harmonic generation (SHG) response in both crystal and glassy forms. The crystalline materials are type-I phase-matchable with SHG coefficients chi((2)) of 151.3 and 149.4 pm V(-1) for K(+) and Rb(+) salts, respectively, which is the highest among phase-matchable nonlinear optical (NLO) materials with band gaps over 1.0 eV. The glass of APSe(6) exhibits comparable SHG intensities to the top infrared NLO material AgGaSe(2) without any poling treatments. APSe(6) exhibit excellent mid-IR transparency. We demonstrate that starting from noncentrosymmetric phase-change materials such as APSe(6) (A = K, Rb), we can obtain optical glass fibers with strong, intrinsic, and temporally stable second-order nonlinear optical (NLO) response. The as-prepared glass fibers exhibit SHG and difference frequency generation (DFG) responses over a wide range of wavelengths. Raman spectroscopy and pair distribution function (PDF) analyses provide further understanding of the local structure in amorphous state of KPSe(6) bulk glass and glass fiber. We propose that this approach can be widely applied to prepare permanent NLO glass from materials that undergo a phase-change process.

  2. THz Induced Nonlinear Effects in Materials at Intensities above 26 GW/cm2

    Science.gov (United States)

    Woldegeorgis, A.; Kurihara, T.; Beleites, B.; Bossert, J.; Grosse, R.; Paulus, G. G.; Ronneberger, F.; Gopal, A.

    2018-04-01

    Nonlinear refractive index and absorption coefficient are measured for common semiconductor material such as silicon and organic molecule such as lactose in the terahertz (THz) spectral regime extending from 0.1 to 3 THz. Terahertz pulses with field strengths in excess of 4.4 MV/cm have been employed. Transmittance and the transmitted spectrum were measured with Z-scan and single shot noncollinear electro-optic pump-probe techniques. The THz-induced change in the refractive index (Δn) shows frequency-dependence and a maximum change of - 0.128 at 1.37 THz in lactose and up to + 0.169 at 0.15 THz in silicon was measured for a peak incident THz intensity of 26 GW/cm2. Furthermore, the refractive index variation shows a quadratic dependence on the incident THz field, implying the dominance of third-order nonlinearity.

  3. Flexural fatigue life prediction of closed hat-section using materially nonlinear axial fatigue characteristics

    Science.gov (United States)

    Razzaq, Zia

    1989-01-01

    Straight or curved hat-section members are often used as structural stiffeners in aircraft. For instance, they are employed as stiffeners for the dorsal skin as well as in the aerial refueling adjacent area structure in F-106 aircraft. The flanges of the hat-section are connected to the aircraft skin. Thus, the portion of the skin closing the hat-section interacts with the section itself when resisting the stresses due to service loads. The flexural fatigue life of such a closed section is estimated using materially nonlinear axial fatigue characteristics. It should be recognized that when a structural shape is subjected to bending, the fatigue life at the neutral axis is infinity since the normal stresses are zero at that location. Conversely, the fatigue life at the extreme fibers where the normal bending stresses are maximum can be expected to be finite. Thus, different fatigue life estimates can be visualized at various distances from the neural axis. The problem becomes compounded further when significant portions away from the neutral axis are stressed into plastic range. A theoretical analysis of the closed hat-section subjected to flexural cyclic loading is first conducted. The axial fatigue characteristics together with the related axial fatigue life formula and its inverted form given by Manson and Muralidharan are adopted for an aluminum alloy used in aircraft construction. A closed-form expression for predicting the flexural fatigue life is then derived for the closed hat-section including materially nonlinear action. A computer program is written to conduct a study of the variables such as the thicknesses of the hat-section and the skin, and the type of alloy used. The study has provided a fundamental understanding of the flexural fatigue life characteristics of a practical structural component used in aircraft when materially nonlinear action is present.

  4. First principles crystal engineering of nonlinear optical materials. I. Prototypical case of urea

    Science.gov (United States)

    Masunov, Artëm E.; Tannu, Arman; Dyakov, Alexander A.; Matveeva, Anastasia D.; Freidzon, Alexandra Ya.; Odinokov, Alexey V.; Bagaturyants, Alexander A.

    2017-06-01

    The crystalline materials with nonlinear optical (NLO) properties are critically important for several technological applications, including nanophotonic and second harmonic generation devices. Urea is often considered to be a standard NLO material, due to the combination of non-centrosymmetric crystal packing and capacity for intramolecular charge transfer. Various approaches to crystal engineering of non-centrosymmetric molecular materials were reported in the literature. Here we propose using global lattice energy minimization to predict the crystal packing from the first principles. We developed a methodology that includes the following: (1) parameter derivation for polarizable force field AMOEBA; (2) local minimizations of crystal structures with these parameters, combined with the evolutionary algorithm for a global minimum search, implemented in program USPEX; (3) filtering out duplicate polymorphs produced; (4) reoptimization and final ranking based on density functional theory (DFT) with many-body dispersion (MBD) correction; and (5) prediction of the second-order susceptibility tensor by finite field approach. This methodology was applied to predict virtual urea polymorphs. After filtering based on packing similarity, only two distinct packing modes were predicted: one experimental and one hypothetical. DFT + MBD ranking established non-centrosymmetric crystal packing as the global minimum, in agreement with the experiment. Finite field approach was used to predict nonlinear susceptibility, and H-bonding was found to account for a 2.5-fold increase in molecular hyperpolarizability to the bulk value.

  5. Non-Reciprocal Geometric Wave Diode by Engineering Asymmetric Shapes of Nonlinear Materials

    Energy Technology Data Exchange (ETDEWEB)

    Ren, Jie [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Li, Nianbei [Tongji Univ., Shanghai Shi (China)

    2014-02-18

    Unidirectional nonreciprocal transport is at the heart of many fundamental problems and applications in both science and technology. Here we study how to design the novel wave diode devices to realize the non-reciprocal wave propagations. Analytical results reveal that such non-reciprocal wave propagation can be purely induced by asymmetric geometry in nonlinear materials. The detailed numerical simulations are performed for a more realistic geometric wave diode model with typical asymmetric shape, where good non-reciprocal wave diode effect has been demonstrated. The results open a way for making wave diodes efficiently simply through shape engineering.

  6. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

    Energy Technology Data Exchange (ETDEWEB)

    Matouš, Karel, E-mail: kmatous@nd.edu [Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556 (United States); Geers, Marc G.D.; Kouznetsova, Varvara G. [Department of Mechanical Engineering, Eindhoven University of Technology, Eindhoven (Netherlands); Gillman, Andrew [Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556 (United States)

    2017-02-01

    Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

  7. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

    International Nuclear Information System (INIS)

    Matouš, Karel; Geers, Marc G.D.; Kouznetsova, Varvara G.; Gillman, Andrew

    2017-01-01

    Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

  8. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

    Science.gov (United States)

    Matouš, Karel; Geers, Marc G. D.; Kouznetsova, Varvara G.; Gillman, Andrew

    2017-02-01

    Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

  9. A nonlinear dynamical system approach for the yielding behaviour of a viscoplastic material.

    Science.gov (United States)

    Burghelea, Teodor; Moyers-Gonzalez, Miguel; Sainudiin, Raazesh

    2017-03-08

    A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stresses recently reported in R. Sainudiin, M. Moyers-Gonzalez and T. Burghelea, Soft Matter, 2015, 11(27), 5531-5545 is presented. The predictions of the model are in fair agreement with microscopic simulations and are in very good agreement with the micro-structural semi-empirical model reported in A. M. V. Putz and T. I. Burghelea, Rheol. Acta, 2009, 48, 673-689. With only two internal parameters, the nonlinear dynamical system model captures several key features of the solid-fluid transition observed in experiments: the effect of the interactions between microscopic constituents on the yield point, the abruptness of solid-fluid transition and the emergence of a hysteresis of the micro-structural states upon increasing/decreasing external forces. The scaling behaviour of the magnitude of the hysteresis with the degree of the steadiness of the flow is consistent with previous experimental observations. Finally, the practical usefulness of the approach is demonstrated by fitting a rheological data set measured with an elasto-viscoplastic material.

  10. A non-linear optimal control problem in obtaining homogeneous concentration for semiconductor materials

    International Nuclear Information System (INIS)

    Huang, C.-H.; Li, J.-X.

    2006-01-01

    A non-linear optimal control algorithm is examined in this study for the diffusion process of semiconductor materials. The purpose of this algorithm is to estimate an optimal control function such that the homogeneity of the concentration can be controlled during the diffusion process and the diffusion-induced stresses for the semiconductor materials can thus be reduced. The validation of this optimal control analysis utilizing the conjugate gradient method of minimization is analysed by using numerical experiments. Three different diffusion processing times are given and the corresponding optimal control functions are to be determined. Results show that the diffusion time can be shortened significantly by applying the optimal control function at the boundary and the homogeneity of the concentration is also guaranteed. This control function can be obtained within a very short CPU time on a Pentium III 600 MHz PC

  11. Performance analysis of flow lines with non-linear flow of material

    CERN Document Server

    Helber, Stefan

    1999-01-01

    Flow line design is one of the major tasks in production management. The decision to install a set of machines and buffers is often highly irreversible. It determines both cost and revenue to a large extent. In order to assess the economic impact of any possible flow line design, production rates and inventory levels have to be estimated. These performance measures depend on the allocation of buffers whenever the flow of material is occasionally disrupted, for example due to machine failures or quality problems. The book describes analytical methods that can be used to evaluate flow lines much faster than with simulation techniques. Based on these fast analytical techniques, it is possible to determine a flow line design that maximizes the net present value of the flow line investment. The flow of material through the line may be non-linear, for example due to assembly operations or quality inspections.

  12. DIESYS—dynamically non-linear dielectric elastomer energy generating synergetic structures: perspectives and challenges

    International Nuclear Information System (INIS)

    Antoniadis, I A; Venetsanos, D T; Papaspyridis, F G

    2013-01-01

    Dielectric elastomer based generators (DEGs) offer some unique properties over energy generators based on other materials. These properties include high energy density, high efficiency over a broad range of frequencies, low compliance, the ability to produce high strain, large area, low cost films with no toxic materials and wide range environmental tolerance. As further shown in this paper, DEG materials can also exhibit a non-linear dynamic behavior, enhancing broad-band energy transfer. More specifically, dielectric elastomer (DE) energy generating synergetic structures (DIESYS) are considered as dynamic energy absorbers. Two elementary characteristic DIESYS design concepts are examined, leading to a typical antagonistic configuration for in-plane oscillations and a typical synagonistic configuration for out-of-plane oscillations. Originally, all the DE elements of the structure are assumed to be always in tension during all the phases of the harvesting cycle, conforming to the traditional concept of operation of DE structures. As shown in this paper, the traditional always-in-tension concept results in a linear dynamic system response, despite the fact that the implemented (DE) parts are considered to have been made of a non-linear (hyperelastic) material. In contrast, the proposed loose-part concept ensures the appearance of a non-linear broad-band system response, enhancing energy transfer from the environmental source. (paper)

  13. A pull-back algorithm to determine the unloaded vascular geometry in anisotropic hyperelastic AAA passive mechanics.

    Science.gov (United States)

    Riveros, Fabián; Chandra, Santanu; Finol, Ender A; Gasser, T Christian; Rodriguez, Jose F

    2013-04-01

    Biomechanical studies on abdominal aortic aneurysms (AAA) seek to provide for better decision criteria to undergo surgical intervention for AAA repair. More accurate results can be obtained by using appropriate material models for the tissues along with accurate geometric models and more realistic boundary conditions for the lesion. However, patient-specific AAA models are generated from gated medical images in which the artery is under pressure. Therefore, identification of the AAA zero pressure geometry would allow for a more realistic estimate of the aneurysmal wall mechanics. This study proposes a novel iterative algorithm to find the zero pressure geometry of patient-specific AAA models. The methodology allows considering the anisotropic hyperelastic behavior of the aortic wall, its thickness and accounts for the presence of the intraluminal thrombus. Results on 12 patient-specific AAA geometric models indicate that the procedure is computational tractable and efficient, and preserves the global volume of the model. In addition, a comparison of the peak wall stress computed with the zero pressure and CT-based geometries during systole indicates that computations using CT-based geometric models underestimate the peak wall stress by 59 ± 64 and 47 ± 64 kPa for the isotropic and anisotropic material models of the arterial wall, respectively.

  14. Light-induced second-order nonlinear optical properties of molecular materials

    International Nuclear Information System (INIS)

    Fiorini, Celine

    1995-01-01

    We present a theoretical and experimental study of all-optical orientation. The work focusses more particularly on the realization of poled polymers for quadratic nonlinear optics. It is shown that the coherent superposition of two beams at fundamental and second harmonic frequencies results in the breaking of the former centro-symmetry of the material. The source is a Neodymium-YAG laser delivering 25 ps pulses at 1064 nm. The incident second-harmonic beam is obtained by frequency doubling in a KDP crystal. Using a phase conjugation configuration based on six-wave mixing interactions, we have Investigated in detail the mechanism of photo-induced second-harmonic generation in initially centrosymmetric materials. It is shown that the light-induced non-centro-symmetry is due to an orientational hole burning of the molecules. The process involves interference effects between one and two photon absorptions. Experiments are performed in various solutions of an azo-dye molecule (Disperse Red One). The possibility of inducing quasi-permanent second-order susceptibility in a PMMA polymer matrix doped with the azo-dye molecule of Disperse Red One is also demonstrated. The method of all-optical poling consists in a seeding type process with alternate writing and probing phases. Permanent orientation of the molecules can be described in terms of photo-isomerization processes. It leads to a poling of the molecules with a spatial modulation which is phase-matched for frequency doubling. Relevant parameters leading to an efficient polarisation of the sample are identified. A theoretical modelling of the different phenomena observed is proposed. Last part of the study is devoted to an enlarged study of the potentialities offered by this dual-frequency holography technique: orientation of octupolar molecules, polarisation of highly transparent materials. We also show that the new techniques developed during this work can also reveal to be complementary methods for nonlinear

  15. A family of hyperelastic models for human brain tissue

    Science.gov (United States)

    Mihai, L. Angela; Budday, Silvia; Holzapfel, Gerhard A.; Kuhl, Ellen; Goriely, Alain

    2017-09-01

    Experiments on brain samples under multiaxial loading have shown that human brain tissue is both extremely soft when compared to other biological tissues and characterized by a peculiar elastic response under combined shear and compression/tension: there is a significant increase in shear stress with increasing axial compression compared to a moderate increase with increasing axial tension. Recent studies have revealed that many widely used constitutive models for soft biological tissues fail to capture this characteristic response. Here, guided by experiments of human brain tissue, we develop a family of modeling approaches that capture the elasticity of brain tissue under varying simple shear superposed on varying axial stretch by exploiting key observations about the behavior of the nonlinear shear modulus, which can be obtained directly from the experimental data.

  16. Mixing of two co-directional Rayleigh surface waves in a nonlinear elastic material.

    Science.gov (United States)

    Morlock, Merlin B; Kim, Jin-Yeon; Jacobs, Laurence J; Qu, Jianmin

    2015-01-01

    The mixing of two co-directional, initially monochromatic Rayleigh surface waves in an isotropic, homogeneous, and nonlinear elastic solid is investigated using analytical, finite element method, and experimental approaches. The analytical investigations show that while the horizontal velocity component can form a shock wave, the vertical velocity component can form a pulse independent of the specific ratios of the fundamental frequencies and amplitudes that are mixed. This analytical model is then used to simulate the development of the fundamentals, second harmonics, and the sum and difference frequency components over the propagation distance. The analytical model is further extended to include diffraction effects in the parabolic approximation. Finally, the frequency and amplitude ratios of the fundamentals are identified which provide maximum amplitudes of the second harmonics as well as of the sum and difference frequency components, to help guide effective material characterization; this approach should make it possible to measure the acoustic nonlinearity of a solid not only with the second harmonics, but also with the sum and difference frequency components. Results of the analytical investigations are then confirmed using the finite element method and the experimental feasibility of the proposed technique is validated for an aluminum specimen.

  17. Geometrically and material non-linear analysis of bubble condenser steel structure

    International Nuclear Information System (INIS)

    Gyoergyi, J.; Lenkei, P.

    2003-01-01

    In frame of the project funded by the European Commission (EC) through the Phare and Tacis Programmes experimentally investigate the behaviour of the bubble condenser system (BCS) during phenomena induced by postulated design basis accidents (DBA). The bubble condenser steel structure consists of 12 trays. To enable the Bubble Condenser Test Prototype to be representative of the majority of trays and sections, it was decided to model a typical tray. The test results demonstrate the integrity of the standard tray pressure retaining boundary (side wall, face wall, ceiling and bottom) against a differential pressure (30 kPa). The stability of the side wall and the face wall of tray level 12 was not assured for this differential pressure. The thermal-hydraulic tests demonstrate that the maximum differential pressure across the tray walls in the case of Large Break Loss of Coolant Accident (LBLOCA) is 20 kPa. We have got from the experiences the differential pressure in function of time. The results of the approximate calculations showed the effect of nonlinearly. In case of calculation by FEM model we have done the elastic and linear analyses, and calculated with the geometrically and material non-linearity. (author)

  18. A micro-macro constitutive model for finite-deformation viscoelasticity of elastomers with nonlinear viscosity

    Science.gov (United States)

    Zhou, Jianyou; Jiang, Liying; Khayat, Roger E.

    2018-01-01

    Elastomers are known to exhibit viscoelastic behavior under deformation, which is linked to the diffusion processes of the highly mobile and flexible polymer chains. Inspired by the theories of polymer dynamics, a micro-macro constitutive model is developed to study the viscoelastic behaviors and the relaxation process of elastomeric materials under large deformation, in which the material parameters all have a microscopic foundation or a microstructural justification. The proposed model incorporates the nonlinear material viscosity into the continuum finite-deformation viscoelasticity theories which represent the polymer networks of elastomers with an elastic ground network and a few viscous subnetworks. The developed modeling framework is capable of adopting most of strain energy density functions for hyperelastic materials and thermodynamics evolution laws of viscoelastic solids. The modeling capacity of the framework is outlined by comparing the simulation results with the experimental data of three commonly used elastomeric materials, namely, VHB4910, HNBR50 and carbon black (CB) filled elastomers. The comparison shows that the stress responses and some typical behaviors of filled and unfilled elastomers can be quantitatively predicted by the model with suitable strain energy density functions. Particularly, the strain-softening effect of elastomers could be explained by the deformation-dependent (nonlinear) viscosity of the polymer chains. The presented modeling framework is expected to be useful as a modeling platform for further study on the performance of different type of elastomeric materials.

  19. Diagnostic tool for structural health monitoring: effect of material nonlinearity and vibro-impact process

    Science.gov (United States)

    Hiwarkar, V. R.; Babitsky, V. I.; Silberschmidt, V. V.

    2013-07-01

    Numerous techniques are available for monitoring structural health. Most of these techniques are expensive and time-consuming. In this paper, vibration-based techniques are explored together with their use as diagnostic tools for structural health monitoring. Finite-element simulations are used to study the effect of material nonlinearity on dynamics of a cracked bar. Additionally, several experiments are performed to study the effect of vibro-impact behavior of crack on its dynamics. It was observed that a change in the natural frequency of the cracked bar due to crack-tip plasticity and vibro-impact behavior linked to interaction of crack faces, obtained from experiments, led to generation of higher harmonics; this can be used as a diagnostic tool for structural health monitoring.

  20. Wave Propagation in Linear and Nonlinear Photonic Band-Gap Materials

    National Research Council Canada - National Science Library

    Venakides, Stephanos

    2003-01-01

    .... Development of 3D boundary element code for EM scattering off photonic crystal slabs. Development of 2D FDTD code that includes nonlinearities and use in studying resonant phenomena. Nonlinear Effects...

  1. Design and characterization of a single channel two-liquid capacitor and its application to hyperelastic strain sensing.

    Science.gov (United States)

    Liu, Shanliangzi; Sun, Xiaoda; Hildreth, Owen J; Rykaczewski, Konrad

    2015-03-07

    Room temperature liquid-metal microfluidic devices are attractive systems for hyperelastic strain sensing. These liquid-phase electronics are intrinsically soft and retain their functionality even when stretched to several times their original length. Currently two types of liquid metal-based strain sensors exist for in-plane measurements: single-microchannel resistive and two-microchannel capacitive devices. With a winding serpentine channel geometry, these sensors typically have a footprint of about a square centimeter. This large footprint of an individual device limits the number of sensors that can be embedded into, for example, electronic fabric or skin. In this work we introduce an alternative capacitor design consisting of two liquid metal electrodes separated by a liquid dielectric material within a single straight channel. Using a liquid insulator instead of a solid elastomer enables us to tailor the system's capacitance by selecting high or low dielectric constant liquids. We quantify the effects of the electrode geometry including the diameter, spacing, and meniscus shape as well as the dielectric constant of the insulating liquid on the overall system's capacitance. We also develop a procedure for fabricating the two-liquid capacitor within a single straight polydiemethylsiloxane channel and demonstrate that this device can have about 25 times higher capacitance per sensor's base area when compared to two-channel liquid metal capacitors. Lastly, we characterize the response of this compact device to strain and identify operational issues arising from complex hydrodynamics near liquid-liquid and liquid-elastomer interfaces.

  2. Nonlinear dynamic modeling for smart material electro-hydraulic actuator development

    Science.gov (United States)

    Larson, John P.; Dapino, Marcelo J.

    2013-03-01

    Smart material electro-hydraulic actuators use hydraulic rectification by one-way check valves to amplify the motion of smart materials, such as magnetostrictives and piezoelectrics, in order to create compact, lightweight actuators. A piston pump driven by a smart material is combined with a hydraulic cylinder to form a self-contained, power-by-wire actuator that can be used in place of a conventional hydraulic system without the need for hydraulic lines and a centralized pump. The performance of an experimental actuator driven by a 12.7 mm diameter, 114 mm length Terfenol-D rod is evaluated over a range of applied input frequencies, loads, and currents. The peak performance achieved is 37 W, moving a 220 N load at a rate of 17 cm/s and producing a blocked pressure of 12.5 MPa. Additional tests are conducted to quantify the dynamic behavior of the one-way reed valves using a scanning laser vibrometer to identify the frequency response of the reeds and the effect of the valve seat and fluid mass loading. A lumped-parameter model is developed for the system that includes valve inertia and fluid response nonlinearities, and the model results are compared with the experimental data.

  3. Study of the Mechanical Behavior of a Hyperelastic Membrane

    Directory of Open Access Journals (Sweden)

    Bourbaba Houaria

    2014-04-01

    Full Text Available The benefits in emloying plastics material in microfluidic devices manufactures are extremely attractive that include reduced cost and simplified manufacturing procedures, particularly when compared to silicon. An additional benefit is the wide range of available plastic materials which allow the manufacturer to choose materials' properties suitable for their specific application. The Polydimethylsiloxane is commonly used in a wide range of microfluidic applications due to its flexibility and low cost. In addition the properties of the Polymethyl methacrylate such as the low cost, high transparency, and good chemical properties are needed in microfluidics applications. In this paper, we have used Finit Elements method to simulate the mechanical behavior of Polydimethylsiloxane and Polymethylmethacrylate using hyper elastic and linear elastic model. Sevral parameters have been studied; such as, thickness and number of mesh in order to optimize the dimension of the membrane. Also, we have studied the impact of the mesh form on the membrane’s displacement.

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

    Science.gov (United States)

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

    2018-02-01

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

  5. Extension of One-Dimensional Models for Hyperelastic String Structures under Coulomb Friction with Adhesion

    Directory of Open Access Journals (Sweden)

    Vladimir Shiryaev

    2018-04-01

    Full Text Available A stretching behavior of knitted and woven textiles is modeled. In our work, the yarns are modeled as one-dimensional hyperelastic strings with frictional contact. Capstan law known for Coulomb’s friction of yarns is extended to an additional adhesion due to gluing of filaments on the yarn surface or some chemical reaction. Two-step Newton’s method is applied for the solution of the large stretching with sliding evolution in the contact nodes. The approach is illustrated on a hysteresis of knitted textile and on the force-strain curve for a woven pattern and both compared with experimental effective curves.

  6. Combining Approach in Stages with Least Squares for fits of data in hyperelasticity

    Science.gov (United States)

    Beda, Tibi

    2006-10-01

    The present work concerns a method of continuous approximation by block of a continuous function; a method of approximation combining the Approach in Stages with the finite domains Least Squares. An identification procedure by sub-domains: basic generating functions are determined step-by-step permitting their weighting effects to be felt. This procedure allows one to be in control of the signs and to some extent of the optimal values of the parameters estimated, and consequently it provides a unique set of solutions that should represent the real physical parameters. Illustrations and comparisons are developed in rubber hyperelastic modeling. To cite this article: T. Beda, C. R. Mecanique 334 (2006).

  7. Hyperelastic modelling of the crystalline lens: Accommodation and presbyopia

    Science.gov (United States)

    Lanchares, Elena; Navarro, Rafael; Calvo, Begoña

    2012-01-01

    Purpose The modification of the mechanical properties of the human crystalline lens with age can be a major cause of presbyopia. Since these properties cannot be measured in vivo, numerical simulation can be used to estimate them. We propose an inverse method to determine age-dependent change in the material properties of the tissues composing the human crystalline lens. Methods A finite element model of a 30-year-old lens in the accommodated state was developed. The force necessary to achieve full accommodation in a 30-year-old lens of known external geometry was computed using this model. Two additional numerical models of the lens corresponding to the ages of 40 and 50 years were then built. Assuming that the accommodative force applied to the lens remains constant with age, the material properties of nucleus and cortex were estimated by inverse analysis. Results The zonular force necessary to reshape the model of a 30-year-old lens from the accommodated to the unaccommodated geometry was 0.078 newton (N). Both nucleus and cortex became stiffer with age. The stiffness of the nucleus increased with age at a higher rate than the cortex. Conclusions In agreement with the classical theory of Helmholtz, on which we based our model, our results indicate that a major cause of presbyopia is that both nucleus and cortex become stiffer with age; therefore, a constant value of the zonular forces with aging does not achieve full accommodation, that is, the accommodation capability decreases.

  8. Nonlinear analysis of thermally and electrically actuated functionally graded material microbeam.

    Science.gov (United States)

    Li, Yingli; Meguid, S A; Fu, Yiming; Xu, Daolin

    2014-02-08

    In this paper, we provide a unified and self-consistent treatment of a functionally graded material (FGM) microbeam with varying thermal conductivity subjected to non-uniform or uniform temperature field. Specifically, it is our objective to determine the effect of the microscopic size of the beam, the electrostatic gap, the temperature field and material property on the pull-in voltage of the microbeam under different boundary conditions. The non-uniform temperature field is obtained by integrating the steady-state heat conduction equation. The governing equations account for the microbeam size by introducing an internal material length-scale parameter that is based on the modified couple stress theory. Furthermore, it takes into account Casimir and van der Waals forces, and the associated electrostatic force with the first-order fringing field effects. The resulting nonlinear differential equations were converted to a coupled system of algebraic equations using the differential quadrature method. The outcome of our work shows the dramatic effect and dependence of the pull-in voltage of the FGM microbeam upon the temperature field, its gradient for a given boundary condition. Specifically, both uniform and non-uniform thermal loading can actuate the FGM microbeam even without an applied voltage. Our work also reveals that the non-uniform temperature field is more effective than the uniform temperature field in actuating a FGM cantilever-type microbeam. For the clamped-clamped case, care must be taken to account for the effective use of thermal loading in the design of microbeams. It is also observed that uniform thermal loading will lead to a reduction in the pull-in voltage of a FGM microbeam for all the three boundary conditions considered.

  9. Determination of the buckling safety of reinforced concrete shells considering the nonlinear material-behavior

    International Nuclear Information System (INIS)

    Zerna, W.; Mungan, I.; Steffen, W.

    1980-01-01

    The equations of the bending and stability theories for the orthotropic shell are solved using the FEM. A biaxial material law for concrete and a nearly bilinear stress-strain diagram for reinforcing steel were considered. Taking a layered ring element the influence of bending moments together with the membrane forces can be followed under increasing load up to failure of concrete or steel. At each level the bucking factor can be calculated considering the stress dependent buckling stiffness. The method of calculation is applied to a cooling tower shell under dead load acting simultaneously with an axi-symmetric loading to compensate for the wind effect. Due to orthotropy and descending tangent modulus at the ultimate load the buckling load factor drops to the half of the value obtained assuming a linear elastic behaviour. Additional parametric studies demonstrate the effect of some hypothetic cracks of different position and depth of the bifurcation results. The variation of the safety factors against buckling and ultimate load is obtained by changing the shell thickness. For the shell investigated it turns out that the buckling safety is influenced much more than the safety against material failure if the wall thickness is varied. It is recommended to split the buckling analysis of reinforced concrete shells in two parts. For shells of parts of a shell under only slightly disturbed membrane stress state the buckling analysis governs, otherwise the ultimate state considering the geometric and material nonlinearities is decisive to obtain not only the wall thickness but also the amount of reinforced necessary. (orig./HP) [de

  10. Solution strategies for linear and nonlinear instability phenomena for arbitrarily thin shell structures

    International Nuclear Information System (INIS)

    Eckstein, U.; Harte, R.; Kraetzig, W.B.; Wittek, U.

    1983-01-01

    In order to describe nonlinear response and instability behaviour the paper starts with the total potential energy considering the basic kinematic equations of a consistent nonlinear shell theory for large displacements and moderate rotations. The material behaviour is assumed to be hyperelastic and isotropic. The incrementation and discretization of the total potential energy leads to the tangent stiffness relation, which is the central equation of computational algorithms based on combined incremental and iterative techniques. Here a symmetrized form of the RIKS/WEMPNER-algorithm for positive and negative load incrementation represents the basis of the nonlinear solution technique. To detect secondary equilibrium branches at points of neutral equilibrium within nonlinear primary paths a quadratic eigenvalue-problem has to be solved. In order to follow those complicated nonlinear response phenomena the RIKS/WEMPNER incrementation/iteration process is combined with a simultaneous solution of the linearized quadratic eigenvalue-problem. Additionally the essentials of a recently derived family of arbitrarily curved shell elements for linear (LACS) and geometrically nonlinear (NACS) shell problems are presented. The main advantage of these elements is the exact description of all geometric properties as well as the energy-equivalent representation of the applied loads in combination with an efficient algorithm to form the stiffness submatrices. Especially the NACS-elements are designed to improve the accuracy of the solution in the deep postbuckling range including moderate rotations. The derived finite elements and solution strategies are applied to a certain number of typical shell problems to prove the precision of the shell elements and to demonstrate the possibilities of tracing linear and nonlinear bifurcation problems as well as snap-through phenomena with and without secondary bifurcation branches. (orig.)

  11. X-ray topographic studies of organic and non-linear optical materials

    International Nuclear Information System (INIS)

    Halfpenny, P. J.; Sherwood, J. N.; Simpson, G. S.

    1997-01-01

    The flexible and non-destructive nature of X-ray topography is ideally suited to the study of large single crystals for both fundamental research and technological applications as well as the optimisation of crystal growth processes. Three examples are discussed, illustrating the application of X-ray topographic methods to non-linear optical (NLO) crystals. Synchrotron radiation section topography has been applied to the examination of large organic crystals. X-ray topography has been used to examine growth defects and the quality of crystals of m-nitroaniline (mNA) grown by the Bridgeman method. These studies allow evaluation of growth parameters together with their influence on defect density and show that in the case of mNA, remarkably low defect densities can be achieved under optimum growth conditions. Double-crystal reflection topography, with synchrotron radiation has been used to image defects intersecting the (011) faces of the inorganic NLO material potassium titanyl phosphate (KTP). X-ray images have been combined with optical microscopy and interferometry to provide valuable information on the crystal growth process

  12. Nonlinear optics in germanium mid-infrared fiber material: Detuning oscillations in femtosecond mid-infrared spectroscopy

    Directory of Open Access Journals (Sweden)

    M. Ordu

    2017-09-01

    Full Text Available Germanium optical fibers hold great promise in extending semiconductor photonics into the fundamentally important mid-infrared region of the electromagnetic spectrum. The demonstration of nonlinear response in fabricated Ge fiber samples is a key step in the development of mid-infrared fiber materials. Here we report the observation of detuning oscillations in a germanium fiber in the mid-infrared region using femtosecond dispersed pump-probe spectroscopy. Detuning oscillations are observed in the frequency-resolved response when mid-infrared pump and probe pulses are overlapped in a fiber segment. The oscillations arise from the nonlinear frequency resolved nonlinear (χ(3 response in the germanium semiconductor. Our work represents the first observation of coherent oscillations in the emerging field of germanium mid-infrared fiber optics.

  13. High-order nonlinear optical processes in ablated carbon-containing materials: Recent approaches in development of the nonlinear spectroscopy using harmonic generation in the extreme ultraviolet range

    Science.gov (United States)

    Ganeev, R. A.

