NASA Astrophysics Data System (ADS)
Kong, Chao; Hai, Kuo; Tan, Jintao; Chen, Hao; Hai, Wenhua
2016-03-01
Nonlinear Kronig-Penney model has been frequently employed to study transmission problem of electron wave in a doped semiconductor superlattice or in a nonlinear electrified chain. Here from an integral equation we derive a novel exact solution of the problem, which contains a simple nonlinear map connecting transmission coefficient with system parameters. Consequently, we propose a scheme to manipulate electronic distribution and transmission by adjusting the system parameters. A new quantum coherence effect is evidenced by the strict expression of transmission coefficient, which results in the aperiodic electronic distributions and different transmission coefficients including the approximate zero transmission and total transmission, and the multiple transmissions. The method based on the concise exact solution can be applied directly to some nonlinear cold atomic systems and a lot of linear Kronig-Penney systems, and also can be extended to investigate electronic transport in different discrete nonlinear systems.
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.
NASA Astrophysics Data System (ADS)
Smirnov, Yu. G.; Valovik, D. V.
2016-10-01
The paper focuses on a transmission eigenvalue problem for Maxwell's equations with cubic nonlinearity that describes the propagation of transverse magnetic waves along the boundaries of a dielectric layer filled with nonlinear (Kerr) medium. Using an original approach, it is proved that even for small values of the nonlinearity coefficient, the nonlinear problem has infinitely many nonperturbative solutions (eigenvalues and eigenwaves), whereas the corresponding linear problem always has a finite number of solutions. This fact implies the theoretical existence of a novel type of eigenwaves that do not reduce to the linear ones in the limit in which the nonlinear coefficient reduces to zero. Asymptotic distribution of the eigenvalues is found, periodicity of the eigenfunctions is proved, the exact formula for the period is found, and the zeros of the eigenfunctions are determined.
NASA Astrophysics Data System (ADS)
Amaral, Marcelo D.; Teixeira, Eduardo V.
2015-08-01
We study transmission problems with free interfaces from one random medium to another. Solutions are required to solve distinct partial differential equations, and , within their positive and negative sets respectively. A corresponding flux balance from one phase to another is also imposed. We establish existence and bounds of solutions. We also prove that variational solutions are non-degenerate and develop the regularity theory for solutions of such free boundary problems.
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.
The Born transmission eigenvalue problem
NASA Astrophysics Data System (ADS)
Cakoni, Fioralba; Colton, David; Rezac, Jacob D.
2016-10-01
In this paper we study the distribution of transmission eigenvalues in the complex plane for obstacles whose contrast is small in magnitude. We use a first order approximation of the refractive index to derive and study an approximate interior transmission problem. In the case of spherically stratified media, we prove existence and discreteness of transmission eigenvalues and derive a condition under which the complex part of transmission eigenvalues cannot lie in a strip parallel to the real axis. For obstacles with general shape, we demonstrate that if transmission eigenvalues exist then they form a discrete set.
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.
Global methods for nonlinear complementarity problems
More, J.J.
1994-04-01
Global methods for nonlinear complementarity problems formulate the problem as a system of nonsmooth nonlinear equations approach, or use continuation to trace a path defined by a smooth system of nonlinear equations. We formulate the nonlinear complementarity problem as a bound-constrained nonlinear least squares problem. Algorithms based on this formulation are applicable to general nonlinear complementarity problems, can be started from any nonnegative starting point, and each iteration only requires the solution of systems of linear equations. Convergence to a solution of the nonlinear complementarity problem is guaranteed under reasonable regularity assumptions. The converge rate is Q-linear, Q-superlinear, or Q-quadratic, depending on the tolerances used to solve the subproblems.
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].
The real problem with Merchant transmission
Blumsack, Seth; Lave, Lester B.; Ilic, Marija
2008-03-15
Current regulatory policy distinguishes transmission investments that have primarily economic benefits from those that primarily enhance reliability. But no such dichotomy exists; congestion and reliability are inter-related in complex ways. Thus, solving the transmission investment problem is more complex than ''fixing'' merchant transmission; investment in the grid must be treated as a systems problem. (author)
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 eigenvalue problems in smectics
Marchenko, V. I. Podolyak, E. R.
2010-01-15
The asymptotic forms of strains in a smectic around the linear distributions of multipole force are determined. The law of a decrease in strains is specified by the indices, which are eigenvalues of nonlinear equations describing the angular dependence of the strains.
The role of nonlinearity in inverse problems
NASA Astrophysics Data System (ADS)
Snieder, Roel
1998-06-01
In many practical inverse problems, one aims to retrieve a model that has infinitely many degrees of freedom from a finite amount of data. It follows from a simple variable count that this cannot be done in a unique way. Therefore, inversion entails more than estimating a model: any inversion is not complete without a description of the class of models that is consistent with the data; this is called the appraisal problem. Nonlinearity makes the appraisal problem particularly difficult. The first reason for this is that nonlinear error propagation is a difficult problem. The second reason is that for some nonlinear problems the model parameters affect the way in which the model is being interrogated by the data. Two examples are given of this, and it is shown how the nonlinearity may make the problem more ill-posed. Finally, three attempts are shown to carry out the model appraisal for nonlinear inverse problems that are based on an analytical approach, a numerical approach and a common sense approach.
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.
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.
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…
Nonlinear transmission of an intense terahertz field through monolayer graphene
Hafez, H. A.; Ibrahim, A.; Ozaki, T.; Al-Naib, I.; Dignam, M. M.; Oguri, K.; Sekine, Y.; Hibino, H.; Cooke, D. G.; Tanaka, S.; Komori, F.
2014-11-15
We report nonlinear terahertz (THz) effects in monolayer graphene, giving rise to transmission enhancement of a single-cycle THz pulse when the incident THz peak electric field is increased. This transmission enhancement is attributed to reduced photoconductivity, due to saturation effects in the field-induced current and increased intraband scattering rates arising from transient heating of electrons. We have developed a tight-binding model of the response using the length gauge interaction Hamiltonian that provides good qualitative agreement. The model fully accounts for the nonlinear response arising from the linear dispersion energy spectrum in graphene. The results reveal a strong dependence of the scattering time on the THz field, which is at the heart of the observed nonlinear response.
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.
On the linear properties of the nonlinear radiative transfer problem
NASA Astrophysics Data System (ADS)
Pikichyan, H. V.
2016-11-01
In this report, we further expose the assertions made in nonlinear problem of reflection/transmission of radiation from a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness, when both of its boundaries are illuminated by intense monochromatic radiative beams. The new conceptual element of well-defined, so-called, linear images is noteworthy. They admit a probabilistic interpretation. In the framework of nonlinear problem of reflection/transmission of radiation, we derive solution which is similar to linear case. That is, the solution is reduced to the linear combination of linear images. By virtue of the physical meaning, these functions describe the reflectivity and transmittance of the medium for a single photon or their beam of unit intensity, incident on one of the boundaries of the layer. Thereby the medium in real regime is still under the bilateral illumination by external exciting radiation of arbitrary intensity. To determine the linear images, we exploit three well known methods of (i) adding of layers, (ii) its limiting form, described by differential equations of invariant imbedding, and (iii) a transition to the, so-called, functional equations of the "Ambartsumyan's complete invariance".
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.
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.
L1 adaptive control of uncertain gear transmission servo systems with deadzone nonlinearity.
Zuo, Zongyu; Li, Xiao; Shi, Zhiguang
2015-09-01
This paper deals with the adaptive control problem of Gear Transmission Servo (GTS) systems in the presence of unknown deadzone nonlinearity and viscous friction. A global differential homeomorphism based on a novel differentiable deadzone model is proposed first. Since there exist both matched and unmatched state-dependent unknown nonlinearities, a full-state feedback L1 adaptive controller is constructed to achieve uniformly bounded transient response in addition to steady-state performance. Finally, simulation results are included to show the elimination of limit cycles, in addition to demonstrating the main results in this paper. PMID:26250588
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.
The transmission interface constraint problem. Revision
Baldick, R.; Kahn, E.
1994-10-01
Electric power transmission systems exhibit a number of complex constraints on their operation and usage. When a network is subject to a constraint that limits the amount of power that can be moved from one region to another, there is said to be an interface limit. The power systems literature gives no general treatment of the engineering-economics of this ubiquitous phenomenon. Particular aspects of interface limits are typically discussed in sophisticated technical detail, but the general engineering-economic trade-offs involved in relieving interface constraints have not been systematically addressed. We approach this problem in the spirit of a heuristic model. Such models are quite valuable under current industry conditions because they delineate technical opportunities and choices in situations where there may be conflicting views among competing parties and regulatory authorities. We organize and enumerate the choices, clarify the practical conditions that dictate the optimum in particular cases, and help to motivate the final choices made by planners.
An identification problem for nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Aksoy, Nigar Yildirim; Yagub, Gabil; Aksoy, Eray
2016-04-01
In this paper, an identification problem on determining the unknown coefficients of nonlinear time-dependent Schrödinger equation is studied. The existence and uniqueness of solutions of identification problem with variational method are proved.
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.
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.
Nonlinear galloping of internally resonant iced transmission lines considering eccentricity
NASA Astrophysics Data System (ADS)
Yan, Zhimiao; Yan, Zhitao; Li, Zhengliang; Tan, Ting
2012-07-01
Based on the curved-beam theory, a nonlinear galloping model considering three displacement (normal, bi-normal and tangential) components and twist is formulated. According to the property of transmission line, one reduced (normal and bi-normal) galloping model, with regard of bending, rotation and eccentricity of cross section, is obtained. Moreover, the initial rotation angle is also introduced in galloping and aerodynamic models. Additionally, based on the reduced model, the bifurcation and stability of the two cases (1:1 resonance and 2:1 resonance) are analyzed. The results turn out that the importance of ice eccentricity needs to be highlighted. Finally, multiple stabilities are found through the analyses of bifurcation and stability and proved by the reduced model and Reduced Amplitude Modulation Equations (RAME) numerically integrated in time history.
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…
Energy and Transmissibility in Nonlinear Viscous Base Isolators
NASA Astrophysics Data System (ADS)
Markou, Athanasios A.; Manolis, George D.
2016-09-01
High damping rubber bearings (HDRB) are the most commonly used base isolators in buildings and are often combined with other systems, such as sliding bearings. Their mechanical behaviour is highly nonlinear and dependent on a number of factors. At first, a physical process is suggested here to explain the empirical formula introduced by J.M. Kelly in 1991, where the dissipated energy of a HDRB under cyclic testing, at constant frequency, is proportional to the amplitude of the shear strain, raised to a power of approximately 1.50. This physical process is best described by non-Newtonian fluid behaviour, originally developed by F.H. Norton in 1929 to describe creep in steel at high-temperatures. The constitutive model used includes a viscous term, that depends on the absolute value of the velocity, raised to a non-integer power. The identification of a three parameter Kelvin model, the simplest possible system with nonlinear viscosity, is also suggested here. Furthermore, a more advanced model with variable damping coefficient is implemented to better model in this complex mechanical process. Next, the assumption of strain-rate dependence in their rubber layers under cyclic loading is examined in order to best interpret experimental results on the transmission of motion between the upper and lower surfaces of HDRB. More specifically, the stress-relaxation phenomenon observed with time in HRDB can be reproduced numerically, only if the constitutive model includes a viscous term, that depends on the absolute value of the velocity raised to a non-integer power, i. e., the Norton fluid previously mentioned. Thus, it becomes possible to compute the displacement transmissibility function between the top and bottom surfaces of HDRB base isolator systems and to draw engineering-type conclusions, relevant to their design under time-harmonic loads.
Solving nonlinear heat transfer constant area fin problems
NASA Technical Reports Server (NTRS)
1968-01-01
Tables and graphs were compiled for solving nonlinear heat transfer constant area fin problems. The differential equation describing one-dimensional steady-state temperature distribution and heat flow under three modes of heat transfer with heat generation was investigated.
A new perturbative approach to nonlinear problems
Bender, C. M.; Milton, K. A.; Pinsky, S. S.; Simmons, L. M., Jr.
1989-07-01
A recently proposed perturbative technique for quantum field theory consistsof replacing nonlinear terms in the Lagrangian such as /phi//sup 4/ by(/phi//sup 2/)/sup 1+delta/ and then treating delta as a small parameter. It is shown herethat the same approach gives excellent results when applied to difficultnonlinear differential equations such as the Lane--Emden, Thomas--Fermi,Blasius, and Duffing equations.
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.
Explanation of the inverse Doppler effect observed in nonlinear transmission lines.
Kozyrev, Alexander B; van der Weide, Daniel W
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.
Iterative methods for solving nonlinear problems of nuclear reactor criticality
Kuz'min, A. M.
2012-12-15
The paper presents iterative methods for calculating the neutron flux distribution in nonlinear problems of nuclear reactor criticality. Algorithms for solving equations for variations in the neutron flux are considered. Convergence of the iterative processes is studied for two nonlinear problems in which macroscopic interaction cross sections are functionals of the spatial neutron distribution. In the first problem, the neutron flux distribution depends on the water coolant density, and in the second one, it depends on the fuel temperature. Simple relationships connecting the vapor content and the temperature with the neutron flux are used.
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 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.
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.
On nonlinear diffusion problems with strong degeneracy
NASA Astrophysics Data System (ADS)
Ammar, Kaouther
In this paper, we study the "triply" degenerate problem: b(-Δg(v)+divΦ(v)=f on Q:=(0,T)×Ω, b(v(0,ṡ))=b(v) on Ω and " g(v)=g(a) on some part of the boundary (0,T)×∂Ω," in the case of continuous nonhomogeneous and nonstationary boundary data a. The functions b,g are assumed to be continuous, locally Lipschitz, nondecreasing and to verify the normalization condition b(0)=g(0)=0 and the range condition R(b+g)=R. Using monotonicity and penalization methods, we prove existence of a weak renormalized entropy solution in the spirit of [K. Ammar, J. Carrillo, P. Wittbold, Scalar conservation laws with general boundary condition and continuous flux function, J. Differential Equations 228 (2006) 111-139].
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.
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.
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.
Some nonlinear problems in the manipulation of beams
Sessler, A.M.
1990-10-01
An overview is given of nonlinear problems that arise in the manipulation of beams. Beams can be made of material particles or photons, can be intense or dilute, can be energetic or not, and they can be propagating in vacuum or in a medium. The nonlinear aspects of the motion are different in each case, and this diversity of behavior is categorized. Many examples are given, which serves to illustrate the categorization and, furthermore, display the richness of behavior encountered in the physics of beams. 25 refs., 5 figs.
Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line
NASA Astrophysics Data System (ADS)
Aslan, İsmail
2016-09-01
Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions (kink/antikink solitons, singular, periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.
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.
Nonlinear singularly perturbed optimal control problems with singular arcs
NASA Technical Reports Server (NTRS)
Ardema, M. D.
1977-01-01
A third order, nonlinear, singularly perturbed optimal control problem is considered under assumptions which assure that the full problem is singular and the reduced problem is nonsingular. The separation between the singular arc of the full problem and the optimal control law of the reduced one, both of which are hypersurfaces in state space, is of the same order as the small parameter of the problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem. A numerical example is included.
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.
Lu, Bao-Liang; Ito, Koji
2003-09-01
In this paper we present a method for converting general nonlinear programming (NLP) problems into separable programming (SP) problems by using feedforward neural networks (FNNs). The basic idea behind the method is to use two useful features of FNNs: their ability to approximate arbitrary continuous nonlinear functions with a desired degree of accuracy and their ability to express nonlinear functions in terms of parameterized compositions of functions of single variables. According to these two features, any nonseparable objective functions and/or constraints in NLP problems can be approximately expressed as separable functions with FNNs. Therefore, any NLP problems can be converted into SP problems. The proposed method has three prominent features. (a) It is more general than existing transformation techniques; (b) it can be used to formulate optimization problems as SP problems even when their precise analytic objective function and/or constraints are unknown; (c) the SP problems obtained by the proposed method may highly facilitate the selection of grid points for piecewise linear approximation of nonlinear functions. We analyze the computational complexity of the proposed method and compare it with an existing transformation approach. We also present several examples to demonstrate the method and the performance of the simplex method with the restricted basis entry rule for solving SP problems.
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.
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.
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.
Modifying PASVART to solve singular nonlinear 2-point boundary problems
NASA Technical Reports Server (NTRS)
Fulton, James P.
1988-01-01
To study the buckling and post-buckling behavior of shells and various other structures, one must solve a nonlinear 2-point boundary problem. Since closed-form analytic solutions for such problems are virtually nonexistent, numerical approximations are inevitable. This makes the availability of accurate and reliable software indispensable. In a series of papers Lentini and Pereyra, expanding on the work of Keller, developed PASVART: an adaptive finite difference solver for nonlinear 2-point boundary problems. While the program does produce extremely accurate solutions with great efficiency, it is hindered by a major limitation. PASVART will only locate isolated solutions of the problem. In buckling problems, the solution set is not unique. It will contain singular or bifurcation points, where different branches of the solution set may intersect. Thus, PASVART is useless precisely when the problem becomes interesting. To resolve this deficiency we propose a modification of PASVART that will enable the user to perform a more complete bifurcation analysis. PASVART would be combined with the Thurston bifurcation solution: as adaptation of Newton's method that was motivated by the work of Koiter 3 are reinterpreted in terms of an iterative computational method by Thurston.
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.
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.
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 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)
Q-factor analysis of nonlinear impairments in ultrahigh-speed Nyquist pulse transmission.
Hirooka, Toshihiko; Nakazawa, Masataka
2015-12-28
We present detailed analytical and numerical results of the dispersion and nonlinear tolerances of RZ and Nyquist optical pulses in ultrahigh-speed TDM transmissions. From a Q-map analysis, i.e. by numerically calculating the Q-factor distribution as a function of transmission power and fiber dispersion, we found that Nyquist TDM transmission has a substantially larger Q margin as regards both dispersion and optical power thanks to ISI-free overlapped TDM. We also show that the optimum transmission power for Nyquist pulses is 2 dB lower than for RZ pulses. An analytical model is provided to explain the overlap-induced nonlinear impairments in Nyquist TDM transmission in a high power regime, which agrees well with numerical results.
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.
Jacobi elliptic functions: A review of nonlinear oscillatory application problems
NASA Astrophysics Data System (ADS)
Kovacic, Ivana; Cveticanin, Livija; Zukovic, Miodrag; Rakaric, Zvonko
2016-10-01
This review paper is concerned with the applications of Jacobi elliptic functions to nonlinear oscillators whose restoring force has a monomial or binomial form that involves cubic and/or quadratic nonlinearity. First, geometric interpretations of three basic Jacobi elliptic functions are given and their characteristics are discussed. It is shown then how their different forms can be utilized to express exact solutions for the response of certain free conservative oscillators. These forms are subsequently used as a starting point for a presentation of different quantitative techniques for obtaining an approximate response for free perturbed nonlinear oscillators. An illustrative example is provided. Further, two types of externally forced nonlinear oscillators are reviewed: (i) those that are excited by elliptic-type excitations with different exact and approximate solutions; (ii) those that are damped and excited by harmonic excitations, but their approximate response is expressed in terms of Jacobi elliptic functions. Characteristics of the steady-state response are discussed and certain qualitative differences with respect to the classical Duffing oscillator excited harmonically are pointed out. Parametric oscillations of the oscillators excited by an elliptic-type forcing are considered as well, and the differences with respect to the stability chart of the classical Mathieu equation are emphasized. The adjustment of the Melnikov method to derive the general condition for the onset of homoclinic bifurcations in a system parametrically excited by an elliptic-type forcing is provided and compared with those corresponding to harmonic excitations. Advantages and disadvantages of the use of Jacobi elliptic functions in nonlinear oscillatory application problems are discussed and some suggestions for future work are given.
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.
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.
Kengne, E; Bozic, V; Viana, M; Vaillancourt, R
2008-08-01
In the semidiscrete limit and in suitably scaled coordinates, the voltage of a system of coupled nonlinear dispersive transmission lines is described by a nonlinear Schrödinger equation. This equation is used to study the transverse stability of solitary waves of the system. Exact results for the growth rate and the corresponding perturbation function of linear transverse perturbations are obtained in terms of the network's and soliton's parameters.
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.
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
Nonlinear Eigenvalue Problems in Elliptic Variational Inequalities: a local study
Conrad, F.; Brauner, C.; Issard-Roch, F.; Nicolaenko, B.
1985-01-01
The authors consider a class of Nonlinear Eigenvalue Problems (N.L.E.P.) associated with Elliptic Variational Inequalities (E.V.I.). First the authors introduce the main tools for a local study of branches of solutions; the authors extend the linearization process required in the case of equations. Next the authors prove the existence of arcs of solutions close to regular vs singular points, and determine their local behavior up to the first order. Finally, the authors discuss the connection between their regularity condition and some stability concept. 37 references, 6 figures.
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.
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.
Zhukovsky, Sergei V.; Smirnov, Andrey G.
2011-02-15
Light propagation in asymmetric Kerr-nonlinear multilayers with perfect transmission resonances is theoretically investigated. It is found that hybrid Fabry-Perot-resonator-photonic-crystal structures of the type (BA){sup k}(AB){sup k}(AABB){sup m} exhibit both pronounced unidirectionality (due to strong spatial asymmetry of the resonant mode) and high transmission (due to the existence of a perfect transmission resonance). This results in nonlinear optical diode action with low reflection losses without need for a pumping beam or input pulse modulation. By slightly perturbing the perfect transmission resonance condition, the operating regime of the optical diode can be tuned, with a tradeoff between minimizing the reflection losses and maximizing the frequency bandwidth where unidirectional transmission exists. Optical diode action is demonstrated in direct numerical simulation, showing >92% transmittance in one direction and about 22% in the other. The effect of perfect transmission resonance restoration induced by nonlinearity was observed analytically and numerically. The proposed geometry is shown to have advantages over previously reported designs based on photonic quasicrystals.
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.
The factorization method for the acoustic transmission problem
NASA Astrophysics Data System (ADS)
Anagnostopoulos, Konstantinos A.; Charalambopoulos, Antonios; Kleefeld, Andreas
2013-11-01
In this work, the shape reconstruction problem of acoustically penetrable bodies from the far-field data corresponding to time-harmonic plane wave incidence is investigated within the framework of the factorization method. Although the latter technique has received considerable attention in inverse scattering problems dealing with impenetrable scatterers and it has not been elaborated for inverse transmission problems with the only exception being a work by the first two authors and co-workers. We aim to bridge this gap in the field of acoustic scattering; the paper on one hand focuses on establishing rigorously the necessary theoretical framework for the application of the factorization method to the inverse acoustic transmission problem. The main outcome of the investigation undertaken is the derivation of an explicit formula for the scatterer's characteristic function, which depends solely on the far-field data feeding the inverse scattering scheme. Extended numerical examples in three dimensions are also presented, where a variety of different surfaces are successfully reconstructed by the factorization method, thus, complementing the method's validation from the computational point of view.
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.
Studies in nonlinear problems of energy. Final report
Matkowsky, B.J.
1998-12-01
The author completed a successful research program on Nonlinear Problems of Energy, with emphasis on combustion and flame propagation. A total of 183 papers associated with the grant has appeared in the literature, and the efforts have twice been recognized by DOE`s Basic Science Division for Top Accomplishment. In the research program the author concentrated on modeling, analysis and computation of combustion phenomena, with particular emphasis on the transition from laminar to turbulent combustion. Thus he investigated the nonlinear dynamics and pattern formation in the successive stages of transition. He described the stability of combustion waves, and transitions to waves exhibiting progressively higher degrees of spatio-temporal complexity. Combustion waves are characterized by large activation energies, so that chemical reactions are significant only in thin layers, termed reaction zones. In the limit of infinite activation energy, the zones shrink to moving surfaces, termed fronts, which must be found during the course of the analysis, so that the problems are moving free boundary problems. The analytical studies were carried out for the limiting case with fronts, while the numerical studies were carried out for the case of finite, though large, activation energy. Accurate resolution of the solution in the reaction zone(s) is essential, otherwise false predictions of dynamical behavior are possible. Since the reaction zones move, and their location is not known a-priori, the author has developed adaptive pseudo-spectral methods, which have proven to be very useful for the accurate, efficient computation of solutions of combustion, and other, problems. The approach is based on a combination of analytical and numerical methods. The numerical computations built on and extended the information obtained analytically. Furthermore, the solutions obtained analytically served as benchmarks for testing the accuracy of the solutions determined computationally. Finally
Science Influence on Policy - A Transmission or Reception Problem? (Invited)
NASA Astrophysics Data System (ADS)
Carlson, D. J.
2009-12-01
Unfortunately we can claim very little scientific influence on climate change policies, nationally or internationally. The weak to non-existent inclusion of green (‘climate-friendly’) practices and policies in various national economic stimulus plans represents a scientific communication failure and an opportunity lost. The ineffective and inconclusive results from the Copenhagen negotiations represent a similar and equally serious failure. When communications fail we can consider errors in transmission (from science) or in reception (by policymakers). As scientists we tend to find fault with the receivers, and to identify solutions that consist, in effect, of ‘turning up’ the transmission volume. I suggest that in fact most problems lie with the transmitters. Those problems consist of speaking in transmit (scientific) terms rather than reception (economic) terms, of ignoring the necessity of converting and comparing our predictions or assessments to real world examples and terms, of misunderstanding the considerable ability of the receivers to process uncertainty, of missing many opportunities to match our transmission technologies to the modern public reception capabilities, and, most fundamentally, of failing, in key opportunities, to transmit a clear message. During IPY we have confronted each of these failures, and at least learned what we did wrong.
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.
Capacity estimates for optical transmission based on the nonlinear Fourier transform
NASA Astrophysics Data System (ADS)
Derevyanko, Stanislav A.; Prilepsky, Jaroslaw E.; Turitsyn, Sergei K.
2016-09-01
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.
Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances
Miroshnichenko, Andrey E.; Kivshar, Yuri S.; Malomed, Boris A.
2011-07-15
We consider a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (in other words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system in the form of a dimer, symmetric and asymmetric eigenstates, including multistable ones, are found analytically. We demonstrate that, if coupled to a linear chain, such a nonlinear PT-symmetric dimer generates previously unexplored types of nonlinear Fano resonances, with completely suppressed or greatly amplified transmission, as well as a regime similar to the electromagnetically induced transparency. The implementation of the systems is possible in various media admitting controllable linear and nonlinear amplification of waves.
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 dBSNR/dBPower 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
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
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.
Word, Daniel P; Cummings, Derek A T; Burke, Donald S; Iamsirithaworn, Sopon; Laird, Carl D
2012-08-01
Mathematical models can enhance our understanding of childhood infectious disease dynamics, but these models depend on appropriate parameter values that are often unknown and must be estimated from disease case data. In this paper, we develop a framework for efficient estimation of childhood infectious disease models with seasonal transmission parameters using continuous differential equations containing model and measurement noise. The problem is formulated using the simultaneous approach where all state variables are discretized, and the discretized differential equations are included as constraints, giving a large-scale algebraic nonlinear programming problem that is solved using a nonlinear primal-dual interior-point solver. The technique is demonstrated using measles case data from three different locations having different school holiday schedules, and our estimates of the seasonality of the transmission parameter show strong correlation to school term holidays. Our approach gives dramatic efficiency gains, showing a 40-400-fold reduction in solution time over other published methods. While our approach has an increased susceptibility to bias over techniques that integrate over the entire unknown state-space, a detailed simulation study shows no evidence of bias. Furthermore, the computational efficiency of our approach allows for investigation of a large model space compared with more computationally intensive approaches.
Word, Daniel P.; Cummings, Derek A. T.; Burke, Donald S.; Iamsirithaworn, Sopon; Laird, Carl D.
2012-01-01
Mathematical models can enhance our understanding of childhood infectious disease dynamics, but these models depend on appropriate parameter values that are often unknown and must be estimated from disease case data. In this paper, we develop a framework for efficient estimation of childhood infectious disease models with seasonal transmission parameters using continuous differential equations containing model and measurement noise. The problem is formulated using the simultaneous approach where all state variables are discretized, and the discretized differential equations are included as constraints, giving a large-scale algebraic nonlinear programming problem that is solved using a nonlinear primal–dual interior-point solver. The technique is demonstrated using measles case data from three different locations having different school holiday schedules, and our estimates of the seasonality of the transmission parameter show strong correlation to school term holidays. Our approach gives dramatic efficiency gains, showing a 40–400-fold reduction in solution time over other published methods. While our approach has an increased susceptibility to bias over techniques that integrate over the entire unknown state-space, a detailed simulation study shows no evidence of bias. Furthermore, the computational efficiency of our approach allows for investigation of a large model space compared with more computationally intensive approaches. PMID:22337634
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.
The asymptotic analysis of communications and wave collapse problems in nonlinear optics
NASA Astrophysics Data System (ADS)
Ahrens, Cory D.
This thesis investigates two problems in nonlinear optics. The first is the calculation of collision induced timing shifts in nonlinear fiber optic communication systems, while the second is the use of dispersion management in preventing wave collapse in (2+1) dimensions. Optical fiber communication systems are a key technology in the long distance transmission of information. Long distance propagation implies that nonlinear effects are important. The nonlinear effects of interest here are cross-phase modulation (XPM) and four-wave mixing (FWM). In the first part of this thesis, an asymptotic theory to calculate frequency and timing shifts due to XPM and FWM is developed. The theory is based on a perturbed Nonlinear Schrodinger (NLS) equation. From the NLS equation, ordinary differential equations describing pulse temporal position and frequency are derived. Effects of FWM on temporal position and frequency are then shown to be negligible compared to effects from XPM. By neglecting FWM, computation of the timing and frequency shift is greatly simplified. Using asymptotic methods, formulas for timing and frequency shift due to XPM are derived, giving an accurate, computationally efficient method to estimate frequency and timing shifts. The utility of the theory is demonstrated for several realistic systems. The search for light bullets is an outstanding problem in nonlinear optics. In two or more spatial dimensions, pulses governed by the cubic NLS equation can undergo collapse. Recently, researchers have proposed using dispersion management to prevent pulse collapse. The second part of this thesis investigates the effects of dispersion management in (2+1) dimensions on pulse evolution and development of pulse collapse. A multiple scale analysis is used to derive the (2+1) dimensional dispersion-managed NLS (DMNLS) equation, which describes average pulse dynamics. Local existence of solutions to the DMNLS equation in the Sobolev space HsR2 , s > 1, is established
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.
Nonlinear response of GaAs gratings in the extraordinary transmission regime.
Vincenti, Maria Antonietta; de Ceglia, Domenico; Scalora, Michael
2011-12-01
We theoretically describe a way to enhance harmonic generation from subwavelength slits milled on semiconductor substrates in strongly absorptive regimes. The metal-like response typical of semiconductors, like GaAs and GaP, triggers enhanced transmission and nonlinear optical phenomena in the deep UV range. We numerically study correlations between linear and nonlinear responses and their intricacies in infinite arrays, and highlight differences between nonlinear surface and magnetic sources, and intrinsic χ((2)) and χ((3)) contributions to harmonic generation. The results show promising efficiencies at wavelengths below 120 nm, and reveal coupling of TE and TM polarizations for pump and harmonic signals. A downconversion process that can regenerate pump photons with polarization orthogonal to the incident pump is also discussed. PMID:22139280
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.
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.
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
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.
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.
Design sensitivity analysis for nonlinear magnetostatic problems by continuum approach
NASA Astrophysics Data System (ADS)
Park, Il-Han; Coulomb, J. L.; Hahn, Song-Yop
1992-11-01
Using the material derivative concept of continuum mechanics and an adjoint variable method, in a 2-dimensional nonlinear magnetostatic system the sensitivity formula is derived in a line integral form along the shape modification interface. The sensitivity coefficients are numerically evaluated from the solutions of state and adjoint variables calculated by the existing standard finite element code. To verify this method, the pole shape design problem of a quadrupole is provided. En utilisant la notion de dérivée matérielle de la mécanique des milieux continus et une méthode de variable adjointe, pour des problèmes magnétiques non linéaires bidimensionnels, la formule de sensibilité est dérivée sous forme d'une intégrale de contour sur la surface de modification. Les coefficients de sensibilité sont numériquement évalués avec les variables d'état et adjointes calculées à partir du logiciel existant d'éléments finis. Pour vérifier cette méthode, le problème d'optimisation de forme d'un quadripôle est décrit.
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.
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
A quadratic-tensor model algorithm for nonlinear least-squares problems with linear constraints
NASA Technical Reports Server (NTRS)
Hanson, R. J.; Krogh, Fred T.
1992-01-01
A new algorithm for solving nonlinear least-squares and nonlinear equation problems is proposed which is based on approximating the nonlinear functions using the quadratic-tensor model by Schnabel and Frank. The algorithm uses a trust region defined by a box containing the current values of the unknowns. The algorithm is found to be effective for problems with linear constraints and dense Jacobian matrices.
NASA Astrophysics Data System (ADS)
Rai, Buddhi; McGurn, Arthur R.
2015-02-01
Photonic crystal and split ring resonator (SRR) metamaterial waveguides with Kerr nonlinear dielectric impurities are studied. The transmission coefficients for two guided modes of different frequencies scattering from the Kerr impurities are computed. The systems are shown to exhibit multiple transmission coefficient solutions arising from the Kerr nonlinearity. Multiple transmission coefficients occur when different input intensities into a waveguide result in the same transmitted output intensities past its nonlinear impurities. (In the case of a single incident guided mode the multiplicity of transmission coefficients is known as optical bistability.) The analytical conditions under which the transmission coefficients are single and multiple valued are determined, and specific examples of both single and multiple valued transmission coefficient scattering are presented. Both photonic crystal and split ring resonator systems are studied as the Kerr nonlinearity enters the photonic crystal and SRR systems in different ways. This allows for an interesting comparison of the differences in behaviors of these two types of system which are described by distinctly different mathematical structures. Both the photonic crystal and SRR models used in the calculations are based on a difference equation approach to the system dynamics. The difference equation approach has been extensively employed in previous papers to model the basic properties of these systems. The paper is a continuation of work on the optical bistability of single guided modes interacting with Kerr impurities in photonic crystals originally considered by McGurn [Chaos 13, 754 (2003), 10.1063/1.1568691] and work on the resonant scattering from Kerr impurities in photonic crystal waveguides considered by McGurn [J. Phys.: Condens. Matter 16, S5243 (2004), 10.1088/0953-8984/16/44/021]. It generalizes this work making the extension to the more complex interaction of two guided modes at different frequencies
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.
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.
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.
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.
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
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
NASA Astrophysics Data System (ADS)
Man, Weining; Fardad, Shima; Zhang, Ze; Prakash, Jai; Lau, Michael; Zhang, Peng; Heinrich, Matthias; Christodoulides, Demetrios N.; Chen, Zhigang
2013-11-01
We demonstrate a new class of synthetic colloidal suspensions capable of exhibiting negative polarizabilities, and observe for the first time robust propagation and enhanced transmission of self-trapped light over long distances that would have been otherwise impossible in conventional suspensions with positive polarizabilities. Such light penetration through the strong scattering environment is attributed to the interplay between optical forces and self-activated transparency effects while no thermal effect is involved. By judiciously mixing colloidal particles of both negative and positive polarizabilities, we show that the resulting nonlinear response of these systems can be fine-tuned. Our experimental observations are in agreement with theoretical analysis based on a thermodynamic model that takes into account particle-particle interactions. These results may open up new opportunities in developing soft-matter systems with engineered optical nonlinearities.
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.
[Post-transmission Schistosomiasis: the Problem of Hepatic Fibrosis].
Wang, Yong
2015-12-01
Hepatic fibrosis caused by schistosomiasis japonica is becoming an important issue in areas when the transmission of schitosomiasis has been interrupted. Schistosomiasis control programme should therefore be adjusted to involve the routine monitoring and intervention of hepatic fibrosis of schistosomiasis in those areas with effective transmission control, to inhibit the development of advanced schistosomiasis.
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.
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.
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.
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.
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.
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…
NASA Astrophysics Data System (ADS)
Miyanaga, S.; Sato, T.
2015-04-01
Polarization-dependent nonlinear transmissions are investigated by a pump-probe method in saturable-dye-doped films in which optically anisotropic saturable dyes are rigidly held with random orientations. The nonlinear transmissions measured by using uranine-doped poly(vinyl alcohol) films are compared with the theoretical predictions that are obtained by considering the effects of pump propagation and molecular orientation on the basis of a rate equation analysis for a four-energy-level model including an excited-state absorption. The measurements were conducted for the two cases of polarization states for which the polarization direction of the probe wave is either parallel or perpendicular to that of the pump wave; the experimental results considerably deviated from the theoretical ones for the probe wave perpendicularly polarized to the pump wave. It is shown that this is explained by modifying the energy level model to include the existence of a nearly-orthogonal component of the transition dipole moment associated with the ground-state absorption in uranine dyes.
