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.
Dielectric Nonlinear Transmission Line (Postprint)
2011-12-01
Technical Paper 3. DATES COVERED (From - To) 2011 4. TITLE AND SUBTITLE Dielectric Nonlinear Transmission Line (POSTPRINT) 5a. CONTRACT NUMBER...14. ABSTRACT A parallel plate nonlinear transmission line (NLTL) was constructed. Periodic loading of nonlinear dielectric slabs provides the...846-9101 Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std. 239.18 Dielectric Nonlinear Transmission Line David M. French, Brad W. Hoff
Problems of nonlinear deformation
NASA Astrophysics Data System (ADS)
Grigoliuk, E. I.; Shalashilin, V. I.
A method of continuing the solution is discussed with respect to a parameter for a certain class of nonlinear problems in solid mechanics. Modifications of the method are developed in order to implement a unified continuation process at regular and limit points in the set of solutions, with extensions to nonlinear boundary value problems. Algorithms are developed for solving large deflection problems of elastic arches and large axisymmetric deflection problems for shells of revolution. In particular, the algorithms are used for the analysis of large deflections of circular arches and toroidal shells. Examples of natural vibration and stability problems for parallelograms and trapezoidal membranes and panels are given.
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.
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.
Scalar discrete nonlinear multipoint boundary value problems
NASA Astrophysics Data System (ADS)
Rodriguez, Jesus; Taylor, Padraic
2007-06-01
In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].
Nonlinear transmission line based electron beam driver
French, David M.; Hoff, Brad W.; Tang Wilkin; Heidger, Susan; 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.
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.
Nonlinearity of superconducting transmission line and microstrip resonator
Vendik, O.G.; Vendik, I.B.; Samoilova, T.B.
1997-02-01
The simplest model of nonlinear response of a superconducting thin film is used for modeling the nonlinear phenomena in a superconducting transmission line and a microstrip resonator. The specified characteristic power of the transmission line is suggested to use as a fitting parameter for numerical description of the microstrip line nonlinearity at microwaves. Quantitative agreement of simulated and experimental data has been obtained for the incident power dependent transmission coefficient of a microstrip line section and a high quality microstrip resonator. Numerical results have also been obtained for the power of the third harmonic radiated from the nonlinear resonator.
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.
A nonlinear supercooled Stefan problem
NASA Astrophysics Data System (ADS)
Briozzo, Adriana C.; Natale, Maria F.
2017-04-01
We study the supercooled one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity at the fixed face x=0. We obtain sufficient conditions for data in order to have existence of a solution of similarity type, local in time and finite-time blow-up occurs. This explicit solution is obtained through the unique solution of an integral equation with the time as a parameter.
Nonlinear transmission conditions for thin curvilinear low-conductive interphases
NASA Astrophysics Data System (ADS)
Andreeva, Daria; Miszuris, Wiktoria
2017-01-01
In this paper, we consider the heat transfer problem in a cylindrical composite material with an adhesive interphase of closed curvilinear shape. The interphase exhibits nonlinear behaviour and at the same time has physical characteristics (size, thermal conductivity) that significantly vary from the properties of the surrounding components. As the latter complicates the direct use of FEM, we use asymptotic method to replace the interphase with an imperfect interface of zero thickness, preserving the essential features of the thermal behaviour of the interphase through the evaluated transmission conditions. Carefully designed numerical simulations verify their validity. We place special emphasis on the impact of geometric properties of the interphase, in particular, the curvature of its boundaries, on the accuracy of the conditions.
Bounding solutions of geometrically nonlinear viscoelastic problems
NASA Technical Reports Server (NTRS)
Stubstad, J. M.; Simitses, G. J.
1986-01-01
Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.
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…
The transmissibility of nonlinear energy sink based on nonlinear output frequency-response functions
NASA Astrophysics Data System (ADS)
Yang, Kai; Zhang, Ye-Wei; Ding, Hu; Chen, Li-Qun
2017-03-01
For the first time, a new representation of transmissibility based on nonlinear output frequency-response functions (NOFRFs) is proposed in the present study. Furthermore, the transmissibility is applied to evaluate the vibration isolation performance of a nonlinear energy sink (NES) in frequency domain. A two-degree-of-freedom (2-DOF) structure with the NES attached system is adopted. Numerical simulations have been performed for the 2-DOF structure. Moreover, the effects of NES parameters on the transmissibility of the nonlinear system are evaluated. By increasing the viscous damping and mass, as well as decreasing the cubic nonlinear stiffness of the NES, the analytical results show that the transmissibility of the 2-DOF structure with NES is reduced over all resonance regions. Therefore, the present paper produces a novel method for NES design in frequency domain.
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.
Landesman-Lazer condition for nonlinear problems with jumping nonlinearities
NASA Astrophysics Data System (ADS)
Drábek, Pavel
This paper was motivated by the result of Iannacci and Nkashama ( J. Differential Equations69 (1987) , 289-309) concerning the existence of at least one solution for the differential equation x″( t) + m2x( t) + g( t, x( t)) = e( t) with periodic boundary data x(0) - x(2 π) = x'(0) - x'(2 π) = 0, where m ⩾ 0 is an integer, e is integrable, and g satisfies Carathéodory's conditions. We intend to prove that the Landesman-Lazer type condition is sufficient for solvability of this periodic problem under rather more general assumptions on the growth of the nonlinear term g. Particularly, our hypotheses cover the nonlinearities which may "jump over" the eigenvalues different from m2 while the assumptions of Iannacci and Nkashama allow g only to asymptotically "touch" the neighbour eigenvalues. Our approach may be used also for two-point boundary value problems. The proofs are based on the Leray-Schauder degree theory and on the shooting method for ordinary differential equations.
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.
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'.
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.
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".
The fully nonlinear stratified geostrophic adjustment problem
NASA Astrophysics Data System (ADS)
Coutino, Aaron; Stastna, Marek
2017-01-01
The study of the adjustment to equilibrium by a stratified fluid in a rotating reference frame is a classical problem in geophysical fluid dynamics. We consider the fully nonlinear, stratified adjustment problem from a numerical point of view. We present results of smoothed dam break simulations based on experiments in the published literature, with a focus on both the wave trains that propagate away from the nascent geostrophic state and the geostrophic state itself. We demonstrate that for Rossby numbers in excess of roughly 2 the wave train cannot be interpreted in terms of linear theory. This wave train consists of a leading solitary-like packet and a trailing tail of dispersive waves. However, it is found that the leading wave packet never completely separates from the trailing tail. Somewhat surprisingly, the inertial oscillations associated with the geostrophic state exhibit evidence of nonlinearity even when the Rossby number falls below 1. We vary the width of the initial disturbance and the rotation rate so as to keep the Rossby number fixed, and find that while the qualitative response remains consistent, the Froude number varies, and these variations are manifested in the form of the emanating wave train. For wider initial disturbances we find clear evidence of a wave train that initially propagates toward the near wall, reflects, and propagates away from the geostrophic state behind the leading wave train. We compare kinetic energy inside and outside of the geostrophic state, finding that for long times a Rossby number of around one-quarter yields an equal split between the two, with lower (higher) Rossby numbers yielding more energy in the geostrophic state (wave train). Finally we compare the energetics of the geostrophic state as the Rossby number varies, finding long-lived inertial oscillations in the majority of the cases and a general agreement with the past literature that employed either hydrostatic, shallow-water equation-based theory or
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.
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.
Exact solutions of the derivative nonlinear Schrödinger equation for a nonlinear transmission line.
Kengne, E; Liu, W M
2006-02-01
We consider the derivative nonlinear Schrödinger equation with constant potential as a model for wave propagation on a discrete nonlinear transmission line. This equation can be derived in the small amplitude and long wavelength limit using the standard reductive perturbation method and complex expansion. We construct some exact soliton and elliptic solutions of the mentioned equation by perturbation of its Stokes wave solutions. We find that for some values of the coefficients of the equation and for some parameters of solutions, the graphical representations show some kinds of symmetries such as mirror symmetry and rotational symmetry.
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.
A Unified Theory of Intrachannel Nonlinearity in Pseudolinear Transmission
NASA Astrophysics Data System (ADS)
Mecozzi, Antonio
The material of this chapter originates from a visit of the author the AT&T Laboratory in Red Bank, NJ in the summer of 2000. During that visit, the author was exposed to some experimental work on transmission using short pulses, which spread very rapidly upon propagation and for this reason were dubbed by Jay Wiesenfeld into "Tedons" from "to ted" which, according to Merriam-Webster's Collegiate Dictionary, means "to spread or turn from the swath and scatter (as new-mown grass) for drying." Tedons minimize the effects of nonlinearity by a quick spread, unlike solitons that instead resist to nonlinearity by balancing nonlinearity with dispersion, so that their shape does not change. He teamed up with Carl Clausen and Mark Shtaif and developed a perturbative theory, whose results were presented in a series of three papers [1-3]. The details of that theory and of its derivations were, however, never published in the open literature. The presentation of these details, together with some later improvements, is the purpose of this chapter.
Some control problems of continuously variable belt transmission
NASA Astrophysics Data System (ADS)
Radzymiński, B.
2016-09-01
Control problems of continuously variable belt transmission used in passenger cars have been discussed. Pulley adjustment solutions and choice of control and feedback signals are the main topics. Intention to use such a transmission as part of a complex system containing mechanical energy storage caused that the adjustment transition time become crucial problem.
Nonlinear Multidimensional Assignment Problems Efficient Conic Optimization Methods and Applications
2015-06-24
problems. The size 16 three-dimensional quadratic assignment problem Q3AP from wireless communications was solved using a sophisticated approach...combinatorial optimization problem, the Directional Sensor Problem, was solved in two ways. First, heuristically in an engineering fashion and second, exactly...the sensor problem was solved as a nonlinear MINLP problem. Specifically, the information gain obtained was maximized in order to determine the optimal
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.
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.
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.
Matrix iteration method for nonlinear eigenvalue problems with applications
NASA Astrophysics Data System (ADS)
Ram, Y. M.
2016-12-01
A simple and intuitive matrix iteration method for solving nonlinear eigenvalue problems is described and demonstrated in detail by two problems: (i) the boundary value problem associated with large deflection of a flexible rod, and (ii) the initial value problem associated with normal mode motion of a double pendulum. The two problems are solved by two approaches, the finite difference approach and a continuous realization approach which is similar in spirit to the Rayleigh-Ritz method.
Solving a Class of Nonlinear Eigenvalue Problems by Newton's Method
Gao, Weiguo; Yang, Chao; Meza, Juan C.
2009-07-02
We examine the possibility of using the standard Newton's method for solving a class of nonlinear eigenvalue problems arising from electronic structure calculation. We show that the Jacobian matrix associated with this nonlinear system has a special structure that can be exploited to reduce the computational complexity of the Newton's method. Preliminary numerical experiments indicate that the Newton's method can be more efficient for small problems in which a few smallest eigenpairs are needed.
Nonlinear Transient Problems Using Structure Compatible Heat Transfer Code
NASA Technical Reports Server (NTRS)
Hou, Gene
2000-01-01
The report documents the recent effort to enhance a transient linear heat transfer code so as to solve nonlinear problems. The linear heat transfer code was originally developed by Dr. Kim Bey of NASA Largely and called the Structure-Compatible Heat Transfer (SCHT) code. The report includes four parts. The first part outlines the formulation of the heat transfer problem of concern. The second and the third parts give detailed procedures to construct the nonlinear finite element equations and the required Jacobian matrices for the nonlinear iterative method, Newton-Raphson method. The final part summarizes the results of the numerical experiments on the newly enhanced SCHT code.
Parabolic Perturbation of a Nonlinear Hyperbolic Problem Arising in Physiology
NASA Astrophysics Data System (ADS)
Colli, P.; Grasselli, M.
We study a transport-diffusion initial value problem where the diffusion codlicient is "small" and the transport coefficient is a time function depending on the solution in a nonlinear and nonlocal way. We show the existence and the uniqueness of a weak solution of this problem. Moreover we discuss its asymptotic behaviour as the diffusion coefficient goes to zero, obtaining a well-posed first-order nonlinear hyperbolic problem. These problems arise from mathematical models of muscle contraction in the framework of the sliding filament theory.
Reale, D V; Parson, J M; Neuber, A A; Dickens, J C; Mankowski, J J
2016-03-01
A stripline gyromagnetic nonlinear transmission line (NLTL) was constructed out of yttrium iron garnet ferrite and tested at charge voltages of 35 kV-55 kV with bias fields ranging from 10 kA/m to 20 kA/m. Typically, high power gyromagnetic NLTLs are constructed in a coaxial geometry. While this approach has many advantages, including a uniform transverse electromagnetic (TEM) mode, simple interconnection between components, and the ability to use oil or pressurized gas as an insulator, the coaxial implementation suffers from complexity of construction, especially when using a solid insulator. By moving to a simpler transmission line geometry, NLTLs can be constructed more easily and arrayed on a single substrate. This work represents a first step in exploring the suitability of various transmission line structures, such as microstrips and coplanar waveguides. The resulting high power microwave (HPM) source operates in ultra high frequency (UHF) band with an average bandwidth of 40.1% and peak rf power from 2 MW to 12.7 MW.
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.
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.
Multigrid Reduction in Time for Nonlinear Parabolic Problems
Falgout, R. D.; Manteuffel, T. A.; O'Neill, B.; Schroder, J. B.
2016-01-04
The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.
A reduced basis Landweber method for nonlinear inverse problems
NASA Astrophysics Data System (ADS)
Garmatter, Dominik; Haasdonk, Bernard; Harrach, Bastian
2016-03-01
We consider parameter identification problems in parametrized partial differential equations (PDEs). These lead to nonlinear ill-posed inverse problems. One way of solving them is using iterative regularization methods, which typically require numerous amounts of forward solutions during the solution process. In this article we consider the nonlinear Landweber method and couple it with the reduced basis method as a model order reduction technique in order to reduce the overall computational time. In particular, we consider PDEs with a high-dimensional parameter space, which are known to pose difficulties in the context of reduced basis methods. We present a new method that is able to handle such high-dimensional parameter spaces by combining the nonlinear Landweber method with adaptive online reduced basis updates. It is then applied to the inverse problem of reconstructing the conductivity in the stationary heat equation.
Yang, Zengtao; Yang, Jiashi; Hu, Yuantai
2008-11-01
Weakly nonlinear behavior of electric power transmission through an elastic wall by piezoelectric transducers and acoustic waves near resonance is studied based on the cubic theory of nonlinear electroelasticity. An approximate analytical solution is obtained. Output voltage is calculated and plotted. Basic nonlinear behaviors of the power transmission structure are examined. It is found that near nonlinear resonance the electrical input-output relation loses its linearity, becomes multi-valued, and experiences jumps due to large mechanical deformations. The behavior below and above resonance is qualitatively different and is qualitatively material dependent.
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.
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.
Nonlinear phase noise in coherent optical OFDM transmission systems.
Zhu, Xianming; Kumar, Shiva
2010-03-29
We derive an analytical formula to estimate the variance of nonlinear phase noise caused by the interaction of amplified spontaneous emission (ASE) noise with fiber nonlinearity such as self-phase modulation (SPM), cross-phase modulation (XPM), and four-wave mixing (FWM) in coherent orthogonal frequency division multiplexing (OFDM) systems. The analytical results agree very well with numerical simulations, enabling the study of the nonlinear penalties in long-haul coherent OFDM systems without extensive numerical simulation. Our results show that the nonlinear phase noise induced by FWM is significantly larger than that induced by SPM and XPM, which is in contrast to traditional WDM systems where ASE-FWM interaction is negligible in quasi-linear systems. We also found that fiber chromatic dispersion can reduce the nonlinear phase noise. The variance of the total phase noise increases linearly with the bit rate, and does not depend significantly on the number of subcarriers for systems with moderate fiber chromatic dispersion.
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.
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.
2014-03-14
AFRL-OSR-VA-TR-2014-0068 Equipment for Nonlinear Photonics Research Zhigang Chen SAN FRANCISCO STATE UNIVERSITY Final Report 03/14/2014 DISTRIBUTION...34Equipment for Nonlinear Photonics Research - Light control and image transmission in specially-designed photonic " Contract/Grant #: FA9550...project is to develop research programs at the frontier of nonlinear optics/ photonics that could lead to fundamental understandings in scientific
Nonlinear eigenvalue problems in Density Functional Theory calculations
Fattebert, J
2009-08-28
Developed in the 1960's by W. Kohn and coauthors, Density Functional Theory (DFT) is a very popular quantum model for First-Principles simulations in chemistry and material sciences. It allows calculations of systems made of hundreds of atoms. Indeed DFT reduces the 3N-dimensional Schroedinger electronic structure problem to the search for a ground state electronic density in 3D. In practice it leads to the search for N electronic wave functions solutions of an energy minimization problem in 3D, or equivalently the solution of an eigenvalue problem with a non-linear operator.
Numerical solution of control problems governed by nonlinear differential equations
Heinkenschloss, M.
1994-12-31
In this presentation the author investigates an iterative method for the solution of optimal control problems. These problems are formulated as constrained optimization problems with constraints arising from the state equation and in the form of bound constraints on the control. The method for the solution of these problems uses the special structure of the problem arising from the bound constraint and the state equation. It is derived from SQP methods and projected Newton methods and combines the advantages of both methods. The bound constraint is satisfied by all iterates using a projection, the nonlinear state equation is satisfied in the limit. Only a linearized state equation has to be solved in every iteration. The solution of the linearized problems are done using multilevel methods and GMRES.
Ndzana, Fabien; Mohamadou, Alidou; Kofané, Timoléon C
2008-12-01
We study wave propagation in a nonlinear transmission line with dissipative elements. We show analytically that the telegraphers' equations of the electrical transmission line can be modeled by a pair of continuous coupled complex Ginzburg-Landau equations, coupled by purely nonlinear terms. Based on this system, we investigated both analytically and numerically the modulational instability (MI). We produce characteristics of the MI in the form of typical dependence of the instability growth rate on the wavenumbers and system parameters. Generic outcomes of the nonlinear development of the MI are investigated by dint of direct simulations of the underlying equations. We find that the initial modulated plane wave disintegrates into waves train. An apparently turbulent state takes place in the system during the propagation.
NASA Astrophysics Data System (ADS)
Royston, T. J.; Singh, R.
1996-07-01
While significant non-linear behavior has been observed in many vibration mounting applications, most design studies are typically based on the concept of linear system theory in terms of force or motion transmissibility. In this paper, an improved analytical strategy is presented for the design optimization of complex, active of passive, non-linear mounting systems. This strategy is built upon the computational Galerkin method of weighted residuals, and incorporates order reduction and numerical continuation in an iterative optimization scheme. The overall dynamic characteristics of the mounting system are considered and vibratory power transmission is minimized via adjustment of mount parameters by using both passive and active means. The method is first applied through a computational example case to the optimization of basic passive and active, non-linear isolation configurations. It is found that either active control or intentionally introduced non-linearity can improve the mount's performance; but a combination of both produces the greatest benefit. Next, a novel experimental, active, non-linear isolation system is studied. The effect of non-linearity on vibratory power transmission and active control are assessed via experimental measurements and the enhanced Galerkin method. Results show how harmonic excitation can result in multiharmonic vibratory power transmission. The proposed optimization strategy offers designers some flexibility in utilizing both passive and active means in combination with linear and non-linear components for improved vibration mounts.
Investigation of non-linear imaging in high-resolution transmission electron microscopy.
Chang, Yunjie; Wang, Yumei; Cui, Yanxiang; Ge, Binghui
2016-12-01
Transmission cross-coefficient theory and pseudo-weak-phase object approximation theory were combined to investigate the non-linear imaging in high-resolution transmission electron microscopy (HRTEM). The analytical expressions of linear and non-linear imaging components in diffractogram were obtained and changes of linear and non-linear components over sample thickness were analyzed. Moreover, the linear and non-linear components are found to be an odd and even-function of the defocus and Cs, respectively. Based on this, a method for separating the linear and non-linear contrasts in Cs-corrected (non-zero Cs conditions included) HRTEM images was proposed, and its effectiveness was confirmed by image simulations with AlN as an example.
Adapting a truly nonlinear filter to the ocean acoustic inverse problem
NASA Astrophysics Data System (ADS)
Ganse, Andrew A.; Odom, Robert I.
2005-04-01
Nonlinear inverse problems including the ocean acoustic problem have been solved by Monte Carlo, locally-linear, and filter based techniques such as the Extended Kalman Filter (EKF). While these techniques do provide statistical information about the solution (e.g., mean and variance), each suffers from inherent limitations in their approach to nonlinear problems. Monte Carlo techniques are expensive to compute and do not contribute to intuitive interpretation of a problem, and locally-linear techniques (including the EKF) are limited by the multimodal objective landscape of nonlinear problems. A truly nonlinear filter, based on recent work in nonlinear tracking, estimates state information for a nonlinear problem in continual measurement updates and is adapted to solving nonlinear inverse problems. Additional terms derived from the system's state PDF are added to the mean and covariance of the solution to address the nonlinearities of the problem, and overall the technique offers improved performance in nonlinear inversion. [Work supported by ONR.
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1984-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems. Previously announced in STAR as N83-33589
Difference equation state approximations for nonlinear hereditary control problems
NASA Technical Reports Server (NTRS)
Rosen, I. G.
1982-01-01
Discrete approximation schemes for the solution of nonlinear hereditary control problems are constructed. The methods involve approximation by a sequence of optimal control problems in which the original infinite dimensional state equation has been approximated by a finite dimensional discrete difference equation. Convergence of the state approximations is argued using linear semigroup theory and is then used to demonstrate that solutions to the approximating optimal control problems in some sense approximate solutions to the original control problem. Two schemes, one based upon piecewise constant approximation, and the other involving spline functions are discussed. Numerical results are presented, analyzed and used to compare the schemes to other available approximation methods for the solution of hereditary control problems.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
NASA Technical Reports Server (NTRS)
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
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.
On the Cauchy problem for strongly nonlinear intense wave groups
NASA Astrophysics Data System (ADS)
Slunyaev, Alexey
2015-04-01
Stable long-living nonlinear groups of gravity water waves (very steep and very short envelope solitons) were first observed in numerical simulations [1, 2] and then - in laboratory conditions [3]. In [2] their interaction was shown to be almost elastic in some (but not all) situations. Therefore the Cauchy problem for localized wave groups beyond the weakly nonlinear assumption is of interest. In general, the formation of a few solitary wave groups from the initial condition may take place [4]. We have focused on the unidentified reason, why some experimental tests of solitary wave groups in [3] were not successful (while other runs with slightly different experimental parameters were successful). In this paper we consider the initial problem, when the initial condition is taken in the form of a scaled intense envelope soliton of the nonlinear Schrodinger equation, and is simulated by means of the fully nonlinear code of potential Euler equations. The result of the long-term evolution (which is generally represented by a solitary wave group and smaller scale waves) is compared with the prediction of the weakly nonlinear theory. We show reasonable agreement between the weakly nonlinear theory and the strongly nonlinear simulations. In particular, a 10% decrease of the initial perturbation results in 20% smaller amplitude of the eventual envelope soliton. This fact explains the failure of reproduction of envelope solitons in some experimental tests in the finite-depth flume [3]. The solution of the nonlinear Schrodinger equation for finite-depth water may be transformed to the infinite-depth solution with reduced amplitude. [1] A.I. Dyachenko, V.E. Zakharov, On the formation of freak waves on the surface of deep water. J. Exp. Theor. Phys. Lett. 88, 307-311 (2008). [2] A.V. Slunyaev, Numerical simulation of "limiting" envelope solitons of gravity waves on deep water. JETP 109, 676-686 (2009). [3] A. Slunyaev, G.F. Clauss, M. Klein, M. Onorato, Simulations and
Software Performance on Nonlinear Least-Squares Problems
1989-01-01
Murray, and Wright [1981), Dennis and Schnabel (1983], and Mori and Sorensen [19841. Section 3 reviews the principal approaches that are used in software...2.3.1) where R1, is upper-triangular and nonsingular (see, e. g., Stewart [19731, Chapter 3 ). Gill and Murray alter the Cholesky factorization...problem, JTJo can be used as the initial estimate, provided the columns of Jo are linearly independent. 1 I 3 . Methods for Nonlinear Least Squares 3.1
Control of terahertz nonlinear transmission with electrically gated graphene metadevices
NASA Astrophysics Data System (ADS)
Choi, Hyun Joo; Baek, In Hyung; Kang, Bong Joo; Kim, Hyeon-Don; Oh, Sang Soon; Hamm, Joachim M.; Pusch, Andreas; Park, Jagang; Lee, Kanghee; Son, Jaehyeon; Jeong, Young U. K.; Hess, Ortwin; Rotermund, Fabian; Min, Bumki
2017-02-01
Graphene, which is a two-dimensional crystal of carbon atoms arranged in a hexagonal lattice, has attracted a great amount of attention due to its outstanding mechanical, thermal and electronic properties. Moreover, graphene shows an exceptionally strong tunable light-matter interaction that depends on the Fermi level - a function of chemical doping and external gate voltage - and the electromagnetic resonance provided by intentionally engineered structures. In the optical regime, the nonlinearities of graphene originated from the Pauli blocking have already been exploited for mode-locking device applications in ultrafast laser technology, whereas nonlinearities in the terahertz regime, which arise from a reduction in conductivity due to carrier heating, have only recently been confirmed experimentally. Here, we investigated two key factors for controlling nonlinear interactions of graphene with an intense terahertz field. The induced transparencies of graphene can be controlled effectively by engineering meta-atoms and/or changing the number of charge carriers through electrical gating. Additionally, nonlinear phase changes of the transmitted terahertz field can be observed by introducing the resonances of the meta-atoms.
Control of terahertz nonlinear transmission with electrically gated graphene metadevices.
Choi, Hyun Joo; Baek, In Hyung; Kang, Bong Joo; Kim, Hyeon-Don; Oh, Sang Soon; Hamm, Joachim M; Pusch, Andreas; Park, Jagang; Lee, Kanghee; Son, Jaehyeon; Jeong, Young U K; Hess, Ortwin; Rotermund, Fabian; Min, Bumki
2017-02-20
Graphene, which is a two-dimensional crystal of carbon atoms arranged in a hexagonal lattice, has attracted a great amount of attention due to its outstanding mechanical, thermal and electronic properties. Moreover, graphene shows an exceptionally strong tunable light-matter interaction that depends on the Fermi level - a function of chemical doping and external gate voltage - and the electromagnetic resonance provided by intentionally engineered structures. In the optical regime, the nonlinearities of graphene originated from the Pauli blocking have already been exploited for mode-locking device applications in ultrafast laser technology, whereas nonlinearities in the terahertz regime, which arise from a reduction in conductivity due to carrier heating, have only recently been confirmed experimentally. Here, we investigated two key factors for controlling nonlinear interactions of graphene with an intense terahertz field. The induced transparencies of graphene can be controlled effectively by engineering meta-atoms and/or changing the number of charge carriers through electrical gating. Additionally, nonlinear phase changes of the transmitted terahertz field can be observed by introducing the resonances of the meta-atoms.