    2017-08-01

    The nonlinear spectroscopy using harmonic generation in the extreme ultraviolet range became a versatile tool for the analysis of the optical, structural and morphological properties of matter. The carbon-contained materials have shown the advanced properties among other studied species, which allowed both the definition of the role of structural properties on the nonlinear optical response and the analysis of the fundamental features of carbon as the attractive material for generation of coherent short-wavelength radiation. We review the studies of the high-order harmonic generation by focusing ultrashort pulses into the plasmas produced during laser ablation of various organic compounds. We discuss the role of ionic transitions of ablated carbon-containing molecules on the harmonic yield. We also show the similarities and distinctions of the harmonic and plasma spectra of organic compounds and graphite. We discuss the studies of the generation of harmonics up to the 27th order (λ = 29.9 nm) of 806 nm radiation in the boron carbide plasma and analyze the advantages and disadvantages of this target compared with the ingredients comprising B4C (solid boron and graphite) by comparing plasma emission and harmonic spectra from three species. We also show that the coincidence of harmonic and plasma emission wavelengths in most cases does not cause the enhancement or decrease of the conversion efficiency of this harmonic.

  14. A nonlinear beam model to describe the postbuckling of wide neo-Hookean beams

    Science.gov (United States)

    Lubbers, Luuk A.; van Hecke, Martin; Coulais, Corentin

    2017-09-01

    Wide beams can exhibit subcritical buckling, i.e. the slope of the force-displacement curve can become negative in the postbuckling regime. In this paper, we capture this intriguing behaviour by constructing a 1D nonlinear beam model, where the central ingredient is the nonlinearity in the stress-strain relation of the beams constitutive material. First, we present experimental and numerical evidence of a transition to subcritical buckling for wide neo-Hookean hyperelastic beams, when their width-to-length ratio exceeds a critical value of 12%. Second, we construct an effective 1D energy density by combining the Mindlin-Reissner kinematics with a nonlinearity in the stress-strain relation. Finally, we establish and solve the governing beam equations to analytically determine the slope of the force-displacement curve in the postbuckling regime. We find, without any adjustable parameters, excellent agreement between the 1D theory, experiments and simulations. Our work extends the understanding of the postbuckling of structures made of wide elastic beams and opens up avenues for the reverse-engineering of instabilities in soft and metamaterials.

  15. A general nonlinear magnetomechanical model for ferromagnetic materials under a constant weak magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Shi, Pengpeng; Zheng, Xiaojing, E-mail: xjzheng@xidian.edu.cn [School of Mechano-Electronic Engineering, Xidian University, Xi' an 710071, Shaanxi (China); Jin, Ke [School of Aerospace Science and Technology, Xidian University, Xi' an 710071, Shaanxi (China)

    2016-04-14

    Weak magnetic nondestructive testing (e.g., metal magnetic memory method) concerns the magnetization variation of ferromagnetic materials due to its applied load and a weak magnetic surrounding them. One key issue on these nondestructive technologies is the magnetomechanical effect for quantitative evaluation of magnetization state from stress–strain condition. A representative phenomenological model has been proposed to explain the magnetomechanical effect by Jiles in 1995. However, the Jiles' model has some deficiencies in quantification, for instance, there is a visible difference between theoretical prediction and experimental measurements on stress–magnetization curve, especially in the compression case. Based on the thermodynamic relations and the approach law of irreversible magnetization, a nonlinear coupled model is proposed to improve the quantitative evaluation of the magnetomechanical effect. Excellent agreement has been achieved between the predictions from the present model and previous experimental results. In comparison with Jiles' model, the prediction accuracy is improved greatly by the present model, particularly for the compression case. A detailed study has also been performed to reveal the effects of initial magnetization status, cyclic loading, and demagnetization factor on the magnetomechanical effect. Our theoretical model reveals that the stable weak magnetic signals of nondestructive testing after multiple cyclic loads are attributed to the first few cycles eliminating most of the irreversible magnetization. Remarkably, the existence of demagnetization field can weaken magnetomechanical effect, therefore, significantly reduces the testing capability. This theoretical model can be adopted to quantitatively analyze magnetic memory signals, and then can be applied in weak magnetic nondestructive testing.

  16. 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

  17. Hyperelastic skin

    Science.gov (United States)

    ... is most often seen in people who have Ehlers-Danlos syndrome. People with this disorder have very elastic skin. ... any member of your family been diagnosed with Ehlers-Danlos syndrome? What other symptoms are present? Genetic counseling may ...

  18. Evaluation of solution procedures for material and/or geometrically nonlinear structural analysis by the direct stiffness method.

    Science.gov (United States)

    Stricklin, J. A.; Haisler, W. E.; Von Riesemann, W. A.

    1972-01-01

    This paper presents an assessment of the solution procedures available for the analysis of inelastic and/or large deflection structural behavior. A literature survey is given which summarized the contribution of other researchers in the analysis of structural problems exhibiting material nonlinearities and combined geometric-material nonlinearities. Attention is focused at evaluating the available computation and solution techniques. Each of the solution techniques is developed from a common equation of equilibrium in terms of pseudo forces. The solution procedures are applied to circular plates and shells of revolution in an attempt to compare and evaluate each with respect to computational accuracy, economy, and efficiency. Based on the numerical studies, observations and comments are made with regard to the accuracy and economy of each solution technique.

  19. Modeling the Creep of Rib-Reinforced Composite Media Made from Nonlinear Hereditary Phase Materials 2. Verification of the Model

    Science.gov (United States)

    Yankovskii, A. P.

    2015-05-01

    An indirect verification of a structural model describing the creep of a composite medium reinforced by honeycombs and made of nonlinear hereditary phase materials obeying the Rabotnov theory of creep is presented. It is shown that the structural model proposed is trustworthy and can be used in practical calculations. For different kinds of loading, creep curves for a honeycomb core made of a D16T aluminum alloy are calculated.

  20. Growth and characterization of benzaldehyde 4-nitro phenyl hydrazone (BPH) single crystal: A proficient second order nonlinear optical material

    Science.gov (United States)

    Saravanan, M.; Abraham Rajasekar, S.

    2016-04-01

    The crystals (benzaldehyde 4-nitro phenyl hydrazone (BPH)) appropriate for NLO appliance were grown by the slow cooling method. The solubility and metastable zone width measurement of BPH specimen was studied. The material crystallizes in the monoclinic crystal system with noncentrosymmetric space group of Cc. The optical precision in the whole visible region was found to be excellent for non-linear optical claim. Excellence of the grown crystal is ascertained by the HRXRD and etching studies. Laser Damage Threshold and Photoluminescence studies designate that the grown crystal contains less imperfection. The mechanical behaviour of BPH sample at different temperatures was investigated to determine the hardness stability of the grown specimen. The piezoelectric temperament and the relative Second Harmonic Generation (for diverse particle sizes) of the material were also studied. The dielectric studies were executed at varied temperatures and frequencies to investigate the electrical properties. Photoconductivity measurement enumerates consummate of inducing dipoles due to strong incident radiation and also divulge the nonlinear behaviour of the material. The third order nonlinear optical properties of BPH crystals were deliberate by Z-scan method.

  1. Mathematical and numerical analysis of hyper-elastic systems and introduction of plasticity

    International Nuclear Information System (INIS)

    Kluth, G.

    2008-12-01

    The goal is to model mathematically and numerically the dynamic phenomenons for solids in finite plasticity. We suggest a model that we call hyper-elasto-plastic based on hyper-elastic systems of conservation laws and on the use of an equation of state that we have constructed so as to achieve the plastic yield criterion of Von Mises. This model gives exact (analytic) solutions with shock split to flyer-plate experiments. The mathematical analysis of this model is done (hyperbolicity, characteristic fields, involutions and entropy). In the numerical part, we give 1D and 2D Lagrangian schemes which satisfy an entropy criterion. Moreover, thanks to a special discretization of the equations on deformation gradient, we satisfy some discrete involutions. In this work, the degeneracy of the solid model into hydrodynamic models is studied at the continuous level, and achieved at the numerical one. On different problems, we show the validity of our model and our numerical schemes. (author)

  2. 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

  3. Synthesis, crystal structure, growth, optical and third order nonlinear optical studies of 8HQ2C5N single crystal - An efficient third-order nonlinear optical material

    Energy Technology Data Exchange (ETDEWEB)

    Divya Bharathi, M.; Ahila, G.; Mohana, J. [Department of Physics, Presidency College, Chennai 600005 (India); Chakkaravarthi, G. [Department of Physics, CPCL Polytechnic College, Chennai 600068 (India); Anbalagan, G., E-mail: anbu24663@yahoo.co.in [Department of Nuclear Physics, University of Madras, Chennai 600025 (India)

    2017-05-01

    A neoteric organic third order nonlinear optical material 8-hydroxyquinolinium 2-chloro-5-nitrobenzoate dihydrate (8HQ2C5N) was grown by slow cooling technique using ethanol: water (1:1) mixed solvent. The calculated low value of average etch pit solidity (4.12 × 10{sup 3} cm{sup −2}) indicated that the title crystal contain less defects. From the single crystal X-ray diffraction data, it was endowed that 8HQ2C5N crystal belongs to the monoclinic system with centrosymmetric space group P2{sub 1}/c and the cell parameters values, a = 9.6546 (4) Ǻ, b = 7.1637(3) Ǻ, c = 24.3606 (12) Ǻ, α = γ = 90°, β = 92.458(2)° and volume = 1683.29(13) Ǻ{sup 3}. The FT-IR and FT-Raman spectrum were used to affirm the functional group of the title compound. The chemical structure of 8HQ2C5N was scrutinized by {sup 13}C and {sup 1}H NMR spectral analysis and thermal stability through the differential scanning calorimetry study. Using optical studies the lower cut-off wavelength and optical band gap of 8HQ2C5N were found to be 364 nm and 3.17 eV respectively. Using the single oscillator model suggested by Wemple – Didomenico, the oscillator energy (E{sub o}), the dispersion energy (E{sub d}) and static dielectric constant (ε{sub o}) were estimated. The third-order susceptibility were determined as Im χ{sup (3)} = 2.51 × 10{sup −5} esu and Re χ{sup (3)} = 4.46 × 10{sup −7} esu. The theoretical third-order nonlinear optical susceptibility χ{sup (3)} was calculated and the results were compared with experimental value. Photoluminescence spectrum of 8HQ2C5N crystal showed the yellow emission. The crystal had the single shot laser damage threshold of 5.562 GW/cm{sup 2}. Microhardness measurement showed that 8HQ2C5N belongs to a soft material category. - Highlights: • A new organic single crystals were grown and the crystal structure was reported. • Crystal possess, good transmittance, thermal and mechanical stability. • Single shot LDT value is found to be

  4. Reconstruction of the residual stresses in a hyperelastic body using ultrasound techniques

    KAUST Repository

    Joshi, Sunnie

    2013-09-01

    This paper focuses on a novel approach for characterizing the residual stress field in soft tissue using ultrasound interrogation. A nonlinear inverse spectral technique is developed that makes fundamental use of the finite strain nonlinear response of the material to a quasi-static loading. The soft tissue is modeled as a nonlinear, prestressed and residually stressed, isotropic, slightly compressible elastic body with a rectangular geometry. A boundary value problem is formulated for the residually stressed and prestressed soft tissue, the boundary of which is subjected to a quasi-static pressure, and then an idealized model for the ultrasound interrogation is constructed by superimposing small amplitude time harmonic infinitesimal vibrations on static finite deformation via an asymptotic construction. The model is studied, through a semi-inverse approach, for a specific class of deformations that leads to a system of second order differential equations with homogeneous boundary conditions of Sturm-Liouville type. By making use of the classical theory of inverse Sturm-Liouville problems, and root finding and optimization techniques, several inverse spectral algorithms are developed to approximate the residual stress distribution in the body, given the first few eigenfrequencies of several induced static pressures. © 2013 Elsevier Ltd. All rights reserved.

  5. Nonlinear and anisotropic polarization rotation in two-dimensional Dirac materials

    Science.gov (United States)

    Singh, Ashutosh; Ghosh, Saikat; Agarwal, Amit

    2018-05-01

    We predict nonlinear optical polarization rotation in two-dimensional massless Dirac systems including graphene and 8-P m m n borophene. When illuminated, a continuous-wave optical field leads to a nonlinear steady state of photoexcited carriers in the medium. The photoexcited population inversion and the interband coherence give rise to a finite transverse optical conductivity σx y(ω ) . This in turn leads to definitive signatures in associated Kerr and Faraday polarization rotation, which are measurable in a realistic experimental scenario.

  6. Growth and characterizaion of urea p-nitrophenol crystal: an organic nonlinear optical material for optoelectronic device application

    Science.gov (United States)

    Suresh, A.; Manikandan, N.; Jauhar, RO. MU.; Murugakoothan, P.; Vinitha, G.

    2018-06-01

    Urea p-nitrophenol, an organic nonlinear optical crystal was synthesized and grown adopting slow evaporation and seed rotation method. Single crystal X-ray diffraction study confirmed the formation of the desired crystal. High resolution X-ray diffraction study showed the defect nature of the crystal. The presence of functional groups in the material was confirmed by FTIR analysis. UV-Vis-NIR study indicates that the grown crystal has a wider transparency region with the lower cutoff wavelength at 423 nm. The grown crystal is thermally stable up to 120 °C as assessed by TG-DTA analysis. The optical homogeneity of the grown crystal was confirmed by birefringence study. The 1064 nm Nd-YAG laser was used to obtain laser induced surface damage threshold which was found to be 0.38, 0.25 and 0.33 GW/cm2 for (0 1 0), (1 1 - 1) and (0 1 1) planes, respectively. The dielectric study was performed to find the charge distribution inside the crystal. The hardness property of the titular material has been found using Vicker's microhardness study. The optical nonlinearity obtained from third order nonlinear optical measurements carried out using Z-scan technique showed that these samples could be exploited for optical limiting studies.

  7. Comparison of linear and non-linear models for the adsorption of fluoride onto geo-material: limonite.

    Science.gov (United States)

    Sahin, Rubina; Tapadia, Kavita

    2015-01-01

    The three widely used isotherms Langmuir, Freundlich and Temkin were examined in an experiment using fluoride (F⁻) ion adsorption on a geo-material (limonite) at four different temperatures by linear and non-linear models. Comparison of linear and non-linear regression models were given in selecting the optimum isotherm for the experimental results. The coefficient of determination, r², was used to select the best theoretical isotherm. The four Langmuir linear equations (1, 2, 3, and 4) are discussed. Langmuir isotherm parameters obtained from the four Langmuir linear equations using the linear model differed but they were the same when using the nonlinear model. Langmuir-2 isotherm is one of the linear forms, and it had the highest coefficient of determination (r² = 0.99) compared to the other Langmuir linear equations (1, 3 and 4) in linear form, whereas, for non-linear, Langmuir-4 fitted best among all the isotherms because it had the highest coefficient of determination (r² = 0.99). The results showed that the non-linear model may be a better way to obtain the parameters. In the present work, the thermodynamic parameters show that the absorption of fluoride onto limonite is both spontaneous (ΔG 0). Scanning electron microscope and X-ray diffraction images also confirm the adsorption of F⁻ ion onto limonite. The isotherm and kinetic study reveals that limonite can be used as an adsorbent for fluoride removal. In future we can develop new technology for fluoride removal in large scale by using limonite which is cost-effective, eco-friendly and is easily available in the study area.

  8. Nonlinear dynamic analysis and state space representation of a manipulator under viscoelastic material conditions

    Directory of Open Access Journals (Sweden)

    Esfandiar, H.

    2013-05-01

    Full Text Available In this paper, based on the VoigtKelvin constitutive model, nonlinear dynamic modelling and state space representation of a viscoelastic beam acting as a flexible robotic manipulator is investigated. Complete nonlinear dynamic modelling of a viscoelastic beam without premature linearisation of dynamic equations is developed. The adopted method is capable of reproducing nonlinear dynamic effects, such as beam stiffening due to centrifugal and Coriolis forces induced by rotation of the joints. Structural damping effects on the models dynamic behaviour are also shown. A reliable model for a viscoelastic beam is subsequently presented. The governing equations of motion are derived using Hamiltons principle, and using the finite difference method, nonlinear partial differential equations are reduced to ordinary differential equations. For the purpose of flexible manipulator control, the standard form of state space equations for the viscoelastic link and the actuator is obtained. Simulation results indicate substantial improvements in dynamic behaviour, and a parameter sensitivity study is carried out to investigate the effect of structural damping on the vibration amplitude.

  9. Nonlinear and anisotropic tensile properties of graft materials used in soft tissue applications.

    Science.gov (United States)

    Yoder, Jonathon H; Elliott, Dawn M

    2010-05-01

    The mechanical properties of extracellular matrix grafts that are intended to augment or replace soft tissues should be comparable to the native tissue. Such grafts are often used in fiber-reinforced tissue applications that undergo multi-axial loading and therefore knowledge of the anisotropic and nonlinear properties are needed, including the moduli and Poisson's ratio in two orthogonal directions within the plane of the graft. The objective of this study was to measure the tensile mechanical properties of several marketed grafts: Alloderm, Restore, CuffPatch, and OrthADAPT. The degree of anisotropy and non-linearity within each graft was evaluated from uniaxial tensile tests and compared to their native tissue. The Alloderm graft was anisotropic in both the toe- and linear-region of the stress-strain response, was highly nonlinear, and generally had low properties. The Restore and CuffPatch grafts had similar stress-strain responses, were largely isotropic, had a linear-region modulus of 18MPa, and were nonlinear. OrthADAPT was anisotropic in the linear-region (131 MPA vs 47MPa in the toe-region) and was highly nonlinear. The Poisson ratio for all grafts was between 0.4 and 0.7, except for the parallel orientation of Restore which was greater than 1.0. Having an informed understanding of how the available grafts perform mechanically will allow for better assessment by the physician for which graft to apply depending upon its application. Copyright 2010 Elsevier Ltd. All rights reserved.

  10. A continuum mechanics framework for hyperelastic materials: connecting experiments and modelling

    OpenAIRE

    García González, Daniel

    2016-01-01

    Mención Internacional en el título de doctor La investigación llevada a cabo en esta Tesis Doctoral proporciona nuevas ideas y metodologías para el desarrollo de modelos constitutivos con base hiperelástica, con fundamentación física y basados en evidencias experimentales. Estos modelos han sido aplicados al estudio del comportamiento termomecánico de polímeros termoplásticos y tejidos blandos en un amplio intervalo de condiciones de trabajo. La simulación de este tipo de só...

  11. Recovery of material parameters of soft hyperelastic tissue by an inverse spectral technique

    KAUST Repository

    Gou, Kun; Joshi, Sunnie; Walton, Jay R.

    2012-01-01

    An inverse spectral method is developed for recovering a spatially inhomogeneous shear modulus for soft tissue. The study is motivated by a novel use of the intravascular ultrasound technique to image arteries. The arterial wall is idealized as a

  12. Computation of the current density in nonlinear materials subjected to large current pulses

    International Nuclear Information System (INIS)

    Hodgdon, M.L.; Hixson, R.S.; Parsons, W.M.

    1991-01-01

    This paper reports that the finite element method and the finite difference method are used to calculate the current distribution in two nonlinear conductors. The first conductor is a small ferromagnetic wire subjected to a current pulse that rises to 10,000 Amperes in 10 microseconds. Results from the transient thermal and transient magnetic solvers of the finite element code FLUX2D are used to compute the current density in the wire. The second conductor is a metal oxide varistor. Maxwell's equations, Ohm's law and the varistor relation for the resistivity and the current density of p = αj -β are used to derive a nonlinear differential equation. The solutions of the differential equation are obtained by a finite difference approximation and a shooting method. The behavior predicted by these calculations is in agreement with experiments

  13. Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material

    Directory of Open Access Journals (Sweden)

    M. Awais

    2018-03-01

    Full Text Available The present analysis is related to the dynamics of polymeric liquids (Oldroyd-B model with the presence of nanoparticles. The rheological system is considered under the application of nonlinear thermal radiations. Energy and concentration equations are presented when thermophoresis and Brownian motion effects are present. Bidirectional form of stretching is considered to interpret the three-dimensional flow dynamics of polymeric liquid. Making use of the similarity transformations, problem is reduced into ordinary differential system which is approximated by using HAM. Influence of physical parameters including Deborah number, thermophoresis and Brownian motion on velocity, temperature and mass fraction expressions are plotted and analyzed. Numerical values for local Sherwood and Nusselt numbers are presented and discussed. Keywords: Nanoparticles, Polymeric liquid, Oldroyd-B model, Nonlinear thermal radiation

  14. Updated Lagrangian finite element formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review.

    Science.gov (United States)

    Townsend, Molly T; Sarigul-Klijn, Nesrin

    2016-01-01

    Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated Lagrangian formulation comprehensive procedure of various non-linear material models for the application of finite element analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.

  15. GEOMETRIC AND MATERIAL NONLINEAR ANALYSIS OF REINFORCED CONCRETE SLABS AT FIRE ENVIRONMENT

    Directory of Open Access Journals (Sweden)

    Ayad A. Abdul -Razzak

    2013-05-01

    Full Text Available In the present study a nonlinear finite element analysis is presented  to predict the fire resistance of reinforced concrete slabs at fire environment. An eight node layered degenerated shell element utilizing Mindlin/Reissner thick plate theory is employed. The proposed model considered cracking, crushing and yielding of concrete and steel at elevated temperatures. The layered approach is used to represent the steel reinforcement and discretize the concrete slab through the thickness. The reinforcement steel is represented as a smeared layer of equivalent thickness with uniaxial strength and rigidity properties.Geometric nonlinear analysis may play an important role in the behavior of reinforced concrete slabs at high temperature. Geometrical nonlinearity in the layered approach is considered in the mathematical model, which is based on the total Lagrangian approach taking into account Von Karman assumptions.Finally two examples for which experimental results are available are analyzed, using the proposed model .The comparison showed good agreement with experimental results. 

  16. FY 1991 Report on the results of the researches on nonlinear photoelectronic materials; 1991 nendo hisenkei hikari denshi zairyo no kenkyu kaihatsu seika hokokusho

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1992-03-01

    The nonlinear optics with light-light conversion and electro-optical effects are expected to be the optical materials of the next generation for their functions of, e.g., conversion of the infrared laser beams into visual light, and optical switching. The efforts are directed to development of the procedures for exploring and designing various raw materials, and technologies for synthesizing the raw materials and for producing and evaluating the materials, in order to develop highly nonlinear, high-speed responding materials. Three areas are studied; for the organic materials, the chiral nonlinear effects are demonstrated and the new procedure for determining electrical susceptibility ({gamma}) is developed; for the dispersed materials, highly nonlinear susceptibility of glass dispersed with fine particles of semiconductors, e.g., CuCl, is realized, and possibility of controlled dispersion of fine semiconductor particles in an organic polymer is established; and for development of the superlattice-based materials, the layered structures of thin organic superlattice films are studied, the thin semiconductor films of high purity and little defects are prepared, and development of the three-dimensional structures is started. The individual researches are conducted, 3 for the organic materials, 4 for the dispersed materials, and 2 for the superlattice-based materials. The targets of susceptibility and response are 10{sup -8}esu or more and 10ps or less, respectively. (NEDO)

  17. FY 1998 annual report on the research and development of non-linear, opto-electronic materials; 1998 nendo hisenkei hikari denshi zairyo no kenkyu kaihatsu seika hokokusho

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1999-03-01

    The final assessment of researches on non-linear, opto-electronic materials was conducted in FY 1988. These researches are evaluated as the world-level basic researches, high in potential of giving ripple effects on various areas. The R and D themes are organic, low-molecular-weight materials; technology for orientation-controlled crystal growth; conjugated polymer films; microcrystallite-doped glasses using vapor deposition and stuffing method; glass composite materials using sol-gel method and ultra-low melting point glass; nanoparticle-dispersed glasses using super-cooling technology; materials dispersed in organic compounds; organic superlattice formation; three-dimensionally superstructured materials; and comprehensive surveys and researches. The researches and surveys on the common basic techniques were recommissioned to Universities of Tokyo, Keio Gijuku, Nagoya, Tohoku and Hokkaido. These themes are analytical methods for non-linear optical characteristics; morphology-controlled crystal growth of nonlinear-optical organic materials and fundamental studies on all-optical devices; large enhancement of optical nonlinearity and its mechanism in nanocrystals embedded in matrices; improvement of organic materials for high performance; and ultrafast nonlinear optical processes and their application for controlling ultrafast optical pulses. (NEDO)

  18. Asymmetric induced cubic nonlinearities in homogeneous and quasi-phase-matched quadratic materials: signature and importance

    DEFF Research Database (Denmark)

    Bang, Ole; Corney, Joel Frederick

    2001-01-01

    In continuous-wave operation asymmetric induced nonlinearities induce an intensity-dependent phase mismatch that implies a nonzero so-called separatrix intensity, the crossing of which changes the one-period phase shift of the fundamental by Pi , with obvious use in switching applications.......We derived a formula for this QPM-induced separatrix intensity that corrects earlier estimates by a factor of 5.3, and we found the optimum crystal lengths for a flat phase-versus-intensity response on each side of the separatrix...

  19. Nonlinear optics

    CERN Document Server

    Boyd, Robert W

    2013-01-01

    Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q

  20. Nonlinear inversion of borehole-radar tomography data to reconstruct velocity and attenuation distribution in earth materials

    Science.gov (United States)

    Zhou, C.; Liu, L.; Lane, J.W.

    2001-01-01

    A nonlinear tomographic inversion method that uses first-arrival travel-time and amplitude-spectra information from cross-hole radar measurements was developed to simultaneously reconstruct electromagnetic velocity and attenuation distribution in earth materials. Inversion methods were developed to analyze single cross-hole tomography surveys and differential tomography surveys. Assuming the earth behaves as a linear system, the inversion methods do not require estimation of source radiation pattern, receiver coupling, or geometrical spreading. The data analysis and tomographic inversion algorithm were applied to synthetic test data and to cross-hole radar field data provided by the US Geological Survey (USGS). The cross-hole radar field data were acquired at the USGS fractured-rock field research site at Mirror Lake near Thornton, New Hampshire, before and after injection of a saline tracer, to monitor the transport of electrically conductive fluids in the image plane. Results from the synthetic data test demonstrate the algorithm computational efficiency and indicate that the method robustly can reconstruct electromagnetic (EM) wave velocity and attenuation distribution in earth materials. The field test results outline zones of velocity and attenuation anomalies consistent with the finding of previous investigators; however, the tomograms appear to be quite smooth. Further work is needed to effectively find the optimal smoothness criterion in applying the Tikhonov regularization in the nonlinear inversion algorithms for cross-hole radar tomography. ?? 2001 Elsevier Science B.V. All rights reserved.

  1. Non-Linear Optical Phenomena in Detecting Materials as a Possibility for Fast Timing in Detectors of Ionizing Radiation

    CERN Document Server

    Korjik, M. V.; Buganov, O.; Fedorov, A. A.; Emelianchik, I.; Griesmayer, E.; Mechinsky, V.; Nargelas, S.; Sidletskiy, O.; Tamulaitis, G.; Tikhomirov, S. N.; Vaitkevicius, A.

    2016-01-01

    The time resolution of the detectors currently in use is limited by 50-70 ps due to the spontaneous processes involved in the development of the response signal, which forms after the relaxation of carriers generated during the interaction. In this study, we investigate the feasibility of exploiting sub-picosecond phenomena occurring after the interaction of scintillator material with ionizing radiation by probing the material with ultra-short laser pulses. One of the phenomena is the elastic polarization due to the local lattice distortion caused by the displacement of electrons and holes generated by ionization. The key feature of the elastic polarization is its short response time, which makes it prospective for using as an optically detectable time mark. The nonlinear optical absorption of femtosecond light pulses of appropriate wavelength is demonstrated to be a prospective tool to form the mark. This study was aimed at searching for inorganic crystalline media combining scintillation properties and non-...

  2. Achievement report on research and development in fiscal 1989. Research and development of non-linear photoelectron materials; 1989 nendo hisenkei hikari denshi zairyo no kenkyu kaihatsu

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1990-03-01

    With an objective to realize the communication and information processing utilizing the high velocity and parallelism of light, search for materials having non-linear susceptibility and high-speed responsiveness, and research and development of the material using technology have begun. This paper reports the achievements in fiscal 1989. In developing organic materials, investigations and preliminary experiments were performed on three-dimensional non-linear photoelectron materials of organic low molecular systems, such as chiral non-linear photoelectron material. Fundamental studies were made on growth of orientation controlled crystals. Researches were carried out on polymeric films of organic and conjugate systems. In developing the dispersed system materials, researches were executed on a technology to deposit CuCl particulates using the air phase method and porous glass impregnation method, and on evaluation of non-linear photoelectron properties of CuCl particulate dispersed glass. In addition, glass dispersed system materials were studied by using the sol-gel method, the ultra-low melting point glass method, and the ultra quenching method. Furthermore, for the organic dispersed system materials, synthesizing conditions were discussed on CdS/polymer dispersing element films, and ultra-particulate synthesizing experiments were performed. In developing the ultra-grid system materials, researches were performed on the organic ultra grid making technology and the three-dimensional ultra-structuring technology. (NEDO)

  3. Reconstruction of the residual stresses in a hyperelastic body using ultrasound techniques

    KAUST Repository

    Joshi, Sunnie; Walton, Jay R.

    2013-01-01

    This paper focuses on a novel approach for characterizing the residual stress field in soft tissue using ultrasound interrogation. A nonlinear inverse spectral technique is developed that makes fundamental use of the finite strain nonlinear response

  4. Comparison of procedures for determination of acoustic nonlinearity of some inhomogeneous materials

    DEFF Research Database (Denmark)

    Jensen, Leif Bjørnø

    1983-01-01

    for an evaluation of the second order nonlinearity ratio B/A as a tissue characterizing parameter on a par with attenuation, impedance, etc. The several techniques used for the determination of B/A roughly fall into two main groups, finite-amplitude methods and thermo-dynamic-acoustic methods. The B/A values...... determined using various techniques of the two main groups are strongly scattered, showing a dependence on the procedure used, which makes it difficult to draw any valid conclusions. The paper discusses advantages and disadvantages of the techniques used hitherto, aiming at an explanation of the reasons...... for the deviations between the present B/A results for biological media. The necessary accuracy in the determination and the reliability in the exploitation of B/A as a tissue characterizing parameter for clinical use are emphasized....

  5. Nanoparticles and nonlinear thermal radiation properties in the rheology of polymeric material

    Science.gov (United States)

    Awais, M.; Hayat, T.; Muqaddass, N.; Ali, A.; Aqsa; Awan, Saeed Ehsan

    2018-03-01

    The present analysis is related to the dynamics of polymeric liquids (Oldroyd-B model) with the presence of nanoparticles. The rheological system is considered under the application of nonlinear thermal radiations. Energy and concentration equations are presented when thermophoresis and Brownian motion effects are present. Bidirectional form of stretching is considered to interpret the three-dimensional flow dynamics of polymeric liquid. Making use of the similarity transformations, problem is reduced into ordinary differential system which is approximated by using HAM. Influence of physical parameters including Deborah number, thermophoresis and Brownian motion on velocity, temperature and mass fraction expressions are plotted and analyzed. Numerical values for local Sherwood and Nusselt numbers are presented and discussed.

  6. Sensitivity of corneal biomechanical and optical behavior to material parameters using design of experiments method.

    Science.gov (United States)

    Xu, Mengchen; Lerner, Amy L; Funkenbusch, Paul D; Richhariya, Ashutosh; Yoon, Geunyoung

    2018-02-01

    The optical performance of the human cornea under intraocular pressure (IOP) is the result of complex material properties and their interactions. The measurement of the numerous material parameters that define this material behavior may be key in the refinement of patient-specific models. The goal of this study was to investigate the relative contribution of these parameters to the biomechanical and optical responses of human cornea predicted by a widely accepted anisotropic hyperelastic finite element model, with regional variations in the alignment of fibers. Design of experiments methods were used to quantify the relative importance of material properties including matrix stiffness, fiber stiffness, fiber nonlinearity and fiber dispersion under physiological IOP. Our sensitivity results showed that corneal apical displacement was influenced nearly evenly by matrix stiffness, fiber stiffness and nonlinearity. However, the variations in corneal optical aberrations (refractive power and spherical aberration) were primarily dependent on the value of the matrix stiffness. The optical aberrations predicted by variations in this material parameter were sufficiently large to predict clinically important changes in retinal image quality. Therefore, well-characterized individual variations in matrix stiffness could be critical in cornea modeling in order to reliably predict optical behavior under different IOPs or after corneal surgery.

  7. 3D printed hyperelastic "bone" scaffolds and regional gene therapy: A novel approach to bone healing.

