Hydrophone area-averaging correction factors in nonlinearly generated ultrasonic beams

Science.gov (United States)

Cooling, M. P.; Humphrey, V. F.; Wilkens, V.

2011-02-01

The nonlinear propagation of an ultrasonic wave can be used to produce a wavefield rich in higher frequency components that is ideally suited to the calibration, or inter-calibration, of hydrophones. These techniques usually use a tone-burst signal, limiting the measurements to harmonics of the fundamental calibration frequency. Alternatively, using a short pulse enables calibration at a continuous spectrum of frequencies. Such a technique is used at PTB in conjunction with an optical measurement technique to calibrate devices. Experimental findings indicate that the area-averaging correction factor for a hydrophone in such a field demonstrates a complex behaviour, most notably varying periodically between frequencies that are harmonics of the centre frequency of the original pulse and frequencies that lie midway between these harmonics. The beam characteristics of such nonlinearly generated fields have been investigated using a finite difference solution to the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a focused field. The simulation results are used to calculate the hydrophone area-averaging correction factors for 0.2 mm and 0.5 mm devices. The results clearly demonstrate a number of significant features observed in the experimental investigations, including the variation with frequency, drive level and hydrophone element size. An explanation for these effects is also proposed.

Nonlinear Eddy Viscosity Models applied to Wind Turbine Wakes

DEFF Research Database (Denmark)

Laan, van der, Paul Maarten; Sørensen, Niels N.; Réthoré, Pierre-Elouan

2013-01-01

The linear k−ε eddy viscosity model and modified versions of two existing nonlinear eddy viscosity models are applied to single wind turbine wake simulations using a Reynolds Averaged Navier-Stokes code. Results are compared with field wake measurements. The nonlinear models give better results...

Nonlinear adaptive optics: aberration correction in three photon fluorescence microscopy for mouse brain imaging

Science.gov (United States)

Sinefeld, David; Paudel, Hari P.; Wang, Tianyu; Wang, Mengran; Ouzounov, Dimitre G.; Bifano, Thomas G.; Xu, Chris

2017-02-01

Multiphoton fluorescence microscopy is a well-established technique for deep-tissue imaging with subcellular resolution. Three-photon microscopy (3PM) when combined with long wavelength excitation was shown to allow deeper imaging than two-photon microscopy (2PM) in biological tissues, such as mouse brain, because out-of-focus background light can be further reduced due to the higher order nonlinear excitation. As was demonstrated in 2PM systems, imaging depth and resolution can be improved by aberration correction using adaptive optics (AO) techniques which are based on shaping the scanning beam using a spatial light modulator (SLM). In this way, it is possible to compensate for tissue low order aberration and to some extent, to compensate for tissue scattering. Here, we present a 3PM AO microscopy system for brain imaging. Soliton self-frequency shift is used to create a femtosecond source at 1675 nm and a microelectromechanical (MEMS) SLM serves as the wavefront shaping device. We perturb the 1020 segment SLM using a modified nonlinear version of three-point phase shifting interferometry. The nonlinearity of the fluorescence signal used for feedback ensures that the signal is increasing when the spot size decreases, allowing compensation of phase errors in an iterative optimization process without direct phase measurement. We compare the performance for different orders of nonlinear feedback, showing an exponential growth in signal improvement as the nonlinear order increases. We demonstrate the impact of the method by applying the 3PM AO system for in-vivo mouse brain imaging, showing improvement in signal at 1-mm depth inside the brain.

Respiratory lung motion analysis using a nonlinear motion correction technique for respiratory-gated lung perfusion SPECT images

International Nuclear Information System (INIS)

Ue, Hidenori; Haneishi, Hideaki; Iwanaga, Hideyuki; Suga, Kazuyoshi

2007-01-01

This study evaluated the respiratory motion of lungs using a nonlinear motion correction technique for respiratory-gated single photon emission computed tomography (SPECT) images. The motion correction technique corrects the respiratory motion of the lungs nonlinearly between two-phase images obtained by respiratory-gated SPECT. The displacement vectors resulting from respiration can be computed at every location of the lungs. Respiratory lung motion analysis is carried out by calculating the mean value of the body axis component of the displacement vector in each of the 12 small regions into which the lungs were divided. In order to enable inter-patient comparison, the 12 mean values were normalized by the length of the lung region along the direction of the body axis. This method was applied to 25 Technetium (Tc)-99m-macroaggregated albumin (MAA) perfusion SPECT images, and motion analysis results were compared with the diagnostic results. It was confirmed that the respiratory lung motion reflects the ventilation function. A statistically significant difference in the amount of the respiratory lung motion was observed between the obstructive pulmonary diseases and other conditions, based on an unpaired Student's t test (P<0.0001). A difference in the motion between normal lungs and lungs with a ventilation obstruction was detected by the proposed method. This method is effective for evaluating obstructive pulmonary diseases such as pulmonary emphysema and diffuse panbronchiolitis. (author)

Synchronizing movements with the metronome: nonlinear error correction and unstable periodic orbits.

Science.gov (United States)

Engbert, Ralf; Krampe, Ralf Th; Kurths, Jürgen; Kliegl, Reinhold

2002-02-01

The control of human hand movements is investigated in a simple synchronization task. We propose and analyze a stochastic model based on nonlinear error correction; a mechanism which implies the existence of unstable periodic orbits. This prediction is tested in an experiment with human subjects. We find that our experimental data are in good agreement with numerical simulations of our theoretical model. These results suggest that feedback control of the human motor systems shows nonlinear behavior. Copyright 2001 Elsevier Science (USA).

Correction of detector nonlinearity for the balloonborne Michelson Interferometer for Passive Atmospheric Sounding.

Science.gov (United States)

Kleinert, Anne

2006-01-20

The detectors used in the cryogenic limb-emission sounder MIPAS-B2 (Michelson Interferometer for Passive Atmospheric Sounding) show a nonlinear response, which leads to radiometric errors in the calibrated spectra if the nonlinearity is not taken into account. In the case of emission measurements, the dominant error that arises from the nonlinearity is the changing detector responsivity as the incident photon load changes. The effect of the distortion of a single interferogram can be neglected. A method to characterize the variable responsivity and to correct for this effect is proposed. Furthermore, a detailed error estimation is presented.

Probing hysteretic elasticity in weakly nonlinear materials

Energy Technology Data Exchange (ETDEWEB)

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

2010-12-07

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

Photon attenuation correction technique in SPECT based on nonlinear optimization

International Nuclear Information System (INIS)

Suzuki, Shigehito; Wakabayashi, Misato; Okuyama, Keiichi; Kuwamura, Susumu

1998-01-01

Photon attenuation correction in SPECT was made using a nonlinear optimization theory, in which an optimum image is searched so that the sum of square errors between observed and reprojected projection data is minimized. This correction technique consists of optimization and step-width algorithms, which determine at each iteration a pixel-by-pixel directional value of search and its step-width, respectively. We used the conjugate gradient and quasi-Newton methods as the optimization algorithm, and Curry rule and the quadratic function method as the step-width algorithm. Statistical fluctuations in the corrected image due to statistical noise in the emission projection data grew as the iteration increased, depending on the combination of optimization and step-width algorithms. To suppress them, smoothing for directional values was introduced. Computer experiments and clinical applications showed a pronounced reduction in statistical fluctuations of the corrected image for all combinations. Combinations using the conjugate gradient method were superior in noise characteristic and computation time. The use of that method with the quadratic function method was optimum if noise property was regarded as important. (author)

Diffraction corrections for second harmonic beam fields and effects on the nonlinearity parameter evaluation

Energy Technology Data Exchange (ETDEWEB)

Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)

2016-04-15

The nonlinearity parameter is frequently measured as a sensitive indicator in damaged material characterization or tissue harmonic imaging. Several previous studies have employed the plane wave solution, and ignored the effects of beam diffraction when measuring the non-linearity parameter β. This paper presents a multi-Gaussian beam approach to explicitly derive diffraction corrections for fundamental and second harmonics under quasilinear and paraxial approximation. Their effects on the nonlinearity parameter estimation demonstrate complicated dependence of β on the transmitter-receiver geometries, frequency, and propagation distance. The diffraction effects on the non-linearity parameter estimation are important even in the nearfield region. Experiments are performed to show that improved β values can be obtained by considering the diffraction effects.

Nonlinear effect of the structured light profilometry in the phase-shifting method and error correction

International Nuclear Information System (INIS)

Zhang Wan-Zhen; Chen Zhe-Bo; Xia Bin-Feng; Lin Bin; Cao Xiang-Qun

2014-01-01

Digital structured light (SL) profilometry is increasingly used in three-dimensional (3D) measurement technology. However, the nonlinearity of the off-the-shelf projectors and cameras seriously reduces the measurement accuracy. In this paper, first, we review the nonlinear effects of the projector–camera system in the phase-shifting structured light depth measurement method. We show that high order harmonic wave components lead to phase error in the phase-shifting method. Then a practical method based on frequency domain filtering is proposed for nonlinear error reduction. By using this method, the nonlinear calibration of the SL system is not required. Moreover, both the nonlinear effects of the projector and the camera can be effectively reduced. The simulations and experiments have verified our nonlinear correction method. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Use Residual Correction Method and Monotone Iterative Technique to Calculate the Upper and Lower Approximate Solutions of Singularly Perturbed Non-linear Boundary Value Problems

Directory of Open Access Journals (Sweden)

Chi-Chang Wang

2013-09-01

Full Text Available This paper seeks to use the proposed residual correction method in coordination with the monotone iterative technique to obtain upper and lower approximate solutions of singularly perturbed non-linear boundary value problems. First, the monotonicity of a non-linear differential equation is reinforced using the monotone iterative technique, then the cubic-spline method is applied to discretize and convert the differential equation into the mathematical programming problems of an inequation, and finally based on the residual correction concept, complex constraint solution problems are transformed into simpler questions of equational iteration. As verified by the four examples given in this paper, the method proposed hereof can be utilized to fast obtain the upper and lower solutions of questions of this kind, and to easily identify the error range between mean approximate solutions and exact solutions.

Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions

KAUST Repository

De Pascalis, Riccardo

2010-07-22

Euler\\'s celebrated buckling formula gives the critical load N for the buckling of a slender cylindrical column with radius B and length L as N/(π3B2)=(E/4)(B/L)2 where E is Young\\'s modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness (B/L) is an infinitesimal quantity. Here we ask the following question: What is the first non-linear correction in the right hand-side of this equation when terms up to (B/L)4 are kept? To answer this question, we specialize the exact solution of incremental non-linear elasticity for the homogeneous compression of a thick compressible cylinder with lubricated ends to the theory of third-order elasticity. In particular, we highlight the way second- and third-order constants-including Poisson\\'s ratio-all appear in the coefficient of (B/L)4. © 2010 Springer Science+Business Media B.V.

Nonlinear Correction to the Euler Buckling Formula for Compressed Cylinders with Guided-Guided End Conditions

KAUST Repository

De Pascalis, Riccardo; Destrade, Michel; Goriely, Alain

2010-01-01

Euler's celebrated buckling formula gives the critical load N for the buckling of a slender cylindrical column with radius B and length L as N/(π3B2)=(E/4)(B/L)2 where E is Young's modulus. Its derivation relies on the assumptions that linear elasticity applies to this problem, and that the slenderness (B/L) is an infinitesimal quantity. Here we ask the following question: What is the first non-linear correction in the right hand-side of this equation when terms up to (B/L)4 are kept? To answer this question, we specialize the exact solution of incremental non-linear elasticity for the homogeneous compression of a thick compressible cylinder with lubricated ends to the theory of third-order elasticity. In particular, we highlight the way second- and third-order constants-including Poisson's ratio-all appear in the coefficient of (B/L)4. © 2010 Springer Science+Business Media B.V.

Correction of Non-Linear Propagation Artifact in Contrast-Enhanced Ultrasound Imaging of Carotid Arteries: Methods and in Vitro Evaluation.

Science.gov (United States)

Yildiz, Yesna O; Eckersley, Robert J; Senior, Roxy; Lim, Adrian K P; Cosgrove, David; Tang, Meng-Xing

2015-07-01

Non-linear propagation of ultrasound creates artifacts in contrast-enhanced ultrasound images that significantly affect both qualitative and quantitative assessments of tissue perfusion. This article describes the development and evaluation of a new algorithm to correct for this artifact. The correction is a post-processing method that estimates and removes non-linear artifact in the contrast-specific image using the simultaneously acquired B-mode image data. The method is evaluated on carotid artery flow phantoms with large and small vessels containing microbubbles of various concentrations at different acoustic pressures. The algorithm significantly reduces non-linear artifacts while maintaining the contrast signal from bubbles to increase the contrast-to-tissue ratio by up to 11 dB. Contrast signal from a small vessel 600 μm in diameter buried in tissue artifacts before correction was recovered after the correction. Copyright © 2015 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

A simple predistortion technique for suppression of nonlinear effects in periodic signals generated by nonlinear transducers

Science.gov (United States)

Novak, A.; Simon, L.; Lotton, P.

2018-04-01

Mechanical transducers, such as shakers, loudspeakers and compression drivers that are used as excitation devices to excite acoustical or mechanical nonlinear systems under test are imperfect. Due to their nonlinear behaviour, unwanted contributions appear at their output besides the wanted part of the signal. Since these devices are used to study nonlinear systems, it should be required to measure properly the systems under test by overcoming the influence of the nonlinear excitation device. In this paper, a simple method that corrects distorted output signal of the excitation device by means of predistortion of its input signal is presented. A periodic signal is applied to the input of the excitation device and, from analysing the output signal of the device, the input signal is modified in such a way that the undesirable spectral components in the output of the excitation device are cancelled out after few iterations of real-time processing. The experimental results provided on an electrodynamic shaker show that the spectral purity of the generated acceleration output approaches 100 dB after few iterations (1 s). This output signal, applied to the system under test, is thus cleaned from the undesirable components produced by the excitation device; this is an important condition to ensure a correct measurement of the nonlinear system under test.

Partial fourier and parallel MR image reconstruction with integrated gradient nonlinearity correction.

Science.gov (United States)

Tao, Shengzhen; Trzasko, Joshua D; Shu, Yunhong; Weavers, Paul T; Huston, John; Gray, Erin M; Bernstein, Matt A

2016-06-01

To describe how integrated gradient nonlinearity (GNL) correction can be used within noniterative partial Fourier (homodyne) and parallel (SENSE and GRAPPA) MR image reconstruction strategies, and demonstrate that performing GNL correction during, rather than after, these routines mitigates the image blurring and resolution loss caused by postreconstruction image domain based GNL correction. Starting from partial Fourier and parallel magnetic resonance imaging signal models that explicitly account for GNL, noniterative image reconstruction strategies for each accelerated acquisition technique are derived under the same core mathematical assumptions as their standard counterparts. A series of phantom and in vivo experiments on retrospectively undersampled data were performed to investigate the spatial resolution benefit of integrated GNL correction over conventional postreconstruction correction. Phantom and in vivo results demonstrate that the integrated GNL correction reduces the image blurring introduced by the conventional GNL correction, while still correcting GNL-induced coarse-scale geometrical distortion. Images generated from undersampled data using the proposed integrated GNL strategies offer superior depiction of fine image detail, for example, phantom resolution inserts and anatomical tissue boundaries. Noniterative partial Fourier and parallel imaging reconstruction methods with integrated GNL correction reduce the resolution loss that occurs during conventional postreconstruction GNL correction while preserving the computational efficiency of standard reconstruction techniques. Magn Reson Med 75:2534-2544, 2016. © 2015 Wiley Periodicals, Inc. © 2015 Wiley Periodicals, Inc.

QIN DAWG Validation of Gradient Nonlinearity Bias Correction Workflow for Quantitative Diffusion-Weighted Imaging in Multicenter Trials.

Science.gov (United States)

Malyarenko, Dariya I; Wilmes, Lisa J; Arlinghaus, Lori R; Jacobs, Michael A; Huang, Wei; Helmer, Karl G; Taouli, Bachir; Yankeelov, Thomas E; Newitt, David; Chenevert, Thomas L

2016-12-01

Previous research has shown that system-dependent gradient nonlinearity (GNL) introduces a significant spatial bias (nonuniformity) in apparent diffusion coefficient (ADC) maps. Here, the feasibility of centralized retrospective system-specific correction of GNL bias for quantitative diffusion-weighted imaging (DWI) in multisite clinical trials is demonstrated across diverse scanners independent of the scanned object. Using corrector maps generated from system characterization by ice-water phantom measurement completed in the previous project phase, GNL bias correction was performed for test ADC measurements from an independent DWI phantom (room temperature agar) at two offset locations in the bore. The precomputed three-dimensional GNL correctors were retrospectively applied to test DWI scans by the central analysis site. The correction was blinded to reference DWI of the agar phantom at magnet isocenter where the GNL bias is negligible. The performance was evaluated from changes in ADC region of interest histogram statistics before and after correction with respect to the unbiased reference ADC values provided by sites. Both absolute error and nonuniformity of the ADC map induced by GNL (median, 12%; range, -35% to +10%) were substantially reduced by correction (7-fold in median and 3-fold in range). The residual ADC nonuniformity errors were attributed to measurement noise and other non-GNL sources. Correction of systematic GNL bias resulted in a 2-fold decrease in technical variability across scanners (down to site temperature range). The described validation of GNL bias correction marks progress toward implementation of this technology in multicenter trials that utilize quantitative DWI.

Multigrid and defect correction for the steady Navier-Stokes equations

NARCIS (Netherlands)

Koren, B.

1990-01-01

Theoretical and experimental convergence results are presented for nonlinear multigrid and iterative defect correction applied to finite volume discretizations of the full, steady, 2D, compressible Navier-Stokes equations. Iterative defect correction is introduced for circumventing the difficulty in

Linear and nonlinear schemes applied to pitch control of wind turbines.

Science.gov (United States)

Geng, Hua; Yang, Geng

2014-01-01

Linear controllers have been employed in industrial applications for many years, but sometimes they are noneffective on the system with nonlinear characteristics. This paper discusses the structure, performance, implementation cost, advantages, and disadvantages of different linear and nonlinear schemes applied to the pitch control of the wind energy conversion systems (WECSs). The linear controller has the simplest structure and is easily understood by the engineers and thus is widely accepted by the industry. In contrast, nonlinear schemes are more complicated, but they can provide better performance. Although nonlinear algorithms can be implemented in a powerful digital processor nowadays, they need time to be accepted by the industry and their reliability needs to be verified in the commercial products. More information about the system nonlinear feature is helpful to simplify the controller design. However, nonlinear schemes independent of the system model are more robust to the uncertainties or deviations of the system parameters.

Inducing in situ, nonlinear soil response applying an active source

Science.gov (United States)

Johnson, P.A.; Bodin, P.; Gomberg, J.; Pearce, F.; Lawrence, Z.; Menq, F.-Y.

2009-01-01

[1] It is well known that soil sites have a profound effect on ground motion during large earthquakes. The complex structure of soil deposits and the highly nonlinear constitutive behavior of soils largely control nonlinear site response at soil sites. Measurements of nonlinear soil response under natural conditions are critical to advancing our understanding of soil behavior during earthquakes. Many factors limit the use of earthquake observations to estimate nonlinear site response such that quantitative characterization of nonlinear behavior relies almost exclusively on laboratory experiments and modeling of wave propagation. Here we introduce a new method for in situ characterization of the nonlinear behavior of a natural soil formation using measurements obtained immediately adjacent to a large vibrator source. To our knowledge, we are the first group to propose and test such an approach. Employing a large, surface vibrator as a source, we measure the nonlinear behavior of the soil by incrementally increasing the source amplitude over a range of frequencies and monitoring changes in the output spectra. We apply a homodyne algorithm for measuring spectral amplitudes, which provides robust signal-to-noise ratios at the frequencies of interest. Spectral ratios are computed between the receivers and the source as well as receiver pairs located in an array adjacent to the source, providing the means to separate source and near-source nonlinearity from pervasive nonlinearity in the soil column. We find clear evidence of nonlinearity in significant decreases in the frequency of peak spectral ratios, corresponding to material softening with amplitude, observed across the array as the source amplitude is increased. The observed peak shifts are consistent with laboratory measurements of soil nonlinearity. Our results provide constraints for future numerical modeling studies of strong ground motion during earthquakes.

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Science.gov (United States)

Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

2018-03-01

We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Genetic algorithms applied to nonlinear and complex domains

International Nuclear Information System (INIS)

Barash, D; Woodin, A E

1999-01-01

The dissertation, titled ''Genetic Algorithms Applied to Nonlinear and Complex Domains'', describes and then applies a new class of powerful search algorithms (GAS) to certain domains. GAS are capable of solving complex and nonlinear problems where many parameters interact to produce a ''final'' result such as the optimization of the laser pulse in the interaction of an atom with an intense laser field. GAS can very efficiently locate the global maximum by searching parameter space in problems which are unsuitable for a search using traditional methods. In particular, the dissertation contains new scientific findings in two areas. First, the dissertation examines the interaction of an ultra-intense short laser pulse with atoms. GAS are used to find the optimal frequency for stabilizing atoms in the ionization process. This leads to a new theoretical formulation, to explain what is happening during the ionization process and how the electron is responding to finite (real-life) laser pulse shapes. It is shown that the dynamics of the process can be very sensitive to the ramp of the pulse at high frequencies. The new theory which is formulated, also uses a novel concept (known as the (t,t') method) to numerically solve the time-dependent Schrodinger equation Second, the dissertation also examines the use of GAS in modeling decision making problems. It compares GAS with traditional techniques to solve a class of problems known as Markov Decision Processes. The conclusion of the dissertation should give a clear idea of where GAS are applicable, especially in the physical sciences, in problems which are nonlinear and complex, i.e. difficult to analyze by other means

Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Directory of Open Access Journals (Sweden)

Vitanov Nikolay K.