Control of terahertz nonlinear transmission with electrically gated graphene metadevices
Choi, Hyun Joo; Baek, In Hyung; Kang, Bong Joo; Kim, Hyeon-Don; Oh, Sang Soon; Hamm, Joachim M.; Pusch, Andreas; Park, Jagang; Lee, Kanghee; Son, Jaehyeon; Jeong, Young U. k.; Hess, Ortwin; Rotermund, Fabian; Min, Bumki
2017-01-01
Graphene, which is a two-dimensional crystal of carbon atoms arranged in a hexagonal lattice, has attracted a great amount of attention due to its outstanding mechanical, thermal and electronic properties. Moreover, graphene shows an exceptionally strong tunable light-matter interaction that depends on the Fermi level - a function of chemical doping and external gate voltage - and the electromagnetic resonance provided by intentionally engineered structures. In the optical regime, the nonlinearities of graphene originated from the Pauli blocking have already been exploited for mode-locking device applications in ultrafast laser technology, whereas nonlinearities in the terahertz regime, which arise from a reduction in conductivity due to carrier heating, have only recently been confirmed experimentally. Here, we investigated two key factors for controlling nonlinear interactions of graphene with an intense terahertz field. The induced transparencies of graphene can be controlled effectively by engineering meta-atoms and/or changing the number of charge carriers through electrical gating. Additionally, nonlinear phase changes of the transmitted terahertz field can be observed by introducing the resonances of the meta-atoms. PMID:28216677
Solving nonlinear equality constrained multiobjective optimization problems using neural networks.
Mestari, Mohammed; Benzirar, Mohammed; Saber, Nadia; Khouil, Meryem
2015-10-01
This paper develops a neural network architecture and a new processing method for solving in real time, the nonlinear equality constrained multiobjective optimization problem (NECMOP), where several nonlinear objective functions must be optimized in a conflicting situation. In this processing method, the NECMOP is converted to an equivalent scalar optimization problem (SOP). The SOP is then decomposed into several-separable subproblems processable in parallel and in a reasonable time by multiplexing switched capacitor circuits. The approach which we propose makes use of a decomposition-coordination principle that allows nonlinearity to be treated at a local level and where coordination is achieved through the use of Lagrange multipliers. The modularity and the regularity of the neural networks architecture herein proposed make it suitable for very large scale integration implementation. An application to the resolution of a physical problem is given to show that the approach used here possesses some advantages of the point of algorithmic view, and provides processes of resolution often simpler than the usual techniques.
An Algorithm for Linearly Constrained Nonlinear Programming Programming Problems.
1980-01-01
ALGORITHM FOR LINEARLY CONSTRAINED NONLINEAR PROGRAMMING PROBLEMS Mokhtar S. Bazaraa and Jamie J. Goode In this paper an algorithm for solving a linearly...distance pro- gramr.ing, as in the works of Bazaraa and Goode 12], and Wolfe [16 can be used for solving this problem. Special methods that take advantage of...34 Pacific Journal of Mathematics, Volume 16, pp. 1-3, 1966. 2. M. S. Bazaraa and J. j. Goode, "An Algorithm for Finding the Shortest Element of a
A convergence theory for a class of nonlinear programming problems.
NASA Technical Reports Server (NTRS)
Rauch, S. W.
1973-01-01
A recent convergence theory of Elkin concerning methods for unconstrained minimization is extended to a certain class of nonlinear programming problems. As in Elkin's original approach, the analysis of a variety of step-length algorithms is treated entirely separately from that of several direction algorithms. This allows for their combination into many different methods for solving the constrained problem. These include some of the methods of Rosen and Zoutendijk. We also extend the results of Topkis and Veinott to nonconvex sets and drop their requirement of the uniform feasibility of a subsequence of the search directions.
Application of nonlinear Krylov acceleration to radiative transfer problems
Till, A. T.; Adams, M. L.; Morel, J. E.
2013-07-01
The iterative solution technique used for radiative transfer is normally nested, with outer thermal iterations and inner transport iterations. We implement a nonlinear Krylov acceleration (NKA) method in the PDT code for radiative transfer problems that breaks nesting, resulting in more thermal iterations but significantly fewer total inner transport iterations. Using the metric of total inner transport iterations, we investigate a crooked-pipe-like problem and a pseudo-shock-tube problem. Using only sweep preconditioning, we compare NKA against a typical inner / outer method employing GMRES / Newton and find NKA to be comparable or superior. Finally, we demonstrate the efficacy of applying diffusion-based preconditioning to grey problems in conjunction with NKA. (authors)
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.
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.
Rademacher, Georg; Warm, Stefan; Petermann, Klaus
2015-01-12
We analyze the impact of Differential Mode Delay (DMD) Management on the nonlinear impairments in mode-division multiplexed transmission systems. It is found out that DMD Management can lead to a degraded performance, due to enhanced intermodal nonlinear interaction. This can be attributed to an increased correlation of co-propagating channels, similar to the effects that show up in dispersion managed single-mode systems.
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.
Nonlinear programming for classification problems in machine learning
NASA Astrophysics Data System (ADS)
Astorino, Annabella; Fuduli, Antonio; Gaudioso, Manlio
2016-10-01
We survey some nonlinear models for classification problems arising in machine learning. In the last years this field has become more and more relevant due to a lot of practical applications, such as text and web classification, object recognition in machine vision, gene expression profile analysis, DNA and protein analysis, medical diagnosis, customer profiling etc. Classification deals with separation of sets by means of appropriate separation surfaces, which is generally obtained by solving a numerical optimization model. While linear separability is the basis of the most popular approach to classification, the Support Vector Machine (SVM), in the recent years using nonlinear separating surfaces has received some attention. The objective of this work is to recall some of such proposals, mainly in terms of the numerical optimization models. In particular we tackle the polyhedral, ellipsoidal, spherical and conical separation approaches and, for some of them, we also consider the semisupervised versions.
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.
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.
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.
Transmission of matter-wave solitons through nonlinear traps and barriers
Garnier, Josselin; Abdullaev, Fatkhulla Kh.
2006-07-15
The transmissions of matter-wave solitons through linear and nonlinear inhomogeneities induced by the spatial variations of the trap and the scattering length in Bose-Einstein condensates are investigated. The enhanced transmission of a soliton through a linear trap by a modulation of the scattering length, is exhibited. The theory is based on the perturbed inverse scattering transform for solitons, and we show that radiation effects are important. Numerical simulations of the Gross-Pitaevskii equation confirm the theoretical predictions.
Application of genetic algorithms in nonlinear heat conduction problems.
Kadri, Muhammad Bilal; 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.
Computer-aided analysis of nonlinear problems in transport phenomena
NASA Technical Reports Server (NTRS)
Brown, R. A.; Scriven, L. E.; Silliman, W. J.
1980-01-01
The paper describes algorithms for equilibrium and steady-state problems with coefficients in the expansions derived by the Galerkin weighted residual method and calculated from the resulting sets of nonlinear algebraic equations by the Newton-Raphson method. Initial approximations are obtained from nearby solutions by continuation techniques as parameters are varied. The Newton-Raphson technique is preferred because the Jacobian of the solution is useful for continuation, for analyzing the stability of solutions, for detecting bifurcation of solution families, and for computing asymptotic estimates of the effects on any solution of small changes in parameters, boundary conditions, and boundary shape.
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.
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.
Nonlinear problems of the theory of heterogeneous slightly curved shells
NASA Technical Reports Server (NTRS)
Kantor, B. Y.
1973-01-01
An account if given of the variational method of the solution of physically and geometrically nonlinear problems of the theory of heterogeneous slightly curved shells. Examined are the bending and supercritical behavior of plates and conical and spherical cupolas of variable thickness in a temperature field, taking into account the dependence of the elastic parameters on temperature. The bending, stability in general and load-bearing capacity of flexible isotropic elastic-plastic shells with different criteria of plasticity, taking into account compressibility and hardening. The effect of the plastic heterogeneity caused by heat treatment, surface work hardening and irradiation by fast neutron flux is investigated. Some problems of the dynamic behavior of flexible shells are solved. Calculations are performed in high approximations. Considerable attention is given to the construction of a machine algorithm and to the checking of the convergence of iterative processes.
Nonlinear high voltage transmission line for transversely excited CO{sub 2} lasers
Ishi, Akira; Yasuoka, Koichi; Tamagawa, Tohru
1995-12-31
A high voltage Pulse with the risetime less than a few hundreds nanoseconds and the amplitude of several tens kilovolts is required to establish stable glow discharge excitation in high power pulsed gas lasers. To make the high voltage pulse fast, we have developed a nonlinear high voltage transmission line for transversely excited CO{sub 2} lasers. Fig.1 shows the electrical circuit of switching unit, pulse sharpening unit with nonlinear high voltage transmission line and discharge electrodes for TE-CO{sub 2} laser. The nonlinear high voltage transmission line is a 15-step LC ladder circuit that consists of linear inductors (L=6 {mu}H) and nonlinear BaTiO{sub 3} capacitors. Fig.2 shows a capacitance dependence on applied voltages. If an LC ladder circuit is constructed using a capacitor with the characteristics, the transmission velocity is fast at the high-voltage section and is slow at the low-voltage section. High voltage pulse with slow risetime is expected to be sharpen. The voltage and the current waveforms of the discharge measured at the point {open_quotes}c{close_quotes}. The risetime of 1{mu}s of the input voltage pulse was compressed to less than 200 ns at the output terminal of the LC ladder circuit and the outout pulse was applied to the discharge gap of the laser.
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
Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers.
Le, Son Thai; Prilepsky, Jaroslaw E; Turitsyn, Sergei K
2014-11-03
In linear communication channels, spectral components (modes) defined by the Fourier transform of the signal propagate without interactions with each other. In certain nonlinear channels, such as the one modelled by the classical nonlinear Schrödinger equation, there are nonlinear modes (nonlinear signal spectrum) that also propagate without interacting with each other and without corresponding nonlinear cross talk, effectively, in a linear manner. Here, we describe in a constructive way how to introduce such nonlinear modes for a given input signal. We investigate the performance of the nonlinear inverse synthesis (NIS) method, in which the information is encoded directly onto the continuous part of the nonlinear signal spectrum. This transmission technique, combined with the appropriate distributed Raman amplification, can provide an effective eigenvalue division multiplexing with high spectral efficiency, thanks to highly suppressed channel cross talk. The proposed NIS approach can be integrated with any modulation formats. Here, we demonstrate numerically the feasibility of merging the NIS technique in a burst mode with high spectral efficiency methods, such as orthogonal frequency division multiplexing and Nyquist pulse shaping with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 4.5 dB, which is comparable to results achievable with multi-step per span digital back propagation.
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.
Modulated waves and pattern formation in coupled discrete nonlinear LC transmission lines.
Ndzana, Fabien Ii; Mohamadou, Alidou; Kofané, Timoléon C; English, Lars Q
2008-07-01
The conditions for the propagation of modulated waves on a system of two coupled discrete nonlinear LC transmission lines with negative nonlinear resistance are examined, each line of the network containing a finite number of cells. Our theoretical analysis shows that the telegrapher equations of the electrical transmission line can be reduced to a set of two coupled discrete complex Ginzburg-Landau equations. Using the standard linear stability analysis, we derive the expression for the growth rate of instability as a function of the wave numbers and system parameters, then obtain regions of modulational instability. Using numerical simulations, we examine the long-time dynamics of modulated waves in the line. This leads to the generation of nonlinear modulated waves which have the shape of a soliton for the fast and low modes. The effects of dissipative elements on the propagation are also shown. The analytical results are corroborated by numerical simulations.
2008-11-01
focused onto the films with a 10 cm focal length lens. The in- cident and transmitted laser energy were collected with a lens and measured...Laghumavarapu, J. Devulapalli, D. Rao, B. R. Kimball, M. Nakashima, and B. S. DeCristofano, “Optical power limiting with photoinduced anisotropy of azo ...benzene films ,” Appl. Opt. 42, 4560–4565 (2003). 8. N. Venkatram and D. N. Rao, “Nonlinear absorption, scatter- ing and optical limiting studies of CdS
Blind post processed nonlinearity mitigation in multiband OFDM radio over fiber optical transmission
NASA Astrophysics Data System (ADS)
Park, Hyoung-Joon; Jung, Sun-Young; Han, Sang-Kook
2016-02-01
We propose a blind adaptive post-processing method to reduce nonlinear distortion in multiband radio over fiber (RoF) transmission. Mitigating nonlinear distortion has been a critical challenge to enhance signal quality in RoF system due to analog optical transmission. To keep up with explosive increase in number of mobiles and their data capacity demands, remote antenna unit (RAU) has to be widely and densely distributed with RoF system. Consequently, RAU should be simple and compensation should be fully processed in central office (CO). In optical uplink transmission of RoF system, post-processing of distortion mitigation will be effective. In this paper, we propose post compensation structure constructed by means of Hammerstein equalizer without inserting preamble. Specifically, Hammerstein equalizer, which is separated into linear and nonlinear parts, was used to compensate both linear and nonlinear distortion of RoF system. The filter coefficients were updated adaptively by using LMS algorithm to adjust variable channel environments. In our experiment, multiband OFDM signal, which is LTE standard according to 3GPP, was optically transmitted through RoF channel. Experimental demonstration for the improvement of EVM performance with proposed post-processing was verified.
Word, Daniel P; Cummings, Derek A T; Burke, Donald S; Iamsirithaworn, Sopon; Laird, Carl D
2012-08-07
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
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.
Long-time dynamics of modulated waves in a nonlinear discrete LC transmission line.
Yemélé, David; Marquié, Patrick; Bilbault, Jean Marie
2003-07-01
The long-time dynamics of modulated waves in a nonlinear LC transmission line is investigated. Considering the higher-order nonlinear Schrödinger equation, we define analytically the conditions leading to the instability of modulated waves. We show that two kinds of instabilities may develop in the network depending on the frequency range of the chosen carrier wave and on the magnitude of its initial amplitude, which is confirmed by our numerical simulations. The nonreproducibility of numerical experiments on modulated waves is also considered.
NASA Astrophysics Data System (ADS)
Afshari, E.; Bhat, H. S.; Hajimiri, A.; Marsden, J. E.
2006-03-01
We propose a class of electrical circuits for extremely wideband (EWB) signal shaping. A one-dimensional, nonlinear, nonuniform transmission line is proposed for narrow pulse generation. A two-dimensional transmission lattice is proposed for EWB signal combining. Model equations for the circuits are derived. Theoretical and numerical solutions of the model equations are presented, showing that the circuits can be used for the desired application. The procedure by which the circuits are designed exemplifies a modern, mathematical design methodology for EWB circuits.
Skidin, Anton S; Sidelnikov, Oleg S; Fedoruk, Mikhail P; Turitsyn, Sergei K
2016-12-26
The impact of the fiber Kerr effect on error statistics in the nonlinear (high power) transmission of the OFDM 16-QAM signal over a 2000 km EDFA-based link is examined. We observed and quantified the difference in the error statistics for constellation points located at three power-defined rings. Theoretical analysis of a trade-off between redundancy and error rate reduction using probabilistic coding of three constellation power rings decreasing the symbol-error rate of OFDM 16-QAM signal is presented. Based on this analysis, we propose to mitigate the nonlinear impairments using the adaptive modulation technique applied to the OFDM 16-QAM signal. We demonstrate through numerical modelling the system performance improvement by the adaptive modulation for the large number of OFDM subcarriers (more than 100). We also show that a similar technique can be applied to single carrier transmission.
Khoo, Iam Choon; Hong, Kuan Lung; Zhao, Shuo; Ma, Ding; Lin, Tsung-Hsien
2013-02-25
Blue-phase liquid crystal (BPLC) is introduced into the pores of capillary arrays to fabricate fiber arrays. Owing to the photonic-crystals like properties of BPLC, these fiber arrays exhibit temperature dependent photonic bandgaps in the visible spectrum. With the cores maintained in isotropic as well as the Blue phases, the fiber arrays allow high quality image transmission when inserted in the focal plane of a 1x telescope. Nonlinear transmission and optical limiting action on a cw white-light continuum laser is also observed and is attributed to laser induced self-defocusing and propagation modes changing effects caused by some finite absorption of the broadband laser at the short wavelength regime. These nonlinear and other known electro-optical properties of BPLC, in conjunction with their fabrication ease make these fiber arrays highly promising for imaging, electro-optical or all-optical modulation, switching and passive optical limiting applications.
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.
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.
A Parametric Study of Nonlinear Seismic Response Analysis of Transmission Line Structures
Wang, Yanming; Yi, Zhenhua
2014-01-01
A parametric study of nonlinear seismic response analysis of transmission line structures subjected to earthquake loading is studied in this paper. The transmission lines are modeled by cable element which accounts for the nonlinearity of the cable based on a real project. Nonuniform ground motions are generated using a stochastic approach based on random vibration analysis. The effects of multicomponent ground motions, correlations among multicomponent ground motions, wave travel, coherency loss, and local site on the responses of the cables are investigated using nonlinear time history analysis method, respectively. The results show the multicomponent seismic excitations should be considered, but the correlations among multicomponent ground motions could be neglected. The wave passage effect has a significant influence on the responses of the cables. The change of the degree of coherency loss has little influence on the response of the cables, but the responses of the cables are affected significantly by the effect of coherency loss. The responses of the cables change little with the degree of the difference of site condition changing. The effect of multicomponent ground motions, wave passage, coherency loss, and local site should be considered for the seismic design of the transmission line structures. PMID:25133215
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.
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.
Nonlinear phase noise mitigation in phase-sensitive amplified transmission systems.
Olsson, Samuel L I; Karlsson, Magnus; Andrekson, Peter A
2015-05-04
We investigate the impact of in-line amplifier noise in transmission systems amplified by two-mode phase-sensitive amplifiers (PSAs) and present the first experimental demonstration of nonlinear phase noise (NLPN) mitigation in a modulation format independent PSA-amplified transmission system. The NLPN mitigation capability is attributed to the correlated noise on the signal and idler waves at the input of the transmission span. We study a single-span system with noise loading in the transmitter but the results are expected to be applicable also in multi-span systems. The experimental investigation is supported by numerical simulations showing excellent agreement with the experiments. In addition to demonstrating NLPN mitigation we also present a record high sensitivity receiver, enabled by low-noise PSA-amplification, requiring only 4.1 photons per bit to obtain a bit error ratio (BER) of 1 × 10(-3) with 10 GBd quadrature phase-shift keying (QPSK) data.
Linear or Nonlinear Problems with Input Sets. II.
1987-03-06
particular, the Burgers’ equation , the KdV equation , and the Lin-Tsien equation are analyzed. In all cases the particular group includes arbitrary...Construction of Approximate Solutions 1. Bounds for Spatially Nonhomogeneous Model Boltzmann Energy Equations (E. Adams, J. Herod, H. Spreuer) Nonlinear...Journal of Nonlinear Analysis and Applications. 2. Nonlinear Constitutive Equations and Uniform Boundedness of Perturbed Solutions of Evolution-Type (E
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
Scaling properties of weakly nonlinear coefficients in the Faraday problem.
Skeldon, A C; Porter, J
2011-07-01
Interesting and exotic surface wave patterns have regularly been observed in the Faraday experiment. Although symmetry arguments provide a qualitative explanation for the selection of some of these patterns (e.g., superlattices), quantitative analysis is hindered by mathematical difficulties inherent in a time-dependent, free-boundary Navier-Stokes problem. More tractable low viscosity approximations are available, but these do not necessarily capture the moderate viscosity regime of the most interesting experiments. Here we focus on weakly nonlinear behavior and compare the scaling results derived from symmetry arguments in the low viscosity limit with the computed coefficients of appropriate amplitude equations using both the full Navier-Stokes equations and a reduced set of partial differential equations due to Zhang and Vinãls. We find the range of viscosities over which one can expect "low viscosity" theories to hold. We also find that there is an optimal viscosity range for locating superlattice patterns experimentally-large enough that the region of parameters giving stable patterns is not impracticably small, yet not so large that crucial resonance effects are washed out. These results help explain some of the discrepancies between theory and experiment.
Problem of inflation in nonlinear multidimensional cosmological models
Saidov, Tamerlan; Zhuk, Alexander
2009-01-15
We consider a multidimensional cosmological model with nonlinear quadratic R{sup 2} and quartic R{sup 4} actions. As a matter source, we include a monopole form field, a D-dimensional bare cosmological constant and the tensions of branes located at fixed points. In the spirit of the universal extra dimension model, the standard model fields are not localized on branes, but rather they can move in the bulk. We define conditions that ensure stable compactification of the internal space in zero minima of the effective potentials. Such effective potentials may have a rather complicated form with a number of local minima, maxima, and saddle points. We investigate inflation in such models. It is shown that the R{sup 2}- and R{sup 4} models can produce up to 10 and 22 e-foldings, respectively. These values are not sufficient to solve the homogeneity and isotropy problem, but they are large enough to explain recent cosmic microwave background data. Additionally, the R{sup 4} model can provide conditions for eternal topological inflation. The main drawback of the obtained inflationary models consists in a spectral index n{sub s} that is less than the presently observed n{sub s}{approx_equal}1. For the R{sup 4} model we find, e.g., n{sub s}{approx_equal}0.61.
Research progress of wireless power transmission technology and the related problems
NASA Astrophysics Data System (ADS)
Li, Jianliang
2017-03-01
Wireless Power Transfer (WPT) has been widely used in recent years, it has the advantages of high transmission efficiency, long transmission distance, and so on. Firstly, this paper introduces the application progress of transmission technology at home and abroad. Secondly, combined with the development of the current technology, this paper puts forward the basic problems of wireless power transmission technology from four aspects. Lastly, the paper summarizes and puts forward the current hot and difficult problems.
Dynamical systems approaches to nonlinear problems in systems and circuits
Salam, F.M.A.; Levi, M.L.
1988-01-01
Applications of dynamical-systems analysis to nonlinear circuits and physical systems are discussed in reviews and reports. Topics addressed include general analytical methods, general simulation methods, nonlinear circuits and systems in electrical engineering, control systems, solids and vibrations, and mechanical systems. Consideration is given to the applicability of the Mel'nikov method to highly dissipative systems, damping in nonlinear solid mechanics, a three-dimensional rotation instrument for displaying strange attractors, a chaotic saddle catastrophe in forced oscillators, soliton experiments in annular Josephson junctions, local bifurcation control, periodic and chaotic motions of a buckled beam experiencing parametric and external excitation, and robust nonlinear computed torque control for robot manipulators.
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.
Transmission scattering problem via a DtN map
NASA Astrophysics Data System (ADS)
Lee, Kuo-Ming
2017-03-01
In this paper, we consider the scattering problem of time-harmonic waves from a penetrable obstacle. A Dirichlet-to-Neumann map is defined to convert this problem into an exterior boundary value problem which mimics an impedance problem. This process reduces the size of the problem and thus enables an elegant treatment of the scattering problem.
Repetitive sub-gigawatt rf source based on gyromagnetic nonlinear transmission line
NASA Astrophysics Data System (ADS)
Romanchenko, Ilya V.; Rostov, Vladislav V.; Gubanov, Vladimir P.; Stepchenko, Alexey S.; Gunin, Alexander V.; Kurkan, Ivan K.
2012-07-01
We demonstrate a high power repetitive rf source using gyromagnetic nonlinear transmission line to produce rf oscillations. Saturated NiZn ferrites act as active nonlinear medium first sharpening the pumping high voltage nanosecond pulse and then radiating at central frequency of about 1 GHz: shock rise time excites gyromagnetic precession in ferrites forming damping rf oscillations. The optimal length of nonlinear transmission line was found to be of about 1 m. SINUS-200 high voltage driver with Tesla transformer incorporated into pulse forming line has been designed and fabricated to produce bursts of 1000 pulses with 200 Hz repetition rate. A band-pass filter and mode-converter have been designed to extract rf pulse from low-frequency component and to form TE11 mode of circular waveguide with linear polarization. A wide-band horn antenna has been fabricated to form Gaussian distribution of radiation pattern. The peak value of electric field strength of a radiated pulse at the distance of 3.5 m away from antenna is measured to be 160 kV/m. The corresponding rf peak power of 260 MW was achieved.
Repetitive sub-gigawatt rf source based on gyromagnetic nonlinear transmission line.
Romanchenko, Ilya V; Rostov, Vladislav V; Gubanov, Vladimir P; Stepchenko, Alexey S; Gunin, Alexander V; Kurkan, Ivan K
2012-07-01
We demonstrate a high power repetitive rf source using gyromagnetic nonlinear transmission line to produce rf oscillations. Saturated NiZn ferrites act as active nonlinear medium first sharpening the pumping high voltage nanosecond pulse and then radiating at central frequency of about 1 GHz: shock rise time excites gyromagnetic precession in ferrites forming damping rf oscillations. The optimal length of nonlinear transmission line was found to be of about 1 m. SINUS-200 high voltage driver with Tesla transformer incorporated into pulse forming line has been designed and fabricated to produce bursts of 1000 pulses with 200 Hz repetition rate. A band-pass filter and mode-converter have been designed to extract rf pulse from low-frequency component and to form TE(11) mode of circular waveguide with linear polarization. A wide-band horn antenna has been fabricated to form Gaussian distribution of radiation pattern. The peak value of electric field strength of a radiated pulse at the distance of 3.5 m away from antenna is measured to be 160 kV/m. The corresponding rf peak power of 260 MW was achieved.
Transmission of pulses in a dispersion-managed fiber link with extra nonlinear segments
NASA Astrophysics Data System (ADS)
Driben, Rodislav; Malomed, Boris A.; Chu, P. L.
2005-01-01
We introduce an extended version of the dispersion-management (DM) model, which includes an extra nonlinear element, and consider transmission of return-to-zero pulses in this system (they are not solitons). The pulses feature self-compression, accompanied by generation of side peaks (in the temporal domain). An optimal transmission distance, zopt, is identified, up to which the pulse continues to compress itself (the eventual width-compression factor is ≃2), while the amplitude of the side peaks remains small enough. The distance zopt virtually does not depend on the strength S of the DM part of the system in the interval 1.5 < S < 11, but it is sensitive to the nonlinearity strength in the extra segment. The system provides essentially stronger suppression of the noise-induced jitter of the pulses than the ordinary DM model. The most important issue is interaction between adjacent pulses, which is a basic difficulty in the case of DM solitons. In a broad parameter region, the system provides effective isolation between pulses. The minimum initial temporal distance between them, necessary for the isolation, is quite small, slightly larger than 1.5 the pulse's width. The transmission actually improves the quality of multi-pulse arrays, as it leads to deepening of hiatuses between originally overlapping pulses.
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.
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
Zibar, Darko; Winther, Ole; Franceschi, Niccolo; Borkowski, Robert; Caballero, Antonio; Arlunno, Valeria; Schmidt, Mikkel N; Gonzales, Neil Guerrero; Mao, Bangning; Ye, Yabin; Larsen, Knud J; Monroy, Idelfonso Tafur
2012-12-10
In this paper, we show numerically and experimentally that expectation maximization (EM) algorithm is a powerful tool in combating system impairments such as fibre nonlinearities, inphase and quadrature (I/Q) modulator imperfections and laser linewidth. The EM algorithm is an iterative algorithm that can be used to compensate for the impairments which have an imprint on a signal constellation, i.e. rotation and distortion of the constellation points. The EM is especially effective for combating non-linear phase noise (NLPN). It is because NLPN severely distorts the signal constellation and this can be tracked by the EM. The gain in the nonlinear system tolerance for the system under consideration is shown to be dependent on the transmission scenario. We show experimentally that for a dispersion managed polarization multiplexed 16-QAM system at 14 Gbaud a gain in the nonlinear system tolerance of up to 3 dB can be obtained. For, a dispersion unmanaged system this gain reduces to 0.5 dB.
NASA Astrophysics Data System (ADS)
Swaidan, Waleeda; Hussin, Amran
2015-10-01
Most direct methods solve finite time horizon optimal control problems with nonlinear programming solver. In this paper, we propose a numerical method for solving nonlinear optimal control problem with state and control inequality constraints. This method used quasilinearization technique and Haar wavelet operational matrix to convert the nonlinear optimal control problem into a quadratic programming problem. The linear inequality constraints for trajectories variables are converted to quadratic programming constraint by using Haar wavelet collocation method. The proposed method has been applied to solve Optimal Control of Multi-Item Inventory Model. The accuracy of the states, controls and cost can be improved by increasing the Haar wavelet resolution.
