NASA Astrophysics Data System (ADS)
Kohr, Mirela; de Cristoforis, Massimo Lanza; Wendland, Wolfgang L.
2016-06-01
The purpose of this paper is to study a boundary value problem of Robin-transmission type for the nonlinear Darcy-Forchheimer-Brinkman and Navier-Stokes systems in two adjacent bounded Lipschitz domains in {{{R}}n (nin {2,3})}, with linear transmission conditions on the internal Lipschitz interface and a linear Robin condition on the remaining part of the Lipschitz boundary. We also consider a Robin-transmission problem for the same nonlinear systems subject to nonlinear transmission conditions on the internal Lipschitz interface and a nonlinear Robin condition on the remaining part of the boundary. For each of these problems we exploit layer potential theoretic methods combined with fixed point theorems in order to show existence results in Sobolev spaces, when the given data are suitably small in {L^2}-based Sobolev spaces or in some Besov spaces. For the first mentioned problem, which corresponds to linear Robin and transmission conditions, we also show a uniqueness result. Note that the Brinkman-Forchheimer-extended Darcy equation is a nonlinear equation that describes saturated porous media fluid flows.
Detonator comprising a nonlinear transmission line
Elizondo-Decanini, Juan M
2014-12-30
Detonators are described herein. In a general embodiment, the detonator includes a nonlinear transmission line that has a variable capacitance. Capacitance of the nonlinear transmission line is a function of voltage on the nonlinear transmission line. The nonlinear transmission line receives a voltage pulse from a voltage source and compresses the voltage pulse to generate a trigger signal. Compressing the voltage pulse includes increasing amplitude of the voltage pulse and decreasing length of the voltage pulse in time. An igniter receives the trigger signal and detonates an explosive responsive to receipt of the trigger signal.
Problems in nonlinear resistive MHD
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L.
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
NASA Astrophysics Data System (ADS)
Skerget, P.; Brebbia, C. A.
In many practical applications of boundary elements, the potential problems may be nonlinear. The use of Kirchoff's transform provides an approach to convert a nonlinear material problem into a linear one. A description of several different shape functions to define the conductivity is presented. Attention is given to the type of integral equations which are obtained if the Kirchoff's transform is applied for nonlinear material in the presence of mixed boundary conditions. The integral formulation for nonlinear radiation boundary conditions with and without potential dependent conductivity is also considered. For steady heat conduction problems with constant conductivity a boundary integral equation relating boundary values for temperatures (or potentials) and its normal derivatives over the boundary can be obtained. Applications which concern the solution of steady state conduction problems are investigated. The problems are related to a hollow cylinder, a nuclear reactor pressure vessel, and an industrial furnace.
Networks of nonlinear superconducting transmission line resonators
NASA Astrophysics Data System (ADS)
Leib, M.; Deppe, F.; Marx, A.; Gross, R.; Hartmann, M. J.
2012-07-01
We investigate a network of coupled superconducting transmission line resonators, each of them made nonlinear with a capacitively shunted Josephson junction coupling to the odd flux modes of the resonator. The resulting eigenmode spectrum shows anticrossings between the plasma mode of the shunted junction and the odd resonator modes. Notably, we find that the combined device can inherit the complete nonlinearity of the junction, allowing for a description as a harmonic oscillator with a Kerr nonlinearity. Using a dc SQUID instead of a single junction, the nonlinearity can be tuned between 10 kHz and 4 MHz while maintaining resonance frequencies of a few gigahertz for realistic device parameters. An array of such nonlinear resonators can be considered a scalable superconducting quantum simulator for a Bose-Hubbard Hamiltonian. The device would be capable of accessing the strongly correlated regime and be particularly well suited for investigating quantum many-body dynamics of interacting particles under the influence of drive and dissipation.
Nonlinear problems in flight dynamics
NASA Technical Reports Server (NTRS)
Chapman, G. T.; Tobak, M.
1984-01-01
A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.
NOVEL SIGNAL PROCESSING WITH NONLINEAR TRANSMISSION LINES
D. REAGOR; ET AL
2000-08-01
Nonlinear dielectrics offer uniquely strong and tunable nonlinearities that make them attractive for current devices (for example, frequency-agile microwave filters) and for future signal-processing technologies. The goal of this project is to understand pulse propagation on nonlinear coplanar waveguide prototype devices. We have performed time-domain and frequency-domain experimental studies of simple waveguide structures and pursued a theoretical understanding of the propagation of signals on these nonlinear waveguides. To realistically assess the potential applications, we used a time-domain measurement and analysis technique developed during this project to perform a broadband electrodynamics characterization in terms of nonlinear, dispersive, and dissipative effects. We completed a comprehensive study of coplanar waveguides made from high-temperature superconducting thin-film YBa{sub 2}Cu{sub 3}O{sub 7{minus}{delta}} electrodes on nonlinear dielectric single-crystal SrTiO{sub 3} substrates. By using parameters determined from small-signal (linear) transmission characteristics of the waveguides, we develop a model equation that successfully predicts and describes large-signal (nonlinear) behavior.
Nonlinear transmission spectroscopy with dual frequency combs
NASA Astrophysics Data System (ADS)
Glenn, Rachel; Mukamel, Shaul
2014-08-01
We show how two frequency combs E1, E2 can be used to measure single-photon, two-photon absorption (TPA), and Raman resonances in a molecule with three electronic bands, by detecting the radio frequency modulation of the nonlinear transmission signal. Some peaks are independent of the carrier frequency of the comb and others shift with that frequency and have a width close to the comb width. TPA and Raman resonances independent of the carrier frequency are selected by measuring the transmission signal ˜E12E22 and the single-photon resonances are selected by measuring the transmission signal ˜E13E2. Sinusoidal spectral phase shaping strongly affects the TPA, but not the Raman resonances.
Scalar discrete nonlinear multipoint boundary value problems
NASA Astrophysics Data System (ADS)
Rodriguez, Jesus; Taylor, Padraic
2007-06-01
In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].
Nonlinear transmission line based electron beam driver.
French, David M; Hoff, Brad W; Tang, Wilkin; Heidger, Susan; Allen-Flowers, Jordan; Shiffler, Don
2012-12-01
Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique. PMID:23277977
Nonlinear transmission line based electron beam driver
NASA Astrophysics Data System (ADS)
French, David M.; Hoff, Brad W.; Tang, Wilkin; Heidger, Susan; Allen-Flowers, Jordan; Shiffler, Don
2012-12-01
Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique.
Nonlinear transmission line based electron beam driver
French, David M.; Hoff, Brad W.; Tang Wilkin; Heidger, Susan; Shiffler, Don; Allen-Flowers, Jordan
2012-12-15
Gated field emission cathodes can provide short electron pulses without the requirement of laser systems or cathode heating required by photoemission or thermionic cathodes. The large electric field requirement for field emission to take place can be achieved by using a high aspect ratio cathode with a large field enhancement factor which reduces the voltage requirement for emission. In this paper, a cathode gate driver based on the output pulse train from a nonlinear transmission line is experimentally demonstrated. The application of the pulse train to a tufted carbon fiber field emission cathode generates short electron pulses. The pulses are approximately 2 ns in duration with emission currents of several mA, and the train contains up to 6 pulses at a frequency of 100 MHz. Particle-in-cell simulation is used to predict the characteristic of the current pulse train generated from a single carbon fiber field emission cathode using the same technique.
Nonlinearity management in fiber transmission systems with hybrid amplification
NASA Astrophysics Data System (ADS)
Ania-Castañón, J. D.; Nasieva, I. O.; Kurukitkoson, N.; Turitsyn, S. K.; Borsier, C.; Pincemin, E.
2004-04-01
Nonlinearity management in transmission lines with periodic dispersion compensation and hybrid Raman-Erbium doped fiber amplification is studied both analytically and numerically. Different transmission/compensating fiber pairs are considered, with particular focus on the SMF/DCF case.
Studies of Nonlinear Problems. I
DOE R&D Accomplishments Database
Fermi, E.; Pasta, J.; Ulam, S.
1955-05-01
A one-dimensional dynamical system of 64 particles with forces between neighbors containing nonlinear terms has been studied on the Los Alamos computer MANIAC I. The nonlinear terms considered are quadratic, cubic, and broken linear types. The results are analyzed into Fourier components and plotted as a function of time. The results show very little, if any, tendency toward equipartition of energy among the degrees of freedom.
Nonlinear system guidance in the presence of transmission zero dynamics
NASA Technical Reports Server (NTRS)
Meyer, G.; Hunt, L. R.; Su, R.
1995-01-01
An iterative procedure is proposed for computing the commanded state trajectories and controls that guide a possibly multiaxis, time-varying, nonlinear system with transmission zero dynamics through a given arbitrary sequence of control points. The procedure is initialized by the system inverse with the transmission zero effects nulled out. Then the 'steady state' solution of the perturbation model with the transmission zero dynamics intact is computed and used to correct the initial zero-free solution. Both time domain and frequency domain methods are presented for computing the steady state solutions of the possibly nonminimum phase transmission zero dynamics. The procedure is illustrated by means of linear and nonlinear examples.
Generalized spectral decomposition for stochastic nonlinear problems
Nouy, Anthony Le Maitre, Olivier P.
2009-01-10
We present an extension of the generalized spectral decomposition method for the resolution of nonlinear stochastic problems. The method consists in the construction of a reduced basis approximation of the Galerkin solution and is independent of the stochastic discretization selected (polynomial chaos, stochastic multi-element or multi-wavelets). Two algorithms are proposed for the sequential construction of the successive generalized spectral modes. They involve decoupled resolutions of a series of deterministic and low-dimensional stochastic problems. Compared to the classical Galerkin method, the algorithms allow for significant computational savings and require minor adaptations of the deterministic codes. The methodology is detailed and tested on two model problems, the one-dimensional steady viscous Burgers equation and a two-dimensional nonlinear diffusion problem. These examples demonstrate the effectiveness of the proposed algorithms which exhibit convergence rates with the number of modes essentially dependent on the spectrum of the stochastic solution but independent of the dimension of the stochastic approximation space.
Bounding solutions of geometrically nonlinear viscoelastic problems
NASA Technical Reports Server (NTRS)
Stubstad, J. M.; Simitses, G. J.
1986-01-01
Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.
Bounding solutions of geometrically nonlinear viscoelastic problems
NASA Technical Reports Server (NTRS)
Stubstad, J. M.; Simitses, G. J.
1985-01-01
Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.
Some Legal Problems of Satellite Transmission.
ERIC Educational Resources Information Center
Siebert, Fred S.
Now that the technical aspects of satellite transmission have been solved, there remain the more complex and difficult problems of maintaining both order in outer space and the rights of nations and individuals as these rights may be affected by broadcasts transmitted by satellite stations. These broadcasts, whether beamed to a ground station or…
Multigrid Methods for Nonlinear Problems: An Overview
Henson, V E
2002-12-23
Since their early application to elliptic partial differential equations, multigrid methods have been applied successfully to a large and growing class of problems, from elasticity and computational fluid dynamics to geodetics and molecular structures. Classical multigrid begins with a two-grid process. First, iterative relaxation is applied, whose effect is to smooth the error. Then a coarse-grid correction is applied, in which the smooth error is determined on a coarser grid. This error is interpolated to the fine grid and used to correct the fine-grid approximation. Applying this method recursively to solve the coarse-grid problem leads to multigrid. The coarse-grid correction works because the residual equation is linear. But this is not the case for nonlinear problems, and different strategies must be employed. In this presentation we describe how to apply multigrid to nonlinear problems. There are two basic approaches. The first is to apply a linearization scheme, such as the Newton's method, and to employ multigrid for the solution of the Jacobian system in each iteration. The second is to apply multigrid directly to the nonlinear problem by employing the so-called Full Approximation Scheme (FAS). In FAS a nonlinear iteration is applied to smooth the error. The full equation is solved on the coarse grid, after which the coarse-grid error is extracted from the solution. This correction is then interpolated and applied to the fine grid approximation. We describe these methods in detail, and present numerical experiments that indicate the efficacy of them.
Nonlinear transmission through a tapered fiber in rubidium vapor
Hendrickson, S. M.; Pittman, T. B.; Franson, J. D.
2009-02-15
Subwavelength-diameter tapered optical fibers surrounded by rubidium vapor can undergo a substantial decrease in transmission at high atomic densities due to the accumulation of rubidium atoms on the surface of the fiber. Here we demonstrate the ability to control these changes in transmission using light guided within the taper. We observe transmission through a tapered fiber that is a nonlinear function of the incident power. This effect can also allow a strong control beam to change the transmission of a weak probe beam.
Nonlinear waves propagating in the electrical transmission line
NASA Astrophysics Data System (ADS)
Duan, W.-S.
2004-04-01
A coupled Zakharov-Kuznetsov (ZK) equation is derived for a nonlinear transmission line in which the nonlinear capacitance C is of a general form C = C0(1 + k1V + k2V2 + ...). For a solitary-wave solution of the ZK equation, there is an instability region which is given numerically in this paper. It is in agreement with the analytical results for special cases.
Variational approach to stochastic nonlinear problems
Phythian, R.; Curtis, W.D.
1986-03-01
A variational principle is formulated which enables the mean value and higher moments of the solution of a stochastic nonlinear differential equation to be expressed as stationary values of certain quantities. Approximations are generated by using suitable trial functions in this variational principle and some of these are investigated numerically for the case of a Bernoulli oscillator driven by white noise. Comparison with exact data available for this system show that the variational approach to such problems can be quite effective.
On the transmissibilities of nonlinear vibration isolation system
NASA Astrophysics Data System (ADS)
Lu, Zeqi; Brennan, Michael J.; Chen, Li-Qun
2016-08-01
Transmissibility is a key parameter to quantify the effectiveness of a vibration isolation system. Under harmonic excitation, the force transmissibility of a linear vibration isolation system is defined as the ratio between the amplitude of the force transmitted to the host structure and the excitation force amplitude, and the displacement transmissibility is the ratio between the displacement amplitude of the payload and that of the base. For a nonlinear vibration isolation system, the force or the displacement responses usually have more frequency components than the excitation. For a harmonic excitation, the response may be periodic, quasi-periodic or chaotic. Therefore, the amplitude ratio cannot well define the transmissibility. The root-mean-square ratio of the response to the excitation is suggested to define the transmissibility. The significance of the modified transmissibility is highlighted in a nonlinear two-stage vibration isolation system consisting of two linear spring connected linear vibration isolators with two additional horizontal linear springs. Harmonic balance method (HBM) is applied to determine the responses with the fundamental and third harmonic. Numerical simulations reveal that chaos may occur in the responses. In both cases, the modified transmissibility works while the original definition cannot be applied to chaotic response.
OPEN PROBLEM: Some nonlinear challenges in biology
NASA Astrophysics Data System (ADS)
Mosconi, Francesco; Julou, Thomas; Desprat, Nicolas; Sinha, Deepak Kumar; Allemand, Jean-François; Croquette, Vincent; Bensimon, David
2008-08-01
Driven by a deluge of data, biology is undergoing a transition to a more quantitative science. Making sense of the data, building new models, asking the right questions and designing smart experiments to answer them are becoming ever more relevant. In this endeavour, nonlinear approaches can play a fundamental role. The biochemical reactions that underlie life are very often nonlinear. The functional features exhibited by biological systems at all levels (from the activity of an enzyme to the organization of a colony of ants, via the development of an organism or a functional module like the one responsible for chemotaxis in bacteria) are dynamically robust. They are often unaffected by order of magnitude variations in the dynamical parameters, in the number or concentrations of actors (molecules, cells, organisms) or external inputs (food, temperature, pH, etc). This type of structural robustness is also a common feature of nonlinear systems, exemplified by the fundamental role played by dynamical fixed points and attractors and by the use of generic equations (logistic map, Fisher-Kolmogorov equation, the Stefan problem, etc.) in the study of a plethora of nonlinear phenomena. However, biological systems differ from these examples in two important ways: the intrinsic stochasticity arising from the often very small number of actors and the role played by evolution. On an evolutionary time scale, nothing in biology is frozen. The systems observed today have evolved from solutions adopted in the past and they will have to adapt in response to future conditions. The evolvability of biological system uniquely characterizes them and is central to biology. As the great biologist T Dobzhansky once wrote: 'nothing in biology makes sense except in the light of evolution'.
Kurtosis Approach to Solution of a Nonlinear ICA Problem
NASA Technical Reports Server (NTRS)
Duong, Vu; Stubberud, Allen
2009-01-01
An algorithm for solving a particular nonlinear independent-component-analysis (ICA) problem, that differs from prior algorithms for solving the same problem, has been devised. The problem in question of a type known in the art as a post nonlinear mixing problem is a useful approximation of the problem posed by the mixing and subsequent nonlinear distortion of sensory signals that occur in diverse scientific and engineering instrumentation systems.
Nonlinearities of biopolymer gels increase the range of force transmission.
Xu, Xinpeng; Safran, Samuel A
2015-09-01
We present a model of biopolymer gels that includes two types of elastic nonlinearities, stiffening under extension and softening (due to buckling) under compression, to predict the elastic anisotropy induced by both external as well as internal (e.g., due to cell contractility) stresses in biopolymer gels. We show how the stretch-induced anisotropy and the strain-stiffening nonlinearity increase both the amplitude and power-law range of transmission of internal, contractile, cellular forces, and relate this to recent experiments. PMID:26465519
Nonlinearities of biopolymer gels increase the range of force transmission
NASA Astrophysics Data System (ADS)
Xu, Xinpeng; Safran, Samuel A.
2015-09-01
We present a model of biopolymer gels that includes two types of elastic nonlinearities, stiffening under extension and softening (due to buckling) under compression, to predict the elastic anisotropy induced by both external as well as internal (e.g., due to cell contractility) stresses in biopolymer gels. We show how the stretch-induced anisotropy and the strain-stiffening nonlinearity increase both the amplitude and power-law range of transmission of internal, contractile, cellular forces, and relate this to recent experiments.
Soliton transmission in optical fibers with loss and saturable nonlinearity
NASA Astrophysics Data System (ADS)
Aicklen, Gregory H.; Tamil, Lakshman S.
1996-09-01
Optical solitons propagating in media exhibiting saturable nonlinearity offer advantages over Kerr-medium solitons for transmission over large distances through optical fibers with loss. Soliton pulses in saturable media offer greater energy for a given peak power, and upper-branch solitons decrease in width with distance traveled. These properties result in pulses that remain distinct and detectable for greater distances than Kerr-medium solitons do with the same peak power. .
Studies in nonlinear problems of energy
Matkowsky, B.J.
1992-07-01
Emphasis has been on combustion and flame propagation. The research program was on modeling, analysis and computation of combustion phenomena, with emphasis on transition from laminar to turbulent combustion. Nonlinear dynamics and pattern formation were investigated in the transition. Stability of combustion waves, and transitions to complex waves are described. Combustion waves possess large activation energies, so that chemical reactions are significant only in thin layers, or reaction zones. In limit of infinite activation energy, the zones shrink to moving surfaces, (fronts) which must be found during the analysis, so that (moving free boundary problems). The studies are carried out for limiting case with fronts, while the numerical studies are carried out for finite, though large, activation energy. Accurate resolution of the solution in the reaction zones is essential, otherwise false predictions of dynamics are possible. Since the the reaction zones move, adaptive pseudo-spectral methods were developed. The approach is based on a synergism of analytical and computational methods. The numerical computations build on and extend the analytical information. Furthermore, analytical solutions serve as benchmarks for testing the accuracy of the computation. Finally, ideas from analysis (singular perturbation theory) have induced new approaches to computations. The computational results suggest new analysis to be considered. Among the recent interesting results, was spatio-temporal chaos in combustion. One goal is extension of the adaptive pseudo-spectral methods to adaptive domain decomposition methods. Efforts have begun to develop such methods for problems with multiple reaction zones, corresponding to problems with more complex, and more realistic chemistry. Other topics included stochastics, oscillators, Rysteretic Josephson junctions, DC SQUID, Markov jumps, laser with saturable absorber, chemical physics, Brownian movement, combustion synthesis, etc.
Social Emotional Optimization Algorithm for Nonlinear Constrained Optimization Problems
NASA Astrophysics Data System (ADS)
Xu, Yuechun; Cui, Zhihua; Zeng, Jianchao
Nonlinear programming problem is one important branch in operational research, and has been successfully applied to various real-life problems. In this paper, a new approach called Social emotional optimization algorithm (SEOA) is used to solve this problem which is a new swarm intelligent technique by simulating the human behavior guided by emotion. Simulation results show that the social emotional optimization algorithm proposed in this paper is effective and efficiency for the nonlinear constrained programming problems.
Multisplitting for linear, least squares and nonlinear problems
Renaut, R.
1996-12-31
In earlier work, presented at the 1994 Iterative Methods meeting, a multisplitting (MS) method of block relaxation type was utilized for the solution of the least squares problem, and nonlinear unconstrained problems. This talk will focus on recent developments of the general approach and represents joint work both with Andreas Frommer, University of Wupertal for the linear problems and with Hans Mittelmann, Arizona State University for the nonlinear problems.
A Signal Transmission Technique for Stability Analysis of Multivariable Non-Linear Control Systems
NASA Technical Reports Server (NTRS)
Jackson, Mark; Zimpfer, Doug; Adams, Neil; Lindsey, K. L. (Technical Monitor)
2000-01-01
Among the difficulties associated with multivariable, non-linear control systems is the problem of assessing closed-loop stability. Of particular interest is the class of non-linear systems controlled with on/off actuators, such as spacecraft thrusters or electrical relays. With such systems, standard describing function techniques are typically too conservative, and time-domain simulation analysis is prohibitively extensive, This paper presents an open-loop analysis technique for this class of non-linear systems. The technique is centered around an innovative use of multivariable signal transmission theory to quantify the plant response to worst case control commands. The technique has been applied to assess stability of thruster controlled flexible space structures. Examples are provided for Space Shuttle attitude control with attached flexible payloads.
Minimax theory for a class of nonlinear statistical inverse problems
NASA Astrophysics Data System (ADS)
Ray, Kolyan; Schmidt-Hieber, Johannes
2016-06-01
We study a class of statistical inverse problems with nonlinear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the nonlinearity. This reduces the initial nonlinear problem to a linear inverse problem with deterministic noise, which is then solved in a second step. The noise reduction step is based on wavelet thresholding and is shown to be minimax optimal (up to logarithmic factors) in a pointwise function-dependent sense. Our analysis is based on a modified notion of Hölder smoothness scales that are natural in this setting.
Nonlinear transmission of CO2 laser radiation by graphene
NASA Astrophysics Data System (ADS)
Sorochenko, V. R.; Obraztsova, Elena D.; Rusakov, P. S.; Rybin, M. G.
2012-10-01
The nonlinear transmission of multilayer (~12 layers) graphene at the wavelength λ ~ 10 μm is measured for the first time. The absorption saturation intensity in graphene (~330 kW cm-2) and the ablation threshold of its outer layers (~1 MW cm-2, 0.11 J cm-2) under action of a CO2 laser pulse with a duration of 70 — 85 ns at λ = 10.55 μm are determined. The residual absorption of graphene at its partial saturation was 48 % of the initial value. This is significantly smaller than the value measured previously for samples with a close number of layers at λ = 1.55 μm (92.3 % — 93.8 %). It is shown that the ablation threshold of two graphene layers adjacent to the BaF2 substrate (after successive ablation of outer layers) exceeds 0.27 J cm-2.