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.
Nonlinear problems of complex natural systems: Sun and climate dynamics.
Bershadskii, A
2013-01-13
The universal role of the nonlinear one-third subharmonic resonance mechanism in generation of strong fluctuations in complex natural dynamical systems related to global climate is discussed using wavelet regression detrended data. The role of the oceanic Rossby waves in the year-scale global temperature fluctuations and the nonlinear resonance contribution to the El Niño phenomenon have been discussed in detail. The large fluctuations in the reconstructed temperature on millennial time scales (Antarctic ice core data for the past 400,000 years) are also shown to be dominated by the one-third subharmonic resonance, presumably related to the Earth's precession effect on the energy that the intertropical regions receive from the Sun. The effects of galactic turbulence on the temperature fluctuations are also discussed. PMID:23185052
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.
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.
NASA Astrophysics Data System (ADS)
Wang, Qing; Yao, Jing-Zheng
2010-12-01
Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for large variation nonlinear dynamic problems. For this purpose, algorithms and a framework related to SFEM based on the stochastic virtual work principle were studied. To prove the validity and practicality of the algorithms and framework, numerical examples for nonlinear dynamic problems with large variations were calculated and compared with the Monte-Carlo Simulation method. This comparison shows that the proposed approaches are accurate and effective for the nonlinear dynamic analysis of structures with random parameters.
Solving chemical equilibrium problems using nonlinear optimization. [NEWT
Parkinson, W.J.; Sanderson, J.G.
1984-06-01
This report describes a program that will solve general chemical equilibrium problems of the type found in synthetic fossil-fuel plants. The program described here will also solve chemical equilibrium problems that are associated with unit operations that are found in refineries and ammonia plants. The most common problem encountered involves finding the equilibrium composition of a mixture, given feed composition, and the desired equilibrium temperature and pressure. Another less common problem requires the computation of the equilibrium temperature as well as the equilibrium composition for an adiabatic or other nonisothermal reaction. A constrained multidimensional Newton's method is used to solve the common isothermal equilibrium problem. The nonisothermal problem is solved by nesting the same multidimensional Newton's method inside a one-dimensional Newton's method that iterates on temperature. The program allows a gas phase with up to 20 reacting gases and the possibility of one solid phase (graphitic carbon).
Willert, Jeffrey; Park, H.; Taitano, William
2015-11-01
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.
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.
Morsy-Osman, Mohamed; Zhuge, Qunbi; Chen, Lawrence R; Plant, David V
2011-12-12
We propose the use of pilot-aided (PA) transmission, enabled by single-sideband-subcarrier modulation of both quadratures in the DSP-domain, in single-carrier systems to mitigate jointly laser phase noise and fiber nonlinearity. In addition to tolerance against laser phase noise, we show that the proposed scheme also improves the nonlinear tolerance of both polarization-division-multiplexed (PDM) QPSK and 16-QAM coherent transmission systems by increasing the maximum allowable launch power by 1 dB and 1.5 dB, respectively. The improved nonlinear performance of both systems also manifests itself as an increase in the maximum reach by 720 km and 480 km, respectively. Finally, when digital-to-analog converters (DACs) with lower bit resolutions are used at the transmitter, PA transmission is shown to preserve the same performance improvement over the non-PA case.
Dynamics of parabolic problems with memory. Subcritical and critical nonlinearities
NASA Astrophysics Data System (ADS)
Li, Xiaojun
2016-08-01
In this paper, we study the long-time behavior of the solutions of non-autonomous parabolic equations with memory in cases when the nonlinear term satisfies subcritical and critical growth conditions. In order to do this, we show that the family of processes associated to original systems with heat source f(x, t) being translation bounded in Lloc 2 ( R ; L 2 ( Ω ) ) is dissipative in higher energy space M α , 0 < α ≤ 1, and possesses a compact uniform attractor in M 0 .
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.
NASA Astrophysics Data System (ADS)
Li, Dongfang; Zhang, Jiwei
2016-10-01
Anomalous diffusion behavior in many practical problems can be described by the nonlinear time-fractional parabolic problems on unbounded domain. The numerical simulation is a challenging problem due to the dependence of global information from time fractional operators, the nonlinearity of the problem and the unboundedness of the spacial domain. To overcome the unboundedness, conventional computational methods lead to extremely expensive costs, especially in high dimensions with a simple treatment of boundary conditions by making the computational domain large enough. In this paper, based on unified approach proposed in [25], we derive the efficient nonlinear absorbing boundary conditions (ABCs), which reformulates the problem on unbounded domain to an initial boundary value problem on bounded domain. To overcome nonlinearity, we construct a linearized finite difference scheme to solve the reduced nonlinear problem such that iterative methods become dispensable. And the stability and convergence of our linearized scheme are proved. Most important, we prove that the numerical solutions are bounded by the initial values with a constant coefficient, i.e., the constant coefficient is independent of the time. Overall, the computational cost can be significantly reduced comparing with the usual implicit schemes and a simple treatment of boundary conditions. Finally, numerical examples are given to demonstrate the efficiency of the artificial boundary conditions and theoretical results of the schemes.
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
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)
Jalali, Tahmineh
2014-12-01
The multiple multipoles (MMP) method is used to solve a nonlinear eigenvalue problem for analysis of a 2D metallic and dielectric photonic crystal. Simulation space is implemented in the first Brillouin zone, in order to obtain band structure and modal fields and in the supercell to calculate waveguide modes. The Bloch theorem is used to implement fictitious periodic boundary conditions for the first Brillouin zone and supercell. This method successfully computes the transmission and reflection coefficients of photonic crystal waveguide without significant error for termination of the computational space. To validate our code, the band structure of a cubic lattice is simulated and results are compared with results of the plane wave expansion method. The proposed method is shown to be applicable to photonic crystals of irregular shape and frequency dependent (independent) materials, such as dielectric or dispersive material, and experimental data for different lattice structures. Numerical calculations show that the MMP method is stable, accurate and fast and can be used on personal computers.
Nonlinear effects in gases in the Couette problem
Chernyak, V. G. Polikarpov, A. Ph.
2010-01-15
The nonlinear processes of heat and mass transfer in a rarefied gas confined between two infinite parallel plates maintained at different temperatures and moving at a relative velocity are considered. The profiles of the gas macroscopic flow velocity, density, temperature, heat fluxes, and shear stress were calculated on the basis of kinetic equations by the discrete velocity method in a wide range of Knudsen numbers at different values of temperature difference between the plates and plate velocities. It was shown that under certain conditions, the direction of gas flow near the 'hot' plate can change to the opposite. It was discovered that the longitudinal and normal components of heat flux at a certain temperature difference between the plates change their orientation to the opposite in transition and nearly free molecular regimes.
Numerical nonlinear inverse problem of determining wall heat flux
NASA Astrophysics Data System (ADS)
Zueco, J.; Alhama, F.; González Fernández, C. F.
2005-03-01
The inverse problem of determining time-variable surface heat flux in a plane wall, with constant or temperature dependent thermal properties, is numerically studied. Different kinds of incident heat flux, including rectangular waveform, are assumed. The solution is numerically solved as a function estimation problem, so that no a priori information for the functional waveforms of the unknown heat flux is needed. In all cases, a solution in the form of a piece-wise function is used to approach the incident flux. Transient temperature measurements at the boundary, from the solution of the direct problem, served as the simulated experimental data needed as input for the inverse analysis. Both direct and inverse heat conduction problems are solved using the network simulation method. The solution is obtained step-by-step by minimising the classical functional that compares the above input data with those obtained from the solution of the inverse problem. A straight line of variable slope and length is used for each one of the stretches of the desired solution. The influence of random error, number of functional terms and the effect of sensor location are studied. In all cases, the results closely agree with the solution.
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.
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.
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.
Mathematical modeling of multiresonance problems in nonlinear optics
NASA Astrophysics Data System (ADS)
Byrne, Julie A.
2000-10-01
We have explored asymptotic and exact solution methods for equations modeling multi-resonant interactions of light with optical media. For two-level media that are inhomogeneously broadened, we find small amplitude asymptotic solutions using the method of multiple scales. For Λ-type three level media, in which the ground state of the two level atom has two degenerated ground sublevels, we employ the inverse scattering transform to find exact solutions and then use parametrizations to plot the solutions on simple manifolds such as spheres and ellipses. We have used the method of multiple scales on completely integrable two-level Maxwell-Bloch system in order to find the leading order behavior of ``small'' solutions. The solution technique we have employed involves computing the small-amplitude expansion on the equations and also directly on the Lax Pair at every step of the calculation to ensure that integrability is retained. Thus, the ``secularity condition,'' which eliminates the growing terms and produces the successive approximate equations in the method of multiple scales, must also satisfy the compatibility condition of the Lax pair at each level of approximation. In the limit of low intensity, the electric field becomes a sum of plane waves with small and slowly-modulated amplitudes. These amplitudes are described by the nonlinear Schrodinger equations. We have calculated solutions of the three-level Maxwell- Bloch equations in the ``Lambda'' configuration that represent the switching of light polarization in a nonlinear resonant optically active medium. These are special solutions of soliton type, and correspond to the physical setup in which initially only one of the two less energetic atomic quantum levels in the optical medium is populated by electrons. In order to display the physical properties of the polarization switching solutions, we used the Stokes' sphere representation from optics to display the polarization of light. We also used the Euler
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?'
Estimates of reachable sets of impulsive control problems with special nonlinearity
NASA Astrophysics Data System (ADS)
Filippova, T. F.
2016-10-01
The problem of estimating reachable sets of nonlinear dynamical control systems with quadratic or bilinear nonlinearity and with uncertainty in initial states is studied. We assume that the uncertainty is of a set-membership kind when we know only the bounding set for unknown items and any additional statistical information on their behavior is not available. We present here approaches that allow finding ellipsoidal estimates of reachable sets, which use the special structure of nonlinearity of studied control system. The algorithms of constructing such ellipsoidal set-valued estimates and numerical simulation results are given in two cases, for control systems with classical controls and for measure driven (impulsive) control systems.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Kasai, Seiya; Tadokoro, Yukihiro; Ichiki, Akihisa
2013-12-01
We design nonlinear functions for the transmission of a small signal with non-Gaussian noise and perform experiments to characterize their responses. Using statistical design theory [A. Ichiki and Y. Tadokoro, Phys. Rev. E 87, 012124 (2013), 10.1103/PhysRevE.87.012124], a static nonlinear function is estimated from the probability density function of the given noise in order to maximize the signal-to-noise ratio of the output. Using an electronic system that implements the optimized nonlinear function, we confirm the recovery of a small signal from a signal with non-Gaussian noise. In our experiment, the non-Gaussian noise is a mixture of Gaussian noises. A similar technique is also applied to the optimization of the threshold value of the function. We find that, for non-Gaussian noise, the response of the optimized nonlinear systems is better than that of the linear system.
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.
Neural networks for nonlinear and mixed complementarity problems and their applications.
Dang, Chuangyin; Leung, Yee; Gao, Xing-Bao; Chen, Kai-zhou
2004-03-01
This paper presents two feedback neural networks for solving a nonlinear and mixed complementarity problem. The first feedback neural network is designed to solve the strictly monotone problem. This one has no parameter and possesses a very simple structure for implementation in hardware. Based on a new idea, the second feedback neural network for solving the monotone problem is constructed by using the first one as a subnetwork. This feedback neural network has the least number of state variables. The stability of a solution of the problem is proved. When the problem is strictly monotone, the unique solution is uniformly and asymptotically stable in the large. When the problem has many solutions, it is guaranteed that, for any initial point, the trajectory of the network does converge to an exact solution of the problem. Feasibility and efficiency of the proposed neural networks are supported by simulation experiments. Moreover, the feedback neural network can also be applied to solve general nonlinear convex programming and nonlinear monotone variational inequalities problems with convex constraints.
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.
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.
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
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.
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.
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.)…
On some transmission problems set in a biological cell, analysis and resolution
NASA Astrophysics Data System (ADS)
Labbas, Rabah; Lemrabet, Keddour; Limam, Kheira; Medeghri, Ahmed; Meisner, Maëlis
2015-10-01
Some transmission problems are set in bodies with a crown of small thickness ε > 0. For instance, those concerning the conductivity in the biological cell. By a natural change of variables, we transform them in transmission problems set in two cylindrical bodies ] - ∞, 0 [ × ] - π, π [ and ] 0, δ [ × ] - π, π [ (where δ = ln (1 + ε)) and then, in some general elliptic abstract differential equations (Pδ) δ > 0. The goal of this work is to give a complete study of these problems (Pδ) δ > 0 for every δ > 0. Existence, uniqueness and maximal regularity results are obtained for the classical solutions essentially by using the semigroups theory.
A high-performance feedback neural network for solving convex nonlinear programming problems.
Leung, Yee; Chen, Kai-Zhou; Gao, Xing-Bao
2003-01-01
Based on a new idea of successive approximation, this paper proposes a high-performance feedback neural network model for solving convex nonlinear programming problems. Differing from existing neural network optimization models, no dual variables, penalty parameters, or Lagrange multipliers are involved in the proposed network. It has the least number of state variables and is very simple in structure. In particular, the proposed network has better asymptotic stability. For an arbitrarily given initial point, the trajectory of the network converges to an optimal solution of the convex nonlinear programming problem under no more than the standard assumptions. In addition, the network can also solve linear programming and convex quadratic programming problems, and the new idea of a feedback network may be used to solve other optimization problems. Feasibility and efficiency are also substantiated by simulation examples.
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.
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
NASA Astrophysics Data System (ADS)
Koleva, M. N.
2007-10-01
We consider stationary linear and nonlinear problems on non-connected layers with distinct material properties. A version of the finite element method (FEM) is used for discretization of the continuous problems. We formulate sufficient conditions under which we prove the discrete maximum principle and convergence of the numerical higher-order finite elements solution. Efficient algorithm for solution of the FEM algebraic equations is proposed. Numerical experiments are also discussed.
An iterative regularization method for nonlinear problems based on Bregman projections
NASA Astrophysics Data System (ADS)
Maaß, Peter; Strehlow, Robin
2016-11-01
In this paper, we present an iterative method for the regularization of ill-posed, nonlinear problems. The approach is based on the Bregman projection onto stripes the width of which is controlled by both the noise level and the structure of the operator. In our investigations, we follow (Lorenz et al 2014 SIAM J. Imaging Sci. 7 1237–62) and extend the respective method to the setting of nonlinear operators. Furthermore, we present a proof for the regularizing properties of the method.
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.
A monotonic method for nonlinear optimal control problems with concave dependence on the state
NASA Astrophysics Data System (ADS)
Salomon, Julien; Turinici, Gabriel
2011-03-01
Initially introduced in the framework of quantum control, the so-called monotonic algorithms have demonstrated very good numerical performance when dealing with bilinear optimal control problems. This article presents a unified formulation that can be applied to more general nonlinear settings compatible with the hypothesis detailed below. In this framework, we show that the well-posedness of the general algorithm is related to a nonlinear evolution equation. We prove the existence of the solution to the evolution equation and give important properties of the optimal control functional. Finally we show how the algorithm works for selected models from the literature. We also compare the algorithm with the gradient algorithm.
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.
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.
Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
NASA Astrophysics Data System (ADS)
Lakshtanov, E.; Vainberg, B.
2013-10-01
The paper concerns the isotropic interior transmission eigenvalue (ITE) problem. This problem is not elliptic, but we show that, using the Dirichlet-to-Neumann map, it can be reduced to an elliptic one. This leads to the discreteness of the spectrum as well as to certain results on a possible location of the transmission eigenvalues. If the index of refraction \\sqrt{n(x)} is real, then we obtain a result on the existence of infinitely many positive ITEs and the Weyl-type lower bound on its counting function. All the results are obtained under the assumption that n(x) - 1 does not vanish at the boundary of the obstacle or it vanishes identically, but its normal derivative does not vanish at the boundary. We consider the classical transmission problem as well as the case when the inhomogeneous medium contains an obstacle. Some results on the discreteness and localization of the spectrum are obtained for complex valued n(x).
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.
NASA Astrophysics Data System (ADS)
Srivastava, Nilabh; Haque, Imtiaz
2009-03-01
Over the past two decades, extensive research has been conducted on developing vehicle transmissions that meet the goals of reduced exhaust emissions and increased vehicle efficiency. A continuously variable transmission is an emerging automotive transmission technology that offers a continuum of gear ratios between desired limits. A chain CVT is a friction-limited drive whose dynamic performance and torque capacity rely significantly on the friction characteristic of the contact patch between the chain and the pulley. Although a CVT helps to maximize the vehicle fuel economy, its complete potential has not been accomplished in a mass-production vehicle. The present research focuses on developing models to analyze friction-induced nonlinear dynamics of a chain CVT drive and identify possible mechanisms that cause degradation of the overall dynamic performance by inducing chaos and self-sustained vibrations in the system. Two different mathematical models of friction, which characterize different operating or loading conditions, are embedded into a detailed planar multibody model of chain CVT in order to capture the various friction-induced effects in the system. Tools such as stick-slip oscillator dynamics, Lyapunov exponents, phase-space reconstruction, and recurrence plotting are incorporated to characterize the nonlinear dynamics of such a friction-limited system. The mathematical models, the computational scheme, and the results corresponding to different loading scenarios are discussed. The results discuss the influence of friction characteristics on the nonlinear dynamics and torque transmitting capacity of a chain CVT drive.
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.
NASA Astrophysics Data System (ADS)
Korpusov, M. O.; Panin, A. A.
2014-10-01
We consider an abstract Cauchy problem for a formally hyperbolic equation with double non-linearity. Under certain conditions on the operators in the equation, we prove its local (in time) solubility and give sufficient conditions for finite-time blow-up of solutions of the corresponding abstract Cauchy problem. The proof uses a modification of a method of Levine. We give examples of Cauchy problems and initial-boundary value problems for concrete non-linear equations of mathematical physics.
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.
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.
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
NASA Astrophysics Data System (ADS)
Liu, Shaobin; Canfield, Robert A.
2013-07-01
A Continuum Sensitivity Equation (CSE) method was developed in local derivative form for fluid-structure shape design problems. The boundary velocity method was used to derive the continuum sensitivity equations and sensitivity boundary conditions in local derivative form for a built-up joined beam structure under transient aerodynamic loads. For nonlinear problems, when the Newton-Raphson method is used, the tangent stiffness matrix yields the desired sensitivity coefficient matrix for solving the linear sensitivity equations in the Galerkin finite element formulation. For built-up structures with strain discontinuity, the local sensitivity variables are not continuous at the joints, requiring special treatment to assemble the elemental local sensitivities and the generalized force vector. The coupled fluid-structure physics and continuum sensitivity equations for gust response of a nonlinear joined beam with an airfoil model were posed and solved. The results were compared to the results obtained by finite difference (FD) method.
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.
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.
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.
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.
Analytical Approximation Method for the Center Manifold in the Nonlinear Output Regulation Problem
NASA Astrophysics Data System (ADS)
Suzuki, Hidetoshi; Sakamoto, Noboru; Celikovský, Sergej
In nonlinear output regulation problems, it is necessary to solve the so-called regulator equations consisting of a partial differential equation and an algebraic equation. It is known that, for the hyperbolic zero dynamics case, solving the regulator equations is equivalent to calculating a center manifold for zero dynamics of the system. The present paper proposes a successive approximation method for obtaining center manifolds and shows its effectiveness by applying it for an inverted pendulum example.
Solution of nonlinear optimal control problems by the interpolating scaling functions
NASA Astrophysics Data System (ADS)
Foroozandeh, Z.; Shamsi, M.
2012-03-01
This paper presents a numerical method for solving nonlinear optimal control problems including state and control inequality constraints. The method is based upon interpolating scaling functions. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique.
A Two-point Boundary Value Problem in Nonlinear Stability Analysis
NASA Astrophysics Data System (ADS)
Luyckx, Liesbeth; Loccufier, Mia; Noldus, Erik
2002-09-01
Computational methods combining simulation and geometrical analysis are presented to estimate a set point's basin of attraction in the state space of autonomous nonlinear systems. Dynamical systems are considered which possess global Lyapunov functions. The Lyapunov function is used to analyse the geometrical structure of the stability boundary, which determines the numerical procedure to be followed. Moreover the problem is studied of visualizing the estimated stability boundary in a higher dimensional state space.
Nonlinear random response of large-scale sparse finite element plate bending problems
NASA Astrophysics Data System (ADS)
Chokshi, Swati
Acoustic fatigue is one of the major design considerations for skin panels exposed to high levels of random pressure at subsonic/supersonic/hypersonic speeds. The nonlinear large deflection random response of the single-bay panels aerospace structures subjected to random excitations at various sound pressure levels (SPLs) is investigated. The nonlinear responses of plate analyses are limited to determine the root-mean-square displacement under uniformly distributed pressure random loads. Efficient computational technologies like sparse storage schemes and parallel computation are proposed and incorporated to solve large-scale, nonlinear large deflection random vibration problems for both types of loading cases: (1) synchronized in time and (2) unsynchronized and statistically uncorrelated in time. For the first time, large scale plate bending problems subjected to unsynchronized load are solved using parallel computing capabilities to account for computational burden due to the simulation of the unsynchronized random pressure fluctuations. The main focus of the research work is placed upon computational issues involved in the nonlinear modal methodologies. A nonlinear FEM method in time domain is incorporated with the Monte Carlo simulation and sparse computational technologies, including the efficient sparse Subspace Eigen-solutions are presented and applied to accurately determine the random response with a refined, large finite element mesh for the first time. Sparse equation solver and sparse matrix operations embedded inside the subspace Eigen-solution algorithms are also exploited. The approach uses the von-Karman nonlinear strain-displacement relations and the classical plate theory. In the proposed methodologies, the solution for a small number (say less than 100) of lowest linear, sparse Eigen-pairs need to be solved for only once, in order to transform nonlinear large displacements from the conventional structural degree-of-freedom (dof) into the modal
Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin
2016-01-01
This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness. PMID:27006888
Modeling of the wave transmission properties of large arteries using nonlinear elastic tubes.
Pythoud, F; Stergiopulos, N; Meister, J J
1994-11-01
We propose a new, simple way of constructing elastic tubes which can be used to model the nonlinear elastic properties of large arteries. The tube models are constructed from a silicon elastomer (Sylgard 184, Dow Corning), which exhibits a nonlinear behavior with increased stiffness at high strains. Tests conducted on different tube models showed that, with the proper choice of geometric parameters, the elastic properties, in terms of area-pressure relation and compliance, can be similar to that of real arteries.
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.
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.
NASA Astrophysics Data System (ADS)
Sengupta, Parijat; Bellotti, Enrico
2016-09-01
We study the optical behavior of an arrangement in which the interface between a linear and non-linear dielectric media is covered by an embedded mono-layer of transition metal dichalcogenides (TMDC). The optical behavior is qualitatively obtained through transmission and reflection coefficients which are a function of the third order non-linear susceptibility of the Kerr-type dielectric and the inter-band optical conductivity of the TMDC mono-layer. The inter-band optical conductivity of the TMDC mono-layer is calculated using the Kubo formalism from the linear response theory. In particular, we theoretically demonstrate that the optical response of this structure can be switched between the total internal reflection and a normal transmission regime by controlling the intensity of the incident radiation. The reflection and transmission functions are shown to be amenable to further control by altering the inter-band optical conductivity of the embedded TMDC mono-layer. The optical conductivity is directly related to its energy dispersion. We specifically choose two TMDC mono-layers, MoS2 and WSe2, which have nearly identical dispersion parameters apart from a much stronger spin-orbit coupling in the latter. The stronger spin-orbit coupling in WSe2 does not significantly alter the inter-band optical conductivity to manifest as an enhanced reflection spectrum. However, we find that application of an external perturbation such as strain could be effectively used to modulate the overall optical response. We conclude by discussing briefly the phenomenon of optical bistability which arises in materials exhibiting optical non-linearity via an intensity-dependent refractive index.
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.
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.
Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology
2014-01-01
We introduce an efficient recursive scheme based on Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples. PMID:24707221
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 Astrophysics Data System (ADS)
Hill, M. C.; Hanson, R. T.; Kauffman, L. J.
2012-12-01
A synthetic test case illustrates the importance of a transparency (revealed importance) and refutability (tested hypotheses) in model development. The test case represents transport of an environmental tracer (cfc) and contaminant (pce) in a heterogeneous groundwater system. A locally refined grid is used to represent selected features and the dynamics of pumping. Observations include hydraulic heads for which simulated values are obtained with MODFLOW, and four types of observations for which simulated values are produced with particle tracking using the new program MODPATH-OBS. These include (1) proximity observations that measure whether particles arrive at expected locations, (2) time-of-travel observations that measure whether particles arrive when they are expected, (3) concentration observations of cfc and pce where the simulated values are obtained by assigning each particle a concentration that is allowed to decay during transport, and (4) source water type observations that measure the dominance of sources of water that reach a given destination. There are eight transmissivity and porosity parameters. One model run requires 20 minutes; computationally frugal model analysis methods that required 10s to 100s of model runs enabled rapid access to the insights obtained. Three sets of parameter values are considered: (a) starting parameter values for which the sum-of-squared weighted residuals (SOSWR) exceeds 11,000, (b) estimated parameter values for which SOSWR equals 326, and (c) true parameter values that are known for this synthetic problem and for which SOSWR equals 457. SOSWR is not zero for the true parameter values because most of the locally refined model grid used in these simulations is coarser than the globally refined model grid used to generate the observations in this synthetic problem. SOSWR is smaller for the estimated parameter values than the true values because of fitting typical of model calibration, regardless of how calibrated results
NASA Astrophysics Data System (ADS)
Kohr, Mirela; Lanza de Cristoforis, Massimo; Mikhailov, Sergey E.; Wendland, Wolfgang L.
2016-10-01
The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the nonlinear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain {Ω} with connected boundary, and the other one is the exterior Lipschitz domain R3 setminus overline{Ω}. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces.
A pegging algorithm for separable continuous nonlinear knapsack problems with box constraints
NASA Astrophysics Data System (ADS)
Kim, Gitae; Wu, Chih-Hang
2012-10-01
This article proposes an efficient pegging algorithm for solving separable continuous nonlinear knapsack problems with box constraints. A well-known pegging algorithm for solving this problem is the Bitran-Hax algorithm, a preferred choice for large-scale problems. However, at each iteration, it must calculate an optimal dual variable and update all free primal variables, which is time consuming. The proposed algorithm checks the box constraints implicitly using the bounds on the Lagrange multiplier without explicitly calculating primal variables at each iteration as well as updating the dual solution in a more efficient manner. Results of computational experiments have shown that the proposed algorithm consistently outperforms the Bitran-Hax in all baseline testing and two real-time application models. The proposed algorithm shows significant potential for many other mathematical models in real-world applications with straightforward extensions.
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.
Solving nonlinear system of third-order boundary value problems using block method
NASA Astrophysics Data System (ADS)
See, Phang Pei; Majid, Zanariah Abdul; Suleiman, Mohamed; Ismail, Fudziah Bt; Othman, Khairil Iskandar
2015-05-01
In this paper, we propose an algorithm of two-point block method to solve the nonlinear system of third-order boundary value problems directly. The proposed method is presented in a simple form of Adams type and two approximate solutions will be obtained simultaneously with the block method using variable step size strategy. The method will be implemented with the multiple shooting technique via the three-step iterative method to generate the missing initial value. Most of the existence method will reduce the third-order boundary value problems to a system of first order equations where the systems of six equations need to be solved. The method we proposed in this paper will solve the third-order boundary value problems directly. Two numerical examples are given to illustrate the efficiency of the proposed method.
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)
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
Quasi-static solution algorithms for kinematically/materially nonlinear thermomechanical problems
NASA Technical Reports Server (NTRS)
Padovan, J.; Pai, S. S.
1984-01-01
This paper develops an algorithmic solution strategy which allows the handling of positive/indefinite stiffness characteristics associated with the pre- and post-buckling of structures subject to complex thermomechanical loading fields. The flexibility of the procedure is such that it can be applied to both finite difference and element-type simulations. Due to the generality of the algorithmic approach developed, both kinematic and thermal/mechanical type material nonlinearity including inelastic effects can be treated. This includes the possibility of handling completely general thermomechanical boundary conditions. To demonstrate the scheme, the results of several benchmark problems is presented.
Large time behavior in a nonlinear age-dependent population dynamics problem with spatial diffusion.
Langlais, M
1988-01-01
In this work we analyze the large time behavior in a nonlinear model of population dynamics with age-dependence and spatial diffusion. We show that when t----+ infinity either the solution of our problem goes to 0 or it stabilizes to a nontrivial stationary solution. We give two typical examples where the stationary solutions can be evaluated upon solving very simple partial differential equations. As a by-product of the extinction case we find a necessary condition for a nontrivial periodic solution to exist. Numerical computations not described below show a rapid stabilization.
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.
Pinkerton, Steven D.; Chesson, Harrell W.; Crosby, Richard A.; Layde, Peter M.
2014-01-01
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 behavior change measures as indicators of the effectiveness of HIV/STI risk-reduction interventions. Findings indicate that the risk of acquiring HIV through vaginal intercourse is essentially a linear function of the number of unprotected sex acts and is nearly independent of the number of sex partners. Consequently, the number of unprotected sex acts is an excellent marker for the risk of acquiring HIV through vaginal intercourse, whereas the number of sex partners is largely uninformative. In general, the number of unprotected sex acts is not an adequate marker for the risk of acquiring a highly infectious STI due to the highly nonlinear per act transmission dynamics of these STIs. The number of sex partners is a reasonable indicator of STI risk only under highly circumscribed conditions. A theoretical explanation for this pattern of results is provided. The contrasting extent to which HIV and highly infectious STIs deviate from the linearity assumption that underlies sexual behavior outcome measures has important implications for the use of these measures to assess the effectiveness of HIV/STI risk-reduction interventions. PMID:22201639
Mitter, S.K.
1980-06-01
The main thesis of this paper is that there are striking similarities between the mathematical problems of stochastic system theory, notably linear and non-linear filtering theory, and mathematical developments underlying quantum mechanics and quantum field theory. Thus the mathematical developments of the past thirty years in functional analysis, lie groups and lie algebras, group representations, and probabilistic methods of quantum theory can serve as a guide and indicator to search for an appropriate theory of stochastic systems. In the current state of development of linear and non-linear filtering theory, it is best to proceed by 'analogy' and with care, since 'unitarity' which plays such an important part in quantum mechanics and quantum field theory is not necessarily relevant to linear and non-linear filtering theory. The partial differential equations that arise in quantum theory are generally wave equations, whereas the partial differential equations arising in filtering theory are stochastic parabolic equations. Nevertheless the possibility of passing to a wave equation by appropriate analytic continuation from the parabolic equation, reminiscent of the current program in euclidean field theory, should not be overlooked.
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 nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem
NASA Astrophysics Data System (ADS)
Golse, François; Salvarani, Francesco
2007-04-01
Consider the initial-boundary value problem for the 2-speed Carleman model of the Boltzmann equation of the kinetic theory of gases, (see Carleman 1957 Problèmes Mathématiques Dans la Théorie Cinétique des Gaz (Uppsala: Almqvist-Wiksells)), set in some bounded interval with boundary conditions prescribing the density of particles entering the interval. Under the usual parabolic scaling, a nonlinear diffusion limit is established for this problem. In fact, the techniques presented here allow treatment generalizations of the Carleman system where the collision frequency is proportional to the αth power of the macroscopic density, with α ∈ [-1, 1].
Solution of non-linear inverse heat conduction problems using the method of lines
NASA Astrophysics Data System (ADS)
Taler, J.; Duda, P.
Two space marching methods for solving the one-dimensional nonlinear inverse heat conduction problems are presented. The temperature-dependent thermal properties and the boundary condition on the accessible part of the boundary of the body are known. Additional temperature measurements in time are taken with a sensor located in an arbitrary position within the solid, and the objective is to determine the surface temperature and heat flux on the remaining part of the unspecified boundary. The methods have the advantage that time derivatives are not replaced by finite differences and the good accuracy of the method results from an appropriate approximation of the first time derivative using smoothing polynomials. The extension of the first method presented in this study to higher dimensions inverse heat conduction problems is straightforward.
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.
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 Technical Reports Server (NTRS)
Antoniewicz, Robert F.; Duke, Eugene L.; Menon, P. K. A.
1991-01-01
The design of nonlinear controllers has relied on the use of detailed aerodynamic and engine models that must be associated with the control law in the flight system implementation. Many of these controllers were applied to vehicle flight path control problems and have attempted to combine both inner- and outer-loop control functions in a single controller. An approach to the nonlinear trajectory control problem is presented. This approach uses linearizing transformations with measurement feedback to eliminate the need for detailed aircraft models in outer-loop control applications. By applying this approach and separating the inner-loop and outer-loop functions two things were achieved: (1) the need for incorporating detailed aerodynamic models in the controller is obviated; and (2) the controller is more easily incorporated into existing aircraft flight control systems. An implementation of the controller is discussed, and this controller is tested on a six degree-of-freedom F-15 simulation and in flight on an F-15 aircraft. Simulation data are presented which validates this approach over a large portion of the F-15 flight envelope. Proof of this concept is provided by flight-test data that closely matches simulation results. Flight-test data are also presented.
Voss, Tobias; Svacha, Geoffry T; Mazur, Eric; Müller, Sven; Ronning, Carsten
2009-03-01
We perform a transmission experiment on a ZnO nanowire waveguide to study its transmission characteristics under nonlinear femtosecond-pulse excitation. We find that both the second harmonic and the photoluminescence couple into low-order waveguide modes of the nanowires but with distinctly different efficiencies. We measure the transmission spectrum of a single ZnO nanowire waveguide for near-UV light generated by interband recombination processes. The transmission spectrum allows us to determine the absorption edge of the excited nanowire and to study the temperature profile of the nanowire under femtosecond-pulse excitation.
NASA Astrophysics Data System (ADS)
Miller, Eric L.; Willsky, Alan S.
1996-01-01
In this paper, we present an approach to the nonlinear inverse scattering problem using the extended Born approximation (EBA) on the basis of methods from the fields of multiscale and statistical signal processing. By posing the problem directly in the wavelet transform domain, regularization is provided through the use of a multiscale prior statistical model. Using the maximum a posteriori (MAP) framework, we introduce the relative Cramér-Rao bound (RCRB) as a tool for analyzing the level of detail in a reconstruction supported by a data set as a function of the physics, the source-receiver geometry, and the nature of our prior information. The MAP estimate is determined using a novel implementation of the Levenberg-Marquardt algorithm in which the RCRB is used to achieve a substantial reduction in the effective dimensionality of the inversion problem with minimal degradation in performance. Additional reduction in complexity is achieved by taking advantage of the sparse structure of the matrices defining the EBA in scale space. An inverse electrical conductivity problem arising in geophysical prospecting applications provides the vehicle for demonstrating the analysis and algorithmic techniques developed in this paper.
NASA Astrophysics Data System (ADS)
Pikichyan, H. V.
2016-06-01
It is shown that for the nonlinear boundary value problem of determining the radiation field inside a one-dimensional anisotropic medium illuminated from outside at its boundaries on both sides, the formulas for adding layers in semilinear systems of differential equations for radiative transfer, invariant embedding, and total Ambartsumyan invariance can be used to reduce the equations for the problem to separable equations with initial conditions. The fields travelling to the left and right are thereby found independently of one another. In addition, when one of them has been determined, the other can be found directly using an explicit expression. A general equivalence property of operators with respect to a certain mathematical form, expression, or functional is formulated mathematically. New equations, referred to as kinetic equations of equivalency, are derived from the mutual equivalence of the differential operators of the Boltzmann kinetic equation (the equations of radiative transfer) and the functional equation of the Ambartsumian's complete invariance. Besides separability, these new equations also have the property of linearity. Formulas are also introduced for special problems of single sided illumination of a medium that in this case serve as supplementary information in the initial conditions for formulating Cauchy problems.
NASA Astrophysics Data System (ADS)
Buchler, J. R.; Detweiler, Steven L.; Ipser, James R.
1991-08-01
Consideration is given to 3D numerical cosmology, sources of chaos in mixmaster cosmologies, growth of nonlinear cosmological structure, galactic oscillations, cosmic-string traveling waves, post-Newtonian effects on the oscillations of rotating stars, a new method for treating nonradial pulsations in general relativity, mathematical results on gravitational collapse, and slowly evolving black hole binary systems. Attention is also given to detectability of gravitational radiation from stellar-core collapse, the Cauchy problem on space times with closed timelike curves, exact solutions to conformal Weyl gravity, astrophysical aspects of Weyl gravity; rotating black holes, complex geometry, and thermodynamics; nonlinear operators on spacetime manifolds; and exact solutions, asymptotic structure, and quadrupole radiation.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1976-01-01
Some results of studies of convergence and accuracy of finite element approximations of certain nonlinear problems encountered in finite elasticity are presented. A general technique for obtaining error bounds is also described together with an existence theorem. Numerical results obtained by solving a representative problem are also included.