Inference of Stochastic Nonlinear Oscillators with Applications to Physiological Problems
NASA Technical Reports Server (NTRS)
Smelyanskiy, Vadim N.; Luchinsky, Dmitry G.
2004-01-01
A new method of inferencing of coupled stochastic nonlinear oscillators is described. The technique does not require extensive global optimization, provides optimal compensation for noise-induced errors and is robust in a broad range of dynamical models. We illustrate the main ideas of the technique by inferencing a model of five globally and locally coupled noisy oscillators. Specific modifications of the technique for inferencing hidden degrees of freedom of coupled nonlinear oscillators is discussed in the context of physiological applications.
Some problems of nonlinear waves in solid propellant rocket motors
NASA Technical Reports Server (NTRS)
Culick, F. E. C.
1979-01-01
An approximate technique for analyzing nonlinear waves in solid propellant rocket motors is presented which inexpensively provides accurate results up to amplitudes of ten percent. The connection with linear stability analysis is shown. The method is extended to third order in the amplitude of wave motion in order to study nonlinear stability, or triggering. Application of the approximate method to the behavior of pulses is described.
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.
From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation
Egozcue, J. Meziat, R. Pedregal, P.
2002-12-19
We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature.
NASA Astrophysics Data System (ADS)
Saïdou, Abdoulkary; Alidou, Mohamadou; Ousmanou, Dafounansou; Serge Yamigno, Doka
2014-12-01
We investigated exact traveling soliton solutions for the nonlinear electrical transmission line. By applying a concise and straightforward method, the variable-coefficient discrete (G'/G)-expansion method, we solve the nonlinear differential—difference equations associated with the network. We obtain some exact traveling wave solutions which include hyperbolic function solution, trigonometric function solution, rational solutions with arbitrary function, bright as well as dark solutions.
Lossless Convexification of Control Constraints for a Class of Nonlinear Optimal Control Problems
NASA Technical Reports Server (NTRS)
Blackmore, Lars; Acikmese, Behcet; Carson, John M.,III
2012-01-01
In this paper we consider a class of optimal control problems that have continuous-time nonlinear dynamics and nonconvex control constraints. We propose a convex relaxation of the nonconvex control constraints, and prove that the optimal solution to the relaxed problem is the globally optimal solution to the original problem with nonconvex control constraints. This lossless convexification enables a computationally simpler problem to be solved instead of the original problem. We demonstrate the approach in simulation with a planetary soft landing problem involving a nonlinear gravity field.
NASA 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.
Freeform illumination design: a nonlinear boundary problem for the elliptic Monge-Ampére equation.
Wu, Rengmao; Xu, Liang; Liu, Peng; Zhang, Yaqin; Zheng, Zhenrong; Li, Haifeng; Liu, Xu
2013-01-15
We propose an approach to deal with the problem of freeform surface illumination design without assuming any symmetry based on the concept that this problem is similar to the problem of optimal mass transport. With this approach, the freeform design is converted into a nonlinear boundary problem for the elliptic Monge-Ampére equation. The theory and numerical method are given for solving this boundary problem. Experimental results show the feasibility of this approach in tackling this freeform design problem.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
NASA Technical Reports Server (NTRS)
Cerro, J. A.; Scotti, S. J.
1991-01-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
Evaluation of a transfinite element numerical solution method for nonlinear heat transfer problems
NASA Astrophysics Data System (ADS)
Cerro, J. A.; Scotti, S. J.
1991-07-01
Laplace transform techniques have been widely used to solve linear, transient field problems. A transform-based algorithm enables calculation of the response at selected times of interest without the need for stepping in time as required by conventional time integration schemes. The elimination of time stepping can substantially reduce computer time when transform techniques are implemented in a numerical finite element program. The coupling of transform techniques with spatial discretization techniques such as the finite element method has resulted in what are known as transfinite element methods. Recently attempts have been made to extend the transfinite element method to solve nonlinear, transient field problems. This paper examines the theoretical basis and numerical implementation of one such algorithm, applied to nonlinear heat transfer problems. The problem is linearized and solved by requiring a numerical iteration at selected times of interest. While shown to be acceptable for weakly nonlinear problems, this algorithm is ineffective as a general nonlinear solution method.
NASA Astrophysics Data System (ADS)
Zou, Li; Liang, Songxin; Li, Yawei; Jeffrey, David J.
2017-03-01
Nonlinear boundary value problems arise frequently in physical and mechanical sciences. An effective analytic approach with two parameters is first proposed for solving nonlinear boundary value problems. It is demonstrated that solutions given by the two-parameter method are more accurate than solutions given by the Adomian decomposition method (ADM). It is further demonstrated that solutions given by the ADM can also be recovered from the solutions given by the two-parameter method. The effectiveness of this method is demonstrated by solving some nonlinear boundary value problems modeling beam-type nano-electromechanical systems.
NASA Astrophysics Data System (ADS)
Moreira, Diego; Wang, Lihe
2014-08-01
In this paper, we prove a Hausdorff measure estimate for the free boundaries of subsolutions of fully nonlinear and quasilinear equations of the type and where and μ is a signed Radon measure with some appropriate growth condition. Gradient estimates for nonnegative harmonic functions with bounded normal derivatives along the boundary obtained by Caffarelli and Salsa (Geometric Approach to Free Boundary Problems,
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.
NASA Astrophysics Data System (ADS)
Duarte, Vanessa C.; Drummond, Miguel V.; Nogueira, Rogério N.
2013-11-01
Advanced modulation formats are an emerging area since they allow reducing the symbol rate while encoding more bits per symbol. This allows higher spectral efficiencies. In addition, we can achieve higher data rates using lower-speed equipment like in all-optical format conversion systems, an important step for the development of systems with high transmission rates. In this paper we study the impact of some impairments found in all-optical advanced format conversions based on cross phase modulation (XPM) on a highly nonlinear fiber (HNLF), such as amplified spontaneous emission (ASE), nonlinear fiber length and group velocity dispersion (GVD), and analyze its performance based on error vector magnitude (EVM) for different bitrate transmissions. This simulation study is applied on earlier proposed phase modulated format conversion where n nonreturn-to-zero on-off keying (NRZ-OOK) channels at 10 Gb/s are converted into a return-to-zero m phase shift keying (RZ-mPSK) at 20Gb/s. We extend the work with simulations and show the results for n NRZ-OOK channels at 20Gb/s, 40 Gb/s and 50Gb/s to RZ-PSK at 40Gb/s, 80 Gb/s and 100Gb/s, respectively.
Nonlinear Programming Problems Associated with Closed Range Operators
Aizicovici, S.; Motreanu, D.; Pavel, N. H.
1999-09-15
Necessary conditions for the optimality of a pair (y-bar, u-bar) with respect to a locally Lipschitz cost functional L(y,u) , subject to Ay + F(y) = Cu + B(u) , are given in terms of generalized gradients. Here A and C are densely defined, closed, linear operators on some Banach spaces, while F and B are (Frechet) differentiable maps, which are suitably related to A and C . Various examples and potential applications to nonlinear programming models and nonlinear optimal control of partial differential equations are also discussed.
Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design
Liao, Ben-Shan; Bai, Zhaojun; Lee, Lie-Quan; Ko, Kwok; /SLAC
2006-09-28
A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.
NASA Astrophysics Data System (ADS)
Goldsworthy, Ray L.; Greenberg, Julie E.
2004-12-01
The Speech Transmission Index (STI) is a physical metric that is well correlated with the intelligibility of speech degraded by additive noise and reverberation. The traditional STI uses modulated noise as a probe signal and is valid for assessing degradations that result from linear operations on the speech signal. Researchers have attempted to extend the STI to predict the intelligibility of nonlinearly processed speech by proposing variations that use speech as a probe signal. This work considers four previously proposed speech-based STI methods and four novel methods, studied under conditions of additive noise, reverberation, and two nonlinear operations (envelope thresholding and spectral subtraction). Analyzing intermediate metrics in the STI calculation reveals why some methods fail for nonlinear operations. Results indicate that none of the previously proposed methods is adequate for all of the conditions considered, while four proposed methods produce qualitatively reasonable results and warrant further study. The discussion considers the relevance of this work to predicting the intelligibility of cochlear-implant processed speech. .
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.
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…
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
2014-05-01
Gyromagnetic Nonlinear Transmission Lines (NLTLs) generate microwaves through the damped gyromagnetic precession of the magnetic moments in ferrimagnetic material, and are thus utilized as compact, solid-state, frequency agile, high power microwave (HPM) sources. The output frequency of a NLTL can be adjusted by control of the externally applied bias field and incident voltage pulse without physical alteration to the structure of the device. This property provides a frequency tuning capability not seen in many conventional e-beam based HPM sources. The NLTLs developed and tested are mesoband sources capable of generating MW power levels in the L, S, and C bands of the microwave spectrum. For an individual NLTL the output power at a given frequency is determined by several factors including the intrinsic properties of the ferrimagnetic material and the transmission line structure. Hence, if higher power levels are to be achieved, it is necessary to combine the outputs of multiple NLTLs. This can be accomplished in free space using antennas or in a transmission line via a power combiner. Using a bias-field controlled delay, a transient, high voltage, coaxial, three port, power combiner was designed and tested. Experimental results are compared with the results of a transient COMSOL simulation to evaluate combiner performance.
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 Technical Reports Server (NTRS)
Gabrielsen, R. E.; Karel, S.
1975-01-01
An algorithm for solving the nonlinear stationary Navier-Stokes problem is developed. Explicit error estimates are given. This mathematical technique is potentially adaptable to the separation problem.
Fundamental immunological problems associated with "transmissible spongiform encephalopathies".
Ebringer, Alan; Rashid, Taha; Wilson, Clyde
2015-02-01
"Bovine spongiform encephalopathy", "scrapie", as well as Creutzfeldt-Jakob disease and kuru belong to a group of related neurological conditions termed "transmissible spongiform encephalopathies". These diseases are based on the LD50 measurement whereby saline brain homogenates are injected into experimental animals and when 50% of them develop symptoms, this is considered as transmission of the disease, but the gold standard for diagnosis is autopsy examination. However, an untenable assumption is being made in that saline brain homogenates do not cause tissue damage but it is known since the time of Pasteur, that they give rise to "post-rabies vaccination allergic encephalomyelitis". This is the fundamental flaw in the diagnosis of these diseases. A way forward, however, is to examine infectious agents, such as Acinetobacter which show molecular mimicry with myelin and elevated levels of antibodies to this microbe are found in multiple sclerosis patients and animals affected by "bovine spongiform encephalopathy".
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.
Zhang, Songchuan; Xia, Youshen
2016-12-28
Much research has been devoted to complex-variable optimization problems due to their engineering applications. However, the complex-valued optimization method for solving complex-variable optimization problems is still an active research area. This paper proposes two efficient complex-valued optimization methods for solving constrained nonlinear optimization problems of real functions in complex variables, respectively. One solves the complex-valued nonlinear programming problem with linear equality constraints. Another solves the complex-valued nonlinear programming problem with both linear equality constraints and an ℓ₁-norm constraint. Theoretically, we prove the global convergence of the proposed two complex-valued optimization algorithms under mild conditions. The proposed two algorithms can solve the complex-valued optimization problem completely in the complex domain and significantly extend existing complex-valued optimization algorithms. Numerical results further show that the proposed two algorithms have a faster speed than several conventional real-valued optimization algorithms.
Nonlinear Problems in Fluid Dynamics and Inverse Scattering
1993-05-31
We have demonstrated that a certain class of multidimensional extensions of the well- known Korteweg - deVries equations , often referred to as higher...ion and multiplication in the wavelets bases. Several additional algorithms relevant to solving the nonlinear equations and capturing the...algorithms for solving n1ow linear equations grew into a sizable effort. I work now with two graduate students. .laies IKeiser and Robert Cramer. With
Nonlinear wave interaction problems in the three-dimensional case
NASA Astrophysics Data System (ADS)
Curró, C.; Manganaro, N.; Pavlov, M. V.
2017-01-01
Three-dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three-dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous semi-Hamiltonian hydrodynamic type systems (i.e. possess diagonal form and infinitely many conservation laws). The interaction of N waves was studied. In particular we prove that they behave like simple waves and they distort after the collision region. The amount of the distortion can be analytically computed.
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.
Existence and multiplicity results for some nonlinear problems with singular ϕ-Laplacian
NASA Astrophysics Data System (ADS)
Bereanu, C.; Mawhin, J.
Using Leray-Schauder degree theory we obtain various existence and multiplicity results for nonlinear boundary value problems (ϕ(u))=f(t,u,u), l(u,u)=0 where l(u,u)=0 denotes the Dirichlet, periodic or Neumann boundary conditions on [0,T], ϕ :]-a,a[→R is an increasing homeomorphism, ϕ(0)=0. The Dirichlet problem is always solvable. For Neumann or periodic boundary conditions, we obtain in particular existence conditions for nonlinearities which satisfy some sign conditions, upper and lower solutions theorems, Ambrosetti-Prodi type results. We prove Lazer-Solimini type results for singular nonlinearities and periodic boundary conditions.
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.
Semrau, Daniel; Xu, Tianhua; Shevchenko, Nikita A; Paskov, Milen; Alvarado, Alex; Killey, Robert I; Bayvel, Polina
2017-01-01
Achievable information rates (AIRs) of wideband optical communication systems using a ∼40 nm (∼5 THz) erbium-doped fiber amplifier and ∼100 nm (∼12.5 THz) distributed Raman amplification are estimated based on a first-order perturbation analysis. The AIRs of each individual channel have been evaluated for DP-64QAM, DP-256QAM, and DP-1024QAM modulation formats. The impact of full-field nonlinear compensation (FF-NLC) and probabilistically shaped constellations using a Maxwell-Boltzmann distribution were studied and compared to electronic dispersion compensation. It has been found that a probabilistically shaped DP-1024QAM constellation, combined with FF-NLC, yields achievable information rates of ∼75 Tbit/s for the EDFA scheme and ∼223 Tbit/s for the Raman amplification scheme over a 2000 km standard single-mode fiber transmission.
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 .
Inverse Problem of Variational Calculus for Nonlinear Evolution Equations
NASA Astrophysics Data System (ADS)
Ali, Sk. Golam; Talukdar, B.; Das, U.
2007-06-01
We couple a nonlinear evolution equation with an associated one and derive the action principle. This allows us to write the Lagrangian density of the system in terms of the original field variables rather than Casimir potentials. We find that the corresponding Hamiltonian density provides a natural basis to recast the pair of equations in the canonical form. Amongst the case studies presented the KdV and modified KdV pairs exhibit bi-Hamiltonian structure and allow one to realize the associated fields in physical terms.
Characterization of the shape stability for nonlinear elliptic problems
NASA Astrophysics Data System (ADS)
Bucur, Dorin
We characterize all geometric perturbations of an open set, for which the solution of a nonlinear elliptic PDE of p-Laplacian type with Dirichlet boundary condition is stable in the L-norm. The necessary and sufficient conditions are jointly expressed by a geometric property associated to the γ-convergence. If the dimension N of the space satisfies N-1
NASA Astrophysics Data System (ADS)
Cotta, R. M.; Naveira-Cotta, C. P.; Knupp, D. C.; Zotin, J. L. Z.; Pontes, P. C.
2016-09-01
This lecture offers an updated review on the Generalized Integral Transform Technique (GITT), with focus on handling complex geometries, coupled problems, and nonlinear convection-diffusion, so as to illustrate some new application paradigms. Special emphasis is given to demonstrating novel developments, such as a single domain reformulation strategy that simplifies the treatment of complex geometries, an integral balance scheme in handling multiscale problems, the adoption of convective eigenvalue problems in dealing with strongly convective formulations, and the direct integral transformation of nonlinear convection-diffusion problems based on nonlinear eigenvalue problems. Representative application examples are then provided that employ recent extensions on the Generalized Integral Transform Technique (GITT), and a few numerical results are reported to illustrate the convergence characteristics of the proposed eigenfunction expansions.
Xia, Youshen; Feng, Gang; Wang, Jun
2008-08-01
This paper presents a novel recurrent neural network for solving nonlinear optimization problems with inequality constraints. Under the condition that the Hessian matrix of the associated Lagrangian function is positive semidefinite, it is shown that the proposed neural network is stable at a Karush-Kuhn-Tucker point in the sense of Lyapunov and its output trajectory is globally convergent to a minimum solution. Compared with variety of the existing projection neural networks, including their extensions and modification, for solving such nonlinearly constrained optimization problems, it is shown that the proposed neural network can solve constrained convex optimization problems and a class of constrained nonconvex optimization problems and there is no restriction on the initial point. Simulation results show the effectiveness of the proposed neural network in solving nonlinearly constrained optimization problems.
NASA Astrophysics Data System (ADS)
Enokida, Ryuta; Takewaki, Izuru; Stoten, David
2014-12-01
The problem of control system design can be conceptualised as identifying an input signal to a plant (the system to be controlled) so that the corresponding output matches that of a pre-defined reference signal. Primarily, this problem is solved via well-known techniques based upon the principle of feedback design, an essential component for ensuring stability and robustness of the controlled system. However, feedforward design techniques also have a large part to play, whereby (in the absence of feedback control and assuming that the plant is stable) a model of the plant dynamics can be used to modify the reference signal so that the resultant feedforward input signal generates a plant output signal that is sufficiently close to the original reference signal. The principal objective of this paper is to introduce a new nonlinear control method, called nonlinear signal-based control (NSBC) that can be executed as an on-line technique of feedforward compensation (used synonymously here with the phrase 'input identification') and an off-line technique of feedback compensation. NSBC determines the feedforward input signal to the plant by using an error signal, determined from the difference between the output signals from a linear model of the plant and from the nonlinear plant, under the same input signal. The efficacy of NSBC is examined via numerical examples using Matlab/Simulink and compared with alternative well-known methods based upon inverse transfer function compensation and also the method of high gain feedback control. NSBC was found to provide the most accurate input identification in all the examined cases of linear or nonlinear single-input, single-output and single-input, multi-output (SIMO) systems. Furthermore, in problems of structural and earthquake engineering, NSBC was also found to be particularly effective in estimating the original ground motion from a nonlinear SIMO system and its response.
NASA Astrophysics Data System (ADS)
Bianchi, Matteo; Scarpa, Fabrizio
2013-08-01
This work describes the vibration transmissibility behaviour in conventional and auxetic (negative Poisson’s ratio) foams under low and high amplitude vibrations. Auxetic foam pads were manufactured from conventional open cell PU-PE based blocks using an alternative manufacturing process to the one currently used in the mainstream literature. The dynamic behaviour of both conventional and auxetic porous materials was assessed within the frequency bandwidth 5-500 Hz using a base excitation technique with a calibrated seismic mass. The foam pads were subjected to white noise broadband excitation at low dynamic strain, followed by a sine sweep around the resonance of the foam-mass system. The experimental data have been used to perform an inverse identification of the nonlinear dependence of the foam permeability versus the amplitude and frequency of excitation using a single-degree-of-freedom poroelastic vibration model. The auxetic foam shows higher dynamic stiffness and enhanced viscous dissipation characteristics, in particular when subjected to nonlinear vibration loading.
A Robust Bayesian Random Effects Model for Nonlinear Calibration Problems
Fong, Y.; Wakefield, J.; De Rosa, S.; Frahm, N.
2013-01-01
Summary In the context of a bioassay or an immunoassay, calibration means fitting a curve, usually nonlinear, through the observations collected on a set of samples containing known concentrations of a target substance, and then using the fitted curve and observations collected on samples of interest to predict the concentrations of the target substance in these samples. Recent technological advances have greatly improved our ability to quantify minute amounts of substance from a tiny volume of biological sample. This has in turn led to a need to improve statistical methods for calibration. In this paper, we focus on developing calibration methods robust to dependent outliers. We introduce a novel normal mixture model with dependent error terms to model the experimental noise. In addition, we propose a re-parameterization of the five parameter logistic nonlinear regression model that allows us to better incorporate prior information. We examine the performance of our methods with simulation studies and show that they lead to a substantial increase in performance measured in terms of mean squared error of estimation and a measure of the average prediction accuracy. A real data example from the HIV Vaccine Trials Network Laboratory is used to illustrate the methods. PMID:22551415
Solution algorithms for non-linear singularly perturbed optimal control problems
NASA Technical Reports Server (NTRS)
Ardema, M. D.
1983-01-01
The applicability and usefulness of several classical and other methods for solving the two-point boundary-value problem which arises in non-linear singularly perturbed optimal control are assessed. Specific algorithms of the Picard, Newton and averaging types are formally developed for this class of problem. The computational requirements associated with each algorithm are analysed and compared with the computational requirement of the method of matched asymptotic expansions. Approximate solutions to a linear and a non-linear problem are obtained by each method and compared.
Continuous Dependence on Modeling in the Cauchy Problem for Nonlinear Elliptic Equations.
1987-04-01
parameter 4. AMON INTRODUCTION A problem in ordinary or partial differential equations is said to properly posed if it has a unique solution in the...problem for second-order nonlinear partial differential equations , Doctoral thesis, Cornell University, Ithaca, N.Y., 1986. [6] J. Conlan and G. N. Trytten...IModeling in the Cauchy Problem for Nonlinear Elliptic Equations by Allan Bennett DT1C A z1t17n m (It C ltd n Inttt " CENTER.FOR.NAVAL.ANALYSFS 4401
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.
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.
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.
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.
Asymptotic solutions of weakly nonlinear, dispersive wave-propagation problems by Fourier analysis
Srinivasan, R.
1989-01-01
A perturbation method based on Fourier analysis and multiple scales is introduced for solving weakly nonlinear, dispersive wave propagation problems with Fourier transformable initial conditions. Asymptotic solutions are derived for the weakly nonlinear cubic Schroedinger (NLS) equation with variable coefficients and the weakly nonlinear Kortewegde-Vries (KdV) equation; the results for the NLS equation are verified by comparison with numerical solutions. In the special case of constant coefficients, the asymptotic solution for the weakly nonlinear NLS equation agrees to leading order with previously derived results in the literature; in general, this is not true to higher orders. Therefore previous asymptotic results for the strongly nonlinear Schroedinger equation can be valid only for restricted initial conditions. Similar conclusions apply to the KdV equation.
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…
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.
NASA Astrophysics Data System (ADS)
Gou, Pengqi; Wang, Kaihui; Qin, Chaoyi; Yu, Jianjun
2017-03-01
We experimentally demonstrate a 16-ary quadrature amplitude modulation (16QAM) DFT-spread optical orthogonal frequency division multiplexing (OFDM) transmission system utilizing a cost-effective directly modulated laser (DML) and direct detection. For 20-Gbaud 16QAM-OFDM signal, with the aid of nonlinear equalization (NLE) algorithm, we respectively provide 6.2-dB and 5.2-dB receiver sensitivity improvement under the hard-decision forward-error-correction (HD-FEC) threshold of 3.8×10-3 for the back-to-back (BTB) case and after transmission over 10-km standard single mode fiber (SSMF) case, related to only adopt post-equalization scheme. To our knowledge, this is the first time to use dynamic nonlinear equalizer (NLE) based on the summation of the square of the difference between samples in one IM/DD OFDM system with DML to mitigate nonlinear distortion.
1986-04-30
TenCate , who is supported by ONR Contract NOOO I 4-84-K-0574, in the completion of work on pure tones that interact in higher order modes of a...rectangular duct.26 Through collaboration with TenCate , Lind has acquired experience with the same experimental apparatus that he will use beginning I June...34 J. Acoust. Soc. " .. Am. 65.1127-1133(1979). 36. J. A TenCate and K F. Hamilton, "Dispersive nonlinear wave interactions in a rectangular duct," In
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.
Upper error bounds on calculated outputs of interest for linear and nonlinear structural problems
NASA Astrophysics Data System (ADS)
Ladevèze, Pierre
2006-07-01
This Note introduces new strict upper error bounds on outputs of interest for linear as well as time-dependent nonlinear structural problems calculated by the finite element method. Small-displacement problems without softening, such as (visco)plasticity problems, are included through the standard thermodynamics framework involving internal state variables. To cite this article: P. Ladevèze, C. R. Mecanique 334 (2006).
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.
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.)…
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.
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.
Kaikina, Elena I.
2013-11-15
We consider the inhomogeneous Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation, formulated on a half-line. We study traditionally important problems of the theory of nonlinear partial differential equations, such as global in time existence of solutions to the initial-boundary value problem and the asymptotic behavior of solutions for large time.
Bouaricha, A.; Schnabel, R.B.
1996-12-31
This paper describes a modular software package for solving systems of nonlinear equations and nonlinear least squares problems, using a new class of methods called tensor methods. It is intended for small to medium-sized problems, say with up to 100 equations and unknowns, in cases where it is reasonable to calculate the Jacobian matrix or approximate it by finite differences at each iteration. The software allows the user to select between a tensor method and a standard method based upon a linear model. The tensor method models F({ital x}) by a quadratic model, where the second-order term is chosen so that the model is hardly more expensive to form, store, or solve than the standard linear model. Moreover, the software provides two different global strategies, a line search and a two- dimensional trust region approach. Test results indicate that, in general, tensor methods are significantly more efficient and robust than standard methods on small and medium-sized problems in iterations and function evaluations.
Johnson, J M; Reale, D V; Cravey, W H; Garcia, R S; Barnett, D H; Neuber, A A; Dickens, J C; Mankowski, J J
2015-08-01
Implementing nonlinear transmission line (NLTL) technology in the design of a high power microwave source has the benefits of producing a comparatively small and lightweight solid-state system where the emission frequency is easily tuned. Usually, smaller in physical size, single NLTLs may produce significantly less power than its vacuum based counterparts. However, combining individual NLTL outputs electrically or in free-space is an attractive solution to achieve greater output power. This paper discusses a method for aligning a four element NLTL antenna array with coaxial geometry using easily adjustable temporal delay lines. These delay lines, sometimes referred to as pulse shock lines or pulse sharpening lines, are placed serially in front of the main NLTL line. The propagation velocity in each delay line is set by the voltage amplitude of an incident pulse as well as the magnetic field bias. Each is adjustable although for the system described in this paper, the voltage is held constant while the bias is changed through applying an external DC magnetic field of varying magnitude. Three different ferrimagnetic materials are placed in the temporal delay line to evaluate which yields the greatest range of electrical delay with the least amount of variability from consecutive shots.
Solid-State Radio Frequency Plasma Heating Using a Nonlinear Transmission Line
NASA Astrophysics Data System (ADS)
Miller, Kenneth; Ziemba, Timothy; Prager, James; Slobodov, Ilia
2015-11-01
Radio Frequency heating systems are rarely used by the small-scale validation platform experiments due to the high cost and complexity of these systems, which typically require high power gyrotrons or klystrons, associated power supplies, waveguides and vacuum systems. The cost and complexity of these systems can potentially be reduced with a nonlinear transmission line (NLTL) based system. In the past, NLTLs have lacked a high voltage driver that could produce long duration high voltage pulses with fast rise times at high pulse repetition frequency. Eagle Harbor Technologies, Inc. (EHT) has created new high voltage nanosecond pulser, which combined with NLTL technology will produce a low-cost, fully solid-state architecture for the generation of the RF frequencies (0.5 to 10 GHz) and peak power levels (~ 10 MW) necessary for plasma heating and diagnostic systems for the validation platform experiments within the fusion science community. The proposed system does not require the use of vacuum tube technology, is inherently lower cost, and is more robust than traditional high power RF heating schemes. Design details and initial bench testing results for the new RF system will be presented. This work is supported under DOE Grant # DE-SC0013747.
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.
Solvability of a nonlinear model Boltzmann equation in the problem of a plane shock wave
NASA Astrophysics Data System (ADS)
Khachatryan, A. Kh.; Khachatryan, Kh. A.