    Science.gov (United States)

    Alluri, Ram; Jakus, Adam; Bougioukli, Sofia; Pannell, William; Sugiyama, Osamu; Tang, Amy; Shah, Ramille; Lieberman, Jay R

    2018-04-01

    The purpose of this study was to evaluate the viability of human adipose-derived stem cells (ADSCs) transduced with a lentiviral (LV) vector to overexpress bone morphogenetic protein-2 (BMP-2) loaded onto a novel 3D printed scaffold. Human ADSCs were transduced with a LV vector carrying the cDNA for BMP-2. The transduced cells were loaded onto a 3D printed Hyperelastic "Bone" (HB) scaffold. In vitro BMP-2 production was assessed using enzyme-linked immunosorbent assay analysis. The ability of ADSCs loaded on the HB scaffold to induce in vivo bone formation in a hind limb muscle pouch model was assessed in the following groups: ADSCs transduced with LV-BMP-2, LV-green fluorescent protein, ADSCs alone, and empty HB scaffolds. Bone formation was assessed using radiographs, histology and histomorphometry. Transduced ADSCs BMP-2 production on the HB scaffold at 24 hours was similar on 3D printed HB scaffolds versus control wells with transduced cells alone, and continued to increase after 1 and 2 weeks of culture. Bone formation was noted in LV-BMP-2 animals on plain radiographs at 2 and 4 weeks after implantation; no bone formation was noted in the other groups. Histology demonstrated that the LV-BMP-2 group was the only group that formed woven bone and the mean bone area/tissue area was significantly greater when compared with the other groups. 3D printed HB scaffolds are effective carriers for transduced ADSCs to promote bone repair. The combination of gene therapy and tissue engineered scaffolds is a promising multidisciplinary approach to bone repair with significant clinical potential. © 2018 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 106A: 1104-1110, 2018. © 2018 Wiley Periodicals, Inc.

  8. Effects of material non-linearity on the residual stresses in a dendritic silicon crystal ribbon

    Science.gov (United States)

    Ray, Sujit K.; Utku, Senol

    1990-01-01

    Thermal stresses developed in a dendritic silicon crystal ribbon have been shown to cause plastic deformation and residual stresses in the ribbon. This paper presents an implementation of a numerical model proposed for thermoelastoplastic behavior of a material. The model has been used to study the effects of plasticity of silicon on the residual stresses. The material properties required to implement this model are all assumed, and the response of the material to the variations in these assumed parameters of the constitutive law and in the finite element mesh is investigated. The steady state growth process is observed to be periodic with nonzero residual stresses. Numerical difficulties are also encountered in the computer solution process, resulting in sharp jumps and large oscillations in the stress responses.

  9. Study on the Unsteady Creep of Composite Beams with an Irregular Laminar Fibrous Structure Made from Nonlinear Hereditary Materials

    Science.gov (United States)

    Yankovskii, A. P.

    2017-09-01

    The creep of homogenous and hybrid composite beams of an irregular laminar fibrous structure is investigated. The beams consist of thin walls and flanges (load-carrying layers). The walls may be reinforced longitudinally or crosswise in the plane, and the load-carrying layers are reinforced in the longitudinal direction. The mechanical behavior of phase materials is described by the Rabotnov nonlinear hereditary theory of creep taking into account their possible different resistance to tension and compression. On the basis of hypotheses of the Timoshenko theory, with using the method of time steps, a problem is formulated for the inelastic bending deformation of such beams with account of the weakened resistance of their walls to the transverse shear. It is shown that, at discrete instants of time, the mechanical behavior of such structures can formally be described by the governing relations for composite beams made of nonlinear elastic anisotropic materials with a known initial stress state. The method of successive iterations, similar to the method of variable parameters of elasticity, is used to linearize the boundary-value problem at each instant of time. The bending deformation is investigated for homogeneous and reinforced cantilever and simply supported beams in creep under the action of a uniformly distributed transverse load. The cross sections of the beams considered are I-shaped. It is found that the use of the classical theory for such beams leads to the prediction of indefensibly underestimated flexibility, especially in long-term loading. It is shown that, in beams with reinforced load-carrying layers, the creep mainly develops due to the shear strains of walls. It is found that, in short- and long-term loadings of composite beams, the reinforcement structures rational by the criterion of minimum flexibility are different.

  10. Inclusion of Material Non-Linearity and Inelasticity into a Continuum-Level Material Model for Soda-Lime Glass

    Science.gov (United States)

    2012-01-01

    Grujicic et al. /Materials and Design 35 (2012) 144–155 where Zsh is the average size of the shielding zone defined as: ktðtÞZshðtÞ ¼ Z t 0 dkt dt...of the flaws at time s, given as 1kt ðtÞ dkt dt s withR t 0 ktðtÞ dkt dt sds ¼ 1 (since for a shielding zone to exist the crack must have...the term dktdt s can be written as: dkt dt ¼ k0m _r mtm1 Sm0 ð12Þ After substitution of Eq. (12) into Eq. (11) and, in turn, into Eq. (10

  11. A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

    NARCIS (Netherlands)

    Matous, K.; Geers, M.G.D.; Kouznetsova, V.; Gillman, A.

    2017-01-01

    Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today’s electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous

  12. NLO 󈨞. Nonlinear Optics: Materials, Phenomena and Devices Digest. Internation Meeting on Nonlinear Optics (1st) Held in Kauai, Hawaii on 16-20 July 1990

    Science.gov (United States)

    1991-03-13

    combination50 with a dynamic grating diffraction modelO . Considering o 0 a polarlsatlon grating on a homoetropic aligned nematlc ’-i 40 filmi the optical...nonlinearities of solutions of chloroaluminumphthalocyanine (CAP) in methanol and a silicon naphthalocyanine (Nc) derivative, SiNc( OSi (hexyl)3)2 or

  13. Second-order nonlinear optical properties of composite material of an azo-chromophore with a tricyanodiphenyl acceptor in a poly(styrene-co-methyl methacrylate) matrix

    Science.gov (United States)

    Shelkovnikov, Vladimir; Selivanova, Galina; Lyubas, Gleb; Korotaev, Sergey; Shundrina, Inna; Tretyakov, Evgeny; Zueva, Ekaterina; Plekhanov, Alexander; Mikerin, Sergey; Simanchuk, Andrey

    2017-07-01

    The composite material of new synthesized 4-((4-(N,N-n-dibutylamino) phenyl)diazenyl)-biphenyl-2,3,4-tricarbonitrile (GAS dye) in commercial poly(styrene-co-methyl methacrylate) (PSMMA) was prepared, poled and its nonlinear optical properties compared with DR1 dye were studied. High thermal stability of the composite material was revealed, and the maximal concentration of the chromophore was found to reach ∼20 wt%. The dipole moment, polarizability tensor, and first hyperpolarizability tensor of the investigated dyes were calculated by within the framework of the coupled perturbed density functional theory. A nanosecond second-harmonic generation Maker fringes technique was used which is capable of providing the magnitude of the second-order nonlinearity of optical materials at a wavelength of 1064 nm. For the tested GAS-PSMMA composite material, maximal coefficient d33 was found to be 50 pm/V. The nonlinear optical response, which was achieved here, shows possible usefulness of the GAS dye as a component for molecular design of nonlinear-optical materials with advanced characteristics.

  14. Theoretical analysis of open aperture reflection Z-scan on materials with high-order optical nonlinearities

    International Nuclear Information System (INIS)

    Petris, Adrian I.; Vlad, Valentin I.

    2010-03-01

    We present a theoretical analysis of open aperture reflection Z-scan in nonlinear media with third-, fifth-, and higher-order nonlinearities. A general analytical expression for the normalized reflectance when third-, fifth- and higher-order optical nonlinearities are excited is derived and its consequences on RZ-scan in media with high-order nonlinearities are discussed. We show that by performing RZ-scan experiments at different incident intensities it is possible to put in evidence the excitation of different order nonlinearities in the medium. Their contributions to the overall nonlinear response can be discriminated by using formulas derived by us. A RZ-scan numerical simulation using these formulas and data taken from literature, measured by another method for the third-, fifth-, and seventh-order nonlinear refractive indices of As 2 S 3 chalcogenide glass, is performed. (author)

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

    International Nuclear Information System (INIS)

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

    2011-01-01

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

  16. Material component to non-linear relation between sediment yield and drainage network development: an flume experimental study

    Institute of Scientific and Technical Information of China (English)

    2001-01-01

    This paper examines the experimental study on influence ofmaterial component to non linear relation between sediment yield and drainage network development completed in the Lab. The area of flume drainage system is 81.2 m2, the longitudinal gradient and cross section slope are from 0.0348 to 0.0775 and from 0.0115 to 0.038, respectively. Different model materials with a medium diameter of 0.021 mm, 0.076 mm and 0.066 mm cover three experiments each. An artificial rainfall equipment is a sprinkler-system composed of 7 downward nozzles, distributed by hexagon type and a given rainfall intensity is 35.56 mm/hr.cm2. Three experiments are designed by process-response principle at the beginning the ψ shaped small network is dug in the flume. Running time spans are 720 m, 1440 minutes and 540 minutes for Runs Ⅰ, Ⅳ and Ⅵ, respectively. Three experiments show that the sediment yield processes are characterized by delaying with a vibration. During network development the energy of a drainage system is dissipated by two ways, of which one is increasing the number of channels (rill and gully), and the other one is enlarging the channel length. The fractal dimension of a drainage network is exactly an index of energy dissipation of a drainage morphological system. Change of this index with time is an unsymmetrical concave curve. Comparison of three experiments explains that the vibration and the delaying ratio of sediment yield processes increase with material coarsening, while the number of channel decreases. The length of channel enlarges with material fining. There exists non-linear relationship between fractal dimension and sediment yield with an unsymmetrical hyperbolic curve. The bsolute value of delaying ratio of the curve reduces with time unning and material fining. It is characterized by substitution of situation to time.

  17. Simulation of High-current Pulse Effect on the Electrode with Nonlinear Material Characteristics and Phase Transitions Taken into Account

    Directory of Open Access Journals (Sweden)

    R. V. Arutjunjan

    2016-01-01

    Full Text Available The article investigates the thermal and electrical processes when heating the metal electrode by a high current pulse. The aim is to understand an impact nature of the nonlinearities of thermal parameters, the phase transitions of melting and evaporation, and the type of boundary conditions in the current spot. To solve the problem was formulated a mathematical model, and were also developed a finite-difference method and computer programmes which allow an effective computer simulations of thermal and electrical processes under the high current pulse impact on the metal electrodes. The Stefan problem is solved by the through "enthalpy" method. Calculation of the electric field is performed by Seidel iteration. Thermal and current balance and comparison with solution results of model problems allow computer error monitoring.The work involved a series of calculations for an informative case of iron. It enabled to find a significant influence of the nonlinearities of thermal parameters, the phase transitions of melting and evaporation, the type of boundary conditions on the values of the temperature and electric fields, especially in the vicinity of the current spot. The presence of high current density and temperature, respectively, in the vicinity of the current spot edge confirms the well-known hypothesis about the causes of contact welding on the edges of the contact area. It has been found that the impact of losses on radiation and convection cooling is negligible. The article continues and complements the well-known research in the theory of electrical contacts and welding processes based on detailed consideration of the electrode material properties, the nonlinearities, and a type of boundary conditions for temperature and electric fields.The results can be used in the practice in research and design of electrical machines and other electrical devices.The study has revealed the need to improve the enthalpy finite- difference method for

  18. Growth, optical, thermal and dielectric studies of an amino acid organic nonlinear optical material: L-Alanine

    International Nuclear Information System (INIS)

    Caroline, M. Lydia; Sankar, R.; Indirani, R.M.; Vasudevan, S.

    2009-01-01

    Good transparent bulk single crystals of L-alanine (nonlinear optical material) have been grown successfully by slow cooling technique from aqueous solution at pH value of 2.0. Optically transparent crystals with dimensions 2.4 cm x 1.2 cm x 1.6 cm, were grown by optimizing the growth parameters within a growth period of 2 weeks. The crystallinity of L-alanine crystal was confirmed by the powder X-ray diffraction study and diffraction peaks are indexed. The vibrational structure of the molecule is elucidated from FTIR spectra. The thermal behaviour of the grown crystal was investigated by thermogravimetric (TG) and differential thermal analyses (DTA) techniques in a nitrogen atmosphere. The result showed that the material starts decomposing at 297 deg. C. Its optical behaviour has been examined by UV-vis spectral analysis, which shows the absence of absorbance between the wavelengths ranging from 200 to 1200 nm. The NLO property was confirmed by the powder technique of Kurtz and Perry. The dielectric behaviour of the sample was also studied for the first time

  19. Comparison between isotropic linear-elastic law and isotropic hyperelastic law in the finite element modeling of the brachial plexus.

    Science.gov (United States)

    Perruisseau-Carrier, A; Bahlouli, N; Bierry, G; Vernet, P; Facca, S; Liverneaux, P

    2017-12-01

    Augmented reality could help the identification of nerve structures in brachial plexus surgery. The goal of this study was to determine which law of mechanical behavior was more adapted by comparing the results of Hooke's isotropic linear elastic law to those of Ogden's isotropic hyperelastic law, applied to a biomechanical model of the brachial plexus. A model of finite elements was created using the ABAQUS ® from a 3D model of the brachial plexus acquired by segmentation and meshing of MRI images at 0°, 45° and 135° of shoulder abduction of a healthy subject. The offset between the reconstructed model and the deformed model was evaluated quantitatively by the Hausdorff distance and qualitatively by the identification of 3 anatomical landmarks. In every case the Hausdorff distance was shorter with Ogden's law compared to Hooke's law. On a qualitative aspect, the model deformed by Ogden's law followed the concavity of the reconstructed model whereas the model deformed by Hooke's law remained convex. In conclusion, the results of this study demonstrate that the behavior of Ogden's isotropic hyperelastic mechanical model was more adapted to the modeling of the deformations of the brachial plexus. Copyright © 2017 Elsevier Masson SAS. All rights reserved.

  20. A nonlinear electromechanical coupling model for electropore expansion in cell electroporation

    KAUST Repository

    Deng, Peigang

    2014-10-15

    Under an electric field, the electric tractions acting on a cell membrane containing a pore-nucleus are investigated by using a nonlinear electromechanical coupling model, in which the cell membrane is treated as a hyperelastic material. Iterations between the electric field and the structure field are performed to reveal the electrical forces exerting on the pore region and the subsequent pore expansion process. An explicit exponential decay of the membrane\\'s edge energy as a function of pore radius is defined for a hydrophilic pore and the transition energy as a hydrophobic pore converts to a hydrophilic pore during the initial stage of pore formation is investigated. It is found that the edge energy for the creation of an electropore edge plays an important role at the atomistic scale and it determines the hydrophobic-hydrophilic transition energy barrier. Various free energy evolution paths are exhibited, depending on the applied electric field, which provides further insight towards the electroporation (EP) phenomenon. In comparison with previous EP models, the proposed model has the ability to predict the metastable point on the free energy curve that is relevant to the lipid ion channel. In addition, the proposed model can also predict the critical transmembrane potential for the activation of an effective electroporation that is in a good agreement with previously published experimental data.

  1. Synthesis, growth and characterization of 4-bromo-4'-nitrobenzylidene aniline (BNBA): a novel nonlinear optical material with a (3+1)-dimensional incommensurately modulated structure

    Czech Academy of Sciences Publication Activity Database

    Subashini, A.; Leela, S.; Ramamurthi, K.; Arakcheeva, A.; Stoeckli-Evans, H.; Petříček, Václav; Chapuis, G.; Pattison, P.; Reji, P.

    2013-01-01

    Roč. 15, č. 13 (2013), s. 2474-2481 ISSN 1466-8033 Grant - others:AV ČR(CZ) AP0701 Program:Akademická prémie - Praemium Academiae Institutional support: RVO:68378271 Keywords : organic nonlinear optical material * crystal structure analysis * incommensurately modulated structures Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.858, year: 2013

  2. Influence of material non-linearity on the thermo-mechanical response of polymer foam cored sandwich structures - FE modelling and preliminary experiemntal results

    DEFF Research Database (Denmark)

    Palleti, Hara Naga Krishna Teja; Thomsen, Ole Thybo; Fruehmann, Richard.K

    In this paper, the polymer foam cored sandwich structures with fibre reinforced composite face sheets will be analyzed using the commercial FE code ABAQUS/Standard® incorporating the material and geometrical non-linearity. Large deformations are allowed which attributes geometric non linearity...

  3. Solution of problems with material nonlinearities with a coupled finite element/boundary element scheme using an iterative solver. Yucca Mountain Site Characterization Project

    International Nuclear Information System (INIS)

    Koteras, J.R.

    1996-01-01

    The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region

  4. Gamma ray processing of ZnGeP2: A nonlinear optical material for the infrared

    International Nuclear Information System (INIS)

    Schunemann, P.G.; Drevinsky, P.J.; Ohmer, M.C.

    1995-01-01

    Zinc germanium phosphide, an important frequency-conversion material for producing mid-infrared lasers, is plagued by a defect-related absorption band extending from the fundamental edge (0.62 microns) to ∼3 microns. The level of absorption varies with melt composition, and can be reduced by post-growth annealing treatments. In these experiments, further reduction of the near-band-edge absorption was achieved by irradiating with 1.173 MeV and 1.3325 MeV gamma rays. A 40 KiloCurie 60 Co source was used to irradiate a series of crystals at an average flux of 4.8 x 10 6 rads/hr to cumulative doses up to 3.91 x 10 10 rads. The absorption coefficient in the near-infrared was reduced by nearly a factor of two, and the penetration depth of the ionizing radiation was sufficient to uniformly reduce the absorption in the largest samples tested (up to 7x8x23 mm 3 ). The loss coefficients achieved at 1 micron (4.28 cm -1 ) and at 2.05 microns (0.19 -1 ) are lower than the best results achievable by conventional thermal annealing alone. No saturation effects or absorption increases at longer wavelengths were observed

  5. Nonlinear optimization

    CERN Document Server

    Ruszczynski, Andrzej

    2011-01-01

    Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern top...

  6. Synthesis, growth and characterization of organic nonlinear optical material: N-benzyl-2-methyl-4-nitroaniline (BNA)

    Science.gov (United States)

    Kalaivanan, R.; Srinivasan, K.

    2017-05-01

    Synthesis of the organic nonlinear optical compound N-benzyl-2-methyl-4-nitroaniline (BNA) was carried out in a newer chemical environment using the mixture of benzyl chloride and 2-methl-4-nitroaniline by a preferred laboratory synthesis process. The synthesized BNA compound was separated by column chromatography (CC) with low pressure silica gell using petrollium benzine and purity of the separated resultant product was confirmed by thin layer chromatography (TLC). Further, the material was recrystallized atleast four times in methanol and the highly purified BNA was used for the growth of single crystals from solutions with selected solvents by slow evaporation method at room temperature. Single crystals having natural growth morphology were harvested and their different growth faces were identified by optical goniometry. The grown crystals were subjected to different characterization techniques such as powder x-ray diffraction (PXRD), fourier transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC) and UV-vis-Near IR spectroscopy. Further, the second harmonic generation (SHG) efficiency of the grown BNA crystal was studied by Kurtz and Perry powder technique using Nd:YAG laser as fundamental source and found to be twice that of inorganic standard KDP.

  7. Contribution to concrete modelling towards aging and durability: interactions between creep deformations and non-linear behaviour of the material

    International Nuclear Information System (INIS)

    Berthollet, A.

    2003-10-01

    Concrete structures are examined during their lifetime and often present important cracking states, which can progress with time and lead to change the structural behavior. The civil engineering works that the main function corresponds to protection's wall are very sensitive to this damage and its evolution. The growth of the time - dependent cracks represents an aging pathology linked with interaction between creep mechanism and the non-linear behavior of the material. In this thesis, a modeling for these mechanisms and their coupling are proposed. It based on creep strains analysis under different load levels, on the influence of the rate effect to the mechanical behavior. A stress limit is put on prominent manner, where beyond it, the creep - cracking interaction becomes important with the introduction of the ultimate tertiary creep kinetic. This level of strength is identified for infinitely slow loading rates and is also called intrinsic strength. It defines the limit on this side the viscous behavior of the cement paste limits the irreversibility processes as cracking. Thus, a constitutive law of viscoelastic - viscoplastic behavior with a high coupling between the cracking mechanism and the creep strains is proposed. The developments of the model are built on DUVAUT - LIONS approach integrated a generalized MAXWELL chain model. For one part, the viscoelastic behavior translates the creep mechanism under low stresses. For a second part, it associated with the viscoplastic behavior, which allows introducing both creep effect under high stresses and rate effect acting on micro-cracked zones. The cracking mechanism is described throughout a plasticity theory with multi-criteria, which induce a property of anisotropy for hardening. Qualitatively, ails of the creep kinetics are reproduced. An additional validation is based on experimental tests in compression, traction and flexion where the main parameters of the modeling are detailed. Thus, we can conclude on the

  8. DOE Final Report -NON-LINEAR WAVES IN CONTINUOUS MEDIA- BES- Division of Engineering and Materials Science

    International Nuclear Information System (INIS)

    Seth J. Putterman

    2006-01-01

    FINAL REPORT ON : NON-LINEAR WAVES IN CONTINUOUS MEDIA Doe DE FG03-87ER13686 (001312-001) Submitted January 10, 2006 by Seth J. Putterman 310-8252269 Physics Department University of California Los Angeles, CA 90095 puherman at ritva.physics.ucla.edu NON-LINEAR WAVES IN CONTINUOUS MEDIA I am happy to report that this project has been a big success. For over 10 years the DOE [Division of Materials Sciences and Engineering] has funded our research program on the overarching theme of spontaneous energy focusing phenomena. These effects occur when a nonlinear macroscopic system is excited so as to drive it far from equilibrium. The subsequent relaxation to equilibrium does not occur smoothly but instead is accompanied by the formation of structured domains where the energy density is highly concentrated. A signature example is picosecond sonoluminescence [1] wherein a smooth sound wave has its energy density focused by 12 orders of magnitude to generate a clock-like string of picosecond flashes of ultraviolet light. Our earlier work on solitons [2] demonstrated how uniform surface waves break up into stable localized structures. Our experimental work on turbulence produced photos of localized structures lying many standard deviations outside the range of gaussian statistics[3]. This effect is referred to as intermittency. Our recent work on friction finds its motivation in those theories of sonoluminescence which invoke frictional electricity. In its most common form this is the generation of a spark when we touch a doorknob after walking over a carpet. Our reading of the literature on this subject indicated that frictional electricity like sonoluminescence is not understood. So to probe triboelectrification we set up a modern version of an experiment performed by Bernoulli in 1700. Here sparking is caused by the rubbing of glass against mercury. We indeed observed flashes of light which were accompanied by events of stick-slip friction at the interface between the

  9. Numerical simulation of shear and the Poynting effects by the finite element method: An application of the generalised empirical inequalities in non-linear elasticity

    KAUST Repository

    Angela Mihai, L.

    2013-03-01

    Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.

  10. Quantum Nonlinear Optics

    CERN Document Server

    Hanamura, Eiichi; Yamanaka, Akio

    2007-01-01

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

  11. [?]Nonlinear Issues in the Aerothermochemistry of Gases and Materials and the Associated Physics and Dynamics of Interfaces

    Science.gov (United States)

    Johnson, Joseph A., III

    1996-01-01

    Our research and technology are focused on nonlinear issues in the aerothermochemistry of gases and materials and the associated physics and dynamics of interfaces. Our program is now organized to aggressively support the NASA Aeronautics Enterprise so as to: (a) develop a new generation of environmentally compatible, economic subsonic aircraft; (b) develop the technology base for an economically viable and environmentally compatible high-speed civil transport; (c) develop the technology options for new capabilities in high-performance aircraft; (d) develop hypersonic technologies for air-breathing flight; and (e) develop advanced concepts, understanding of physical phenomena, and theoretical, experimental, and computational tools for advanced aerospace systems. The implications from our research for aeronautical and aerospace technology have been both broad and deep. For example, using advanced computational techniques, we have determined exact solutions for the Schrodinger equation in electron-molecule scattering allowing us to evaluate atmospheric models important to reentry physics. We have also found a new class of exact solutions for the Navier Stokes equations. In experimental fluid dynamics, we have found explicit evidence of turbulence modification of droplet sizes in shock tube flow with condensation. We have developed a new diagnostic tool for the direct estimation of flow velocities at MHz sampling rates in quasi-one dimensional turbulent flow. This procedure suggests an unexpected confirmation of the possibility of 'natural' closure in Reynolds stresses with deep implications for the development of turbulent models. A transient increase is observed in both the spectral energy decay rate and the degree of chaotic complexity at the interface of a shock wave and a turbulent ionized gas. Even though the gas is apparently brought to rest by the shock wave, no evidence is found either of the expected relaminarization. A unique diamond-shaped nozzle has been

  12. Stress analysis of liners for prestressed concrete reactor pressure vessels with regard to non-linear behaviour of liner material and of anchor-characteristics

    International Nuclear Information System (INIS)

    Oberpichler, R.; Schnellenbach, G.

    1975-01-01

    The thin liner attached by anchors like a membrane to the interior wall of a prestressed concrete reactor pressure vessel (PCRV) has to provide the leak-tightness of the vessel. Furthermore the liner may serve as internal shuttering for placing of concrete as well as a support for the cooling system. The two-dimensional behaviour of the liner is investigated with regard to non-linear anchor-characteristics and non-linear material behaviour of the liner. The analysis is based on a plane stress model under the assumption of a membrane state of the liner. Calculations are performed by the dynamic relaxation method. With the aid of available non-linear stress-strain diagrams, describing the post-buckling behaviour, individual panels are considered as buckled ones. The adjacent unbuckled panels are calculated on other non-linear diagrams. Strains and stresses in the liner and additional shear loads in the anchors can be calculated with arbitrary sizing and spacing of the anchors. With respect to the parameters they are easily controlled. Since actual loads on the liner are defined by the PCRV-behaviour, an economical and safe design is possible. Finally an extreme case is calculated to assess the maximum value of the shear-forces assuming zero post-buckling capacity for the buckled panel. (Auth.)

  13. A model for acoustic vaporization dynamics of a bubble/droplet system encapsulated within a hyperelastic shell.

    Science.gov (United States)

    Lacour, Thomas; Guédra, Matthieu; Valier-Brasier, Tony; Coulouvrat, François

    2018-01-01

    Nanodroplets have great, promising medical applications such as contrast imaging, embolotherapy, or targeted drug delivery. Their functions can be mechanically activated by means of focused ultrasound inducing a phase change of the inner liquid known as the acoustic droplet vaporization (ADV) process. In this context, a four-phases (vapor + liquid + shell + surrounding environment) model of ADV is proposed. Attention is especially devoted to the mechanical properties of the encapsulating shell, incorporating the well-known strain-softening behavior of Mooney-Rivlin material adapted to very large deformations of soft, nearly incompressible materials. Various responses to ultrasound excitation are illustrated, depending on linear and nonlinear mechanical shell properties and acoustical excitation parameters. Different classes of ADV outcomes are exhibited, and a relevant threshold ensuring complete vaporization of the inner liquid layer is defined. The dependence of this threshold with acoustical, geometrical, and mechanical parameters is also provided.

  14. Design of steel-liners and their anchorage with regard to non-linear behaviour of liner-material and anchorage

    International Nuclear Information System (INIS)

    Oberpichler, R.

    1979-01-01

    The thin steel liner attached by studs or rib-type anchors to the interior wall of a Prestressed Concrete Reactor Pressure Vessel (PCRV) or a Concrete Containment Vessel (PCCV) has to provide the leak-tightness of the vessel. The liner also may serve as internal shuttering for placing concrete as well as a support for the cooling system or thermal isolation. Mainly strained by self-limited loads imposed on the liner by deformations of the vessel-wall or by heatup inside the vessel the liner predominantly will function in a compressive biaxially strained state like a membrane. The vessel-wall is assumed to be a rigid boundary without reactions caused by the liner-anchor-restraints. Furthermore it is assumed that the liner supported in a close-spaced pattern to the concrete with respect to self-limited loads and all effects of non-linear behaviour of liner-material and non-linear anchor-characteristics will not fail by instability, especially not by an effect of snapthrough. Only one essential mode of failure, the shear connector failure is assumed to be basis for all liner investigations. Design of the liner and its anchorage therefore is based on the analysis of large deformations with regard to elastic-plastic behaviour of liner-material and non-linear anchor characteristics. By this method both economical and safe sizing and spacing of the anchors can be calculated. (orig.)

  15. CsB{sub 4}O{sub 6}F. A congruent-melting deep-ultraviolet nonlinear optical material by combining superior functional units

    Energy Technology Data Exchange (ETDEWEB)

    Wang, Xuefei [Key Lab. of Functional Materials and Devices for Special Environments, Xinjiang Technical Inst. of Physics and Chemistry, Chinese Academy of Sciences, Xinjiang Key Lab. of Electronic Information Materials and Devices, Urumqi (China); University of Chinese Academy of Sciences, Beijing (China); Wang, Ying; Zhang, Bingbing; Zhang, Fangfang; Yang, Zhihua; Pan, Shilie [Key Lab. of Functional Materials and Devices for Special Environments, Xinjiang Technical Inst. of Physics and Chemistry, Chinese Academy of Sciences, Xinjiang Key Lab. of Electronic Information Materials and Devices, Urumqi (China)

    2017-11-06

    The discovery of new nonlinear optical (NLO) materials for coherent light generation in the deep-ultraviolet (DUV, wavelength below 200 nm) region is essential for the development of laser technologies. Herein, we report a new material CsB{sub 4}O{sub 6}F (CBF), which combines the superior structural properties of two well-known NLO materials, β-BaB{sub 2}O{sub 4} (BBO) and KBe{sub 2}BO{sub 3}F{sub 2} (KBBF). CBF exhibits excellent DUV optical properties including a short cutoff edge (155 nm), a large SHG response (∼1.9 x KDP), and a suitable birefringence that enables frequency doubling down to 171.6 nm. Remarkably, CBF melts congruently and shows an improved growth habit. In addition, our rational design strategy will contribute to the discovery of DUV NLO materials. (copyright 2017 Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim)

  16. CsB_4O_6F. A congruent-melting deep-ultraviolet nonlinear optical material by combining superior functional units

    International Nuclear Information System (INIS)

    Wang, Xuefei; Wang, Ying; Zhang, Bingbing; Zhang, Fangfang; Yang, Zhihua; Pan, Shilie

    2017-01-01

    The discovery of new nonlinear optical (NLO) materials for coherent light generation in the deep-ultraviolet (DUV, wavelength below 200 nm) region is essential for the development of laser technologies. Herein, we report a new material CsB_4O_6F (CBF), which combines the superior structural properties of two well-known NLO materials, β-BaB_2O_4 (BBO) and KBe_2BO_3F_2 (KBBF). CBF exhibits excellent DUV optical properties including a short cutoff edge (155 nm), a large SHG response (∼1.9 x KDP), and a suitable birefringence that enables frequency doubling down to 171.6 nm. Remarkably, CBF melts congruently and shows an improved growth habit. In addition, our rational design strategy will contribute to the discovery of DUV NLO materials. (copyright 2017 Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim)

  17. Synthesis, structure and characterization of a hybrid centrosymmetric material (4-dimethylaminopyridinium nitrate gallic acid monohydrate) well-designed for non-linear optics

    Science.gov (United States)

    Ennaceur, Nasreddine; Jalel, Boutheina; Henchiri, Rokaya; Cordier, Marie; Ledoux-Rak, Isabelle

    2018-01-01

    Hybrid material: 4-Dimethylaminopyridinium nitrate gallic acid monohydrate abbreviated DNGA monohydrate has been successfully synthesized by slow evaporation method at room temperature. X-ray diffraction (XRD) on a single crystal showed that the latter was crystallized in P-1 space group. Likewise, thermal analyses demonstrated the stability of our crystal up to 80 °C. Besides, the analysis of the infrared spectrum (FTIR), allowed us to confirm the presence of the different groups present in the structure. Furthermore, by studying the UV-Visible spectrum, the transparency of our crystal was proven. Despite the fact that of having a centrosymmetric structure, the nonlinear optical properties of our single crystal, which was tested by Kurtz-Perry technique, proved that its second harmonic generation efficiency was 1.22 times more than that of KDP (potassium dihydrogen phosphate) single crystal. This nonlinear optical behavior of the studied compound was also determined through the calculations of polarizability and first hyperpolarizability values.

  18. Local-in-space blow-up criteria for a class of nonlinear dispersive wave equations

    Science.gov (United States)

    Novruzov, Emil

    2017-11-01

    This paper is concerned with blow-up phenomena for the nonlinear dispersive wave equation on the real line, ut -uxxt +[ f (u) ] x -[ f (u) ] xxx +[ g (u) + f″/(u) 2 ux2 ] x = 0 that includes the Camassa-Holm equation as well as the hyperelastic-rod wave equation (f (u) = ku2 / 2 and g (u) = (3 - k) u2 / 2) as special cases. We establish some a local-in-space blow-up criterion (i.e., a criterion involving only the properties of the data u0 in a neighborhood of a single point) simplifying and precising earlier blow-up criteria for this equation.