2018-03-01

Full Text Available We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Correction of Gradient Nonlinearity Bias in Quantitative Diffusion Parameters of Renal Tissue with Intra Voxel Incoherent Motion.

Science.gov (United States)

Malyarenko, Dariya I; Pang, Yuxi; Senegas, Julien; Ivancevic, Marko K; Ross, Brian D; Chenevert, Thomas L

2015-12-01

Spatially non-uniform diffusion weighting bias due to gradient nonlinearity (GNL) causes substantial errors in apparent diffusion coefficient (ADC) maps for anatomical regions imaged distant from magnet isocenter. Our previously-described approach allowed effective removal of spatial ADC bias from three orthogonal DWI measurements for mono-exponential media of arbitrary anisotropy. The present work evaluates correction feasibility and performance for quantitative diffusion parameters of the two-component IVIM model for well-perfused and nearly isotropic renal tissue. Sagittal kidney DWI scans of a volunteer were performed on a clinical 3T MRI scanner near isocenter and offset superiorly. Spatially non-uniform diffusion weighting due to GNL resulted both in shift and broadening of perfusion-suppressed ADC histograms for off-center DWI relative to unbiased measurements close to isocenter. Direction-average DW-bias correctors were computed based on the known gradient design provided by vendor. The computed bias maps were empirically confirmed by coronal DWI measurements for an isotropic gel-flood phantom. Both phantom and renal tissue ADC bias for off-center measurements was effectively removed by applying pre-computed 3D correction maps. Comparable ADC accuracy was achieved for corrections of both b -maps and DWI intensities in presence of IVIM perfusion. No significant bias impact was observed for IVIM perfusion fraction.

Algorithms For Integrating Nonlinear Differential Equations

Science.gov (United States)

Freed, A. D.; Walker, K. P.

1994-01-01

Improved algorithms developed for use in numerical integration of systems of nonhomogenous, nonlinear, first-order, ordinary differential equations. In comparison with integration algorithms, these algorithms offer greater stability and accuracy. Several asymptotically correct, thereby enabling retention of stability and accuracy when large increments of independent variable used. Accuracies attainable demonstrated by applying them to systems of nonlinear, first-order, differential equations that arise in study of viscoplastic behavior, spread of acquired immune-deficiency syndrome (AIDS) virus and predator/prey populations.

Multigrid and defect correction for the steady Navier-Stokes equations : application to aerodynamics

NARCIS (Netherlands)

Koren, B.

1991-01-01

Theoretical and expcrimental convergence results are presented for nonlinear multigrid and iterative defect correction applied to finite volume discretizations of the full, steady, 2D, compressible NavierStokes equations. lterative defect correction is introduced for circumventing the difficulty in

Significance of accurate diffraction corrections for the second harmonic wave in determining the acoustic nonlinearity parameter

International Nuclear Information System (INIS)

Jeong, Hyunjo; Zhang, Shuzeng; Li, Xiongbing; Barnard, Dan

2015-01-01

The accurate measurement of acoustic nonlinearity parameter β for fluids or solids generally requires making corrections for diffraction effects due to finite size geometry of transmitter and receiver. These effects are well known in linear acoustics, while those for second harmonic waves have not been well addressed and therefore not properly considered in previous studies. In this work, we explicitly define the attenuation and diffraction corrections using the multi-Gaussian beam (MGB) equations which were developed from the quasilinear solutions of the KZK equation. The effects of making these corrections are examined through the simulation of β determination in water. Diffraction corrections are found to have more significant effects than attenuation corrections, and the β values of water can be estimated experimentally with less than 5% errors when the exact second harmonic diffraction corrections are used together with the negligible attenuation correction effects on the basis of linear frequency dependence between attenuation coefficients, α 2 ≃ 2α 1

Significance of accurate diffraction corrections for the second harmonic wave in determining the acoustic nonlinearity parameter

Energy Technology Data Exchange (ETDEWEB)

Jeong, Hyunjo, E-mail: hjjeong@wku.ac.kr [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan, Jeonbuk 570-749 (Korea, Republic of); Zhang, Shuzeng; Li, Xiongbing [School of Traffic and Transportation Engineering, Central South University, Changsha, Hunan 410075 (China); Barnard, Dan [Center for Nondestructive Evaluation, Iowa State University, Ames, IA 50010 (United States)

2015-09-15

The accurate measurement of acoustic nonlinearity parameter β for fluids or solids generally requires making corrections for diffraction effects due to finite size geometry of transmitter and receiver. These effects are well known in linear acoustics, while those for second harmonic waves have not been well addressed and therefore not properly considered in previous studies. In this work, we explicitly define the attenuation and diffraction corrections using the multi-Gaussian beam (MGB) equations which were developed from the quasilinear solutions of the KZK equation. The effects of making these corrections are examined through the simulation of β determination in water. Diffraction corrections are found to have more significant effects than attenuation corrections, and the β values of water can be estimated experimentally with less than 5% errors when the exact second harmonic diffraction corrections are used together with the negligible attenuation correction effects on the basis of linear frequency dependence between attenuation coefficients, α{sub 2} ≃ 2α{sub 1}.

Significance of accurate diffraction corrections for the second harmonic wave in determining the acoustic nonlinearity parameter

Science.gov (United States)

Jeong, Hyunjo; Zhang, Shuzeng; Barnard, Dan; Li, Xiongbing

2015-09-01

The accurate measurement of acoustic nonlinearity parameter β for fluids or solids generally requires making corrections for diffraction effects due to finite size geometry of transmitter and receiver. These effects are well known in linear acoustics, while those for second harmonic waves have not been well addressed and therefore not properly considered in previous studies. In this work, we explicitly define the attenuation and diffraction corrections using the multi-Gaussian beam (MGB) equations which were developed from the quasilinear solutions of the KZK equation. The effects of making these corrections are examined through the simulation of β determination in water. Diffraction corrections are found to have more significant effects than attenuation corrections, and the β values of water can be estimated experimentally with less than 5% errors when the exact second harmonic diffraction corrections are used together with the negligible attenuation correction effects on the basis of linear frequency dependence between attenuation coefficients, α2 ≃ 2α1.

Nonlinear evolution equations for waves in random media

International Nuclear Information System (INIS)

Pelinovsky, E.; Talipova, T.

1994-01-01

The scope of this paper is to highlight the main ideas of asymptotical methods applying in modern approaches of description of nonlinear wave propagation in random media. We start with the discussion of the classical conception of ''mean field''. Then an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters is considered in order to demonstrate that the ''mean field'' method is not correct. We develop new asymptotic procedures of obtaining the nonlinear evolution equations for the wave fields in random media. (author). 16 refs

Genetic algorithms applied to nonlinear and complex domains; TOPICAL

International Nuclear Information System (INIS)

Barash, D; Woodin, A E

1999-01-01

The dissertation, titled ''Genetic Algorithms Applied to Nonlinear and Complex Domains'', describes and then applies a new class of powerful search algorithms (GAS) to certain domains. GAS are capable of solving complex and nonlinear problems where many parameters interact to produce a ''final'' result such as the optimization of the laser pulse in the interaction of an atom with an intense laser field. GAS can very efficiently locate the global maximum by searching parameter space in problems which are unsuitable for a search using traditional methods. In particular, the dissertation contains new scientific findings in two areas. First, the dissertation examines the interaction of an ultra-intense short laser pulse with atoms. GAS are used to find the optimal frequency for stabilizing atoms in the ionization process. This leads to a new theoretical formulation, to explain what is happening during the ionization process and how the electron is responding to finite (real-life) laser pulse shapes. It is shown that the dynamics of the process can be very sensitive to the ramp of the pulse at high frequencies. The new theory which is formulated, also uses a novel concept (known as the (t,t') method) to numerically solve the time-dependent Schrodinger equation Second, the dissertation also examines the use of GAS in modeling decision making problems. It compares GAS with traditional techniques to solve a class of problems known as Markov Decision Processes. The conclusion of the dissertation should give a clear idea of where GAS are applicable, especially in the physical sciences, in problems which are nonlinear and complex, i.e. difficult to analyze by other means

Acceleration of the AFEN method by two-node nonlinear iteration

Energy Technology Data Exchange (ETDEWEB)

Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1999-12-31

A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)

Acceleration of the AFEN method by two-node nonlinear iteration

Energy Technology Data Exchange (ETDEWEB)

Moon, Kap Suk; Cho, Nam Zin; Noh, Jae Man; Hong, Ser Gi [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)

1998-12-31

A nonlinear iterative scheme developed to reduce the computing time of the AFEN method was tested and applied to two benchmark problems. The new nonlinear method for the AFEN method is based on solving two-node problems and use of two nonlinear correction factors at every interface instead of one factor in the conventional scheme. The use of two correction factors provides higher-order accurate interface fluxes as well as currents which are used as the boundary conditions of the two-node problem. The numerical results show that this new method gives exactly the same solution as that of the original AFEN method and the computing time is significantly reduced in comparison with the original AFEN method. 7 refs., 1 fig., 1 tab. (Author)

A Robust In-Situ Warp-Correction Algorithm For VISAR Streak Camera Data at the National Ignition Facility

International Nuclear Information System (INIS)

Labaria, George R.; Warrick, Abbie L.; Celliers, Peter M.; Kalantar, Daniel H.

2015-01-01

The National Ignition Facility (NIF) at the Lawrence Livermore National Laboratory is a 192-beam pulsed laser system for high-energy-density physics experiments. Sophisticated diagnostics have been designed around key performance metrics to achieve ignition. The Velocity Interferometer System for Any Reflector (VISAR) is the primary diagnostic for measuring the timing of shocks induced into an ignition capsule. The VISAR system utilizes three streak cameras; these streak cameras are inherently nonlinear and require warp corrections to remove these nonlinear effects. A detailed calibration procedure has been developed with National Security Technologies (NSTec) and applied to the camera correction analysis in production. However, the camera nonlinearities drift over time, affecting the performance of this method. An in-situ fiber array is used to inject a comb of pulses to generate a calibration correction in order to meet the timing accuracy requirements of VISAR. We develop a robust algorithm for the analysis of the comb calibration images to generate the warp correction that is then applied to the data images. Our algorithm utilizes the method of thin-plate splines (TPS) to model the complex nonlinear distortions in the streak camera data. In this paper, we focus on the theory and implementation of the TPS warp-correction algorithm for the use in a production environment.

A Robust In-Situ Warp-Correction Algorithm For VISAR Streak Camera Data at the National Ignition Facility

Energy Technology Data Exchange (ETDEWEB)

Labaria, George R. [Univ. of California, Santa Cruz, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Warrick, Abbie L. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Celliers, Peter M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kalantar, Daniel H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2015-01-12

The National Ignition Facility (NIF) at the Lawrence Livermore National Laboratory is a 192-beam pulsed laser system for high-energy-density physics experiments. Sophisticated diagnostics have been designed around key performance metrics to achieve ignition. The Velocity Interferometer System for Any Reflector (VISAR) is the primary diagnostic for measuring the timing of shocks induced into an ignition capsule. The VISAR system utilizes three streak cameras; these streak cameras are inherently nonlinear and require warp corrections to remove these nonlinear effects. A detailed calibration procedure has been developed with National Security Technologies (NSTec) and applied to the camera correction analysis in production. However, the camera nonlinearities drift over time, affecting the performance of this method. An in-situ fiber array is used to inject a comb of pulses to generate a calibration correction in order to meet the timing accuracy requirements of VISAR. We develop a robust algorithm for the analysis of the comb calibration images to generate the warp correction that is then applied to the data images. Our algorithm utilizes the method of thin-plate splines (TPS) to model the complex nonlinear distortions in the streak camera data. In this paper, we focus on the theory and implementation of the TPS warp-correction algorithm for the use in a production environment.

Nonlinear resonant ultrasound spectroscopy (NRUS) applied to damage assessment in bone

Science.gov (United States)

Muller, Marie; Sutin, Alexander; Guyer, Robert; Talmant, Maryline; Laugier, Pascal; Johnson, Paul A.

2005-12-01

Nonlinear resonant ultrasound spectroscopy (NRUS) is a resonance-based technique exploiting the significant nonlinear behavior of damaged materials. In NRUS, the resonant frequency(ies) of an object is studied as a function of the excitation level. As the excitation level increases, the elastic nonlinearity is manifest by a shift in the resonance frequency. This study shows the feasibility of this technique for application to damage assessment in bone. Two samples of bovine cortical bone were subjected to progressive damage induced by application of mechanical cycling. Before cycling commenced, and at each step in the cycling process, NRUS was applied for damage assessment. For independent assessment of damage, high-energy x-ray computed tomography imaging was performed but was only useful in identifying the prominent cracks. As the integral quantity of damage increased, NRUS revealed a corresponding increase in the nonlinear response. The measured change in nonlinear response is much more sensitive than the change in linear modulus. The results suggest that NRUS could be a potential tool for micro-damage assessment in bone. Further work must be carried out for a better understanding of the physical nature of damaged bone and for the ultimate goal of the challenging in vivo implementation of the technique.

Electromagnetic fields with vanishing quantum corrections

Czech Academy of Sciences Publication Activity Database

Ortaggio, Marcello; Pravda, Vojtěch

2018-01-01

Roč. 779, 10 April (2018), s. 393-395 ISSN 0370-2693 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : nonlinear electrodynamics * quantum corrections Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.807, year: 2016 https://www.sciencedirect.com/science/article/pii/S0370269318300327?via%3Dihub

Electromagnetic fields with vanishing quantum corrections

Czech Academy of Sciences Publication Activity Database

Ortaggio, Marcello; Pravda, Vojtěch

2018-01-01

Roč. 779, 10 April (2018), s. 393-395 ISSN 0370-2693 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : nonlinear electrodynamics * quantum corrections Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 4.807, year: 2016 https://www. science direct.com/ science /article/pii/S0370269318300327?via%3Dihub

Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system

Science.gov (United States)

Kurt, Mehmet; Moore, Keegan J.; Eriten, Melih; McFarland, D. Michael; Bergman, Lawrence A.; Vakakis, Alexander F.

2017-05-01

We consider the application of a new nonlinear model updating strategy to a computational benchmark system. The approach relies on analyzing system response time series in the frequency-energy domain by constructing both Hamiltonian and forced and damped frequency-energy plots (FEPs). The system parameters are then characterized and updated by matching the backbone branches of the FEPs with the frequency-energy wavelet transforms of experimental and/or computational time series. The main advantage of this method is that no nonlinearity model is assumed a priori, and the system model is updated solely based on simulation and/or experimental measured time series. By matching the frequency-energy plots of the benchmark system and its reduced-order model, we show that we are able to retrieve the global strongly nonlinear dynamics in the frequency and energy ranges of interest, identify bifurcations, characterize local nonlinearities, and accurately reconstruct time series. We apply the proposed methodology to a benchmark problem, which was posed to the system identification community prior to the IMAC XXXII (2014) and XXXIII (2015) Conferences as a "Round Robin Exercise on Nonlinear System Identification". We show that we are able to identify the parameters of the non-linear element in the problem with a priori knowledge about its position.

Nonlinear Modeling of the PEMFC Based On NNARX Approach

OpenAIRE

Shan-Jen Cheng; Te-Jen Chang; Kuang-Hsiung Tan; Shou-Ling Kuo

2015-01-01

Polymer Electrolyte Membrane Fuel Cell (PEMFC) is such a time-vary nonlinear dynamic system. The traditional linear modeling approach is hard to estimate structure correctly of PEMFC system. From this reason, this paper presents a nonlinear modeling of the PEMFC using Neural Network Auto-regressive model with eXogenous inputs (NNARX) approach. The multilayer perception (MLP) network is applied to evaluate the structure of the NNARX model of PEMFC. The validity and accurac...

Controller Design of Complex System Based on Nonlinear Strength

Directory of Open Access Journals (Sweden)

Rongjun Mu

2015-01-01

Full Text Available This paper presents a new idea of controller design for complex systems. The nonlinearity index method was first developed for error propagation of nonlinear system. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of the system model. The algorithm of nonlinearity index according to engineering application is first proposed in this paper. Applying this method on nonlinear systems is an effective way to measure the nonlinear strength of dynamics model over the full flight envelope. The nonlinearity indices access the boundary between the strong and the weak nonlinearities of system model. According to the different nonlinear strength of dynamical model, the control system is designed. The simulation time of dynamical complex system is selected by the maximum value of dynamic nonlinearity indices. Take a missile as example; dynamical system and control characteristic of missile are simulated. The simulation results show that the method is correct and appropriate.

A method for nonlinear exponential regression analysis

Science.gov (United States)

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.

Bayesian Estimation and Selection of Nonlinear Vector Error Correction Models: The Case of the Sugar-Ethanol-Oil Nexus in Brazil

OpenAIRE

Kelvin Balcombe; George Rapsomanikis

2008-01-01

Nonlinear adjustment toward long-run price equilibrium relationships in the sugar-ethanol-oil nexus in Brazil is examined. We develop generalized bivariate error correction models that allow for cointegration between sugar, ethanol, and oil prices, where dynamic adjustments are potentially nonlinear functions of the disequilibrium errors. A range of models are estimated using Bayesian Monte Carlo Markov Chain algorithms and compared using Bayesian model selection methods. The results suggest ...

On the p4-corrections to K → 3π decay amplitudes in nonlinear and linear chiral models

International Nuclear Information System (INIS)

Bel'kov, A.A.; Bolnn, G.; Lanyov, A.V.; Schaale, A.

1993-09-01

The calculations of isotopic amplitudes and their results for the direct CP-violating charge asymmetry in K ± → 3π decays within the nonlinear and linear (σ-model) chiral Lagrangian approach are compared with each other. It is shown, that the latter, taking into account intermediate scalar resonances, does not reproduce the p 4 -corrections of the nonlinear approach introduced by Gasser and Leutwyler, being saturated mainly by vector resonance exchange. The resulting differences concerning the CP violation effect are traced in some detail. (author). 31 refs., 1 tab

Correction method of nonlinearity due to logarithm operation for X-ray CT projection data with noise in photon-starved state

International Nuclear Information System (INIS)

Iwamoto, Shin-ichiro; Shiozaki, Akira

2007-01-01

In the acquisition of projection data of X-ray CT, logarithm operation is indispensable. But noise distribution is nonlinearly projected by the logarithm operation, and this deteriorates the precision of CT number. This influence becomes particularly remarkable when only a few photons are caught with a detector. It generates a strong streak artifact (SA) in a reconstructed image. Previously we have clarified the influence of the nonlinearity by statistical analysis and proposed a correction method for such nonlinearity. However, there is a problem that the compensation for clamp processing cannot be performed and that the suppression of SA is not enough in photon shortage state. In this paper, we propose a new technique for correcting the nonlinearity due to logarithm operation for noisy data by combining the previously presented method and an adaptive filtering method. The technique performs an adaptive filtering only when the number of captured photons is very few. Moreover we quantitatively evaluate the influence of noise on the reconstructed image in the proposed method by the experiment using numerical phantoms. The experimental results show that there is less influence on spatial resolution despite suppressing SA effectively and that CT number are hardly dependent on the number of the incident photons. (author)

Nonlinear responses of chiral fluids from kinetic theory

Science.gov (United States)

Hidaka, Yoshimasa; Pu, Shi; Yang, Di-Lun

2018-01-01

The second-order nonlinear responses of inviscid chiral fluids near local equilibrium are investigated by applying the chiral kinetic theory (CKT) incorporating side-jump effects. It is shown that the local equilibrium distribution function can be nontrivially introduced in a comoving frame with respect to the fluid velocity when the quantum corrections in collisions are involved. For the study of anomalous transport, contributions from both quantum corrections in anomalous hydrodynamic equations of motion and those from the CKT and Wigner functions are considered under the relaxation-time (RT) approximation, which result in anomalous charge Hall currents propagating along the cross product of the background electric field and the temperature (or chemical-potential) gradient and of the temperature and chemical-potential gradients. On the other hand, the nonlinear quantum correction on the charge density vanishes in the classical RT approximation, which in fact satisfies the matching condition given by the anomalous equation obtained from the CKT.

Phase estimation for global defocus correction in optical coherence tomography

DEFF Research Database (Denmark)

Jensen, Mikkel; Israelsen, Niels Møller; Podoleanu, Adrian

2017-01-01

In this work we investigate three techniques for estimation of the non-linear phase present due to defocus in opticalcoherence tomography, and apply them with the angular spectrum method. The techniques are: Least squarestting the of unwrapped phase of the angular spectrum, iterative optimization......, and sub-aperture correlations. The estimated phase of a single en-face image is used to extrapolate the non-linear phase at all depths, whichin the end can be used to correct the entire 3-D tomogram, and any other tomogram from the same system.......In this work we investigate three techniques for estimation of the non-linear phase present due to defocus in opticalcoherence tomography, and apply them with the angular spectrum method. The techniques are: Least squarestting the of unwrapped phase of the angular spectrum, iterative optimization...