2016-11-01
We consider a nonlinear system of integral equations describing the structure of a plane shock wave. Based on physical reasoning, we propose an iterative method for constructing an approximate solution of this system. The problem reduces to studying decoupled scalar nonlinear and linear integral equations for the gas temperature, density, and velocity. We formulate a theorem on the existence of a positive bounded solution of a nonlinear equation of the Uryson type. We also prove theorems on the existence and uniqueness of bounded positive solutions for linear integral equations in the space L 1[-r, r] for all finite r < +∞. For a more general nonlinear integral equation, we prove a theorem on the existence of a positive solution and also find a lower bound and an integral upper bound for the constructed solution.
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.
A composite Chebyshev finite difference method for nonlinear optimal control problems
NASA Astrophysics Data System (ADS)
Marzban, H. R.; Hoseini, S. M.
2013-06-01
In this paper, a composite Chebyshev finite difference method is introduced and is successfully employed for solving nonlinear optimal control problems. The proposed method is an extension of the Chebyshev finite difference scheme. This method can be regarded as a non-uniform finite difference scheme and is based on a hybrid of block-pulse functions and Chebyshev polynomials using the well-known Chebyshev-Gauss-Lobatto points. The convergence of the method is established. The nice properties of hybrid functions are then used to convert the nonlinear optimal control problem into a nonlinear mathematical programming one that can be solved efficiently by a globally convergent algorithm. The validity and applicability of the proposed method are demonstrated through some numerical examples. The method is simple, easy to implement and yields very accurate results.
Initial value problem solution of nonlinear shallow water-wave equations.
Kânoğlu, 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.
Kim, T; Pasciak, J E; Vassilevski, P S
2004-09-20
In this paper, we consider an inexact Newton method applied to a second order nonlinear problem with higher order nonlinearities. We provide conditions under which the method has a mesh-independent rate of convergence. To do this, we are required to first, set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced with one iterative step provided that the initial nonlinear iterate is accurate enough. The closeness criteria can be taken independent of the mesh size. Finally, the results of numerical experiments are given to support the theory.
NASA Astrophysics Data System (ADS)
Kounadis, A. N.
1992-05-01
An efficient and easily applicable, approximate analytic technique for the solution of nonlinear initial and boundary-value problems associated with nonlinear ordinary differential equations (O.D.E.) of any order and variable coefficients, is presented. Convergence, uniqueness and upper bound error estimates of solutions, obtained by the successive approximations scheme of the proposed technique, are thoroughly established. Important conclusions regarding the improvement of convergence for large time and large displacement solutions in case of nonlinear initial-value problems are also assessed. The proposed technique is much more efficient than the perturbations schemes for establishing the large postbuckling response of structural systems. The efficiency, simplicity and reliability of the proposed technique is demonstrated by two illustrative examples for which available numerical results exist.
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.
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.
NASA Astrophysics Data System (ADS)
Roul, Pradip
2016-06-01
This paper presents a new iterative technique for solving nonlinear singular two-point boundary value problems with Neumann and Robin boundary conditions. The method is based on the homotopy perturbation method and the integral equation formalism in which a recursive scheme is established for the components of the approximate series solution. This method does not involve solution of a sequence of nonlinear algebraic or transcendental equations for the unknown coefficients as in some other iterative techniques developed for singular boundary value problems. The convergence result for the proposed method is established in the paper. The method is illustrated by four numerical examples, two of which have physical significance: The first problem is an application of the reaction-diffusion process in a porous spherical catalyst and the second problem arises in the study of steady-state oxygen-diffusion in a spherical cell with Michaelis-Menten uptake kinetics.
The solution of singular optimal control problems using direct collocation and nonlinear programming
NASA Astrophysics Data System (ADS)
Downey, James R.; Conway, Bruce A.
1992-08-01
This paper describes work on the determination of optimal rocket trajectories which may include singular arcs. In recent years direct collocation and nonlinear programming has proven to be a powerful method for solving optimal control problems. Difficulties in the application of this method can occur if the problem is singular. Techniques exist for solving singular problems indirectly using the associated adjoint formulation. Unfortunately, the adjoints are not a part of the direct formulation. It is shown how adjoint information can be obtained from the direct method to allow the solution of singular problems.
Numerical solutions of nonlinear STIFF initial value problems by perturbed functional iterations
NASA Technical Reports Server (NTRS)
Dey, S. K.
1982-01-01
Numerical solution of nonlinear stiff initial value problems by a perturbed functional iterative scheme is discussed. The algorithm does not fully linearize the system and requires only the diagonal terms of the Jacobian. Some examples related to chemical kinetics are presented.
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
Error estimations of mixed finite element methods for nonlinear problems of shallow shell theory
NASA Astrophysics Data System (ADS)
Karchevsky, M.
2016-11-01
The variational formulations of problems of equilibrium of a shallow shell in the framework of the geometrically and physically nonlinear theory by boundary conditions of different main types, including non-classical, are considered. Necessary and sufficient conditions for their solvability are derived. Mixed finite element methods for the approximate solutions to these problems based on the use of second derivatives of the bending as auxiliary variables are proposed. Estimations of accuracy of approximate solutions are established.
Makovejs, Sergejs; Millar, David S; Lavery, Domanic; Behrens, Carsten; Killey, Robert I; Savory, Seb J; Bayvel, Polina
2010-06-07
In this paper long-haul, single channel, polarization multiplexed 16-state quadrature amplitude modulation (PDM-QAM-16) transmission at 112 Gbit/s is investigated. Novel digital signal processing techniques are used to perform carrier phase estimation and symbol estimation, in combination with nonlinear digital backpropagation. The results obtained demonstrate that the use of digital nonlinear backpropagation increases the optimum launch power from -4 dBm to -1 dBm with a consequent increase in maximum reach from 1440 km to 2400 km, which is a record transmission distance for QAM-16 reported to date for an SMF link with EDFAs only. Furthermore, experimental measurements are supported by simulations, based on the link used in the experiment.
Response of Non-Linear Shock Absorbers-Boundary Value Problem Analysis
NASA Astrophysics Data System (ADS)
Rahman, M. A.; Ahmed, U.; Uddin, M. S.
2013-08-01
A nonlinear boundary value problem of two degrees-of-freedom (DOF) untuned vibration damper systems using nonlinear springs and dampers has been numerically studied. As far as untuned damper is concerned, sixteen different combinations of linear and nonlinear springs and dampers have been comprehensively analyzed taking into account transient terms. For different cases, a comparative study is made for response versus time for different spring and damper types at three important frequency ratios: one at r = 1, one at r > 1 and one at r <1. The response of the system is changed because of the spring and damper nonlinearities; the change is different for different cases. Accordingly, an initially stable absorber may become unstable with time and vice versa. The analysis also shows that higher nonlinearity terms make the system more unstable. Numerical simulation includes transient vibrations. Although problems are much more complicated compared to those for a tuned absorber, a comparison of the results generated by the present numerical scheme with the exact one shows quite a reasonable agreement
NASA Astrophysics Data System (ADS)
Lazo, Edmundo; Garrido, Alejandro; Neira, Félix
2016-11-01
This study investigates the localization properties of dual electric transmission lines with non-linear capacitances. The VC,n voltage across each capacitor is selected as a non-linear function of the electric charge qn, i.e., VC,n = qn(1/Cn -ɛn|qn|2) where Cn is the linear part of the capacitance and ɛn the amplitude of the non-linear term. We follow a binary distribution of values of ɛn, according to the Thue-Morse m-tupling sequence. The localization behavior of this non-linear case indicates that the case m = 2 does not belong to the m ≥ 3, family because when m changes from m = 2 to m = 3, the number of extended states diminishes dramatically. This proves the topological difference of the m = 2 and m = 3 families. However, by increasing m values, localization behavior of the m-tupling family resembles that of the m = 2, case because the system begins to regain its extended states. The exact same result was obtained recently in the study of linear direct transmission lines with m-tupling distribution of inductances. Consequently, we state that the localization behavior of the m-tupling family as a function of the m value is independent of both the linear and the non-linear system under study, but independent of the kind of transmission line (dual or direct). This is curious behavior of the m-tupling family and thus deserves more scholarly attention.
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.
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.
Semi-analytical method for solving nonlinear heat diffusion problems in spherical medium
NASA Astrophysics Data System (ADS)
Abd-El-Malek, Mina B.; Helal, Medhat M.
2006-08-01
A semi-analytical methodology, based on the finite integral transform technique, is proposed to solve the heat diffusion problem in a spherical medium subject to nonlinear boundary conditions due to radiation exchange at the interface according to the fourth power law. The method proceeds by treating the nonlinearity term in the boundary condition as a source in the differential equation and keeping other conditions unchanged. The results obtained from this semi-analytical solutions are compared with those obtained from a numerical solution developed using an explicit finite difference method, which showed very good agreement.
Local-instantaneous filtering in the integral transform solution of nonlinear diffusion problems
NASA Astrophysics Data System (ADS)
Macêdo, E. N.; Cotta, R. M.; Orlande, H. R. B.
A novel filtering strategy is proposed to be utilized in conjunction with the Generalized Integral Transform Technique (GITT), in the solution of nonlinear diffusion problems. The aim is to optimize convergence enhancement, yielding computationally efficient eigenfunction expansions. The proposed filters include space and time dependence, extracted from linearized versions of the original partial differential system. The scheme automatically updates the filter along the time integration march, as the required truncation orders for the user requested accuracy begin to exceed a prescribed maximum system size. A fully nonlinear heat conduction example is selected to illustrate the computational performance of the filtering strategy, against the classical single-filter solution behavior.
Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's
NASA Technical Reports Server (NTRS)
Cai, Wei; Wang, Jian-Zhong
1993-01-01
We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.
A fast nonlinear conjugate gradient based method for 3D concentrated frictional contact problems
NASA Astrophysics Data System (ADS)
Zhao, Jing; Vollebregt, Edwin A. H.; Oosterlee, Cornelis W.
2015-05-01
This paper presents a fast numerical solver for a nonlinear constrained optimization problem, arising from 3D concentrated frictional shift and rolling contact problems with dry Coulomb friction. The solver combines an active set strategy with a nonlinear conjugate gradient method. One novelty is to consider the tractions of each slip element in a polar coordinate system, using azimuth angles as variables instead of conventional traction variables. The new variables are scaled by the diagonal of the underlying Jacobian. The fast Fourier transform (FFT) technique accelerates all matrix-vector products encountered, exploiting the matrix' Toeplitz structure. Numerical tests demonstrate a significant reduction of the computational time compared to existing solvers for concentrated contact problems.
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.
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.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-01-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer. PMID
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
Use of kernel functions in artificial immune systems for the nonlinear classification problems.
Ozşen, Seral; Güneş, Salih; Kara, Sadik; Latifoğlu, Fatma
2009-07-01
Due to the fact that there exist only a small number of complex systems in artificial immune systems (AISs) that solve nonlinear problems, there is a need to develop nonlinear AIS approaches that would be among the well-known solution methods. In this study, we developed a kernel-based AIS to compensate for this deficiency by providing a nonlinear structure via transformation of distance calculations in the clonal selection models of classical AIS to kernel space. Applications of the developed system were conducted on Statlog heart disease dataset, which was taken from the University of California, Irvine Machine-Learning Repository, and on Doppler sonograms to diagnose atherosclerosis disease. The system obtained a classification accuracy of 85.93% for the Statlog heart disease dataset, while it achieved a 99.09% classification success for the Doppler dataset. With these results, our system seems to be a potential solution method, and it may be considered as a suitable method for hard nonlinear classification problems.
NASA Astrophysics Data System (ADS)
Yildiz, Nihat; San, Sait Eren; Köysal, Oğuz
2010-09-01
In this paper, two complementary objectives related to optical transmission spectra of nematic liquid crystals (NLCs) were achieved. First, at room temperature, for both pure and dye (DR9) doped E7 NLCs, the 10-250 W halogen lamp transmission spectra (wavelength 400-1200 nm) were measured at various bias voltages. Second, because the measured spectra were inherently highly nonlinear, it was difficult to construct explicit empirical physical formulas (EPFs) to employ as transmittance functions. To avoid this difficulty, layered feedforward neural networks (LFNNs) were used to construct explicit EPFs for these theoretically unknown nonlinear NLC transmittance functions. As we theoretically showed in a previous work, a LFNN, as an excellent nonlinear function approximator, is highly relevant to EPF construction. The LFNN-EPFs efficiently and consistently estimated both the measured and yet-to-be-measured nonlinear transmittance response values. The experimentally obtained doping ratio dependencies and applied bias voltage responses of transmittance were also confirmed by LFFN-EPFs. This clearly indicates that physical laws embedded in the physical data can be faithfully extracted by the suitable LFNNs. The extraordinary success achieved with LFNN here suggests two potential applications. First, although not attempted here, these LFNN-EPFs, by such mathematical operations as derivation, integration, minimization etc., can be used to obtain further transmittance related functions of NLCs. Second, for a given NLC response function, whose theoretical nonlinear functional form is yet unknown, a suitable experimental data based LFNN-EPF can be constructed to predict the yet-to-be-measured values.
Computing FEM Solutions of Plasticity Problems via Nonlinear Mixed Variational Inequalities
NASA Astrophysics Data System (ADS)
Venini, Paolo; Nascimbene, Roberto
A fixed-point algorithm for the solution of hardening plasticity problems is proposed. The continuous problem may be classified as a mixed nonlinear non-differentiable variational inequality of the second type that is discretized by means of a truly mixed finite-element scheme. The non-differentiability of the dissipation functional is coped with via regularization whereas the nonlinearity is approached with a fixed-point iterative strategy. Numerical results are proposed to assess the sensitivity of the approach with respect to the mesh size and the regularization parameter. The simplicity of the proposed fixed-point scheme with respect to more classical return mapping approaches seems to represent one of the key features of our algorithm. Eventually an extension is proposed that allows to analyze the propagation of a cohesive crack within an elastoplastic bulk. A suitable modification of the variational formulation is introduced to this scope that takes full advantage of the inherent discontinuity of the displacement field.
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.
NASA Technical Reports Server (NTRS)
Baum, J. D.; Levine, J. N.
1980-01-01
The selection of a satisfactory numerical method for calculating the propagation of steep fronted shock life waveforms in a solid rocket motor combustion chamber is discussed. A number of different numerical schemes were evaluated by comparing the results obtained for three problems: the shock tube problems; the linear wave equation, and nonlinear wave propagation in a closed tube. The most promising method--a combination of the Lax-Wendroff, Hybrid and Artificial Compression techniques, was incorporated into an existing nonlinear instability program. The capability of the modified program to treat steep fronted wave instabilities in low smoke tactical motors was verified by solving a number of motor test cases with disturbance amplitudes as high as 80% of the mean pressure.
Solution of the nonlinear inverse scattering problem by T -matrix completion. II. Simulations
NASA Astrophysics Data System (ADS)
Levinson, Howard W.; Markel, Vadim A.
2016-10-01
This is Part II of the paper series on data-compatible T -matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043317 (2016), 10.1103/PhysRevE.94.043317] contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object, but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.
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.
Wang, Xinwei; Peng, Haijun; Zhang, Sheng; Chen, Biaosong; Zhong, Wanxie
2017-03-16
A symplectic pseudospectral method based on the dual variational principle and the quasilinearization method is proposed and is successfully applied to solve nonlinear optimal control problems with inequality constraints in this paper. Nonlinear optimal control problem is firstly converted into a series of constraint linear-quadratic optimal control problems with the help of quasilinearization techniques. Then a symplectic pseudospectral method based on dual variational principle for solving the converted constrained linear-quadratic optimal control problems is developed. In the proposed method, inequality constraints which can be functions of pure state, pure control and mixed state-control are transformed into equality constraints with the help of parameteric variables. After that, state variables, costate variables and parametric variables are interpolated locally at Legendre-Gauss-Lobatto points. Finally, based on the parametric variational principle and complementary conditions, the converted problem is transformed into a standard linear complementary problem which can be solved easily. Numerical examples show that the proposed method is of high accuracy and efficiency.
Landau-Zener problem in a three-level neutrino system with nonlinear time dependence
Keraenen, P.; Maalampi, J.; Myyrylaeinen, M.; Riittinen, J.
2007-02-01
We consider the level-crossing problem in a three-level system with nonlinearly time-varying Hamiltonian (time-dependence t{sup -3}). We study the validity of the so-called independent crossing approximation in the Landau-Zener model by making comparison with results obtained numerically in the density matrix approach. We also demonstrate the failure of the so-called 'nearest zero' approximation of the Landau-Zener level-crossing probability integral.
Carey, G.F.; Young, D.M.
1993-12-31
The program outlined here is directed to research on methods, algorithms, and software for distributed parallel supercomputers. Of particular interest are finite element methods and finite difference methods together with sparse iterative solution schemes for scientific and engineering computations of very large-scale systems. Both linear and nonlinear problems will be investigated. In the nonlinear case, applications with bifurcation to multiple solutions will be considered using continuation strategies. The parallelizable numerical methods of particular interest are a family of partitioning schemes embracing domain decomposition, element-by-element strategies, and multi-level techniques. The methods will be further developed incorporating parallel iterative solution algorithms with associated preconditioners in parallel computer software. The schemes will be implemented on distributed memory parallel architectures such as the CRAY MPP, Intel Paragon, the NCUBE3, and the Connection Machine. We will also consider other new architectures such as the Kendall-Square (KSQ) and proposed machines such as the TERA. The applications will focus on large-scale three-dimensional nonlinear flow and reservoir problems with strong convective transport contributions. These are legitimate grand challenge class computational fluid dynamics (CFD) problems of significant practical interest to DOE. The methods developed and algorithms will, however, be of wider interest.
Nickel, J; Schürmann, H W
2007-03-01
In a recent article Kengne and Liu [Phys. Rev. E 73, 026603 (2006)] have presented a number of exact elliptic solutions for a derivative nonlinear Schrödinger equation. It is the aim of this Comment to point out that all these solutions given in Secs. II and III of this article (referred to as KL in the following) are subcases of the general solution of Eq. (KL.9). Conditions for the parameters A-E of the solutions given by Kengne and Liu can be found from general conditions for solitary and periodic elliptic solutions as shown in the following. Positive and bounded solutions can be found by considering the phase diagram. Therefore, the comment of Kengne and Liu that "we find its particular positive bounded solutions" can be specified.
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.
NASA Astrophysics Data System (ADS)
Fu, Libi; Song, Weiguo; Lo, Siuming
2017-01-01
Emergencies involved in mass events are related to a variety of factors and processes. An important factor is the transmission of information on danger that has an influence on nonlinear crowd dynamics during the process of crowd dispersion. Due to much uncertainty in this process, there is an urgent need to propose a method to investigate the influence. In this paper, a novel fuzzy-theory-based method is presented to study crowd dynamics under the influence of information transmission. Fuzzy functions and rules are designed for the ambiguous description of human states. Reasonable inference is employed to decide the output values of decision making such as pedestrian movement speed and directions. Through simulation under four-way pedestrian situations, good crowd dispersion phenomena are achieved. Simulation results under different conditions demonstrate that information transmission cannot always induce successful crowd dispersion in all situations. This depends on whether decision strategies in response to information on danger are unified and effective, especially in dense crowds. Results also suggest that an increase in drift strength at low density and the percentage of pedestrians, who choose one of the furthest unoccupied Von Neumann neighbors from the dangerous source as the drift direction at high density, is helpful in crowd dispersion. Compared with previous work, our comprehensive study improves an in-depth understanding of nonlinear crowd dynamics under the effect of information on danger.
Non-Linear Noise Contributions in Highly Dispersive Optical Transmission Systems
NASA Astrophysics Data System (ADS)
Matera, Francesco
2016-01-01
This article reports an analytical investigation, confirmed by numerical simulations, about the non-linear noise contribution in single-channel systems adopting generic modulation-detection formats in long links with both managed and unmanaged dispersion compensation and its impact in system performance. This noise contribution is expressed in terms of a pulse non-linear interaction length and permits a simple calculation of the Q-factor. Results point out the dependence of this non-linear noise on the number of amplifiers spans, N, according to the adopted chromatic dispersion compensation scheme, the modulation-detection format, and the signal baud rate. It is also shown how the effects of polarization multiplexing can be taken into account and how this single-channel non-linear noise contribution can be used in a wavelength-division multiplexing (WDM) environment.
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.
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)
Azou, Stéphane; Bejan, Șerban; Morel, Pascal; Sharaiha, Ammar
2015-02-01
Coherent-Optical OFDM systems are known to be sensitive to large peak-to-average power ratio (PAPR) at the transmitter output, due to nonlinear properties of some components involved in the transmission link. In this paper, we investigate the impact of an amplification of such signals via a semiconductor optical amplifier (SOA), considering some recent experimental results. An efficient tradeoff between BER performance, computational complexity and power efficiency is performed by a proper design of Wang's nonlinear companding function, considered for the first time in an optical communication context. A BER advantage of around 3 dB can hence be obtained over a standard system implementation not using PAPR reduction. The designed function also proves to be more efficient than μ-law function, considered in the literature as an efficient companding scheme.
NASA Astrophysics Data System (ADS)
Cakoni, Fioralba; Haddar, Houssem
2013-10-01
In inverse scattering theory, transmission eigenvalues can be seen as the extension of the notion of resonant frequencies for impenetrable objects to the case of penetrable dielectrics. The transmission eigenvalue problem is a relatively late arrival to the spectral theory of partial differential equations. Its first appearance was in 1986 in a paper by Kirsch who was investigating the denseness of far-field patterns for scattering solutions of the Helmholtz equation or, in more modern terminology, the injectivity of the far-field operator [1]. The paper of Kirsch was soon followed by a more systematic study by Colton and Monk in the context of developing the dual space method for solving the inverse scattering problem for acoustic waves in an inhomogeneous medium [2]. In this paper they showed that for a spherically stratified media transmission eigenvalues existed and formed a discrete set. Numerical examples were also given showing that in principle transmission eigenvalues could be determined from the far-field data. This first period of interest in transmission eigenvalues was concluded with papers by Colton et al in 1989 [3] and Rynne and Sleeman in 1991 [4] showing that for an inhomogeneous medium (not necessarily spherically stratified) transmission eigenvalues, if they existed, formed a discrete set. For the next seventeen years transmission eigenvalues were ignored. This was mainly due to the fact that, with the introduction of various sampling methods to determine the shape of an inhomogeneous medium from far-field data, transmission eigenvalues were something to be avoided and hence the fact that transmission eigenvalues formed at most a discrete set was deemed to be sufficient. In addition, questions related to the existence of transmission eigenvalues or the structure of associated eigenvectors were recognized as being particularly difficult due to the nonlinearity of the eigenvalue problem and the special structure of the associated transmission
NASA Astrophysics Data System (ADS)
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.
Arbitrary Lagrangian-Eulerian method for non-linear problems of geomechanics
NASA Astrophysics Data System (ADS)
Nazem, M.; Carter, J. P.; Airey, D. W.
2010-06-01
In many geotechnical problems it is vital to consider the geometrical non-linearity caused by large deformation in order to capture a more realistic model of the true behaviour. The solutions so obtained should then be more accurate and reliable, which should ultimately lead to cheaper and safer design. The Arbitrary Lagrangian-Eulerian (ALE) method originated from fluid mechanics, but has now been well established for solving large deformation problems in geomechanics. This paper provides an overview of the ALE method and its challenges in tackling problems involving non-linearities due to material behaviour, large deformation, changing boundary conditions and time-dependency, including material rate effects and inertia effects in dynamic loading applications. Important aspects of ALE implementation into a finite element framework will also be discussed. This method is then employed to solve some interesting and challenging geotechnical problems such as the dynamic bearing capacity of footings on soft soils, consolidation of a soil layer under a footing, and the modelling of dynamic penetration of objects into soil layers.
Solution of the nonlinear elasticity imaging inverse problem: The incompressible case.
Goenezen, Sevan; Barbone, Paul; Oberai, Assad A
2011-03-01
We have recently developed and tested an efficient algorithm for solving the nonlinear inverse elasticity problem for a compressible hyperelastic material. The data for this problem are the quasi-static deformation fields within the solid measured at two distinct overall strain levels. The main ingredients of our algorithm are a gradient based quasi-Newton minimization strategy, the use of adjoint equations and a novel strategy for continuation in the material parameters. In this paper we present several extensions to this algorithm. First, we extend it to incompressible media thereby extending its applicability to tissues which are nearly incompressible under slow deformation. We achieve this by solving the forward problem using a residual-based, stabilized, mixed finite element formulation which circumvents the Ladyzenskaya-Babuska-Brezzi condition. Second, we demonstrate how the recovery of the spatial distribution of the nonlinear parameter can be improved either by preconditioning the system of equations for the material parameters, or by splitting the problem into two distinct steps. Finally, we present a new strain energy density function with an exponential stress-strain behavior that yields a deviatoric stress tensor, thereby simplifying the interpretation of pressure when compared with other exponential functions. We test the overall approach by solving for the spatial distribution of material parameters from noisy, synthetic deformation fields.
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.
Molnar, Alyosha; Hsueh, Hain-Ann; Roska, Botond; Werblin, Frank S
2009-12-01
In the mammalian retina, complementary ON and OFF visual streams are formed at the bipolar cell dendrites, then carried to amacrine and ganglion cells via nonlinear excitatory synapses from bipolar cells. Bipolar, amacrine and ganglion cells also receive a nonlinear inhibitory input from amacrine cells. The most common form of such inhibition crosses over from the opposite visual stream: Amacrine cells carry ON inhibition to the OFF cells and carry OFF inhibition to the ON cells ("crossover inhibition"). Although these synapses are predominantly nonlinear, linear signal processing is required for computing many properties of the visual world such as average intensity across a receptive field. Linear signaling is also necessary for maintaining the distinction between brightness and contrast. It has long been known that a subset of retinal outputs provide exactly this sort of linear representation of the world; we show here that rectifying (nonlinear) synaptic currents, when combined thorough crossover inhibition can generate this linear signaling. Using simple mathematical models we show that for a large set of cases, repeated rounds of synaptic rectification without crossover inhibition can destroy information carried by those synapses. A similar circuit motif is employed in the electronics industry to compensate for transistor nonlinearities in analog circuits.
Nonlinear Schrödinger equation on graphs: recent results and open problems.
Noja, Diego
2014-01-28
In this paper, an introduction to the new subject of nonlinear dispersive Hamiltonian equations on graphs is given. The focus is on recently established properties of solutions in the case of the nonlinear Schrödinger (NLS) equation. Special consideration is given to the existence and behaviour of solitary solutions. Two subjects are discussed in some detail concerning the NLS equation on a star graph: the standing waves of the NLS equation on a graph with a δ interaction at the vertex, and the scattering of fast solitons through a Y-junction in the cubic case. The emphasis is on a description of concepts and results and on physical context, without reporting detailed proofs; some perspectives and more ambitious open problems are discussed.
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
Khairuzzaman, Md; Zhang, Chao; Igarashi, Koji; Katoh, Kazuhiro; Kikuchi, Kazuro
2010-03-01
We describe a successful introduction of maximum-likelihood-sequence estimation (MLSE) into digital coherent receivers together with finite-impulse response (FIR) filters in order to equalize both linear and nonlinear fiber impairments. The MLSE equalizer based on the Viterbi algorithm is implemented in the offline digital signal processing (DSP) core. We transmit 20-Gbit/s quadrature phase-shift keying (QPSK) signals through a 200-km-long standard single-mode fiber. The bit-error rate performance shows that the MLSE equalizer outperforms the conventional adaptive FIR filter, especially when nonlinear impairments are predominant.
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.
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.