Nonlinear band gap transmission in optical waveguide arrays.
Khomeriki, Ramaz
2004-02-13
The effect of nonlinear transmission in coupled optical waveguide arrays is theoretically investigated and a realistic experimental setup is suggested. The beam is injected in a single boundary waveguide, linear refractive index of which (n(0)) is larger than refractive indexes (n) of other identical waveguides in the array. Particularly, the effect holds if omega(n(0)-n)/c>2Q, where Q is a linear coupling constant between array waveguides, omega is a carrier wave frequency, and c is a light velocity. Numerical experiments show that the energy transfers from the boundary waveguide to the waveguide array above a certain threshold intensity of the injected beam. This effect is due to the creation and the propagation of gap solitons in full analogy with a similar phenomenon in sine-Gordon lattice [Phys. Rev. Lett. 89, 134102 (2002)
Monolithic high voltage nonlinear transmission line fabrication process
Cooper, Gregory A.
1994-01-01
A process for fabricating sequential inductors and varactor diodes of a monolithic, high voltage, nonlinear, transmission line in GaAs is disclosed. An epitaxially grown laminate is produced by applying a low doped active n-type GaAs layer to an n-plus type GaAs substrate. A heavily doped p-type GaAs layer is applied to the active n-type layer and a heavily doped n-type GaAs layer is applied to the p-type layer. Ohmic contacts are applied to the heavily doped n-type layer where diodes are desired. Multiple layers are then either etched away or Oxygen ion implanted to isolate individual varactor diodes. An insulator is applied between the diodes and a conductive/inductive layer is thereafter applied on top of the insulator layer to complete the process.
Monolithic high voltage nonlinear transmission line fabrication process
Cooper, G.A.
1994-10-04
A process for fabricating sequential inductors and varistor diodes of a monolithic, high voltage, nonlinear, transmission line in GaAs is disclosed. An epitaxially grown laminate is produced by applying a low doped active n-type GaAs layer to an n-plus type GaAs substrate. A heavily doped p-type GaAs layer is applied to the active n-type layer and a heavily doped n-type GaAs layer is applied to the p-type layer. Ohmic contacts are applied to the heavily doped n-type layer where diodes are desired. Multiple layers are then either etched away or Oxygen ion implanted to isolate individual varistor diodes. An insulator is applied between the diodes and a conductive/inductive layer is thereafter applied on top of the insulator layer to complete the process. 6 figs.
Non-conforming finite element methods for transmission eigenvalue problem
NASA Astrophysics Data System (ADS)
Yang, Yidu; Han, Jiayu; Bi, Hai
2016-08-01
The transmission eigenvalue problem is an important and challenging topic arising in the inverse scattering theory. In this paper, for the Helmholtz transmission eigenvalue problem, we give a weak formulation which is a nonselfadjoint linear eigenvalue problem. Based on the weak formulation, we first discuss the non-conforming finite element approximation, and prove the error estimates of the discrete eigenvalues obtained by the Adini element, Morley-Zienkiewicz element, modified-Zienkiewicz element et. al. And we report some numerical examples to validate the efficiency of our approach for solving transmission eigenvalue problem.
A Unified Approach for Solving Nonlinear Regular Perturbation Problems
ERIC Educational Resources Information Center
Khuri, S. A.
2008-01-01
This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…
Nonlinear Transient Problems Using Structure Compatible Heat Transfer Code
NASA Technical Reports Server (NTRS)
Hou, Gene
2000-01-01
The report documents the recent effort to enhance a transient linear heat transfer code so as to solve nonlinear problems. The linear heat transfer code was originally developed by Dr. Kim Bey of NASA Largely and called the Structure-Compatible Heat Transfer (SCHT) code. The report includes four parts. The first part outlines the formulation of the heat transfer problem of concern. The second and the third parts give detailed procedures to construct the nonlinear finite element equations and the required Jacobian matrices for the nonlinear iterative method, Newton-Raphson method. The final part summarizes the results of the numerical experiments on the newly enhanced SCHT code.
Parabolic Perturbation of a Nonlinear Hyperbolic Problem Arising in Physiology
NASA Astrophysics Data System (ADS)
Colli, P.; Grasselli, M.
We study a transport-diffusion initial value problem where the diffusion codlicient is "small" and the transport coefficient is a time function depending on the solution in a nonlinear and nonlocal way. We show the existence and the uniqueness of a weak solution of this problem. Moreover we discuss its asymptotic behaviour as the diffusion coefficient goes to zero, obtaining a well-posed first-order nonlinear hyperbolic problem. These problems arise from mathematical models of muscle contraction in the framework of the sliding filament theory.
Explanation of the Inverse Doppler Effect Observed in Nonlinear Transmission Lines
Kozyrev, Alexander B.; Weide, Daniel W. van der
2005-05-27
The theory of the inverse Doppler effect recently observed in magnetic nonlinear transmission lines is developed. We explain the crucial role of the backward spatial harmonic in the occurrence of an inverse Doppler effect and draw analogies of the magnetic nonlinear transmission line to the backward wave oscillator.
Studies in nonlinear problems of energy
Matkowsky, B.J.
1990-11-01
We carry out a research program with primary emphasis on the applications of Bifurcation and Stability Theory to Problems of energy, with specific emphasis on Problems of Combustion and Flame Propagation. In particular we consider the problem of transition from laminar to turbulent flame propagation. A great deal of progress has been made in our investigations. More than one hundred and thirty papers citing this project have been prepared for publication in technical journals. A list of the papers, including abstracts for each paper, is appended to this report.
NASA Astrophysics Data System (ADS)
Reale, D. V.; Parson, J. M.; Neuber, A. A.; Dickens, J. C.; Mankowski, J. J.
2016-03-01
A stripline gyromagnetic nonlinear transmission line (NLTL) was constructed out of yttrium iron garnet ferrite and tested at charge voltages of 35 kV-55 kV with bias fields ranging from 10 kA/m to 20 kA/m. Typically, high power gyromagnetic NLTLs are constructed in a coaxial geometry. While this approach has many advantages, including a uniform transverse electromagnetic (TEM) mode, simple interconnection between components, and the ability to use oil or pressurized gas as an insulator, the coaxial implementation suffers from complexity of construction, especially when using a solid insulator. By moving to a simpler transmission line geometry, NLTLs can be constructed more easily and arrayed on a single substrate. This work represents a first step in exploring the suitability of various transmission line structures, such as microstrips and coplanar waveguides. The resulting high power microwave (HPM) source operates in ultra high frequency (UHF) band with an average bandwidth of 40.1% and peak rf power from 2 MW to 12.7 MW.
Reale, D V; Parson, J M; Neuber, A A; Dickens, J C; Mankowski, J J
2016-03-01
A stripline gyromagnetic nonlinear transmission line (NLTL) was constructed out of yttrium iron garnet ferrite and tested at charge voltages of 35 kV-55 kV with bias fields ranging from 10 kA/m to 20 kA/m. Typically, high power gyromagnetic NLTLs are constructed in a coaxial geometry. While this approach has many advantages, including a uniform transverse electromagnetic (TEM) mode, simple interconnection between components, and the ability to use oil or pressurized gas as an insulator, the coaxial implementation suffers from complexity of construction, especially when using a solid insulator. By moving to a simpler transmission line geometry, NLTLs can be constructed more easily and arrayed on a single substrate. This work represents a first step in exploring the suitability of various transmission line structures, such as microstrips and coplanar waveguides. The resulting high power microwave (HPM) source operates in ultra high frequency (UHF) band with an average bandwidth of 40.1% and peak rf power from 2 MW to 12.7 MW. PMID:27036802
On the Dirichlet problem for a nonlinear elliptic equation
NASA Astrophysics Data System (ADS)
Egorov, Yu V.
2015-04-01
We prove the existence of an infinite set of solutions to the Dirichlet problem for a nonlinear elliptic equation of the second order. Such a problem for a nonlinear elliptic equation with Laplace operator was studied earlier by Krasnosel'skii, Bahri, Berestycki, Lions, Rabinowitz, Struwe and others. We study the spectrum of this problem and prove the weak convergence to 0 of the sequence of normed eigenfunctions. Moreover, we obtain some estimates for the 'Fourier coefficients' of functions in W^1p,0(Ω). This allows us to improve the preceding results. Bibliography: 8 titles.
On the Inverse Problems of Nonlinear Acoustics and Acoustic Turbulence
NASA Astrophysics Data System (ADS)
Gurbatov, S. N.; Rudenko, O. V.
2015-12-01
We consider the problem of retrieval of the radiated acoustic signal parameters from the measured wave field in some cross section of the nonlinear medium. The possibilities of solving regular and statistical inverse problems are discussed on the basis of the solution of the Burgers equation for zero and infinitesimal viscosities.
On a Highly Nonlinear Self-Obstacle Optimal Control Problem
Di Donato, Daniela; Mugnai, Dimitri
2015-10-15
We consider a non-quadratic optimal control problem associated to a nonlinear elliptic variational inequality, where the obstacle is the control itself. We show that, fixed a desired profile, there exists an optimal solution which is not far from it. Detailed characterizations of the optimal solution are given, also in terms of approximating problems.
Differential eigenvalue problems in which the parameter appears nonlinearly
NASA Technical Reports Server (NTRS)
Bridges, T. J.; Morris, P. J.
1984-01-01
Several methods are examined for determining the eigenvalues of a system of equations in which the parameter appears nonlinearly. The equations are the result of the discretization of differential eigenvalue problems using a finite Chebyshev series. Two global methods are considered which determine the spectrum of eigenvalues without an initial estimate. A local iteration scheme with cubic convergence is presented. Calculations are performed for a model second order differential problem and the Orr-Sommerfeld problem for plane Poiseuille flow.
A reduced basis Landweber method for nonlinear inverse problems
NASA Astrophysics Data System (ADS)
Garmatter, Dominik; Haasdonk, Bernard; Harrach, Bastian
2016-03-01
We consider parameter identification problems in parametrized partial differential equations (PDEs). These lead to nonlinear ill-posed inverse problems. One way of solving them is using iterative regularization methods, which typically require numerous amounts of forward solutions during the solution process. In this article we consider the nonlinear Landweber method and couple it with the reduced basis method as a model order reduction technique in order to reduce the overall computational time. In particular, we consider PDEs with a high-dimensional parameter space, which are known to pose difficulties in the context of reduced basis methods. We present a new method that is able to handle such high-dimensional parameter spaces by combining the nonlinear Landweber method with adaptive online reduced basis updates. It is then applied to the inverse problem of reconstructing the conductivity in the stationary heat equation.
Finite element methods for nonlinear elastostatic problems in rubber elasticity
NASA Technical Reports Server (NTRS)
Oden, J. T.; Becker, E. B.; Miller, T. H.; Endo, T.; Pires, E. B.
1983-01-01
A number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined. Several different finite element schemes are discussed. These include the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations. Algorithms for the analysis of limit point behavior and bifurcations are described and the results of several numerical experiments are presented. In addition, a brief survey of some recent work on modelling contact and friction in elasticity problems is given. These results pertain to the use of new nonlocal and nonlinear friction laws.
Frequency dependence of the nonlinear response in YBa2Cu3O7-x transmission lines
NASA Astrophysics Data System (ADS)
Mateu, Jordi; Booth, James C.; Moeckly, Brian H.
2007-01-01
The authors evaluate the frequency dependence of the nonlinear response in high-temperature superconductor YBa2Cu3O7-x thin films by simultaneously measuring the nonlinear intermodulation products and harmonic generation in broadband superconducting transmission lines at 76K. The frequencies of the two-tone incident signal are set to produce spurious signals from 1to21GHz. They extract a nonlinear term ∣ΔR2+jωΔL2∣ by applying a model of spurious signal generation in superconducting transmission lines to their measurement results. They found that this nonlinear term follows a linear dependence on frequency, indicating a dominant contribution of the nonlinear inductance ΔL2 over the nonlinear resistance ΔR2, (ωΔL2≫ΔR2), for the superconducting nonlinear response.
Multiply scaled constrained nonlinear equation solvers. [for nonlinear heat conduction problems
NASA Technical Reports Server (NTRS)
Padovan, Joe; Krishna, Lala
1986-01-01
To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.
The problem of applying information theory to efficient image transmission.
NASA Technical Reports Server (NTRS)
Sakrison, D. J.
1973-01-01
The main ideas of Shannon's (1948, 1960) theory of source encoding with a fidelity constraint, more commonly known as rate distortion theory, are summarized. The theory was specifically intended to provide a theoretical basis for efficient transmission of information such as images. What the theory has to contribute to the problem is demonstrated. Difficulties that impeded application of the theory to image transmission, and current efforts to solve these difficulties are discussed.
Particle swarm optimization for complex nonlinear optimization problems
NASA Astrophysics Data System (ADS)
Alexandridis, Alex; Famelis, Ioannis Th.; Tsitouras, Charalambos
2016-06-01
This work presents the application of a technique belonging to evolutionary computation, namely particle swarm optimization (PSO), to complex nonlinear optimization problems. To be more specific, a PSO optimizer is setup and applied to the derivation of Runge-Kutta pairs for the numerical solution of initial value problems. The effect of critical PSO operational parameters on the performance of the proposed scheme is thoroughly investigated.
Position-momentum-entangled photon pairs in nonlinear waveguides and transmission lines
NASA Astrophysics Data System (ADS)
Sherkunov, Y.; Whittaker, David M.; Fal'ko, Vladimir
2016-04-01
We analyze the correlation properties of light in nonlinear waveguides and transmission lines, predict the position-momentum realization of the Einstein-Podolsky-Rosen paradox for photon pairs in Kerr-type nonlinear photonic circuits, and we show how two-photon entangled states can be generated and detected.
Time domain adjoint sensitivity analysis of electromagnetic problems with nonlinear media.
Bakr, Mohamed H; Ahmed, Osman S; El Sherif, Mohamed H; Nomura, Tsuyoshi
2014-05-01
In this paper, we propose a theory for wideband adjoint sensitivity analysis of problems with nonlinear media. We show that the sensitivities of the desired response with respect to all shape and material parameters are obtained through one extra adjoint simulation. Unlike linear problems, the system matrices of this adjoint simulation are time varying. Their values are determined during the original simulation. The proposed theory exploits the time-domain transmission line modeling (TLM) and provides an efficient AVM approach for sensitivity analysis of general time domain objective functions. The theory has been illustrated through a number of examples. PMID:24921783
Nonlinear eigenvalue problems in Density Functional Theory calculations
Fattebert, J
2009-08-28
Developed in the 1960's by W. Kohn and coauthors, Density Functional Theory (DFT) is a very popular quantum model for First-Principles simulations in chemistry and material sciences. It allows calculations of systems made of hundreds of atoms. Indeed DFT reduces the 3N-dimensional Schroedinger electronic structure problem to the search for a ground state electronic density in 3D. In practice it leads to the search for N electronic wave functions solutions of an energy minimization problem in 3D, or equivalently the solution of an eigenvalue problem with a non-linear operator.
Numerical solution of control problems governed by nonlinear differential equations
Heinkenschloss, M.
1994-12-31
In this presentation the author investigates an iterative method for the solution of optimal control problems. These problems are formulated as constrained optimization problems with constraints arising from the state equation and in the form of bound constraints on the control. The method for the solution of these problems uses the special structure of the problem arising from the bound constraint and the state equation. It is derived from SQP methods and projected Newton methods and combines the advantages of both methods. The bound constraint is satisfied by all iterates using a projection, the nonlinear state equation is satisfied in the limit. Only a linearized state equation has to be solved in every iteration. The solution of the linearized problems are done using multilevel methods and GMRES.
Nonlinear transmission properties in bacteriorhodopsin-embedded photonic crystal
NASA Astrophysics Data System (ADS)
Okada-Shudo, Yoshiko; Ishihara, Teruya
2003-11-01
Transmission spectra and photoinduced transmission change are observed in periodic waveguide which consist of a quartz grating substrate and a thin protein film of bacteriorhodopsin. We propose a scheme to achieve all optical switching using the photoinduced refractive index change of bacteriorhodopsin.
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1984-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1982-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Discrete Element Method Simulation of Nonlinear Viscoelastic Stress Wave Problems
NASA Astrophysics Data System (ADS)
Tang, Zhiping; Horie, Y.; Wang, Wenqiang
2002-07-01
A DEM(Discrete Element Method) simulation of nonlinear viscoelastic stress wave problems is carried out. The interaction forces among elements are described using a model in which neighbor elements are linked by a nonlinear spring and a certain number of Maxwell components in parallel. By making use of exponential relaxation moduli, it is shown that numerical computation of the convolution integral does not require storing and repeatedly calculating strain history, so that the computational cost is dramatically reduced. To validate the viscoelastic DM2 code1, stress wave propagation in a Maxwell rod with one end subjected to a constant stress loading is simulated. Results excellently fit those from the characteristics calculation. The code is then used to investigate the problem of meso-scale damage in a plastic-bonded explosive under shock loading. Results not only show "compression damage", but also reveal a complex damage evolution. They demonstrate a unique capability of DEM in modeling heterogeneous materials.
Discrete Element Method Simulation of Nonlinear Viscoelastic Stress Wave Problems
NASA Astrophysics Data System (ADS)
Wang, Wenqiang; Tang, Zhiping; Horie, Y.
2002-07-01
A DEM(Discrete Element Method) simulation of nonlinear viscoelastic stress wave problems is carried out. The interaction forces among elements are described using a model in which neighbor elements are linked by a nonlinear spring and a certain number of Maxwell components in parallel. By making use of exponential relaxation moduli, it is shown that numerical computation of the convolution integral does not require storing and repeatedly calculating strain history, so that the computational cost is dramatically reduced. To validate the viscoelastic DM2 code[1], stress wave propagation in a Maxwell rod with one end subjected to a constant stress loading is simulated. Results excellently fit those from the characteristics calculation. The code is then used to investigate the problem of meso-scale damage in a plastic-bonded explosive under shock loading. Results not only show "compression damage", but also reveal a complex damage evolution. They demonstrate a unique capability of DEM in modeling heterogeneous materials.
NASA Astrophysics Data System (ADS)
Cao, Wenhua
2016-05-01
Predispersion for reduction of intrachannel nonlinear impairments in quasi-linear strongly dispersion-managed transmission system is analyzed in detail by numerical simulations. We show that for moderate amount of predispersion there is an optimal value at which reduction of the nonlinear impairments can be obtained, which is consistent with previous well-known predictions. However, we found that much better transmission performance than that of the previous predictions can be obtained if predispersion is increased to some extent. For large predispersion, the nonlinear impairments reduce monotonically with increasing predispersion and then they tend to be stabilized when predispersion is further increased. Thus, transmission performance can be efficiently improved by inserting a high-dispersive element, such as a chirped fiber bragg grating (CFBG), at the input end of the transmission link to broaden the signal pulses while, at the output end, using another CFBG with the opposite dispersion to recompress the signal.
On the Cauchy problem for strongly nonlinear intense wave groups
NASA Astrophysics Data System (ADS)
Slunyaev, Alexey
2015-04-01
Stable long-living nonlinear groups of gravity water waves (very steep and very short envelope solitons) were first observed in numerical simulations [1, 2] and then - in laboratory conditions [3]. In [2] their interaction was shown to be almost elastic in some (but not all) situations. Therefore the Cauchy problem for localized wave groups beyond the weakly nonlinear assumption is of interest. In general, the formation of a few solitary wave groups from the initial condition may take place [4]. We have focused on the unidentified reason, why some experimental tests of solitary wave groups in [3] were not successful (while other runs with slightly different experimental parameters were successful). In this paper we consider the initial problem, when the initial condition is taken in the form of a scaled intense envelope soliton of the nonlinear Schrodinger equation, and is simulated by means of the fully nonlinear code of potential Euler equations. The result of the long-term evolution (which is generally represented by a solitary wave group and smaller scale waves) is compared with the prediction of the weakly nonlinear theory. We show reasonable agreement between the weakly nonlinear theory and the strongly nonlinear simulations. In particular, a 10% decrease of the initial perturbation results in 20% smaller amplitude of the eventual envelope soliton. This fact explains the failure of reproduction of envelope solitons in some experimental tests in the finite-depth flume [3]. The solution of the nonlinear Schrodinger equation for finite-depth water may be transformed to the infinite-depth solution with reduced amplitude. [1] A.I. Dyachenko, V.E. Zakharov, On the formation of freak waves on the surface of deep water. J. Exp. Theor. Phys. Lett. 88, 307-311 (2008). [2] A.V. Slunyaev, Numerical simulation of "limiting" envelope solitons of gravity waves on deep water. JETP 109, 676-686 (2009). [3] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and
Nonlinear optical transmission in VOx nanotubes and VOx nanotube composites
NASA Astrophysics Data System (ADS)
Xu, J.-F.; Czerw, R.; Webster, S.; Carroll, D. L.; Ballato, J.; Nesper, R.
2002-08-01
Optical-limiting behavior of vanadium oxide nanotubes is characterized for the visible and infrared spectral ranges using 8 ns pulses from a Nd:YAG laser with an f/40 optical system. Vanadium oxide nanotube dispersions were investigated in both water suspensions and embedded in solid polymethyl methacrylate films. In each case, these nanotubes exhibit strong optical-limiting at 532 nm (in comparison to carbon nanotubes); however, no nonlinear behavior is observed for 1064 nm. This suggests that a two photon or excited state absorption mechanism is responsible for the observed nonlinearity.
Kumar, Shiva; Liu, Ling
2007-03-01
An analytical expression for the variance of nonlinear phase noise for a quasi-linear system using the midpoint optical phase conjugation (OPC) is obtained. It is shown that the the system with OPC and dispersion inversion (DI) can exactly cancel the nonlinear phase noise up to the first order in nonlinear coefficient if the amplifier and the end point of the system are equidistant from the OPC. It is found that the nonlinear phase noise variance of the midpoint phase-conjugated optical transmission system with DI is smaller than that of the system without DI. PMID:19532453
NASA Astrophysics Data System (ADS)
McGurn, Arthur R.
2013-10-01
The barrier transmission characteristics of a one-dimensional chain of optically linear split-ring resonators (SRRs) containing a barrier composed of optically nonlinear split-ring resonators are studied. (This is an analogy to the quantum mechanical problem of the resonant transmission of a particle through a finite barrier potential.) The SRRs are idealized as inductor-resistor-capacitor-equivalent resonator circuits where the capacitance is either from a linear dielectric medium (optically linear SRRs) or from a Kerr-type nonlinear dielectric medium (optically nonlinear SRRs). The SRRs are arrayed in a one-dimensional chain and interact with one another through weak nearest-neighbor mutually inductive couplings. The transmission maxima of the SRR barrier problem are studied as they are located in a two-dimensional parameter space characterizing the linear mutually inductive coupling and the nonlinear Kerr dielectric of the SRRs of the barrier. The result is a two-dimensional map giving the conditions for the existence of the resonant-barrier modes that are excited in the transmission process. The various lines of transmission maxima in the two-dimensional plot are associated with different types of resonant excitations in the barrier. The map is similar to one recently made in McGurn [Phys. Rev. BPRBMDO0163-182910.1103/PhysRevB.77.115105 77, 115105 (2008)] for the resonant-transmission modes of a nonlinear barrier in a photonic crystal waveguide. The SRR problem, however, is quite different from the photonic crystal problem as the nonlinear difference equations of the two systems are different in the nature of their nonlinear interactions. Consequently, the results for the two systems are briefly compared. The transmission maxima of the SRR system occur along lines in the two-dimensional plot, which are associated with modes resonantly excited in the barrier. These lines of resonant modes either originate as a simple evolution from the resonant modes of the
Application of bifurcation methods to nonlinear flight dynamics problems
NASA Astrophysics Data System (ADS)
Goman, M. G.; Zagainov, G. I.; Khramtsovsky, A. V.