Keanini, R.G.
2011-04-15
Research Highlights: > Systematic approach for physically probing nonlinear and random evolution problems. > Evolution of vortex sheets corresponds to evolution of an Ornstein-Uhlenbeck process. > Organization of near-molecular scale vorticity mediated by hydrodynamic modes. > Framework allows calculation of vorticity evolution within random strain fields. - Abstract: A framework which combines Green's function (GF) methods and techniques from the theory of stochastic processes is proposed for tackling nonlinear evolution problems. The framework, established by a series of easy-to-derive equivalences between Green's function and stochastic representative solutions of linear drift-diffusion problems, provides a flexible structure within which nonlinear evolution problems can be analyzed and physically probed. As a preliminary test bed, two canonical, nonlinear evolution problems - Burgers' equation and the nonlinear Schroedinger's equation - are first treated. In the first case, the framework provides a rigorous, probabilistic derivation of the well known Cole-Hopf ansatz. Likewise, in the second, the machinery allows systematic recovery of a known soliton solution. The framework is then applied to a fairly extensive exploration of physical features underlying evolution of randomly stretched and advected Burger's vortex sheets. Here, the governing vorticity equation corresponds to the Fokker-Planck equation of an Ornstein-Uhlenbeck process, a correspondence that motivates an investigation of sub-sheet vorticity evolution and organization. Under the assumption that weak hydrodynamic fluctuations organize disordered, near-molecular-scale, sub-sheet vorticity, it is shown that these modes consist of two weakly damped counter-propagating cross-sheet acoustic modes, a diffusive cross-sheet shear mode, and a diffusive cross-sheet entropy mode. Once a consistent picture of in-sheet vorticity evolution is established, a number of analytical results, describing the motion
Zylberberg, Joel; Shea-Brown, Eric
2015-12-01
While recent recordings from neural populations show beyond-pairwise, or higher-order, correlations (HOC), we have little understanding of how HOC arise from network interactions and of how they impact encoded information. Here, we show that input nonlinearities imply HOC in spin-glass-type statistical models. We then discuss one such model with parametrized pairwise- and higher-order interactions, revealing conditions under which beyond-pairwise interactions increase the mutual information between a given stimulus type and the population responses. For jointly Gaussian stimuli, coding performance is improved by shaping output HOC only when neural firing rates are constrained to be low. For stimuli with skewed probability distributions (like natural image luminances), performance improves for all firing rates. Our work suggests surprising connections between nonlinear integration of neural inputs, stimulus statistics, and normative theories of population coding. Moreover, it suggests that the inclusion of beyond-pairwise interactions could improve the performance of Boltzmann machines for machine learning and signal processing applications. PMID:26764727
hp-Pseudospectral method for solving continuous-time nonlinear optimal control problems
NASA Astrophysics Data System (ADS)
Darby, Christopher L.
2011-12-01
In this dissertation, a direct hp-pseudospectral method for approximating the solution to nonlinear optimal control problems is proposed. The hp-pseudospectral method utilizes a variable number of approximating intervals and variable-degree polynomial approximations of the state within each interval. Using the hp-discretization, the continuous-time optimal control problem is transcribed to a finite-dimensional nonlinear programming problem (NLP). The differential-algebraic constraints of the optimal control problem are enforced at a finite set of collocation points, where the collocation points are either the Legendre-Gauss or Legendre-Gauss-Radau quadrature points. These sets of points are chosen because they correspond to high-accuracy Gaussian quadrature rules for approximating the integral of a function. Moreover, Runge phenomenon for high-degree Lagrange polynomial approximations to the state is avoided by using these points. The key features of the hp-method include computational sparsity associated with low-order polynomial approximations and rapid convergence rates associated with higher-degree polynomials approximations. Consequently, the hp-method is both highly accurate and computationally efficient. Two hp-adaptive algorithms are developed that demonstrate the utility of the hp-approach. The algorithms are shown to accurately approximate the solution to general continuous-time optimal control problems in a computationally efficient manner without a priori knowledge of the solution structure. The hp-algorithms are compared empirically against local (h) and global (p) collocation methods over a wide range of problems and are found to be more efficient and more accurate. The hp-pseudospectral approach developed in this research not only provides a high-accuracy approximation to the state and control of an optimal control problem, but also provides high-accuracy approximations to the costate of the optimal control problem. The costate is approximated by
Blow-up problems for the heat equation with a local nonlinear Neumann boundary condition
NASA Astrophysics Data System (ADS)
Yang, Xin; Zhou, Zhengfang
2016-09-01
This paper estimates the blow-up time for the heat equation ut = Δu with a local nonlinear Neumann boundary condition: The normal derivative ∂ u / ∂ n =uq on Γ1, one piece of the boundary, while on the rest part of the boundary, ∂ u / ∂ n = 0. The motivation of the study is the partial damage to the insulation on the surface of space shuttles caused by high speed flying subjects. We show the finite time blow-up of the solution and estimate both upper and lower bounds of the blow-up time in terms of the area of Γ1. In many other work, they need the convexity of the domain Ω and only consider the problem with Γ1 = ∂ Ω. In this paper, we remove the convexity condition and only require ∂Ω to be C2. In addition, we deal with the local nonlinearity, namely Γ1 can be just part of ∂Ω.
Advances in the study of boundary value problems for nonlinear integrable PDEs
NASA Astrophysics Data System (ADS)
Pelloni, Beatrice
2015-02-01
In this review I summarize some of the most significant advances of the last decade in the analysis and solution of boundary value problems for integrable partial differential equations (PDEs) in two independent variables. These equations arise widely in mathematical physics, and in order to model realistic applications, it is essential to consider bounded domain and inhomogeneous boundary conditions. I focus specifically on a general and widely applicable approach, usually referred to as the unified transform or Fokas transform, that provides a substantial generalization of the classical inverse scattering transform. This approach preserves the conceptual efficiency and aesthetic appeal of the more classical transform approaches, but presents a distinctive and important difference. While the inverse scattering transform follows the ‘separation of variables’ philosophy, albeit in a nonlinear setting, the unified transform is based on the idea of synthesis, rather than separation, of variables. I will outline the main ideas in the case of linear evolution equations, and then illustrate their generalization to certain nonlinear cases of particular significance.
NASA Astrophysics Data System (ADS)
Klofaï, Yerima; Essimbi, B. Z.; Jäger, D.
2015-02-01
In this paper the electronic implementation of FitzHugh-Nagumo (F-N) neurons via monolithic microwave integrated circuits (MMIC) based upon a resonant tunneling diode (RTD) nonlinear transmission line (NLTL) using a coplanar waveguide (CPW) is considered. The goals are twofold. In the framework of electrical equivalent circuit emulating nonlinear active wave propagation effects, it is shown, on one hand, how different physical mechanisms are responsible for the time evolution of given input signals. A key result is that this medium supports stable and stationary pulse propagation that is only determined by the parameters of the RTD-NLTL and is independent of the boundary conditions. On the other hand, the influence of specific line elements on the output signal waveform is discussed in a most systematic manner. This leads, for the first time, to a more physical interpretation of the properties of the RTD-NLTL and, furthermore, to interesting technical applications at multi-GHz frequencies and on picosecond time scales. As a result, physically based ways are elucidated regarding how the technical design of those compact neuromorphic electrical circuits can be optimized by numerical simulations and performed using standard MMIC technologies.
NASA Astrophysics Data System (ADS)
Sumin, M. I.
2015-06-01
A parametric nonlinear programming problem in a metric space with an operator equality constraint in a Hilbert space is studied assuming that its lower semicontinuous value function at a chosen individual parameter value has certain subdifferentiability properties in the sense of nonlinear (nonsmooth) analysis. Such subdifferentiability can be understood as the existence of a proximal subgradient or a Fréchet subdifferential. In other words, an individual problem has a corresponding generalized Kuhn-Tucker vector. Under this assumption, a stable sequential Kuhn-Tucker theorem in nondifferential iterative form is proved and discussed in terms of minimizing sequences on the basis of the dual regularization method. This theorem provides necessary and sufficient conditions for the stable construction of a minimizing approximate solution in the sense of Warga in the considered problem, whose initial data can be approximately specified. A substantial difference of the proved theorem from its classical same-named analogue is that the former takes into account the possible instability of the problem in the case of perturbed initial data and, as a consequence, allows for the inherited instability of classical optimality conditions. This theorem can be treated as a regularized generalization of the classical Uzawa algorithm to nonlinear programming problems. Finally, the theorem is applied to the "simplest" nonlinear optimal control problem, namely, to a time-optimal control problem.
Minimax terminal approach problem in two-level hierarchical nonlinear discrete-time dynamical system
Shorikov, A. F.
2015-11-30
We consider a discrete–time dynamical system consisting of three controllable objects. The motions of all objects are given by the corresponding vector nonlinear or linear discrete–time recurrent vector relations, and control system for its has two levels: basic (first or I level) that is dominating and subordinate level (second or II level) and both have different criterions of functioning and united a priori by determined informational and control connections defined in advance. For the dynamical system in question, we propose a mathematical formalization in the form of solving a multistep problem of two-level hierarchical minimax program control over the terminal approach process with incomplete information and give a general scheme for its solving.
Probabilistic collocation method for strongly nonlinear problems: 3. Transform by time
NASA Astrophysics Data System (ADS)
Liao, Qinzhuo; Zhang, Dongxiao
2016-03-01
The probabilistic collocation method (PCM) has drawn wide attention for stochastic analysis recently. Its results may become inaccurate in case of a strongly nonlinear relation between random parameters and model responses. To tackle this problem, we proposed a location-based transformed PCM (xTPCM) and a displacement-based transformed PCM (dTPCM) in previous parts of this series. Making use of the transform between response and space, the above two methods, however, have certain limitations. In this study, we introduce a time-based transformed PCM (tTPCM) employing the transform between response and time. We conduct numerical experiments to investigate its performance in uncertainty quantification. The results show that the tTPCM greatly improves the accuracy of the traditional PCM in a cost-effective manner and is more general and convenient than the xTPCM/dTPCM.
NASA Astrophysics Data System (ADS)
Korpusov, M. O.
2016-06-01
We obtain blowup conditions for the solutions of initial boundary-value problems for the nonlinear equation of ion sound waves in a hydrogen plasma in the approximation of "hot" electrons and "heavy" ions. A specific characteristic of this nonlinear equation is the noncoercive nonlinearity of the form ∂ t|∇ u|2, which complicates its study by any energy method. We solve this problem by the Mitidieri-Pohozaev method of nonlinear capacity.
NASA Technical Reports Server (NTRS)
Keyes, David E.; Smooke, Mitchell D.
1987-01-01
A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n.
Blanford, M.
1997-12-31
Most commercially-available quasistatic finite element programs assemble element stiffnesses into a global stiffness matrix, then use a direct linear equation solver to obtain nodal displacements. However, for large problems (greater than a few hundred thousand degrees of freedom), the memory size and computation time required for this approach becomes prohibitive. Moreover, direct solution does not lend itself to the parallel processing needed for today`s multiprocessor systems. This talk gives an overview of the iterative solution strategy of JAS3D, the nonlinear large-deformation quasistatic finite element program. Because its architecture is derived from an explicit transient-dynamics code, it does not ever assemble a global stiffness matrix. The author describes the approach he used to implement the solver on multiprocessor computers, and shows examples of problems run on hundreds of processors and more than a million degrees of freedom. Finally, he describes some of the work he is presently doing to address the challenges of iterative convergence for ill-conditioned problems.
NASA Astrophysics Data System (ADS)
Tsysar, S. A.; Nikolaeva, A. V.; Svet, V. D.; Khokhlova, V. A.; Yuldashev, P. V.; Sapozhnikov, O. A.
2015-10-01
In the paper the use of receiving and radiating system, which allows to determine the parameters of bone by nonlinear pulse-echo technique and to image of brain structures through the skull bones, was proposed. Accuracy of the skull bone characterization is due to higher measured harmonic and is significantly better than in linear case. In the experimental part focused piezoelectric transducer with diameter 100 mm, focal distance 100 mm, the frequency of 1.092 MHz was used. It was shown that skull bone profiling can be performed with the use of 3rd harmonic since 1st harmonic can be used for visualization of the underlying objects. The use of wideband systems for both skull profiling and brain visualization is restricted by skull attenuation and resulting low effective sensitivity.
Tsysar, S. A. Nikolaeva, A. V.; Khokhlova, V. A.; Yuldashev, P. V.; Svet, V. D.; Sapozhnikov, O. A.
2015-10-28
In the paper the use of receiving and radiating system, which allows to determine the parameters of bone by nonlinear pulse-echo technique and to image of brain structures through the skull bones, was proposed. Accuracy of the skull bone characterization is due to higher measured harmonic and is significantly better than in linear case. In the experimental part focused piezoelectric transducer with diameter 100 mm, focal distance 100 mm, the frequency of 1.092 MHz was used. It was shown that skull bone profiling can be performed with the use of 3rd harmonic since 1st harmonic can be used for visualization of the underlying objects. The use of wideband systems for both skull profiling and brain visualization is restricted by skull attenuation and resulting low effective sensitivity.
Transmission and reflection of strongly nonlinear solitary waves at granular interfaces.
Tichler, A M; Gómez, L R; Upadhyaya, N; Campman, X; Nesterenko, V F; Vitelli, V
2013-07-26
The interaction of a solitary wave with an interface formed by two strongly nonlinear noncohesive granular lattices displays rich behavior, characterized by the breakdown of continuum equations of motion in the vicinity of the interface. By treating the solitary wave as a quasiparticle with an effective mass, we construct an intuitive (energy- and linear-momentum-conserving) discrete model to predict the amplitudes of the transmitted solitary waves generated when an incident solitary-wave front, parallel to the interface, moves from a denser to a lighter granular hexagonal lattice. Our findings are corroborated with simulations. We then successfully extend this model to oblique interfaces, where we find that the angle of refraction and reflection of a solitary wave follows, below a critical value, an analogue of Snell's law in which the solitary-wave speed replaces the speed of sound, which is zero in the sonic vacuum.
Windhorst, U; Kokkoroyiannis, T; Laouris, Y; Meyer-Lohmann, J
1994-03-01
Spinal recurrent inhibition via Renshaw cells and proprioceptive feedback via skeletal muscle and muscle spindle afferents have been hypothesized to constitute a compound feedback system [Windhorst (1989) Afferent Control of Posture and Locomotion; Windhorst (1993) Robots and Biological Systems--Towards a New Bionics]. To assess their detailed functions, it is necessary to know their dynamic characteristics. Previously we have extensively described the properties of signal transmission from motor axons to Renshaw cells using random motor axon stimulation and data analysis methods based thereupon. Using the same methods, we here compare these properties, in the cat, with those between motor axons and group Ia muscle spindle afferents in terms of frequency responses and nonlinear features. The frequency responses depend on the mean rate (carrier rate) of activation of motor axons and on the strength of coupling between motor units and spindles. In general, they are those of a second-order low-pass system with a cut-off at fairly low frequencies. This contrasts with the dynamics of motor axon-Renshaw cell couplings which are those of a much broader band-pass with its peak in the range of c. 2-15 Hz [Christakos (1987) Neuroscience 23, 613-623]. The second-order non-linearities in motor unit-muscle spindle signal lines are much more diverse than those in motor axon-Renshaw cell couplings. Although the average strength of response declines with mean stimulus rate in both subsystems, there is no systematic relationship between the amount of non-linearity and the average response in the former, whilst there is in the latter. The qualitative appearance of motor unit-muscle spindle non-linearities was complicated as was the average response to motor unit twitches. Thus, whilst Renshaw cells appear to dynamically reflect motor output rather faithfully, muscle spindles seem to signal local muscle fibre length changes and their dynamics. This would be consistent with the
NASA Technical Reports Server (NTRS)
Nguyen, Duc T.
1990-01-01
Practical engineering application can often be formulated in the form of a constrained optimization problem. There are several solution algorithms for solving a constrained optimization problem. One approach is to convert a constrained problem into a series of unconstrained problems. Furthermore, unconstrained solution algorithms can be used as part of the constrained solution algorithms. Structural optimization is an iterative process where one starts with an initial design, a finite element structure analysis is then performed to calculate the response of the system (such as displacements, stresses, eigenvalues, etc.). Based upon the sensitivity information on the objective and constraint functions, an optimizer such as ADS or IDESIGN, can be used to find the new, improved design. For the structural analysis phase, the equation solver for the system of simultaneous, linear equations plays a key role since it is needed for either static, or eigenvalue, or dynamic analysis. For practical, large-scale structural analysis-synthesis applications, computational time can be excessively large. Thus, it is necessary to have a new structural analysis-synthesis code which employs new solution algorithms to exploit both parallel and vector capabilities offered by modern, high performance computers such as the Convex, Cray-2 and Cray-YMP computers. The objective of this research project is, therefore, to incorporate the latest development in the parallel-vector equation solver, PVSOLVE into the widely popular finite-element production code, such as the SAP-4. Furthermore, several nonlinear unconstrained optimization subroutines have also been developed and tested under a parallel computer environment. The unconstrained optimization subroutines are not only useful in their own right, but they can also be incorporated into a more popular constrained optimization code, such as ADS.
NASA Astrophysics Data System (ADS)
Ibrahima, Fayadhoi; Meyer, Daniel; Tchelepi, Hamdi
2016-04-01
Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are crucial to explore possible scenarios and assess risks in subsurface problems. In particular, nonlinear two-phase flows in porous media are essential, yet challenging, in reservoir simulation and hydrology. Adding highly heterogeneous and uncertain input, such as the permeability and porosity fields, transforms the estimation of the flow response into a tough stochastic problem for which computationally expensive Monte Carlo (MC) simulations remain the preferred option.We propose an alternative approach to evaluate the probability distribution of the (water) saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the (water) saturation. The distribution method draws inspiration from a Lagrangian approach of the stochastic transport problem and expresses the saturation PDF and CDF essentially in terms of a deterministic mapping and the distribution and statistics of scalar random fields. In a large class of applications these random fields can be estimated at low computational costs (few MC runs), thus making the distribution method attractive. Even though the method relies on a key assumption of fixed streamlines, we show that it performs well for high input variances, which is the case of interest. Once the saturation distribution is determined, any one-point statistics thereof can be obtained, especially the saturation average and standard deviation. Moreover, the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be efficiently derived from the distribution method. These statistics can then be used for risk assessment, as well as data assimilation and uncertainty reduction
Kharibegashvili, S. S.; Jokhadze, O. M. E-mail: ojokhadze@yahoo.com
2014-04-30
A mixed problem for a one-dimensional semilinear wave equation with nonlinear boundary conditions is considered. Conditions of this type occur, for example, in the description of the longitudinal oscillations of a spring fastened elastically at one end, but not in accordance with Hooke's linear law. Uniqueness and existence questions are investigated for global and blowup solutions to this problem, in particular how they depend on the nature of the nonlinearities involved in the equation and the boundary conditions. Bibliography: 14 titles. (paper)
NASA Astrophysics Data System (ADS)
Alibubin, M. U.; Sunarto, A.; Sulaiman, J.
2016-04-01
The aim of this paper is to consider the Quarter-sweep Successive Over Relaxation (QSSOR) iteration for solving nonlinear two-point boundary value problems. The second order finite difference (FD) method is applied to derive the quarter-sweep nonlocal discretization scheme for the sake of transforming the system of nonlinear approximation equations into the corresponding system of linear equations. The formulation and the implementation of the methods are discussed. In addition, the numerical results by solving the proposed problems using QSSOR method are included and compared with the Full-sweep Successive Over Relaxation (FSSOR) and Half-sweep Successive Over Relaxation (HSSOR) methods.
NASA Astrophysics Data System (ADS)
Alibubin, M. U.; Sunarto, A.; Sulaiman, J.
2016-06-01
In this paper, we present the concept of Half-sweep Accelerated OverRelaxation (HSAOR) iterative method with a nonlocal discretization scheme for solving nonlinear two-point boundary value problems. Second order finite difference scheme has been used to derive the half-sweep finite difference (HSFD) approximations of the problems. Then, the nonlocal discretization scheme is applied in order to transform the system of nonlinear approximation equations into the corresponding system of linear equations. Numerical results showed that HSAOR method is superior compared to Full-sweep Gauss-seidel (FSGS), Full-sweep Successive OverRelaxation (FSSOR) and Full-sweep Accelerated Over Relaxation (FSAOR) methods.
Transient even and odd order nonlinearity of a YBCO transmission line
NASA Astrophysics Data System (ADS)
Huizen, Richard; Remillard, Stephen
Second (IMD2) and third (IMD3) order intermodulation distortions were found to exhibit dependencies on temperature and magnetic field. A carrier wave at the 890 MHz resonant frequency of the type-II YBa2Cu3O7-δ superconducting resonator circuit, with TC = 89K, was introduced into the circuit via an electric coupling antenna. Two off-resonance probe signals were injected into the circuit via a separate magnetic coupling element. The combination of these three signals locally excited synchronous second and third order IMD. A static magnetic field was applied perpendicularly to the film which induced magnetic flux vortices in the sample. Upon removal of the static magnetic field, IMD2 and IMD3 exhibited distinct transient decay modes correlating to temperature. Between 85.0K and 87.5K, IMD3 decayed exponentially. Above 87.5K, IMD3 exhibited bounded exponential growth, while within a narrow temperature range around 87.5K, removal of a static magnetic field strongly suppressed IMD3. IMD2 exhibited exponential decay at all temperatures. Even and odd order microwave nonlinearities were thus shown to result from different, magnetically coupled, physical mechanisms. Funding for this project was provided by Award Number DMR-1206149 from the National Science Foundation.
Initial-Boundary Value Problem Solution of the Nonlinear Shallow-water Wave Equations
NASA Astrophysics Data System (ADS)
Kanoglu, U.; Aydin, B.
2014-12-01
The hodograph transformation solutions of the one-dimensional nonlinear shallow-water wave (NSW) equations are usually obtained through integral transform techniques such as Fourier-Bessel transforms. However, the original formulation of Carrier and Greenspan (1958 J Fluid Mech) and its variant Carrier et al. (2003 J Fluid Mech) involve evaluation integrals. Since elliptic integrals are highly singular as discussed in Carrier et al. (2003), this solution methodology requires either approximation of the associated integrands by smooth functions or selection of regular initial/boundary data. It should be noted that Kanoglu (2004 J Fluid Mech) partly resolves this issue by simplifying the resulting integrals in closed form. Here, the hodograph transform approach is coupled with the classical eigenfunction expansion method rather than integral transform techniques and a new analytical model for nonlinear long wave propagation over a plane beach is derived. This approach is based on the solution methodology used in Aydın & Kanoglu (2007 CMES-Comp Model Eng) for wind set-down relaxation problem. In contrast to classical initial- or boundary-value problem solutions, here, the NSW equations are formulated to yield an initial-boundary value problem (IBVP) solution. In general, initial wave profile with nonzero initial velocity distribution is assumed and the flow variables are given in the form of Fourier-Bessel series. The results reveal that the developed method allows accurate estimation of the spatial and temporal variation of the flow quantities, i.e., free-surface height and depth-averaged velocity, with much less computational effort compared to the integral transform techniques such as Carrier et al. (2003), Kanoglu (2004), Tinti & Tonini (2005 J Fluid Mech), and Kanoglu & Synolakis (2006 Phys Rev Lett). Acknowledgments: This work is funded by project ASTARTE- Assessment, STrategy And Risk Reduction for Tsunamis in Europe. Grant 603839, 7th FP (ENV.2013.6.4-3 ENV
An efficient distribution method for nonlinear transport problems in stochastic porous media
NASA Astrophysics Data System (ADS)
Ibrahima, F.; Tchelepi, H.; Meyer, D. W.
2015-12-01
Because geophysical data are inexorably sparse and incomplete, stochastic treatments of simulated responses are convenient to explore possible scenarios and assess risks in subsurface problems. In particular, understanding how uncertainties propagate in porous media with nonlinear two-phase flow is essential, yet challenging, in reservoir simulation and hydrology. We give a computationally efficient and numerically accurate method to estimate the one-point probability density (PDF) and cumulative distribution functions (CDF) of the water saturation for the stochastic Buckley-Leverett problem when the probability distributions of the permeability and porosity fields are available. The method draws inspiration from the streamline approach and expresses the distributions of interest essentially in terms of an analytically derived mapping and the distribution of the time of flight. In a large class of applications the latter can be estimated at low computational costs (even via conventional Monte Carlo). Once the water saturation distribution is determined, any one-point statistics thereof can be obtained, especially its average and standard deviation. Moreover, rarely available in other approaches, yet crucial information such as the probability of rare events and saturation quantiles (e.g. P10, P50 and P90) can be derived from the method. We provide various examples and comparisons with Monte Carlo simulations to illustrate the performance of the method.
Lorber, A.A.; Carey, G.F.; Bova, S.W.; Harle, C.H.
1996-12-31
The connection between the solution of linear systems of equations by iterative methods and explicit time stepping techniques is used to accelerate to steady state the solution of ODE systems arising from discretized PDEs which may involve either physical or artificial transient terms. Specifically, a class of Runge-Kutta (RK) time integration schemes with extended stability domains has been used to develop recursion formulas which lead to accelerated iterative performance. The coefficients for the RK schemes are chosen based on the theory of Chebyshev iteration polynomials in conjunction with a local linear stability analysis. We refer to these schemes as Chebyshev Parameterized Runge Kutta (CPRK) methods. CPRK methods of one to four stages are derived as functions of the parameters which describe an ellipse {Epsilon} which the stability domain of the methods is known to contain. Of particular interest are two-stage, first-order CPRK and four-stage, first-order methods. It is found that the former method can be identified with any two-stage RK method through the correct choice of parameters. The latter method is found to have a wide range of stability domains, with a maximum extension of 32 along the real axis. Recursion performance results are presented below for a model linear convection-diffusion problem as well as non-linear fluid flow problems discretized by both finite-difference and finite-element methods.
Li, Xiaolin; Zhang, Fan; Zhang, Xiaoru; Zhang, Dechao; Chen, Zhangyuan; Xu, Anshi
2008-02-01
For differential decoding, direct detection of DPSK signal needs a delay line interferometer with a free spectral range normally equal to the transmitted bit-rate. We numerically demonstrate that free spectral range optimization can increase tolerance to fiber Kerr nonlinearities for 40 Gbit/s RZ-DPSK transmission, especially for multi-format (RZ-DPSK and RZ-OOK) systems, in which Kerr nonlinearities is quite serious mainly due to cross-phase modulation. The optimal delay time of the delay line interferometer in DPSK signal demodulation is shorter than one bit-period. Joint optimization of free spectral range and optical filter bandwidth will further enhance system tolerance to nonlinear transmission.
Glass, Micheal W.; Hogan, Roy E., Jr.; Gartling, David K.
2010-03-01
The need for the engineering analysis of systems in which the transport of thermal energy occurs primarily through a conduction process is a common situation. For all but the simplest geometries and boundary conditions, analytic solutions to heat conduction problems are unavailable, thus forcing the analyst to call upon some type of approximate numerical procedure. A wide variety of numerical packages currently exist for such applications, ranging in sophistication from the large, general purpose, commercial codes, such as COMSOL, COSMOSWorks, ABAQUS and TSS to codes written by individuals for specific problem applications. The original purpose for developing the finite element code described here, COYOTE, was to bridge the gap between the complex commercial codes and the more simplistic, individual application programs. COYOTE was designed to treat most of the standard conduction problems of interest with a user-oriented input structure and format that was easily learned and remembered. Because of its architecture, the code has also proved useful for research in numerical algorithms and development of thermal analysis capabilities. This general philosophy has been retained in the current version of the program, COYOTE, Version 5.0, though the capabilities of the code have been significantly expanded. A major change in the code is its availability on parallel computer architectures and the increase in problem complexity and size that this implies. The present document describes the theoretical and numerical background for the COYOTE program. This volume is intended as a background document for the user's manual. Potential users of COYOTE are encouraged to become familiar with the present report and the simple example analyses reported in before using the program. The theoretical and numerical background for the finite element computer program, COYOTE, is presented in detail. COYOTE is designed for the multi-dimensional analysis of nonlinear heat conduction problems
Transmission Loss Calculation using A and B Loss Coefficients in Dynamic Economic Dispatch Problem
NASA Astrophysics Data System (ADS)
Jethmalani, C. H. Ram; Dumpa, Poornima; Simon, Sishaj P.; Sundareswaran, K.
2016-04-01
This paper analyzes the performance of A-loss coefficients while evaluating transmission losses in a Dynamic Economic Dispatch (DED) Problem. The performance analysis is carried out by comparing the losses computed using nominal A loss coefficients and nominal B loss coefficients in reference with load flow solution obtained by standard Newton-Raphson (NR) method. Density based clustering method based on connected regions with sufficiently high density (DBSCAN) is employed in identifying the best regions of A and B loss coefficients. Based on the results obtained through cluster analysis, a novel approach in improving the accuracy of network loss calculation is proposed. Here, based on the change in per unit load values between the load intervals, loss coefficients are updated for calculating the transmission losses. The proposed algorithm is tested and validated on IEEE 6 bus system, IEEE 14 bus, system IEEE 30 bus system and IEEE 118 bus system. All simulations are carried out using SCILAB 5.4 (www.scilab.org) which is an open source software.
Studies in nonlinear problems of energy. Progress report, January 1, 1992--December 31, 1992
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.
Bulgakov, Evgeny; Sadreev, Almas
2011-08-10
Using coupled mode theory we consider transmission in a T-shaped waveguide coupled with two identical symmetrically positioned nonlinear micro-cavities with mirror symmetry. For input power injected into the central waveguide we show the existence of a symmetry breaking solution which is a result of mixing of the symmetrical input wave with an antisymmetric standing wave in the Fabry-Pérot interferometer. With growth of the input power, a feature in the form of loops arises in the solution which originates from bistability in the transmission in the output left/right waveguide coupled with the first/second nonlinear cavity. The domains of stability of the solution are found. The breaking of mirror symmetry gives rise to nonsymmetrical left and right outputs. We demonstrate that this phenomenon can be explored for all-optical switching of light transmission from the left output waveguide to the right one by application of input pulses.
NASA Astrophysics Data System (ADS)
Jain, Ruchika; Sinha, Deepa
2014-09-01
The non-linear stability of L 4 in the restricted three-body problem when both primaries are finite straight segments in the presence of third and fourth order resonances has been investigated. Markeev's theorem (Markeev in Libration Points in Celestial Mechanics and Astrodynamics, 1978) is used to examine the non-linear stability for the resonance cases 2:1 and 3:1. It is found that the non-linear stability of L 4 depends on the lengths of the segments in both resonance cases. It is also found that the range of stability increases when compared with the classical restricted problem. The results have been applied in the following asteroids systems: (i) 216 Kleopatra-951 Gaspara, (ii) 9 Metis-433 Eros, (iii) 22 Kalliope-243 Ida.
Fourth-order solutions of nonlinear two-point boundary value problems by Newton-HSSOR iteration
NASA Astrophysics Data System (ADS)
Sulaiman, Jumat; Hasan, Mohd. Khatim; Othman, Mohamed; Karim, Samsul Ariffin Abdul
2014-06-01
In this paper, the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method together with Newton scheme namely Newton-HSSOR is investigated in solving the nonlinear systems generated from the fourth-order half-sweep finite difference approximation equation for nonlinear two-point boundary value problems. The Newton scheme is proposed to linearize the nonlinear system into the form of linear system. On top of that, we also present the basic formulation and implementation of Newton-HSSOR iterative method. For comparison purpose, combinations between the Full-Sweep Gauss-Seidel (FSGS) and Full-Sweep Successive Over-Relaxation (FSSOR) iterative methods with Newton scheme, which are indicated as Newton-FSGS and Newton-FSSOR methods respectively have been implemented numerically. Numerical experiments of two problems are given to illustrate that the Newton-HSSOR method is more superior compared with the tested methods.
ERIC Educational Resources Information Center
Fulcher, Lewis P.
1979-01-01
Presents an exact solution to the nonlinear Faraday's law problem of a rod sliding on frictionless rails with resistance. Compares the results with perturbation calculations based on the methods of Poisson and Pincare and of Kryloff and Bogoliuboff. (Author/GA)
Inverse Tasks In The Tsunami Problem: Nonlinear Regression With Inaccurate Input Data
NASA Astrophysics Data System (ADS)
Lavrentiev, M.; Shchemel, A.; Simonov, K.
A variant of modified training functional that allows considering inaccurate input data is suggested. A limiting case when a part of input data is completely undefined, and, therefore, a problem of reconstruction of hidden parameters should be solved, is also considered. Some numerical experiments are presented. It is assumed that a dependence of known output variables on known input ones should be found is the classic problem definition, which is widely used in the majority of neural nets algorithms. The quality of approximation is evaluated as a performance function. Often the error of the task is evaluated as squared distance between known input data and predicted data multiplied by weighed coefficients. These coefficients may be named "precision coefficients". When inputs are not known exactly, natural generalization of performance function is adding member that responsible for distance between known inputs and shifted inputs, which lessen model's error. It is desirable that the set of variable parameters is compact for training to be con- verging. In the above problem it is possible to choose variants of demands of a priori compactness, which allow meaningful interpretation in the smoothness of the model dependence. Two kinds of regularization was used, first limited squares of coefficients responsible for nonlinearity and second limited multiplication of the above coeffi- cients and linear coefficients. Asymptotic universality of neural net ability to approxi- mate various smooth functions with any accuracy by increase of the number of tunable parameters is often the base for selecting a type of neural net approximation. It is pos- sible to show that used neural net will approach to Fourier integral transform, which approximate abilities are known, with increasing of the number of tunable parameters. In the limiting case, when input data is set with zero precision, the problem of recon- struction of hidden parameters with observed output data appears. The
Studies in nonlinear problems of energy. Progress report, October 1, 1993--September 30, 1994
Matkowsky, B.J.
1994-09-01
The authors concentrate on modeling, analysis and large scale scientific computation of combustion and flame propagation phenomena, with emphasis on the transition from laminar to turbulent combustion. In the transition process a flame passed through a stages exhibiting increasingly complex spatial and temporal patterns which serve as signatures identifying each stage. Often the transitions arise via bifurcation. The authors investigate nonlinear dynamics, bifurcation and pattern formation in the successive stage of transition. They describe the stability of combustion waves, and transitions to combustion waves exhibiting progressively higher degrees of spatio-temporal complexity. One aspect of this research program is the systematic derivation of appropriate, approximate models from the original models governing combustion. The approximate models are then analyzed. The authors are particularly interested in understanding the basic mechanisms affecting combustion, which is a prerequisite to effective control of the process. They are interested in determining the effects of varying various control parameters, such as Nusselt number, Lewis number, heat release, activation energy, Damkohler number, Reynolds number, Prandtl number, Peclet number, etc. The authors have also considered a number of problems in self-propagating high-temperature synthesis (SHS), in which combustion waves are employed to synthesize advanced materials. Efforts are directed toward understanding fundamental mechanisms. 167 refs.
Final state problem for the cubic nonlinear Klein-Gordon equation
Hayashi, Nakao; Naumkin, Pavel I.
2009-10-15
We study the final state problem for the nonlinear Klein-Gordon equation, u{sub tt}+u-u{sub xx}={mu}u{sup 3}, t is an element of R,x is an element of R, where {mu} is an element of R. We prove the existence of solutions in the neighborhood of the approximate solutions 2 Re U(t)w{sub +}(t), where U(t) is the free evolution group defined by U(t)=F{sup -1}e{sup -it<{xi}}{sup >}F,
Zhao, Sangen; Kang, Lei; Shen, Yaoguo; Wang, Xiaodong; Asghar, Muhammad Adnan; Lin, Zheshuai; Xu, Yingying; Zeng, Siyuan; Hong, Maochun; Luo, Junhua
2016-03-01
A beryllium-free deep-ultraviolet (deep-UV) nonlinear optical (NLO) material K3Ba3Li2Al4B6O20F is developed mainly by the element substitution of Be for Al and Li from Sr2Be2B2O7 that was considered as one of the most promising deep-UV NLO materials. K3Ba3Li2Al4B6O20F preserves the structural merits of Sr2Be2B2O7 and thus exhibits no layering growth tendency and possesses the optical properties required for deep-UV NLO applications, including deep-UV transparency, phase-matchability, and sufficiently large second-harmonic generation (1.5 × KH2PO4). Furthermore, it overcomes the structural instability problem of Sr2Be2B2O7, which is confirmed by the obtainment of large single crystals and phonon dispersion calculations. These attributes make it very attractive for next-generation deep-UV NLO materials. The substitution of Be for Al and Li in beryllium borates provides a new opportunity to design beryllium-free deep-UV NLO materials with good performance.