  19. TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material

    International Nuclear Information System (INIS)

    Sciancalepore, C; Agostiano, A; Cassano, T; Valentini, A; Curri, M L; Striccoli, M; Mecerreyes, D; Tommasi, R

    2008-01-01

    Original nanocomposites have been obtained by direct incorporation of pre-synthesized oleic acid capped TiO 2 nanorods into properly functionalized poly(methyl methacrylate) copolymers, carrying carboxylic acid groups on the repeating polymer unit. The presence of carboxylic groups on the alkyl chain of the host functionalized copolymer allows an highly homogeneous dispersion of the nanorods in the organic matrix. The prepared TiO 2 /PMMA-co-MA nanocomposites show high optical transparency in the visible region, even at high TiO 2 nanorod content, and tunable linear refractive index depending on the nanoparticle concentration. Finally measurements of nonlinear optical properties of TiO 2 polymer nanocomposites demonstrate a negligible two-photon absorption and a negative value of nonlinear refractive index, highlighting the potential of the nanocomposite for efficient optical devices operating in the visible region

  20. TiO2 nanorods/PMMA copolymer-based nanocomposites: highly homogeneous linear and nonlinear optical material

    Science.gov (United States)

    Sciancalepore, C.; Cassano, T.; Curri, M. L.; Mecerreyes, D.; Valentini, A.; Agostiano, A.; Tommasi, R.; Striccoli, M.

    2008-05-01

    Original nanocomposites have been obtained by direct incorporation of pre-synthesized oleic acid capped TiO2 nanorods into properly functionalized poly(methyl methacrylate) copolymers, carrying carboxylic acid groups on the repeating polymer unit. The presence of carboxylic groups on the alkyl chain of the host functionalized copolymer allows an highly homogeneous dispersion of the nanorods in the organic matrix. The prepared TiO2/PMMA-co-MA nanocomposites show high optical transparency in the visible region, even at high TiO2 nanorod content, and tunable linear refractive index depending on the nanoparticle concentration. Finally measurements of nonlinear optical properties of TiO2 polymer nanocomposites demonstrate a negligible two-photon absorption and a negative value of nonlinear refractive index, highlighting the potential of the nanocomposite for efficient optical devices operating in the visible region.

  1. Growth and characterization of materials for infrared detectors and nonlinear optical switches; Proceedings of the Meeting, Orlando, FL, Apr. 2, 3, 1991

    Science.gov (United States)

    Longshore, Randolph E.; Baars, Jan W.

    Papers included in these proceedings are grouped under the topics of infrared material growth and characterization, infrared detector physics, and nonlinear optics. Attention is given to interface demarcation in Bridgman-Stockbarger crystal growth of II-VI compounds, growth of CdTe-CdMnTe heterostructures by molecular beam epitaxy, and a photoconductivity decay method for determining the minority carrier lifetime of p-type HgCdTe. Consideration is also given to anodic oxides on HgZnTe, the characterization of anodic fluoride films on Hg(1-x)Cd(x)Te, optical response in high-temperature superconducting thin films, and pyroelectric linear array IR detectors with CCD multiplexer. Other papers are on structural and optical properties of melt-processed calcium aluminate fibers, the preparation and characterization of a new thermistor material for thermistor bolometer, and photoemission from quantum-confined structure of nonlinear optical materials. (For individual items see A93-26893 to A93-26895)

  2. Nonlinear transient heat transfer and thermoelastic analysis of thick-walled FGM cylinder with temperature-dependent material properties using Hermitian transfinite element

    Energy Technology Data Exchange (ETDEWEB)

    Azadi, Mohammad [Sharif University of Technology, Tehran (Iran, Islamic Republic of); Azadi, Mahboobeh [Shiraz University, Shiraz (Iran, Islamic Republic of)

    2009-10-15

    Nonlinear transient heat transfer and thermoelastic stress analyses of a thick-walled FGM cylinder with temperature dependent materials are performed by using the Hermitian transfinite element method. Temperature-dependency of the material properties has not been taken into account in transient thermoelastic analysis, so far. Due to the mentioned dependency, the resulting governing FEM equations of transient heat transfer are highly nonlinear. Furthermore, in all finite element analysis performed so far in the field, Lagrangian elements have been used. To avoid an artificial local heat source at the mutual boundaries of the elements, Hermitian elements are used instead in the present research. Another novelty of the present paper is simultaneous use of the transfinite element method and updating technique. Time variations of the temperature, displacements, and stresses are obtained through a numerical Laplace inversion. Finally, results obtained considering the temperature-dependency of the material properties are compared with those derived based on temperature independency assumption. Furthermore, the temperature distribution and the radial and circumferential stresses are investigated versus time, geometrical parameters and index of power law. Results reveal that the temperature-dependency effect is significant

  3. All-optical conversion scheme from binary to its MTN form with the help of nonlinear material based tree-net architecture

    Science.gov (United States)

    Maiti, Anup Kumar; Nath Roy, Jitendra; Mukhopadhyay, Sourangshu

    2007-08-01

    In the field of optical computing and parallel information processing, several number systems have been used for different arithmetic and algebraic operations. Therefore an efficient conversion scheme from one number system to another is very important. Modified trinary number (MTN) has already taken a significant role towards carry and borrow free arithmetic operations. In this communication, we propose a tree-net architecture based all optical conversion scheme from binary number to its MTN form. Optical switch using nonlinear material (NLM) plays an important role.

  4. Double lens device for tunable harmonic generation of laser beams in KBBF/RBBF crystals or other non-linear optic materials

    Science.gov (United States)

    Kaminski, Adam

    2017-08-22

    A method and apparatus to generate harmonically related laser wavelengths includes a pair of lenses at opposing faces of a non-linear optical material. The lenses are configured to promote incoming and outgoing beams to be normal to each outer lens surface over a range of acceptance angles of the incoming laser beam. This reduces reflection loss for higher efficiency operation. Additionally, the lenses allow a wider range of wavelengths for lasers for more universal application. Examples of the lenses include plano-cylindrical and plano-spherical form factors.

  5. The nonlinear Maxwell-type model for viscoelastoplastic materials: simulation of temperature influence on creep, relaxation and strain-stress curves

    Directory of Open Access Journals (Sweden)

    Andrew V. Khokhlov

    2017-04-01

    Full Text Available The nonlinear Maxwell-type constitutive relation with two arbitrary material functions for viscoelastoplastic multi-modulus materials is studied analytically in uniaxial isothermic case to reveal the model abilities and applicability scope and to develop techniques of its identification, tuning and fitting. The constitutive equation is aimed at adequate modeling of the rheological phenomena set which is typical for reonomic materials exhibiting non-linear hereditary properties, strong strain rate sensitivity, secondary creep, yielding at constant stress, tension compression asymmetry and such temperature effects as increase of material compliance, strain rate sensitivity and rates of dissipation, relaxation, creep and plastic strain accumulation with temperature growth. The model is applicable for simulation of mechanical behaviour of various polymers, their solutions and melts, solid propellants, sand-asphalt concretes, composite materials, titanium and aluminum alloys, ceramics at high temperature and so on. To describe the influence of temperature on material mechanical behavior (under isothermic conditions, two scalar material parameters of the model (viscosity coefficient and “modulus of elasticity” are considered as a functions of temperature level. The general restrictions on their properties which are necessary and sufficient for adequate qualitative description of the basic thermomechanical phenomena related to typical temperature influence on creep and relaxation curves, creep recovery curves, creep curves under step-wise loading and quasi-static stress-strain curves of viscoelastoplastic materials are obtained. The restrictions are derived using systematic analytical study of general qualitative features of the theoretic creep and relaxation curves, creep curves under step-wise loading, long-term strength curves and stress-strain curves at constant strain or stress rates generated by the constitutive equation (under minimal

  6. Introduction of non-linear elasticity models for characterization of shape and deformation statistics: application to contractility assessment of isolated adult cardiocytes.

    Science.gov (United States)

    Bazan, Carlos; Hawkins, Trevor; Torres-Barba, David; Blomgren, Peter; Paolini, Paul

    2011-08-22

    We are exploring the viability of a novel approach to cardiocyte contractility assessment based on biomechanical properties of the cardiac cells, energy conservation principles, and information content measures. We define our measure of cell contraction as being the distance between the shapes of the contracting cell, assessed by the minimum total energy of the domain deformation (warping) of one cell shape into another. To guarantee a meaningful vis-à-vis correspondence between the two shapes, we employ both a data fidelity term and a regularization term. The data fidelity term is based on nonlinear features of the shapes while the regularization term enforces the compatibility between the shape deformations and that of a hyper-elastic material. We tested the proposed approach by assessing the contractile responses in isolated adult rat cardiocytes and contrasted these measurements against two different methods for contractility assessment in the literature. Our results show good qualitative and quantitative agreements with these methods as far as frequency, pacing, and overall behavior of the contractions are concerned. We hypothesize that the proposed methodology, once appropriately developed and customized, can provide a framework for computational cardiac cell biomechanics that can be used to integrate both theory and experiment. For example, besides giving a good assessment of contractile response of the cardiocyte, since the excitation process of the cell is a closed system, this methodology can be employed in an attempt to infer statistically significant model parameters for the constitutive equations of the cardiocytes.

  7. Understanding of Materials State and its Degradation using Non-Linear Ultrasound Approaches for Lamb Wave Propagation

    Science.gov (United States)

    2015-05-31

    welded as well as HAZ region. Nonlinear Ultrasonic (NLU) is also now used to characterise the creep damage. Sony Baby et al. used the NLU technique...Šohaj, R Foret, “Microstructural stability of 316TI/P92 and 17242/P91 weld joints”, METAL 2011, 18th – 20th May 2011, Brno, Czech Republic, EU. [60] P J...harmonic generation”, J. Appl. Phys., 81(7); 2957-2962 (1997). [63] G E Dieter, Mechanical Metallurgy , McGraw-Hill Book Co., 1988 [64] J H Cantrell, and W

  8. Crystal growth, structural, spectral, thermal, dielectric, linear and nonlinear optical characteristics of a new organic acentric material: L-Methionine-Succinic acid (2/1)

    Science.gov (United States)

    Nageshwari, M.; Kumari, C. Rathika Thaya; Vinitha, G.; Mohamed, M. Peer; Sudha, S.; Caroline, M. Lydia

    2018-03-01

    L-Methionine-Succinic acid (2/1) (LMSA), 2C5H11NO2S·C4H6O4, a novel nonlinear optical material which belongs to the class of organic category was grown-up for the first time by the technique of slow evaporation. Purity of LMSA was improved using repetitive recrystallization. LMSA was analyzed by single crystal and powder X-ray diffraction investigation to affirm the crystal structure and crystalline character. The single crystal XRD revealed that LMSA corresponds to the crystal system of triclinic with P1 as space group showing the asymmetric unit consists of a neutral succinic acid molecule and two methionine residues which are crystallographically independent existing in zwitterionic form. The functional groups existing in LMSA was accomplished using Fourier transform infrared spectroscopy. The optical transparency and the band gap energy were identified utilizing UV-Visible spectrum. The optical constants specifically reflectance and extinction coefficient clearly indicate the elevated transparency of LMSA. The thermal analyses affirmed its thermal stability. The luminescence behavior of LMSA has been analyzed by Photoluminescence (PL) spectral study. The mechanical, laser damage threshold and dielectric investigation of LMSA was done to suggest the material for practical applications. The second and third harmonic generation efficacy was confirmed by means of Kurtz-Perry and Z-scan procedure which attest its potentiality in the domain of nonlinear optics.

  9. Nonlinear optical switching of PDA/Ag hybrid materials based on temperature- and pH-responsive threading and dethreading of cyclodextrin polypseudorotaxane

    Energy Technology Data Exchange (ETDEWEB)

    Rao, Jinan; Wen, Xiaolei; Leng, Jing; Wang, Jin; Zou, Gang; Zhang, Qijin [University of Science and Technology of China, CAS Key Laboratory of Soft Matter Chemistry, Department of Polymer Science and Engineering, Key Laboratory of Optoelectronic Science and Technology in Anhui Province, Anhui (China)

    2012-11-15

    We developed a novel temperature and pH dual-responsive supramolecular system in which the aggregation and disaggregation of polydiacetylene/silver (PDA/Ag) hybrid nanocrystals can be mediated by environmentally responsive threading and dethreading processes of polypseudorotaxane. The PDA/Ag hybrid nanocrystals provide a nonlinear optical (NLO) property. The host-guest interaction between poly(ethylene glycol) (PEG) and cyclodextrin (CD) cavities on the surface of the hybrid nanocrystals causes the PDA/Ag hybrid nanocrystals to be sufficiently close to each other for providing an enhanced surface plasmon resonance and a corresponding NLO effect. NLO switching of the colloidal materials can be easily realized by varying temperature and pH. The facile preparation procedures and their response to the surrounding media render these novel hybrid colloidal materials potential candidates for applications in sensors, catalysis and optical/electronic devices. (orig.)

  10. Nonlinear Optics and Applications

    Science.gov (United States)

    Abdeldayem, Hossin A. (Editor); Frazier, Donald O. (Editor)

    2007-01-01

    Nonlinear optics is the result of laser beam interaction with materials and started with the advent of lasers in the early 1960s. The field is growing daily and plays a major role in emerging photonic technology. Nonlinear optics play a major role in many of the optical applications such as optical signal processing, optical computers, ultrafast switches, ultra-short pulsed lasers, sensors, laser amplifiers, and many others. This special review volume on Nonlinear Optics and Applications is intended for those who want to be aware of the most recent technology. This book presents a survey of the recent advances of nonlinear optical applications. Emphasis will be on novel devices and materials, switching technology, optical computing, and important experimental results. Recent developments in topics which are of historical interest to researchers, and in the same time of potential use in the fields of all-optical communication and computing technologies, are also included. Additionally, a few new related topics which might provoke discussion are presented. The book includes chapters on nonlinear optics and applications; the nonlinear Schrodinger and associated equations that model spatio-temporal propagation; the supercontinuum light source; wideband ultrashort pulse fiber laser sources; lattice fabrication as well as their linear and nonlinear light guiding properties; the second-order EO effect (Pockels), the third-order (Kerr) and thermo-optical effects in optical waveguides and their applications in optical communication; and, the effect of magnetic field and its role in nonlinear optics, among other chapters.

  11. A Numerical Approach for Non-Linear Moisture Flow in Porous Materials with Account to Sorption Hysteresis

    DEFF Research Database (Denmark)

    Johannesson, Björn; Nyman, U.

    2010-01-01

    . History-dependent sorption behaviour is introduced by considering scanning curves between the bounding desorption and absorption curves. The method, therefore, makes it possible to calculate equilibrium water contents for arbitrary relative humidity variations at every material point considered...

  12. Nonlinear optics

    International Nuclear Information System (INIS)

    Boyd, R.W.

    1992-01-01

    Nonlinear optics is the study of the interaction of intense laser light with matter. This book is a textbook on nonlinear optics at the level of a beginning graduate student. The intent of the book is to provide an introduction to the field of nonlinear optics that stresses fundamental concepts and that enables the student to go on to perform independent research in this field. This book covers the areas of nonlinear optics, quantum optics, quantum electronics, laser physics, electrooptics, and modern optics

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

    International Nuclear Information System (INIS)

    Gelebart, Lionel; Mondon-Cancel, Romain

    2013-01-01

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

  14. Refined Modeling of Flexural Deformation of Layered Plates with a Regular Structure Made from Nonlinear Hereditary Materials

    Science.gov (United States)

    Yankovskii, A. P.

    2018-01-01

    On the basis of constitutive equations of the Rabotnov nonlinear hereditary theory of creep, the problem on the rheonomic flexural behavior of layered plates with a regular structure is formu-lated. Equations allowing one to describe, with different degrees of accuracy, the stress-strain state of such plates with account of their weakened resistance to transverse shear were ob-tained. From them, the relations of the nonclassical Reissner- and Reddytype theories can be found. For axially loaded annular plates clamped at one edge and loaded quasistatically on the other edge, a simplified version of the refined theory, whose complexity is comparable to that of the Reissner and Reddy theories, is developed. The flexural strains of such metal-composite annular plates in shortterm and long-term loadings at different levels of heat action are calcu-lated. It is shown that, for plates with a relative thickness of order of 1/10, neither the classical theory, nor the traditional nonclassical Reissner and Reddy theories guarantee reliable results for deflections even with the rough 10% accuracy. The accuracy of these theories decreases at elevated temperatures and with time under long-term loadings of structures. On the basic of relations of the refined theory, it is revealed that, in bending of layered metal-composite heat-sensitive plates under elevated temperatures, marked edge effects arise in the neighborhood of the supported edge, which characterize the shear of these structures in the transverse direction

  15. Nonlinear optics

    CERN Document Server

    Bloembergen, Nicolaas

    1996-01-01

    Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe

  16. Numerical simulation of the roll levelling of third generation fortiform 1050 steel using a nonlinear combined hardening material model

    Science.gov (United States)

    Galdos, L.; Saenz de Argandoña, E.; Mendiguren, J.; Silvestre, E.

    2017-09-01

    The roll levelling is a flattening process used to remove the residual stresses and imperfections of metal strips by means of plastic deformations. During the process, the metal sheet is subjected to cyclic tension-compression deformations leading to a flat product. The process is especially important to avoid final geometrical errors when coils are cold formed or when thick plates are cut by laser. In the last years, and due to the appearance of high strength materials such as Ultra High Strength Steels, machine design engineers are demanding reliable tools for the dimensioning of the levelling facilities. Like in other metal forming fields, finite element analysis seems to be the most widely used solution to understand the occurring phenomena and to calculate the processing loads. In this paper, the roll levelling process of the third generation Fortiform 1050 steel is numerically analysed. The process has been studied using the MSC MARC software and two different material laws. A pure isotropic hardening law has been used and set as the baseline study. In the second part, tension-compression tests have been carried out to analyse the cyclic behaviour of the steel. With the obtained data, a new material model using a combined isotropic-kinematic hardening formulation has been fitted. Finally, the influence of the material model in the numerical results has been analysed by comparing a pure isotropic model and the later combined mixed hardening model.

  17. 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.

  18. An Experimental and Finite Element Investigation into the Nonlinear Material Behavior of Pin-Loaded Composite Laminates

    Science.gov (United States)

    1991-01-01

    shear formulation. This phenomenon was thought to be highly span dependent. A mathematical representation of this formulation was found by introducing a...U) (N I- - +-4 UV IfX Figue 964 [+ 5-45)]s onlnearElatic oupn Ci an C1 Contittiv Equtio Costats 120 lb lod lvel 201 I I Iw z 110 W- (0 to U (IO...Failure Analysis of composite Bolted Joints", Journal of Composite Materials, 20, May 1986, pp. 236-252. 3 1Hill, R., "The Mathematical Theory of

  19. Growth, structural, physical and computational perspectives of trans-4-hydroxy-l-proline: a promising organic nonlinear optical material with large laser-induced damage threshold

    Science.gov (United States)

    Thirumurugan, Ramaiah; Anitha, Kandasamy

    2017-05-01

    In this work, a systematic study of an organic nonlinear optical (NLO) material, trans-4-hydroxy-l-proline (THP), C5H9NO3 is reported. An optical quality single crystals of THP have been successfully grown by using slow evaporation solution growth technique (SEST). The single crystal x-ray diffraction (SXRD) analysis reveals that grown crystal belongs to the orthorhombic system with non-centrosymmetric space group (NCS), P212121. Powder x-ray diffraction (PXRD) analysis shows relatively a good crystalline nature. The molecular structure of THP was recognized by NMR (1H and 13C) studies and its vibrational modes were confirmed by FTIR and FT-Raman vibrational studies. UV-Vis-NIR spectrum of grown crystal shows high optical transparency in the visible and near-IR region with low near-UV cut-off wavelength at 218 nm. Photoluminescence study confirms ultraviolet wavelength emission of THP crystal. The second harmonic generation (SHG) efficiency of grown crystal is 1.6 times greater with respect to standard potassium dihydrogen phosphate (KDP). Nonlinear refractive index (n 2) and nonlinear absorption coefficient (β) were determined using the Z-scan technique. The title compound owns high thermal stability of 294 °C and specific heat capacity (C P) of 1.21 J g-1 K-1 at 300 K and 11.33 J g-1 K-1 at 539 K (melting point). The laser-induced damage threshold (LDT) value of grown crystal was measured as 7.25 GW cm-2. The crystal growth mechanism and defects of grown crystal were studied by chemical etching technique. Mechanical strength was extensively studied by Vickers microhardness test and crystal void percentage analysis. Moreover, density functional theory (DFT) studies were carried out to probe the Mulliken charge distribution, frontier molecular orbitals (FMOs) and first order hyperpolarizability (β) of the optimized molecular structure to get a better insight of the molecular properties. These characterization results endorse that grown THP crystal as a

  20. The Effect of Material Property on the Critical Velocity of Randomly Excited Nonlinear Axially Travelling Functionally Graded Plates

    Directory of Open Access Journals (Sweden)

    M. Abedi

    Full Text Available Abstract In this paper, the critical axial speeds of three types of sigmoid, power law and exponential law functionally graded plates for both isotropic and orthotropic cases are obtained via a completely analytic method. The plates are subjected to lateral white noise excitation and show evidence of large deformations. Due to randomness, the conventional deterministic methods fail and a statistical approach must be selected. Here, the probability density function is evaluated analytically for prescribed plates and used to investigate the critical axial velocity of them. Specifically the effect of in-plane forces, mean value of lateral load and the material property on the critical axial speed are studied and discussed for both isotropic and orthotropic functionally graded plates. Since the governing equation is transformed to a non dimensional format, the results can be used for a wide range of plate dimensions. It is shown that the material heterogeneity palys an essential and significant role in increasing or decreasing the critical speed of both isotropic and orthotropic functionally graded plates.

  1. Grain size and nanoscale effects on the nonlinear pull-in instability and vibrations of electrostatic actuators made of nanocrystalline material

    Science.gov (United States)

    Gholami, R.; Ansari, R.

    2018-01-01

    Presented herein is the study of grain size, grain surface energy and small scale effects on the nonlinear pull-in instability and free vibration of electrostatic nanoscale actuators made of nanocrystalline silicon (Nc-Si). A Mori-Tanaka micromechanical model is utilized to calculate the effective material properties of Nc-Si considering material structure inhomogeneity, grain size and grain surface energy. The small-scale effect is also taken into account using Mindlin’s strain gradient theory. Governing equations are derived in the discretized weak form using the variational differential quadrature method based on the third-order shear defamation beam theory in conjunction with the von Kármán hypothesis. The electrostatic actuation is modeled considering the fringing field effects based upon the parallel plate approximation. Moreover, the Casimir force effect is considered. The pseudo arc-length continuation technique is used to obtain the applied voltage-deflection curve of Nc-Si actuators. Then, a time-dependent small disturbance around the deflected configuration is assumed to solve the free vibration problem. By performing a numerical study, the influences of various factors such as length scale parameter, volume fraction of the inclusion phase, density ratio, average inclusion radius and Casimir force on the pull-in instability and free vibration of Nc-Si actuators are investigated.

  2. Nonlinear dynamics of structures

    CERN Document Server

    Oller, Sergio

    2014-01-01

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

  3. Nonlinear Science

    CERN Document Server

    Yoshida, Zensho

    2010-01-01

    This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl

  4. Nonlinear photonic metasurfaces

    Science.gov (United States)

    Li, Guixin; Zhang, Shuang; Zentgraf, Thomas

    2017-03-01

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

  5. 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

  6. Terahertz semiconductor nonlinear optics

    DEFF Research Database (Denmark)

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

    2013-01-01

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

  7. Finite element model for nonlinear shells of revolution

    International Nuclear Information System (INIS)

    Cook, W.A.

    1979-01-01

    Nuclear material shipping containers have shells of revolution as basic structural components. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Existing models are limited to large displacements, small rotations, and nonlinear materials. The paper presents a finite element model for a nonlinear shell of revolution that will account for large displacements, large strains, large rotations, and nonlinear materials

  8. Local-metrics error-based Shepard interpolation as surrogate for highly non-linear material models in high dimensions

    Science.gov (United States)

    Lorenzi, Juan M.; Stecher, Thomas; Reuter, Karsten; Matera, Sebastian

    2017-10-01

    Many problems in computational materials science and chemistry require the evaluation of expensive functions with locally rapid changes, such as the turn-over frequency of first principles kinetic Monte Carlo models for heterogeneous catalysis. Because of the high computational cost, it is often desirable to replace the original with a surrogate model, e.g., for use in coupled multiscale simulations. The construction of surrogates becomes particularly challenging in high-dimensions. Here, we present a novel version of the modified Shepard interpolation method which can overcome the curse of dimensionality for such functions to give faithful reconstructions even from very modest numbers of function evaluations. The introduction of local metrics allows us to take advantage of the fact that, on a local scale, rapid variation often occurs only across a small number of directions. Furthermore, we use local error estimates to weigh different local approximations, which helps avoid artificial oscillations. Finally, we test our approach on a number of challenging analytic functions as well as a realistic kinetic Monte Carlo model. Our method not only outperforms existing isotropic metric Shepard methods but also state-of-the-art Gaussian process regression.

  9. Accuracy of specimen-specific nonlinear finite element analysis for evaluation of distal radius strength in cadaver material.

    Science.gov (United States)

    Matsuura, Yusuke; Kuniyoshi, Kazuki; Suzuki, Takane; Ogawa, Yasufumi; Sukegawa, Koji; Rokkaku, Tomoyuki; Takahashi, Kazuhisa

    2014-11-01

    Distal radius fracture, which often occurs in the setting of osteoporosis, can lead to permanent deformity and disability. Great effort has been directed toward developing noninvasive methods for evaluating the distal radius strength, with the goal of assessing fracture risk. The aim of this study was to evaluate distal radius strength using a finite element model and to gauge the accuracy of finite element model measurement using cadaver material. Ten wrists were obtained from cadavers with a mean age of 89.5 years at death. CT images of each wrist in an extended position were obtained. CT-based finite element models were prepared with Mechanical Finder software. Fracture on the models was simulated by applying a mechanical load to the palm in a direction parallel to the forearm axis, after which the fracture load and the site at which the fracture began were identified. For comparison, the wrists were fractured using a universal testing machine and the fracture load and the site of fracture were identified. The fracture load was 970.9 N in the finite element model group and 990.0 N in the actual measurement group. The site of the initial fracture was extra-articular to the distal radius in both groups. The finite element model was predictive for distal radius fracture when compared to the actual measurement. In this study, a finite element model for evaluation of distal radius strength was validated and can be used to predict fracture risk. We conclude that a finite element model is useful for the evaluation of distal radius strength. Knowing distal radius strength might avoid distal radius fracture because appropriate antiosteoporotic treatment can be initiated.

  10. Nonlinear systems

    CERN Document Server

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

    2018-01-01

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

  11. Quantitative analysis of Ni2+/Ni3+ in Li[NixMnyCoz]O2 cathode materials: Non-linear least-squares fitting of XPS spectra

    Science.gov (United States)

    Fu, Zewei; Hu, Juntao; Hu, Wenlong; Yang, Shiyu; Luo, Yunfeng

    2018-05-01

    Quantitative analysis of Ni2+/Ni3+ using X-ray photoelectron spectroscopy (XPS) is important for evaluating the crystal structure and electrochemical performance of Lithium-nickel-cobalt-manganese oxide (Li[NixMnyCoz]O2, NMC). However, quantitative analysis based on Gaussian/Lorentzian (G/L) peak fitting suffers from the challenges of reproducibility and effectiveness. In this study, the Ni2+ and Ni3+ standard samples and a series of NMC samples with different Ni doping levels were synthesized. The Ni2+/Ni3+ ratios in NMC were quantitatively analyzed by non-linear least-squares fitting (NLLSF). Two Ni 2p overall spectra of synthesized Li [Ni0.33Mn0.33Co0.33]O2(NMC111) and bulk LiNiO2 were used as the Ni2+ and Ni3+ reference standards. Compared to G/L peak fitting, the fitting parameters required no adjustment, meaning that the spectral fitting process was free from operator dependence and the reproducibility was improved. Comparison of residual standard deviation (STD) showed that the fitting quality of NLLSF was superior to that of G/L peaks fitting. Overall, these findings confirmed the reproducibility and effectiveness of the NLLSF method in XPS quantitative analysis of Ni2+/Ni3+ ratio in Li[NixMnyCoz]O2 cathode materials.

  12. Establishment of the evaluation method of the tendon effective stress in the containment building and the concrete material nonlinear model(II)

    International Nuclear Information System (INIS)

    Chung, Chul Hun; Park, Jae Gyun; Kim, Jong Suk; Yun, Yeon Suk; Kim, Se Hun; Chung, Dong Jin

    2006-12-01

    To elevate the structural integrity of the NPP containment building more rigorously, the effective prestress, which is one of the most affecting elements, needs to be estimated exactly. In the second year study, we evaluated the proposed effective prestress measuring method which uses pressure decreasing technique through experiments. It is possible to improve the effective prestress measuring method by test beam, which is being applied for the investigation of the Nuclear Power Plant in operation. We performed a finite element analysis to evaluate the effect of the prestress loss of the tendon to the behavior of the structure. According to the results, the effect of the prestress loss of the vertical and circumventive tendon to some level in the confinement building was analyzed. Another requirement for te rigorous evaluation of the structural soundness is the fast and exact analysis of structural responses under such extreme loads as earthquakes. To achieve this goal, we need analysis models that can describe nonlinear behavior of each material well. In this second year, based on the analysis results during first year, we propose a guideline for the concrete modeling via ABAQUS, a multi-purpose finite element analysis program, and perform static and dynamic analyses

  13. Development of nonlinear optical materials using inorganic-organic complexes; Hisenkei kogaku zairyo to shite no yuki-muki fukugotai no kaihatsu

    Energy Technology Data Exchange (ETDEWEB)

    Mizuno, N. [Hokkaido University, Sapporo (Japan). Catalysis Research Center

    1994-12-15

    Development was attempted on organic-inorganic complexes as nonlinear optical materials. The objective is to develop elements with SHG activity (generating second harmonics) to change a visible ray into an ultraviolet ray by inserting P-nitroaniline (pNA) into such solid acids having strong static electric field as zeolite, laminar compounds, and heteropolyacid, and utilizing the static electric field and the molecule coordination field of inorganic compounds. Used for the pNA{center_dot}Bronsted acid composite are HBr, HCl, HNO3, and H2SO4. The pNA that has a center of symmetry in the crystalline structure and does not generate the second harmonics shows SHG when it is formed into a composite with HBr. No SHG is recognized in other acid composites. This difference is due to the difference in the crystalline structure. The SHG activity was generated when pNA is loaded onto alumina and silica as solid oxides. When zeolites are used as carriers, no SHG was observed. A composite of pNA{center_dot}AlCl3 has high SHG intensity, which reached a maximum when the pNA/AlCl3 ratio was two. This composite showed four new peaks that belong to the SHG activity phase. 8 refs., 2 figs., 2 tabs.

  14. Mathematical and numerical analysis of hyper-elastic systems and introduction of plasticity; Analyse mathematique et numerique de systemes hyperelastiques et introduction de la plasticite

    Energy Technology Data Exchange (ETDEWEB)

    Kluth, G

    2008-12-15

    The goal is to model mathematically and numerically the dynamic phenomenons for solids in finite plasticity. We suggest a model that we call hyper-elasto-plastic based on hyper-elastic systems of conservation laws and on the use of an equation of state that we have constructed so as to achieve the plastic yield criterion of Von Mises. This model gives exact (analytic) solutions with shock split to flyer-plate experiments. The mathematical analysis of this model is done (hyperbolicity, characteristic fields, involutions and entropy). In the numerical part, we give 1D and 2D Lagrangian schemes which satisfy an entropy criterion. Moreover, thanks to a special discretization of the equations on deformation gradient, we satisfy some discrete involutions. In this work, the degeneracy of the solid model into hydrodynamic models is studied at the continuous level, and achieved at the numerical one. On different problems, we show the validity of our model and our numerical schemes. (author)

  15. 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

  16. Long Distance Enhancement of Nonlinear Optical Properties Using Low Concentration of Plasmonic Nanostructures in Dye Doped Monolithic SolGel Materials (Postprint)

    Science.gov (United States)

    2016-05-31

    Incorporation of effi cient nonlinear dyes into a solid matrix at high concentration is a real challenge. This has been achieved through the sol...NIR Lambda 750 spectrometer. The nonlinear absorption measurements at 532 and 600 nm were made with the same method and on the same occasion as for

  17. Particles geometry influence in the thermal stress level in an SiC reinforced aluminum matrix composite considering the material non-linear behavior

    International Nuclear Information System (INIS)

    Miranda, Carlos A. de J.; Libardi, Rosani M.P.; Boari, Zoroastro de M.