A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

International Nuclear Information System (INIS)

Zhang Huiqun

2009-01-01

By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

Analysis of efficient preconditioned defect correction methods for nonlinear water waves

DEFF Research Database (Denmark)

Engsig-Karup, Allan Peter

2014-01-01

Robust computational procedures for the solution of non-hydrostatic, free surface, irrotational and inviscid free-surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable...... prediction of free-surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow...... equations. We present new detailed fundamental analysis using finite-amplitude wave solutions for iterative solvers. We demonstrate that the PDC method in combination with a high-order discretization method enables efficient and scalable solution of the linear system of equations arising in potential flow...

Stack emission monitoring using non-dispersive infrared spectroscopy with an optimized nonlinear absorption cross interference correction algorithm

Directory of Open Access Journals (Sweden)

Y. W. Sun

2013-08-01

Full Text Available In this paper, we present an optimized analysis algorithm for non-dispersive infrared (NDIR to in situ monitor stack emissions. The proposed algorithm simultaneously compensates for nonlinear absorption and cross interference among different gases. We present a mathematical derivation for the measurement error caused by variations in interference coefficients when nonlinear absorption occurs. The proposed algorithm is derived from a classical one and uses interference functions to quantify cross interference. The interference functions vary proportionally with the nonlinear absorption. Thus, interference coefficients among different gases can be modeled by the interference functions whether gases are characterized by linear or nonlinear absorption. In this study, the simultaneous analysis of two components (CO2 and CO serves as an example for the validation of the proposed algorithm. The interference functions in this case can be obtained by least-squares fitting with third-order polynomials. Experiments show that the results of cross interference correction are improved significantly by utilizing the fitted interference functions when nonlinear absorptions occur. The dynamic measurement ranges of CO2 and CO are improved by about a factor of 1.8 and 3.5, respectively. A commercial analyzer with high accuracy was used to validate the CO and CO2 measurements derived from the NDIR analyzer prototype in which the new algorithm was embedded. The comparison of the two analyzers show that the prototype works well both within the linear and nonlinear ranges.

Real-Time Correction By Optical Tracking with Integrated Geometric Distortion Correction for Reducing Motion Artifacts in fMRI

Science.gov (United States)

Rotenberg, David J.

Artifacts caused by head motion are a substantial source of error in fMRI that limits its use in neuroscience research and clinical settings. Real-time scan-plane correction by optical tracking has been shown to correct slice misalignment and non-linear spin-history artifacts, however residual artifacts due to dynamic magnetic field non-uniformity may remain in the data. A recently developed correction technique, PLACE, can correct for absolute geometric distortion using the complex image data from two EPI images, with slightly shifted k-space trajectories. We present a correction approach that integrates PLACE into a real-time scan-plane update system by optical tracking, applied to a tissue-equivalent phantom undergoing complex motion and an fMRI finger tapping experiment with overt head motion to induce dynamic field non-uniformity. Experiments suggest that including volume by volume geometric distortion correction by PLACE can suppress dynamic geometric distortion artifacts in a phantom and in vivo and provide more robust activation maps.

Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes

DEFF Research Database (Denmark)

Zhang, H.W.; Schäffer, Hemming Andreas

2007-01-01

An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....

Intense laser effects on nonlinear optical absorption and optical rectification in single quantum wells under applied electric and magnetic field

International Nuclear Information System (INIS)

Duque, C.A.; Kasapoglu, E.; Sakiroglu, S.; Sari, H.; Soekmen, I.

2011-01-01

In this work the effects of intense laser on the electron-related nonlinear optical absorption and nonlinear optical rectification in GaAs-Ga 1-x Al x As quantum wells are studied under, applied electric and magnetic field. The electric field is applied along the growth direction of the quantum well whereas the magnetic field has been considered to be in-plane. The calculations were performed within the density matrix formalism with the use of the effective mass and parabolic band approximations. The intense laser effects are included through the Floquet method, by modifying the confining potential associated to the heterostructure. Results are presented for the nonlinear optical absorption, the nonlinear optical rectification and the resonant peak of these two optical processes. Several configurations of the dimensions of the quantum well, the applied electric and magnetic fields, and the incident intense laser radiation have been considered. The outcome of the calculation suggests that the nonlinear optical absorption and optical rectification are non-monotonic functions of the dimensions of the heterostructure and of the external perturbations considered in this work.

C code generation applied to nonlinear model predictive control for an artificial pancreas

DEFF Research Database (Denmark)

Boiroux, Dimitri; Jørgensen, John Bagterp

2017-01-01

This paper presents a method to generate C code from MATLAB code applied to a nonlinear model predictive control (NMPC) algorithm. The C code generation uses the MATLAB Coder Toolbox. It can drastically reduce the time required for development compared to a manual porting of code from MATLAB to C...

Effects of nonlinear error correction of measurements obtained by peak flowmeter using the Wright scale to assess asthma attack severity in children

Directory of Open Access Journals (Sweden)

Stamatović Dragana

2007-01-01

Full Text Available Introduction: Monitoring of peak expiratory flow (PEF is recommended in numerous guidelines for management of asthma. Improvements in calibration methods have demonstrated the inaccuracy of original Wright scale of peak flowmeter. A new standard, EN 13826 that was applied to peak flowmeter was adopted on 1st September 2004 by some European countries. Correction of PEF readings obtained with old type devices for measurement is possible by Dr M. Miller’s original predictive equation. Objective. Assessment of PEF correction effect on the interpretation of measurement results and management decisions. Method. In children with intermittent (35 or stable persistent asthma (75 aged 6-16 years, there were performed 8393 measurements of PEF by Vitalograph normal-range peak flowmeter with traditional Wright scale. Readings were expressed as percentage of individual best values (PB before and after correction. The effect of correction was analyzed based on The British Thoracic Society guidelines for asthma attack treatment. Results. In general, correction reduced the values of PEF (p<0.01. The highest mean percentage error (20.70% in the measured values was found in the subgroup in which PB ranged between 250 and 350 l/min. Nevertheless, the interpretation of PEF after the correction in this subgroup changed in only 2.41% of measurements. The lowest mean percentage error (15.72%, and, at the same time, the highest effect of correction on measurement results interpretation (in 22.65% readings were in children with PB above 450 l/min. In 73 (66.37% subjects, the correction changed the clinical interpretation of some values of PEF after correction. In 13 (11.8% patients, some corrected values indicated the absence or a milder degree of airflow obstruction. In 27 (24.54% children, more than 10%, and in 12 (10.93%, more than 20% of the corrected readings indicated a severe degree of asthma exacerbation that needed more aggressive treatment. Conclusion

A nonlinear adaptive backstepping approach applied to a three phase PWM AC-DC converter feeding induction heating

Science.gov (United States)

Hadri-Hamida, A.; Allag, A.; Hammoudi, M. Y.; Mimoune, S. M.; Zerouali, S.; Ayad, M. Y.; Becherif, M.; Miliani, E.; Miraoui, A.

2009-04-01

This paper presents a new control strategy for a three phase PWM converter, which consists of applying an adaptive nonlinear control. The input-output feedback linearization approach is based on the exact cancellation of the nonlinearity, for this reason, this technique is not efficient, because system parameters can vary. First a nonlinear system modelling is derived with state variables of the input current and the output voltage by using power balance of the input and output, the nonlinear adaptive backstepping control can compensate the nonlinearities in the nominal system and the uncertainties. Simulation results are obtained using Matlab/Simulink. These results show how the adaptive backstepping law updates the system parameters and provide an efficient control design both for tracking and regulation in order to improve the power factor.

Thermal nucleation of kink-antikink pairs in a deformable chain: Influence of the non-Gaussian correction

International Nuclear Information System (INIS)

Woulache, R.L.; Kofane, T.C.; Yemele, D.

2005-08-01

Thermal nucleation of kink-antikink pairs in a nonlinear Klein- Gordon model with Remoissenet-Peyrard substrate potential coupled to an applied field is analyzed in the limits of moderate temperature and strong damping. We derive analytically the non- Gaussian correction to the nucleation rate formula of kink- antikink pairs previously calculated by Yemele and Kofane and show that the correction factor depends on the intensity of the applied field, the temperature of the system and the shape of the substrate potential. (author)

Wave equation of a nonlinear triatomic molecule and the adiabatic correction to the Born--Oppenheimer approximation

International Nuclear Information System (INIS)

Bardo, R.D.; Wolfsberg, M.

1977-01-01

The wave equation for a nonlinear polyatomic molecule is formulated in molecule-fixed coordinates by a method originally due to Hirschfelder and Wigner. Application is made to a triatomic molecule, and the wave equation is explicitly presented in a useful molecule-fixed coordinate system. The formula for the adiabatic correction to the Born--Oppenheimer approximation for a triatomic molecule is obtained. The extension of the present formulation to larger polyatomic molecules is pointed out. Some terms in the triatomic molecule wave equation are discussed in detail

Non-linear corrections to the time-covariance function derived from a multi-state chemical master equation.

Science.gov (United States)

Scott, M

2012-08-01

The time-covariance function captures the dynamics of biochemical fluctuations and contains important information about the underlying kinetic rate parameters. Intrinsic fluctuations in biochemical reaction networks are typically modelled using a master equation formalism. In general, the equation cannot be solved exactly and approximation methods are required. For small fluctuations close to equilibrium, a linearisation of the dynamics provides a very good description of the relaxation of the time-covariance function. As the number of molecules in the system decrease, deviations from the linear theory appear. Carrying out a systematic perturbation expansion of the master equation to capture these effects results in formidable algebra; however, symbolic mathematics packages considerably expedite the computation. The authors demonstrate that non-linear effects can reveal features of the underlying dynamics, such as reaction stoichiometry, not available in linearised theory. Furthermore, in models that exhibit noise-induced oscillations, non-linear corrections result in a shift in the base frequency along with the appearance of a secondary harmonic.

LDV measurement of small nonlinearities in flat and curved membranes. A model for eardrum nonlinear acoustic behaviour

Science.gov (United States)

Kilian, Gladiné; Pieter, Muyshondt; Joris, Dirckx

2016-06-01

Laser Doppler Vibrometry is an intrinsic highly linear measurement technique which makes it a great tool to measure extremely small nonlinearities in the vibration response of a system. Although the measurement technique is highly linear, other components in the experimental setup may introduce nonlinearities. An important source of artificially introduced nonlinearities is the speaker, which generates the stimulus. In this work, two correction methods to remove the effects of stimulus nonlinearity are investigated. Both correction methods were found to give similar results but have different pros and cons. The aim of this work is to investigate the importance of the conical shape of the eardrum as a source of nonlinearity in hearing. We present measurements on flat and indented membranes. The data shows that the curved membrane exhibit slightly higher levels of nonlinearity compared to the flat membrane.

Derivation of an applied nonlinear Schroedinger equation

Energy Technology Data Exchange (ETDEWEB)

Pitts, Todd Alan [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Laine, Mark Richard [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Schwarz, Jens [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Rambo, Patrick K. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Karelitz, David B. [Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

2015-01-01

We derive from first principles a mathematical physics model useful for understanding nonlinear optical propagation (including filamentation). All assumptions necessary for the development are clearly explained. We include the Kerr effect, Raman scattering, and ionization (as well as linear and nonlinear shock, diffraction and dispersion). We explain the phenomenological sub-models and each assumption required to arrive at a complete and consistent theoretical description. The development includes the relationship between shock and ionization and demonstrates why inclusion of Drude model impedance effects alters the nature of the shock operator. Unclassified Unlimited Release

A Lagrangian meshfree method applied to linear and nonlinear elasticity.

Science.gov (United States)

Walker, Wade A

2017-01-01

The repeated replacement method (RRM) is a Lagrangian meshfree method which we have previously applied to the Euler equations for compressible fluid flow. In this paper we present new enhancements to RRM, and we apply the enhanced method to both linear and nonlinear elasticity. We compare the results of ten test problems to those of analytic solvers, to demonstrate that RRM can successfully simulate these elastic systems without many of the requirements of traditional numerical methods such as numerical derivatives, equation system solvers, or Riemann solvers. We also show the relationship between error and computational effort for RRM on these systems, and compare RRM to other methods to highlight its strengths and weaknesses. And to further explain the two elastic equations used in the paper, we demonstrate the mathematical procedure used to create Riemann and Sedov-Taylor solvers for them, and detail the numerical techniques needed to embody those solvers in code.

A new nonlinear parameter in the developed strain-to-applied strain of the soft tissues and its application in ultrasound elasticity imaging.

Science.gov (United States)

Xu, Jingping; Tripathy, Sakya; Rubin, Jonathan M; Stidham, Ryan W; Johnson, Laura A; Higgins, Peter D R; Kim, Kang

2012-03-01

Strain developed under quasi-static deformation has been mostly used in ultrasound elasticity imaging (UEI) to determine the stiffness change of tissues. However, the strain measure in UEI is often less sensitive to a subtle change of stiffness. This is particularly true for Crohn's disease where we have applied strain imaging to the differentiation of acutely inflamed bowel from chronically fibrotic bowel. In this study, a new nonlinear elastic parameter of the soft tissues is proposed to overcome this limit. The purpose of this study is to evaluate the newly proposed method and demonstrate its feasibility in the UEI. A nonlinear characteristic of soft tissues over a relatively large dynamic range of strain was investigated. A simplified tissue model based on a finite element (FE) analysis was integrated with a laboratory developed ultrasound radio-frequency (RF) signal synthesis program. Two-dimensional speckle tracking was applied to this model to simulate the nonlinear behavior of the strain developed in a target inclusion over the applied average strain to the surrounding tissues. A nonlinear empirical equation was formulated and optimized to best match the developed strain-to-applied strain relation obtained from the FE simulation. The proposed nonlinear equation was applied to in vivo measurements and nonlinear parameters were further empirically optimized. For an animal model, acute and chronic inflammatory bowel disease was induced in Lewis rats with trinitrobenzene sulfonic acid (TNBS)-ethanol treatments. After UEI, histopathology and direct mechanical measurements were performed on the excised tissues. The extracted nonlinear parameter from the developed strain-to-applied strain relation differentiated the three different tissue types with 1.96 ± 0.12 for normal, 1.50 ± 0.09 for the acutely inflamed and 1.03 ± 0.08 for the chronically fibrotic tissue. T-tests determined that the nonlinear parameters between normal, acutely inflamed and fibrotic tissue

Receiver calibration and the nonlinearity parameter measurement of thick solid samples with diffraction and attenuation corrections.

Science.gov (United States)

Jeong, Hyunjo; Barnard, Daniel; Cho, Sungjong; Zhang, Shuzeng; Li, Xiongbing

2017-11-01

This paper presents analytical and experimental techniques for accurate determination of the nonlinearity parameter (β) in thick solid samples. When piezoelectric transducers are used for β measurements, the receiver calibration is required to determine the transfer function from which the absolute displacement can be calculated. The measured fundamental and second harmonic displacement amplitudes should be modified to account for beam diffraction and material absorption. All these issues are addressed in this study and the proposed technique is validated through the β measurements of thick solid samples. A simplified self-reciprocity calibration procedure for a broadband receiver is described. The diffraction and attenuation corrections for the fundamental and second harmonics are explicitly derived. Aluminum alloy samples in five different thicknesses (4, 6, 8, 10, 12cm) are prepared and β measurements are made using the finite amplitude, through-transmission method. The effects of diffraction and attenuation corrections on β measurements are systematically investigated. When diffraction and attenuation corrections are all properly made, the variation of β between different thickness samples is found to be less than 3.2%. Copyright © 2017 Elsevier B.V. All rights reserved.

Self-interaction corrections applied to Mg-porphyrin, C60, and pentacene molecules

International Nuclear Information System (INIS)

Pederson, Mark R.; Baruah, Tunna; Basurto, Luis; Kao, Der-you

2016-01-01

We have applied a recently developed method to incorporate the self-interaction correction through Fermi orbitals to Mg-porphyrin, C 60 , and pentacene molecules. The Fermi-Löwdin orbitals are localized and unitarily invariant to the Kohn-Sham orbitals from which they are constructed. The self-interaction-corrected energy is obtained variationally leading to an optimum set of Fermi-Löwdin orbitals (orthonormalized Fermi orbitals) that gives the minimum energy. A Fermi orbital, by definition, is dependent on a certain point which is referred to as the descriptor position. The degree to which the initial choice of descriptor positions influences the variational approach to the minimum and the complexity of the energy landscape as a function of Fermi-orbital descriptors is examined in detail for Mg-porphyrin. The applications presented here also demonstrate that the method can be applied to larger molecular systems containing a few hundred electrons. The atomization energy of the C 60 molecule within the Fermi-Löwdin-orbital self-interaction-correction approach is significantly improved compared to local density approximation in the Perdew-Wang 92 functional and generalized gradient approximation of Perdew-Burke-Ernzerhof functionals. The eigenvalues of the highest occupied molecular orbitals show qualitative improvement.

Real-space post-processing correction of thermal drift and piezoelectric actuator nonlinearities in scanning tunneling microscope images

Science.gov (United States)

Yothers, Mitchell P.; Browder, Aaron E.; Bumm, Lloyd A.

2017-01-01

We have developed a real-space method to correct distortion due to thermal drift and piezoelectric actuator nonlinearities on scanning tunneling microscope images using Matlab. The method uses the known structures typically present in high-resolution atomic and molecularly resolved images as an internal standard. Each image feature (atom or molecule) is first identified in the image. The locations of each feature's nearest neighbors are used to measure the local distortion at that location. The local distortion map across the image is simultaneously fit to our distortion model, which includes thermal drift in addition to piezoelectric actuator hysteresis and creep. The image coordinates of the features and image pixels are corrected using an inverse transform from the distortion model. We call this technique the thermal-drift, hysteresis, and creep transform. Performing the correction in real space allows defects, domain boundaries, and step edges to be excluded with a spatial mask. Additional real-space image analyses are now possible with these corrected images. Using graphite(0001) as a model system, we show lattice fitting to the corrected image, averaged unit cell images, and symmetry-averaged unit cell images. Statistical analysis of the distribution of the image features around their best-fit lattice sites measures the aggregate noise in the image, which can be expressed as feature confidence ellipsoids.

Real-space post-processing correction of thermal drift and piezoelectric actuator nonlinearities in scanning tunneling microscope images.

Science.gov (United States)

Yothers, Mitchell P; Browder, Aaron E; Bumm, Lloyd A

2017-01-01

We have developed a real-space method to correct distortion due to thermal drift and piezoelectric actuator nonlinearities on scanning tunneling microscope images using Matlab. The method uses the known structures typically present in high-resolution atomic and molecularly resolved images as an internal standard. Each image feature (atom or molecule) is first identified in the image. The locations of each feature's nearest neighbors are used to measure the local distortion at that location. The local distortion map across the image is simultaneously fit to our distortion model, which includes thermal drift in addition to piezoelectric actuator hysteresis and creep. The image coordinates of the features and image pixels are corrected using an inverse transform from the distortion model. We call this technique the thermal-drift, hysteresis, and creep transform. Performing the correction in real space allows defects, domain boundaries, and step edges to be excluded with a spatial mask. Additional real-space image analyses are now possible with these corrected images. Using graphite(0001) as a model system, we show lattice fitting to the corrected image, averaged unit cell images, and symmetry-averaged unit cell images. Statistical analysis of the distribution of the image features around their best-fit lattice sites measures the aggregate noise in the image, which can be expressed as feature confidence ellipsoids.

Three-Step Predictor-Corrector of Exponential Fitting Method for Nonlinear Schroedinger Equations

International Nuclear Information System (INIS)

Tang Chen; Zhang Fang; Yan Haiqing; Luo Tao; Chen Zhanqing

2005-01-01

We develop the three-step explicit and implicit schemes of exponential fitting methods. We use the three-step explicit exponential fitting scheme to predict an approximation, then use the three-step implicit exponential fitting scheme to correct this prediction. This combination is called the three-step predictor-corrector of exponential fitting method. The three-step predictor-corrector of exponential fitting method is applied to numerically compute the coupled nonlinear Schroedinger equation and the nonlinear Schroedinger equation with varying coefficients. The numerical results show that the scheme is highly accurate.

Effects produced by oscillations applied to nonlinear dynamic systems: a general approach and examples

DEFF Research Database (Denmark)

Blekhman, I. I.; Sorokin, V. S.

2016-01-01

A general approach to study effects produced by oscillations applied to nonlinear dynamic systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics.......g., the requirement for the involved nonlinearities to be weak. The approach is illustrated by several relevant examples from various fields of science, e.g., mechanics, physics, chemistry and biophysics....... equations). The approach is named as the oscillatory strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that capture the averaged effect of oscillations. The method of direct separation of motions appears to be an efficient...

Overview of magnetic nonlinear beam dynamics in the RHIC

International Nuclear Information System (INIS)

Luo, Y.; Bai, M.; Beebe-Wang, J.; Bengtsson, J.; Calaga, R.; Fischer, W.; Jain, A.; Pilat, F.; Ptitsyn, V.; Malitsky, N.; Robert-Demolaize, G.; Satogata, T.; Tepikian, S.; Tomas, R.; Trbojevic, D.

