Sample records for nonlinear transmission problems

  1. Improvement of SPM nonlinear limit by chirped duobinary PolSK transmission

    NASA Astrophysics Data System (ADS)

    Yang, Lixiu; Fan, Jiayu; Wang, Lutang; Huang, Zhaoming

    2005-02-01

    In today's terrestrial long-haul optical fiber communication systems, high channel powers are required to obtain a large transmission distance with reasonable optical amplifier spacing. In such systems, however, the presence of nonlinear effects such as the self-phase modulation (SPM) and the fiber dispersion as well as their combined effects, called SPM-induced nonlinear limitation or SPM limit, will seriously degrade the system performances in respect of the effective transmission distance and ultimately become a limiting factor in high-speed, long-haul optical fiber transmission.In this paper, a new transmission format: chirped duobinary PolSK transmission, has been proposed to generate a pre-chirped duobianry signal with fixed polarity (either positive or negative), which is modulated by a PolSK modulator. This format is based on a transmitter setup consisting of a duobinary PolSK Modulation transmitter followed by an additional phase modulator. The chirped duobinary PolSK transmission reduces the signal degradation and spectral broadening in the nonlinear regime significantly. Thus it shifts this SPM nonlinear limit to enable more relaxed dispersion compensation at high optical power compared to the conventional duobinary schemes.The simulation results show chirped duobinary PolSK transmission enlarges the dispersion limited transmission distance, increases the dispersion tolerance and overcome the SPM nonlinear limit.

  2. Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

    NASA Astrophysics Data System (ADS)

    Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent

    2018-02-01

    We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

  3. 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.

  4. L1 adaptive control of uncertain gear transmission servo systems with deadzone nonlinearity.

    PubMed

    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. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  5. Co-operation of digital nonlinear equalizers and soft-decision LDPC FEC in nonlinear transmission.

    PubMed

    Tanimura, Takahito; Oda, Shoichiro; Hoshida, Takeshi; Aoki, Yasuhiko; Tao, Zhenning; Rasmussen, Jens C

    2013-12-30

    We experimentally and numerically investigated the characteristics of 128 Gb/s dual polarization - quadrature phase shift keying signals received with two types of nonlinear equalizers (NLEs) followed by soft-decision (SD) low-density parity-check (LDPC) forward error correction (FEC). Successful co-operation among SD-FEC and NLEs over various nonlinear transmissions were demonstrated by optimization of parameters for NLEs.

  6. 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].

  7. Experimental investigation of alternative transmission functions: Quantitative evidence for the importance of nonlinear transmission dynamics in host-parasite systems.

    PubMed

    Orlofske, Sarah A; Flaxman, Samuel M; Joseph, Maxwell B; Fenton, Andy; Melbourne, Brett A; Johnson, Pieter T J

    2018-05-01

    Understanding pathogen transmission is crucial for predicting and managing disease. Nonetheless, experimental comparisons of alternative functional forms of transmission remain rare, and those experiments that are conducted are often not designed to test the full range of possible forms. To differentiate among 10 candidate transmission functions, we used a novel experimental design in which we independently varied four factors-duration of exposure, numbers of parasites, numbers of hosts and parasite density-in laboratory infection experiments. We used interactions between amphibian hosts and trematode parasites as a model system and all candidate models incorporated parasite depletion. An additional manipulation involving anaesthesia addressed the effects of host behaviour on transmission form. Across all experiments, nonlinear transmission forms involving either a power law or a negative binomial function were the best-fitting models and consistently outperformed the linear density-dependent and density-independent functions. By testing previously published data for two other host-macroparasite systems, we also found support for the same nonlinear transmission forms. Although manipulations of parasite density are common in transmission studies, the comprehensive set of variables tested in our experiments revealed that variation in density alone was least likely to differentiate among competing transmission functions. Across host-pathogen systems, nonlinear functions may often more accurately represent transmission dynamics and thus provide more realistic predictions for infection. © 2017 The Authors. Journal of Animal Ecology published by John Wiley & Sons Ltd on behalf of British Ecological Society.

  8. Large predispersion for reduction of intrachannel nonlinear impairments in strongly dispersion-managed transmissions

    NASA Astrophysics Data System (ADS)

    Cao, Wenhua

    2016-05-01

    Predispersion for reduction of intrachannel nonlinear impairments in quasi-linear strongly dispersion-managed transmission system is analyzed in detail by numerical simulations. We show that for moderate amount of predispersion there is an optimal value at which reduction of the nonlinear impairments can be obtained, which is consistent with previous well-known predictions. However, we found that much better transmission performance than that of the previous predictions can be obtained if predispersion is increased to some extent. For large predispersion, the nonlinear impairments reduce monotonically with increasing predispersion and then they tend to be stabilized when predispersion is further increased. Thus, transmission performance can be efficiently improved by inserting a high-dispersive element, such as a chirped fiber bragg grating (CFBG), at the input end of the transmission link to broaden the signal pulses while, at the output end, using another CFBG with the opposite dispersion to recompress the signal.

  9. Chameleon's behavior of modulable nonlinear electrical transmission line

    NASA Astrophysics Data System (ADS)

    Togueu Motcheyo, A. B.; Tchinang Tchameu, J. D.; Fewo, S. I.; Tchawoua, C.; Kofane, T. C.

    2017-12-01

    We show that modulable discrete nonlinear transmission line can adopt Chameleon's behavior due to the fact that, without changing its appearance structure, it can become alternatively purely right or left handed line which is different to the composite one. Using a quasidiscrete approximation, we derive a nonlinear Schrödinger equation, that predicts accurately the carrier frequency threshold from the linear analysis. It appears that the increasing of the linear capacitor in parallel in the series branch induced the selectivity of the filter in the right-handed region while it increases band pass filter in the left-handed region. Numerical simulations of the nonlinear model confirm the forward wave in the right handed line and the backward wave in the left handed one.

  10. Determinants of Rotavirus Transmission: A Lag Nonlinear Time Series Analysis.

    PubMed

    van Gaalen, Rolina D; van de Kassteele, Jan; Hahné, Susan J M; Bruijning-Verhagen, Patricia; Wallinga, Jacco

    2017-07-01

    Rotavirus is a common viral infection among young children. As in many countries, the infection dynamics of rotavirus in the Netherlands are characterized by an annual winter peak, which was notably low in 2014. Previous study suggested an association between weather factors and both rotavirus transmission and incidence. From epidemic theory, we know that the proportion of susceptible individuals can affect disease transmission. We investigated how these factors are associated with rotavirus transmission in the Netherlands, and their impact on rotavirus transmission in 2014. We used available data on birth rates and rotavirus laboratory reports to estimate rotavirus transmission and the proportion of individuals susceptible to primary infection. Weather data were directly available from a central meteorological station. We developed an approach for detecting determinants of seasonal rotavirus transmission by assessing nonlinear, delayed associations between each factor and rotavirus transmission. We explored relationships by applying a distributed lag nonlinear regression model with seasonal terms. We corrected for residual serial correlation using autoregressive moving average errors. We inferred the relationship between different factors and the effective reproduction number from the most parsimonious model with low residual autocorrelation. Higher proportions of susceptible individuals and lower temperatures were associated with increases in rotavirus transmission. For 2014, our findings suggest that relatively mild temperatures combined with the low proportion of susceptible individuals contributed to lower rotavirus transmission in the Netherlands. However, our model, which overestimated the magnitude of the peak, suggested that other factors were likely instrumental in reducing the incidence that year.

  11. A direct method for nonlinear ill-posed problems

    NASA Astrophysics Data System (ADS)

    Lakhal, A.

    2018-02-01

    We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.

  12. Well-posed and stable transmission problems

    NASA Astrophysics Data System (ADS)

    Nordström, Jan; Linders, Viktor

    2018-07-01

    We introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability are analysed for continuous and discrete problems using both strong and weak formulations, and a general transmission condition is obtained. The theory is applied to the coupling of fluid-acoustic models, multi-grid implementations, adaptive mesh refinements, multi-block formulations and numerical filtering.

  13. Two-dimensional solitary waves and periodic waves on coupled nonlinear electrical transmission lines

    NASA Astrophysics Data System (ADS)

    Wang, Heng; Zheng, Shuhua

    2017-06-01

    By using the dynamical system approach, the exact travelling wave solutions for a system of coupled nonlinear electrical transmission lines are studied. Based on this method, the bifurcations of phase portraits of a dynamical system are given. The two-dimensional solitary wave solutions and periodic wave solutions on coupled nonlinear transmission lines are obtained. With the aid of Maple, the numerical simulations are conducted for solitary wave solutions and periodic wave solutions to the model equation. The results presented in this paper improve upon previous studies.

  14. A Parametric Study of Nonlinear Seismic Response Analysis of Transmission Line Structures

    PubMed Central

    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

  15. Intergenerational Transmission of Childhood Conduct Problems

    PubMed Central

    D’Onofrio, Brian M.; Slutske, Wendy S.; Turkheimer, Eric; Emery, Robert E.; Paige Harden, K.; Heath, Andrew C.; Madden, Pamela A. F.; Martin, Nicholas G.

    2010-01-01

    Context The familial nature of childhood conduct problems has been well documented, but few genetically informed studies have explicitly explored the processes through which parental conduct problems influence an offspring’s behavior problems. Objective To delineate the genetic and environmental processes underlying the intergenerational transmission of childhood conduct problems. Design We used hierarchical linear models to analyze data from a Children of Twins Study, a quasiexperimental design, to explore the extent to which genetic factors common to both generations, unmeasured environmental factors that are shared by twins, or measured characteristics of both parents confound the intergenerational association. Setting Participants were recruited from the community and completed a semistructured diagnostic telephone interview. Participants The research used a high-risk sample of twins, their spouses, and their young adult offspring (n=2554) from 889 twin families in the Australian Twin Registry, but the analyses used sample weights to produce parameter estimates for the community-based volunteer sample of twins. Main Outcome Measure Number of conduct disorder symptoms. Results The magnitude of the intergenerational transmission was significant for all offspring, though it was stronger for males (effect size [Cohen d]=0.21; 95% confidence interval, 0.15–0.17) than females (d=0.09; 95% confidence interval, 0.05–0.14). The use of the Children of Twins design and measured covariates indicated that the intergenerational transmission of conduct problems for male offspring was largely mediated by environmental variables specifically related to parental conduct disorder (d=0.13; 95% confidence interval, 0.02–0.23). In contrast, the intergenerational transmission of conduct problems was not because of environmentally mediated causal processes for female offspring (d=−0.09; 95% confidence interval, −0.20 to 0.03); a common genetic liability accounted for the

  16. Nonlinear force feedback control of piezoelectric-hydraulic pump actuator for automotive transmission shift control

    NASA Astrophysics Data System (ADS)

    Kim, Gi-Woo; Wang, K. W.

    2008-03-01

    In recent years, researchers have investigated the feasibility of utilizing piezoelectric-hydraulic pump based actuation systems for automotive transmission controls. This new concept could eventually reduce the complexity, weight, and fuel consumption of the current transmissions. In this research, we focus on how to utilize this new approach on the shift control of automatic transmissions (AT), which generally requires pressure profiling for friction elements during the operation. To illustrate the concept, we will consider the 1--> 2 up shift control using band brake friction elements. In order to perform the actuation force tracking for AT shift control, nonlinear force feedback control laws are designed based on the sliding mode theory for the given nonlinear system. This paper will describe the modeling of the band brake actuation system, the design of the nonlinear force feedback controller, and simulation and experimental results for demonstration of the new concept.

  17. Solving intuitionistic fuzzy multi-objective nonlinear programming problem

    NASA Astrophysics Data System (ADS)

    Anuradha, D.; Sobana, V. E.

    2017-11-01

    This paper presents intuitionistic fuzzy multi-objective nonlinear programming problem (IFMONLPP). All the coefficients of the multi-objective nonlinear programming problem (MONLPP) and the constraints are taken to be intuitionistic fuzzy numbers (IFN). The IFMONLPP has been transformed into crisp one and solved by using Kuhn-Tucker condition. Numerical example is provided to illustrate the approach.

  18. Bounding solutions of geometrically nonlinear viscoelastic problems

    NASA Technical Reports Server (NTRS)

    Stubstad, J. M.; Simitses, G. J.

    1985-01-01

    Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

  19. 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.

  20. Nonlinearity-dependent asymmetric transmission in a sawtooth photonic lattice with defects

    NASA Astrophysics Data System (ADS)

    Ji, Kaiwen; Qi, Xinyuan; Li, Shasha; Han, Kun; Wen, Zengrun; Zhang, Guoquan; Bai, Jintao

    2018-04-01

    We study both theoretically and numerically the asymetric transmission of a Gaussian beam in a two-dimensional nonlinear sawtooth lattice with two defects. The results show that quasi-total reflection, asymmetric propagation and asymmetric reflection can all be achieved in such a system by adjusting the input intensity, the magnitude of defects and the number of nonlinear waveguides. This study may provide a new way to realize an optical switch and optical diode.

  1. 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.

  2. Nonlinear interaction in differential mode delay managed mode-division multiplexed transmission systems.

    PubMed

    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.

  3. 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.

  4. Analog nonlinear MIMO receiver for optical mode division multiplexing transmission.

    PubMed

    Spalvieri, Arnaldo; Boffi, Pierpaolo; Pecorino, Simone; Barletta, Luca; Magarini, Maurizio; Gatto, Alberto; Martelli, Paolo; Martinelli, Mario

    2013-10-21

    The complexity and the power consumption of digital signal processing are crucial issues in optical transmission systems based on mode division multiplexing and coherent multiple-input multiple-output (MIMO) processing at the receiver. In this paper the inherent characteristic of spatial separation between fiber modes is exploited, getting a MIMO system where joint demultiplexing and detection is based on spatially separated photodetectors. After photodetection, one has a MIMO system with nonlinear crosstalk between modes. The paper shows that the nonlinear crosstalk can be dealt with by a low-complexity and non-adaptive detection scheme, at least in the cases presented in the paper.

  5. Scrambled coherent superposition for enhanced optical fiber communication in the nonlinear transmission regime.

    PubMed

    Liu, Xiang; Chandrasekhar, S; Winzer, P J; Chraplyvy, A R; Tkach, R W; Zhu, B; Taunay, T F; Fishteyn, M; DiGiovanni, D J

    2012-08-13

    Coherent superposition of light waves has long been used in various fields of science, and recent advances in digital coherent detection and space-division multiplexing have enabled the coherent superposition of information-carrying optical signals to achieve better communication fidelity on amplified-spontaneous-noise limited communication links. However, fiber nonlinearity introduces highly correlated distortions on identical signals and diminishes the benefit of coherent superposition in nonlinear transmission regime. Here we experimentally demonstrate that through coordinated scrambling of signal constellations at the transmitter, together with appropriate unscrambling at the receiver, the full benefit of coherent superposition is retained in the nonlinear transmission regime of a space-diversity fiber link based on an innovatively engineered multi-core fiber. This scrambled coherent superposition may provide the flexibility of trading communication capacity for performance in future optical fiber networks, and may open new possibilities in high-performance and secure optical communications.

  6. Modulational Instability in a Pair of Non-identical Coupled Nonlinear Electrical Transmission Lines

    NASA Astrophysics Data System (ADS)

    Eric, Tala-Tebue; Aurelien, Kenfack-Jiotsa; Marius Hervé, Tatchou-Ntemfack; Timoléon Crépin, Kofané

    2013-07-01

    In this work, we investigate the dynamics of modulated waves non-identical coupled nonlinear transmission lines. Traditional methods for avoiding mode mixing in identical coupled nonlinear electrical lines consist of adding the same number of linear inductors in each branch. Adding linear inductors in a single line leads to asymmetric coupled nonlinear electrical transmission lines which propagate the signal and the mode mixing. On one hand, the difference between the two lines induced the fission for only one mode of propagation. This fission is influenced by the amplitude of the signal and the amount of the input energy as well; it also narrows the width of the input pulse soliton, leading to a possible increasing of the bit rate. On the other hand, the dissymmetry of the two lines converts the network into a good amplifier for the ω_ mode which corresponds to the regime admitting low frequencies.

  7. Multiply scaled constrained nonlinear equation solvers. [for nonlinear heat conduction problems

    NASA Technical Reports Server (NTRS)

    Padovan, Joe; Krishna, Lala

    1986-01-01

    To improve the numerical stability of nonlinear equation solvers, a partitioned multiply scaled constraint scheme is developed. This scheme enables hierarchical levels of control for nonlinear equation solvers. To complement the procedure, partitioned convergence checks are established along with self-adaptive partitioning schemes. Overall, such procedures greatly enhance the numerical stability of the original solvers. To demonstrate and motivate the development of the scheme, the problem of nonlinear heat conduction is considered. In this context the main emphasis is given to successive substitution-type schemes. To verify the improved numerical characteristics associated with partitioned multiply scaled solvers, results are presented for several benchmark examples.

  8. Nonlinear response of GaAs gratings in the extraordinary transmission regime.

    PubMed

    Vincenti, Maria Antonietta; de Ceglia, Domenico; Scalora, Michael

    2011-12-01

    We theoretically describe a way to enhance harmonic generation from subwavelength slits milled on semiconductor substrates in strongly absorptive regimes. The metal-like response typical of semiconductors, like GaAs and GaP, triggers enhanced transmission and nonlinear optical phenomena in the deep UV range. We numerically study correlations between linear and nonlinear responses and their intricacies in infinite arrays, and highlight differences between nonlinear surface and magnetic sources, and intrinsic χ((2)) and χ((3)) contributions to harmonic generation. The results show promising efficiencies at wavelengths below 120 nm, and reveal coupling of TE and TM polarizations for pump and harmonic signals. A downconversion process that can regenerate pump photons with polarization orthogonal to the incident pump is also discussed. © 2011 Optical Society of America

  9. Recent advances in reduction methods for nonlinear problems. [in structural mechanics

    NASA Technical Reports Server (NTRS)

    Noor, A. K.

    1981-01-01

    Status and some recent developments in the application of reduction methods to nonlinear structural mechanics problems are summarized. The aspects of reduction methods discussed herein include: (1) selection of basis vectors in nonlinear static and dynamic problems, (2) application of reduction methods in nonlinear static analysis of structures subjected to prescribed edge displacements, and (3) use of reduction methods in conjunction with mixed finite element models. Numerical examples are presented to demonstrate the effectiveness of reduction methods in nonlinear problems. Also, a number of research areas which have high potential for application of reduction methods are identified.

  10. Algorithms for Nonlinear Least-Squares Problems

    DTIC Science & Technology

    1988-09-01

    O -,i(x) 2 , where each -,(x) is a smooth function mapping Rn to R. J - The m x n Jacobian matrix of f. ... x g - The gradient of the nonlinear least...V211f(X*)I112~ l~ l) J(xk)T J(xk) 2 + O(k - X*) For more convergence results and detailed convergence analysis for the Gauss-Newton method, see, e. g ...for a class of nonlinear least-squares problems that includes zero-residual prob- lems. The function Jt is the pseudo-inverse of Jk (see, e. g

  11. 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.

  12. Advanced linear and nonlinear compensations for 16QAM SC-400G unrepeatered transmission system

    NASA Astrophysics Data System (ADS)

    Zhang, Junwen; Yu, Jianjun; Chien, Hung-Chang

    2018-02-01

    Digital signal processing (DSP) with both linear equalization and nonlinear compensations are studied in this paper for the single-carrier 400G system based on 65-GBaud 16-quadrature amplitude modulation (QAM) signals. The 16-QAM signals are generated and pre-processed with pre-equalization (Pre-EQ) and Look-up-Table (LUT) based pre-distortion (Pre-DT) at the transmitter (Tx)-side. The implementation principle of training-based equalization and pre-distortion are presented here in this paper with experimental studies. At the receiver (Rx)-side, fiber-nonlinearity compensation based on digital backward propagation (DBP) are also utilized to further improve the transmission performances. With joint LUT-based Pre-DT and DBP-based post-compensation to mitigate the opto-electronic components and fiber nonlinearity impairments, we demonstrate the unrepeatered transmission of 1.6Tb/s based on 4-lane 400G single-carrier PDM-16QAM over 205-km SSMF without distributed amplifier.

  13. Nonlinear Fourier transform—towards the construction of nonlinear Fourier modes

    NASA Astrophysics Data System (ADS)

    Saksida, Pavle

    2018-01-01

    We study a version of the nonlinear Fourier transform associated with ZS-AKNS systems. This version is suitable for the construction of nonlinear analogues of Fourier modes, and for the perturbation-theoretic study of their superposition. We provide an iterative scheme for computing the inverse of our transform. The relevant formulae are expressed in terms of Bell polynomials and functions related to them. In order to prove the validity of our iterative scheme, we show that our transform has the necessary analytic properties. We show that up to order three of the perturbation parameter, the nonlinear Fourier mode is a complex sinusoid modulated by the second Bernoulli polynomial. We describe an application of the nonlinear superposition of two modes to a problem of transmission through a nonlinear medium.

  14. An efficient variable projection formulation for separable nonlinear least squares problems.

    PubMed

    Gan, Min; Li, Han-Xiong

    2014-05-01

    We consider in this paper a class of nonlinear least squares problems in which the model can be represented as a linear combination of nonlinear functions. The variable projection algorithm projects the linear parameters out of the problem, leaving the nonlinear least squares problems involving only the nonlinear parameters. To implement the variable projection algorithm more efficiently, we propose a new variable projection functional based on matrix decomposition. The advantage of the proposed formulation is that the size of the decomposed matrix may be much smaller than those of previous ones. The Levenberg-Marquardt algorithm using finite difference method is then applied to minimize the new criterion. Numerical results show that the proposed approach achieves significant reduction in computing time.

  15. COPS: Large-scale nonlinearly constrained optimization problems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bondarenko, A.S.; Bortz, D.M.; More, J.J.

    2000-02-10

    The authors have started the development of COPS, a collection of large-scale nonlinearly Constrained Optimization Problems. The primary purpose of this collection is to provide difficult test cases for optimization software. Problems in the current version of the collection come from fluid dynamics, population dynamics, optimal design, and optimal control. For each problem they provide a short description of the problem, notes on the formulation of the problem, and results of computational experiments with general optimization solvers. They currently have results for DONLP2, LANCELOT, MINOS, SNOPT, and LOQO.

  16. Nonlinearity in the vertical transmissibility of seating: the role of the human body apparent mass and seat dynamic stiffness

    NASA Astrophysics Data System (ADS)

    Tufano, Saverio; Griffin, Michael J.

    2013-01-01

    The efficiency of a seat in reducing vibration depends on the characteristics of the vibration, the dynamic characteristics of the seat, and the dynamic characteristics of the person sitting on the seat. However, it is not known whether seat cushions influence the dynamic response of the human body, whether the human body influences the dynamic response of seat cushions, or the relative importance of human body nonlinearity and seat nonlinearity in causing nonlinearity in measures of seat transmissibility. This study was designed to investigate the nonlinearity of the coupled seat and human body systems and to compare the apparent mass of the human body supported on rigid and foam seats. A frequency domain model was used to identify the dynamic parameters of seat foams and investigate their dependence on the subject-sitting weight and hip breadth. With 15 subjects, the force and acceleration at the seat base and acceleration at the subject interface were measured during random vertical vibration excitation (0.25-25 Hz) at each of five vibration magnitudes, (0.25-1.6 ms-2 r.m.s.) with four seating conditions (rigid flat seat and three foam cushions). The measurements are presented in terms of the subject's apparent mass on the rigid and foam seat surfaces, and the transmissibility and dynamic stiffness of each of the foam cushions. Both the human body and the foams showed nonlinear softening behaviour, which resulted in nonlinear cushion transmissibility. The apparent masses of subjects sitting on the rigid seat and on foam cushions were similar, but with an apparent increase in damping when sitting on the foams. The foam dynamic stiffness showed complex correlations with characteristics of the human body, which differed between foams. The nonlinearities in cushion transmissibilities, expressed in terms of changes in resonance frequencies and moduli, were more dependent on human body nonlinearity than on cushion nonlinearity.

  17. Correcting nonlinear drift distortion of scanning probe and scanning transmission electron microscopies from image pairs with orthogonal scan directions

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Ophus, Colin; Ciston, Jim; Nelson, Chris T.

    Unwanted motion of the probe with respect to the sample is a ubiquitous problem in scanning probe and scanning transmission electron microscopies, causing both linear and nonlinear artifacts in experimental images. We have designed a procedure to correct these artifacts by using orthogonal scan pairs to align each measurement line-by-line along the slow scan direction, by fitting contrast variation along the lines. We demonstrate the accuracy of our algorithm on both synthetic and experimental data and provide an implementation of our method.

  18. Correcting nonlinear drift distortion of scanning probe and scanning transmission electron microscopies from image pairs with orthogonal scan directions

    DOE PAGES

    Ophus, Colin; Ciston, Jim; Nelson, Chris T.

    2015-12-10

    Unwanted motion of the probe with respect to the sample is a ubiquitous problem in scanning probe and scanning transmission electron microscopies, causing both linear and nonlinear artifacts in experimental images. We have designed a procedure to correct these artifacts by using orthogonal scan pairs to align each measurement line-by-line along the slow scan direction, by fitting contrast variation along the lines. We demonstrate the accuracy of our algorithm on both synthetic and experimental data and provide an implementation of our method.

  19. Multiplicity of transmission coefficients in photonic crystal and split ring resonator waveguides with Kerr nonlinear impurities

    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

  20. Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

    NASA Astrophysics Data System (ADS)

    Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

    2010-12-01

    Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

  1. A Unified Approach for Solving Nonlinear Regular Perturbation Problems

    ERIC Educational Resources Information Center

    Khuri, S. A.

    2008-01-01

    This article describes a simple alternative unified method of solving nonlinear regular perturbation problems. The procedure is based upon the manipulation of Taylor's approximation for the expansion of the nonlinear term in the perturbed equation. An essential feature of this technique is the relative simplicity used and the associated unified…

  2. Some New Results in Astrophysical Problems of Nonlinear Theory of Radiative Transfer

    NASA Astrophysics Data System (ADS)

    Pikichyan, H. V.

    2017-07-01

    In the interpretation of the observed astrophysical spectra, a decisive role is related to nonlinear problems of radiative transfer, because the processes of multiple interactions of matter of cosmic medium with the exciting intense radiation ubiquitously occur in astrophysical objects, and in their vicinities. Whereas, the intensity of the exciting radiation changes the physical properties of the original medium, and itself was modified, simultaneously, in a self-consistent manner under its influence. In the present report, we show that the consistent application of the principle of invariance in the nonlinear problem of bilateral external illumination of a scattering/absorbing one-dimensional anisotropic medium of finite geometrical thickness allows for simplifications that were previously considered as a prerogative only of linear problems. The nonlinear problem is analyzed through the three methods of the principle of invariance: (i) an 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". Thereby, as an alternative to the Boltzmann equation, a new type of equations, so-called "kinetic equations of equivalence", are obtained. By the introduction of new functions - the so-called "linear images" of solution of nonlinear problem of radiative transfer, the linear structure of the solution of the nonlinear problem under study is further revealed. Linear images allow to convert naturally the statistical characteristics of random walk of a "single quantum" or their "beam of unit intensity", as well as widely known "probabilistic interpretation of phenomena of transfer", to the field of nonlinear problems. The structure of the equations obtained for determination of linear images is typical of linear problems.

  3. Nonlinear impairment compensation for DFT-S OFDM signal transmission with directly modulated laser and direct detection

    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.

  4. Using Algorithms in Solving Synapse Transmission Problems.

    ERIC Educational Resources Information Center

    Stencel, John E.

    1992-01-01

    Explains how a simple three-step algorithm can aid college students in solving synapse transmission problems. Reports that all of the students did not completely understand the algorithm. However, many learn a simple working model of synaptic transmission and understand why an impulse will pass across a synapse quantitatively. Students also see…

  5. 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.

  6. The intergenerational transmission of conduct problems.

    PubMed

    Raudino, Alessandra; Fergusson, David M; Woodward, Lianne J; Horwood, L John

    2013-03-01

    Drawing on prospective longitudinal data, this paper examines the intergenerational transmission of childhood conduct problems in a sample of 209 parents and their 331 biological offspring studied as part of the Christchurch Health and Developmental Study. The aims were to estimate the association between parental and offspring conduct problems and to examine the extent to which this association could be explained by (a) confounding social/family factors from the parent's childhood and (b) intervening factors reflecting parental behaviours and family functioning. The same item set was used to assess childhood conduct problems in parents and offspring. Two approaches to data analysis (generalised estimating equation regression methods and latent variable structural equation modelling) were used to examine possible explanations of the intergenerational continuity in behaviour. Regression analysis suggested that there was moderate intergenerational continuity (r = 0.23, p < 0.001) between parental and offspring conduct problems. This continuity was not explained by confounding factors but was partially mediated by parenting behaviours, particularly parental over-reactivity. Latent variable modelling designed to take account of non-observed common genetic and environmental factors underlying the continuities in problem behaviours across generations also suggested that parenting behaviour played a role in mediating the intergenerational transmission of conduct problems. There is clear evidence of intergenerational continuity in conduct problems. In part this association reflects a causal chain process in which parental conduct problems are associated (directly or indirectly) with impaired parenting behaviours that in turn influence risks of conduct problems in offspring.

  7. 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.

  8. 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

  9. Investigation of a stripline transmission line structure for gyromagnetic nonlinear transmission line high power microwave sources.

    PubMed

    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.

  10. Investigation of a stripline transmission line structure for gyromagnetic nonlinear transmission line high power microwave sources

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Reale, D. V., E-mail: david.reale@ttu.edu; Parson, J. M.; Neuber, A. A.

    2016-03-15

    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 constructedmore » 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.« less

  11. SEACAS Theory Manuals: Part 1. Problem Formulation in Nonlinear Solid Mechancis

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    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. Themore » 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.« less

  12. Simultaneous multigrid techniques for nonlinear eigenvalue problems: Solutions of the nonlinear Schrödinger-Poisson eigenvalue problem in two and three dimensions

    NASA Astrophysics Data System (ADS)

    Costiner, Sorin; Ta'asan, Shlomo

    1995-07-01

    Algorithms for nonlinear eigenvalue problems (EP's) often require solving self-consistently a large number of EP's. Convergence difficulties may occur if the solution is not sought in an appropriate region, if global constraints have to be satisfied, or if close or equal eigenvalues are present. Multigrid (MG) algorithms for nonlinear problems and for EP's obtained from discretizations of partial differential EP have often been shown to be more efficient than single level algorithms. This paper presents MG techniques and a MG algorithm for nonlinear Schrödinger Poisson EP's. The algorithm overcomes the above mentioned difficulties combining the following techniques: a MG simultaneous treatment of the eigenvectors and nonlinearity, and with the global constrains; MG stable subspace continuation techniques for the treatment of nonlinearity; and a MG projection coupled with backrotations for separation of solutions. These techniques keep the solutions in an appropriate region, where the algorithm converges fast, and reduce the large number of self-consistent iterations to only a few or one MG simultaneous iteration. The MG projection makes it possible to efficiently overcome difficulties related to clusters of close and equal eigenvalues. Computational examples for the nonlinear Schrödinger-Poisson EP in two and three dimensions, presenting special computational difficulties that are due to the nonlinearity and to the equal and closely clustered eigenvalues are demonstrated. For these cases, the algorithm requires O(qN) operations for the calculation of q eigenvectors of size N and for the corresponding eigenvalues. One MG simultaneous cycle per fine level was performed. The total computational cost is equivalent to only a few Gauss-Seidel relaxations per eigenvector. An asymptotic convergence rate of 0.15 per MG cycle is attained.

  13. 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.

  14. 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.

  15. 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.

  16. On Some Separated Algorithms for Separable Nonlinear Least Squares Problems.

    PubMed

    Gan, Min; Chen, C L Philip; Chen, Guang-Yong; Chen, Long

    2017-10-03

    For a class of nonlinear least squares problems, it is usually very beneficial to separate the variables into a linear and a nonlinear part and take full advantage of reliable linear least squares techniques. Consequently, the original problem is turned into a reduced problem which involves only nonlinear parameters. We consider in this paper four separated algorithms for such problems. The first one is the variable projection (VP) algorithm with full Jacobian matrix of Golub and Pereyra. The second and third ones are VP algorithms with simplified Jacobian matrices proposed by Kaufman and Ruano et al. respectively. The fourth one only uses the gradient of the reduced problem. Monte Carlo experiments are conducted to compare the performance of these four algorithms. From the results of the experiments, we find that: 1) the simplified Jacobian proposed by Ruano et al. is not a good choice for the VP algorithm; moreover, it may render the algorithm hard to converge; 2) the fourth algorithm perform moderately among these four algorithms; 3) the VP algorithm with the full Jacobian matrix perform more stable than that of the VP algorithm with Kuafman's simplified one; and 4) the combination of VP algorithm and Levenberg-Marquardt method is more effective than the combination of VP algorithm and Gauss-Newton method.

  17. Selected Problems in Nonlinear Dynamics and Sociophysics

    NASA Astrophysics Data System (ADS)

    Westley, Alexandra Renee

    This Ph.D. dissertation focuses on a collection of problems on the dynamical behavior of nonlinear many-body systems, drawn from two substantially different areas. First, the dynamical behavior seen in strongly nonlinear lattices such as in the Fermi-Pasta-Ulam-Tsingou (FPUT) system (part I) and second, time evolution behavior of interacting living objects which can be broadly considered as sociophysics systems (part II). The studies on FPUT-like systems will comprise of five chapters, dedicated to the properties of solitary and anti-solitary waves in the system, how localized nonlinear excitations decay and spread throughout these lattices, how two colliding solitary waves can precipitate highly localized and stable excitations, a possible alternative way to view these localized excitations through Duffing oscillators, and finally an exploration of parametric resonance in an FPUT-like lattice. Part II consists of two problems in the context of sociophysics. I use molecular dynamics inspired simulations to study the size and the stability of social groups of chimpanzees (such as those seen in central Africa) and compare the results with existing observations on the stability of chimpanzee societies. Secondly, I use an agent-based model to simulate land battles between an intelligent army and an insurgency when both have access to equally powerful weaponry. The study considers genetic algorithm based adaptive strategies to infer the strategies needed for the intelligent army to win the battles.

  18. Non-linear analytic and coanalytic problems ( L_p-theory, Clifford analysis, examples)

    NASA Astrophysics Data System (ADS)

    Dubinskii, Yu A.; Osipenko, A. S.

    2000-02-01

    Two kinds of new mathematical model of variational type are put forward: non-linear analytic and coanalytic problems. The formulation of these non-linear boundary-value problems is based on a decomposition of the complete scale of Sobolev spaces into the "orthogonal" sum of analytic and coanalytic subspaces. A similar decomposition is considered in the framework of Clifford analysis. Explicit examples are presented.

  19. Electronic transmission in non-linear potential profile of GaAs/AlxGa1-xAs biased quantum well structure

    NASA Astrophysics Data System (ADS)

    Meghoufel, F. Z.; Bentata, S.; Terkhi, S.; Bendahma, F.; Cherid, S.

    2013-05-01

    We study the effect of the nonlinearity on electrons transmission properties in a double barriers structure GaAs/AlxGa1-xAs superlattices. The nonlinearity is introduced as an effective potential in the Schrödinger equation and translates the electronic Colombian repulsion. We have used the transfer matrix formalism and the plane wave functions approximation to solve numerically the equation and calculate the electronic transmission coefficient. We have shown the occurrence of two allowed states within the same well instead of a single, translating the presence of two resonant states at two different energies. The first allowed state intensity strongly decreases with increasing the nonlinear parameter, whereas the second one called the degeneracy state increases. Both the two states evolve towards higher resonances energies.

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

    NASA Astrophysics Data System (ADS)

    Avdyushev, Victor A.

    2017-12-01

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

  1. Monolithic high voltage nonlinear transmission line fabrication process

    DOEpatents

    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.

  2. Nonlinear Dynamics of a Multistage Gear Transmission System with Multi-Clearance

    NASA Astrophysics Data System (ADS)

    Xiang, Ling; Zhang, Yue; Gao, Nan; Hu, Aijun; Xing, Jingtang

    The nonlinear torsional model of a multistage gear transmission system which consists of a planetary gear and two parallel gear stages is established with time-varying meshing stiffness, comprehensive gear error and multi-clearance. The nonlinear dynamic responses are analyzed by applying the reference of backlash bifurcation parameters. The motions of the system on the change of backlash are identified through global bifurcation diagram, largest Lyapunov exponent (LLE), FFT spectra, Poincaré maps, the phase diagrams and time series. The numerical results demonstrate that the system exhibits rich features of nonlinear dynamics such as the periodic motion, nonperiodic states and chaotic states. It is found that the sun-planet backlash has more complex effect on the system than the ring-planet backlash. The motions of the system with backlash of parallel gear are diverse including some different multi-periodic motions. Furthermore, the state of the system can change from chaos into quasi-periodic behavior, which means that the dynamic behavior of the system is composed of more stable components with the increase of the backlash. Correspondingly, the parameters of the system should be designed properly and controlled timely for better operation and enhancing the life of the system.

  3. Rogue waves generation in a left-handed nonlinear transmission line with series varactor diodes

    NASA Astrophysics Data System (ADS)

    Onana Essama, B. G.; Atangana, J.; Biya Motto, F.; Mokhtari, B.; Cherkaoui Eddeqaqi, N.; Kofane, Timoleon C.

    2014-07-01

    We investigate the electromagnetic wave behavior and its characterization using collective variables technique. Second-order dispersion, first- and second-order nonlinearities, which strongly act in a left-handed nonlinear transmission line with series varactor diodes, are taken into account. Four frequency ranges have been found. The first one gives the so-called energetic soliton due to a perfect combination of second-order dispersion and first-order nonlinearity. The second frequency range presents a dispersive soliton leading to the collapse of the electromagnetic wave at the third frequency range. But the fourth one shows physical conditions which are able to provoke the appearance of wave trains generation with some particular waves, the rogue waves. Moreover, we demonstrate that the number of rogue waves increases with frequency. The soliton, thereafter, gains a relative stability when second-order nonlinearity comes into play with some specific values in the fourth frequency range. Furthermore, the stability conditions of the electromagnetic wave at high frequencies have been also discussed.

  4. Six different roles for crossover inhibition in the retina: correcting the nonlinearities of synaptic transmission.

    PubMed

    Werblin, Frank S

    2010-03-01

    Early retinal studies categorized ganglion cell behavior as either linear or nonlinear and rectifying as represented by the familiar X- and Y-type ganglion cells in cat. Nonlinear behavior is in large part a consequence of the rectifying nonlinearities inherent in synaptic transmission. These nonlinear signals underlie many special functions in retinal processing, including motion detection, motion in motion, and local edge detection. But linear behavior is also required for some visual processing tasks. For these tasks, the inherently nonlinear signals are "linearized" by "crossover inhibition." Linearization utilizes a circuitry whereby nonlinear ON inhibition adds with nonlinear OFF excitation or ON excitation adds with OFF inhibition to generate a more linear postsynaptic voltage response. Crossover inhibition has now been measured in most bipolar, amacrine, and ganglion cells. Functionally crossover inhibition enhances edge detection, allows ganglion cells to recognize luminance-neutral patterns with their receptive fields, permits ganglion cells to distinguish contrast from luminance, and maintains a more constant conductance during the light response. In some cases, crossover extends the operating range of cone-driven OFF ganglion cells into the scotopic levels. Crossover inhibition is also found in neurons of the lateral geniculate nucleus and V1.

  5. Numerical method for solving the nonlinear four-point boundary value problems

    NASA Astrophysics Data System (ADS)

    Lin, Yingzhen; Lin, Jinnan

    2010-12-01

    In this paper, a new reproducing kernel space is constructed skillfully in order to solve a class of nonlinear four-point boundary value problems. The exact solution of the linear problem can be expressed in the form of series and the approximate solution of the nonlinear problem is given by the iterative formula. Compared with known investigations, the advantages of our method are that the representation of exact solution is obtained in a new reproducing kernel Hilbert space and accuracy of numerical computation is higher. Meanwhile we present the convergent theorem, complexity analysis and error estimation. The performance of the new method is illustrated with several numerical examples.

  6. Monolithic high voltage nonlinear transmission line fabrication process

    DOEpatents

    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.

  7. 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…

  8. Experimental demonstration of a frequency-domain Volterra series nonlinear equalizer in polarization-multiplexed transmission.

    PubMed

    Guiomar, Fernando P; Reis, Jacklyn D; Carena, Andrea; Bosco, Gabriella; Teixeira, António L; Pinto, Armando N

    2013-01-14

    Employing 100G polarization-multiplexed quaternary phase-shift keying (PM-QPSK) signals, we experimentally demonstrate a dual-polarization Volterra series nonlinear equalizer (VSNE) applied in frequency-domain, to mitigate intra-channel nonlinearities. The performance of the dual-polarization VSNE is assessed in both single-channel and in wavelength-division multiplexing (WDM) scenarios, providing direct comparisons with its single-polarization version and with the widely studied back-propagation split-step Fourier (SSF) approach. In single-channel transmission, the optimum power has been increased by about 1 dB, relatively to the single-polarization equalizers, and up to 3 dB over linear equalization, with a corresponding bit error rate (BER) reduction of up to 63% and 85%, respectively. Despite of the impact of inter-channel nonlinearities, we show that intra-channel nonlinear equalization is still able to provide approximately 1 dB improvement in the optimum power and a BER reduction of ~33%, considering a 66 GHz WDM grid. By means of simulation, we demonstrate that the performance of nonlinear equalization can be substantially enhanced if both optical and electrical filtering are optimized, enabling the VSNE technique to outperform its SSF counterpart at high input powers.