    2009-01-01

    An analytical methodology was developed to predict the thermal stress level that occurs in a metallic matrix composite reinforced with SiC particles, when the temperature decreases from 600 deg C to 20 deg C during the fabrication process. This analytical development is based on the Eshelby method, dislocation mechanisms, and the Maxwell-Boltzmann distribution model. The material was assumed to have a linear elastic behavior. The analytical results from this formulation were verified against numerical linear analyses that were performed over a set of random non-uniform distribution of particles that covers a wide range of volumetric ratios. To stick with the analytical hypothesis, particles with round geometry were used. Each stress distribution, represented by the isostress curves at ΔT=-580 deg C, was analyzed with an image analyzer. A statistical procedure was applied to obtain the most probable thermal stress level. Analytical and numerical results compared very well. Plastic deformation as well as particle geometry can alter significantly the stress field in the material. To account for these effects, in this work, several numerical analyses were performed considering the non-linear behavior for the aluminum matrix and distinct particle geometries. Two distinct sets of data with were used. To allow a direct comparison, the first set has the same models (particle form, size and distribution) as used previously. The second set analyze quadrilateral particles and present very tight range of volumetric ratio, closer to what is found in actual SiC composites. A simple and fast algorithm was developed to analyze the new results. The comparison of these results with the previous ones shows, as expected, the strong influence of the elastic-plastic behavior of the aluminum matrix on the composite thermal stress distribution due to its manufacturing process and shows, also, a small influence of the particles geometry and volumetric ratio. (author)

  18. Nonlinear systems

    National Research Council Canada - National Science Library

    Drazin, P. G

    1992-01-01

    This book is an introduction to the theories of bifurcation and chaos. It treats the solution of nonlinear equations, especially difference and ordinary differential equations, as a parameter varies...

  19. Nonlinear analysis

    CERN Document Server

    Gasinski, Leszek

    2005-01-01

    Hausdorff Measures and Capacity. Lebesgue-Bochner and Sobolev Spaces. Nonlinear Operators and Young Measures. Smooth and Nonsmooth Analysis and Variational Principles. Critical Point Theory. Eigenvalue Problems and Maximum Principles. Fixed Point Theory.

  20. Oscillations in nonlinear systems

    CERN Document Server

    Hale, Jack K

    2015-01-01

    By focusing on ordinary differential equations that contain a small parameter, this concise graduate-level introduction to the theory of nonlinear oscillations provides a unified approach to obtaining periodic solutions to nonautonomous and autonomous differential equations. It also indicates key relationships with other related procedures and probes the consequences of the methods of averaging and integral manifolds.Part I of the text features introductory material, including discussions of matrices, linear systems of differential equations, and stability of solutions of nonlinear systems. Pa

  1. Nonlinear Optics: Principles and Applications

    DEFF Research Database (Denmark)

    Rottwitt, Karsten; Tidemand-Lichtenberg, Peter

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

  2. Quantum mechanical design of efficient second-order nonlinear optical materials based on heteroaromatic imido-substituted hexamolybdates: first theoretical framework of POM-based heterocyclic aromatic rings.

    Science.gov (United States)

    Janjua, Muhammad Ramzan Saeed Ashraf

    2012-11-05

    This work was inspired by a previous report (Janjua et al. J. Phys. Chem. A 2009, 113, 3576-3587) in which the nonlinear-optical (NLO) response strikingly improved with an increase in the conjugation path of the ligand and the nature of hexamolybdates (polyoxometalates, POMs) was changed into a donor by altering the direction of charge transfer with a second aromatic ring. Herein, the first theoretical framework of POM-based heteroaromatic rings is found to be another class of excellent NLO materials having double heteroaromatic rings. First hyperpolarizabilities of a large number of push-pull-substituted conjugated systems with heteroaromatic rings have been calculated. The β components were computed at the density functional theory (DFT) level (BP86 geometry optimizations and LB94 time-dependent DFT). The largest β values are obtained with a donor (hexamolybdates) on the benzene ring and an acceptor (-NO(2)) on pyrrole, thiophene, and furan rings. The pyrrole imido-substituted hexamolybdate (system 1c) has a considerably large first hyperpolarizability, 339.00 × 10(-30) esu, and it is larger than that of (arylimido)hexamolybdate, calculated as 0.302 × 10(-30) esu (reference system 1), because of the double aromatic rings in the heteroaromatic imido-substituted hexamolybdates. The heteroaromatic rings act as a conjugation bridge between the electron acceptor (-NO(2)) and donor (polyanion). The introduction of an electron donor into heteroaromatic rings significantly enhances the first hyperpolarizabilities because the electron-donating ability is substantially enhanced when the electron donor is attached to the heterocyclic aromatic rings. Interposing five-membered auxiliary fragments between strong donor (polyanion) or acceptor (-NO(2)) groups results in a large computed second-order NLO response. The present investigation provides important insight into the NLO properties of (heteroaromatic) imido-substituted hexamolybdate derivatives because these compounds

  3. Polymeric Materials Models in the Warrior Injury Assessment Manikin (WIAMan) Anthropomorphic Test Device (ATD) Tech Demonstrator

    Science.gov (United States)

    2017-01-01

    analytical model currently used by military vehicle analysts has been continuously updated to address the model’s inherent deficiencies and make the... model is a hyperelastic polymer model based upon statistical mechanics and the finite extensibility of a polymer chain.23 Its rheological ...ARL-TR-7927 ● JAN 2017 US Army Research Laboratory Polymeric Materials Models in the Warrior Injury Assessment Manikin (WIAMan

  4. Fracture as a material sink

    Science.gov (United States)

    Volokh, K. Y.

    2017-12-01

    Cracks are created by massive breakage of molecular or atomic bonds. The latter, in its turn, leads to the highly localized loss of material, which is the reason why even closed cracks are visible by a naked eye. Thus, fracture can be interpreted as the local material sink. Mass conservation is violated locally in the area of material failure. We consider a theoretical formulation of the coupled mass and momenta balance equations for a description of fracture. Our focus is on brittle fracture and we propose a finite strain hyperelastic thermodynamic framework for the coupled mass-flow-elastic boundary value problem. The attractiveness of the proposed framework as compared to the traditional continuum damage theories is that no internal parameters (like damage variables, phase fields, etc.) are used while the regularization of the failure localization is provided by the physically sound law of mass balance.

  5. Topology optimization of nonlinear optical devices

    DEFF Research Database (Denmark)

    Jensen, Jakob Søndergaard

    2011-01-01

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

  6. Nonlinear silicon photonics

    Science.gov (United States)

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

    2017-09-01

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

  7. Investigation on the growth, spectral, lifetime, mechanical analysis and third-order nonlinear optical studies of L-methionine admixtured D-mandelic acid single crystal: A promising material for nonlinear optical applications

    Science.gov (United States)

    Jayaprakash, P.; Sangeetha, P.; Kumari, C. Rathika Thaya; Caroline, M. Lydia

    2017-08-01

    A nonlinear optical bulk single crystal of L-methionine admixtured D-mandelic acid (LMDMA) has been grown by slow solvent evaporation technique using water as solvent at ambient temperature. The crystallized LMDMA single crystal subjected to single crystal X-ray diffraction study confirmed monoclinic system with the acentric space group P21. The FTIR analysis gives information about the modes of vibration in the various functional groups present in LMDMA. The UV-visible spectral analysis assessed the optical quality and linear optical properties such as extinction coefficient, reflectance, refractive index and from which optical conductivity and electric susceptibility were also evaluated. The frequency doubling efficiency was observed using Kurtz Perry powder technique. A multiple shot laser was utilized to evaluate the laser damage threshold energy of the crystal. Discrete thermodynamic properties were carried out by TG-DTA studies. The hardness, Meyer's index, yield strength, elastic stiffness constant, Knoop hardness, fracture toughness and brittleness index were analyzed using Vickers microhardness tester. Layer growth pattern and the surface defect were examined by chemical etching studies using optical microscope. Fluorescence emission spectrum was recorded and lifetime was also studied. The electric field response of crystal was investigated from the dielectric studies at various temperatures at different frequencies. The third-order nonlinear optical response in LMDMA has been investigated using Z-scan technique with He-Ne laser at 632.8 nm and nonlinear parameters such as refractive index (n2), absorption coefficient (β) and susceptibility (χ3) investigated extensively for they are in optical phase conjucation, high-speed optical switches and optical dielectric devices.

  8. Algorithm for the treatment of the material plastic anisotropy and its introduction into a non-linear structural analysis code (NOSA)

    Energy Technology Data Exchange (ETDEWEB)

    Toselli, G. [ENEA, Centro Ricerche Ezio Clementel, Bologna, (Italy). Dipt. Innovazione; Mirco, A. M. [Bologna Univ., Bologna (Italy). Dipt. di Matematica

    1999-07-01

    In this technical report the thesis of doctor's degree in Mathematics of A.M. Mirco is reported; it has been developed at ENEA research centre 'E. Clementel' in Bologna (Italy) in the frame of a collaboration between the section MACO (Applied Physics Division - Innovation Department) of ENEA at Bologna and the Department of Mathematics of the mathematical, physical and natural sciences faculty of Bologna University. Substantially, studies and research work, developed in these last years at MACO section, are here presented; they have led to the development of a constitutive model, based on Hill potential theory, for the treatment, in plastic field, of metal material anisotropy induced by previous workings and to the construction of the corresponding FEM algorithm for the non-linear structural analysis NOSA, oriented in particular to the numerical simulation of metal forming. Subsequently, an algorithm extension (proper object of the thesis), which has given, beyond a more rigorous formalization, also significant improvements. [Italian] In questo rapporto tecnico viene riportata la tesi di laurea in matematica di A. M. Mirco, tesi svolta presso il centro ricerche E. Clementel dell'ENEA di Bologna nell'ambito di un accordo di collaborazione fra la sezione MACO (Divisione Fisica Applicata - Dipartimento di Innovazione) dell'ENEA di Bologna ed il Dipartimento di matematica della facolta' di scienze matematiche, fisiche e naturali dell'universita' degli studi di Bologna. Sostanzialmente, vengono presentati gli studi ed il lavoro di ricerca, svolti in questi ultimi anni presso la sezione MACO, che hanno portato allo sviluppo di un modello costitutivo, basato sulla teoria del potenziale di Hill, per il trattamento in campo plastico, dell'anisotropia indotta da lavorazioni precedenti per un materiale metallico ed alla costruzione del corrispondente algoritmo basato sul metodo degli elementi finiti per il codice di analisi

  9. Nonlinear hyperbolic waves in multidimensions

    CERN Document Server

    Prasad, Phoolan

    2001-01-01

    The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...

  10. Nonlinear optics principles and applications

    CERN Document Server

    Rottwitt, Karsten

    2014-01-01

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

  11. FY 1992 Report on the results of the research and development project for the industrial base technologies of the next generation. Research and development of nonlinear optoelectronic materials; 1992 nendo hisenkei hikari denshi zairyo no kenkyu kaihatsu seika hokokusho

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1993-03-01

    Described herein are the FY 1992 results of the research and development project for the optoelectronic materials. The FY 1992 is the last year for the phase-I project of the basic plan, and the results are evaluated mainly viewed from extent of attainment of the interim targets. For the organic materials, the highly unique chiral nonlinear compounds are further developed, and direction for the investigations of the conjugated low-molecular-weight compounds is established. The excellent high-molecular-weight films are developed. For the dispersed materials, those developed include CuCl-dispersed glass, CdTe laminated glass developed by the laser evaporation method, glass dispersed with semiconductors at high concentrations, and dispersed materials with high-molecular-weight materials as the matrices. For the material development, those technologies investigated are orientation controlling of the crystals for thin organic films, and development of superlattices. A total of 9 research themes are recommissioned to 9 enterprises. They include organic, low-molecular-weight materials, growth of orientation-controlled crystals, films of high-molecular-weight organic conjugated compounds, glass-dispersed materials (prepared by the vapor-phase, impregnation of porous glass, sol-gel, superlow-melting glass and super-cooling methods), organic dispersed materials, development of the organic superlattices, and development of the three-dimensional superstructures. (NEDO)

  12. FY 1990 Report on the results of the research and development project for the industrial base technologies of the next generation. Research and development of nonlinear optoelectronic materials; 1990 nendo hisenkei hikari denshi zairyo no kenkyu kaihatsu seika hokokusho

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1991-03-01

    Described herein are the FY 1990 results of the research and development project for the optoelectronic materials, implemented to cope with the highly information-oriented societies. The FY 1990 is the second year for the phase-I project of the basic plan, and the R and D efforts are directed to elucidation of the mechanisms involved in the nonlinear phenomena, exploration and designs of various materials, and investigations of the technologies for, e.g., the material synthesis and evaluation. The themes to be investigated by the long-term project include exploration and preparation of the superfine particles and base materials for the organic materials; and crystal growth, dispersion of the fine particles and development of the superlattices for development of the materials. The comprehensive investigation and research program investigates the trends of the related technologies, both domestic and foreign. A total of 9 research themes are recommissioned to 9 enterprises. They include organic, low-molecular-weight materials, growth of orientation-controlled crystals, films of high-molecular-weight organic conjugated compounds, glass-dispersed materials (prepared by the vapor-phase, impregnation of porous glass, sol-gel, superlow-melting glass and super-cooling methods), organic dispersed materials, development of the organic superlattices, and development of the three-dimensional superstructures. (NEDO)

  13. Measuring Regional Changes in the Diastolic Deformation of the Left Ventricle of SHR Rats Using microPET Technology and Hyperelastic Warping

    Energy Technology Data Exchange (ETDEWEB)

    Gullberg, Grant T; VERESS , ALEXANDER I.; WEISS, JEFFREY A.; HUESMAN, RONALD H.; REUTTER, BRYAN W.; TAYLOR , SCOTT E.; SITEK , AREK; FENG, BING; YANG , YONGFENG; GULLBERG, GRANT T.

    2008-04-04

    The objective of this research was to assess applicability of a technique known as hyperelastic warping for the measurement of local strains in the left ventricle (LV) directly from microPET image data sets. The technique uses differences in image intensities between template (reference) and target (loaded) image data sets to generate a body force that deforms a finite element (FE) representation of the template so that it registers with the target images. For validation, the template image was defined as the end-systolic microPET image data set from a Wistar Kyoto (WKY) rat. The target image was created by mapping the template image using the deformation results obtained from a FE model of diastolic filling. Regression analysis revealed highly significant correlations between the simulated forward FE solution and image derived warping predictions for fiber stretch (R2 = 0.96), circumferential strain (R2 = 0.96), radial strain (R2 = 0.93), and longitudinal strain (R2 = 0.76) (p<0.001for all cases). The technology was applied to microPET image data of two spontaneously hypertensive rats (SHR) and a WKY control. Regional analysis revealed that, the lateral freewall in the SHR subjects showed the greatest deformation compared with the other wall segments. This work indicates that warping can accurately predict the strain distributions during diastole from the analysis of microPET data sets.

  14. Measuring Regional Changes in the Diastolic Deformation of the Left Ventricle of SHR Rats Using microPET Technology and Hyperelastic Warping

    International Nuclear Information System (INIS)

    Gullberg, Grant T; VERESS, ALEXANDER I.; WEISS, JEFFREY A.; HUESMAN, RONALD H.; REUTTER, BRYAN W.; TAYLOR, SCOTT E.; SITEK, AREK; FENG, BING; YANG, YONGFENG; GULLBERG, GRANT T.

    2008-01-01

    The objective of this research was to assess applicability of a technique known as hyperelastic warping for the measurement of local strains in the left ventricle (LV) directly from microPET image data sets. The technique uses differences in image intensities between template (reference) and target (loaded) image data sets to generate a body force that deforms a finite element (FE) representation of the template so that it registers with the target images. For validation, the template image was defined as the end-systolic microPET image data set from a Wistar Kyoto (WKY) rat. The target image was created by mapping the template image using the deformation results obtained from a FE model of diastolic filling. Regression analysis revealed highly significant correlations between the simulated forward FE solution and image derived warping predictions for fiber stretch (R2 = 0.96), circumferential strain (R2 = 0.96), radial strain (R2 = 0.93), and longitudinal strain (R2 = 0.76) (p < 0.001 for all cases). The technology was applied to microPET image data of two spontaneously hypertensive rats (SHR) and a WKY control. Regional analysis revealed that, the lateral freewall in the SHR subjects showed the greatest deformation compared with the other wall segments. This work indicates that warping can accurately predict the strain distributions during diastole from the analysis of microPET data sets

  15. Materialism.

    Science.gov (United States)

    Melnyk, Andrew

    2012-05-01

    Materialism is nearly universally assumed by cognitive scientists. Intuitively, materialism says that a person's mental states are nothing over and above his or her material states, while dualism denies this. Philosophers have introduced concepts (e.g., realization and supervenience) to assist in formulating the theses of materialism and dualism with more precision, and distinguished among importantly different versions of each view (e.g., eliminative materialism, substance dualism, and emergentism). They have also clarified the logic of arguments that use empirical findings to support materialism. Finally, they have devised various objections to materialism, objections that therefore serve also as arguments for dualism. These objections typically center around two features of mental states that materialism has had trouble in accommodating. The first feature is intentionality, the property of representing, or being about, objects, properties, and states of affairs external to the mental states. The second feature is phenomenal consciousness, the property possessed by many mental states of there being something it is like for the subject of the mental state to be in that mental state. WIREs Cogn Sci 2012, 3:281-292. doi: 10.1002/wcs.1174 For further resources related to this article, please visit the WIREs website. Copyright © 2012 John Wiley & Sons, Ltd.

  16. Nonlinear fiber optics formerly quantum electronics

    CERN Document Server

    Agrawal, Govind

    1995-01-01

    The field of nonlinear fiber optics has grown substantially since the First Edition of Nonlinear Fiber Optics, published in 1989. Like the First Edition, this Second Edition is a comprehensive, tutorial, and up-to-date account of nonlinear optical phenomena in fiber optics. It synthesizes widely scattered research material and presents it in an accessible manner for students and researchers already engaged in or wishing to enter the field of nonlinear fiber optics. Particular attention is paid to the importance of nonlinear effects in the design of optical fiber communication systems. This is

  17. Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

    Indian Academy of Sciences (India)

    In this paper we study nonlinear elliptic boundary value problems with monotone and nonmonotone multivalued nonlinearities. First we consider the case of monotone nonlinearities. In the first result we assume that the multivalued nonlinearity is defined on all R R . Assuming the existence of an upper and of a lower ...

  18. A method for determination of X-ray elastic constants of materials showing non-linear sin2ψ diagrams and its application to Zn-Ni-alloy electroplate

    International Nuclear Information System (INIS)

    Sasaki, Toshihiko; Kuramoto, Makoto; Yoshioka, Yasuo.

    1990-01-01

    This paper describes the method and the experiment for the determination of the x-ray elastic constants of Zn-Ni-alloy electroplate. For this material, the sin 2 ψ method is not adequate to use because this material shows severely curved sin 2 ψ diagrams. Therefore, a new method developed by the authors was explained first. This new method is effective for materials showing nonlinear sin 2 ψ diagrams. Secondly, the experiment was made on the application of this method to the Zn-Ni-alloy electroplate. And it was found out that the experimental data agreed well to the theory of this method. As a result, the following values were obtained as the x-ray elastic constants of the sample measured: (1+ν)/E=8.44 TPa -1 ν/E=2.02 TPa -1 (author)

  19. Materials

    CSIR Research Space (South Africa)

    Van Wyk, Llewellyn V

    2009-02-01

    Full Text Available . It is generally included as part of a structurally insulated panel (SIP) where the foam is sandwiched between external skins of steel, wood or cement. Cement composites Cement bonded composites are an important class of building materials. These products... for their stone buildings, including the Egyptians, Aztecs and Inca’s. As stone is a very dense material it requires intensive heating to become warm. Rocks were generally stacked dry but mud, and later cement, can be used as a mortar to hold the rocks...

  20. Extreme Nonlinear Optics An Introduction

    CERN Document Server

    Wegener, Martin

    2005-01-01

    Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged. Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself. This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The followi...

  1. Nonlinear Elasticity

    Science.gov (United States)

    Fu, Y. B.; Ogden, R. W.

    2001-05-01

    This collection of papers by leading researchers in the field of finite, nonlinear elasticity concerns itself with the behavior of objects that deform when external forces or temperature gradients are applied. This process is extremely important in many industrial settings, such as aerospace and rubber industries. This book covers the various aspects of the subject comprehensively with careful explanations of the basic theories and individual chapters each covering a different research direction. The authors discuss the use of symbolic manipulation software as well as computer algorithm issues. The emphasis is placed firmly on covering modern, recent developments, rather than the very theoretical approach often found. The book will be an excellent reference for both beginners and specialists in engineering, applied mathematics and physics.

  2. Nonlinear resonances

    CERN Document Server

    Rajasekar, Shanmuganathan

    2016-01-01

    This introductory text presents the basic aspects and most important features of various types of resonances and anti-resonances in dynamical systems. In particular, for each resonance, it covers the theoretical concepts, illustrates them with case studies, and reviews the available information on mechanisms, characterization, numerical simulations, experimental realizations, possible quantum analogues, applications and significant advances made over the years. Resonances are one of the most fundamental phenomena exhibited by nonlinear systems and refer to specific realizations of maximum response of a system due to the ability of that system to store and transfer energy received from an external forcing source. Resonances are of particular importance in physical, engineering and biological systems - they can prove to be advantageous in many applications, while leading to instability and even disasters in others. The book is self-contained, providing the details of mathematical derivations and techniques invo...

  3. Nonlinear optimal control theory

    CERN Document Server

    Berkovitz, Leonard David

    2012-01-01

    Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also dis

  4. Studying Maximum Plantar Stress per Insole Design Using Foot CT-Scan Images of Hyperelastic Soft Tissues

    Directory of Open Access Journals (Sweden)

    Ali Sarikhani

    2016-01-01

    Full Text Available The insole shape and the resulting plantar stress distribution have a pivotal impact on overall health. In this paper, by Finite Element Method, maximum stress value and stress distribution of plantar were studied for different insoles designs, which are the flat surface and the custom-molded (conformal surface. Moreover, insole thickness, heel’s height, and different materials were used to minimize the maximum stress and achieve the most uniform stress distribution. The foot shape and its details used in this paper were imported from online CT-Scan images. Results show that the custom-molded insole reduced maximum stress 40% more than the flat surface insole. Upon increase of thickness in both insole types, stress distribution becomes more uniform and maximum stress value decreases up to 10%; however, increase of thickness becomes ineffective above a threshold of 1 cm. By increasing heel height (degree of insole, maximum stress moves from heel to toes and becomes more uniform. Therefore, this scenario is very helpful for control of stress in 0.2° to 0.4° degrees for custom-molded insole and over 1° for flat insole. By changing the material of the insole, the value of maximum stress remains nearly constant. The custom-molded (conformal insole which has 0.5 to 1 cm thickness and 0.2° to 0.4° degrees is found to be the most compatible form for foot.

  5. [Nonlinear magnetohydrodynamics

    International Nuclear Information System (INIS)

    1994-01-01

    Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday's law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm's law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile

  6. Fiscal 1997 R and D project on industrial science technology under consignment from NEDO. Report on the R and D of nonlinear optoelectronic materials; 1997 nendo sangyo kagaku gijutsu kenkyu kaihatsu jigyo Shin energy Sangyo Gijutsu Sogo Kaihatsu Kiko itaku. Hisenkei hikari denshi zairyo no kenkyu kaihatsu seika hokokusho

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1998-03-01

    As to the development of organic base materials, the paper is going ahead with an evaluation, higher performance and further use as materials of basic optical properties of quirale nonlinear materials and organic conjugate base materials which are promising among organic low molecular materials. As the development of orientation control crystal growth technology, grooves for orientation control were formed on the surface of the lead glass substrate, from which thin film single crystals were obtained. The nonlinear response was studied of the glass where semiconducting fine particles dispersed in matrix glass. Glass scattering base prototype materials were selected by the sol-gel method and ultra-low melting-point glass method. The glass dispersion base materials by the very fast cooling method was also studied. For the purpose of realizing a high speed switching characteristic, a processing technology was developed of ultra fine particle dispersing polymer light waveguide. As to the technology for super lattice, the optimum nonlinear performance materials were selected mainly with the optimum complex super lattice base. Moreover, the three-dimensional super structuring technology was constructed to improve nonlinear optical characteristics. The comprehensive investigational study was conducted for effective promotion of the research development. 177 refs., 260 figs., 27 tabs.

  7. Theory and design of nonlinear metamaterials

    Science.gov (United States)

    Rose, Alec Daniel

    If electronics are ever to be completely replaced by optics, a significant possibility in the wake of the fiber revolution, it is likely that nonlinear materials will play a central and enabling role. Indeed, nonlinear optics is the study of the mechanisms through which light can change the nature and properties of matter and, as a corollary, how one beam or color of light can manipulate another or even itself within such a material. However, of the many barriers preventing such a lofty goal, the narrow and limited range of properties supported by nonlinear materials, and natural materials in general, stands at the forefront. Many industries have turned instead to artificial and composite materials, with homogenizable metamaterials representing a recent extension of such composites into the electromagnetic domain. In particular, the inclusion of nonlinear elements has caused metamaterials research to spill over into the field of nonlinear optics. Through careful design of their constituent elements, nonlinear metamaterials are capable of supporting an unprecedented range of interactions, promising nonlinear devices of novel design and scale. In this context, I cast the basic properties of nonlinear metamaterials in the conventional formalism of nonlinear optics. Using alternately transfer matrices and coupled mode theory, I develop two complementary methods for characterizing and designing metamaterials with arbitrary nonlinear properties. Subsequently, I apply these methods in numerical studies of several canonical metamaterials, demonstrating enhanced electric and magnetic nonlinearities, as well as predicting the existence of nonlinear magnetoelectric and off-diagonal nonlinear tensors. I then introduce simultaneous design of the linear and nonlinear properties in the context of phase matching, outlining five different metamaterial phase matching methods, with special emphasis on the phase matching of counter propagating waves in mirrorless parametric amplifiers

  8. Influence of quantum confinement on the carrier contribution to the elastic constants in quantum confined heavily doped non-linear optical and optoelectronic materials: simplified theory and the suggestion for experimental determination

    International Nuclear Information System (INIS)

    Baruah, D; Choudhury, S; Singh, K M; Ghatak, K P

    2007-01-01

    In this paper we study the carrier contribution to elastic constants in quantum confined heavily doped non-linear optical compounds on the basis of a newly formulated electron dispersion law taking into account the anisotropies of the effective electron masses and spin orbit splitting constants together with the proper inclusion of the crystal field splitting in the Hamiltonian within the framework of k.p formalism. All the results of heavily doped three, and two models of Kane for heavily doped III-V materials form special cases of our generalized analysis. It has been found, taking different heavily doped quantum confined materials that, the carrier contribution to the elastic constants increases with increase in electron statistics and decrease in film thickness in ladder like manners for all types of quantum confinements with different numerical values which are totally dependent on the energy band constants. The said contribution is greatest in quantum dots and least in quantum wells together with the fact the heavy doping enhances the said contributions for all types of quantum confined materials. We have suggested an experimental method of determining the carrier contribution to the elastic constants in nanostructured materials having arbitrary band structures

  9. Nonlinear optical crystals a complete survey

    CERN Document Server

    Nikogosyan, David N

    2005-01-01

    Nonlinear optical crystals are widely used in modern optical science and technology for frequency conversion of laser light, i.e. to generate laser radiation at any specific wavelength in visible, UV or IR spectral regions. This unrivalled reference book contains the most complete and up-to-date information on properties of nonlinear optical crystals. It includes: * Database of 63 common and novel nonlinear optical crystals * Periodically-poled and self-frequency-doubling materials * Full description of linear and nonlinear optical properties * Significant amount of crystallophysical, thermophysical, spectroscopic, electro-optic and magneto-optic information * 7 mini-reviews on novel applications, such as deep-UV light generation, terahertz-wave generation, ultrashort laser pulse compression, photonic band-gap crystals, x3 nonlinearity, etc. * More than 1500 different references with full titles It is a vital source of information for scientists and engineers dealing with modern applications of nonlinear opti...

  10. Introduction to nonlinear finite element analysis

    CERN Document Server

    Kim, Nam-Ho

    2015-01-01

    This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: ·         Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems ·         Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory ·    ...

  11. 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

  12. Applications of Nonlinear Electrochemical Impedance Spectroscopy (NLEIS)

    KAUST Repository

    Adler, S. B.

    2013-01-01

    This paper reviews the use of nonlinear electrochemical impedance spectroscopy (NLEIS) in the analysis of SOFC electrode reactions. By combining EIS and NLEIS, as well as other independent information about an electrode material, it becomes possible

  13. Nonlinear and Nonequilibrium Dynamics in Geomaterials

    OpenAIRE

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

    2004-01-01

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

  14. FY 1993 Report on the industrial science and technology research and development project results. Research and development of non-linear photoelectronic materials; 1993 nendo hisenkei hikari denshi zairyo no kenkyu kaihatsu seika hokokusho

    Energy Technology Data Exchange (ETDEWEB)

    NONE

    1994-11-01

    Described herein are the results of the industrial science and technology research and development project for nonlinear optoelectronic materials. The more functional chiral and pi-conjugated compounds are investigated as the organic, low-molecular-weight materials. The technologies for the orientation-controlled crystal growth are continuously investigated. Polyacetylene is investigated as the conjugated pi-electron system. The glass-dispersed systems, prepared by the sol-gel, superlow-melting glass and super-cooling methods, are investigated. In order to elucidate the relationship between the organic superlattice and properties (e.g., photoelectronic properties), the intramolecular interactions under the superlattice conditions are estimated by the theoretical chemical calculations, and the optimum structures deduced from the measured properties are proposed. The thin, composite films of fine metallic particles and glass are prepared by the multi-dimensional sputtering, to explore the constituent materials suitable for the three-dimensional superstructures, and their properties are analyzed. The thin semiconductor films of superlattices are prepared by the molecular beam epitaxy method, to investigate the optimization of the structures and compositions. The basic aspects of the three-dimensional superstructures, prepared by the superfine machining, are investigated. The results of the comprehensive investigations and researches are also described. (NEDO)

  15. Electronic structure and optical properties of LiGa0.5In0.5Se2 single crystal, a nonlinear optical mid-IR material

    Science.gov (United States)

    Lavrentyev, A. A.; Gabrelian, B. V.; Vu, Tuan V.; Isaenko, L. I.; Yelisseyev, A. P.; Khyzhun, O. Y.

    2018-06-01

    Measurements of X-ray photoelectron core-level and valence-band spectra for pristine and irradiated with Ar+ ions surfaces of LiGa0.5In0.5Se2 single crystal, novel nonlinear optical mid-IR selenide grown by a modified vertical Bridgman-Stockbarger technique, are reported. Electronic structure of LiGa0.5In0.5Se2 is elucidated from theoretical and experimental points of view. Notably, total and partial densities of states (DOSs) of the LiGa0.5In0.5Se2 compound are calculated based on density functional theory (DFT) using the augmented plane wave + local orbitals (APW + lo) method. In accordance with the DFT calculations, the principal contributors to the valence band are the Se 4p states, making the main input at the top and in the upper part of the band, while its bottom is dominated by contributions of the valence s states associated with Ga and In atoms. The theoretical total DOS curve peculiarities are found to be in excellent agreement with the shape of the X-ray photoelectron valence-band spectrum of the LiGa0.5In0.5Se2 single crystal. The bottom of the conduction band of LiGa0.5In0.5Se2 is formed mainly by contributions of the unoccupied Ga 4s and In 5s states in almost equal proportion, with somewhat smaller contributions of the unoccupied Se 4p states as well. Our calculations indicate that the LiGa0.5In0.5Se2 compound is a direct gap semiconductor. The principal optical constants of LiGa0.5In0.5Se2 are calculated in the present work.

  16. Growth, spectral and optical characterization of a novel nonlinear optical organic material: D-Alanine DL-Mandelic acid single crystal

    Science.gov (United States)

    Jayaprakash, P.; Mohamed, M. Peer; Caroline, M. Lydia

    2017-04-01

    An organic nonlinear optical single crystal, D-alanine DL-mandelic acid was synthesized and successfully grown by slow evaporation solution growth technique at ambient temperature using solvent of aqueous solution. The unit cell parameters were assessed from single crystal X-ray diffraction analysis. The presence of diverse functional groups and vibrational modes were identified using Fourier Transform Infra Red and Fourier Transform Raman spectral analyses. The chemical structure of grown crystal has been identified by Nuclear Magnetic Resonance spectroscopic study. Ultraviolet-visible spectral analysis reveal that the crystal has lower cut-off wavelength down to 259 nm, is a key factor to exhibit second harmonic generation signal. The electronic optical band gap and Urbach energy is calculated as 5.31 eV and 0.2425 eV respectively from the UV absorption profile. The diverse optical properties such as, extinction coefficient, reflectance, linear refractive index, optical conductivity was calculated using UV-visible data. The relative second harmonic efficiency of the compound is found to be 0.81 times greater than that of KH2PO4 (KDP). The thermal stability of the grown crystal was studied by thermogravimetric analysis and differential thermal analysis techniques. The luminescence spectrum exhibited two peaks (520 nm, 564 nm) due to the donation of protons from carboxylic acid to amino group. The Vickers microhardness test was carried out employing one of the as-grown hard crystal and there by hardness number (Hv), Meyer's index (n), yield strength (σy), elastic stiffness constant (C11) and Knoop hardness number (HK) were assessed. The dielectric behaviour of the as-grown crystal was analyzed for different temperatures (313 K, 333 K, 353 K, and 373 K) at different frequencies.