2009-01-01

In this article we review our studies of nonlinear beam dynamics due to the nonlinear magnetic field errors in the Relativistic Heavy Ion Collider (RHIC). Nonlinear magnetic field errors, including magnetic field errors in interaction regions (IRs), chromatic sextupoles, and sextupole components from arc main dipoles are discussed. Their effects on beam dynamics and beam dynamic aperture are evaluated. The online methods to measure and correct the IR nonlinear field errors, second order chromaticities, and horizontal third order resonance are presented. The overall strategy for nonlinear corrections in RHIC is discussed

Non-uniformity Correction of Infrared Images by Midway Equalization

Directory of Open Access Journals (Sweden)

Yohann Tendero

2012-07-01

Full Text Available The non-uniformity is a time-dependent noise caused by the lack of sensor equalization. We present here the detailed algorithm and on line demo of the non-uniformity correction method by midway infrared equalization. This method was designed to suit infrared images. Nevertheless, it can be applied to images produced for example by scanners, or by push-broom satellites. The obtained single image method works on static images, is fully automatic, having no user parameter, and requires no registration. It needs no camera motion compensation, no closed aperture sensor equalization and is able to correct for a fully non-linear non-uniformity.

Simultaneous use of linear and nonlinear gradients for B1+ inhomogeneity correction.

Science.gov (United States)

Ertan, Koray; Atalar, Ergin

2017-09-01

The simultaneous use of linear spatial encoding magnetic fields (L-SEMs) and nonlinear spatial encoding magnetic fields (N-SEMs) in B 1 + inhomogeneity problems is formulated and demonstrated with both simulations and experiments. Independent excitation k-space variables for N-SEMs are formulated for the simultaneous use of L-SEMs and N-SEMs by assuming a small tip angle. The formulation shows that, when N-SEMs are considered as an independent excitation k-space variable, numerous different k-space trajectories and frequency weightings differing in dimension, length, and energy can be designed for a given target transverse magnetization distribution. The advantage of simultaneous use of L-SEMs and N-SEMs is demonstrated by B 1 + inhomogeneity correction with spoke excitation. To fully utilize the independent k-space formulations, global optimizations are performed for 1D, 2D RF power limited, and 2D RF power unlimited simulations and experiments. Three different cases are compared: L-SEMs alone, N-SEMs alone, and both used simultaneously. In all cases, the simultaneous use of L-SEMs and N-SEMs leads to a decreased standard deviation in the ROI compared with using only L-SEMs or N-SEMs. The simultaneous use of L-SEMs and N-SEMs results in better B 1 + inhomogeneity correction than using only L-SEMs or N-SEMs due to the increased number of degrees of freedom. Copyright © 2017 John Wiley & Sons, Ltd.

Nonlinear streak computation using boundary region equations

Energy Technology Data Exchange (ETDEWEB)

Martin, J A; Martel, C, E-mail: juanangel.martin@upm.es, E-mail: carlos.martel@upm.es [Depto. de Fundamentos Matematicos, E.T.S.I Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid (Spain)

2012-08-01

The boundary region equations (BREs) are applied for the simulation of the nonlinear evolution of a spanwise periodic array of streaks in a flat plate boundary layer. The well-known BRE formulation is obtained from the complete Navier-Stokes equations in the high Reynolds number limit, and provides the correct asymptotic description of three-dimensional boundary layer streaks. In this paper, a fast and robust streamwise marching scheme is introduced to perform their numerical integration. Typical streak computations present in the literature correspond to linear streaks or to small-amplitude nonlinear streaks computed using direct numerical simulation (DNS) or the nonlinear parabolized stability equations (PSEs). We use the BREs to numerically compute high-amplitude streaks, a method which requires much lower computational effort than DNS and does not have the consistency and convergence problems of the PSE. It is found that the flow configuration changes substantially as the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-streamwise plane) becomes more important and strongly distorts the streamwise velocity profiles, which end up being quite different from those of the linear case. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks and compare them with available experimental results. (paper)

Nonlinear correction to the longitudinal structure function at small x

International Nuclear Information System (INIS)

Boroun, G.R.

2010-01-01

We computed the longitudinal proton structure function F L , using the nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation approach at small x. For the gluon distribution, the nonlinear effects are related to the longitudinal structure function. As the very small-x behavior of the gluon distribution is obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear shadowing term incorporated, we show that the strong rise that corresponds to the linear QCD evolution equations can be tamed by screening effects. Consequently, the obtained longitudinal structure function shows a tamed growth at small x. We computed the predictions for all details of the nonlinear longitudinal structure function in the kinematic range where it has been measured by the H1 Collaboration and made comparisons with the computation by Moch, Vermaseren and Vogt at the second order with input data from the MRST QCD fit. (orig.)

Model Equation for Acoustic Nonlinear Measurement of Dispersive Specimens at High Frequency

Science.gov (United States)

Zhang, Dong; Kushibiki, Junichi; Zou, Wei

2006-10-01

We present a theoretical model for acoustic nonlinearity measurement of dispersive specimens at high frequency. The nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation governs the nonlinear propagation in the SiO2/specimen/SiO2 multi-layer medium. The dispersion effect is considered in a special manner by introducing the frequency-dependant sound velocity in the KZK equation. Simple analytic solutions are derived by applying the superposition technique of Gaussian beams. The solutions are used to correct the diffraction and dispersion effects in the measurement of acoustic nonlinearity of cottonseed oil in the frequency range of 33-96 MHz. Regarding two different ultrasonic devices, the accuracies of the measurements are improved to ±2.0% and ±1.3% in comparison with ±9.8% and ±2.9% obtained from the previous plane wave model.

A solution to nonlinearity problems

International Nuclear Information System (INIS)

Neuffer, D.V.

1989-01-01

New methods of correcting dynamic nonlinearities resulting from the multipole content of a synchrotron or transport line are presented. In a simplest form, correction elements are places at the center (C) of the accelerator half-cells as well as near the focusing (F) and defocusing (D) quadrupoles. In a first approximation, the corrector strengths follow Simpson's Rule, forming an accurate quasi-local canceling approximation to the nonlinearity. The F, C, and D correctors may also be used to obtain precise control of the horizontal, coupled, and vertical motion. Correction by three or more orders of magnitude can be obtained, and simple solutions to a fundamental problem in beam transport have been obtained. 13 refs., 1 fig., 1 tab

Suppression of nonlinear frequency-sweeping of resonant interchange modes in a magnetic dipole with applied radio frequency fields

International Nuclear Information System (INIS)

Maslovsky, D.; Levitt, B.; Mauel, M. E.

2003-01-01

Interchange instabilities excited by energetic electrons trapped by a magnetic dipole nonlinearly saturate and exhibit complex, coherent spectral characteristics and frequency sweeping [H. P. Warren and M. E. Mauel, Phys. Plasmas 2, 4185 (1995)]. When monochromatic radio frequency (rf) fields are applied in the range of 100-1000 MHz, the saturation behavior of the interchange instability changes dramatically. For applied fields of sufficient intensity and pulse-length, coherent interchange fluctuations are suppressed and frequency sweeping is eliminated. When rf fields are switched off, coherent frequency sweeping reappears. Since low frequency interchange instabilities preserve the electron's first and second adiabatic invariants, these observations can be interpreted as resulting from nonlinear resonant wave-particle interactions described within a particle phase-space, (ψ,φ), comprised of the third adiabatic invariant and the azimuthal angle. Self-consistent numerical simulation is used to study (1) the nonlinear development of the instability, (2) the radial mode structure of the interchange instability, and (3) the suppression of frequency sweeping. When the applied rf heating is modeled as an 'rf collisionality', the simulation reproduces frequency sweeping suppression and suggests an explanation for the observations that is consistent with Berk and co-workers [H. L. Berk et al., Phys. Plasmas 6, 3102 (1999)

Linear and Non-Linear Control Techniques Applied to Actively Lubricated Journal Bearings

DEFF Research Database (Denmark)

Nicoletti, Rodrigo; Santos, Ilmar

2003-01-01

The main objectives of actively lubricated bearings are the simultaneous reduction of wear and vibration between rotating and stationary machinery parts. For reducing wear and dissipating vibration energy until certain limits, one can count with the conventional hydrodynamic lubrication. For furt......The main objectives of actively lubricated bearings are the simultaneous reduction of wear and vibration between rotating and stationary machinery parts. For reducing wear and dissipating vibration energy until certain limits, one can count with the conventional hydrodynamic lubrication....... For further reduction of shaft vibrations one can count with the active lubrication action, which is based on injecting pressurised oil into the bearing gap through orifices machined in the bearing sliding surface. The design and efficiency of some linear (PD, PI and PID) and non-linear controllers, applied...... vibration reduction of unbalance response of a rigid rotor, where the PD and the non-linear P controllers show better performance for the frequency range of study (0 to 80 Hz). The feasibility of eliminating rotor-bearing instabilities (phenomena of whirl) by using active lubrication is also investigated...

Self-interaction corrections applied to Mg-porphyrin, C{sub 60}, and pentacene molecules

Energy Technology Data Exchange (ETDEWEB)

Pederson, Mark R. [Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218 (United States); Baruah, Tunna; Basurto, Luis [Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968 (United States); Kao, Der-you [Department of Mechanical and Aerospace Engineering, George Washington University, Washington, DC 20052 (United States)

2016-04-28

We have applied a recently developed method to incorporate the self-interaction correction through Fermi orbitals to Mg-porphyrin, C{sub 60}, and pentacene molecules. The Fermi-Löwdin orbitals are localized and unitarily invariant to the Kohn-Sham orbitals from which they are constructed. The self-interaction-corrected energy is obtained variationally leading to an optimum set of Fermi-Löwdin orbitals (orthonormalized Fermi orbitals) that gives the minimum energy. A Fermi orbital, by definition, is dependent on a certain point which is referred to as the descriptor position. The degree to which the initial choice of descriptor positions influences the variational approach to the minimum and the complexity of the energy landscape as a function of Fermi-orbital descriptors is examined in detail for Mg-porphyrin. The applications presented here also demonstrate that the method can be applied to larger molecular systems containing a few hundred electrons. The atomization energy of the C{sub 60} molecule within the Fermi-Löwdin-orbital self-interaction-correction approach is significantly improved compared to local density approximation in the Perdew-Wang 92 functional and generalized gradient approximation of Perdew-Burke-Ernzerhof functionals. The eigenvalues of the highest occupied molecular orbitals show qualitative improvement.

Non-linear effects in electron cyclotron current drive applied for the stabilization of neoclassical tearing modes

NARCIS (Netherlands)

Ayten, B.; Westerhof, E.; ASDEX Upgrade team,

2014-01-01

Due to the smallness of the volumes associated with the flux surfaces around the O-point of a magnetic island, the electron cyclotron power density applied inside the island for the stabilization of neoclassical tearing modes (NTMs) can exceed the threshold for non-linear effects as derived

Three dimensional topography correction applied to magnetotelluric data from Sikkim Himalayas

Science.gov (United States)

Kumar, Sushil; Patro, Prasanta K.; Chaudhary, B. S.

2018-06-01

Magnetotelluric (MT) method is one of the powerful tools to investigate the deep crustal image of mountainous regions such as Himalayas. Topographic variations due to irregular surface terrain distort the resistivity curves and hence may not give accurate interpretation of magnetotelluric data. The two-dimensional (2-D) topographic effects in Transverse Magnetic (TM) mode is only galvanic whereas inductive in Transverse Electric (TE) mode, thus TM mode responses is much more important than TE mode responses in 2-D. In three-dimensional (3-D), the topography effect is both galvanic and inductive in each element of impedance tensor and hence the interpretation is complicated. In the present work, we investigate the effects of three-dimensional (3-D) topography for a hill model. This paper presents the impedance tensor correction algorithm to reduce the topographic effects in MT data. The distortion caused by surface topography effectively decreases by using homogeneous background resistivity in impedance correction method. In this study, we analyze the response of ramp, distance from topographic edges, conductive and resistive dykes. The new correction method is applied to the real data from Sikkim Himalayas, which brought out the true nature of the basement in this region.

What do we know about real exchange rate non-linearities?

DEFF Research Database (Denmark)

Kruse, Robinson; Frömmel, Michael; Menkhoff, Lukas

correctly and misspecified non-linear alternatives is analyzed by means of a Monte Carlo study. The chosen parametrization is obtained by real-life exchange rates. The test against ESTAR has low power against all alternatives whereas the proposed unit root test against a Markov Switching autoregressive......This research points to the serious problem of potentially misspecified alternative hypotheses when testing for unit roots in real exchange rates. We apply a popular unit root test against nonlinear ESTAR and develop a Markov Switching unit root test. The empirical power of these tests against...... model performs clearly better. An empirical application of these tests suggests that real exchange rates may indeed be explained by Markov-Switching dynamics....

Vector velocity volume flow estimation: Sources of error and corrections applied for arteriovenous fistulas

DEFF Research Database (Denmark)

Jensen, Jonas; Olesen, Jacob Bjerring; Stuart, Matthias Bo

2016-01-01

radius. The error sources were also studied in vivo under realistic clinical conditions, and the theoretical results were applied for correcting the volume flow errors. Twenty dialysis patients with arteriovenous fistulas were scanned to obtain vector flow maps of fistulas. When fitting an ellipsis......A method for vector velocity volume flow estimation is presented, along with an investigation of its sources of error and correction of actual volume flow measurements. Volume flow errors are quantified theoretically by numerical modeling, through flow phantom measurements, and studied in vivo...

A GENERALIZED NON-LINEAR METHOD FOR DISTORTION CORRECTION AND TOP-DOWN VIEW CONVERSION OF FISH EYE IMAGES

Directory of Open Access Journals (Sweden)

Vivek Singh Bawa

2017-06-01

Full Text Available Advanced driver assistance systems (ADAS have been developed to automate and modify vehicles for safety and better driving experience. Among all computer vision modules in ADAS, 360-degree surround view generation of immediate surroundings of the vehicle is very important, due to application in on-road traffic assistance, parking assistance etc. This paper presents a novel algorithm for fast and computationally efficient transformation of input fisheye images into required top down view. This paper also presents a generalized framework for generating top down view of images captured by cameras with fish-eye lenses mounted on vehicles, irrespective of pitch or tilt angle. The proposed approach comprises of two major steps, viz. correcting the fish-eye lens images to rectilinear images, and generating top-view perspective of the corrected images. The images captured by the fish-eye lens possess barrel distortion, for which a nonlinear and non-iterative method is used. Thereafter, homography is used to obtain top-down view of corrected images. This paper also targets to develop surroundings of the vehicle for wider distortion less field of view and camera perspective independent top down view, with minimum computation cost which is essential due to limited computation power on vehicles.

Applying nonlinear MODM model to supply chain management with quantity discount policy under complex fuzzy environment

Directory of Open Access Journals (Sweden)

Zhe Zhang

2014-06-01

Full Text Available Purpose: The aim of this paper is to deal with the supply chain management (SCM with quantity discount policy under the complex fuzzy environment, which is characterized as the bi-fuzzy variables. By taking into account the strategy and the process of decision making, a bi-fuzzy nonlinear multiple objective decision making (MODM model is presented to solve the proposed problem.Design/methodology/approach: The bi-fuzzy variables in the MODM model are transformed into the trapezoidal fuzzy variables by the DMs's degree of optimism ?1 and ?2, which are de-fuzzified by the expected value index subsequently. For solving the complex nonlinear model, a multi-objective adaptive particle swarm optimization algorithm (MO-APSO is designed as the solution method.Findings: The proposed model and algorithm are applied to a typical example of SCM problem to illustrate the effectiveness. Based on the sensitivity analysis of the results, the bi-fuzzy nonlinear MODM SCM model is proved to be sensitive to the possibility level ?1.Practical implications: The study focuses on the SCM under complex fuzzy environment in SCM, which has a great practical significance. Therefore, the bi-fuzzy MODM model and MO-APSO can be further applied in SCM problem with quantity discount policy.Originality/value: The bi-fuzzy variable is employed in the nonlinear MODM model of SCM to characterize the hybrid uncertain environment, and this work is original. In addition, the hybrid crisp approach is proposed to transferred to model to an equivalent crisp one by the DMs's degree of optimism and the expected value index. Since the MODM model consider the bi-fuzzy environment and quantity discount policy, so this paper has a great practical significance.

Neoclassical transport including collisional nonlinearity.

Science.gov (United States)

Candy, J; Belli, E A

2011-06-10

In the standard δf theory of neoclassical transport, the zeroth-order (Maxwellian) solution is obtained analytically via the solution of a nonlinear equation. The first-order correction δf is subsequently computed as the solution of a linear, inhomogeneous equation that includes the linearized Fokker-Planck collision operator. This equation admits analytic solutions only in extreme asymptotic limits (banana, plateau, Pfirsch-Schlüter), and so must be solved numerically for realistic plasma parameters. Recently, numerical codes have appeared which attempt to compute the total distribution f more accurately than in the standard ordering by retaining some nonlinear terms related to finite-orbit width, while simultaneously reusing some form of the linearized collision operator. In this work we show that higher-order corrections to the distribution function may be unphysical if collisional nonlinearities are ignored.

Method of moments as applied to arbitrarily shaped bounded nonlinear scatterers

Science.gov (United States)

Caorsi, Salvatore; Massa, Andrea; Pastorino, Matteo

1994-01-01

In this paper, we explore the possibility of applying the moment method to determine the electromagnetic field distributions inside three-dimensional bounded nonlinear dielectric objects of arbitrary shapes. The moment method has usually been employed to solve linear scattering problems. We start with an integral equation formulation, and derive a nonlinear system of algebraic equations that allows us to obtain an approximate solution for the harmonic vector components of the electric field. Preliminary results of some numerical simulations are reported. Dans cet article nous explorons la possibilité d'appliquer la méthode des moments pour déterminer la distribution du champ électromagnétique dans des objets tridimensionnels diélectriques, non-linéaires, limités et de formes arbitraires. La méthode des moments a été communément employée pour les problèmes de diffusion linéaire. Nous commençons par une formulation basée sur l'équation intégrale et nous dérivons un système non-linéaire d'équations algébriques qui nous permet d'obtenir une solution approximative pour les composantes harmoniques du vecteur du champ électrique. Les résultats préliminaires de quelques simulations numériques sont présentés.

Small-χ singlet structure functions from the nonlinear GLR equation

International Nuclear Information System (INIS)

Kim, V.T.; Ryskin, M.G.

1991-06-01

The effect of absorptive corrections in the nonlinear GLR evolution equation is considered. A simple method how to estimate the corrections numerically is described. In the case of the parametrization based on semihard hadron phenomenology developed earlier a visible difference between linear and nonlinear evolution is expected at HERA energies. (orig.)

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

Science.gov (United States)

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.

Linear and nonlinear stability analysis in BWRs applying a reduced order model

Energy Technology Data Exchange (ETDEWEB)

Olvera G, O. A.; Espinosa P, G.; Prieto G, A., E-mail: omar_olverag@hotmail.com [Universidad Autonoma Metropolitana, Unidad Iztapalapa, San Rafael Atlixco No. 186, Col. Vicentina, 09340 Ciudad de Mexico (Mexico)

2016-09-15

Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

Linear and nonlinear stability analysis in BWRs applying a reduced order model

International Nuclear Information System (INIS)

Olvera G, O. A.; Espinosa P, G.; Prieto G, A.

2016-09-01

Boiling Water Reactor (BWR) stability studies are generally conducted through nonlinear reduced order models (Rom) employing various techniques such as bifurcation analysis and time domain numerical integration. One of those models used for these studies is the March-Leuba Rom. Such model represents qualitatively the dynamic behavior of a BWR through a one-point reactor kinetics, a one node representation of the heat transfer process in fuel, and a two node representation of the channel Thermal hydraulics to account for the void reactivity feedback. Here, we study the effect of this higher order model on the overall stability of the BWR. The change in the stability boundaries is determined by evaluating the eigenvalues of the Jacobian matrix. The nonlinear model is also integrated numerically to show that in the nonlinear region, the system evolves to stable limit cycles when operating close to the stability boundary. We also applied a new technique based on the Empirical Mode Decomposition (Emd) to estimate a parameter linked with stability in a BWR. This instability parameter is not exactly the classical Decay Ratio (Dr), but it will be linked with it. The proposed method allows decomposing the analyzed signal in different levels or mono-component functions known as intrinsic mode functions (Imf). One or more of these different modes can be associated to the instability problem in BWRs. By tracking the instantaneous frequencies (calculated through Hilbert Huang Transform (HHT) and the autocorrelation function (Acf) of the Imf linked to instability. The estimation of the proposed parameter can be achieved. The current methodology was validated with simulated signals of the studied model. (Author)

Effects of image distortion correction on voxel-based morphometry

International Nuclear Information System (INIS)

Goto, Masami; Abe, Osamu; Kabasawa, Hiroyuki

2012-01-01

We aimed to show that correcting image distortion significantly affects brain volumetry using voxel-based morphometry (VBM) and to assess whether the processing of distortion correction reduces system dependency. We obtained contiguous sagittal T 1 -weighted images of the brain from 22 healthy participants using 1.5- and 3-tesla magnetic resonance (MR) scanners, preprocessed images using Statistical Parametric Mapping 5, and tested the relation between distortion correction and brain volume using VBM. Local brain volume significantly increased or decreased on corrected images compared with uncorrected images. In addition, the method used to correct image distortion for gradient nonlinearity produced fewer volumetric errors from MR system variation. This is the first VBM study to show more precise volumetry using VBM with corrected images. These results indicate that multi-scanner or multi-site imaging trials require correction for distortion induced by gradient nonlinearity. (author)

Nonlinear vibration behaviors of high-Tc superconducting bulks in an applied permanent magnetic array field

Science.gov (United States)

Li, Jipeng; Li, Haitao; Zheng, Jun; Zheng, Botian; Huang, Huan; Deng, Zigang

2017-06-01

The nonlinear vibration of high temperature superconducting (HTS) bulks in an applied permanent magnetic array (Halbach array) field, as a precondition for commercial application to HTS maglev train and HTS bearing, is systematically investigated. This article reports the actual vibration rules of HTS bulks from three aspects. First, we propose a new numerical model to simplify the calculation of levitation force. This model could provide precise simulations, especially the estimation of eigenfrequency. Second, an approximate analytic solution of the vibration of the HTS bulks is obtained by using the method of harmonic balance. Finally, to verify the results mentioned above, we measure the vertical vibration acceleration signals of an HTS maglev model, consisting of eight YBaCuO bulks, oscillating freely above a Halbach array with large displacement excitation. Higher order harmonic components, which indicate the nonlinear vibration phenomenon, are detected in the responses. All the three results are compared and agreed well with each other. This study combines the experimental and theoretical analyses and provides a deep understanding of the physical phenomenon of the nonlinear vibration and is meaningful for the vibration control of the relevant applications.