  9. 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.

  10. Middle School Students' Reasoning in Nonlinear Proportional Problems in Geometry

    ERIC Educational Resources Information Center

    Ayan, Rukiye; Isiksal Bostan, Mine

    2018-01-01

    In this study, we investigate sixth, seventh, and eighth grade students' achievement in nonlinear (quadratic or cubic) proportional problems regarding length, area, and volume of enlarged figures. In addition, we examine students' solution strategies for the problems and obstacles that prevent students from answering the problems correctly by…

  11. The existence of semiregular solutions to elliptic spectral problems with discontinuous nonlinearities

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Pavlenko, V N; Potapov, D K

    2015-09-30

    This paper is concerned with the existence of semiregular solutions to the Dirichlet problem for an equation of elliptic type with discontinuous nonlinearity and when the differential operator is not assumed to be formally self-adjoint. Theorems on the existence of semiregular (positive and negative) solutions for the problem under consideration are given, and a principle of upper and lower solutions giving the existence of semiregular solutions is established. For positive values of the spectral parameter, elliptic spectral problems with discontinuous nonlinearities are shown to have nontrivial semiregular (positive and negative) solutions. Bibliography: 32 titles.

  12. Optical stealth transmission based on super-continuum generation in highly nonlinear fiber over WDM network.

    PubMed

    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.

  13. 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.

  14. Calculation of transmission probability by solving an eigenvalue problem

    NASA Astrophysics Data System (ADS)

    Bubin, Sergiy; Varga, Kálmán

    2010-11-01

    The electron transmission probability in nanodevices is calculated by solving an eigenvalue problem. The eigenvalues are the transmission probabilities and the number of nonzero eigenvalues is equal to the number of open quantum transmission eigenchannels. The number of open eigenchannels is typically a few dozen at most, thus the computational cost amounts to the calculation of a few outer eigenvalues of a complex Hermitian matrix (the transmission matrix). The method is implemented on a real space grid basis providing an alternative to localized atomic orbital based quantum transport calculations. Numerical examples are presented to illustrate the efficiency of the method.

  15. A fixed energy fixed angle inverse scattering in interior transmission problem

    NASA Astrophysics Data System (ADS)

    Chen, Lung-Hui

    2017-06-01

    We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

  16. Transmission eigenvalues

    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

  17. 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.

  18. High current nonlinear transmission line based electron beam driver

    NASA Astrophysics Data System (ADS)

    Hoff, B. W.; French, D. M.; Simon, D. S.; Lepell, P. D.; Montoya, T.; Heidger, S. L.

    2017-10-01

    A gigawatt-class nonlinear transmission line based electron beam driver is experimentally demonstrated. Four experimental series, each with a different Marx bank charge voltage (15, 20, 25, and 30 kV), were completed. Within each experimental series, shots at peak frequencies ranging from 950 MHz to 1.45 GHz were performed. Peak amplitude modulations of the NLTL output voltage signal were found to range between 18% and 35% for the lowest frequency shots and between 5% and 20% for the highest frequency shots (higher modulation at higher Marx charge voltage). Peak amplitude modulations of the electron beam current were found to range between 10% and 20% for the lowest frequency shots and between 2% and 7% for the highest frequency shots (higher modulation at higher Marx charge voltage).

  19. New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem

    NASA Astrophysics Data System (ADS)

    Rahman, Md. Saifur; Lee, Yiu-Yin

    2017-10-01

    In this study, a new modified multi-level residue harmonic balance method is presented and adopted to investigate the forced nonlinear vibrations of axially loaded double beams. Although numerous nonlinear beam or linear double-beam problems have been tackled and solved, there have been few studies of this nonlinear double-beam problem. The geometric nonlinear formulations for a double-beam model are developed. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. This heavily reduces the computational effort compared with solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The proposed method can generate the higher-level nonlinear solutions that are neglected by the previous modified harmonic balance method. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, and excitation magnitude on the nonlinear vibrational behaviour are examined.

  20. 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.

  1. Nonlinear experimental dye-doped nematic liquid crystal optical transmission spectra estimated by neural network empirical physical formulas

    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.

  2. Multigrid techniques for nonlinear eigenvalue probems: Solutions of a nonlinear Schroedinger eigenvalue problem in 2D and 3D

    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.

  3. The piecewise parabolic method for Riemann problems in nonlinear elasticity.

    PubMed

    Zhang, Wei; Wang, Tao; Bai, Jing-Song; Li, Ping; Wan, Zhen-Hua; Sun, De-Jun

    2017-10-18

    We present the application of Harten-Lax-van Leer (HLL)-type solvers on Riemann problems in nonlinear elasticity which undergoes high-load conditions. In particular, the HLLD ("D" denotes Discontinuities) Riemann solver is proved to have better robustness and efficiency for resolving complex nonlinear wave structures compared with the HLL and HLLC ("C" denotes Contact) solvers, especially in the shock-tube problem including more than five waves. Also, Godunov finite volume scheme is extended to higher order of accuracy by means of piecewise parabolic method (PPM), which could be used with HLL-type solvers and employed to construct the fluxes. Moreover, in the case of multi material components, level set algorithm is applied to track the interface between different materials, while the interaction of interfaces is realized through HLLD Riemann solver combined with modified ghost method. As seen from the results of both the solid/solid "stick" problem with the same material at the two sides of contact interface and the solid/solid "slip" problem with different materials at the two sides, this scheme composed of HLLD solver, PPM and level set algorithm can capture the material interface effectively and suppress spurious oscillations therein significantly.

  4. 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

  5. Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering

    DOE PAGES

    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.

  6. A Bifurcation Problem for a Nonlinear Partial Differential Equation of Parabolic Type,

    DTIC Science & Technology

    NONLINEAR DIFFERENTIAL EQUATIONS, INTEGRATION), (*PARTIAL DIFFERENTIAL EQUATIONS, BOUNDARY VALUE PROBLEMS), BANACH SPACE , MAPPING (TRANSFORMATIONS), SET THEORY, TOPOLOGY, ITERATIONS, STABILITY, THEOREMS

  7. Topics on data transmission problem in software definition network

    NASA Astrophysics Data System (ADS)

    Gao, Wei; Liang, Li; Xu, Tianwei; Gan, Jianhou

    2017-08-01

    In normal computer networks, the data transmission between two sites go through the shortest path between two corresponding vertices. However, in the setting of software definition network (SDN), it should monitor the network traffic flow in each site and channel timely, and the data transmission path between two sites in SDN should consider the congestion in current networks. Hence, the difference of available data transmission theory between normal computer network and software definition network is that we should consider the prohibit graph structures in SDN, and these forbidden subgraphs represent the sites and channels in which data can't be passed by the serious congestion. Inspired by theoretical analysis of an available data transmission in SDN, we consider some computational problems from the perspective of the graph theory. Several results determined in the paper imply the sufficient conditions of data transmission in SDN in the various graph settings.

  8. Analysis of Classes of Superlinear Semipositone Problems with Nonlinear Boundary Conditions

    NASA Astrophysics Data System (ADS)

    Morris, Quinn A.

    We study positive radial solutions for classes of steady state reaction diffusion problems on the exterior of a ball with both Dirichlet and nonlinear boundary conditions. We consider p-Laplacian problems (p > 1) with reaction terms which are superlinear at infinity and semipositone. In the case p = 2, using variational methods, we establish the existence of a solution, and via detailed analysis of the Green's function, we prove the positivity of the solution. In the case p ≠ 2, we again use variational methods to establish the existence of a solution, but the positivity of the solution is achieved via sophisticated a priori estimates. In the case p ≠ 2, the Green's function analysis is no longer available. Our results significantly enhance the literature on superlinear semipositone problems. Finally, we provide algorithms for the numerical generation of exact bifurcation curves for one-dimensional problems. In the autonomous case, we extend and analyze a quadrature method, and using nonlinear solvers in Mathematica, generate bifurcation curves. In the nonautonomous case, we employ shooting methods in Mathematica to generate bifurcation curves.

  9. Linearity and Nonlinearity in HIV/STI Transmission: Implications for the Evaluation of Sexual Risk Reduction Interventions

    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…

  10. The relative degree enhancement problem for MIMO nonlinear systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Schoenwald, D.A.; Oezguener, Ue.

    1995-07-01

    The authors present a result for linearizing a nonlinear MIMO system by employing partial feedback - feedback at all but one input-output channel such that the SISO feedback linearization problem is solvable at the remaining input-output channel. The partial feedback effectively enhances the relative degree at the open input-output channel provided the feedback functions are chosen to satisfy relative degree requirements. The method is useful for nonlinear systems that are not feedback linearizable in a MIMO sense. Several examples are presented to show how these feedback functions can be computed. This strategy can be combined with decentralized observers for amore » completely decentralized feedback linearization result for at least one input-output channel.« less

  11. Analytical expressions for the nonlinear interference in dispersion managed transmission coherent optical systems

    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.

  12. Bias-field controlled phasing and power combination of gyromagnetic nonlinear transmission lines

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Reale, D. V., E-mail: david.reale@ttu.edu; Bragg, J.-W. B.; Gonsalves, N. R.

    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 bandsmore » 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.« less

  13. Bias-field controlled phasing and power combination of gyromagnetic nonlinear transmission lines.

    PubMed

    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.

  14. 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.

  15. Theoretical Investigation of Light Transmission in a Slab Cavity via Kerr Nonlinearity of Carbon Nanotube Quantum Dot Nanostructure

    NASA Astrophysics Data System (ADS)

    Solookinejad, Gh.; Jabbari, M.; Sangachin, E. Ahmadi; Asadpour, S. H.

    2018-01-01

    In this paper, we discuss the transmission properties of weak probe laser field propagate through slab cavity with defect layer of carbon-nanotube quantum dot (CNT-QD) nanostructure. We show that due to spin-orbit coupling, the double electromagnetically induced transparency (EIT) windows appear and the giant Kerr nonlinearity of the intracavity medium can lead to manipulating of transmission coefficient of weak probe light. The thickness effect of defect layer medium has also been analyzed on transmission properties of probe laser field. Our proposed model may be useful for integrated photonics devices based on CNT-QD for applications in all-optical systems which require multiple EIT effect.

  16. Clutch pressure estimation for a power-split hybrid transmission using nonlinear robust observer

    NASA Astrophysics Data System (ADS)

    Zhou, Bin; Zhang, Jianwu; Gao, Ji; Yu, Haisheng; Liu, Dong

    2018-06-01

    For a power-split hybrid transmission, using the brake clutch to realize the transition from electric drive mode to hybrid drive mode is an available strategy. Since the pressure information of the brake clutch is essential for the mode transition control, this research designs a nonlinear robust reduced-order observer to estimate the brake clutch pressure. Model uncertainties or disturbances are considered as additional inputs, thus the observer is designed in order that the error dynamics is input-to-state stable. The nonlinear characteristics of the system are expressed as the lookup tables in the observer. Moreover, the gain matrix of the observer is solved by two optimization procedures under the constraints of the linear matrix inequalities. The proposed observer is validated by offline simulation and online test, the results have shown that the observer achieves significant performance during the mode transition, as the estimation error is within a reasonable range, more importantly, it is asymptotically stable.

  17. 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.

  18. Global gradient estimates for divergence-type elliptic problems involving general nonlinear operators

    NASA Astrophysics Data System (ADS)

    Cho, Yumi

    2018-05-01

    We study nonlinear elliptic problems with nonstandard growth and ellipticity related to an N-function. We establish global Calderón-Zygmund estimates of the weak solutions in the framework of Orlicz spaces over bounded non-smooth domains. Moreover, we prove a global regularity result for asymptotically regular problems which are getting close to the regular problems considered, when the gradient variable goes to infinity.

  19. The intergenerational transmission of at-risk/problem gambling: The moderating role of parenting practices.

    PubMed

    Dowling, Nicki A; Shandley, Kerrie A; Oldenhof, Erin; Affleck, Julia M; Youssef, George J; Frydenberg, Erica; Thomas, Shane A; Jackson, Alun C

    2017-10-01

    Although parenting practices are articulated as underlying mechanisms or protective factors in several theoretical models, their role in the intergenerational transmission of gambling problems has received limited research attention. This study therefore examined the degree to which parenting practices (positive parenting, parental involvement, and inconsistent discipline) moderated the intergenerational transmission of paternal and maternal problem gambling. Students aged 12-18 years (N = 612) recruited from 17 Australian secondary schools completed a survey measuring parental problem gambling, problem gambling severity, and parenting practices. Participants endorsing paternal problem gambling (23.3%) were 4.3 times more likely to be classified as at-risk/problem gamblers than their peers (5.4%). Participants endorsing maternal problem gambling (6.9%) were no more likely than their peers (4.0%) to be classified as at-risk/problem gamblers. Paternal problem gambling was a significant predictor of offspring at-risk/problem gambling after controlling for maternal problem gambling and participant demographic characteristics. The relationship between maternal problem gambling and offspring at-risk/problem gambling was buffered by parental involvement. Paternal problem gambling may be important in the development of adolescent at-risk/problem gambling behaviours and higher levels of parental involvement buffers the influence of maternal problem gambling in the development of offspring gambling problems. Further research is therefore required to identify factors that attenuate the seemingly greater risk of transmission associated with paternal gambling problems. Parental involvement is a potential candidate for prevention and intervention efforts designed to reduce the intergenerational transmission of gambling problems. (Am J Addict 2017;26:707-712). © 2017 American Academy of Addiction Psychiatry.

  20. Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems

    NASA Astrophysics Data System (ADS)

    Cianchi, Andrea; Maz'ya, Vladimir G.

    2018-05-01

    Best possible second-order regularity is established for solutions to p-Laplacian type equations with {p \\in (1, ∞)} and a square-integrable right-hand side. Our results provide a nonlinear counterpart of the classical L 2-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are obtained. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required, although our conclusions are new even for smooth domains. If the domain is convex, no regularity of its boundary is needed at all.

  1. 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.

  2. A fuzzy-theory-based method for studying the effect of information transmission on nonlinear crowd dispersion dynamics

    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.

  3. Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

    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.

  4. Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem

    NASA Astrophysics Data System (ADS)

    Lakshtanov, E.; Vainberg, B.

    2013-10-01

    The paper concerns the isotropic interior transmission eigenvalue (ITE) problem. This problem is not elliptic, but we show that, using the Dirichlet-to-Neumann map, it can be reduced to an elliptic one. This leads to the discreteness of the spectrum as well as to certain results on a possible location of the transmission eigenvalues. If the index of refraction \\sqrt{n(x)} is real, then we obtain a result on the existence of infinitely many positive ITEs and the Weyl-type lower bound on its counting function. All the results are obtained under the assumption that n(x) - 1 does not vanish at the boundary of the obstacle or it vanishes identically, but its normal derivative does not vanish at the boundary. We consider the classical transmission problem as well as the case when the inhomogeneous medium contains an obstacle. Some results on the discreteness and localization of the spectrum are obtained for complex valued n(x).

  5. Studies in nonlinear problems of energy. Final report

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    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 wavesmore » 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

  6. A numerical method for solving a nonlinear 2-D optimal control problem with the classical diffusion equation

    NASA Astrophysics Data System (ADS)

    Mamehrashi, K.; Yousefi, S. A.

    2017-02-01

    This paper presents a numerical solution for solving a nonlinear 2-D optimal control problem (2DOP). The performance index of a nonlinear 2DOP is described with a state and a control function. Furthermore, dynamic constraint of the system is given by a classical diffusion equation. It is preferred to use the Ritz method for finding the numerical solution of the problem. The method is based upon the Legendre polynomial basis. By using this method, the given optimisation nonlinear 2DOP reduces to the problem of solving a system of algebraic equations. The benefit of the method is that it provides greater flexibility in which the given initial and boundary conditions of the problem are imposed. Moreover, compared with the eigenfunction method, the satisfactory results are obtained only in a small number of polynomials order. This numerical approach is applicable and effective for such a kind of nonlinear 2DOP. The convergence of the method is extensively discussed and finally two illustrative examples are included to observe the validity and applicability of the new technique developed in the current work.

  7. Waterjet and laser etching: the nonlinear inverse problem

    NASA Astrophysics Data System (ADS)

    Bilbao-Guillerna, A.; Axinte, D. A.; Billingham, J.; Cadot, G. B. J.

    2017-07-01

    In waterjet and laser milling, material is removed from a solid surface in a succession of layers to create a new shape, in a depth-controlled manner. The inverse problem consists of defining the control parameters, in particular, the two-dimensional beam path, to arrive at a prescribed freeform surface. Waterjet milling (WJM) and pulsed laser ablation (PLA) are studied in this paper, since a generic nonlinear material removal model is appropriate for both of these processes. The inverse problem is usually solved for this kind of process by simply controlling dwell time in proportion to the required depth of milling at a sequence of pixels on the surface. However, this approach is only valid when shallow surfaces are etched, since it does not take into account either the footprint of the beam or its overlapping on successive passes. A discrete adjoint algorithm is proposed in this paper to improve the solution. Nonlinear effects and non-straight passes are included in the optimization, while the calculation of the Jacobian matrix does not require large computation times. Several tests are performed to validate the proposed method and the results show that tracking error is reduced typically by a factor of two in comparison to the pixel-by-pixel approach and the classical raster path strategy with straight passes. The tracking error can be as low as 2-5% and 1-2% for WJM and PLA, respectively, depending on the complexity of the target surface.

  8. The Fisher-KPP problem with doubly nonlinear diffusion

    NASA Astrophysics Data System (ADS)

    Audrito, Alessandro; Vázquez, Juan Luis

    2017-12-01

    The famous Fisher-KPP reaction-diffusion model combines linear diffusion with the typical KPP reaction term, and appears in a number of relevant applications in biology and chemistry. It is remarkable as a mathematical model since it possesses a family of travelling waves that describe the asymptotic behaviour of a large class solutions 0 ≤ u (x , t) ≤ 1 of the problem posed in the real line. The existence of propagation waves with finite speed has been confirmed in some related models and disproved in others. We investigate here the corresponding theory when the linear diffusion is replaced by the "slow" doubly nonlinear diffusion and we find travelling waves that represent the wave propagation of more general solutions even when we extend the study to several space dimensions. A similar study is performed in the critical case that we call "pseudo-linear", i.e., when the operator is still nonlinear but has homogeneity one. With respect to the classical model and the "pseudo-linear" case, the "slow" travelling waves exhibit free boundaries.

  9. 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.

  10. Nonlinear gearshifts control of dual-clutch transmissions during inertia phase.

    PubMed

    Hu, Yunfeng; Tian, Lu; Gao, Bingzhao; Chen, Hong

    2014-07-01

    In this paper, a model-based nonlinear gearshift controller is designed by the backstepping method to improve the shift quality of vehicles with a dual-clutch transmission (DCT). Considering easy-implementation, the controller is rearranged into a concise structure which contains a feedforward control and a feedback control. Then, robustness of the closed-loop error system is discussed in the framework of the input to state stability (ISS) theory, where model uncertainties are considered as the additive disturbance inputs. Furthermore, due to the application of the backstepping method, the closed-loop error system is ordered as a linear system. Using the linear system theory, a guideline for selecting the controller parameters is deduced which could reduce the workload of parameters tuning. Finally, simulation results and Hardware in the Loop (HiL) simulation are presented to validate the effectiveness of the designed controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

  11. Fuzzy control for a nonlinear mimo-liquid level problem

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Smith, R. E.; Mortensen, F. N.; Wantuck, P. J.

    2001-01-01

    Nonlinear systems are very common in the chemical process industries. Control of these systems, particularly multivariable systems, is extremely difficult. In many chemical plants, because of this difficulty, control is seldom optimal. Quite often, the best control is obtained in the manual mode using experienced operators. Liquid level control is probably one of the most common control problems in a chemical plant. Liquid level is important in heat exchanger control where heat and mass transfer rates can be controlled by the amount of liquid covering the tubes. Distillation columns, mixing tanks, and surge tanks are other examples where liquid levelmore » control is very important. The problem discussed in this paper is based on the simultaneous level control of three tanks connected in series. Each tank holds slightly less than 0.01 m{sup 3} of liquid. All three tanks are connected, Liquid is pumped into the first and the third tanks to maintain their levels. The third tank in the series drains to the system exit. The levels in the first and third tank control the level in the middle tank. The level in the middle tank affects the levels in the two end tanks. Many other chemical plant systems can be controlled in a manner similar to this three-tank system. For example, in any distillation column liquid level control problems can be represented as a total condenser with liquid level control, a reboiler with liquid level control, with the interactive column in between. The solution to the three-tank-problem can provide insight into many of the nonlinear control problems in the chemical process industries. The system was tested using the fuzzy logic controller and a proportional-integral (PI) controller, in both the setpoint tracking mode and disturbance rejection mode. The experimental results are discussed and comparisons between fuzzy controller and the standard PI controller are made.« less

  12. Initial-value problem for the Gardner equation applied to nonlinear internal waves

    NASA Astrophysics Data System (ADS)

    Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim

    2017-04-01

    The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of

  13. Guaranteed estimation of solutions to Helmholtz transmission problems with uncertain data from their indirect noisy observations

    NASA Astrophysics Data System (ADS)

    Podlipenko, Yu. K.; Shestopalov, Yu. V.

    2017-09-01

    We investigate the guaranteed estimation problem of linear functionals from solutions to transmission problems for the Helmholtz equation with inexact data. The right-hand sides of equations entering the statements of transmission problems and the statistical characteristics of observation errors are supposed to be unknown and belonging to certain sets. It is shown that the optimal linear mean square estimates of the above mentioned functionals and estimation errors are expressed via solutions to the systems of transmission problems of the special type. The results and techniques can be applied in the analysis and estimation of solution to forward and inverse electromagnetic and acoustic problems with uncertain data that arise in mathematical models of the wave diffraction on transparent bodies.

  14. Mitigation of nonlinear fiber distortion using optical phase conjugation for mode-division multiplexed transmission

    NASA Astrophysics Data System (ADS)

    Zhang, Kai; Gao, Guanjun; Zhang, Jie; Fei, Aimei; Cvijetic, Milorad

    2018-07-01

    We have investigated and proposed the use of optical phase conjugation (OPC) technique to mitigate the impact of fiber nonlinearities in mode-division multiplexed transmission systems. Numerical simulations are performed for three wavelengths, each loaded with 200 Gb/s dual-polarization 16-level quadrature amplitude modulation (DP-16QAM) format, in weakly guided two-mode fiber. It is known that differential mode group delay (DMGD) in mode-division multiplexed (MDM) transmission systems could be beneficial for system performance of MDM system with MIMO compensation in place. On the other side, for MDM system with OPC in place, the presence of DMGD may limit the overall benefits since signal power evolution per spatial modes should be symmetrical at the system midpoint in order to realize an effective compensation of the nonlinear effects. Our simulation results show that in the reference case (in the absence of DMGD), the employment of OPC module would lead to an average Q-factor improvement of approximately 10 dB. At the same time, in the presence of DMGD, an average Q-factor improvement would be ∼2.8 dB for WDM case. In addition, due to asymmetrical signal power map, the penalties induced by a periodic amplification process cannot be ideally compensated by the midpoint insertion of OPC. However, by accounting the impacts of both DMGD and asymmetrical signal power map, the insertion of the OPC system will still lead to an average Q-factor improvement of ∼1 dB for WDM channel arrangement.

  15. 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.

  16. A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints

    NASA Astrophysics Data System (ADS)

    Li, Jinquan; Feng, Shuang; Mi, Honghai

    In this work, a kind of nonlinear programming problem with non-differential objective function and under the constraints expressed by a system of mixed fuzzy relation equations is investigated. First, some properties of this kind of optimization problem are obtained. Then, a polynomial-time algorithm for this kind of optimization problem is proposed based on these properties. Furthermore, we show that this algorithm is optimal for the considered optimization problem in this paper. Finally, numerical examples are provided to illustrate our algorithms.

  17. An Algorithm for Efficient Maximum Likelihood Estimation and Confidence Interval Determination in Nonlinear Estimation Problems

    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.

  18. A family of approximate solutions and explicit error estimates for the nonlinear stationary Navier-Stokes problem

    NASA Technical Reports Server (NTRS)

    Gabrielsen, R. E.; Karel, S.

    1975-01-01

    An algorithm for solving the nonlinear stationary Navier-Stokes problem is developed. Explicit error estimates are given. This mathematical technique is potentially adaptable to the separation problem.

  19. 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.

  20. An efficient computational method for solving nonlinear stochastic Itô integral equations: Application for stochastic problems in physics

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Heydari, M.H., E-mail: heydari@stu.yazd.ac.ir; The Laboratory of Quantum Information Processing, Yazd University, Yazd; Hooshmandasl, M.R., E-mail: hooshmandasl@yazd.ac.ir

    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. Errormore » 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.« less

  1. CSOLNP: Numerical Optimization Engine for Solving Non-linearly Constrained Problems.

    PubMed

    Zahery, Mahsa; Maes, Hermine H; Neale, Michael C

    2017-08-01

    We introduce the optimizer CSOLNP, which is a C++ implementation of the R package RSOLNP (Ghalanos & Theussl, 2012, Rsolnp: General non-linear optimization using augmented Lagrange multiplier method. R package version, 1) alongside some improvements. CSOLNP solves non-linearly constrained optimization problems using a Sequential Quadratic Programming (SQP) algorithm. CSOLNP, NPSOL (a very popular implementation of SQP method in FORTRAN (Gill et al., 1986, User's guide for NPSOL (version 4.0): A Fortran package for nonlinear programming (No. SOL-86-2). Stanford, CA: Stanford University Systems Optimization Laboratory), and SLSQP (another SQP implementation available as part of the NLOPT collection (Johnson, 2014, The NLopt nonlinear-optimization package. Retrieved from http://ab-initio.mit.edu/nlopt)) are three optimizers available in OpenMx package. These optimizers are compared in terms of runtimes, final objective values, and memory consumption. A Monte Carlo analysis of the performance of the optimizers was performed on ordinal and continuous models with five variables and one or two factors. While the relative difference between the objective values is less than 0.5%, CSOLNP is in general faster than NPSOL and SLSQP for ordinal analysis. As for continuous data, none of the optimizers performs consistently faster than the others. In terms of memory usage, we used Valgrind's heap profiler tool, called Massif, on one-factor threshold models. CSOLNP and NPSOL consume the same amount of memory, while SLSQP uses 71 MB more memory than the other two optimizers.

  2. A one-dimensional nonlinear problem of thermoelasticity in extended thermodynamics

    NASA Astrophysics Data System (ADS)

    Rawy, E. K.

    2018-06-01

    We solve a nonlinear, one-dimensional initial boundary-value problem of thermoelasticity in generalized thermodynamics. A Cattaneo-type evolution equation for the heat flux is used, which differs from the one used extensively in the literature. The hyperbolic nature of the associated linear system is clarified through a study of the characteristic curves. Progressive wave solutions with two finite speeds are noted. A numerical treatment is presented for the nonlinear system using a three-step, quasi-linearization, iterative finite-difference scheme for which the linear system of equations is the initial step in the iteration. The obtained results are discussed in detail. They clearly show the hyperbolic nature of the system, and may be of interest in investigating thermoelastic materials, not only at low temperatures, but also during high temperature processes involving rapid changes in temperature as in laser treatment of surfaces.

  3. Efficient nonlinear equalizer for intra-channel nonlinearity compensation for next generation agile and dynamically reconfigurable optical networks.

    PubMed

    Malekiha, Mahdi; Tselniker, Igor; Plant, David V

    2016-02-22

    In this work, we propose and experimentally demonstrate a novel low-complexity technique for fiber nonlinearity compensation. We achieved a transmission distance of 2818 km for a 32-GBaud dual-polarization 16QAM signal. For efficient implantation, and to facilitate integration with conventional digital signal processing (DSP) approaches, we independently compensate fiber nonlinearities after linear impairment equalization. Therefore this algorithm can be easily implemented in currently deployed transmission systems after using linear DSP. The proposed equalizer operates at one sample per symbol and requires only one computation step. The structure of the algorithm is based on a first-order perturbation model with quantized perturbation coefficients. Also, it does not require any prior calculation or detailed knowledge of the transmission system. We identified common symmetries between perturbation coefficients to avoid duplicate and unnecessary operations. In addition, we use only a few adaptive filter coefficients by grouping multiple nonlinear terms and dedicating only one adaptive nonlinear filter coefficient to each group. Finally, the complexity of the proposed algorithm is lower than previously studied nonlinear equalizers by more than one order of magnitude.

  4. Characteristics of a four element gyromagnetic nonlinear transmission line array high power microwave source.

    PubMed

    Johnson, J M; Reale, D V; Krile, J T; Garcia, R S; Cravey, W H; Neuber, A A; Dickens, J C; Mankowski, J J

    2016-05-01

    In this paper, a solid-state four element array gyromagnetic nonlinear transmission line high power microwave system is presented as well as a detailed description of its subsystems and general output capabilities. This frequency agile S-band source is easily adjusted from 2-4 GHz by way of a DC driven biasing magnetic field and is capable of generating electric fields of 7.8 kV/m at 10 m correlating to 4.2 MW of RF power with pulse repetition frequencies up to 1 kHz. Beam steering of the array at angles of ±16.7° is also demonstrated, and the associated general radiation pattern is detailed.

  5. Characteristics of a four element gyromagnetic nonlinear transmission line array high power microwave source

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Johnson, J. M., E-mail: jared.johnson@ttu.edu; Reale, D. V.; Garcia, R. S.

    2016-05-15

    In this paper, a solid-state four element array gyromagnetic nonlinear transmission line high power microwave system is presented as well as a detailed description of its subsystems and general output capabilities. This frequency agile S-band source is easily adjusted from 2-4 GHz by way of a DC driven biasing magnetic field and is capable of generating electric fields of 7.8 kV/m at 10 m correlating to 4.2 MW of RF power with pulse repetition frequencies up to 1 kHz. Beam steering of the array at angles of ±16.7° is also demonstrated, and the associated general radiation pattern is detailed.

  6. Stable sequential Kuhn-Tucker theorem in iterative form or a regularized Uzawa algorithm in a regular nonlinear programming problem

    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.

  7. Application of genetic algorithms in nonlinear heat conduction problems.

    PubMed

    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.

  8. A Description of the Strategic Knowledge of Experts Solving Transmission Genetics Problems.

    ERIC Educational Resources Information Center

    Collins, Angelo

    Descriptions of the problem-solving strategies of experts solving realistic, computer-generated transmission genetics problems are presented in this paper and implications for instruction are discussed. Seven experts were involved in the study. All of the experts had a doctoral degree and experience in both teaching and doing research in genetics.…

  9. The intergenerational transmission of problem gambling: The mediating role of parental psychopathology.

    PubMed

    Dowling, N A; Shandley, K; Oldenhof, E; Youssef, G J; Thomas, S A; Frydenberg, E; Jackson, A C

    2016-08-01

    The present study investigated the intergenerational transmission of problem gambling and the potential mediating role of parental psychopathology (problem drinking, drug use problems, and mental health issues). The study comprised 3953 participants (1938 males, 2015 females) recruited from a large-scale Australian community telephone survey of adults retrospectively reporting on parental problem gambling and psychopathology during their childhood. Overall, 4.0% [95%CI 3.0, 5.0] (n=157) of participants reported paternal problem gambling and 1.7% [95%CI 1.0, 2.0] (n=68) reported maternal problem gambling. Compared to their peers, participants reporting paternal problem gambling were 5.1 times more likely to be moderate risk gamblers and 10.7 times more likely to be problem gamblers. Participants reporting maternal problem gambling were 1.7 times more likely to be moderate risk gamblers and 10.6 times more likely to be problem gamblers. The results revealed that the relationships between paternal-and-participant and maternal-and-participant problem gambling were significant, but that only the relationship between paternal-and-participant problem gambling remained statistically significant after controlling for maternal problem gambling and sociodemographic factors. Paternal problem drinking and maternal drug use problems partially mediated the relationship between paternal-and-participant problem gambling, and fully mediated the relationship between maternal-and-participant problem gambling. In contrast, parental mental health issues failed to significantly mediate the transmission of gambling problems by either parent. When parental problem gambling was the mediator, there was full mediation of the effect between parental psychopathology and offspring problem gambling for fathers but not mothers. Overall, the study highlights the vulnerability of children from problem gambling households and suggests that it would be of value to target prevention and intervention

  10. Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

    PubMed

    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.

  11. 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.

  12. The Characteristics of Vibration Isolation System with Damping and Stiffness Geometrically Nonlinear

    NASA Astrophysics Data System (ADS)

    Lu, Ze-Qi; Chen, Li-Qun; Brennan, Michael J.; Li, Jue-Ming; Ding, Hu

    2016-09-01

    The paper concerns an investigation into the use of both stiffness and damping nonlinearity in the vibration isolator to improve its effectiveness. The nonlinear damping and nonlinear stiffness are both achieved by horizontal damping and stiffness as the way of the geometrical nonlinearity. The harmonic balance method is used to analyze the force transmissibility of such vibration isolation system. It is found that as the horizontal damping increasing, the height of the force transmissibility peak is decreased and the high-frequency force transmissibility is almost the same. The results are also validated by some numerical method. Then the RMS of transmissibility under Gaussian white noise is calculated numerically, the results demonstrate that the beneficial effects of the damping nonlinearity can be achieved under random excitation.

  13. 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.

  14. Iterative algorithms for a non-linear inverse problem in atmospheric lidar

    NASA Astrophysics Data System (ADS)

    Denevi, Giulia; Garbarino, Sara; Sorrentino, Alberto

    2017-08-01

    We consider the inverse problem of retrieving aerosol extinction coefficients from Raman lidar measurements. In this problem the unknown and the data are related through the exponential of a linear operator, the unknown is non-negative and the data follow the Poisson distribution. Standard methods work on the log-transformed data and solve the resulting linear inverse problem, but neglect to take into account the noise statistics. In this study we show that proper modelling of the noise distribution can improve substantially the quality of the reconstructed extinction profiles. To achieve this goal, we consider the non-linear inverse problem with non-negativity constraint, and propose two iterative algorithms derived using the Karush-Kuhn-Tucker conditions. We validate the algorithms with synthetic and experimental data. As expected, the proposed algorithms out-perform standard methods in terms of sensitivity to noise and reliability of the estimated profile.

  15. Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

    NASA Astrophysics Data System (ADS)

    Koleva, M. N.

    2011-11-01

    In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

  16. Stable scalable control of soliton propagation in broadband nonlinear optical waveguides

    NASA Astrophysics Data System (ADS)

    Peleg, Avner; Nguyen, Quan M.; Huynh, Toan T.

    2017-02-01

    We develop a method for achieving scalable transmission stabilization and switching of N colliding soliton sequences in optical waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss. We show that dynamics of soliton amplitudes in N-sequence transmission is described by a generalized N-dimensional predator-prey model. Stability and bifurcation analysis for the predator-prey model are used to obtain simple conditions on the physical parameters for robust transmission stabilization as well as on-off and off-on switching of M out of N soliton sequences. Numerical simulations for single-waveguide transmission with a system of N coupled nonlinear Schrödinger equations with 2 ≤ N ≤ 4 show excellent agreement with the predator-prey model's predictions and stable propagation over significantly larger distances compared with other broadband nonlinear single-waveguide systems. Moreover, stable on-off and off-on switching of multiple soliton sequences and stable multiple transmission switching events are demonstrated by the simulations. We discuss the reasons for the robustness and scalability of transmission stabilization and switching in waveguides with broadband delayed Raman response and narrowband nonlinear gain-loss, and explain their advantages compared with other broadband nonlinear waveguides.

  17. 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.

  18. Nonlinear multilayers as optical limiters

    NASA Astrophysics Data System (ADS)

    Turner-Valle, Jennifer Anne

    1998-10-01

    In this work we present a non-iterative technique for computing the steady-state optical properties of nonlinear multilayers and we examine nonlinear multilayer designs for optical limiters. Optical limiters are filters with intensity-dependent transmission designed to curtail the transmission of incident light above a threshold irradiance value in order to protect optical sensors from damage due to intense light. Thin film multilayers composed of nonlinear materials exhibiting an intensity-dependent refractive index are used as the basis for optical limiter designs in order to enhance the nonlinear filter response by magnifying the electric field in the nonlinear materials through interference effects. The nonlinear multilayer designs considered in this work are based on linear optical interference filter designs which are selected for their spectral properties and electric field distributions. Quarter wave stacks and cavity filters are examined for their suitability as sensor protectors and their manufacturability. The underlying non-iterative technique used to calculate the optical response of these filters derives from recognizing that the multi-valued calculation of output irradiance as a function of incident irradiance may be turned into a single-valued calculation of incident irradiance as a function of output irradiance. Finally, the benefits and drawbacks of using nonlinear multilayer for optical limiting are examined and future research directions are proposed.

  19. Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications☆

    PubMed Central

    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

  20. Flexible traffic control of the synfire-mode transmission by inhibitory modulation: Nonlinear noise reduction

    NASA Astrophysics Data System (ADS)

    Shinozaki, Takashi; Okada, Masato; Reyes, Alex D.; Câteau, Hideyuki

    2010-01-01

    Intermingled neural connections apparent in the brain make us wonder what controls the traffic of propagating activity in the brain to secure signal transmission without harmful crosstalk. Here, we reveal that inhibitory input but not excitatory input works as a particularly useful traffic controller because it controls the degree of synchrony of population firing of neurons as well as controlling the size of the population firing bidirectionally. Our dynamical system analysis reveals that the synchrony enhancement depends crucially on the nonlinear membrane potential dynamics and a hidden slow dynamical variable. Our electrophysiological study with rodent slice preparations show that the phenomenon happens in real neurons. Furthermore, our analysis with the Fokker-Planck equations demonstrates the phenomenon in a semianalytical manner.

  1. Numerical techniques for solving nonlinear instability problems in smokeless tactical solid rocket motors. [finite difference technique

    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.

  2. Solving deterministic non-linear programming problem using Hopfield artificial neural network and genetic programming techniques

    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.

  3. 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.

  4. Prediction of transmission distortion for wireless video communication: analysis.

    PubMed

    Chen, Zhifeng; Wu, Dapeng

    2012-03-01

    Transmitting video over wireless is a challenging problem since video may be seriously distorted due to packet errors caused by wireless channels. The capability of predicting transmission distortion (i.e., video distortion caused by packet errors) can assist in designing video encoding and transmission schemes that achieve maximum video quality or minimum end-to-end video distortion. This paper is aimed at deriving formulas for predicting transmission distortion. The contribution of this paper is twofold. First, we identify the governing law that describes how the transmission distortion process evolves over time and analytically derive the transmission distortion formula as a closed-form function of video frame statistics, channel error statistics, and system parameters. Second, we identify, for the first time, two important properties of transmission distortion. The first property is that the clipping noise, which is produced by nonlinear clipping, causes decay of propagated error. The second property is that the correlation between motion-vector concealment error and propagated error is negative and has dominant impact on transmission distortion, compared with other correlations. Due to these two properties and elegant error/distortion decomposition, our formula provides not only more accurate prediction but also lower complexity than the existing methods.

  5. Nonlinear Problems in Fluid Dynamics and Inverse Scattering

    DTIC Science & Technology

    1993-05-31

    nonlinear Kadomtsev - Petviashvili (KP) equations , have solutions which will become infinite in finite time. This phenomenon is sometimes referred to as...40 (November 1992). 4 7. Wave Collapse and Instability of Solitary Waves of a Generalized Nonlinear Kaoiomtsev- Petviashvili Equation , X.P. Wang, M.J...words) The inverse scattering of a class of differential-difference equations and multidimensional operators has been constructed. Solutions of nonlinear

  6. Absorption spectra and nonlinear transmission (at λ = 2940 nm) of a diffusion-doped Fe{sup 2+}:ZnSe single crystal

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bufetova, G A; Gulyamova, E S; Il'ichev, N N

    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:more » 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)« less

  7. A hybrid Boundary Element Unstructured Transmission-line (BEUT) method for accurate 2D electromagnetic simulation

    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.

  8. A hybrid Boundary Element Unstructured Transmission-line (BEUT) method for accurate 2D electromagnetic simulation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Simmons, Daniel, E-mail: daniel.simmons@nottingham.ac.uk; Cools, Kristof; Sewell, Phillip

    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 removesmore » 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. - Graphical abstract:.« less

  9. Compensation of nonlinearity in a fiber-optic transmission system using frequency-degenerate phase conjugation through counter-propagating dual pump FWM in a semiconductor optical amplifier

    NASA Astrophysics Data System (ADS)

    Anchal, Abhishek; K, Pradeep Kumar; O'Duill, Sean; Anandarajah, Prince M.; Landais, Pascal

    2018-04-01

    We present a scheme of frequency-degenerate mid-span spectral inversion (MSSI) for nonlinearity compensation in fiber-optic transmission systems. The spectral inversion is obtained by using counter-propagating dual pump four-wave mixing in a semiconductor optical amplifier (SOA). Frequency-degeneracy between signal and conjugate is achieved by keeping two pump frequencies symmetrical about the signal frequency. We simulate the performance of MSSI for nonlinearity compensation by scrutinizing the improvement of the Q-factor of a 200 Gbps QPSK signal transmitted over a standard single mode fiber, as a function of launch power for different span lengths and number of spans. We demonstrate a 7.5 dB improvement in the input power dynamic range and an almost 83% increase in the transmission length for optimum MSSI parameters of -2 dBm pump power and 400 mA SOA current.