Applications of global stability and bifurcational analysis methods are presented for different nonlinear flight dynamics problems, such as roll-coupling, stall, spin, etc. Based on the results for different real aircraft, F-4, F-14, F-15, High Incidence Research Model, (HIRM), the general methods developed by many authors are presented. The outline of basic concepts and methods from dynamcal system theory are also introduced.
Parallel computation of three-dimensional nonlinear magnetostatic problems.
Levine, D.; Gropp, W.; Forsman, K.; Kettunen, L.; Mathematics and Computer Science; Tampere Univ. of Tech.
1999-02-01
We describe a general-purpose parallel electromagnetic code for computing accurate solutions to large computationally demanding, 3D, nonlinear magnetostatic problems. The code, CORAL, is based on a volume integral equation formulation. Using an IBM SP parallel computer and iterative solution methods, we successfully solved the dense linear systems inherent in such formulations. A key component of our work was the use of the PETSc library, which provides parallel portability and access to the latest linear algebra solution technology.
Nonlinear Stefan problem with convective boundary condition in Storm's materials
NASA Astrophysics Data System (ADS)
Briozzo, Adriana C.; Natale, Maria F.
2016-04-01
We consider a nonlinear one-dimensional Stefan problem for a semi-infinite material x > 0, with phase change temperature T f . We assume that the heat capacity and the thermal conductivity satisfy a Storm's condition, and we assume a convective boundary condition at the fixed face x = 0. A unique explicit solution of similarity type is obtained. Moreover, asymptotic behavior of the solution when {h→ + ∞} is studied.
Solving nonlinear equality constrained multiobjective optimization problems using neural networks.
Mestari, Mohammed; Benzirar, Mohammed; Saber, Nadia; Khouil, Meryem
2015-10-01
This paper develops a neural network architecture and a new processing method for solving in real time, the nonlinear equality constrained multiobjective optimization problem (NECMOP), where several nonlinear objective functions must be optimized in a conflicting situation. In this processing method, the NECMOP is converted to an equivalent scalar optimization problem (SOP). The SOP is then decomposed into several-separable subproblems processable in parallel and in a reasonable time by multiplexing switched capacitor circuits. The approach which we propose makes use of a decomposition-coordination principle that allows nonlinearity to be treated at a local level and where coordination is achieved through the use of Lagrange multipliers. The modularity and the regularity of the neural networks architecture herein proposed make it suitable for very large scale integration implementation. An application to the resolution of a physical problem is given to show that the approach used here possesses some advantages of the point of algorithmic view, and provides processes of resolution often simpler than the usual techniques. PMID:25647664
A convergence theory for a class of nonlinear programming problems.
NASA Technical Reports Server (NTRS)
Rauch, S. W.
1973-01-01
A recent convergence theory of Elkin concerning methods for unconstrained minimization is extended to a certain class of nonlinear programming problems. As in Elkin's original approach, the analysis of a variety of step-length algorithms is treated entirely separately from that of several direction algorithms. This allows for their combination into many different methods for solving the constrained problem. These include some of the methods of Rosen and Zoutendijk. We also extend the results of Topkis and Veinott to nonconvex sets and drop their requirement of the uniform feasibility of a subsequence of the search directions.
Application of nonlinear Krylov acceleration to radiative transfer problems
Till, A. T.; Adams, M. L.; Morel, J. E.
2013-07-01
The iterative solution technique used for radiative transfer is normally nested, with outer thermal iterations and inner transport iterations. We implement a nonlinear Krylov acceleration (NKA) method in the PDT code for radiative transfer problems that breaks nesting, resulting in more thermal iterations but significantly fewer total inner transport iterations. Using the metric of total inner transport iterations, we investigate a crooked-pipe-like problem and a pseudo-shock-tube problem. Using only sweep preconditioning, we compare NKA against a typical inner / outer method employing GMRES / Newton and find NKA to be comparable or superior. Finally, we demonstrate the efficacy of applying diffusion-based preconditioning to grey problems in conjunction with NKA. (authors)
Implicit solvers for large-scale nonlinear problems
Keyes, D E; Reynolds, D; Woodward, C S
2006-07-13
Computational scientists are grappling with increasingly complex, multi-rate applications that couple such physical phenomena as fluid dynamics, electromagnetics, radiation transport, chemical and nuclear reactions, and wave and material propagation in inhomogeneous media. Parallel computers with large storage capacities are paving the way for high-resolution simulations of coupled problems; however, hardware improvements alone will not prove enough to enable simulations based on brute-force algorithmic approaches. To accurately capture nonlinear couplings between dynamically relevant phenomena, often while stepping over rapid adjustments to quasi-equilibria, simulation scientists are increasingly turning to implicit formulations that require a discrete nonlinear system to be solved for each time step or steady state solution. Recent advances in iterative methods have made fully implicit formulations a viable option for solution of these large-scale problems. In this paper, we overview one of the most effective iterative methods, Newton-Krylov, for nonlinear systems and point to software packages with its implementation. We illustrate the method with an example from magnetically confined plasma fusion and briefly survey other areas in which implicit methods have bestowed important advantages, such as allowing high-order temporal integration and providing a pathway to sensitivity analyses and optimization. Lastly, we overview algorithm extensions under development motivated by current SciDAC applications.
Correct averaging in transmission radiography: Analysis of the inverse problem
NASA Astrophysics Data System (ADS)
Wagner, Michael; Hampel, Uwe; Bieberle, Martina
2016-05-01
Transmission radiometry is frequently used in industrial measurement processes as a means to assess the thickness or composition of a material. A common problem encountered in such applications is the so-called dynamic bias error, which results from averaging beam intensities over time while the material distribution changes. We recently reported on a method to overcome the associated measurement error by solving an inverse problem, which in principle restores the exact average attenuation by considering the Poisson statistics of the underlying particle or photon emission process. In this paper we present a detailed analysis of the inverse problem and its optimal regularized numerical solution. As a result we derive an optimal parameter configuration for the inverse problem.
The relative degree enhancement problem for MIMO nonlinear systems
Schoenwald, D.A.; Oezguener, Ue.
1995-07-01
The authors present a result for linearizing a nonlinear MIMO system by employing partial feedback - feedback at all but one input-output channel such that the SISO feedback linearization problem is solvable at the remaining input-output channel. The partial feedback effectively enhances the relative degree at the open input-output channel provided the feedback functions are chosen to satisfy relative degree requirements. The method is useful for nonlinear systems that are not feedback linearizable in a MIMO sense. Several examples are presented to show how these feedback functions can be computed. This strategy can be combined with decentralized observers for a completely decentralized feedback linearization result for at least one input-output channel.
Exact Null Controllability of a Nonlinear Thermoelastic Contact Problem
Sivergina, Irina F. Polis, Michael P.
2005-01-15
We study the controllability properties of a nonlinear parabolic system that models the temperature evolution of a one-dimensional thermoelastic rod that may come into contact with a rigid obstacle. Basically the system dynamics is described by a one-dimensional nonlocal heat equation with a nonlinear and nonlocal boundary condition of Newmann type.We focus on the control problem and treat the case when the control is distributed over the whole space domain. In this case the system is proved to be exactly null controllable provided the parameters of the system are smooth.The proof is based on changing the control variable and using Aubin's Compactness Lemma to obtain an invariant set for the linearized controllability map. Then, by proving that the found solution is sufficiently smooth, we get the null controllability for the original system.
Ding, Yaqiong; Xue, Chunhua; Sun, Yong; Jiang, Haitao; Li, Yunhui; Li, Hongqiang; Chen, Hong
2012-10-22
We propose a scheme for subwavelength electromagnetic switch by employing nonlinear meta-atom. Bistable response is conceptually demonstrated on a microwave transmission line, which is side-coupled to a varactor-loaded split ring resonator acting as a nonlinear meta-atom. Calculations and experiments show that by applying conductive coupling instead of near-field interaction between the transmission line and the nonlinear meta-atom, switch performances are improved. The switch threshold of low to -5.8 dBm and the transmission contrast of up to 4.0 dB between the two bistable states were achieved. Subwavelength size of our switch should be useful for miniaturization of integrated optical nanocircuits. PMID:23187246
Russell, Steven J.; Carlsten, Bruce E.
2012-06-26
We will quickly go through the history of the non-linear transmission lines (NLTLs). We will describe how they work, how they are modeled and how they are designed. Note that the field of high power, NLTL microwave sources is still under development, so this is just a snap shot of their current state. Topics discussed are: (1) Introduction to solitons and the KdV equation; (2) The lumped element non-linear transmission line; (3) Solution of the KdV equation; (4) Non-linear transmission lines at microwave frequencies; (5) Numerical methods for NLTL analysis; (6) Unipolar versus bipolar input; (7) High power NLTL pioneers; (8) Resistive versus reactive load; (9) Non-lineaer dielectrics; and (10) Effect of losses.
The role of spiking nonlinearity in contrast gain control and information transmission.
Yu, Yuguo; Potetz, Brian; Lee, Tai Sing
2005-03-01
Threshold and saturation are two nonlinear features common to almost all spiking neurons. How these nonlinearities affect the performance gain of the transfer function and coding properties of the neurons has attracted much attention. Here, we deduce basic analytical relationships among these nonlinearities (threshold and saturation), performance gain and information transmission in neurons. We found that performance gain and information transmission can be maximized by input signals with optimal variance. The threshold and saturation inside the model determines the gain tuning property and maximum coding capacity. This framework provides an understanding of some basic design principles underlying information processing systems that can be adjusted to match the statistics of signals in the environment. This study also isolates the exact contributions of the nonlinearities on the contrast adaptation phenomena observed in real visual neurons. PMID:15621176
Inverse problem of nonlinear dynamical systems: a constructive approach
Gonzalez-Gascon, F.; Moreno-Insertis, F.; Rodriguez-Camino, E.
1980-08-01
A quite simple and practical method is developed for the construction of two dimensional nonlinear dynamical systems (plane vector fields) possessing an arbitrary number of given limit cycles. The method is applied to the construction of n-dimensional dynamical systems (R/sup n/ vector fields) possessing at least one limit cycle and, under certain circumstances, more than one, or even a numerable infinity. Interesting open problems arise when n is greater than two, or where more than one limit cycle appears. Our constructive algorithm for this type of inverse problem is also applied to the construction of second order differential equations (Newtonian differential equations) possessing a finite or infinite number of invariant speeds. This last problem is relevant for certain aspects of the special theory of relativity.
Optimizing material properties of composite plates for sound transmission problem
NASA Astrophysics Data System (ADS)
Tsai, Yu-Ting; Pawar, S. J.; Huang, Jin H.
2015-01-01
To calculate the specific transmission loss (TL) of a composite plate, the conjugate gradient optimization method is utilized to estimate and optimize material properties of the composite plate in this study. For an n-layer composite plate, a nonlinear dynamic stiffness matrix based on the thick plate theory is formulated. To avoid huge computational efforts due to the combination of different composite material plates, a transfer matrix approach is proposed to restrict the dynamic stiffness matrix of the composite plate to a 4×4 matrix. Moreover, the transfer matrix approach has also been used to simplify the complexity of the objective function gradient for the optimization method. Numerical simulations are performed to validate the present algorithm by comparing the TL of the optimal composite plate with that of the original plate. Small number of iterations required during convergence tests illustrates the efficiency of the optimization method. The results indicate that an excellent estimation for the composite plate can be obtained for the desired sound transmission.
NASA Astrophysics Data System (ADS)
Moshonas, Nikolaos; Pagiatakis, Gerasimos K.; Papagiannis, Panagiotis; Savaidis, Stylianos P.; Stathopoulos, Nikolaos A.
2014-11-01
In this work, we numerically investigate and analyze the properties of an optical structure composed of successive thin film layers that can possess high values of nonlinear susceptibility, affecting the refractive index and/or the absorption coefficient. By applying the transmission line method properly modified to resolve the inclusion of third-order nonlinearity, the spectral reflectivity and transmission of such a device are presented. Specifically, the method is applied to a conceptual design of a distributed Bragg reflector. Optical bistability can be observed, which translates not only to a change in the value of reflectivity as the input power increases, but also to a shift of the Bragg wavelength.
Numerical solution of nonlinear heat problem with moving boundary
NASA Astrophysics Data System (ADS)
AL-Mannai, Mona; Khabeev, Nail
2012-01-01
Two phase gas-liquid flow in pipes is widely spread in space applications: bubble flows appear in cryogenic components transport through fuel/oxidant supply lines. Another important application is based on the fact that in liquid flows with small bubbles a close contact between the two phases occurs resulting in high rates of transfer between them. The compactness of a system makes it ideally suited to serve as a space-based two-phase bio-reactor which forms an important unit in environmental control and life support system deployed onboard. A numerical method was developed for solving a nonlinear problem of thermal interaction between a spherical gas bubble and surrounding liquid. The system of equations for describing this interaction was formulated. It includes ordinary and nonlinear partial differential equations. The problem was solved using finite-difference technique by dividing the system into spherical layers inside the bubble and employing the new variable which "freezes" the moving boundary of the bubble. A numerical solution is obtained for the problem of radial bubble motion induced by a sudden pressure change in the liquid—a situation which corresponds to the behavior of bubbles beyond a shock wave front when the latter enters a bubble curtain.
Zhong, Zhi-Jian; Xu, Yi; Lan, Sheng; Dai, Qiao-Feng; Wu, Li-Jun
2010-01-01
Based on the excitation of surface plasmon polaritons (SPPs), we analytically and numerically investigate the transmission response in metal-dielectric-metal (MDM) plasmonic waveguides with a side coupled nanocavity (SCNC). By filling the nanocavity with a Kerr nonlinear medium, the position of the resonant dip in the transmission spectrum can be tuned by the incident light intensity. The oscillation of a Fabry-Perot nanocavity formed by incorporating a finite length of the same Kerr nonlinear media into the MDM waveguide acts as a background for the transmission response of the system and induces a sharp and asymmetric response line shape. As a result, the wavelength shift required for the plasmonic device to be switched from the maximum to the minimum transmission can be reduced by half in a structure less than 400 nm long. Such an effect may be potentially applied to constructing SPP-based all-optical switching with low power threshold at nanoscale. PMID:20173825
Application of Genetic Algorithms in Nonlinear Heat Conduction Problems
Khan, Waqar A.
2014-01-01
Genetic algorithms are employed to optimize dimensionless temperature in nonlinear heat conduction problems. Three common geometries are selected for the analysis and the concept of minimum entropy generation is used to determine the optimum temperatures under the same constraints. The thermal conductivity is assumed to vary linearly with temperature while internal heat generation is assumed to be uniform. The dimensionless governing equations are obtained for each selected geometry and the dimensionless temperature distributions are obtained using MATLAB. It is observed that GA gives the minimum dimensionless temperature in each selected geometry. PMID:24695517
Fuzzy control for a nonlinear mimo-liquid level problem
Smith, R. E.; Mortensen, F. N.; Wantuck, P. J.; Parkinson, W. J. ,
2001-01-01
Nonlinear systems are very common in the chemical process industries. Control of these systems, particularly multivariable systems, is extremely difficult. In many chemical plants, because of this difficulty, control is seldom optimal. Quite often, the best control is obtained in the manual mode using experienced operators. Liquid level control is probably one of the most common control problems in a chemical plant. Liquid level is important in heat exchanger control where heat and mass transfer rates can be controlled by the amount of liquid covering the tubes. Distillation columns, mixing tanks, and surge tanks are other examples where liquid level control is very important. The problem discussed in this paper is based on the simultaneous level control of three tanks connected in series. Each tank holds slightly less than 0.01 m{sup 3} of liquid. All three tanks are connected, Liquid is pumped into the first and the third tanks to maintain their levels. The third tank in the series drains to the system exit. The levels in the first and third tank control the level in the middle tank. The level in the middle tank affects the levels in the two end tanks. Many other chemical plant systems can be controlled in a manner similar to this three-tank system. For example, in any distillation column liquid level control problems can be represented as a total condenser with liquid level control, a reboiler with liquid level control, with the interactive column in between. The solution to the three-tank-problem can provide insight into many of the nonlinear control problems in the chemical process industries. The system was tested using the fuzzy logic controller and a proportional-integral (PI) controller, in both the setpoint tracking mode and disturbance rejection mode. The experimental results are discussed and comparisons between fuzzy controller and the standard PI controller are made.
NASA Astrophysics Data System (ADS)
Nguyen, Ba Phi; Kim, Kihong
2014-06-01
We study theoretically the influence of nonlinear gain effects on the transmission and the Anderson localization of waves in both uniform and random one-dimensional amplifying media by using the discrete nonlinear Schrödinger equation. In uniform amplifying media with nonlinear gain, we find that the strong oscillatory behavior of the transmittance and the reflectance for odd and even values of the sample length disappears for large nonlinearities. The exponential decay rate of the transmittance in the asymptotic limit is found to be independent of nonlinear gain. In random amplifying media, we find that the maximum values of the disorder-averaged logarithmic transmittance and reflectance depend nonmonotonically on the strength of nonlinear gain. We also find that the localization length is independent of nonlinear gain. In other words, the Anderson localization is neither enhanced nor weakened due to nonlinear gain. In both the uniform and the random cases, the crossover length, which is the critical length for the amplification to be efficient, is strongly reduced by the nonlinear nature of the gain.
Topology optimization for nonlinear dynamic problems: Considerations for automotive crashworthiness
NASA Astrophysics Data System (ADS)
Kaushik, Anshul; Ramani, Anand
2014-04-01
Crashworthiness of automotive structures is most often engineered after an optimal topology has been arrived at using other design considerations. This study is an attempt to incorporate crashworthiness requirements upfront in the topology synthesis process using a mathematically consistent framework. It proposes the use of equivalent linear systems from the nonlinear dynamic simulation in conjunction with a discrete-material topology optimizer. Velocity and acceleration constraints are consistently incorporated in the optimization set-up. Issues specific to crash problems due to the explicit solution methodology employed, nature of the boundary conditions imposed on the structure, etc. are discussed and possible resolutions are proposed. A demonstration of the methodology on two-dimensional problems that address some of the structural requirements and the types of loading typical of frontal and side impact is provided in order to show that this methodology has the potential for topology synthesis incorporating crashworthiness requirements.
Nonlinear problems of the theory of heterogeneous slightly curved shells
NASA Technical Reports Server (NTRS)
Kantor, B. Y.
1973-01-01
An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.
Nonlinear optical transmission of cyanobacteria-derived optical materials
NASA Astrophysics Data System (ADS)
Zhao, Edward H.; Watanabe, Fumiya; Zhao, Wei
2015-08-01
Cyanobacteria-derived optical materials for optical limiting applications have been studied in this work. Six samples have been prepared from cyanobacteria including cyanobacteria suspension in water, extracts in water, methanol, and N,N-dimethylformamide, and pyrolyzed cyanobacteria (PCYB) dispersed in dsDNA (sodium salt from salmon testes) solution and sodium dodecyl sulfate solution, respectively. The extracts contain phycocyanin, chlorophyll a, and carotenoids as measured by optical absorption spectroscopy, while the PCYB is a nanostructural composite composed of multi-walled carbon nanotubes, carbon nanoringes, and multilayer graphenes, as revealed by transmission electron microscopy. The optical limiting responses of the samples have been measured at 532 and 756 nm. The PCYB in dsDNA solution has the best limiting performance out of all the cyanobacteria-derived samples. It outperforms carbon black suspension standard at 532 nm and is a broadband limiter, which makes it attractive for optical limiting applications.
Channel Capacity of Non-Linear Transmission Systems
NASA Astrophysics Data System (ADS)
Ellis, Andrew D.; Zhao, Jian
Since their introduction in the late 1970s, the capacity of optical communication links has grown exponentially, fuelled by a series of key innovations including movement between the three telecommunication windows of 850 nm, 1,310 nm and 1,550 nm, distributed feedback laser, erbium-doped fibre amplifiers (EDFAs), dispersion-shifted and dispersion-managed fibre links, external modulation, wavelength division multiplexing, optical switching, forward error correction (FEC), Raman amplification, and most recently, coherent detection, electronic signal processing and optical orthogonal frequency division multiplexing (OFDM). Throughout this evolution, one constant factor has been the use of single-mode optical fibre, whose fundamental principles dated back to the 1800s, when Irish scientist, John Tyndall demonstrated in a lecture to the Royal Society in London that light could be guided through a curved stream of water [1]. Following many developments, including the proposal for waveguides by J.J. Thompson [2], the presentation of detailed calculations for dielectric waveguides by Snitzer [3], the proposal [4] and fabrication [5] of ultra low loss fibres, single-mode fibres were first adopted for non-experimental use in Dorset, UK in 1975, and are still in use today, despite the evolving designs to control chromatic dispersion and non-linearity.
Ophus, Colin; Ciston, Jim; Nelson, Chris T
2016-03-01
Unwanted motion of the probe with respect to the sample is a ubiquitous problem in scanning probe and scanning transmission electron microscopies, causing both linear and nonlinear artifacts in experimental images. We have designed a procedure to correct these artifacts by using orthogonal scan pairs to align each measurement line-by-line along the slow scan direction, by fitting contrast variation along the lines. We demonstrate the accuracy of our algorithm on both synthetic and experimental data and provide an implementation of our method. PMID:26716724
Liu, Xiang; Chandrasekhar, S; Winzer, P J; Chraplyvy, A R; Tkach, R W; Zhu, B; Taunay, T F; Fishteyn, M; DiGiovanni, D J
2012-08-13
Coherent superposition of light waves has long been used in various fields of science, and recent advances in digital coherent detection and space-division multiplexing have enabled the coherent superposition of information-carrying optical signals to achieve better communication fidelity on amplified-spontaneous-noise limited communication links. However, fiber nonlinearity introduces highly correlated distortions on identical signals and diminishes the benefit of coherent superposition in nonlinear transmission regime. Here we experimentally demonstrate that through coordinated scrambling of signal constellations at the transmitter, together with appropriate unscrambling at the receiver, the full benefit of coherent superposition is retained in the nonlinear transmission regime of a space-diversity fiber link based on an innovatively engineered multi-core fiber. This scrambled coherent superposition may provide the flexibility of trading communication capacity for performance in future optical fiber networks, and may open new possibilities in high-performance and secure optical communications. PMID:23038549
Zhang, Fan; Yang, Chuanchuan; Fang, Xi; Zhang, Tingting; Chen, Zhangyuan
2013-03-11
Orthogonal transmission with frequency division multiplexing technique is investigated for next generation optical communication systems. Coherent optical orthogonal frequency division multiplexing (OFDM) and single-carrier frequency division multiplexing (SCFDM) schemes are compared in combination with polarization-division multiplexing quadrature phase shift keying (QPSK) or 16-QAM (quadrature amplitude modulation) formats. Multi-granularity transmission with flexible bandwidth can be realized through ultra-dense wavelength division multiplexing (UDWDM) based on the orthogonal technique. The system performance is numerically studied with special emphasis on transmission degradations due to fiber Kerr nonlinearity. The maximum reach and fiber capacity for different spectral efficiencies are investigated for systems with nonlinear propagation over uncompensated standard single-mode fiber (SSMF) links with lumped amplification. PMID:23482180
Linear and nonlinear transfer functions of single mode fiber for optical transmission systems.