NASA Astrophysics Data System (ADS)
Tang, Yao-Zong; Li, Xiao-Lin
2017-03-01
We first give a stabilized improved moving least squares (IMLS) approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis. Project supported by the National Natural Science Foundation of China (Grant No. 11471063), the Chongqing Research Program of Basic Research and Frontier Technology, China (Grant No. cstc2015jcyjBX0083), and the Educational Commission Foundation of Chongqing City, China (Grant No. KJ1600330).
Daly, Edoardo; Porporato, Amilcare
2004-11-01
Similarity solutions of the shallow-water equation with a generalized resistance term are studied for open channel flows when both inertial and gravity forces are negligible. The resulting model encompasses various particular cases that appear, in addition to mathematical hydraulics, in diverse physical phenomena, such as gravity currents, creeping flows of Newtonian and non-Newtonian fluids, thin films, and nonlinear Fokker-Planck equations. Solutions of both source-type and dam-break problems are analyzed. Closed-form solutions are discussed, when possible, along with a qualitative study of two phase-plane formulations based on two different variable transformations.
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.
2017-03-01
We shall give the proof of existence results for the entropy solutions of the following nonlinear parabolic problem ... 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.
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).
Optimal homotopy perturbation method for solving a nonlinear problem in elasticity
NASA Astrophysics Data System (ADS)
Ene, R.-D.; Marinca, V.; Cãruntu, B.
2012-09-01
In this paper we present an analytical method - the Optimal Homotopy Perturbation Method (OHPM), and we apply it to find approximate solutions for a nonlinear problem related to the stress and deformation states of a thin elastic plate. OHPM combines the features of the homotopy approach with an efficient computational algorithm which provides a convenient way to control the convergence of the approximation series. The comparison of the results obtained by OHPM with results obtained by numerical integration show a very good agreement proving the effectiveness and accuracy of the method.
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.
NASA Astrophysics Data System (ADS)
Ekanayake, N.
1983-10-01
An expression is derived for the bit error probability of minimum shift keying (MSK) and offset quaternary phase shift keying (OQPSK) signals which have been transmitted through nonlinear satellite channels after bandlimiting. The transponder nonlinearity considered in the paper is of the bandpass type, which exhibits AM/AM and AM/PM conversion effects. The effects of up-link and down-link thermal noise are also taken into consideration in the analysis. The resulting expression for the bit error probability is an infinite series containing double integrals. In order to illustrate the usefulness of the method, the error rates of MSK and OQPSK signals are computed for a Butterworth bandlimiting filter hard limiting transponder channel model. The error rates of MSK and OQPSK signals are compared with the error rate of binary PSK signals for this communication system model.
Detailed discussion of the optimum baud rate of nonlinearity in WDM transmission
NASA Astrophysics Data System (ADS)
Wang, Wanli; Qiao, Yaojun; Yang, Lin
2017-01-01
Different numbers of sub-channels correspond to different baud rates per sub-channel when the total baud rate is fixed. The optimum baud rate of nonlinearity in WDM systems is investigated in this paper. We find that the phase matching effect produces an optimum baud rate of nonlinearity, which is related to the chromatic dispersion accumulation of a single span. Then other factors that influence the optimum baud rate are analyzed. By mathematical derivation and simulation verification, larger number of spans and larger spectrum gap between sub-channels both make the optimum value decrease. We also find that different modulation formats barely change the optimum baud rate if other system settings are the same and all sub-channels have the same modulation format.
Discrete and continuum links to a nonlinear coupled transport problem of interacting populations
NASA Astrophysics Data System (ADS)
Duong, M. H.; Muntean, A.; Richardson, O. M.
2017-02-01
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.
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.
Verified solutions of two-point boundary value problems for nonlinear oscillators
NASA Astrophysics Data System (ADS)
Bünger, Florian
Using techniques introduced by Nakao [4], Oishi [5, 6] and applied by Takayasu, Oishi, Kubo [11, 12] to certain nonlinear two-point boundary value problems (see also Rump [7], Chapter 15), we provide a numerical method for verifying the existence of weak solutions of two-point boundary value problems of the form -u″ = a(x, u) + b(x, u)u‧, 0 < x < 1, u(0) = 0 = u(1), in the vicinity of a given approximate numerical solution, where a and b are functions that fulfill some regularity properties. The numerical approximation is done by cubic spline interpolation. Finally, the method is applied to the Duffing, the van der Pol and the Toda oscillator. The rigorous numerical computations were done with INTLAB [8].
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.
Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem
NASA Astrophysics Data System (ADS)
Terekhov, Kirill M.; Mallison, Bradley T.; Tchelepi, Hamdi A.
2017-02-01
We present two new cell-centered nonlinear finite-volume methods for the heterogeneous, anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and transversal components. Specifically, linear combinations of the transversal vector and the co-normal are used that lead to significant improvements in terms of the mesh-locking effects. The harmonic component of the flux is represented using a conventional monotone two-point flux approximation; the component along the parameterized direction is treated nonlinearly to satisfy either positivity of the solution as in [29], or the discrete maximum principle as in [9]. In order to make the method purely cell-centered, we derive a homogenization function that allows for seamless interpolation in the presence of heterogeneity following a strategy similar to [46]. The performance of the new schemes is compared with existing multi-point flux approximation methods [3,5]. The robustness of the scheme with respect to the mesh-locking problem is demonstrated using several challenging test cases.
Solution of the nonlinear inverse scattering problem by T -matrix completion. I. Theory
NASA Astrophysics Data System (ADS)
Levinson, Howard W.; Markel, Vadim A.
2016-10-01
We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V . An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T -matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016), 10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.
Vanin, Evgeny; Jacobsen, Gunnar; Berntson, Anders
2007-06-15
We propose a novel method for effective simulation of optical fiber transmission system performance with nonlinear interaction between the amplified spontaneous emission noise and the modulated optical signal employing on-off keying. The method enables a standard analytical description of the receiver operation even when the detected optical field obeys non-Gaussian statistics with a substantial amount of nonlinear phase noise accumulated along the fiber link due to strong signal-noise interaction.
An optimal control problem arising from a dengue disease transmission model.
Aldila, Dipo; Götz, Thomas; Soewono, Edy
2013-03-01
An optimal control problem for a host-vector Dengue transmission model is discussed here. In the model, treatments with mosquito repellent are given to adults and children and those who undergo treatment are classified in treated compartments. With this classification, the model consists of 11 dynamic equations. The basic reproductive ratio that represents the epidemic indicator is obtained from the largest eigenvalue of the next generation matrix. The optimal control problem is designed with four control parameters, namely the treatment rates for children and adult compartments, and the drop-out rates from both compartments. The cost functional accounts for the total number of the infected persons, the cost of the treatment, and the cost related to reducing the drop-out rates. Numerical results for the optimal controls and the related dynamics are shown for the case of epidemic prevention and outbreak reduction strategies.
NASA Astrophysics Data System (ADS)
Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Perez-Pinacho, Claudia A.
2014-06-01
The main issue of this work is related with the design of a class of nonlinear observer in order to synchronize chaotic dynamical systems in a master-slave scheme, considering different initial conditions. The oscillator of Chen is proposed as a benchmark model and a bounded-type observer is proposed to reach synchronicity between both two chaotic systems. The proposed observer contains a proportional and sigmoid form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Some numerical simulations were carrying out in order to show the operation of the proposed methodology, with possible applications to secure data communications issues.
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)
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.
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.
Li, Xiaolin; Zhang, Fan; Chen, Zhangyuan; Xu, Anshi
2007-12-24
We numerically investigate XPM effect and XPM-induced nonlinear phase noise in both RZ-DPSK and multi-format (RZ-DPSK and RZ-OOK) WDM systems operating at 40 Gbit/s with different dispersion maps. The relative strength of XPM effect and XPM-induced nonlinear phase noise is discussed for both RZ-DPSK and multi-format WDM transmission. With optimum dispersion mapping, XPM and XPM-induced nonlinear phase noise from neighboring channels carrying either OOK or DPSK signals can both be effectively suppressed.
Analysis of steady-state and dynamical radially-symmetric problems of nonlinear viscoelasticity
NASA Astrophysics Data System (ADS)
Stepanov, Alexey B.
This thesis treats radially symmetric steady states and radially symmetric motions of nonlinearly elastic and viscoelastic plates and shells subject to dead-load and hydrostatic pressures on their boundaries and with the plate subject to centrifugal force. The plates and shells are described by specializations of the exact (nonlinear) equations of three-dimensional continuum mechanics. The treatment in every case is very general and encompasses large classes of constitutive functions (characterizing the material response). We first treat the radially symmetric steady states of plates and shells and the radially symmetric steady rotations of plates. We show that the existence, multiplicity, and qualitative behavior of solutions for problems accounting for the live loads due to hydrostatic pressure and centrifugal force depend critically on the material properties of the bodies, physically reasonable refined descriptions of which are given and examined here with great care, and on the nature of boundary conditions. he treatment here, giving new and sharp results, employs several different mathematical tools, ranging from phase-plane analysis to the mathematically more sophisticated direct methods of the Calculus of Variations, fixed-point theorems, and global continuation methods, each of which has different strengths and weaknesses for handling intrinsic difficulties in the mechanics. We then treat the initial-boundary-value problems for the radially symmetric motions of annular plates and spherical shells that consist of a nonlinearly viscoelastic material of strain-rate type. We discuss a range of physically natural constitutive equations. We first show that when the material is strong in a suitable sense relative to externally applied loads, solutions exist for all time, depend continuously on the data, and consequently are unique. We study the role of the constitutive restrictions and that of the regularity of the data in ensuring the preclusion of a total
NASA Astrophysics Data System (ADS)
Marinca, Vasile; Ene, Remus-Daniel
2017-01-01
In this paper, the Optimal Homotopy Perturbation Method (OHPM) is employed to determine an analytic approximate solution for the nonlinear MHD Jeffery-Hamel flow and heat transfer problem. The Navier-Stokes equations, taking into account Maxwell's electromagnetism and heat transfer, lead to two nonlinear ordinary differential equations. The results obtained by means of OHPM show very good agreement with numerical results and with Homotopy Perturbation Method (HPM) results.
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
Sugano, K.
1988-12-27
A transmission is described which consists of: an input shaft; an output shaft; a first planetary gear set including a first sun gear selectively connectable by a first clutch to the input shaft, a first carrier selectively connectable by a second clutch to the input shaft and a first ring gear connected to the output shaft. The first sun gear selectively held stationary by a first brake, the first carrier is allowed to rotate in the same forward direction as the input shaft when the second clutch is engaged, but prevented from rotating in a reverse direction opposite to the forward direction by a first one-way clutch, the first carrier being selectively held stationary by a second brake; a second planetary gear set including a second sun gear connected to the input shaft, a second carrier connected to the first ring gear and also the the output shaft, and a second ring gear.
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.
A linear stability analysis for nonlinear, grey, thermal radiative transfer problems
Wollaber, Allan B.; Larsen, Edward W.
2011-02-20
We present a new linear stability analysis of three time discretizations and Monte Carlo interpretations of the nonlinear, grey thermal radiative transfer (TRT) equations: the widely used 'Implicit Monte Carlo' (IMC) equations, the Carter Forest (CF) equations, and the Ahrens-Larsen or 'Semi-Analog Monte Carlo' (SMC) equations. Using a spatial Fourier analysis of the 1-D Implicit Monte Carlo (IMC) equations that are linearized about an equilibrium solution, we show that the IMC equations are unconditionally stable (undamped perturbations do not exist) if {alpha}, the IMC time-discretization parameter, satisfies 0.5 < {alpha} {<=} 1. This is consistent with conventional wisdom. However, we also show that for sufficiently large time steps, unphysical damped oscillations can exist that correspond to the lowest-frequency Fourier modes. After numerically confirming this result, we develop a method to assess the stability of any time discretization of the 0-D, nonlinear, grey, thermal radiative transfer problem. Subsequent analyses of the CF and SMC methods then demonstrate that the CF method is unconditionally stable and monotonic, but the SMC method is conditionally stable and permits unphysical oscillatory solutions that can prevent it from reaching equilibrium. This stability theory provides new conditions on the time step to guarantee monotonicity of the IMC solution, although they are likely too conservative to be used in practice. Theoretical predictions are tested and confirmed with numerical experiments.
NASA Astrophysics Data System (ADS)
Liu, Tianyu; Jiao, Licheng; Ma, Wenping; Shang, Ronghua
2017-03-01
In this paper, an improved quantum-behaved particle swarm optimization (CL-QPSO), which adopts a new collaborative learning strategy to generate local attractors for particles, is proposed to solve nonlinear numerical problems. Local attractors, which directly determine the convergence behavior of particles, play an important role in quantum-behaved particle swarm optimization (QPSO). In order to get a promising and efficient local attractor for each particle, a collaborative learning strategy is introduced to generate local attractors in the proposed algorithm. Collaborative learning strategy consists of two operators, namely orthogonal operator and comparison operator. For each particle, orthogonal operator is used to discover the useful information that lies in its personal and global best positions, while comparison operator is used to enhance the particle's ability of jumping out of local optima. By using a probability parameter, the two operators cooperate with each other to generate local attractors for particles. A comprehensive comparison of CL-QPSO with some state-of-the-art evolutionary algorithms on nonlinear numeric optimization functions demonstrates the effectiveness of the proposed algorithm.
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.
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.
Lin, Chien-Yu; Asif, Rameez; Holtmannspoetter, Michael; Schmauss, Bernhard
2012-12-10
We investigate the performance of carrier phase estimation (CPE) and digital backward propagation (DBP) in compensating fiber nonlinearity for 224 Gbps polarization-multiplexed quadrature-amplitude-modulation coherent systems with level of 4 and 16 (PM-4-QAM and PM-16-QAM) over standard single-mode fiber (SSMF) uncompensated link. The results from numerical simulation show the individual performance of CPE and DBP as well as their mutual influence. With DBP compensation, required CPE tap number for optimal performance can be reduced by 50% for 4-QAM signal and 67% for 16-QAM signal compared to linear compensation. On the other hand, employing CPE compensation after DBP also allows to reduce DBP steps. In the mentioned PM-16-QAM system, 60% reduction in the required number of DBP steps to achieve BER=10(-3) is possible, with a step-size of 200 km, which reveals great potential to reduce the complexity for future real time implementation.
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.
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.
An efficient numerical technique for the solution of nonlinear singular boundary value problems
NASA Astrophysics Data System (ADS)
Singh, Randhir; Kumar, Jitendra
2014-04-01
In this work, a new technique based on Green's function and the Adomian decomposition method (ADM) for solving nonlinear singular boundary value problems (SBVPs) is proposed. The technique relies on constructing Green's function before establishing the recursive scheme for the solution components. In contrast to the existing recursive schemes based on the ADM, the proposed technique avoids solving a sequence of transcendental equations for the undetermined coefficients. It approximates the solution in the form of a series with easily computable components. Additionally, the convergence analysis and the error estimate of the proposed method are supplemented. The reliability and efficiency of the proposed method are demonstrated by several numerical examples. The numerical results reveal that the proposed method is very efficient and accurate.
NASA Astrophysics Data System (ADS)
Emmrich, Etienne; Thalhammer, Mechthild
2010-04-01
Stiffly accurate implicit Runge-Kutta methods are studied for the time discretisation of nonlinear first-order evolution equations. The equation is supposed to be governed by a time-dependent hemicontinuous operator that is (up to a shift) monotone and coercive, and fulfills a certain growth condition. It is proven that the piecewise constant as well as the piecewise linear interpolant of the time-discrete solution converges towards the exact weak solution, provided the Runge-Kutta method is consistent and satisfies a stability criterion that implies algebraic stability; examples are the Radau IIA and Lobatto IIIC methods. The convergence analysis is also extended to problems involving a strongly continuous perturbation of the monotone main part.
Modelling of hydrogen thermal desorption spectrum in nonlinear dynamical boundary-value problem
NASA Astrophysics Data System (ADS)
Kostikova, E. K.; Zaika, Yu V.
2016-11-01
One of the technological challenges for hydrogen materials science (including the ITER project) is the currently active search for structural materials with various potential applications that will have predetermined limits of hydrogen permeability. One of the experimental methods is thermal desorption spectrometry (TDS). A hydrogen-saturated sample is degassed under vacuum and monotone heating. The desorption flux is measured by mass spectrometer to determine the character of interactions of hydrogen isotopes with the solid. We are interested in such transfer parameters as the coefficients of diffusion, dissolution, desorption. The paper presents a distributed boundary-value problem of thermal desorption and a numerical method for TDS spectrum simulation, where only integration of a nonlinear system of low order (compared with, e.g., the method of lines) ordinary differential equations (ODE) is required. This work is supported by the Russian Foundation for Basic Research (project 15-01-00744).
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.
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.
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.
2016-06-01
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.
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
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.
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
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.
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.
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
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.
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.
Crama, Y.; Mazzola, J.
1994-12-31
This paper defines the dense subhypergraph problem (DSP), which provides a generalized modelling framework for the nonlinear knapsack problem and other well-known problems arising in areas such as capital budgeting, flexible manufacturing system production planning, repair-kit selection, and compiler construction. We define several families of valid inequalities and state conditions under which these inequalities are facet-defining for DSP. We also explore the polyhedral structure of the cardinality-constrained DSP. Finally, we examine a special case of this problem that arises, for example, within the context of Lagrangian decomposition. For this case, we present a complete description of the convex hull of the feasible region.
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)
NASA Astrophysics Data System (ADS)
Rozhdestvenskaya, Ekaterina A.
2011-02-01
The existence of a solution of the Dirichlet problem for a second order elliptic equation with non-linear part discontinuous in the phase variable is proved in the cases of resonance on the left and resonance on the right of the first eigenvalue of the differential operator in the situation where the Landesman-Lazer conditions do not hold.
Hoyos-Idrobo, A; Weiss, P; Massire, A; Amadon, A; Boulant, N
2014-03-01
Parallel transmission is a very promising candidate technology to mitigate the inevitable radio-frequency (RF) field inhomogeneity in magnetic resonance imaging at ultra-high field. For the first few years, pulse design utilizing this technique was expressed as a least squares problem with crude power regularizations aimed at controlling the specific absorption rate (SAR), hence the patient safety. This approach being suboptimal for many applications sensitive mostly to the magnitude of the spin excitation, and not its phase, the magnitude least squares (MLS) problem then was first formulated in 2007. Despite its importance and the availability of other powerful numerical optimization methods, the MLS problem yet has been faced almost exclusively by the pulse designer with the so-called variable exchange method. In this paper, we investigate various two-stage strategies consisting of different initializations and nonlinear programming approaches, and incorporate directly the strict SAR and hardware constraints. Several schemes such as sequential quadratic programming, interior point methods, semidefinite programming and magnitude squared least squares relaxations are studied both in the small and large tip angle regimes with RF and static field maps obtained in vivo on a human brain at 7T. Convergence and robustness of the different approaches are analyzed, and recommendations to tackle this specific problem are finally given. Small tip angle and inversion pulses are returned in a few seconds and in under a minute respectively while respecting the constraints, allowing the use of the proposed approach in routine.
NASA Astrophysics Data System (ADS)
Yamgoué, Serge Bruno; Pelap, François Beceau
2016-05-01
We revisit the derivation of the equation modeling envelope waves in a discrete nonlinear electrical transmission line (NLTL) considered a few years back in Physics Letters A 373 (2009) 3801-3809. Using a combination of rotating wave approximation and the Gardner-Morikawa transformation, we show that the modulated waves are described by a new type of extended nonlinear Schrödinger equation. In addition the expressions of several coefficients of this equation are found to be strongly different from those given earlier. As a consequence, key relationships between these coefficients that sustained the previous analysis are broken.
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.
Zhao, Sangen; Kang, Lei; Shen, Yaoguo; Wang, Xiaodong; Asghar, Muhammad Adnan; Lin, Zheshuai; Xu, Yingying; Zeng, Siyuan; Hong, Maochun; Luo, Junhua
2016-03-09
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.
Band selection for nonlinear unmixing of hyperspectral images as a maximal clique problem.
Imbiriba, Tales; Bermudez, Jose Carlos; Richard, Cedric
2017-03-01
Kernel-based nonlinear mixing models have been applied to unmix spectral information of hyperspectral images when the type of mixing occurring in the scene is too complex or unknown. Such methods, however, usually require the inversion of matrices of sizes equal to the number of spectral bands. Reducing the computational load of these methods remains a challenge in large scale applications. This paper proposes a centralized band selection (BS) method for supervised unmixing in the reproducing kernel Hilbert space (RKHS). It is based upon the coherence criterion, which sets the largest value allowed for correlations between the basis kernel functions characterizing the selected bands in the unmixing model. We show that the proposed BS approach is equivalent to solving a maximum clique problem (MCP), i.e., searching for the biggest complete subgraph in a graph. Furthermore, we devise a strategy for selecting the coherence threshold and the Gaussian kernel bandwidth using coherence bounds for linearly independent bases. Simulation results illustrate the efficiency of the proposed method.
NASA Astrophysics Data System (ADS)
Siddheshwar, P. G.; Mahabaleswar, U. S.; Andersson, H. I.
2013-08-01
The paper discusses a new analytical procedure for solving the non-linear boundary layer equation arising in a linear stretching sheet problem involving a Newtonian/non-Newtonian liquid. On using a technique akin to perturbation the problem gives rise to a system of non-linear governing differential equations that are solved exactly. An analytical expression is obtained for the stream function and velocity as a function of the stretching parameters. The Clairaut equation is obtained on consideration of consistency and its solution is shown to be that of the stretching sheet boundary layer equation. The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem
NASA Astrophysics Data System (ADS)
Zhang, Fangzheng; Wu, Jian; Li, Yan; Lin, Jintong
2012-10-01
We numerically investigate the nonlinear transmission performance of 112 Gb/s coherent transmission systems using polarization multiplexed quadrature-phase-shift-keying (QPSK), offset QPSK (OQPSK) and minimum-shift-keying (MSK) formats, and compare the fiber nonlinear tolerances of the three modulation formats. Simulation results show that in both single channel and wavelength-division-multiplexed (WDM) systems, OQPSK is slightly more resistant to fiber nonlinearities than QPSK, and MSK has the best fiber nonlinear tolerance. The advantage of MSK format over QPSK and OQPSK is particularly notable in WDM systems. When digital back propagation (DBP) is used in the digital coherent receiver for intra-channel fiber nonlinearity compensation, system performance is improved with better Q-factor, enlarged input optical power range and extended transmission distance. It is found that the use of DBP brings the largest performance improvement in QPSK system and the least performance improvement in MSK system although MSK system has better fiber nonlinear tolerance.
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.
The late Universe with non-linear interaction in the dark sector: The coincidence problem
NASA Astrophysics Data System (ADS)
Bouhmadi-López, Mariam; Morais, João; Zhuk, Alexander
2016-12-01
We study the Universe at the late stage of its evolution and deep inside the cell of uniformity. At such a scale the Universe is highly inhomogeneous and filled with discretely distributed inhomogeneities in the form of galaxies and groups of galaxies. As a matter source, we consider dark matter (DM) and dark energy (DE) with a non-linear interaction Q = 3 HγεbarDEεbarDM /(εbarDE +εbarDM) , where γ is a constant. We assume that DM is pressureless and DE has a constant equation of state parameter w. In the considered model, the energy densities of the dark sector components present a scaling behaviour with εbarDM /εbarDE ∼(a0 / a) - 3(w + γ). We investigate the possibility that the perturbations of DM and DE, which are interacting among themselves, could be coupled to the galaxies with the former being concentrated around them. To carry our analysis, we consider the theory of scalar perturbations (within the mechanical approach), and obtain the sets of parameters (w , γ) which do not contradict it. We conclude that two sets: (w = - 2 / 3 , γ = 1 / 3) and (w = - 1 , γ = 1 / 3) are of special interest. First, the energy densities of DM and DE on these cases are concentrated around galaxies confirming that they are coupled fluids. Second, we show that for both of them, the coincidence problem is less severe than in the standard ΛCDM. Third, the set (w = - 1 , γ = 1 / 3) is within the observational constraints. Finally, we also obtain an expression for the gravitational potential in the considered model.
Sokhoyan, R.; Azizbekyan, H.; Leroy, C.; Ishkhanyan, A.
2011-04-15
We discuss the strong-coupling regime of the nonlinear Landau-Zener problem occurring at coherent photo- and magneto-association of ultracold atoms. We apply a variational approach to an exact third-order nonlinear differential equation for the molecular state probability and construct an accurate approximation describing the time dynamics of the coupled atom-molecule system. The resultant solution improves the accuracy of the previous approximation [22]. The obtained results reveal a remarkable observation that in the strong-coupling limit, the resonance crossing is mostly governed by the nonlinearity, while the coherent atom-molecule oscillations occurring soon after crossing the resonance are principally of a linear nature. This observation is supposedly general for all nonlinear quantum systems having the same generic quadratic nonlinearity, due to the basic attributes of the resonance crossing processes in such systems. The constructed approximation turns out to have a larger applicability range than it was initially expected, covering the whole moderate-coupling regime for which the proposed solution accurately describes ail the main characteristics of the system evolution except the amplitude of the coherent atom-molecule oscillation, which is rather overestimated.
2015-08-27
called as Lead-Zirconium-Titanate (PZT). For reduced dielectric losses, PZT is acquired normally de- poled . The acquired PZT material (type 4) was...line. In low-voltage NLTLs, varactor diodes are used as nonlinear medium since their diode junction capacitance varies with the inverse of the...nonlinearity and frequency response. For these tests, we used circular PZT samples de- poled by manufacturer (type 4 and type 8) of 20/25 mm diameter
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.
NASA Astrophysics Data System (ADS)
Maksimyuk, V. A.; Storozhuk, E. A.; Chernyshenko, I. S.
2012-11-01
Variational finite-difference methods of solving linear and nonlinear problems for thin and nonthin shells (plates) made of homogeneous isotropic (metallic) and orthotropic (composite) materials are analyzed and their classification principles and structure are discussed. Scalar and vector variational finite-difference methods that implement the Kirchhoff-Love hypotheses analytically or algorithmically using Lagrange multipliers are outlined. The Timoshenko hypotheses are implemented in a traditional way, i.e., analytically. The stress-strain state of metallic and composite shells of complex geometry is analyzed numerically. The numerical results are presented in the form of graphs and tables and used to assess the efficiency of using the variational finite-difference methods to solve linear and nonlinear problems of the statics of shells (plates)
1992-12-01
manufactura - bility, and quality while reducing time to market (31). Considering these advantages, reduced cost and improved customer satisfaction...widely applicable mainly due to the flexibility of ASTROS’ bulk data deck By assigning a material card to each element, the changing nature of the...stresses, this nonlinear materials capability allows ASTROS users flexibility . There is benefit in modeling materials nonlinearly; as materials get even
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.
NASA Astrophysics Data System (ADS)
Shivanian, Elyas; Hosseini Ghoncheh, S. J.
2017-02-01
In this paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. A method based on the traditional shooting method and the homotopy analysis method is applied, the so-called shooting homotopy analysis method (SHHAM), to the governing nonlinear differential equation. In this technique, more high-order approximate solutions are computable and multiple solutions are easily searched and discovered due to being free of the symbolic variable. It is found that the solution might be empty, unique or dual depending on the values of the parameters of the model. Furthermore, corresponding fin efficiencies with high accuracy are computed. As a consequence, a new branch solution for this nonlinear problem by a new proposed method, based on the traditional shooting method and the homotopy analysis method, is obtained.