  10. On a local solvability and stability of the inverse transmission eigenvalue problem

    NASA Astrophysics Data System (ADS)

    Bondarenko, Natalia; Buterin, Sergey

    2017-11-01

    We prove a local solvability and stability of the inverse transmission eigenvalue problem posed by McLaughlin and Polyakov (1994 J. Diff. Equ. 107 351-82). In particular, this result establishes the minimality of the data used therein. The proof is constructive.

  11. Supratransmission in a metastable modular metastructure for tunable non-reciprocal wave transmission

    NASA Astrophysics Data System (ADS)

    Wu, Zhen; Wang, K. W.

    2018-03-01

    In this research, we numerically and analytically investigate the nonlinear energy transmission phenomenon in a metastable modular metastructure. Numerical studies on a 1D metastable chain provide clear evidence that when driving frequency is within the stopband of the periodic structure, there exists a threshold for the driving amplitude, above which sudden increase in the energy transmission can be observed. This onset of transmission is due to nonlinear instability and is known as supratransmission. We discover that due to spatial asymmetry of strategically configured constituents, such transmission thresholds are considerably different when structure is excited from different ends and this discrepancy creates a region of non-reciprocal energy transmission. We demonstrate that when the loss of stability is due to saddlenode bifurcation, the transmission threshold can be predicted analytically using a localized nonlinear-linear system model, and analyzed via combining harmonic balancing and transfer matrix methods. These investigations elucidate the rich and complex dynamics achievable by nonlinearity and metastabilities, and provide synthesize tools for tunable bandgaps and non-reciprocal wave transmissions.

  12. Global and blowup solutions of a mixed problem with nonlinear boundary conditions for a one-dimensional semilinear wave equation

    NASA Astrophysics Data System (ADS)

    Kharibegashvili, S. S.; Jokhadze, O. M.

    2014-04-01

    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.

  13. A parallel multi-domain solution methodology applied to nonlinear thermal transport problems in nuclear fuel pins

    DOE PAGES

    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

  14. Two Studies of Complex Nonlinear Systems: Engineered Granular Crystals and Coarse-Graining Optimization Problems

    NASA Astrophysics Data System (ADS)

    Pozharskiy, Dmitry

    In recent years a nonlinear, acoustic metamaterial, named granular crystals, has gained prominence due to its high accessibility, both experimentally and computationally. The observation of a wide range of dynamical phenomena in the system, due to its inherent nonlinearities, has suggested its importance in many engineering applications related to wave propagation. In the first part of this dissertation, we explore the nonlinear dynamics of damped-driven granular crystals. In one case, we consider a highly nonlinear setting, also known as a sonic vacuum, and derive a nonlinear analogue of a linear spectrum, corresponding to resonant periodic propagation and antiresonances. Experimental studies confirm the computational findings and the assimilation of experimental data into a numerical model is demonstrated. In the second case, global bifurcations in a precompressed granular crystal are examined, and their involvement in the appearance of chaotic dynamics is demonstrated. Both results highlight the importance of exploring the nonlinear dynamics, to gain insight into how a granular crystal responds to different external excitations. In the second part, we borrow established ideas from coarse-graining of dynamical systems, and extend them to optimization problems. We combine manifold learning algorithms, such as Diffusion Maps, with stochastic optimization methods, such as Simulated Annealing, and show that we can retrieve an ensemble, of few, important parameters that should be explored in detail. This framework can lead to acceleration of convergence when dealing with complex, high-dimensional optimization, and could potentially be applied to design engineered granular crystals.

  15. Topology optimization for nonlinear dynamic problems: Considerations for automotive crashworthiness

    NASA Astrophysics Data System (ADS)

    Kaushik, Anshul; Ramani, Anand

    2014-04-01

    Crashworthiness of automotive structures is most often engineered after an optimal topology has been arrived at using other design considerations. This study is an attempt to incorporate crashworthiness requirements upfront in the topology synthesis process using a mathematically consistent framework. It proposes the use of equivalent linear systems from the nonlinear dynamic simulation in conjunction with a discrete-material topology optimizer. Velocity and acceleration constraints are consistently incorporated in the optimization set-up. Issues specific to crash problems due to the explicit solution methodology employed, nature of the boundary conditions imposed on the structure, etc. are discussed and possible resolutions are proposed. A demonstration of the methodology on two-dimensional problems that address some of the structural requirements and the types of loading typical of frontal and side impact is provided in order to show that this methodology has the potential for topology synthesis incorporating crashworthiness requirements.

  16. Multitrace/singletrace formulations and Domain Decomposition Methods for the solution of Helmholtz transmission problems for bounded composite scatterers

    NASA Astrophysics Data System (ADS)

    Jerez-Hanckes, Carlos; Pérez-Arancibia, Carlos; Turc, Catalin

    2017-12-01

    We present Nyström discretizations of multitrace/singletrace formulations and non-overlapping Domain Decomposition Methods (DDM) for the solution of Helmholtz transmission problems for bounded composite scatterers with piecewise constant material properties. We investigate the performance of DDM with both classical Robin and optimized transmission boundary conditions. The optimized transmission boundary conditions incorporate square root Fourier multiplier approximations of Dirichlet to Neumann operators. While the multitrace/singletrace formulations as well as the DDM that use classical Robin transmission conditions are not particularly well suited for Krylov subspace iterative solutions of high-contrast high-frequency Helmholtz transmission problems, we provide ample numerical evidence that DDM with optimized transmission conditions constitute efficient computational alternatives for these type of applications. In the case of large numbers of subdomains with different material properties, we show that the associated DDM linear system can be efficiently solved via hierarchical Schur complements elimination.

  17. Nonlinear Waves.

    DTIC Science & Technology

    1988-02-01

    in Multi- dimensions II, P.M. Santini and A.S. Fokas, preprint INS#67, 1986. The Recursion Operator of the Kadomtsev - Petviashvili Equation and the...solitons, multidimensional inverse problems, Painleve equations , direct linearizations of certain nonlinear wave equations , DBAR problems, Riemann...the Navy is (a) the recent discovery that many of the equations describing ship hydrodynamics in channels of finite depth obey nonlinear equations

  18. Recent advances in nonlinear passive vibration isolators

    NASA Astrophysics Data System (ADS)

    Ibrahim, R. A.

    2008-07-01

    The theory of nonlinear vibration isolation has witnessed significant developments due to pressing demands for the protection of structural installations, nuclear reactors, mechanical components, and sensitive instruments from earthquake ground motion, shocks, and impact loads. In view of these demands, engineers and physicists have developed different types of nonlinear vibration isolators. This article presents a comprehensive assessment of recent developments of nonlinear isolators in the absence of active control means. It does not deal with other means of linear or nonlinear vibration absorbers. It begins with the basic concept and features of nonlinear isolators and inherent nonlinear phenomena. Specific types of nonlinear isolators are then discussed, including ultra-low-frequency isolators. For vertical vibration isolation, the treatment of the Euler spring isolator is based on the post-buckling dynamic characteristics of the column elastica and axial stiffness. Exact and approximate analyses of axial stiffness of the post-buckled Euler beam are outlined. Different techniques of reducing the resonant frequency of the isolator are described. Another group is based on the Gospodnetic-Frisch-Fay beam, which is free to slide on two supports. The restoring force of this beam resembles to a great extent the restoring roll moment of biased ships. The base isolation of buildings, bridges, and liquid storage tanks subjected to earthquake ground motion is then described. Base isolation utilizes friction elements, laminated-rubber bearings, and the friction pendulum. Nonlinear viscoelastic and composite material springs, and smart material elements are described in terms of material mechanical characteristics and the dependence of their transmissibility on temperature and excitation amplitude. The article is closed by conclusions, which highlight resolved and unresolved problems and recommendations for future research directions.

  19. Near-optimal alternative generation using modified hit-and-run sampling for non-linear, non-convex problems

    NASA Astrophysics Data System (ADS)

    Rosenberg, D. E.; Alafifi, A.

    2016-12-01

    Water resources systems analysis often focuses on finding optimal solutions. Yet an optimal solution is optimal only for the modelled issues and managers often seek near-optimal alternatives that address un-modelled objectives, preferences, limits, uncertainties, and other issues. Early on, Modelling to Generate Alternatives (MGA) formalized near-optimal as the region comprising the original problem constraints plus a new constraint that allowed performance within a specified tolerance of the optimal objective function value. MGA identified a few maximally-different alternatives from the near-optimal region. Subsequent work applied Markov Chain Monte Carlo (MCMC) sampling to generate a larger number of alternatives that span the near-optimal region of linear problems or select portions for non-linear problems. We extend the MCMC Hit-And-Run method to generate alternatives that span the full extent of the near-optimal region for non-linear, non-convex problems. First, start at a feasible hit point within the near-optimal region, then run a random distance in a random direction to a new hit point. Next, repeat until generating the desired number of alternatives. The key step at each iterate is to run a random distance along the line in the specified direction to a new hit point. If linear equity constraints exist, we construct an orthogonal basis and use a null space transformation to confine hits and runs to a lower-dimensional space. Linear inequity constraints define the convex bounds on the line that runs through the current hit point in the specified direction. We then use slice sampling to identify a new hit point along the line within bounds defined by the non-linear inequity constraints. This technique is computationally efficient compared to prior near-optimal alternative generation techniques such MGA, MCMC Metropolis-Hastings, evolutionary, or firefly algorithms because search at each iteration is confined to the hit line, the algorithm can move in one

  20. The Nonlinear Steepest Descent Method to Long-Time Asymptotics of the Coupled Nonlinear Schrödinger Equation

    NASA Astrophysics Data System (ADS)

    Geng, Xianguo; Liu, Huan

    2018-04-01

    The Riemann-Hilbert problem for the coupled nonlinear Schrödinger equation is formulated on the basis of the corresponding 3× 3 matrix spectral problem. Using the nonlinear steepest descent method, we obtain leading-order asymptotics for the Cauchy problem of the coupled nonlinear Schrödinger equation.

  1. Model-based nonlinear control of hydraulic servo systems: Challenges, developments and perspectives

    NASA Astrophysics Data System (ADS)

    Yao, Jianyong

    2018-06-01

    Hydraulic servo system plays a significant role in industries, and usually acts as a core point in control and power transmission. Although linear theory-based control methods have been well established, advanced controller design methods for hydraulic servo system to achieve high performance is still an unending pursuit along with the development of modern industry. Essential nonlinearity is a unique feature and makes model-based nonlinear control more attractive, due to benefit from prior knowledge of the servo valve controlled hydraulic system. In this paper, a discussion for challenges in model-based nonlinear control, latest developments and brief perspectives of hydraulic servo systems are presented: Modelling uncertainty in hydraulic system is a major challenge, which includes parametric uncertainty and time-varying disturbance; some specific requirements also arise ad hoc difficulties such as nonlinear friction during low velocity tracking, severe disturbance, periodic disturbance, etc.; to handle various challenges, nonlinear solutions including parameter adaptation, nonlinear robust control, state and disturbance observation, backstepping design and so on, are proposed and integrated, theoretical analysis and lots of applications reveal their powerful capability to solve pertinent problems; and at the end, some perspectives and associated research topics (measurement noise, constraints, inner valve dynamics, input nonlinearity, etc.) in nonlinear hydraulic servo control are briefly explored and discussed.

  2. 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.

  3. An iterative kernel based method for fourth order nonlinear equation with nonlinear boundary condition

    NASA Astrophysics Data System (ADS)

    Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

    2018-06-01

    This article discusses an iterative reproducing kernel method with respect to its effectiveness and capability of solving a fourth-order boundary value problem with nonlinear boundary conditions modeling beams on elastic foundations. Since there is no method of obtaining reproducing kernel which satisfies nonlinear boundary conditions, the standard reproducing kernel methods cannot be used directly to solve boundary value problems with nonlinear boundary conditions as there is no knowledge about the existence and uniqueness of the solution. The aim of this paper is, therefore, to construct an iterative method by the use of a combination of reproducing kernel Hilbert space method and a shooting-like technique to solve the mentioned problems. Error estimation for reproducing kernel Hilbert space methods for nonlinear boundary value problems have yet to be discussed in the literature. In this paper, we present error estimation for the reproducing kernel method to solve nonlinear boundary value problems probably for the first time. Some numerical results are given out to demonstrate the applicability of the method.

  4. Optimal packing for cascaded regenerative transmission based on phase sensitive amplifiers.

    PubMed

    Sorokina, Mariia; Sygletos, Stylianos; Ellis, Andrew D; Turitsyn, Sergei

    2013-12-16

    We investigate the transmission performance of advanced modulation formats in nonlinear regenerative channels based on cascaded phase sensitive amplifiers. We identify the impact of amplitude and phase noise dynamics along the transmission line and show that after a cascade of regenerators, densely packed single ring PSK constellations outperform multi-ring constellations. The results of this study will greatly simplify the design of future nonlinear regenerative channels for ultra-high capacity transmission.

  5. The intergenerational transmission of problem gambling: The mediating role of offspring gambling expectancies and motives.

    PubMed

    Dowling, N A; Oldenhof, E; Shandley, K; Youssef, G J; Vasiliadis, S; Thomas, S A; Frydenberg, E; Jackson, A C

    2018-02-01

    The risk for developing a gambling problem is greater among offspring who have a problem gambling parent, yet little research has directly examined the mechanisms by which this transmission of problem gambling occurs. For this reason, the present study sought to examine the degree to which children's expectancies and motives relating to gambling explain, at least in part, the intergenerational transmission of problem gambling. Participants (N=524; 56.5% male) were recruited from educational institutions, and retrospectively reported on parental problem gambling. Problem gambling was measured using the Problem Gambling Severity Index and a range of positive and negative expectancies and gambling motives were explored as potential mediators of the relationship between parent-and-participant problem gambling. The relationship between parent-and-participant problem gambling was significant, and remained so after controlling for sociodemographic factors and administration method. Significant mediators of this relationship included self-enhancement expectancies (feeling in control), money expectancies (financial gain), over-involvement (preoccupation with gambling) and emotional impact expectancies (guilt, shame, and loss), as well as enhancement motives (gambling to increase positive feelings) and coping motives (gambling to reduce or avoid negative emotions). All mediators remained significant when entered into the same model. The findings highlight that gambling expectancies and motives present unique pathways to the development of problem gambling in the offspring of problem gambling parents, and suggest that gambling cognitions may be potential candidates for targeted interventions for the offspring of problem gamblers. Copyright © 2017 Elsevier Ltd. All rights reserved.

  6. A new impedance accounting for short- and long-range effects in mixed substructured formulations of nonlinear problems

    NASA Astrophysics Data System (ADS)

    Negrello, Camille; Gosselet, Pierre; Rey, Christian

    2018-05-01

    An efficient method for solving large nonlinear problems combines Newton solvers and Domain Decomposition Methods (DDM). In the DDM framework, the boundary conditions can be chosen to be primal, dual or mixed. The mixed approach presents the advantage to be eligible for the research of an optimal interface parameter (often called impedance) which can increase the convergence rate. The optimal value for this parameter is often too expensive to be computed exactly in practice: an approximate version has to be sought for, along with a compromise between efficiency and computational cost. In the context of parallel algorithms for solving nonlinear structural mechanical problems, we propose a new heuristic for the impedance which combines short and long range effects at a low computational cost.

  7. Control of terahertz nonlinear transmission with electrically gated graphene metadevices.

    PubMed

    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.

  8. Model-Based Adaptive Event-Triggered Control of Strict-Feedback Nonlinear Systems.

    PubMed

    Li, Yuan-Xin; Yang, Guang-Hong

    2018-04-01

    This paper is concerned with the adaptive event-triggered control problem of nonlinear continuous-time systems in strict-feedback form. By using the event-sampled neural network (NN) to approximate the unknown nonlinear function, an adaptive model and an associated event-triggered controller are designed by exploiting the backstepping method. In the proposed method, the feedback signals and the NN weights are aperiodically updated only when the event-triggered condition is violated. A positive lower bound on the minimum intersample time is guaranteed to avoid accumulation point. The closed-loop stability of the resulting nonlinear impulsive dynamical system is rigorously proved via Lyapunov analysis under an adaptive event sampling condition. In comparing with the traditional adaptive backstepping design with a fixed sample period, the event-triggered method samples the state and updates the NN weights only when it is necessary. Therefore, the number of transmissions can be significantly reduced. Finally, two simulation examples are presented to show the effectiveness of the proposed control method.

  9. Study on Heat Transfer Agent Models of Transmission Line and Transformer

    NASA Astrophysics Data System (ADS)

    Wang, B.; Zhang, P. P.

    2018-04-01

    When using heat transfer simulation to study the dynamic overload of transmission line and transformer, it needs to establish the mathematical expression of heat transfer. However, the formula is a nonlinear differential equation or equation set and it is not easy to get general solutions. Aiming at this problem, some different temperature change processes caused by different initial conditions are calculated by differential equation and equation set. New agent models are developed according to the characteristics of different temperature change processes. The results show that the agent models have high precision and can solve the problem that the original equation cannot be directly applied in some practical engineers.

  10. Advanced Computational Methods for Security Constrained Financial Transmission Rights

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kalsi, Karanjit; Elbert, Stephen T.; Vlachopoulou, Maria

    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 reformulationmore » 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.« less

  11. Linear SFM: A hierarchical approach to solving structure-from-motion problems by decoupling the linear and nonlinear components

    NASA Astrophysics Data System (ADS)

    Zhao, Liang; Huang, Shoudong; Dissanayake, Gamini

    2018-07-01

    This paper presents a novel hierarchical approach to solving structure-from-motion (SFM) problems. The algorithm begins with small local reconstructions based on nonlinear bundle adjustment (BA). These are then joined in a hierarchical manner using a strategy that requires solving a linear least squares optimization problem followed by a nonlinear transform. The algorithm can handle ordered monocular and stereo image sequences. Two stereo images or three monocular images are adequate for building each initial reconstruction. The bulk of the computation involves solving a linear least squares problem and, therefore, the proposed algorithm avoids three major issues associated with most of the nonlinear optimization algorithms currently used for SFM: the need for a reasonably accurate initial estimate, the need for iterations, and the possibility of being trapped in a local minimum. Also, by summarizing all the original observations into the small local reconstructions with associated information matrices, the proposed Linear SFM manages to preserve all the information contained in the observations. The paper also demonstrates that the proposed problem formulation results in a sparse structure that leads to an efficient numerical implementation. The experimental results using publicly available datasets show that the proposed algorithm yields solutions that are very close to those obtained using a global BA starting with an accurate initial estimate. The C/C++ source code of the proposed algorithm is publicly available at https://github.com/LiangZhaoPKUImperial/LinearSFM.

  12. Non-intrusive reduced order modeling of nonlinear problems using neural networks

    NASA Astrophysics Data System (ADS)

    Hesthaven, J. S.; Ubbiali, S.

    2018-06-01

    We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial differential equations (PDEs). The method extracts a reduced basis from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD) and employs artificial neural networks (ANNs), particularly multi-layer perceptrons (MLPs), to accurately approximate the coefficients of the reduced model. The search for the optimal number of neurons and the minimum amount of training samples to avoid overfitting is carried out in the offline phase through an automatic routine, relying upon a joint use of the Latin hypercube sampling (LHS) and the Levenberg-Marquardt (LM) training algorithm. This guarantees a complete offline-online decoupling, leading to an efficient RB method - referred to as POD-NN - suitable also for general nonlinear problems with a non-affine parametric dependence. Numerical studies are presented for the nonlinear Poisson equation and for driven cavity viscous flows, modeled through the steady incompressible Navier-Stokes equations. Both physical and geometrical parametrizations are considered. Several results confirm the accuracy of the POD-NN method and show the substantial speed-up enabled at the online stage as compared to a traditional RB strategy.

  13. Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods. Ph.D. Thesis - Paris Univ.; [mathematical models of transonic flow using nonlinear equations

    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.

  14. Variational finite-difference methods in linear and nonlinear problems of the deformation of metallic and composite shells (review)

    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)

  15. Fundamental bounds on the operation of Fano nonlinear isolators

    NASA Astrophysics Data System (ADS)

    Sounas, Dimitrios L.; Alù, Andrea

    2018-03-01

    Nonlinear isolators have attracted significant attention for their ability to break reciprocity and provide isolation without the need of an external bias. A popular approach for the design of such devices is based on Fano resonators, which, due to their sharp frequency response, can lead to very large isolation for moderate input intensities. Here, we show that, independent of their specific implementation, these devices are subject to fundamental bounds on the transmission coefficient in the forward direction versus their quality factor, input power, and nonreciprocal intensity range. Our analysis quantifies a general tradeoff between forward transmission and these metrics, stemming directly from time-reversal symmetry, and that unitary transmission is only possible for vanishing nonreciprocity. Our results also shed light on the operation of resonant nonlinear isolators, reveal their fundamental limitations, and provide indications on how it is possible to design nonlinear isolators with optimal performance.

  16. Arnold tongues in a billiard problem in nonlinear and nonequilibrium systems

    NASA Astrophysics Data System (ADS)

    Miyaji, Tomoyuki

    2017-02-01

    We study a billiard problem in nonlinear and nonequilibrium systems. This is motivated by the motions of a traveling spot in a reaction-diffusion system (RDS) in a rectangular domain. We consider a four-dimensional dynamical system, defined by ordinary differential equations. This was first derived by S.-I. Ei et al. (2006), based on a reduced system on the center manifold in a neighborhood of a pitchfork bifurcation of a stationary spot for the RDS. In contrast to the classical billiard problem, this defines a dynamical system that is dissipative rather than conservative, and has an attractor. According to previous numerical studies, the attractor of the system changes depending on parameters such as the aspect ratio of the domain. It may be periodic, quasi-periodic, or chaotic. In this paper, we elucidate that it results from parameters crossing Arnold tongues and that the organizing center is a Hopf-Hopf bifurcation of the trivial equilibrium.

  17. Solid-state repetitive generator with a gyromagnetic nonlinear transmission line operating as a peak power amplifier

    NASA Astrophysics Data System (ADS)

    Gusev, A. I.; Pedos, M. S.; Rukin, S. N.; Timoshenkov, S. P.

    2017-07-01

    In this work, experiments were made in which gyromagnetic nonlinear transmission line (NLTL) operates as a peak power amplifier of the input pulse. At such an operating regime, the duration of the input pulse is close to the period of generated oscillations, and the main part of the input pulse energy is transmitted only to the first peak of the oscillations. Power amplification is achieved due to the voltage amplitude of the first peak across the NLTL output exceeding the voltage amplitude of the input pulse. In the experiments, the input pulse with an amplitude of 500 kV and a half-height pulse duration of 7 ns is applied to the NLTL with a natural oscillation frequency of ˜300 MHz. At the output of the NLTL in 40 Ω coaxial transmission line, the pulse amplitude is increased to 740 kV and the pulse duration is reduced to ˜2 ns, which correspond to power amplification of the input pulse from ˜6 to ˜13 GW. As a source of input pulses, a solid-state semiconductor opening switch generator was used, which allowed carrying out experiments at pulse repetition frequency up to 1 kHz in the burst mode of operation.

  18. Parallel-vector computation for linear structural analysis and non-linear unconstrained optimization problems

    NASA Technical Reports Server (NTRS)

    Nguyen, D. T.; Al-Nasra, M.; Zhang, Y.; Baddourah, M. A.; Agarwal, T. K.; Storaasli, O. O.; Carmona, E. A.

    1991-01-01

    Several parallel-vector computational improvements to the unconstrained optimization procedure are described which speed up the structural analysis-synthesis process. A fast parallel-vector Choleski-based equation solver, pvsolve, is incorporated into the well-known SAP-4 general-purpose finite-element code. The new code, denoted PV-SAP, is tested for static structural analysis. Initial results on a four processor CRAY 2 show that using pvsolve reduces the equation solution time by a factor of 14-16 over the original SAP-4 code. In addition, parallel-vector procedures for the Golden Block Search technique and the BFGS method are developed and tested for nonlinear unconstrained optimization. A parallel version of an iterative solver and the pvsolve direct solver are incorporated into the BFGS method. Preliminary results on nonlinear unconstrained optimization test problems, using pvsolve in the analysis, show excellent parallel-vector performance indicating that these parallel-vector algorithms can be used in a new generation of finite-element based structural design/analysis-synthesis codes.

  19. 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.

    2017-07-01

    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.

  20. Analysis of influence and improvement measures on laser weapons induced by laser atmospheric transmission

    NASA Astrophysics Data System (ADS)

    Che, Jinxi; Zhang, Jinchun; Yang, Haiqiang; Li, Yu; Wang, Hongjun

    2018-02-01

    In the course of atmospheric transmission, laser atmospheric transmission study a series of linear optical effect produced by the interaction of atmosphere and laser and non-linear effect and the influence of laser transmission due to these effects. In this paper, the linear effects of atmosphere refringence, absorption, scattering and turbulence affecting laser transmission were analyzed. And the non-linear effects affecting laser atmosphere transmission were also analyzed. On this basis, the corresponding improvement measures were analyzed. To understand and master the laws of laser atmospheric transmission and study avoiding or as far as possible decreasing the influence of laser transmission induced by atmosphere, the outcome can be referred.

  1. Optimal temperature for malaria transmission is dramaticallylower than previously predicted

    USGS Publications Warehouse

    Mordecai, Eerin A.; Paaijmans, Krijin P.; Johnson, Leah R.; Balzer, Christian; Ben-Horin, Tal; de Moor, Emily; McNally, Amy; Pawar, Samraat; Ryan, Sadie J.; Smith, Thomas C.; Lafferty, Kevin D.

    2013-01-01

    The ecology of mosquito vectors and malaria parasites affect the incidence, seasonal transmission and geographical range of malaria. Most malaria models to date assume constant or linear responses of mosquito and parasite life-history traits to temperature, predicting optimal transmission at 31 °C. These models are at odds with field observations of transmission dating back nearly a century. We build a model with more realistic ecological assumptions about the thermal physiology of insects. Our model, which includes empirically derived nonlinear thermal responses, predicts optimal malaria transmission at 25 °C (6 °C lower than previous models). Moreover, the model predicts that transmission decreases dramatically at temperatures > 28 °C, altering predictions about how climate change will affect malaria. A large data set on malaria transmission risk in Africa validates both the 25 °C optimum and the decline above 28 °C. Using these more accurate nonlinear thermal-response models will aid in understanding the effects of current and future temperature regimes on disease transmission.

  2. Superconducting nanowires as nonlinear inductive elements for qubits

    NASA Astrophysics Data System (ADS)

    Ku, Jaseung; Manucharyan, Vladimir; Bezryadin, Alexey

    2011-03-01

    We report microwave transmission measurements of superconducting Fabry-Perot resonators, having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low-quality factor sample exhibits a ``crater'' at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. NSF DMR-1005645, DOE DO-FG02-07ER46453.

  3. Breaking beta: deconstructing the parasite transmission function

    PubMed Central

    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

  4. Highly accurate adaptive finite element schemes for nonlinear hyperbolic problems

    NASA Astrophysics Data System (ADS)

    Oden, J. T.

    1992-08-01

    This document is a final report of research activities supported under General Contract DAAL03-89-K-0120 between the Army Research Office and the University of Texas at Austin from July 1, 1989 through June 30, 1992. The project supported several Ph.D. students over the contract period, two of which are scheduled to complete dissertations during the 1992-93 academic year. Research results produced during the course of this effort led to 6 journal articles, 5 research reports, 4 conference papers and presentations, 1 book chapter, and two dissertations (nearing completion). It is felt that several significant advances were made during the course of this project that should have an impact on the field of numerical analysis of wave phenomena. These include the development of high-order, adaptive, hp-finite element methods for elastodynamic calculations and high-order schemes for linear and nonlinear hyperbolic systems. Also, a theory of multi-stage Taylor-Galerkin schemes was developed and implemented in the analysis of several wave propagation problems, and was configured within a general hp-adaptive strategy for these types of problems. Further details on research results and on areas requiring additional study are given in the Appendix.

  5. FAST TRACK PAPER: Non-iterative multiple-attenuation methods: linear inverse solutions to non-linear inverse problems - II. BMG approximation

    NASA Astrophysics Data System (ADS)

    Ikelle, Luc T.; Osen, Are; Amundsen, Lasse; Shen, Yunqing

    2004-12-01

    The classical linear solutions to the problem of multiple attenuation, like predictive deconvolution, τ-p filtering, or F-K filtering, are generally fast, stable, and robust compared to non-linear solutions, which are generally either iterative or in the form of a series with an infinite number of terms. These qualities have made the linear solutions more attractive to seismic data-processing practitioners. However, most linear solutions, including predictive deconvolution or F-K filtering, contain severe assumptions about the model of the subsurface and the class of free-surface multiples they can attenuate. These assumptions limit their usefulness. In a recent paper, we described an exception to this assertion for OBS data. We showed in that paper that a linear and non-iterative solution to the problem of attenuating free-surface multiples which is as accurate as iterative non-linear solutions can be constructed for OBS data. We here present a similar linear and non-iterative solution for attenuating free-surface multiples in towed-streamer data. For most practical purposes, this linear solution is as accurate as the non-linear ones.

  6. A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions.

    PubMed

    Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin

    2016-01-01

    This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.

  7. Mapping Environmental Suitability for Malaria Transmission, Greece

    PubMed Central

    Sudre, Bertrand; Rossi, Massimiliano; Van Bortel, Wim; Danis, Kostas; Baka, Agoritsa; Vakalis, Nikos

    2013-01-01

    During 2009–2012, Greece experienced a resurgence of domestic malaria transmission. To help guide malaria response efforts, we used spatial modeling to characterize environmental signatures of areas suitable for transmission. Nonlinear discriminant analysis indicated that sea-level altitude and land-surface temperature parameters are predictive in this regard. PMID:23697370

  8. 77 FR 32183 - Transmission Planning and Cost Allocation by Transmission Owning and Operating Public Utilities

    Federal Register 2010, 2011, 2012, 2013, 2014

    2012-05-31

    ... it would not wait for systemic problems to undermine transmission planning before action is taken... that the development of transmission facilities can involve long lead times and complex problems... rather than allowing the problems in transmission planning and cost allocation to continue or to increase...

  9. Conditional nonlinear optimal perturbations based on the particle swarm optimization and their applications to the predictability problems

    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

  10. A numerical scheme for nonlinear Helmholtz equations with strong nonlinear optical effects.

    PubMed

    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.

  11. 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.

  12. Performance bounds for nonlinear systems with a nonlinear ℒ2-gain property

    NASA Astrophysics Data System (ADS)

    Zhang, Huan; Dower, Peter M.

    2012-09-01

    Nonlinear ℒ2-gain is a finite gain concept that generalises the notion of conventional (linear) finite ℒ2-gain to admit the application of ℒ2-gain analysis tools of a broader class of nonlinear systems. The computation of tight comparison function bounds for this nonlinear ℒ2-gain property is important in applications such as small gain design. This article presents an approximation framework for these comparison function bounds through the formulation and solution of an optimal control problem. Key to the solution of this problem is the lifting of an ℒ2-norm input constraint, which is facilitated via the introduction of an energy saturation operator. This admits the solution of the optimal control problem of interest via dynamic programming and associated numerical methods, leading to the computation of the proposed bounds. Two examples are presented to demonstrate this approach.

  13. Exact Solution of a Faraday's Law Problem that Includes a Nonlinear Term and Its Implication for Perturbation Theory.

    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)

  14. FRF decoupling of nonlinear systems

    NASA Astrophysics Data System (ADS)

    Kalaycıoğlu, Taner; Özgüven, H. Nevzat

    2018-03-01

    Structural decoupling problem, i.e. predicting dynamic behavior of a particular substructure from the knowledge of the dynamics of the coupled structure and the other substructure, has been well investigated for three decades and led to several decoupling methods. In spite of the inherent nonlinearities in a structural system in various forms such as clearances, friction and nonlinear stiffness, all decoupling studies are for linear systems. In this study, decoupling problem for nonlinear systems is addressed for the first time. A method, named as FRF Decoupling Method for Nonlinear Systems (FDM-NS), is proposed for calculating FRFs of a substructure decoupled from a coupled nonlinear structure where nonlinearity can be modeled as a single nonlinear element. Depending on where nonlinear element is, i.e., either in the known or unknown subsystem, or at the connection point, the formulation differs. The method requires relative displacement information between two end points of the nonlinear element, in addition to point and transfer FRFs at some points of the known subsystem. However, it is not necessary to excite the system from the unknown subsystem even when the nonlinear element is in that subsystem. The validation of FDM-NS is demonstrated with two different case studies using nonlinear lumped parameter systems. Finally, a nonlinear experimental test structure is used in order to show the real-life application and accuracy of FDM-NS.

  15. 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.

  16. Nonlinear problems in data-assimilation : Can synchronization help?

    NASA Astrophysics Data System (ADS)

    Tribbia, J. J.; Duane, G. S.

    2009-12-01

    Over the past several years, operational weather centers have initiated ensemble prediction and assimilation techniques to estimate the error covariance of forecasts in the short and the medium range. The ensemble techniques used are based on linear methods. The theory This technique s been shown to be a useful indicator of skill in the linear range where forecast errors are small relative to climatological variance. While this advance has been impressive, there are still ad hoc aspects of its use in practice, like the need for covariance inflation which are troubling. Furthermore, to be of utility in the nonlinear range an ensemble assimilation and prediction method must be capable of giving probabilistic information for the situation where a probability density forecast becomes multi-modal. A prototypical, simplest example of such a situation is the planetary-wave regime transition where the pdf is bimodal. Our recent research show how the inconsistencies and extensions of linear methodology can be consistently treated using the paradigm of synchronization which views the problems of assimilation and forecasting as that of optimizing the forecast model state with respect to the future evolution of the atmosphere.

  17. Optimal temperature for malaria transmission is dramatically lower than previously predicted

    USGS Publications Warehouse

    Mordecai, Erin A.; Paaijmans, Krijn P.; Johnson, Leah R.; Balzer, Christian; Ben-Horin, Tal; de Moor, Emily; McNally, Amy; Pawar, Samraat; Ryan, Sadie J.; Smith, Thomas C.; Lafferty, Kevin D.

    2013-01-01

    The ecology of mosquito vectors and malaria parasites affect the incidence, seasonal transmission and geographical range of malaria. Most malaria models to date assume constant or linear responses of mosquito and parasite life-history traits to temperature, predicting optimal transmission at 31 °C. These models are at odds with field observations of transmission dating back nearly a century. We build a model with more realistic ecological assumptions about the thermal physiology of insects. Our model, which includes empirically derived nonlinear thermal responses, predicts optimal malaria transmission at 25 °C (6 °C lower than previous models). Moreover, the model predicts that transmission decreases dramatically at temperatures > 28 °C, altering predictions about how climate change will affect malaria. A large data set on malaria transmission risk in Africa validates both the 25 °C optimum and the decline above 28 °C. Using these more accurate nonlinear thermal-response models will aid in understanding the effects of current and future temperature regimes on disease transmission.

  18. Transmission sputtering under diatomic molecule bombardment. Model calculations

    NASA Astrophysics Data System (ADS)

    Bitensky, I. S.

    1996-04-01

    Transmission sputtering means that emission of secondary particles is studied from the downstream side of a bombarded foil. Nonlinear effects in sputtering manifest themselves as a deviation of sputtering yield under molecular ion bombardment from the sum of the yields induced by the constituents at the same velocity. In the reflection geometry the overlap of the spike regions reaches maximum, while in transmission the degree of overlap depends on the projectile and on the foil thickness. It has been shown that the transmission sputtering yield can be described by a function of a scaling parameter determined by beam-foil characteristics and a mechanism of nonlinear sputtering. Calculations of the transmission yield have been made in the thermal spike and shock wave models. The results of calculations are compared with experimental data on phenylalanine molecular ion desorption from organic targets induced by Au + and Au 2+ impact. Suggestions for further experimental study are made.

  19. Recasting the theory of mosquito-borne pathogen transmission dynamics and control.

    PubMed

    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.

  20. Recasting the theory of mosquito-borne pathogen transmission dynamics and control

    PubMed Central

    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

  1. A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wollaber, Allan B., E-mail: wollaber@lanl.go; Larsen, Edward W., E-mail: edlarsen@umich.ed

    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, wemore » 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.« less

  2. A linear stability analysis for nonlinear, grey, thermal radiative transfer problems

    NASA Astrophysics Data System (ADS)

    Wollaber, Allan B.; Larsen, Edward W.

    2011-02-01

    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 α, the IMC time-discretization parameter, satisfies 0.5 < α ⩽ 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.

  3. Superconducting nanowires as nonlinear inductive elements for qubits

    NASA Astrophysics Data System (ADS)

    Ku, Jaseung; Manucharyan, Vladimir; Bezryadin, Alexey

    2010-10-01

    We report microwave transmission measurements of superconducting Fabry-Perot resonators, having a superconducting nanowire placed at a supercurrent antinode. As the plasma oscillation is excited, the supercurrent is forced to flow through the nanowire. The microwave transmission of the resonator-nanowire device shows a nonlinear resonance behavior, significantly dependent on the amplitude of the supercurrent oscillation. We show that such amplitude-dependent response is due to the nonlinearity of the current-phase relationship of the nanowire. The results are explained within a nonlinear oscillator model of the Duffing oscillator, in which the nanowire acts as a purely inductive element, in the limit of low temperatures and low amplitudes. The low-quality factor sample exhibits a “crater” at the resonance peak at higher driving power, which is due to dissipation. We observe a hysteretic bifurcation behavior of the transmission response to frequency sweep in a sample with a higher quality factor. The Duffing model is used to explain the Duffing bistability diagram. We also propose a concept of a nanowire-based qubit that relies on the current dependence of the kinetic inductance of a superconducting nanowire.

  4. Nonlinear Wavefront Control with All-Dielectric Metasurfaces

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wang, Lei; Kruk, Sergey; Koshelev, Kirill

    Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

  5. Nonlinear Wavefront Control with All-Dielectric Metasurfaces.

    PubMed

    Wang, Lei; Kruk, Sergey; Koshelev, Kirill; Kravchenko, Ivan; Luther-Davies, Barry; Kivshar, Yuri

    2018-06-13

    Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront of parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Our nonlinear metasurfaces produce phase gradients over a full 0-2π phase range with a 92% diffraction efficiency.

  6. Nonlinear Wavefront Control with All-Dielectric Metasurfaces

    DOE PAGES

    Wang, Lei; Kruk, Sergey; Koshelev, Kirill; ...

    2018-05-11

    Metasurfaces, two-dimensional lattices of nanoscale resonators, offer unique opportunities for functional flat optics and allow the control of the transmission, reflection, and polarization of a wavefront of light. Recently, all-dielectric metasurfaces reached remarkable efficiencies, often matching or out-performing conventional optical elements. The exploitation of the nonlinear optical response of metasurfaces offers a paradigm shift in nonlinear optics, and dielectric nonlinear metasurfaces are expected to enrich subwavelength photonics by enhancing substantially nonlinear response of natural materials combined with the efficient control of the phase of nonlinear waves. Here, we suggest a novel and rather general approach for engineering the wavefront ofmore » parametric waves of arbitrary complexity generated by a nonlinear metasurface. We design all-dielectric nonlinear metasurfaces, achieve a highly efficient wavefront control of a third-harmonic field, and demonstrate the generation of nonlinear beams at a designed angle and the generation of nonlinear focusing vortex beams. Lastly, our nonlinear metasurfaces produce phase gradients over a full 0–2π phase range with a 92% diffraction efficiency.« less

  7. Steady induction effects in geomagnetism. Part 1B: Geomagnetic estimation of steady surficial core motions: A non-linear inverse problem

    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.

  8. 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).

  9. Dispersion and nonlinear effects in OFDM-RoF system

    NASA Astrophysics Data System (ADS)

    Alhasson, Bader H.; Bloul, Albe M.; Matin, M.

    2010-08-01

    The radio-over-fiber (RoF) network has been a proven technology to be the best candidate for the wireless-access technology, and the orthogonal frequency division multiplexing (OFDM) technique has been established as the core technology in the physical layer of next generation wireless communication system, as a result OFDM-RoF has drawn attentions worldwide and raised many new research topics recently. At the present time, the trend of information industry is towards mobile, wireless, digital and broadband. The next generation network (NGN) has motivated researchers to study higher-speed wider-band multimedia communication to transmit (voice, data, and all sorts of media such as video) at a higher speed. The NGN would offer services that would necessitate broadband networks with bandwidth higher than 2Mbit/s per radio channel. Many new services emerged, such as Internet Protocol TV (IPTV), High Definition TV (HDTV), mobile multimedia and video stream media. Both speed and capacity have been the key objectives in transmission. In the meantime, the demand for transmission bandwidth increased at a very quick pace. The coming of 4G and 5G era will provide faster data transmission and higher bit rate and bandwidth. Taking advantages of both optical communication and wireless communication, OFDM Radio over Fiber (OFDM-RoF) system is characterized by its high speed, large capacity and high spectral efficiency. However, up to the present there are some problems to be solved, such as dispersion and nonlinearity effects. In this paper we will study the dispersion and nonlinearity effects and their elimination in OFDM-radio-over-fiber system.

  10. State estimation with incomplete nonlinear constraint

    NASA Astrophysics Data System (ADS)

    Huang, Yuan; Wang, Xueying; An, Wei

    2017-10-01

    A problem of state estimation with a new constraints named incomplete nonlinear constraint is considered. The targets are often move in the curve road, if the width of road is neglected, the road can be considered as the constraint, and the position of sensors, e.g., radar, is known in advance, this info can be used to enhance the performance of the tracking filter. The problem of how to incorporate the priori knowledge is considered. In this paper, a second-order sate constraint is considered. A fitting algorithm of ellipse is adopted to incorporate the priori knowledge by estimating the radius of the trajectory. The fitting problem is transformed to the nonlinear estimation problem. The estimated ellipse function is used to approximate the nonlinear constraint. Then, the typical nonlinear constraint methods proposed in recent works can be used to constrain the target state. Monte-Carlo simulation results are presented to illustrate the effectiveness proposed method in state estimation with incomplete constraint.