  17. Bulk monocrystal growth, optical, dielectric, third order nonlinear, thermal and mechanical studies on HCl added L-alanine: An organic NLO material

    Energy Technology Data Exchange (ETDEWEB)

    Shkir, Mohd, E-mail: shkirphysics@gmail.com [Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Physics Department, Faculty of Science, King Khalid University, Abha (Saudi Arabia); Yahia, I.S., E-mail: dr_isyahia@yahoo.com [Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Physics Department, Faculty of Science, King Khalid University, Abha (Saudi Arabia); Nano-Science & Semiconductor Labs, Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo (Egypt); Al-Qahtani, A.M.A. [Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Physics Department, Faculty of Science, King Khalid University, Abha (Saudi Arabia)

    2016-12-01

    In the current work, good quality bulk size (∼32 mm × 23 mm × 10 mm) single crystals of HCl added L-alanine with well-defined morphology are successfully grown using slow evaporation technique. Crystal structure and other structural parameters were evaluated from X-ray diffraction data. Vibrational assessment of the grown crystal was done by FT-Raman analysis. The presence of chlorine and good quality of the grown crystal was confirmed by SEM/EDX analysis. Solid state UV–Vis–NIR diffused reflectance was measured and direct and indirect optical band gap was calculated using Kubelka-Munk relation and found to be 5.64 and 5 eV respectively. Dielectric measurement was carried out in high frequency range. Third order nonlinear optical susceptibility value was found to be enhanced from 1.91 × 10{sup −6} (pure) to 8.6 × 10{sup −6} esu (LAHCl). Good thermal stability of grown crystals was confirmed from DSC analysis. The enhancement in mechanical strength and crystalline perfection was also observed. - Highlights: • Bulk size (32 mm × 23 mm × 10 mm), good crystalline perfection HCl added L-alanine monocrystal is grown. • The shift in X-ray diffraction and vibrational peaks confirms the interaction of HCl. • The high optical transparency and band gap confirms its application in optoelectronic devices. • Third order NLO properties are found to be enhanced in HCl added L-alanine crystals. • The mechanical strength of the grown crystals is found to be enhanced due HCl addition.

  18. Nonlinear optical studies of curcumin metal derivatives with cw laser

    Energy Technology Data Exchange (ETDEWEB)

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

    2015-03-30

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

  19. Nonlinear optical studies of curcumin metal derivatives with cw laser

    International Nuclear Information System (INIS)

    Henari, F. Z.; Cassidy, S.

    2015-01-01

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

  20. Correlation between ultrasonic nonlinearity and elastic nonlinearity in heat-treated aluminum alloy

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Jong Beom; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)

    2017-04-15

    The nonlinear ultrasonic technique is a potential nondestructive method to evaluate material degradation, in which the ultrasonic nonlinearity parameter is usually measured. The ultrasonic nonlinearity parameter is defined by the elastic nonlinearity coefficients of the nonlinear Hooke’s equation. Therefore, even though the ultrasonic nonlinearity parameter is not equal to the elastic nonlinearity parameter, they have a close relationship. However, there has been no experimental verification of the relationship between the ultrasonic and elastic nonlinearity parameters. In this study, the relationship is experimentally verified for a heat-treated aluminum alloy. Specimens of the aluminum alloy were heat-treated at 300°C for different periods of time (0, 1, 2, 5, 10, 20, and 50 h). The relative ultrasonic nonlinearity parameter of each specimen was then measured, and the elastic nonlinearity parameter was determined by fitting the stress-strain curve obtained from a tensile test to the 5th-order-polynomial nonlinear Hooke’s equation. The results showed that the variations in these parameters were in good agreement with each other.

  1. Introduction to nonlinear dispersive equations

    CERN Document Server

    Linares, Felipe

    2015-01-01

    This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

  2. Model of anisotropic nonlinearity in self-defocusing photorefractive media.

    Science.gov (United States)

    Barsi, C; Fleischer, J W

    2015-09-21

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

  3. Effect of platform connection and abutment material on stress distribution in single anterior implant-supported restorations: a nonlinear 3-dimensional finite element analysis.

    Science.gov (United States)

    Carvalho, Marco Aurélio; Sotto-Maior, Bruno Salles; Del Bel Cury, Altair Antoninha; Pessanha Henriques, Guilherme Elias

    2014-11-01

    Although various abutment connections and materials have recently been introduced, insufficient data exist regarding the effect of stress distribution on their mechanical performance. The purpose of this study was to investigate the effect of different abutment materials and platform connections on stress distribution in single anterior implant-supported restorations with the finite element method. Nine experimental groups were modeled from the combination of 3 platform connections (external hexagon, internal hexagon, and Morse tapered) and 3 abutment materials (titanium, zirconia, and hybrid) as follows: external hexagon-titanium, external hexagon-zirconia, external hexagon-hybrid, internal hexagon-titanium, internal hexagon-zirconia, internal hexagon-hybrid, Morse tapered-titanium, Morse tapered-zirconia, and Morse tapered-hybrid. Finite element models consisted of a 4×13-mm implant, anatomic abutment, and lithium disilicate central incisor crown cemented over the abutment. The 49 N occlusal loading was applied in 6 steps to simulate the incisal guidance. Equivalent von Mises stress (σvM) was used for both the qualitative and quantitative evaluation of the implant and abutment in all the groups and the maximum (σmax) and minimum (σmin) principal stresses for the numerical comparison of the zirconia parts. The highest abutment σvM occurred in the Morse-tapered groups and the lowest in the external hexagon-hybrid, internal hexagon-titanium, and internal hexagon-hybrid groups. The σmax and σmin values were lower in the hybrid groups than in the zirconia groups. The stress distribution concentrated in the abutment-implant interface in all the groups, regardless of the platform connection or abutment material. The platform connection influenced the stress on abutments more than the abutment material. The stress values for implants were similar among different platform connections, but greater stress concentrations were observed in internal connections

  4. Growth, spectral, optical, laser damage threshold and DFT investigations on 2-amino 4-methyl pyridinium 4-methoxy benzoate (2A4MP4MB): A potential organic third order nonlinear optical material for optoelectronic applications

    Science.gov (United States)

    Krishnakumar, M.; Karthick, S.; Thirupugalmani, K.; Babu, B.; Vinitha, G.

    2018-05-01

    In present investigation, single crystals of organic charge transfer complex, 2-amino-4-methyl pyridinium-4-methoxy benzoate (2A4MP4MB) was grown by controlled slow evaporation solution growth technique using methanol as a solvent at room temperature. Single crystal XRD analysis confirmed the crystal system and lattice parameters of 2A4MP4MB. The crystalline nature, presence of various vibrational modes and other chemical bonds in the compound have been recognized and confirmed by powder X-ray diffraction, FT-IR and FT-Raman spectroscopic techniques respectively. The presence of various proton and carbon positions in title compound was confirmed using 1H NMR and 13C NMR spectral studies. The wide optical operating window and cut-off wavelength were identified and band gap value of the title compound was calculated using UV-vis-NIR study. The specific heat capacity (cp) values of the title compound, 1.712 J g-1·K-1 at 300 K and 13.6 J g-1 K-1 at 433 K (melting point) were measured using Modulated Differential Scanning Calorimetric studies (MDSC). From Z-scan study, nonlinear refractive index (n2), nonlinear absorption (β) and third order nonlinear susceptibility (χ(3)) values were determined. The self-defocusing effect and saturable absorption behavior of the material were utilized to exhibit the optical limiting action at λ = 532 nm by employing the same continuous wave (cw) Nd: YAG laser source. The laser damage threshold (LDT) study of title compound was carried out using Nd: YAG laser of 532 nm wavelength. The Vickers' micro hardness test was carried out at room temperature and obtained results were investigated using classical Meyer's law. In addition, DFT calculations were carried out for the first time for this compound. These characterization studies performed on the title compound planned to probe the valuable and safe region of optical, thermal and mechanical properties to improve efficacy of 2A4MP4MB single crystals in optoelectronic device

  5. Nonlinear Water Waves

    CERN Document Server

    2016-01-01

    This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...

  6. NH4 Be2 BO3 F2 and γ-Be2 BO3 F: Overcoming the Layering Habit in KBe2 BO3 F2 for the Next-Generation Deep-Ultraviolet Nonlinear Optical Materials.

    Science.gov (United States)

    Peng, Guang; Ye, Ning; Lin, Zheshuai; Kang, Lei; Pan, Shilie; Zhang, Min; Lin, Chensheng; Long, Xifa; Luo, Min; Chen, Yu; Tang, Yu-Huan; Xu, Feng; Yan, Tao

    2018-05-12

    KBe 2 BO 3 F 2 (KBBF) is still the only practically usable crystal that can generate deep-ultraviolet (DUV) coherent light by direct second harmonic generation (SHG). However, applications are hindered by layering, leading to difficulty in the growth of thick crystals and compromised mechanical integrity. Despite efforts, it is still a great challenge to discover new nonlinear optical (NLO) materials that overcome the layering while keeping the DUV SHG available. Now, two new DUV NLO beryllium borates have been successfully designed and synthesized, NH 4 Be 2 BO 3 F 2 (ABBF) and γ-Be 2 BO 3 F (γ-BBF), which not only overcome the layering but also can be used as next-generation DUV NLO materials with the shortest type I phase-matching second-harmonic wavelength down to 173.9 nm and 146 nm, respectively. Significantly, γ-BBF is superior to KBBF in all metrics and would be the most outstanding DUV NLO crystal. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

  7. A finite element model of myocardial infarction using a composite material approach.

    Science.gov (United States)

    Haddad, Seyyed M H; Samani, Abbas

    2018-01-01

    Computational models are effective tools to study cardiac mechanics under normal and pathological conditions. They can be used to gain insight into the physiology of the heart under these conditions while they are adaptable to computer assisted patient-specific clinical diagnosis and therapeutic procedures. Realistic cardiac mechanics models incorporate tissue active/passive response in conjunction with hyperelasticity and anisotropy. Conventional formulation of such models leads to mathematically-complex problems usually solved by custom-developed non-linear finite element (FE) codes. With a few exceptions, such codes are not available to the research community. This article describes a computational cardiac mechanics model developed such that it can be implemented using off-the-shelf FE solvers while tissue pathologies can be introduced in the model in a straight-forward manner. The model takes into account myocardial hyperelasticity, anisotropy, and active contraction forces. It follows a composite tissue modeling approach where the cardiac tissue is decomposed into two major parts: background and myofibers. The latter is modelled as rebars under initial stresses mimicking the contraction forces. The model was applied in silico to study the mechanics of infarcted left ventricle (LV) of a canine. End-systolic strain components, ejection fraction, and stress distribution attained using this LV model were compared quantitatively and qualitatively to corresponding data obtained from measurements as well as to other corresponding LV mechanics models. This comparison showed very good agreement.

  8. On Poisson Nonlinear Transformations

    Directory of Open Access Journals (Sweden)

    Nasir Ganikhodjaev

    2014-01-01

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

  9. Simulation of nonlinear transient elastography: finite element model for the propagation of shear waves in homogeneous soft tissues.

    Science.gov (United States)

    Ye, W; Bel-Brunon, A; Catheline, S; Combescure, A; Rochette, M

    2018-01-01

    In this study, visco-hyperelastic Landau's model, which is widely used in acoustical physic field, is introduced into a finite element formulation. It is designed to model the nonlinear behaviour of finite amplitude shear waves in soft solids, typically, in biological tissues. This law is used in finite element models based on elastography, experiments reported in Jacob et al, the simulations results show a good agreement with the experimental study: It is observed in both that a plane shear wave generates only odd harmonics and a nonplane wave generates both odd and even harmonics in the spectral domain. In the second part, a parametric study is performed to analyse the influence of different factors on the generation of odd harmonics of plane wave. A quantitative relation is fitted between the odd harmonic amplitudes and the non-linear elastic parameter of Landau's model, which provides a practical guideline to identify the non-linearity of homogeneous tissues using elastography experiment. Copyright © 2017 John Wiley & Sons, Ltd.

  10. 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.

  11. 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

  12. Advances in nonlinear optics

    CERN Document Server

    Chen, Xianfeng; Zeng, Heping; Guo, Qi; She, Weilong

    2015-01-01

    This book presents an overview of the state of the art of nonlinear optics from weak light nonlinear optics, ultrafast nonlinear optics to electro-optical theory and applications. Topics range from the fundamental studies of the interaction between matter and radiation to the development of devices, components, and systems of tremendous commercial interest for widespread applications in optical telecommunications, medicine, and biotechnology.

  13. Design of a nonlinear torsional vibration absorber

    Science.gov (United States)

    Tahir, Ammaar Bin

    larger than that in the latter. A nonlinear absorber design has been proposed comprising of thin beams as elastic elements. The geometric configuration of the proposed design has been shown to provide cubic stiffness nonlinearity in torsion. The values of design variables, namely the strength of nonlinearity alpha and torsional stiffness kalpha, were obtained by optimizing dimensions and material properties of the beams for a maximum vibration energy dissipation in the nonlinear absorber. A parametric study has also been conducted to analyze the effect of the magnitude of excitation provided to the system on the performance of a nonlinear absorber. It has been shown that the nonlinear absorber turns out to be more effective in terms of energy dissipation as compared to a linear absorber with an increase in the excitation level applied to the system.

  14. Numerical study of surface plasmon enhanced nonlinear absorption and refraction.

    Science.gov (United States)

    Kohlgraf-Owens, Dana C; Kik, Pieter G

    2008-07-07

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

  15. 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.

  16. Evaluation of polymer based third order nonlinear integrated optics devices

    NARCIS (Netherlands)

    Driessen, A.; Hoekstra, Hugo; Blom, F.C.; Horst, F.; Horst, F.; Krijnen, Gijsbertus J.M.; van Schoot, J.B.P.; van Schoot, J.B.P.; Lambeck, Paul; Popma, T.J.A.; Diemeer, Mart

    Nonlinear polymers are promising materials for high speed active integrated optics devices. In this paper we evaluate the perspectives polymer based nonlinear optical devices can offer. Special attention is directed to the materials aspects. In our experimental work we applied mainly Akzo Nobel DANS

  17. Distributed nonlinear optical response

    DEFF Research Database (Denmark)

    Nikolov, Nikola Ivanov

    2005-01-01

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

  18. Enhanced Nonlinear Effects in Metamaterials and Plasmonics

    Directory of Open Access Journals (Sweden)

    C. Argyropoulos

    2012-07-01

    Full Text Available In this paper we provide an overview of the anomalous and enhanced nonlinear effects available when optical nonlinear materials are combined inside plasmonic waveguide structures. Broad, bistable and all-optical switching responses are exhibited at the cut-off frequency of these waveguides, characterized by reduced Q-factor resonances. These phenomena are due to the large field enhancement obtained inside specific plasmonic gratings, which ensures a significant boosting of the nonlinear operation. Several exciting applications are proposed, which may potentially lead to new optical components and add to the optical nanocircuit paradigm.

  19. Teaching nonlinear dynamics through elastic cords

    International Nuclear Information System (INIS)

    Chacon, R; Galan, C A; Sanchez-Bajo, F

    2011-01-01

    We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.

  20. 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

  1. Dynamic nonlinear analysis of shells of revolution

    International Nuclear Information System (INIS)

    Riesemann, W.A. von; Stricklin, J.A.; Haisler, W.E.

    1975-01-01

    Over the past few years a series of finite element computer programs have been developed at Texas A and M University for the static and dynamic nonlinear analysis of shells of revolution. This paper discusses one of these, DYNAPLAS, which is a program for the transient response of ring stiffened shells of revolution subjected to either asymmetric initial velocities or to asymmetric pressure loadings. Both material and geometric nonlinearities may be considered. (Auth.)

  2. On conservation laws in geometrically nonlinear elasto-dynamic field of non-homogenous materials%论非均匀材料几何非线性弹性动力学场的守恒律

    Institute of Scientific and Technical Information of China (English)

    施伟辰; 高庆海; 李欢欢

    2006-01-01

    对基于Lagrange框架描述的非均匀弹性材料的Lagrange泛函应用Noether原理,开展材料的几何非线性弹性动力学场守恒律的研究,并给出其物质空间守恒律与物质平衡定律之间关系的清晰图景.研究发现,质量密度和弹性系数需满足一组一阶线性偏微分方程,该组方程不但包含来自Newton力学时-空观的全部时-空对称变换,而且控制着材料物质空间守恒律的存在性和存在的形式.特别需指出的是,惯性坐标系的平移和旋转是Lagrange泛函的对称变换,这些对称变换可导致均匀材料的物质空间守恒律和非均匀材料的物质平衡定律,但是时-空坐标的标度改变并不是对称变换.然而,若质量密度和弹性系数满足由上述方程简化而来的一组特殊的一阶线性偏微分方程,则时-空坐标的标度改变可成为Lagrange泛函的对称变换并导致相关守恒律的存在,但此时与该守恒律关联的物质平衡定律仍然不存在.为构造适合力学分析的功能梯度材料的物质空间守恒律,进行了质量密度和弹性系数需满足的方程的应用研究.对于粘合于基底的功能梯度材料层,给出全部非平凡的物质空间守恒律.%By applying Noether's theorem to the Lagrangian density of non-homogenous elastic materials in the so-called Lagrangian framework, conservation laws in geometrically nonlinear elasto-dynamic field have been studied, and a clear picture of relations between the conservation laws in material space and the material balance laws is given. It is found that the mass density and Lamé's moduli have to satisfy a set of first-order linear partial differential equations, which contain all the symmetry-transformations of space-time based on Newtonian viewpoint of mechanics. The existence and existent forms of conservation laws in material space are governed by these equations. Especially, translation and rotation of coordinates are symmetry

  3. Computational assessment of promising mid-infrared nonlinear optical materials Mg–IV–V2 (IV = Si, Ge, Sn; V = P, As): a first-principles study

    Science.gov (United States)

    Xiao, Jianping; Zhu, Shifu; Zhao, Beijun; Chen, Baojun; Liu, Hui; He, Zhiyu

    2018-03-01

    The mid-infrared (mid-IR) nonlinear optical (NLO) capabilities of Mg–IV–V2 (IV = Si, Ge, Sn; V = P, As) are systematically assessed by the first-principles calculation. The results show that the compounds in this group except MgSiP2 and MgSnP2 have moderate birefringence values to fulfill the phase-matching conditions. In particular, MgGeP2 and MgSiAs2 possess relatively large band gaps and almost three to four times larger static SHG coefficients than the benchmark material AgGaSe2, exhibiting good potential for mid-IR NLO application. According to the detailed analysis of the electronic structures, it is found that the dominant SHG contributions are from the orbitals of the asymmetry anionic unit [IV–V2]2‑. Moreover, the further evaluation reveals that MgSiAs2, MgGeAs2, MgSnP2 and MgSnAs2 are not thermodynamically stable and the new synthesis strategy (i.e. synthesis under non-equilibrium conditions) should be considered.

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

    Science.gov (United States)

    Bache, Morten; Lavrinenko, Andrei V.

    2017-09-01

    Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still under investigation. We consider the propagation of pulses in ultrathin gold strip waveguides, modeled by the nonlinear Schrödinger equation. The nonlinear response of gold is accounted for by the two-temperature model, revealing it as a delayed nonlinearity intrinsic in gold. The consequence is that the measured nonlinearities are strongly dependent on pulse duration. This issue has so far only been addressed phenomenologically, but we provide an accurate estimate of the quantitative connection as well as a phenomenological theory to understand the enhanced nonlinear response as the gold thickness is reduced. In comparison with previous works, the analytical model for the power-loss equation has been improved, and can be applied now to cases with a high laser peak power. We show new fits to experimental data from the literature and provide updated values for the real and imaginary parts of the nonlinear susceptibility of gold for various pulse durations and gold layer thicknesses. Our simulations show that the nonlinear loss is inhibiting efficient nonlinear interaction with low-power laser pulses. We therefore propose to design waveguides suitable for the mid-IR, where the ponderomotive instantaneous nonlinearity can dominate over the delayed hot-electron nonlinearity and provide a suitable plasmonics platform for efficient ultrafast nonlinear optics.

  5. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  6. Nonlinear graphene plasmonics

    Science.gov (United States)

    Ooi, Kelvin J. A.; Tan, Dawn T. H.

    2017-10-01

    The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.

  7. Rapid assessment of nonlinear optical propagation effects in dielectrics

    Science.gov (United States)

    Hoyo, J. Del; de La Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

    2015-01-01

    Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

  8. Stationary nonlinear Airy beams

    International Nuclear Information System (INIS)

    Lotti, A.; Faccio, D.; Couairon, A.; Papazoglou, D. G.; Panagiotopoulos, P.; Tzortzakis, S.; Abdollahpour, D.

    2011-01-01

    We demonstrate the existence of an additional class of stationary accelerating Airy wave forms that exist in the presence of third-order (Kerr) nonlinearity and nonlinear losses. Numerical simulations and experiments, in agreement with the analytical model, highlight how these stationary solutions sustain the nonlinear evolution of Airy beams. The generic nature of the Airy solution allows extension of these results to other settings, and a variety of applications are suggested.

  9. Generalized Nonlinear Yule Models

    OpenAIRE

    Lansky, Petr; Polito, Federico; Sacerdote, Laura

    2016-01-01

    With the aim of considering models with persistent memory we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macrovolution. 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...

  10. Nonlinear theory of electroelastic and magnetoelastic interactions

    CERN Document Server

    Dorfmann, Luis

    2014-01-01

    This book provides a unified theory of nonlinear electro-magnetomechanical interactions of soft materials capable of large elastic deformations. The authors include an overview of the basic principles of the classical theory of electromagnetism from the fundamental notions of point charges and magnetic dipoles through to distributions of charge and current in a non-deformable continuum, time-dependent electromagnetic fields and Maxwell’s equations. They summarize the basic ingredients of continuum mechanics that are required to account for the deformability of material and present nonlinear constitutive frameworks for electroelastic and magnetoelastic interactions in a highly deformable material. The equations contained in the book are used to formulate and solve a variety of representative boundary-value problems for both nonlinear electroelasticity and magnetoelasticity.

  11. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  12. Nonlinear Physics of Plasmas

    CERN Document Server

    Kono, Mitsuo

    2010-01-01

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

  13. Nonlinear optics at interfaces

    International Nuclear Information System (INIS)

    Chen, C.K.

    1980-12-01

    Two aspects of surface nonlinear optics are explored in this thesis. The first part is a theoretical and experimental study of nonlinear intraction of surface plasmons and bulk photons at metal-dielectric interfaces. The second part is a demonstration and study of surface enhanced second harmonic generation at rough metal surfaces. A general formulation for nonlinear interaction of surface plasmons at metal-dielectric interfaces is presented and applied to both second and third order nonlinear processes. Experimental results for coherent second and third harmonic generation by surface plasmons and surface coherent antiStokes Raman spectroscopy (CARS) are shown to be in good agreement with the theory

  14. 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

  15. Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers

    International Nuclear Information System (INIS)

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

    2005-01-01

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

  16. Nonlinear Analysis of Cavities in Rock Salt

    DEFF Research Database (Denmark)

    Ottosen, N. S.; Krenk, Steen

    1979-01-01

    The paper covers some material and computational aspects of the rock mechanics of leached cavities in salt. A material model is presented in which the instantaneous stiffness of the salt is obtained by interpolation between the unloaded state and a relevant failure state. The model enables predic...... prediction of short term triaxial behaviour from uniaxial stress-strain curves. Key results from a nonlinear finite element calculation of a gas-filled cavity are given, and the general features are related to a simple nonlinear method of stress evaluation....

  17. 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...

  18. Nonlinear viscoelasticity of pre-compressed layered polymeric composite under oscillatory compression

    KAUST Repository

    Xu, Yangguang; Tao, Ran; Lubineau, Gilles

    2018-01-01

    remains elusive because the dynamic moduli (storage modulus and loss modulus) are not very convenient when the material falls into nonlinear viscoelastic range. In this study, we utilize two methods, Fourier transform and geometrical nonlinear analysis

  19. Nonlinear dynamics in Nuclotron

    International Nuclear Information System (INIS)

    Dinev, D.

    1997-01-01

    The paper represents an extensive study of the nonlinear beam dynamics in the Nuclotron. Chromatic effects, including the dependence of the betatron tunes on the amplitude, and chromatic perturbations have been investigated taking into account the measured field imperfections. Beam distortion, smear, dynamic aperture and nonlinear acceptance have been calculated for different particle energies and betatron tunes

  20. An anisotropic elastoplastic constitutive formulation generalised for orthotropic materials

    Science.gov (United States)

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

    2018-03-01

    This paper presents a finite strain constitutive model to predict a complex elastoplastic deformation behaviour that involves very high pressures and shockwaves in orthotropic materials using an anisotropic Hill's yield criterion by means of the evolving structural tensors. The yield surface of this hyperelastic-plastic constitutive model is aligned uniquely within the principal stress space due to the combination of Mandel stress tensor and a new generalised orthotropic pressure. The formulation is developed in the isoclinic configuration and allows for a unique treatment for elastic and plastic orthotropy. An isotropic hardening is adopted to define the evolution of plastic orthotropy. The important feature of the proposed hyperelastic-plastic constitutive model is the introduction of anisotropic effect in the Mie-Gruneisen equation of state (EOS). The formulation is further combined with Grady spall failure model to predict spall failure in the materials. The proposed constitutive model is implemented as a new material model in the Lawrence Livermore National Laboratory (LLNL)-DYNA3D code of UTHM's version, named Material Type 92 (Mat92). The combination of the proposed stress tensor decomposition and the Mie-Gruneisen EOS requires some modifications in the code to reflect the formulation of the generalised orthotropic pressure. The validation approach is also presented in this paper for guidance purpose. The \\varvec{ψ} tensor used to define the alignment of the adopted yield surface is first validated. This is continued with an internal validation related to elastic isotropic, elastic orthotropic and elastic-plastic orthotropic of the proposed formulation before a comparison against range of plate impact test data at 234, 450 and {895 ms}^{-1} impact velocities is performed. A good agreement is obtained in each test.

  1. Nonlinear optical systems

    CERN Document Server

    Lugiato, Luigi; Brambilla, Massimo

    2015-01-01

    Guiding graduate students and researchers through the complex world of laser physics and nonlinear optics, this book provides an in-depth exploration of the dynamics of lasers and other relevant optical systems, under the umbrella of a unitary spatio-temporal vision. Adopting a balanced approach, the book covers traditional as well as special topics in laser physics, quantum electronics and nonlinear optics, treating them from the viewpoint of nonlinear dynamical systems. These include laser emission, frequency generation, solitons, optically bistable systems, pulsations and chaos and optical pattern formation. It also provides a coherent and up-to-date treatment of the hierarchy of nonlinear optical models and of the rich variety of phenomena they describe, helping readers to understand the limits of validity of each model and the connections among the phenomena. It is ideal for graduate students and researchers in nonlinear optics, quantum electronics, laser physics and photonics.

  2. Homogenized description and retrieval method of nonlinear metasurfaces

    Science.gov (United States)

    Liu, Xiaojun; Larouche, Stéphane; Smith, David R.

    2018-03-01

    A patterned, plasmonic metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical device. When the metasurface is patterned uniformly, its linear optical properties can be expressed using effective surface electric and magnetic polarizabilities obtained through a homogenization procedure. The homogenized description of a nonlinear metasurface, however, presents challenges both because of the inherent anisotropy of the medium as well as the much larger set of potential wave interactions available, making it challenging to assign effective nonlinear parameters to the otherwise inhomogeneous layer of metamaterial elements. Here we show that a homogenization procedure can be developed to describe nonlinear metasurfaces, which derive their nonlinear response from the enhanced local fields arising within the structured plasmonic elements. With the proposed homogenization procedure, we are able to assign effective nonlinear surface polarization densities to a nonlinear metasurface, and link these densities to the effective nonlinear surface susceptibilities and averaged macroscopic pumping fields across the metasurface. These effective nonlinear surface polarization densities are further linked to macroscopic nonlinear fields through the generalized sheet transition conditions (GSTCs). By inverting the GSTCs, the effective nonlinear surface susceptibilities of the metasurfaces can be solved for, leading to a generalized retrieval method for nonlinear metasurfaces. The application of the homogenization procedure and the GSTCs are demonstrated by retrieving the nonlinear susceptibilities of a SiO2 nonlinear slab. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry

  3. Nonlinear Optimization with Financial Applications

    CERN Document Server

    Bartholomew-Biggs, Michael

    2005-01-01

    The book introduces the key ideas behind practical nonlinear optimization. Computational finance - an increasingly popular area of mathematics degree programs - is combined here with the study of an important class of numerical techniques. The financial content of the book is designed to be relevant and interesting to specialists. However, this material - which occupies about one-third of the text - is also sufficiently accessible to allow the book to be used on optimization courses of a more general nature. The essentials of most currently popular algorithms are described, and their performan

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

    International Nuclear Information System (INIS)

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

    2003-01-01

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

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2003-03-01

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

  6. Nonlinear wave equations

    CERN Document Server

    Li, Tatsien

    2017-01-01

    This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.

  7. Sinusoidal velaroidal shell – numerical modelling of the nonlinear ...

    African Journals Online (AJOL)

    The nonlinearity, applied to a sinusoidal velaroidal shell with the inner radius r0, the outer variables radii from 10m to 20m and the number of waves n=8, will give rise to the investigation of its nonlinear buckling resistance. The building material is a high-performant concrete. The investigation emphasizes more on the ...

  8. A Photonic Basis for Deriving Nonlinear Optical Response

    Science.gov (United States)

    Andrews, David L.; Bradshaw, David S.

    2009-01-01

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

  9. Pressure tunable cascaded third order nonlinearity and temporal pulse switching

    DEFF Research Database (Denmark)

    Eilenberger, Falk; Bache, Morten; Minardi, Stefano

    2013-01-01

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

  10. Nonlinear dynamics of semiconductors in strong THz electric fields

    DEFF Research Database (Denmark)

    Tarekegne, Abebe Tilahun

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

  11. Research on Fatigue Damage of Compressor Blade Steel KMN-I Using Nonlinear Ultrasonic Testing

    Directory of Open Access Journals (Sweden)

    Pengfei Wang

    2017-01-01

    Full Text Available The fatigue damage of compressor blade steel KMN-I was investigated using nonlinear ultrasonic testing and the relation curve between the material nonlinearity parameter β and the fatigue life was obtained. The results showed that the nonlinearity parameter increased first and then decreased with the increase of the fatigue cycles. The microstructures were observed by scanning electron microscopy (SEM. It was found that some small defects like holes and pits appeared in the material matrix with the increase of the fatigue cycles, and the nonlinearity parameter increased correspondingly. The nonlinearity parameter reached the peak value when the microcracks initiated, and the nonlinearity parameter began to decrease when the microcracks further propagated to macrocracks. Therefore, it is proved that the nonlinearity parameter can be used to characterize the initiation of microcracks at the early stage of fatigue, and a method of evaluating the fatigue life of materials by nonlinear ultrasonic testing is proposed.

  12. Nonlinear finite element modeling of corrugated board

    Science.gov (United States)

    A. C. Gilchrist; J. C. Suhling; T. J. Urbanik

    1999-01-01

    In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...

  13. Materializing Superghosts

    OpenAIRE

    Alexandrov, Victor; Krotov, Dmitry; Losev, Andrei; Lysov, Vyacheslav

    2007-01-01

    We construct the off-shell BV realization of N=1, d=10 SYM with 7 auxillary fields. This becomes possible due to materialized ghost phenomenon. Namely, supersymmetry ghosts are coordinates on a manifold B of 10-dimensional spinors with pure spinors cut out. Auxillary fields are sections of a bundle over B, and supersymmetry transformations are nonlinear in ghosts. By integrating out axillary fields we obtain on-shell supersymmetric BV action with terms quadratic in antifields. Exactly this on...

  14. Progress in nonlinear nano-optics

    CERN Document Server

    Lienau, Christoph; Grunwald, Rüdiger

    2015-01-01

    This book presents the state of the art in nonlinear nanostructures for ultrafast laser applications. Most recent results in two emerging fields are presented: (i) generation of laser-induced nanostructures in materials like metals, metal oxides and semiconductors, and (ii) ultrafast excitation and energy transfer in nanoscale physical, chemical and hybrid systems. Particular emphasis is laid on the up-to-date controversially discussed mechanisms of sub-wavelength ripple formation including models of self-organized material transport and multiphoton excitation channels, nonlinear optics of plasmonic structures (nanotips, nanowires, 3D-metamaterials), and energy localization and transport on ultrafast time scale and spatial nanoscale. High-resolution spectroscopy, simulation and characterization techniques are reported. New applications of ultrashort-pulsed lasers for materials processing and the use of nanostructured materials for characterizing laser fields and laser-matter-interactions are discussed.