Nonlinear optics principles and applications

CERN Document Server

Rottwitt, Karsten

2014-01-01

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

On the correct implementation of Fermi-Dirac statistics and electron trapping in nonlinear electrostatic plane wave propagation in collisionless plasmas

Science.gov (United States)

Schamel, Hans; Eliasson, Bengt

2016-05-01

Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes, the holes become of cnoidal wave type and the electron density is shown to be described by a ϕ ( x ) 1 / 2 rather than a ϕ ( x ) expansion, where ϕ ( x ) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of ϕ ( x ) and the nonlinear dispersion relation, which describes their phase velocity.

Theory of plasmonic effects in nonlinear optics: the case of graphene

Science.gov (United States)

Rostami, Habib; Katsnelson, Mikhail I.; Polini, Marco; Mikhail I. Katsnelson Collaboration; Habib Rostami; Marco Polini Collaboration

The nonlinear optical properties of two-dimensional electronic systems are beginning to attract considerable interest both in the theoretical and experimental sectors. Recent experiments on the nonlinear optical properties of graphene reveal considerably strong third harmonic generation and four-wave mixing of this single-atomic-layer electronic system. We develop a large-N theory of electron-electron interaction corrections to multi-legged Feynman diagrams describing second- and third-order nonlinear response functions. Our theory is completely general and is useful to understand all second- and third-order nonlinear effects, including harmonic generation, wave mixing, and photon drag. We apply our theoretical framework to the case of graphene, by carrying out microscopic calculations of the second- and third-order nonlinear response functions of an interacting two-dimensional gas of massless Dirac fermions. We compare our results with recent measurements, where all-optical launching of graphene plasmons has been achieved. This work was supported by Fondazione Istituto Italiano di Tecnologia, the European Union's Horizon 2020 research and innovation programme under Grant agreement No. 696656 GrapheneCore, and the ERC Advanced Grant 338957 FEMTO/NANO (M.I.K.).

Nonlinear approaches in engineering applications applied mechanics, vibration control, and numerical analysis

CERN Document Server

Jazar, Reza

2015-01-01

This book focuses on the latest applications of nonlinear approaches in different disciplines of engineering. For each selected topic, detailed concept development, derivations, and relevant knowledge are provided for the convenience of the readers. The topics range from dynamic systems and control to optimal approaches in nonlinear dynamics. The volume includes invited chapters from world class experts in the field. The selected topics are of great interest in the fields of engineering and physics and this book is ideal for engineers and researchers working in a broad range of practical topics and approaches. This book also: ·         Explores the most up-to-date applications and underlying principles of nonlinear approaches to problems in engineering and physics, including sections on analytic nonlinearity and practical nonlinearity ·         Enlightens readers to the conceptual significance of nonlinear approaches with examples of applications in scientific and engineering problems from v...

Role of nonlinear dynamics and chaos in applied sciences

International Nuclear Information System (INIS)

Lawande, Quissan V.; Maiti, Nirupam

2000-02-01

Nonlinear dynamics manifests itself in a number of phenomena in both laboratory and day to day dealings. However, little attention was being paid to this dynamically rich field. With the advent of high speed computers with visual graphics, the field has proliferated over past few years. One of the most rewarding realization from nonlinear dynamics is the universally acclaimed field of chaos. Chaos has brought in order and has broken the disciplinary boundaries that existed until recently. With its universal phenomena, almost all disciplines following an evolutionary character can be treated on same footing. Chaotic dynamics has its grounding in the multidisciplinary field of synergetics founded by Professor Hermann Haken. In this report, we address some of the basics related to the field of chaos. We have discussed simple mechanisms for generating chaotic trajectories, ways and means of characterizing such systems and the manifestation of their signatures in the evolutions. We have mentioned the links of this field with other existing theories. We have outlined the topics on bifurcation and stability of dynamical systems. Information theoretic aspects and notions on fractal geometry are reviewed in the light of dynamical characterization of chaotic systems. Application oriented views of this novel dynamical phenomena are discussed through examples on simple nonlinear electronic circuits and a BWR reactor. Some ideas relating to control and synchronization in chaotic systems also addressed. In conclusion, we have explored the possibilities of exploiting nonlinear dynamics and chaos in the context of multidisciplinary character of BARC. (author)

Nonlinearity Mechanism and Correction of Sapphire Fiber Temperature Sensor on Blackbody Cavity

Directory of Open Access Journals (Sweden)

Tiejun Cao

2014-06-01

Full Text Available Based on the principle of blackbody radiation, sapphire optic fiber temperature sensor has been more widely used in recent years, and its temperature range is between 800 ~ 2000 oC, and the response time is in 10-2 magnitude, and transient temperature measurement can be high precision in harsh environments. Nonlinear constraints on sapphire fiber temperature sensor affect the accuracy and stability of the sensor. In order to solve the nonlinear problems which exist in the measurement, at first, the sapphire fiber optic temperature sensor temperature measurement principle and nonlinear generation mechanism are studied; secondly piecewise linear interpolation and spline interpolation linearization algorithm is designed with combining the nonlinear characteristics of sapphire optical fiber temperature sensor, and the program is designed on its linear and associated signal processing. Experimental results show that a good linearization of sapphire fiber optic temperature sensor can been achieved in this method.

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-03-31

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

Applied nonlinear optics in the journal 'Quantum Electronics'

International Nuclear Information System (INIS)

Grechin, Sergei G; Dmitriev, Valentin G; Chirkin, Anatolii S

2011-01-01

A brief historical review of the experimental and theoretical works on nonlinear optical frequency conversion (generation of harmonics, up- and down-conversion, parametric oscillation), which have been published in the journal 'Quantum Electronics' for the last 40 years, is presented.

On applying safety archetypes to the Fukushima accident to identify nonlinear influencing factors

Energy Technology Data Exchange (ETDEWEB)

Sousa, A.L., E-mail: alsousa@cnen.gov.br [Comissao Nacional de Energia Nuclear (CNEN), Rio de Janeiro, RJ (Brazil); Ribeiro, A.C.O., E-mail: antonio.ribeiro@bayer.com [Bayer Crop Science Brasil S.A., Belford Roxo, RJ (Brazil); Duarte, J.P., E-mail: julianapduarte@poli.ufrj.br [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Escola Politecnica. Departamento de Engenharia Nuclear; Frutuoso e Melo, P.F., E-mail: frutuoso@nuclear.ufrj.br [Coordenacao dos Programas de Pos-Graduacao em Engenharia (COOPE/UFRJ), RJ (Brazil). Programa de Engenharia Nuclear

2013-07-01

Nuclear power plants are typically characterized as high reliable organizations. In other words, they are organizations defined as relatively error free over a long period of time. Another relevant characteristic of the nuclear industry is that safety efforts are credited to design. However, major accidents, like the Fukushima accident, have shown that new tools are needed to identify latent deficiencies and help improve their safety level. Safety archetypes proposed elsewhere (e. g., safety issues stalled in the face of technological advances and eroding safety) consonant with International Atomic Energy Agency (IAEA) efforts are used to examine different aspects of accidents in a systemic perspective of the interaction between individuals, technology and organizational factors. Safety archetypes can help consider nonlinear interactions. Effects are rarely proportional to causes and what happens locally in a system (near the current operating point) often does not apply to distant regions (other system states), so that one has to consider the so-called nonlinear interactions. This is the case, for instance, with human probability failure estimates and safety level identification. In this paper, we discuss the Fukushima accident in order to show how archetypes can highlight nonlinear interactions of factors that influenced it and how to maintain safety levels in order to prevent other accidents. The initial evaluation of the set of archetypes suggested in the literature showed that at least four of them are applicable to the Fukushima accident, as is inferred from official reports on the accident. These are: complacency (that is, the effects of complacency on safety), decreased safety awareness, fixing on symptoms and not the real causes and eroding safety. (author)

On applying safety archetypes to the Fukushima accident to identify nonlinear influencing factors

International Nuclear Information System (INIS)

Sousa, A.L.; Ribeiro, A.C.O.; Duarte, J.P.; Frutuoso e Melo, P.F.

2013-01-01

Nuclear power plants are typically characterized as high reliable organizations. In other words, they are organizations defined as relatively error free over a long period of time. Another relevant characteristic of the nuclear industry is that safety efforts are credited to design. However, major accidents, like the Fukushima accident, have shown that new tools are needed to identify latent deficiencies and help improve their safety level. Safety archetypes proposed elsewhere (e. g., safety issues stalled in the face of technological advances and eroding safety) consonant with International Atomic Energy Agency (IAEA) efforts are used to examine different aspects of accidents in a systemic perspective of the interaction between individuals, technology and organizational factors. Safety archetypes can help consider nonlinear interactions. Effects are rarely proportional to causes and what happens locally in a system (near the current operating point) often does not apply to distant regions (other system states), so that one has to consider the so-called nonlinear interactions. This is the case, for instance, with human probability failure estimates and safety level identification. In this paper, we discuss the Fukushima accident in order to show how archetypes can highlight nonlinear interactions of factors that influenced it and how to maintain safety levels in order to prevent other accidents. The initial evaluation of the set of archetypes suggested in the literature showed that at least four of them are applicable to the Fukushima accident, as is inferred from official reports on the accident. These are: complacency (that is, the effects of complacency on safety), decreased safety awareness, fixing on symptoms and not the real causes and eroding safety. (author)

Nonlinear dynamics and complexity

CERN Document Server

Luo, Albert; Fu, Xilin

2014-01-01

This important collection presents recent advances in nonlinear dynamics including analytical solutions, chaos in Hamiltonian systems, time-delay, uncertainty, and bio-network dynamics. Nonlinear Dynamics and Complexity equips readers to appreciate this increasingly main-stream approach to understanding complex phenomena in nonlinear systems as they are examined in a broad array of disciplines. The book facilitates a better understanding of the mechanisms and phenomena in nonlinear dynamics and develops the corresponding mathematical theory to apply nonlinear design to practical engineering.

Renormalization group and instantons in stochastic nonlinear dynamics, from self-organized criticality to thermonuclear reactors

International Nuclear Information System (INIS)

Volchenkov, D.

2009-01-01

Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magnetohydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications. (author)

Renormalization group and instantons in stochastic nonlinear dynamics, from self-organized criticality to thermonuclear reactors

Energy Technology Data Exchange (ETDEWEB)

Volchenkov, D. [Bielefeld Univ., Center of Excellence Cognitive Interaction Technology (CITEC) (Germany)

2009-03-15

Stochastic counterparts of nonlinear dynamics are studied by means of nonperturbative functional methods developed in the framework of quantum field theory (QFT). In particular, we discuss fully developed turbulence, including leading corrections on possible compressibility of fluids, transport through porous media, theory of waterspouts and tsunami waves, stochastic magnetohydrodynamics, turbulent transport in crossed fields, self-organized criticality, and dynamics of accelerated wrinkled flame fronts advancing in a wide canal. This report would be of interest to the broad auditorium of physicists and applied mathematicians, with a background in nonperturbative QFT methods or nonlinear dynamical systems, having an interest in both methodological developments and interdisciplinary applications. (author)

A Second-Order Maximum Principle Preserving Lagrange Finite Element Technique for Nonlinear Scalar Conservation Equations

KAUST Repository

Guermond, Jean-Luc; Nazarov, Murtazo; Popov, Bojan; Yang, Yong

2014-01-01

© 2014 Society for Industrial and Applied Mathematics. This paper proposes an explicit, (at least) second-order, maximum principle satisfying, Lagrange finite element method for solving nonlinear scalar conservation equations. The technique is based on a new viscous bilinear form introduced in Guermond and Nazarov [Comput. Methods Appl. Mech. Engrg., 272 (2014), pp. 198-213], a high-order entropy viscosity method, and the Boris-Book-Zalesak flux correction technique. The algorithm works for arbitrary meshes in any space dimension and for all Lipschitz fluxes. The formal second-order accuracy of the method and its convergence properties are tested on a series of linear and nonlinear benchmark problems.

Noise level estimation in weakly nonlinear slowly time-varying systems

International Nuclear Information System (INIS)

Aerts, J R M; Dirckx, J J J; Lataire, J; Pintelon, R

2008-01-01

Recently, a method using multisine excitation was proposed for estimating the frequency response, the nonlinear distortions and the disturbing noise of weakly nonlinear time-invariant systems. This method has been demonstrated on the measurement of nonlinear distortions in the vibration of acoustically driven systems such as a latex membrane, which is a good example of a time-invariant system [1]. However, not all systems are perfectly time invariant, e.g. biomechanical systems. This time variation can be misinterpreted as an elevated noise floor, and the classical noise estimation method gives a wrong result. Two improved methods to retrieve the correct noise information from the measurements are presented. Both of them make use of multisine excitations. First, it is demonstrated that the improved methods give the same result as the classical noise estimation method when applied to a time-invariant system (high-quality microphone membrane). Next, it is demonstrated that the new methods clearly give an improved estimate of the noise level on time-varying systems. As an application example results for the vibration response of an eardrum are shown

Nonlinear Response of Strong Nonlinear System Arisen in Polymer Cushion

Directory of Open Access Journals (Sweden)

Jun Wang

2013-01-01

Full Text Available A dynamic model is proposed for a polymer foam-based nonlinear cushioning system. An accurate analytical solution for the nonlinear free vibration of the system is derived by applying He's variational iteration method, and conditions for resonance are obtained, which should be avoided in the cushioning design.

Pescara benchmarks: nonlinear identification

Science.gov (United States)

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

2011-07-01

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

Pescara benchmarks: nonlinear identification

International Nuclear Information System (INIS)

Gandino, E; Garibaldi, L; Marchesiello, S

2011-01-01

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

Nonlinear dynamics and astrophysics

International Nuclear Information System (INIS)

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

2000-01-01

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

Effects of applied electromagnetic fields on the linear and nonlinear optical properties in an inverse parabolic quantum well

International Nuclear Information System (INIS)

Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sökmen, I.

2012-01-01

In this present work, we have investigated theoretically the effects of applied electric and magnetic fields on the linear and nonlinear optical properties in a GaAs/Al x Ga 1−x As inverse parabolic quantum well for different Al concentrations at the well center. The Al concentration at the barriers was always x max =0.3. The energy levels and wave functions are calculated within the effective mass approximation and the envelope function approach. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The linear, third-order nonlinear and total absorption and refractive index changes depending on the Al concentration at the well center are investigated as a function of the incident photon energy for the different values of the applied electric and magnetic fields. The results show that the applied electric and magnetic fields have a great effect on these optical quantities. - Highlights: ► The x c concentration has a great effect on the optical characteristics of these structures. ► The EM fields have a great effect on the optical properties of these structures. ► The total absorption coefficients increased as the electric and magnetic field increases. ► The RICs reduced as the electric and magnetic field increases.

Equation-Method for correcting clipping errors in OFDM signals.

Science.gov (United States)

Bibi, Nargis; Kleerekoper, Anthony; Muhammad, Nazeer; Cheetham, Barry

2016-01-01

Orthogonal frequency division multiplexing (OFDM) is the digital modulation technique used by 4G and many other wireless communication systems. OFDM signals have significant amplitude fluctuations resulting in high peak to average power ratios which can make an OFDM transmitter susceptible to non-linear distortion produced by its high power amplifiers (HPA). A simple and popular solution to this problem is to clip the peaks before an OFDM signal is applied to the HPA but this causes in-band distortion and introduces bit-errors at the receiver. In this paper we discuss a novel technique, which we call the Equation-Method, for correcting these errors. The Equation-Method uses the Fast Fourier Transform to create a set of simultaneous equations which, when solved, return the amplitudes of the peaks before they were clipped. We show analytically and through simulations that this method can, correct all clipping errors over a wide range of clipping thresholds. We show that numerical instability can be avoided and new techniques are needed to enable the receiver to differentiate between correctly and incorrectly received frequency-domain constellation symbols.

A Photonic Basis for Deriving Nonlinear Optical Response

Science.gov (United States)

Andrews, David L.; Bradshaw, David S.

2009-01-01

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

Interaction of Lyapunov vectors in the formulation of the nonlinear extension of the Kalman filter.

Science.gov (United States)

Palatella, Luigi; Trevisan, Anna

2015-04-01

When applied to strongly nonlinear chaotic dynamics the extended Kalman filter (EKF) is prone to divergence due to the difficulty of correctly forecasting the forecast error probability density function. In operational forecasting applications ensemble Kalman filters circumvent this problem with empirical procedures such as covariance inflation. This paper presents an extension of the EKF that includes nonlinear terms in the evolution of the forecast error estimate. This is achieved starting from a particular square-root implementation of the EKF with assimilation confined in the unstable subspace (EKF-AUS), that is, the span of the Lyapunov vectors with non-negative exponents. When the error evolution is nonlinear, the space where it is confined is no more restricted to the unstable and neutral subspace causing filter divergence. The algorithm presented here, denominated EKF-AUS-NL, includes the nonlinear terms in the error dynamics: These result from the nonlinear interaction among the leading Lyapunov vectors and account for all directions where the error growth may take place. Numerical results show that with the nonlinear terms included, filter divergence can be avoided. We test the algorithm on the Lorenz96 model, showing very promising results.

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

Science.gov (United States)

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Model of anisotropic nonlinearity in self-defocusing photorefractive media.

Science.gov (United States)

Barsi, C; Fleischer, J W

2015-09-21

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

Temporal Gain Correction for X-Ray Calorimeter Spectrometers

Science.gov (United States)

Porter, F. S.; Chiao, M. P.; Eckart, M. E.; Fujimoto, R.; Ishisaki, Y.; Kelley, R. L.; Kilbourne, C. A.; Leutenegger, M. A.; McCammon, D.; Mitsuda, K.

2016-01-01

Calorimetric X-ray detectors are very sensitive to their environment. The boundary conditions can have a profound effect on the gain including heat sink temperature, the local radiation temperature, bias, and the temperature of the readout electronics. Any variation in the boundary conditions can cause temporal variations in the gain of the detector and compromise both the energy scale and the resolving power of the spectrometer. Most production X-ray calorimeter spectrometers, both on the ground and in space, have some means of tracking the gain as a function of time, often using a calibration spectral line. For small gain changes, a linear stretch correction is often sufficient. However, the detectors are intrinsically non-linear and often the event analysis, i.e., shaping, optimal filters etc., add additional non-linearity. Thus for large gain variations or when the best possible precision is required, a linear stretch correction is not sufficient. Here, we discuss a new correction technique based on non-linear interpolation of the energy-scale functions. Using Astro-HSXS calibration data, we demonstrate that the correction can recover the X-ray energy to better than 1 part in 104 over the entire spectral band to above 12 keV even for large-scale gain variations. This method will be used to correct any temporal drift of the on-orbit per-pixel gain using on-board calibration sources for the SXS instrument on the Astro-H observatory.

Nonlinear Model-Based Predictive Control applied to Large Scale Cryogenic Facilities

CERN Document Server

Blanco Vinuela, Enrique; de Prada Moraga, Cesar

2001-01-01

The thesis addresses the study, analysis, development, and finally the real implementation of an advanced control system for the 1.8 K Cooling Loop of the LHC (Large Hadron Collider) accelerator. The LHC is the next accelerator being built at CERN (European Center for Nuclear Research), it will use superconducting magnets operating below a temperature of 1.9 K along a circumference of 27 kilometers. The temperature of these magnets is a control parameter with strict operating constraints. The first control implementations applied a procedure that included linear identification, modelling and regulation using a linear predictive controller. It did improve largely the overall performance of the plant with respect to a classical PID regulator, but the nature of the cryogenic processes pointed out the need of a more adequate technique, such as a nonlinear methodology. This thesis is a first step to develop a global regulation strategy for the overall control of the LHC cells when they will operate simultaneously....