  11. Application and flight test of linearizing transformations using measurement feedback to the nonlinear control problem

    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.

  12. The neural network approximation method for solving multidimensional nonlinear inverse problems of geophysics

    NASA Astrophysics Data System (ADS)

    Shimelevich, M. I.; Obornev, E. A.; Obornev, I. E.; Rodionov, E. A.

    2017-07-01

    The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters n × 103 of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.

  13. Solution of large nonlinear quasistatic structural mechanics problems on distributed-memory multiprocessor computers

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    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 assemblemore » 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.« less

  14. [Problems in the transmission of information during within-hospital medical consultations and referrals].

    PubMed

    Montero Ruiz, E; Rebollar Merino, Á; Melgar Molero, V; Barbero Allende, J M; Culebras López, A; López Álvarez, J

    2014-01-01

    Within-hospital medical consultations and referrals (MCR) have many problems, among them are those related to the oral and written transmission of information. Our aim is to analyze problems in the transmission of information related to MCR, and possible differences between medical (MS) and surgical (SS) services. A prospective, observational study was conducted on the MCR requested to Internal Medicine Service over an 8 month period. The following variables were collected: age, sex, the requester, MCR type, type of admission, comorbidity, hospital stay and mortality, length of MCR, the number of physicians responsible for the patient requesting service during the MCR, MCR repeats, information on the request, available medical records, verbal contact, conflict between doctors, and medical information in the discharge summary. Of the total 215 MCR received, 66 (30.7%) were requested by MS, and 149 (69.3%) per SS. MCR duration was 3 days (standard deviation [SD] 4.8. The number of doctors responsible was 1.7 (SD 1.1), with, Repeats 43 (20%) and Urgent 14 (6.5%). Minimum information on the request, 6 (9.1%) MS and 21 (27.5%) SS. Low availability of medical record, 2 (3%) MS and 50 (33.6%) SS. No verbal contact, 33 (15.4%). Conflict between doctors 13 (6%). Information acceptably good in MCR urgent request 100% MS, and 80% SS. Two out of three MCR were without reference to the discharge report. There are significant losses in the transmission of information during the process of the MCR, which is higher in surgical than in medical departments. Copyright © 2013 SECA. Published by Elsevier Espana. All rights reserved.

  15. 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.

  16. Advanced Computational Methods for Security Constrained Financial Transmission Rights: Structure and Parallelism

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Elbert, Stephen T.; Kalsi, Karanjit; Vlachopoulou, Maria

    Financial Transmission Rights (FTRs) 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, a novel non-linear dynamical system (NDS) approach is proposed tomore » 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 large-scale systems using data from the Western Electricity Coordinating Council (WECC). The NDS is demonstrated to outperform the widely used CPLEX algorithms while exhibiting superior scalability. Furthermore, the NDS based solver can be easily parallelized which results in significant computational improvement.« less

  17. Nonlinear damping based semi-active building isolation system

    NASA Astrophysics Data System (ADS)

    Ho, Carmen; Zhu, Yunpeng; Lang, Zi-Qiang; Billings, Stephen A.; Kohiyama, Masayuki; Wakayama, Shizuka

    2018-06-01

    Many buildings in Japan currently have a base-isolation system with a low stiffness that is designed to shift the natural frequency of the building below the frequencies of the ground motion due to earthquakes. However, the ground motion observed during the 2011 Tohoku earthquake contained strong long-period waves that lasted for a record length of 3 min. To provide a novel and better solution against the long-period waves while maintaining the performance of the standard isolation range, the exploitation of the characteristics of nonlinear damping is proposed in this paper. This is motivated by previous studies of the authors, which have demonstrated that nonlinear damping can achieve desired performance over both low and high frequency regions and the optimal nonlinear damping force can be realized by closed loop controlled semi-active dampers. Simulation results have shown strong vibration isolation performance on a building model with identified parameters and have indicated that nonlinear damping can achieve low acceleration transmissibilities round the structural natural frequency as well as the higher ground motion frequencies that have been frequently observed during most earthquakes in Japan. In addition, physical building model based laboratory experiments are also conducted, The results demonstrate the advantages of the proposed nonlinear damping technologies over both traditional linear damping and more advanced Linear-Quadratic Gaussian (LQG) feedback control which have been used in practice to address building isolation system design and implementation problems. In comparison with the tuned-mass damper and other active control methods, the proposed solution offers a more pragmatic, low-cost, robust and effective alternative that can be readily installed into the base-isolation system of most buildings.

  18. Computation of Transonic Nozzle Sound Transmission and Rotor Problems by the Dispersion-Relation-Preserving Scheme

    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.

  19. A two steps solution approach to solving large nonlinear models: application to a problem of conjunctive use.

    PubMed

    Vieira, J; Cunha, M C

    2011-01-01

    This article describes a solution method of solving large nonlinear problems in two steps. The two steps solution approach takes advantage of handling smaller and simpler models and having better starting points to improve solution efficiency. The set of nonlinear constraints (named as complicating constraints) which makes the solution of the model rather complex and time consuming is eliminated from step one. The complicating constraints are added only in the second step so that a solution of the complete model is then found. The solution method is applied to a large-scale problem of conjunctive use of surface water and groundwater resources. The results obtained are compared with solutions determined with the direct solve of the complete model in one single step. In all examples the two steps solution approach allowed a significant reduction of the computation time. This potential gain of efficiency of the two steps solution approach can be extremely important for work in progress and it can be particularly useful for cases where the computation time would be a critical factor for having an optimized solution in due time.

  20. Broadband ultrafast nonlinear absorption and nonlinear refraction of layered molybdenum dichalcogenide semiconductors

    NASA Astrophysics Data System (ADS)

    Wang, Kangpeng; Feng, Yanyan; Chang, Chunxia; Zhan, Jingxin; Wang, Chengwei; Zhao, Quanzhong; Coleman, Jonathan N.; Zhang, Long; Blau, Werner J.; Wang, Jun

    2014-08-01

    A series of layered molybdenum dichalcogenides, i.e., MoX2 (X = S, Se and Te), were prepared in cyclohexyl pyrrolidinone by a liquid-phase exfoliation technique. The high quality of the two-dimensional nanostructures was verified by transmission electron microscopy and absorption spectroscopy. Open- and closed-aperture Z-scans were employed to study the nonlinear absorption and nonlinear refraction of the MoX2 dispersions, respectively. All the three-layered nanostructures exhibit prominent ultrafast saturable absorption (SA) for both femtosecond (fs) and picosecond (ps) laser pulses over a broad wavelength range from the visible to the near infrared. While the dispersions treated with low-speed centrifugation (1500 rpm) have an SA response, and the MoS2 and MoSe2 dispersions after higher speed centrifugation (10 000 rpm) possess two-photon absorption for fs pulses at 1030 nm, which is due to the significant reduction of the average thickness of the nanosheets; hence, the broadening of band gap. In addition, all dispersions show obvious nonlinear self-defocusing for ps pulses at both 1064 nm and 532 nm, resulting from the thermally-induced nonlinear refractive index. The versatile ultrafast nonlinear properties imply a huge potential of the layered MoX2 semiconductors in the development of nanophotonic devices, such as mode-lockers, optical limiters, optical switches, etc.A series of layered molybdenum dichalcogenides, i.e., MoX2 (X = S, Se and Te), were prepared in cyclohexyl pyrrolidinone by a liquid-phase exfoliation technique. The high quality of the two-dimensional nanostructures was verified by transmission electron microscopy and absorption spectroscopy. Open- and closed-aperture Z-scans were employed to study the nonlinear absorption and nonlinear refraction of the MoX2 dispersions, respectively. All the three-layered nanostructures exhibit prominent ultrafast saturable absorption (SA) for both femtosecond (fs) and picosecond (ps) laser pulses over a broad

  1. Mathematical nonlinear optics

    NASA Astrophysics Data System (ADS)

    McLaughlin, David W.

    1995-08-01

    The principal investigator, together with a post-doctoral fellows Tetsuji Ueda and Xiao Wang, several graduate students, and colleagues, has applied the modern mathematical theory of nonlinear waves to problems in nonlinear optics and to equations directly relevant to nonlinear optics. Projects included the interaction of laser light with nematic liquid crystals and chaotic, homoclinic, small dispersive, and random behavior of solutions of the nonlinear Schroedinger equation. In project 1, the extremely strong nonlinear response of a continuous wave laser beam in a nematic liquid crystal medium has produced striking undulation and filamentation of the laser beam which has been observed experimentally and explained theoretically. In project 2, qualitative properties of the nonlinear Schroedinger equation (which is the fundamental equation for nonlinear optics) have been identified and studied. These properties include optical shocking behavior in the limit of very small dispersion, chaotic and homoclinic behavior in discretizations of the partial differential equation, and random behavior.

  2. Nonlinear Waves and Inverse Scattering

    DTIC Science & Technology

    1990-09-18

    to be published Proceedings: conference Chaos in Australia (February 1990). 5. On the Kadomtsev Petviashvili Equation and Associated Constraints by...Scattering Transfoni (IST). IST is a method which alows one to’solve nonlinear wave equations by solving certain related direct and inverse scattering...problems. We use these results to find solutions to nonlinear wave equations much like one uses Fourier analysis for linear problems. Moreover the

  3. TORO II: A finite element computer program for nonlinear quasi-static problems in electromagnetics: Part 1, Theoretical background

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gartling, D.K.

    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.

  4. 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.

  5. Graded meshes in bio-thermal problems with transmission-line modeling method.

    PubMed

    Milan, Hugo F M; Carvalho, Carlos A T; Maia, Alex S C; Gebremedhin, Kifle G

    2014-10-01

    In this study, the transmission-line modeling (TLM) applied to bio-thermal problems was improved by incorporating several novel computational techniques, which include application of graded meshes which resulted in 9 times faster in computational time and uses only a fraction (16%) of the computational resources used by regular meshes in analyzing heat flow through heterogeneous media. Graded meshes, unlike regular meshes, allow heat sources to be modeled in all segments of the mesh. A new boundary condition that considers thermal properties and thus resulting in a more realistic modeling of complex problems is introduced. Also, a new way of calculating an error parameter is introduced. The calculated temperatures between nodes were compared against the results obtained from the literature and agreed within less than 1% difference. It is reasonable, therefore, to conclude that the improved TLM model described herein has great potential in heat transfer of biological systems. Copyright © 2014 Elsevier Ltd. All rights reserved.

  6. On Interactions of Oscillation Modes for a Weakly Non-Linear Undamped Elastic Beam with AN External Force

    NASA Astrophysics Data System (ADS)

    BOERTJENS, G. J.; VAN HORSSEN, W. T.

    2000-08-01

    In this paper an initial-boundary value problem for the vertical displacement of a weakly non-linear elastic beam with an harmonic excitation in the horizontal direction at the ends of the beam is studied. The initial-boundary value problem can be regarded as a simple model describing oscillations of flexible structures like suspension bridges or iced overhead transmission lines. Using a two-time-scales perturbation method an approximation of the solution of the initial-boundary value problem is constructed. Interactions between different oscillation modes of the beam are studied. It is shown that for certain external excitations, depending on the phase of an oscillation mode, the amplitude of specific oscillation modes changes.

  7. Event-based recursive filtering for a class of nonlinear stochastic parameter systems over fading channels

    NASA Astrophysics Data System (ADS)

    Shen, Yuxuan; Wang, Zidong; Shen, Bo; Alsaadi, Fuad E.

    2018-07-01

    In this paper, the recursive filtering problem is studied for a class of time-varying nonlinear systems with stochastic parameter matrices. The measurement transmission between the sensor and the filter is conducted through a fading channel characterized by the Rice fading model. An event-based transmission mechanism is adopted to decide whether the sensor measurement should be transmitted to the filter. A recursive filter is designed such that, in the simultaneous presence of the stochastic parameter matrices and fading channels, the filtering error covariance is guaranteed to have an upper bound and such an upper bound is then minimized by appropriately choosing filter gain matrix. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed filtering scheme.

  8. Event-Triggered Fault Detection of Nonlinear Networked Systems.

    PubMed

    Li, Hongyi; Chen, Ziran; Wu, Ligang; Lam, Hak-Keung; Du, Haiping

    2017-04-01

    This paper investigates the problem of fault detection for nonlinear discrete-time networked systems under an event-triggered scheme. A polynomial fuzzy fault detection filter is designed to generate a residual signal and detect faults in the system. A novel polynomial event-triggered scheme is proposed to determine the transmission of the signal. A fault detection filter is designed to guarantee that the residual system is asymptotically stable and satisfies the desired performance. Polynomial approximated membership functions obtained by Taylor series are employed for filtering analysis. Furthermore, sufficient conditions are represented in terms of sum of squares (SOSs) and can be solved by SOS tools in MATLAB environment. A numerical example is provided to demonstrate the effectiveness of the proposed results.

  9. Linear and nonlinear dynamics of isospectral granular chains

    NASA Astrophysics Data System (ADS)

    Chaunsali, R.; Xu, H.; Yang, J.; Kevrekidis, P. G.

    2017-04-01

    We study the dynamics of isospectral granular chains that are highly tunable due to the nonlinear Hertz contact law interaction between the granular particles. The system dynamics can thus be tuned easily from being linear to strongly nonlinear by adjusting the initial compression applied to the chain. In particular, we introduce both discrete and continuous spectral transformation schemes to generate a family of granular chains that are isospectral in their linear limit. Inspired by the principle of supersymmetry in quantum systems, we also introduce a methodology to add or remove certain eigenfrequencies, and we demonstrate numerically that the corresponding physical system can be constructed in the setting of one-dimensional granular crystals. In the linear regime, we highlight the similarities in the elastic wave transmission characteristics of such isospectral systems, and emphasize that the presented mathematical framework allows one to suitably tailor the wave transmission through a general class of granular chains, both ordered and disordered. Moreover, we show how the dynamic response of these structures deviates from its linear limit as we introduce Hertzian nonlinearity in the chain and how nonlinearity breaks the notion of linear isospectrality.

  10. An overview of adaptive model theory: solving the problems of redundancy, resources, and nonlinear interactions in human movement control.

    PubMed

    Neilson, Peter D; Neilson, Megan D

    2005-09-01

    Adaptive model theory (AMT) is a computational theory that addresses the difficult control problem posed by the musculoskeletal system in interaction with the environment. It proposes that the nervous system creates motor maps and task-dependent synergies to solve the problems of redundancy and limited central resources. These lead to the adaptive formation of task-dependent feedback/feedforward controllers able to generate stable, noninteractive control and render nonlinear interactions unobservable in sensory-motor relationships. AMT offers a unified account of how the nervous system might achieve these solutions by forming internal models. This is presented as the design of a simulator consisting of neural adaptive filters based on cerebellar circuitry. It incorporates a new network module that adaptively models (in real time) nonlinear relationships between inputs with changing and uncertain spectral and amplitude probability density functions as is the case for sensory and motor signals.

  11. Enhanced transmission by a grating composed of left-handed materials

    NASA Astrophysics Data System (ADS)

    Premlal, Prabhakaran Letha; Tiwari, Dinesh Chandra; Chaturvedi, Vandana

    2018-04-01

    We present a detailed theoretical analysis about the influence of surface polaritons on the transmission properties of electromagnetic waves at the periodically corrugated interface between the vacuum and left-handed material by using nonlinear boundary condition approach. The principle behind this approach is to match the wave fields across the grating interface by using a set of linear wave equation with nonlinear boundary conditions. The resonant transmission of the incident electromagnetic radiation in this structure is feasible within a certain frequency band, where there is a range of frequency over which both the electric permittivity and the magnetic permeability are simultaneously negative. The enhanced transmission is attributed to the coupling of the incident electromagnetic wave with the excited surface polaritons on grating interface. Finally, we present the numerical results illustrating the effect of the structural parameters and angle of incidence on the transmission spectra of a TM polarized electromagnetic wave.

  12. Detecting nonlinearity and chaos in epidemic data

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    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 ofmore » 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.« less

  13. A comparison of several methods of solving nonlinear regression groundwater flow problems

    USGS Publications Warehouse

    Cooley, Richard 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. The fastest method per iteration was the Fletcher-Reeves method, and this was followed closely by the quasi-Newton method. The Marquardt and quasi-linearization methods were slower. For all four methods the speed per iteration was directly related to the number of parameters in the model. However, this effect was much more pronounced for the Marquardt and quasi-linearization methods than for the other two. Hence the quasi-Newton (and perhaps Fletcher-Reeves) method might be more efficient than either the Marquardt or quasi-linearization methods if the number of parameters in a particular model were large, although this remains to be proven. The Marquardt method required somewhat less central memory than the quasi-linearization metilod for three of the four problems. For all four problems the quasi-Newton method required roughly two thirds to three quarters of the memory required by the Marquardt method, and the Fletcher-Reeves method required slightly less memory than the quasi-Newton method. Memory requirements were not excessive for any of the four methods.

  14. Parallel-vector computation for structural analysis and nonlinear unconstrained optimization problems

    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.

  15. Transmission problems for Mindlin–Timoshenko plates: frictional versus viscous damping mechanisms

    NASA Astrophysics Data System (ADS)

    Ferreira, Marcio V.; Muñoz Rivera, Jaime E.; Suárez, Fredy M. S.

    2018-06-01

    In this article, we make a comparative analysis of the stabilizing effect of the frictional dissipation with the dissipation produced by viscous materials of Kelvin-Voigt type both located in a part of a Mindlin-Timoshenko plate. We model these dissipative mechanisms through transmission problems and show that localized frictional damping, when effective over a strategic component of the plate, produces exponential stability of the corresponding semigroup. On the other hand, although the dissipation of Kelvin-Voigt is considered a strong dissipation, we prove that it loses its uniform stabilizing properties when localized over a component of the material and provides only a slower polynomial decay.

  16. Broadband ultrafast nonlinear absorption and nonlinear refraction of layered molybdenum dichalcogenide semiconductors.

    PubMed

    Wang, Kangpeng; Feng, Yanyan; Chang, Chunxia; Zhan, Jingxin; Wang, Chengwei; Zhao, Quanzhong; Coleman, Jonathan N; Zhang, Long; Blau, Werner J; Wang, Jun

    2014-09-21

    A series of layered molybdenum dichalcogenides, i.e., MoX₂ (X = S, Se and Te), were prepared in cyclohexyl pyrrolidinone by a liquid-phase exfoliation technique. The high quality of the two-dimensional nanostructures was verified by transmission electron microscopy and absorption spectroscopy. Open- and closed-aperture Z-scans were employed to study the nonlinear absorption and nonlinear refraction of the MoX₂ dispersions, respectively. All the three-layered nanostructures exhibit prominent ultrafast saturable absorption (SA) for both femtosecond (fs) and picosecond (ps) laser pulses over a broad wavelength range from the visible to the near infrared. While the dispersions treated with low-speed centrifugation (1500 rpm) have an SA response, and the MoS₂ and MoSe₂ dispersions after higher speed centrifugation (10,000 rpm) possess two-photon absorption for fs pulses at 1030 nm, which is due to the significant reduction of the average thickness of the nanosheets; hence, the broadening of band gap. In addition, all dispersions show obvious nonlinear self-defocusing for ps pulses at both 1064 nm and 532 nm, resulting from the thermally-induced nonlinear refractive index. The versatile ultrafast nonlinear properties imply a huge potential of the layered MoX2 semiconductors in the development of nanophotonic devices, such as mode-lockers, optical limiters, optical switches, etc.

  17. Inverse atmospheric radiative transfer problems - A nonlinear minimization search method of solution. [aerosol pollution monitoring

    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.

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

    NASA Astrophysics Data System (ADS)

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

    2007-12-01

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

  19. Simulation of stochastic wind action on transmission power lines

    NASA Astrophysics Data System (ADS)

    Wielgos, Piotr; Lipecki, Tomasz; Flaga, Andrzej

    2018-01-01

    The paper presents FEM analysis of the wind action on overhead transmission power lines. The wind action is based on a stochastic simulation of the wind field in several points of the structure and on the wind tunnel tests on aerodynamic coefficients of the single conductor consisting of three wires. In FEM calculations the section of the transmission power line composed of three spans is considered. Non-linear analysis with deadweight of the structure is performed first to obtain the deformed shape of conductors. Next, time-dependent wind forces are applied to respective points of conductors and non-linear dynamic analysis is carried out.

  20. Soliton production with nonlinear homogeneous lines

    DOE PAGES

    Elizondo-Decanini, Juan M.; Coleman, Phillip D.; Moorman, Matthew W.; ...

    2015-11-24

    Low- and high-voltage Soliton waves were produced and used to demonstrate collision and compression using diode-based nonlinear transmission lines. Experiments demonstrate soliton addition and compression using homogeneous nonlinear lines. We built the nonlinear lines using commercially available diodes. These diodes are chosen after their capacitance versus voltage dependence is used in a model and the line design characteristics are calculated and simulated. Nonlinear ceramic capacitors are then used to demonstrate high-voltage pulse amplification and compression. The line is designed such that a simple capacitor discharge, input signal, develops soliton trains in as few as 12 stages. We also demonstrated outputmore » voltages in excess of 40 kV using Y5V-based commercial capacitors. The results show some key features that determine efficient production of trains of solitons in the kilovolt range.« less

  1. A methodology for airplane parameter estimation and confidence interval determination in nonlinear estimation problems. Ph.D. Thesis - George Washington Univ., Apr. 1985

    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.

  2. A problem in non-linear Diophantine approximation

    NASA Astrophysics Data System (ADS)

    Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon

    2018-05-01

    In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

  3. Spacecraft nonlinear control

    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.

  4. Optimization-Based Approach for Joint X-Ray Fluorescence and Transmission Tomographic Inversion

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Di, Zichao; Leyffer, Sven; Wild, Stefan M.

    2016-01-01

    Fluorescence tomographic reconstruction, based on the detection of photons coming from fluorescent emission, can be used for revealing the internal elemental composition of a sample. On the other hand, conventional X-ray transmission tomography can be used for reconstructing the spatial distribution of the absorption coefficient inside a sample. In this work, we integrate both X-ray fluorescence and X-ray transmission data modalities and formulate a nonlinear optimization-based approach for reconstruction of the elemental composition of a given object. This model provides a simultaneous reconstruction of both the quantitative spatial distribution of all elements and the absorption effect in the sample. Mathematicallymore » speaking, we show that compared with the single-modality inversion (i.e., the X-ray transmission or fluorescence alone), the joint inversion provides a better-posed problem, which implies a better recovery. Therefore, the challenges in X-ray fluorescence tomography arising mainly from the effects of self-absorption in the sample are partially mitigated. The use of this technique is demonstrated on the reconstruction of several synthetic samples.« less

  5. 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…

  6. 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.

  7. Principles of Nonlinear Optics

    DTIC Science & Technology

    1989-11-01

    modelled by a ring cavity. The nonlinear meterial is between mirrors I and 2. E., E and I r E denote the incident, reflected and transmitted electric...Pasta and S. Ulam, "Studies of Nonlinear Problems I," Los Alamos Rep. LA 1940, 1955. 10. L. F. McGoldrick, "Resonant Interactions among Capillary- gravity ...34 Proc. IEEE, vol. 67, pp. 1442-1443, 1979. 23. P. P. Banerjee, A. Korpel and K. E. Lonngren," Self-refraction of Nonlinear Capillary- gravity Waves

  8. Guided particle swarm optimization method to solve general nonlinear optimization problems

    NASA Astrophysics Data System (ADS)

    Abdelhalim, Alyaa; Nakata, Kazuhide; El-Alem, Mahmoud; Eltawil, Amr

    2018-04-01

    The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder-Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and competitive.

  9. Optical isolation with nonlinear topological photonics

    NASA Astrophysics Data System (ADS)

    Zhou, Xin; Wang, You; Leykam, Daniel; Chong, Y. D.

    2017-09-01

    It is shown that the concept of topological phase transitions can be used to design nonlinear photonic structures exhibiting power thresholds and discontinuities in their transmittance. This provides a novel route to devising nonlinear optical isolators. We study three representative designs: (i) a waveguide array implementing a nonlinear 1D Su-Schrieffer-Heeger model, (ii) a waveguide array implementing a nonlinear 2D Haldane model, and (iii) a 2D lattice of coupled-ring waveguides. In the first two cases, we find a correspondence between the topological transition of the underlying linear lattice and the power threshold of the transmittance, and show that the transmission behavior is attributable to the emergence of a self-induced topological soliton. In the third case, we show that the topological transition produces a discontinuity in the transmittance curve, which can be exploited to achieve sharp jumps in the power-dependent isolation ratio.

  10. Spectrally Shaped DP-16QAM Super-Channel Transmission with Multi-Channel Digital Back-Propagation

    PubMed Central

    Maher, Robert; Xu, Tianhua; Galdino, Lidia; Sato, Masaki; Alvarado, Alex; Shi, Kai; Savory, Seb J.; Thomsen, Benn C.; Killey, Robert I.; Bayvel, Polina

    2015-01-01

    The achievable transmission capacity of conventional optical fibre communication systems is limited by nonlinear distortions due to the Kerr effect and the difficulty in modulating the optical field to effectively use the available fibre bandwidth. In order to achieve a high information spectral density (ISD), while simultaneously maintaining transmission reach, multi-channel fibre nonlinearity compensation and spectrally efficient data encoding must be utilised. In this work, we use a single coherent super-receiver to simultaneously receive a DP-16QAM super-channel, consisting of seven spectrally shaped 10GBd sub-carriers spaced at the Nyquist frequency. Effective nonlinearity mitigation is achieved using multi-channel digital back-propagation (MC-DBP) and this technique is combined with an optimised forward error correction implementation to demonstrate a record gain in transmission reach of 85%; increasing the maximum transmission distance from 3190 km to 5890 km, with an ISD of 6.60 b/s/Hz. In addition, this report outlines for the first time, the sensitivity of MC-DBP gain to linear transmission line impairments and defines a trade-off between performance and complexity. PMID:25645457

  11. An Optimization Code for Nonlinear Transient Problems of a Large Scale Multidisciplinary Mathematical Model

    NASA Astrophysics Data System (ADS)

    Takasaki, Koichi

    This paper presents a program for the multidisciplinary optimization and identification problem of the nonlinear model of large aerospace vehicle structures. The program constructs the global matrix of the dynamic system in the time direction by the p-version finite element method (pFEM), and the basic matrix for each pFEM node in the time direction is described by a sparse matrix similarly to the static finite element problem. The algorithm used by the program does not require the Hessian matrix of the objective function and so has low memory requirements. It also has a relatively low computational cost, and is suited to parallel computation. The program was integrated as a solver module of the multidisciplinary analysis system CUMuLOUS (Computational Utility for Multidisciplinary Large scale Optimization of Undense System) which is under development by the Aerospace Research and Development Directorate (ARD) of the Japan Aerospace Exploration Agency (JAXA).

  12. From solitons to rogue waves in nonlinear left-handed metamaterials.

    PubMed

    Shen, Yannan; Kevrekidis, P G; Veldes, G P; Frantzeskakis, D J; DiMarzio, D; Lan, X; Radisic, V

    2017-03-01

    In the present work, we explore soliton and roguelike wave solutions in the transmission line analog of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltage-dependent, symmetric capacitance motivated by recently developed ferroelectric barium strontium titanate thin-film capacitor designs. We develop both the corresponding nonlinear dynamical lattice and its reduction via a multiple scales expansion to a nonlinear Schrödinger (NLS) model for the envelope of a given carrier wave. The reduced model can feature either a focusing or a defocusing nonlinearity depending on the frequency (wave number) of the carrier. We then consider the robustness of different types of solitary waves of the reduced model within the original nonlinear left-handed medium. We find that both bright and dark solitons persist in a suitable parametric regime, where the reduction to the NLS model is valid. Additionally, for suitable initial conditions, we observe a rogue wave type of behavior that differs significantly from the classic Peregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like pattern into solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized members of the family of the Peregrine solitons, namely, Akhmediev breathers and Kuznetsov-Ma solitons, and explore how these evolve in the left-handed transmission line.

  13. Improving the Energy Market: Algorithms, Market Implications, and Transmission Switching

    NASA Astrophysics Data System (ADS)

    Lipka, Paula Ann

    corresponding to the accuracy and AC-feasiblity of the solution. This linearization was tested on the IEEE and Polish systems, which range from 14 to 3375 buses and 20 to 4161 transmission lines. It had an accuracy of 0.5% or less for all but the 30-bus system. It also solved in linear time with CPLEX, while the non-linear version solved in O(n1.11) to O(n1.39). The sequential linearization is slower than the nonlinear formulation for smaller problems, but faster for larger problems, and its linear computational time means it would continue solving faster for larger problems. A major consideration to implementing algorithms to solve the optimal generator dispatch is ensuring that the resulting prices from the algorithm will support the market. Since the sequential linearization is linear, it is convex, its marginal values are well-defined, and there is no duality gap. The prices and settlements obtained from the sequential linearization therefore can be used to run a market. This market will include extra prices and settlements for reactive power and voltage, compared to the present-day market, which is based on real power. An advantage of this is that there is a very clear pool that can be used for reactive power/voltage support payments, while presently there is not a clear pool to take them out of. This method also reveals how valuable reactive power and voltage are at different locations, which can enable better planning of reactive resource construction. Transmission switching increases the feasible region of the generator dispatch, which means there may be a better solution than without transmission switching. Power flows on transmission lines are not directly controllable; rather, the power flows according to how it is injected and the physical characteristics of the lines. Changing the network topology changes the physical characteristics, which changes the flows. This means that sets of generator dispatch that may have previously been infeasible due to the flow

  14. Nonlinear dynamics analysis of the spur gear system for railway locomotive

    NASA Astrophysics Data System (ADS)

    Wang, Junguo; He, Guangyue; Zhang, Jie; Zhao, Yongxiang; Yao, Yuan

    2017-02-01

    Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincaré maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

  15. Broadband parametric amplifiers based on nonlinear kinetic inductance artificial transmission lines

    NASA Astrophysics Data System (ADS)

    Chaudhuri, S.; Li, D.; Irwin, K. D.; Bockstiegel, C.; Hubmayr, J.; Ullom, J. N.; Vissers, M. R.; Gao, J.

    2017-04-01

    We present broadband parametric amplifiers based on the kinetic inductance of superconducting NbTiN thin films in an artificial (lumped-element) transmission line architecture. We demonstrate two amplifier designs implementing different phase matching techniques: periodic impedance loading and resonator phase shifters placed periodically along the transmission line. Our design offers several advantages over previous CPW-based amplifiers, including intrinsic 50 Ω characteristic impedance, natural suppression of higher pump harmonics, lower required pump power, and shorter total trace length. Experimental realizations of both versions of the amplifiers are demonstrated. With a transmission line length of 20 cm, we have achieved gains of 15 dB over several GHz of bandwidth.

  16. Multilevel algorithms for nonlinear optimization

    NASA Technical Reports Server (NTRS)

    Alexandrov, Natalia; Dennis, J. E., Jr.

    1994-01-01

    Multidisciplinary design optimization (MDO) gives rise to nonlinear optimization problems characterized by a large number of constraints that naturally occur in blocks. We propose a class of multilevel optimization methods motivated by the structure and number of constraints and by the expense of the derivative computations for MDO. The algorithms are an extension to the nonlinear programming problem of the successful class of local Brown-Brent algorithms for nonlinear equations. Our extensions allow the user to partition constraints into arbitrary blocks to fit the application, and they separately process each block and the objective function, restricted to certain subspaces. The methods use trust regions as a globalization strategy, and they have been shown to be globally convergent under reasonable assumptions. The multilevel algorithms can be applied to all classes of MDO formulations. Multilevel algorithms for solving nonlinear systems of equations are a special case of the multilevel optimization methods. In this case, they can be viewed as a trust-region globalization of the Brown-Brent class.

  17. Nonlinear Fano-Resonant Dielectric Metasurfaces

    DOE PAGES

    Yang, Yuanmu; Wang, Wenyi; Boulesbaa, Abdelaziz; ...

    2015-10-26

    Strong nonlinear light matter interaction is highly sought-after for a variety of applications including lasing and all-optical light modulation. Recently, resonant plasmonic structures have been considered promising candidates for enhancing nonlinear optical processes due to their ability to greatly enhance the optical near-field; however, their small mode volumes prevent the inherently large nonlinear susceptibility of the metal from being efficiently exploited. We present an alternative approach that utilizes a Fano-resonant silicon metasurface. The metasurface results in strong near-field enhancement within the volume of the silicon resonator while minimizing two photon absorption. Here, we measure a third harmonic generation enhancement factormore » of 1.5 105 with respect to an unpatterned silicon film and an absolute conversion efficiency of 1.2 10 6 with a peak pump intensity of 3.2 GW cm 2. The enhanced nonlinearity, combined with a sharp linear transmittance spectrum, results in transmission modulation with a modulation depth of 36%. Finally, the modulation mechanism is studied by pump probe experiments« less

  18. Broadband parametric amplifiers based on nonlinear kinetic inductance artificial transmission lines

    DOE PAGES

    Chaudhuri, S.; Li, D.; Irwin, K. D.; ...

    2017-04-10

    Here, we present broadband parametric amplifiers based on the kinetic inductance of superconducting NbTiN thin films in an artificial (lumped-element) transmission line architecture. We demonstrate two amplifier designs implementing different phase matching techniques: periodic impedance loading and resonator phase shifters placed periodically along the transmission line. Our design offers several advantages over previous CPW-based amplifiers, including intrinsic 50 Ω characteristic impedance, natural suppression of higher pump harmonics, lower required pump power, and shorter total trace length. Experimental realizations of both versions of the amplifiers are demonstrated. In conclusion, with a transmission line length of 20 cm, we have achieved gainsmore » of 15 dB over several GHz of bandwidth.« less

  19. Broadband parametric amplifiers based on nonlinear kinetic inductance artificial transmission lines

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Chaudhuri, S.; Li, D.; Irwin, K. D.

    Here, we present broadband parametric amplifiers based on the kinetic inductance of superconducting NbTiN thin films in an artificial (lumped-element) transmission line architecture. We demonstrate two amplifier designs implementing different phase matching techniques: periodic impedance loading and resonator phase shifters placed periodically along the transmission line. Our design offers several advantages over previous CPW-based amplifiers, including intrinsic 50 Ω characteristic impedance, natural suppression of higher pump harmonics, lower required pump power, and shorter total trace length. Experimental realizations of both versions of the amplifiers are demonstrated. In conclusion, with a transmission line length of 20 cm, we have achieved gainsmore » of 15 dB over several GHz of bandwidth.« less

  20. 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.

  1. The Thinnest Path Problem

    DTIC Science & Technology

    2016-07-22

    their corresponding transmission powers . At first glance, one may wonder whether the thinnest path problem is simply a shortest path problem with the...nature of the shortest path problem. Another aspect that complicates the problem is the choice of the transmission power at each node (within a maximum...fixed transmission power at each node (in this case, the resulting hypergraph degenerates to a standard graph), the thinnest path problem is NP

  2. Computational strategy for the solution of large strain nonlinear problems using the Wilkins explicit finite-difference approach

    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.

  3. Minimax terminal approach problem in two-level hierarchical nonlinear discrete-time dynamical system

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Shorikov, A. F., E-mail: afshorikov@mail.ru

    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 terminalmore » approach process with incomplete information and give a general scheme for its solving.« less

  4. 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.

  5. Rogue wave in coupled electric transmission line

    NASA Astrophysics Data System (ADS)

    Duan, J. K.; Bai, Y. L.

    2018-03-01

    Distributed electrical transmission lines that consist of a large number of identical sections have been theoretically studied in the present paper. The rogue wave is analyzed and predicted using the nonlinear Schrodinger equation (NLSE). The results indicate that, in the continuum limit, the voltage for the transmission line is described in some cases by the NLSE that is obtained using the traditional perturbation technique. The dependences of the characteristics of the rouge wave parameters on the coupled electric transmission line are shown in the paper. As is well known, rogue waves can be found for a large number of oceanic disasters, and such waves may be disastrous. However, the results of the present paper for coupled electric transmission lines may be useful.

  6. Analysis of a parallelized nonlinear elliptic boundary value problem solver with application to reacting flows

    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.

  7. Nonlinear transport theory in the metal with tunnel barrier

    NASA Astrophysics Data System (ADS)

    Zubov, E. E.

    2018-02-01

    Within the framework of the scattering matrix formalism, the nonlinear Kubo theory for electron transport in the metal with a tunnel barrier has been considered. A general expression for the mean electrical current was obtained. It significantly simplifies the calculation of nonlinear contributions to the conductivity of various hybrid structures. In the model of the tunnel Hamiltonian, all linear and nonlinear contributions to a mean electrical current are evaluated. The linear approximation agrees with results of other theories. For effective barrier transmission ?, the ballistic transport is realised with a value of the Landauer conductivity equal to ?.

  8. Determination of unknown coefficient in a non-linear elliptic problem related to the elastoplastic torsion of a bar

    NASA Astrophysics Data System (ADS)

    Hasanov, Alemdar; Erdem, Arzu

    2008-08-01

    The inverse problem of determining the unknown coefficient of the non-linear differential equation of torsional creep is studied. The unknown coefficient g = g({xi}2) depends on the gradient{xi} : = |{nabla}u| of the solution u(x), x [isin] {Omega} [sub] Rn, of the direct problem. It is proved that this gradient is bounded in C-norm. This permits one to choose the natural class of admissible coefficients for the considered inverse problem. The continuity in the norm of the Sobolev space H1({Omega}) of the solution u(x;g) of the direct problem with respect to the unknown coefficient g = g({xi}2) is obtained in the following sense: ||u(x;g) - u(x;gm)||1 [->] 0 when gm({eta}) [->] g({eta}) point-wise as m [->] {infty}. Based on these results, the existence of a quasi-solution of the inverse problem in the considered class of admissible coefficients is obtained. Numerical examples related to determination of the unknown coefficient are presented.

  9. 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.

  10. Global dynamic modeling of a transmission system

    NASA Technical Reports Server (NTRS)

    Choy, F. K.; Qian, W.

    1993-01-01

    The work performed on global dynamic simulation and noise correlation of gear transmission systems at the University of Akron is outlined. The objective is to develop a comprehensive procedure to simulate the dynamics of the gear transmission system coupled with the effects of gear box vibrations. The developed numerical model is benchmarked with results from experimental tests at NASA Lewis Research Center. The modal synthesis approach is used to develop the global transient vibration analysis procedure used in the model. Modal dynamic characteristics of the rotor-gear-bearing system are calculated by the matrix transfer method while those of the gear box are evaluated by the finite element method (NASTRAN). A three-dimensional, axial-lateral coupled bearing model is used to couple the rotor vibrations with the gear box motion. The vibrations between the individual rotor systems are coupled through the nonlinear gear mesh interactions. The global equations of motion are solved in modal coordinates and the transient vibration of the system is evaluated by a variable time-stepping integration scheme. The relationship between housing vibration and resulting noise of the gear transmission system is generated by linear transfer functions using experimental data. A nonlinear relationship of the noise components to the fundamental mesh frequency is developed using the hypercoherence function. The numerically simulated vibrations and predicted noise of the gear transmission system are compared with the experimental results from the gear noise test rig at NASA Lewis Research Center. Results of the comparison indicate that the global dynamic model developed can accurately simulate the dynamics of a gear transmission system.

  11. Scaling properties of weakly nonlinear coefficients in the Faraday problem.

    PubMed

    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.

  12. 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.

  13. Nonlinear frequency response based adaptive vibration controller design for a class of nonlinear systems

    NASA Astrophysics Data System (ADS)

    Thenozhi, Suresh; Tang, Yu

    2018-01-01

    Frequency response functions (FRF) are often used in the vibration controller design problems of mechanical systems. Unlike linear systems, the FRF derivation for nonlinear systems is not trivial due to their complex behaviors. To address this issue, the convergence property of nonlinear systems can be studied using convergence analysis. For a class of time-invariant nonlinear systems termed as convergent systems, the nonlinear FRF can be obtained. The present paper proposes a nonlinear FRF based adaptive vibration controller design for a mechanical system with cubic damping nonlinearity and a satellite system. Here the controller gains are tuned such that a desired closed-loop frequency response for a band of harmonic excitations is achieved. Unlike the system with cubic damping, the satellite system is not convergent, therefore an additional controller is utilized to achieve the convergence property. Finally, numerical examples are provided to illustrate the effectiveness of the proposed controller.

  14. Spurious Solutions Of Nonlinear Differential Equations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Sweby, P. K.; Griffiths, D. F.

    1992-01-01

    Report utilizes nonlinear-dynamics approach to investigate possible sources of errors and slow convergence and non-convergence of steady-state numerical solutions when using time-dependent approach for problems containing nonlinear source terms. Emphasizes implications for development of algorithms in CFD and computational sciences in general. Main fundamental conclusion of study is that qualitative features of nonlinear differential equations cannot be adequately represented by finite-difference method and vice versa.

  15. An approximation theory for the identification of nonlinear distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Reich, Simeon; Rosen, I. G.

    1988-01-01

    An abstract approximation framework for the identification of nonlinear distributed parameter systems is developed. Inverse problems for nonlinear systems governed by strongly maximal monotone operators (satisfying a mild continuous dependence condition with respect to the unknown parameters to be identified) are treated. Convergence of Galerkin approximations and the corresponding solutions of finite dimensional approximating identification problems to a solution of the original finite dimensional identification problem is demonstrated using the theory of nonlinear evolution systems and a nonlinear analog of the Trotter-Kato approximation result for semigroups of bounded linear operators. The nonlinear theory developed here is shown to subsume an existing linear theory as a special case. It is also shown to be applicable to a broad class of nonlinear elliptic operators and the corresponding nonlinear parabolic partial differential equations to which they lead. An application of the theory to a quasilinear model for heat conduction or mass transfer is discussed.