  15. Rectangular-cladding silicon slot waveguide with improved nonlinear performance

    Science.gov (United States)

    Huang, Zengzhi; Huang, Qingzhong; Wang, Yi; Xia, Jinsong

    2018-04-01

    Silicon slot waveguides have great potential in hybrid silicon integration to realize nonlinear optical applications. We propose a rectangular-cladding hybrid silicon slot waveguide. Simulation result shows that, with a rectangular-cladding, the slot waveguide can be formed by narrower silicon strips, so the two-photon absorption (TPA) loss in silicon is decreased. When the cladding material is a nonlinear polymer, the calculated TPA figure of merit (FOMTPA) is 4.4, close to the value of bulk nonlinear polymer of 5.0. This value confirms the good nonlinear performance of rectangular-cladding silicon slot waveguides.

  16. 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.

  17. Photostable nonlinear optical polycarbonates

    NARCIS (Netherlands)

    Faccini, M.; Balakrishnan, M.; Diemeer, Mart; Torosantucci, Riccardo; Driessen, A.; Reinhoudt, David; Verboom, Willem

    2008-01-01

    Highly thermal and photostable nonlinear optical polymers were obtained by covalently incorporating the tricyanovinylidenediphenylaminobenzene (TCVDPA) chromophore to a polycarbonate backbone. NLO polycarbonates with different chromophore attachment modes and flexibilities were synthesized. In spite

  18. Nonlinear singular elliptic equations

    International Nuclear Information System (INIS)

    Dong Minh Duc.

    1988-09-01

    We improve the Poincare inequality, the Sobolev imbedding theorem and the Trudinger imbedding theorem and prove a Mountain pass theorem. Applying these results we study a nonlinear singular mixed boundary problem. (author). 22 refs

  19. Nonlinear Optical Terahertz Technology

    Data.gov (United States)

    National Aeronautics and Space Administration — We develop a new approach to generation of THz radiation. Our method relies on mixing two optical frequency beams in a nonlinear crystalline Whispering Gallery Mode...

  20. Nonlinear differential equations

    CERN Document Server

    Struble, Raimond A

    2017-01-01

    Detailed treatment covers existence and uniqueness of a solution of the initial value problem, properties of solutions, properties of linear systems, stability of nonlinear systems, and two-dimensional systems. 1962 edition.

  1. Ultrafast nonlinear optics

    CERN Document Server

    Leburn, Christopher; Reid, Derryck

    2013-01-01

    The field of ultrafast nonlinear optics is broad and multidisciplinary, and encompasses areas concerned with both the generation and measurement of ultrashort pulses of light, as well as those concerned with the applications of such pulses. Ultrashort pulses are extreme events – both in terms of their durations, and also the high peak powers which their short durations can facilitate. These extreme properties make them powerful experiment tools. On one hand, their ultrashort durations facilitate the probing and manipulation of matter on incredibly short timescales. On the other, their ultrashort durations can facilitate high peak powers which can drive highly nonlinear light-matter interaction processes. Ultrafast Nonlinear Optics covers a complete range of topics, both applied and fundamental in nature, within the area of ultrafast nonlinear optics. Chapters 1 to 4 are concerned with the generation and measurement of ultrashort pulses. Chapters 5 to 7 are concerned with fundamental applications of ultrasho...

  2. Nonlinear surface Alfven waves

    International Nuclear Information System (INIS)

    Cramer, N.F.

    1991-01-01

    The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)

  3. Nonlinear Structural Analysis

    Indian Academy of Sciences (India)

    The Structures Panel of the Aeronautics Research and Development Board of India ... A great variety of topics was covered, including themes such as nonlinear finite ... or shell structures, and three are on the composite form of construction, ...

  4. A nonlinear oscillatory problem

    International Nuclear Information System (INIS)

    Zhou Qingqing.

    1991-10-01

    We have studied the nonlinear oscillatory problem of orthotropic cylindrical shell, we have analyzed the character of the oscillatory system. The stable condition of the oscillatory system has been given. (author). 6 refs

  5. Degenerate nonlinear diffusion equations

    CERN Document Server

    Favini, Angelo

    2012-01-01

    The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

  6. Introduction to nonlinear science

    CERN Document Server

    Nicolis, G

    1995-01-01

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

  7. Nonlinear Wave Propagation

    Science.gov (United States)

    2015-05-07

    associated with the lattice background; the nonlinearity is derived from the inclusion of cubic nonlinearity. Often the background potential is periodic...dispersion branch we can find discrete evolution equations for the envelope associated with the lattice NLS equation (1) by looking for solutions of...spatial operator in the above NLS equation can be elliptic, hyperbolic or parabolic . We remark that further reduction is possible by going into a moving

  8. Nonlinear dynamics and astrophysics

    International Nuclear Information System (INIS)

    Vallejo, J. C.; Sanjuan, M. A. F.

    2000-01-01

    Concepts and techniques from Nonlinear Dynamics, also known as Chaos Theory, have been applied successfully to several astrophysical fields such as orbital motion, time series analysis or galactic dynamics, providing answers to old questions but also opening a few new ones. Some of these topics are described in this review article, showing the basis of Nonlinear Dynamics, and how it is applied in Astrophysics. (Author)

  9. Applications of Nonlinear Electrochemical Impedance Spectroscopy (NLEIS)

    KAUST Repository

    Adler, S. B.

    2013-08-31

    This paper reviews the use of nonlinear electrochemical impedance spectroscopy (NLEIS) in the analysis of SOFC electrode reactions. By combining EIS and NLEIS, as well as other independent information about an electrode material, it becomes possible to establish quantitative links between electrochemical kinetics and materials properties, even when systems are unstable with time. After a brief review of the method, this paper summarizes recent results analyzing the effects of Sr segregation in thin-film LSC electrodes. © The Electrochemical Society.

  10. Pescara benchmarks: nonlinear identification

    Science.gov (United States)

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

    2011-07-01

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

  11. Nonlinear Multiantenna Detection Methods

    Directory of Open Access Journals (Sweden)

    Chen Sheng

    2004-01-01

    Full Text Available A nonlinear detection technique designed for multiple-antenna assisted receivers employed in space-division multiple-access systems is investigated. We derive the optimal solution of the nonlinear spatial-processing assisted receiver for binary phase shift keying signalling, which we refer to as the Bayesian detector. It is shown that this optimal Bayesian receiver significantly outperforms the standard linear beamforming assisted receiver in terms of a reduced bit error rate, at the expense of an increased complexity, while the achievable system capacity is substantially enhanced with the advent of employing nonlinear detection. Specifically, when the spatial separation expressed in terms of the angle of arrival between the desired and interfering signals is below a certain threshold, a linear beamformer would fail to separate them, while a nonlinear detection assisted receiver is still capable of performing adequately. The adaptive implementation of the optimal Bayesian detector can be realized using a radial basis function network. Two techniques are presented for constructing block-data-based adaptive nonlinear multiple-antenna assisted receivers. One of them is based on the relevance vector machine invoked for classification, while the other on the orthogonal forward selection procedure combined with the Fisher ratio class-separability measure. A recursive sample-by-sample adaptation procedure is also proposed for training nonlinear detectors based on an amalgam of enhanced -means clustering techniques and the recursive least squares algorithm.

  12. Pescara benchmarks: nonlinear identification

    International Nuclear Information System (INIS)

    Gandino, E; Garibaldi, L; Marchesiello, S

    2011-01-01

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

  13. Theoretical models for ultrashort electromagnetic pulse propagation in nonlinear metamaterials

    International Nuclear Information System (INIS)

    Wen, Shuangchun; Xiang, Yuanjiang; Dai, Xiaoyu; Tang, Zhixiang; Su, Wenhua; Fan, Dianyuan

    2007-01-01

    A metamaterial (MM) differs from an ordinary optical material mainly in that it has a dispersive magnetic permeability and offers greatly enhanced design freedom to alter the linear and nonlinear properties. This makes it possible for us to control the propagation of ultrashort electromagnetic pulses at will. Here we report on generic features of ultrashort electromagnetic pulse propagation and demonstrate the controllability of both the linear and nonlinear parameters of models for pulse propagation in MMs. First, we derive a generalized system of coupled three-dimensional nonlinear Schroedinger equations (NLSEs) suitable for few-cycle pulse propagation in a MM with both nonlinear electric polarization and nonlinear magnetization. The coupled equations recover previous models for pulse propagation in both ordinary material and a MM under the same conditions. Second, by using the coupled NLSEs in the Drude dispersive model as an example, we identify the respective roles of the dispersive electric permittivity and magnetic permeability in ultrashort pulse propagation and disclose some additional features of pulse propagation in MMs. It is shown that, for linear propagation, the sign and magnitude of space-time focusing can be controlled through adjusting the linear dispersive permittivity and permeability. For nonlinear propagation, the linear dispersive permittivity and permeability are incorporated into the nonlinear magnetization and nonlinear polarization, respectively, resulting in controllable magnetic and electric self-steepening effects and higher-order dispersively nonlinear terms in the propagation models

  14. Nonlinear damage detection in composite structures using bispectral analysis

    Science.gov (United States)

    Ciampa, Francesco; Pickering, Simon; Scarselli, Gennaro; Meo, Michele

    2014-03-01

    Literature offers a quantitative number of diagnostic methods that can continuously provide detailed information of the material defects and damages in aerospace and civil engineering applications. Indeed, low velocity impact damages can considerably degrade the integrity of structural components and, if not detected, they can result in catastrophic failure conditions. This paper presents a nonlinear Structural Health Monitoring (SHM) method, based on ultrasonic guided waves (GW), for the detection of the nonlinear signature in a damaged composite structure. The proposed technique, based on a bispectral analysis of ultrasonic input waveforms, allows for the evaluation of the nonlinear response due to the presence of cracks and delaminations. Indeed, such a methodology was used to characterize the nonlinear behaviour of the structure, by exploiting the frequency mixing of the original waveform acquired from a sparse array of sensors. The robustness of bispectral analysis was experimentally demonstrated on a damaged carbon fibre reinforce plastic (CFRP) composite panel, and the nonlinear source was retrieved with a high level of accuracy. Unlike other linear and nonlinear ultrasonic methods for damage detection, this methodology does not require any baseline with the undamaged structure for the evaluation of the nonlinear source, nor a priori knowledge of the mechanical properties of the specimen. Moreover, bispectral analysis can be considered as a nonlinear elastic wave spectroscopy (NEWS) technique for materials showing either classical or non-classical nonlinear behaviour.

  15. Research on nonlinearity effect of secondary electron multiplier

    International Nuclear Information System (INIS)

    Wei Xingjian; Liao Junsheng; Deng Dachao; Yu Chunrong; Yuan Li

    2007-01-01

    The nonlinearity of secondary electron multiplier (SEM) of a thermal ionization mass spectrometer has been researched by using UTB-500 uranium isotope reference material and multi-collecting technique. The results show that the nonlinearity effect of SEM exists in the whole ion counting range, and there is an extreme point of the nonlinearity when the ion counting rate is about 20000 cps. The deviation between measured value of the extreme point and the reference value of the reference sample can be up to 3%, and the nonlinearity obeys logarithm linearity law on both sides of extreme point. A kind of mathematics model of nonlinearity calibration has been put forward. Using this model, the nonlinearity of SEM of TIMS can be calibrated. (authors)

  16. Multi-frequency Defect Selective Imaging via Nonlinear Ultrasound

    Science.gov (United States)

    Solodov, Igor; Busse, Gerd

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

  17. Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis.

    Science.gov (United States)

    Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping

    2015-10-01

    We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.

  18. Linear and nonlinear optical properties of borate crystals as ...

    Indian Academy of Sciences (India)

    Unknown

    crystal series, with an accuracy acceptable for materials development/design, and answer the questions often ... Optical property; nonlinear optical crystals; first principles calculation. 1. ..... system, and is not in concept suitable to excitation pro-.

  19. Weyl geometry and the nonlinear mechanics of distributed point defects

    KAUST Repository

    Yavari, A.; Goriely, A.

    2012-01-01

    The residual stress field of a nonlinear elastic solid with a spherically symmetric distribution of point defects is obtained explicitly using methods from differential geometry. The material manifold of a solid with distributed point defects

  20. Advances in nonlinear polymers and inorganic crystals, liquid crystals, and laser media

    International Nuclear Information System (INIS)

    Musikant, S.

    1987-01-01

    These proceedings collect papers on laser materials. Topics include: solid state lasers, fracture mechanics in laser materials, optical second harmonic generation, nonlinear optics, molecular crystals, crystal-phase transformation, and materials for laser fusion reactors

  1. Nonlinear Approaches in Engineering Applications

    CERN Document Server

    Jazar, Reza

    2012-01-01

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

  2. Ring vortex solitons in nonlocal nonlinear media

    DEFF Research Database (Denmark)

    Briedis, D.; Petersen, D.E.; Edmundson, D.

    2005-01-01

    We study the formation and propagation of two-dimensional vortex solitons, i.e. solitons with a phase singularity, in optical materials with a nonlocal focusing nonlinearity. We show that nonlocality stabilizes the dynamics of an otherwise unstable vortex beam. This occurs for either single...... or higher charge fundamental vortices as well as higher order (multiple ring) vortex solitons. Our results pave the way for experimental observation of stable vortex rings in other nonlocal nonlinear systems including Bose-Einstein condensates with pronounced long-range interparticle interaction....

  3. 50 years of nonlinear optics

    International Nuclear Information System (INIS)

    Shen Yuanrang

    2011-01-01

    This article presents a brief introduction to the birth and early investigations of nonlinear optics, such as second harmonic generation,sum and difference frequency generation, stimulated Raman scattering,and self-action of light etc. Several important research achievements and applications of nonlinear optics are presented as well, including nonlinear optical spectroscopy, phase conjugation and adaptive optics, coherent nonlinear optics, and high-order harmonic generation. In the end, current and future research topics in nonlinear optics are summarized. (authors)

  4. 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.

  5. Nonlinear AC susceptibility, surface and bulk shielding

    Science.gov (United States)

    van der Beek, C. J.; Indenbom, M. V.; D'Anna, G.; Benoit, W.

    1996-02-01

    We calculate the nonlinear AC response of a thin superconducting strip in perpendicular field, shielded by an edge current due to the geometrical barrier. A comparison with the results for infinite samples in parallel field, screened by a surface barrier, and with those for screening by a bulk current in the critical state, shows that the AC response due to a barrier has general features that are independent of geometry, and that are significantly different from those for screening by a bulk current in the critical state. By consequence, the nonlinear (global) AC susceptibility can be used to determine the origin of magnetic irreversibility. A comparison with experiments on a Bi 2Sr 2CaCu 2O 8+δ crystal shows that in this material, the low-frequency AC screening at high temperature is mainly due to the screening by an edge current, and that this is the unique source of the nonlinear magnetic response at temperatures above 40 K.

  6. A non-linear kinematic hardening function

    International Nuclear Information System (INIS)

    Ottosen, N.S.

    1977-05-01

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

  7. Photonic surfaces for designable nonlinear power shaping

    Energy Technology Data Exchange (ETDEWEB)

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

    2015-02-09

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

  8. Photonic surfaces for designable nonlinear power shaping

    International Nuclear Information System (INIS)

    Biswas, Roshni; Povinelli, Michelle L.

    2015-01-01

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

  9. Z-scan: A simple technique for determination of third-order optical nonlinearity

    Energy Technology Data Exchange (ETDEWEB)

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

    2015-08-28

    Z-scan is a simple experimental technique to measure intensity dependent nonlinear susceptibilities of third-order nonlinear optical materials. This technique is used to measure the sign and magnitude of both real and imaginary part of the third order nonlinear susceptibility (χ{sup (3)}) of nonlinear optical materials. In this paper, we investigate third-order nonlinear optical properties of Ag-polymer composite film by using single beam z-scan technique with Q-switched, frequency doubled Nd: YAG laser (λ=532 nm) at 5 ns pulse. The values of nonlinear absorption coefficient (β), nonlinear refractive index (n{sub 2}) and third-order nonlinear optical susceptibility (χ{sup (3)}) of permethylazine were found to be 9.64 × 10{sup −7} cm/W, 8.55 × 10{sup −12} cm{sup 2}/W and 5.48 × 10{sup −10} esu, respectively.

  10. Nonlinear control of magnetic signatures

    Science.gov (United States)

    Niemoczynski, Bogdan

    Magnetic properties of ferrite structures are known to cause fluctuations in Earth's magnetic field around the object. These fluctuations are known as the object's magnetic signature and are unique based on the object's geometry and material. It is a common practice to neutralize magnetic signatures periodically after certain time intervals, however there is a growing interest to develop real time degaussing systems for various applications. Development of real time degaussing system is a challenging problem because of magnetic hysteresis and difficulties in measurement or estimation of near-field flux data. The goal of this research is to develop a real time feedback control system that can be used to minimize magnetic signatures for ferrite structures. Experimental work on controlling the magnetic signature of a cylindrical steel shell structure with a magnetic disturbance provided evidence that the control process substantially increased the interior magnetic flux. This means near field estimation using interior sensor data is likely to be inaccurate. Follow up numerical work for rectangular and cylindrical cross sections investigated variations in shell wall flux density under a variety of ambient excitation and applied disturbances. Results showed magnetic disturbances could corrupt interior sensor data and magnetic shielding due to the shell walls makes the interior very sensitive to noise. The magnetic flux inside the shell wall showed little variation due to inner disturbances and its high base value makes it less susceptible to noise. This research proceeds to describe a nonlinear controller to use the shell wall data as an input. A nonlinear plant model of magnetics is developed using a constant tau to represent domain rotation lag and a gain function k to describe the magnetic hysteresis curve for the shell wall. The model is justified by producing hysteresis curves for multiple materials, matching experimental data using a particle swarm algorithm, and

  11. Nonlinear Dot Plots.

    Science.gov (United States)

    Rodrigues, Nils; Weiskopf, Daniel

    2018-01-01

    Conventional dot plots use a constant dot size and are typically applied to show the frequency distribution of small data sets. Unfortunately, they are not designed for a high dynamic range of frequencies. We address this problem by introducing nonlinear dot plots. Adopting the idea of nonlinear scaling from logarithmic bar charts, our plots allow for dots of varying size so that columns with a large number of samples are reduced in height. For the construction of these diagrams, we introduce an efficient two-way sweep algorithm that leads to a dense and symmetrical layout. We compensate aliasing artifacts at high dot densities by a specifically designed low-pass filtering method. Examples of nonlinear dot plots are compared to conventional dot plots as well as linear and logarithmic histograms. Finally, we include feedback from an expert review.

  12. Multidimensional nonlinear descriptive analysis

    CERN Document Server

    Nishisato, Shizuhiko

    2006-01-01

    Quantification of categorical, or non-numerical, data is a problem that scientists face across a wide range of disciplines. Exploring data analysis in various areas of research, such as the social sciences and biology, Multidimensional Nonlinear Descriptive Analysis presents methods for analyzing categorical data that are not necessarily sampled randomly from a normal population and often involve nonlinear relations. This reference not only provides an overview of multidimensional nonlinear descriptive analysis (MUNDA) of discrete data, it also offers new results in a variety of fields. The first part of the book covers conceptual and technical preliminaries needed to understand the data analysis in subsequent chapters. The next two parts contain applications of MUNDA to diverse data types, with each chapter devoted to one type of categorical data, a brief historical comment, and basic skills peculiar to the data types. The final part examines several problems and then concludes with suggestions for futu...

  13. Nonlinear Source Emulator

    DEFF Research Database (Denmark)

    Nguyen-Duy, Khiem

    of a proposed NSE system with high dynamic performance. The goal of the work is to achieve a state-of-the art transient time of 10 µs. In order to produce the arbitrary nonlinear curve, the exponential function of a typical diode is used, but the diode can be replaced by other nonlinear curve reference...... of conductive common-mode current produced by the high rate of change of voltage over time (high dv/dt) at the NSE output. v/xvii The contributions of the thesis are based on the development of both units: the low Cio isolated power supply and the high dynamic performance NSE. Both units are investigated......-of-the-art dynamic performance among devices of the same kind. It also offers a complete solution for simulation of nonlinear source systems of different sizes, both in terrestrial and non-terrestrial applications. Key words: Current transformers, dc-dc power converters, hysteresis, parasitic capacitance, system...

  14. Nonlinear excitations in biomolecules

    International Nuclear Information System (INIS)

    Peyrard, M.

    1995-01-01

    The aim of the workshop entitled ''Nonlinear Excitations in Biomolecules'' is to attempt to bridge the gap between the physicists and biologists communities which is mainly due to language and cultural barriers. The progress of nonlinear science in the last few decades which have shown that the combination of nonlinearity, which characterize most biological phenomena, and cooperative effects in a system having a large number of degrees of freedom, can give rise to coherent excitations with remarkable properties. New concepts, such as solitons nd nonlinear energy localisation have become familiar to physicists and applied mathematicians. It is thus tempting to make an analogy between these coherent excitations and the exceptional stability of some biological processes, such as for instance DNA transcription, which require the coordination of many events in the ever changing environment of a cell. Physicists are now invoking nonlinear excitations to describe and explain many bio-molecular processes while biologists often doubt that the seemingly infinite variety of phenomena that they are attempting to classify can be reduced to such simple concepts. A large part of the meeting is devoted to tutorial lectures rather than to latest research results. The book provides a pedagogical introduction to the two topics forming the backbone of the meeting: the theory of nonlinear excitations and solitons, and their application in biology; and the structure and function of biomolecules, as well as energy and charge transport in biophysics. In order to emphasize the link between physics and biology, the volume is not divided along these two topics but according to biological subjects. Each chapter starts with a short introduction attempting to help the reader to find his way among the contributions and point out the connection between them. 23 lectures over the 32 presented have been selected and refers to quantum properties of macro-molecules. (J.S.)

  15. Energia total de ruptura: um teste biomecânico para avaliação de material biológico com propriedade viscoelástica não linear Total energy of rupture: a biomechanical test to evaluate non-linear viscoelastic biological material

    Directory of Open Access Journals (Sweden)

    Feng Chung Wu

    2004-12-01

    Full Text Available Objetivo: Apresentação do teste biomecânico Energia Total de Ruptura para o estudo da resistência intrínseca de material biológico com propriedade viscoelástica não-linear representado neste trabalho por segmento íntegro de cólon descendente de rato. Métodos: Implementação do teste biomecânico Energia Total de Ruptura e do Sistema de Aquisição e Análise de dados Biomecânicos - SABI 2.0. Para esse fim, foram utilizados conceitos físico-mecânicos, computacionais e biomecânicos e como corpos de teste, 15 espécimes de cólon descendente de ratos. Resultados: O teste biomecânico Energia Total de Ruptura permitiu o cálculo da energia total acumulada necessária para promover a ruptura dos corpos de prova durante os ensaios mecânicos. Por meio da automatização e gerenciamento da aquisição e análise dos dados capturados foi possível a geração de gráficos e relatórios descritivos e estatísticos. Conclusão: Fundamentado em conceitos físico-mecânicos, computacionais e biomecânicos, o teste Energia Total de Ruptura pôde proporcionar análise matemática do comportamento dos segmentos de cólon descendente de ratos durante os ensaios, demonstrando ser um possível método de medição da resistência intrínseca desse material biológico com propriedade viscoelástica não-linear.Purpose: Presentation of the Total Energy of Rupture biomechanical test to evaluate the intrinsic resistance of the rat’s left colon which presents a non-linear viscoelastic property. Methods: Implementation of Total Energy of Rupture test (ETR and the Biomechanical Data Acquisition and Analysis System (SABI 2.0 based on physic-mechanical, computational and biomechanical concepts. Fifteen specimens of Wistar adults rat’s left colon where considered for experiments. Results: Using the TER biomechanical test it was possible calculate the accumulated total energy necessary to promote the specimens rupture during the mechanical trial. It was

  16. Nonlinearity in nanomechanical cantilevers

    DEFF Research Database (Denmark)

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

    2013-01-01

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

  17. Coupled nonlinear oscillators

    Energy Technology Data Exchange (ETDEWEB)

    Chandra, J; Scott, A C

    1983-01-01

    Topics discussed include transitions in weakly coupled nonlinear oscillators, singularly perturbed delay-differential equations, and chaos in simple laser systems. Papers are presented on truncated Navier-Stokes equations in a two-dimensional torus, on frequency locking in Josephson point contacts, and on soliton excitations in Josephson tunnel junctions. Attention is also given to the nonlinear coupling of radiation pulses to absorbing anharmonic molecular media, to aspects of interrupted coarse-graining in stimulated excitation, and to a statistical analysis of long-term dynamic irregularity in an exactly soluble quantum mechanical model.

  18. Engineered nonlinear lattices

    DEFF Research Database (Denmark)

    Clausen, Carl A. Balslev; Christiansen, Peter Leth; Torner, L.

    1999-01-01

    We show that with the quasi-phase-matching technique it is possible to fabricate stripes of nonlinearity that trap and guide light like waveguides. We investigate an array of such stripes and find that when the stripes are sufficiently narrow, the beam dynamics is governed by a quadratic nonlinear...... discrete equation. The proposed structure therefore provides an experimental setting for exploring discrete effects in a controlled manner. In particular, we show propagation of breathers that are eventually trapped by discreteness. When the stripes are wide the beams evolve in a structure we term...

  19. Nonlinear fiber optics

    CERN Document Server

    Agrawal, Govind

    2012-01-01

    Since the 4e appeared, a fast evolution of the field has occurred. The 5e of this classic work provides an up-to-date account of the nonlinear phenomena occurring inside optical fibers, the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research, this new edition includes major new content: slow light effects, which offers a reduction in noise and power consumption and more ordered network traffic-stimulated Brillouin scattering; vectorial treatment of highly nonlinear fibers; and a brand new chapter o

  20. Linear and nonlinear symmetrically loaded shells of revolution approximated with the finite element method

    International Nuclear Information System (INIS)

    Cook, W.A.

    1978-10-01

    Nuclear Material shipping containers have shells of revolution as a basic structural component. Analytically modeling the response of these containers to severe accident impact conditions requires a nonlinear shell-of-revolution model that accounts for both geometric and material nonlinearities. Present models are limited to large displacements, small rotations, and nonlinear materials. This report discusses a first approach to developing a finite element nonlinear shell of revolution model that accounts for these nonlinear geometric effects. The approach uses incremental loads and a linear shell model with equilibrium iterations. Sixteen linear models are developed, eight using the potential energy variational principle and eight using a mixed variational principle. Four of these are suitable for extension to nonlinear shell theory. A nonlinear shell theory is derived, and a computational technique used in its solution is presented

  1. 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.

  2. Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

    International Nuclear Information System (INIS)

    Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

    2011-01-01

    This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.

  3. Nonlinear Vibration and Mode Shapes of FG Cylindrical Shells

    Directory of Open Access Journals (Sweden)

    Saeed Mahmoudkhani

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

  4. BOOK REVIEW: Nonlinear Magnetohydrodynamics

    Science.gov (United States)

    Shafranov, V.

    1998-08-01

    Nonlinear magnetohydrodynamics by Dieter Biskamp is a thorough introduction to the physics of the most impressive non-linear phenomena that occur in conducting magnetoplasmas. The basic systems, in which non-trivial dynamic processes are observed, accompanied by changes of geometry of the magnetic field and the effects of energy transformation (magnetic energy into kinetic energy or the opposite effect in magnetic dynamos), are the plasma magnetic confinement systems for nuclear fusion and space plasmas, mainly the solar plasma. A significant number of the examples of the dynamic processes considered are taken from laboratory plasmas, for which an experimental check of the theory is possible. Therefore, though the book is intended for researchers and students interested in both laboratory, including nuclear fusion, and astrophysical plasmas, it is most probably closer to the first category of reader. In the Introduction the author notes that unlike the hydrodynamics of non-conducting fluids, where the phenomena caused by rapid fluid motions are the most interesting, for plasmas in a strong magnetic field the quasi-static configurations inside which the local dynamic processes occur are often the most important. Therefore, the reader will also find in this book rather traditional material on the theory of plasma equilibrium and stability in magnetic fields. In addition, it is notable that, as opposed to a linear theory, the non-linear theory, as a rule, cannot give quite definite explanations or predictions of phenomena, and consequently there are in the book many results obtained by consideration of numerical models with the use of supercomputers. The treatment of non-linear dynamics is preceded by Chapters 2 to 4, in which the basics of MHD theory are presented with an emphasis on the role of integral invariants of the magnetic helicity type, a derivation of the reduced MHD equations is given, together with examples of the exact solutions of the equilibrium

  5. A novel nonlinear damage resonance intermodulation effect for structural health monitoring

    Science.gov (United States)

    Ciampa, Francesco; Scarselli, Gennaro; Meo, Michele

    2017-04-01

    This paper is aimed at developing a theoretical model able to predict the generation of nonlinear elastic effects associated to the interaction of ultrasonic waves with the steady-state nonlinear response of local defect resonance (LDR). The LDR effect is used in nonlinear elastic wave spectroscopy to enhance the excitation of the material damage at its local resonance, thus to dramatically increase the vibrational amplitude of material nonlinear phenomena. The main result of this work is to prove both analytically and experimentally the generation of novel nonlinear elastic wave effects, here named as nonlinear damage resonance intermodulation, which correspond to a nonlinear intermodulation between the driving frequency and the LDR one. Beside this intermodulation effect, other nonlinear elastic wave phenomena such as higher harmonics of the input frequency and superharmonics of LDR frequency were found. The analytical model relies on solving the nonlinear equation of motion governing bending displacement under the assumption of both quadratic and cubic nonlinear defect approximation. Experimental tests on a damaged composite laminate confirmed and validated these predictions and showed that using continuous periodic excitation, the nonlinear structural phenomena associated to LDR could also be featured at locations different from the damage resonance. These findings will provide new opportunities for material damage detection using nonlinear ultrasounds.

  6. Nonlinear coherent structures in granular crystals

    Science.gov (United States)

    Chong, C.; Porter, Mason A.; Kevrekidis, P. G.; Daraio, C.

    2017-10-01

    The study of granular crystals, which are nonlinear metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures—which include traveling solitary waves, dispersive shock waves, and discrete breathers—have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research to date has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

  7. Nonlinear silicon photonics

    Science.gov (United States)

    Tsia, Kevin K.; Jalali, Bahram

    2010-05-01

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

  8. Nonlinear Regression with R

    CERN Document Server

    Ritz, Christian; Parmigiani, Giovanni

    2009-01-01

    R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. This book provides a coherent treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.

  9. 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.

  10. Intramolecular and nonlinear dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Davis, M.J. [Argonne National Laboratory, IL (United States)

    1993-12-01

    Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.

  11. Balancing for nonlinear systems

    NARCIS (Netherlands)

    Scherpen, J.M.A.

    1993-01-01

    We present a method of balancing for nonlinear systems which is an extension of balancing for linear systems in the sense that it is based on the input and output energy of a system. It is a local result, but gives 'broader' results than we obtain by just linearizing the system. Furthermore, the

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

    DEFF Research Database (Denmark)

    Bache, Morten; Lavrinenko, Andrei

    2017-01-01

    Using long-range surface plasmon polaritons light can propagate in metal nano-scale waveguides for ultracompact opto-electronic devices. Gold is an important material for plasmonic waveguides, but although its linear optical properties are fairly well understood, the nonlinear response is still...

  13. Development of a 3D cell-centered Lagrangian scheme for the numerical modeling of the gas dynamics and hyper-elasticity systems

    International Nuclear Information System (INIS)

    Georges, Gabriel

    2016-01-01

    High Energy Density Physics (HEDP) flows are multi-material flows characterized by strong shock waves and large changes in the domain shape due to rare faction waves. Numerical schemes based on the Lagrangian formalism are good candidates to model this kind of flows since the computational grid follows the fluid motion. This provides accurate results around the shocks as well as a natural tracking of multi-material interfaces and free-surfaces. In particular, cell-centered Finite Volume Lagrangian schemes such as GLACE (Godunov-type Lagrangian scheme Conservative for total Energy) and EUCCLHYD (Explicit Unstructured Cell-Centered Lagrangian Hydrodynamics) provide good results on both the modeling of gas dynamics and elastic-plastic equations. The work produced during this PhD thesis is in continuity with the work of Maire and Nkonga [JCP, 2009] for the hydrodynamic part and the work of Kluth and Despres [JCP, 2010] for the hyper elasticity part. More precisely, the aim of this thesis is to develop robust and accurate methods for the 3D extension of the EUCCLHYD scheme with a second-order extension based on MUSCL (Monotonic Upstream-centered Scheme for Conservation Laws) and GRP (Generalized Riemann Problem) procedures. A particular care is taken on the preservation of symmetries and the monotonicity of the solutions. The scheme robustness and accuracy are assessed on numerous Lagrangian test cases for which the 3D extensions are very challenging. (author) [fr

  14. Identification of nonlinear anelastic models

    International Nuclear Information System (INIS)

    Draganescu, G E; Bereteu, L; Ercuta, A

    2008-01-01

    A useful nonlinear identification technique applied to the anelastic and rheologic models is presented in this paper. First introduced by Feldman, the method is based on the Hilbert transform, and is currently used for identification of the nonlinear vibrations

  15. Nonlinear chaos control and synchronization

    NARCIS (Netherlands)

    Huijberts, H.J.C.; Nijmeijer, H.; Schöll, E.; Schuster, H.G.