NASA Astrophysics Data System (ADS)
Jeng, Jin-Tsong; Lee, Tsu-Tian
1998-03-01
In this paper, we propose a neural network model with a faster learning speed and a good approximate capability in the function approximation for solving worst-case identification of nonlinear systems H(infinity ) problems. Specifically, via the approximate transformable technique, we develop a Chebyshev Polynomials Based unified model neural network for solving the worst-case identification of nonlinear systems H(infinity ) problems. Based on this approximate transformable technique, the relationship between the single-layered neural network and multi-layered perceptron neural network is derived. It is shown that the Chebyshev Polynomials Based unified model neural network can be represented as a functional link network that is based on Chebyshev polynomials. We also derive a new learning algorithm such that the infinity norm of the transfer function from the input to the output is under a prescribed level. It turns out that the Chebyshev Polynomials Based unified model neural network not only has the same capability of universal approximator, but also has a faster learning speed than multi-layered perceptron or the recurrent neural network in the deterministic worst-case identification of nonlinear systems H(infinity ) problems.
NASA Astrophysics Data System (ADS)
Timergaliev, S. N.
2009-06-01
This paper deals with the proof of the existence of solutions of a geometrically and physically nonlinear boundary value problem for shallow Timoshenko shells with the transverse shear strains taken into account. The shell edge is assumed to be partly fixed. It is proposed to study the problem by a variational method based on searching the points of minimum of the total energy functional for the shell-load system in the space of generalized displacements. We show that there exists a generalized solution of the problemon which the total energy functional attains its minimum on a weakly closed subset of the space of generalized displacements.
NASA Astrophysics Data System (ADS)
Hiller, M.; Sorg, H.
Various papers on the theory and applications of nonlinear problems in dynamical systems are presented. The topics considered include: feedback control of nonlinear systems on equilibratable set, canonical forms for nonlinear systems, optimality of linear feedback control for nonlinear systems, second-order nonlinear mapping in symmetric matrix space, nonlinear oscillations in many degrees of freedom systems, optimal solution to the LQG problem with random delay and incomplete information, chaos induced by the generalized Euler's method, domains of attraction in systems with limit cycles. Also addressed are: period doubling and chaotic behavior, number theory in science and communication, modelling of complex vehicle systems, dynamics of spatial multibar mechanisms, impact noise generated from circulated plate, bilinear model for the chemotherapeutic process of acute leukemia, asymmetric model of auditory systems, aspects of the modelling and control of the drop-on-demand ink jet system, prediction and control of moldability in sand mixing, and stability analysis of linear time-delay systems.
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.
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.
Philip, Bobby; Berrill, Mark A.; Allu, Srikanth; ...
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
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.
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…
Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Amir, Muhammad; Haq, Ihsanul
2014-01-01
We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.
Malik, Suheel Abdullah; Qureshi, Ijaz Mansoor; Haq, Ihsanul
2014-01-01
We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions. PMID:24672381
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.
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.
1989-06-15
following surprising situation. Namely associated with the integrable nonlinear Schrodinger equations are standard numerical schemes which exhibit at...36. An Initial Boundary Value Problem for the Nonlinear Schrodinger Equations , A.S. Fokas, Physica D March 1989. 37. Evolution Theory, Periodic... gravity waves and wave excitation phenomena related to moving pressure distributions; numerical approximation and computation; nonlinear optics; and
NASA Astrophysics Data System (ADS)
Chandra, S.; Vardhanan, A. Vishnu; Gangopadhyay, R.
2007-11-01
Optical phase conjugation (OPC) and distributed Raman amplifier (DRA) combination (OPC-DRA) is demonstrated as a potential enabling solution for simultaneous reduction of fiber non-linearities and dispersion compensation of a sub-carrier multiplexed (SCM) optical transmission link. The present work is focused on the use of OPC-DRA combination for system performance improvement in terms of composite second order distortion (CSO) and carrier to noise ratio (CNR) of the SCM link. The analysis further shows that, introduction of DRA with proper pumping scheme significantly reduce fiber non-linearity resulting in improvement of the system performance in terms of CNR, compared to the situation where only mid-way optical phase conjugation is used.
2016-01-27
industrial applications, called as Lead-Zirconium-Titanate (PZT). For reduced dielectric losses, PZT is acquired normally de- poled . The acquired PZT...with the inverse of the applied reverse voltage [8], [9]. In this report, the experimental results of a varactor diode NLTL built with 30 sections are...breakdown (BD) strength, nonlinearity and frequency response. For these tests, we used circular PZT samples de- poled by manufacturer (type 4 and
NASA Astrophysics Data System (ADS)
Vorotnikov, V. I.; Martyshenko, Yu. G.
2013-09-01
The nonlinear game problem of the three-axis reorientation of an asymmetric solid body with three flywheels (rotors) has been solved. Acceptable levels of uncontrollable noise depending on given constraints of control moments have been estimated.
Finite Dimensional Approximation of a Class of Constrained Nonlinear Optimal Control Problems
1994-03-01
property for Schr ~ dinger Hanxiltonians, Helvetica Physiea Acta, 52 (1979), pp. 655-670. [13) V. GIRAULT AND P. RAVIART, Finite Element Methods for Navier...involves the von Kirma.n plate equations of nonlinear elasticity, the second the Ginzburg-Landau equations of superconductivity, and the third the...Navier-Stokes equations for incompressible, viscous flows. ’This research was supported by the National Aeronautics and Space Administration under NASA
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 Astrophysics Data System (ADS)
Geniet, F.; Leon, J.
2003-05-01
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Bufetova, G A; Gulyamova, E S; Il'ichev, N N; Pashinin, P P; Shapkin, P V; Nasibov, A S
2015-06-30
Transmission spectra of a ZnSe sample diffusion-doped with Fe{sup 2+} ions have been measured in the wavelength range 500 – 7000 nm. A broad absorption band in the range 500 – 1500 nm has been observed in both doped and undoped regions of the sample. This band is possibly due to deviations from stoichiometry in the course of diffusion doping. The transmission of the Fe{sup 2+}:ZnSe sample at a wavelength of 2940 nm has been measured at various dopant concentrations and high peak pulse intensities (up to 8 MW cm{sup -2}). The samples have been shown to be incompletely bleached: during a laser pulse, the transmission first increases, reaches a maximum, and then falls off. Our results suggest that the incomplete bleaching cannot be accounted for by excited-state absorption. The incomplete bleaching (as well as the transmission maximum) is due to the heating of the sample, which leads to a reduction in upper level lifetime and, accordingly, to an increase in absorption saturation intensity. (nonlinear optical phenomena)
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.
Explicit Solutions for a Class of Nonlinear PDE that Arise in Allocation Problems
2006-05-12
approximations for allocation and occupancy problems one must solve a deterministic optimal control problem (or equiv- alently, a calculus of variations...to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 12 MAY 2006 2. REPORT TYPE 3...significant underlying simplification. In the first example it is the fact that the value function for the control problem is expected to be quadratic
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.
A new Liu-Storey type nonlinear conjugate gradient method for unconstrained optimization problems
NASA Astrophysics Data System (ADS)
Zhang, Li
2009-03-01
Although the Liu-Storey (LS) nonlinear conjugate gradient method has a similar structure as the well-known Polak-Ribière-Polyak (PRP) and Hestenes-Stiefel (HS) methods, research about this method is very rare. In this paper, based on the memoryless BFGS quasi-Newton method, we propose a new LS type method, which converges globally for general functions with the Grippo-Lucidi line search. Moreover, we modify this new LS method such that the modified scheme is globally convergent for nonconvex minimization if the strong Wolfe line search is used. Numerical results are also reported.
NASA Astrophysics Data System (ADS)
Zheng, Qin; Yang, Zubin; Sha, Jianxin; Yan, Jun
2017-02-01
In predictability problem research, the conditional nonlinear optimal perturbation (CNOP) describes the initial perturbation that satisfies a certain constraint condition and causes the largest prediction error at the prediction time. The CNOP has been successfully applied in estimation of the lower bound of maximum predictable time (LBMPT). Generally, CNOPs are calculated by a gradient descent algorithm based on the adjoint model, which is called ADJ-CNOP. This study, through the two-dimensional Ikeda model, investigates the impacts of the nonlinearity on ADJ-CNOP and the corresponding precision problems when using ADJ-CNOP to estimate the LBMPT. Our conclusions are that (1) when the initial perturbation is large or the prediction time is long, the strong nonlinearity of the dynamical model in the prediction variable will lead to failure of the ADJ-CNOP method, and (2) when the objective function has multiple extreme values, ADJ-CNOP has a large probability of producing local CNOPs, hence making a false estimation of the LBMPT. Furthermore, the particle swarm optimization (PSO) algorithm, one kind of intelligent algorithm, is introduced to solve this problem. The method using PSO to compute CNOP is called PSO-CNOP. The results of numerical experiments show that even with a large initial perturbation and long prediction time, or when the objective function has multiple extreme values, PSO-CNOP can always obtain the global CNOP. Since the PSO algorithm is a heuristic search algorithm based on the population, it can overcome the impact of nonlinearity and the disturbance from multiple extremes of the objective function. In addition, to check the estimation accuracy of the LBMPT presented by PSO-CNOP and ADJ-CNOP, we partition the constraint domain of initial perturbations into sufficiently fine grid meshes and take the LBMPT obtained by the filtering method as a benchmark. The result shows that the estimation presented by PSO-CNOP is closer to the true value than the
An Optimization-Based Method for Feature Ranking in Nonlinear Regression Problems.
Bravi, Luca; Piccialli, Veronica; Sciandrone, Marco
2016-02-03
In this paper, we consider the feature ranking problem, where, given a set of training instances, the task is to associate a score with the features in order to assess their relevance. Feature ranking is a very important tool for decision support systems, and may be used as an auxiliary step of feature selection to reduce the high dimensionality of real-world data. We focus on regression problems by assuming that the process underlying the generated data can be approximated by a continuous function (for instance, a feedforward neural network). We formally state the notion of relevance of a feature by introducing a minimum zero-norm inversion problem of a neural network, which is a nonsmooth, constrained optimization problem. We employ a concave approximation of the zero-norm function, and we define a smooth, global optimization problem to be solved in order to assess the relevance of the features. We present the new feature ranking method based on the solution of instances of the global optimization problem depending on the available training data. Computational experiments on both artificial and real data sets are performed, and point out that the proposed feature ranking method is a valid alternative to existing methods in terms of effectiveness. The obtained results also show that the method is costly in terms of CPU time, and this may be a limitation in the solution of large-dimensional problems.
Arc-Length Continuation and Multi-Grid Techniques for Nonlinear Elliptic Eigenvalue Problems,
1981-03-19
8217 MG Algorithm 13 3.3 Indefinite Problems 17 3.4 Continuation Methods 17 4. Application to the Bratu Problem 20 4.1 Bratu’s Problem 20 4.2 Arc-length...hierarchy of grids (G0 ,G1 . .... . G"), with GM being the finest one, defined on a domain 0 with corresponding meab sizes (h0 > hi > ..... > h,). and all...1 vM-1 FM-1 a M-RM oGM -1 Li Ml 1 Ml IM K onG • M (3.4) vM ’’I = 0 on aGM - 1 After this problem is solved we can interpolate the solution vM- I
Granmo, Ole-Christoffer; Oommen, B John; Myrer, Svein Arild; Olsen, Morten Goodwin
2007-02-01
This paper considers the nonlinear fractional knapsack problem and demonstrates how its solution can be effectively applied to two resource allocation problems dealing with the World Wide Web. The novel solution involves a "team" of deterministic learning automata (LA). The first real-life problem relates to resource allocation in web monitoring so as to "optimize" information discovery when the polling capacity is constrained. The disadvantages of the currently reported solutions are explained in this paper. The second problem concerns allocating limited sampling resources in a "real-time" manner with the purpose of estimating multiple binomial proportions. This is the scenario encountered when the user has to evaluate multiple web sites by accessing a limited number of web pages, and the proportions of interest are the fraction of each web site that is successfully validated by an HTML validator. Using the general LA paradigm to tackle both of the real-life problems, the proposed scheme improves a current solution in an online manner through a series of informed guesses that move toward the optimal solution. At the heart of the scheme, a team of deterministic LA performs a controlled random walk on a discretized solution space. Comprehensive experimental results demonstrate that the discretization resolution determines the precision of the scheme, and that for a given precision, the current solution (to both problems) is consistently improved until a nearly optimal solution is found--even for switching environments. Thus, the scheme, while being novel to the entire field of LA, also efficiently handles a class of resource allocation problems previously not addressed in the literature.
Inverse backscattering problem for the generalized nonlinear Schrödinger operator in two dimensions
NASA Astrophysics Data System (ADS)
Serov, V.; Sandhu, J.
2010-08-01
The inverse Born approximation is studied for the generalized nonlinear two-dimensional Schrödinger equation - \\Delta u + \\sum _ {l = 0} ^ m \\alpha _ l |u| ^ l u = k ^ 2 u, where the real-valued unknown potentials αl belong to L ^ {p} _ {\\mathrm{comp}} (\\mathbb {R} ^ 2) for some 2 <= p <= ∞ and their Fourier transforms belong to the space L ^ {s} (\\mathbb {R} ^ 2) for some 1 < s < 2. We prove that the leading-order singularities of the sum of the unknown potentials can be recovered from the inverse Born approximation. We also prove that the approximation is equal to the true function up to sum of two functions: one of them from the Sobolev space Ht while the other being a continuous function.
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…
Iannella, Nicolangelo; Tanaka, Shigeru
2007-06-01
In order to gain a better theoretical understanding of the interaction between voltage and calcium influx, we present the simulation results for saltatory transmission in a sparsely excitable model of a continuous cylindrical segment of nerve fiber, where calcium diffuses internally and various ion channels are distributed as hotspots along the cable. A standard set of ion channel descriptions is used to illustrate how different numbers and distributions of ion channel hotspots affect the propagation and transmission of a single action potential and/or a spike train and how such hotspots affect calcium influx and diffusion within continuous cylindrical segment of nerve fiber.
NASA Astrophysics Data System (ADS)
Fonseca, Daniel; Cartaxo, Adolfo V. T.; Monteiro, Paulo P.
2007-06-01
The impact of the extinction ratio (ER) on the performance of a 40-Gb/s return-to-zero transmission system over standard single-mode fiber (SSMF) is presented. Several dispersion maps are analyzed in order to minimize the distortion due to the intrachannel nonlinear effects, namely, intrachannel cross-phase modulation and intrachannel four wave mixing (IFWM). The decrease of the ER until a specific value leads to an increase of the intensity distortion, which is mainly due to IFWM. As a consequence, two distinct transmission regimes are identified, depending on the input average power of each section and the ER of the optical signals. The first regime has previously been called the pseudolinear regime in the literature and occurs when high ERs are considered. The optimum dispersion map of this regime has a given optical precompensation and a total residual dispersion near zero. The second regime occurs with the decrease of the ER. Under such a circumstance, the optimum dispersion map obtained in the pseudolinear regime leads to significant degradation, which is mainly due to ghost pulses appearing in the symbol “0.” This effect can be reduced by a system with residual dispersion that is significantly different from zero, leading to a detected eye pattern with low degradation in the symbol “0” but high timing jitter, which limits the use of such signals in feasible transmission systems. We call this new regime pseudosolitonic as the intrachannel nonlinear effects are apparently reduced by the residual group velocity dispersion (as it is observed in the solitonic regime occurring at lower bit rates), but strong waveform degradation occurs along the SSMF transmission. The exact value of ER for which the change between the two transmission regimes is observed depends on the optical average power at the input of each section. A simple expression to predict the system conditions (namely, ER, input average power of each section, and number of sections) for which
Reduction of nonlinear embedded boundary models for problems with evolving interfaces
NASA Astrophysics Data System (ADS)
Balajewicz, Maciej; Farhat, Charbel
2014-10-01
Embedded boundary methods alleviate many computational challenges, including those associated with meshing complex geometries and solving problems with evolving domains and interfaces. Developing model reduction methods for computational frameworks based on such methods seems however to be challenging. Indeed, most popular model reduction techniques are projection-based, and rely on basis functions obtained from the compression of simulation snapshots. In a traditional interface-fitted computational framework, the computation of such basis functions is straightforward, primarily because the computational domain does not contain in this case a fictitious region. This is not the case however for an embedded computational framework because the computational domain typically contains in this case both real and ghost regions whose definitions complicate the collection and compression of simulation snapshots. The problem is exacerbated when the interface separating both regions evolves in time. This paper addresses this issue by formulating the snapshot compression problem as a weighted low-rank approximation problem where the binary weighting identifies the evolving component of the individual simulation snapshots. The proposed approach is application independent and therefore comprehensive. It is successfully demonstrated for the model reduction of several two-dimensional, vortex-dominated, fluid-structure interaction problems.
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…
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.
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.
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.
The nurse scheduling problem: a goal programming and nonlinear optimization approaches
NASA Astrophysics Data System (ADS)
Hakim, L.; Bakhtiar, T.; Jaharuddin
2017-01-01
Nurses scheduling is an activity of allocating nurses to conduct a set of tasks at certain room at a hospital or health centre within a certain period. One of obstacles in the nurse scheduling is the lack of resources in order to fulfil the needs of the hospital. Nurse scheduling which is undertaken manually will be at risk of not fulfilling some nursing rules set by the hospital. Therefore, this study aimed to perform scheduling models that satisfy all the specific rules set by the management of Bogor State Hospital. We have developed three models to overcome the scheduling needs. Model 1 is designed to schedule nurses who are solely assigned to a certain inpatient unit and Model 2 is constructed to manage nurses who are assigned to an inpatient room as well as at Polyclinic room as conjunct nurses. As the assignment of nurses on each shift is uneven, then we propose Model 3 to minimize the variance of the workload in order to achieve equitable assignment on every shift. The first two models are formulated in goal programming framework, while the last model is in nonlinear optimization form.
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.
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)
Khan, Junaid Ali; Zahoor Raja, Muhammad Asif; Rashidi, Mohammad Mehdi; Syam, Muhammad Ibrahim; Majid Wazwaz, Abdul
2015-10-01
In this research, the well-known non-linear Lane-Emden-Fowler (LEF) equations are approximated by developing a nature-inspired stochastic computational intelligence algorithm. A trial solution of the model is formulated as an artificial feed-forward neural network model containing unknown adjustable parameters. From the LEF equation and its initial conditions, an energy function is constructed that is used in the algorithm for the optimisation of the networks in an unsupervised way. The proposed scheme is tested successfully by applying it on various test cases of initial value problems of LEF equations. The reliability and effectiveness of the scheme are validated through comprehensive statistical analysis. The obtained numerical results are in a good agreement with their corresponding exact solutions, which confirms the enhancement made by the proposed approach.
NASA Astrophysics Data System (ADS)
Xiao, Jinyou; Zhou, Hang; Zhang, Chuanzeng; Xu, Chao
2016-11-01
This paper focuses on the development and engineering applications of a new resolvent sampling based Rayleigh-Ritz method (RSRR) for solving large-scale nonlinear eigenvalue problems (NEPs) in finite element analysis. There are three contributions. First, to generate reliable eigenspaces the resolvent sampling scheme is derived from Keldysh's theorem for holomorphic matrix functions following a more concise and insightful algebraic framework. Second, based on the new derivation a two-stage solution strategy is proposed for solving large-scale NEPs, which can greatly enhance the computational cost and accuracy of the RSRR. The effects of the user-defined parameters are studied, which provides a useful guide for real applications. Finally, the RSRR and the two-stage scheme is applied to solve two NEPs in the FE analysis of viscoelastic damping structures with up to 1 million degrees of freedom. The method is versatile, robust and suitable for parallelization, and can be easily implemented into other packages.
NASA Astrophysics Data System (ADS)
Xiao, Jinyou; Zhou, Hang; Zhang, Chuanzeng; Xu, Chao
2017-02-01
This paper focuses on the development and engineering applications of a new resolvent sampling based Rayleigh-Ritz method (RSRR) for solving large-scale nonlinear eigenvalue problems (NEPs) in finite element analysis. There are three contributions. First, to generate reliable eigenspaces the resolvent sampling scheme is derived from Keldysh's theorem for holomorphic matrix functions following a more concise and insightful algebraic framework. Second, based on the new derivation a two-stage solution strategy is proposed for solving large-scale NEPs, which can greatly enhance the computational cost and accuracy of the RSRR. The effects of the user-defined parameters are studied, which provides a useful guide for real applications. Finally, the RSRR and the two-stage scheme is applied to solve two NEPs in the FE analysis of viscoelastic damping structures with up to 1 million degrees of freedom. The method is versatile, robust and suitable for parallelization, and can be easily implemented into other packages.
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)
Lin, Ray-Qing
We apply a symbolic manipulation program (MACSYMA, 1977) and a second-order perturbation approach to develop a hierarchy of adjustable M-mode models to study nonlinear phenomena in geophysical fluid dynamics. The automated symbolic manipulation provides, for each value of M, a Fortran program of nonlinear algebraic equations for stationary solutions, and of ordinary differential equations (ODES) for time-dependent solutions. These equations are then solved numerically to determine successive bifurcations in the solution structure, and to study the stability characteristics and dynamical behavior of each solution branch. We illustrate this methodology by studying nonlinear, thermally and rotationally-driven convection in a rapidly -rotating cylindrical annulus, which is heated from the outside and cooled from the inside. This annulus model is a tool for investigating convection in the equatorial regions of major planets. The cylinder has slightly inclined end boundaries to simulate the geometry of thick atmospheres in an equatorial region. both these boundaries and the side walls are stress-free. The problem is based on the two-dimensional vorticity equation and thermodynamic equation in the Boussinesq approximation. We adopt two distinct approaches (Runge-Kutta and Fourier-decomposition) to solve the time-dependent nonlinear differential equations. We found the same solution, involving a large phase shift between waves, as Or and Busse, who used a Galerkin-type method, Additionally we found a new solution with a small phase shift between waves. The increased number of waves permitted by our hierarchic approach allows one to study wave-wave interactions, in addition to wave/mean -flow interactions. More generally, it opens the road to a study of transitions from simple solutions to chaos in systems with a moderately large number of degrees of freedom. Symbolic manipulation greatly reduces the chances of numerical and human errors in the detailed study of this
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.
A free boundary problem of a diffusive SIRS model with nonlinear incidence
NASA Astrophysics Data System (ADS)
Cao, Jia-Feng; Li, Wan-Tong; Wang, Jie; Yang, Fei-Ying
2017-04-01
This paper is concerned with the spreading (persistence) and vanishing (extinction) of a disease which is characterized by a diffusive SIRS model with a bilinear incidence rate and free boundary. Through discussing the dynamics of a free boundary problem of an SIRS model, the spreading of a disease is described. We get the sufficient conditions which ensure the disease spreading or vanishing. In addition, the estimate of the expanding speed is also given when the free boundaries extend to the whole R.
On solvability of a elliptic-parabolic problem of nonlinear filtration theory
NASA Astrophysics Data System (ADS)
Pavlova, M. F.; Rung, E. V.
2016-11-01
Existence of a strong solution of the initial-boundary value problem modeling the process of liquid filtration in an arbitrary bounded region Ω of space Rn is proven. For determining a generalized solution, the Kirchhoff transform is used, and it is assumed that the domain of the Kirchhoff function constitutes only a part of the real axis. For proving the existence theorem, the method of semidiscretization with respect to the variable t and the Galerkin method are used.
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.
Sackey, Isaac; Da Ros, Francesco; Jazayerifar, Mahmoud; Richter, Thomas; Meuer, Christian; Nölle, Markus; Molle, Lutz; Peucheret, Christophe; Petermann, Klaus; Schubert, Colja
2014-11-03
We present experimental and numerical investigations of Kerr nonlinearity compensation in a 400-km standard single-mode fiber link with distributed Raman amplification with backward pumping. A dual-pump polarization-independent fiber-based optical parametric amplifier is used for mid-link spectral inversion of 5 × 28-GBd polarization-multiplexed 16-QAM signals. Signal quality factor (Q-factor) improvements of 1.1 dB and 0.8 dB were obtained in the cases of a single-channel and a five-channel wavelength-division multiplexing (WDM) system, respectively. The experimental results are compared to numerical simulations with good agreement. It is also shown with simulations that a maximum transmission reach of 2400 km enabled by the optical phase conjugator is possible for the WDM signal.
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 grandparents. Results indicated that G1 MDD conferred risk for G2 MDD, but not for G3 CBCL scores. G2 MDD predicted higher G3 Internalizing and Anxious/Depressed scores. Also, there was an interaction between G1 MDD and G2 MDD in predicting higher G3 Anxious/Depressed scores such that scores were highest among children with both depressed parents and grandparents. These effects were robust to statistical adjustments for status variables and parental relationship measures but not to adjustment for concurrent parental depressive symptoms. PMID:18645754
NASA Astrophysics Data System (ADS)
Chappell, James M.; Gunn, Lachlan J.; Abbott, Derek
2014-09-01
The idealized Kish-Sethuraman (KS) cipher is theoretically known to offer perfect security through a classical information channel. However, realization of the protocol is hitherto an open problem, as the required mathematical operators have not been identified in the previous literature. A mechanical analogy of this protocol can be seen as sending a message in a box using two padlocks; one locked by the Sender and the other locked by the Receiver, so that theoretically the message remains secure at all times. We seek a mathematical representation of this process, considering that it would be very unusual if there was a physical process with no mathematical description. We select Clifford's geometric algebra for this task as it is a natural formalism to handle rotations in spaces of various dimension. The significance of finding a mathematical description that describes the protocol, is that it is a possible step toward a physical realization having benefits in increased security with reduced complexity.
NASA Astrophysics Data System (ADS)
Cherednichenko, Kirill D.; Smyshlyaev, Valery P.
2004-12-01
We consider a scalar quasilinear equation in the divergence form with periodic rapid oscillations, which may be a model of, e.g., nonlinear conducting, dielectric, or deforming in a restricted way hardening elastic-plastic composites, with “outer” periodicity conditions of a fixed large period. Under some natural growth assumptions on the stored-energy function, we construct for uniformly elliptic problems a full two-scale asymptotic expansion, which has a precise “double-series” structure, separating the slow and the fast variables “in all orders”, so that its “slowly varying” part solves asymptotically an “infinite-order homogenised equation” (cf. Bakhvalov, N.S., Panasenko, G.P.: Homogenisation: Averaging Processes in Periodic Media. Nauka, Moscow, 1984 (in Russian); English translation: Kluwer, 1989), and whose higher-order terms depend on the higher gradients of the slowly varying part. We prove the error bound, i.e., that the truncated asymptotic expansion is “higher-order” close to the actual solution in appropriate norms. The approach is extended to a non-uniformly elliptic case: for two-dimensional power-law potentials we prove the “non-degeneracy” using topological index methods. Examples and explicit formulae for the higher-order terms are given. In particular, we prove that the first term in the higher-order homogenised equations is related to the first-order corrector to the “mean” flux, and has in general the form of a fully nonlinear operator which is quadratic with respect to its highest (second) derivative being a linear combination of the second minors of the Hessian with coefficients depending on the first gradient, and in dimension two is of Monge-Ampère type. We show that this term is present at least for some examples (three-phase power-law laminates).
Kikuchi, Kazuro
2008-01-21
We demonstrate electronic post-compensation for nonlinear phase fluctuation in a 1000-km 20-Gbit/s optical quadrature phase-shift keying (QPSK) transmission system, where group-velocity dispersion is well managed. The inter-symbol interference (ISI) at the transmitter induces the nonlinear phase fluctuation through self-phase modulation (SPM) of the signal transmitted through a fiber. However, when the optimized phase shift proportional to the intensity fluctuation is given to the complex amplitude of the signal electric field by using a digital coherent receiver, the nonlinear phase fluctuation can be reduced effectively.
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, improves 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.