Performance assessment of a non-linear eddy-viscosity turbulence model applied to the anisotropic wake flow of a low-pressure turbine blade

International Nuclear Information System (INIS)

Vlahostergios, Z.; Sideridis, A.; Yakinthos, K.; Goulas, A.

2012-01-01

Highlights: ► We model the wake flow produced by a LPT blade using a non-linear turbulence model. ► We use two interpolation schemes for the convection terms with different accuracy. ► We investigate the effect of each term of the non-linear constitutive expression. ► The results are compared with available experimental measurements. ► The model predicts with a good accuracy the velocity and stress distributions. - Abstract: The wake flow produced by a low-pressure turbine blade is modeled using a non-linear eddy-viscosity turbulence model. The theoretical benefit of using a non-linear eddy-viscosity model is strongly related to the capability of resolving highly anisotropic flows in contrast to the linear turbulence models, which are unable to correctly predict anisotropy. The main aim of the present work is to practically assess the performance of the model, by examining its ability to capture the anisotropic behavior of the wake-flow, mainly focusing on the measured velocity and Reynolds-stress distributions and to provide accurate results for the turbulent kinetic energy balance terms. Additionally, the contribution of each term of its non-linear constitutive expression for the Reynolds stresses is also investigated, in order to examine their direct effect on the modeling of the wake flow. The assessment is based on the experimental measurements that have been carried-out by the same group in Thessaloniki, Sideridis et al. (2011). The computational results show that the non-linear eddy viscosity model is capable to predict, with a good accuracy, all the flow and turbulence parameters while it is easy to program it in a computer code thus meeting the expectations of its originators.

Nonlinear acceleration of transport criticality problems

International Nuclear Information System (INIS)

Park, H.; Knoll, D.A.; Newman, C.K.

2011-01-01

We present a nonlinear acceleration algorithm for the transport criticality problem. The algorithm combines the well-known nonlinear diffusion acceleration (NDA) with a recently developed, Newton-based, nonlinear criticality acceleration (NCA) algorithm. The algorithm first employs the NDA to reduce the system to scalar flux, then the NCA is applied to the resulting drift-diffusion system. We apply a nonlinear elimination technique to eliminate the eigenvalue from the Jacobian matrix. Numerical results show that the algorithm reduces the CPU time a factor of 400 in a very diffusive system, and a factor of 5 in a non-diffusive system. (author)

Correction of Misclassifications Using a Proximity-Based Estimation Method

Directory of Open Access Journals (Sweden)

Shmulevich Ilya

2004-01-01

Full Text Available An estimation method for correcting misclassifications in signal and image processing is presented. The method is based on the use of context-based (temporal or spatial information in a sliding-window fashion. The classes can be purely nominal, that is, an ordering of the classes is not required. The method employs nonlinear operations based on class proximities defined by a proximity matrix. Two case studies are presented. In the first, the proposed method is applied to one-dimensional signals for processing data that are obtained by a musical key-finding algorithm. In the second, the estimation method is applied to two-dimensional signals for correction of misclassifications in images. In the first case study, the proximity matrix employed by the estimation method follows directly from music perception studies, whereas in the second case study, the optimal proximity matrix is obtained with genetic algorithms as the learning rule in a training-based optimization framework. Simulation results are presented in both case studies and the degree of improvement in classification accuracy that is obtained by the proposed method is assessed statistically using Kappa analysis.

Applying volumetric weather radar data for rainfall runoff modeling: The importance of error correction.

Science.gov (United States)

Hazenberg, P.; Leijnse, H.; Uijlenhoet, R.; Delobbe, L.; Weerts, A.; Reggiani, P.

2009-04-01

In the current study half a year of volumetric radar data for the period October 1, 2002 until March 31, 2003 is being analyzed which was sampled at 5 minutes intervals by C-band Doppler radar situated at an elevation of 600 m in the southern Ardennes region, Belgium. During this winter half year most of the rainfall has a stratiform character. Though radar and raingauge will never sample the same amount of rainfall due to differences in sampling strategies, for these stratiform situations differences between both measuring devices become even larger due to the occurrence of a bright band (the point where ice particles start to melt intensifying the radar reflectivity measurement). For these circumstances the radar overestimates the amount of precipitation and because in the Ardennes bright bands occur within 1000 meter from the surface, it's detrimental effects on the performance of the radar can already be observed at relatively close range (e.g. within 50 km). Although the radar is situated at one of the highest points in the region, very close to the radar clutter is a serious problem. As a result both nearby and farther away, using uncorrected radar results in serious errors when estimating the amount of precipitation. This study shows the effect of carefully correcting for these radar errors using volumetric radar data, taking into account the vertical reflectivity profile of the atmosphere, the effects of attenuation and trying to limit the amount of clutter. After applying these correction algorithms, the overall differences between radar and raingauge are much smaller which emphasizes the importance of carefully correcting radar rainfall measurements. The next step is to assess the effect of using uncorrected and corrected radar measurements on rainfall-runoff modeling. The 1597 km2 Ourthe catchment lies within 60 km of the radar. Using a lumped hydrological model serious improvement in simulating observed discharges is found when using corrected radar

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

Science.gov (United States)

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

Saturation at Low X and Nonlinear Evolution

International Nuclear Information System (INIS)

Stasto, A.M.

2002-01-01

In this talk the results of the analytical and numerical analysis of the nonlinear Balitsky-Kovchegov equation are presented. The characteristic BFKL diffusion into infrared regime is suppressed by the generation of the saturation scale Q s . We identify the scaling and linear regimes for the solution. We also study the impact of subleading corrections onto the nonlinear evolution. (author)

Enhanced nonlinear iterative techniques applied to a nonequilibrium plasma flow

International Nuclear Information System (INIS)

Knoll, D.A.

1998-01-01

The authors study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. They use Newton's method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. They investigate both a modified and a matrix-free Newton-Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, mesh sequencing, and a pseudotransient continuation technique is used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with incomplete lower-upper (ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a mesh sequencing implementation provides significant CPU savings for fine grid calculations. Performance comparisons of modified Newton-Krylov and matrix-free Newton-Krylov algorithms will be presented

A variable age of onset segregation model for linkage analysis, with correction for ascertainment, applied to glioma

DEFF Research Database (Denmark)

Sun, Xiangqing; Vengoechea, Jaime; Elston, Robert

2012-01-01

We propose a 2-step model-based approach, with correction for ascertainment, to linkage analysis of a binary trait with variable age of onset and apply it to a set of multiplex pedigrees segregating for adult glioma....

Characterization, prediction, and correction of geometric distortion in 3 T MR images

International Nuclear Information System (INIS)

Baldwin, Lesley N.; Wachowicz, Keith; Thomas, Steven D.; Rivest, Ryan; Gino Fallone, B.

2007-01-01

The work presented herein describes our methods and results for predicting, measuring and correcting geometric distortions in a 3 T clinical magnetic resonance (MR) scanner for the purpose of image guidance in radiation treatment planning. Geometric inaccuracies due to both inhomogeneities in the background field and nonlinearities in the applied gradients were easily visualized on the MR images of a regularly structured three-dimensional (3D) grid phantom. From a computed tomography scan, the locations of just under 10 000 control points within the phantom were accurately determined in three dimensions using a MATLAB-based computer program. MR distortion was then determined by measuring the corresponding locations of the control points when the phantom was imaged using the MR scanner. Using a reversed gradient method, distortions due to gradient nonlinearities were separated from distortions due to inhomogeneities in the background B 0 field. Because the various sources of machine-related distortions can be individually characterized, distortions present in other imaging sequences (for which 3D distortion cannot accurately be measured using phantom methods) can be predicted negating the need for individual distortion calculation for a variety of other imaging sequences. Distortions were found to be primarily caused by gradient nonlinearities and maximum image distortions were reported to be less than those previously found by other researchers at 1.5 T. Finally, the image slices were corrected for distortion in order to provide geometrically accurate phantom images

SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2015-01-01

minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two

The relationship between crude oil spot and futures prices: Cointegration, linear and nonlinear causality

International Nuclear Information System (INIS)

Bekiros, Stelios D.; Diks, Cees G.H.

2008-01-01

The present study investigates the linear and nonlinear causal linkages between daily spot and futures prices for maturities of one, two, three and four months of West Texas Intermediate (WTI) crude oil. The data cover two periods October 1991-October 1999 and November 1999-October 2007, with the latter being significantly more turbulent. Apart from the conventional linear Granger test we apply a new nonparametric test for nonlinear causality by Diks and Panchenko after controlling for cointegration. In addition to the traditional pairwise analysis, we test for causality while correcting for the effects of the other variables. To check if any of the observed causality is strictly nonlinear in nature, we also examine the nonlinear causal relationships of VECM filtered residuals. Finally, we investigate the hypothesis of nonlinear non-causality after controlling for conditional heteroskedasticity in the data using a GARCH-BEKK model. Whilst the linear causal relationships disappear after VECM cointegration filtering, nonlinear causal linkages in some cases persist even after GARCH filtering in both periods. This indicates that spot and futures returns may exhibit asymmetric GARCH effects and/or statistically significant higher order conditional moments. Moreover, the results imply that if nonlinear effects are accounted for, neither market leads or lags the other consistently, videlicet the pattern of leads and lags changes over time. (author)

Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction

Czech Academy of Sciences Publication Activity Database

Převorovský, Zdeněk

..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics

Calibration of the Nonlinear Accelerator Model at the Diamond Storage Ring

CERN Document Server

Bartolini, Riccardo; Rowland, James; Martin, Ian; Schmidt, Frank

2010-01-01

The correct implementation of the nonlinear ring model is crucial to achieve the top performance of a synchrotron light source. Several dynamics quantities can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these methods are based on the analysis of turn-by-turn data of excited betatron oscillations. We present the experimental results of the campaign of measurements carried out at the Diamond. A combination of Frequency Map Analysis (FMA) and detuning with momentum measurements has allowed a precise calibration of the nonlinear model capable of reproducing the nonlinear beam dynamics in the storage ring

Calibration of the nonlinear ring model at the Diamond Light Source

Directory of Open Access Journals (Sweden)

R. Bartolini

2011-05-01

Full Text Available Nonlinear beam dynamics plays a crucial role in defining the performance of a storage ring. The beam lifetime, the injection efficiency, and the dynamic and momentum apertures available to the beam are optimized during the design phase by a proper optimization of the linear lattice and of the distribution of sextupole families. The correct implementation of the design model, especially the nonlinear part, is a nontrivial accelerator physics task. Several parameters of the nonlinear dynamics can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these parameters are extracted from the analysis of turn-by-turn data after the excitation of betatron oscillations of the particles in the ring. We present the experimental results of the campaign of measurements carried out at the Diamond storage ring to characterize the nonlinear beam dynamics. A combination of frequency map analysis with the detuning with momentum measurements has allowed for a precise calibration of the nonlinear model that can accurately reproduce the nonlinear beam dynamics in Diamond.

Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders

KAUST Repository

El Beltagy, Mohamed

2016-01-01

In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.

Solution of stochastic nonlinear PDEs using Wiener-Hermite expansion of high orders

KAUST Repository

El Beltagy, Mohamed

2016-01-06

In this work, the Wiener-Hermite Expansion (WHE) is used to solve stochastic nonlinear PDEs excited with noise. The generation of the equivalent set of deterministic integro-differential equations is automated and hence allows for high order terms of WHE. The automation difficulties are discussed, solved and implemented to output the final system to be solved. A numerical Pikard-like algorithm is suggested to solve the resulting deterministic system. The automated WHE is applied to the 1D diffusion equation and to the heat equation. The results are compared with previous solutions obtained with WHEP (WHE with perturbation) technique. The solution obtained using the suggested WHE technique is shown to be the limit of the WHEP solutions with infinite number of corrections. The automation is extended easily to account for white-noise of higher dimension and for general nonlinear PDEs.

On the non-linear scale of cosmological perturbation theory

Energy Technology Data Exchange (ETDEWEB)

Blas, Diego [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Garny, Mathias; Konstandin, Thomas [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2013-04-15

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

On the non-linear scale of cosmological perturbation theory

International Nuclear Information System (INIS)

Blas, Diego; Garny, Mathias; Konstandin, Thomas

2013-04-01

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

On the non-linear scale of cosmological perturbation theory

CERN Document Server

Blas, Diego; Konstandin, Thomas

2013-01-01

We discuss the convergence of cosmological perturbation theory. We prove that the polynomial enhancement of the non-linear corrections expected from the effects of soft modes is absent in equal-time correlators like the power or bispectrum. We first show this at leading order by resumming the most important corrections of soft modes to an arbitrary skeleton of hard fluctuations. We derive the same result in the eikonal approximation, which also allows us to show the absence of enhancement at any order. We complement the proof by an explicit calculation of the power spectrum at two-loop order, and by further numerical checks at higher orders. Using these insights, we argue that the modification of the power spectrum from soft modes corresponds at most to logarithmic corrections. Finally, we discuss the asymptotic behavior in the large and small momentum regimes and identify the expansion parameter pertinent to non-linear corrections.

Applying a pelvic corrective force induces forced use of the paretic leg and improves paretic leg EMG activities of individuals post-stroke during treadmill walking.

Science.gov (United States)

Hsu, Chao-Jung; Kim, Janis; Tang, Rongnian; Roth, Elliot J; Rymer, William Z; Wu, Ming

2017-10-01

To determine whether applying a mediolateral corrective force to the pelvis during treadmill walking would enhance muscle activity of the paretic leg and improve gait symmetry in individuals with post-stroke hemiparesis. Fifteen subjects with post-stroke hemiparesis participated in this study. A customized cable-driven robotic system based over a treadmill generated a mediolateral corrective force to the pelvis toward the paretic side during early stance phase. Three different amounts of corrective force were applied. Electromyographic (EMG) activity of the paretic leg, spatiotemporal gait parameters and pelvis lateral displacement were collected. Significant increases in integrated EMG of hip abductor, medial hamstrings, soleus, rectus femoris, vastus medialis and tibialis anterior were observed when pelvic corrective force was applied, with pelvic corrective force at 9% of body weight inducing greater muscle activity than 3% or 6% of body weight. Pelvis lateral displacement was more symmetric with pelvic corrective force at 9% of body weight. Applying a mediolateral pelvic corrective force toward the paretic side may enhance muscle activity of the paretic leg and improve pelvis displacement symmetry in individuals post-stroke. Forceful weight shift to the paretic side could potentially force additional use of the paretic leg and improve the walking pattern. Copyright © 2017 International Federation of Clinical Neurophysiology. Published by Elsevier B.V. All rights reserved.

Statistical approach of weakly nonlinear ablative Rayleigh-Taylor instability

International Nuclear Information System (INIS)

Garnier, J.; Masse, L.

2005-01-01

A weakly nonlinear model is proposed for the Rayleigh-Taylor instability in presence of ablation and thermal transport. The nonlinear effects for a single-mode disturbance are computed, included the nonlinear correction to the exponential growth of the fundamental modulation. Mode coupling in the spectrum of a multimode disturbance is thoroughly analyzed by a statistical approach. The exponential growth of the linear regime is shown to be reduced by the nonlinear mode coupling. The saturation amplitude is around 0.1λ for long wavelengths, but higher for short instable wavelengths in the ablative regime

Linear versus Nonlinear Filtering with Scale-Selective Corrections for Balanced Dynamics in a Simple Atmospheric Model

KAUST Repository

Subramanian, Aneesh C.

2012-11-01

This paper investigates the role of the linear analysis step of the ensemble Kalman filters (EnKF) in disrupting the balanced dynamics in a simple atmospheric model and compares it to a fully nonlinear particle-based filter (PF). The filters have a very similar forecast step but the analysis step of the PF solves the full Bayesian filtering problem while the EnKF analysis only applies to Gaussian distributions. The EnKF is compared to two flavors of the particle filter with different sampling strategies, the sequential importance resampling filter (SIRF) and the sequential kernel resampling filter (SKRF). The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode. It can also be configured either to evolve on a so-called slow manifold, where the fast motion is suppressed, or such that the fast-varying variables are diagnosed from the slow-varying variables as slaved modes. Identical twin experiments show that EnKF and PF capture the variables on the slow manifold well as the dynamics is very stable. PFs, especially the SKRF, capture slaved modes better than the EnKF, implying that a full Bayesian analysis estimates the nonlinear model variables better. The PFs perform significantly better in the fully coupled nonlinear model where fast and slow variables modulate each other. This suggests that the analysis step in the PFs maintains the balance in both variables much better than the EnKF. It is also shown that increasing the ensemble size generally improves the performance of the PFs but has less impact on the EnKF after a sufficient number of members have been used.

Linear versus Nonlinear Filtering with Scale-Selective Corrections for Balanced Dynamics in a Simple Atmospheric Model

KAUST Repository

Subramanian, Aneesh C.; Hoteit, Ibrahim; Cornuelle, Bruce; Miller, Arthur J.; Song, Hajoon

2012-01-01

This paper investigates the role of the linear analysis step of the ensemble Kalman filters (EnKF) in disrupting the balanced dynamics in a simple atmospheric model and compares it to a fully nonlinear particle-based filter (PF). The filters have a very similar forecast step but the analysis step of the PF solves the full Bayesian filtering problem while the EnKF analysis only applies to Gaussian distributions. The EnKF is compared to two flavors of the particle filter with different sampling strategies, the sequential importance resampling filter (SIRF) and the sequential kernel resampling filter (SKRF). The model admits a chaotic vortical mode coupled to a comparatively fast gravity wave mode. It can also be configured either to evolve on a so-called slow manifold, where the fast motion is suppressed, or such that the fast-varying variables are diagnosed from the slow-varying variables as slaved modes. Identical twin experiments show that EnKF and PF capture the variables on the slow manifold well as the dynamics is very stable. PFs, especially the SKRF, capture slaved modes better than the EnKF, implying that a full Bayesian analysis estimates the nonlinear model variables better. The PFs perform significantly better in the fully coupled nonlinear model where fast and slow variables modulate each other. This suggests that the analysis step in the PFs maintains the balance in both variables much better than the EnKF. It is also shown that increasing the ensemble size generally improves the performance of the PFs but has less impact on the EnKF after a sufficient number of members have been used.

Exploitation of jet properties for energy scale corrections for the CMS calorimeters

International Nuclear Information System (INIS)

Kirschenmann, Henning

2011-02-01

Jets form important event signatures in proton-proton collisions at the Large Hadron Collider (LHC) and the precise measurement of their energy is a crucial premise for a manifold of physics studies. Jets, which are reconstructed exclusively from calorimeter information, have been widely used within the CMS collaboration. However, the response of the calorimeters to incident particles depends heavily on their energy. In addition, it has been observed at previous experiments that the charged particle multiplicity and the radial distribution of constituents differ for jets induced by light quarks or by gluons. In conjunction with the non-linearity of the CMS calorimeters, this contributes to a mean energy response deviating from unity for calorimeter jets, depending on the jet-flavour. This thesis describes a jet-energy correction to be applied in addition to the default corrections within the CMS collaboration. This correction aims at decreasing the flavour dependence of the jet-energy response and improving the energy resolution. As many different effects contribute to the observed jet-energy response, a set of observables are introduced and corrections based on these observables are tested with respect to the above aims. A jet-width variable, which is defined from energy measured in the calorimeter, shows the best performance: A correction based on this observable improves the energy resolution by up to 20% at high transverse momenta in the central detector region and decreases the flavour dependence of the jet-energy response by a factor of two. A parametrisation of the correction is both derived from and validated on simulated data. First results from experimental data, to which the correction has been applied, are presented. The proposed jet-width correction shows a promising level of performance. (orig.)

Exploitation of jet properties for energy scale corrections for the CMS calorimeters

Energy Technology Data Exchange (ETDEWEB)

Kirschenmann, Henning

2011-02-15

Jets form important event signatures in proton-proton collisions at the Large Hadron Collider (LHC) and the precise measurement of their energy is a crucial premise for a manifold of physics studies. Jets, which are reconstructed exclusively from calorimeter information, have been widely used within the CMS collaboration. However, the response of the calorimeters to incident particles depends heavily on their energy. In addition, it has been observed at previous experiments that the charged particle multiplicity and the radial distribution of constituents differ for jets induced by light quarks or by gluons. In conjunction with the non-linearity of the CMS calorimeters, this contributes to a mean energy response deviating from unity for calorimeter jets, depending on the jet-flavour. This thesis describes a jet-energy correction to be applied in addition to the default corrections within the CMS collaboration. This correction aims at decreasing the flavour dependence of the jet-energy response and improving the energy resolution. As many different effects contribute to the observed jet-energy response, a set of observables are introduced and corrections based on these observables are tested with respect to the above aims. A jet-width variable, which is defined from energy measured in the calorimeter, shows the best performance: A correction based on this observable improves the energy resolution by up to 20% at high transverse momenta in the central detector region and decreases the flavour dependence of the jet-energy response by a factor of two. A parametrisation of the correction is both derived from and validated on simulated data. First results from experimental data, to which the correction has been applied, are presented. The proposed jet-width correction shows a promising level of performance. (orig.)

Beam Stability and Nonlinear Dynamics. Proceedings

International Nuclear Information System (INIS)

Parsa, Z.