Binh, Le Nguyen
2009-07-01
The transmittance transfer function of single mode optical fibers operating in both linear and nonlinear regions is presented. For the linear domain, Fresnel sine and cosine integrals are obtained via the Fourier transform. In the nonlinear region dominated by self-phase-modulation effects, the Volterra series is essential to obtain the nonlinear transfer function. A convergence criterion for the Volterra series transfer function (VSTF) approach is described for solving the nonlinear Schrödinger wave propagation equation. Soliton transmission over single fibers is demonstrated as a case study of the application of the VSTF and a modified VSTF with a number of segmented steps whose distance is within the limit of the convergence of the VSTF. PMID:19568291
Al-Khateeb, Mohammad A Z; McCarthy, Mary; Sánchez, Christian; Ellis, Andrew
2016-04-15
In this Letter, we theoretically and numerically analyze the performance of coherent optical transmission systems that deploy inline or transceiver based nonlinearity compensation techniques. For systems where signal-signal nonlinear interactions are fully compensated, we find that beyond the performance peak the signal-to-noise ratio degradation has a slope of 3 dB_{SNR}/dB_{Power} suggesting a quartic rather than quadratic dependence on signal power. This is directly related to the fact that signals in a given span will interact not only with linear amplified spontaneous emission noise, but also with the nonlinear four-wave mixing products generated from signal-noise interaction in previous (hitherto) uncompensated spans. The performance of optical systems employing different nonlinearity compensation schemes were numerically simulated and compared against analytical predictions, showing a good agreement within a 0.4 dB margin of error. PMID:27082361
Experimental analysis of nonlinear problems by optical methods
NASA Astrophysics Data System (ADS)
Laermann, Karl-Hans
1994-11-01
As an example of a geometrical nonlinear problem a thin plate-in-bending under large deflection is considered. To determine the inplane- as well as the bending stress-state the photoelastic reflection method and Ligtenberg's moire method are used; the measured information is evaluated according to the principles of integrated photoelasticity. As yet in photoelasticity it has always been supposed Hooke's law of elasticity is valid and consequently linear relations between birefringent effects and stresses are existing. However, in areas of high stress concentration and with reference to some of the mainly used photoelastic material nonlinear strain-stress relations must be introduced. A proper constitutive equation yields an advanced principal photoelastic equation, the solution of which is performed in an iterative procedure. It should be mentioned that extended material testing is demanded to get the various material parameters. Finally proper algorithms and the respective numerical evaluation procedures are described, to analyze plane stress-states, if the material shows viscoelastic response. Then the mechanical as well as the optical rheological response of material must be considered.
Wave reflection and transmission reduction using a piezoelectric semipassive nonlinear technique.
Guyomar, D; Faiz, A; Petit, L; Richard, C
2006-01-01
This study addresses the problem of noise reduction using piezoelements. The nonlinear technique, synchronized switch damping (SSD), is implemented. The device is a pulse-tube termination equipped with piezoelements, which allows performant damping of the vibration resulting from an incident acoustic wave. Due to this damping, both reflected and transmitted wave are reduced. In the semipassive damping approach proposed in this paper, energy degradation is strongly enhanced when the piezoelements are continuously switched from open to short circuit synchronously to the strain. This technique has been developed following two strategies. The first is SSD on a short circuit in which the piezoelement is always in open circuit, except for a very brief period at each strain extremum where it is short-circuited. The second approach is SSD on an inductor. The process is very similar, except that instead of forcing the voltage to zero, the voltage is exactly reversed using a controlled oscillating discharge of the piezoelement capacitor on an inductor during switch drive. Due to this switching mechanism, a phase shift appears between the strain and the resulting voltage, thus creating energy dissipation. Following SSD on an piezoelement, attenuations of 15 dB in reflection and 7 dB in transmission were obtained. PMID:16454284
Zhang, H.
1994-10-01
In this paper the author considers a nonlinear evolution problem denoted in the paper as P. Problem (P) arises in the study of thermal evaporation of atoms and molecules from locally heated surface regions (spikes) invoked as one of several mechanisms of ion-bombardment-induced particle emission (sputtering). Then in the case of particle-induced evaporation, the Stefan-Boltzman law of heat loss by radiation is replaced by some activation law describing the loss of heat by evaporation. The equation in P is the so-called degenerate diffusion problem, which has been extensively studied in recent years. However, when dealing with the nonlinear flux boundary condition, {beta}({center_dot}) is usually assumed to be monotene. The purpose of this paper is to provide a general theory for problem P under a different assumption on {beta}({center_dot}), i.e., Lipschitz continuity instead of monotonicity. The main idea of the proof used here is to choose an appropriate test function from the corresponding linearized dual space of the solution. The similar idea has been used by many authors, e.g., Aronson, Crandall and Peletier, Bertsch and Hilhorst and Friedman. The author follows the proof of Bertsch and Hilhorst. The paper is organized as follows. They begin by stating the precise assumptions on the functions involved in P and by defining a weak solution. Then, in Section 2 they prove the existence of the solution by the method of parabolic regularization. The uniqueness is proved in Section 3. Finally, they study the large time behavior of the solution in Section 4.
Nonlinear Quantum Mechanics Implies Polynomial-Time Solution for NP-Complete and # P Problems
NASA Astrophysics Data System (ADS)
Abrams, Daniel S.; Lloyd, Seth
1998-11-01
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete and # P problems in polynomial time. We provide algorithms that solve NP-complete and # P oracle problems by exploiting nonlinear quantum logic gates. Using the Weinberg model as a simple example, the explicit construction of these gates is derived from the underlying physics. Nonlinear quantum algorithms are also presented using Polchinski type nonlinearities which do not allow for superluminal communication.
Nonlinear Control of Wind Turbines with Hydrostatic Transmission Based on Takagi-Sugeno Model
NASA Astrophysics Data System (ADS)
Schulte, Horst; Georg, Soren
2014-06-01
A nonlinear model-based control concept for wind turbines with hydrostatic transmission is proposed. The complete mathematical model of a wind turbine drive train with variable displacement pump and variable displacement motor is presented. The controller design takes into consideration the nonlinearity of the aerodynamic maps and hydrostatic drive train by an convex combination of state space controller with measurable generator speed and hydraulic motor displacement as scheduling parameters. The objectives are the set point control of generator speed and tracking control of the rotor speed to reach the maximum power according to the power curve in the partial-load region.
Modified semi-classical methods for nonlinear quantum oscillations problems
Moncrief, Vincent; Marini, Antonella; Maitra, Rachel
2012-10-15
We develop a modified semi-classical approach to the approximate solution of Schroedinger's equation for certain nonlinear quantum oscillations problems. In our approach, at lowest order, the Hamilton-Jacobi equation of the conventional semi-classical formalism is replaced by an inverted-potential-vanishing-energy variant thereof. With suitable smoothness, convexity and coercivity properties imposed on its potential energy function, we prove, using methods drawn from the calculus of variations together with the (Banach space) implicit function theorem, the existence of a global, smooth 'fundamental solution' to this equation. Higher order quantum corrections thereto, for both ground and excited states, can then be computed through the integration of associated systems of linear transport equations, derived from Schroedinger's equation, and formal expansions for the corresponding energy eigenvalues obtained therefrom by imposing the natural demand for smoothness on the (successively computed) quantum corrections to the eigenfunctions. For the special case of linear oscillators our expansions naturally truncate, reproducing the well-known exact solutions for the energy eigenfunctions and eigenvalues. As an explicit application of our methods to computable nonlinear problems, we calculate a number of terms in the corresponding expansions for the one-dimensional anharmonic oscillators of quartic, sectic, octic, and dectic types and compare the results obtained with those of conventional Rayleigh/Schroedinger perturbation theory. To the orders considered (and, conjecturally, to all orders) our eigenvalue expansions agree with those of Rayleigh/Schroedinger theory whereas our wave functions more accurately capture the more-rapid-than-gaussian decay known to hold for the exact solutions to these problems. For the quartic oscillator in particular our results strongly suggest that both the ground state energy eigenvalue expansion and its associated wave function expansion
Highly accurate adaptive finite element schemes for nonlinear hyperbolic problems
NASA Astrophysics Data System (ADS)
Oden, J. T.
1992-08-01
This document is a final report of research activities supported under General Contract DAAL03-89-K-0120 between the Army Research Office and the University of Texas at Austin from July 1, 1989 through June 30, 1992. The project supported several Ph.D. students over the contract period, two of which are scheduled to complete dissertations during the 1992-93 academic year. Research results produced during the course of this effort led to 6 journal articles, 5 research reports, 4 conference papers and presentations, 1 book chapter, and two dissertations (nearing completion). It is felt that several significant advances were made during the course of this project that should have an impact on the field of numerical analysis of wave phenomena. These include the development of high-order, adaptive, hp-finite element methods for elastodynamic calculations and high-order schemes for linear and nonlinear hyperbolic systems. Also, a theory of multi-stage Taylor-Galerkin schemes was developed and implemented in the analysis of several wave propagation problems, and was configured within a general hp-adaptive strategy for these types of problems. Further details on research results and on areas requiring additional study are given in the Appendix.
Khoo, Iam Choon; Hong, Kuan Lung; Zhao, Shuo; Ma, Ding; Lin, Tsung-Hsien
2013-02-25
Blue-phase liquid crystal (BPLC) is introduced into the pores of capillary arrays to fabricate fiber arrays. Owing to the photonic-crystals like properties of BPLC, these fiber arrays exhibit temperature dependent photonic bandgaps in the visible spectrum. With the cores maintained in isotropic as well as the Blue phases, the fiber arrays allow high quality image transmission when inserted in the focal plane of a 1x telescope. Nonlinear transmission and optical limiting action on a cw white-light continuum laser is also observed and is attributed to laser induced self-defocusing and propagation modes changing effects caused by some finite absorption of the broadband laser at the short wavelength regime. These nonlinear and other known electro-optical properties of BPLC, in conjunction with their fabrication ease make these fiber arrays highly promising for imaging, electro-optical or all-optical modulation, switching and passive optical limiting applications. PMID:23481965
NASA Astrophysics Data System (ADS)
Moshonas, Nikolaos; Pagiatakis, Gerasimos K.; Papagiannis, Panagiotis; Savaidis, Stylianos P.; Stathopoulos, Nikolaos A.
2014-05-01
In this work we numerically investigate and analyse the properties of an optical structure comprised of successive thin film layers that can possess high values of nonlinear susceptibility, affecting the refractive index and/or the absorption coefficient. By applying the Transmission Line Method (TLM), properly modified to resolve the inclusion of third order nonlinearity, the spectral reflectivity and transmission of such a device are presented. Specifically, the method is applied for the case of conceptual design of a Distributed Bragg Reflector (DBR). Optical bistability can be observed, which translates not only to a change in the value of reflectivity, as the input power increases, but also to a shift of the Bragg wavelength.
Electrical short pulses generation using a resonant tunneling diode nonlinear transmission line
NASA Astrophysics Data System (ADS)
Essimbi, B. Z.; Jäger, D.
2012-03-01
In this paper, the generation of short electrical pulses based on nonlinear active wave propagation effects along the resonant tunneling diode transmission line is studied. The principle of operation is discussed and it is shown by computer experiments that an input rectangular pulse as well as a sinusoidal input signal can be converted into a set of output spikes, suitable for A/D conversion at millimeter wave frequencies.
Nonlinear absorption and transmission properties of Ge, Te and InAs using tuneable IR FEL
Amirmadhi, F.; Becker, K.; Brau, C.A.
1995-12-31
Nonlinear absorption properties of Ge, Te and InAs are being investigated using the transmission of FEL optical pulses through these semiconductors (z-scan method). Wavelength, intensity and macropulse dependence are used to differentiate between two-photon and free-carrier absorption properties of these materials. Macropulse dependence is resolved by using a Pockles Cell to chop the 4-{mu}s macropulse down to 100 ns. Results of these experiments will be presented and discussed.
NASA Astrophysics Data System (ADS)
Li, Jibin; Chen, Fengjuan
In this paper, we consider a modulated equation in a discrete nonlinear electrical transmission line. This model is an integrable planar dynamical system having three singular straight lines. By using the theory of singular systems to investigate the dynamical behavior for this system, we obtain bifurcations of phase portraits under different parameter conditions. Corresponding to some special level curves, we derive exact explicit parametric representations of solutions (including smooth solitary wave solutions, peakons, compactons, periodic cusp wave solutions) under different parameter conditions.
Effect of non-linear capacitance on a non-uniform transmission line
NASA Astrophysics Data System (ADS)
Kumar, L.; Shankar Pandey, V.; Parthasarathy, H.; Shrimali, V.; Varshney, G.
2016-05-01
In this paper we derive a non-linear polarization electric field relationship in a dielectric by considering harmonics binding of the electrons to its nuclei. We apply this theory to a transmission line to model the non-linear, inhomogeneous frequency-dependent capacitance of the line and approximate an expression for the line current when the line is terminated by load impedance. We then suggest a method for estimating the inhomogeneous, frequency-dependent non-linear component of the line capacitance from the measurements of the far field electromagnetic field radiated by the line current. The far field magnetic vector potential is calculated from the line current by the standard Green's function integration in free space.
A Parametric Study of Nonlinear Seismic Response Analysis of Transmission Line Structures
Wang, Yanming; Yi, Zhenhua
2014-01-01
A parametric study of nonlinear seismic response analysis of transmission line structures subjected to earthquake loading is studied in this paper. The transmission lines are modeled by cable element which accounts for the nonlinearity of the cable based on a real project. Nonuniform ground motions are generated using a stochastic approach based on random vibration analysis. The effects of multicomponent ground motions, correlations among multicomponent ground motions, wave travel, coherency loss, and local site on the responses of the cables are investigated using nonlinear time history analysis method, respectively. The results show the multicomponent seismic excitations should be considered, but the correlations among multicomponent ground motions could be neglected. The wave passage effect has a significant influence on the responses of the cables. The change of the degree of coherency loss has little influence on the response of the cables, but the responses of the cables are affected significantly by the effect of coherency loss. The responses of the cables change little with the degree of the difference of site condition changing. The effect of multicomponent ground motions, wave passage, coherency loss, and local site should be considered for the seismic design of the transmission line structures. PMID:25133215
A parametric study of nonlinear seismic response analysis of transmission line structures.
Tian, Li; Wang, Yanming; Yi, Zhenhua; Qian, Hui
2014-01-01
A parametric study of nonlinear seismic response analysis of transmission line structures subjected to earthquake loading is studied in this paper. The transmission lines are modeled by cable element which accounts for the nonlinearity of the cable based on a real project. Nonuniform ground motions are generated using a stochastic approach based on random vibration analysis. The effects of multicomponent ground motions, correlations among multicomponent ground motions, wave travel, coherency loss, and local site on the responses of the cables are investigated using nonlinear time history analysis method, respectively. The results show the multicomponent seismic excitations should be considered, but the correlations among multicomponent ground motions could be neglected. The wave passage effect has a significant influence on the responses of the cables. The change of the degree of coherency loss has little influence on the response of the cables, but the responses of the cables are affected significantly by the effect of coherency loss. The responses of the cables change little with the degree of the difference of site condition changing. The effect of multicomponent ground motions, wave passage, coherency loss, and local site should be considered for the seismic design of the transmission line structures. PMID:25133215
Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line.
Sato, M; Mukaide, T; Nakaguchi, T; Sievers, A J
2016-07-01
The experimental properties of intrinsic localized modes (ILMs) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest-neighbor intersite potentials. Here it is shown for a one-dimensional lumped electrical transmission line that a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis, the nonlinear inductive current equations are transformed to flux transmission line equations with analog onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice, ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally, this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice. PMID:27575139
Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line
NASA Astrophysics Data System (ADS)
Sato, M.; Mukaide, T.; Nakaguchi, T.; Sievers, A. J.
2016-07-01
The experimental properties of intrinsic localized modes (ILMs) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest-neighbor intersite potentials. Here it is shown for a one-dimensional lumped electrical transmission line that a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis, the nonlinear inductive current equations are transformed to flux transmission line equations with analog onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice, ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally, this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.
The treatment of contact problems as a non-linear complementarity problem
Bjorkman, G.
1994-12-31
Contact and friction problems are of great importance in many engineering applications, for example in ball bearings, bolted joints, metal forming and also car crashes. In these problems the behavior on the contact surface has a great influence on the overall behavior of the structure. Often problems such as wear and initiation of cracks occur on the contact surface. Contact problems are often described using complementarity conditions, w {>=} 0, p {>=} 0, w{sup T}p = 0, which for example represents the following behavior: (i) two bodies can not penetrate each other, i.e. the gap must be greater than or equal to zero, (ii) the contact pressure is positive and different from zero only if the two bodies are in contact with each other. Here it is shown that by using the theory of non-linear complementarity problems the unilateral behavior of the problem can be treated in a straightforward way. It is shown how solution methods for discretized frictionless contact problem can be formulated. By formulating the problem either as a generalized equation or as a B-differentiable function, it is pointed out how Newton`s method may be extended to contact problems. Also an algorithm for tracing the equilibrium path of frictionless contact problems is described. It is shown that, in addition to the {open_quotes}classical{close_quotes} bifurcation and limit points, there can be points where the equilibrium path has reached an end point or points where bifurcation is possible even if the stiffness matrix is non-singular.
Nonlinear problems in data-assimilation : Can synchronization help?
NASA Astrophysics Data System (ADS)
Tribbia, J. J.; Duane, G. S.
2009-12-01
Over the past several years, operational weather centers have initiated ensemble prediction and assimilation techniques to estimate the error covariance of forecasts in the short and the medium range. The ensemble techniques used are based on linear methods. The theory This technique s been shown to be a useful indicator of skill in the linear range where forecast errors are small relative to climatological variance. While this advance has been impressive, there are still ad hoc aspects of its use in practice, like the need for covariance inflation which are troubling. Furthermore, to be of utility in the nonlinear range an ensemble assimilation and prediction method must be capable of giving probabilistic information for the situation where a probability density forecast becomes multi-modal. A prototypical, simplest example of such a situation is the planetary-wave regime transition where the pdf is bimodal. Our recent research show how the inconsistencies and extensions of linear methodology can be consistently treated using the paradigm of synchronization which views the problems of assimilation and forecasting as that of optimizing the forecast model state with respect to the future evolution of the atmosphere.
Zhu, Huatao; Wang, Rong; Pu, Tao; Fang, Tao; Xiang, Peng; Zheng, Jilin; Chen, Dalei
2015-06-01
In this Letter, the optical stealth transmission carried by super-continuum spectrum optical pulses generated in highly nonlinear fiber is proposed and experimentally demonstrated. In the proposed transmission scheme, super-continuum signals are reshaped in the spectral domain through a wavelength-selective switch and are temporally spread by a chromatic dispersion device to achieve the same noise-like characteristic as the noise in optical networks, so that in both the time domain and the spectral domain, the stealth signals are hidden in public channel. Our experimental results show that compared with existing schemes where stealth channels are carried by amplified spontaneous emission noise, super-continuum signal can increase the transmission performance and robustness. PMID:26030557
Impulsive two-point boundary value problems for nonlinear qk-difference equations
NASA Astrophysics Data System (ADS)
Mardanov, Misir J.; Sharifov, Yagub A.
2016-08-01
In this study, impulsive two-point boundary value problems for nonlinear qk -difference equations is considered. Note that this problem contains the similar problem with antiperiodic boundary conditions as a partial case. The theorems on existence and uniqueness of the solution of the considered problem are proved. Obtained here results not only enlarges the class of considered boundary problems and also strengthens them.
Repetitive sub-gigawatt rf source based on gyromagnetic nonlinear transmission line.
Romanchenko, Ilya V; Rostov, Vladislav V; Gubanov, Vladimir P; Stepchenko, Alexey S; Gunin, Alexander V; Kurkan, Ivan K
2012-07-01
We demonstrate a high power repetitive rf source using gyromagnetic nonlinear transmission line to produce rf oscillations. Saturated NiZn ferrites act as active nonlinear medium first sharpening the pumping high voltage nanosecond pulse and then radiating at central frequency of about 1 GHz: shock rise time excites gyromagnetic precession in ferrites forming damping rf oscillations. The optimal length of nonlinear transmission line was found to be of about 1 m. SINUS-200 high voltage driver with Tesla transformer incorporated into pulse forming line has been designed and fabricated to produce bursts of 1000 pulses with 200 Hz repetition rate. A band-pass filter and mode-converter have been designed to extract rf pulse from low-frequency component and to form TE(11) mode of circular waveguide with linear polarization. A wide-band horn antenna has been fabricated to form Gaussian distribution of radiation pattern. The peak value of electric field strength of a radiated pulse at the distance of 3.5 m away from antenna is measured to be 160 kV/m. The corresponding rf peak power of 260 MW was achieved. PMID:22852710
Minzioni, Paolo; Pusino, Vincenzo; Cristiani, Ilaria; Marazzi, Lucia; Martinelli, Mario; Langrock, Carsten; Fejer, M M; Degiorgio, Vittorio
2010-08-16
We experimentally compare the effectiveness of three different optical-phase-conjugation-based nonlinearity-compensation strategies on a transmission system employing phase-modulated signals, and hence affected by the Gordon-Mollenauer effect. We demonstrate that it is possible to obtain significant nonlinearity compensation, but that no improvement is obtained using configurations specifically aimed at the compensation of the nonlinear phase noise. PMID:20721200
Multigrid approaches to non-linear diffusion problems on unstructured meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.
NASA Astrophysics Data System (ADS)
Nguyen, Quan M.; Peleg, Avner; Tran, Thinh P.
2015-01-01
We develop a method for transmission stabilization and robust dynamic switching for colliding optical soliton sequences in broadband waveguide systems with nonlinear gain and loss. The method is based on employing hybrid waveguides, consisting of spans with linear gain and cubic loss, and spans with linear loss, cubic gain, and quintic loss. We show that the amplitude dynamics is described by a hybrid Lotka-Volterra (LV) model, and use the model to determine the physical parameter values required for enhanced transmission stabilization and switching. Numerical simulations with coupled nonlinear Schrödinger equations confirm the predictions of the LV model, and show complete suppression of radiative instability and pulse distortion. This enables stable transmission over distances larger by an order of magnitude compared with uniform waveguides with linear gain and cubic loss. Moreover, multiple on-off and off-on dynamic switching events are demonstrated over a wide range of soliton amplitudes, showing the superiority of hybrid waveguides compared with static switching in uniform waveguides.
NASA Astrophysics Data System (ADS)
Swaidan, Waleeda; Hussin, Amran
2015-10-01
Most direct methods solve finite time horizon optimal control problems with nonlinear programming solver. In this paper, we propose a numerical method for solving nonlinear optimal control problem with state and control inequality constraints. This method used quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a quadratic programming problem. The linear inequality constraints for trajectories variables are converted to quadratic programming constraint by using Haar wavelet collocation method. The proposed method has been applied to solve Optimal Control of Multi-Item Inventory Model. The accuracy of the states, controls and cost can be improved by increasing the Haar wavelet resolution.