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
Non-Linear Problems in NMR: Application of the DFM Variation of Parameters Method
NASA Astrophysics Data System (ADS)
Erker, Jay Charles
This Dissertation introduces, develops, and applies the Dirac-McLachlan-Frenkel (DFM) time dependent variation of parameters approach to Nuclear Magnetic Resonance (NMR) problems. Although never explicitly used in the treatment of time domain NMR problems to date, the DFM approach has successfully predicted the dynamics of optically prepared wave packets on excited state molecular energy surfaces. Unlike the Floquet, average Hamiltonian, and Van Vleck transformation methods, the DFM approach is not restricted by either the size or symmetry of the time domain perturbation. A particularly attractive feature of the DFM method is that measured data can be used to motivate a parameterized trial function choice and that the DFM theory provides the machinery to provide the optimum, minimum error choices for these parameters. Indeed a poor parameterized trial function choice will lead to a poor match with real experiments, even with optimized parameters. Although there are many NMR problems available to demonstrate the application of the DFM variation of parameters, five separate cases that have escaped analytical solution and thus require numerical methods are considered here: molecular diffusion in a magnetic field gradient, radiation damping in the presence of inhomogeneous broadening, multi-site chemical exchange, and the combination of molecular diffusion in a magnetic field gradient with chemical exchange. The application to diffusion in a gradient is used as an example to develop the DFM method for application to NMR. The existence of a known analytical solution and experimental results allows for direct comparison between the theoretical results of the DFM method and Torrey's solution to the Bloch equations corrected for molecular diffusion. The framework of writing classical Bloch equations in matrix notation is then applied to problems without analytical solution. The second example includes the generation of a semi-analytical functional form for the free
On Algorithms for Nonlinear Minimax and Min-Max-Min Problems and Their Efficiency
2011-03-01
Monterey CA 93943-5000 The views expressed in this thesis are those of the author and do not reflect the official policy or position of the Department of...MINIMAX AND MIN-MAX-MIN PROBLEMS AND THEIR EFFICIENCY Pee Eng Yau Principal Analyst, Singapore Defence Science and Technology Agency B.Eng., National...BLANK xii LIST OF TABLES 1. Run times based on ϵ for ϵ- PPP . The word “local” means that the algorithm converges to a locally optimal solution that does
FEDOROVA,A.; ZEITLIN,M.; PARSA,Z.
2000-03-31
In this paper the authors present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to a variational approach in the general case they have the solution as a multiresolution (multiscales) expansion on the base of compactly supported wavelet basis. They give an extension of their results to the cases of periodic orbital particle motion and arbitrary variable coefficients. Then they consider more flexible variational method which is based on a biorthogonal wavelet approach. Also they consider a different variational approach, which is applied to each scale.
On the nonlinear stability of viscous modes within the Rayleigh problem on an infinite flat plate
NASA Technical Reports Server (NTRS)
Webb, J. C.; Otto, S. R.; Lilley, G. M.
1994-01-01
The stability has been investigated of the unsteady flow past an infinite flat plate when it is moved impulsively from rest, in its own plane. For small times the instantaneous stability of the flow depends on the linearized equations of motion which reduce in this problem to the Orr-Sommerfeld equation. It is known that the flow for certain values of Reynolds number, frequency and wave number is unstable to Tollmien-Schlichting waves, as in the case of the Blasius boundary layer flow past a flat plate. With increase in time, the unstable waves only undergo growth for a finite time interval, and this growth rate is itself a function of time. The influence of finite amplitude effects is studied by solving the full Navier-Stokes equations. It is found that the stability characteristics are markedly changed both by the consideration of the time evolution of the flow, and by the introduction of finite amplitude effects.
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
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.
Jan Hesthaven
2012-02-06
Final report for DOE Contract DE-FG02-98ER25346 entitled Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences. Principal Investigator Jan S. Hesthaven Division of Applied Mathematics Brown University, Box F Providence, RI 02912 Jan.Hesthaven@Brown.edu February 6, 2012 Note: This grant was originally awarded to Professor David Gottlieb and the majority of the work envisioned reflects his original ideas. However, when Prof Gottlieb passed away in December 2008, Professor Hesthaven took over as PI to ensure proper mentoring of students and postdoctoral researchers already involved in the project. This unusual circumstance has naturally impacted the project and its timeline. However, as the report reflects, the planned work has been accomplished and some activities beyond the original scope have been pursued with success. Project overview and main results The effort in this project focuses on the development of high order accurate computational methods for the solution of hyperbolic equations with application to problems with strong shocks. While the methods are general, emphasis is on applications to gas dynamics with strong shocks.
Zhai, Chengbo; Hao, Mengru
2014-01-01
By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by -D(0+)(ν1)y1(t) = λ1a1(t)f(y1(t), y2(t)), - D(0+)(ν2)y2(t) = λ2a2(t)g(y1(t), y2(t)), where D(0+)(ν) is the standard Riemann-Liouville fractional derivative, ν1, ν2 ∈ (n - 1, n] for n > 3 and n ∈ N, subject to the boundary conditions y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = 0 = [D(0+ (α)y2(t)] t=1, for 1 ≤ α ≤ n - 2, or y1((i))(0) = 0 = y ((i))(0), for 0 ≤ i ≤ n - 2, and [D(0+)(α)y1(t)] t=1 = ϕ1(y1), [D(0+)(α)y2(t)] t=1 = ϕ2(y2), for 1 ≤ α ≤ n - 2, ϕ1, ϕ2 ∈ C([0,1], R). Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.
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.
Koteras, J.R.
1996-01-01
The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region.
Nonlinear magnetic metamaterials.
Shadrivov, Ilya V; Kozyrev, Alexander B; van der Weide, Daniel W; Kivshar, Yuri S
2008-12-08
We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission.
NASA Astrophysics Data System (ADS)
Singh, Palwinder; Sharma, Pankaj; Sharma, Vineet; Thakur, Anup
2017-04-01
In this paper we have studied the effect of Ag addition on linear and non-linear optical properties of thermally evaporated (Ge2Sb2Te5)100‑x Ag x (x = 0, 1, 3 and 10) thin films (thickness ∼700 nm) from single transmission spectra. Energy dispersive spectroscopy, x-ray diffraction and Raman spectroscopy were used to verify the composition, amorphous nature and structure of the fabricated thin films respectively. Swanpoel’s method was used to calculate the thickness (d), refractive index (n) and extinction coefficient (k). The refractive index and extinction coefficient were used to obtain all linear and non linear optical parameters. The compositional dependence of the refractive index, extinction coefficient, volume energy loss function, surface energy loss function, dielectric constant, dielectric loss function, optical conductivity and third order non-linear optical susceptibility were determined. All these optical parameters have minimum values for 3% Ag-doped Ge2Sb2Te5 (GST). The decrease in measured optical parameters up to 3% Ag doping is due to a decrease in the density of localized states in the mobility gap. The increase in the optical parameters at 10% Ag doping was ascribed to the distortion of the host lattice, because incorporation of Ag has been done at the expense of Ge, Sb and Te. The optical parameters of the GST films were found to be strongly dependent upon Ag content. The results revealed that 3% Ag-doped GST is a promising candidate for phase change optical storage applications.
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.
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)
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.
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
Kheifets, S.
1983-01-01
A perturbation method which allows one to find the distribution function and the beam size for a broad class of storage ring nonlinear problems is described in Part I of this work. In present note I apply this method to a particular problem. Namely, I want to evaluate an enhancement of the vertical beam size of a bunch due to the presence of the ring of nonlinear magnetic fields. The main part of the work deals with sextupole magnets. Formula for the beam size in the presence of octupole fields are also developed to the first order in the octupole strength, although octupole magnets are not widely used in present storage ring designs. This calculation is done mainly because the octupole field has the same symmetry as the beam-beam force for the head-on collision. This will give us the opportunity to compare the conduct of the bunch due to this two types of nonlinear kicks. The general terms of the applicability of the Green's function method is discussed in the first part of this work.
NASA Astrophysics Data System (ADS)
Kir'yanov, Alexander V.; Barmenkov, Yuri O.
2006-07-01
We reply to the comment [R. Paschotta and A.C. Tropper, Opt. Express, to be published (2006)] on our recent work reporting a study of the cooperative absorption and emission in heavily-doped Ytterbium silica fibers and mechanisms of the fiber nonlinear transmission coefficient reduction due to the Ytterbium ion-pairs’ effect [A.V. Kir’yanov et al., Opt. Express, 14 (9), 3981 (2006)]. We provide some additional evidences for that our work hypotheses and conclusions.
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)
Nourazar, Salman; Nazari-Golshan, Akbar; Yıldırım, Ahmet; Nourazar, Maryam
2012-07-01
The physical science importance of the Cauchy problem of the reaction-diffusion equation appears in the modelling of a wide variety of nonlinear systems in physics, chemistry, ecology, biology, and engineering. A hybrid of Fourier transform and Adomian decomposition method (FTADM) is developed for solving the nonlinear non-homogeneous partial differential equations of the Cauchy problem of reaction-diffusion. The results of the FTADM and the ADM are compared with the exact solution. The comparison reveals that for the same components of the recursive sequences, the errors associated with the FTADM are much lesser than those of the ADM. We show that as time increases the results of the FTADM approaches 1 with only six recursive terms. This is in agreement with the physical property of the density-dependent nonlinear diffusion of the Cauchy problem which is also in agreement with the exact solution. The monotonic and very rapid convergence of the results of the FTADM towards the exact solution is shown to be much faster than that of the ADM
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.
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.
NASA Technical Reports Server (NTRS)
Moyer, E. T., Jr.
1984-01-01
The nonlinear vibration response of a double cantilevered beam subjected to pulse loading over a central sector is studied. The initial response is generated in detail to ascertain the energetics of the response. The total energy is used as a gauge of the stability and accuracy of the solution. It is shown that to obtain accurate and stable initial solutions an extremely high spatial and time resolution is required. This requirement was only evident through an examination of the energy of the system. It is proposed, therefore, to use the total energy of the system as a necessary stability and accuracy criterion for the nonlinear response of conservative systems. The results also demonstrate that even for moderate nonlinearities, the effects of membrane forces have a significant influence on the system. It is also shown that while the fundamental response is contained in a first mode envelope, the fluctuations caused by the higher order modes must be resolved.
NASA Astrophysics Data System (ADS)
Tian, Shou-Fu
2017-01-01
Boundary value problems for integrable nonlinear differential equations can be analyzed via the Fokas method. In this paper, this method is employed in order to study initial-boundary value problems of the general coupled nonlinear Schrödinger equation formulated on the finite interval with 3 × 3 Lax pairs. The solution can be written in terms of the solution of a 3 × 3 Riemann-Hilbert problem. The relevant jump matrices are explicitly expressed in terms of the three matrix-value spectral functions s (k), S (k), and SL (k). The associated general Dirichlet to Neumann map is also analyzed via the global relation. It is interesting that the relevant formulas can be reduced to the analogous formulas derived for boundary value problems formulated on the half-line in the limit when the length of the interval tends to infinity. It is shown that the formulas characterizing the Dirichlet to Neumann map coincide with the analogous formulas obtained via a Gelfand-Levitan-Marchenko representation.
Baksmaty, Leslie O; Yannouleas, Constantine; Landman, Uzi
2008-09-26
Systematic trends of nonuniversal behavior of electron-transmission phases through a quantum dot, with no phase lapse for the transition N = 1-->N = 2 and a lapse of pi for the N = 2-->N = 3 transition, are predicted, in agreement with experiments, from many-body transport calculations involving exact diagonalization of the dot Hamiltonian. The results favor shape anisotropy of the dot and strong e-e repulsion with consequent electron localization, showing dependence on spin configurations and the participation of excited doorway transmission channels.
1990-12-07
Proceedings of the 13th Interna- tional Congress on Acoustics, Belgrade, Yugoslavia, August 1989, edited by P. Pravica and G. Drakulic (Sava Centar...Congress on Acoustics (Sava Centar, Belgrade, 1989), edited by P. Pravica and G. Drakulic , Vol. 1, pp. 145-148. [11] K.-E. Froysa, "Weakly nonlinear...Congress on Acoustics (Sava Centar, Belgrade, 1989), edited by P. Pravica and G. Drakulic , Vol. 1, pp. 283-286. [41] C. M. Darvennes, M. F. Hamilton, J
Carrassi, Alberto; Ghil, Michael; Trevisan, Anna; Uboldi, Francesco
2008-06-01
We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system leads to the uniqueness of its sequentially estimated solutions and is required for the convergence of these solutions to the system's true, chaotic evolution. The key ideas of our approach are illustrated for a linearized Lorenz system. Stability of two nonlinear prediction-assimilation systems from dynamic meteorology is studied next via the complete spectrum of their Lyapunov exponents; these two systems are governed by a large set of ordinary and of partial differential equations, respectively. The degree of data-induced stabilization is crucial for the performance of such a system. This degree, in turn, depends on two key ingredients: (i) the observational network, either fixed or data-adaptive, and (ii) the assimilation method.
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.
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.
Alexandrov, D V; Nizovtseva, I G; Malygin, A P; Huang, H-N; Lee, D
2008-03-19
A model is presented that describes nonstationary solidification of binary melts or solutions from a cooled boundary maintained at a time-dependent temperature. Heat and mass transfer processes are described on the basis of the principles of a mushy layer, which divides pure solid material and a liquid phase. Nonlinear equations characterizing the dynamics of the phase transition boundaries are deduced. Approximate analytical solutions of the model under consideration are constructed. A method for controlling the external temperature at a cooled wall in order to obtain a required solidification velocity is discussed.
Nonlinear Ultrasonic Phased Array Imaging
NASA Astrophysics Data System (ADS)
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.
Nonlinear ultrasonic phased array imaging.
Potter, J N; Croxford, A J; Wilcox, P D
2014-10-03
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)
Vozhakov, I. S.; Arkhipov, D. G.; Tsvelodub, O. Yu
2016-10-01
The work is devoted to numerical simulation of the dynamics of nonlinear periodic waves on the surface of freely flowing liquid film realized with the use of the previously discovered symmetry of model equations. The calculation results have been presented for the dynamics of amplitudes of significant harmonics and for the wave surface evolution. They prove to be in good agreement with previously calculated steady-state traveling solutions obtained on the full and the reduced bases. In addition, the work has identified intervals of wavenumbers in which the evolution of perturbations with small initial amplitude leads to a wave signal periodically changing in time rather than to the steady-state traveling solution.
Kheifets, S.
1982-07-01
For an electron storage ring the beam size evaluation including beam-beam interaction gives an example of such a problem. Another good example is finding the beam size for a nonlinear machine. The present work gives a way to solve some of these problems, at least in principle. The approach described here is an application of the well known Green's function method, which in this case is applied to the Fokker-Planck equation governing the distribution function in the phase space of particle motion. The new step made in this paper is to consider the particle motion in two degrees of freedom rather than in one dimension, a characteristic of all the previous work. This step seems to be necessary for an adequate description of the problem, at least for the class of problems which are considered below. This work consists of the formal solution of the Fokker-Planck equation in terms of its Green's function and describing the Green's function itself. The Green's function and the description of some of its properties can be found in the Appendices. I discuss the distribution function in the transverse phase space of a particle and it's Fokker-Planck equation for a simple case of a weak focusing machine. Part of this paper is devoted to describing the Green's function and solution of this equation. Then this technique is applied to a strong focusing machine and finally there is a discussion of applicability of this method, its limitations and relation to other methods. 13 refs.
NASA Astrophysics Data System (ADS)
Petra, N.; Alexanderian, A.; Stadler, G.; Ghattas, O.
2015-12-01
We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs). The inverse problem seeks to infer a parameter field (e.g., the log permeability field in a porous medium flow model problem) from synthetic observations at a set of sensor locations and from the governing PDEs. The goal of the OED problem is to find an optimal placement of sensors so as to minimize the uncertainty in the inferred parameter field. We formulate the OED objective function by generalizing the classical A-optimal experimental design criterion using the expected value of the trace of the posterior covariance. This expected value is computed through sample averaging over the set of likely experimental data. Due to the infinite-dimensional character of the parameter field, we seek an optimization method that solves the OED problem at a cost (measured in the number of forward PDE solves) that is independent of both the parameter and the sensor dimension. To facilitate this goal, we construct a Gaussian approximation to the posterior at the maximum a posteriori probability (MAP) point, and use the resulting covariance operator to define the OED objective function. We use randomized trace estimation to compute the trace of this covariance operator. The resulting OED problem includes as constraints the system of PDEs characterizing the MAP point, and the PDEs describing the action of the covariance (of the Gaussian approximation to the posterior) to vectors. We control the sparsity of the sensor configurations using sparsifying penalty functions, and solve the resulting penalized bilevel optimization problem via an interior-point quasi-Newton method, where gradient information is computed via adjoints. We elaborate our OED method for the problem of determining the optimal sensor configuration to best infer the log permeability field in a porous medium flow problem. Numerical results show that the number of PDE
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.
Homentcovschi, Dorel; Miles, Ronald N.
2008-01-01
An analysis is presented of the diffraction of a pressure wave by a periodic grating including the influence of the air viscosity. The direction of the incoming pressure wave is arbitrary. As opposed to the classical nonviscous case, the problem cannot be reduced to a plane problem having a definite 3-D character. The system of partial differential equations used for solving the problem consists of the compressible Navier-Stokes equations associated with no-slip boundary conditions on solid surfaces. The problem is reduced to a system of two hypersingular integral equations for determining the velocity components in the slits’ plane and a hypersingular integral equation for the normal component of velocity. These equations are solved by using Galerkin’s method with some special trial functions. The results can be applied in designing protective screens for miniature microphones realized in MEMS technology. In this case, the physical dimensions of the device are on the order of the viscous boundary layer so that the viscosity cannot be neglected. The analysis indicates that the openings in the screen should be on the order of 10 microns in order to avoid excessive attenuation of the signal. This paper also provides the variation of the transmission coefficient with frequency in the acoustical domain. PMID:19122753
NASA Astrophysics Data System (ADS)
Bukhenskiĭ, M. F.; Novikov, V. D.
1985-08-01
A review is given of the papers presented at a plenary meeting of the Scientific Council of the USSR Academy of Sciences on the Problem of Coherent and Nonlinear Optics, held in Kishinev on December 3-5, 1984. The following topics were discussed at this meeting: nonlinear optical properties of semiconductors, semiconductors at high excitation rates, waveguide systems, applications of lasers in biology, optical instrumentation.
1986-03-31
generation, and the resulting thermomechanical response. Examine role of thermomechanical effects in damage processes such as fatigue and wear. 4.) Conduct...deformations, rotations, large strains, and thermomechanical inter- actions, with due consideration of frictional resistance. 2.) Conduct preliminary...studies of simple quasi-static problems with the characteristics listed above. 3.) Investigate dynamic friction mechanisms, their role in heat
1988-04-01
Moreover, if e2 > 61 and we further assume (f.1) f(x,y) is locally Lipschitz continuous in y then inequalities (1.37) and (1.38) are strict. 17 Proof MI...Univ. Math. J. 20 (1971), 983-996.[I 124 18. J. A. Hempel, Superlinear variational boundary value problems and nonuniqueness , Thesis, University of
NASA Astrophysics Data System (ADS)
Steward, David R.
2016-11-01
Recharge from surface to groundwater is an important component of the hydrological cycle, yet its rate is difficult to quantify. Percolation through two-dimensional circular inhomogeneities in the vadose zone is studied where one soil type is embedded within a uniform background, and nonlinear interface conditions in the quasilinear formulation are solved using Newton's method with the Analytic Element Method. This numerical laboratory identifies detectable variations in pathline and pressure head distributions that manifest due to a shift in recharge rate through in a heterogeneous media. Pathlines either diverge about or converge through coarser and finer grained materials with inverse patterns forming across lower and upper elevations; however, pathline geometry is not significantly altered by recharge. Analysis of pressure head in lower regions near groundwater identifies a new phenomenon: its distribution is not significantly impacted by an inhomogeneity soil type, nor by its placement nor by recharge rate. Another revelation is that pressure head for coarser grained inhomogeneities in upper regions is completely controlled by geometry and conductivity contrasts; a shift in recharge generates a difference Δp that becomes an additive constant with the same value throughout this region. In contrast, shifts in recharge for finer grained inhomogeneities reveal patterns with abrupt variations across their interfaces. Consequently, measurements aimed at detecting shifts in recharge in a heterogeneous vadose zone by deciphering the corresponding patterns of change in pressure head should focus on finer grained inclusions well above a groundwater table.
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).
NASA Technical Reports Server (NTRS)
Beckett, P. M.
1981-01-01
The proposed method for the treatment of two dimensional solidification problems is based on quasilinearization of the transformed heat conduction equation and latent heat condition at the interface and an iterative sequence in which these are solved simultaneously. Modern algorithms for solving such sparse systems mean that most of the storage advantage of other methods are reduced and the speed of solution can be improved.
NASA Astrophysics Data System (ADS)
Pulkkinen, Antti; Lindahl, Sture; Viljanen, Ari; Pirjola, Risto
2005-08-01
On 30 October 2003, an ongoing geomagnetic superstorm knocked down a part of the high-voltage power transmission system in southern Sweden. The blackout lasted for an hour and left about 50,000 customers without electricity. The incident was probably the most severe geomagnetically induced current (GIC) failure observed since the well-known March 1989 Québec blackout. The "three-phase" storm produced exceptionally large geomagnetic activity at the Fennoscandian auroral region. Although the diversity of the GIC drivers is addressed in the study, the problems in operating the Swedish system during the storm are attributed geophysically to substorms, storm sudden commencement, and enhanced ionospheric convection, all of which created large and complex geoelectric fields capable of driving large GIC. On the basis of the basic twofold nature of the failure-related geoelectric field characteristics, a semideterministic approach for forecasting GIC-related geomagnetic activity in which average overall activity is supplemented with statistical estimations of the amplitudes of GIC fluctuations is suggested. The study revealed that the primary mode of GIC-related failures in the Swedish high-voltage power transmission system were via harmonic distortions produced by GIC combined with too sensitive operation of the protective relays. The outage in Malmö on 30 October 2003 was caused by a combination of an abnormal switching state of the system and tripping of a low-set residual overcurrent relay that had a high sensitivity for the third harmonic of the fundamental frequency.
Dishion, Thomas J; Forgatch, Marion; Van Ryzin, Mark; Winter, Charlotte
2012-07-01
In this study we examined the videotaped family interactions of a community sample of adolescents and their parents. Youths were assessed in early to late adolescence on their levels of antisocial behavior. At age 16-17, youths and their parents were videotaped interacting while completing a variety of tasks, including family problem solving. The interactions were coded and compared for three developmental patterns of antisocial behavior: early onset, persistent; adolescence onset; and typically developing. The mean duration of conflict bouts was the only interaction pattern that discriminated the 3 groups. In the prediction of future antisocial behavior, parent and youth reports of transition entropy and conflict resolution interacted to account for antisocial behavior at age 18-19. Families with low entropy and peaceful resolutions predicted low levels of youth antisocial behavior at age 18-19. These findings suggest the need to study both attractors and repellers to understand family dynamics associated with health and social and emotional development.
Christiansen, H; Chen, W; Oades, R D; Asherson, P; Taylor, E A; Lasky-Su, J; Zhou, K; Banaschewski, T; Buschgens, C; Franke, B; Gabriels, I; Manor, I; Marco, R; Müller, U C; Mulligan, A; Psychogiou, L; Rommelse, N N J; Uebel, H; Buitelaar, J; Ebstein, R P; Eisenberg, J; Gill, M; Miranda, A; Mulas, F; Roeyers, H; Rothenberger, A; Sergeant, J A; Sonuga-Barke, E J S; Steinhausen, H-C; Thompson, M; Faraone, S V
2008-01-01
Common disorders of childhood and adolescence are attention-deficit/hyperactivity disorder (ADHD), oppositional defiant disorder (ODD) and conduct disorder (CD). For one to two cases in three diagnosed with ADHD the disorders may be comorbid. However, whether comorbid conduct problems (CP) represents a separate disorder or a severe form of ADHD remains controversial. We investigated familial recurrence patterns of the pure or comorbid condition in families with at least two children and one definite case of DSM-IV ADHDct (combined-type) as part of the International Multicentre ADHD Genetics Study (IMAGE). Using case diagnoses (PACS, parental account) and symptom ratings (Parent/Teacher Strengths and Difficulties [SDQ], and Conners Questionnaires [CPTRS]) we studied 1009 cases (241 with ADHDonly and 768 with ADHD + CP), and their 1591 siblings. CP was defined as > or =4 on the SDQ conduct-subscale, and T > or = 65, on Conners' oppositional-score. Multinomial logistic regression was used to ascertain recurrence risks of the pure and comorbid conditions in the siblings as predicted by the status of the cases. There was a higher relative risk to develop ADHD + CP for siblings of cases with ADHD + CP (RRR = 4.9; 95%CI: 2.59-9.41); p < 0.001) than with ADHDonly. Rates of ADHDonly in siblings of cases with ADHD + CP were lower but significant (RRR = 2.9; 95%CI: 1.6-5.3, p < 0.001). Children with ADHD + CP scored higher on the Conners ADHDct symptom-scales than those with ADHDonly. Our finding that ADHD + CP can represent a familial distinct subtype possibly with a distinct genetic etiology is consistent with a high risk for cosegregation. Further, ADHD + CP can be a more severe disorder than ADHDonly with symptoms stable from childhood through adolescence. The findings provide partial support for the ICD-10 distinction between hyperkinetic disorder (F90.0) and hyperkinetic conduct disorder (F90.1).
Nonlinear terahertz superconducting plasmonics
NASA Astrophysics Data System (ADS)
Wu, Jingbo; Zhang, Caihong; Liang, Lanju; Jin, Biaobing; Kawayama, Iwao; Murakami, Hironaru; Kang, Lin; Xu, Weiwei; Wang, Huabing; Chen, Jian; Tonouchi, Masayoshi; Wu, Peiheng
2014-10-01
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.
NASA Astrophysics Data System (ADS)
Bukhenskiĭ, M. F.; Novikov, V. D.
1984-02-01
A review is given of the papers presented at a plenary meeting of the Scientific Council of the USSR Academy of Sciences on the Problem of Coherent and Nonlinear Optics, held in Gorki on June 6-8, 1983. The following topics were discussed at this meeting: precision laser interferometry, laser polarization measurements, fundamental laser experiments, optical instrumentation.
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.
Kheifets, S.
1982-10-01
In the first part of this work I described a general approach to some storage ring problems. The basic concept and the main equations were developed there. The next natural step in this work should be an application of the developed technique to some particular nonlinear problem. Instead, I found it useful to apply the method to the case of a field gradient perturbation first. This happened to be plausible not only as a check of the method, but, more importantly, as a way to resolve several troublesome difficulties encountered in subsequent calculations. The present note does not contain any new results. Still, the work is felt to be necessary as a support for all the future applications of the method. I consider here the effect of a global gradient error in a weak-focusing machine and the effect of a local gradient error in a strong focusing machine. The distribution function of a particle bunch for a perturbed lattice in these cases can be written explicitly. The expansion of this distribution function as a series perturbation terms produces the first and the second order corrections to the unperturbed function. From them we calculate, then, corresponding second moments. A similar expansion of the distribution function is found by the Green's function method described of this work. The second moments are found independently with the help of this distribution function. The comparison of these two results is one way to check the method and the correctness of the calculations. This comparison is done for the first and second order perturbations. 4 refs., 2 tabs.
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.
Dark solitons near potential and nonlinearity steps
NASA Astrophysics Data System (ADS)
Tsitoura, F.; Anastassi, Z. A.; Marzuola, J. L.; Kevrekidis, P. G.; Frantzeskakis, D. J.