    2007-01-01

    This chapter contains sections titled: Introduction Nonlinear Geometric Control Some Differential Geometric Concepts Nonlinear Controllability Chaos Control Through Feedback Linearization Chaos Control Through Input-Output Linearization Lyapunov Design Lyapunov Stability and Lyapunov's First Method

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

    Energy Technology Data Exchange (ETDEWEB)

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

    2012-06-28

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

  17. 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...

  18. Second-order nonlinear optical metamaterials: ABC-type nanolaminates

    International Nuclear Information System (INIS)

    Alloatti, L.; Kieninger, C.; Lauermann, M.; Köhnle, K.; Froelich, A.; Wegener, M.; Frenzel, T.; Freude, W.; Leuthold, J.; Koos, C.

    2015-01-01

    We demonstrate a concept for second-order nonlinear metamaterials that can be obtained from non-metallic centrosymmetric constituents with inherently low optical absorption. The concept is based on iterative atomic-layer deposition of three different materials, A = Al 2 O 3 , B = TiO 2 , and C = HfO 2 . The centrosymmetry of the resulting ABC stack is broken since the ABC and the inverted CBA sequences are not equivalent—a necessary condition for non-zero second-order nonlinearity. In our experiments, we find that the bulk second-order nonlinear susceptibility depends on the density of interfaces, leading to a nonlinear susceptibility of 0.26 pm/V at a wavelength of 800 nm. ABC-type nanolaminates can be deposited on virtually any substrate and offer a promising route towards engineering of second-order optical nonlinearities at both infrared and visible wavelengths

  19. 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....

  20. 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....

  1. FRF decoupling of nonlinear systems

    Science.gov (United States)

    Kalaycıoğlu, Taner; Özgüven, H. Nevzat

    2018-03-01

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

  2. Rogue waves in nonlinear science

    International Nuclear Information System (INIS)

    Yan Zhenya

    2012-01-01

    Rogue waves, as a special type of solitary waves, play an important role in nonlinear optics, Bose-Einstein condensates, ocean, atmosphere, and even finance. In this report, we mainly review on the history of the rogue wave phenomenon and recent development of rogue wave solutions in some nonlinear physical models arising in the fields of nonlinear science.

  3. H∞ Balancing for Nonlinear Systems

    NARCIS (Netherlands)

    Scherpen, Jacquelien M.A.

    1996-01-01

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

  4. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  5. Nonlinear (Anharmonic Casimir Oscillator

    Directory of Open Access Journals (Sweden)

    Habibollah Razmi

    2011-01-01

    Full Text Available We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an nonlinear (anharmonic Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has no exact solvable (analytical solution and the turning point(s of the system has (have no fixed position(s; however, for particular values of the stiffness of the micro spring and at appropriately well-chosen distance scales and conditions, there is (are approximately sinusoidal solution(s for the problem (the variable turning points are collected in a very small interval of positions. This, as a simple and elementary plan, may be useful in controlling the Casimir stiction problem in micromechanical devices.

  6. Limits to Nonlinear Inversion

    DEFF Research Database (Denmark)

    Mosegaard, Klaus

    2012-01-01

    For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...... pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag....

  7. Nonlinear Photonics 2014: introduction.

    Science.gov (United States)

    Akhmediev, N; Kartashov, Yaroslav

    2015-01-12

    International Conference "Nonlinear Photonics-2014" took place in Barcelona, Spain on July 27-31, 2014. It was a part of the "Advanced Photonics Congress" which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.

  8. Nonlinear data assimilation

    CERN Document Server

    Van Leeuwen, Peter Jan; Reich, Sebastian

    2015-01-01

    This book contains two review articles on nonlinear data assimilation that deal with closely related topics but were written and can be read independently. Both contributions focus on so-called particle filters. The first contribution by Jan van Leeuwen focuses on the potential of proposal densities. It discusses the issues with present-day particle filters and explorers new ideas for proposal densities to solve them, converging to particle filters that work well in systems of any dimension, closing the contribution with a high-dimensional example. The second contribution by Cheng and Reich discusses a unified framework for ensemble-transform particle filters. This allows one to bridge successful ensemble Kalman filters with fully nonlinear particle filters, and allows a proper introduction of localization in particle filters, which has been lacking up to now.

  9. Essentials of nonlinear optics

    CERN Document Server

    Murti, Y V G S

    2014-01-01

    Current literature on Nonlinear Optics varies widely in terms of content, style, and coverage of specific topics, relative emphasis of areas and the depth of treatment. While most of these books are excellent resources for the researchers, there is a strong need for books appropriate for presenting the subject at the undergraduate or postgraduate levels in Universities. The need for such a book to serve as a textbook at the level of the bachelors and masters courses was felt by the authors while teaching courses on nonlinear optics to students of both science and engineering during the past two decades. This book has emerged from an attempt to address the requirement of presenting the subject at college level. A one-semester course covering the essentials can effectively be designed based on this.

  10. Nonlinear differential equations

    International Nuclear Information System (INIS)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

  11. Inducing in situ, nonlinear soil response applying an active source

    Science.gov (United States)

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

    2009-01-01

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

  12. Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

    Energy Technology Data Exchange (ETDEWEB)

    Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg [School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 (Singapore); Zhou, Yu [Advanced Remanufacturing and Technology Center (ARTC), 3 Clean Tech Loop, CleanTech Two, Singapore 637143 (Singapore)

    2016-07-15

    Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonant frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.

  13. The forced nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Kaup, D.J.; Hansen, P.J.

    1985-01-01

    The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

  14. Nonlinear electrodynamics and cosmology

    International Nuclear Information System (INIS)

    Breton, Nora

    2010-01-01

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

  15. Nonlinear fibre optics overview

    DEFF Research Database (Denmark)

    Travers, J. C.; Frosz, Michael Henoch; Dudley, J. M.

    2010-01-01

    The optical fiber based supercontinuum source has recently become a significant scientific and commercial success, with applications ranging from frequency comb production to advanced medical imaging. This one-of-a-kind book explains the theory of fiber supercontinuum broadening, describes......, provides a background to the associated nonlinear optical processes, treats the generation mechanisms from continuous wave to femtosecond pulse pump regimes and highlights the diverse applications. A full discussion of numerical methods and comprehensive computer code are also provided, enabling readers...

  16. Damped nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Nicholson, D.R.; Goldman, M.V.

    1976-01-01

    High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time

  17. A finite element model for nonlinear shells of revolution

    International Nuclear Information System (INIS)

    Cook, W.A.

    1979-01-01

    A shell-of-revolution model was developed to analyze impact problems associated with the safety analysis of nuclear material shipping containers. The nonlinear shell theory presented by Eric Reissner in 1972 was used to develop our model. Reissner's approach includes transverse shear deformation and moments turning about the middle surface normal. With these features, this approach is valid for both thin and thick shells. His theory is formulated in terms of strain and stress resultants that refer to the undeformed geometry. This nonlinear shell model is developed using the virtual work principle associated with Reissner's equilibrium equations. First, the virtual work principle is modified for incremental loading; then it is linearized by assuming that the nonlinear portions of the strains are known. By iteration, equilibrium is then approximated for each increment. A benefit of this approach is that this iteration process makes it possible to use nonlinear material properties. (orig.)

  18. Nonlinearity without superluminality

    International Nuclear Information System (INIS)

    Kent, Adrian

    2005-01-01

    Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schroedinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality

  19. Nonlinear flow model for well production in an underground formation

    Directory of Open Access Journals (Sweden)

    J. C. Guo

    2013-05-01

    Full Text Available Fluid flow in underground formations is a nonlinear process. In this article we modelled the nonlinear transient flow behaviour of well production in an underground formation. Based on Darcy's law and material balance equations, we used quadratic pressure gradients to deduce diffusion equations and discuss the origins of nonlinear flow issues. By introducing an effective-well-radius approach that considers skin factor, we established a nonlinear flow model for both gas and liquid (oil or water. The liquid flow model was solved using a semi-analytical method, while the gas flow model was solved using numerical simulations because the diffusion equation of gas flow is a stealth function of pressure. For liquid flow, a series of standard log-log type curves of pressure transients were plotted and nonlinear transient flow characteristics were analyzed. Qualitative and quantitative analyses were used to compare the solutions of the linear and nonlinear models. The effect of nonlinearity upon pressure transients should not be ignored. For gas flow, pressure transients were simulated and compared with oil flow under the same formation and well conditions, resulting in the conclusion that, under the same volume rate production, oil wells demand larger pressure drops than gas wells. Comparisons between theoretical data and field data show that nonlinear models will describe fluid flow in underground formations realistically and accurately.

  20. Phase-space topography characterization of nonlinear ultrasound waveforms.

    Science.gov (United States)

    Dehghan-Niri, Ehsan; Al-Beer, Helem

    2018-03-01

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

  1. Organic nonlinear crystals and high power frequency conversion

    International Nuclear Information System (INIS)

    Velsko, S.P.; Davis, L.; Wang, F.; Monaco, S.; Eimerl, D.

    1987-12-01

    We are searching for a new second- and third-harmonic generators among the salts of chiral organic acids and bases. We discuss the relevant properties of crystals from this group of compounds, including their nonlinear and phasematching characteristics, linear absorption, damage threshold and crystal growth. In addition, we summarize what is known concerning other nonlinear optical properties of these crystals, such as two-photon absorption, nonlinear refractive index, and stimulated Raman thresholds. A preliminary assessment is made of the potential of these materials for use in future high power, large aperture lasers such as those used for inertial confinement fusion experiments. 14 refs., 1 fig., 3 tabs

  2. Organic nonlinear crystals and high power frequency conversion

    International Nuclear Information System (INIS)

    Velsko, S.P.; Davis, L.; Wang, F.; Monaco, S.; Eimerl, D.

    1987-01-01

    The authors are searching for new second and third harmonic generators among the salts of organic acids and bases. They discuss the relevant properties of crystals from this group of compounds, including their nonlinear and phasematching characteristics, linear absorption, damage threshold and crystal growth. In addition, they summarize what is known concerning other nonlinear optical properties of these crystals, such as two-photon absorption, nonlinear refractive index, and stimulated Raman thresholds. A preliminary assessment is made of the potential of these materials for use in future high power, large aperture lasers such as those used for inertial confinement fusion experiments

  3. Study of large nonlinear change phase in Hibiscus Sabdariffa

    Science.gov (United States)

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

    2015-09-01

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

  4. Non-linear programming method in optimization of fast reactors

    International Nuclear Information System (INIS)

    Pavelesku, M.; Dumitresku, Kh.; Adam, S.

    1975-01-01

    Application of the non-linear programming methods on optimization of nuclear materials distribution in fast reactor is discussed. The programming task composition is made on the basis of the reactor calculation dependent on the fuel distribution strategy. As an illustration of this method application the solution of simple example is given. Solution of the non-linear program is done on the basis of the numerical method SUMT. (I.T.)

  5. On Maximally Dissipative Shock Waves in Nonlinear Elasticity

    OpenAIRE

    Knowles, James K.

    2010-01-01

    Shock waves in nonlinearly elastic solids are, in general, dissipative. We study the following question: among all plane shock waves that can propagate with a given speed in a given one-dimensional nonlinearly elastic bar, which one—if any—maximizes the rate of dissipation? We find that the answer to this question depends strongly on the qualitative nature of the stress-strain relation characteristic of the given material. When maximally dissipative shocks do occur, they propagate according t...

  6. Nonlinear internal friction, chaos, fractal and musical instruments

    International Nuclear Information System (INIS)

    Sun, Z.Q.; Lung, C.W.

    1995-08-01

    Nonlinear and structure sensitive internal friction phenomena in materials are used for characterizing musical instruments. It may be one of the most important factors influencing timbre of instruments. As a nonlinear dissipated system, chaos and fractals are fundamental peculiarities of sound spectra. It is shown that the concept of multi range fractals can be used to decompose the frequency spectra of melody. New approaches are suggested to improve the fabrication, property characterization and physical understanding of instruments. (author). 18 refs, 4 figs

  7. Nonlinear left-handed transmission line metamaterials

    International Nuclear Information System (INIS)

    Kozyrev, A B; Weide, D W van der

    2008-01-01

    Metamaterials, exhibiting simultaneously negative permittivity ε and permeability μ, more commonly referred to as left-handed metamaterials (LHMs) and also known as negative-index materials, have received substantial attention in the scientific and engineering communities [1]. Most studies of LHMs (and electromagnetic metamaterials in general) have been in the linear regime of wave propagation and have already inspired new types of microwave circuits and devices. The results of these studies have already been the subject of numerous reviews and books. This review covers a less explored but rapidly developing area of investigation involving media that combine nonlinearity (dependence of the permittivity and permeability on the magnitude of the propagating field) with the anomalous dispersion exhibited by LHM. The nonlinear phenomena in such media will be considered on the example of a model system: the nonlinear left-handed transmission line. These nonlinear phenomena include parametric generation and amplification, harmonic and subharmonic generation as well as modulational instabilities and envelope solitons. (topical review)

  8. Iterative analysis of concrete gravity dam-nonlinear foundation ...

    African Journals Online (AJOL)

    The solution of the coupled system is accomplished by solving the two systems separately and then considering the interaction effects at the soil–structure interface enforced by a developed iterative scheme. Emphasis has been laid on the study of material nonlinearity of the foundation material in the interaction analysis.

  9. Noise in nonlinear nanoelectromechanical resonators

    Science.gov (United States)

    Guerra Vidal, Diego N.

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

  10. Parametric model of servo-hydraulic actuator coupled with a nonlinear system: Experimental validation

    Science.gov (United States)

    Maghareh, Amin; Silva, Christian E.; Dyke, Shirley J.

    2018-05-01

    Hydraulic actuators play a key role in experimental structural dynamics. In a previous study, a physics-based model for a servo-hydraulic actuator coupled with a nonlinear physical system was developed. Later, this dynamical model was transformed into controllable canonical form for position tracking control purposes. For this study, a nonlinear device is designed and fabricated to exhibit various nonlinear force-displacement profiles depending on the initial condition and the type of materials used as replaceable coupons. Using this nonlinear system, the controllable canonical dynamical model is experimentally validated for a servo-hydraulic actuator coupled with a nonlinear physical system.

  11. Advances in dynamic relaxation techniques for nonlinear finite element analysis

    International Nuclear Information System (INIS)

    Sauve, R.G.; Metzger, D.R.

    1995-01-01

    Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented. They include: (1) nonlinear geometric cantilever plate; (2) moment-loaded nonlinear beam; and (3) creep of nuclear fuel channel assemblies

  12. Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging

    KAUST Repository

    Desmal, Abdulla

    2016-03-01

    Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using

  13. Synthesis, growth, structure and characterization of 1-Ethyl-2-(2-p-tolyl-vinyl)-pyridinium iodide (TASI) – An efficient material for third-order nonlinear optical applications

    Energy Technology Data Exchange (ETDEWEB)

    Nivetha, K. [Centre for Crystal Growth, School of Advanced Sciences, VIT University, Vellore 632 014 (India); Kalainathan, S., E-mail: kalainathan@yahoo.com [Centre for Crystal Growth, School of Advanced Sciences, VIT University, Vellore 632 014 (India); Yamada, M. [Research Center for Engineering Science, Graduate School of Engineering Science, Akita University, 1-1 Tegatagakuen-machi, Akita 010-8502 (Japan); Kondo, Y. [Department of Life Science, Graduate School of Engineering Science, Akita University, 1-1 Tegatagakuen-machi, Akita 010-8502 (Japan); Hamada, F. [Department of Applied Chemistry, Graduate School of Engineering Science, Akita University, 1-1 Tegatagakuen-machi, Akita 010-8502 (Japan)

    2017-02-15

    A new organic stilbazolium derivative, 1-Ethyl-2-(2-p-tolyl-vinyl)-pyridinium iodide (TASI), was grown from methanol:acetonitrile (1:3) mixed solvent by slow evaporation technique. Single crystal X-ray diffraction analysis revealed that TASI crystallizes in triclinic system with a centrosymmetric space group P-1. The molecular structure and the presence of expected functional groups of TASI were confirmed by {sup 1}H NMR and FT-IR spectroscopic studies. The HOMO and LUMO energies influence the charge transfer takes place within the molecule. The grown crystal was thermally stable up to 210 °C as determined by TG/DTA analysis. UV-Vis-NIR spectral study showed that the grown crystal was transparent in the wavelength range of 438–1100 nm. Mechanical behaviour and surface laser damage threshold were studied to find the suitability of the grown crystal for device fabrication. Studies of its third-order nonlinear optical properties using a Z-scan technique demonstrates that TASI crystal is capable of exhibiting reverse saturable absorption and self-focusing performance with the second-order molecular hyperpolarizability (γ) 4.983 × 10{sup −34} esu. The third-order nonlinear susceptibility of TASI was found to be 8.931 × 10{sup −6} esu, which is higher than a few other stilbazolium derivative crystals. - Highlights: • TASI is a new organic stilbazolium derivative and was grown by slow evaporation technique. • HOMO-LUMO analysis helps to explain charge transfer interaction within the molecule. • The grown crystal has 80% transmittance in the visible and near-IR spectral range. • Thermally, electrically and mechanically efficient for NLO applications. • Z-scan measurements reveal the aptness of the grown crystal for third order NLO applications.

  14. Synthesis and electrical, spectroscopic and nonlinear optical properties of cobalt molecular materials obtained from PcCo(CN)L (L = ethylenediamine, 1,4-diaminebutane, 1,12-diaminododecane and 2,6-diamineanthraquinone)

    Energy Technology Data Exchange (ETDEWEB)

    Morales-Saavedra, O.G., E-mail: omar.morales@ccadet.unam.mx [Lab. of Nonlinear Optics, Centro de Ciencias Aplicadas y Desarrollo Tecnologico, Universidad Nacional Autonoma de Mexico, CCADET-UNAM, Apdo, Postal 70-186, C.P. 04510 Coyoacan, Cd. Universitaria, Mexico D. F. (Mexico); Sanchez-Vergara, M.E. [Coordinacion de Ingenieria Mecatronica, Facultad de Ingenieria, Universidad Anahuac del Norte, Avenida Universidad Anahuac 46, Col. Lomas Anahuac, 52786 Huixquilucan, Estado de Mexico (Mexico); Rodriguez-Rosales, A.A.; Ortega-Martinez, R. [Lab. of Nonlinear Optics, Centro de Ciencias Aplicadas y Desarrollo Tecnologico, Universidad Nacional Autonoma de Mexico, CCADET-UNAM, Apdo, Postal 70-186, C.P. 04510 Coyoacan, Cd. Universitaria, Mexico D. F. (Mexico); Ortiz-Rebollo, A. [Instituto de Investigaciones en Materiales, Universidad Nacional Autonoma de Mexico, IIM-UNAM, A.P. 70-360 Coyoacan, 04510 Mexico D. F. (Mexico); Frontana-Uribe, B.A. [Centro Conjunto de Investigacion en Quimica Sustentable UAEM-UNAM Km. 14.5, Carretera Toluca-Atlacomulco, C.P. 50200 Toluca, Estado de Mexico (Mexico); Garcia-Montalvo, V. [Instituto de Quimica, Universidad Nacional Autonoma de Mexico, Circuito Exterior, Ciudad Universitaria, Mexico D. F. 04510 (Mexico)

    2010-10-01

    Novel PcCo(CN)L monomeric complexes were synthesized from [PcCoCN]{sub n} compounds and bidentate axial ligands (L) such as ethylenediamine, 1,4-diaminebutane, 1,12-diaminedodecane and 2,6-diamineanthraquinone. These complexes were implemented to fabricate pellets and thin films by the vacuum thermal evaporation technique. The obtained compounds and deposited thin films were characterized by different spectroscopic techniques. Measurements of the electrical conductivity and the electrical current as a function of temperature were also carried out. IR-spectroscopy studies showed that the ligand attaches to the [PcCoCN]{sub n} unit. The C=N vibrational band is found in the PcCo(et)CN and PcCo(bu)CN molecular solids, although it is displaced with respect to other reported values. Compounds PcCo(do){sub 2} and PcCo(an){sub 2} do not show C=N vibrational bands. This fact suggests a double bond between the ligand and the macrocycle and a coordination at the fifth and sixth position on the Co(III) atom. UV-vis spectra of the thin films exhibited higher conjugation degree for the CN-based samples. Electrical conductivity for the PcCo(an){sub 2} complex was consistently low for all temperature ranges under measurement, whereas the other synthesized compounds showed a semiconductor-like dependence of electric current with temperature. Additionally, cubic nonlinear optical (NLO) characterizations of the film samples were performed with the Z-Scan and third harmonic generation (THG) techniques, all samples exhibit outstandingly high nonlinear activity.

  15. Synthesis and electrical, spectroscopic and nonlinear optical properties of cobalt molecular materials obtained from PcCo(CN)L (L = ethylenediamine, 1,4-diaminebutane, 1,12-diaminododecane and 2,6-diamineanthraquinone)

    International Nuclear Information System (INIS)

    Morales-Saavedra, O.G.; Sanchez-Vergara, M.E.; Rodriguez-Rosales, A.A.; Ortega-Martinez, R.; Ortiz-Rebollo, A.; Frontana-Uribe, B.A.; Garcia-Montalvo, V.

    2010-01-01

    Novel PcCo(CN)L monomeric complexes were synthesized from [PcCoCN] n compounds and bidentate axial ligands (L) such as ethylenediamine, 1,4-diaminebutane, 1,12-diaminedodecane and 2,6-diamineanthraquinone. These complexes were implemented to fabricate pellets and thin films by the vacuum thermal evaporation technique. The obtained compounds and deposited thin films were characterized by different spectroscopic techniques. Measurements of the electrical conductivity and the electrical current as a function of temperature were also carried out. IR-spectroscopy studies showed that the ligand attaches to the [PcCoCN] n unit. The C=N vibrational band is found in the PcCo(et)CN and PcCo(bu)CN molecular solids, although it is displaced with respect to other reported values. Compounds PcCo(do) 2 and PcCo(an) 2 do not show C=N vibrational bands. This fact suggests a double bond between the ligand and the macrocycle and a coordination at the fifth and sixth position on the Co(III) atom. UV-vis spectra of the thin films exhibited higher conjugation degree for the CN-based samples. Electrical conductivity for the PcCo(an) 2 complex was consistently low for all temperature ranges under measurement, whereas the other synthesized compounds showed a semiconductor-like dependence of electric current with temperature. Additionally, cubic nonlinear optical (NLO) characterizations of the film samples were performed with the Z-Scan and third harmonic generation (THG) techniques, all samples exhibit outstandingly high nonlinear activity.

  16. Nonlinear robust hierarchical control for nonlinear uncertain systems

    Directory of Open Access Journals (Sweden)

    Leonessa Alexander

    1999-01-01

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

  17. Physically Functional Materials

    DEFF Research Database (Denmark)

    2002-01-01

    acids or peptides having azobenzenes or other physicially functional groups, e.g., photoresponsive groups, as side chains. These compounds may be synthesized using solid phase peptide synthesis techniques. Materials, e.g., thin films, comprising such compounds may be used for optical storage...... of information (holographic data storage), nonlinear optics (NLO), as photoconductors, photonic band-gap materials, electrically conducting materials, electroluminescent materials, piezo-electric materials, pyroelectric materials, magnetic materials, ferromagnetic materials, ferroelectric materials......, photorefractive materials, or materials in which light-induced conformational changes can be produced. Optical anisotropy may reversibly be generated with polarized laser light whereby a hologram is formed. First order diffraction efficiencies of up to around 80% have been obtained....

  18. 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...

  19. Non-linear osmosis

    Science.gov (United States)

    Diamond, Jared M.

    1966-01-01

    1. The relation between osmotic gradient and rate of osmotic water flow has been measured in rabbit gall-bladder by a gravimetric procedure and by a rapid method based on streaming potentials. Streaming potentials were directly proportional to gravimetrically measured water fluxes. 2. As in many other tissues, water flow was found to vary with gradient in a markedly non-linear fashion. There was no consistent relation between the water permeability and either the direction or the rate of water flow. 3. Water flow in response to a given gradient decreased at higher osmolarities. The resistance to water flow increased linearly with osmolarity over the range 186-825 m-osM. 4. The resistance to water flow was the same when the gall-bladder separated any two bathing solutions with the same average osmolarity, regardless of the magnitude of the gradient. In other words, the rate of water flow is given by the expression (Om — Os)/[Ro′ + ½k′ (Om + Os)], where Ro′ and k′ are constants and Om and Os are the bathing solution osmolarities. 5. Of the theories advanced to explain non-linear osmosis in other tissues, flow-induced membrane deformations, unstirred layers, asymmetrical series-membrane effects, and non-osmotic effects of solutes could not explain the results. However, experimental measurements of water permeability as a function of osmolarity permitted quantitative reconstruction of the observed water flow—osmotic gradient curves. Hence non-linear osmosis in rabbit gall-bladder is due to a decrease in water permeability with increasing osmolarity. 6. The results suggest that aqueous channels in the cell membrane behave as osmometers, shrinking in concentrated solutions of impermeant molecules and thereby increasing membrane resistance to water flow. A mathematical formulation of such a membrane structure is offered. PMID:5945254

  20. Nonlinear diffusion equations

    CERN Document Server

    Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

    2001-01-01

    Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which

  1. Methods of nonlinear analysis

    CERN Document Server

    Bellman, Richard Ernest

    1970-01-01

    In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat

  2. Topics in Nonlinear Dynamics

    DEFF Research Database (Denmark)

    Mosekilde, Erik

    Through a significant number of detailed and realistic examples this book illustrates how the insights gained over the past couple of decades in the fields of nonlinear dynamics and chaos theory can be applied in practice. Aomng the topics considered are microbiological reaction systems, ecological...... food-web systems, nephron pressure and flow regulation, pulsatile secretion of hormones, thermostatically controlled radiator systems, post-stall maneuvering of aircrafts, transfer electron devices for microwave generation, economic long waves, human decision making behavior, and pattern formation...... in chemical reaction-diffusion systems....

  3. Nonlinear dynamics in psychology

    Directory of Open Access Journals (Sweden)

    Stephen J. Guastello

    2001-01-01

    Full Text Available This article provides a survey of the applications of nonlinear dynamical systems theory to substantive problems encountered in the full scope of psychological science. Applications are organized into three topical areas – cognitive science, social and organizational psychology, and personality and clinical psychology. Both theoretical and empirical studies are considered with an emphasis on works that capture the broadest scope of issues that are of substantive interest to psychological theory. A budding literature on the implications of NDS principles in professional practice is reported also.

  4. Nonlinear Hamiltonian systems

    DEFF Research Database (Denmark)

    Jørgensen, Michael Finn

    1995-01-01

    It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...

  5. Nonlinear surface electromagnetic phenomena

    CERN Document Server

    Ponath, H-E

    1991-01-01

    In recent years the physics of electromagnetic surface phenomena has developed rapidly, evolving into technologies for communications and industry, such as fiber and integrated optics. The variety of phenomena based on electromagnetism at surfaces is rich and this book was written with the aim of summarizing the available knowledge in selected areas of the field. The book contains reviews written by solid state and optical physicists on the nonlinear interaction of electromagnetic waves at and with surfaces and films. Both the physical phenomena and some potential applications are

  6. Oscillators from nonlinear realizations

    Science.gov (United States)

    Kozyrev, N.; Krivonos, S.

    2018-02-01

    We construct the systems of the harmonic and Pais-Uhlenbeck oscillators, which are invariant with respect to arbitrary noncompact Lie algebras. The equations of motion of these systems can be obtained with the help of the formalism of nonlinear realizations. We prove that it is always possible to choose time and the fields within this formalism in such a way that the equations of motion become linear and, therefore, reduce to ones of ordinary harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce these equations, can also be provided. As particular examples of this construction, we discuss the so(2, 3) and G 2(2) algebras.

  7. 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...

  8. Global Analysis of Nonlinear Dynamics

    CERN Document Server

    Luo, Albert

    2012-01-01

    Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.  

  9. 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

  10. Collapse of nonlinear Langmuir waves

    International Nuclear Information System (INIS)

    Malkin, V.M.

    1986-01-01

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

  11. One-dimensional motion of a material with a strain theshold

    Directory of Open Access Journals (Sweden)

    A. Farina

    2007-12-01

    Full Text Available We consider the one-dimensional shearing motion of a material exhibiting elastic behaviour when the stress is below some threshold. The threshold represents a limit to the deformability, i.e. no further deformation can occur on increasing the stress. The mathematical formulation leads to a free boundary problem for the wave equation, whose structure depends on whether the stress (and the velocity are continuous across the propagating interface for the strain threshold .Local existence and uniqueness are proved for the continuous case (in which the interface propagation is subsonic. Some explicit solutions are calculated for another case (with a supersonic interface. It is shown that the model with strain threshold is never the limit of hyperelastic systems.

  12. 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.

  13. Nonlinear viscoelasticity of pre-compressed layered polymeric composite under oscillatory compression

    KAUST Repository

    Xu, Yangguang

    2018-05-03

    Describing nonlinear viscoelastic properties of polymeric composites when subjected to dynamic loading is essential for development of practical applications of such materials. An efficient and easy method to analyze nonlinear viscoelasticity remains elusive because the dynamic moduli (storage modulus and loss modulus) are not very convenient when the material falls into nonlinear viscoelastic range. In this study, we utilize two methods, Fourier transform and geometrical nonlinear analysis, to quantitatively characterize the nonlinear viscoelasticity of a pre-compressed layered polymeric composite under oscillatory compression. We discuss the influences of pre-compression, dynamic loading, and the inner structure of polymeric composite on the nonlinear viscoelasticity. Furthermore, we reveal the nonlinear viscoelastic mechanism by combining with other experimental results from quasi-static compressive tests and microstructural analysis. From a methodology standpoint, it is proved that both Fourier transform and geometrical nonlinear analysis are efficient tools for analyzing the nonlinear viscoelasticity of a layered polymeric composite. From a material standpoint, we consequently posit that the dynamic nonlinear viscoelasticity of polymeric composites with complicated inner structures can also be well characterized using these methods.

  14. Applications of nonlinear fiber optics

    CERN Document Server

    Agrawal, Govind

    2008-01-01

    * The only book describing applications of nonlinear fiber optics * Two new chapters on the latest developments: highly nonlinear fibers and quantum applications* Coverage of biomedical applications* Problems provided at the end of each chapterThe development of new highly nonlinear fibers - referred to as microstructured fibers, holey fibers and photonic crystal fibers - is the next generation technology for all-optical signal processing and biomedical applications. This new edition has been thoroughly updated to incorporate these key technology developments.The bo

  15. Recent topics in nonlinear PDE

    International Nuclear Information System (INIS)

    Mimura, Masayasu; Nishida, Takaaki

    1984-01-01

    The meeting on the subject of nonlinear partial differential equations was held at Hiroshima University in February, 1983. Leading and active mathematicians were invited to talk on their current research interests in nonlinear pdes occuring in the areas of fluid dynamics, free boundary problems, population dynamics and mathematical physics. This volume contains the theory of nonlinear pdes and the related topics which have been recently developed in Japan. (Auth.)

  16. 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...

  17. Nonlinear and quantum optics near nanoparticles

    Science.gov (United States)

    Dhayal, Suman

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

  18. Nonlinear analysis of reinforced concrete structures using software package abaqus

    Directory of Open Access Journals (Sweden)

    Marković Nemanja

    2014-01-01

    Full Text Available Reinforced concrete (AB is characterized by huge inhomogeneity resulting from the material characteristics of the concrete, then, quasi-brittle behavior during failure. These and other phenomena require the introduction of material nonlinearity in the modeling of reinforced concrete structures. This paper presents the modeling reinforced concrete in the software package ABAQUS. A brief theoretical overview is presented of methods such as: Concrete Damage Plasticity (CDP, Smeared Concrete Cracking (CSC, Cap Plasticity (CP and Drucker-Prager model (DPM. We performed a nonlinear analysis of two-storey reinforced concrete frame by applying CDP method for modeling material nonlinearity of concrete. We have analyzed damage zones, crack propagation and loading-deflection ratio.

  19. Perspectives of nonlinear dynamics

    International Nuclear Information System (INIS)

    Jackson, E.A.

    1985-03-01

    Four lectures were given weekly in October and November, 1984, and some of the ideas presented here will be of use in the future. First, a brief survey of the historical development of nonlinear dynamics since about 1890 was given, and then, a few topics were discussed in detail. The objective was to introduce some of many concepts and methods which are presently used for describing nonlinear dynamics. The symbiotic relationship between sciences of all types and mathematics, two main categories of the models describing nature, the method for describing the dynamics of a system, the idea of control parameters and topological dimension, the asymptotic properties of dynamics, abstract dynamics, the concept of embedding, singular perturbation theory, strange attractor, Fermi-Pasta-Ulam phenomena, an example of computer heuristics, the idea of elementary catastrophe theory and so on were explained. The logistic map is the simplest introduction to complex dynamics. The complicated dynamics is referred to as strange attractors. Two-dimensional maps are the highest dimensional maps commonly studied. These were discussed in detail. (Kako, I.)

  20. Nonlinearities in Behavioral Macroeconomics.

    Science.gov (United States)

    Gomes, Orlando

    2017-07-01

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