Zhao, Sangen; Kang, Lei; Shen, Yaoguo; Wang, Xiaodong; Asghar, Muhammad Adnan; Lin, Zheshuai; Xu, Yingying; Zeng, Siyuan; Hong, Maochun; Luo, Junhua
2016-03-01
A beryllium-free deep-ultraviolet (deep-UV) nonlinear optical (NLO) material K3Ba3Li2Al4B6O20F is developed mainly by the element substitution of Be for Al and Li from Sr2Be2B2O7 that was considered as one of the most promising deep-UV NLO materials. K3Ba3Li2Al4B6O20F preserves the structural merits of Sr2Be2B2O7 and thus exhibits no layering growth tendency and possesses the optical properties required for deep-UV NLO applications, including deep-UV transparency, phase-matchability, and sufficiently large second-harmonic generation (1.5 × KH2PO4). Furthermore, it overcomes the structural instability problem of Sr2Be2B2O7, which is confirmed by the obtainment of large single crystals and phonon dispersion calculations. These attributes make it very attractive for next-generation deep-UV NLO materials. The substitution of Be for Al and Li in beryllium borates provides a new opportunity to design beryllium-free deep-UV NLO materials with good performance. PMID:26889570
Taming the non-linearity problem in GPR full-waveform inversion for high contrast media
NASA Astrophysics Data System (ADS)
Meles, Giovanni; Greenhalgh, Stewart; van der Kruk, Jan; Green, Alan; Maurer, Hansruedi
2012-03-01
We present a new algorithm for the inversion of full-waveform ground-penetrating radar (GPR) data. It is designed to tame the non-linearity issue that afflicts inverse scattering problems, especially in high contrast media. We first investigate the limitations of current full-waveform time-domain inversion schemes for GPR data and then introduce a much-improved approach based on a combined frequency-time-domain analysis. We show by means of several synthetic tests and theoretical considerations that local minima trapping (common in full bandwidth time-domain inversion) can be avoided by starting the inversion with only the low frequency content of the data. Resolution associated with the high frequencies can then be achieved by progressively expanding to wider bandwidths as the iterations proceed. Although based on a frequency analysis of the data, the new method is entirely implemented by means of a time-domain forward solver, thus combining the benefits of both frequency-domain (low frequency inversion conveys stability and avoids convergence to a local minimum; whereas high frequency inversion conveys resolution) and time-domain methods (simplicity of interpretation and recognition of events; ready availability of FDTD simulation tools).
NASA Astrophysics Data System (ADS)
Tadmor, Eitan
We study the entropy stability of difference approximations to nonlinear hyperbolic conservation laws, and related time-dependent problems governed by additional dissipative and dispersive forcing terms. We employ a comparison principle as the main tool for entropy stability analysis, comparing the entropy production of a given scheme against properly chosen entropy-conservative schemes.To this end, we introduce general families of entropy-conservative schemes, interesting in their own right. The present treatment of such schemes extends our earlier recipe for construction of entropy-conservative schemes, introduced in Tadmor (1987b). The new families of entropy-conservative schemes offer two main advantages, namely, (i) their numerical fluxes admit an explicit, closed-form expression, and (ii) by a proper choice of their path of integration in phase space, we can distinguish between different families of waves within the same computational cell; in particular, entropy stability can be enforced on rarefactions while keeping the sharp resolution of shock discontinuities.A comparison with the numerical viscosities associated with entropy-conservative schemes provides a useful framework for the construction and analysis of entropy-stable schemes. We employ this framework for a detailed study of entropy stability for a host of first- and second-order accurate schemes. The comparison approach yields a precise characterization of the entropy stability of semi-discrete schemes for both scalar problems and systems of equations.We extend these results to fully discrete schemes. Here, spatial entropy dissipation is balanced by the entropy production due to time discretization with a suffciently small time-step, satisfying a suitable CFL condition. Finally, we revisit the question of entropy stability for fully discrete schemes using a different approach based on homotopy arguments. We prove entropy stability under optimal CFL conditions.
On parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems
NASA Astrophysics Data System (ADS)
Lastra, A.; Malek, S.
2015-11-01
We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter ɛ with vanishing initial data at complex time t = 0 and whose coefficients depend analytically on (ɛ, t) near the origin in C2 and are bounded holomorphic on some horizontal strip in C w.r.t. the space variable. This problem is assumed to be non-Kowalevskian in time t, therefore analytic solutions at t = 0 cannot be expected in general. Nevertheless, we are able to construct a family of actual holomorphic solutions defined on a common bounded open sector with vertex at 0 in time and on the given strip above in space, when the complex parameter ɛ belongs to a suitably chosen set of open bounded sectors whose union form a covering of some neighborhood Ω of 0 in C*. These solutions are achieved by means of Laplace and Fourier inverse transforms of some common ɛ-depending function on C × R, analytic near the origin and with exponential growth on some unbounded sectors with appropriate bisecting directions in the first variable and exponential decay in the second, when the perturbation parameter belongs to Ω. Moreover, these solutions satisfy the remarkable property that the difference between any two of them is exponentially flat for some integer order w.r.t. ɛ. With the help of the classical Ramis-Sibuya theorem, we obtain the existence of a formal series (generally divergent) in ɛ which is the common Gevrey asymptotic expansion of the built up actual solutions considered above.
NASA Astrophysics Data System (ADS)
Kelbert, A.; Schultz, A.; Egbert, G.
2006-12-01
We address the non-linear ill-posed inverse problem of reconstructing the global three-dimensional distribution of electrical conductivity in Earth's mantle. The authors have developed a numerical regularized least-squares inverse solution based on the non-linear conjugate gradients approach. We apply this methodology to the most current low-frequency global observatory data set by Fujii &Schultz (2002), that includes c- and d-responses. We obtain 4-8 layer models satisfying the data. We then describe the features common to all these models and discuss the resolution of our method.
Gartling, D.K.
1996-05-01
The theoretical and numerical background for the finite element computer program, TORO II, is presented in detail. TORO II is designed for the multi-dimensional analysis of nonlinear, electromagnetic field problems described by the quasi-static form of Maxwell`s equations. 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 TORO II are also outlined. Instructions for the use of the code are documented in SAND96-0903; examples of problems analyzed with the code are also provided in the user`s manual. 24 refs., 8 figs.
Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves
NASA Astrophysics Data System (ADS)
El, G. A.; Khamis, E. G.; Tovbis, A.
2016-09-01
We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.
NASA Astrophysics Data System (ADS)
Anishchenko, V. S.; Boev, Ya. I.; Semenova, N. I.; Strelkova, G. I.
2015-07-01
We review rigorous and numerical results on the statistics of Poincaré recurrences which are related to the modern development of the Poincaré recurrence problem. We analyze and describe the rigorous results which are achieved both in the classical (local) approach and in the recently developed global approach. These results are illustrated by numerical simulation data for simple chaotic and ergodic systems. It is shown that the basic theoretical laws can be applied to noisy systems if the probability measure is ergodic and stationary. Poincaré recurrences are studied numerically in nonautonomous systems. Statistical characteristics of recurrences are analyzed in the framework of the global approach for the cases of positive and zero topological entropy. We show that for the positive entropy, there is a relationship between the Afraimovich-Pesin dimension, Lyapunov exponents and the Kolmogorov-Sinai entropy either without and in the presence of external noise. The case of zero topological entropy is exemplified by numerical results for the Poincare recurrence statistics in the circle map. We show and prove that the dependence of minimal recurrence times on the return region size demonstrates universal properties for the golden and the silver ratio. The behavior of Poincaré recurrences is analyzed at the critical point of Feigenbaum attractor birth. We explore Poincaré recurrences for an ergodic set which is generated in the stroboscopic section of a nonautonomous oscillator and is similar to a circle shift. Based on the obtained results we show how the Poincaré recurrence statistics can be applied for solving a number of nonlinear dynamics issues. We propose and illustrate alternative methods for diagnosing effects of external and mutual synchronization of chaotic systems in the context of the local and global approaches. The properties of the recurrence time probability density can be used to detect the stochastic resonance phenomenon. We also discuss how
NASA Astrophysics Data System (ADS)
Foufoula-Georgiou, Efi; Schwenk, Jon; Tejedor, Alejandro
2015-04-01
Are the dynamics of meandering rivers non-linear? What information does the shape of an oxbow lake carry about its forming process? How to characterize self-dissimilar landscapes carrying the signature of larger-scale geologic or tectonic controls? Do we have proper frameworks for quantifying the topology and dynamics of deltaic systems? What can the structural complexity of river networks (erosional and depositional) reveal about their vulnerability and response to change? Can the structure and dynamics of river networks reveal potential hotspots of geomorphic change? All of the above problems are at the heart of understanding landscape evolution, relating process to structure and form, and developing methodologies for inferring how a system might respond to future changes. We argue that a new surge of rigorous methodologies is needed to address these problems. The innovations introduced herein are: (1) gradual wavelet reconstruction for depicting threshold nonlinearity (due to cutoffs) versus inherent nonlinearity (due to underlying dynamics) in river meandering, (2) graph theory for studying the topology and dynamics of deltaic river networks and their response to change, and (3) Lagrangian approaches combined with topology and non-linear dynamics for inferring sediment-driven hotspots of geomorphic change.
Xie, Lie-Jun; Zhou, Cai-Lian; Xu, Song
2016-01-01
In this work, an effective numerical method is developed to solve a class of singular boundary value problems arising in various physical models by using the improved differential transform method (IDTM). The IDTM applies the Adomian polynomials to handle the differential transforms of the nonlinearities arising in the given differential equation. The relation between the Adomian polynomials of those nonlinear functions and the coefficients of unknown truncated series solution is given by a simple formula, through which one can easily deduce the approximate solution which takes the form of a convergent series. An upper bound for the estimation of approximate error is presented. Several physical problems are discussed as illustrative examples to testify the validity and applicability of the proposed method. Comparisons are made between the present method and the other existing methods. PMID:27462514
NASA Technical Reports Server (NTRS)
Hofmann, R.
1980-01-01
The STEALTH code system, which solves large strain, nonlinear continuum mechanics problems, was rigorously structured in both overall design and programming standards. The design is based on the theoretical elements of analysis while the programming standards attempt to establish a parallelism between physical theory, programming structure, and documentation. These features have made it easy to maintain, modify, and transport the codes. It has also guaranteed users a high level of quality control and quality assurance.
Gartling, D.K.; Hogan, R.E.
1994-10-01
User instructions are given for the finite element computer program, COYOTE II. COYOTE II is designed for the multi-dimensional analysis of nonlinear heat conduction problems including the effects of enclosure radiation and chemical reaction. The theoretical background and numerical methods used in the program are documented in SAND94-1173. Examples of the use of the code are presented in SAND94-1180.
A nonlinear eigenvalue problem for self-similar spherical force-free magnetic fields
Lerche, I.; Low, B. C.
2014-10-15
An axisymmetric force-free magnetic field B(r, θ) in spherical coordinates is defined by a function r sin θB{sub φ}=Q(A) relating its azimuthal component to its poloidal flux-function A. The power law r sin θB{sub φ}=aA|A|{sup 1/n}, n a positive constant, admits separable fields with A=(A{sub n}(θ))/(r{sup n}) , posing a nonlinear boundary-value problem for the constant parameter a as an eigenvalue and A{sub n}(θ) as its eigenfunction [B. C. Low and Y. Q Lou, Astrophys. J. 352, 343 (1990)]. A complete analysis is presented of the eigenvalue spectrum for a given n, providing a unified understanding of the eigenfunctions and the physical relationship between the field's degree of multi-polarity and rate of radial decay via the parameter n. These force-free fields, self-similar on spheres of constant r, have basic astrophysical applications. As explicit solutions they have, over the years, served as standard benchmarks for testing 3D numerical codes developed to compute general force-free fields in the solar corona. The study presented includes a set of illustrative multipolar field solutions to address the magnetohydrodynamics (MHD) issues underlying the observation that the solar corona has a statistical preference for negative and positive magnetic helicities in its northern and southern hemispheres, respectively; a hemispherical effect, unchanging as the Sun's global field reverses polarity in successive eleven-year cycles. Generalizing these force-free fields to the separable form B=(H(θ,φ))/(r{sup n+2}) promises field solutions of even richer topological varieties but allowing for φ-dependence greatly complicates the governing equations that have remained intractable. The axisymmetric results obtained are discussed in relation to this generalization and the Parker Magnetostatic Theorem. The axisymmetric solutions are mathematically related to a family of 3D time-dependent ideal MHD solutions for a polytropic fluid of index γ = 4/3 as
NASA Astrophysics Data System (ADS)
Payette, G. S.; Reddy, J. N.
2011-05-01
In this paper we examine the roles of minimization and linearization in the least-squares finite element formulations of nonlinear boundary-values problems. The least-squares principle is based upon the minimization of the least-squares functional constructed via the sum of the squares of appropriate norms of the residuals of the partial differential equations (in the present case we consider L2 norms). Since the least-squares method is independent of the discretization procedure and the solution scheme, the least-squares principle suggests that minimization should be performed prior to linearization, where linearization is employed in the context of either the Picard or Newton iterative solution procedures. However, in the least-squares finite element analysis of nonlinear boundary-value problems, it has become common practice in the literature to exchange the sequence of application of the minimization and linearization operations. The main purpose of this study is to provide a detailed assessment on how the finite element solution is affected when the order of application of these operators is interchanged. The assessment is performed mathematically, through an examination of the variational setting for the least-squares formulation of an abstract nonlinear boundary-value problem, and also computationally, through the numerical simulation of the least-squares finite element solutions of both a nonlinear form of the Poisson equation and also the incompressible Navier-Stokes equations. The assessment suggests that although the least-squares principle indicates that minimization should be performed prior to linearization, such an approach is often impractical and not necessary.
Philip, Bobby; Berrill, Mark A.; Allu, Srikanth; Hamilton, Steven P.; Sampath, Rahul S.; Clarno, Kevin T.; Dilts, Gary A.
2015-01-26
We describe an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors are described. The details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstrating the achieved efficiency of the algorithm are presented. Moreover, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.
Stamovlasis, Dimitrios
2011-04-01
In this study, an attempt is made to integrate Nonlinear Dynamical Systems theory and neo-Piagetian theories applied to creative mental processes, such as problem solving. A catastrophe theory model is proposed, which implements three neo-Piagetian constructs as controls: the functional M-capacity as asymmetry and logical thinking and the degree of field dependence independence as bifurcation. Data from achievement scores of students in tenth grade physics were analyzed using dynamic difference equations and statistical regression techniques. The cusp catastrophe model proved superior comparing to the pre-post linear counterpart and demonstrated nonlinearity at the behavioral level. The nonlinear phenomenology, such as hysteresis effects and bifurcation, is explained by an analysis, which provides a causal interpretation via the mathematical theory of self-organization and thus building bridges between NDS-theory concepts and neo-Piagetian theories. The contribution to theory building is made, by also addressing the emerging philosophical, - ontological and epistemological- questions about the processes of problem solving and creativity.
Philip, Bobby; Berrill, Mark A.; Allu, Srikanth; Hamilton, Steven P.; Sampath, Rahul S.; Clarno, Kevin T.; Dilts, Gary A.
2015-01-26
We describe an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors are described. The details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstratingmore » the achieved efficiency of the algorithm are presented. Moreover, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.« less
Philip, Bobby; Berrill, Mark A; Allu, Srikanth; Hamilton, Steven P; Clarno, Kevin T; Dilts, Gary
2014-08-01
This paper describes an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors is described. Details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstrating the achieved efficiency of the algorithm are presented. Furthermore, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.
NASA Astrophysics Data System (ADS)
Philip, Bobby; Berrill, Mark A.; Allu, Srikanth; Hamilton, Steven P.; Sampath, Rahul S.; Clarno, Kevin T.; Dilts, Gary A.
2015-04-01
This paper describes an efficient and nonlinearly consistent parallel solution methodology for solving coupled nonlinear thermal transport problems that occur in nuclear reactor applications over hundreds of individual 3D physical subdomains. Efficiency is obtained by leveraging knowledge of the physical domains, the physics on individual domains, and the couplings between them for preconditioning within a Jacobian Free Newton Krylov method. Details of the computational infrastructure that enabled this work, namely the open source Advanced Multi-Physics (AMP) package developed by the authors is described. Details of verification and validation experiments, and parallel performance analysis in weak and strong scaling studies demonstrating the achieved efficiency of the algorithm are presented. Furthermore, numerical experiments demonstrate that the preconditioner developed is independent of the number of fuel subdomains in a fuel rod, which is particularly important when simulating different types of fuel rods. Finally, we demonstrate the power of the coupling methodology by considering problems with couplings between surface and volume physics and coupling of nonlinear thermal transport in fuel rods to an external radiation transport code.
NASA Astrophysics Data System (ADS)
Campbell, David K.
2010-03-01
In 1953, Enrico Fermi, John Pasta, and Stan Ulam initiated a series of computer studies aimed at exploring how simple, multi-degree of freedom nonlinear mechanical systems obeying reversible deterministic dynamics evolve in time to an equilibrium state describable by statistical mechanics. Their expectation was that this would occur by mixing behavior among the many linear modes. Their intention was then to study more complex nonlinear systems, with the hope of modeling turbulence computationally. The results of this first study of the so-called Fermi-Pasta-Ulam (FPU) problem, which were published in 1955 and characterized by Fermi as a ``little discovery,'' showed instead of the expected mixing of linear modes a striking series of (near) recurrences of the initial state and no evidence of equipartition. This work heralded the beginning of both computational physics and (modern) nonlinear science. In particular, the work marked the first systematic study of a nonlinear system by digital computers (``experimental mathematics'') and led directly to the discovery of ``solitons,'' as well as to deep insights into deterministic chaos and statistical mechanics. In this talk, I will review the original FPU studies and show how they led to the understanding of two key paradigms of nonlinear science. Specifically, I will show how a continuum approximation to the original discrete system led to the discovery of ``solitions'' whereas a low-mode approximation led to an early example of ``deterministic chaos.'' I will close with a brief indication of how the recurrence phenomenon observed by behavior by FPU can be reconciled with mixing, equipartition, and statistical mechanics.
NASA Technical Reports Server (NTRS)
Stahara, S. S.; Elliott, J. P.; Spreiter, J. R.
1983-01-01
An investigation was conducted to continue the development of perturbation procedures and associated computational codes for rapidly determining approximations to nonlinear flow solutions, with the purpose of establishing a method for minimizing computational requirements associated with parametric design studies of transonic flows in turbomachines. The results reported here concern the extension of the previously developed successful method for single parameter perturbations to simultaneous multiple-parameter perturbations, and the preliminary application of the multiple-parameter procedure in combination with an optimization method to blade design/optimization problem. In order to provide as severe a test as possible of the method, attention is focused in particular on transonic flows which are highly supercritical. Flows past both isolated blades and compressor cascades, involving simultaneous changes in both flow and geometric parameters, are considered. Comparisons with the corresponding exact nonlinear solutions display remarkable accuracy and range of validity, in direct correspondence with previous results for single-parameter perturbations.
Loeber, Rolf; Hipwell, Alison; Battista, Deena; Sembower, Mark; Stouthamer-Loeber, Magda
2009-11-01
Much of the research examining intergenerational continuity of problems from mother to offspring has focused on homotypic continuity (e.g., depression), despite the fact that different types of mental health problems tend to cluster in both adults and children. It remains unclear whether mothers with multiple mental health problems compared to mothers with fewer or no problems are more likely to have daughters with multiple mental health problems during middle childhood (ages 7 to 11). Six waves of maternal and child data from the Pittsburgh Girls Study (n = 2,451) were used to examine the specificity of effects of maternal psychopathology on child adjustment. Child multiple mental health problems comprised disruptive behavior, ADHD symptoms, depressed mood, anxiety symptoms and somatic complaints, while maternal multiple mental health problems consisted of depression, prior conduct problems and somatic complaints. Generalized Estimating Equations (GEE) was used to examine the prospective relationships between mother's single and multiple mental health problems and their daughter's single and multiple mental health problems across the elementary school-aged period (ages 7-11 years). The results show that multiple mental health problems in the mothers predicted multiple mental health problems in the daughters even when earlier mental health problem of the daughters, demographic factors, and childrearing practices were controlled. Maternal low parental warmth and harsh punishment independently contributed to the prediction of multiple mental health problems in their daughter, but mediation analyses showed that the contribution of parenting behaviors to the explanation of girls' mental health problems was small.
Loeber, Rolf; Hipwell, Alison; Battista, Deena; Sembower, Mark; Stouthamer-Loeber, Magda
2009-11-01
Much of the research examining intergenerational continuity of problems from mother to offspring has focused on homotypic continuity (e.g., depression), despite the fact that different types of mental health problems tend to cluster in both adults and children. It remains unclear whether mothers with multiple mental health problems compared to mothers with fewer or no problems are more likely to have daughters with multiple mental health problems during middle childhood (ages 7 to 11). Six waves of maternal and child data from the Pittsburgh Girls Study (n = 2,451) were used to examine the specificity of effects of maternal psychopathology on child adjustment. Child multiple mental health problems comprised disruptive behavior, ADHD symptoms, depressed mood, anxiety symptoms and somatic complaints, while maternal multiple mental health problems consisted of depression, prior conduct problems and somatic complaints. Generalized Estimating Equations (GEE) was used to examine the prospective relationships between mother's single and multiple mental health problems and their daughter's single and multiple mental health problems across the elementary school-aged period (ages 7-11 years). The results show that multiple mental health problems in the mothers predicted multiple mental health problems in the daughters even when earlier mental health problem of the daughters, demographic factors, and childrearing practices were controlled. Maternal low parental warmth and harsh punishment independently contributed to the prediction of multiple mental health problems in their daughter, but mediation analyses showed that the contribution of parenting behaviors to the explanation of girls' mental health problems was small. PMID:19639406
NASA Astrophysics Data System (ADS)
Kohr, Mirela; Mikhailov, Sergey E.; Wendland, Wolfgang L.
2016-07-01
The purpose of this paper is to study boundary value problems of transmission type for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in two complementary Lipschitz domains on a compact Riemannian manifold of dimension {m in {2, 3}} . We exploit a layer potential method combined with a fixed point theorem in order to show existence and uniqueness results when the given data are suitably small in L 2-based Sobolev spaces.
ERIC Educational Resources Information Center
Loeber, Rolf; Hipwell, Alison; Battista, Deena; Sembower, Mark; Stouthamer-Loeber, Magda
2009-01-01
Much of the research examining intergenerational continuity of problems from mother to offspring has focused on homotypic continuity (e.g., depression), despite the fact that different types of mental health problems tend to cluster in both adults and children. It remains unclear whether mothers with multiple mental health problems compared to…
NASA Astrophysics Data System (ADS)
Zheng, Guangtai; Qiu, Yi; Griffin, Michael J.
2012-12-01
The vertical apparent mass of the human body exhibits nonlinearity, with the principal resonance frequency reducing as the vibration magnitude increases. Measures of the transmission of vibration to the spine and the pelvis have suggested complex modes are responsible for the dominant resonance during vertical excitation, but the modes present with dual-axis excitation have not been investigated. This study was designed to examine how the apparent mass and transmissibility of the human body depend on the magnitude of vertical excitation and the addition of fore-and-aft excitation, and the relation between the apparent mass and the transmissibility of the body. The movement of the body (over the first, fifth and twelfth thoracic vertebrae, the third lumbar vertebra, and the pelvis) in the fore-and-aft and vertical directions (and in pitch at the pelvis) was measured in 12 male subjects sitting with their hands on their laps during random vertical vibration excitation (over the range 0.25-20 Hz) at three vibration magnitudes (0.25, 0.5 and 1.0 m s-2 rms). At the highest magnitude of vertical excitation (1.0 m s-2 rms) the effect of adding fore-aft vibration (at 0.25, 0.5, and 1.0 m s-2 rms) was investigated. The forces in the vertical and fore-and-aft directions on the seat surface were also measured so as to calculate apparent masses. Resonances in the apparent mass and transmissibility to the spine and pelvis in the fore-and-aft and vertical directions, and pitch transmissibility to the pelvis, shifted to lower frequencies as the magnitude of vertical excitation increased and as the magnitude of the additional fore-and-aft excitation increased. The nonlinear resonant behaviour of the apparent mass and transmissibility during dual-axis vibration excitation suggests coupling between the principal mode associated with vertical excitation and the cross-axis influence of fore-and-aft excitation. The transmissibility measures are consistent with complex modes
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1985-01-01
Elliptic and hyperbolic problems in unbounded regions are considered. These problems, when one wants to solve them numerically, have the difficulty of prescribing boundary conditions at infinity. Computationally, one needs a finite region in which to solve these problems. The corresponding conditions at infinity imposed on the finite distance boundaries should dictate the boundary conditions at infinity and be accurate with respect to the interior numerical scheme. The treatment of these boundary conditions for wave-like equations is discussed.
Linear and nonlinear pattern selection in Rayleigh-Benard stability problems
NASA Technical Reports Server (NTRS)
Davis, Sanford S.
1993-01-01
A new algorithm is introduced to compute finite-amplitude states using primitive variables for Rayleigh-Benard convection on relatively coarse meshes. The algorithm is based on a finite-difference matrix-splitting approach that separates all physical and dimensional effects into one-dimensional subsets. The nonlinear pattern selection process for steady convection in an air-filled square cavity with insulated side walls is investigated for Rayleigh numbers up to 20,000. The internalization of disturbances that evolve into coherent patterns is investigated and transient solutions from linear perturbation theory are compared with and contrasted to the full numerical simulations.
Stability of discrete time recurrent neural networks and nonlinear optimization problems.
Singh, Jayant; Barabanov, Nikita
2016-02-01
We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for Absolute Stability of these essentially nonlinear systems produce rather weak results. The method mentioned above is proved to be more powerful. It involves a multi-step procedure with maximization of special nonconvex functions over polytopes on every step. We derive conditions which guarantee an existence of at most one point of local maximum for such functions over every hyperplane. This nontrivial result is valid for wide range of neuron transfer functions.
Cauchy problem for non-linear systems of equations in the critical case
NASA Astrophysics Data System (ADS)
Kaikina, E. I.; Naumkin, P. I.; Shishmarev, I. A.
2004-12-01
The large-time asymptotic behaviour is studied for a system of non-linear evolution dissipative equations \\displaystyle u_t+\\mathscr N(u,u)+\\mathscr Lu=0, \\qquad x\\in\\mathbb R^n, \\quad t>0, \\displaystyle u(0,x)=\\widetilde u(x), \\qquad x\\in\\mathbb R^n, where \\mathscr L is a linear pseudodifferential operator \\mathscr Lu=\\overline{\\mathscr F}_{\\xi\\to x}(L(\\xi)\\widehat u(\\xi)) and the non-linearity \\mathscr N is a quadratic pseudodifferential operator \\displaystyle \\mathscr N(u,u)=\\overline{\\mathscr F}_{\\xi\\to x}\\sum_{k,l=1}^m\\int_{\\mathbb R^n}A^{kl}(t,\\xi,y)\\widehat u_k(t,\\xi-y)\\widehat u_l(t,y)\\,dy,where \\widehat u\\equiv\\mathscr F_{x\\to\\xi}u is the Fourier transform. Under the assumptions that the initial data \\widetilde u\\in\\mathbf H^{\\beta,0}\\cap\\mathbf H^{0,\\beta}, \\beta>n/2 are sufficiently small, where \\displaystyle \\mathbf H^{n,m}=\\{\\phi\\in\\mathbf L^2:\\Vert\\langle x\\rangle^m\\lang......\\phi(x)\\Vert _{\\mathbf L^2}<\\infty\\}, \\qquad \\langle x\\rangle=\\sqrt{1+x^2}\\,,is a Sobolev weighted space, and that the total mass vector \\displaystyle M=\\int\\widetilde u(x)\\,dx\
Samet Y. Kadioglu; Robert R. Nourgaliev; Vincent A. Mousseau
2008-03-01
We perform a comparative study for the harmonic versus arithmetic averaging of the heat conduction coefficient when solving non-linear heat transfer problems. In literature, the harmonic average is the method of choice, because it is widely believed that the harmonic average is more accurate model. However, our analysis reveals that this is not necessarily true. For instance, we show a case in which the harmonic average is less accurate when a coarser mesh is used. More importantly, we demonstrated that if the boundary layers are finely resolved, then the harmonic and arithmetic averaging techniques are identical in the truncation error sense. Our analysis further reveals that the accuracy of these two techniques depends on how the physical problem is modeled.
NASA Technical Reports Server (NTRS)
Ardema, M. D.
1979-01-01
Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.
NASA Astrophysics Data System (ADS)
Lesnic, D.; Elliott, L.; Ingham, D. B.
1996-07-01
In this study the inverse problem of the identification of temperature dependent thermal properties of a heat conducting body is investigated. The solution of the corresponding direct problem is obtained using a time marching boundary element method (BEM), which allows, without any need of interpolation and solution domain discretisation, efficient and accurate evaluation of the temperature everywhere inside the space-time dependent domain. Since the inverse problem, which requires the determination of the thermal conductivity and heat capacity from a finite set of temperature measurements taken inside the body, possesses poor uniqueness features, additional information is achieved by assuming that the thermal properties belong to a set of polynomials. Thus the inverse problem reduces to a parameter system estimation problem which is solved using the nonlinear least-squares method. Convergent and stable numerical results are obtained for the finite set of parameters which characterise the thermal properties for various test examples. Once the thermal properties are accurately obtained then the BEM determines automatically the temperature inside the solution domain and the remaining unspecified boundary values and the numerically obtained results show good agreement with the corresponding analytical solutions.
Nonlinear inverse problem for the estimation of time-and-space dependent heat transfer coefficients
NASA Astrophysics Data System (ADS)
Osman, A. M.; Beck, J. V.
1987-01-01
The aim of this paper is to describe a method and an algorithm for the direct estimation of the time-and-space dependent heat transfer coefficients from transient temperature data measured at approximate points inside a heat conducting solid. This inverse estimation problem is called herein the inverse heat transfer coefficient problem. An application considered in the present is the quenching of a solid in a liquid. The solution method used here is an extension of the sequential temperature future-information method introduced by Beck for solving the inverse heat conduction problem. The finite-difference method, based on the control volume approach, was used for the discretization of the direct heat conduction problem. Numerical results show that the proposed method is accurate and efficient.
Dmitriy Y. Anistratov; Adrian Constantinescu; Loren Roberts; William Wieselquist
2007-04-30
This is a project in the field of fundamental research on numerical methods for solving the particle transport equation. Numerous practical problems require to use unstructured meshes, for example, detailed nuclear reactor assembly-level calculations, large-scale reactor core calculations, radiative hydrodynamics problems, where the mesh is determined by hydrodynamic processes, and well-logging problems in which the media structure has very complicated geometry. Currently this is an area of very active research in numerical transport theory. main issues in developing numerical methods for solving the transport equation are the accuracy of the numerical solution and effectiveness of iteration procedure. The problem in case of unstructured grids is that it is very difficult to derive an iteration algorithm that will be unconditionally stable.
NASA Astrophysics Data System (ADS)
Moroni, Giovanni; Syam, Wahyudin P.; Petrò, Stefano
2014-08-01
Product quality is a main concern today in manufacturing; it drives competition between companies. To ensure high quality, a dimensional inspection to verify the geometric properties of a product must be carried out. High-speed non-contact scanners help with this task, by both speeding up acquisition speed and increasing accuracy through a more complete description of the surface. The algorithms for the management of the measurement data play a critical role in ensuring both the measurement accuracy and speed of the device. One of the most fundamental parts of the algorithm is the procedure for fitting the substitute geometry to a cloud of points. This article addresses this challenge. Three relevant geometries are selected as case studies: a non-linear least-squares fitting of a circle, sphere and cylinder. These geometries are chosen in consideration of their common use in practice; for example the sphere is often adopted as a reference artifact for performance verification of a coordinate measuring machine (CMM) and a cylinder is the most relevant geometry for a pin-hole relation as an assembly feature to construct a complete functioning product. In this article, an improvement of the initial point guess for the Levenberg-Marquardt (LM) algorithm by employing a chaos optimization (CO) method is proposed. This causes a performance improvement in the optimization of a non-linear function fitting the three geometries. The results show that, with this combination, a higher quality of fitting results a smaller norm of the residuals can be obtained while preserving the computational cost. Fitting an ‘incomplete-point-cloud’, which is a situation where the point cloud does not cover a complete feature e.g. from half of the total part surface, is also investigated. Finally, a case study of fitting a hemisphere is presented.
Il'ichev, N N; Pashinin, P P; Gulyamova, E S; Bufetova, G A; Shapkin, P V; Nasibov, A S
2014-03-28
The linear and nonlinear transmission of Fe{sup 2+}:ZnSe crystals is measured at a wavelength of 2940 nm in the temperature range 20 – 220 °C. It is found that, with increasing temperature from 20 °C to 150 – 220 °C, the transmission of Fe{sup 2+}:ZnSe crystals decreases in the case of incident radiation with an intensity of ∼5.5 MW cm{sup -2} and increases in the case of radiation with an intensity of 28 kW cm{sup -2}. At a temperature of 220 °C, the linear transmission almost coincides with the nonlinear transmission. The transmission spectra of Fe{sup 2+}:ZnSe crystals at temperatures of 22 and 220 °C in the wavelength range 500 – 7000 nm are presented. (active media)
NASA Technical Reports Server (NTRS)
Atluri, S. N.; Nakagaki, M.; Kathiresan, K.
1980-01-01
In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.
Construction of solutions for some nonlinear two-point boundary value problems
NASA Technical Reports Server (NTRS)
Pennline, J. A.
1982-01-01
Constructive existence and uniqueness results for boundary value problems associated with some simple special cases of the second order equation y'' = f(x,y,y') 0 or = x or = 1, are sought. The approach considered is to convert the differential equation and boundary conditions to an integral equation via Green's functions, and then to apply fixed point and contraction map principles to a sequence of successive approximations. The approach is tested on several applied problems. Difficulties in trying to prove general theorems are discussed.
NASA Astrophysics Data System (ADS)
Li, Enying; Wang, Hu; Li, Guangyao
2012-09-01
High-dimensional model representation (HDMR) is a general set of metamodel assessment and analysis tools to improve the efficiency of high dimensional underlying system behavior. Compared with the current popular modeling methods, such as Kriging (KG), radial basis function (RBF), and the moving least square approximation method (MLS), the distinctive characteristic of the HDMR is to decouple the input variables. Therefore, a high dimensional problem can be transformed as a low, middle or combination of middle dimensional function. Although the HDMR is a feasible method for high dimensional problems, the computational cost is still a bottleneck for complex engineering problems. To improve the efficiency of the HDMR method further, the purpose of this study is to use an intelligent sampling method for the HDMR. Because the HDMR cannot be integrated with the sampling method directly, a projection-based intelligent method is suggested. Compared with the popular HDMR methods, the construction procedure for the HDMR-based model is optimized. To validate the performance of the suggested method, multiple mathematical test functions are given to illustrate the modeling principles, procedures, and the efficiency and accuracy of HDMR models with problems of a wide scope of dimensionalities.
Rijlaarsdam, Jolien; Stevens, Gonneke W J M; Jansen, Pauline W; Ringoot, Ank P; Jaddoe, Vincent W V; Hofman, Albert; Ayer, Lynsay; Verhulst, Frank C; Hudziak, James J; Tiemeier, Henning
2014-03-18
This study examined hostility and harsh discipline of both mothers and fathers as potential mechanisms explaining the association between a maternal maltreatment history and her offspring's internalizing and externalizing problems. Prospective data from fetal life to age 6 were collected from a total of 4,438 families participating in the Generation R Study. Maternal maltreatment was assessed during pregnancy using a self-administered questionnaire. Mothers and fathers each reported on their psychological distress and harsh discipline when the child was 3 years. Children's internalizing and externalizing problems were assessed by parental reports and child interview at age 6. Findings from structural equation modeling showed that the association between a maternal maltreatment history and her offspring's externalizing problems was explained by maternal hostility and harsh discipline and, at least partially, also by paternal hostility and harsh discipline. Child interview data provided support for both these indirect paths, with associations largely similar to those observed for parent reports.