  16. Nonlinear functional approximation with networks using adaptive neurons

    NASA Technical Reports Server (NTRS)

    Tawel, Raoul

    1992-01-01

    A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.

  17. Asymmetric nonlinear system is not sufficient for a nonreciprocal wave diode

    NASA Astrophysics Data System (ADS)

    Wu, Gaomin; Long, Yang; Ren, Jie

    2018-05-01

    We demonstrate symmetric wave propagations in asymmetric nonlinear systems. By solving the nonlinear Schördinger equation, we first analytically prove the existence of symmetric transmission in asymmetric systems with a single nonlinear delta-function interface. We then point out that a finite width of the nonlinear interface region is necessary to produce nonreciprocity in asymmetric systems. However, a geometrical resonant condition for breaking nonreciprocal propagation is then identified theoretically and verified numerically. With such a resonant condition, the nonlinear interface region of finite width behaves like a single nonlinear delta-barrier so that wave propagations in the forward and backward directions are identical under arbitrary incident wave intensity. As such, reciprocity reemerges periodically in the asymmetric nonlinear system when changing the width of interface region. Finally, similar resonant conditions of discrete nonlinear Schördinger equation are discussed. Therefore, we have identified instances of reciprocity that breaking spatial symmetry in nonlinear interface systems is not sufficient to produce nonreciprocal wave propagation.

  18. Linear and nonlinear Fano resonance in the main chain-structure of additional defects with an isolated ring composed of defects

    NASA Astrophysics Data System (ADS)

    Ding, Xiu-Huan; Wang, Rui; Qiao, Qian; Zhang, Cun-Xi

    2018-03-01

    As is well known, Fano resonance originates from the interference between a continuum energy band and an embedded discrete energy level. We study transmission properties of the discrete chain-structure of additional defects with an isolated ring composed of N defect states, and obtain the analytical transmission coefficient of similar Fano formula. Using the formula, we reveal conditions for perfect reflections and transmissions due to either destructive or constructive interferences. It is found that a nonlinear Kerr-like response leads to bistable transmission, and for either linear cases or nonlinear ones, the defects in main arrays have a major impact on perfect reflections, but has no effect on perfect transmission.

  19. Transmission dynamics: critical questions and challenges

    PubMed Central

    2017-01-01

    This article overviews the dynamics of disease transmission in one-host–one-parasite systems. Transmission is the result of interacting host and pathogen processes, encapsulated with the environment in a ‘transmission triangle’. Multiple transmission modes and their epidemiological consequences are often not understood because the direct measurement of transmission is difficult. However, its different components can be analysed using nonlinear transmission functions, contact matrices and networks. A particular challenge is to develop such functions for spatially extended systems. This is illustrated for vector transmission where a ‘perception kernel’ approach is developed that incorporates vector behaviour in response to host spacing. A major challenge is understanding the relative merits of the large number of approaches to quantifying transmission. The evolution of transmission mode itself has been a rather neglected topic, but is important in the context of understanding disease emergence and genetic variation in pathogens. Disease impacts many biological processes such as community stability, the evolution of sex and speciation, yet the importance of different transmission modes in these processes is not understood. Broader approaches and ideas to disease transmission are important in the public health realm for combating newly emerging infections. This article is part of the themed issue ‘Opening the black box: re-examining the ecology and evolution of parasite transmission’. PMID:28289255

  20. Optimal control in adaptive optics modeling of nonlinear systems

    NASA Astrophysics Data System (ADS)

    Herrmann, J.

    The problem of using an adaptive optics system to correct for nonlinear effects like thermal blooming is addressed using a model containing nonlinear lenses through which Gaussian beams are propagated. The best correction of this nonlinear system can be formulated as a deterministic open loop optimal control problem. This treatment gives a limit for the best possible correction. Aspects of adaptive control and servo systems are not included at this stage. An attempt is made to determine that control in the transmitter plane which minimizes the time averaged area or maximizes the fluence in the target plane. The standard minimization procedure leads to a two-point-boundary-value problem, which is ill-conditioned in the case. The optimal control problem was solved using an iterative gradient technique. An instantaneous correction is introduced and compared with the optimal correction. The results of the calculations show that for short times or weak nonlinearities the instantaneous correction is close to the optimal correction, but that for long times and strong nonlinearities a large difference develops between the two types of correction. For these cases the steady state correction becomes better than the instantaneous correction and approaches the optimum correction.

  1. Handling times and saturating transmission functions in a snail-worm symbiosis.

    PubMed

    Hopkins, Skylar R; McGregor, Cari M; Belden, Lisa K; Wojdak, Jeremy M

    2018-06-16

    All dynamic species interaction models contain an assumption that describes how contact rates scale with population density. Choosing an appropriate contact-density function is important, because different functions have different implications for population dynamics and stability. However, this choice can be challenging, because there are many possible functions, and most are phenomenological and thus difficult to relate to underlying ecological processes. Using one such phenomenological function, we described a nonlinear relationship between field transmission rates and host density in a common snail-oligochaete symbiosis. We then used a well-known contact function from predator-prey models, the Holling Type II functional response, to describe and predict host snail contact rates in the laboratory. The Holling Type II functional response accurately described both the nonlinear contact-density relationship and the average contact duration that we observed. Therefore, we suggest that contact rates saturate with host density in this system because each snail contact requires a non-instantaneous handling time, and additional possible contacts do not occur during that handling time. Handling times and nonlinear contact rates might also explain the nonlinear relationship between symbiont transmission and snail density that we observed in the field, which could be confirmed by future work that controls for other potential sources of seasonal variation in transmission rates. Because most animal contacts are not instantaneous, the Holling Type II functional response might be broadly relevant to diverse host-symbiont systems.

  2. Transmission Measurement of the Third-Order Susceptibility of Gold

    NASA Technical Reports Server (NTRS)

    Smith, David D.; Yoon, Youngkwon; Boyd, Robert W.; Crooks, Richard M.; George, Michael

    1999-01-01

    Gold nanoparticle composites are known to display large optical nonlinearities. In order to assess the validity of generalized effective medium theories (EMT's) for describing the linear and nonlinear optical properties of metal nanoparticle composites, knowledge of the linear and nonlinear susceptibilities of the constituent materials is a prerequisite. In this study the inherent nonlinearity of the metal is measured directly (rather than deduced from a suitable EMT) using a very thin gold film. Specifically, we have used the z-scan technique at a wavelength near the transmission window of bulk gold to measure the third-order susceptibility of a continuous thin gold film deposited on a quartz substrate surface-modified with a self-assembled monolayer to promote adhesion and uniformity without affecting the optical properties. We compare our results with predictions which ascribe the nonlinear response to a Fermi-smearing mechanism. Further, we note that the sign of the nonlinear susceptibility is reversed from that of gold nanoparticle composites.

  3. Drill string transmission line

    DOEpatents

    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.

  4. Asymmetric wave transmission in a diatomic acoustic/elastic metamaterial

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Li, Bing; Tan, K. T., E-mail: ktan@uakron.edu

    2016-08-21

    Asymmetric acoustic/elastic wave transmission has recently been realized using nonlinearity, wave diffraction, or bias effects, but always at the cost of frequency distortion, direction shift, large volumes, or external energy. Based on the self-coupling of dual resonators, we propose a linear diatomic metamaterial, consisting of several small-sized unit cells, to realize large asymmetric wave transmission in low frequency domain (below 1 kHz). The asymmetric transmission mechanism is theoretically investigated, and numerically verified by both mass-spring and continuum models. This passive system does not require any frequency conversion or external energy, and the asymmetric transmission band can be theoretically predicted andmore » mathematically controlled, which extends the design concept of unidirectional transmission devices.« less

  5. Method for nonlinear exponential regression analysis

    NASA Technical Reports Server (NTRS)

    Junkin, B. G.

    1972-01-01

    Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.

  6. Portfolios with nonlinear constraints and spin glasses

    NASA Astrophysics Data System (ADS)

    Gábor, Adrienn; Kondor, I.

    1999-12-01

    In a recent paper Galluccio, Bouchaud and Potters demonstrated that a certain portfolio problem with a nonlinear constraint maps exactly onto finding the ground states of a long-range spin glass, with the concomitant nonuniqueness and instability of the optimal portfolios. Here we put forward geometric arguments that lead to qualitatively similar conclusions, without recourse to the methods of spin glass theory, and give two more examples of portfolio problems with convex nonlinear constraints.

  7. Chirped femtosecond pulses in the higher-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities

    NASA Astrophysics Data System (ADS)

    Triki, Houria; Biswas, Anjan; Milović, Daniela; Belić, Milivoj

    2016-05-01

    We consider a high-order nonlinear Schrödinger equation with competing cubic-quintic-septic nonlinearities, non-Kerr quintic nonlinearity, self-steepening, and self-frequency shift. The model describes the propagation of ultrashort (femtosecond) optical pulses in highly nonlinear optical fibers. A new ansatz is adopted to obtain nonlinear chirp associated with the propagating femtosecond soliton pulses. It is shown that the resultant elliptic equation of the problem is of high order, contains several new terms and is more general than the earlier reported results, thus providing a systematic way to find exact chirped soliton solutions of the septic model. Novel soliton solutions, including chirped bright, dark, kink and fractional-transform soliton solutions are obtained for special choices of parameters. Furthermore, we present the parameter domains in which these optical solitons exist. The nonlinear chirp associated with each of the solitonic solutions is also determined. It is shown that the chirping is proportional to the intensity of the wave and depends on higher-order nonlinearities. Of special interest is the soliton solution of the bright and dark type, determined for the general case when all coefficients in the equation have nonzero values. These results can be useful for possible chirped-soliton-based applications of highly nonlinear optical fiber systems.

  8. The influence of the uplink noise on the performance of satellite data transmission systems

    NASA Astrophysics Data System (ADS)

    Dewal, Vrinda P.

    The problem of transmission of binary phase shift keying (BPSK) modulated digital data through a bandlimited nonlinear satellite channel in the presence of uplink, downlink Gaussian noise and intersymbol interface is examined. The satellite transponder is represented by a zero memory bandpass nonlinearity, with AM/AM conversion. The proposed optimum linear receiver structure consists of tapped-delay lines followed by a decision device. The linear receiver is designed to minimize the mean square error that is a function of the intersymbol interface, the uplink and the downlink noise. The minimum mean square error equalizer (MMSE) is derived using the Wiener-Kolmogorov theory. In this receiver, the decision about the transmitted signal is made by taking into account the received sequence of present sample, and the interfering past and future samples, which represent the intersymbol interference (ISI). Illustrative examples of the receiver structures are considered for the nonlinear channels with a symmetrical and asymmetrical frequency responses of the transmitter filter. The transponder nonlinearity is simulated by a polynomial using only the first and the third orders terms. A computer simulation determines the tap gain coefficients of the MMSE equalizer that adapt to the various uplink and downlink noise levels. The performance of the MMSE equalizer is evaluated in terms of an estimate of the average probability of error.

  9. Normal modes of a superconducting transmission-line resonator with embedded lumped element circuit components

    NASA Astrophysics Data System (ADS)

    Mortensen, Henrik Lund; Mølmer, Klaus; Andersen, Christian Kraglund

    2016-11-01

    We present a method to identify the coupled, normal modes of a superconducting transmission line with an embedded lumped element circuit. We evaluate the effective transmission-line nonlinearities in the case of Kerr-like Josephson interactions in the circuit and in the case where the embedded circuit constitutes a qubit degree of freedom, which is Rabi coupled to the field in the transmission line. Our theory quantitatively accounts for the very high and positive Kerr nonlinearities observed in a recent experiment [M. Rehák, P. Neilinger, M. Grajcar, G. Oelsner, U. Hübner, E. Il'ichev, and H.-G. Meyer, Appl. Phys. Lett. 104, 162604 (2014), 10.1063/1.4873719], and we can evaluate the accomplishments of modified versions of the experimental circuit.

  10. Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

    NASA Astrophysics Data System (ADS)

    Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

    2018-01-01

    We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

  11. On parametric Gevrey asymptotics for some nonlinear initial value Cauchy problems

    NASA Astrophysics Data System (ADS)

    Lastra, A.; Malek, S.

    2015-11-01

    We study a nonlinear initial value Cauchy problem depending upon a complex perturbation parameter ɛ with vanishing initial data at complex time t = 0 and whose coefficients depend analytically on (ɛ, t) near the origin in C2 and are bounded holomorphic on some horizontal strip in C w.r.t. the space variable. This problem is assumed to be non-Kowalevskian in time t, therefore analytic solutions at t = 0 cannot be expected in general. Nevertheless, we are able to construct a family of actual holomorphic solutions defined on a common bounded open sector with vertex at 0 in time and on the given strip above in space, when the complex parameter ɛ belongs to a suitably chosen set of open bounded sectors whose union form a covering of some neighborhood Ω of 0 in C*. These solutions are achieved by means of Laplace and Fourier inverse transforms of some common ɛ-depending function on C × R, analytic near the origin and with exponential growth on some unbounded sectors with appropriate bisecting directions in the first variable and exponential decay in the second, when the perturbation parameter belongs to Ω. Moreover, these solutions satisfy the remarkable property that the difference between any two of them is exponentially flat for some integer order w.r.t. ɛ. With the help of the classical Ramis-Sibuya theorem, we obtain the existence of a formal series (generally divergent) in ɛ which is the common Gevrey asymptotic expansion of the built up actual solutions considered above.

  12. Mitigation of Power Quality Problems in Grid-Interactive Distributed Generation System

    NASA Astrophysics Data System (ADS)

    Bhende, C. N.; Kalam, A.; Malla, S. G.

    2016-04-01

    Having an inter-tie between low/medium voltage grid and distributed generation (DG), both exposes to power quality (PQ) problems created by each other. This paper addresses various PQ problems arise due to integration of DG with grid. The major PQ problems are due to unbalanced and non-linear load connected at DG, unbalanced voltage variations on transmission line and unbalanced grid voltages which severely affect the performance of the system. To mitigate the above mentioned PQ problems, a novel integrated control of distribution static shunt compensator (DSTATCOM) is presented in this paper. DSTATCOM control helps in reducing the unbalance factor of PCC voltage. It also eliminates harmonics from line currents and makes them balanced. Moreover, DSTATCOM supplies the reactive power required by the load locally and hence, grid need not to supply the reactive power. To show the efficacy of the proposed controller, several operating conditions are considered and verified through simulation using MATLAB/SIMULINK.

  13. State-Dependent Riccati Equation Regulation of Systems with State and Control Nonlinearities

    NASA Technical Reports Server (NTRS)

    Beeler, Scott C.; Cox, David E. (Technical Monitor)

    2004-01-01

    The state-dependent Riccati equations (SDRE) is the basis of a technique for suboptimal feedback control of a nonlinear quadratic regulator (NQR) problem. It is an extension of the Riccati equation used for feedback control of linear problems, with the addition of nonlinearities in the state dynamics of the system resulting in a state-dependent gain matrix as the solution of the equation. In this paper several variations on the SDRE-based method will be considered for the feedback control problem with control nonlinearities. The control nonlinearities may result in complications in the numerical implementation of the control, which the different versions of the SDRE method must try to overcome. The control methods will be applied to three test problems and their resulting performance analyzed.

  14. Nonlinear Waves and Inverse Scattering

    DTIC Science & Technology

    1989-01-01

    transform provides a linearization.’ Well known systems include the Kadomtsev - Petviashvili , Davey-Stewartson and Self-Dual Yang-Mills equations . The d...which employs inverse scattering theory in order to linearize the given nonlinear equation . I.S.T. has led to new developments in both fields: inverse...scattering and nonlinear wave equations . Listed below are some of the problems studied and a short description of results. - Multidimensional

  15. Building Blocks for Reliable Complex Nonlinear Numerical Simulations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.

    2005-01-01

    This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations.

  16. 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.

  17. Nonlinear single-spin spectrum analyzer.

    PubMed

    Kotler, Shlomi; Akerman, Nitzan; Glickman, Yinnon; Ozeri, Roee

    2013-03-15

    Qubits have been used as linear spectrum analyzers of their environments. Here we solve the problem of nonlinear spectral analysis, required for discrete noise induced by a strongly coupled environment. Our nonperturbative analytical model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We develop a noise characterization scheme adapted to this nonlinearity. We then apply it using a single trapped ion as a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. Finally, we experimentally compared the performance of equidistant vs Uhrig modulation schemes for spectral analysis.

  18. Numerical Studies of Localized Vibrating Structures in Nonlinear Lattices

    DTIC Science & Technology

    1991-03-01

    transmit soliton pulses, greatly increasing the permissible time-bandwidth product of a given system ( Hasegawa and Tappert [1973]). Solitons, which are...CIO CD 0 Fi->ue111.4 F ia aknlk tt fe rg ndcy 8 !78 CoI I o (0))ep Udw FiUeI1.4 FiaIak lk tt afe riho dcy I 78 IV. THE NONLINEAR LATTICE II...equation", PysiCa. D41, 341-355. Hasegawa , A. and Tappert, F. : ’Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers

  19. Learning automata-based solutions to the nonlinear fractional knapsack problem with applications to optimal resource allocation.

    PubMed

    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.

  20. Development of a multiple-parameter nonlinear perturbation procedure for transonic turbomachinery flows: Preliminary application to design/optimization problems

    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.

  1. Nonlinear Dot Plots.

    PubMed

    Rodrigues, Nils; Weiskopf, Daniel

    2018-01-01

    Conventional dot plots use a constant dot size and are typically applied to show the frequency distribution of small data sets. Unfortunately, they are not designed for a high dynamic range of frequencies. We address this problem by introducing nonlinear dot plots. Adopting the idea of nonlinear scaling from logarithmic bar charts, our plots allow for dots of varying size so that columns with a large number of samples are reduced in height. For the construction of these diagrams, we introduce an efficient two-way sweep algorithm that leads to a dense and symmetrical layout. We compensate aliasing artifacts at high dot densities by a specifically designed low-pass filtering method. Examples of nonlinear dot plots are compared to conventional dot plots as well as linear and logarithmic histograms. Finally, we include feedback from an expert review.

  2. Third order nonlinearity in pulsed laser deposited LiNbO{sub 3} thin films

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tumuluri, Anil; Rapolu, Mounika; Rao, S. Venugopal, E-mail: kcjrsp@uohyd.ernet.in, E-mail: svrsp@uohyd.ernet.in

    2016-05-06

    Lithium niobate (LiNbO{sub 3}) thin films were prepared using pulsed laser deposition technique. Structural properties of the same were examined from XRD and optical band gap of the thin films were measured from transmittance spectra recorded using UV-Visible spectrophotometer. Nonlinear optical properties of the thin films were recorded using Z-Scan technique. The films were exhibiting third order nonlinearity and their corresponding two photon absorption, nonlinear refractive index, real and imaginary part of nonlinear susceptibility were calculated from open aperture and closed aperture transmission curves. From these studies, it suggests that these films have potential applications in nonlinear optical devices.

  3. Advanced RF Sources Based on Novel Nonlinear Transmission Lines

    DTIC Science & Technology

    2015-01-26

    microwave (HPM) sources. It is also critical to thin film devices and integrated circuits, carbon nanotube based cathodes and interconnects, field emitters ... line model (TLM) in Fig. 6b. Our model is compared with TLM, shown in Fig. 7a. When the interface resistance rc is small, TLM becomes inaccurate...due to current crowding. Fig. 6. (a) Electrical contact including specific interfacial resistivity ρc, and (b) its transmission line model

  4. Stability analysis of nonlinear systems with slope restricted nonlinearities.

    PubMed

    Liu, Xian; Du, Jiajia; Gao, Qing

    2014-01-01

    The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

  5. Multiplayer games and HIV transmission via casual encounters.

    PubMed

    Tully, Stephen; Cojocaru, Monica-Gabriela; Bauch, Chris T

    2017-04-01

    Population transmission models have been helpful in studying the spread of HIV. They assess changes made at the population level for different intervention strategies. To further understand how individual changes affect the population as a whole, game-theoretical models are used to quantify the decision-making process. Investigating multiplayer nonlinear games that model HIV transmission represents a unique approach in epidemiological research. We present here 2-player and multiplayer noncooperative games where players are defined by HIV status and age and may engage in casual (sexual) encounters. The games are modelled as generalized Nash games with shared constraints, which is completely novel in the context of our applied problem. Each player's HIV status is known to potential partners, and players have personal preferences ranked via utility values of unprotected and protected sex outcomes. We model a player's strategy as their probability of being engaged in a casual unprotected sex encounter (USE), which may lead to HIV transmission; however, we do not incorporate a transmission model here. We study the sensitivity of Nash strategies with respect to varying preference rankings, and the impact of a prophylactic vaccine introduced in players of youngest age groups. We also study the effect of these changes on the overall increase in infection level, as well as the effects that a potential prophylactic treatment may have on age-stratified groups of players. We conclude that the biggest impacts on increasing the infection levels in the overall population are given by the variation in the utilities assigned to individuals for unprotected sex with others of opposite HIV status, while the introduction of a prophylactic vaccine in youngest age group (15-20 yr olds) slows down the increase in HIV infection.

  6. Experimental gaze at nonlinear phenomena

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Libchaber, A.

    1988-09-20

    Experimental observations of nonlinear problems in physics are presented, including liquid crystal phase transformations, convection of mercury, and the transition to turbulence in helium gas thermal convection./aip/.

  7. SEACAS Theory Manuals: Part II. Nonlinear Continuum Mechanics

    DOE Office of Scientific and Technical Information (OSTI.GOV)

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

    1998-09-01

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

  8. High-order statistical equalizer for nonlinearity compensation in dispersion-managed coherent optical communications.

    PubMed

    Koike-Akino, Toshiaki; Duan, Chunjie; Parsons, Kieran; Kojima, Keisuke; Yoshida, Tsuyoshi; Sugihara, Takashi; Mizuochi, Takashi

    2012-07-02

    Fiber nonlinearity has become a major limiting factor to realize ultra-high-speed optical communications. We propose a fractionally-spaced equalizer which exploits a trained high-order statistics to deal with data-pattern dependent nonlinear impairments in fiber-optic communications. The computer simulation reveals that the proposed 3-tap equalizer improves Q-factor by more than 2 dB for long-haul transmissions of 5,230 km distance and 40 Gbps data rate. We also demonstrate that the joint use of a digital backpropagation (DBP) and the proposed equalizer offers an additional 1-2 dB performance improvement due to the channel shortening gain. A performance in high-speed transmissions of 100 Gbps and beyond is evaluated as well.

  9. Numerical investigation of an all-optical switch in a graded nonlinear plasmonic grating.

    PubMed

    Wang, Guoxi; Lu, Hua; Liu, Xueming; Gong, Yongkang

    2012-11-09

    We have proposed and numerically investigated an all-optical switch based on a metal-insulator-metal waveguide with graded nonlinear plasmonic gratings. The influences of grating depth and refractive index of a Kerr nonlinear medium on the transmission of the switch are exactly analyzed by utilizing transmission line theory. The finite-difference time-domain simulation results show that the highly compact structure possesses excellent switch function by tuning the incident electric field intensity. In addition, the simulation results show that this all-optical switch has an ultrawide operating frequency regime and femtosecond-scale response time (~130 fs). Such a switch can find potential applications for all-optical signal processing and optical communication.

  10. User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures

    NASA Technical Reports Server (NTRS)

    Whitcomb, J. D.; Dattaguru, B.

    1984-01-01

    GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.

  11. The non-linear power spectrum of the Lyman alpha forest

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Arinyo-i-Prats, Andreu; Miralda-Escudé, Jordi; Viel, Matteo

    2015-12-01

    The Lyman alpha forest power spectrum has been measured on large scales by the BOSS survey in SDSS-III at z∼ 2.3, has been shown to agree well with linear theory predictions, and has provided the first measurement of Baryon Acoustic Oscillations at this redshift. However, the power at small scales, affected by non-linearities, has not been well examined so far. We present results from a variety of hydrodynamic simulations to predict the redshift space non-linear power spectrum of the Lyα transmission for several models, testing the dependence on resolution and box size. A new fitting formula is introduced to facilitate themore » comparison of our simulation results with observations and other simulations. The non-linear power spectrum has a generic shape determined by a transition scale from linear to non-linear anisotropy, and a Jeans scale below which the power drops rapidly. In addition, we predict the two linear bias factors of the Lyα forest and provide a better physical interpretation of their values and redshift evolution. The dependence of these bias factors and the non-linear power on the amplitude and slope of the primordial fluctuations power spectrum, the temperature-density relation of the intergalactic medium, and the mean Lyα transmission, as well as the redshift evolution, is investigated and discussed in detail. A preliminary comparison to the observations shows that the predicted redshift distortion parameter is in good agreement with the recent determination of Blomqvist et al., but the density bias factor is lower than observed. We make all our results publicly available in the form of tables of the non-linear power spectrum that is directly obtained from all our simulations, and parameters of our fitting formula.« less

  12. Building Blocks for Reliable Complex Nonlinear Numerical Simulations

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

    2002-01-01

    This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

  13. Modified Taylor series method for solving nonlinear differential equations with mixed boundary conditions defined on finite intervals.

    PubMed

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel Antonio; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Marin-Hernandez, Antonio; Herrera-May, Agustin Leobardo; Diaz-Sanchez, Alejandro; Huerta-Chua, Jesus

    2014-01-01

    In this article, we propose the application of a modified Taylor series method (MTSM) for the approximation of nonlinear problems described on finite intervals. The issue of Taylor series method with mixed boundary conditions is circumvented using shooting constants and extra derivatives of the problem. In order to show the benefits of this proposal, three different kinds of problems are solved: three-point boundary valued problem (BVP) of third-order with a hyperbolic sine nonlinearity, two-point BVP for a second-order nonlinear differential equation with an exponential nonlinearity, and a two-point BVP for a third-order nonlinear differential equation with a radical nonlinearity. The result shows that the MTSM method is capable to generate easily computable and highly accurate approximations for nonlinear equations. 34L30.

  14. Status of the Monte Carlo library least-squares (MCLLS) approach for non-linear radiation analyzer problems

    NASA Astrophysics Data System (ADS)

    Gardner, Robin P.; Xu, Libai

    2009-10-01

    The Center for Engineering Applications of Radioisotopes (CEAR) has been working for over a decade on the Monte Carlo library least-squares (MCLLS) approach for treating non-linear radiation analyzer problems including: (1) prompt gamma-ray neutron activation analysis (PGNAA) for bulk analysis, (2) energy-dispersive X-ray fluorescence (EDXRF) analyzers, and (3) carbon/oxygen tool analysis in oil well logging. This approach essentially consists of using Monte Carlo simulation to generate the libraries of all the elements to be analyzed plus any other required background libraries. These libraries are then used in the linear library least-squares (LLS) approach with unknown sample spectra to analyze for all elements in the sample. Iterations of this are used until the LLS values agree with the composition used to generate the libraries. The current status of the methods (and topics) necessary to implement the MCLLS approach is reported. This includes: (1) the Monte Carlo codes such as CEARXRF, CEARCPG, and CEARCO for forward generation of the necessary elemental library spectra for the LLS calculation for X-ray fluorescence, neutron capture prompt gamma-ray analyzers, and carbon/oxygen tools; (2) the correction of spectral pulse pile-up (PPU) distortion by Monte Carlo simulation with the code CEARIPPU; (3) generation of detector response functions (DRF) for detectors with linear and non-linear responses for Monte Carlo simulation of pulse-height spectra; and (4) the use of the differential operator (DO) technique to make the necessary iterations for non-linear responses practical. In addition to commonly analyzed single spectra, coincidence spectra or even two-dimensional (2-D) coincidence spectra can also be used in the MCLLS approach and may provide more accurate results.

  15. Nonlinear model predictive control of a wave energy converter based on differential flatness parameterisation

    NASA Astrophysics Data System (ADS)

    Li, Guang

    2017-01-01

    This paper presents a fast constrained optimization approach, which is tailored for nonlinear model predictive control of wave energy converters (WEC). The advantage of this approach relies on its exploitation of the differential flatness of the WEC model. This can reduce the dimension of the resulting nonlinear programming problem (NLP) derived from the continuous constrained optimal control of WEC using pseudospectral method. The alleviation of computational burden using this approach helps to promote an economic implementation of nonlinear model predictive control strategy for WEC control problems. The method is applicable to nonlinear WEC models, nonconvex objective functions and nonlinear constraints, which are commonly encountered in WEC control problems. Numerical simulations demonstrate the efficacy of this approach.

  16. Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations.

    PubMed

    Hu, Eric Y; Bouteiller, Jean-Marie C; Song, Dong; Baudry, Michel; Berger, Theodore W

    2015-01-01

    Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

  17. Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations

    PubMed Central

    Hu, Eric Y.; Bouteiller, Jean-Marie C.; Song, Dong; Baudry, Michel; Berger, Theodore W.

    2015-01-01

    Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations. PMID:26441622

  18. Neural networks for feedback feedforward nonlinear control systems.

    PubMed

    Parisini, T; Zoppoli, R

    1994-01-01

    This paper deals with the problem of designing feedback feedforward control strategies to drive the state of a dynamic system (in general, nonlinear) so as to track any desired trajectory joining the points of given compact sets, while minimizing a certain cost function (in general, nonquadratic). Due to the generality of the problem, conventional methods are difficult to apply. Thus, an approximate solution is sought by constraining control strategies to take on the structure of multilayer feedforward neural networks. After discussing the approximation properties of neural control strategies, a particular neural architecture is presented, which is based on what has been called the "linear-structure preserving principle". The original functional problem is then reduced to a nonlinear programming one, and backpropagation is applied to derive the optimal values of the synaptic weights. Recursive equations to compute the gradient components are presented, which generalize the classical adjoint system equations of N-stage optimal control theory. Simulation results related to nonlinear nonquadratic problems show the effectiveness of the proposed method.

  19. Fully Nonlinear Modeling and Analysis of Precision Membranes

    NASA Technical Reports Server (NTRS)

    Pai, P. Frank; Young, Leyland G.

    2003-01-01

    High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

  20. High efficiency all-optical plasmonic diode based on a nonlinear side-coupled waveguide-cavity structure with broken symmetry

    NASA Astrophysics Data System (ADS)

    Liang, Hong-Qin; Liu, Bin; Hu, Jin-Feng; He, Xing-Dao

    2018-05-01

    An all-optical plasmonic diode, comprising a metal-insulator-metal waveguide coupled with a stub cavity, is proposed based on a nonlinear Fano structure. The key technique used is to break structural spatial symmetry by a simple reflector layer in the waveguide. The spatial asymmetry of the structure gives rise to the nonreciprocity of coupling efficiencies between the Fano cavity and waveguides on both sides of the reflector layer, leading to a nonreciprocal nonlinear response. Transmission properties and dynamic responses are numerically simulated and investigated by the nonlinear finite-difference time-domain method. In the proposed structure, high-efficiency nonreciprocal transmission can be achieved with a low power threshold and an ultrafast response time (subpicosecond level). A high maximum transmittance of 89.3% and an ultra-high transmission contrast ratio of 99.6% can also be obtained. The device can be flexibly adjusted for working wavebands by altering the stub cavity length.

  1. A programmable nonlinear acoustic metamaterial

    NASA Astrophysics Data System (ADS)

    Yang, Tianzhi; Song, Zhi-Guang; Clerkin, Eoin; Zhang, Ye-Wei; Sun, Jia-He; Su, Yi-Shu; Chen, Li-Qun; Hagedorn, Peter

    2017-09-01

    Acoustic metamaterials with specifically designed lattices can manipulate acoustic/elastic waves in unprecedented ways. Whereas there are many studies that focus on passive linear lattice, with non-reconfigurable structures. In this letter, we present the design, theory and experimental demonstration of an active nonlinear acoustic metamaterial, the dynamic properties of which can be modified instantaneously with reversibility. By incorporating active and nonlinear elements in a single unit cell, a real-time tunability and switchability of the band gap is achieved. In addition, we demonstrate a dynamic "editing" capability for shaping transmission spectra, which can be used to create the desired band gap and resonance. This feature is impossible to achieve in passive metamaterials. These advantages demonstrate the versatility of the proposed device, paving the way toward smart acoustic devices, such as logic elements, diode and transistor.

  2. An adaptive model order reduction by proper snapshot selection for nonlinear dynamical problems

    NASA Astrophysics Data System (ADS)

    Nigro, P. S. B.; Anndif, M.; Teixeira, Y.; Pimenta, P. M.; Wriggers, P.

    2016-04-01

    Model Order Reduction (MOR) methods are employed in many fields of Engineering in order to reduce the processing time of complex computational simulations. A usual approach to achieve this is the application of Galerkin projection to generate representative subspaces (reduced spaces). However, when strong nonlinearities in a dynamical system are present and this technique is employed several times along the simulation, it can be very inefficient. This work proposes a new adaptive strategy, which ensures low computational cost and small error to deal with this problem. This work also presents a new method to select snapshots named Proper Snapshot Selection (PSS). The objective of the PSS is to obtain a good balance between accuracy and computational cost by improving the adaptive strategy through a better snapshot selection in real time (online analysis). With this method, it is possible a substantial reduction of the subspace, keeping the quality of the model without the use of the Proper Orthogonal Decomposition (POD).

  3. Method for solving the problem of nonlinear heating a cylindrical body with unknown initial temperature

    NASA Astrophysics Data System (ADS)

    Yaparova, N.

    2017-10-01

    We consider the problem of heating a cylindrical body with an internal thermal source when the main characteristics of the material such as specific heat, thermal conductivity and material density depend on the temperature at each point of the body. We can control the surface temperature and the heat flow from the surface inside the cylinder, but it is impossible to measure the temperature on axis and the initial temperature in the entire body. This problem is associated with the temperature measurement challenge and appears in non-destructive testing, in thermal monitoring of heat treatment and technical diagnostics of operating equipment. The mathematical model of heating is represented as nonlinear parabolic PDE with the unknown initial condition. In this problem, both the Dirichlet and Neumann boundary conditions are given and it is required to calculate the temperature values at the internal points of the body. To solve this problem, we propose the numerical method based on using of finite-difference equations and a regularization technique. The computational scheme involves solving the problem at each spatial step. As a result, we obtain the temperature function at each internal point of the cylinder beginning from the surface down to the axis. The application of the regularization technique ensures the stability of the scheme and allows us to significantly simplify the computational procedure. We investigate the stability of the computational scheme and prove the dependence of the stability on the discretization steps and error level of the measurement results. To obtain the experimental temperature error estimates, computational experiments were carried out. The computational results are consistent with the theoretical error estimates and confirm the efficiency and reliability of the proposed computational scheme.

  4. Equalization of nonlinear transmission impairments by maximum-likelihood-sequence estimation in digital coherent receivers.

    PubMed

    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.

  5. Non-linear vibrations of sandwich viscoelastic shells

    NASA Astrophysics Data System (ADS)

    Benchouaf, Lahcen; Boutyour, El Hassan; Daya, El Mostafa; Potier-Ferry, Michel

    2018-04-01

    This paper deals with the non-linear vibration of sandwich viscoelastic shell structures. Coupling a harmonic balance method with the Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. This permits to get the non-linear frequency and the non-linear loss factor as functions of the displacement amplitude. To validate our approach, these relationships are illustrated in the case of a circular sandwich ring.

  6. Hyperextended Cosmological Perturbation Theory: Predicting Nonlinear Clustering Amplitudes

    NASA Astrophysics Data System (ADS)

    Scoccimarro, Román; Frieman, Joshua A.

    1999-07-01

    We consider the long-standing problem of predicting the hierarchical clustering amplitudes Sp in the strongly nonlinear regime of gravitational evolution. N-body results for the nonlinear evolution of the bispectrum (the Fourier transform of the three-point density correlation function) suggest a physically motivated Ansatz that yields the strongly nonlinear behavior of the skewness, S3, starting from leading-order perturbation theory. When generalized to higher order (p>3) polyspectra or correlation functions, this Ansatz leads to a good description of nonlinear amplitudes in the strongly nonlinear regime for both scale-free and cold dark matter models. Furthermore, these results allow us to provide a general fitting formula for the nonlinear evolution of the bispectrum that interpolates between the weakly and strongly nonlinear regimes, analogous to previous expressions for the power spectrum.

  7. Analysis of dynamic channel power equalization by using nonlinear amplifying Sagnac interferometer for ASK-WDM optical transmission

    NASA Astrophysics Data System (ADS)

    Qu, Feng; Liu, Xiaoming; Zhao, Jianhui

    2004-05-01

    A power equalization using an asymmetric nonlinear amplifying Sagnac interferometer (NASI) for ASK modulation is studied numerically. A nonreciprocal phase bias was proposed to be introduced into the structure. The nonreciprocal phase bias reduces not only the demanding for amplifier power or fiber non-linearity, but also increase the dynamic input power range. The power equalization is demonstrated for RZ modulation by nonlinear phase analysis and eye diagram simulation.

  8. Use of Picard and Newton iteration for solving nonlinear ground water flow equations

    USGS Publications Warehouse

    Mehl, S.

    2006-01-01

    This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.

  9. Development of solution techniques for nonlinear structural analysis

    NASA Technical Reports Server (NTRS)

    Vos, R. G.; Andrews, J. S.

    1974-01-01

    Nonlinear structural solution methods in the current research literature are classified according to order of the solution scheme, and it is shown that the analytical tools for these methods are uniformly derivable by perturbation techniques. A new perturbation formulation is developed for treating an arbitrary nonlinear material, in terms of a finite-difference generated stress-strain expansion. Nonlinear geometric effects are included in an explicit manner by appropriate definition of an applicable strain tensor. A new finite-element pilot computer program PANES (Program for Analysis of Nonlinear Equilibrium and Stability) is presented for treatment of problems involving material and geometric nonlinearities, as well as certain forms on nonconservative loading.

  10. Indirect learning control for nonlinear dynamical systems

    NASA Technical Reports Server (NTRS)

    Ryu, Yeong Soon; Longman, Richard W.

    1993-01-01

    In a previous paper, learning control algorithms were developed based on adaptive control ideas for linear time variant systems. The learning control methods were shown to have certain advantages over their adaptive control counterparts, such as the ability to produce zero tracking error in time varying systems, and the ability to eliminate repetitive disturbances. In recent years, certain adaptive control algorithms have been developed for multi-body dynamic systems such as robots, with global guaranteed convergence to zero tracking error for the nonlinear system euations. In this paper we study the relationship between such adaptive control methods designed for this specific class of nonlinear systems, and the learning control problem for such systems, seeking to converge to zero tracking error in following a specific command repeatedly, starting from the same initial conditions each time. The extension of these methods from the adaptive control problem to the learning control problem is seen to be trivial. The advantages and disadvantages of using learning control based on such adaptive control concepts for nonlinear systems, and the use of other currently available learning control algorithms are discussed.

  11. Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential

    NASA Astrophysics Data System (ADS)

    Cipolatti, R.; de Macedo Lira, Y.; Trallero-Giner, C.

    2018-03-01

    We consider a generalized nonlinear Schrödinger equation (GNLS) with a single power nonlinearity of the form λ ≤ft\\vert \\varphi \\right\\vert p , with p  >  0 and λ\\in{R} , in the presence of a harmonic confinement. We report the conditions that p and λ must fulfill for the existence and uniqueness of ground states of the GNLS. We discuss the Cauchy problem and summarize which conditions are required for the nonlinear term λ ≤ft\\vert \\varphi \\right\\vert p to render the ground state solutions orbitally stable. Based on a new variational method we provide exact formulæ for the minimum energy for each index p and the changing range of values of the nonlinear parameter λ. Also, we report an approximate close analytical expression for the ground state energy, performing a comparative analysis of the present variational calculations with those obtained by a generalized Thomas-Fermi approach, and soliton solutions for the respective ranges of p and λ where these solutions can be implemented to describe the minimum energy.

  12. Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations

    NASA Technical Reports Server (NTRS)

    Tessler, Alexander; Sleight, David W.

    2006-01-01

    Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.

  13. Linear and nonlinear dynamic analysis of redundant load path bearingless rotor systems

    NASA Technical Reports Server (NTRS)

    Murthy, V. R.; Shultz, Louis A.

    1994-01-01

    The goal of this research is to develop the transfer matrix method to treat nonlinear autonomous boundary value problems with multiple branches. The application is the complete nonlinear aeroelastic analysis of multiple-branched rotor blades. Once the development is complete, it can be incorporated into the existing transfer matrix analyses. There are several difficulties to be overcome in reaching this objective. The conventional transfer matrix method is limited in that it is applicable only to linear branch chain-like structures, but consideration of multiple branch modeling is important for bearingless rotors. Also, hingeless and bearingless rotor blade dynamic characteristics (particularly their aeroelasticity problems) are inherently nonlinear. The nonlinear equations of motion and the multiple-branched boundary value problem are treated together using a direct transfer matrix method. First, the formulation is applied to a nonlinear single-branch blade to validate the nonlinear portion of the formulation. The nonlinear system of equations is iteratively solved using a form of Newton-Raphson iteration scheme developed for differential equations of continuous systems. The formulation is then applied to determine the nonlinear steady state trim and aeroelastic stability of a rotor blade in hover with two branches at the root. A comprehensive computer program is developed and is used to obtain numerical results for the (1) free vibration, (2) nonlinearly deformed steady state, (3) free vibration about the nonlinearly deformed steady state, and (4) aeroelastic stability tasks. The numerical results obtained by the present method agree with results from other methods.