Inference of Stochastic Nonlinear Oscillators with Applications to Physiological Problems
NASA Technical Reports Server (NTRS)
Smelyanskiy, Vadim N.; Luchinsky, Dmitry G.
2004-01-01
A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of dynamical models. We illustrate the main ideas of the technique by inferencing a model of five globally and locally coupled noisy oscillators. Specific modifications of the technique for inferencing hidden degrees of freedom of coupled nonlinear oscillators is discussed in the context of physiological applications.
Capacity estimates for optical transmission based on the nonlinear Fourier transform.
Derevyanko, Stanislav A; Prilepsky, Jaroslaw E; Turitsyn, Sergei K
2016-01-01
What is the maximum rate at which information can be transmitted error-free in fibre-optic communication systems? For linear channels, this was established in classic works of Nyquist and Shannon. However, despite the immense practical importance of fibre-optic communications providing for >99% of global data traffic, the channel capacity of optical links remains unknown due to the complexity introduced by fibre nonlinearity. Recently, there has been a flurry of studies examining an expected cap that nonlinearity puts on the information-carrying capacity of fibre-optic systems. Mastering the nonlinear channels requires paradigm shift from current modulation, coding and transmission techniques originally developed for linear communication systems. Here we demonstrate that using the integrability of the master model and the nonlinear Fourier transform, the lower bound on the capacity per symbol can be estimated as 10.7 bits per symbol with 500 GHz bandwidth over 2,000 km. PMID:27611059
Dynamical analysis of transmission line cables. Part 3—Nonlinear theory
NASA Astrophysics Data System (ADS)
Barbieri, Renato; Barbieri, Nilson; de Souza Júnior, Oswaldo Honorato
2008-05-01
In this work the authors use nonlinear mathematical models for simulation of the dynamical behavior of transmission lines cables. The numerical models are obtained through the finite element method. For validation of the mathematical nonlinear models, the simulated results are compared with experimental data obtained in an automated testing system for overhead line cables. Many sample lengths and load situations were used. The forced response is obtained through an impulsive excitation (impact hammer) or electromechanical shaker and, the vibration signals are collected through accelerometers placed along the half sample. The eigenbehavior is analyzed using the Irvine parameter for straight and inclinated cables. It also showed the numeric and experimental dynamical behavior results for the load cable fluctuation in function of the excitation frequency, the influence of concentrated mass of straight cable and the beat condition.
NASA Astrophysics Data System (ADS)
Qiao, Yaojun; Li, Ming; Yang, Qiuhong; Xu, Yanfei; Ji, Yuefeng
2015-01-01
Closed-form expressions of nonlinear interference of dense wavelength-division-multiplexed (WDM) systems with dispersion managed transmission (DMT) are derived. We carry out a simulative validation by addressing an ample and significant set of the Nyquist-WDM systems based on polarization multiplexed quadrature phase-shift keying (PM-QPSK) subcarriers at a baud rate of 32 Gbaud per channel. Simulation results show the simple closed-form analytical expressions can provide an effective tool for the quick and accurate prediction of system performance in DMT coherent optical systems.
NASA Technical Reports Server (NTRS)
Costiner, Sorin; Taasan, Shlomo
1994-01-01
This paper presents multigrid (MG) techniques for nonlinear eigenvalue problems (EP) and emphasizes an MG algorithm for a nonlinear Schrodinger EP. The algorithm overcomes the mentioned difficulties combining the following techniques: an MG projection coupled with backrotations for separation of solutions and treatment of difficulties related to clusters of close and equal eigenvalues; MG subspace continuation techniques for treatment of the nonlinearity; an MG simultaneous treatment of the eigenvectors at the same time with the nonlinearity and with the global constraints. The simultaneous MG techniques reduce the large number of self consistent iterations to only a few or one MG simultaneous iteration and keep the solutions in a right neighborhood where the algorithm converges fast.
Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems
NASA Technical Reports Server (NTRS)
Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III
2012-01-01
In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.
NASA Astrophysics Data System (ADS)
Huang, Ya; Griffin, Michael J.
2009-07-01
Resonance frequencies evident in the apparent mass and the transmissibility of the human body decrease with increasing vibration magnitude, but the mechanisms responsible for this nonlinearity have not been established. This experiment was designed to explore the effects of body location on the nonlinearity of the body in supine postures. In a group of 12 male subjects, the apparent mass and transmissibility to the sternum, upper abdomen, and lower abdomen were measured in three postures (relaxed semi-supine, flat supine and constrained semi-supine) with vertical random vibration (0.25-20 Hz) at seven vibration magnitudes (nominally 0.0313, 0.0625, 0.125, 0.25, 0.5, 0.75, and 1.0 ms -2 rms). In all three postures, the apparent mass resonance frequencies and the primary peak frequencies in the transmissibilities to the upper and lower abdomen decreased with increases in vibration magnitude from 0.25 to 1.0 ms -2 rms. Nonlinearity generally apparent in transmissibility to the abdomen was less evident in transmissibility to the sternum and less evident in transmissibilities to the abdomen at vibration magnitudes less than 0.125 ms -2 rms. The nonlinearity was more apparent in the flat supine posture than in the semi-supine postures. The findings are consistent with the nonlinearity being associated with the response of soft tissues, more likely a consequence of passive thixotropy than muscle activity.
Solving nonlinear heat conduction problems with multigrid preconditioned Newton-Krylov methods
Rider, W.J.; Knoll, D.A.
1997-09-01
Our objective is to investigate the utility of employing multigrid preconditioned Newton-Krylov methods for solving initial value problems. Multigrid based method promise better performance from the linear scaling associated with them. Our model problem is nonlinear heat conduction which can model idealized Marshak waves. Here we will investigate the efficiency of using a linear multigrid method to precondition a Krylov subspace method. In effect we will show that a fixed point nonlinear iterative method provides an effective preconditioner for the nonlinear problem.
Nonlinear Schwarz-Fas Methods for Unstructured Finite Element Elliptic Problems
Jones, J E; Vassilevski, P S; Woodward, C S
2002-09-30
This paper provides extensions of an element agglomeration AMG method to nonlinear elliptic problems discretized by the finite element method on general unstructured meshes. The method constructs coarse discretization spaces and corresponding coarse nonlinear operators as well as their Jacobians. We introduce both standard (fairly quasi-uniformly coarsened) and non-standard (coarsened away) coarse meshes and respective finite element spaces. We use both kind of spaces in FAS type coarse subspace correction (or Schwarz) algorithms. Their performance is illustrated on a number of model problems. The coarsened away spaces seem to perform better than the standard spaces for problems with nonlinearities in the principal part of the elliptic operator.
Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design
Liao, Ben-Shan; Bai, Zhaojun; Lee, Lie-Quan; Ko, Kwok; /SLAC
2006-09-28
A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.
NASA Astrophysics Data System (ADS)
Nakao, Mitsuhiro
We prove the existence of global decaying solutions to the exterior problem for the Klein-Gordon equation with a nonlinear localized dissipation and a derivative nonlinearity. To derive the required estimates of solutions we employ a 'loan' method.
Cognitive Variables in Problem Solving: A Nonlinear Approach
ERIC Educational Resources Information Center
Stamovlasis, Dimitrios; Tsaparlis, Georgios
2005-01-01
We employ tools of complexity theory to examine the effect of cognitive variables, such as working-memory capacity, degree of field dependence-independence, developmental level and the mobility-fixity dimension. The nonlinear method correlates the subjects' rank-order achievement scores with each cognitive variable. From the achievement scores in…
An application of a linear programing technique to nonlinear minimax problems
NASA Technical Reports Server (NTRS)
Schiess, J. R.
1973-01-01
A differential correction technique for solving nonlinear minimax problems is presented. The basis of the technique is a linear programing algorithm which solves the linear minimax problem. By linearizing the original nonlinear equations about a nominal solution, both nonlinear approximation and estimation problems using the minimax norm may be solved iteratively. Some consideration is also given to improving convergence and to the treatment of problems with more than one measured quantity. A sample problem is treated with this technique and with the least-squares differential correction method to illustrate the properties of the minimax solution. The results indicate that for the sample approximation problem, the minimax technique provides better estimates than the least-squares method if a sufficient amount of data is used. For the sample estimation problem, the minimax estimates are better if the mathematical model is incomplete.
Algorithm for nonlinear stationary Navier-Stokes problem
NASA Technical Reports Server (NTRS)
Gabrielsen, R. E.; Karel, S.
1975-01-01
Results of applications of algorithm suggest that it has potential application to variety of related fluid flow problems, such as presently intractable separation problem of aerodynamics. Details of mathematical development, as well as computation of explicit error estimates, are available.
NASA Astrophysics Data System (ADS)
Tufano, Saverio; Griffin, Michael J.
2013-01-01
The efficiency of a seat in reducing vibration depends on the characteristics of the vibration, the dynamic characteristics of the seat, and the dynamic characteristics of the person sitting on the seat. However, it is not known whether seat cushions influence the dynamic response of the human body, whether the human body influences the dynamic response of seat cushions, or the relative importance of human body nonlinearity and seat nonlinearity in causing nonlinearity in measures of seat transmissibility. This study was designed to investigate the nonlinearity of the coupled seat and human body systems and to compare the apparent mass of the human body supported on rigid and foam seats. A frequency domain model was used to identify the dynamic parameters of seat foams and investigate their dependence on the subject-sitting weight and hip breadth. With 15 subjects, the force and acceleration at the seat base and acceleration at the subject interface were measured during random vertical vibration excitation (0.25-25 Hz) at each of five vibration magnitudes, (0.25-1.6 ms-2 r.m.s.) with four seating conditions (rigid flat seat and three foam cushions). The measurements are presented in terms of the subject's apparent mass on the rigid and foam seat surfaces, and the transmissibility and dynamic stiffness of each of the foam cushions. Both the human body and the foams showed nonlinear softening behaviour, which resulted in nonlinear cushion transmissibility. The apparent masses of subjects sitting on the rigid seat and on foam cushions were similar, but with an apparent increase in damping when sitting on the foams. The foam dynamic stiffness showed complex correlations with characteristics of the human body, which differed between foams. The nonlinearities in cushion transmissibilities, expressed in terms of changes in resonance frequencies and moduli, were more dependent on human body nonlinearity than on cushion nonlinearity.
Solving mixed integer nonlinear programming problems using spiral dynamics optimization algorithm
NASA Astrophysics Data System (ADS)
Kania, Adhe; Sidarto, Kuntjoro Adji
2016-02-01
Many engineering and practical problem can be modeled by mixed integer nonlinear programming. This paper proposes to solve the problem with modified spiral dynamics inspired optimization method of Tamura and Yasuda. Four test cases have been examined, including problem in engineering and sport. This method succeeds in obtaining the optimal result in all test cases.
Fundamental immunological problems associated with "transmissible spongiform encephalopathies".
Ebringer, Alan; Rashid, Taha; Wilson, Clyde
2015-02-01
"Bovine spongiform encephalopathy", "scrapie", as well as Creutzfeldt-Jakob disease and kuru belong to a group of related neurological conditions termed "transmissible spongiform encephalopathies". These diseases are based on the LD50 measurement whereby saline brain homogenates are injected into experimental animals and when 50% of them develop symptoms, this is considered as transmission of the disease, but the gold standard for diagnosis is autopsy examination. However, an untenable assumption is being made in that saline brain homogenates do not cause tissue damage but it is known since the time of Pasteur, that they give rise to "post-rabies vaccination allergic encephalomyelitis". This is the fundamental flaw in the diagnosis of these diseases. A way forward, however, is to examine infectious agents, such as Acinetobacter which show molecular mimicry with myelin and elevated levels of antibodies to this microbe are found in multiple sclerosis patients and animals affected by "bovine spongiform encephalopathy". PMID:25573495
Bias-field controlled phasing and power combination of gyromagnetic nonlinear transmission lines
Reale, D. V. Bragg, J.-W. B.; Gonsalves, N. R.; Johnson, J. M.; Neuber, A. A.; Dickens, J. C.; Mankowski, J. J.
2014-05-15
Gyromagnetic Nonlinear Transmission Lines (NLTLs) generate microwaves through the damped gyromagnetic precession of the magnetic moments in ferrimagnetic material, and are thus utilized as compact, solid-state, frequency agile, high power microwave (HPM) sources. The output frequency of a NLTL can be adjusted by control of the externally applied bias field and incident voltage pulse without physical alteration to the structure of the device. This property provides a frequency tuning capability not seen in many conventional e-beam based HPM sources. The NLTLs developed and tested are mesoband sources capable of generating MW power levels in the L, S, and C bands of the microwave spectrum. For an individual NLTL the output power at a given frequency is determined by several factors including the intrinsic properties of the ferrimagnetic material and the transmission line structure. Hence, if higher power levels are to be achieved, it is necessary to combine the outputs of multiple NLTLs. This can be accomplished in free space using antennas or in a transmission line via a power combiner. Using a bias-field controlled delay, a transient, high voltage, coaxial, three port, power combiner was designed and tested. Experimental results are compared with the results of a transient COMSOL simulation to evaluate combiner performance.
Bias-field controlled phasing and power combination of gyromagnetic nonlinear transmission lines.
Reale, D V; Bragg, J-W B; Gonsalves, N R; Johnson, J M; Neuber, A A; Dickens, J C; Mankowski, J J
2014-05-01
Gyromagnetic Nonlinear Transmission Lines (NLTLs) generate microwaves through the damped gyromagnetic precession of the magnetic moments in ferrimagnetic material, and are thus utilized as compact, solid-state, frequency agile, high power microwave (HPM) sources. The output frequency of a NLTL can be adjusted by control of the externally applied bias field and incident voltage pulse without physical alteration to the structure of the device. This property provides a frequency tuning capability not seen in many conventional e-beam based HPM sources. The NLTLs developed and tested are mesoband sources capable of generating MW power levels in the L, S, and C bands of the microwave spectrum. For an individual NLTL the output power at a given frequency is determined by several factors including the intrinsic properties of the ferrimagnetic material and the transmission line structure. Hence, if higher power levels are to be achieved, it is necessary to combine the outputs of multiple NLTLs. This can be accomplished in free space using antennas or in a transmission line via a power combiner. Using a bias-field controlled delay, a transient, high voltage, coaxial, three port, power combiner was designed and tested. Experimental results are compared with the results of a transient COMSOL simulation to evaluate combiner performance. PMID:24880394
Bias-field controlled phasing and power combination of gyromagnetic nonlinear transmission lines
NASA Astrophysics Data System (ADS)
Reale, D. V.; Bragg, J.-W. B.; Gonsalves, N. R.; Johnson, J. M.; Neuber, A. A.; Dickens, J. C.; Mankowski, J. J.
2014-05-01
Gyromagnetic Nonlinear Transmission Lines (NLTLs) generate microwaves through the damped gyromagnetic precession of the magnetic moments in ferrimagnetic material, and are thus utilized as compact, solid-state, frequency agile, high power microwave (HPM) sources. The output frequency of a NLTL can be adjusted by control of the externally applied bias field and incident voltage pulse without physical alteration to the structure of the device. This property provides a frequency tuning capability not seen in many conventional e-beam based HPM sources. The NLTLs developed and tested are mesoband sources capable of generating MW power levels in the L, S, and C bands of the microwave spectrum. For an individual NLTL the output power at a given frequency is determined by several factors including the intrinsic properties of the ferrimagnetic material and the transmission line structure. Hence, if higher power levels are to be achieved, it is necessary to combine the outputs of multiple NLTLs. This can be accomplished in free space using antennas or in a transmission line via a power combiner. Using a bias-field controlled delay, a transient, high voltage, coaxial, three port, power combiner was designed and tested. Experimental results are compared with the results of a transient COMSOL simulation to evaluate combiner performance.
Nonlinear phase noise mitigation in phase-sensitive amplified transmission systems.
Olsson, Samuel L I; Karlsson, Magnus; Andrekson, Peter A
2015-05-01
We investigate the impact of in-line amplifier noise in transmission systems amplified by two-mode phase-sensitive amplifiers (PSAs) and present the first experimental demonstration of nonlinear phase noise (NLPN) mitigation in a modulation format independent PSA-amplified transmission system. The NLPN mitigation capability is attributed to the correlated noise on the signal and idler waves at the input of the transmission span. We study a single-span system with noise loading in the transmitter but the results are expected to be applicable also in multi-span systems. The experimental investigation is supported by numerical simulations showing excellent agreement with the experiments. In addition to demonstrating NLPN mitigation we also present a record high sensitivity receiver, enabled by low-noise PSA-amplification, requiring only 4.1 photons per bit to obtain a bit error ratio (BER) of 1 × 10(-3) with 10 GBd quadrature phase-shift keying (QPSK) data. PMID:25969263
On solvability of inverse coefficient problems for nonlinear convection—diffusion—reaction equation
NASA Astrophysics Data System (ADS)
Brizitskii, R. V.; Saritskaya, Zh Yu
2016-06-01
An inverse coefficient problem is considered for a stationary nonlinear convection- diffusion-reaction equation, in which reaction coefficient has a rather common dependence on substance concentration and on spacial variable. The solvability of the considered nonlinear boundary value problem is proved in a general case. The existence of solutions of the inverse problem is proved for the reaction coefficients, which are defined by the product of two functions. The first function depends on a spatial variable, the second one depends nonlinearly on the solution of the boundary value problem. The mentioned inverse problem consists in reconstructing the first function with the help of additional information provided by the solution of the boundary value problem.
NASA Technical Reports Server (NTRS)
Gabrielsen, R. E.; Karel, S.
1975-01-01
An algorithm for solving the nonlinear stationary Navier-Stokes problem is developed. Explicit error estimates are given. This mathematical technique is potentially adaptable to the separation problem.
NASA Astrophysics Data System (ADS)
Djordjevic, Ivan B.; Vasic, Bane
2006-01-01
A problem of suppression of intrachannel nonlinearities through the use of constrained coding is considered. Three different techniques are proposed and compared with respect to their efficiency, namely 1) constrained coding; 2) combined constrained and error control coding; and 3) deliberate error insertion. Significant Q-factor improvement up to 16 dB depending on code rate and number of spans is demonstrated. A combined constrained-iterative forward error correction (FEC) scheme can operate in the presence of strong intrachannel nonlinearities when even advanced FEC schemes would be overwhelmed with errors. It provides a coding gain of 12.1 dB at a bit error rate (BER) of 10-9. Deliberate error insertion is an efficient approach to balance the encoder complexity and the achievable coding gain.
Fast and Robust Newton strategies for non-linear geodynamics problems
NASA Astrophysics Data System (ADS)
Le Pourhiet, Laetitia; May, Dave
2014-05-01
Geodynamic problems are inherently non-linear, with sources of non-inearities arising from the (i) rheology, (ii) boundary conditions and (iii) the choice of time integration scheme. We have developed a robust non-linear scheme utilizing PETSc's non-linear solver framework; SNES. Through the SNES framework, we have access to a wide range of globalization techniques. In this work we extensively use line search implementation. We explored a wide range different strategies for solving a variety of non-linear problems specific to geodynamics. In this presentation, we report of the most robust line-searching techniques which we have found for the three classes of non-linearities previously identified. Among the class of rheological non-linearities, the shear banding instability using visco-plastic flow rules is the most difficult to solve. Distinctively from its sibling, the elasto-plastic rheology, the visco-plastic rheology causes instantaneous shear localisation. As a results, decreasing time-stepping is not a viable approach to better capture the initial phase of localisation. Furthermore, return map algorithms based on a consistent tangent cannot be used as the slope of the tangent is infinite. Obtaining a converged non-linear solution to this problem only relies on the robustness non-linear solver. After presenting a Newton methodology suitable for rheological non-linearities, we examine the performance of this formulation when frictional sliding boundary conditions are introduced. We assess the robustness of the non-linear solver when applied to critical taper type problems.
Willert, Jeffrey; Park, H.; Taitano, William
2015-10-12
High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.
Weakly nonlinear analysis of the Saffman-Taylor problem
NASA Astrophysics Data System (ADS)
Miranda, Jose A.
The Saffman-Taylor viscous fingering instability occurs when a less viscous fluid displaces a more viscous one between narrowly spaced parallel plates in a Hele-Shaw cell. Experiments in radial and rectangular flow geometries form finger-like patterns, in which fingers of different lengths compete, spread and split. Our weakly nonlinear analysis of the instability predicts these phenomena, which are beyond the scope of linear stability theory. Finger competition arises through enhanced growth of sub-harmonic perturbations, while spreading and splitting occur through the growth of harmonic modes. Nonlinear mode-coupling enhances the growth of these specific perturbations with appropriate relative phases, as we demonstrate through a symmetry analysis of the mode coupling equations. We extend our mode coupling theory to include the situation in which one of the fluids is a ferrofluid and a magnetic field is applied normal to the Hele-Shaw cell. Our analysis indicates that the onset of interface symmetry breaking observed in experiments involving ferrofluids depends on viscosity contrast, not on the applied magnetic field. We also show how magnetic fields lead to finger tip-splitting.
Johnson, J M; Reale, D V; Krile, J T; Garcia, R S; Cravey, W H; Neuber, A A; Dickens, J C; Mankowski, J J
2016-05-01
In this paper, a solid-state four element array gyromagnetic nonlinear transmission line high power microwave system is presented as well as a detailed description of its subsystems and general output capabilities. This frequency agile S-band source is easily adjusted from 2-4 GHz by way of a DC driven biasing magnetic field and is capable of generating electric fields of 7.8 kV/m at 10 m correlating to 4.2 MW of RF power with pulse repetition frequencies up to 1 kHz. Beam steering of the array at angles of ±16.7° is also demonstrated, and the associated general radiation pattern is detailed. PMID:27250448
NASA Astrophysics Data System (ADS)
Johnson, J. M.; Reale, D. V.; Krile, J. T.; Garcia, R. S.; Cravey, W. H.; Neuber, A. A.; Dickens, J. C.; Mankowski, J. J.
2016-05-01
In this paper, a solid-state four element array gyromagnetic nonlinear transmission line high power microwave system is presented as well as a detailed description of its subsystems and general output capabilities. This frequency agile S-band source is easily adjusted from 2-4 GHz by way of a DC driven biasing magnetic field and is capable of generating electric fields of 7.8 kV/m at 10 m correlating to 4.2 MW of RF power with pulse repetition frequencies up to 1 kHz. Beam steering of the array at angles of ±16.7° is also demonstrated, and the associated general radiation pattern is detailed.
Nonlinear gearshifts control of dual-clutch transmissions during inertia phase.
Hu, Yunfeng; Tian, Lu; Gao, Bingzhao; Chen, Hong
2014-07-01
In this paper, a model-based nonlinear gearshift controller is designed by the backstepping method to improve the shift quality of vehicles with a dual-clutch transmission (DCT). Considering easy-implementation, the controller is rearranged into a concise structure which contains a feedforward control and a feedback control. Then, robustness of the closed-loop error system is discussed in the framework of the input to state stability (ISS) theory, where model uncertainties are considered as the additive disturbance inputs. Furthermore, due to the application of the backstepping method, the closed-loop error system is ordered as a linear system. Using the linear system theory, a guideline for selecting the controller parameters is deduced which could reduce the workload of parameters tuning. Finally, simulation results and Hardware in the Loop (HiL) simulation are presented to validate the effectiveness of the designed controller. PMID:24815082
High power microwave beam steering based on gyromagnetic nonlinear transmission lines
NASA Astrophysics Data System (ADS)
Romanchenko, I. V.; Rostov, V. V.; Gunin, A. V.; Konev, V. Yu.