NASA Technical Reports Server (NTRS)
Hall, Philip
1989-01-01
Goertler vortices are thought to be the cause of transition in many fluid flows of practical importance. A review of the different stages of vortex growth is given. In the linear regime, nonparallel effects completely govern this growth, and parallel flow theories do not capture the essential features of the development of the vortices. A detailed comparison between the parallel and nonparallel theories is given and it is shown that at small vortex wavelengths, the parallel flow theories have some validity; otherwise nonparallel effects are dominant. New results for the receptivity problem for Goertler vortices are given; in particular vortices induced by free stream perturbations impinging on the leading edge of the walls are considered. It is found that the most dangerous mode of this type can be isolated and it's neutral curve is determined. This curve agrees very closely with the available experimental data. A discussion of the different regimes of growth of nonlinear vortices is also given. Again it is shown that, unless the vortex wavelength is small, nonparallel effects are dominant. Some new results for nonlinear vortices of 0(1) wavelengths are given and compared to experimental observations.
Makarov, V A; Petnikova, V M; Potravkin, N N; Shuvalov, V V
2014-02-28
Using the linearization method, we obtain approximate solutions to a one-dimensional nonintegrable problem of propagation of elliptically polarised light waves in an isotropic gyrotropic medium with local and nonlocal components of the Kerr nonlinearity and group-velocity dispersion. The consistent evolution of two orthogonal circularly polarised components of the field is described analytically in the case when their phases vary linearly during propagation. The conditions are determined for the excitation of waves with a regular and 'chaotic' change in the polarisation state. The character of the corresponding nonlinear solutions, i.e., periodic analogues of multisoliton complexes, is analysed. (nonlinear optical phenomena)
Problems associated with application of a wellbore heat transmission computer code
Dash, Z.V.; Zyvoloski, G.A.
1982-01-01
An analysis of the discrepancies between actual temperature surveys and results obtained from a wellbore heat transmission computer code are presented for recent workover operations in well EE-2 at the Fenton Hill Hot Dry Rock Geothermal site. Several sources of error in modeling the thermal behavior of wellbores are considered. These are errors in the estimation of in-situ properties, particularly thermal conductivity, the failure to include frictional heating effects when high flow rates are involved, and error in reporting the flow rate history. These errors were also found to have a cumulative effect. A sensitivity analysis of the computed results to each error type is presented for countercurrent flow. It is concluded that all the errors considered can cause temperature discrepancies between measured and computed temperature. Wellbore codes should have provisions for variable thermal properties and frictional heating. In addition, modeling efforts should be coordinated with periodic temperature surveys so cumulative errors can be minimized.
NASA Technical Reports Server (NTRS)
Periaux, J.
1979-01-01
The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.
ERIC Educational Resources Information Center
Pettit, Jeremy W.; Olino, Thomas M.; Roberts, Robert E.; Seeley, John R.; Lewinsohn, Peter M.
2008-01-01
Effects of lifetime histories of grandparental (G1) and parental (G2) major depressive disorder (MDD) on children's (G3) internalizing problems were investigated among 267 G3 children (ages 2-18 years) who received Child Behavior Checklist (CBCL) ratings and had diagnostic data available on 267 biological G2 parents and 527 biological G1…
Existence of Multiple Solutions for a p-Kirchhoff Problem with Nonlinear Boundary Conditions
Xiu, Zonghu
2013-01-01
The paper considers the existence of multiple solutions of the singular nonlocal elliptic problem −M(∫Ω | x|−ap | ∇u|p)div(|x|−ap | ∇u|p−2∇u) = λh(x) | u|r−2u, x ∈ Ω, M(∫Ω | x|−ap | ∇u|p) | x|−ap | ∇u|p−2 (∂u/∂ν) = g(x) | u|q−2u, on ∂Ω, where 1 < (N + 1)/2 < p < N, a < (N − p)/p. By the variational method on the Nehari manifold, we prove that the problem has at least two positive solutions when some conditions are satisfied. PMID:23983636
Cobb, J.W.
1995-02-01
There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.
NASA Astrophysics Data System (ADS)
Elizondo, D.; Cappelaere, B.; Faure, Ch.
2002-04-01
Emerging tools for automatic differentiation (AD) of computer programs should be of great benefit for the implementation of many derivative-based numerical methods such as those used for inverse modeling. The Odyssée software, one such tool for Fortran 77 codes, has been tested on a sample model that solves a 2D non-linear diffusion-type equation. Odyssée offers both the forward and the reverse differentiation modes, that produce the tangent and the cotangent models, respectively. The two modes have been implemented on the sample application. A comparison is made with a manually-produced differentiated code for this model (MD), obtained by solving the adjoint equations associated with the model's discrete state equations. Following a presentation of the methods and tools and of their relative advantages and drawbacks, the performances of the codes produced by the manual and automatic methods are compared, in terms of accuracy and of computing efficiency (CPU and memory needs). The perturbation method (finite-difference approximation of derivatives) is also used as a reference. Based on the test of Taylor, the accuracy of the two AD modes proves to be excellent and as high as machine precision permits, a good indication of Odyssée's capability to produce error-free codes. In comparison, the manually-produced derivatives (MD) sometimes appear to be slightly biased, which is likely due to the fact that a theoretical model (state equations) and a practical model (computer program) do not exactly coincide, while the accuracy of the perturbation method is very uncertain. The MD code largely outperforms all other methods in computing efficiency, a subject of current research for the improvement of AD tools. Yet these tools can already be of considerable help for the computer implementation of many numerical methods, avoiding the tedious task of hand-coding the differentiation of complex algorithms.
NASA Astrophysics Data System (ADS)
Grayver, Alexander V.; Kuvshinov, Alexey V.
2016-05-01
This paper presents a methodology to sample equivalence domain (ED) in nonlinear partial differential equation (PDE)-constrained inverse problems. For this purpose, we first applied state-of-the-art stochastic optimization algorithm called Covariance Matrix Adaptation Evolution Strategy (CMAES) to identify low-misfit regions of the model space. These regions were then randomly sampled to create an ensemble of equivalent models and quantify uncertainty. CMAES is aimed at exploring model space globally and is robust on very ill-conditioned problems. We show that the number of iterations required to converge grows at a moderate rate with respect to number of unknowns and the algorithm is embarrassingly parallel. We formulated the problem by using the generalized Gaussian distribution. This enabled us to seamlessly use arbitrary norms for residual and regularization terms. We show that various regularization norms facilitate studying different classes of equivalent solutions. We further show how performance of the standard Metropolis-Hastings Markov chain Monte Carlo algorithm can be substantially improved by using information CMAES provides. This methodology was tested by using individual and joint inversions of magneotelluric, controlled-source electromagnetic (EM) and global EM induction data.
NASA Astrophysics Data System (ADS)
Mena, Andres; Ferrero, Jose M.; Rodriguez Matas, Jose F.
2015-11-01
Solving the electric activity of the heart possess a big challenge, not only because of the structural complexities inherent to the heart tissue, but also because of the complex electric behaviour of the cardiac cells. The multi-scale nature of the electrophysiology problem makes difficult its numerical solution, requiring temporal and spatial resolutions of 0.1 ms and 0.2 mm respectively for accurate simulations, leading to models with millions degrees of freedom that need to be solved for thousand time steps. Solution of this problem requires the use of algorithms with higher level of parallelism in multi-core platforms. In this regard the newer programmable graphic processing units (GPU) has become a valid alternative due to their tremendous computational horsepower. This paper presents results obtained with a novel electrophysiology simulation software entirely developed in Compute Unified Device Architecture (CUDA). The software implements fully explicit and semi-implicit solvers for the monodomain model, using operator splitting. Performance is compared with classical multi-core MPI based solvers operating on dedicated high-performance computer clusters. Results obtained with the GPU based solver show enormous potential for this technology with accelerations over 50 × for three-dimensional problems.
NASA Astrophysics Data System (ADS)
Mena, Andres; Ferrero, Jose M.; Rodriguez Matas, Jose F.
2015-11-01
Solving the electric activity of the heart possess a big challenge, not only because of the structural complexities inherent to the heart tissue, but also because of the complex electric behaviour of the cardiac cells. The multi-scale nature of the electrophysiology problem makes difficult its numerical solution, requiring temporal and spatial resolutions of 0.1 ms and 0.2 mm respectively for accurate simulations, leading to models with millions degrees of freedom that need to be solved for thousand time steps. Solution of this problem requires the use of algorithms with higher level of parallelism in multi-core platforms. In this regard the newer programmable graphic processing units (GPU) has become a valid alternative due to their tremendous computational horsepower. This paper presents results obtained with a novel electrophysiology simulation software entirely developed in Compute Unified Device Architecture (CUDA). The software implements fully explicit and semi-implicit solvers for the monodomain model, using operator splitting. Performance is compared with classical multi-core MPI based solvers operating on dedicated high-performance computer clusters. Results obtained with the GPU based solver show enormous potential for this technology with accelerations over 50 × for three-dimensional problems.
New Nonlinear Multigrid Analysis
NASA Technical Reports Server (NTRS)
Xie, Dexuan
1996-01-01
The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.
Intergenerational Transmission of Child Problem Behaviors: A Longitudinal, Population-Based Study
ERIC Educational Resources Information Center
van Meurs, Inge; Reef, Joni; Verhulst, Frank C.; van der Ende, Jan
2009-01-01
The scores of 4- to 16-year-olds on a child behavior checklist made in 1983 is compared with those of their 6- to 18-year-old offsprings that were done in 2007. It is found that most forms of problem behavior in children were predicted by their parent's behavior as children and that continuity is stronger in mothers than fathers and in sons than…
Reed, B W; LaGrange, T; Shuttlesworth, R M; Gibson, D J; Campbell, G H; Browning, N D
2009-12-29
We describe a modification to a transmission electron microscope (TEM) that allows it to briefly (using a pulsed-laser-driven photocathode) operate at currents in excess of 10 mA while keeping the effects of condenser lens aberrations to a minimum. This modification allows real-space imaging of material microstructure with a resolution of order 10 nm over regions several {micro}m across with an exposure time of 15 ns. This is more than 6 orders of magnitude faster than typical video-rate TEM imaging. The key is the addition of a weak magnetic lens to couple the large-diameter high-current beam exiting the accelerator into the acceptance aperture of a conventional TEM condenser lens system. We show that the performance of the system is essentially consistent with models derived from ray tracing and finite element simulations. The instrument can also be operated as a conventional TEM by using the electron gun in a thermionic mode. The modification enables very high electron current densities in {micro}m-sized areas and could also be used in a non-pulsed system for high-throughput imaging and analytical TEM.
Yamabe type equations with a sign-changing nonlinearity, and the prescribed curvature problem
NASA Astrophysics Data System (ADS)
Bianchini, Bruno; Mari, Luciano; Rigoli, Marco
2016-05-01
In this paper, we investigate the prescribed scalar curvature problem on a non-compact Riemannian manifold (M , < , >), namely the existence of a conformal deformation of the metric < , > realizing a given function s ˜ (x) as its scalar curvature. In particular, the work focuses on the case when s ˜ (x) changes sign. Our main achievement are two new existence results requiring minimal assumptions on the underlying manifold, and ensuring a control on the stretching factor of the conformal deformation in such a way that the conformally deformed metric be bi-Lipschitz equivalent to the original one. The topological-geometrical requirements we need are all encoded in the spectral properties of the standard and conformal Laplacians of M. Our techniques can be extended to investigate the existence of entire positive solutions of quasilinear equations of the type
NASA Astrophysics Data System (ADS)
Popescu, Mihai; Dumitrache, Alexandru
2011-05-01
This study refers to minimization of quadratic functionals in infinite time. The coefficients of the quadratic form are quadratic matrix, function of the state variable. Dynamic constraints are represented by bilinear differential systems of the form x˙=A(x)x+B(x)u,x(0)=x0. One selects an adequate factorization of A( x) such that the analyzed system should be controllable. Employing the Hamilton-Jacobi equation it results the matrix algebraic equation of Riccati associated to the optimum problem. The necessary extremum conditions determine the adjoint variables λ and the control variables u as functions of state variable, as well as the adjoint system corresponding to those functions. Thus one obtains a matrix differential equation where the solution representing the positive defined symmetric matrix P( x), verifies the Riccati algebraic equation. The stability analysis for the autonomous systems solution resulting for the determined feedback control is performed using the Liapunov function method. Finally we present certain significant cases.
Sensitivity Analysis of Boundary Value Problems: Application to Nonlinear Reaction-Diffusion Systems
NASA Astrophysics Data System (ADS)
Reuven, Yakir; Smooke, Mitchell D.; Rabitz, Herschel
1986-05-01
A direct and very efficient approach for obtaining sensitivities of two-point boundary value problems solved by Newton's method is studied. The link between the solution method and the sensitivity equations is investigated together with matters of numerical accuracy and efficiency. This approach is employed in the analysis of a model three species, unimolecular, steady-state, premixed laminar flame. The numerical accuracy of the sensitivities is verified and their values are utilized for interpretation of the model results. It is found that parameters associated directly with the temperature play a dominant role. The system's Green's functions relating dependent variables are also controlled strongly by the temperature. In addition, flame speed sensitivities are calculated and shown to be a special class of derived sensitivity coefficients. Finally, some suggestions for the physical interpretation of sensitivities in model analysis are given.
NASA Astrophysics Data System (ADS)
Luo, Tao; Xin, Zhouping; Zeng, Huihui
2016-11-01
The nonlinear asymptotic stability of Lane-Emden solutions is proved in this paper for spherically symmetric motions of viscous gaseous stars with the density dependent shear and bulk viscosities which vanish at the vacuum, when the adiabatic exponent {γ} lies in the stability regime {(4/3, 2)}, by establishing the global-in-time regularity uniformly up to the vacuum boundary for the vacuum free boundary problem of the compressible Navier-Stokes-Poisson systems with spherical symmetry, which ensures the global existence of strong solutions capturing the precise physical behavior that the sound speed is {C^{{1}/{2}}}-Hölder continuous across the vacuum boundary, the large time asymptotic uniform convergence of the evolving vacuum boundary, density and velocity to those of Lane-Emden solutions with detailed convergence rates, and the detailed large time behavior of solutions near the vacuum boundary. Those uniform convergence are of fundamental importance in the study of vacuum free boundary problems which are missing in the previous results for global weak solutions. Moreover, the results obtained in this paper apply to much broader cases of viscosities than those in Fang and Zhang (Arch Ration Mech Anal 191:195-243, 2009) for the theory of weak solutions when the adiabatic exponent {γ} lies in the most physically relevant range. Finally, this paper extends the previous local-in-time theory for strong solutions to a global-in-time one.
Cameron, M.K.; Fomel, S.B.; Sethian, J.A.
2009-01-01
In the present work we derive and study a nonlinear elliptic PDE coming from the problem of estimation of sound speed inside the Earth. The physical setting of the PDE allows us to pose only a Cauchy problem, and hence is ill-posed. However we are still able to solve it numerically on a long enough time interval to be of practical use. We used two approaches. The first approach is a finite difference time-marching numerical scheme inspired by the Lax-Friedrichs method. The key features of this scheme is the Lax-Friedrichs averaging and the wide stencil in space. The second approach is a spectral Chebyshev method with truncated series. We show that our schemes work because of (1) the special input corresponding to a positive finite seismic velocity, (2) special initial conditions corresponding to the image rays, (3) the fact that our finite-difference scheme contains small error terms which damp the high harmonics; truncation of the Chebyshev series, and (4) the need to compute the solution only for a short interval of time. We test our numerical scheme on a collection of analytic examples and demonstrate a dramatic improvement in accuracy in the estimation of the sound speed inside the Earth in comparison with the conventional Dix inversion. Our test on the Marmousi example confirms the effectiveness of the proposed approach.
Xu, Y; Li, N
2014-09-01
Biological species have produced many simple but efficient rules in their complex and critical survival activities such as hunting and mating. A common feature observed in several biological motion strategies is that the predator only moves along paths in a carefully selected or iteratively refined subspace (or manifold), which might be able to explain why these motion strategies are effective. In this paper, a unified linear algebraic formulation representing such a predator-prey relationship is developed to simplify the construction and refinement process of the subspace (or manifold). Specifically, the following three motion strategies are studied and modified: motion camouflage, constant absolute target direction and local pursuit. The framework constructed based on this varying subspace concept could significantly reduce the computational cost in solving a class of nonlinear constrained optimal trajectory planning problems, particularly for the case with severe constraints. Two non-trivial examples, a ground robot and a hypersonic aircraft trajectory optimization problem, are used to show the capabilities of the algorithms in this new computational framework.
NASA Astrophysics Data System (ADS)
Menelaou, K.; Yau, M. K.; Martinez, Y.
2014-09-01
Some aspects of the problem of secondary eyewall formation (SEF) are investigated with the aid of an idealized model. A series of experiments are conducted, starting with a strong annular vortex embedded in a quiescent background flow and forced by the sustained heating associated with a spiral rainband (control experiment). Following this, two experiments are configured to assess the impact of vertical wind shear (VWS) in the SEF process. The importance of the boundary layer force imbalance is finally investigated in a number of simulations in which surface and boundary layer physics are included. From the control experiment, it is found that in the absence of background environmental flow, the sustained latent heating associated with a spiral rainband can form a secondary eyewall even in the absence of a frictional boundary layer. The presence of VWS acts negatively in the SEF process by disrupting the organization of the potential vorticity induced by the rainband. When boundary layer physics is included, some similarities with previous studies are seen, but there is no SEF. These results suggest that the boundary layer most likely contributes to, rather than initiate, a secondary eyewall. This article was corrected on 10 OCT 2014. See the end of the full text for details.
Development of MLPG and LBIE Methods for Nonlinear Problems of Fracture
NASA Technical Reports Server (NTRS)
Atluri, Satya N.; Raju, Ivatury S. (Technical Monitor)
2002-01-01
The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation are defined only from the primary nodes, and the secondary nodes use the same sub-domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and/or moved without an additional mesh. The essential boundary conditions can be imposed exactly, and non-convex boundaries can be treated without special techniques. Several numerical examples are presented to illustrate the performance of the present method.
Munoz, F. D.; Hobbs, B. F.; Watson, J. -P.
2016-02-01
A novel two-phase bounding and decomposition approach to compute optimal and near-optimal solutions to large-scale mixed-integer investment planning problems is proposed and it considers a large number of operating subproblems, each of which is a convex optimization. Our motivating application is the planning of power transmission and generation in which policy constraints are designed to incentivize high amounts of intermittent generation in electric power systems. The bounding phase exploits Jensen’s inequality to define a lower bound, which we extend to stochastic programs that use expected-value constraints to enforce policy objectives. The decomposition phase, in which the bounds are tightened, improvesmore » upon the standard Benders’ algorithm by accelerating the convergence of the bounds. The lower bound is tightened by using a Jensen’s inequality-based approach to introduce an auxiliary lower bound into the Benders master problem. Upper bounds for both phases are computed using a sub-sampling approach executed on a parallel computer system. Numerical results show that only the bounding phase is necessary if loose optimality gaps are acceptable. But, the decomposition phase is required to attain optimality gaps. Moreover, use of both phases performs better, in terms of convergence speed, than attempting to solve the problem using just the bounding phase or regular Benders decomposition separately.« less
Abgrall, Rémi; Congedo, Pietro Marco
2013-02-15
This paper deals with the formulation of a semi-intrusive (SI) method allowing the computation of statistics of linear and non linear PDEs solutions. This method shows to be very efficient to deal with probability density function of whatsoever form, long-term integration and discontinuities in stochastic space. Given a stochastic PDE where randomness is defined on Ω, starting from (i) a description of the solution in term of a space variables, (ii) a numerical scheme defined for any event ω∈Ω and (iii) a (family) of random variables that may be correlated, the solution is numerically described by its conditional expectancies of point values or cell averages and its evaluation constructed from the deterministic scheme. One of the tools is a tessellation of the random space as in finite volume methods for the space variables. Then, using these conditional expectancies and the geometrical description of the tessellation, a piecewise polynomial approximation in the random variables is computed using a reconstruction method that is standard for high order finite volume space, except that the measure is no longer the standard Lebesgue measure but the probability measure. This reconstruction is then used to formulate a scheme on the numerical approximation of the solution from the deterministic scheme. This new approach is said semi-intrusive because it requires only a limited amount of modification in a deterministic solver to quantify uncertainty on the state when the solver includes uncertain variables. The effectiveness of this method is illustrated for a modified version of Kraichnan–Orszag three-mode problem where a discontinuous pdf is associated to the stochastic variable, and for a nozzle flow with shocks. The results have been analyzed in terms of accuracy and probability measure flexibility. Finally, the importance of the probabilistic reconstruction in the stochastic space is shown up on an example where the exact solution is computable, the viscous
Serkin, Vladimir N; Belyaeva, T L
2001-11-30
It is shown that optical solitons in nonlinear fibre-optic communication systems and soliton lasers can be represented as nonlinear Bloch waves in periodic structures. The Bloch theorem is proved for solitons of the nonlinear Schrodinger equation in systems with the dispersion, the nonlinearity, and the gain (absorption coefficient) periodically changing over the length. The dynamics of formation and interaction, as well as stability of the coupled states of nonlinear Bloch waves are investigated. It is shown that soliton Bloch waves exist only under certain self-matching conditions for the basic parameters of the system and reveal a structural instability with respect to the mismatch between the periods of spatial modulation of the dispersion, nonlinearity or gain. (solitons)
NASA Astrophysics Data System (ADS)
De Conti, Alberto; Silveira, Fernando H.; Visacro, Silvério
2015-07-01
A theoretical study is presented to investigate lightning strikes to towers, with focus on wave interactions occurring at the return-stroke front due to the arrival of current pulses that propagate upward on the channel after being transmitted from the tower. The lightning channel is represented as a transmission line including corona and nonlinear losses. Analyses for the hypothetical case of a lossless channel considering matched tower and channel impedances show that the arrival of current pulses at the upward moving return-stroke front leads to an increase in corona currents leaving the channel. This transient process generates current pulses whose arrival at the tower top can be interpreted as the effect of a current reflection at the upward moving front, even though no impedance discontinuity exists at that point if return-stroke and leader channel properties are assumed the same. In the more realistic case of a lossy channel considering unmatched channel and tower impedances, the nonlinear channel resistance modifies the current pulses that propagate along the channel so that they merge smoothly with the return-stroke front. In this case, the interaction of the current pulses transmitted from the tower to the channel with the upward moving return-stroke front does not lead to features that can be clearly interpreted as the result of current reflections at that point in the evaluated conditions. Finally, it is argued that the current reflection coefficient at the tower top should be viewed as a current dependent parameter as opposed to a constant, linear value.
Research in nonlinear structural and solid mechanics
NASA Technical Reports Server (NTRS)
Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)
1980-01-01
Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.
Diaz, J. I.; Galiano, G.; Padial, J. F.
1999-01-15
We study the uniqueness of solutions of a semilinear elliptic problem obtained from an inverse formulation when the nonlinear terms of the equation are prescribed in a general class of real functions. The inverse problem arises in the modeling of the magnetic confinement of a plasma in a Stellarator device. The uniqueness proof relies on an L{sup {infinity}} -estimate on the solution of an auxiliary nonlocal problem formulated in terms of the relative rearrangement of a datum with respect to the solution.
NASA Astrophysics Data System (ADS)
You, Yi-Zhuang; Bi, Zhen; Mao, Dan; Xu, Cenke
2016-03-01
We propose a series of simple two-dimensional (2D) lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry-protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction, the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a Sp (N ) principal chiral model with a topological Θ term, whose boundary is described by a Sp (N ) principal chiral model with a Wess-Zumino-Witten term at level 1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning Θ in the field theory, and the phase transition occurs at Θ =π . The simplest version of these models with N =1 is equivalent to the familiar O(4) nonlinear sigma model (NLSM) with a topological term, whose boundary is a (1 +1 )D conformal field theory with central charge c =1 . After breaking the O(4) symmetry to its subgroups, this model can be viewed as bosonic SPT states with U(1), or Z2 symmetries, etc. All of these fermion models, including the bulk quantum phase transitions, can be simulated with the determinant quantum Monte Carlo method without the sign problem. Recent numerical results strongly suggest that the quantum disordered phase of the O(4) NLSM with precisely Θ =π is a stable (2 +1 )D conformal field theory with gapless bosonic modes.
Aloo, P A
2000-01-01
The majority of the numerous fish parasites are harmless to man and many domestic animals because when eaten with their fish hosts, they are digested. However, some of the fish parasites with larval stages in freshwater or marine teleosts have zoonotic potential if eaten raw or partially cooked. These are usually parasites, which have a piscivorous mammalian carnivore as their normal final host and are able to infect man because of the low host specificity of the adult stage. The major groups of fish parasite that are known as potentially dangerous pathogens of man belong to the helminth groups cestoda, trematoda, nematoda and rarely acanthocephala. However, bacterial and viral disease of man transmitted through fish are not uncommon. Toxic substances, metals and insecticides used to control human diseases in aquatic environments may accumulate in fish in po1lluted waters at such levels as to constitute a health risk to the consumer. Other health problems associated with fish arise from its perishable nature for example, in adequate handling, processing and storage, which may lead to the accumulation of microbes enhancing the risk of food poisoning. The aquatic environment in Africa constitutes a breeding habitat to several vectors of human diseases such as mosquitoes, snails and black flies. This paper reviews the role played by fish in transmitting diseases to humans as well as the importance of the aquatic environments in the transmission of human diseases such as Malaria, Schistosomiasis and onchocerciasis.
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-06-23
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.
NASA Astrophysics Data System (ADS)
Shen, Jianhe; Han, Maoan
2014-08-01
This paper considers the existence and uniformly valid asymptotic approximation of canard solutions in a second-order nonlinear singularly perturbed boundary value problem with a turning point. We get the main results by constructing the asymptotic solution first and then defining a couple of upper and lower solutions suitably on the basis of the asymptotic solution. Two examples are carried out to illustrate and verify the theoretical results.
NASA Technical Reports Server (NTRS)
Murphy, P. C.
1986-01-01
An algorithm for maximum likelihood (ML) estimation is developed with an efficient method for approximating the sensitivities. 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. With the fitted surface, sensitivity information can be updated at each iteration with less computational effort than that required by either a finite-difference method or integration of the analytically determined sensitivity equations. MNRES eliminates the need to derive sensitivity equations for each new model, and thus provides flexibility to use model equations in any convenient format. 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. 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. Beale's measure of nonlinearity is developed in this study for airplane identification problems; it is used to empirically correct confidence levels and to predict the degree of agreement between CR bounds and search estimates.
NASA Astrophysics Data System (ADS)
Santucci, F.; Santini, P. M.
2016-10-01
We study the generalization of the dispersionless Kadomtsev-Petviashvili (dKP) equation in n+1 dimensions and with nonlinearity of degree m+1, a model equation describing the propagation of weakly nonlinear, quasi one-dimensional waves in the absence of dispersion and dissipation, and arising in several physical contexts, like acoustics, plasma physics, hydrodynamics and nonlinear optics. In 2 + 1 dimensions and with quadratic nonlinearity, this equation is integrable through a novel inverse scattering transform, and it has been recently shown to be a prototype model equation in the description of the two-dimensional wave breaking of localized initial data. In higher dimensions and with higher nonlinearity, the generalized dKP equations are not integrable, but their invariance under motions on the paraboloid allows one to construct in this paper a family of exact solutions describing waves constant on their paraboloidal wave front and breaking simultaneously in all points of it, developing after breaking either multivaluedness or single-valued discontinuous profiles (shocks). Then such exact solutions are used to build the longtime behavior of the solutions of the Cauchy problem, for small and localized initial data, showing that wave breaking of small initial data takes place in the longtime regime if and only if m(n-1)≤slant 2. Lastly, the analytic aspects of such wave breaking are investigated in detail in terms of the small initial data, in both cases in which the solution becomes multivalued after breaking or it develops a shock. These results, contained in the 2012 master’s thesis of one of the authors (FS) [1], generalize those obtained in [2] for the dKP equation in n+1 dimensions with quadratic nonlinearity, and are obtained following the same strategy.
Currie, Thomas E.; Greenhill, Simon J.; Mace, Ruth
2010-01-01
Phylogenetic comparative methods (PCMs) provide a potentially powerful toolkit for testing hypotheses about cultural evolution. Here, we build on previous simulation work to assess the effect horizontal transmission between cultures has on the ability of both phylogenetic and non-phylogenetic methods to make inferences about trait evolution. We found that the mode of horizontal transmission of traits has important consequences for both methods. Where traits were horizontally transmitted separately, PCMs accurately reported when trait evolution was not correlated even at the highest levels of horizontal transmission. By contrast, linear regression analyses often incorrectly concluded that traits were correlated. Where simulated trait evolution was not correlated and traits were horizontally transmitted as a pair, both methods inferred increased levels of positive correlation with increasing horizontal transmission. Where simulated trait evolution was correlated, increasing rates of separate horizontal transmission led to decreasing levels of inferred correlation for both methods, but increasing rates of paired horizontal transmission did not. Furthermore, the PCM was also able to make accurate inferences about the ancestral state of traits. These results suggest that under certain conditions, PCMs can be robust to the effects of horizontal transmission. We discuss ways that future work can investigate the mode and tempo of horizontal transmission of cultural traits. PMID:21041214
Kerfriden, P.; Gosselet, P.; Adhikari, S.; Bordas, S.
2013-01-01
This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, “on-the-fly”, the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved. PMID:27076688
NASA Technical Reports Server (NTRS)
Voorhies, Coerte V.
1993-01-01
The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.
NASA Astrophysics Data System (ADS)
Kawai, Yusuke; Yamada, Yoshio
2016-07-01
This paper deals with a free boundary problem for diffusion equation with a certain class of bistable nonlinearity which allows two positive stable equilibrium states as an ODE model. This problem models the invasion of a biological species and the free boundary represents the spreading front of its habitat. Our main interest is to study large-time behaviors of solutions for the free boundary problem. We will completely classify asymptotic behaviors of solutions and, in particular, observe two different types of spreading phenomena corresponding to two positive stable equilibrium states. Moreover, it will be proved that, if the free boundary expands to infinity, an asymptotic speed of the moving free boundary for large time can be uniquely determined from the related semi-wave problem.
Kir'yanov, Alexander V; Barmenkov, Yuri O; Martinez, Itzel L; Kurkov, Audrey S; Dianov, Evgenii M
2006-05-01
An experimental and theoretical investigation of the nonlinear transmission coefficient in a set of Ytterbium-doped silica fibers (YFs) with various concentrations of Yb(3+) ions at continuous-wave 980-nm pumping is reported. An analysis of the obtained experimental data shows that YF transmission coefficient is notably affected by the presence of Yb(3+) - Yb(3+) ion-pairs in the fibers, especially in heavily-doped ones. The last fact is confirmed by the study of the cooperative luminescence and absorption effects in the fibers, where a detailed inspection of their dependence on Yb3+ concentration is presented. The pairs' effect is shown to seriously modify both the nonlinear character of YF transmission coefficient at lambda = 980 nm and Yb(3+) excited-state relaxation. A modeling of the experimental data is performed, which allows to find the coefficients addressing the pairs' effect in each of YFs under study and, as a result, to fit the experimentally measured dependences of YF transmission coefficient on pump power, fiber length, and Yb(3+) concentration. PMID:19516545
NASA Astrophysics Data System (ADS)
Kir'yanov, Alexander V.; Barmenkov, Yuri O.; Martinez, Itzel L.; Kurkov, Audrey S.; Dianov, Evgenii M.
2006-05-01
An experimental and theoretical investigation of the nonlinear transmission coefficient in a set of Ytterbium-doped silica fibers (YFs) with various concentrations of Yb3+ ions at continuous-wave 980-nm pumping is reported. An analysis of the obtained experimental data shows that YF transmission coefficient is notably affected by the presence of Yb3+ - Yb3+ ion-pairs in the fibers, especially in heavily-doped ones. The last fact is confirmed by the study of the cooperative luminescence and absorption effects in the fibers, where a detailed inspection of their dependence on Yb3+ concentration is presented. The pairs’ effect is shown to seriously modify both the nonlinear character of YF transmission coefficient at λ = 980 nm and Yb3+ excited-state relaxation. A modeling of the experimental data is performed, which allows to find the coefficients addressing the pairs’ effect in each of YFs under study and, as a result, to fit the experimentally measured dependences of YF transmission coefficient on pump power, fiber length, and Yb3+ concentration.
Traveltime tomography and nonlinear constrained optimization
Berryman, J.G.
1988-10-01
Fermat's principle of least traveltime states that the first arrivals follow ray paths with the smallest overall traveltime from the point of transmission to the point of reception. This principle determines a definite convex set of feasible slowness models - depending only on the traveltime data - for the fully nonlinear traveltime inversion problem. The existence of such a convex set allows us to transform the inversion problem into a nonlinear constrained optimization problem. Fermat's principle also shows that the standard undamped least-squares solution to the inversion problem always produces a slowness model with many ray paths having traveltime shorter than the measured traveltime (an impossibility even if the trial ray paths are not the true ray paths). In a damped least-squares inversion, the damping parameter may be varied to allow efficient location of a slowness model on the feasibility boundary. 13 refs., 1 fig., 1 tab.
Xia, Cen; Liu, Xiang; Chandrasekhar, S; Fontaine, N K; Zhu, Likai; Li, G
2014-03-10
We demonstrate nonlinearity compensation of 37.5-GHz-spaced 128-Gb/s PDM-QPSK signals using dispersion-folded digital-backward-propagation and a spectrally-sliced receiver that simultaneously receives three WDM signals, showing mitigation of intra-channel and inter-channel nonlinear effects in a 2560-km dispersion-managed TWRS-fiber link. Intra-channel and adjacent inter-channel nonlinear compensation gains when WDM channels are fully populated in the C-band are estimated based on the GN-model. PMID:24663923
Xia, Cen; Liu, Xiang; Chandrasekhar, S; Fontaine, N K; Zhu, Likai; Li, G
2014-03-10
We demonstrate nonlinearity compensation of 37.5-GHz-spaced 128-Gb/s PDM-QPSK signals using dispersion-folded digital-backward-propagation and a spectrally-sliced receiver that simultaneously receives three WDM signals, showing mitigation of intra-channel and inter-channel nonlinear effects in a 2560-km dispersion-managed TWRS-fiber link. Intra-channel and adjacent inter-channel nonlinear compensation gains when WDM channels are fully populated in the C-band are estimated based on the GN-model.
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-01
This Letter reports a technique for the imaging of acoustic nonlinearity. By contrasting the energy of the diffuse field produced through the focusing of an ultrasonic array by delayed parallel element transmission with that produced by postprocessing of sequential transmission data, acoustic nonlinearity local to the focal point is measured. Spatially isolated wave distortion is inferred without requiring interrogation of the wave at the inspection point, thereby allowing nonlinear imaging through depth.
NASA Astrophysics Data System (ADS)
Kulikovskii, A. G.; Chugainova, A. P.; Shargatov, V. A.
2016-07-01
Solutions of the Riemann problem for a generalized Hopf equation are studied. The solutions are constructed using a sequence of non-overturning Riemann waves and shock waves with stable stationary and nonstationary structures.
NASA Astrophysics Data System (ADS)
Zeevaert, A. E.
1980-03-01
A mathematical formulation to model the behavior under load of a reinforced soil system, where a fabric is placed over a soft soil and covered with stone for use as a temporary haul road is discussed. This approach is used to improve the behavior of temporary roadways, particularly where very soft soils are encountered. The stress distribution and the load-deformation characteristics of the soil-fabric system for varying geometries and material properties are defined. Included in the mathematical formulation are such features as: nonlinear behavior of the soil and fabric materials, friction parameters of the interface, tension characteristics of the fabric materials, large displacements in finite deformation, "no tension" conditions of the cohesionless materials, and yielding of plastic materials. The mathematical model is a more complete approximation of the actual fabric-soil system than is presently available.
Generation and transmission expansion planning for renewable energy integration
Bent, Russell W; Berscheid, Alan; Toole, G. Loren
2010-11-30
In recent years the expansion planning problem has become increasingly complex. As expansion planning (sometimes called composite or integrated resource planning) is a non-linear and non-convex optimization problem, researchers have traditionally focused on approximate models of power flows to solve the problem. The problem has also been split into generation expansion planning (GEP) and transmission network expansion planning (TNEP) to improve computational tractability. Until recently these approximations have produced results that are straight-forward to combine and adapt to the more complex and complete problem. However, the power grid is evolving towards a state where the adaptations are no longer easy (e.g. large amounts of limited control, renewable generation, comparable generation and transmission construction costs) and necessitates new approaches. Recent work on deterministic Discrepancy Bounded Local Search (DBLS) has shown it to be quite effective in addressing the TNEP. In this paper, we propose a generalization of DBLS to handle simultaneous generation and transmission planning.