  14. Deer density and disease prevalence influence transmission of Chronic Wasting Disease in White-tailed Deer

    USGS Publications Warehouse

    Samuel, Michael D.; Richards, Bryan J.; Storm, Daniel J.; Rolley, Robert E.; Shelton, Paul; Nicholas S. Keuler,; Timothy R. Van Deelen,

    2013-01-01

    Host-parasite dynamics and strategies for managing infectious diseases of wildlife depend on the functional relationship between disease transmission rates and host density. However, the disease transmission function is rarely known for free-living wildlife, leading to uncertainty regarding the impacts of diseases on host populations and effective control actions. We evaluated the influence of deer density, landscape features, and soil clay content on transmission of chronic wasting disease (CWD) in young (<2-year-old) white-tailed deer (Odocoileus virginianus) in south-central Wisconsin, USA. We evaluated how frequency-dependent, density-dependent, and intermediate transmission models predicted CWD incidence rates in harvested yearling deer. An intermediate transmission model, incorporating both disease prevalence and density of infected deer, performed better than simple density- and frequency-dependent models. Our results indicate a combination of social structure, non-linear relationships between infectious contact and deer density, and distribution of disease among groups are important factors driving CWD infection in young deer. The landscape covariates % deciduous forest cover and forest edge density also were positively associated with infection rates, but soil clay content had no measurable influences on CWD transmission. Lack of strong density-dependent transmission rates indicates that controlling CWD by reducing deer density will be difficult. The consequences of non-linear disease transmission and aggregation of disease on cervid populations deserves further consideration.

  15. Solution algorithms for nonlinear transient heat conduction analysis employing element-by-element iterative strategies

    NASA Technical Reports Server (NTRS)

    Winget, J. M.; Hughes, T. J. R.

    1985-01-01

    The particular problems investigated in the present study arise from nonlinear transient heat conduction. One of two types of nonlinearities considered is related to a material temperature dependence which is frequently needed to accurately model behavior over the range of temperature of engineering interest. The second nonlinearity is introduced by radiation boundary conditions. The finite element equations arising from the solution of nonlinear transient heat conduction problems are formulated. The finite element matrix equations are temporally discretized, and a nonlinear iterative solution algorithm is proposed. Algorithms for solving the linear problem are discussed, taking into account the form of the matrix equations, Gaussian elimination, cost, and iterative techniques. Attention is also given to approximate factorization, implementational aspects, and numerical results.

  16. Computational Methods for Nonlinear Dynamics Problems in Solid and Structural Mechanics: Models of Dynamic Frictional Phenomena in Metallic Structures.

    DTIC Science & Technology

    1986-03-31

    Martins, J.A.C. and Campos , L.T. [1986], "Existence and Local Uniqueness of Solutions to Contact Problems in Elasticity with Nonlinear Friction...noisy and ttoubl esome vibt.t4ons. If the sound generated by the friction-induced oscillations of Rviolin strings may be the delight of all music lovers...formulation. See 0den and Martins - [1985] and Rabier, Martins, Oden and Campos [1986]. - It is now simple to show, in a 6o’uman manner, that, for

  17. Nonlinear dynamics and quantum entanglement in optomechanical systems.

    PubMed

    Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso

    2014-03-21

    To search for and exploit quantum manifestations of classical nonlinear dynamics is one of the most fundamental problems in physics. Using optomechanical systems as a paradigm, we address this problem from the perspective of quantum entanglement. We uncover strong fingerprints in the quantum entanglement of two common types of classical nonlinear dynamical behaviors: periodic oscillations and quasiperiodic motion. There is a transition from the former to the latter as an experimentally adjustable parameter is changed through a critical value. Accompanying this process, except for a small region about the critical value, the degree of quantum entanglement shows a trend of continuous increase. The time evolution of the entanglement measure, e.g., logarithmic negativity, exhibits a strong dependence on the nature of classical nonlinear dynamics, constituting its signature.

  18. Nonlinear time-series-based adaptive control applications

    NASA Technical Reports Server (NTRS)

    Mohler, R. R.; Rajkumar, V.; Zakrzewski, R. R.

    1991-01-01

    A control design methodology based on a nonlinear time-series reference model is presented. It is indicated by highly nonlinear simulations that such designs successfully stabilize troublesome aircraft maneuvers undergoing large changes in angle of attack as well as large electric power transients due to line faults. In both applications, the nonlinear controller was significantly better than the corresponding linear adaptive controller. For the electric power network, a flexible AC transmission system with series capacitor power feedback control is studied. A bilinear autoregressive moving average reference model is identified from system data, and the feedback control is manipulated according to a desired reference state. The control is optimized according to a predictive one-step quadratic performance index. A similar algorithm is derived for control of rapid changes in aircraft angle of attack over a normally unstable flight regime. In the latter case, however, a generalization of a bilinear time-series model reference includes quadratic and cubic terms in angle of attack.

  19. Magnetoplasmonic RF mixing and nonlinear frequency generation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Firby, C. J., E-mail: firby@ualberta.ca; Elezzabi, A. Y.

    2016-07-04

    We present the design of a magnetoplasmonic Mach-Zehnder interferometer (MZI) modulator facilitating radio-frequency (RF) mixing and nonlinear frequency generation. This is achieved by forming the MZI arms from long-range dielectric-loaded plasmonic waveguides containing bismuth-substituted yttrium iron garnet (Bi:YIG). The magnetization of the Bi:YIG can be driven in the nonlinear regime by RF magnetic fields produced around adjacent transmission lines. Correspondingly, the nonlinear temporal dynamics of the transverse magnetization component are mapped onto the nonreciprocal phase shift in the MZI arms, and onto the output optical intensity signal. We show that this tunable mechanism can generate harmonics, frequency splitting, and frequencymore » down-conversion with a single RF excitation, as well as RF mixing when driven by two RF signals. This magnetoplasmonic component can reduce the number of electrical sources required to generate distinct optical modulation frequencies and is anticipated to satisfy important applications in integrated optics.« less

  20. Nonlinear field equations for aligning self-propelled rods.

    PubMed

    Peshkov, Anton; Aranson, Igor S; Bertin, Eric; Chaté, Hugues; Ginelli, Francesco

    2012-12-28

    We derive a set of minimal and well-behaved nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.

  1. Special discontinuities in nonlinearly elastic media

    NASA Astrophysics Data System (ADS)

    Chugainova, A. P.

    2017-06-01

    Solutions of a nonlinear hyperbolic system of equations describing weakly nonlinear quasitransverse waves in a weakly anisotropic elastic medium are studied. The influence of small-scale processes of dissipation and dispersion is investigated. The small-scale processes determine the structure of discontinuities (shocks) and a set of discontinuities with a stationary structure. Among the discontinuities with a stationary structure, there are special ones that, in addition to relations following from conservation laws, satisfy additional relations required for the existence of their structure. In the phase plane, the structure of such discontinuities is represented by an integral curve joining two saddles. Special discontinuities lead to nonunique self-similar solutions of the Riemann problem. Asymptotics of non-self-similar problems for equations with dissipation and dispersion are found numerically. These asymptotics correspond to self-similar solutions of the problems.

  2. Kinetic theory of nonlinear diffusion in a weakly disordered nonlinear Schrödinger chain in the regime of homogeneous chaos.

    PubMed

    Basko, D M

    2014-02-01

    We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ρ satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(ρ) = D(0)ρ(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed.

  3. Nonlinear optical transmittance of semiconductors in the presence of high-intensity radiation fields

    NASA Astrophysics Data System (ADS)

    Dong, H. M.; Han, F. W.; Duan, Y. F.; Huang, F.; Liu, J. L.

    2018-04-01

    We developed a systematic theoretical study of nonlinear optical properties of semiconductors. The eight-band kṡp model and the energy-balance equation are employed to calculate the transmission and optical absorption coefficients in the presence of both the linear one-photon absorption and the nonlinear two-photon absorption (TPA) processes. A substantial reduction of the optical transmittance far below the band-gap can be observed under relatively high-intensity radiation fields due to the nonlinear TPA. The TPA-induced optical transmittance decreases with increasing intensity of the radiation fields. Our theoretical results are in line with those observed experimentally. The theoretical approach can be applied to understand the nonlinear optical properties of semiconductors under high-field conditions.

  4. Nonlinear optical waves with the second Painleve transcendent shape of envelope in Kerr media

    NASA Astrophysics Data System (ADS)

    Shcherbakov, Alexandre S.; Tepichin Rodriguez, Eduardo; Sanchez Sanchez, Mauro

    2004-05-01

    Nonlinear optical wave packets with the second Painleve transcendent shape of envelope are revealed in Kerr media, manifesting weakly focusing cubic nonlinearity, square-law dispersion, and linear losses. When the state of nonlinear optical transmission is realized, two possible types of boundary conditions turn out to be satisfied for these wave packets. The propagation of initially unchirped optical wave packets under consideration could be supported by lossless medium in both normal and anomalous dispersion regimes. At the same time initially chirped optical waves with the second Painleve transcendent shape in low-loss medium and need matching the magnitude of optical losses by the dispersion and nonlinear properties of that medium.

  5. Z-Scan Measurement of the Nonlinear Absorption of a Thin Gold Film

    NASA Technical Reports Server (NTRS)

    Smith, David D.; Yoon, Youngkwon; Boyd, Robert W.; Campbell, Joseph K.; Baker, Lane A.; Crooks, Richard M.; George, Michael

    1999-01-01

    We have used the z-scan technique at a wavelength (532 nm) near the transmission window of bulk gold to measure the nonlinear absorption coefficient of continuous approximately 50-Angstrom-thick gold films, deposited onto surface-modified quartz substrates. For highly absorbing media such as metals, we demonstrate that determination of either the real or imaginary part of the third-order susceptibility requires a measurement of both nonlinear absorption and nonlinear refraction, i.e. both open- and closed-aperture z-scans must be performed. Closed-aperture z-scans did not yield a sufficient signal for the determination of the nonlinear refraction. However, open-aperture z-scans yielded values ranging from Beta = 1.9 x 10(exp -3) to 5.3 x 10(exp -3) cm/W in good agreement with predictions which ascribe the nonlinear response to a Fermi smearing mechanism. We note that the sign of the nonlinearity is reversed from that of gold nanoparticle composites, in accordance with the predictions of mean field theories.

  6. Study of optical nonlinearities in Se-Te-Bi thin films

    NASA Astrophysics Data System (ADS)

    Sharma, Ambika; Yadav, Preeti; Kumari, Anshu

    2014-04-01

    The present work reports the nonlinear refractive index of Se85-xTe15Bix thin films calculated by Ticha and Tichy relation. The nonlinear refractive index of Chalcogenide amorphous semiconductor is well correlated with the linear refractive index and WDD parameters which in turn depend on the density and molar volume of the system. The density of the system is calculated theoretical as well as experimentally by using Archimedes principle. The linear refractive index and WDD parameters are calculated using single transmission spectra in the spectral range of 400-1500 nm. It is observed that linear as well as nonlinear refractive index increases with Bi content. The results are analyzed on the basis of increasing polarizability due to larger radii of Bi.

  7. Transmission degradation and preservation for tapered optical fibers in rubidium vapor.

    PubMed

    Lai, Meimei; Franson, James D; Pittman, Todd B

    2013-04-20

    The use of subwavelength diameter tapered optical fibers (TOFs) in warm rubidium vapor has recently been identified as a promising system for realizing ultralow-power nonlinear optical effects. However, at the relatively high atomic densities needed for many of these experiments, rubidium atoms accumulating on the TOF surface can cause a significant loss of overall transmission through the fiber. Here we report direct measurements of the time scale associated with this transmission degradation for various rubidium density conditions. Transmission is affected almost immediately after the introduction of rubidium vapor into the system, and declines rapidly as the density is increased. More significantly, we show how a heating element designed to raise the TOF temperature can be used to reduce this transmission loss and dramatically extend the effective TOF transmission lifetime.

  8. Exploring equivalence domain in nonlinear inverse problems using Covariance Matrix Adaption Evolution Strategy (CMAES) and random sampling

    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.

  9. Bright breathers in nonlinear left-handed metamaterial lattices

    NASA Astrophysics Data System (ADS)

    Koukouloyannis, V.; Kevrekidis, P. G.; Veldes, G. P.; Frantzeskakis, D. J.; DiMarzio, D.; Lan, X.; Radisic, V.

    2018-02-01

    In the present work, we examine a prototypical model for the formation of bright breathers in nonlinear left-handed metamaterial lattices. Utilizing the paradigm of nonlinear transmission lines, we build a relevant lattice and develop a quasi-continuum multiscale approximation that enables us to appreciate both the underlying linear dispersion relation and the potential for bifurcation of nonlinear states. We focus here, more specifically, on bright discrete breathers which bifurcate from the lower edge of the linear dispersion relation at wavenumber k=π . Guided by the multiscale analysis, we calculate numerically both the stable inter-site centered and the unstable site-centered members of the relevant family. We quantify the associated stability via Floquet analysis and the Peierls-Nabarro barrier of the energy difference between these branches. Finally, we explore the dynamical implications of these findings towards the potential mobility or lack thereof (pinning) of such breather solutions.

  10. Vibration isolation using extreme geometric nonlinearity

    NASA Astrophysics Data System (ADS)

    Virgin, L. N.; Santillan, S. T.; Plaut, R. H.

    2008-08-01

    A highly deformed, slender beam (or strip), attached to a vertically oscillating base, is used in a vibration isolation application to reduce the motion of a supported mass. The isolator is a thin strip that is bent so that the two ends are clamped together, forming a loop. The clamped ends are attached to an excitation source and the supported system is attached at the loop midpoint directly above the base. The strip is modeled as an elastica, and the resulting nonlinear boundary value problem is solved numerically using a shooting method. First the equilibrium shapes of the loop with varying static loads and lengths are studied. The analysis reveals a large degree of stiffness tunability; the stiffness is dependent on the geometric configuration, which itself is determined by the supported mass, loop length, and loop self-weight. Free vibration frequencies and mode shapes are also found. Finally, the case of forced vibration is studied, and the displacement transmissibility over a large range of forcing frequencies is determined for varying parameter values. Experiments using polycarbonate strips are conducted to verify equilibrium and dynamic behavior.

  11. NOLIN: A nonlinear laminate analysis program

    NASA Technical Reports Server (NTRS)

    Kibler, J. J.

    1975-01-01

    A nonlinear, plane-stress, laminate analysis program, NOLIN, was developed which accounts for laminae nonlinearity under inplane shear and transverse extensional stress. The program determines the nonlinear stress-strain behavior of symmetric laminates subjected to any combination of inplane shear and biaxial extensional loadings. The program has the ability to treat different stress-strain behavior in tension and compression, and predicts laminate failure using any or all of maximum stress, maximum strain, and quadratic interaction failure criteria. A brief description of the program is presented including discussion of the flow of information and details of the input required. Sample problems and a complete listing of the program is also provided.

  12. NONLINEAR OPTICAL EFFECTS AND FIBER OPTICS: Theory of four-wave mixing in photorefractive media when the response of a medium is nonlinear in respect of the modulation parameter

    NASA Astrophysics Data System (ADS)

    Zozulya, A. A.

    1988-12-01

    A theoretical model is constructed for four-wave mixing in a photorefractive crystal where a transmission grating is formed by the drift-diffusion nonlinearity mechanism in the absence of an external electrostatic field and the response of the medium is nonlinear in respect of the modulation parameter. A comparison is made with a model in which the response of the medium is linear in respect of the modulation parameter. Theoretical models of four-wave and two-wave mixing are also compared with experiments.

  13. Nonlinear plasmonic behavior of nanohole arrays in thin gold films for imaging lipids

    NASA Astrophysics Data System (ADS)

    Subramaniyam, Nagarajan; Shah, Ali; Dreser, Christoph; Isomäki, Antti; Fleischer, Monika; Sopanen, Markku

    2018-06-01

    We demonstrate linear and nonlinear plasmonic behaviors of periodic nanohole arrays in thin gold (Au) films with varying periodicities. As expected, the linear optical transmission spectra of the nanohole arrays show a red-shift of the resonance wavelength and Wood's anomaly with increasing hole spacing. The optical transmission and electric near-field intensity distribution of the nanohole arrays are simulated using the finite element method. The nonlinear plasmonic behavior of the nanohole arrays is studied by using picosecond pulsed excitation at near-infrared wavelengths. The characteristic nonlinear signals indicating two-photon excited luminescence (TPEL), sum frequency generation, second harmonic generation, and four-wave mixing (FWM) are observed. A maximum FWM/TPEL signal intensity ratio is achieved for nanohole arrays with a periodicity of 500 nm. Furthermore, the significant FWM signal intensity and contrast compared to the background were harnessed to demonstrate the ability of surface-enhanced coherent anti-Stokes Raman scattering to visualize low concentrations of lipids deposited on the nanohole array with a periodicity of 500 nm.

  14. Approximation Methods for Inverse Problems Governed by Nonlinear Parabolic Systems

    DTIC Science & Technology

    1999-12-17

    We present a rigorous theoretical framework for approximation of nonlinear parabolic systems with delays in the context of inverse least squares...numerical results demonstrating the convergence are given for a model of dioxin uptake and elimination in a distributed liver model that is a special case of the general theoretical framework .

  15. Nonlinear coherent optical image processing using logarithmic transmittance of bacteriorhodopsin films

    NASA Astrophysics Data System (ADS)

    Downie, John D.

    1995-08-01

    The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

  16. Nonlinear Coherent Optical Image Processing Using Logarithmic Transmittance of Bacteriorhodopsin Films

    NASA Technical Reports Server (NTRS)

    Downie, John D.

    1995-01-01

    The transmission properties of some bacteriorhodopsin-film spatial light modulators are uniquely suited to allow nonlinear optical image-processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude-transmission characteristic of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. I present experimental results demonstrating the principle and the capability for several different image and noise situations, including deterministic noise and speckle. The bacteriorhodopsin film studied here displays the logarithmic transmission response for write intensities spanning a dynamic range greater than 2 orders of magnitude.

  17. Transmission Planning Analysis Tool

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    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 analysismore » and voltage stability analysis and QV analysis of many scenarios of study and arrange them in a systematic way to aid power system planning engineers or transmission operators in effective decision]making process or in the off]line study environment.« less

  18. Finite difference time domain calculation of transients in antennas with nonlinear loads

    NASA Technical Reports Server (NTRS)

    Luebbers, Raymond J.; Beggs, John H.; Kunz, Karl S.; Chamberlin, Kent

    1991-01-01

    Determining transient electromagnetic fields in antennas with nonlinear loads is a challenging problem. Typical methods used involve calculating frequency domain parameters at a large number of different frequencies, then applying Fourier transform methods plus nonlinear equation solution techniques. If the antenna is simple enough so that the open circuit time domain voltage can be determined independently of the effects of the nonlinear load on the antennas current, time stepping methods can be applied in a straightforward way. Here, transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain (FDTD) methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case, the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets, including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

  19. Solutions for a Kirchhoff equation with critical Caffarelli–Kohn–Nirenberg growth and discontinuous nonlinearity

    NASA Astrophysics Data System (ADS)

    dos Santos, Gelson G.; Figueiredo, Giovany M.

    2018-06-01

    In this paper, we study the existence of nonegative solutions to a class of nonlinear boundary value problems of the Kirchhoff type. We prove existence results when the problem has discontinuous nonlinearity and critical Caffarelli-Kohn-Nirenberg growth.

  20. Adaptive Nonlinear RF Cancellation for Improved Isolation in Simultaneous Transmit–Receive Systems

    NASA Astrophysics Data System (ADS)

    Kiayani, Adnan; Waheed, Muhammad Zeeshan; Anttila, Lauri; Abdelaziz, Mahmoud; Korpi, Dani; Syrjala, Ville; Kosunen, Marko; Stadius, Kari; Ryynanen, Jussi; Valkama, Mikko

    2018-05-01

    This paper proposes an active radio frequency (RF) cancellation solution to suppress the transmitter (TX) passband leakage signal in radio transceivers supporting simultaneous transmission and reception. The proposed technique is based on creating an opposite-phase baseband equivalent replica of the TX leakage signal in the transceiver digital front-end through adaptive nonlinear filtering of the known transmit data, to facilitate highly accurate cancellation under a nonlinear TX power amplifier (PA). The active RF cancellation is then accomplished by employing an auxiliary transmitter chain, to generate the actual RF cancellation signal, and combining it with the received signal at the receiver (RX) low noise amplifier (LNA) input. A closed-loop parameter learning approach, based on the decorrelation principle, is also developed to efficiently estimate the coefficients of the nonlinear cancellation filter in the presence of a nonlinear TX PA with memory, finite passive isolation, and a nonlinear RX LNA. The performance of the proposed cancellation technique is evaluated through comprehensive RF measurements adopting commercial LTE-Advanced transceiver hardware components. The results show that the proposed technique can provide an additional suppression of up to 54 dB for the TX passband leakage signal at the RX LNA input, even at considerably high transmit power levels and with wide transmission bandwidths. Such novel cancellation solution can therefore substantially improve the TX-RX isolation, hence reducing the requirements on passive isolation and RF component linearity, as well as increasing the efficiency and flexibility of the RF spectrum use in the emerging 5G radio networks.

  1. ISS method for coordination control of nonlinear dynamical agents under directed topology.

    PubMed

    Wang, Xiangke; Qin, Jiahu; Yu, Changbin

    2014-10-01

    The problems of coordination of multiagent systems with second-order locally Lipschitz continuous nonlinear dynamics under directed interaction topology are investigated in this paper. A completely nonlinear input-to-state stability (ISS)-based framework, drawing on ISS methods, with the aid of results from graph theory, matrix theory, and the ISS cyclic-small-gain theorem, is proposed for the coordination problem under directed topology, which can effectively tackle the technical challenges caused by locally Lipschitz continuous dynamics. Two coordination problems, i.e., flocking with a virtual leader and containment control, are considered. For both problems, it is assumed that only a portion of the agents can obtain the information from the leader(s). For the first problem, the proposed strategy is shown effective in driving a group of nonlinear dynamical agents reach the prespecified geometric pattern under the condition that at least one agent in each strongly connected component of the information-interconnection digraph with zero in-degree has access to the state information of the virtual leader; and the strategy proposed for the second problem can guarantee the nonlinear dynamical agents moving to the convex hull spanned by the positions of multiple leaders under the condition that for each agent there exists at least one leader that has a directed path to this agent.

  2. Optical rogue waves for the inhomogeneous generalized nonlinear Schrödinger equation.

    PubMed

    Loomba, Shally; Kaur, Harleen

    2013-12-01

    We present optical rogue wave solutions for a generalized nonlinear Schrodinger equation by using similarity transformation. We have predicted the propagation of rogue waves through a nonlinear optical fiber for three cases: (i) dispersion increasing (decreasing) fiber, (ii) periodic dispersion parameter, and (iii) hyperbolic dispersion parameter. We found that the rogue waves and their interactions can be tuned by properly choosing the parameters. We expect that our results can be used to realize improved signal transmission through optical rogue waves.

  3. Design sensitivity analysis of nonlinear structural response

    NASA Technical Reports Server (NTRS)

    Cardoso, J. B.; Arora, J. S.

    1987-01-01

    A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use.

  4. Overdetermined elliptic problems in topological disks

    NASA Astrophysics Data System (ADS)

    Mira, Pablo

    2018-06-01

    We introduce a method, based on the Poincaré-Hopf index theorem, to classify solutions to overdetermined problems for fully nonlinear elliptic equations in domains diffeomorphic to a closed disk. Applications to some well-known nonlinear elliptic PDEs are provided. Our result can be seen as the analogue of Hopf's uniqueness theorem for constant mean curvature spheres, but for the general analytic context of overdetermined elliptic problems.

  5. Operational Risk Management is Ineffective at Addressing Nonlinear Problems

    DTIC Science & Technology

    2009-02-20

    brains are not linear: even though the sound of an oboe and the sound of a string section may be independent when they enter your ear, the emotional...impact of both sounds together may be very much greater than either one alone. (This is what keeps symphony orchestras in business .) Nor is the...involving people. “In nonlinear systems... chaos theory tells you that the slightest uncertainty in your knowledge of the initial conditions will often

  6. Measurement Model Nonlinearity in Estimation of Dynamical Systems

    NASA Astrophysics Data System (ADS)

    Majji, Manoranjan; Junkins, J. L.; Turner, J. D.

    2012-06-01

    The role of nonlinearity of the measurement model and its interactions with the uncertainty of measurements and geometry of the problem is studied in this paper. An examination of the transformations of the probability density function in various coordinate systems is presented for several astrodynamics applications. Smooth and analytic nonlinear functions are considered for the studies on the exact transformation of uncertainty. Special emphasis is given to understanding the role of change of variables in the calculus of random variables. The transformation of probability density functions through mappings is shown to provide insight in to understanding the evolution of uncertainty in nonlinear systems. Examples are presented to highlight salient aspects of the discussion. A sequential orbit determination problem is analyzed, where the transformation formula provides useful insights for making the choice of coordinates for estimation of dynamic systems.

  7. Theoretical and experimental study on PMD-supported transmission using polarization diversity in coherent optical OFDM systems.

    PubMed

    Shieh, W; Yi, X; Ma, Y; Tang, Y

    2007-08-06

    In this paper, we conduct theoretical and experimental study on the PMD-supported transmission with coherent optical orthogonal frequency-division multiplexing (CO-OFDM). We first present the model for the optical fiber communication channel in the presence of the polarization effects. It shows that the optical fiber channel model can be treated as a special kind of multiple-input multiple-output (MIMO) model, namely, a two-input two-output (TITO) model which is intrinsically represented by a two-element Jones vector familiar to the optical communications community. The detailed discussions on various coherent optical MIMO-OFDM (CO-MIMO-OFDM) models are presented. Furthermore, we show the first experiment of polarization-diversity detection in CO-OFDM systems. In particular, a CO-OFDM signal at 10.7 Gb/s is successfully recovered after 900 ps differential-group-delay (DGD) and 1000-km transmission through SSMF fiber without optical dispersion compensation. The transmission experiment with higher-order PMD further confirms the immunity of the CO-OFDM signal to PMD in the transmission fiber. The nonlinearity performance of PMD-supported transmission is also reported. For the first time, nonlinear phase noise mitigation based on receiver digital signal processing is experimentally demonstrated for CO-OFDM transmission.

  8. Goertler vortices in growing boundary layers: The leading edge receptivity problem, linear growth and the nonlinear breakdown stage

    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.

  9. Theoretical investigation of dielectric corona pre-ionization TEA nitrogen laser based on transmission line method

    NASA Astrophysics Data System (ADS)

    Bahrampour, Alireza; Fallah, Robabeh; Ganjovi, Alireza A.; Bahrampour, Abolfazl

    2007-07-01

    This paper models the dielectric corona pre-ionization, capacitor transfer type of flat-plane transmission line traveling wave transverse excited atmospheric pressure nitrogen laser by a non-linear lumped RLC electric circuit. The flat-plane transmission line and the pre-ionizer dielectric are modeled by a lumped linear RLC and time-dependent non-linear RC circuit, respectively. The main discharge region is considered as a time-dependent non-linear RLC circuit where its resistance value is also depends on the radiated pre-ionization ultra violet (UV) intensity. The UV radiation is radiated by the resistance due to the surface plasma on the pre-ionizer dielectric. The theoretical predictions are in a very good agreement with the experimental observations. The electric circuit equations (including the ionization rate equations), the equations of laser levels population densities and propagation equation of laser intensities, are solved numerically. As a result, the effects of pre-ionizer dielectric parameters on the electrical behavior and output laser intensity are obtained.

  10. Sound transmission in ducts containing nearly choked flows

    NASA Technical Reports Server (NTRS)

    Callegari, A. J.; Myers, M. K.

    1979-01-01

    The nonlinear theory previously developed by the authors (1977, 1978) is used to obtain numerical results for sound transmission through a nearly choked throat in a variable-area duct. Parametric studies are performed for different source locations, strengths and frequencies. It is shown that the nonlinear interactions in the throat region generate superharmonics of the fundamental (source) frequency throughout the duct. The amplitudes of these superharmonics increase as the source parameters (frequency and strength) are increased toward values leading to acoustic shocks. For a downstream source, superharmonics carry about 20% of the total acoustic power as shocking conditions are approached. For the source strength levels and frequencies considered, streaming effects are negligible.

  11. Non-linear dynamic analysis of geared systems, part 2

    NASA Technical Reports Server (NTRS)

    Singh, Rajendra; Houser, Donald R.; Kahraman, Ahmet

    1990-01-01

    A good understanding of the steady state dynamic behavior of a geared system is required in order to design reliable and quiet transmissions. This study focuses on a system containing a spur gear pair with backlash and periodically time-varying mesh stiffness, and rolling element bearings with clearance type non-linearities. A dynamic finite element model of the linear time-invariant (LTI) system is developed. Effects of several system parameters, such as torsional and transverse flexibilities of the shafts and prime mover/load inertias, on free and force vibration characteristics are investigated. Several reduced order LTI models are developed and validated by comparing their eigen solution with the finite element model results. Several key system parameters such as mean load and damping ratio are identified and their effects on the non-linear frequency response are evaluated quantitatively. Other fundamental issues such as the dynamic coupling between non-linear modes, dynamic interactions between component non-linearities and time-varying mesh stiffness, and the existence of subharmonic and chaotic solutions including routes to chaos have also been examined in depth.

  12. Towards adjoint-based inversion for rheological parameters in nonlinear viscous mantle flow

    NASA Astrophysics Data System (ADS)

    Worthen, Jennifer; Stadler, Georg; Petra, Noemi; Gurnis, Michael; Ghattas, Omar

    2014-09-01

    We address the problem of inferring mantle rheological parameter fields from surface velocity observations and instantaneous nonlinear mantle flow models. We formulate this inverse problem as an infinite-dimensional nonlinear least squares optimization problem governed by nonlinear Stokes equations. We provide expressions for the gradient of the cost functional of this optimization problem with respect to two spatially-varying rheological parameter fields: the viscosity prefactor and the exponent of the second invariant of the strain rate tensor. Adjoint (linearized) Stokes equations, which are characterized by a 4th order anisotropic viscosity tensor, facilitates efficient computation of the gradient. A quasi-Newton method for the solution of this optimization problem is presented, which requires the repeated solution of both nonlinear forward Stokes and linearized adjoint Stokes equations. For the solution of the nonlinear Stokes equations, we find that Newton’s method is significantly more efficient than a Picard fixed point method. Spectral analysis of the inverse operator given by the Hessian of the optimization problem reveals that the numerical eigenvalues collapse rapidly to zero, suggesting a high degree of ill-posedness of the inverse problem. To overcome this ill-posedness, we employ Tikhonov regularization (favoring smooth parameter fields) or total variation (TV) regularization (favoring piecewise-smooth parameter fields). Solution of two- and three-dimensional finite element-based model inverse problems show that a constant parameter in the constitutive law can be recovered well from surface velocity observations. Inverting for a spatially-varying parameter field leads to its reasonable recovery, in particular close to the surface. When inferring two spatially varying parameter fields, only an effective viscosity field and the total viscous dissipation are recoverable. Finally, a model of a subducting plate shows that a localized weak zone at the

  13. Nonlinearization and waves in bounded media: old wine in a new bottle

    NASA Astrophysics Data System (ADS)

    Mortell, Michael P.; Seymour, Brian R.

    2017-02-01

    We consider problems such as a standing wave in a closed straight tube, a self-sustained oscillation, damped resonance, evolution of resonance and resonance between concentric spheres. These nonlinear problems, and other similar ones, have been solved by a variety of techniques when it is seen that linear theory fails. The unifying approach given here is to initially set up the appropriate linear difference equation, where the difference is the linear travel time. When the linear travel time is replaced by a corrected nonlinear travel time, the nonlinear difference equation yields the required solution.

  14. Nonlinear Optical Image Processing with Bacteriorhodopsin Films

    NASA Technical Reports Server (NTRS)

    Downie, John D.; Deiss, Ron (Technical Monitor)

    1994-01-01

    The transmission properties of some bacteriorhodopsin film spatial light modulators are uniquely suited to allow nonlinear optical image processing operations to be applied to images with multiplicative noise characteristics. A logarithmic amplitude transmission feature of the film permits the conversion of multiplicative noise to additive noise, which may then be linearly filtered out in the Fourier plane of the transformed image. The bacteriorhodopsin film displays the logarithmic amplitude response for write beam intensities spanning a dynamic range greater than 2.0 orders of magnitude. We present experimental results demonstrating the principle and capability for several different image and noise situations, including deterministic noise and speckle. Using the bacteriorhodopsin film, we successfully filter out image noise from the transformed image that cannot be removed from the original image.

  15. A Sequential Linear Quadratic Approach for Constrained Nonlinear Optimal Control with Adaptive Time Discretization and Application to Higher Elevation Mars Landing Problem

    NASA Astrophysics Data System (ADS)

    Sandhu, Amit

    A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state only constraints. The proposed algorithm further develops on the approach proposed in [1] with objective to eliminate the use of a high number of time intervals for arriving at an optimal solution. This is done by introducing an adaptive time discretization to allow formation of a desirable control profile without utilizing a lot of intervals. The use of fewer time intervals reduces the computation time considerably. This algorithm is further used in this thesis to solve a trajectory planning problem for higher elevation Mars landing.

  16. Impulsive response of an automatic transmission system with multiple clearances: Formulation, simulation and experiment

    NASA Astrophysics Data System (ADS)

    Crowther, Ashley R.; Singh, Rajendra; Zhang, Nong; Chapman, Chris

    2007-10-01

    Impulsive responses in geared systems with multiple clearances are studied when the mean torque excitation and system load change abruptly, with application to a vehicle driveline with an automatic transmission. First, torsional lumped-mass models of the planetary and differential gear sets are formulated using matrix elements. The model is then reduced to address tractable nonlinear problems while successfully retaining the main modes of interest. Second, numerical simulations for the nonlinear model are performed for transient conditions and a typical driving situation that induces an impulsive behaviour simulated. However, initial conditions and excitation and load profiles have to be carefully defined before the model can be numerically solved. It is shown that the impacts within the planetary or differential gears may occur under combinations of engine, braking and vehicle load transients. Our analysis shows that the shaping of the engine transient by the torque converter before reaching the clearance locations is more critical. Third, a free vibration experiment is developed for an analogous driveline with multiple clearances and three experiments that excite different response regimes have been carried out. Good correlations validate the proposed methodology.

  17. Volterra-series-based nonlinear system modeling and its engineering applications: A state-of-the-art review

    NASA Astrophysics Data System (ADS)

    Cheng, C. M.; Peng, Z. K.; Zhang, W. M.; Meng, G.

    2017-03-01

    Nonlinear problems have drawn great interest and extensive attention from engineers, physicists and mathematicians and many other scientists because most real systems are inherently nonlinear in nature. To model and analyze nonlinear systems, many mathematical theories and methods have been developed, including Volterra series. In this paper, the basic definition of the Volterra series is recapitulated, together with some frequency domain concepts which are derived from the Volterra series, including the general frequency response function (GFRF), the nonlinear output frequency response function (NOFRF), output frequency response function (OFRF) and associated frequency response function (AFRF). The relationship between the Volterra series and other nonlinear system models and nonlinear problem solving methods are discussed, including the Taylor series, Wiener series, NARMAX model, Hammerstein model, Wiener model, Wiener-Hammerstein model, harmonic balance method, perturbation method and Adomian decomposition. The challenging problems and their state of arts in the series convergence study and the kernel identification study are comprehensively introduced. In addition, a detailed review is then given on the applications of Volterra series in mechanical engineering, aeroelasticity problem, control engineering, electronic and electrical engineering.

  18. On the dispersionless Kadomtsev-Petviashvili equation with arbitrary nonlinearity and dimensionality: exact solutions, longtime asymptotics of the Cauchy problem, wave breaking and shocks

    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.

  19. Building Blocks for Reliable Complex Nonlinear Numerical Simulations. Chapter 2

    NASA Technical Reports Server (NTRS)

    Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

    2001-01-01

    This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

  20. Direct application of Padé approximant for solving nonlinear differential equations.

    PubMed

    Vazquez-Leal, Hector; Benhammouda, Brahim; Filobello-Nino, Uriel; Sarmiento-Reyes, Arturo; Jimenez-Fernandez, Victor Manuel; Garcia-Gervacio, Jose Luis; Huerta-Chua, Jesus; Morales-Mendoza, Luis Javier; Gonzalez-Lee, Mario

    2014-01-01

    This work presents a direct procedure to apply Padé method to find approximate solutions for nonlinear differential equations. Moreover, we present some cases study showing the strength of the method to generate highly accurate rational approximate solutions compared to other semi-analytical methods. The type of tested nonlinear equations are: a highly nonlinear boundary value problem, a differential-algebraic oscillator problem, and an asymptotic problem. The high accurate handy approximations obtained by the direct application of Padé method shows the high potential if the proposed scheme to approximate a wide variety of problems. What is more, the direct application of the Padé approximant aids to avoid the previous application of an approximative method like Taylor series method, homotopy perturbation method, Adomian Decomposition method, homotopy analysis method, variational iteration method, among others, as tools to obtain a power series solutions to post-treat with the Padé approximant. 34L30.

  1. Fourier series expansion for nonlinear Hamiltonian oscillators.

    PubMed

    Méndez, Vicenç; Sans, Cristina; Campos, Daniel; Llopis, Isaac

    2010-06-01

    The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relationship. We compare our results with other recent approaches such as variational methods or heuristic approximations, in particular the Ren-He's method. Based on its application to the Duffing oscillator, the nonlinear pendulum and the eardrum equation, it is shown that the Fourier series expansion method is the most accurate.

  2. Nonlinear Spectroscopy.

    DTIC Science & Technology

    1985-03-20

    Finally, the (linear) .response of a Fabry - Perot cavity to a phase modulated light wave is considered because of its relevance to phase locking a laser...prepared and therefore doesn’t contribute. This effect provides the remaining factor of two. IV. FABRY - PEROT We now calculate the response of a plane...mirror Fabry - Perot cavity to a phase-modulated laser beam. This linear problem, which contrasts with the nonlinear atomic case, is the basis of an

  3. Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

    NASA Astrophysics Data System (ADS)

    Pipkins, Daniel Scott

    Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially. problem involves a simply supported rhombic plate. &The bending moments in the non-linear model are compared to those

  4. A study of selected radiation and propagation problems related to antennas and probes in magneto-ionic media

    NASA Technical Reports Server (NTRS)

    1973-01-01

    Research consisted of computations toward the solution of the problem of the current distribution on a cylindrical antenna in a magnetoplasma. The case of an antenna parallel to the applied magnetic field was investigated. A systematic method of asymptotic expansion was found which simplifies the solution in the general case by giving the field of a dipole even at relatively short range. Some useful properties of the dispersion surfaces in a lossy medium have also been found. A laboratory experiment was directed toward evaluating nonlinear effects, such as those due to power level, bias voltage and electron heating. The problem of reflection and transmission of waves in an electron heated plasma was treated theoretically. The profile inversion problem has been pursued. Some results are very encouraging, however, the general question of stability of the solution remains unsolved.

  5. Reflection and Transmission of a Focused Finite Amplitude Sound Beam Incident on a Curved Interface

    NASA Astrophysics Data System (ADS)

    Makin, Inder Raj Singh

    Reflection and transmission of a finite amplitude focused sound beam at a weakly curved interface separating two fluid-like media are investigated. The KZK parabolic wave equation, which accounts for thermoviscous absorption, diffraction, and nonlinearity, is used to describe the high intensity focused beam. The first part of the work deals with the quasilinear analysis of a weakly nonlinear beam after its reflection and transmission from a curved interface. A Green's function approach is used to define the field integrals describing the primary and the nonlinearly generated second harmonic beam. Closed-form solutions are obtained for the primary and second harmonic beams when a Gaussian amplitude distribution at the source is assumed. The second part of the research uses a numerical frequency domain solution of the KZK equation for a fully nonlinear analysis of the reflected and transmitted fields. Both piston and Gaussian sources are considered. Harmonic components generated in the medium due to propagation of the focused beam are evaluated, and formation of shocks in the reflected and transmitted beams is investigated. A finite amplitude focused beam is observed to be modified due to reflection and transmission from a curved interface in a manner distinct from that in the case of a small signal beam. Propagation curves, beam patterns, phase plots and time waveforms for various parameters defining the source and media pairs are presented, highlighting the effect of the interface curvature on the reflected and transmitted beams. Relevance of the current work to biomedical applications of ultrasound is discussed.

  6. Experimental observation of the generation of cutoff solitons in a discrete L C nonlinear electrical line

    NASA Astrophysics Data System (ADS)

    Koon, K. Tse Ve; Marquié, P.; Dinda, P. Tchofo

    2014-11-01

    We address the problem of supratransmission of waves in a discrete nonlinear system, driven at one end by a periodic excitation at a frequency lying above the phonon band edge. In an experimental electrical transmission line made of 200 inductance-capacitance LC cells, we establish the existence of a voltage threshold for a supratransmission enabling the generation and propagation of cut-off solitons within the line. The decisive role of modulational instability in the onset and development of the process of generation of cut-off solitons is clearly highlighted. The phenomenon of dissipation is identified as being particularly harmful for the soliton generation, but we show that its impact can be managed by a proper choice of the amplitude of the voltage excitation of the system.

  7. An efficient distribution method for nonlinear transport problems in highly heterogeneous stochastic porous media

    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

  8. Asymptotic Stability of Interconnected Passive Non-Linear Systems

    NASA Technical Reports Server (NTRS)

    Isidori, A.; Joshi, S. M.; Kelkar, A. G.