2015-06-01
We demonstrate electronically controlled beam steering by high power RF pulses produced by two gyromagnetic nonlinear transmission lines (NLTLs) connected to a one high voltage driver. Each NLTL is capable of producing several ns RF pulses with peak power from 50 to 700 MW (6% standard deviation) at frequencies from 0.5 to 1.7 GHz (1% standard deviation) with 100 Hz repetition rate. Using a helix antenna allows irradiating of RF pulses with almost circular polarization and 350 MW maximum peak power, which corresponds to 350 kV effective potential of radiation. At the installation of two identical channels, we demonstrate the possibility of beam steering within ±15° in the horizontal plane by coherent RF pulses with circular polarization at 1.0 GHz center frequency. Fourfold increase in the power flux density for in-phase irradiation of RF pulses is confirmed by comparison with one-channel operation.
NASA Astrophysics Data System (ADS)
Shinozaki, Takashi; Okada, Masato; Reyes, Alex D.; Câteau, Hideyuki
2010-01-01
Intermingled neural connections apparent in the brain make us wonder what controls the traffic of propagating activity in the brain to secure signal transmission without harmful crosstalk. Here, we reveal that inhibitory input but not excitatory input works as a particularly useful traffic controller because it controls the degree of synchrony of population firing of neurons as well as controlling the size of the population firing bidirectionally. Our dynamical system analysis reveals that the synchrony enhancement depends crucially on the nonlinear membrane potential dynamics and a hidden slow dynamical variable. Our electrophysiological study with rodent slice preparations show that the phenomenon happens in real neurons. Furthermore, our analysis with the Fokker-Planck equations demonstrates the phenomenon in a semianalytical manner.
From Self-consistency to SOAR: Solving Large Scale NonlinearEigenvalue Problems
Bai, Zhaojun; Yang, Chao
2006-02-01
What is common among electronic structure calculation, design of MEMS devices, vibrational analysis of high speed railways, and simulation of the electromagnetic field of a particle accelerator? The answer: they all require solving large scale nonlinear eigenvalue problems. In fact, these are just a handful of examples in which solving nonlinear eigenvalue problems accurately and efficiently is becoming increasingly important. Recognizing the importance of this class of problems, an invited minisymposium dedicated to nonlinear eigenvalue problems was held at the 2005 SIAM Annual Meeting. The purpose of the minisymposium was to bring together numerical analysts and application scientists to showcase some of the cutting edge results from both communities and to discuss the challenges they are still facing. The minisymposium consisted of eight talks divided into two sessions. The first three talks focused on a type of nonlinear eigenvalue problem arising from electronic structure calculations. In this type of problem, the matrix Hamiltonian H depends, in a non-trivial way, on the set of eigenvectors X to be computed. The invariant subspace spanned by these eigenvectors also minimizes a total energy function that is highly nonlinear with respect to X on a manifold defined by a set of orthonormality constraints. In other applications, the nonlinearity of the matrix eigenvalue problem is restricted to the dependency of the matrix on the eigenvalues to be computed. These problems are often called polynomial or rational eigenvalue problems In the second session, Christian Mehl from Technical University of Berlin described numerical techniques for solving a special type of polynomial eigenvalue problem arising from vibration analysis of rail tracks excited by high-speed trains.
Influence of impurities on solitons in the nonlinear LC transmission line.
Pan, Jun-ting; Chen, Wei-zhong; Tao, Feng; Xu, Wen
2011-01-01
This paper studies the propagation of solitons in the nonlinear LC transmission line (NLCTL) with capacitor impurity. Based on Kirchhoff's laws, the numerical simulation shows that the amplitude of the soliton will be increased or decreased when it is close to the positive or negative impurity. Then, it will be split into reflected and transmitted waves by both the positive and negative impurities. Furthermore, their final amplitude and propagating speeds are almost independent of the impurity polarity. The observations near the impurity can be understood in the physical picture of the linear uncoupled energy absorption. By these results, we find that the impurity-soliton interactions (ISIs) in NLCTLs for both inductance and capacitance impurities, which have been seen to be different before, actually can be unified. They also indicate that the ISIs in NLCTLs essentially can be integrated with those in many other soliton systems, such as the Frenkel-Kontorova model and hydrodynamics. Moreover, the impurity-induced influence on the NLCTL solitons can also be well interpreted in the framework of the nonlinear Schrödinger model with an impurity term derived from the discrete voltage propagation equations by means of the perturbation method. PMID:21405785
NASA Astrophysics Data System (ADS)
Bianchi, Matteo; Scarpa, Fabrizio
2013-08-01
This work describes the vibration transmissibility behaviour in conventional and auxetic (negative Poisson’s ratio) foams under low and high amplitude vibrations. Auxetic foam pads were manufactured from conventional open cell PU-PE based blocks using an alternative manufacturing process to the one currently used in the mainstream literature. The dynamic behaviour of both conventional and auxetic porous materials was assessed within the frequency bandwidth 5-500 Hz using a base excitation technique with a calibrated seismic mass. The foam pads were subjected to white noise broadband excitation at low dynamic strain, followed by a sine sweep around the resonance of the foam-mass system. The experimental data have been used to perform an inverse identification of the nonlinear dependence of the foam permeability versus the amplitude and frequency of excitation using a single-degree-of-freedom poroelastic vibration model. The auxetic foam shows higher dynamic stiffness and enhanced viscous dissipation characteristics, in particular when subjected to nonlinear vibration loading.
Pan, Shuokai; Elliott, Stephen J; Teal, Paul D; Lineton, Ben
2015-06-01
Nonlinear models of the cochlea are best implemented in the time domain, but their computational demands usually limit the duration of the simulations that can reasonably be performed. This letter presents a modified state space method and its application to an example nonlinear one-dimensional transmission-line cochlear model. The sparsity pattern of the individual matrices for this alternative formulation allows the use of significantly faster numerical algorithms. Combined with a more efficient implementation of the saturating nonlinearity, the computational speed of this modified state space method is more than 40 times faster than that of the original formulation. PMID:26093443
NASA Astrophysics Data System (ADS)
Ravasi, Matteo; Vasconcelos, Ivan; Curtis, Andrew
2014-08-01
Source-receiver interferometric imaging can be used to synthesize a subsurface acoustic or elastic image, consisting of a zero-time, zero-offset response (or Green's function) between a colocated pseudo-source and pseudo-receiver placed at each point in the subsurface image. However, if the imaging process does not properly account for multiple reflections, and enclosing boundaries of sources and receivers are not available, the image shows artefacts, poorly illuminated areas and distorted image amplitudes. Here we demonstrate with numerical examples that two-sided non-linear imaging provides the best elastic pure-mode (PP and SS) and converted-mode (PS) images, having higher resolution and more uniform illumination than those obtained from both one-sided linear imaging and from other intermediate steps of imaging (e.g. non-linear one-sided, linear two-sided). We also propose practical approaches to construct the additional fields required by two-sided non-linear imaging without the need for a detailed velocity model and receivers (and/or sources) in the subsurface. Moreover, when conversions are used for imaging, `true-amplitude' images (here true-amplitude means properly retrieving amplitudes that represent the zero-time, zero-offset elastic response) should theoretically vanish because neither P-to-S or S-to-P conversions arise at zero-time and zero-offset. Applying a correction procedure that accounts for the polarity reversal in PS (or SP) single-shot images helps with their structural interpretation but results in an unphysical estimate of the subsurface response and uninterpretable amplitudes. This suggests that there are advantages in exploiting pure-mode SS reflections/transmissions, in addition to converted waves only, because they require no polarity correction and the resulting image contains meaningful amplitudes that are proportional to the local shear-wave properties of the medium.
Differential geometry measures of nonlinearity for the bearing-only tracking problem
NASA Astrophysics Data System (ADS)
Mallick, Mahendra; La Scala, Barbara F.; Arulampalam, M. S.
2005-05-01
The bearing-only tracking problem arises in many radar and sonar tracking applications. Since the bearing measurement model is a nonlinear function of the target state, the filtering problem is nonlinear in nature. A great deal of attention has been focused on this problem due to the difficulty posed by the so-called high degree of nonlinearity (DoN) in the problem. However, a quantitative measure of the DoN is not calculated in previous works. It has been observed that the extended Kalman filter (EKF) in which the state vector consists of the Cartesian components of position and velocity is unstable and diverges in some cases. The range parametrized EKF (RPEKF) and particle filter (PF) have been shown to produce improved estimates for the bearing-only tracking problem. In this paper, we calculate two measures of nonlinearity, (1) the parameter-effects curvature and (2) intrinsic curvature for the bearing-only tracking problem using the differential geometry measures of nonlinearity. We present numerical results using simulated data for the constant velocity motion of a target in 2D with bearing-only measurements where the sensor platform uses a higher order motion than the target to achieve observability. We analyze the DoN by varying the distance between the target and sensor.
Solution algorithms for non-linear singularly perturbed optimal control problems
NASA Technical Reports Server (NTRS)
Ardema, M. D.
1983-01-01
The applicability and usefulness of several classical and other methods for solving the two-point boundary-value problem which arises in non-linear singularly perturbed optimal control are assessed. Specific algorithms of the Picard, Newton and averaging types are formally developed for this class of problem. The computational requirements associated with each algorithm are analysed and compared with the computational requirement of the method of matched asymptotic expansions. Approximate solutions to a linear and a non-linear problem are obtained by each method and compared.
Periodic boundary value problems for nonlinear impulsive evolution equations on Banach spaces
NASA Astrophysics Data System (ADS)
Yu, Xiulan; Wang, JinRong
2015-05-01
In this paper, we consider periodic boundary value problems for two new type nonlinear impulsive evolution equations on Banach spaces. By using the theory of semigroup, a mixed type Gronwall inequality and fixed point methods, we establish several sufficient conditions on the existence of mild solutions for such problems. Finally, examples are given to illustrate our main results.
COYOTE: a finite-element computer program for nonlinear heat-conduction problems
Gartling, D.K.
1982-10-01
COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program.
A hybrid symbolic/finite-element algorithm for solving nonlinear optimal control problems
NASA Technical Reports Server (NTRS)
Bless, Robert R.; Hodges, Dewey H.
1991-01-01
The general code described is capable of solving difficult nonlinear optimal control problems by using finite elements and a symbolic manipulator. Quick and accurate solutions are obtained with a minimum for user interaction. Since no user programming is required for most problems, there are tremendous savings to be gained in terms of time and money.
On high-continuity transfinite element formulations for linear-nonlinear transient thermal problems
NASA Technical Reports Server (NTRS)
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
This paper describes recent developments in the applicability of a hybrid transfinite element methodology with emphasis on high-continuity formulations for linear/nonlinear transient thermal problems. The proposed concepts furnish accurate temperature distributions and temperature gradients making use of a relatively smaller number of degrees of freedom; and the methodology is applicable to linear/nonlinear thermal problems. Characteristic features of the formulations are described in technical detail as the proposed hybrid approach combines the major advantages and modeling features of high-continuity thermal finite elements in conjunction with transform methods and classical Galerkin schemes. Several numerical test problems are evaluated and the results obtained validate the proposed concepts for linear/nonlinear thermal problems.
SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis
Attaway, S.W.; Laursen, T.A.; Zadoks, R.I.
1998-08-01
This report gives an introduction to the basic concepts and principles involved in the formulation of nonlinear problems in solid mechanics. By way of motivation, the discussion begins with a survey of some of the important sources of nonlinearity in solid mechanics applications, using wherever possible simple one dimensional idealizations to demonstrate the physical concepts. This discussion is then generalized by presenting generic statements of initial/boundary value problems in solid mechanics, using linear elasticity as a template and encompassing such ideas as strong and weak forms of boundary value problems, boundary and initial conditions, and dynamic and quasistatic idealizations. The notational framework used for the linearized problem is then extended to account for finite deformation of possibly inelastic solids, providing the context for the descriptions of nonlinear continuum mechanics, constitutive modeling, and finite element technology given in three companion reports.
The eigenvalue problem associated with the nonlinear buckling of a shear bending column
NASA Astrophysics Data System (ADS)
Nishimura, Isao
2011-04-01
This paper discusses the eigenvalue problem of a nonlinear differential equation that governs the stability of a shear bending column under extremely large deformation. What is taken into consideration is the geometrical nonlinearity while the material is supposed to be linear. The reason of a superbly stable buckling behavior of a slender rubber bearing is physically explained by pointing out the analogy that is similar to the nonlinear wave propagation expressed in KdV equation. The nonlinear boundary condition and the nonlinear term of the differential equation cancel each other and make the associated eigenvalue rather constant. In other words, as far as the material is supposed to be linear, the column does not buckle no matter how large the deformation is. This theoretical prediction is experimentally verified and successfully applied to a base isolation system of a lightweight structure.
Singular layers for transmission problems in thin shallow shell theory: Rigid junction case
NASA Astrophysics Data System (ADS)
Merabet, Ismail; Chacha, D. A.; Nicaise, S.
2010-02-01
In this Note we study two-dimensional transmission problems for the linear Koiter's model of an elastic multi-structure composed of two thin shallow shells. This work enters in the framework of singular perturbation of problems depending on a small parameter ɛ. The formal limit problem fails to give a solution satisfying all boundary and transmission conditions; it gives only the outer solution. Both in the case of regular or singular loadings, we derive a limit problem which allows us to determine the inner solution explicitly.
Boundary-element shape sensitivity analysis for thermal problems with nonlinear boundary conditions
NASA Technical Reports Server (NTRS)
Kane, James H.; Wang, Hua
1991-01-01
Implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solid objects subjected to nonlinear boundary conditions is shown to generate an accurate and economical approach for the computation of shape sensitivities for this class of problems. This approach involves the employment of analytical derivatives of boundary-element kernel functions with respect to shape design variables. A formulation is presented that can consistently account for both temperature-dependent convection and radiation boundary conditions. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems are presented that have closed-form solutions.
NASA Technical Reports Server (NTRS)
Muravyov, Alexander A.
1999-01-01
In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.
The effect of problem perturbations on nonlinear dynamical systems and their reduced order models
Serban, R; Homescu, C; Petzold, L
2005-03-03
Reduced order models are used extensively in many areas of science and engineering for simulation, design, and control. Reduction techniques for nonlinear dynamical systems produce models that depend strongly on the nominal set of parameters for which the reduction is carried out. In this paper we address the following two questions: 'What is the effect of perturbations in the problem parameters on the output functional of a nonlinear dynamical system?' and 'To what extent does the reduced order model capture this effect?'
ERIC Educational Resources Information Center
Pinkerton, Steven D.; Chesson, Harrell W.; Crosby, Richard A.; Layde, Peter M.
2011-01-01
A mathematical model of HIV/sexually transmitted infections (STI) transmission was used to examine how linearity or nonlinearity in the relationship between the number of unprotected sex acts (or the number of sex partners) and the risk of acquiring HIV or a highly infectious STI (such as gonorrhea or chlamydia) affects the utility of sexual…
Application of traditional CFD methods to nonlinear computational aeroacoustics problems
NASA Technical Reports Server (NTRS)
Chyczewski, Thomas S.; Long, Lyle N.
1995-01-01
This paper describes an implementation of a high order finite difference technique and its application to the category 2 problems of the ICASE/LaRC Workshop on Computational Aeroacoustics (CAA). Essentially, a popular Computational Fluid Dynamics (CFD) approach (central differencing, Runge-Kutta time integration and artificial dissipation) is modified to handle aeroacoustic problems. The changes include increasing the order of the spatial differencing to sixth order and modifying the artificial dissipation so that it does not significantly contaminate the wave solution. All of the results were obtained from the CM5 located at the Numerical Aerodynamic Simulation Laboratory. lt was coded in CMFortran (very similar to HPF), using programming techniques developed for communication intensive large stencils, and ran very efficiently.
Some comparison of restarted GMRES and QMR for linear and nonlinear problems
Morgan, R.; Joubert, W.
1994-12-31
Comparisons are made between the following methods: QMR including its transpose-free version, restarted GMRES, and a modified restarted GMRES that uses approximate eigenvectors to improve convergence, For some problems, the modified GMRES is competitive with or better than QMR in terms of the number of matrix-vector products. Also, the GMRES methods can be much better when several similar systems of linear equations must be solved, as in the case of nonlinear problems and ODE problems.
CUERVO: A finite element computer program for nonlinear scalar transport problems
Sirman, M.B.; Gartling, D.K.
1995-11-01
CUERVO is a finite element code that is designed for the solution of multi-dimensional field problems described by a general nonlinear, advection-diffusion equation. The code is also applicable to field problems described by diffusion, Poisson or Laplace equations. The finite element formulation and the associated numerical methods used in CUERVO are outlined here; detailed instructions for use of the code are also presented. Example problems are provided to illustrate the use of the code.
On the Value Function of Weakly Coercive Problems in Nonlinear Stochastic Control
Motta, Monica; Sartori, Caterina
2011-08-15
In this paper we investigate via a dynamic programming approach some nonlinear stochastic control problems where the control set is unbounded and a classical coercivity hypothesis is replaced by some weaker assumptions. We prove that these problems can be approximated by finite fuel problems; show the continuity of the relative value functions and characterize them as unique viscosity solutions of a quasi-variational inequality with suitable boundary conditions.
An iterative method to solve the heat transfer problem under the non-linear boundary conditions
NASA Astrophysics Data System (ADS)
Zhu, Zhenggang; Kaliske, Michael
2012-02-01
The aim of the paper is to determine the approximation of the tangential matrix for solving the non-linear heat transfer problem. Numerical model of the strongly non-linear heat transfer problem based on the theory of the finite element method is presented. The tangential matrix of the Newton method is formulated. A method to solve the heat transfer with the non-linear boundary conditions, based on the secant slope of a reference function, is developed. The contraction mapping principle is introduced to verify the convergence of this method. The application of the method is shown by two examples. Numerical results of these examples are comparable to the ones solved with the Newton method and the commercial software COMSOL for the heat transfer problem under the radiative boundary conditions.
Finite dimensional approximation of a class of constrained nonlinear optimal control problems
NASA Technical Reports Server (NTRS)
Gunzburger, Max D.; Hou, L. S.
1994-01-01
An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.
ERIC Educational Resources Information Center
Thomson, Norman; Stewart, James
2003-01-01
Presents a study to determine the methods inquiry geneticists use to solve dynamic complex computer-generated transmission genetics problems; specifically, their strategies and conceptual knowledge. Develops a hierarchical framework and pathway for solving problems through geneticist solution protocols and interviews. (Contains 32 references.)…
NASA Astrophysics Data System (ADS)
Abramov, A. A.; Yukhno, L. F.
2016-07-01
A nonlinear eigenvalue problem for a linear system of ordinary differential equations is examined on a semi-infinite interval. The problem is supplemented by nonlocal conditions specified by a Stieltjes integral. At infinity, the solution must be bounded. In addition to these basic conditions, the solution must satisfy certain redundant conditions, which are also nonlocal. A numerically stable method for solving such a singular overdetermined eigenvalue problem is proposed and analyzed. The essence of the method is that this overdetermined problem is replaced by an auxiliary problem consistent with all the above conditions.
A new algorithm for constrained nonlinear least-squares problems, part 1
NASA Technical Reports Server (NTRS)
Hanson, R. J.; Krogh, F. T.
1983-01-01
A Gauss-Newton algorithm is presented for solving nonlinear least squares problems. The problem statement may include simple bounds or more general constraints on the unknowns. The algorithm uses a trust region that allows the objective function to increase with logic for retreating to best values. The computations for the linear problem are done using a least squares system solver that allows for simple bounds and linear constraints. The trust region limits are defined by a box around the current point. In its current form the algorithm is effective only for problems with small residuals, linear constraints and dense Jacobian matrices. Results on a set of test problems are encouraging.
Dowling, N A; Shandley, K; Oldenhof, E; Youssef, G J; Thomas, S A; Frydenberg, E; Jackson, A C
2016-08-01
The present study investigated the intergenerational transmission of problem gambling and the potential mediating role of parental psychopathology (problem drinking, drug use problems, and mental health issues). The study comprised 3953 participants (1938 males, 2015 females) recruited from a large-scale Australian community telephone survey of adults retrospectively reporting on parental problem gambling and psychopathology during their childhood. Overall, 4.0% [95%CI 3.0, 5.0] (n=157) of participants reported paternal problem gambling and 1.7% [95%CI 1.0, 2.0] (n=68) reported maternal problem gambling. Compared to their peers, participants reporting paternal problem gambling were 5.1 times more likely to be moderate risk gamblers and 10.7 times more likely to be problem gamblers. Participants reporting maternal problem gambling were 1.7 times more likely to be moderate risk gamblers and 10.6 times more likely to be problem gamblers. The results revealed that the relationships between paternal-and-participant and maternal-and-participant problem gambling were significant, but that only the relationship between paternal-and-participant problem gambling remained statistically significant after controlling for maternal problem gambling and sociodemographic factors. Paternal problem drinking and maternal drug use problems partially mediated the relationship between paternal-and-participant problem gambling, and fully mediated the relationship between maternal-and-participant problem gambling. In contrast, parental mental health issues failed to significantly mediate the transmission of gambling problems by either parent. When parental problem gambling was the mediator, there was full mediation of the effect between parental psychopathology and offspring problem gambling for fathers but not mothers. Overall, the study highlights the vulnerability of children from problem gambling households and suggests that it would be of value to target prevention and intervention
Bouaricha, A.; Schnabel, R.B.
1996-12-31
This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.
Kaikina, Elena I.
2013-11-15
We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.
NASA Astrophysics Data System (ADS)
Teschke, Gerd; Borries, Claudia
2010-02-01
This paper is concerned with the construction of an iterative algorithm to solve nonlinear inverse problems with an ell1 constraint on x. One extensively studied method to obtain a solution of such an ell1 penalized problem is iterative soft-thresholding. Regrettably, such iteration schemes are computationally very intensive. A subtle alternative to iterative soft-thresholding is the projected gradient method that was quite recently proposed by Daubechies et al (2008 J. Fourier Anal. Appl. 14 764-92). The authors have shown that the proposed scheme is indeed numerically much thriftier. However, its current applicability is limited to linear inverse problems. In this paper we provide an extension of this approach to nonlinear problems. Adequately adapting the conditions on the (variable) thresholding parameter to the nonlinear nature, we can prove convergence in norm for this projected gradient method, with and without acceleration. A numerical verification is given in the context of nonlinear and non-ideal sensing. For this particular recovery problem we can achieve an impressive numerical performance (when comparing it to non-accelerated procedures).
NASA Astrophysics Data System (ADS)
Johnson, J. M.; Reale, D. V.; Cravey, W. H.; Garcia, R. S.; Barnett, D. H.; Neuber, A. A.; Dickens, J. C.; Mankowski, J. J.