NASA Astrophysics Data System (ADS)
Muha, Boris; Canić, Suncica
2013-03-01
We study a nonlinear, unsteady, moving boundary, fluid-structure interaction (FSI) problem arising in modeling blood flow through elastic and viscoelastic arteries. The fluid flow, which is driven by the time-dependent pressure data, is governed by two-dimensional incompressible Navier-Stokes equations, while the elastodynamics of the cylindrical wall is modeled by the one-dimensional cylindrical Koiter shell model. Two cases are considered: the linearly viscoelastic and the linearly elastic Koiter shell. The fluid and structure are fully coupled (two-way coupling) via the kinematic and dynamic lateral boundary conditions describing continuity of velocity (the no-slip condition), and the balance of contact forces at the fluid-structure interface. We prove the existence of weak solutions to the two FSI problems (the viscoelastic and the elastic case) as long as the cylinder radius is greater than zero. The proof is based on a novel semi-discrete, operator splitting numerical scheme, known as the kinematically coupled scheme, introduced in Guidoboni et al. (J Comput Phys 228(18):6916-6937, 2009) to numerically solve the underlying FSI problems. The backbone of the kinematically coupled scheme is the well-known Marchuk-Yanenko scheme, also known as the Lie splitting scheme. We effectively prove convergence of that numerical scheme to a solution of the corresponding FSI problem.
Computational method for transmission eigenvalues for a spherically stratified medium.
Cheng, Xiaoliang; Yang, Jing
2015-07-01
We consider a computational method for the interior transmission eigenvalue problem that arises in acoustic and electromagnetic scattering. The transmission eigenvalues contain useful information about some physical properties, such as the index of refraction. Instead of the existence and estimation of the spectral property of the transmission eigenvalues, we focus on the numerical calculation, especially for spherically stratified media in R^{3}. Due to the nonlinearity and the special structure of the interior transmission eigenvalue problem, there are not many numerical methods to date. First, we reduce the problem into a second-order ordinary differential equation. Then, we apply the Hermite finite element to the weak formulation of the equation. With proper rewriting of the matrix-vector form, we change the original nonlinear eigenvalue problem into a quadratic eigenvalue problem, which can be written as a linear system and solved by the eigs function in MATLAB. This numerical method is fast, effective, and can calculate as many transmission eigenvalues as needed at a time. PMID:26367151
NASA Technical Reports Server (NTRS)
Sidi, Avram; Pennline, James A.
1999-01-01
In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + definite integral of g(x, t)F(t,y(t))dt with limits between 0 and 1,0 less than or equal to x les than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integral equations arise, e.g., when one applied Green's function techniques to nonlinear two-point boundary value problems of the form y "(x) =f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and y(l) = y(sub l), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trepezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal rule, thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.
NASA Technical Reports Server (NTRS)
Sidi, Avram; Pennline, James A.
1999-01-01
In this paper we are concerned with high-accuracy quadrature method solutions of nonlinear Fredholm integral equations of the form y(x) = r(x) + integral(0 to 1) g(x,t) F(t, y(t)) dt, 0 less than or equal to x less than or equal to 1, where the kernel function g(x,t) is continuous, but its partial derivatives have finite jump discontinuities across x = t. Such integrals equations arise, e.g., when one applies Green's function techniques to nonlinear two-point boundary value problems of the form U''(x) = f(x,y(x)), 0 less than or equal to x less than or equal to 1, with y(0) = y(sub 0) and g(l) = y(sub 1), or other linear boundary conditions. A quadrature method that is especially suitable and that has been employed for such equations is one based on the trapezoidal rule that has a low accuracy. By analyzing the corresponding Euler-Maclaurin expansion, we derive suitable correction terms that we add to the trapezoidal thus obtaining new numerical quadrature formulas of arbitrarily high accuracy that we also use in defining quadrature methods for the integral equations above. We prove an existence and uniqueness theorem for the quadrature method solutions, and show that their accuracy is the same as that of the underlying quadrature formula. The solution of the nonlinear systems resulting from the quadrature methods is achieved through successive approximations whose convergence is also proved. The results are demonstrated with numerical examples.
NASA Astrophysics Data System (ADS)
Farhat, Charbel; Geuzaine, Philippe; Grandmont, Céline
2001-12-01
Discrete geometric conservation laws (DGCLs) govern the geometric parameters of numerical schemes designed for the solution of unsteady flow problems on moving grids. A DGCL requires that these geometric parameters, which include among others grid positions and velocities, be computed so that the corresponding numerical scheme reproduces exactly a constant solution. Sometimes, this requirement affects the intrinsic design of an arbitrary Lagrangian Eulerian (ALE) solution method. In this paper, we show for sample ALE schemes that satisfying the corresponding DGCL is a necessary and sufficient condition for a numerical scheme to preserve the nonlinear stability of its fixed grid counterpart. We also highlight the impact of this theoretical result on practical applications of computational fluid dynamics.
Kalashnikova, Irina
2012-05-01
A numerical study aimed to evaluate different preconditioners within the Trilinos Ifpack and ML packages for the Quantum Computer Aided Design (QCAD) non-linear Poisson problem implemented within the Albany code base and posed on the Ottawa Flat 270 design geometry is performed. This study led to some new development of Albany that allows the user to select an ML preconditioner with Zoltan repartitioning based on nodal coordinates, which is summarized. Convergence of the numerical solutions computed within the QCAD computational suite with successive mesh refinement is examined in two metrics, the mean value of the solution (an L{sup 1} norm) and the field integral of the solution (L{sup 2} norm).
Recent advances in nonlinear passive vibration isolators
NASA Astrophysics Data System (ADS)
Ibrahim, R. A.
2008-07-01
The theory of nonlinear vibration isolation has witnessed significant developments due to pressing demands for the protection of structural installations, nuclear reactors, mechanical components, and sensitive instruments from earthquake ground motion, shocks, and impact loads. In view of these demands, engineers and physicists have developed different types of nonlinear vibration isolators. This article presents a comprehensive assessment of recent developments of nonlinear isolators in the absence of active control means. It does not deal with other means of linear or nonlinear vibration absorbers. It begins with the basic concept and features of nonlinear isolators and inherent nonlinear phenomena. Specific types of nonlinear isolators are then discussed, including ultra-low-frequency isolators. For vertical vibration isolation, the treatment of the Euler spring isolator is based on the post-buckling dynamic characteristics of the column elastica and axial stiffness. Exact and approximate analyses of axial stiffness of the post-buckled Euler beam are outlined. Different techniques of reducing the resonant frequency of the isolator are described. Another group is based on the Gospodnetic-Frisch-Fay beam, which is free to slide on two supports. The restoring force of this beam resembles to a great extent the restoring roll moment of biased ships. The base isolation of buildings, bridges, and liquid storage tanks subjected to earthquake ground motion is then described. Base isolation utilizes friction elements, laminated-rubber bearings, and the friction pendulum. Nonlinear viscoelastic and composite material springs, and smart material elements are described in terms of material mechanical characteristics and the dependence of their transmissibility on temperature and excitation amplitude. The article is closed by conclusions, which highlight resolved and unresolved problems and recommendations for future research directions.
Nonlinear terahertz superconducting plasmonics
Wu, Jingbo; Liang, Lanju; Jin, Biaobing E-mail: tonouchi@ile.osaka-u.ac.jp Kang, Lin; Xu, Weiwei; Chen, Jian; Wu, Peiheng E-mail: tonouchi@ile.osaka-u.ac.jp; Zhang, Caihong; Kawayama, Iwao; Murakami, Hironaru; Tonouchi, Masayoshi E-mail: tonouchi@ile.osaka-u.ac.jp; Wang, Huabing
2014-10-20
Nonlinear terahertz (THz) transmission through subwavelength hole array in superconducting niobium nitride (NbN) film is experimentally investigated using intense THz pulses. The good agreement between the measurement and numerical simulations indicates that the field strength dependent transmission mainly arises from the nonlinear properties of the superconducting film. Under weak THz pulses, the transmission peak can be tuned over a frequency range of 145 GHz which is attributed to the high kinetic inductance of 50 nm-thick NbN film. Utilizing the THz pump-THz probe spectroscopy, we study the dynamic process of transmission spectra and demonstrate that the transition time of such superconducting plasmonic device is within 5 ps.
Identifying nonlinear biomechanical models by multicriteria analysis
NASA Astrophysics Data System (ADS)
Srdjevic, Zorica; Cveticanin, Livija
2012-02-01
In this study, the methodology developed by Srdjevic and Cveticanin (International Journal of Industrial Ergonomics 34 (2004) 307-318) for the nonbiased (objective) parameter identification of the linear biomechanical model exposed to vertical vibrations is extended to the identification of n-degree of freedom (DOF) nonlinear biomechanical models. The dynamic performance of the n-DOF nonlinear model is described in terms of response functions in the frequency domain, such as the driving-point mechanical impedance and seat-to-head transmissibility function. For randomly generated parameters of the model, nonlinear equations of motion are solved using the Runge-Kutta method. The appropriate data transformation from the time-to-frequency domain is performed by a discrete Fourier transformation. Squared deviations of the response functions from the target values are used as the model performance evaluation criteria, thus shifting the problem into the multicriteria framework. The objective weights of criteria are obtained by applying the Shannon entropy concept. The suggested methodology is programmed in Pascal and tested on a 4-DOF nonlinear lumped parameter biomechanical model. The identification process over the 2000 generated sets of parameters lasts less than 20 s. The model response obtained with the imbedded identified parameters correlates well with the target values, therefore, justifying the use of the underlying concept and the mathematical instruments and numerical tools applied. It should be noted that the identified nonlinear model has an improved accuracy of the biomechanical response compared to the accuracy of a linear model.
Nonlinear rotordynamics analysis
NASA Technical Reports Server (NTRS)
Day, W. B.
1985-01-01
The special nonlinearities of the Jeffcott equations in rotordynamics are examined. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot firing ground testing. Deadband, side force and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency is defined and used to develop the solutions of the nonlinear Jeffcott equations as asympotic expansions. This nonlinear natural frequency which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies. Numerical solutions are included for comparison with the analysis. Also, nonlinear frequency-response tables are made for a typical range of values.
Quadratic eigenvalue problems.
Walsh, Timothy Francis; Day, David Minot
2007-04-01
In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.
NASA Astrophysics Data System (ADS)
McLaughlin, David W.
1994-01-01
The principal investigator, together with two post-doctoral fellows, several graduate students, and colleagues, has applied the modern mathematical theory of nonlinear waves to problems in nonlinear optics. Projects included the interaction of laser light with nematic liquid crystals, propagation through random nonlinear media, cross polarization instabilities and optical shocks for propagation along nonlinear optical fibers, and the dynamics of bistable optical switches coupled through both diffusion and diffraction. In the first project the extremely strong nonlinear response of a CW laser beam in a nematic liquid crystal medium produced striking undulation and filamentation of the CW beam which was observed experimentally and explained theoretically. In the second project the interaction of randomness with nonlinearity was investigated, as well as an effective randomness due to the simultaneous presence of many nonlinear instabilities. In the polarization problems theoretical hyperbolic structure (instabilities and homoclinic orbits) in the coupled nonlinear Schroedinger (NLS) equations was identified and used to explain cross polarization instabilities in both the focusing and defocusing cases, as well as to describe optical shocking phenomena. For the coupled bistable optical switches, a numerical code was carefully developed in two spatial and one temporal dimensions. The code was used to study the decay of temporal transients to 'on-off' steady states in a geometry which includes forward and backward longitudinal propagation, together with one dimensional transverse coupling of both electromagnetic diffraction and carrier diffusion.
Detecting nonlinearity and chaos in epidemic data
Ellner, S.; Gallant, A.R.; Theiler, J. |
1993-08-01
Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude of epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.
NASA Technical Reports Server (NTRS)
Sheen, Jyh-Jong; Bishop, Robert H.
1992-01-01
The feedback linearization technique is applied to the problem of spacecraft attitude control and momentum management with control moment gyros (CMGs). The feedback linearization consists of a coordinate transformation, which transforms the system to a companion form, and a nonlinear feedback control law to cancel the nonlinear dynamics resulting in a linear equivalent model. Pole placement techniques are then used to place the closed-loop poles. The coordinate transformation proposed here evolves from three output functions of relative degree four, three, and two, respectively. The nonlinear feedback control law is presented. Stability in a neighborhood of a controllable torque equilibrium attitude (TEA) is guaranteed and this fact is demonstrated by the simulation results. An investigation of the nonlinear control law shows that singularities exist in the state space outside the neighborhood of the controllable TEA. The nonlinear control law is simplified by a standard linearization technique and it is shown that the linearized nonlinear controller provides a natural way to select control gains for the multiple-input, multiple-output system. Simulation results using the linearized nonlinear controller show good performance relative to the nonlinear controller in the neighborhood of the TEA.
Chatterjee, Kausik; Roadcap, John R.; Singh, Surendra
2014-11-01
The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson–Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.
NASA Astrophysics Data System (ADS)
Chatterjee, Kausik; Roadcap, John R.; Singh, Surendra
2014-11-01
The objective of this paper is the exposition of a recently-developed, novel Green's function Monte Carlo (GFMC) algorithm for the solution of nonlinear partial differential equations and its application to the modeling of the plasma sheath region around a cylindrical conducting object, carrying a potential and moving at low speeds through an otherwise neutral medium. The plasma sheath is modeled in equilibrium through the GFMC solution of the nonlinear Poisson-Boltzmann (NPB) equation. The traditional Monte Carlo based approaches for the solution of nonlinear equations are iterative in nature, involving branching stochastic processes which are used to calculate linear functionals of the solution of nonlinear integral equations. Over the last several years, one of the authors of this paper, K. Chatterjee has been developing a philosophically-different approach, where the linearization of the equation of interest is not required and hence there is no need for iteration and the simulation of branching processes. Instead, an approximate expression for the Green's function is obtained using perturbation theory, which is used to formulate the random walk equations within the problem sub-domains where the random walker makes its walks. However, as a trade-off, the dimensions of these sub-domains have to be restricted by the limitations imposed by perturbation theory. The greatest advantage of this approach is the ease and simplicity of parallelization stemming from the lack of the need for iteration, as a result of which the parallelization procedure is identical to the parallelization procedure for the GFMC solution of a linear problem. The application area of interest is in the modeling of the communication breakdown problem during a space vehicle's re-entry into the atmosphere. However, additional application areas are being explored in the modeling of electromagnetic propagation through the atmosphere/ionosphere in UHF/GPS applications.
Transmission Planning Analysis Tool
2015-06-23
Developed to solve specific problem: Assist transmission planning for regional transfers in interconnected power systems. This work was originated in a study for the U.S. Department of State, to recommend transmission reinforcements for the Central American regional system that interconnects 6 countries. Transmission planning analysis is currently performed by engineers with domainspecific and systemspecific knowledge without a unique methodology. The software codes of this disclosure assists engineers by defining systematic analysis procedures to help identify weak points and make decisions on transmission planning of regional interconnected power systems. Transmission Planning Analysis Tool groups PSS/E results of multiple AC contingency analysis and voltage stability analysis and QV analysis of many scenarios of study and arrange them in a systematic way to aid power system planning engineers or transmission operators in effective decision]making process or in the off]line study environment.
Transmission Planning Analysis Tool
2015-06-23
Developed to solve specific problem: Assist transmission planning for regional transfers in interconnected power systems. This work was originated in a study for the U.S. Department of State, to recommend transmission reinforcements for the Central American regional system that interconnects 6 countries. Transmission planning analysis is currently performed by engineers with domainspecific and systemspecific knowledge without a unique methodology. The software codes of this disclosure assists engineers by defining systematic analysis procedures to help identifymore » weak points and make decisions on transmission planning of regional interconnected power systems. Transmission Planning Analysis Tool groups PSS/E results of multiple AC contingency analysis and voltage stability analysis and QV analysis of many scenarios of study and arrange them in a systematic way to aid power system planning engineers or transmission operators in effective decision]making process or in the off]line study environment.« less
Nonlinear optomechanical pressure
NASA Astrophysics Data System (ADS)
Conti, Claudio; Boyd, Robert
2014-03-01
A transparent material exhibits ultrafast optical nonlinearity and is subject to optical pressure if irradiated by a laser beam. However, the effect of nonlinearity on optical pressure is often overlooked, even if a nonlinear optical pressure may be potentially employed in many applications, such as optical manipulation, biophysics, cavity optomechanics, quantum optics, and optical tractors, and is relevant in fundamental problems such as the Abraham-Minkoswky dilemma or the Casimir effect. Here, we show that an ultrafast nonlinear polarization gives indeed a contribution to the optical pressure that also is negative in certain spectral ranges; the theoretical analysis is confirmed by first-principles simulations. An order-of-magnitude estimate shows that the effect can be observable by measuring the deflection of a membrane made by graphene.
Coherent-incoherent phenomena in nonlinear optics and imaging
NASA Astrophysics Data System (ADS)
Dylov, Dmitry V.
While the majority of modern experimentation in optics and optical technology relies on pure and highly coherent sources, the light encountered in nature is of inferior quality. The low-quality, or noisy, light creates problems in nonlinear signal processing, as the random, multi-mode distribution inhibits phase matching and wave mixing. In this dissertation, we will discover new incoherent phenomena using nonlinear optics and characterize many fundamental, and useful, features pertinent to waves with inferior coherence. The first part of the thesis will be devoted to a new theory describing the nonlinear propagation of statistical light. The essence of the theory is to represent incoherent light as a gas of particles (speckles) that can interact collectively via nonlinearity, effectively forming a photonic plasma. We carried out a set of basic plasma-like experiments in optics and showed that this representation is valid and promising. Experiments were conducted using a nonlinear photorefractive crystal and basic phenomena such as modulation and bump-on-tail instabilities, optical turbulence, etc., were observed. In the second part of the thesis, we will apply this plasma formalism to the recovery and amplification of weak, noise-hidden images. The signal fidelity will be shown to improve by exploiting signal-noise interaction in the nonlinear medium. This new, dynamical type of stochastic resonance (a process in which signal can grow at expense of the noise) is treated as an equivalent beam-plasma instability, allowing an analytical characterization of the resonance as a function of coupling strength, noise statistics, modal content of the signal and wavelength. The theory also suggests an exponential limit to the amount of information transmissible in nonlinear communications systems. The results link the fields of optics, plasma and information theory, and pave the way for a variety of nonlinear, instability-driven imaging techniques.
Spatiotemporal soliton supported by parity-time symmetric potential with competing nonlinearities
NASA Astrophysics Data System (ADS)
Xu, Si-Liu; Zhao, Yuan; Petrović, Nikola Z.; Belić, Milivoj R.
2016-07-01
We construct explicit spatiotemporal or light bullet (LB) solutions to the (3 + 1)-dimensional nonlinear Schrödinger equation (NLSE) with inhomogeneous diffraction/dispersion and nonlinearity in the presence of parity-time (PT) symmetric potential with competing nonlinearities. The solution is based on the similarity transformation, by which the initial inhomogeneous problem is reduced to the standard NLSE with constant coefficients but with redefined variables and potential. Transmission characteristics of LB solutions, such as the phase change, half width and chirp, are studied in the media with exponentially decreasing diffraction/dispersion and with periodic modulation. Our outcomes demonstrate that diffraction/dispersion and nonlinearity management can prolong the stability of LBs in a PT potential.
Nonlinear trajectory navigation
NASA Astrophysics Data System (ADS)
Park, Sang H.
Trajectory navigation entails the solution of many different problems that arise due to uncertain knowledge of the spacecraft state, including orbit prediction, correction maneuver design, and trajectory estimation. In practice, these problems are usually solved based on an assumption that linear dynamical models sufficiently approximate the local trajectory dynamics and their associated statistics. However, astrodynamics problems are nonlinear in general and linear spacecraft dynamics models can fail to characterize the true trajectory dynamics when the system is subject to a highly unstable environment or when mapped over a long time period. This limits the performance of traditional navigation techniques and can make it difficult to perform precision analysis or robust navigation. This dissertation presents an alternate method for spacecraft trajectory navigation based on a nonlinear local trajectory model and their statistics in an analytic framework. For a given reference trajectory, we first solve for the higher order Taylor series terms that describe the localized nonlinear motion and develop an analytic expression for the relative solution flow. We then discuss the nonlinear dynamical mapping of a spacecraft's probability density function by solving the Fokker-Planck equation for a deterministic system. From this result we derive an analytic method for orbit uncertainty propagation which can replicate Monte-Carlo simulations with the benefit of added flexibility in initial orbit statistics. Using this approach, we introduce the concept of the statistically correct trajectory where we directly incorporate statistical information about an orbit state into the trajectory design process. As an extension of this concept, we define a nonlinear statistical targeting method where we solve for a correction maneuver which intercepts the desired target on average. Then we apply our results to a Bayesian filtering problem to obtain a general filtering algorithm for
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Vasylkiv, Yurij; Skab, Ihor; Vlokh, Rostyslav
2014-09-01
In this work, we analyze the behavior of topological defects of optical indicatrix orientation induced by a conically shaped electric field in crystals in a crossover regime that appears at intermediate fields separating the regimes of prevailing Pockels and Kerr electro-optic nonlinearities. We have found that increases in the electric voltage applied to a crystal induce neither topological defects, with the strengths being not multiples of ½, or the optical vortices with fractional charges. Instead, there appear some additional topological defects of the optical indicatrix orientation, the behavior of which we have studied in detail.
Spline approximations for nonlinear hereditary control systems
NASA Technical Reports Server (NTRS)
Daniel, P. L.
1982-01-01
A sline-based approximation scheme is discussed for optimal control problems governed by nonlinear nonautonomous delay differential equations. The approximating framework reduces the original control problem to a sequence of optimization problems governed by ordinary differential equations. Convergence proofs, which appeal directly to dissipative-type estimates for the underlying nonlinear operator, are given and numerical findings are summarized.
Nonlinear systems in medicine.
Higgins, John P.
2002-01-01
Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states. PMID:14580107
Photonic surfaces for designable nonlinear power shaping
Biswas, Roshni Povinelli, Michelle L.
2015-02-09
We propose a method for designing nonlinear input-output power response based on absorptive resonances of nanostructured surfaces. We show that various power transmission trends can be obtained by placing a photonic resonance mode at the appropriate detuning from the laser wavelength. We demonstrate our results in a silicon photonic crystal slab at a laser wavelength of 808 nm. We quantify the overall spectral red shift as a function of laser power. The shift results from absorptive heating and the thermo-optic effect. We then demonstrate devices with increasing, decreasing, and non-monotonic transmission as a function of laser power. The transmission changes are up to 7.5 times larger than in unpatterned silicon. The strong nonlinear transmission is due to a combination of resonantly enhanced absorption, reduced thermal conductivity, and the resonant transmission lineshape. Our results illustrate the possibility of designing different nonlinear power trends within a single materials platform at a given wavelength of interest.
Nonlinear optics and nonlinear dynamics
NASA Astrophysics Data System (ADS)
Chen, C. H.
1990-08-01
The author was invited by the Institute of Atomic and Molecular Sciences, Academia Sinica, in Taiwan to give six lectures on nonlinear optics. The participants included graduate students, postdoctoral fellows, research staff, and professors from several research organizations and universities. Extensive discussion followed each lecture. Since both the Photophysics Group at Oak Ridge National Laboratory (ORNL) and Institute of Atomic and Molecular Sciences in Taiwan have been actively participating in nonlinear optics research, the discussions are very beneficial to ORNL programs. The author also visited several laboratories at IAMS to exchange research ideas on nonlinear optics.
Grant, A E
1996-04-01
Some provincial regulators of nursing are setting out professional standards for the use of facsimile transmissions. While the facsimile machine is a tool that can improve client care through the timely, accurate transmission of vital information, nurses should recognize the potential hazards. Clear policies and procedures for the usage and management of facsimile transmissions are necessary to ensure that legal and professional standards are met.
Linearization of acousto-optic modulator transmission function
NASA Astrophysics Data System (ADS)
Korol, G.; Moskaletz, D.; Moskaletz, O.
2016-08-01
The procedure of linearization of nonlinear transmission function of the optical transparency in the form of an acousto-optic modulator by the methods of nonlinear functional analysis is described. The transmission function of a pair of acousto-optic modulators is linearized in the context of generalized superposition principle.
NASA Astrophysics Data System (ADS)
Finney, Ben; Bentley, Jerry
The transmission of ancient Greek learning and science to medieval western Europe via the translation of Greek and Arab texts is often cited as a terrestrial example of "learning at a distance" that could occur by means of the decipherment of radio messages from advanced extraterrestrial civilizations. However, the translation between such closely related languages as Greek, Latin and Arabic and the decipherment of radio messages from an extraterrestrial civilization to the point where humans could understand them are only nominally analogous tasks. A terrestrial example of such "learning at a distance" from an ancient civilization that perhaps better prepares us for thinking about the immense task inherent in any interstellar knowledge transmission is provided by the lengthy and troubled efforts of western scholars to decipher the inscriptions left by the ancient Maya and to learn from them about this ancient civilization. Only recently, with the rejection of the ideographic fallacy that Maya glyphs symbolized ideas directly without the mediation of language and with the application of linguistic knowledge of Maya languages has it been possible to decipher the Maya inscriptions and learn from them about their science and culture. This experience suggests that without any knowledge of languages in which extraterrestrial messages might be composed, their decipherment could be most problematic. The Maya case is also relevant to the common suggestion that advanced extraterrestrials would deliberately compose messages not in their own natural languages but in artificial ones using logic, numbers, and scientific constants presumably shared among all intelligent civilizations, or at least those in their radio-communicative phases. Numbers and calendrical dating system were the first parts of the Mayan inscriptions to be translated, albeit with the aid of partial "Rosetta stones" left by the Spanish conquerors. This success served, however, to reinforce the ideographic
Evaluation of groundwater resources requires the knowledge of the capacity of aquifers to store and transmit ground water. This requires estimates of key hydraulic parameters, such as the transmissivity, among others. The transmissivity T (m^{2}/sec) is a hydrauli...
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D; Leung, Daniel; Liu, Norman; Meadows, Brian K; Gordon, Frank; Bulsara, Adi R; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
Drill string transmission line
Hall, David R.; Hall, Jr., H. Tracy; Pixton, David S.; Bradford, Kline; Fox, Joe
2006-03-28
A transmission line assembly for transmitting information along a downhole tool comprising a pin end, a box end, and a central bore traveling between the pin end and the box end, is disclosed in one embodiment of the invention as including a protective conduit. A transmission line is routed through the protective conduit. The protective conduit is routed through the central bore and the ends of the protective conduit are routed through channels formed in the pin end and box end of the downhole tool. The protective conduit is elastically forced into a spiral or other non-linear path along the interior surface of the central bore by compressing the protective conduit to a length within the downhole tool shorter than the protective conduit.
Variational algorithms for nonlinear smoothing applications
NASA Technical Reports Server (NTRS)
Bach, R. E., Jr.
1977-01-01
A variational approach is presented for solving a nonlinear, fixed-interval smoothing problem with application to offline processing of noisy data for trajectory reconstruction and parameter estimation. The nonlinear problem is solved as a sequence of linear two-point boundary value problems. Second-order convergence properties are demonstrated. Algorithms for both continuous and discrete versions of the problem are given, and example solutions are provided.
Dilemmas of Cultural Transmission
ERIC Educational Resources Information Center
Kováts-Németh, Mária
2016-01-01
The fundamental problem of the 21st century is that in the modern civilization "the transmission of values is not stable." There is nothing, except for the natural sense of justice and some legal traditions, which would exercise selective power on social behavior. At a critical time in 1949 Albert Szent-Györgyi drew the attention to the…
Chen, Chang-Hua; Lin, Li-Chen; Chang, Yu-Jun; Chen, Yu-Min; Chang, Chin-Yen; Huang, Chieh-Chen
2015-01-01
Background: Acinetobacter baumannii complex (A. baumannii) has been isolated worldwide. The rapid spread of multidrug-resistant A. baumannii complex (MDRAB) in clinical settings has made choosing an appropriate antibiotic to treat these infections and executing contact precautions difficult for clinicians. Although controlling the transmission of MDRAB is a high priority for institutions, there is little information about MDRAB control. Therefore, this study evaluated infection control measures for A. baumannii infections, clusters and outbreaks in the literature. Methods: We performed a review of OVID Medline (from 1980 to 2015), and analyzed the literature. Results: We propose that both infection control programs and antibiotic control programs are essential for control of MDRAB. The first, effective control of MDRAB infections, requires compliance with a series of infection control methods including strict environmental cleaning, effective sterilization of reusable medical equipment, concentration on proper hand hygiene practices, and use of contact precautions, together with appropriate administrative guidance. The second strategy, effective antibiotic control programs to decrease A. baumannii, is also of paramount importance. Conclusion: We believe that both infection control programs and antibiotics stewardship programs are essential for control of MDRAB infections. PMID:26264006
Bertola, Marco
2015-06-15
Two-phase solutions of focusing NLS equation are classically constructed out of an appropriate Riemann surface of genus two and expressed in terms of the corresponding theta-function. We show here that in a certain limiting regime, such solutions reduce to some elementary ones called “Solitons on unstable condensate.” This degeneration turns out to be conveniently studied by means of basic tools from the theory of Riemann-Hilbert problems. In particular, no acquaintance with Riemann surfaces and theta-function is required for such analysis.
Maximized Gust Loads of a Closed-Loop, Nonlinear Aeroelastic System Using Nonlinear Systems Theory
NASA Technical Reports Server (NTRS)
Silva, Walter A.
1999-01-01
The problem of computing the maximized gust load for a nonlinear, closed-loop aeroelastic aircraft is discusses. The Volterra theory of nonlinear systems is applied in order to define a linearized system that provides a bounds on the response of the nonlinear system of interest. The method is applied to a simplified model of an Airbus A310.
ERIC Educational Resources Information Center
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
Optical nonlinearities in plasmonic metamaterials (Conference Presentation)
NASA Astrophysics Data System (ADS)
Zayats, Anatoly V.
2016-04-01
Metals exhibit strong and fast nonlinearities making metallic, plasmonic, structures very promising for ultrafast all-optical applications at low light intensities. Combining metallic nanostructures in metamaterials provides additional functionalities via prospect of precise engineering of spectral response and dispersion. From this point of view, hyperbolic metamaterials, in particular those based on plasmonic nanorod arrays, provide wealth of exciting possibilities in nonlinear optics offering designed linear and nonlinear properties, polarization control, spontaneous emission control and many others. Experiments and modeling have already demonstrated very strong Kerr-nonlinear response and its ultrafast recovery due to the nonlocal nature of the plasmonic mode of the metamaterial, so that small changes in the permittivity of the metallic component under the excitation modify the nonlocal response that in turn leads to strong changes of the metamaterial transmission. In this talk, we will discuss experimental studies and numerical modeling of second- and third-order nonlinear optical processes in hyperbolic metamaterials based on metallic nanorods and other plasmonic systems where coupling between the resonances plays important role in defining nonlinear response. Second-harmonic generation and ultrafast Kerr-type nonlinearity originating from metallic component of the metamaterial will be considered, including nonlinear magneto-optical effects. Nonlinear optical response of stand-alone as well as integrated metamaterial components will be presented. Some of the examples to be discussed include nonlinear polarization control, nonlinear metamaterial integrated in silicon photonic circuitry and second-harmonic generation, including magneto-optical effects.
Advanced Computational Methods for Security Constrained Financial Transmission Rights
Kalsi, Karanjit; Elbert, Stephen T.; Vlachopoulou, Maria; Zhou, Ning; Huang, Zhenyu
2012-07-26
Financial Transmission Rights (FTRs) are financial insurance tools to help power market participants reduce price risks associated with transmission congestion. FTRs are issued based on a process of solving a constrained optimization problem with the objective to maximize the FTR social welfare under power flow security constraints. Security constraints for different FTR categories (monthly, seasonal or annual) are usually coupled and the number of constraints increases exponentially with the number of categories. Commercial software for FTR calculation can only provide limited categories of FTRs due to the inherent computational challenges mentioned above. In this paper, first an innovative mathematical reformulation of the FTR problem is presented which dramatically improves the computational efficiency of optimization problem. After having re-formulated the problem, a novel non-linear dynamic system (NDS) approach is proposed to solve the optimization problem. The new formulation and performance of the NDS solver is benchmarked against widely used linear programming (LP) solvers like CPLEX™ and tested on both standard IEEE test systems and large-scale systems using data from the Western Electricity Coordinating Council (WECC). The performance of the NDS is demonstrated to be comparable and in some cases is shown to outperform the widely used CPLEX algorithms. The proposed formulation and NDS based solver is also easily parallelizable enabling further computational improvement.
Nonlinear growing neutrino cosmology
NASA Astrophysics Data System (ADS)
Ayaita, Youness; Baldi, Marco; Führer, Florian; Puchwein, Ewald; Wetterich, Christof
2016-03-01
The energy scale of dark energy, ˜2 ×10-3 eV , is a long way off compared to all known fundamental scales—except for the neutrino masses. If dark energy is dynamical and couples to neutrinos, this is no longer a coincidence. The time at which dark energy starts to behave as an effective cosmological constant can be linked to the time at which the cosmic neutrinos become nonrelativistic. This naturally places the onset of the Universe's accelerated expansion in recent cosmic history, addressing the why-now problem of dark energy. We show that these mechanisms indeed work in the growing neutrino quintessence model—even if the fully nonlinear structure formation and backreaction are taken into account, which were previously suspected of spoiling the cosmological evolution. The attractive force between neutrinos arising from their coupling to dark energy grows as large as 106 times the gravitational strength. This induces very rapid dynamics of neutrino fluctuations which are nonlinear at redshift z ≈2 . Nevertheless, a nonlinear stabilization phenomenon ensures only mildly nonlinear oscillating neutrino overdensities with a large-scale gravitational potential substantially smaller than that of cold dark matter perturbations. Depending on model parameters, the signals of large-scale neutrino lumps may render the cosmic neutrino background observable.
A Genetic Algorithm Approach to Nonlinear Least Squares Estimation
ERIC Educational Resources Information Center
Olinsky, Alan D.; Quinn, John T.; Mangiameli, Paul M.; Chen, Shaw K.
2004-01-01
A common type of problem encountered in mathematics is optimizing nonlinear functions. Many popular algorithms that are currently available for finding nonlinear least squares estimators, a special class of nonlinear problems, are sometimes inadequate. They might not converge to an optimal value, or if they do, it could be to a local rather than…
Tjernberg, L O; Rising, A; Johansson, J; Jaudzems, K; Westermark, P
2016-08-01
There are around 30 human diseases associated with protein misfolding and amyloid formation, each one caused by a certain protein or peptide. Many of these diseases are lethal and together they pose an enormous burden to society. The prion protein has attracted particular interest as being shown to be the pathogenic agent in transmissible diseases such as kuru, Creutzfeldt-Jakob disease and bovine spongiform encephalopathy. Whether similar transmission could occur also in other amyloidoses such as Alzheimer's disease, Parkinson's disease and serum amyloid A amyloidosis is a matter of intense research and debate. Furthermore, it has been suggested that novel biomaterials such as artificial spider silk are potentially amyloidogenic. Here, we provide a brief introduction to amyloid, prions and other proteins involved in amyloid disease and review recent evidence for their potential transmission. We discuss the similarities and differences between amyloid and silk, as well as the potential hazards associated with protein-based biomaterials. PMID:27002185
Maddison, Ben C
2010-01-01
Prion diseases range from being highly infectious, for example scrapie and CWD, which show facile transmission between susceptible individuals, to showing negligible horizontal transmission, such as BSE and CJD, which are spread via food or iatrogenically, respectively. Scrapie and CWD display considerable in vivo dissemination, with PrPSc and infectivity being found in a range of peripheral tissues. This in vivo dissemination appears to facilitate the recently reported excretion of prion through multiple routes such as from skin, feces, urine, milk, nasal secretions, saliva and placenta. Furthermore, excreted scrapie and CWD agent is detected within environmental samples such as water and on the surfaces of inanimate objects. The cycle of “uptake of prion from the environment—widespread in vivo prion dissemination—prion excretion—prion persistence in the environment” is likely to explain the facile transmission and maintenance of these diseases within wild and farmed populations over many years. PMID:20948292
NASA Technical Reports Server (NTRS)
Coy, John J.
1990-01-01
Highlighted here is that portion of the Lewis Research Center's helicopter propulsion systems program that deals with drive train technology and the related mechanical components. The major goals of the program are to increase life, reliability, and maintainability, to reduce weight, noise, and vibration, and to maintain the relatively high mechanical efficiency of the gear train. The current activity emphasizes noise reduction technology and analytical code development, followed by experimental verification. Selected significant advances in technology for transmissions are reviewed, including advanced configurations and new analytical tools. Finally, the plan for transmission research in the future is presented.