    1999-01-01

    This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

  9. Cascaded two-photon nonlinearity in a one-dimensional waveguide with multiple two-level emitters

    PubMed Central

    Roy, Dibyendu

    2013-01-01

    We propose and theoretically investigate a model to realize cascaded optical nonlinearity with few atoms and photons in one-dimension (1D). The optical nonlinearity in our system is mediated by resonant interactions of photons with two-level emitters, such as atoms or quantum dots in a 1D photonic waveguide. Multi-photon transmission in the waveguide is nonreciprocal when the emitters have different transition energies. Our theory provides a clear physical understanding of the origin of nonreciprocity in the presence of cascaded nonlinearity. We show how various two-photon nonlinear effects including spatial attraction and repulsion between photons, background fluorescence can be tuned by changing the number of emitters and the coupling between emitters (controlled by the separation). PMID:23948782

  10. Analytical-numerical solution of a nonlinear integrodifferential equation in econometrics

    NASA Astrophysics Data System (ADS)

    Kakhktsyan, V. M.; Khachatryan, A. Kh.

    2013-07-01

    A mixed problem for a nonlinear integrodifferential equation arising in econometrics is considered. An analytical-numerical method is proposed for solving the problem. Some numerical results are presented.

  11. Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems.

    PubMed

    Jiménez, Noé; Romero-García, Vicent; Pagneux, Vincent; Groby, Jean-Philippe

    2017-10-19

    Perfect, broadband and asymmetric sound absorption is theoretically, numerically and experimentally reported by using subwavelength thickness panels in a transmission problem. The panels are composed of a periodic array of varying crosssection waveguides, each of them being loaded by Helmholtz resonators (HRs) with graded dimensions. The low cut-off frequency of the absorption band is fixed by the resonance frequency of the deepest HR, that reduces drastically the transmission. The preceding HR is designed with a slightly higher resonance frequency with a geometry that allows the impedance matching to the surrounding medium. Therefore, reflection vanishes and the structure is critically coupled. This results in perfect sound absorption at a single frequency. We report perfect absorption at 300 Hz for a structure whose thickness is 40 times smaller than the wavelength. Moreover, this process is repeated by adding HRs to the waveguide, each of them with a higher resonance frequency than the preceding one. Using this frequency cascade effect, we report quasi-perfect sound absorption over almost two frequency octaves ranging from 300 to 1000 Hz for a panel composed of 9 resonators with a total thickness of 11 cm, i.e., 10 times smaller than the wavelength at 300 Hz.

  12. Exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium.

    PubMed

    Petrov, E Yu; Kudrin, A V

    2010-05-14

    The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of special importance and, at the same time, is an extremely complicated problem. It seems almost impossible to find a rigorous solution to such a problem even for any model of nonlinearity. We obtain the first exact solution of this type. We present a new method for deriving exact solutions of the Maxwell equations in a nonlinear medium without dispersion and give examples of the obtained solutions that describe propagation of cylindrical electromagnetic waves in a nonlinear nondispersive medium and free electromagnetic oscillations in a cylindrical cavity resonator filled with such a medium.

  13. Inverting Monotonic Nonlinearities by Entropy Maximization

    PubMed Central

    López-de-Ipiña Pena, Karmele; Caiafa, Cesar F.

    2016-01-01

    This paper proposes a new method for blind inversion of a monotonic nonlinear map applied to a sum of random variables. Such kinds of mixtures of random variables are found in source separation and Wiener system inversion problems, for example. The importance of our proposed method is based on the fact that it permits to decouple the estimation of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source separation matrix or deconvolution filter), which can be solved by applying any convenient linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes the idea of Gaussianization of the observation by maximizing its entropy instead. We developed two versions of our algorithm based either in a polynomial or a neural network parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear function and the probability distribution that gives a guarantee for the MaxEnt method to succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is compared with existing algorithms for blind approximation of nonlinear maps. Experiments show that MaxEnt is able to successfully compensate monotonic distortions outperforming other methods in terms of the obtained Signal to Noise Ratio in many important cases, for example when the number of variables in a mixture is small. Besides its ability for compensating nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results. PMID:27780261

  14. Inverting Monotonic Nonlinearities by Entropy Maximization.

    PubMed

    Solé-Casals, Jordi; López-de-Ipiña Pena, Karmele; Caiafa, Cesar F

    2016-01-01

    This paper proposes a new method for blind inversion of a monotonic nonlinear map applied to a sum of random variables. Such kinds of mixtures of random variables are found in source separation and Wiener system inversion problems, for example. The importance of our proposed method is based on the fact that it permits to decouple the estimation of the nonlinear part (nonlinear compensation) from the estimation of the linear one (source separation matrix or deconvolution filter), which can be solved by applying any convenient linear algorithm. Our new nonlinear compensation algorithm, the MaxEnt algorithm, generalizes the idea of Gaussianization of the observation by maximizing its entropy instead. We developed two versions of our algorithm based either in a polynomial or a neural network parameterization of the nonlinear function. We provide a sufficient condition on the nonlinear function and the probability distribution that gives a guarantee for the MaxEnt method to succeed compensating the distortion. Through an extensive set of simulations, MaxEnt is compared with existing algorithms for blind approximation of nonlinear maps. Experiments show that MaxEnt is able to successfully compensate monotonic distortions outperforming other methods in terms of the obtained Signal to Noise Ratio in many important cases, for example when the number of variables in a mixture is small. Besides its ability for compensating nonlinearities, MaxEnt is very robust, i.e. showing small variability in the results.

  15. Nonlinear Modeling by Assembling Piecewise Linear Models

    NASA Technical Reports Server (NTRS)

    Yao, Weigang; Liou, Meng-Sing

    2013-01-01

    To preserve nonlinearity of a full order system over a parameters range of interest, we propose a simple modeling approach by assembling a set of piecewise local solutions, including the first-order Taylor series terms expanded about some sampling states. The work by Rewienski and White inspired our use of piecewise linear local solutions. The assembly of these local approximations is accomplished by assigning nonlinear weights, through radial basis functions in this study. The efficacy of the proposed procedure is validated for a two-dimensional airfoil moving at different Mach numbers and pitching motions, under which the flow exhibits prominent nonlinear behaviors. All results confirm that our nonlinear model is accurate and stable for predicting not only aerodynamic forces but also detailed flowfields. Moreover, the model is robustness-accurate for inputs considerably different from the base trajectory in form and magnitude. This modeling preserves nonlinearity of the problems considered in a rather simple and accurate manner.

  16. Nonlinear system identification technique validation

    NASA Astrophysics Data System (ADS)

    Rudko, M.; Bussgang, J. J.

    1982-01-01

    This final technical report describes the results obtained by SIGNATRON, Inc. of Lexington MA on Air Force Contract F30602-80-C-0104 for Rome Air Development Center. The objective of this effort is to develop a technique for identifying system response of nonlinear circuits by measurements of output response to known inputs. The report describes results of a study into the system identification technique based on the pencil-of-function method previously explored by Jain (1974) and Ewen (1979). The procedure identified roles of the linear response and is intended as a first step in nonlinear response and is intended as a first step in nonlinear circuit identification. There are serious implementation problems associated with the original approach such as loss of accuracy due to repeated integrations, lack of good measures of accuracy and computational iteration to identify the number of poles.

  17. Optimisation of micro-perforated cylindrical silencers in linear and nonlinear regimes

    NASA Astrophysics Data System (ADS)

    Bravo, Teresa; Maury, Cédric; Pinhède, Cédric

    2016-02-01

    This paper describes analytical and experimental studies conducted to understand the potential of lightweight non-fibrous alternatives to dissipative mufflers for in-duct noise control problems, especially under high sound pressure levels (SPLs) and in the low frequency domain. The cost-efficient multi-modal propagation method has been extended to predict nonlinear effects in the dissipation and the transmission loss (TL) of micro-perforated cylindrical liners with sub-millimetric holes diameter. A validation experiment was performed in a standing wave tube to measure the power dissipated and transmitted by a nonlocally reacting liner under moderate and high SPLs. Although nonlinear effects significantly reduce the dissipation and TL around the liner maximum damping frequency, these power quantities may be enhanced below the half-bandwidth resonance. An optimal value of the in-hole peak particle velocity has been found that maximizes the TL of locally reacting liners at low frequencies. Optimisation studies based on dissipation or TL maximization showed the sensitivity of the liner constituting parameters to variations in the design target range such as the center frequency, the levels of acoustic excitation and the nature of the surface impedance (locally or nonlocally reacting). An analysis is proposed of the deviation observed at low frequencies between the optimum impedance of the locally reacting liner under moderate SPLs and Cremer's optimum impedances.

  18. Optical fiber sources and transmission controls for multi-Tb/s systems

    NASA Astrophysics Data System (ADS)

    Nowak, George Adelbert

    The accelerating demand for bandwidth capacity in backbone links of terrestrial communications systems is projected to exceed 1Tb/s by 2002. Lightwave carrier frequencies and fused-silica optical fibers provide the natural combination of high passband frequencies and low- loss medium to satisfy this evolving demand for bandwidth capacity. This thesis addresses three key technologies for enabling multi-Tb/s optical fiber communication systems. The first technology is a broadband source based on supercontinuum generation in optical fiber. Using a single modelocked laser with output pulsewidths of 0.5psec pulses, we generate in ~2m of dispersion-shifted fiber more that 200nm of spectral continuum in the vicinity of 1550nm that is flat to better than +/- 0.5 dB over more than 60nm. The short fiber length prevents degradation of timing jitter of the seed pulses and preserves coherence of the continuum by inhibiting environmental perturbations and mapping of random noise from the vicinity of the input pulse across the continuum. Through experiments and simulations, we find that the continuum characteristics result from 3rd order dispersion effects on higher-order soliton compression. We determine optimal fiber properties to provide desired continuum broadness and flatness for given input pulsewidth and energy conditions. The second technology is a novel delay-shifted nonlinear optical loop mirror (DS-NOLM) that performs a transmission control function by serving as an intensity filter and frequency compensator for <5psec soliton transmission systems. A theoretical and experimental study of the DS-NOLM as a transmission control element in a periodically amplified soliton transmission system is presented. We show that DS-NOLMs enable 4ps soliton transmission over 75km of standard dispersion fiber, with 25km spacing between amplifiers, by filtering the dispersive waves and compensating for Raman-induced soliton self-frequency shift. The third technology is all

  19. Influence of biofilm lubricity on shear-induced transmission of staphylococcal biofilms from stainless steel to silicone rubber.

    PubMed

    Gusnaniar, Niar; Sjollema, Jelmer; Jong, Ed D; Woudstra, Willem; de Vries, Joop; Nuryastuti, Titik; van der Mei, Henny C; Busscher, Henk J

    2017-11-01

    In real-life situations, bacteria are often transmitted from biofilms growing on donor surfaces to receiver ones. Bacterial transmission is more complex than adhesion, involving bacterial detachment from donor and subsequent adhesion to receiver surfaces. Here, we describe a new device to study shear-induced bacterial transmission from a (stainless steel) pipe to a (silicone rubber) tube and compare transmission of EPS-producing and non-EPS-producing staphylococci. Transmission of an entire biofilm from the donor to the receiver tube did not occur, indicative of cohesive failure in the biofilm rather than of adhesive failure at the donor-biofilm interface. Biofilm was gradually transmitted over an increasing length of receiver tube, occurring mostly to the first 50 cm of the receiver tube. Under high-shearing velocity, transmission of non-EPS-producing bacteria to the second half decreased non-linearly, likely due to rapid thinning of the lowly lubricious biofilm. Oppositely, transmission of EPS-producing strains to the second tube half was not affected by higher shearing velocity due to the high lubricity and stress relaxation of the EPS-rich biofilms, ensuring continued contact with the receiver. The non-linear decrease of ongoing bacterial transmission under high-shearing velocity is new and of relevance in for instance, high-speed food slicers and food packaging. © 2017 The Authors. Microbial Biotechnology published by John Wiley & Sons Ltd and Society for Applied Microbiology.

  20. Optical properties of solid-core photonic crystal fibers filled with nonlinear absorbers.

    PubMed

    Butler, James J; Bowcock, Alec S; Sueoka, Stacey R; Montgomery, Steven R; Flom, Steven R; Friebele, E Joseph; Wright, Barbara M; Peele, John R; Pong, Richard G S; Shirk, James S; Hu, Jonathan; Menyuk, Curtis R; Taunay, T F

    2013-09-09

    A theoretical and experimental investigation of the transmission of solid-core photonic crystal fibers (PCFs) filled with nonlinear absorbers shows a sharp change in the threshold for optical limiting and in leakage loss as the refractive index of the material in the holes approaches that of the glass matrix. Theoretical calculations of the mode profiles and leakage loss of the PCF are in agreement with experimental results and indicate that the change in limiting response is due to the interaction of the evanescent field of the guided mode with the nonlinear absorbers in the holes.

  1. Problem-Solving Rules for Genetics.

    ERIC Educational Resources Information Center

    Collins, Angelo

    The categories and applications of strategic knowledge as these relate to problem solving in the area of transmission genetics are examined in this research study. The role of computer simulations in helping students acquire the strategic knowledge necessary to solve realistic transmission genetics problems was emphasized. The Genetics…

  2. Robust nonlinear variable selective control for networked systems

    NASA Astrophysics Data System (ADS)

    Rahmani, Behrooz

    2016-10-01

    This paper is concerned with the networked control of a class of uncertain nonlinear systems. In this way, Takagi-Sugeno (T-S) fuzzy modelling is used to extend the previously proposed variable selective control (VSC) methodology to nonlinear systems. This extension is based upon the decomposition of the nonlinear system to a set of fuzzy-blended locally linearised subsystems and further application of the VSC methodology to each subsystem. To increase the applicability of the T-S approach for uncertain nonlinear networked control systems, this study considers the asynchronous premise variables in the plant and the controller, and then introduces a robust stability analysis and control synthesis. The resulting optimal switching-fuzzy controller provides a minimum guaranteed cost on an H2 performance index. Simulation studies on three nonlinear benchmark problems demonstrate the effectiveness of the proposed method.

  3. The numerical dynamic for highly nonlinear partial differential equations

    NASA Technical Reports Server (NTRS)

    Lafon, A.; Yee, H. C.

    1992-01-01

    Problems associated with the numerical computation of highly nonlinear equations in computational fluid dynamics are set forth and analyzed in terms of the potential ranges of spurious behaviors. A reaction-convection equation with a nonlinear source term is employed to evaluate the effects related to spatial and temporal discretizations. The discretization of the source term is described according to several methods, and the various techniques are shown to have a significant effect on the stability of the spurious solutions. Traditional linearized stability analyses cannot provide the level of confidence required for accurate fluid dynamics computations, and the incorporation of nonlinear analysis is proposed. Nonlinear analysis based on nonlinear dynamical systems complements the conventional linear approach and is valuable in the analysis of hypersonic aerodynamics and combustion phenomena.

  4. Dynamic investigation of a locomotive with effect of gear transmissions under tractive conditions

    NASA Astrophysics Data System (ADS)

    Chen, Zaigang; Zhai, Wanming; Wang, Kaiyun

    2017-11-01

    Locomotive is used to drag trailers to move or supply the braking forces to slow the running speed of a train. The electromagnetic torque of the motor is always transmitted by the gear transmission system to the wheelset for generation of the tractive or braking forces at the wheel-rail contact interface. Consequently, gear transmission system is significant for power delivery of a locomotive. This paper develops a comprehensive locomotive-track vertical-longitudinal coupled dynamics model with dynamic effect of gear transmissions. This dynamics model enables considering the coupling interactions between the gear transmission motion, the vertical and the longitudinal motions of the vehicle, and the vertical vibration of the track structure. In this study, some complicated dynamic excitations, such as the gear time-varying mesh stiffness, nonlinear gear tooth backlash, the nonlinear wheel-rail normal contact force and creep force, and the rail vertical geometrical irregularity, are considered. Then, the dynamic responses of the locomotive under the tractive conditions are demonstrated by numerical simulations based on the established dynamics model and by experimental test. The developed dynamics model is validated by the good agreement between the experimental and the theoretical results. The calculated results reveal that the gear transmission system has strong dynamic interactions with the wheel-rail contact interface including both the vertical and the longitudinal motions, and it has negligible effect on the vibrations of the bogie frame and carbody.

  5. Fatigue damage evaluation of austenitic stainless steel using nonlinear ultrasonic waves in low cycle regime

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Zhang, Jianfeng; Xuan, Fu-Zhen, E-mail: fzxuan@ecust.edu.cn

    The interrupted low cycle fatigue test of austenitic stainless steel was conducted and the dislocation structure and fatigue damage was evaluated subsequently by using both transmission electron microscope and nonlinear ultrasonic wave techniques. A “mountain shape” correlation between the nonlinear acoustic parameter and the fatigue life fraction was achieved. This was ascribed to the generation and evolution of planar dislocation structure and nonplanar dislocation structure such as veins, walls, and cells. The “mountain shape” correlation was interpreted successfully by the combined contribution of dislocation monopole and dipole with an internal-stress dependent term of acoustic nonlinearity.

  6. Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

    PubMed

    Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem

    2018-01-01

    In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

  7. Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

    NASA Astrophysics Data System (ADS)

    Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

    2016-06-01

    This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

  8. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  9. Nonlinear bending models for beams and plates

    PubMed Central

    Antipov, Y. A.

    2014-01-01

    A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler–Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition. PMID:25294960

  10. Refinement and application of acoustic impulse technique to study nozzle transmission characteristics

    NASA Technical Reports Server (NTRS)

    Salikuddin, M.; Brown, W. H.; Ramakrishnan, R.; Tanna, H. K.

    1983-01-01

    An improved acoustic impulse technique was developed and was used to study the transmission characteristics of duct/nozzle systems. To accomplish the above objective, various problems associated with the existing spark-discharge impulse technique were first studied. These included (1) the nonlinear behavior of high intensity pulses, (2) the contamination of the signal with flow noise, (3) low signal-to-noise ratio at high exhaust velocities, and (4) the inability to control or shape the signal generated by the source, specially when multiple spark points were used as the source. The first step to resolve these problems was the replacement of the spark-discharge source with electroacoustic driver(s). These included (1) synthesizing on acoustic impulse with acoustic driver(s) to control and shape the output signal, (2) time domain signal averaging to remove flow noise from the contaminated signal, (3) signal editing to remove unwanted portions of the time history, (4) spectral averaging, and (5) numerical smoothing. The acoustic power measurement technique was improved by taking multiple induct measurements and by a modal decomposition process to account for the contribution of higher order modes in the power computation. The improved acoustic impulse technique was then validated by comparing the results derived by an impedance tube method. The mechanism of acoustic power loss, that occurs when sound is transmitted through nozzle terminations, was investigated. Finally, the refined impulse technique was applied to obtain more accurate results for the acoustic transmission characteristics of a conical nozzle and a multi-lobe multi-tube supressor nozzle.

  11. Tapered polysilicon core fibers for nonlinear photonics.

    PubMed

    Suhailin, Fariza H; Shen, Li; Healy, Noel; Xiao, Limin; Jones, Maxwell; Hawkins, Thomas; Ballato, John; Gibson, Ursula J; Peacock, Anna C

    2016-04-01

    We propose and demonstrate a novel approach to obtaining small-core polysilicon waveguides from the silicon fiber platform. The fibers were fabricated via a conventional drawing tower method and, subsequently, tapered down to achieve silicon core diameters of ∼1  μm, the smallest optical cores for this class of fiber to date. Characterization of the material properties have shown that the taper process helps to improve the local crystallinity of the silicon core, resulting in a significant reduction in the material loss. By exploiting the combination of small cores and low losses, these tapered fibers have enabled the first observation of nonlinear transmission within a polycrystalline silicon waveguide of any type. As the fiber drawing method is highly scalable, it opens a route for the development of low-cost and flexible nonlinear silicon photonic systems.

  12. Application of Contraction Mappings to the Control of Nonlinear Systems. Ph.D. Thesis

    NASA Technical Reports Server (NTRS)

    Killingsworth, W. R., Jr.

    1972-01-01

    The theoretical and applied aspects of successive approximation techniques are considered for the determination of controls for nonlinear dynamical systems. Particular emphasis is placed upon the methods of contraction mappings and modified contraction mappings. It is shown that application of the Pontryagin principle to the optimal nonlinear regulator problem results in necessary conditions for optimality in the form of a two point boundary value problem (TPBVP). The TPBVP is represented by an operator equation and functional analytic results on the iterative solution of operator equations are applied. The general convergence theorems are translated and applied to those operators arising from the optimal regulation of nonlinear systems. It is shown that simply structured matrices and similarity transformations may be used to facilitate the calculation of the matrix Green functions and the evaluation of the convergence criteria. A controllability theory based on the integral representation of TPBVP's, the implicit function theorem, and contraction mappings is developed for nonlinear dynamical systems. Contraction mappings are theoretically and practically applied to a nonlinear control problem with bounded input control and the Lipschitz norm is used to prove convergence for the nondifferentiable operator. A dynamic model representing community drug usage is developed and the contraction mappings method is used to study the optimal regulation of the nonlinear system.

  13. Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks

    NASA Astrophysics Data System (ADS)

    Rozdeba, Paul J.

    The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.

  14. Incremental passivity and output regulation for switched nonlinear systems

    NASA Astrophysics Data System (ADS)

    Pang, Hongbo; Zhao, Jun

    2017-10-01

    This paper studies incremental passivity and global output regulation for switched nonlinear systems, whose subsystems are not required to be incrementally passive. A concept of incremental passivity for switched systems is put forward. First, a switched system is rendered incrementally passive by the design of a state-dependent switching law. Second, the feedback incremental passification is achieved by the design of a state-dependent switching law and a set of state feedback controllers. Finally, we show that once the incremental passivity for switched nonlinear systems is assured, the output regulation problem is solved by the design of global nonlinear regulator controllers comprising two components: the steady-state control and the linear output feedback stabilising controllers, even though the problem for none of subsystems is solvable. Two examples are presented to illustrate the effectiveness of the proposed approach.

  15. Simulation program of nonlinearities applied to telecommunication systems

    NASA Technical Reports Server (NTRS)

    Thomas, C.

    1979-01-01

    In any satellite communication system, the problems of distorsion created by nonlinear devices or systems must be considered. The subject of this paper is the use of the Fast Fourier Transform (F.F.T.) in the prediction of the intermodulation performance of amplifiers, mixers, filters. A nonlinear memory-less model is chosen to simulate amplitude and phase nonlinearities of the device in the simulation program written in FORTRAN 4. The experimentally observed nonlinearity parameters of a low noise 3.7-4.2 GHz amplifier are related to the gain and phase coefficients of Fourier Service Series. The measured results are compared with those calculated from the simulation in the cases where the input signal is composed of two, three carriers and noise power density.

  16. GHM method for obtaining rationalsolutions of nonlinear differential equations.

    PubMed

    Vazquez-Leal, Hector; Sarmiento-Reyes, Arturo

    2015-01-01

    In this paper, we propose the application of the general homotopy method (GHM) to obtain rational solutions of nonlinear differential equations. It delivers a high precision representation of the nonlinear differential equation using a few linear algebraic terms. In order to assess the benefits of this proposal, three nonlinear problems are solved and compared against other semi-analytic methods or numerical methods. The obtained results show that GHM is a powerful tool, capable to generate highly accurate rational solutions. AMS subject classification 34L30.

  17. Perturbation solutions of combustion instability problems

    NASA Technical Reports Server (NTRS)

    Googerdy, A.; Peddieson, J., Jr.; Ventrice, M.

    1979-01-01

    A method involving approximate modal analysis using the Galerkin method followed by an approximate solution of the resulting modal-amplitude equations by the two-variable perturbation method (method of multiple scales) is applied to two problems of pressure-sensitive nonlinear combustion instability in liquid-fuel rocket motors. One problem exhibits self-coupled instability while the other exhibits mode-coupled instability. In both cases it is possible to carry out the entire linear stability analysis and significant portions of the nonlinear stability analysis in closed form. In the problem of self-coupled instability the nonlinear stability boundary and approximate forms of the limit-cycle amplitudes and growth and decay rates are determined in closed form while the exact limit-cycle amplitudes and growth and decay rates are found numerically. In the problem of mode-coupled instability the limit-cycle amplitudes are found in closed form while the growth and decay rates are found numerically. The behavior of the solutions found by the perturbation method are in agreement with solutions obtained using complex numerical methods.

  18. Design and implementation of optical switches based on nonlinear plasmonic ring resonators: Circular, square and octagon

    NASA Astrophysics Data System (ADS)

    Ghadrdan, Majid; Mansouri-Birjandi, Mohammad Ali

    2018-05-01

    In this paper, all-optical plasmonic switches (AOPS) based on various configurations of circular, square and octagon nonlinear plasmonic ring resonators (NPRR) were proposed and numerically investigated. Each of these configurations consisted of two metal-insulator-metal (MIM) waveguides coupled to each other by a ring resonator (RR). Nonlinear Kerr effect was used to show switching performance of the proposed NPRR. The result showed that the octagon switch structure had lower threshold power and higher transmission ratio than square and circular switch structures. The octagon switch structure had a low threshold power equal to 7.77 MW/cm2 and the high transmission ratio of approximately 0.6. Therefore, the octagon switch structure was an appropriate candidate to be applied in optical integration circuits as an AOPS.

  19. NONLINEAR AND FIBER OPTICS: Transmission of submillimeter laser beams along hollow-core dielectric waveguides

    NASA Astrophysics Data System (ADS)

    Epishin, V. A.; Maslov, Vyacheslav A.; Ryabykh, V. N.; Svich, V. A.; Topkov, A. N.

    1990-04-01

    Theoretical and experimental investigations are reported of the propagation of axisymmetric linearly polarized laser radiation beams along hollow-core dielectric waveguides. The conditions for transmission with minimum distortion of the complex amplitude and minimum excitation losses are established for beams in the form of Gaussian-Laguerre modes. A scaling relationship is obtained for the attenuation constant of the EH11 mode in glass waveguides acting as transmission lines and for laser cells handling submillimeter wavelengths.

  20. Solution of Nonlinear Systems

    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.

  1. A Robust Bayesian Random Effects Model for Nonlinear Calibration Problems

    PubMed Central

    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

  2. Privacy-preserving outlier detection through random nonlinear data distortion.

    PubMed

    Bhaduri, Kanishka; Stefanski, Mark D; Srivastava, Ashok N

    2011-02-01

    Consider a scenario in which the data owner has some private or sensitive data and wants a data miner to access them for studying important patterns without revealing the sensitive information. Privacy-preserving data mining aims to solve this problem by randomly transforming the data prior to their release to the data miners. Previous works only considered the case of linear data perturbations--additive, multiplicative, or a combination of both--for studying the usefulness of the perturbed output. In this paper, we discuss nonlinear data distortion using potentially nonlinear random data transformation and show how it can be useful for privacy-preserving anomaly detection from sensitive data sets. We develop bounds on the expected accuracy of the nonlinear distortion and also quantify privacy by using standard definitions. The highlight of this approach is to allow a user to control the amount of privacy by varying the degree of nonlinearity. We show how our general transformation can be used for anomaly detection in practice for two specific problem instances: a linear model and a popular nonlinear model using the sigmoid function. We also analyze the proposed nonlinear transformation in full generality and then show that, for specific cases, it is distance preserving. A main contribution of this paper is the discussion between the invertibility of a transformation and privacy preservation and the application of these techniques to outlier detection. The experiments conducted on real-life data sets demonstrate the effectiveness of the approach.

  3. Analysis on nonlinear optical properties of Cd (Zn) Se quantum dots synthesized using three different stabilizing agents

    NASA Astrophysics Data System (ADS)

    J, Joy Sebastian Prakash; G, Vinitha; Ramachandran, Murugesan; Rajamanickam, Karunanithi

    2017-10-01

    Three different stabilizing agents, namely, L-cysteine, Thioglycolic acid and cysteamine hydrochloride were used to synthesize Cd(Zn)Se quantum dots (QDs). It was characterized using UV-vis spectroscopy, x-ray diffraction (XRD) and transmission electron microscopy (TEM). The non-linear optical properties (non-linear absorption and non-linear refraction) of synthesized Cd(Zn)Se quantum dots were studied with z-scan technique using diode pumped continuous wavelaser system at a wavelength of 532 nm. Our (organic) synthesized quantum dots showed optical properties similar to the inorganic materials reported elsewhere.

  4. Cost Considerations in Nonlinear Finite-Element Computing

    NASA Technical Reports Server (NTRS)

    Utku, S.; Melosh, R. J.; Islam, M.; Salama, M.

    1985-01-01

    Conference paper discusses computational requirements for finiteelement analysis using quasi-linear approach to nonlinear problems. Paper evaluates computational efficiency of different computer architecturtural types in terms of relative cost and computing time.

  5. An efficient flexible-order model for 3D nonlinear water waves

    NASA Astrophysics Data System (ADS)

    Engsig-Karup, A. P.; Bingham, H. B.; Lindberg, O.

    2009-04-01

    The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal scaling of the solution effort multigrid is employed to precondition a GMRES iterative solution of the discretized Laplace problem. A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom. A new discretization scheme using one layer of grid points outside the fluid domain is presented and shown to provide convergent solutions over the full physical and discrete parameter space of interest. Linear analysis of the fundamental properties of the scheme with respect to accuracy, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental measurements and other calculations from the literature.

  6. Nonlinear THz absorption and cyclotron resonance in InSb

    NASA Astrophysics Data System (ADS)

    Heffernan, Kate; Yu, Shukai; Talbayev, Diyar

    The emergence of coherent high-field terahertz (THz) sources in the past decade has allowed the exploration of nonlinear light-matter interaction at THz frequencies. Nonlinear THz response of free electrons in semiconductors has received a great deal of attention. Such nonlinear phenomena as saturable absorption and self-phase modulation have been reported. InSb is a narrow-gap (bandgap 0.17 eV) semiconductor with a very low electron effective mass and high electron mobility. Previous high-field THz work on InSb reported the observation of ultrafast electron cascades via impact ionization. We study the transmission of an intense THz electric field pulse by an InSb wafer at different incident THz amplitudes and 10 K temperature. Contrary to previous reports, we observe an increased transmission at higher THz field. Our observation appears similar to the saturable THz absorption reported in other semiconductors. Along with the increased absorption, we observe a strong modulation of the THz phase at high incident fields, most likely due to the self-phase modulation of the THz pulse. We also study the dependence of the cyclotron resonance on the incident THz field amplitude. The cyclotron resonance exhibits a lower strength and frequency at the higher incident THz field. The work at Tulane was supported by the Louisiana Board of Regents through the Board of Regents Support Fund Contract No. LEQSF(2012-15)-RD-A-23 and through the Pilot Funding for New Research (PFund) Contract No. LEQSF-EPS(2014)-PFUND-378.

  7. Nonlinearity measure and internal model control based linearization in anti-windup design

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Perev, Kamen

    2013-12-18

    This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequencymore » ranges.« less

  8. Nonlinear multivariable design by total synthesis. [of gas turbine engine control systems

    NASA Technical Reports Server (NTRS)

    Sain, M. K.; Peczkowski, J. L.

    1982-01-01

    The Nominal Design Problem (NDP) is extended to nonlinear cases, and a new case study of robust feedback synthesis for gas turbine control design is presented. The discussion of NDP extends and builds on earlier Total Synthesis Problem theory and ideas. Some mathematical preliminaries are given in which a bijection from a set S onto a set T is considered, with T admitting the structure of an F-vector space. NDP is then discussed for a nonlinear plant, and nonlinear nominal design is defined and characterized. The design of local controllers for a turbojet and the scheduling of these controls into a global control are addressed.

  9. Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Agaltsov, A. D., E-mail: agalets@gmail.com; Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr; IEPT RAS, 117997 Moscow

    2014-10-15

    We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

  10. Extremely broadband, on-chip optical nonreciprocity enabled by mimicking nonlinear anti-adiabatic quantum jumps near exceptional points

    NASA Astrophysics Data System (ADS)

    Choi, Youngsun; Hahn, Choloong; Yoon, Jae Woong; Song, Seok Ho; Berini, Pierre

    2017-01-01

    Time-asymmetric state-evolution properties while encircling an exceptional point are presently of great interest in search of new principles for controlling atomic and optical systems. Here, we show that encircling-an-exceptional-point interactions that are essentially reciprocal in the linear interaction regime make a plausible nonlinear integrated optical device architecture highly nonreciprocal over an extremely broad spectrum. In the proposed strategy, we describe an experimentally realizable coupled-waveguide structure that supports an encircling-an-exceptional-point parametric evolution under the influence of a gain saturation nonlinearity. Using an intuitive time-dependent Hamiltonian and rigorous numerical computations, we demonstrate strictly nonreciprocal optical transmission with a forward-to-backward transmission ratio exceeding 10 dB and high forward transmission efficiency (~100%) persisting over an extremely broad bandwidth approaching 100 THz. This predicted performance strongly encourages experimental realization of the proposed concept to establish a practical on-chip optical nonreciprocal element for ultra-short laser pulses and broadband high-density optical signal processing.

  11. [On the problems of the evolutionary optimization of life history. II. To justification of optimization criterion for nonlinear Leslie model].

    PubMed

    Pasekov, V P

    2013-03-01

    The paper considers the problems in the adaptive evolution of life-history traits for individuals in the nonlinear Leslie model of age-structured population. The possibility to predict adaptation results as the values of organism's traits (properties) that provide for the maximum of a certain function of traits (optimization criterion) is studied. An ideal criterion of this type is Darwinian fitness as a characteristic of success of an individual's life history. Criticism of the optimization approach is associated with the fact that it does not take into account the changes in the environmental conditions (in a broad sense) caused by evolution, thereby leading to losses in the adequacy of the criterion. In addition, the justification for this criterion under stationary conditions is not usually rigorous. It has been suggested to overcome these objections in terms of the adaptive dynamics theory using the concept of invasive fitness. The reasons are given that favor the application of the average number of offspring for an individual, R(L), as an optimization criterion in the nonlinear Leslie model. According to the theory of quantitative genetics, the selection for fertility (that is, for a set of correlated quantitative traits determined by both multiple loci and the environment) leads to an increase in R(L). In terms of adaptive dynamics, the maximum R(L) corresponds to the evolutionary stability and, in certain cases, convergent stability of the values for traits. The search for evolutionarily stable values on the background of limited resources for reproduction is a problem of linear programming.

  12. Transmission rights and market power

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bushnell, J.

    1999-10-01

    Most of the concerns about physical transmission rights relate to the ability to implicitly or explicitly remove that transmission capacity from the market-place. Under a very strict form of physical right, owners could simply choose not to sell it if they don't want to use it. Modifications that require the release of spare capacity back into an open market could potentially alleviate this problem but there is concern that such releases would not occur far enough in advance to be of much use to schedulers. Similarly, the transmission capacity that is made available for use by non-rights holders can alsomore » be manipulated by the owners of transmission rights. The alternative form, financial transmission rights, provide to their owners congestion payments, but physical control of transmission paths. In electricity markets such as California's, even financial transmission rights could potentially be utilized to effectively withhold transmission capacity from the marketplace. However, methods for withholding transmission capacity are somewhat more convoluted, and probably more difficult, for owners of financial rights than for owners of physical rights. In this article, the author discusses some of the potential concerns over transmission rights and their use for the exercise of various forms of market power.« less

  13. Numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains.

    PubMed

    Li, Hongwei; Guo, Yue

    2017-12-01

    The numerical solution of the general coupled nonlinear Schrödinger equations on unbounded domains is considered by applying the artificial boundary method in this paper. In order to design the local absorbing boundary conditions for the coupled nonlinear Schrödinger equations, we generalize the unified approach previously proposed [J. Zhang et al., Phys. Rev. E 78, 026709 (2008)PLEEE81539-375510.1103/PhysRevE.78.026709]. Based on the methodology underlying the unified approach, the original problem is split into two parts, linear and nonlinear terms, and we then achieve a one-way operator to approximate the linear term to make the wave out-going, and finally we combine the one-way operator with the nonlinear term to derive the local absorbing boundary conditions. Then we reduce the original problem into an initial boundary value problem on the bounded domain, which can be solved by the finite difference method. The stability of the reduced problem is also analyzed by introducing some auxiliary variables. Ample numerical examples are presented to verify the accuracy and effectiveness of our proposed method.

  14. Non-linear aeroelastic prediction for aircraft applications

    NASA Astrophysics Data System (ADS)

    de C. Henshaw, M. J.; Badcock, K. J.; Vio, G. A.; Allen, C. B.; Chamberlain, J.; Kaynes, I.; Dimitriadis, G.; Cooper, J. E.; Woodgate, M. A.; Rampurawala, A. M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.

    2007-05-01

    Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the methods have served the industry well, it is clear that for a number of reasons the inclusion of non-linearity in the mathematical and computational aeroelastic prediction tools is highly desirable. The increase in available and affordable computational resources, together with major advances in algorithms, mean that non-linear aeroelastic tools are now viable within the aircraft design and qualification environment. The Partnership for Unsteady Methods in Aerodynamics (PUMA) Defence and Aerospace Research Partnership (DARP) was sponsored in 2002 to conduct research into non-linear aeroelastic prediction methods and an academic, industry, and government consortium collaborated to address the following objectives: To develop useable methodologies to model and predict non-linear aeroelastic behaviour of complete aircraft. To evaluate the methodologies on real aircraft problems. To investigate the effect of non-linearities on aeroelastic behaviour and to determine which have the greatest effect on the flutter qualification process. These aims have been very effectively met during the course of the programme and the research outputs include: New methods available to industry for use in the flutter prediction process, together with the appropriate coaching of industry engineers. Interesting results in both linear and non-linear aeroelastics, with comprehensive comparison of methods and approaches for challenging problems. Additional embryonic techniques that, with further research, will further improve aeroelastics capability. This paper describes the methods that have been developed and how they are deployable within the industrial environment. We present a thorough review of the PUMA aeroelastics programme together with a comprehensive review of the relevant research

  15. Anatomy of Ag/Hafnia-Based Selectors with 10 10 Nonlinearity

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Midya, Rivu; Wang, Zhongrui; Zhang, Jiaming

    We developed a novel Ag/oxide-based threshold switching device with attractive features including ≈10 10 nonlinearity. Furthermore, in a high-resolution transmission electron microscopic analysis of the nanoscale crosspoint device it is suggested that elongation of an Ag nanoparticle under voltage bias followed by spontaneous reformation of a more spherical shape after power off, is responsible for the observed threshold switching.

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

    NASA Technical Reports Server (NTRS)

    Polchinski, Joseph

    1991-01-01

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

  17. Anatomy of Ag/Hafnia-Based Selectors with 10 10 Nonlinearity

    DOE PAGES

    Midya, Rivu; Wang, Zhongrui; Zhang, Jiaming; ...

    2017-01-30

    We developed a novel Ag/oxide-based threshold switching device with attractive features including ≈10 10 nonlinearity. Furthermore, in a high-resolution transmission electron microscopic analysis of the nanoscale crosspoint device it is suggested that elongation of an Ag nanoparticle under voltage bias followed by spontaneous reformation of a more spherical shape after power off, is responsible for the observed threshold switching.

  18. Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints.

    PubMed

    Fan, Quan-Yong; Yang, Guang-Hong

    2017-01-01

    The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  19. Macroscopic response in active nonlinear photonic crystals.

    PubMed

    Alagappan, Gandhi; John, Sajeev; Li, Er Ping

    2013-09-15

    We derive macroscopic equations of motion for the slowly varying electric field amplitude in three-dimensional active nonlinear optical nanostructures. We show that the microscopic Maxwell equations and polarization dynamics can be simplified to a macroscopic one-dimensional problem in the direction of group velocity. For a three-level active material, we derive the steady-state equations for normal mode frequency, threshold pumping, nonlinear Bloch mode amplitude, and lasing in photonic crystals. Our analytical results accurately recapture the results of exact numerical methods.

  20. The effect of sexual transmission on Zika virus dynamics.

    PubMed

    Saad-Roy, C M; Ma, Junling; van den Driessche, P

    2018-04-25

    Zika virus is a human disease that may lead to neurological disorders in affected individuals, and may be transmitted vectorially (by mosquitoes) or sexually. A mathematical model of Zika virus transmission is formulated, taking into account mosquitoes, sexually active males and females, inactive individuals, and considering both vector transmission and sexual transmission from infectious males to susceptible females. Basic reproduction numbers are computed, and disease control strategies are evaluated. The effect of the incidence function used to model sexual transmission from infectious males to susceptible females is investigated. It is proved that for such functions that are sublinear, if the basic reproduction [Formula: see text], then the disease dies out and [Formula: see text] is a sharp threshold. Moreover, under certain conditions on model parameters and assuming mass action incidence for sexual transmission, it is proved that if [Formula: see text], there exists a unique endemic equilibrium that is globally asymptotically stable. However, under nonlinear incidence, it is shown that for certain functions backward bifurcation and Hopf bifurcation may occur, giving rise to subthreshold equilibria and periodic solutions, respectively. Numerical simulations for various parameter values are displayed to illustrate these behaviours.

  1. Nonlinear spectral singularities for confined nonlinearities.

    PubMed

    Mostafazadeh, Ali

    2013-06-28

    We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrödinger operators involving a confined nonlinearity. The presence of the nonlinearity does not break the parity-reflection symmetry of spectral singularities but makes them amplitude dependent. Nonlinear spectral singularities are, therefore, associated with a resonance effect that produces amplified waves with a specific amplitude-wavelength profile. We explore the consequences of this phenomenon for a complex δ-function potential that is subject to a general confined nonlinearity.