2016-12-01
We study dark solitons near potential and nonlinearity steps and combinations thereof, forming rectangular barriers. This setting is relevant to the contexts of atomic Bose-Einstein condensates (where such steps can be realized by using proper external fields) and nonlinear optics (for beam propagation near interfaces separating optical media of different refractive indices). We use perturbation theory to develop an equivalent particle theory, describing the matter-wave or optical soliton dynamics as the motion of a particle in an effective potential. This Newtonian dynamical problem provides information for the soliton statics and dynamics, including scenarios of reflection, transmission, or quasitrapping at such steps. The case of multiple such steps and its connection to barrier potentials is additionally touched upon. The range of validity of the analytical approximation and radiation effects are also investigated. Our analytical predictions are found to be in very good agreement with the corresponding numerical results, where appropriate.
NASA Astrophysics Data System (ADS)
Rulevskiy, V. M.; Bukreev, V. G.; Shandarova, E. B.; Kuleshova, E. O.; Shandarov, S. M.; Vasilyeva, Yu Z.
2017-02-01
A modeling problem of the power system, which provides an AC power transmission to a submersible device over the conducting rope, was considered. The power supply system units and their parameters are described. The system multi-dimensional mathematical model in the variables state space with regard to the nonlinear characteristic of system elements is proposed.
2015-09-01
Nonlinear-Spring Lattice Structure by Steven B Segletes Approved for public release; distribution is unlimited. NOTICES Disclaimers The findings in this...of a One-Dimensional, Fully Connected, Nonlinear-Spring Lattice Structure by Steven B Segletes Weapons and Materials Research Directorate, ARL... Structure Steven B Segletes ARL-MR-0900 Approved for public release; distribution is unlimited. June 2015 AH80 U.S. Army Research Laboratory ATTN: RDRL-WMP-C
Efficient numerical methods for nonlinear Schrodinger equations
NASA Astrophysics Data System (ADS)
Liang, Xiao
The nonlinear Schrodinger equations are widely used to model a number of important physical phenomena, including solitary wave propagations in optical fibers, deep water turbulence, laser beam transmissions, and the Bose-Einstein condensation, just to mention a few. In the field of optics and photonics, the systems of nonlinear Schrodinger equations can be used to model multi-component solitons and the interaction of self-focusing laser beams. In three spatial dimensions, the nonlinear Schrodinger equation is known as the Gross-Pitaevskii equation, which models the soliton in a low-cost graded-index fiber. Recently, research on nonlinear space fractional Schrodinger equations, which capture the self-similarity in the fractional environment, has become prevalent. Our study includes the systems of multi-dimensional nonlinear space fractional Schrodinger equations. To solve the systems of multi-dimensional nonlinear Schrodinger equations efficiently, several novel numerical methods are presented. The central difference and quartic spline approximation based exponential time differencing Crank-Nicolson method is introduced for solving systems of one- and two-dimensional nonlinear Schrodinger equations. A local extrapolation is employed to achieve fourth-order accuracy in time. The numerical examples include the transmission of a self-focusing laser beam. The local discontinuous Galerkin methods combined with the fourth-order exponential time differencing Runge-Kutta time discretization are studied for solving the systems of nonlinear Schrodinger equations with hyperbolic terms, which are critical in modeling optical solitons in the birefringent fibers. The local discontinuous Galerkin method is able to achieve any order of accuracy in space, thanks to the usage of piecewise polynomial spaces. The exponential time differencing methods are employed to deal with the coupled nonlinearities for the reason that there is no need to solve nonlinear systems at every time step
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.
Finite elements of nonlinear continua.
NASA Technical Reports Server (NTRS)
Oden, J. T.
1972-01-01
The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.
Adaptive and Nonlinear Control
1992-02-29
in [22], we also applied the concept of zero dynamics to the problem of exact linearization of a nonlinear control system by dynamic feedback. Exact ...nonlinear systems, although it was well-known that the conditions for exact linearization are very stringent and consequently do not apply to a broad...29th IEEE Conference n Decision and Control, Invited Paper delivered by Dr. Gilliam. Exact Linearization of Zero Dynamics, 29th IEEE Conference on
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.
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.
Modeling and Simulation of Nonlinear Transmission Lines
2010-01-01
consisting of parallel-plate waveguides in which layers of ferroelectric material (specifically, barium strontium titanate , or BST) alternated with...permits; meanwhile, the basic analysis of the NLTL performance benefits greatly from the feasibility of writing transparent software that is easily...where the parameters t, 0, and are used to fit the data. The values of these parameters they found for their particular BST samples
Nonlinear phased array imaging
NASA Astrophysics Data System (ADS)
Croxford, Anthony J.; Cheng, Jingwei; Potter, Jack N.
2016-04-01
A technique is presented for imaging acoustic nonlinearity within a specimen using ultrasonic phased arrays. Acoustic nonlinearity is measured by evaluating the difference in energy of the transmission bandwidth within the diffuse field produced through different focusing modes. The two different modes being classical beam forming, where delays are applied to different element of a phased array to physically focus the energy at a single location (parallel firing) and focusing in post processing, whereby one element at a time is fired and a focused image produced in post processing (sequential firing). Although these two approaches are linearly equivalent the difference in physical displacement within the specimen leads to differences in nonlinear effects. These differences are localized to the areas where the amplitude is different, essentially confining the differences to the focal point. Direct measurement at the focal point are however difficult to make. In order to measure this the diffuse field is used. It is a statistical property of the diffuse field that it represents the total energy in the system. If the energy in the diffuse field for both the sequential and parallel firing case is measured then the difference between these, within the input signal bandwidth, is largely due to differences at the focal spot. This difference therefore gives a localized measurement of where energy is moving out of the transmission bandwidth due to nonlinear effects. This technique is used to image fatigue cracks and other damage types undetectable with conventional linear ultrasonic measurements.
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.
Influence of the Laser Diode Nonlinearity in Fiber-Fed Microcellular Networks
NASA Astrophysics Data System (ADS)
Gameiro, A.
In this paper, the use of an optical fiber-based fixed infrastructure for code division multiple access (CDMA) mobile networks is considered. One of the major problems associated with optical subcarrier multiplexing (SCM) is the nonlinearity of the laser diodes (LD). The LD is modeled by a memoryless nonlinearity, and the effect of the nonlinearity on the SCM transmission of CDMA signals is evaluated. The behavior departs significantly from what happens in frequency division multiple access (FDMA), and depends critically on the nonlinearity being compressing or expanding. In the former case, significant performance degradation may occur, whereas for the latter this is usually not dramatic. When compared against FDMA, the major advantage of CDMA comes from the tight power control function that must be built in such systems, which means that situations of a weak signal corrupted by strong signals do not occur, unlike what happens in FDMA.
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.
Degtyarev, S P
2008-04-30
Instantaneous support shrinking is studied for a doubly non-linear degenerate parabolic equation in the case of slow diffusion when, in general, the Cauchy initial data are Radon measures. For a non-negative solution, a necessary and sufficient condition for instantaneous support shrinking is obtained in terms of the local behaviour of the mass of the initial data. In the same terms, estimates are obtained for the size of the support, that are sharp with respect to order. Bibliography: 24 titles.
Neurodynamics: nonlinear dynamics and neurobiology.
Abarbanel, H D; Rabinovich, M I
2001-08-01
The use of methods from contemporary nonlinear dynamics in studying neurobiology has been rather limited.Yet, nonlinear dynamics has become a practical tool for analyzing data and verifying models. This has led to productive coupling of nonlinear dynamics with experiments in neurobiology in which the neural circuits are forced with constant stimuli, with slowly varying stimuli, with periodic stimuli, and with more complex information-bearing stimuli. Analysis of these more complex stimuli of neural circuits goes to the heart of how one is to understand the encoding and transmission of information by nervous systems.
A Proposal for the Identification of the Hydraulic Transmissivity Parameter in a Confined Aquifer.
NASA Astrophysics Data System (ADS)
ALVAREZ, R.; GOMEZ, S.; GUERRERO, J.
2001-12-01
The parameter estimation in a partial differential equation like the one which governs the groundwater flux in a porous media, is a typical non-linear inverse and ill-posed problem. The concept of regularization, widely used to solve ill-posed problems, is especially important in the presence of errors in the measured data to solve stably inverse problems. In the meeting we will present a proposal based on the discrepance principle to estimate the transmissivity parameter in a numerical stable way.
A feedback control method for the stabilization of a nonlinear diffusion system on a graph
NASA Astrophysics Data System (ADS)
Yu, Xin; Xu, Chao; Lin, Qun
2014-08-01
In this paper, we consider the internal stabilization problems of FitzHugh-Nagumo (FHN) systems on the locally finite connected weighted graphs, which describe the process of signal transmission across axons in neurobiology. We will establish the proper condition on the weighted Dirichlet-Laplace operator on a graph such that the nonlinear FHN system can be stabilized exponentially and globally only using internal actuation over a sub-domain with a linear feedback form.
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.
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 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
Miura, M.; Aoki, H.
1988-02-02
An automatic transmission is described comprising: an automatic transmission mechanism portion comprising a single planetary gear unit and a dual planetary gear unit; carriers of both of the planetary gear units that are integral with one another; an input means for inputting torque to the automatic transmission mechanism, clutches for operatively connecting predetermined ones of planetary gear elements of both of the planetary gear units to the input means and braking means for restricting the rotation of predetermined ones of planetary gear elements of both of the planetary gear units. The clutches are disposed adjacent one another at an end portion of the transmission for defining a clutch portion of the transmission; a first clutch portion which is attachable to the automatic transmission mechanism portion for comprising the clutch portion when attached thereto; a second clutch portion that is attachable to the automatic transmission mechanism portion in place of the first clutch portion for comprising the clutch portion when so attached. The first clutch portion comprising first clutch for operatively connecting the input means to a ring gear of the single planetary gear unit and a second clutch for operatively connecting the input means to a single gear of the automatic transmission mechanism portion. The second clutch portion comprising a the first clutch, the second clutch, and a third clutch for operatively connecting the input member to a ring gear of the dual planetary gear unit.
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...
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
Ruban, V P
2003-06-01
Hamiltonian dynamics of a thin vortex filament in an ideal incompressible fluid near a flat fixed boundary is considered under the conditions that at any point of the curve, determining the shape of the filament, the angle between tangent vector and the boundary plane is small. Also the distance from a point on the curve to the plane is small in comparison with the curvature radius. The dynamics is shown to be effectively described by a nonlinear system of two (1+1)-dimensional partial differential equations. The hodograph transformation reduces this system to a single linear differential equation of the second order with separable variables. Simple solutions of the linear equation are investigated for real values of spectral parameter lambda, when the filament projection on the boundary plane has shape of a two-branch spiral or a smoothed angle, depending on the sign of lambda.
NASA Astrophysics Data System (ADS)
Arefiev, A.; Breizman, B.
2000-10-01
The ion response to the rf-field in the magnetic beach problem can be essentially nonlinear. This paper presents a self-consistent theory of the rf-wave propagation and ion motion through the ion cyclotron resonance. An important ingredient of the problem is the ion flow along the magnetic field. The flow velocity limits the time the ions spend at the resonance, which in turn limits the ion energy gain. A feature that makes the problem nonlinear is that the flow accelerates under the effect of the grad B force and rf-pressure. This acceleration can produce a steep decrease in the plasma density at the resonance, resulting in partial reflection of the incident wave. *Work supported by VASIMR project at NASA and by U.S. DOE Contract DE-FG03-96ER-54346.
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.
Transmission resonances in above-barrier reflection of ultra-cold atoms by the Rosen-Morse potential
NASA Astrophysics Data System (ADS)
Ishkhanyan, H. A.; Krainov, V. P.; Ishkhanyan, A. M.
2010-04-01
Quantum above-barrier reflection of ultra-cold atoms by the Rosen-Morse potential is analytically considered within the mean-field Gross-Pitaevskii approximation. Reformulating the problem of reflectionless transmission as a quasi-linear eigenvalue problem for the potential depth, an approximation for the specific height of the potential that supports reflectionless transmission of the incoming matter wave is derived via modification of the Rayleigh-Schrödinger time-independent perturbation theory. The approximation provides a highly accurate description of the resonance position for all the resonance orders if the nonlinearity parameter is small compared with the incoming particle's chemical potential. Notably, the result for the first transmission resonance turns out to be exact, i.e. the derived formula for the resonant potential height gives the exact value of the first nonlinear resonance's position for all the allowed variation range of the involved parameters, the nonlinearity parameter and chemical potential. This has been demonstrated by constructing the exact solution of the problem for the first resonance. Furthermore, the presented approximation reveals that, in contrast to the linear case, in the nonlinear case reflectionless transmission may occur not only for potential wells but also for potential barriers with positive potential height. It also shows that the nonlinear shift of the resonance position from the position of the corresponding linear resonance is approximately described as a linear function of the resonance order. Finally, a compact (yet, highly accurate) analytic formula for the nth-order resonance position is constructed via combination of analytical and numerical methods.
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…
Nonlinear Behavior in Optical and Other Systems
1987-09-01
numerical analysis). Others will be devoted to ’state of the art ’ discussions of specific problems (e.g. nonlinear waveguides, Anderson localization). It is...Nonlinearity and Statistical Physics. Approximate Cost of Workshop: $5,312. STATE OF THE ART DEVELOPMfENTS IN NONLINEAR OPTICS Organizers: J. Moloney, A... Art Developments in Nonlinear Optics V. List of Preprints and Reprints with Abstracts ANTICIPATED WORKSHOPS 1987 - 1988 I. Workshop on Singularities
NASA Astrophysics Data System (ADS)
Leble, Sergei B.
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
Robust H ∞ control of a nonlinear uncertain system via a stable nonlinear output feedback controller
NASA Astrophysics Data System (ADS)
Harno, Hendra G.; Petersen, Ian R.
2011-04-01
A new approach to solving a nonlinear robust H ∞ control problem using a stable nonlinear output feedback controller is presented in this article. The class of nonlinear uncertain systems being considered is characterised in terms of integral quadratic constraints and global Lipschitz conditions describing the admissible uncertainties and nonlinearities, respectively. The nonlinear controller is able to exploit the plant nonlinearities through the inclusion of a copy of the known plant nonlinearities in the controller. The H ∞ control objective is to obtain an absolutely stable closed-loop system with a specified disturbance attenuation level. The solution to this control problem involves stabilising solutions to parametrised algebraic Riccati equations. We apply a differential evolution algorithm to solve a non-convex nonlinear optimisation problem arising in the controller synthesis.
Asymmetric wave propagation in nonlinear systems.
Lepri, Stefano; Casati, Giulio
2011-04-22
A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, nonmirror-symmetric model described by the one-dimensional discrete nonlinear Schrödinger equation with spatially varying coefficients embedded in an otherwise linear lattice. We construct a class of exact extended solutions such that waves with the same frequency and incident amplitude impinging from left and right directions have very different transmission coefficients. This effect arises already for the simplest case of two nonlinear layers and is associated with the shift of nonlinear resonances. Increasing the number of layers considerably increases the complexity of the family of solutions. Finally, numerical simulations of asymmetric wave packet transmission are presented which beautifully display the rectifying effect.
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.
Kazakopoulos, Pavlos; Moustakas, Aris L
2008-07-01
We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive nonlinear Schrödinger equation with a Gaussian random pulse as an initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We also calculate the distribution of a set of scattering data of the Zakharov-Shabat operator that determine the asymptotics of the eigenfunctions. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of information transmission through nonlinear optical fibers.
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.
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.
Asymptotic expansions in nonlinear rotordynamics
NASA Technical Reports Server (NTRS)
Day, William B.
1987-01-01
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. 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 singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
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.
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.
Yale, O.S.
1989-12-12
This patent describes a power transmission. It comprises: in combination, a master gear having at least one annular tooth set, means for drivingly engaging the master gear with a power source, driven shaft, a yoke member attached to the shaft and including a screw pump housing extending radially with respect to the shaft with a pair of ports in spaced relation, a pump screw rotatable in the housing and a pump gear attached to the screw and engaging the annular tooth set, and a casing for transmission fluid. The pump housing being located for immersion in the fluid.
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.
Disease transmission in horses.
Samper, Juan C; Tibary, Ahmed
2006-08-01
Bacterial, viral and protozoal infections may cause severe reproductive losses. The present paper reviews the risk factors, clinical signs and preventive measures for the most important venereal or potential sexually transmitted diseases in horses. The stallion and use of semen for artificial insemination represent major risk factors for the transmission of bacterial contaminants of the penis, including Streptococcus equi subspecies zooepidemicus, Pseudomonas aeruginosa and Klebsiella pneumoniae, known to cause endometritis and infertility in the mare. The role of the stallion in disease transmission is also due to the non-clinical manifestation of diseases such as contagious equine metritis and equine viral arteritis. Dourine has been eradicated from many countries, but continues to be a problem in other areas of the globe. Strategies for the prevention of introduction and transmission of diseases in breeding operation are discussed.
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…
1974-02-14
Wester- velt. [60] Streaming. In 1831, Michael Faraday [61] noted that currents of air were set up in the neighborhood of vibrating plates-the first... ducei in the case of a paramettc amy (from Berktay an Leahy 141). C’ "". k•, SEC 10.1 NONLINEAR ACOUSTICS 345 The principal results of their analysis
NASA Astrophysics Data System (ADS)
Kevorkian, J.
This report discusses research in the area of slowly varying nonlinear oscillatory systems. Some of the topics discussed are as follows: adiabatic invariants and transient resonance in very slowly varying Hamiltonian systems; sustained resonance in very slowly varying Hamiltonian systems; free-electron lasers with very slow wiggler taper; and bursting oscillators.
... Abroad Treatment Basic Statistics Get Tested Find an HIV testing site near you. Enter ZIP code or city Follow HIV/AIDS CDC HIV CDC HIV/AIDS See RSS | ... on HIV Syndicated Content Website Feedback HIV/AIDS HIV Transmission Language: English TransmisiÃ³n del VIH Recommend on ...
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.
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…
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.
Nonlinear Optical Interactions in Semiconductors.
1985-12-10
completing bnother article for publication. In addition, we have made four invention disclosures o the U.S. Air Force.We received the delivery of two large...of completing another article for publication. In addition, we have made four invention disclosures to the U. S. Air Force. We received the delivery...gives rise to four -photon mixing. Our attempts were focused on observing a number of new optical effects including nonlinear absorption and transmission
Dynamical Imaging using Spatial Nonlinearity
2014-01-29
829- 832. [29] H. Faulkner, J. Rodenburg, Movable Aperture Lensless Transmission Microscopy : A Novel Phase Retrieval Algorithm, Physical Review...Laser Scanning Fluorescence Microscopy , Science, 248 (1990) 73-76. [3] P.J. Campagnola, H.A. Clark, W.A. Mohler, A. Lewis, L.M. Loew, Second-harmonic...imaging microscopy of living cells, J Biomed Opt, 6 (2001) 277-286. [4] C. Barsi, J.W. Fleischer, Nonlinear Abbe theory, Nat Photonics, 7 (2013) 639
High-capacity transmission over multi-core fibers
NASA Astrophysics Data System (ADS)
Awaji, Yoshinari; Sakaguchi, Jun; Puttnam, Benjamin J.; Luís, Ruben S.; Mendinueta, Jose Manuel Delgado; Klaus, Werner; Wada, Naoya
2017-02-01
The ultimate transmission capacity of standard single-mode fiber (SSMF) is limited by fiber nonlinearity which prevents increasing transmission power and finite amplifier bandwidth. In order to overcome such limitation, space-division multiplexing (SDM) has been proposed. Multi-core fiber (MCF) is a strong candidate to realize practical SDM transmission system because of high isolation of individual spatial modes sharing the same cladding, which enables ultra-high capacity transmission in cooperation with wide band WDM.
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.
NASA Technical Reports Server (NTRS)
Turner, L. R.
1960-01-01
The problem of solving systems of nonlinear equations has been relatively neglected in the mathematical literature, especially in the textbooks, in comparison to the corresponding linear problem. Moreover, treatments that have an appearance of generality fail to discuss the nature of the solutions and the possible pitfalls of the methods suggested. Probably it is unrealistic to expect that a unified and comprehensive treatment of the subject will evolve, owing to the great variety of situations possible, especially in the applied field where some requirement of human or mechanical efficiency is always present. Therefore we attempt here simply to pose the problem and to describe and partially appraise the methods of solution currently in favor.
Transmitting information by controlling nonlinear oscillators
NASA Astrophysics Data System (ADS)
Tôrres, Leonardo A. B.; Aguirre, Luis A.
2004-09-01
The transmission of information relying on the perturbation of nonlinear oscillators vector fields can be approached in a unified manner. This can be accomplished by making use of the Information Transmission Via Control principle, which is stated and proved in the present work. In short, this principle establishes that any controller used to identically synchronize pairs of nonlinear oscillators, including chaotic ones as a special case, can be actually employed as demodulator/decoder in the process of information recovery. Other theoretical results related to the practical realization of the ITVC principle are presented and experimental data is provided showing a good agreement with the proposed theory.
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.
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.
Nonlinear Acoustics at the Air-Water Free Surface
NASA Astrophysics Data System (ADS)
Pree, Seth; Naranjo, Brian; Putterman, Seth
2016-11-01
According to linear acoustics, airborne sound incident on a water surface transmits only a tenth of a percent of its energy. This difficulty of transmitting energy across the water surface limits the feasibility of standoff ultrasound imaging. We propose to overcome this long standing problem by developing new methods of coupling into the medium at standoff. In particular, we believe that the acoustic nonlinearity of both the air and the medium may yield a range of effects in the vicinity of the surface permitting an efficient transmission of ultrasound from the air into the medium. The recent commercial availability of parametric speakers that deliver modulated 100kHz ultrasound at 135dB to nonlinearly generate music at 95dB provides an interesting platform with which to revisit the transmission of sound across acoustic impedance mismatches. We show results of experimental studies of the behavior of the air-water free surface when subjected to large amplitude acoustic pressures from the air. This work was supported by the ARO STIR program.
A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.
Xu, Zhengfu; Bao, Gang
2010-11-01
A numerical scheme is presented to solve the nonlinear Helmholtz (NLH) equation modeling second-harmonic generation (SHG) in photonic bandgap material doped with a nonlinear χ((2)) effect and the NLH equation modeling wave propagation in Kerr type gratings with a nonlinear χ((3)) effect in the one-dimensional case. Both of these nonlinear phenomena arise as a result of the combination of high electromagnetic mode density and nonlinear reaction from the medium. When the mode intensity of the incident wave is significantly strong, which makes the nonlinear effect non-negligible, numerical methods based on the linearization of the essentially nonlinear problem will become inadequate. In this work, a robust, stable numerical scheme is designed to simulate the NLH equations with strong nonlinearity.
Breaking beta: deconstructing the parasite transmission function
McCallum, Hamish; Fenton, Andy; Hudson, Peter J.; Lee, Brian; Levick, Beth; Norman, Rachel
2017-01-01
Transmission is a fundamental step in the life cycle of every parasite but it is also one of the most challenging processes to model and quantify. In most host–parasite models, the transmission process is encapsulated by a single parameter β. Many different biological processes and interactions, acting on both hosts and infectious organisms, are subsumed in this single term. There are, however, at least two undesirable consequences of this high level of abstraction. First, nonlinearities and heterogeneities that can be critical to the dynamic behaviour of infections are poorly represented; second, estimating the transmission coefficient β from field data is often very difficult. In this paper, we present a conceptual model, which breaks the transmission process into its component parts. This deconstruction enables us to identify circumstances that generate nonlinearities in transmission, with potential implications for emergent transmission behaviour at individual and population scales. Such behaviour cannot be explained by the traditional linear transmission frameworks. The deconstruction also provides a clearer link to the empirical estimation of key components of transmission and enables the construction of flexible models that produce a unified understanding of the spread of both micro- and macro-parasite infectious disease agents. This article is part of the themed issue ‘Opening the black box: re-examining the ecology and evolution of parasite transmission’. PMID:28289252
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.
Transmission Investment: A Primer
McGarvey, Joe
2006-10-15
This primer highlights recent trends in transmission investment, summarizes the division of jurisdictional authority over transmission, and presents four alternative models for transmission ownership. (author)
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.
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.
Simulating nonlinear neutrino flavor evolution
NASA Astrophysics Data System (ADS)
Duan, H.; Fuller, G. M.; Carlson, J.
2008-10-01
We discuss a new kind of astrophysical transport problem: the coherent evolution of neutrino flavor in core collapse supernovae. Solution of this problem requires a numerical approach which can simulate accurately the quantum mechanical coupling of intersecting neutrino trajectories and the associated nonlinearity which characterizes neutrino flavor conversion. We describe here the two codes developed to attack this problem. We also describe the surprising phenomena revealed by these numerical calculations. Chief among these is that the nonlinearities in the problem can engineer neutrino flavor transformation which is dramatically different to that in standard Mikheyev Smirnov Wolfenstein treatments. This happens even though the neutrino mass-squared differences are measured to be small, and even when neutrino self-coupling is sub-dominant. Our numerical work has revealed potential signatures which, if detected in the neutrino burst from a Galactic core collapse event, could reveal heretofore unmeasurable properties of the neutrinos, such as the mass hierarchy and vacuum mixing angle θ13.
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.
Inverse Problems for Nonlinear Delay Systems
2011-03-15
within the insect population, it is biologically un- realistic to assume that all neonate aphids born on the same day reach the adult age class at the...population dynamics. We consider the delay between birth and adulthood for neonate pea aphids and present a mathematical model that treats this delay as...J.D. Stark, Time-varying vital rates in ecotoxicology: selective pesticides and aphid population dynamics, Ecological Mod- elling, 210 (2008), 155–160
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.
Non-linear dynamics of a spur gear pair
NASA Astrophysics Data System (ADS)
Kahraman, A.; Singh, R.
1990-10-01
Non-linear frequency response characteristics of a spur gear pair with backlash are examined in this paper for both external and internal excitations. The internal excitation is of importance from the high frequency noise and vibration control viewpoint and it represents the overall kinematic or static transmission error. Such problems may be significantly different from the rattle problems associated with external, low frequency torque excitation. Two solution methods, namely the digital simulation technique and the method of harmonic balance, have been used to develop the steady state solutions for the internal sinusoidal excitation. Difficulties associated with the determination of the multiple solutions at a given frequency in the digital simulation technique have been resolved, as one must search the entire initial conditions map. Such solutions and the transition frequencies for various impact situations are easily found by the method of harmonic balance. Further, the principle of superposition can be employed to analyze the periodic transmission error excitation and/or combined excitation problems provided that the excitation frequencies are sufficiently apart from each other. Our analytical predictions match satisfactorily with the limited experimental data available in the literature. Using the digital simulation, we have also observed that the chaotic and subharmonic resonances may exist in a gear pair depending upon the mean or design load, mean to alternating force ratio, damping and backlash. Specifically, the mean load determines the conditions for no impacts, single-sided impacts and double-sided impacts. Our results are different from the frequency response characteristics of the conventional, single-degree-of-freedom, clearance type non-linear system. Our formulation should form the basis of further analytical and experimental work in the geared rotor dynamics area.
Hamane, M.; Ohri, H.
1989-03-21
This patent describes an automatic transmission connected between a drive shaft and a driven shaft and comprising: a planetary gear mechanism including a first gear driven by the drive shaft, a second gear operatively engaged with the first gear to transmit speed change output to the driven shaft, and a third gear operatively engaged with the second gear to control the operation thereof; centrifugally operated clutch means for driving the first gear and the second gear. It also includes a ratchet type one-way clutch for permitting rotation of the third gear in the same direction as that of the drive shaft but preventing rotation in the reverse direction; the clutch means comprising a ratchet pawl supporting plate coaxially disposed relative to the drive shaft and integrally connected to the third gear, the ratchet pawl supporting plate including outwardly projection radial projections united with one another at base portions thereof.
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.