Recasting the theory of mosquito-borne pathogen transmission dynamics and control
Smith, David L.; Perkins, T. Alex; Reiner, Robert C.; Barker, Christopher M.; Niu, Tianchan; Chaves, Luis Fernando; Ellis, Alicia M.; George, Dylan B.; Le Menach, Arnaud; Pulliam, Juliet R. C.; Bisanzio, Donal; Buckee, Caroline; Chiyaka, Christinah; Cummings, Derek A. T.; Garcia, Andres J.; Gatton, Michelle L.; Gething, Peter W.; Hartley, David M.; Johnston, Geoffrey; Klein, Eili Y.; Michael, Edwin; Lloyd, Alun L.; Pigott, David M.; Reisen, William K.; Ruktanonchai, Nick; Singh, Brajendra K.; Stoller, Jeremy; Tatem, Andrew J.; Kitron, Uriel; Godfray, H. Charles J.; Cohen, Justin M.; Hay, Simon I.; Scott, Thomas W.
2014-01-01
Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of the world. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonald's formula for R0 and its entomological derivative, vectorial capacity, are now used to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross–Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context for mosquito blood feeding, the movement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control. PMID:24591453
Recasting the theory of mosquito-borne pathogen transmission dynamics and control.
Smith, David L; Perkins, T Alex; Reiner, Robert C; Barker, Christopher M; Niu, Tianchan; Chaves, Luis Fernando; Ellis, Alicia M; George, Dylan B; Le Menach, Arnaud; Pulliam, Juliet R C; Bisanzio, Donal; Buckee, Caroline; Chiyaka, Christinah; Cummings, Derek A T; Garcia, Andres J; Gatton, Michelle L; Gething, Peter W; Hartley, David M; Johnston, Geoffrey; Klein, Eili Y; Michael, Edwin; Lloyd, Alun L; Pigott, David M; Reisen, William K; Ruktanonchai, Nick; Singh, Brajendra K; Stoller, Jeremy; Tatem, Andrew J; Kitron, Uriel; Godfray, H Charles J; Cohen, Justin M; Hay, Simon I; Scott, Thomas W
2014-04-01
Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of the world. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonald's formula for R0 and its entomological derivative, vectorial capacity, are now used to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross-Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context for mosquito blood feeding, the movement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.
Nonlinear response of tension leg platforms in random sea waves
Ma, R.; Li, G.
1995-12-31
The nonlinear dynamic analysis of a tension leg platform is carried out by using nonlinear spectral analysis in this paper. The nonlinear response spectrum is obtained by introducing Hermite polynomial. The study indicates that it is possible to solve nonlinear vibration problems by using spectral analysis directly. It is not necessary to linearize the nonlinear terms in this method so that the errors introduced by linearization can be eliminated. This method will provide a convenient and accurate tool for solving nonlinear random vibration problems.
Spurious Solutions Of Nonlinear Differential Equations
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sweby, P. K.; Griffiths, D. F.
1992-01-01
Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.
Vibrational Control of a Nonlinear Elastic Panel
NASA Technical Reports Server (NTRS)
Chow, P. L.; Maestrello, L.
1998-01-01
The paper is concerned with the stabilization of the nonlinear panel oscillation by an active control. The control is actuated by a combination of additive and parametric vibrational forces. A general method of vibrational control is presented for stabilizing panel vibration satisfying a nonlinear beam equation. To obtain analytical results, a perturbation technique is used in the case of weak nonlinearity. Possible application to other types of problems is briefly discussed.
NASA Technical Reports Server (NTRS)
Cantrell, John H.; Yost, William T.
1990-01-01
The effects of material structure on the nonlinearity parameters are reviewed. Problems discussed include definition of nonlinearity parameters, square-law nonlinearity and collinear beam-mixing, structure dependence of the nonlinearity parameters, negative nonlinearity parameters, and implications for materials characterization.
NASA Technical Reports Server (NTRS)
Coy, John J.
1987-01-01
The NASA Lewis Research Center and the U.S. Army Aviation Systems Command share an interest in advancing the technology for helicopter propulsion systems. In particular, this presentation outlines that portion of the program that applies to the drive train and its various mechanical components. The major goals of the program are to increase the life, reliability, and maintainability; reduce the weight, noise, and vibration; and maintain the relatively high mechanical efficiency of the gear train. The current activity emphasizes noise reduction technology and analytical code development followed by experimental verification. Selected significant advances in technology for transmissions are reviewed, including advanced configurations and new analytical tools. Finally, the plan for transmission research in the future is presented.
Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Du, Jiajia
2014-01-01
The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results. PMID:24592160
Nonlinear acoustics - History and outlook
NASA Astrophysics Data System (ADS)
Rott, N.
1980-08-01
A historical review of the development of nonlinear acoustics before the epoch beginning with Riemann is presented followed by a review of the more recent developments of the last 20 years, including a cinematical view of nonlinear acoustic waves. The review emphasizes the works of Poisson and his equations and solutions of particle and wave velocity as well as Stoke's theory of sound. Attention is given to the developments of the last two decades through an examination of Lagrange and Chester problems, such as the transition of Euler coordinates into Lagrange coordinates and equations. The nonlinear theory of resonance is discussed by describing a closed tube resonance problem where periodic excitation through a piston characterizes wave movements.
Optical correlator tracking nonlinearity
NASA Astrophysics Data System (ADS)
Gregory, Don A.; Kirsch, James C.; Johnson, John L.
1987-01-01
A limitation observed in the tracking ability of optical correlators is reported. It is shown by calculations that an inherent nonlinearity exists in many optical correlator configurations, with the problem manifesting itself in a mismatch of the input scene with the position of the correlation signal. Results indicate that some care must be given to the selection of components and their configuration in constructing an optical correlator which exhibits true translational invariance. An input test scene is shown along with the correlation spot and cross hairs from a contrast detector; the offset is apparent.
Method for nonlinear exponential regression analysis
NASA Technical Reports Server (NTRS)
Junkin, B. G.
1972-01-01
Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.
Nonlinear gyrokinetic equations
Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.
1983-03-01
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.
Some nonlinear space decomposition algorithms
Tai, Xue-Cheng; Espedal, M.
1996-12-31
Convergence of a space decomposition method is proved for a general convex programming problem. The space decomposition refers to methods that decompose a space into sums of subspaces, which could be a domain decomposition or a multigrid method for partial differential equations. Two algorithms are proposed. Both can be used for linear as well as nonlinear elliptic problems and they reduce to the standard additive and multiplicative Schwarz methods for linear elliptic problems. Two {open_quotes}hybrid{close_quotes} algorithms are also presented. They converge faster than the additive one and have better parallelism than the multiplicative method. Numerical tests with a two level domain decomposition for linear, nonlinear and interface elliptic problems are presented for the proposed algorithms.
Multilayer perceptron for nonlinear programming.
Reifman, J.; Feldman, E. E.; Reactor Analysis
2002-08-01
A new method for solving nonlinear programming problems within the framework of a multilayer neural network perceptron is proposed. The method employs the Penalty Function method to transform a constrained optimization problem into a sequence of unconstrained optimization problems and then solves the sequence of unconstrained optimizations of the transformed problem by training a series of multilayer perceptrons. The neural network formulation is represented in such a way that the multilayer perceptron prediction error to be minimized mimics the objective function of the unconstrained problem, and therefore, the minimization of the objective function for each unconstrained optimization is attained by training a single perceptron. The multilayer perceptron allows for the transformation of problems with two-sided bounding constraints on the decision variables x, e.g., a{<=}x{sub n}{<=}b, into equivalent optimization problems in which these constraints do not explicitly appear. Hence, when these are the only constraints in the problem, the transformed problem is constraint free (i.e., the transformed objective function contains no penalty terms) and is solved by training a multilayer perceptron only once. In addition, we present a new Penalty Function method for solving nonlinear programming problems that is parameter free and guarantees that feasible solutions are obtained when the optimal solution is on the boundary of the feasible region. Simulation results, including an example from operations research, illustrate the proposed methods.
Ohkubo, M.
1988-02-16
An automatic transmission is described combining a stator reversing type torque converter and speed changer having first and second sun gears comprising: (a) a planetary gear train composed of first and second planetary gears sharing one planetary carrier in common; (b) a clutch and requisite brakes to control the planetary gear train; and (c) a speed-increasing or speed-decreasing mechanism is installed both in between a turbine shaft coupled to a turbine of the stator reversing type torque converter and the first sun gear of the speed changer, and in between a stator shaft coupled to a reversing stator and the second sun gear of the speed changer.
Miki, N.
1988-10-11
This patent describes an automatic transmission including a fluid torque converter, a first gear unit having three forward-speed gears and a single reverse gear, a second gear unit having a low-speed gear and a high-speed gear, and a hydraulic control system, the hydraulic control system comprising: a source of pressurized fluid; a first shift valve for controlling the shifting between the first-speed gear and the second-speed gear of the first gear unit; a second shift valve for controlling the shifting between the second-speed gear and the third-speed gear of the first gear unit; a third shift valve equipped with a spool having two positions for controlling the shifting between the low-speed gear and the high-speed gear of the second gear unit; a manual selector valve having a plurality of shift positions for distributing the pressurized fluid supply from the source of pressurized fluid to the first, second and third shift valves respectively; first, second and third solenoid valves corresponding to the first, second and third shift valves, respectively for independently controlling the operation of the respective shift valves, thereby establishing a six forward-speed automatic transmission by combining the low-speed gear and the high-speed gear of the second gear unit with each of the first-speed gear, the second speed gear and the third-speed gear of the first gear unit; and means to fixedly position the spool of the third shift valve at one of the two positions by supplying the pressurized fluid to the third shift valve when the manual selector valve is shifted to a particular shift position, thereby locking the second gear unit in one of low-speed gear and the high-speed gear, whereby the six forward-speed automatic transmission is converted to a three forward-speed automatic transmission when the manual selector valve is shifted to the particular shift position.
Cultural variant interaction in teaching and transmission.
Abrams, Marshall
2015-01-01
Focus on the way in which cultural variants affect other variants' probabilities of transmission in modeling and empirical work can enrich Kline's conceptualization of teaching. For example, the problem of communicating complex cumulative culture is an adaptive problem; teaching methods that manage transmission so that acquisition of some cultural variants increases the probability of acquiring others, provide a partial solution. PMID:26786769
NASA Astrophysics Data System (ADS)
Simmons, Daniel; Cools, Kristof; Sewell, Phillip
2016-11-01
Time domain electromagnetic simulation tools have the ability to model transient, wide-band applications, and non-linear problems. The Boundary Element Method (BEM) and the Transmission Line Modeling (TLM) method are both well established numerical techniques for simulating time-varying electromagnetic fields. The former surface based method can accurately describe outwardly radiating fields from piecewise uniform objects and efficiently deals with large domains filled with homogeneous media. The latter volume based method can describe inhomogeneous and non-linear media and has been proven to be unconditionally stable. Furthermore, the Unstructured TLM (UTLM) enables modelling of geometrically complex objects by using triangular meshes which removes staircasing and unnecessary extensions of the simulation domain. The hybridization of BEM and UTLM which is described in this paper is named the Boundary Element Unstructured Transmission-line (BEUT) method. It incorporates the advantages of both methods. The theory and derivation of the 2D BEUT method is described in this paper, along with any relevant implementation details. The method is corroborated by studying its correctness and efficiency compared to the traditional UTLM method when applied to complex problems such as the transmission through a system of Luneburg lenses and the modelling of antenna radomes for use in wireless communications.
Aoki, H.
1989-03-21
An automatic transmission is described, comprising: a torque converter including an impeller having a connected member, a turbine having an input member and a reactor; and an automatic transmission mechanism having first to third clutches and plural gear units including a single planetary gear unit with a ring gear and a dual planetary gear unit with a ring gear. The single and dual planetary gear units have respective carriers integrally coupled with each other and respective sun gears integrally coupled with each other, the input member of the turbine being coupled with the ring gear of the single planetary gear unit through the first clutch, and being coupled with the sun gear through the second clutch. The connected member of the impeller is coupled with the ring gear of the dual planetary gear of the dual planetary gear unit is made to be and ring gear of the dual planetary gear unit is made to be restrained as required, and the carrier is coupled with an output member.
[Nonlinear magnetohydrodynamics
Not Available
1994-01-01
Resistive MHD equilibrium, even for small resistivity, differs greatly from ideal equilibrium, as do the dynamical consequences of its instabilities. The requirement, imposed by Faraday`s law, that time independent magnetic fields imply curl-free electric fields, greatly restricts the electric fields allowed inside a finite-resistivity plasma. If there is no flow and the implications of the Ohm`s law are taken into account (and they need not be, for ideal equilibria), the electric field must equal the resistivity times the current density. The vanishing of the divergence of the current density then provides a partial differential equation which, together with boundary conditions, uniquely determines the scalar potential, the electric field, and the current density, for any given resistivity profile. The situation parallels closely that of driven shear flows in hydrodynamics, in that while dissipative steady states are somewhat more complex than ideal ones, there are vastly fewer of them to consider. Seen in this light, the vast majority of ideal MHD equilibria are just irrelevant, incapable of being set up in the first place. The steady state whose stability thresholds and nonlinear behavior needs to be investigated ceases to be an arbitrary ad hoc exercise dependent upon the whim of the investigator, but is determined by boundary conditions and choice of resistivity profile.
Hidden hazards of HCV transmission.
Pondé, Robério Amorim de Almeida
2011-02-01
Hepatitis C virus infection is a global health problem that has important epidemiological and clinical consequences. It has been well established that exposure to infected blood is the main risk factor for HCV transmission. However, in 20% of cases the agent transmission occurs by unknown route or in the presence of an unidentified source of infection. Understanding of the epidemiology of HCV is needed to help us define future control and preventive strategies. Herein, we discuss about diagnosis of HCV infection and hepatitis C surveillance in the context of its transmission.
NASA Astrophysics Data System (ADS)
Syusina, O. M.; Chernitsov, A. M.; Tamarov, V. A.
2011-07-01
Simple and mathematically rigorous methods for calculating of nonlinearity coefficients are proposed. These coefficients allow us to make classification for the least squares problem as strongly or weakly nonlinear one. The advices are given on how to reduce a concrete estimation problem to weakly nonlinear one where a more efficient linear approach can be used.
Liu, Xiang; Hu, Hao; Chandrasekhar, S; Jopson, R M; Gnauck, A H; Dinu, M; Xie, C; Winzer, P J
2014-03-24
We experimentally demonstrate the generation of 1.024-Tb/s Nyquist-WDM phase-conjugated vector twin waves (PCTWs), consisting of eight 128-Gb/s polarization-division-multiplexed QPSK signals and their idlers, by a broadband polarization-insensitive fiber optic parametric amplifier. This novel all-optical signal processing approach to generate WDM-PCTWs enables a 2-fold reduction in the needed optical transmitters as compared to the conventional approach where each idler is generated by a dedicated transmitter. Digital coherent superposition of the twin waves at the receiver enables more than doubled reach in a dispersion-managed transmission link. We further study the impact of polarization-mode dispersion on the performance gain brought by the phase-conjugated twin waves, showing a gain of ~3.8 dB in signal quality factors.
Liu, Xiang; Hu, Hao; Chandrasekhar, S; Jopson, R M; Gnauck, A H; Dinu, M; Xie, C; Winzer, P J
2014-03-24
We experimentally demonstrate the generation of 1.024-Tb/s Nyquist-WDM phase-conjugated vector twin waves (PCTWs), consisting of eight 128-Gb/s polarization-division-multiplexed QPSK signals and their idlers, by a broadband polarization-insensitive fiber optic parametric amplifier. This novel all-optical signal processing approach to generate WDM-PCTWs enables a 2-fold reduction in the needed optical transmitters as compared to the conventional approach where each idler is generated by a dedicated transmitter. Digital coherent superposition of the twin waves at the receiver enables more than doubled reach in a dispersion-managed transmission link. We further study the impact of polarization-mode dispersion on the performance gain brought by the phase-conjugated twin waves, showing a gain of ~3.8 dB in signal quality factors. PMID:24663996
NASA Astrophysics Data System (ADS)
Yamasaki, Tadashi; Houseman, Gregory; Hamling, Ian; Postek, Elek
2010-05-01
We have developed a new parallelized 3-D numerical code, OREGANO_VE, for the solution of the general visco-elastic problem in a rectangular block domain. The mechanical equilibrium equation is solved using the finite element method for a (non-)linear Maxwell visco-elastic rheology. Time-dependent displacement and/or traction boundary conditions can be applied. Matrix assembly is based on a tetrahedral element defined by 4 vertex nodes and 6 nodes located at the midpoints of the edges, and within which displacement is described by a quadratic interpolation function. For evaluating viscoelastic relaxation, an explicit time-stepping algorithm (Zienkiewicz and Cormeau, Int. J. Num. Meth. Eng., 8, 821-845, 1974) is employed. We test the accurate implementation of the OREGANO_VE by comparing numerical and analytic (or semi-analytic half-space) solutions to different problems in a range of applications: (1) equilibration of stress in a constant density layer after gravity is switched on at t = 0 tests the implementation of spatially variable viscosity and non-Newtonian viscosity; (2) displacement of the welded interface between two blocks of differing viscosity tests the implementation of viscosity discontinuities, (3) displacement of the upper surface of a layer under applied normal load tests the implementation of time-dependent surface tractions (4) visco-elastic response to dyke intrusion (compared with the solution in a half-space) tests the implementation of all aspects. In each case, the accuracy of the code is validated subject to use of a sufficiently small time step, providing assurance that the OREGANO_VE code can be applied to a range of visco-elastic relaxation processes in three dimensions, including post-seismic deformation and post-glacial uplift. The OREGANO_VE code includes a capability for representation of prescribed fault slip on an internal fault. The surface displacement associated with large earthquakes can be detected by some geodetic observations
Interfacial Nonlinear Dynamics, Phenomena, and Devices
NASA Astrophysics Data System (ADS)
Zhou, Ping
The dynamics of an optical switch based on a dielectric -clad nonlinear film is presented. Two transition processes of the optical switching, from total internal reflection (TIR) to transmission (Tr) and from Tr to TIR, are investigated in theory as well as experiment. Nonlinear dynamic layered transfer matrix theory is developed to study the transition process from TIR to Tr at a nonlinear thin film due to the optically induced refractive index change. A simple theoretical model based on a dynamic nonlinear Fabry-Perot etalon is given for the analysis of the switching process from Tr to TIR. The quantitative analysis can be used for the design and optimization of an optical sensor protector and other devices. Experiments have been done on both the processes of TIR to Tr and Tr to TIR switching for visible as well as infrared wavelengths. A theory for the design of an optimal anti-reflection coating is proposed in order to aid the design and optimization of a nonlinear interfacial switch. Furthermore, a detailed study of the dynamic optical tunneling through the nonlinear interface indicates that the reflected wave would undergo an additional dynamic nonlinear phase shift which is a novel nonlinear interfacial phenomenon, first revealed by this study.
Miller, G.F.
1986-02-04
This patent describes an overdrive transmission device for use with a motor vehicle. It consists of: a housing; a driving shaft rotatably mounted within the housing; a planetary gear-train; a driven shaft rotatably mounted in the housing and driven by the planetary gear train; and, a device for selectively connecting the planetary gear carrier to the housing or to the driven shaft for rotation; a hydraulically actuated piston adapted to forcibly contact the clutch friction members of the second clutch; a source of working fluid; a pump in fluid flow communication with the source of working fluid; a first valve downstream of the pump and in fluid flow communication with the pump and the hydraulically activated piston.
Nerstad, K.A.; Windish, W.E.
1987-04-21
A planetary transmission is described comprising: an input shaft; a first planetary gear set having a first sun gear driven by the input shaft, a first planet carrier serving as the output, a first ring gear, and first brake means for selectively holding the fist ring gear stationary; a second planetary gear set having a second sun gear driven by the input shaft, a second planet carrier connected for joint rotation to the first ring gear, a second ring gear, and second brake means for selectively holding the second ring gear stationary; a third planetary gear set having a third sun gear connected for joint rotation to the second planet carrier, a third planet carrier connected for joint rotation to the second ring gear, a third ring gear, and third brake means for selectively holding the third ring gear stationary; and clutch means for connecting the third sun gear to the input shaft and providing a direct drive mode of operation.
Nonlinear connectivity by Granger causality.
Marinazzo, Daniele; Liao, Wei; Chen, Huafu; Stramaglia, Sebastiano
2011-09-15
The communication among neuronal populations, reflected by transient synchronous activity, is the mechanism underlying the information processing in the brain. Although it is widely assumed that the interactions among those populations (i.e. functional connectivity) are highly nonlinear, the amount of nonlinear information transmission and its functional roles are not clear. The state of the art to understand the communication between brain systems are dynamic causal modeling (DCM) and Granger causality. While DCM models nonlinear couplings, Granger causality, which constitutes a major tool to reveal effective connectivity, and is widely used to analyze EEG/MEG data as well as fMRI signals, is usually applied in its linear version. In order to capture nonlinear interactions between even short and noisy time series, a few approaches have been proposed. We review them and focus on a recently proposed flexible approach has been recently proposed, consisting in the kernel version of Granger causality. We show the application of the proposed approach on EEG signals and fMRI data.
Extremely nonlinear and switchable SQUID metamaterial
NASA Astrophysics Data System (ADS)
Zhang, Daimeng; Trepanier, Melissa; Mukhanov, Oleg; Jung, Philipp; Butz, Susanne; Ustinov, Alexey; Anlage, Steven
2014-03-01
We present experimental results on a superconducting metamaterial with remarkably nonlinear and switchable properties in the microwave range. The meta-atoms are RF Superconducting Quantum Interference Devices (SQUIDs), a superconducting loop interrupted by a single Josephson Junction. RF SQUIDs are similar to split-ring resonators except that the inductance is tunable due to the nonlinear Josephson inductance. This metamaterial has high tunability via DC magnetic field, temperature and applied RF power. Here we focus on the nonlinearity in our metamaterial due to the Josephson effect. The intermodulation measurements show a highly nonlinear response from the metamaterial. In an RF power dependence experiment we observed hysteretic behavior in transmission which indicates the metamaterial is a nonlinear multi-state system. As a result, we can control the transmission by switching between metastable states via manipulating the applied RF power. We also observe a unique self-induced transparency of meta-atoms in a certain applied RF power range. This extremely nonlinear metamaterial has potential application for next-generation digital RF receiver systems. This work is supported by the NSF-GOALI and OISE programs through grant # ECCS-1158644, and CNAM.
Nonlinear acoustic wave propagation in atmosphere
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1985-01-01
A model problem that simulates an atmospheric acoustic wave propagation situation that is nonlinear is considered. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.
Nonlinear acoustic wave propagation in atmosphere
NASA Technical Reports Server (NTRS)
Hariharan, S. I.
1986-01-01
In this paper a model problem is considered that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.
Transmissivity of a heterogeneous formation
NASA Astrophysics Data System (ADS)
Dykaar, Bruce B.; Kitanidis, Peter K.
1993-04-01
The objective of this paper is to derive the transmissivity of an equivalent homogeneous medium having the same macroscopic flow behavior as the actual heterogeneous formation. We apply generalized Taylor-Ans moment analysis in order to determine the phenomenological coefficient of transmissivity for the case of saturated flow confined in a heterogeneous permeable formation with variable thickness. The generalized Taylor-Aris moment analysis yields a two-step procedure for determining the constant two-dimensional transmissivity tensor from the three-dimensional spatially variable conductivity tensor: solve a flow problem and then perform an integration. For the special case that the conductivity is locally isotropic and the impermeable confining surfaces are parallel, the equations governing transmissivity are discretized using a pseudospectral Fourier-Galerkin scheme. The resultant system of linear algebraic equations is solved efficiently, using preconditioned conjugate gradients, in order Nt In (Nt) operations, where Nt is the number of spatial discretization points. The numerical method is used in several examples to compute the transmissivity of lognormally distributed hydraulic conductivity, and the results are compared with the transmissivity found using the usual depth-averaging approach and another method suggested in the literature. The numerical results show that the averaging volume required to obtain an effective value of transmissivity is about 10 horizontal integral scales. When the flow field has a significant three-dimensional character, the standard method of finding transmissivities by depth averaging can lead to significant errors in the prediction of global scale flows. It is shown that depth averaging consistently overestimates transmissivities. An example illustrates how in the case of tilted strata, anisotropic transmissivities arise and how the degree of transmissivity anisotropy depends on the angle of the dip and the horizontal to
Dispersion and nonlinear effects in OFDM-RoF system
NASA Astrophysics Data System (ADS)
Alhasson, Bader H.; Bloul, Albe M.; Matin, M.
2010-08-01
The radio-over-fiber (RoF) network has been a proven technology to be the best candidate for the wireless-access technology, and the orthogonal frequency division multiplexing (OFDM) technique has been established as the core technology in the physical layer of next generation wireless communication system, as a result OFDM-RoF has drawn attentions worldwide and raised many new research topics recently. At the present time, the trend of information industry is towards mobile, wireless, digital and broadband. The next generation network (NGN) has motivated researchers to study higher-speed wider-band multimedia communication to transmit (voice, data, and all sorts of media such as video) at a higher speed. The NGN would offer services that would necessitate broadband networks with bandwidth higher than 2Mbit/s per radio channel. Many new services emerged, such as Internet Protocol TV (IPTV), High Definition TV (HDTV), mobile multimedia and video stream media. Both speed and capacity have been the key objectives in transmission. In the meantime, the demand for transmission bandwidth increased at a very quick pace. The coming of 4G and 5G era will provide faster data transmission and higher bit rate and bandwidth. Taking advantages of both optical communication and wireless communication, OFDM Radio over Fiber (OFDM-RoF) system is characterized by its high speed, large capacity and high spectral efficiency. However, up to the present there are some problems to be solved, such as dispersion and nonlinearity effects. In this paper we will study the dispersion and nonlinearity effects and their elimination in OFDM-radio-over-fiber system.
Relation of deformed nonlinear algebras with linear ones
NASA Astrophysics Data System (ADS)
Nowicki, A.; Tkachuk, V. M.
2014-01-01
The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator.
Analysis of a non-linear structure by considering two non-linear formulations
NASA Astrophysics Data System (ADS)
Majed, R.; Raynaud, J. L.
2003-03-01
In recent years, modal synthesis methods have been extended for solving non-linear dynamic problems subjected to harmonic excitation. These methods are based on the notion of non-linear or linearized modes and exploited in the case of structures affected by localized non-linearity. Actually, the experimental tests executed on non-linear structures are time consuming, particularly when repeated experimental tests are needed. It is often preferable to consider new non-linear methods with a view to decrease significantly the number of attempts during prototype tests and improving the accuracy of the dynamic behaviour. This article describes two fundamental non-linear formulations based on two different strategies. The first formulation exploits the eigensolutions of the associated linear system and the dynamics characteristics of each localized non-linearity. The second formulation is based on the exploitation of the linearized eigensolutions obtained using an iterative process. This article contains a numerical and an experimental study which examines the non-linear behaviour of the structure affected by localized non-linearities. The study is intended to validate the numerical algorithm and to evaluate the problems arising from the introduction of non-linearities. The complex responses are evaluated using the iterative Newton-Raphson method and for a series of discrete frequencies. The theory has been applied to a bi-dimensional structure and consists of evaluating the harmonic responses obtained using the proposed formulations by comparing measured and calculated transfer functions.
Nonlinear Single Spin Spectrum Analyzer
NASA Astrophysics Data System (ADS)
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2014-03-01
Qubits have been used as linear spectrum analyzers of their environments, through the use of decoherence spectroscopy. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013). Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: NIST, Boulder, CO.
On a Nonlinear Model in Adiabatic Evolutions
NASA Astrophysics Data System (ADS)
Sun, Jie; Lu, Song-Feng
2016-08-01
In this paper, we study a kind of nonlinear model of adiabatic evolution in quantum search problem. As will be seen here, for this problem, there always exists a possibility that this nonlinear model can successfully solve the problem, while the linear model can not. Also in the same setting, when the overlap between the initial state and the final stare is sufficiently large, a simple linear adiabatic evolution can achieve O(1) time efficiency, but infinite time complexity for the nonlinear model of adiabatic evolution is needed. This tells us, it is not always a wise choice to use nonlinear interpolations in adiabatic algorithms. Sometimes, simple linear adiabatic evolutions may be sufficient for using. Supported by the National Natural Science Foundation of China under Grant Nos. 61402188 and 61173050. The first author also gratefully acknowledges the support from the China Postdoctoral Science Foundation under Grant No. 2014M552041
Supratransmission in a disordered nonlinear periodic structure
NASA Astrophysics Data System (ADS)
Yousefzadeh, B.; Phani, A. Srikantha
2016-10-01
We study the interaction among dispersion, nonlinearity, and disorder effects in the context of wave transmission through a discrete periodic structure, subjected to continuous harmonic excitation in its stop band. We consider a damped nonlinear periodic structure of finite length with disorder. Disorder is introduced throughout the structure by small changes in the stiffness parameters drawn from a uniform statistical distribution. Dispersion effects forbid wave transmission within the stop band of the linear periodic structure. However, nonlinearity leads to supratransmission phenomenon, by which enhanced wave transmission occurs within the stop band of the periodic structure when forced at an amplitude exceeding a certain threshold. The frequency components of the transmitted waves lie within the pass band of the linear structure, where disorder is known to cause Anderson localization. There is therefore a competition between dispersion, nonlinearity, and disorder in the context of supratransmission. We show that supratransmission persists in the presence of disorder. The influence of disorder decreases in general as the forcing frequency moves away from the pass band edge, reminiscent of dispersion effects subsuming disorder effects in linear periodic structures. We compute the dependence of the supratransmission force threshold on nonlinearity and strength of coupling between units. We observe that nonlinear forces are confined to the driven unit for weakly coupled systems. This observation, together with the truncation of higher-order nonlinear terms, permits us to develop closed-form expressions for the supratransmission force threshold. In sum, in the frequency range studied here, disorder does not influence the supratransmission force threshold in the ensemble-average sense, but it does reduce the average transmitted wave energy.
Quenching phenomena for second-order nonlinear parabolic equation with nonlinear source
NASA Astrophysics Data System (ADS)
Mingyou, Zhang; Huichao, Xu; Runzhang, Xu
2012-09-01
In this paper, we investigate the quenching phenomena of the Cauchy problem for the second-order nonlinear parabolic equation on unbounded domain. It is shown that the solution quenches in finite time under some assumptions on the exponents and the initial data. Our main tools are comparison principle and maximum principle. We extend the result to the case of more generally nonlinear absorption.
Nonlinear time reversal of classical waves: experiment and model.
Frazier, Matthew; Taddese, Biniyam; Xiao, Bo; Antonsen, Thomas; Ott, Edward; Anlage, Steven M
2013-12-01
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
Frequency domain nonlinear optics
NASA Astrophysics Data System (ADS)
Legare, Francois
2016-05-01
The universal dilemma of gain narrowing occurring in fs amplifiers prevents ultra-high power lasers from delivering few-cycle pulses. This problem is overcome by a new amplification concept: Frequency domain Optical Parametric Amplification - FOPA. It enables simultaneous up-scaling of peak power and amplified spectral bandwidth and can be performed at any wavelength range of conventional amplification schemes, however, with the capability to amplify single cycles of light. The key idea for amplification of octave-spanning spectra without loss of spectral bandwidth is to amplify the broad spectrum ``slice by slice'' in the frequency domain, i.e. in the Fourier plane of a 4f-setup. The striking advantages of this scheme, are its capability to amplify (more than) one octave of bandwidth without shorting the corresponding pulse duration. This is because ultrabroadband phase matching is not defined by the properties of the nonlinear crystal employed but the number of crystals employed. In the same manner, to increase the output energy one simply has to increase the spectral extension in the Fourier plane and to add one more crystal. Thus, increasing pulse energy and shortening its duration accompany each other. A proof of principle experiment was carried out at ALLS on the sub-two cycle IR beam line and yielded record breaking performance in the field of few-cycle IR lasers. 100 μJ two-cycle pulses from a hollow core fibre compression setup were amplified to 1.43mJ without distorting spatial or temporal properties. Pulse duration at the input of FOPA and after FOPA remains the same. Recently, we have started upgrading this system to be pumped by 250 mJ to reach 40 mJ two-cycle IR few-cycle pulses and latest results will be presented at the conference. Furthermore, the extension of the concept of FOPA to other nonlinear optical processes will be discussed. Frequency domain nonlinear optics.
Orshansky, Jr. deceased, Elias; Weseloh, William E.
1978-01-01
A power transmission having three planetary assemblies, each having its own carrier and its own planet, sun, and ring gears. A speed-varying module is connected in driving relation to the input shaft and in driving relationship to the three sun gears, all of which are connected together. The speed-varying means may comprise a pair of hydraulic units hydraulically interconnected so that one serves as a pump while the other serves as a motor and vice versa, one of the units having a variable stroke and being connected in driving relation to the input shaft, the other unit, which may have a fixed stroke, being connected in driving relation to the sun gears. The input shaft also drives the carrier of the third planetary assembly. A brake grounds the first carrier in the first range and in reverse and causes drive to be delivered to the output through the first ring gear in a hydrostatic mode. The carrier of the third planetary assembly drives the ring gear of the second planetary assembly, and a first clutching means connects the second carrier with the output in a second range, the brake for grounding the first carrier then being released. A second clutching means enables the third ring gear to drive the output shaft in a third range.
Soliton production with nonlinear homogeneous lines
Elizondo-Decanini, Juan M.; Coleman, Phillip D.; Moorman, Matthew W.; Petney, Sharon Joy Victor; Dudley, Evan C.; Youngman, Kevin; Penner, Tim Dwight; Fang, Lu; Myers, Katherine M.
2015-11-24
Low- and high-voltage Soliton waves were produced and used to demonstrate collision and compression using diode-based nonlinear transmission lines. Experiments demonstrate soliton addition and compression using homogeneous nonlinear lines. We built the nonlinear lines using commercially available diodes. These diodes are chosen after their capacitance versus voltage dependence is used in a model and the line design characteristics are calculated and simulated. Nonlinear ceramic capacitors are then used to demonstrate high-voltage pulse amplification and compression. The line is designed such that a simple capacitor discharge, input signal, develops soliton trains in as few as 12 stages. We also demonstrated outputmore » voltages in excess of 40 kV using Y5V-based commercial capacitors. The results show some key features that determine efficient production of trains of solitons in the kilovolt range.« less
Soliton production with nonlinear homogeneous lines
Elizondo-Decanini, Juan M.; Coleman, Phillip D.; Moorman, Matthew W.; Petney, Sharon Joy Victor; Dudley, Evan C.; Youngman, Kevin; Penner, Tim Dwight; Fang, Lu; Myers, Katherine M.
2015-11-24
Low- and high-voltage Soliton waves were produced and used to demonstrate collision and compression using diode-based nonlinear transmission lines. Experiments demonstrate soliton addition and compression using homogeneous nonlinear lines. We built the nonlinear lines using commercially available diodes. These diodes are chosen after their capacitance versus voltage dependence is used in a model and the line design characteristics are calculated and simulated. Nonlinear ceramic capacitors are then used to demonstrate high-voltage pulse amplification and compression. The line is designed such that a simple capacitor discharge, input signal, develops soliton trains in as few as 12 stages. We also demonstrated output voltages in excess of 40 kV using Y5V-based commercial capacitors. The results show some key features that determine efficient production of trains of solitons in the kilovolt range.
Applying optimization software libraries to engineering problems
NASA Technical Reports Server (NTRS)
Healy, M. J.
1984-01-01
Nonlinear programming, preliminary design problems, performance simulation problems trajectory optimization, flight computer optimization, and linear least squares problems are among the topics covered. The nonlinear programming applications encountered in a large aerospace company are a real challenge to those who provide mathematical software libraries and consultation services. Typical applications include preliminary design studies, data fitting and filtering, jet engine simulations, control system analysis, and trajectory optimization and optimal control. Problem sizes range from single-variable unconstrained minimization to constrained problems with highly nonlinear functions and hundreds of variables. Most of the applications can be posed as nonlinearly constrained minimization problems. Highly complex optimization problems with many variables were formulated in the early days of computing. At the time, many problems had to be reformulated or bypassed entirely, and solution methods often relied on problem-specific strategies. Problems with more than ten variables usually went unsolved.