1997-01-01

These proceedings represent papers presented at the Beam Stability and Nonlinear Dynamics symposium held in Santa Barbara in December 1996. The symposium was sponsored by the National Science Foundation as part of the United States long term accelerator research. The focus of this symposium was on nonlinear dynamics and beam stability. The topics included single-particle and many-particle dynamics, and stability in large circular accelerators such as the Large Hadron Collider(LHC). Other subjects covered were spin dynamics, nonlinear aberration correction, collective effects in the LHC, sawtooth instability and Landau damping in the presence of strong nonlinearity. There were presentations concerning plasma physics including the effect of beam echo. There are 17 papers altogether in these proceedings and 8 of them have been abstracted for the Energy Science and Technology database

MD1831: Single Bunch Instabilities with Q" and Non-Linear Corrections

CERN Document Server

Carver, Lee Robert; De Maria, Riccardo; Li, Kevin Shing Bruce; Amorim, David; Biancacci, Nicolo; Buffat, Xavier; Maclean, Ewen Hamish; Metral, Elias; Lasocha, Kacper; Lefevre, Thibaut; Levens, Tom; Salvant, Benoit; CERN. Geneva. ATS Department

2017-01-01

During MD1751, it was observed that both a full single beam and 964 non-colliding bunches in Beam 1 (B1) and Beam 2 (B2) were both stable at the End of Squeeze (EOS) for 0A in the Landau Octupoles. At ß* = 40cm there is also a significant Q" arising from the lattice, as well as uncorrected non-linearities in the Insertion Regions (IRs). Each of these effects could be capable of fully stabilising the beam. This MD made first use of a Q" knob through variation of the Main Sextupoles (MS) by stabilising a single bunch at Flat Top, before showing at EOS that the non-linearities were the main contributors to the beam stability.

Dynamics and vibrations progress in nonlinear analysis

CERN Document Server

Kachapi, Seyed Habibollah Hashemi

2014-01-01

Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems. There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between th...

Nonlinear Approaches in Engineering Applications

CERN Document Server

Jazar, Reza

2012-01-01

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

Time history nonlinear earthquake response analysis considering materials and geometrical nonlinearity

International Nuclear Information System (INIS)

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

2002-01-01

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

Geometrically Nonlinear Transient Response of Laminated Plates with Nonlinear Elastic Restraints

Directory of Open Access Journals (Sweden)

Shaochong Yang

2017-01-01

Full Text Available To investigate the dynamic behavior of laminated plates with nonlinear elastic restraints, a varied constraint force model and a systematic numerical procedure are presented in this work. Several kinds of typical relationships of force-displacement for spring are established to simulate the nonlinear elastic restraints. In addition, considering the restraining moments of flexible pads, the pads are modeled by translational and rotational springs. The displacement- dependent constraint forces are added to the right-hand side of equations of motion and treated as additional applied loads. These loads can be explicitly defined, via an independent set of nonlinear load functions. The time histories of transverse displacements at typical points of the laminated plate are obtained through the transient analysis. Numerical examples show that the present method can effectively treat the geometrically nonlinear transient response of plates with nonlinear elastic restraints.

Identification of nonlinear anelastic models

International Nuclear Information System (INIS)

Draganescu, G E; Bereteu, L; Ercuta, A

2008-01-01

A useful nonlinear identification technique applied to the anelastic and rheologic models is presented in this paper. First introduced by Feldman, the method is based on the Hilbert transform, and is currently used for identification of the nonlinear vibrations

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

Different methods of solution of linear and nonlinear algebraic systems are applied to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems, methods in general use of alternating directions type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method on nonlinear conjugate gradient is studied as also Newton's method and some of its variants. It should be noted, however that Newton's method is found to be more efficient when coupled with a good method for solution of the linear system. To conclude, such methods are used to solve a nonlinear diffusion problem and the numerical results obtained are to be compared [fr

Solution of linear and nonlinear matrix systems. Application to a nonlinear diffusion equation

International Nuclear Information System (INIS)

Bonnet, M.; Meurant, G.

1978-01-01

The object of this study is to compare different methods of solving linear and nonlinear algebraic systems and to apply them to the nonlinear system obtained by discretizing a nonlinear diffusion equation. For linear systems the conventional methods of alternating direction type or Gauss Seidel's methods are compared to more recent ones of the type of generalized conjugate gradient; the superiority of the latter is shown by numerical examples. For nonlinear systems, a method of nonlinear conjugate gradient is studied together with Newton's method and some of its variants. It should be noted, however, that Newton's method is found to be more efficient when coupled with a good method for solving the linear system. As a conclusion, these methods are used to solve a nonlinear diffusion problem and the numerical results obtained are compared [fr

Physical Limitations To Nonuniformity Correction In IR Focal Plane Arrays

Science.gov (United States)

Scribner, D. A.; Kruer, M. R.; Gridley, J. C.; Sarkady, K.

1988-05-01

Simple nonuniformity correction algorithms currently in use can be severely limited by nonlinear response characteristics of the individual pixels in an IR focal plane array. Although more complicated multi-point algorithms improve the correction process they too can be limited by nonlinearities. Furthermore, analysis of single pixel noise power spectrums usually show some level of 1 /f noise. This in turn causes pixel outputs to drift independent of each other thus causing the spatial noise (often called fixed pattern noise) of the array to increase as a function of time since the last calibration. Measurements are presented for two arrays (a HgCdTe hybrid and a Pt:Si CCD) describing pixel nonlinearities, 1/f noise, and residual spatial noise (after nonuniforming correction). Of particular emphasis is spatial noise as a function of the lapsed time since the last calibration and the calibration process selected. The resulting spatial noise is examined in terms of its effect on the NEAT performance of each array tested and comparisons are made. Finally, a discussion of implications for array developers is given.

Nonlinear earthquake analysis of reinforced concrete frames with fiber and Bernoulli-Euler beam-column element.

Science.gov (United States)

Karaton, Muhammet

2014-01-01

A beam-column element based on the Euler-Bernoulli beam theory is researched for nonlinear dynamic analysis of reinforced concrete (RC) structural element. Stiffness matrix of this element is obtained by using rigidity method. A solution technique that included nonlinear dynamic substructure procedure is developed for dynamic analyses of RC frames. A predicted-corrected form of the Bossak-α method is applied for dynamic integration scheme. A comparison of experimental data of a RC column element with numerical results, obtained from proposed solution technique, is studied for verification the numerical solutions. Furthermore, nonlinear cyclic analysis results of a portal reinforced concrete frame are achieved for comparing the proposed solution technique with Fibre element, based on flexibility method. However, seismic damage analyses of an 8-story RC frame structure with soft-story are investigated for cases of lumped/distributed mass and load. Damage region, propagation, and intensities according to both approaches are researched.

NONLINEAR TIDES IN CLOSE BINARY SYSTEMS

International Nuclear Information System (INIS)

Weinberg, Nevin N.; Arras, Phil; Quataert, Eliot; Burkart, Josh

2012-01-01

We study the excitation and damping of tides in close binary systems, accounting for the leading-order nonlinear corrections to linear tidal theory. These nonlinear corrections include two distinct physical effects: three-mode nonlinear interactions, i.e., the redistribution of energy among stellar modes of oscillation, and nonlinear excitation of stellar normal modes by the time-varying gravitational potential of the companion. This paper, the first in a series, presents the formalism for studying nonlinear tides and studies the nonlinear stability of the linear tidal flow. Although the formalism we present is applicable to binaries containing stars, planets, and/or compact objects, we focus on non-rotating solar-type stars with stellar or planetary companions. Our primary results include the following: (1) The linear tidal solution almost universally used in studies of binary evolution is unstable over much of the parameter space in which it is employed. More specifically, resonantly excited internal gravity waves in solar-type stars are nonlinearly unstable to parametric resonance for companion masses M' ∼> 10-100 M ⊕ at orbital periods P ≈ 1-10 days. The nearly static 'equilibrium' tidal distortion is, however, stable to parametric resonance except for solar binaries with P ∼ 3 [P/10 days] for a solar-type star) and drives them as a single coherent unit with growth rates that are a factor of ≈N faster than the standard three-wave parametric instability. These are local instabilities viewed through the lens of global analysis; the coherent global growth rate follows local rates in the regions where the shear is strongest. In solar-type stars, the dynamical tide is unstable to this collective version of the parametric instability for even sub-Jupiter companion masses with P ∼< a month. (4) Independent of the parametric instability, the dynamical and equilibrium tides excite a wide range of stellar p-modes and g-modes by nonlinear inhomogeneous forcing

A Modal-Based Substructure Method Applied to Nonlinear Rotordynamic Systems

Directory of Open Access Journals (Sweden)

Helmut J. Holl

2009-01-01

Full Text Available The discretisation of rotordynamic systems usually results in a high number of coordinates, so the computation of the solution of the equations of motion is very time consuming. An efficient semianalytic time-integration method combined with a substructure technique is given, which accounts for nonsymmetric matrices and local nonlinearities. The partitioning of the equation of motion into two substructures is performed. Symmetric and linear background systems are defined for each substructure. The excitation of the substructure comes from the given excitation force, the nonlinear restoring force, the induced force due to the gyroscopic and circulatory effects of the substructure under consideration and the coupling force of the substructures. The high effort for the analysis with complex numbers, which is necessary for nonsymmetric systems, is omitted. The solution is computed by means of an integral formulation. A suitable approximation for the unknown coordinates, which are involved in the coupling forces, has to be introduced and the integration results in Green's functions of the considered substructures. Modal analysis is performed for each linear and symmetric background system of the substructure. Modal reduction can be easily incorporated and the solution is calculated iteratively. The numerical behaviour of the algorithm is discussed and compared to other approximate methods of nonlinear structural dynamics for a benchmark problem and a representative example.

Nonlinear optics at interfaces

International Nuclear Information System (INIS)

Chen, C.K.

1980-12-01

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

A new calibration model for pointing a radio telescope that considers nonlinear errors in the azimuth axis

International Nuclear Information System (INIS)

Kong De-Qing; Wang Song-Gen; Zhang Hong-Bo; Wang Jin-Qing; Wang Min

2014-01-01

A new calibration model of a radio telescope that includes pointing error is presented, which considers nonlinear errors in the azimuth axis. For a large radio telescope, in particular for a telescope with a turntable, it is difficult to correct pointing errors using a traditional linear calibration model, because errors produced by the wheel-on-rail or center bearing structures are generally nonlinear. Fourier expansion is made for the oblique error and parameters describing the inclination direction along the azimuth axis based on the linear calibration model, and a new calibration model for pointing is derived. The new pointing model is applied to the 40m radio telescope administered by Yunnan Observatories, which is a telescope that uses a turntable. The results show that this model can significantly reduce the residual systematic errors due to nonlinearity in the azimuth axis compared with the linear model

Rail vehicle dynamic response to a nonlinear physical 'in-service' model of its secondary suspension hydraulic dampers

Science.gov (United States)

Wang, W. L.; Zhou, Z. R.; Yu, D. S.; Qin, Q. H.; Iwnicki, S.

2017-10-01

A full nonlinear physical 'in-service' model was built for a rail vehicle secondary suspension hydraulic damper with shim-pack-type valves. In the modelling process, a shim pack deflection theory with an equivalent-pressure correction factor was proposed, and a Finite Element Analysis (FEA) approach was applied. Bench test results validated the damper model over its full velocity range and thus also proved that the proposed shim pack deflection theory and the FEA-based parameter identification approach are effective. The validated full damper model was subsequently incorporated into a detailed vehicle dynamics simulation to study how its key in-service parameter variations influence the secondary-suspension-related vehicle system dynamics. The obtained nonlinear physical in-service damper model and the vehicle dynamic response characteristics in this study could be used in the product design optimization and nonlinear optimal specifications of high-speed rail hydraulic dampers.

Handbook of Applied Analysis

CERN Document Server

Papageorgiou, Nikolaos S

2009-01-01

Offers an examination of important theoretical methods and procedures in applied analysis. This book details the important theoretical trends in nonlinear analysis and applications to different fields. It is suitable for those working on nonlinear analysis.

Enhanced nonlinear iterative techniques applied to a non-equilibrium plasma flow

Energy Technology Data Exchange (ETDEWEB)

Knoll, D.A.; McHugh, P.R. [Idaho National Engineering Lab., Idaho Falls, ID (United States)

1996-12-31

We study the application of enhanced nonlinear iterative methods to the steady-state solution of a system of two-dimensional convection-diffusion-reaction partial differential equations that describe the partially-ionized plasma flow in the boundary layer of a tokamak fusion reactor. This system of equations is characterized by multiple time and spatial scales, and contains highly anisotropic transport coefficients due to a strong imposed magnetic field. We use Newton`s method to linearize the nonlinear system of equations resulting from an implicit, finite volume discretization of the governing partial differential equations, on a staggered Cartesian mesh. The resulting linear systems are neither symmetric nor positive definite, and are poorly conditioned. Preconditioned Krylov iterative techniques are employed to solve these linear systems. We investigate both a modified and a matrix-free Newton-Krylov implementation, with the goal of reducing CPU cost associated with the numerical formation of the Jacobian. A combination of a damped iteration, one-way multigrid and a pseudo-transient continuation technique are used to enhance global nonlinear convergence and CPU efficiency. GMRES is employed as the Krylov method with Incomplete Lower-Upper(ILU) factorization preconditioning. The goal is to construct a combination of nonlinear and linear iterative techniques for this complex physical problem that optimizes trade-offs between robustness, CPU time, memory requirements, and code complexity. It is shown that a one-way multigrid implementation provides significant CPU savings for fine grid calculations. Performance comparisons of the modified Newton-Krylov and matrix-free Newton-Krylov algorithms will be presented.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter.

Science.gov (United States)

Song, Xuegang; Zhang, Yuexin; Liang, Dakai

2017-10-10

This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter

Directory of Open Access Journals (Sweden)

Xuegang Song

2017-10-01

Full Text Available This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

Complex motions and chaos in nonlinear systems

CERN Document Server

Machado, José; Zhang, Jiazhong

2016-01-01

This book brings together 10 chapters on a new stream of research examining complex phenomena in nonlinear systems—including engineering, physics, and social science. Complex Motions and Chaos in Nonlinear Systems provides readers a particular vantage of the nature and nonlinear phenomena in nonlinear dynamics that can develop the corresponding mathematical theory and apply nonlinear design to practical engineering as well as the study of other complex phenomena including those investigated within social science.

A hybrid filter to mitigate harmonics caused by nonlinear load and resonance caused by power factor correction capacitor

Science.gov (United States)

Adan, N. F.; Soomro, D. M.

2017-01-01

Power factor correction capacitor (PFCC) is commonly installed in industrial applications for power factor correction (PFC). With the expanding use of non-linear equipment such as ASDs, power converters, etc., power factor (PF) improvement has become difficult due to the presence of harmonics. The resulting capacitive impedance of the PFCC may form a resonant circuit with the source inductive reactance at a certain frequency, which is likely to coincide with one of the harmonic frequency of the load. This condition will trigger large oscillatory currents and voltages that may stress the insulation and cause subsequent damage to the PFCC and equipment connected to the power system (PS). Besides, high PF cannot be achieved due to power distortion. This paper presents the design of a three-phase hybrid filter consisting of a single tuned passive filter (STPF) and shunt active power filter (SAPF) to mitigate harmonics and resonance in the PS through simulation using PSCAD/EMTDC software. SAPF was developed using p-q theory. The hybrid filter has resulted in significant improvement on both total harmonic distortion for voltage (THDV) and total demand distortion for current (TDDI) with maximum values of 2.93% and 9.84% respectively which were within the recommended IEEE 519-2014 standard limits. Regarding PF improvement, the combined filters have achieved PF close to desired PF at 0.95 for firing angle, α values up to 40°.

Simultaneous determination of penicillin G salts by infrared spectroscopy: Evaluation of combining orthogonal signal correction with radial basis function-partial least squares regression

Science.gov (United States)

Talebpour, Zahra; Tavallaie, Roya; Ahmadi, Seyyed Hamid; Abdollahpour, Assem

2010-09-01

In this study, a new method for the simultaneous determination of penicillin G salts in pharmaceutical mixture via FT-IR spectroscopy combined with chemometrics was investigated. The mixture of penicillin G salts is a complex system due to similar analytical characteristics of components. Partial least squares (PLS) and radial basis function-partial least squares (RBF-PLS) were used to develop the linear and nonlinear relation between spectra and components, respectively. The orthogonal signal correction (OSC) preprocessing method was used to correct unexpected information, such as spectral overlapping and scattering effects. In order to compare the influence of OSC on PLS and RBF-PLS models, the optimal linear (PLS) and nonlinear (RBF-PLS) models based on conventional and OSC preprocessed spectra were established and compared. The obtained results demonstrated that OSC clearly enhanced the performance of both RBF-PLS and PLS calibration models. Also in the case of some nonlinear relation between spectra and component, OSC-RBF-PLS gave satisfactory results than OSC-PLS model which indicated that the OSC was helpful to remove extrinsic deviations from linearity without elimination of nonlinear information related to component. The chemometric models were tested on an external dataset and finally applied to the analysis commercialized injection product of penicillin G salts.

Nonlinear wave equations

CERN Document Server

Li, Tatsien

2017-01-01

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

Nonlinear filtering for LIDAR signal processing

Directory of Open Access Journals (Sweden)

D. G. Lainiotis

1996-01-01

Full Text Available LIDAR (Laser Integrated Radar is an engineering problem of great practical importance in environmental monitoring sciences. Signal processing for LIDAR applications involves highly nonlinear models and consequently nonlinear filtering. Optimal nonlinear filters, however, are practically unrealizable. In this paper, the Lainiotis's multi-model partitioning methodology and the related approximate but effective nonlinear filtering algorithms are reviewed and applied to LIDAR signal processing. Extensive simulation and performance evaluation of the multi-model partitioning approach and its application to LIDAR signal processing shows that the nonlinear partitioning methods are very effective and significantly superior to the nonlinear extended Kalman filter (EKF, which has been the standard nonlinear filter in past engineering applications.

Holographic conductivity of holographic superconductors with higher-order corrections

Energy Technology Data Exchange (ETDEWEB)

Sheykhi, Ahmad [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Ghazanfari, Afsoon; Dehyadegari, Amin [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)

2018-02-15

We analytically and numerically disclose the effects of the higher-order correction terms in the gravity and in the gauge field on the properties of s-wave holographic superconductors. On the gravity side, we consider the higher curvature Gauss-Bonnet corrections and on the gauge field side, we add a quadratic correction term to the Maxwell Lagrangian. We show that, for this system, one can still obtain an analytical relation between the critical temperature and the charge density. We also calculate the critical exponent and the condensation value both analytically and numerically. We use a variational method, based on the Sturm-Liouville eigenvalue problem for our analytical study, as well as a numerical shooting method in order to compare with our analytical results. For a fixed value of the Gauss-Bonnet parameter, we observe that the critical temperature decreases with increasing the nonlinearity of the gauge field. This implies that the nonlinear correction term to the Maxwell electrodynamics makes the condensation harder. We also study the holographic conductivity of the system and disclose the effects of the Gauss-Bonnet and nonlinear parameters α and b on the superconducting gap. We observe that, for various values of α and b, the real part of the conductivity is proportional to the frequency per temperature, ω/T, as the frequency is large enough. Besides, the conductivity has a minimum in the imaginary part which is shifted toward greater frequency with decreasing temperature. (orig.)

Calibration of the nonlinear ring model at the Diamond Light Source

CERN Document Server

Bartolini, R; Rehm, G; Martin, I P S

2011-01-01

Nonlinear beam dynamics plays a crucial role in defining the performance of a storage ring. The beam lifetime, the injection efficiency, and the dynamic and momentum apertures available to the beam are optimized during the design phase by a proper optimization of the linear lattice and of the distribution of sextupole families. The correct implementation of the design model, especially the nonlinear part, is a nontrivial accelerator physics task. Several parameters of the nonlinear dynamics can be used to compare the real machine with the model and eventually to correct the accelerator. Most of these parameters are extracted from the analysis of turn-by-turn data after the excitation of betatron oscillations of the particles in the ring. We present the experimental results of the campaign of measurements carried out at the Diamond storage ring to characterize the nonlinear beam dynamics. A combination of frequency map analysis with the detuning with momentum measurements has allowed for a precise calibration ...

A Nonlinear Multiparameters Temperature Error Modeling and Compensation of POS Applied in Airborne Remote Sensing System

Directory of Open Access Journals (Sweden)

Jianli Li

2014-01-01

Full Text Available The position and orientation system (POS is a key equipment for airborne remote sensing systems, which provides high-precision position, velocity, and attitude information for various imaging payloads. Temperature error is the main source that affects the precision of POS. Traditional temperature error model is single temperature parameter linear function, which is not sufficient for the higher accuracy requirement of POS. The traditional compensation method based on neural network faces great problem in the repeatability error under different temperature conditions. In order to improve the precision and generalization ability of the temperature error compensation for POS, a nonlinear multiparameters temperature error modeling and compensation method based on Bayesian regularization neural network was proposed. The temperature error of POS was analyzed and a nonlinear multiparameters model was established. Bayesian regularization method was used as the evaluation criterion, which further optimized the coefficients of the temperature error. The experimental results show that the proposed method can improve temperature environmental adaptability and precision. The developed POS had been successfully applied in airborne TSMFTIS remote sensing system for the first time, which improved the accuracy of the reconstructed spectrum by 47.99%.