2015-08-01
Implementing nonlinear transmission line (NLTL) technology in the design of a high power microwave source has the benefits of producing a comparatively small and lightweight solid-state system where the emission frequency is easily tuned. Usually, smaller in physical size, single NLTLs may produce significantly less power than its vacuum based counterparts. However, combining individual NLTL outputs electrically or in free-space is an attractive solution to achieve greater output power. This paper discusses a method for aligning a four element NLTL antenna array with coaxial geometry using easily adjustable temporal delay lines. These delay lines, sometimes referred to as pulse shock lines or pulse sharpening lines, are placed serially in front of the main NLTL line. The propagation velocity in each delay line is set by the voltage amplitude of an incident pulse as well as the magnetic field bias. Each is adjustable although for the system described in this paper, the voltage is held constant while the bias is changed through applying an external DC magnetic field of varying magnitude. Three different ferrimagnetic materials are placed in the temporal delay line to evaluate which yields the greatest range of electrical delay with the least amount of variability from consecutive shots.
Solid-State Radio Frequency Plasma Heating Using a Nonlinear Transmission Line
NASA Astrophysics Data System (ADS)
Miller, Kenneth; Ziemba, Timothy; Prager, James; Slobodov, Ilia
2015-11-01
Radio Frequency heating systems are rarely used by the small-scale validation platform experiments due to the high cost and complexity of these systems, which typically require high power gyrotrons or klystrons, associated power supplies, waveguides and vacuum systems. The cost and complexity of these systems can potentially be reduced with a nonlinear transmission line (NLTL) based system. In the past, NLTLs have lacked a high voltage driver that could produce long duration high voltage pulses with fast rise times at high pulse repetition frequency. Eagle Harbor Technologies, Inc. (EHT) has created new high voltage nanosecond pulser, which combined with NLTL technology will produce a low-cost, fully solid-state architecture for the generation of the RF frequencies (0.5 to 10 GHz) and peak power levels (~ 10 MW) necessary for plasma heating and diagnostic systems for the validation platform experiments within the fusion science community. The proposed system does not require the use of vacuum tube technology, is inherently lower cost, and is more robust than traditional high power RF heating schemes. Design details and initial bench testing results for the new RF system will be presented. This work is supported under DOE Grant # DE-SC0013747.
Johnson, J M; Reale, D V; Cravey, W H; Garcia, R S; Barnett, D H; Neuber, A A; Dickens, J C; Mankowski, J J
2015-08-01
Implementing nonlinear transmission line (NLTL) technology in the design of a high power microwave source has the benefits of producing a comparatively small and lightweight solid-state system where the emission frequency is easily tuned. Usually, smaller in physical size, single NLTLs may produce significantly less power than its vacuum based counterparts. However, combining individual NLTL outputs electrically or in free-space is an attractive solution to achieve greater output power. This paper discusses a method for aligning a four element NLTL antenna array with coaxial geometry using easily adjustable temporal delay lines. These delay lines, sometimes referred to as pulse shock lines or pulse sharpening lines, are placed serially in front of the main NLTL line. The propagation velocity in each delay line is set by the voltage amplitude of an incident pulse as well as the magnetic field bias. Each is adjustable although for the system described in this paper, the voltage is held constant while the bias is changed through applying an external DC magnetic field of varying magnitude. Three different ferrimagnetic materials are placed in the temporal delay line to evaluate which yields the greatest range of electrical delay with the least amount of variability from consecutive shots. PMID:26329216
High power microwave beam steering based on gyromagnetic nonlinear transmission lines
Romanchenko, I. V. Rostov, V. V.; Gunin, A. V.; Konev, V. Yu.
2015-06-07
We demonstrate electronically controlled beam steering by high power RF pulses produced by two gyromagnetic nonlinear transmission lines (NLTLs) connected to a one high voltage driver. Each NLTL is capable of producing several ns RF pulses with peak power from 50 to 700 MW (6% standard deviation) at frequencies from 0.5 to 1.7 GHz (1% standard deviation) with 100 Hz repetition rate. Using a helix antenna allows irradiating of RF pulses with almost circular polarization and 350 MW maximum peak power, which corresponds to 350 kV effective potential of radiation. At the installation of two identical channels, we demonstrate the possibility of beam steering within ±15° in the horizontal plane by coherent RF pulses with circular polarization at 1.0 GHz center frequency. Fourfold increase in the power flux density for in-phase irradiation of RF pulses is confirmed by comparison with one-channel operation.
NASA Astrophysics Data System (ADS)
Abdul Jalil, Nawal A.; Griffin, Michael J.
2007-01-01
The transmissibility of a seat depends on the dynamic response of the human body (which varies between individuals, body locations, and vibration magnitudes) and the dynamic response of the seat (which varies according to seat design). In the fore-and-aft direction, the transmissibility of a seat backrest was therefore expected to vary with vertical position on the backrest. This experimental study with 12 subjects investigated how backrest transmissibility varied with both the vertical measurement position and the magnitude of vibration. The transmissibilities of the backrest of a car seat and a block of solid foam were measured at five heights above the seat surface with random fore-and-aft vibration at five magnitudes (0.1, 0.2, 0.4, 0.8 and 1.6 ms -2 rms) over the range 0.25-20 Hz. The median transmissibilities exhibited resonances in the range 4-5 Hz for the car seat and in the range 3-6 Hz for the foam. The backrests showed clear changes in transmissibility with vertical position, but there were minimal changes in the resonance frequencies. For both backrests, the transmissibilities were greatest at the middle of the backrest. The least transmissibility was measured at the top of the car seat but at the bottom of the foam backrest. At each measurement position on both backrests, the transmissibility was non-linear with vibration magnitude: the resonance frequencies and transmissibilities at resonance decreased with increasing vibration magnitude. The variations in backrest transmissibility with vertical position and with vibration magnitude were sufficiently great to affect assessments of backrest dynamic performance. The results suggest that the fore-and-aft transmissibilities of backrests should be evaluated from more than one measurement location.
Appraisal analysis for nonlinear problems: Tool for image interpretation and survey design
NASA Astrophysics Data System (ADS)
Routh, P. S.
2005-12-01
At present there is no formal theory for nonlinear appraisal analysis. A lthough this makes the problem difficult but there are number of methods proposed in the past such as linearized analysis (Backus and Gilbert, 1 970), funnel function approach (Oldenburg, 1983) and nonlinear Backus-Gi lbert theory (Snieder, 1990) have provided direction to look at this pro blem. In this paper I will briefly review these methods and discuss some new developments in the nonlinear and linearized point spread function analysis as a model const ruction problem. Point spread functions (PSF) describes how an impulse f unction in the model is observed in the inversion result. Knowledge of P SF provides insight into the inverse operator. It allows to carry out image interpretation such as regions of the model supported by data and provides the ability to design focused surveys.Examples from seismic tomography and controlled source EM will be presented.
Initial Value Problem Solution of Nonlinear Shallow Water-Wave Equations
Kanoglu, Utku; Synolakis, Costas
2006-10-06
The initial value problem solution of the nonlinear shallow water-wave equations is developed under initial waveforms with and without velocity. We present a solution method based on a hodograph-type transformation to reduce the nonlinear shallow water-wave equations into a second-order linear partial differential equation and we solve its initial value problem. The proposed solution method overcomes earlier limitation of small waveheights when the initial velocity is nonzero, and the definition of the initial conditions in the physical and transform spaces is consistent. Our solution not only allows for evaluation of differences in predictions when specifying an exact initial velocity based on nonlinear theory and its linear approximation, which has been controversial in geophysical practice, but also helps clarify the differences in runup observed during the 2004 and 2005 Sumatran tsunamigenic earthquakes.
Newton's method: A link between continuous and discrete solutions of nonlinear problems
NASA Technical Reports Server (NTRS)
Thurston, G. A.
1980-01-01
Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.
Kim, T; Pasciak, J E; Vassilevski, P S
2004-09-20
In this paper, we consider an inexact Newton method applied to a second order nonlinear problem with higher order nonlinearities. We provide conditions under which the method has a mesh-independent rate of convergence. To do this, we are required to first, set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced with one iterative step provided that the initial nonlinear iterate is accurate enough. The closeness criteria can be taken independent of the mesh size. Finally, the results of numerical experiments are given to support the theory.
NASA Astrophysics Data System (ADS)
Roul, Pradip
2016-06-01
This paper presents a new iterative technique for solving nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions. The method is based on the homotopy perturbation method and the integral equation formalism in which a recursive scheme is established for the components of the approximate series solution. This method does not involve solution of a sequence of nonlinear algebraic or transcendental equations for the unknown coefficients as in some other iterative techniques developed for singular boundary value problems. The convergence result for the proposed method is established in the paper. The method is illustrated by four numerical examples, two of which have physical significance: The first problem is an application of the reaction-diffusion process in a porous spherical catalyst and the second problem arises in the study of steady-state oxygen-diffusion in a spherical cell with Michaelis-Menten uptake kinetics.
Singular layers for transmission problems in thin shallow shell theory: Elastic junction case
NASA Astrophysics Data System (ADS)
Merabet, Ismail; Chacha, D. A.; Nicaise, Serge
2010-05-01
In this Note we study two-dimensional transmission problems for the linear Koiter's model of an elastic multi-structure composed of two thin shallow shells with the same thickness ɛ≪1, in the elastic junction case. We suppose that the loading is singular, that the elastic coefficients are of different order on each part ( O(ɛ) and O(1) respectively) and that the elastic stiffness coefficient of the hinge is k=O(ɛ). The formal limit problem fails to give a solution satisfying all boundary and transmission conditions; it gives only the outer solution. We derive the inner limit problem which allows us to describe the transmission layer.
Gartling, D.K.; Hogan, R.E.
1994-10-01
The theoretical and numerical background for the finite element computer program, COYOTE II, is presented in detail. COYOTE II is designed for the multi-dimensional analysis of nonlinear heat conduction problems and other types of diffusion problems. A general description of the boundary value problems treated by the program is presented. The finite element formulation and the associated numerical methods used in COYOTE II are also outlined. Instructions for use of the code are documented in SAND94-1179; examples of problems analyzed with the code are provided in SAND94-1180.
Numerical solutions of nonlinear STIFF initial value problems by perturbed functional iterations
NASA Technical Reports Server (NTRS)
Dey, S. K.
1982-01-01
Numerical solution of nonlinear stiff initial value problems by a perturbed functional iterative scheme is discussed. The algorithm does not fully linearize the system and requires only the diagonal terms of the Jacobian. Some examples related to chemical kinetics are presented.
NASA Astrophysics Data System (ADS)
Berezkin, V. E.; Lotov, A. V.; Lotova, E. A.
2014-06-01
Methods for approximating the Edgeworth-Pareto hull (EPH) of the set of feasible criteria vectors in nonlinear multicriteria optimization problems are examined. The relative efficiency of two EPH approximation methods based on classical methods of searching for local extrema of convolutions of criteria is experimentally studied for a large-scale applied problem (with several hundred variables). A hybrid EPH approximation method combining classical and genetic approximation methods is considered.
A comparison of several methods of solving nonlinear regression groundwater flow problems.
Cooley, R.L.
1985-01-01
Computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear-regression steady state groundwater flow problems. The fastest methods were the Marquardt and quasi-linearization methods, which required almost identical computer times and numbers of iterations; the next fastest was the quasi-Newton method, and last was the Fletcher-Reeves method, which did not converge in 100 iterations for two of the problems.-from Author
Makovejs, Sergejs; Millar, David S; Lavery, Domanic; Behrens, Carsten; Killey, Robert I; Savory, Seb J; Bayvel, Polina
2010-06-01
In this paper long-haul, single channel, polarization multiplexed 16-state quadrature amplitude modulation (PDM-QAM-16) transmission at 112 Gbit/s is investigated. Novel digital signal processing techniques are used to perform carrier phase estimation and symbol estimation, in combination with nonlinear digital backpropagation. The results obtained demonstrate that the use of digital nonlinear backpropagation increases the optimum launch power from -4 dBm to -1 dBm with a consequent increase in maximum reach from 1440 km to 2400 km, which is a record transmission distance for QAM-16 reported to date for an SMF link with EDFAs only. Furthermore, experimental measurements are supported by simulations, based on the link used in the experiment. PMID:20588423
NASA Astrophysics Data System (ADS)
Yang, Desen; Zhang, Haoyang; Shi, Shengguo; Li, Di; Shi, Jie; Hu, Bo
2015-10-01
The propagation of plane acoustic waves can be investigated by taking advantage of the electro-acoustical analogy between the one-dimensional acoustic waveguide and the electrical transmission line, because they share the same type of equation. This paper follow the previous studies and expand the analogy into the cases of quadratic nonlinearity and dispersion produced by relaxation process. From the basic equations relating acoustic pressure, density fluctuation and velocity, which are valid for the nonlinear and relaxing media, the equivalent travelling-wave circuits of one-dimensional acoustic waveguide with the consideration of nonlinearity and relaxation processes are obtained. Furthermore, we also discuss the analogy relationship of parameters which exist in the acoustical and electrical systems.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
NASA Technical Reports Server (NTRS)
Cai, Wei; Wang, Jian-Zhong
1993-01-01
We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.
Kim, D.; Ghanem, R.
1994-12-31
Multigrid solution technique to solve a material nonlinear problem in a visual programming environment using the finite element method is discussed. The nonlinear equation of equilibrium is linearized to incremental form using Newton-Rapson technique, then multigrid solution technique is used to solve linear equations at each Newton-Rapson step. In the process, adaptive mesh refinement, which is based on the bisection of a pair of triangles, is used to form grid hierarchy for multigrid iteration. The solution process is implemented in a visual programming environment with distributed computing capability, which enables more intuitive understanding of solution process, and more effective use of resources.
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Cai, X.C.
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
NASA Astrophysics Data System (ADS)
Xu, S.; Ostrikov, K. N.
2000-07-01
The series expansion of the plasma fields and currents in vector spherical harmonics has been demonstrated to be an efficient technique for solution of nonlinear problems in spherically bounded plasmas. Using this technique, it is possible to describe the nonlinear plasma response to the rotating high-frequency magnetic field applied to the magnetically confined plasma sphere. The effect of the external magnetic field on the current drive and field configuration is studied. The results obtained are important for continuous current drive experiments in compact toruses.
The linearized characteristics method and its application to practical nonlinear supersonic problems
NASA Technical Reports Server (NTRS)
Ferri, Antonio
1952-01-01
The methods of characteristics has been linearized by assuming that the flow field can be represented as a basic flow field determined by nonlinearized methods and a linearized superposed flow field that accounts for small changes of boundary conditions. The method has been applied to two-dimensional rotational flow where the basic flow is potential flow and to axially symmetric problems where conical flows have been used as the basic flows. In both cases the method allows the determination of the flow field to be simplified and the numerical work to be reduced to a few calculations. The calculations of axially symmetric flow can be simplified if tabulated values of some coefficients of the conical flow are obtained. The method has also been applied to slender bodies without symmetry and to some three-dimensional wing problems where two-dimensional flow can be used as the basic flow. Both problems were unsolved before in the approximation of nonlinear flow.
Gehre, Matthias; Jin, Bangti
2014-02-15
In this paper, we study a fast approximate inference method based on expectation propagation for exploring the posterior probability distribution arising from the Bayesian formulation of nonlinear inverse problems. It is capable of efficiently delivering reliable estimates of the posterior mean and covariance, thereby providing an inverse solution together with quantified uncertainties. Some theoretical properties of the iterative algorithm are discussed, and the efficient implementation for an important class of problems of projection type is described. The method is illustrated with one typical nonlinear inverse problem, electrical impedance tomography with complete electrode model, under sparsity constraints. Numerical results for real experimental data are presented, and compared with that by Markov chain Monte Carlo. The results indicate that the method is accurate and computationally very efficient.
NASA Technical Reports Server (NTRS)
Murphy, Patrick Charles
1985-01-01
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. The algorithm was developed for airplane parameter estimation problems but is well suited for most nonlinear, multivariable, dynamic systems. The ML algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). MNRES determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort. MNRES determines the sensitivities with less computational effort than using either a finite-difference method or integrating the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, thus eliminating algorithm reformulation with each new model and providing flexibility to use model equations in any format that is convenient. A random search technique for determining the confidence limits of ML parameter estimates is applied to nonlinear estimation problems for airplanes. The confidence intervals obtained by the search are compared with Cramer-Rao (CR) bounds at the same confidence level. It is observed that the degree of nonlinearity in the estimation problem is an important factor in the relationship between CR bounds and the error bounds determined by the search technique. The CR bounds were found to be close to the bounds determined by the search when the degree of nonlinearity was small. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels for the parameter confidence limits. The primary utility of the measure, however, was found to be in predicting the degree of agreement between Cramer-Rao bounds and search estimates.
A new approach to the Pontryagin maximum principle for nonlinear fractional optimal control problems
NASA Astrophysics Data System (ADS)
Ali, Hegagi M.; Pereira, Fernando Lobo; Gama, Sílvio M. A.
2016-09-01
In this paper, we discuss a new general formulation of fractional optimal control problems whose performance index is in the fractional integral form and the dynamics are given by a set of fractional differential equations in the Caputo sense. We use a new approach to prove necessary conditions of optimality in the form of Pontryagin maximum principle for fractional nonlinear optimal control problems. Moreover, a new method based on a generalization of the Mittag-Leffler function is used to solving this class of fractional optimal control problems. A simple example is provided to illustrate the effectiveness of our main result.
Wu, Zong-Sheng; Fu, Wei-Ping; Xue, Ru
2015-01-01
Teaching-learning-based optimization (TLBO) algorithm is proposed in recent years that simulates the teaching-learning phenomenon of a classroom to effectively solve global optimization of multidimensional, linear, and nonlinear problems over continuous spaces. In this paper, an improved teaching-learning-based optimization algorithm is presented, which is called nonlinear inertia weighted teaching-learning-based optimization (NIWTLBO) algorithm. This algorithm introduces a nonlinear inertia weighted factor into the basic TLBO to control the memory rate of learners and uses a dynamic inertia weighted factor to replace the original random number in teacher phase and learner phase. The proposed algorithm is tested on a number of benchmark functions, and its performance comparisons are provided against the basic TLBO and some other well-known optimization algorithms. The experiment results show that the proposed algorithm has a faster convergence rate and better performance than the basic TLBO and some other algorithms as well. PMID:26421005
An iterative HAM approach for nonlinear boundary value problems in a semi-infinite domain
NASA Astrophysics Data System (ADS)
Zhao, Yinlong; Lin, Zhiliang; Liao, Shijun
2013-09-01
In this paper, we propose an iterative approach to increase the computation efficiency of the homotopy analysis method (HAM), a analytic technique for highly nonlinear problems. By means of the Schmidt-Gram process (Arfken et al., 1985) [15], we approximate the right-hand side terms of high-order linear sub-equations by a finite set of orthonormal bases. Based on this truncation technique, we introduce the Mth-order iterative HAM by using each Mth-order approximation as a new initial guess. It is found that the iterative HAM is much more efficient than the standard HAM without truncation, as illustrated by three nonlinear differential equations defined in an infinite domain as examples. This work might greatly improve the computational efficiency of the HAM and also the Mathematica package BVPh for nonlinear BVPs.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer. PMID
NASA Astrophysics Data System (ADS)
Yildiz, Nihat; San, Sait Eren; Köysal, Oğuz
2010-09-01
In this paper, two complementary objectives related to optical transmission spectra of nematic liquid crystals (NLCs) were achieved. First, at room temperature, for both pure and dye (DR9) doped E7 NLCs, the 10-250 W halogen lamp transmission spectra (wavelength 400-1200 nm) were measured at various bias voltages. Second, because the measured spectra were inherently highly nonlinear, it was difficult to construct explicit empirical physical formulas (EPFs) to employ as transmittance functions. To avoid this difficulty, layered feedforward neural networks (LFNNs) were used to construct explicit EPFs for these theoretically unknown nonlinear NLC transmittance functions. As we theoretically showed in a previous work, a LFNN, as an excellent nonlinear function approximator, is highly relevant to EPF construction. The LFNN-EPFs efficiently and consistently estimated both the measured and yet-to-be-measured nonlinear transmittance response values. The experimentally obtained doping ratio dependencies and applied bias voltage responses of transmittance were also confirmed by LFFN-EPFs. This clearly indicates that physical laws embedded in the physical data can be faithfully extracted by the suitable LFNNs. The extraordinary success achieved with LFNN here suggests two potential applications. First, although not attempted here, these LFNN-EPFs, by such mathematical operations as derivation, integration, minimization etc., can be used to obtain further transmittance related functions of NLCs. Second, for a given NLC response function, whose theoretical nonlinear functional form is yet unknown, a suitable experimental data based LFNN-EPF can be constructed to predict the yet-to-be-measured values.
NASA Technical Reports Server (NTRS)
Murio, Diego A.
1991-01-01
An explicit and unconditionally stable finite difference method for the solution of the transient inverse heat conduction problem in a semi-infinite or finite slab mediums subject to nonlinear radiation boundary conditions is presented. After measuring two interior temperature histories, the mollification method is used to determine the surface transient heat source if the energy radiation law is known. Alternatively, if the active surface is heated by a source at a rate proportional to a given function, the nonlinear surface radiation law is then recovered as a function of the interface temperature when the problem is feasible. Two typical examples corresponding to Newton cooling law and Stefan-Boltzmann radiation law respectively are illustrated. In all cases, the method predicts the surface conditions with an accuracy suitable for many practical purposes.
NASA Technical Reports Server (NTRS)
Tamma, Kumar K.; Railkar, Sudhir B.
1988-01-01
The present paper describes the applicability of hybrid transfinite element modeling/analysis formulations for nonlinear heat conduction problems involving phase change. The methodology is based on application of transform approaches and classical Galerkin schemes with finite element formulations to maintain the modeling versatility and numerical features for computational analysis. In addition, in conjunction with the above, the effects due to latent heat are modeled using enthalpy formulations to enable a physically realistic approximation to be dealt computationally for materials exhibiting phase change within a narrow band of temperatures. Pertinent details of the approach and computational scheme adapted are described in technical detail. Numerical test cases of comparative nature are presented to demonstrate the applicability of the proposed formulations for numerical modeling/analysis of nonlinear heat conduction problems involving phase change.
Gropp, W. D.; McInnes, L. C.; Smith, B. F.
1997-10-27
Developing portable and scalable software for the solution of large-scale optimization problems presents many challenges that traditional libraries do not adequately meet. Using object-oriented design in conjunction with other innovative techniques, they address these issues within the SNES (Scalable Nonlinear Equation Solvers) and SUMS (Scalable Unconstrained Minimization Solvers) packages, which are part of the multilevel PETSCs (Portable, Extensible Tools for Scientific computation) library. This paper focuses on the authors design philosophy and its benefits in providing a uniform and versatile framework for developing optimization software and solving large-scale nonlinear problems. They also consider a three-dimensional anisotropic Ginzburg-Landau model as a representative application that exploits the packages' flexible interface with user-specified data structures and customized routines for function evaluation and preconditioning.
NASA Technical Reports Server (NTRS)
Baum, J. D.; Levine, J. N.