Regional Transmission Projects: Finding Solutions
The Keystone Center
2005-06-15
The Keystone Center convened and facilitated a year-long Dialogue on "Regional Transmission Projects: Finding Solutions" to develop recommendations that will help address the difficult and contentious issues related to expansions of regional electric transmission systems that are needed for reliable and economic transmission of power within and across regions. This effort brought together a cross-section of affected stakeholders and thought leaders to address the problem with the collective wisdom of their experience and interests. Transmission owners sat at the table with consumer advocates and environmental organizations. Representatives from regional transmission organizations exchanged ideas with state and federal regulators. Generation developers explored common interests with public power suppliers. Together, the Dialogue participants developed consensus solutions about how to begin unraveling some of the more intractable issues surrounding identification of need, allocation of costs, and reaching consensus on siting issues that can frustrate the development of regional transmission infrastructure. The recommendations fall into three broad categories: 1. Recommendations on appropriate institutional arrangements and processes for achieving regional consensus on the need for new or expanded transmission infrastructure 2. Recommendations on the process for siting of transmission lines 3. Recommendations on the tools needed to support regional planning, cost allocation, and siting efforts. List of Dialogue participants: List of Dialogue Participants: American Electric Power American Transmission Company American Wind Energy Association California ISO Calpine Corporation Cinergy Edison Electric Institute Environmental Defense Federal Energy Regulatory Commission Great River Energy International Transmission Company ISO-New England Iowa Public Utility Board Kanner & Associates Midwest ISO National Association of Regulatory Utility Commissioners National Association
T. MILONNI; G. CSANAK; ET AL
1999-07-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). The project objectives were to explore theoretically various aspects of nonlinear atom optics effects in cold-atom waves and traps. During the project a major development occurred the observation, by as many as a dozen experimental groups, of Bose-Einstein condensation (BEC) in cold-atom traps. This stimulated us to focus our attention on those aspects of nonlinear atom optics relating to BEC, in addition to continuing our work on a nonequilibrium formalism for dealing with the interaction of an electromagnetic field with multi-level atomic systems, allowing for macroscopic coherence effects such as BEC. Studies of several problems in BEC physics have been completed or are near completion, including the suggested use of external electric fields to modify the nature of the interatomic interaction in cold-atom traps; properties of two-phase condensates; and molecular loss processes associated with BEC experiments involving a so-called Feshbach resonance.
Multilevel algorithms for nonlinear optimization
NASA Technical Reports Server (NTRS)
Alexandrov, Natalia; Dennis, J. E., Jr.
1994-01-01
Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.
Ordo, J.P.; Raszkowski, J.A.; Klemen, D.
1991-04-23
This patent describes a transmission. It comprises a housing having first and second end covers; an input shaft rotatably mounted in the first end cover; an output shaft rotatably supported on the input shaft and in the second end cover; first and second countershafts rotatably supported in the end covers for rotation on respective axis parallel with the input shaft and the output shaft; a first head gear continuously rotatable with the input shaft; second and third head gears meshing with the first head gear and continuously rotatable with the first and second countershafts respectively; ratio gears rotatably supported on each of the countershafts including a first ratio gear on the first countershaft and a second ratio gear on the second countershaft; reverse gear means including a first ratio gear on the first countershaft and a second ratio gear on the second countershaft; reverse gear means including a first member rotatable with the first ratio gear means including a first member rotatable with the first ratio gear and a second member rotatably supported on the second countershaft; synchronizer clutch means selectively and alternatively connectible with the second ratio gear and the second member of the reverse gear means; output gear means drivingly connected with the output shaft and including a first ratio output gear meshing with the second ratio gear; first selectively engageable friction clutch means for connecting the first ratio gear with the first countershaft for completing a low forward drive ratio between the input and output shafts; and second selectively engageable friction clutch means for selectively connecting the synchronizer clutch means to the second countershaft and cooperating therewith to selectively alternatively complete a reverse drive ratio between the input shaft and the output shaft and another forward drive ratio between the input and output shafts.
Miura, M.; Inuzuka, T.
1986-08-26
1. An automatic transmission with four forward speeds and one reverse position, is described which consists of: an input shaft; an output member; first and second planetary gear sets each having a sun gear, a ring gear and a carrier supporting a pinion in mesh with the sun gear and ring gear; the carrier of the first gear set, the ring gear of the second gear set and the output member all being connected; the ring gear of the first gear set connected to the carrier of the second gear set; a first clutch means for selectively connecting the input shaft to the sun gear of the first gear set, including friction elements, a piston selectively engaging the friction elements and a fluid servo in which hydraulic fluid is selectively supplied to the piston; a second clutch means for selectively connecting the input shaft to the sun gear of the second gear set a third clutch means for selectively connecting the input shaft to the carrier of the second gear set including friction elements, a piston selectively engaging the friction elements and a fluid servo in which hydraulic fluid is selectively supplied to the piston; a first drive-establishing means for selectively preventing rotation of the ring gear of the first gear set and the carrier of the second gear set in only one direction and, alternatively, in any direction; a second drive-establishing means for selectively preventing rotation of the sun gear of the second gear set; and a drum being open to the first planetary gear set, with a cylindrical intermediate wall, an inner peripheral wall and outer peripheral wall and forming the hydraulic servos of the first and third clutch means between the intermediate wall and the inner peripheral wall and between the intermediate wall and the outer peripheral wall respectively.
Long-distance optical transmission
Saito, Shigeru
1995-12-31
Optical amplifiers, especially, erbium-doped fiber amplifiers, enable optical signals to be transmitted over long distances: several thousands of kilometers or more with the in-line amplifier system configuration. The state of the art, as well as the basic ideas under-lying such long distance transmission, is discussed. Newly discovered critical issues, such as the nonlinear and polarization characteristics of optical fibers, are also discussed with their countermeasures. Shigeru Saito received the B.S., M.S., and Dr. Eng. degrees in electrical communication engineering from Tohoku University, Sendai, Japan, in 1974, 1976 and 1979, respectively. In 1979 he joined Nippon Telegraph and Telephone Public Corporation, Tokyo, Japan, and commenced researching coherent optical fiber transmission systems. In 1985 he was a Guest Professor at the Technical University of Denmark, Lyngby, Denmark. He is currently a Senior Research Engineer, NTT Optical Network Systems Laboratories, Kanagawa, Japan, where is engaged in the research of optical in-line amplifier systems.
Energy minimization versus pseudo force technique for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Kamat, M. P.; Hayduk, R. J.
1980-01-01
The effectiveness of using minimization techniques for the solution of nonlinear structural analysis problems is discussed and demonstrated by comparison with the conventional pseudo force technique. The comparison involves nonlinear problems with a relatively few degrees of freedom. A survey of the state-of-the-art of algorithms for unconstrained minimization reveals that extension of the technique to large scale nonlinear systems is possible.
NASA Astrophysics Data System (ADS)
Lauterborn, Werner; Kurz, Thomas; Akhatov, Iskander
At high sound intensities or long propagation distances at
Nonlinear functional approximation with networks using adaptive neurons
NASA Technical Reports Server (NTRS)
Tawel, Raoul
1992-01-01
A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.
Nonlinear positron acoustic solitary waves
Tribeche, Mouloud; Aoutou, Kamel; Younsi, Smain; Amour, Rabia
2009-07-15
The problem of nonlinear positron acoustic solitary waves involving the dynamics of mobile cold positrons is addressed. A theoretical work is presented to show their existence and possible realization in a simple four-component plasma model. The results should be useful for the understanding of the localized structures that may occur in space and laboratory plasmas as new sources of cold positrons are now well developed.
Nonlinear dynamics aspects of modern storage rings
Helleman, R.H.G.; Kheifets, S.A.
1986-01-01
It is argued that the nonlinearity of storage rings becomes an essential problem as the design parameters of each new machine are pushed further and further. Yet the familiar methods of classical mechanics do not allow determination of single particle orbits over reasonable lengths of time. It is also argued that the single particle dynamics of a storage ring is possibly one of the cleanest and simplest nonlinear dynamical systems available with very few degrees of freedom. Hence, reasons are found for accelerator physicists to be interested in nonlinear dynamics and for researchers in nonlinear dynamics to be interested in modern storage rings. The more familiar methods of treating nonlinear systems routinely used in acclerator theory are discussed, pointing out some of their limitations and pitfalls. 39 refs., 1 fig. (LEW)
Nonlinear Modeling by Assembling Piecewise Linear Models
NASA Technical Reports Server (NTRS)
Yao, Weigang; Liou, Meng-Sing
2013-01-01
To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.
User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures
NASA Technical Reports Server (NTRS)
Whitcomb, J. D.; Dattaguru, B.
1984-01-01
GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.
Nonlinear Hysteretic Torsional Waves
NASA Astrophysics Data System (ADS)
Cabaret, J.; Béquin, P.; Theocharis, G.; Andreev, V.; Gusev, V. E.; Tournat, V.
2015-07-01
We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found to be nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other types of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short-term memory, as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters.
Tomlin, R.
1990-01-27
A nonlinear oscillator design was imported from Cornell modified, and built for the purpose of simulating the chaotic states of a forced pendulum. Similar circuits have been investigated in the recent nonlinear explosion.
... Address What's this? Submit What's this? Submit Button Zika and Sexual Transmission Language: English EspaÃ±ol PortuguÃªs ... Healthcare Providers: Sexual Transmission of Zika Basics of Zika Virus and Sex Transmission Zika can be passed ...
Optimal singular control for nonlinear semistabilisation
NASA Astrophysics Data System (ADS)
L'Afflitto, Andrea; Haddad, Wassim M.
2016-06-01
The singular optimal control problem for asymptotic stabilisation has been extensively studied in the literature. In this paper, the optimal singular control problem is extended to address a weaker version of closed-loop stability, namely, semistability, which is of paramount importance for consensus control of network dynamical systems. Three approaches are presented to address the nonlinear semistable singular control problem. Namely, a singular perturbation method is presented to construct a state-feedback singular controller that guarantees closed-loop semistability for nonlinear systems. In this approach, we show that for a non-negative cost-to-go function the minimum cost of a nonlinear semistabilising singular controller is lower than the minimum cost of a singular controller that guarantees asymptotic stability of the closed-loop system. In the second approach, we solve the nonlinear semistable singular control problem by using the cost-to-go function to cancel the singularities in the corresponding Hamilton-Jacobi-Bellman equation. For this case, we show that the minimum value of the singular performance measure is zero. Finally, we provide a framework based on the concepts of state-feedback linearisation and feedback equivalence to solve the singular control problem for semistabilisation of nonlinear dynamical systems. For this approach, we also show that the minimum value of the singular performance measure is zero. Three numerical examples are presented to demonstrate the efficacy of the proposed singular semistabilisation frameworks.
Nonlinear Krylov acceleration of reacting flow codes
Kumar, S.; Rawat, R.; Smith, P.; Pernice, M.
1996-12-31
We are working on computational simulations of three-dimensional reactive flows in applications encompassing a broad range of chemical engineering problems. Examples of such processes are coal (pulverized and fluidized bed) and gas combustion, petroleum processing (cracking), and metallurgical operations such as smelting. These simulations involve an interplay of various physical and chemical factors such as fluid dynamics with turbulence, convective and radiative heat transfer, multiphase effects such as fluid-particle and particle-particle interactions, and chemical reaction. The governing equations resulting from modeling these processes are highly nonlinear and strongly coupled, thereby rendering their solution by traditional iterative methods (such as nonlinear line Gauss-Seidel methods) very difficult and sometimes impossible. Hence we are exploring the use of nonlinear Krylov techniques (such as CMRES and Bi-CGSTAB) to accelerate and stabilize the existing solver. This strategy allows us to take advantage of the problem-definition capabilities of the existing solver. The overall approach amounts to using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) method and its variants as nonlinear preconditioners for the nonlinear Krylov method. We have also adapted a backtracking approach for inexact Newton methods to damp the Newton step in the nonlinear Krylov method. This will be a report on work in progress. Preliminary results with nonlinear GMRES have been very encouraging: in many cases the number of line Gauss-Seidel sweeps has been reduced by about a factor of 5, and increased robustness of the underlying solver has also been observed.
Nonlinear Single-Spin Spectrum Analyzer
NASA Astrophysics Data System (ADS)
Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee
2013-03-01
Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.
Stochastic resonance for nonlinear sensors with saturation.
Rousseau, David; Rojas Varela, Julio; Chapeau-Blondeau, François
2003-02-01
We analyze the transmission of a noisy signal by sensor devices which are linear for small inputs and saturate at large inputs. Large information-carrying signals are thus distorted in their transmission. We demonstrate conditions where addition of noise to such large input signals can reduce the distortion that they undergo in the transmission. This is established for periodic, as well as aperiodic, and random information-carrying signals. Various measures characterizing the transmission, such as signal-to-noise ratio, input-output cross correlation, and mutual information, are shown improvable by addition of noise. These results constitute another instance of the nonlinear phenomenon of stochastic resonance where addition of noise enhances the signal. PMID:12636648
Stochastic resonance for nonlinear sensors with saturation
NASA Astrophysics Data System (ADS)
Rousseau, David; Rojas Varela, Julio; Chapeau-Blondeau, François
2003-02-01
We analyze the transmission of a noisy signal by sensor devices which are linear for small inputs and saturate at large inputs. Large information-carrying signals are thus distorted in their transmission. We demonstrate conditions where addition of noise to such large input signals can reduce the distortion that they undergo in the transmission. This is established for periodic, as well as aperiodic, and random information-carrying signals. Various measures characterizing the transmission, such as signal-to-noise ratio, input-output cross correlation, and mutual information, are shown improvable by addition of noise. These results constitute another instance of the nonlinear phenomenon of stochastic resonance where addition of noise enhances the signal.
Radio-relay and satellite transmission systems
NASA Astrophysics Data System (ADS)
Nemirovskii, A. S.
The present work is a handbook on the design and analysis of radio-relay, tropospheric, and satellite transmission systems. Particular consideration is given to the propagation of decimeter and centimeter waves; antenna and feed devices for relay and satellite systems; noise and distortions; the signal fading problem; EMC; and the optimization of the transmission systems.
Nonlinear Transport and Noise Properties of Acoustic Phonons
NASA Astrophysics Data System (ADS)
Walczak, Kamil
We examine heat transport carried by acoustic phonons in molecular junctions composed of organic molecules coupled to two thermal baths of different temperatures. The phononic heat flux and its dynamical noise properties are analyzed within the scattering (Landauer) formalism with transmission probability function for acoustic phonons calculated within the method of atomistic Green's functions (AGF technique). The perturbative computational scheme is used to determine nonlinear corrections to phononic heat flux and its noise power spectral density with up to the second order terms with respect to temperature difference. Our results show the limited applicability of ballistic Fourier's law and fluctuation-dissipation theorem to heat transport in quantum systems. We also derive several noise-signal relations applicable to nanoscale heat flow carried by phonons, but valid for electrons as well. We also discuss the extension of the perturbative transport theory to higher order terms in order to address a huge variety of problems related to nonlinear thermal effects which may occur at nanoscale and at strongly non-equilibrium conditions with high-intensity heat fluxes. This work was supported by Pace University Start-up Grant.
Inverting Monotonic Nonlinearities by Entropy Maximization
López-de-Ipiña Pena, Karmele; Caiafa, Cesar F.
2016-01-01
This paper proposes a new method for blind inversion of a monotonic nonlinear map applied to a sum of random variables. Such kinds of mixtures of random variables are found in source separation and Wiener system inversion problems, for example. The importance of our proposed method is based on the fact that it permits to decouple the estimation of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source separation matrix or deconvolution filter), which can be solved by applying any convenient linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes the idea of Gaussianization of the observation by maximizing its entropy instead. We developed two versions of our algorithm based either in a polynomial or a neural network parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear function and the probability distribution that gives a guarantee for the MaxEnt method to succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is compared with existing algorithms for blind approximation of nonlinear maps. Experiments show that MaxEnt is able to successfully compensate monotonic distortions outperforming other methods in terms of the obtained Signal to Noise Ratio in many important cases, for example when the number of variables in a mixture is small. Besides its ability for compensating nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results. PMID:27780261
Nonlinear large-scale optimization with WORHP
NASA Astrophysics Data System (ADS)
Nikolayzik, Tim; Büskens, Christof; Gerdts, Matthias
Nonlinear optimization has grown to a key technology in many areas of aerospace industry, e.g. satellite control, shape-optimization, aerodynamamics, trajectory planning, reentry prob-lems, interplanetary flights. One of the most extensive areas is the optimization of trajectories for aerospace applications. These problems typically are discretized optimal control problems, which leads to large sparse nonlinear optimization problems. In the end all these different problems from different areas can be described in the general formulation as a nonlinear opti-mization problem. WORHP is designed to solve nonlinear optimization problems with more then one million variables and one million constraints. WORHP uses a lot of different advanced techniques, e.g. reverse communication, to organize the optimization process as efficient and controllable by the user as possible. The solver has nine different interfaces, e.g. to MAT-LAB/SIMULINK and AMPL. Tests of WORHP had shown that WORHP is a very robust and promising solver. Several examples from space applications will be presented.
Survey of Transmission Cost Allocation Methodologies for Regional Transmission Organizations
Fink, S.; Porter, K.; Mudd, C.; Rogers, J.
2011-02-01
The report presents transmission cost allocation methodologies for reliability transmission projects, generation interconnection, and economic transmission projects for all Regional Transmission Organizations.
Egorov, Yurii V
2013-04-30
We consider the classical problem on the tallest column which was posed by Euler in 1757. Bernoulli-Euler theory serves today as the basis for the design of high buildings. This problem is reduced to the problem of finding the potential for the Sturm-Liouville equation corresponding to the maximum of the first eigenvalue. The problem has been studied by many mathematicians but we give the first rigorous proof of the existence and uniqueness of the optimal column and we give new formulae which let us find it. Our method is based on a new approach consisting in the study of critical points of a related nonlinear functional. Bibliography: 6 titles.
Development of solution techniques for nonlinear structural analysis
NASA Technical Reports Server (NTRS)
Vos, R. G.; Andrews, J. S.
1974-01-01
Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.
Nonlinear analysis of drought dynamics
NASA Astrophysics Data System (ADS)
Ma, M.
2015-12-01
Drought is an extreme natural hazard and becomes a severe problem in the world. It arises as a result of interactions between climate input and human activity, displaying the nonlinearity and complexity. Nonlinear time series analyses open a way to study the underlying dynamic characteristics of drought, and then provide the forward knowledge to understanding the physical mechanism of drought event. The rationale behind this idea is that information about the representation of nonlinear properties could be used as an additional quality indicator. To that end, the correlation dimension method, a powerful nonlinear time series analysis method based on the chaos theory, has been suggested to assess the intrinsic dimensionality or degree of freedom of time series according to Takens (1981). It can provide an assessment of the dominant processes that is required to map the observed dynamics. In this study, daily discharge and hourly groundwater level data of 63 catchments in Germany and China were investigated with correlation dimension method. The results indicated that the correlation dimension values of studied discharge exhibited none clear spatial patterns, but showed significant correlations with the spatial heterogeneity within the catchments. In contrast, the correlation dimension values of groundwater level displayed spatial patterns due to the different aquifer conditions (confined or unconfined). High correlation dimension values indicate partly confined conditions. In addition, Hurst analysis was involved to qualify the persistence of drought. It seems that drought mechanisms can be learnt from the data themselves in an inverse manner.
Nonlinear programming with feedforward neural networks.
Reifman, J.
1999-06-02
We provide a practical and effective method for solving constrained optimization problems by successively training a multilayer feedforward neural network in a coupled neural-network/objective-function representation. Nonlinear programming problems are easily mapped into this representation which has a simpler and more transparent method of solution than optimization performed with Hopfield-like networks and poses very mild requirements on the functions appearing in the problem. Simulation results are illustrated and compared with an off-the-shelf optimization tool.
Nonlinearities in vegetation functioning
NASA Astrophysics Data System (ADS)
Ceballos-Núñez, Verónika; Müller, Markus; Metzler, Holger; Sierra, Carlos
2016-04-01
Given the current drastic changes in climate and atmospheric CO2 concentrations, and the role of vegetation in the global carbon cycle, there is increasing attention to the carbon allocation component in biosphere terrestrial models. Improving the representation of C allocation in models could be the key to having better predictions of the fate of C once it enters the vegetation and is partitioned to C pools of different residence times. C allocation has often been modeled using systems of ordinary differential equations, and it has been hypothesized that most models can be generalized with a specific form of a linear dynamical system. However, several studies have highlighted discrepancies between empirical observations and model predictions, attributing these differences to problems with model structure. Although efforts have been made to compare different models, the outcome of these qualitative assessments has been a conceptual categorization of them. In this contribution, we introduce a new effort to identify the main properties of groups of models by studying their mathematical structure. For this purpose, we performed a literature research of the relevant models of carbon allocation in vegetation and developed a database with their representation in symbolic mathematics. We used the Python package SymPy for symbolic mathematics as a common language and manipulated the models to calculate their Jacobian matrix at fixed points and their eigenvalues, among other mathematical analyses. Our preliminary results show a tendency of inverse proportionality between model complexity and size of time/space scale; complex interactions between the variables controlling carbon allocation in vegetation tend to operate at shorter time/space scales, and vice-versa. Most importantly, we found that although the linear structure is common, other structures with non-linearities have been also proposed. We, therefore, propose a new General Model that can accommodate these
Nonlinear acceleration of SN transport calculations
Fichtl, Erin D; Warsa, James S; Calef, Matthew T
2010-12-20
The use of nonlinear iterative methods, Jacobian-Free Newton-Krylov (JFNK) in particular, for solving eigenvalue problems in transport applications has recently become an active subject of research. While JFNK has been shown to be effective for k-eigenvalue problems, there are a number of input parameters that impact computational efficiency, making it difficult to implement efficiently in a production code using a single set of default parameters. We show that different selections for the forcing parameter in particular can lead to large variations in the amount of computational work for a given problem. In contrast, we present a nonlinear subspace method that sits outside and effectively accelerates nonlinear iterations of a given form and requires only a single input parameter, the subspace size. It is shown to consistently and significantly reduce the amount of computational work when applied to fixed-point iteration, and this combination of methods is shown to be more efficient than JFNK for our application.
Randomized discrepancy bounded local search for transmission expansion planning
Bent, Russell W; Daniel, William B
2010-11-23
In recent years the transmission network expansion planning problem (TNEP) has become increasingly complex. As the TNEP is a non-linear and non-convex optimization problem, researchers have traditionally focused on approximate models of power flows to solve the TNEP. Existing approaches are often tightly coupled to the approximation choice. Until recently these approximations have produced results that are straight-forward to adapt to the more complex (real) problem. However, the power grid is evolving towards a state where the adaptations are no longer easy (e.g. large amounts of limited control, renewable generation) and necessitates new approaches. Recent work on deterministic Discrepancy Bounded Local Search (DBLS) has shown it to be quite effective in addressing this question. DBLS encapsulates the complexity of power flow modeling in a black box that may be queried for information about the quality of proposed expansions. In this paper, we propose a randomization strategy that builds on DBLS and dramatically increases the computational efficiency of the algorithm.
Nature limits filarial transmission
Chandra, Goutam
2008-01-01
Lymphatic filariasis, caused by Wuchereria bancrofti, Brugia malayi and B. timori is a public health problem of considerable magnitude of the tropics and subtropics. Presently 1.3 billion people are at risk of lymphatic filariasis (LF) infection and about 120 million people are affected in 83 countries. In this context it is worth mentioning that 'nature' itself limits filarial transmission to a great extent in a number of ways such as by reducing vector populations, parasitic load and many other bearings. Possibilities to utilize these bearings of natural control of filariasis should be searched and if manipulations on nature, like indiscriminate urbanization and deforestation, creating sites favourable for the breeding of filarial vectors and unsanitary conditions, water pollution with organic matters etc., are reduced below the threshold level, we will be highly benefited. Understandings of the factors related to natural phenomena of control of filariasis narrated in this article may help to adopt effective control strategies. PMID:18500974
Instantaneous, stepped-frequency, nonlinear radar
NASA Astrophysics Data System (ADS)
Ranney, Kenneth; Gallagher, Kyle; Martone, Anthony; Mazzaro, Gregory; Sherbondy, Kelly; Narayanan, Ram
2015-05-01
Researchers have recently developed radar systems capable of exploiting non-linear target responses to precisely locate targets in range. These systems typically achieve the bandwidth necessary for range resolution through transmission of either a stepped-frequency or chirped waveform. The second harmonic of the reflected waveform is then analyzed to isolate the non-linear target response. In other experiments, researchers have identified certain targets through the inter-modulation products they produce in response to a multi-tone stimulus. These experiments, however, do not exploit the phase information available in the inter-modulation products. We present a method for exploiting both the magnitude and phase information available in the inter-modulation products to create an "instantaneous" stepped frequency, non-linear target response. The new approach enables us to both maintain the unambiguous range dictated by the fundamental, multi-tone separation and obtain the entire target signature from a single transmitted waveform.
Magnetoplasmonic RF mixing and nonlinear frequency generation
NASA Astrophysics Data System (ADS)
Firby, C. J.; Elezzabi, A. Y.
2016-07-01
We present the design of a magnetoplasmonic Mach-Zehnder interferometer (MZI) modulator facilitating radio-frequency (RF) mixing and nonlinear frequency generation. This is achieved by forming the MZI arms from long-range dielectric-loaded plasmonic waveguides containing bismuth-substituted yttrium iron garnet (Bi:YIG). The magnetization of the Bi:YIG can be driven in the nonlinear regime by RF magnetic fields produced around adjacent transmission lines. Correspondingly, the nonlinear temporal dynamics of the transverse magnetization component are mapped onto the nonreciprocal phase shift in the MZI arms, and onto the output optical intensity signal. We show that this tunable mechanism can generate harmonics, frequency splitting, and frequency down-conversion with a single RF excitation, as well as RF mixing when driven by two RF signals. This magnetoplasmonic component can reduce the number of electrical sources required to generate distinct optical modulation frequencies and is anticipated to satisfy important applications in integrated optics.
Blow-up of the solution of a nonlinear system of equations with positive energy
NASA Astrophysics Data System (ADS)
Korpusov, M. O.
2012-06-01
We consider the Dirichlet problem for a nonlinear system of equations, continuing our study of nonlinear hyperbolic equations and systems of equations with an arbitrarily large positive energy. We use a modified Levine method to prove the blow-up.
Code System for Solving Nonlinear Systems of Equations via the Gauss-Newton Method.
1981-08-31
Version 00 REGN solves nonlinear systems of numerical equations in difficult cases: high nonlinearity, poor initial approximations, a large number of unknowns, ill condition or degeneracy of a problem.
Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality
NASA Technical Reports Server (NTRS)
Acikmese, Ahmet Behcet; Martin, Corless
2004-01-01
We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.
Noise in Nonlinear Dynamical Systems
NASA Astrophysics Data System (ADS)
Moss, Frank; McClintock, P. V. E.
2009-08-01
List of contributors; Preface; Introduction to volume three; 1. The effects of coloured quadratic noise on a turbulent transition in liquid He II J. T. Tough; 2. Electrohydrodynamic instability of nematic liquid crystals: growth process and influence of noise S. Kai; 3. Suppression of electrohydrodynamic instabilities by external noise Helmut R. Brand; 4. Coloured noise in dye laser fluctuations R. Roy, A. W. Yu and S. Zhu; 5. Noisy dynamics in optically bistable systems E. Arimondo, D. Hennequin and P. Glorieux; 6. Use of an electronic model as a guideline in experiments on transient optical bistability W. Lange; 7. Computer experiments in nonlinear stochastic physics Riccardo Mannella; 8. Analogue simulations of stochastic processes by means of minimum component electronic devices Leone Fronzoni; 9. Analogue techniques for the study of problems in stochastic nonlinear dynamics P. V. E. McClintock and Frank Moss; Index.
Essays on electricity transmission investment and financial transmission rights
NASA Astrophysics Data System (ADS)
Shang, Wenzhuo
The U.S. electric power industry has been going through fundamental restructuring and realignment since the 1990's. Many issues and problems have emerged during the transition, and both economists and engineers have been looking for the solutions fervently. In this dissertation, which consists primarily of three essays, we apply economics theory and techniques to the power industry and address two related issues, transmission investment and financial transmission rights (FTRs). The first essay takes the decentralized perspective and investigates the efficiency attribute of market-based transmission investment under perfect competition. We clarify, for the first time, the nature of the externality created by loop flows that causes transmission investment to be inefficient. Our findings have important implications for better understanding of transmission market design and creating incentives for efficient transmission investment. In the second essay, we define several rules for allocating transmission investment cost within the framework of cooperative game theory. These rules provide fair, stable or efficient cost allocations in theory and are good benchmarks against which the allocation mechanism in practice can be compared and improved upon. In the last essay, we make exploratory efforts in analyzing and assessing empirically the performance of the Midwest independent system operator (MISO) FTR auction market. We reveal some stylized facts about this young market and find that it is not efficient under the risk-neutrality assumption. We also point out and correct the drawbacks in previous related work and suggest about more complete empirical work in future. In all, this dissertation makes both theoretic and empirical analysis of the two hot issues related to the power industry and comes up with findings that have important implications for the development of this industry.
Nonlinear neutral inclusions: assemblages of coated ellipsoids
Bolaños, Silvia Jiménez; Vernescu, Bogdan
2015-01-01
The problem of determining nonlinear neutral inclusions in (electrical or thermal) conductivity is considered. Neutral inclusions, inserted in a matrix containing a uniform applied electric field, do not disturb the field outside the inclusions. The well-known Hashin-coated sphere construction is an example of a neutral inclusion. In this paper, we consider the problem of constructing neutral inclusions from nonlinear materials. In particular, we discuss assemblages of coated ellipsoids. The proposed construction is neutral for a given applied field. PMID:26064633
Smoothing of mixed complementarity problems
Gabriel, S.A.; More, J.J.
1995-09-01
The authors introduce a smoothing approach to the mixed complementarity problem, and study the limiting behavior of a path defined by approximate minimizers of a nonlinear least squares problem. The main result guarantees that, under a mild regularity condition, limit points of the iterates are solutions to the mixed complementarity problem. The analysis is applicable to a wide variety of algorithms suitable for large-scale mixed complementarity problems.
Dynamically prioritized progressive transmission
NASA Astrophysics Data System (ADS)
Blanford, Ronald
1992-04-01
Retrieval of image data from a centralized database may be subject to bandwidth limitations, whether due to a low-bandwidth communications link or to contention from simultaneous accesses over a high-bandwidth link. Progressive transmission can alleviate this problem by encoding image data so that any prefix of the data stream approximates the complete image at a coarse level of resolution. The longer the prefix, the finer the resolution. In many cases, as little at 1 percent of the image data may be sufficient to decide whether to discard the image, to permit the retrieval to continue, or to restrict retrieval to a subsection of the image. Our approach treats resolution not as a fixed attribute of the image, but rather as a resource which may be allocated to portions of the image at the direction of a user-specified priority function. The default priority function minimizes error by allocating more resolution to regions of high variance. The user may also point to regions of interest requesting priority transmission. More advanced target recognition strategies may be incorporated at the user's discretion. Multispectral imagery is supported. The user engineering implications are profounded. There is immediate response to a query that might otherwise take minutes to complete. The data is transmitted in small increments so that no single user dominates the communications bandwidth. The user-directed improvement means that bandwidth is focused on interesting information. The user may continue working with the first coarse approximations while further image data is still arriving. The algorithm has been implemented in C on Sun, Silicon Graphics, and NeXT workstations, and in Lisp on a Symbolics. Transmission speeds reach as high as 60,000 baud using a Sparc or 68040 processor when storing data to memory; somewhat less if also updating a graphical display. The memory requirements are roughly five bytes per image pixel. Both computational and memory costs may be reduced
Nonlinear coupling between a nitrogen-vacancy-center ensemble and a superconducting qubit.
Chen, Qiong; Wen, Jun; Yang, W L; Feng, M; Du, Jiangfeng
2015-01-26
By exchange of virtual microwave photon induced by a transmission line resonator, the nonlinear interaction between a nitrogen-vacancy-center ensemble (NVE) and a superconducting charge qubit is achieved in circuit quantum electrodynamics, where the nonlinear coupling results from the second order of the coupling between the magnetic field of the transmission line resonator and the charge qubit. In our case, the nonlinear coupling can be much enhanced by a factor of the total spin number in the NVE. As an application, we present a potentially practical scheme to realize the squeezing of the NVE using the nonlinear coupling, which is within reach of the currently available technology. PMID:25835919
Locally nonlinear transformation for facial image superresolution
NASA Astrophysics Data System (ADS)
Zeng, Xiao; Huang, Hua
2013-02-01
Reconstruction of a high-resolution face image, from a low-resolution observation based on a set of high- and low-resolution training image pairs, is an important problem for optical engineering applications. In this paper, we study this facial superresolution problem and propose a novel locally nonlinear transformation based approach. Multiple locally nonlinear transformation are utilized to approximate the global nonlinear connections between low resolution (LR)/high resolution (HR) images. LR/HR images are initially divided into multiple pairs of patches with the corresponding position information. As facial images are highly structured, patches at the same position spanned a subspace. Since the curse of dimensionality is avoided in these subspaces (patches in the same position), the Euclidean distance can express the intrinsic "radial" between samples in the same subspace. Therefore, multiple radial basis functions are utilized to approximate the nonlinear mapping between LR/HR pairs at each position from training examples. The proposed locally nonlinear transformation (LNT)-based reconstruction is achieved by applying the learned nonlinear transformation to each position patch of an LR input. The final SR results are obtained by refining the LNT reconstruction by the projection onto a convex sets algorithm using the consistency constraint. Extensive experiments on benchmark databases and real world images validate the superiority of the proposed method.
Belokoneva, E. L. Al-Ama, A. G.; Stefanovich, S. Yu.; Plachinda, P. A.
2007-09-15
The structural features responsible for the high nonlinear optical activity of crystals of the hilgardite-like anhydrous bromo-borate Pb{sub 2}[B{sub 5}O{sub 9}]Br (space group Pnn2) are analyzed with the use of data obtained from two (precision and conventional) single-crystal X-ray diffraction experiments. The electron-density peaks associated with the stereochemically active lone electron pair are located in free space at two equally probable positions in the vicinity of the Pb(2) atom on the side of the two most distant atoms, Br(1) and Br(2). The stereochemical activity of two nonequivalent lead atoms in the crystal structure increases upon changing over from the Pb(1) atom to the Pb(2) atom. This is in agreement with the behavior of the lone electron pairs in the hilgardite-like hydrated borate Na{sub 0.5}Pb{sub 2}[B{sub 5}O{sub 9}](OH){sub 1.5} . 0.5H{sub 2}O and another nonlinear optical borate, namely, Pb{sub 2}[B{sub 4}O{sub 5}(OH){sub 4}](OH){sub 2} . H{sub 2}O, which is related to the compound BiB{sub 3}O{sub 6}. The most pronounced nonlinear optical properties of the lead bromo-borate Pb{sub 2}[B{sub 5}O{sub 9}]Br as compared to other orthorhombic hilgardites and lead borates are associated with the presence of highly polarized Pb-Br bonds. In this case, the electron density of the lone electron pair of the Pb(2) atom enhances the polarization effect.
PREFACE Integrability and nonlinear phenomena Integrability and nonlinear phenomena
NASA Astrophysics Data System (ADS)
Gómez-Ullate, David; Lombardo, Sara; Mañas, Manuel; Mazzocco, Marta; Nijhoff, Frank; Sommacal, Matteo
2010-10-01
according to the standards of the journal. The selection of papers in this issue aims to bring together recent developments and findings, even though it consists of only a fraction of the impressive developments in recent years which have affected a broad range of fields, including the theory of special functions, quantum integrable systems, numerical analysis, cellular automata, representations of quantum groups, symmetries of difference equations, discrete geometry, among others. The special issue begins with four review papers: Integrable models in nonlinear optics and soliton solutions Degasperis [1] reviews integrable models in nonlinear optics. He presents a number of approximate models which are integrable and illustrates the links between the mathematical and applicative aspects of the theory of integrable dynamical systems. In particular he discusses the recent impact of boomeronic-type wave equations on applications arising in the context of the resonant interaction of three waves. Hamiltonian PDEs: deformations, integrability, solutions Dubrovin [2] presents classification results for systems of nonlinear Hamiltonian partial differential equations (PDEs) in one spatial dimension. In particular he uses a perturbative approach to the theory of integrability of these systems and discusses their solutions. He conjectures universality of the critical behaviour for the solutions, where the notion of universality refers to asymptotic independence of the structure of solutions (at the point of gradient catastrophe) from the choice of generic initial data as well as from the choice of a generic PDE. KP solitons in shallow water Kodama [3] presents a survey of recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. A large variety of exact soliton solutions of the KP equation are presented and classified. The study includes numerical analysis of the stability of the found solution as well as numerical simulations of the initial value problems which