  2. Parallel High Order Accuracy Methods Applied to Non-Linear Hyperbolic Equations and to Problems in Materials Sciences

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    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 themore » 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.« less

  3. An adaptive grid algorithm for one-dimensional nonlinear equations

    NASA Technical Reports Server (NTRS)

    Gutierrez, William E.; Hills, Richard G.

    1990-01-01

    Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and

  4. Planning nonlinear access paths for temporal bone surgery.

    PubMed

    Fauser, Johannes; Sakas, Georgios; Mukhopadhyay, Anirban

    2018-05-01

    Interventions at the otobasis operate in the narrow region of the temporal bone where several highly sensitive organs define obstacles with minimal clearance for surgical instruments. Nonlinear trajectories for potential minimally invasive interventions can provide larger distances to risk structures and optimized orientations of surgical instruments, thus improving clinical outcomes when compared to existing linear approaches. In this paper, we present fast and accurate planning methods for such nonlinear access paths. We define a specific motion planning problem in [Formula: see text] with notable constraints in computation time and goal pose that reflect the requirements of temporal bone surgery. We then present [Formula: see text]-RRT-Connect: two suitable motion planners based on bidirectional Rapidly exploring Random Tree (RRT) to solve this problem efficiently. The benefits of [Formula: see text]-RRT-Connect are demonstrated on real CT data of patients. Their general performance is shown on a large set of realistic synthetic anatomies. We also show that these new algorithms outperform state-of-the-art methods based on circular arcs or Bézier-Splines when applied to this specific problem. With this work, we demonstrate that preoperative and intra-operative planning of nonlinear access paths is possible for minimally invasive surgeries at the otobasis.

  5. Rate and power efficient image compressed sensing and transmission

    NASA Astrophysics Data System (ADS)

    Olanigan, Saheed; Cao, Lei; Viswanathan, Ramanarayanan

    2016-01-01

    This paper presents a suboptimal quantization and transmission scheme for multiscale block-based compressed sensing images over wireless channels. The proposed method includes two stages: dealing with quantization distortion and transmission errors. First, given the total transmission bit rate, the optimal number of quantization bits is assigned to the sensed measurements in different wavelet sub-bands so that the total quantization distortion is minimized. Second, given the total transmission power, the energy is allocated to different quantization bit layers based on their different error sensitivities. The method of Lagrange multipliers with Karush-Kuhn-Tucker conditions is used to solve both optimization problems, for which the first problem can be solved with relaxation and the second problem can be solved completely. The effectiveness of the scheme is illustrated through simulation results, which have shown up to 10 dB improvement over the method without the rate and power optimization in medium and low signal-to-noise ratio cases.

  6. Digital nonlinearity compensation in high-capacity optical communication systems considering signal spectral broadening effect.

    PubMed

    Xu, Tianhua; Karanov, Boris; Shevchenko, Nikita A; Lavery, Domaniç; Liga, Gabriele; Killey, Robert I; Bayvel, Polina

    2017-10-11

    Nyquist-spaced transmission and digital signal processing have proved effective in maximising the spectral efficiency and reach of optical communication systems. In these systems, Kerr nonlinearity determines the performance limits, and leads to spectral broadening of the signals propagating in the fibre. Although digital nonlinearity compensation was validated to be promising for mitigating Kerr nonlinearities, the impact of spectral broadening on nonlinearity compensation has never been quantified. In this paper, the performance of multi-channel digital back-propagation (MC-DBP) for compensating fibre nonlinearities in Nyquist-spaced optical communication systems is investigated, when the effect of signal spectral broadening is considered. It is found that accounting for the spectral broadening effect is crucial for achieving the best performance of DBP in both single-channel and multi-channel communication systems, independent of modulation formats used. For multi-channel systems, the degradation of DBP performance due to neglecting the spectral broadening effect in the compensation is more significant for outer channels. Our work also quantified the minimum bandwidths of optical receivers and signal processing devices to ensure the optimal compensation of deterministic nonlinear distortions.

  7. Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Martin, Corless

    2004-01-01

    We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

  8. Nonlinear second order evolution inclusions with noncoercive viscosity term

    NASA Astrophysics Data System (ADS)

    Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D.

    2018-04-01

    In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and a priori bounds that permit passing to the limit, we prove that the problem has a solution.

  9. Nonlinear vibrations and dynamic stability of viscoelastic orthotropic rectangular plates

    NASA Astrophysics Data System (ADS)

    Eshmatov, B. Kh.

    2007-03-01

    This paper describes the analyses of the nonlinear vibrations and dynamic stability of viscoelastic orthotropic plates. The models are based on the Kirchhoff-Love (K.L.) hypothesis and Reissner-Mindlin (R.M.) generalized theory (with the incorporation of shear deformation and rotatory inertia) in geometrically nonlinear statements. It provides justification for the choice of the weakly singular Koltunov-Rzhanitsyn type kernel, with three rheological parameters. In addition, the implication of each relaxation kernel parameter has been studied. To solve problems of viscoelastic systems with weakly singular kernels of relaxation, a numerical method has been used, based on quadrature formulae. With a combination of the Bubnov-Galerkin and the presented method, problems of nonlinear vibrations and dynamic stability in viscoelastic orthotropic rectangular plates have been solved, according to the K.L. and R.M. hypotheses. A comparison of the results obtained via these theories is also presented. In all problems, the convergence of the Bubnov-Galerkin method has been investigated. The implications of material viscoelasticity on vibration and dynamic stability are presented graphically.

  10. Computing multiple periodic solutions of nonlinear vibration problems using the harmonic balance method and Groebner bases

    NASA Astrophysics Data System (ADS)

    Grolet, Aurelien; Thouverez, Fabrice

    2015-02-01

    This paper is devoted to the study of vibration of mechanical systems with geometric nonlinearities. The harmonic balance method is used to derive systems of polynomial equations whose solutions give the frequency component of the possible steady states. Groebner basis methods are used for computing all solutions of polynomial systems. This approach allows to reduce the complete system to an unique polynomial equation in one variable driving all solutions of the problem. In addition, in order to decrease the number of variables, we propose to first work on the undamped system, and recover solution of the damped system using a continuation on the damping parameter. The search for multiple solutions is illustrated on a simple system, where the influence of the retained number of harmonic is studied. Finally, the procedure is applied on a simple cyclic system and we give a representation of the multiple states versus frequency.

  11. Estimating parameter of influenza transmission using regularized least square

    NASA Astrophysics Data System (ADS)

    Nuraini, N.; Syukriah, Y.; Indratno, S. W.

    2014-02-01

    Transmission process of influenza can be presented in a mathematical model as a non-linear differential equations system. In this model the transmission of influenza is determined by the parameter of contact rate of the infected host and susceptible host. This parameter will be estimated using a regularized least square method where the Finite Element Method and Euler Method are used for approximating the solution of the SIR differential equation. The new infected data of influenza from CDC is used to see the effectiveness of the method. The estimated parameter represents the contact rate proportion of transmission probability in a day which can influence the number of infected people by the influenza. Relation between the estimated parameter and the number of infected people by the influenza is measured by coefficient of correlation. The numerical results show positive correlation between the estimated parameters and the infected people.

  12. Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

    PubMed

    Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

    2016-09-01

    It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

  13. Essays on electricity transmission investment and financial transmission rights

    NASA Astrophysics Data System (ADS)

    Shang, Wenzhuo

    The U.S. electric power industry has been going through fundamental restructuring and realignment since the 1990's. Many issues and problems have emerged during the transition, and both economists and engineers have been looking for the solutions fervently. In this dissertation, which consists primarily of three essays, we apply economics theory and techniques to the power industry and address two related issues, transmission investment and financial transmission rights (FTRs). The first essay takes the decentralized perspective and investigates the efficiency attribute of market-based transmission investment under perfect competition. We clarify, for the first time, the nature of the externality created by loop flows that causes transmission investment to be inefficient. Our findings have important implications for better understanding of transmission market design and creating incentives for efficient transmission investment. In the second essay, we define several rules for allocating transmission investment cost within the framework of cooperative game theory. These rules provide fair, stable or efficient cost allocations in theory and are good benchmarks against which the allocation mechanism in practice can be compared and improved upon. In the last essay, we make exploratory efforts in analyzing and assessing empirically the performance of the Midwest independent system operator (MISO) FTR auction market. We reveal some stylized facts about this young market and find that it is not efficient under the risk-neutrality assumption. We also point out and correct the drawbacks in previous related work and suggest about more complete empirical work in future. In all, this dissertation makes both theoretic and empirical analysis of the two hot issues related to the power industry and comes up with findings that have important implications for the development of this industry.

  14. A method for modeling discontinuities in a microwave coaxial transmission line

    NASA Technical Reports Server (NTRS)

    Otoshi, T. Y.

    1992-01-01

    A method for modeling discontinuities in a coaxial transmission line is presented. The methodology involves the use of a nonlinear least-squares fit program to optimize the fit between theoretical data (from the model) and experimental data. When this method was applied to modeling discontinuities in a slightly damaged Galileo spacecraft S-band (2.295-GHz) antenna cable, excellent agreement between theory and experiment was obtained over a frequency range of 1.70-2.85 GHz. The same technique can be applied for diagnostics and locating unknown discontinuities in other types of microwave transmission lines, such as rectangular, circular, and beam waveguides.

  15. A method for modeling discontinuities in a microwave coaxial transmission line

    NASA Astrophysics Data System (ADS)

    Otoshi, T. Y.

    1992-08-01

    A method for modeling discontinuities in a coaxial transmission line is presented. The methodology involves the use of a nonlinear least-squares fit program to optimize the fit between theoretical data (from the model) and experimental data. When this method was applied to modeling discontinuities in a slightly damaged Galileo spacecraft S-band (2.295-GHz) antenna cable, excellent agreement between theory and experiment was obtained over a frequency range of 1.70-2.85 GHz. The same technique can be applied for diagnostics and locating unknown discontinuities in other types of microwave transmission lines, such as rectangular, circular, and beam waveguides.

  16. A Unified Approach to Adaptive Neural Control for Nonlinear Discrete-Time Systems With Nonlinear Dead-Zone Input.

    PubMed

    Liu, Yan-Jun; Gao, Ying; Tong, Shaocheng; Chen, C L Philip

    2016-01-01

    In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.

  17. Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations That Arise from Nonlinear Two-Point Boundary Value Problems

    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.

  18. Improving the Accuracy of Quadrature Method Solutions of Fredholm Integral Equations that Arise from Nonlinear Two-Point Boundary Value Problems

    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.

  19. Mutation and Chaos in Nonlinear Models of Heredity

    PubMed Central

    Nawi, Ashraf Mohamed

    2014-01-01

    We shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models and observe chaotic behaviors of such models. PMID:25136693

  20. Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium

    PubMed Central

    Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying

    2015-01-01

    A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066

  1. Nonlinear coherent structures in granular crystals

    NASA Astrophysics Data System (ADS)

    Chong, C.; Porter, Mason A.; Kevrekidis, P. G.; Daraio, C.

    2017-10-01

    The study of granular crystals, which are nonlinear metamaterials that consist of closely packed arrays of particles that interact elastically, is a vibrant area of research that combines ideas from disciplines such as materials science, nonlinear dynamics, and condensed-matter physics. Granular crystals exploit geometrical nonlinearities in their constitutive microstructure to produce properties (such as tunability and energy localization) that are not conventional to engineering materials and linear devices. In this topical review, we focus on recent experimental, computational, and theoretical results on nonlinear coherent structures in granular crystals. Such structures—which include traveling solitary waves, dispersive shock waves, and discrete breathers—have fascinating dynamics, including a diversity of both transient features and robust, long-lived patterns that emerge from broad classes of initial data. In our review, we primarily discuss phenomena in one-dimensional crystals, as most research to date has focused on such scenarios, but we also present some extensions to two-dimensional settings. Throughout the review, we highlight open problems and discuss a variety of potential engineering applications that arise from the rich dynamic response of granular crystals.

  2. Boltzmann sampling from the Ising model using quantum heating of coupled nonlinear oscillators.

    PubMed

    Goto, Hayato; Lin, Zhirong; Nakamura, Yasunobu

    2018-05-08

    A network of Kerr-nonlinear parametric oscillators without dissipation has recently been proposed for solving combinatorial optimization problems via quantum adiabatic evolution through its bifurcation point. Here we investigate the behavior of the quantum bifurcation machine (QbM) in the presence of dissipation. Our numerical study suggests that the output probability distribution of the dissipative QbM is Boltzmann-like, where the energy in the Boltzmann distribution corresponds to the cost function of the optimization problem. We explain the Boltzmann distribution by generalizing the concept of quantum heating in a single nonlinear oscillator to the case of multiple coupled nonlinear oscillators. The present result also suggests that such driven dissipative nonlinear oscillator networks can be applied to Boltzmann sampling, which is used, e.g., for Boltzmann machine learning in the field of artificial intelligence.

  3. Nonlinear stability of the 1D Boltzmann equation in a periodic box

    NASA Astrophysics Data System (ADS)

    Wu, Kung-Chien

    2018-05-01

    We study the nonlinear stability of the Boltzmann equation in the 1D periodic box with size , where is the Knudsen number. The convergence rate is for small time region and exponential for large time region. Moreover, the exponential rate depends on the size of the domain (Knudsen number). This problem is highly nonlinear and hence we need more careful analysis to control the nonlinear term.

  4. Nonlinear and Stochastic Dynamics in the Heart

    PubMed Central

    Qu, Zhilin; Hu, Gang; Garfinkel, Alan; Weiss, James N.

    2014-01-01

    In a normal human life span, the heart beats about 2 to 3 billion times. Under diseased conditions, a heart may lose its normal rhythm and degenerate suddenly into much faster and irregular rhythms, called arrhythmias, which may lead to sudden death. The transition from a normal rhythm to an arrhythmia is a transition from regular electrical wave conduction to irregular or turbulent wave conduction in the heart, and thus this medical problem is also a problem of physics and mathematics. In the last century, clinical, experimental, and theoretical studies have shown that dynamical theories play fundamental roles in understanding the mechanisms of the genesis of the normal heart rhythm as well as lethal arrhythmias. In this article, we summarize in detail the nonlinear and stochastic dynamics occurring in the heart and their links to normal cardiac functions and arrhythmias, providing a holistic view through integrating dynamics from the molecular (microscopic) scale, to the organelle (mesoscopic) scale, to the cellular, tissue, and organ (macroscopic) scales. We discuss what existing problems and challenges are waiting to be solved and how multi-scale mathematical modeling and nonlinear dynamics may be helpful for solving these problems. PMID:25267872

  5. SPECIAL ISSUE ON OPTICAL PROCESSING OF INFORMATION: Information transmission systems based on two-mode lasers with controlled emission frequencies

    NASA Astrophysics Data System (ADS)

    Naumov, N. V.; Petrovskii, V. N.; Protsenko, E. D.; Shananin, R. A.

    1995-10-01

    Various information transmission systems, based on two-mode lasers with controlled emission frequencies, are proposed. It is suggested that these systems can be implemented by modulation of the intermode spacing of a two-mode laser. An experimental investigation is reported of frequency control methods. It is shown that these methods should make it possible to construct information transmission systems with high transmission rates subject to weak nonlinear distortions of the information-carrying signal.

  6. Nonlinear versus Ordinary Adaptive Control of Continuous Stirred-Tank Reactor

    PubMed Central

    Dostal, Petr

    2015-01-01

    Unfortunately, the major group of the systems in industry has nonlinear behavior and control of such processes with conventional control approaches with fixed parameters causes problems and suboptimal or unstable control results. An adaptive control is one way to how we can cope with nonlinearity of the system. This contribution compares classic adaptive control and its modification with Wiener system. This configuration divides nonlinear controller into the dynamic linear part and the static nonlinear part. The dynamic linear part is constructed with the use of polynomial synthesis together with the pole-placement method and the spectral factorization. The static nonlinear part uses static analysis of the controlled plant for introducing the mathematical nonlinear description of the relation between the controlled output and the change of the control input. Proposed controller is tested by the simulations on the mathematical model of the continuous stirred-tank reactor with cooling in the jacket as a typical nonlinear system. PMID:26346878

  7. Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network.

    PubMed

    Goto, Hayato

    2016-02-22

    The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

  8. Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

    PubMed Central

    Goto, Hayato

    2016-01-01

    The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence. PMID:26899997

  9. Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network

    NASA Astrophysics Data System (ADS)

    Goto, Hayato

    2016-02-01

    The dynamics of nonlinear systems qualitatively change depending on their parameters, which is called bifurcation. A quantum-mechanical nonlinear oscillator can yield a quantum superposition of two oscillation states, known as a Schrödinger cat state, via quantum adiabatic evolution through its bifurcation point. Here we propose a quantum computer comprising such quantum nonlinear oscillators, instead of quantum bits, to solve hard combinatorial optimization problems. The nonlinear oscillator network finds optimal solutions via quantum adiabatic evolution, where nonlinear terms are increased slowly, in contrast to conventional adiabatic quantum computation or quantum annealing, where quantum fluctuation terms are decreased slowly. As a result of numerical simulations, it is concluded that quantum superposition and quantum fluctuation work effectively to find optimal solutions. It is also notable that the present computer is analogous to neural computers, which are also networks of nonlinear components. Thus, the present scheme will open new possibilities for quantum computation, nonlinear science, and artificial intelligence.

  10. Distributed Optimization for a Class of Nonlinear Multiagent Systems With Disturbance Rejection.

    PubMed

    Wang, Xinghu; Hong, Yiguang; Ji, Haibo

    2016-07-01

    The paper studies the distributed optimization problem for a class of nonlinear multiagent systems in the presence of external disturbances. To solve the problem, we need to achieve the optimal multiagent consensus based on local cost function information and neighboring information and meanwhile to reject local disturbance signals modeled by an exogenous system. With convex analysis and the internal model approach, we propose a distributed optimization controller for heterogeneous and nonlinear agents in the form of continuous-time minimum-phase systems with unity relative degree. We prove that the proposed design can solve the exact optimization problem with rejecting disturbances.

  11. Nonlinear Thermal Instability in Compressible Viscous Flows Without Heat Conductivity

    NASA Astrophysics Data System (ADS)

    Jiang, Fei

    2018-04-01

    We investigate the thermal instability of a smooth equilibrium state, in which the density function satisfies Schwarzschild's (instability) condition, to a compressible heat-conducting viscous flow without heat conductivity in the presence of a uniform gravitational field in a three-dimensional bounded domain. We show that the equilibrium state is linearly unstable by a modified variational method. Then, based on the constructed linearly unstable solutions and a local well-posedness result of classical solutions to the original nonlinear problem, we further construct the initial data of linearly unstable solutions to be the one of the original nonlinear problem, and establish an appropriate energy estimate of Gronwall-type. With the help of the established energy estimate, we finally show that the equilibrium state is nonlinearly unstable in the sense of Hadamard by a careful bootstrap instability argument.

  12. Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example

    DOE PAGES

    Kevrekidis, Panayotis G.; Cuevas–Maraver, Jesús; Saxena, Avadh; ...

    2015-10-01

    In the present work, we combine the notion of parity-time (PT) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called Pöschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power-law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which is absent for the corresponding solutionmore » of the regular nonlinear Schrödinger equation with arbitrary power-law nonlinearity. The spectral properties and dynamical implications of this instability are examined. Furthermore, we believe that these findings may pave the way toward initiating a fruitful interplay between the notions of PT symmetry, supersymmetric partner potentials, and nonlinear interactions.« less

  13. Interplay between parity-time symmetry, supersymmetry, and nonlinearity: An analytically tractable case example

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kevrekidis, Panayotis G.; Cuevas–Maraver, Jesús; Saxena, Avadh

    In the present work, we combine the notion of parity-time (PT) symmetry with that of supersymmetry (SUSY) for a prototypical case example with a complex potential that is related by SUSY to the so-called Pöschl-Teller potential which is real. Not only are we able to identify and numerically confirm the eigenvalues of the relevant problem, but we also show that the corresponding nonlinear problem, in the presence of an arbitrary power-law nonlinearity, has an exact bright soliton solution that can be analytically identified and has intriguing stability properties, such as an oscillatory instability, which is absent for the corresponding solutionmore » of the regular nonlinear Schrödinger equation with arbitrary power-law nonlinearity. The spectral properties and dynamical implications of this instability are examined. Furthermore, we believe that these findings may pave the way toward initiating a fruitful interplay between the notions of PT symmetry, supersymmetric partner potentials, and nonlinear interactions.« less

  14. On a variational approach to some parameter estimation problems

    NASA Technical Reports Server (NTRS)

    Banks, H. T.

    1985-01-01

    Examples (1-D seismic, large flexible structures, bioturbation, nonlinear population dispersal) in which a variation setting can provide a convenient framework for convergence and stability arguments in parameter estimation problems are considered. Some of these examples are 1-D seismic, large flexible structures, bioturbation, and nonlinear population dispersal. Arguments for convergence and stability via a variational approach of least squares formulations of parameter estimation problems for partial differential equations is one aspect of the problem considered.

  15. Tensor-GMRES method for large sparse systems of nonlinear equations

    NASA Technical Reports Server (NTRS)

    Feng, Dan; Pulliam, Thomas H.

    1994-01-01

    This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

  16. Adaptive Fuzzy Output Feedback Control for Switched Nonlinear Systems With Unmodeled Dynamics.

    PubMed

    Tong, Shaocheng; Li, Yongming

    2017-02-01

    This paper investigates a robust adaptive fuzzy control stabilization problem for a class of uncertain nonlinear systems with arbitrary switching signals that use an observer-based output feedback scheme. The considered switched nonlinear systems possess the unstructured uncertainties, unmodeled dynamics, and without requiring the states being available for measurement. A state observer which is independent of switching signals is designed to solve the problem of unmeasured states. Fuzzy logic systems are used to identify unknown lumped nonlinear functions so that the problem of unstructured uncertainties can be solved. By combining adaptive backstepping design principle and small-gain approach, a novel robust adaptive fuzzy output feedback stabilization control approach is developed. The stability of the closed-loop system is proved via the common Lyapunov function theory and small-gain theorem. Finally, the simulation results are given to demonstrate the validity and performance of the proposed control strategy.

  17. Vibration signature analysis of multistage gear transmission

    NASA Technical Reports Server (NTRS)

    Choy, F. K.; Tu, Y. K.; Savage, M.; Townsend, D. P.

    1989-01-01

    An analysis is presented for multistage multimesh gear transmission systems. The analysis predicts the overall system dynamics and the transmissibility to the gear box or the enclosed structure. The modal synthesis approach of the analysis treats the uncoupled lateral/torsional model characteristics of each stage or component independently. The vibration signature analysis evaluates the global dynamics coupling in the system. The method synthesizes the interaction of each modal component or stage with the nonlinear gear mesh dynamics and the modal support geometry characteristics. The analysis simulates transient and steady state vibration events to determine the resulting torque variations, speeds, changes, rotor imbalances, and support gear box motion excitations. A vibration signature analysis examines the overall dynamic characteristics of the system, and the individual model component responses. The gear box vibration analysis also examines the spectral characteristics of the support system.

  18. Finite difference time domain calculation of transients in antennas with nonlinear loads

    NASA Technical Reports Server (NTRS)

    Luebbers, Raymond J.; Beggs, John H.; Kunz, Karl S.; Chamberlin, Kent

    1991-01-01

    In this paper transient fields for antennas with more general geometries are calculated directly using Finite Difference Time Domain methods. In each FDTD cell which contains a nonlinear load, a nonlinear equation is solved at each time step. As a test case the transient current in a long dipole antenna with a nonlinear load excited by a pulsed plane wave is computed using this approach. The results agree well with both calculated and measured results previously published. The approach given here extends the applicability of the FDTD method to problems involving scattering from targets including nonlinear loads and materials, and to coupling between antennas containing nonlinear loads. It may also be extended to propagation through nonlinear materials.

  19. Numerical treatment of a geometrically nonlinear planar Cosserat shell model

    NASA Astrophysics Data System (ADS)

    Sander, Oliver; Neff, Patrizio; Bîrsan, Mircea

    2016-05-01

    We present a new way to discretize a geometrically nonlinear elastic planar Cosserat shell. The kinematical model is similar to the general six-parameter resultant shell model with drilling rotations. The discretization uses geodesic finite elements (GFEs), which leads to an objective discrete model which naturally allows arbitrarily large rotations. GFEs of any approximation order can be constructed. The resulting algebraic problem is a minimization problem posed on a nonlinear finite-dimensional Riemannian manifold. We solve this problem using a Riemannian trust-region method, which is a generalization of Newton's method that converges globally without intermediate loading steps. We present the continuous model and the discretization, discuss the properties of the discrete model, and show several numerical examples, including wrinkling of thin elastic sheets in shear.

  20. Photon transport in a dissipative chain of nonlinear cavities

    NASA Astrophysics Data System (ADS)

    Biella, Alberto; Mazza, Leonardo; Carusotto, Iacopo; Rossini, Davide; Fazio, Rosario

    2015-05-01

    By means of numerical simulations and the input-output formalism, we study photon transport through a chain of coupled nonlinear optical cavities subject to uniform dissipation. Photons are injected from one end of the chain by means of a coherent source. The propagation through the array of cavities is sensitive to the interplay between the photon hopping strength and the local nonlinearity in each cavity. We characterize photon transport by studying the populations and the photon correlations as a function of the cavity position. When complemented with input-output theory, these quantities provide direct information about photon transmission through the system. The position of single-photon and multiphoton resonances directly reflects the structure of the many-body energy levels. This shows how a study of transport along a coupled cavity array can provide rich information about the strongly correlated (many-body) states of light even in presence of dissipation. The numerical algorithm we use, based on the time-evolving block decimation scheme adapted to mixed states, allows us to simulate large arrays (up to 60 cavities). The scaling of photon transmission with the number of cavities does depend on the structure of the many-body photon states inside the array.

  1. Comment on "exact solutions of the derivative nonlinear Schrödinger equation for a nonlinear transmission line".

    PubMed

    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.

  2. Nonlinear amplitude dynamics in flagellar beating

    NASA Astrophysics Data System (ADS)

    Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

    2017-03-01

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

  3. Nonlinear amplitude dynamics in flagellar beating.

    PubMed

    Oriola, David; Gadêlha, Hermes; Casademunt, Jaume

    2017-03-01

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

  4. Nonlinear amplitude dynamics in flagellar beating

    PubMed Central

    Casademunt, Jaume

    2017-01-01

    The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating. PMID:28405357

  5. Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method

    NASA Astrophysics Data System (ADS)

    Vasant, Pandian

    2011-06-01

    Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.

  6. Discrete time learning control in nonlinear systems

    NASA Technical Reports Server (NTRS)

    Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh

    1992-01-01

    In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.

  7. Impulsive interference in communication channels and its mitigation by SPART and other nonlinear filters

    NASA Astrophysics Data System (ADS)

    Nikitin, Alexei V.; Epard, Marc; Lancaster, John B.; Lutes, Robert L.; Shumaker, Eric A.

    2012-12-01

    A strong digital communication transmitter in close physical proximity to a receiver of a weak signal can noticeably interfere with the latter even when the respective channels are tens or hundreds of megahertz apart. When time domain observations are made in the signal chain of the receiver between the first mixer and the baseband, this interference is likely to appear impulsive. The impulsive nature of this interference provides an opportunity to reduce its power by nonlinear filtering, improving the quality of the receiver channel. This article describes the mitigation, by a particular nonlinear filter, of the impulsive out-of-band (OOB) interference induced in High Speed Downlink Packet Access (HSDPA) by WiFi transmissions, protocols which coexist in many 3G smartphones and mobile hotspots. Our measurements show a decrease in the maximum error-free bit rate of a 1.95 GHz HSDPA receiver caused by the impulsive interference from an OOB 2.4 GHz WiFi transmission, sometimes down to a small fraction of the rate observed in the absence of the interference. We apply a nonlinear SPART filter to recover a noticeable portion of the lost rate and maintain an error-free connection under much higher levels of the WiFi interference than a receiver that does not contain such a filter. These measurements support our wider investigation of OOB interference resulting from digital modulation, which appears impulsive in a receiver, and its mitigation by nonlinear filters.

  8. Acoustic nonreciprocity in a lattice incorporating nonlinearity, asymmetry, and internal scale hierarchy: Experimental study

    NASA Astrophysics Data System (ADS)

    Bunyan, Jonathan; Moore, Keegan J.; Mojahed, Alireza; Fronk, Matthew D.; Leamy, Michael; Tawfick, Sameh; Vakakis, Alexander F.

    2018-05-01

    In linear time-invariant systems acoustic reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and it can be broken only by odd external biases, nonlinearities, or time-dependent properties. Recently it was shown that one-dimensional lattices composed of a finite number of identical nonlinear cells with internal scale hierarchy and asymmetry exhibit nonreciprocity both locally and globally. Considering a single cell composed of a large scale nonlinearly coupled to a small scale, local dynamic nonreciprocity corresponds to vibration energy transfer from the large to the small scale, but absence of energy transfer (and localization) from the small to the large scale. This has been recently proven both theoretically and experimentally. Then, considering the entire lattice, global acoustic nonreciprocity has been recently proven theoretically, corresponding to preferential energy transfer within the lattice under transient excitation applied at one of its boundaries, and absence of similar energy transfer (and localization) when the excitation is applied at its other boundary. This work provides experimental validation of the global acoustic nonreciprocity with a one-dimensional asymmetric lattice composed of three cells, with each cell incorporating nonlinearly coupled large and small scales. Due to the intentional asymmetry of the lattice, low impulsive excitations applied to one of its boundaries result in wave transmission through the lattice, whereas when the same excitations are applied to the other end, they lead in energy localization at the boundary and absence of wave transmission. This global nonreciprocity depends critically on energy (i.e., the intensity of the applied impulses), and reduced-order models recover the nonreciprocal acoustics and clarify the nonlinear mechanism generating nonreciprocity in this system.

  9. Exact solutions for the source-excited cylindrical electromagnetic waves in a nonlinear nondispersive medium.

    PubMed

    Es'kin, V A; Kudrin, A V; Petrov, E Yu

    2011-06-01

    The behavior of electromagnetic fields in nonlinear media has been a topical problem since the discovery of materials with a nonlinearity of electromagnetic properties. The problem of finding exact solutions for the source-excited nonlinear waves in curvilinear coordinates has been regarded as unsolvable for a long time. In this work, we present the first solution of this type for a cylindrically symmetric field excited by a pulsed current filament in a nondispersive medium that is simultaneously inhomogeneous and nonlinear. Assuming that the medium has a power-law permittivity profile in the linear regime and lacks a center of inversion, we derive an exact solution for the electromagnetic field excited by a current filament in such a medium and discuss the properties of this solution.

  10. Effect of asymmetrical transfer coefficients of a non-polarizing beam splitter on the nonlinear error of the polarization interferometer

    NASA Astrophysics Data System (ADS)

    Zhao, Chen-Guang; Tan, Jiu-Bin; Liu, Tao

    2010-09-01

    The mechanism of a non-polarizing beam splitter (NPBS) with asymmetrical transfer coefficients causing the rotation of polarization direction is explained in principle, and the measurement nonlinear error caused by NPBS is analyzed based on Jones matrix theory. Theoretical calculations show that the nonlinear error changes periodically, and the error period and peak values increase with the deviation between transmissivities of p-polarization and s-polarization states. When the transmissivity of p-polarization is 53% and that of s-polarization is 48%, the maximum error reaches 2.7 nm. The imperfection of NPBS is one of the main error sources in simultaneous phase-shifting polarization interferometer, and its influence can not be neglected in the nanoscale ultra-precision measurement.

  11. Nonlinearity-aware 200  Gbit/s DMT transmission for C-band short-reach optical interconnects with a single packaged electro-absorption modulated laser.

    PubMed

    Zhang, Lu; Hong, Xuezhi; Pang, Xiaodan; Ozolins, Oskars; Udalcovs, Aleksejs; Schatz, Richard; Guo, Changjian; Zhang, Junwei; Nordwall, Fredrik; Engenhardt, Klaus M; Westergren, Urban; Popov, Sergei; Jacobsen, Gunnar; Xiao, Shilin; Hu, Weisheng; Chen, Jiajia

    2018-01-15

    We experimentally demonstrate the transmission of a 200 Gbit/s discrete multitone (DMT) at the soft forward error correction limit in an intensity-modulation direct-detection system with a single C-band packaged distributed feedback laser and traveling-wave electro absorption modulator (DFB-TWEAM), digital-to-analog converter and photodiode. The bit-power loaded DMT signal is transmitted over 1.6 km standard single-mode fiber with a net rate of 166.7 Gbit/s, achieving an effective electrical spectrum efficiency of 4.93 bit/s/Hz. Meanwhile, net rates of 174.2 Gbit/s and 179.5 Gbit/s are also demonstrated over 0.8 km SSMF and in an optical back-to-back case, respectively. The feature of the packaged DFB-TWEAM is presented. The nonlinearity-aware digital signal processing algorithm for channel equalization is mathematically described, which improves the signal-to-noise ratio up to 3.5 dB.

  12. Joint recognition and discrimination in nonlinear feature space

    NASA Astrophysics Data System (ADS)

    Talukder, Ashit; Casasent, David P.

    1997-09-01

    A new general method for linear and nonlinear feature extraction is presented. It is novel since it provides both representation and discrimination while most other methods are concerned with only one of these issues. We call this approach the maximum representation and discrimination feature (MRDF) method and show that the Bayes classifier and the Karhunen- Loeve transform are special cases of it. We refer to our nonlinear feature extraction technique as nonlinear eigen- feature extraction. It is new since it has a closed-form solution and produces nonlinear decision surfaces with higher rank than do iterative methods. Results on synthetic databases are shown and compared with results from standard Fukunaga- Koontz transform and Fisher discriminant function methods. The method is also applied to an automated product inspection problem (discrimination) and to the classification and pose estimation of two similar objects (representation and discrimination).

  13. A Bayesian approach for estimating under-reported dengue incidence with a focus on non-linear associations between climate and dengue in Dhaka, Bangladesh.

    PubMed

    Sharmin, Sifat; Glass, Kathryn; Viennet, Elvina; Harley, David

    2018-04-01

    Determining the relation between climate and dengue incidence is challenging due to under-reporting of disease and consequent biased incidence estimates. Non-linear associations between climate and incidence compound this. Here, we introduce a modelling framework to estimate dengue incidence from passive surveillance data while incorporating non-linear climate effects. We estimated the true number of cases per month using a Bayesian generalised linear model, developed in stages to adjust for under-reporting. A semi-parametric thin-plate spline approach was used to quantify non-linear climate effects. The approach was applied to data collected from the national dengue surveillance system of Bangladesh. The model estimated that only 2.8% (95% credible interval 2.7-2.8) of all cases in the capital Dhaka were reported through passive case reporting. The optimal mean monthly temperature for dengue transmission is 29℃ and average monthly rainfall above 15 mm decreases transmission. Our approach provides an estimate of true incidence and an understanding of the effects of temperature and rainfall on dengue transmission in Dhaka, Bangladesh.

  14. Fabrication of semiconductor-polymer compound nonlinear photonic crystal slab with highly uniform infiltration based on nano-imprint lithography technique.

    PubMed

    Qin, Fei; Meng, Zi-Ming; Zhong, Xiao-Lan; Liu, Ye; Li, Zhi-Yuan

    2012-06-04

    We present a versatile technique based on nano-imprint lithography to fabricate high-quality semiconductor-polymer compound nonlinear photonic crystal (NPC) slabs. The approach allows one to infiltrate uniformly polystyrene materials that possess large Kerr nonlinearity and ultrafast nonlinear response into the cylindrical air holes with diameter of hundred nanometers that are perforated in silicon membranes. Both the structural characterization via the cross-sectional scanning electron microscopy images and the optical characterization via the transmission spectrum measurement undoubtedly show that the fabricated compound NPC samples have uniform and dense polymer infiltration and are of high quality in optical properties. The compound NPC samples exhibit sharp transmission band edges and nondegraded high quality factor of microcavities compared with those in the bare silicon PC. The versatile method can be expanded to make general semiconductor-polymer hybrid optical nanostructures, and thus it may pave the way for reliable and efficient fabrication of ultrafast and ultralow power all-optical tunable integrated photonic devices and circuits.

  15. Efficient computational nonlinear dynamic analysis using modal modification response technique

    NASA Astrophysics Data System (ADS)

    Marinone, Timothy; Avitabile, Peter; Foley, Jason; Wolfson, Janet

    2012-08-01

    Generally, structural systems contain nonlinear characteristics in many cases. These nonlinear systems require significant computational resources for solution of the equations of motion. Much of the model, however, is linear where the nonlinearity results from discrete local elements connecting different components together. Using a component mode synthesis approach, a nonlinear model can be developed by interconnecting these linear components with highly nonlinear connection elements. The approach presented in this paper, the Modal Modification Response Technique (MMRT), is a very efficient technique that has been created to address this specific class of nonlinear problem. By utilizing a Structural Dynamics Modification (SDM) approach in conjunction with mode superposition, a significantly smaller set of matrices are required for use in the direct integration of the equations of motion. The approach will be compared to traditional analytical approaches to make evident the usefulness of the technique for a variety of test cases.

  16. The effects of maternal working conditions and mastery on child behavior problems: studying the intergenerational transmission of social control.

    PubMed

    Rogers, S J; Parcel, T L; Menaghan, E G

    1991-06-01

    We assess the impact of maternal sense of mastery and maternal working conditions on maternal perceptions of children's behavior problems as a means to study the transmission of social control across generations. We use a sample of 521 employed mothers and their four-to six-year-old children from the National Longitudinal Survey's Youth Cohort in 1986. Regarding working conditions, we consider mother's hourly wage, work hours, and job content including involvement with things (vs. people), the requisite level of physical activity, and occupational complexity. We also consider maternal and child background and current family characteristics, including marital status, family size, and home environment. Maternal mastery was related to fewer reported behavior problems among children. Lower involvement with people and higher involvement with things, as well as low physical activity, were related significantly to higher levels of perceived problems. In addition, recent changes in maternal marital status, including maternal marriage or remarriage, increased reports of problems; stronger home environments had the opposite effect. We interpret these findings as suggesting how maternal experiences of control in the workplace and personal resources of control can influence the internalization of control in children.

  17. Sub transitional and supersonic travelling field response in nonlinear viscoelastic media

    NASA Technical Reports Server (NTRS)

    Padovan, Joe

    1989-01-01

    This paper considers the problem of traveling fields in nonlinearly elastic and viscoelastic media. By introducing the appropriate hierarchical partitioning, the governing equations of motion are shown to be a continuum analogy of Duffing's equation. Through the use of a constrained perturbation procedure, the response behavior is obtained in sub, transitional as well as supersonic ranges of disturbance speed. Due to the generality of the approach taken, the effects of damping can be handled. To quantify the effects of material nonlinearity, strain softening and hardening are considered. Such behavior is quantified in general example problems.

  18. A method for nonlinear exponential regression analysis

    NASA Technical Reports Server (NTRS)

    Junkin, B. G.

    1971-01-01

    A computer-oriented technique is presented for performing a nonlinear exponential regression analysis on decay-type experimental data. The technique involves the least squares procedure wherein the nonlinear problem is linearized by expansion in a Taylor series. A linear curve fitting procedure for determining the initial nominal estimates for the unknown exponential model parameters is included as an integral part of the technique. A correction matrix was derived and then applied to the nominal estimate to produce an improved set of model parameters. The solution cycle is repeated until some predetermined criterion is satisfied.

  19. Parameter estimation in nonlinear distributed systems - Approximation theory and convergence results

    NASA Technical Reports Server (NTRS)

    Banks, H. T.; Reich, Simeon; Rosen, I. G.

    1988-01-01

    An abstract approximation framework and convergence theory is described for Galerkin approximations applied to inverse problems involving nonlinear distributed parameter systems. Parameter estimation problems are considered and formulated as the minimization of a least-squares-like performance index over a compact admissible parameter set subject to state constraints given by an inhomogeneous nonlinear distributed system. The theory applies to systems whose dynamics can be described by either time-independent or nonstationary strongly maximal monotonic operators defined on a reflexive Banach space which is densely and continuously embedded in a Hilbert space. It is demonstrated that if readily verifiable conditions on the system's dependence on the unknown parameters are satisfied, and the usual Galerkin approximation assumption holds, then solutions to the approximating problems exist and approximate a solution to the original infinite-dimensional identification problem.

  20. Engineering aspect of the microwave ionosphere nonlinear interaction experiment (MINIX) with a sounding rocket

    NASA Astrophysics Data System (ADS)

    Nagatomo, Makoto; Kaya, Nobuyuki; Matsumoto, Hiroshi

    The Microwave Ionosphere Nonlinear Interaction Experiment (MINIX) is a sounding rocket experiment to study possible effects of strong microwave fields in case it is used for energy transmission from the Solar Power Satellite (SPS) upon the Earth's atmosphere. Its secondary objective is to develop high power microwave technology for space use. Two rocket-borne magnetrons were used to emit 2.45 GHz microwave in order to make a simulated condition of power transmission from an SPS to a ground station. Sounding of the environment radiated by microwave was conducted by the diagnostic package onboard the daughter unit which was separated slowly from the mother unit. The main design drivers of this experiment were to build such high power equipments in a standard type of sounding rocket, to keep the cost within the budget and to perform a series of experiments without complete loss of the mission. The key technology for this experiment is a rocket-borne magnetron and high voltage converter. Location of position of the daughter unit relative to the mother unit was a difficult requirement for a spin-stabilized rocket. These problems were solved by application of such a low cost commercial products as a magnetron for microwave oven and a video tape recorder and camera.