1980-01-01
The selection of a satisfactory numerical method for calculating the propagation of steep fronted shock life waveforms in a solid rocket motor combustion chamber is discussed. A number of different numerical schemes were evaluated by comparing the results obtained for three problems: the shock tube problems; the linear wave equation, and nonlinear wave propagation in a closed tube. The most promising method--a combination of the Lax-Wendroff, Hybrid and Artificial Compression techniques, was incorporated into an existing nonlinear instability program. The capability of the modified program to treat steep fronted wave instabilities in low smoke tactical motors was verified by solving a number of motor test cases with disturbance amplitudes as high as 80% of the mean pressure.
NASA Astrophysics Data System (ADS)
Vasant, P.; Ganesan, T.; Elamvazuthi, I.
2012-11-01
A fairly reasonable result was obtained for non-linear engineering problems using the optimization techniques such as neural network, genetic algorithms, and fuzzy logic independently in the past. Increasingly, hybrid techniques are being used to solve the non-linear problems to obtain better output. This paper discusses the use of neuro-genetic hybrid technique to optimize the geological structure mapping which is known as seismic survey. It involves the minimization of objective function subject to the requirement of geophysical and operational constraints. In this work, the optimization was initially performed using genetic programming, and followed by hybrid neuro-genetic programming approaches. Comparative studies and analysis were then carried out on the optimized results. The results indicate that the hybrid neuro-genetic hybrid technique produced better results compared to the stand-alone genetic programming method.
Numerical solution of a nonlinear least squares problem in digital breast tomosynthesis
NASA Astrophysics Data System (ADS)
Landi, G.; Loli Piccolomini, E.; Nagy, J. G.
2015-11-01
In digital tomosynthesis imaging, multiple projections of an object are obtained along a small range of different incident angles in order to reconstruct a pseudo-3D representation (i.e., a set of 2D slices) of the object. In this paper we describe some mathematical models for polyenergetic digital breast tomosynthesis image reconstruction that explicitly takes into account various materials composing the object and the polyenergetic nature of the x-ray beam. A polyenergetic model helps to reduce beam hardening artifacts, but the disadvantage is that it requires solving a large-scale nonlinear ill-posed inverse problem. We formulate the image reconstruction process (i.e., the method to solve the ill-posed inverse problem) in a nonlinear least squares framework, and use a Levenberg-Marquardt scheme to solve it. Some implementation details are discussed, and numerical experiments are provided to illustrate the performance of the methods.
Landau-Zener problem in a three-level neutrino system with nonlinear time dependence
Keraenen, P.; Maalampi, J.; Myyrylaeinen, M.; Riittinen, J.
2007-02-01
We consider the level-crossing problem in a three-level system with nonlinearly time-varying Hamiltonian (time-dependence t{sup -3}). We study the validity of the so-called independent crossing approximation in the Landau-Zener model by making comparison with results obtained numerically in the density matrix approach. We also demonstrate the failure of the so-called 'nearest zero' approximation of the Landau-Zener level-crossing probability integral.
Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management
NASA Astrophysics Data System (ADS)
Koleva, M. N.
2011-11-01
In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.
Carey, G.F.; Young, D.M.
1993-12-31
The program outlined here is directed to research on methods, algorithms, and software for distributed parallel supercomputers. Of particular interest are finite element methods and finite difference methods together with sparse iterative solution schemes for scientific and engineering computations of very large-scale systems. Both linear and nonlinear problems will be investigated. In the nonlinear case, applications with bifurcation to multiple solutions will be considered using continuation strategies. The parallelizable numerical methods of particular interest are a family of partitioning schemes embracing domain decomposition, element-by-element strategies, and multi-level techniques. The methods will be further developed incorporating parallel iterative solution algorithms with associated preconditioners in parallel computer software. The schemes will be implemented on distributed memory parallel architectures such as the CRAY MPP, Intel Paragon, the NCUBE3, and the Connection Machine. We will also consider other new architectures such as the Kendall-Square (KSQ) and proposed machines such as the TERA. The applications will focus on large-scale three-dimensional nonlinear flow and reservoir problems with strong convective transport contributions. These are legitimate grand challenge class computational fluid dynamics (CFD) problems of significant practical interest to DOE. The methods developed and algorithms will, however, be of wider interest.
Modeling and analysis of electric and magnetic coupled problems under nonlinear conditions
NASA Astrophysics Data System (ADS)
Geri, A.; La Rosa, M.; Veca, G. M.
1994-05-01
In this paper the authors define a numerical method to solve nonlinear combined magnetic and electric problems using reliable general purpose calculation codes. This method has been applied to analyze the behavior of a busbar system built with a saturable steel enclosure and connected with an arbitrary external circuit. The enclosure magnetic characteristics have been determined by means of experimental tests executed by the authors. To analyze this electrical system, the skin and proximity effects in the massive conductors, as well as the load conditions of the external circuit, must be taken into account. The present formulation permits us to solve the previously described coupled problems by means of an iterative procedure. Using this technique, it is possible to solve separately the field and the circuit equations by means of specific codes. In particular, an iterative procedure it is pointed out so defined: for each estimated load condition, a finite element code has been used to evaluate the relating busbar cross parameters, taking into account the nonlinear behavior of the steel enclosure, while, for each assigned set of the busbar cross parameters, a circuit simulator has been used to determine the relating load conditions of the busbar. In addition, a specialized post-processor has been developed to manage the data flow between the calculation codes. The originality of this work is linked to the use of general purpose commercial software to solve the nonlinear magnetic and electric coupled problems.
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Aganin, Alexei
2000-01-01
The transonic nozzle transmission problem and the open rotor noise radiation problem are solved computationally. Both are multiple length scales problems. For efficient and accurate numerical simulation, the multiple-size-mesh multiple-time-step Dispersion-Relation-Preserving scheme is used to calculate the time periodic solution. To ensure an accurate solution, high quality numerical boundary conditions are also needed. For the nozzle problem, a set of nonhomogeneous, outflow boundary conditions are required. The nonhomogeneous boundary conditions not only generate the incoming sound waves but also, at the same time, allow the reflected acoustic waves and entropy waves, if present, to exit the computation domain without reflection. For the open rotor problem, there is an apparent singularity at the axis of rotation. An analytic extension approach is developed to provide a high quality axis boundary treatment.
Resolution Analysis for Experiment Planning of a Nonlinear Seafloor Acoustic Inverse Problem
NASA Astrophysics Data System (ADS)
Ganse, A. A.; Odom, R. I.
2007-12-01
Geoacoustic inversion is the estimation of physical properties of the ocean bottom as a continuous function of position (or depth) in the seafloor given acoustic receptions in the water column. It is closely related to marine reflection seismology but also has features of refraction seismology, and uses sonar equipment and less than ideal geometries because accurate scientific determination of the seafloor may not be the primary goal of the experiments. However, the authors show how a pre-measurement inverse theory resolution analysis can be used as part of experiment planning regarding sensor placement and ship tracks, such that a desire for an experimental configuration giving the most information in bottom inversion can be quantitatively balanced with that for other needs like tracking and communication. This nonlinear geoacoustic inverse problem is ill-posed, so that one can only estimate the continuous function of seafloor properties to a limited resolution. This limited resolution varies with experiment geometry, frequency, and other such factors, and can be quantified in either a frequentist or Bayesian framework. Given statistics of the measurement noise (but without any new measurements themselves), the resolution can be quantified exactly for a linear inverse problem, and compared between different experiment geometries. Nonlinear problems complicate this picture, but if the problem can be transformed into a weakly nonlinear form then the resolution may still be explored in an approximate sense and used as a tool in the planning phase. The ideal situation is when previous seafloor estimates exist for the same region in which a new experiment with new geometry and configuration is being planned. For the scenario without previous results, a somewhat more ad-hoc approach can still compare changes in resolution across different seafloor models. This presentation demonstrates the technique for a synthetic problem involving a single stationary source and a
NASA Astrophysics Data System (ADS)
Kengne, E.; Lakhssassi, A.
2015-03-01
We consider a lossless one-dimensional nonlinear discrete bi-inductance electrical transmission line made of N identical unit cells. When lattice effects are considered, we use the reductive perturbation method in the semidiscrete limit to show that the dynamics of modulated waves can be modeled by the classical nonlinear Schrödinger (CNLS) equation, which describes the modulational instability and the propagation of bright and dark solitons on a continuous-wave background. Our theoretical analysis based on the CNLS equation predicts either two or four frequency regions with different behavior concerning the modulational instability of a plane wave. With the help of the analytical solutions of the CNLS equation, we investigate analytically the effects of the linear capacitance CS on the dynamics of matter-wave solitons in the network. Our results reveal that the linear parameter CS can be used to manipulate the motion of bright, dark, and kink soliton in the network.
Kengne, E; Lakhssassi, A
2015-03-01
We consider a lossless one-dimensional nonlinear discrete bi-inductance electrical transmission line made of N identical unit cells. When lattice effects are considered, we use the reductive perturbation method in the semidiscrete limit to show that the dynamics of modulated waves can be modeled by the classical nonlinear Schrödinger (CNLS) equation, which describes the modulational instability and the propagation of bright and dark solitons on a continuous-wave background. Our theoretical analysis based on the CNLS equation predicts either two or four frequency regions with different behavior concerning the modulational instability of a plane wave. With the help of the analytical solutions of the CNLS equation, we investigate analytically the effects of the linear capacitance CS on the dynamics of matter-wave solitons in the network. Our results reveal that the linear parameter CS can be used to manipulate the motion of bright, dark, and kink soliton in the network. PMID:25871172
Application of High Order Acoustic Finite Elements to Transmission Losses and Enclosure Problems
NASA Technical Reports Server (NTRS)
Craggs, A.; Stevenson, G.
1985-01-01
A family of acoustic finite elements was developed based on C continuity (acoustic pressure being the nodal variable) and the no-flow condition. The family include triangular, quadrilateral and hexahedral isoparametric elements with linear quadratic and cubic variation in modelling and distortion. Of greatest use in problems with irregular boundaries are the cubic isoparametric elements: the 32 node hexahedral element for three-dimensional systems; and the twelve node quadrilateral and ten node triangular elements for two-dimensional/axisymmetric applications. These elements were applied to problems involving cavity resonances, transmission loss in silencers and the study of end effects, using a Floating Point Systems 164 attached array processor accessed through an Amdahl 5860 mainframe. The elements are presently being used to study the end effects associated with duct terminations within finite enclosures. The transmission losses with various silencers and sidebranches in ducts is also being studied using the same elements.
NASA Astrophysics Data System (ADS)
Rudenko, O. V.; Gurbatov, S. N.
2016-07-01
Inverse problems of nonlinear acoustics have important applied significance. On the one hand, they are necessary for nonlinear diagnostics of media, materials, manufactured articles, building units, and biological and geological structures. On the other hand, they are needed for creating devices that ensure optimal action of acoustic radiation on a target. However, despite the many promising applications, this direction remains underdeveloped, especially for strongly distorted high-intensity waves containing shock fronts. An example of such an inverse problem is synthesis of the spatiotemporal structure of a field in a radiating system that ensures the highest possible energy density in the focal region. This problem is also related to the urgent problems of localizing wave energy and the theory of strongly nonlinear waves. Below we analyze some quite general and simple inverse nonlinear problems.
On large-scale nonlinear programming techniques for solving optimal control problems
Faco, J.L.D.
1994-12-31
The formulation of decision problems by Optimal Control Theory allows the consideration of their dynamic structure and parameters estimation. This paper deals with techniques for choosing directions in the iterative solution of discrete-time optimal control problems. A unified formulation incorporates nonlinear performance criteria and dynamic equations, time delays, bounded state and control variables, free planning horizon and variable initial state vector. In general they are characterized by a large number of variables, mostly when arising from discretization of continuous-time optimal control or calculus of variations problems. In a GRG context the staircase structure of the jacobian matrix of the dynamic equations is exploited in the choice of basic and super basic variables and when changes of basis occur along the process. The search directions of the bound constrained nonlinear programming problem in the reduced space of the super basic variables are computed by large-scale NLP techniques. A modified Polak-Ribiere conjugate gradient method and a limited storage quasi-Newton BFGS method are analyzed and modifications to deal with the bounds on the variables are suggested based on projected gradient devices with specific linesearches. Some practical models are presented for electric generation planning and fishery management, and the application of the code GRECO - Gradient REduit pour la Commande Optimale - is discussed.
Lee, Xing Ju; Drovandi, Christopher C; Pettitt, Anthony N
2015-03-01
Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1-28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens. PMID:25303085
NASA Astrophysics Data System (ADS)
Cakoni, Fioralba; Haddar, Houssem
2013-10-01
In inverse scattering theory, transmission eigenvalues can be seen as the extension of the notion of resonant frequencies for impenetrable objects to the case of penetrable dielectrics. The transmission eigenvalue problem is a relatively late arrival to the spectral theory of partial differential equations. Its first appearance was in 1986 in a paper by Kirsch who was investigating the denseness of far-field patterns for scattering solutions of the Helmholtz equation or, in more modern terminology, the injectivity of the far-field operator [1]. The paper of Kirsch was soon followed by a more systematic study by Colton and Monk in the context of developing the dual space method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium [2]. In this paper they showed that for a spherically stratified media transmission eigenvalues existed and formed a discrete set. Numerical examples were also given showing that in principle transmission eigenvalues could be determined from the far-field data. This first period of interest in transmission eigenvalues was concluded with papers by Colton et al in 1989 [3] and Rynne and Sleeman in 1991 [4] showing that for an inhomogeneous medium (not necessarily spherically stratified) transmission eigenvalues, if they existed, formed a discrete set. For the next seventeen years transmission eigenvalues were ignored. This was mainly due to the fact that, with the introduction of various sampling methods to determine the shape of an inhomogeneous medium from far-field data, transmission eigenvalues were something to be avoided and hence the fact that transmission eigenvalues formed at most a discrete set was deemed to be sufficient. In addition, questions related to the existence of transmission eigenvalues or the structure of associated eigenvectors were recognized as being particularly difficult due to the nonlinearity of the eigenvalue problem and the special structure of the associated transmission
Modeling Granular Materials as Compressible Non-Linear Fluids: Heat Transfer Boundary Value Problems
Massoudi, M.C.; Tran, P.X.
2006-01-01
We discuss three boundary value problems in the flow and heat transfer analysis in flowing granular materials: (i) the flow down an inclined plane with radiation effects at the free surface; (ii) the natural convection flow between two heated vertical walls; (iii) the shearing motion between two horizontal flat plates with heat conduction. It is assumed that the material behaves like a continuum, similar to a compressible nonlinear fluid where the effects of density gradients are incorporated in the stress tensor. For a fully developed flow the equations are simplified to a system of three nonlinear ordinary differential equations. The equations are made dimensionless and a parametric study is performed where the effects of various dimensionless numbers representing the effects of heat conduction, viscous dissipation, radiation, and so forth are presented.
NASA Technical Reports Server (NTRS)
Fymat, A. L.
1976-01-01
The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.
Nonlinear optical transmission of an integrated optical bent coupler in semiconductor-doped glass
NASA Astrophysics Data System (ADS)
Guntau, Matthias; Possner, Torsten; Braeuer, Andreas H.; Dannberg, Peter
1991-08-01
A technology for monomode slab and strip waveguide fabrication in semiconductor-doped glasses (SDG) is presented. On this basis, directional couplers consisting of both parallel (DC) and bent (BC) couplers of strip waveguides were realized. The optically linear and nonlinear behavior of these devices is described.
NASA Astrophysics Data System (ADS)
Cakoni, Fioralba; Haddar, Houssem
2013-10-01
In inverse scattering theory, transmission eigenvalues can be seen as the extension of the notion of resonant frequencies for impenetrable objects to the case of penetrable dielectrics. The transmission eigenvalue problem is a relatively late arrival to the spectral theory of partial differential equations. Its first appearance was in 1986 in a paper by Kirsch who was investigating the denseness of far-field patterns for scattering solutions of the Helmholtz equation or, in more modern terminology, the injectivity of the far-field operator [1]. The paper of Kirsch was soon followed by a more systematic study by Colton and Monk in the context of developing the dual space method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium [2]. In this paper they showed that for a spherically stratified media transmission eigenvalues existed and formed a discrete set. Numerical examples were also given showing that in principle transmission eigenvalues could be determined from the far-field data. This first period of interest in transmission eigenvalues was concluded with papers by Colton et al in 1989 [3] and Rynne and Sleeman in 1991 [4] showing that for an inhomogeneous medium (not necessarily spherically stratified) transmission eigenvalues, if they existed, formed a discrete set. For the next seventeen years transmission eigenvalues were ignored. This was mainly due to the fact that, with the introduction of various sampling methods to determine the shape of an inhomogeneous medium from far-field data, transmission eigenvalues were something to be avoided and hence the fact that transmission eigenvalues formed at most a discrete set was deemed to be sufficient. In addition, questions related to the existence of transmission eigenvalues or the structure of associated eigenvectors were recognized as being particularly difficult due to the nonlinearity of the eigenvalue problem and the special structure of the associated transmission
NASA Astrophysics Data System (ADS)
Gallagher, Kerry; Sambridge, Malcolm; Drijkoningen, Guy
In providing a method for solving non-linear optimization problems Monte Carlo techniques avoid the need for linearization but, in practice, are often prohibitive because of the large number of models that must be considered. A new class of methods known as Genetic Algorithms have recently been devised in the field of Artificial Intelligence. We outline the basic concept of genetic algorithms and discuss three examples. We show that, in locating an optimal model, the new technique is far superior in performance to Monte Carlo techniques in all cases considered. However, Monte Carlo integration is still regarded as an effective method for the subsequent model appraisal.
Entropy solutions for a nonlinear parabolic problems with lower order term in Orlicz spaces
NASA Astrophysics Data System (ADS)
Mabdaoui, M.; Moussa, H.; Rhoudaf, M.
2016-03-01
We shall give the proof of existence results for the entropy solutions of the following nonlinear parabolic problem [Equation not available: see fulltext.]where A is a Leray-Lions operator having a growth not necessarily of polynomial type. The lower order term Φ :Ω × (0,T)× {R}→ {R}^N is a Carathéodory function, for a.e. (x,t)in Q_T and for all sin R , satisfying only a growth condition and the right hand side f belongs to L^1(Q_T).
Solving Nonlinear Solid Mechanics Problems with the Jacobian-Free Newton Krylov Method
J. D. Hales; S. R. Novascone; R. L. Williamson; D. R. Gaston; M. R. Tonks
2012-06-01
The solution of the equations governing solid mechanics is often obtained via Newton's method. This approach can be problematic if the determination, storage, or solution cost associated with the Jacobian is high. These challenges are magnified for multiphysics applications with many coupled variables. Jacobian-free Newton-Krylov (JFNK) methods avoid many of the difficulties associated with the Jacobian by using a finite difference approximation. BISON is a parallel, object-oriented, nonlinear solid mechanics and multiphysics application that leverages JFNK methods. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and solid mechanics coupled to other PDEs using a series of demonstration problems.
A nonlinear control design for energy sink simulation in the Euler-Poinsot problem
NASA Technical Reports Server (NTRS)
Kammer, Daniel C.; Gray, Gary L.
1993-01-01
A nonlinear control design is presented for the purpose of quantitatively simulating the effects of internal damping mechanisms modeled as energy sinks on the attitude dynamics of rigid body spacecraft. Damping is important because it is often the driving mechanism behind passive attitude acquisition maneuvers. Introduction of the controller into the Euler attitude equations of motion allows for the explicit representation of damping without the introduction of additional degrees of freedom required for a physical damping mechanism. This result is significant because perturbation techniques which rely on the closed form solution of the unperturbed problem can then be used to analyze the effects of perturbations upon a damped system. The controller is designed to dissipate kinetic energy while maintaining the magnitude of the angular momentum vector. Control torques are nonlinear functions of the angular momentum components expressed in a body-fixed frame. A numerical simulation of an actual damping mechanism during a decay from minor axis spin into a flat spin is presented showing that the nonlinear controller gives a good qualitative representation and, in many instances, a good quantitative approximation of the attitude motion of a representative spacecraft containing a damping mechanism.
NASA Technical Reports Server (NTRS)
Ungsuwarungsri, T.; Knauss, W. G.
1988-01-01
A numerical method is developed for the determinations of the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement behavior. The problem formulation is based on the superposition of the relevant elasticity Green's function; the solution of the resulting nonlinear problem is obtained by using Picard's successive approximation scheme. The model is used to investigate the effect of nonlinear fibril behavior on the mechanics of craze and crack growth, and the results are compared with the Dugdale model.
Moon, Francis C.
2002-04-01
Large numbers of fluid elastic structures are part of many power plant systems and vibration of these systems sometimes are responsible for plant shut downs. Earlier research at Cornell in this area had centered on nonlinear dynamics of fluid-elastic systems with low degrees of freedom. The focus of current research is the study of the dynamics of thousands of closely arrayed structures in a cross flow under both fluid and impact forces. This research is relevant to two areas: (1) First, fluid-structural problems continue to be important in the power industry, especially in heat exchange systems where up to thousands of pipe-like structures interact with a fluid medium. [Three years ago in Japan for example, there was a shut down of the Monju nuclear power plant due to a failure attributed to flow induced vibrations.] (2) The second area of relevance is to nonlinear systems and complexity phenomena; issues such as spatial temporal dynamics, localization and coherent patterns entropy measures as well as other complexity issues. Early research on flow induced vibrations in tube row and array structures in cross flow goes back to Roberts in 1966 and Connors in 1970. These studies used linear models as have many of the later work in the 1980's. Nonlinear studies of cross flow induced vibrations have been undertaken in the last decade. The research at Cornell sponsored by DOE has explored nonlinear phenomena in fluid-structure problems. In the work at Cornell we have documented a subcritical Hopf bifurcation for flow around a single row of flexible tubes and have developed an analytical model based on nonlinear system identification techniques. (Thothadri, 1998, Thothadri and Moon, 1998, 1999). These techniques have been applied to a wind tunnel experiment with a row of seven cylinders in a cross flow. These system identification methods have been used to calculate fluid force models that have replicated certain quantitative vibration limit cycle behavior of the
Heydari, M.H.; Hooshmandasl, M.R.; Cattani, C.; Maalek Ghaini, F.M.
2015-02-15
Because of the nonlinearity, closed-form solutions of many important stochastic functional equations are virtually impossible to obtain. Thus, numerical solutions are a viable alternative. In this paper, a new computational method based on the generalized hat basis functions together with their stochastic operational matrix of Itô-integration is proposed for solving nonlinear stochastic Itô integral equations in large intervals. In the proposed method, a new technique for computing nonlinear terms in such problems is presented. The main advantage of the proposed method is that it transforms problems under consideration into nonlinear systems of algebraic equations which can be simply solved. Error analysis of the proposed method is investigated and also the efficiency of this method is shown on some concrete examples. The obtained results reveal that the proposed method is very accurate and efficient. As two useful applications, the proposed method is applied to obtain approximate solutions of the stochastic population growth models and stochastic pendulum problem.
The Compressible Viscous Surface-Internal Wave Problem: Nonlinear Rayleigh-Taylor Instability
NASA Astrophysics Data System (ADS)
Jang, Juhi; Tice, Ian; Wang, Yanjin
2016-07-01
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and t he upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The fluids are acted on by gravity in the bulk, and at the free interfaces we consider both the case of surface tension and the case of no surface forces.We are concerned with the Rayleigh-Taylor instability when the upper fluid is heavier than the lower fluid along the equilibrium interface. When the surface tension at the free internal interface is below the critical value, we prove that the problem is nonlinear unstable.