Establishment of regression dependences. Linear and nonlinear dependences

International Nuclear Information System (INIS)

Onishchenko, A.M.

1994-01-01

The main problems of determination of linear and 19 types of nonlinear regression dependences are completely discussed. It is taken into consideration that total dispersions are the sum of measurement dispersions and parameter variation dispersions themselves. Approaches to all dispersions determination are described. It is shown that the least square fit gives inconsistent estimation for industrial objects and processes. The correction methods by taking into account comparable measurement errors for both variable give an opportunity to obtain consistent estimation for the regression equation parameters. The condition of the correction technique application expediency is given. The technique for determination of nonlinear regression dependences taking into account the dependence form and comparable errors of both variables is described. 6 refs., 1 tab

Evaluating Noise Sensitivity on the Time Series Determination of Lyapunov Exponents Applied to the Nonlinear Pendulum

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L.F.P. Franca

2003-01-01

Full Text Available This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.

Simultaneous Mean and Covariance Correction Filter for Orbit Estimation.

Science.gov (United States)

Wang, Xiaoxu; Pan, Quan; Ding, Zhengtao; Ma, Zhengya

2018-05-05

This paper proposes a novel filtering design, from a viewpoint of identification instead of the conventional nonlinear estimation schemes (NESs), to improve the performance of orbit state estimation for a space target. First, a nonlinear perturbation is viewed or modeled as an unknown input (UI) coupled with the orbit state, to avoid the intractable nonlinear perturbation integral (INPI) required by NESs. Then, a simultaneous mean and covariance correction filter (SMCCF), based on a two-stage expectation maximization (EM) framework, is proposed to simply and analytically fit or identify the first two moments (FTM) of the perturbation (viewed as UI), instead of directly computing such the INPI in NESs. Orbit estimation performance is greatly improved by utilizing the fit UI-FTM to simultaneously correct the state estimation and its covariance. Third, depending on whether enough information is mined, SMCCF should outperform existing NESs or the standard identification algorithms (which view the UI as a constant independent of the state and only utilize the identified UI-mean to correct the state estimation, regardless of its covariance), since it further incorporates the useful covariance information in addition to the mean of the UI. Finally, our simulations demonstrate the superior performance of SMCCF via an orbit estimation example.

Nonlinear Poisson equation for heterogeneous media.

Science.gov (United States)

Hu, Langhua; Wei, Guo-Wei

2012-08-22

The Poisson equation is a widely accepted model for electrostatic analysis. However, the Poisson equation is derived based on electric polarizations in a linear, isotropic, and homogeneous dielectric medium. This article introduces a nonlinear Poisson equation to take into consideration of hyperpolarization effects due to intensive charges and possible nonlinear, anisotropic, and heterogeneous media. Variational principle is utilized to derive the nonlinear Poisson model from an electrostatic energy functional. To apply the proposed nonlinear Poisson equation for the solvation analysis, we also construct a nonpolar solvation energy functional based on the nonlinear Poisson equation by using the geometric measure theory. At a fixed temperature, the proposed nonlinear Poisson theory is extensively validated by the electrostatic analysis of the Kirkwood model and a set of 20 proteins, and the solvation analysis of a set of 17 small molecules whose experimental measurements are also available for a comparison. Moreover, the nonlinear Poisson equation is further applied to the solvation analysis of 21 compounds at different temperatures. Numerical results are compared to theoretical prediction, experimental measurements, and those obtained from other theoretical methods in the literature. A good agreement between our results and experimental data as well as theoretical results suggests that the proposed nonlinear Poisson model is a potentially useful model for electrostatic analysis involving hyperpolarization effects. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Generalized Nonlinear Yule Models

Science.gov (United States)

Lansky, Petr; Polito, Federico; Sacerdote, Laura

2016-11-01

With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.

Electron-related nonlinearities in GaAs-Ga{sub 1-x}Al{sub x}As double quantum wells under the effects of intense laser field and applied electric field

Energy Technology Data Exchange (ETDEWEB)

Mora-Ramos, M.E. [Facultad de Ciencias, Universidad Autonoma del Estado de Morelos, Ave. Universidad 1001, CP 62209, Cuernavaca, Morelos, Mexico (Mexico); Instituto de Fisica, Universidad de Antioquia, AA 1226 Medellin (Colombia); Duque, C.A., E-mail: cduque_echeverri@yahoo.es [Instituto de Fisica, Universidad de Antioquia, AA 1226 Medellin (Colombia); Kasapoglu, E.; Sari, H. [Cumhuriyet University, Physics Department, 58140 Sivas (Turkey); Soekmen, I. [Dokuz Eyluel University, Physics Department, 35160 Buca, Izmir (Turkey)

2013-03-15

The combined effects of intense laser radiation and applied electric fields on the intersubband-related linear and nonlinear optical properties in GaAs-based quantum wells are discussed. It is shown that for asymmetric double quantum well, the increasing laser field intensity causes progressive redshifts in the peak positions of the second and third harmonic coefficients. However, the resonant peaks of the nonlinear optical rectification can suffer a blueshift or a redshift, depending on the laser strengths. The same feature appears in the case of the resonant peaks corresponding to the total coefficients of optical absorption and relative change in the refractive index. - Highlights: Black-Right-Pointing-Pointer Nonlinear optical properties in double quantum wells. Black-Right-Pointing-Pointer Increasing laser field intensity causes redshifts in the peak positions. Black-Right-Pointing-Pointer Resonant peak of second order nonlinearities can be blue-shifted. Black-Right-Pointing-Pointer Relative change in refractive index depends of the applied electric field. Black-Right-Pointing-Pointer The energy position depends of the laser field parameter.

Nonlinear crack mechanics

International Nuclear Information System (INIS)

Khoroshun, L.P.

1995-01-01

The characteristic features of the deformation and failure of actual materials in the vicinity of a crack tip are due to their physical nonlinearity in the stress-concentration zone, which is a result of plasticity, microfailure, or a nonlinear dependence of the interatomic forces on the distance. Therefore, adequate models of the failure mechanics must be nonlinear, in principle, although linear failure mechanics is applicable if the zone of nonlinear deformation is small in comparison with the crack length. Models of crack mechanics are based on analytical solutions of the problem of the stress-strain state in the vicinity of the crack. On account of the complexity of the problem, nonlinear models are bason on approximate schematic solutions. In the Leonov-Panasyuk-Dugdale nonlinear model, one of the best known, the actual two-dimensional plastic zone (the nonlinearity zone) is replaced by a narrow one-dimensional zone, which is then modeled by extending the crack with a specified normal load equal to the yield point. The condition of finite stress is applied here, and hence the length of the plastic zone is determined. As a result of this approximation, the displacement in the plastic zone at the abscissa is nonzero

Correction for polychromatic X-ray image distortion in computer tomography images

International Nuclear Information System (INIS)

1979-01-01

A method and apparatus are described which correct the polychromatic distortion of CT images that is produced by the non-linear interaction of body constituents with a polychromatic X-ray beam. A CT image is processed to estimate the proportion of the attenuation coefficients of the constituents in each pixel element. A multiplicity of projections for each constituent are generated from the original image and are combined utilizing a multidimensional polynomial which approximates the non-linear interaction involved. An error image is then generated from the combined projections and is subtracted from the original image to correct for the polychromatic distortion. (Auth.)

Three dimensional nonlinear magnetic AdS solutions through topological defects

International Nuclear Information System (INIS)

Hendi, S.H.; Panah, B.E.; Momennia, M.; Panahiyan, S.

2015-01-01

Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known Born-Infeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appears too. (orig.)

NR-code: Nonlinear reconstruction code

Science.gov (United States)

Yu, Yu; Pen, Ue-Li; Zhu, Hong-Ming

2018-04-01

NR-code applies nonlinear reconstruction to the dark matter density field in redshift space and solves for the nonlinear mapping from the initial Lagrangian positions to the final redshift space positions; this reverses the large-scale bulk flows and improves the precision measurement of the baryon acoustic oscillations (BAO) scale.

Nonlinear plasma waves excited near resonance

International Nuclear Information System (INIS)

Cohen, B.I.; Kaufman, A.N.

1977-01-01

The nonlinear resonant response of a uniform plasma to an external plane-wave field is formulated in terms of the mismatch Δ/sub n l/ between the driving frequency and the time-dependent, complex, nonlinear normal mode frequency at the driving wavenumber. This formalism is applied to computer simulations of this process, yielding a deduced nonlinear frequency shift. The time dependence of the nonlinear phenomena, at frequency Δ/sub n l/ and at the bounce frequency of the resonant particles, is analyzed. The interdependence of the nonlinear features is described by means of energy and momentum relations

Assessment of Atmospheric Correction Methods for Sentinel-2 MSI Images Applied to Amazon Floodplain Lakes

Directory of Open Access Journals (Sweden)

Vitor Souza Martins

2017-03-01

Full Text Available Satellite data provide the only viable means for extensive monitoring of remote and large freshwater systems, such as the Amazon floodplain lakes. However, an accurate atmospheric correction is required to retrieve water constituents based on surface water reflectance ( R W . In this paper, we assessed three atmospheric correction methods (Second Simulation of a Satellite Signal in the Solar Spectrum (6SV, ACOLITE and Sen2Cor applied to an image acquired by the MultiSpectral Instrument (MSI on-board of the European Space Agency’s Sentinel-2A platform using concurrent in-situ measurements over four Amazon floodplain lakes in Brazil. In addition, we evaluated the correction of forest adjacency effects based on the linear spectral unmixing model, and performed a temporal evaluation of atmospheric constituents from Multi-Angle Implementation of Atmospheric Correction (MAIAC products. The validation of MAIAC aerosol optical depth (AOD indicated satisfactory retrievals over the Amazon region, with a correlation coefficient (R of ~0.7 and 0.85 for Terra and Aqua products, respectively. The seasonal distribution of the cloud cover and AOD revealed a contrast between the first and second half of the year in the study area. Furthermore, simulation of top-of-atmosphere (TOA reflectance showed a critical contribution of atmospheric effects (>50% to all spectral bands, especially the deep blue (92%–96% and blue (84%–92% bands. The atmospheric correction results of the visible bands illustrate the limitation of the methods over dark lakes ( R W < 1%, and better match of the R W shape compared with in-situ measurements over turbid lakes, although the accuracy varied depending on the spectral bands and methods. Particularly above 705 nm, R W was highly affected by Amazon forest adjacency, and the proposed adjacency effect correction minimized the spectral distortions in R W (RMSE < 0.006. Finally, an extensive validation of the methods is required for

Ship nonlinear-feedback course keeping algorithm based on MMG model driven by bipolar sigmoid function for berthing

Directory of Open Access Journals (Sweden)

Qiang Zhang

2017-09-01

Full Text Available Course keeping is hard to implement under the condition of the propeller stopping or reversing at slow speed for berthing due to the ship's dynamic motion becoming highly nonlinear. To solve this problem, a practical Maneuvering Modeling Group (MMG ship mathematic model with propeller reversing transverse forces and low speed correction is first discussed to be applied for the right-handed single-screw ship. Secondly, a novel PID-based nonlinear feedback algorithm driven by bipolar sigmoid function is proposed. The PID parameters are determined by a closed-loop gain shaping algorithm directly, while the closed-loop gain shaping theory was employed for effects analysis of this algorithm. Finally, simulation experiments were carried out on an LPG ship. It is shown that the energy consumption and the smoothness performance of the nonlinear feedback control are reduced by 4.2% and 14.6% with satisfactory control effects; the proposed algorithm has the advantages of robustness, energy saving and safety in berthing practice.

Nonlinear effects on bremsstrahlung emission in dusty plasmas

International Nuclear Information System (INIS)

Kim, Young-Woo; Jung, Young-Dae

2004-01-01

Nonlinear effects on the bremsstrahlung process due to ion-dust grain collisions are investigated in dusty plasmas. The nonlinear screened interaction potential is applied to obtain the Fourier coefficients of the force acting on the dust grain. The classical trajectory analysis is applied to obtain the differential bremsstrahlung radiation cross section as a function of the scaled impact parameter, projectile energy, photon energy, and Debye length. The result shows that the nonlinear effects suppress the bremsstrahlung radiation cross section due to collisions of ions with positively charged dust grains. These nonlinear effects decrease with increasing Debye length and temperature, and increase with increasing radiation photon energy

Transport processes in magnetically confined plasmas in the nonlinear regime.

Science.gov (United States)

Sonnino, Giorgio

2006-06-01

A field theory approach to transport phenomena in magnetically confined plasmas is presented. The thermodynamic field theory (TFT), previously developed for treating the generic thermodynamic system out of equilibrium, is applied to plasmas physics. Transport phenomena are treated here as the effect of the field linking the thermodynamic forces with their conjugate flows combined with statistical mechanics. In particular, the Classical and the Pfirsch-Schluter regimes are analyzed by solving the thermodynamic field equations of the TFT in the weak-field approximation. We found that, the TFT does not correct the expressions of the ionic heat fluxes evaluated by the neoclassical theory in these two regimes. On the other hand, the fluxes of matter and electronic energy (heat flow) is further enhanced in the nonlinear Classical and Pfirsch-Schluter regimes. These results seem to be in line with the experimental observations. The complete set of the electronic and ionic transport equations in the nonlinear Banana regime, is also reported. A paper showing the comparison between our theoretic results and the experimental observations in the JET machine is currently in preparation.

Atmospheric correction of APEX hyperspectral data

Directory of Open Access Journals (Sweden)

Sterckx Sindy

2016-03-01

Full Text Available Atmospheric correction plays a crucial role among the processing steps applied to remotely sensed hyperspectral data. Atmospheric correction comprises a group of procedures needed to remove atmospheric effects from observed spectra, i.e. the transformation from at-sensor radiances to at-surface radiances or reflectances. In this paper we present the different steps in the atmospheric correction process for APEX hyperspectral data as applied by the Central Data Processing Center (CDPC at the Flemish Institute for Technological Research (VITO, Mol, Belgium. The MODerate resolution atmospheric TRANsmission program (MODTRAN is used to determine the source of radiation and for applying the actual atmospheric correction. As part of the overall correction process, supporting algorithms are provided in order to derive MODTRAN configuration parameters and to account for specific effects, e.g. correction for adjacency effects, haze and shadow correction, and topographic BRDF correction. The methods and theory underlying these corrections and an example of an application are presented.

Nonlinear optimization

CERN Document Server

Ruszczynski, Andrzej

2011-01-01

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

Anti-D3 branes and moduli in non-linear supergravity

Science.gov (United States)

Garcia del Moral, Maria P.; Parameswaran, Susha; Quiroz, Norma; Zavala, Ivonne

2017-10-01

Anti-D3 branes and non-perturbative effects in flux compactifications spontaneously break supersymmetry and stabilise moduli in a metastable de Sitter vacua. The low energy 4D effective field theory description for such models would be a supergravity theory with non-linearly realised supersymmetry. Guided by string theory modular symmetry, we compute this non-linear supergravity theory, including dependence on all bulk moduli. Using either a constrained chiral superfield or a constrained vector field, the uplifting contribution to the scalar potential from the anti-D3 brane can be parameterised either as an F-term or Fayet-Iliopoulos D-term. Using again the modular symmetry, we show that 4D non-linear supergravities that descend from string theory have an enhanced protection from quantum corrections by non-renormalisation theorems. The superpotential giving rise to metastable de Sitter vacua is robust against perturbative string-loop and α' corrections.

Synchronization of chaos by nonlinear feedback

International Nuclear Information System (INIS)

Cheng Yanxiang

1995-01-01

The authors point out that synchronization of chaos may also be achieved by a nonlinear feedback without decomposing the original system. They apply the idea to the Lorentz system, and discuss several forms of nonlinear feedbacks by Lyapunov function and numerical method

The multi-order envelope periodic solutions to the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Xiao Yafeng; Xue Haili; Zhang Hongqing

2011-01-01

Based on Jacobi elliptic function and the Lame equation, the perturbation method is applied to get the multi-order envelope periodic solutions of the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation. These multi-order envelope periodic solutions can degenerate into the different envelope solitary solutions. (authors)

Influence of Ultrasonic Nonlinear Propagation on Hydrophone Calibration Using Two-Transducer Reciprocity Method

Science.gov (United States)

Yoshioka, Masahiro; Sato, Sojun; Kikuchi, Tsuneo; Matsuda, Yoichi

2006-05-01

In this study, the influence of ultrasonic nonlinear propagation on hydrophone calibration by the two-transducer reciprocity method is investigated quantitatively using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation. It is proposed that the correction for the diffraction and attenuation of ultrasonic waves used in two-transducer reciprocity calibration can be derived using the KZK equation to remove the influence of nonlinear propagation. The validity of the correction is confirmed by comparing the sensitivities calibrated by the two-transducer reciprocity method and laser interferometry.

Global Analysis of Nonlinear Dynamics

CERN Document Server

Luo, Albert

2012-01-01

Global Analysis of Nonlinear Dynamics collects chapters on recent developments in global analysis of non-linear dynamical systems with a particular emphasis on cell mapping methods developed by Professor C.S. Hsu of the University of California, Berkeley. This collection of contributions prepared by a diverse group of internationally recognized researchers is intended to stimulate interests in global analysis of complex and high-dimensional nonlinear dynamical systems, whose global properties are largely unexplored at this time. This book also: Presents recent developments in global analysis of non-linear dynamical systems Provides in-depth considerations and extensions of cell mapping methods Adopts an inclusive style accessible to non-specialists and graduate students Global Analysis of Nonlinear Dynamics is an ideal reference for the community of nonlinear dynamics in different disciplines including engineering, applied mathematics, meteorology, life science, computational science, and medicine.  

Effect of weak nonlinearities on the plane waves in a plasma stream

International Nuclear Information System (INIS)

Seshadri, S.R.

1976-01-01

The effect of weak nonlinearities on the monochromatic plane waves in a cold infinite plasma stream is investigated for the case in which the waves are progressing parallel to the drift velocity. The fast and the slow space-charge waves undergo amplitude-dependent frequency and wave number shifts. There is a long time slow modulation of the amplitude of the electromagnetic mode which becomes unstable to this nonlinear wave modulation. The importance of using the relativistically correct equation of motion for predicting correctly the modulational stability of the electromagnetic mode is pointed out. (author)

Computer Simulation of Hydraulic Systems with Typical Nonlinear Characteristics

Directory of Open Access Journals (Sweden)

D. N. Popov

2017-01-01

Full Text Available The task was to synthesise an adjustable hydraulic system structure, the mathematical model of which takes into account its inherent nonlinearity. Its solution suggests using a successive computer simulations starting with a structure of the linearized stable hydraulic system, which is then complicated by including the essentially non-linear elements. The hydraulic system thus obtained may be unable to meet the Lyapunov stability criterion and be unstable. This can be eliminated through correcting elements. Control of correction results is provided according to the form of transition processes due to stepwise variation of the control signal.Computer simulation of a throttle-controlled electrohydraulic servo drive with the rotary output element illustrates the proposed method application. A constant pressure power source provides fluid feed for the drive under pressure.For drive simulation the following models were involved: the linear model, the model taking into consideration a non-linearity of the flow-dynamic characteristics of a spool-type valve, and the non-linear models that take into account the dry friction in the spool-type valve, the backlash in the steering angle sensor of the motor shaft.The paper shows possibility of damping oscillation caused by variable hydrodynamic forces through introducing a correction device.The list of references attached contains 16 sources, which were used to justify and explain certain factors of the automatic control theory and the fluid mechanics of unsteady flows.The article presents 6 block-diagrams of the electrohydraulic servo drive and their appropriate transition processes, which have been studied.

Logarithmic corrections in a quantization rule. The polaron spectrum

International Nuclear Information System (INIS)

Karasev, M.V.; Pereskokov, A.V.

1994-01-01

A nonlinear integrodifferential equation that arises in polaron theory is considered. The integral nonlinearity is given by a convolution with the Coulomb potential. Radially symmetric solutions are sought. In the semiclassical limit, an equation for the self-consistent potential is found and studied. The potential has a logarithmic singularity at the origin, and also a turning point at 1. The phase shifts at these points are determined. The quantization rule that takes into account the logarithmic corrections gives a simple asymptotic formula for the polaron spectrum. Global semiclassical solutions of the original nonlinear equation are constructed. 18 refs., 1 tab

Nonlinear (super)symmetries and amplitudes

Energy Technology Data Exchange (ETDEWEB)

Kallosh, Renata [Physics Department, Stanford University,382 Via Pueblo Mall, Stanford, CA 94305-4060 (United States)

2017-03-07

There is an increasing interest in nonlinear supersymmetries in cosmological model building. Independently, elegant expressions for the all-tree amplitudes in models with nonlinear symmetries, like D3 brane Dirac-Born-Infeld-Volkov-Akulov theory, were recently discovered. Using the generalized background field method we show how, in general, nonlinear symmetries of the action, bosonic and fermionic, constrain amplitudes beyond soft limits. The same identities control, for example, bosonic E{sub 7(7)} scalar sector symmetries as well as the fermionic goldstino symmetries. We present a universal derivation of the vanishing amplitudes in the single (bosonic or fermionic) soft limit. We explain why, universally, the double-soft limit probes the coset space algebra. We also provide identities describing the multiple-soft limit. We discuss loop corrections to N≥5 supergravity, to the D3 brane, and the UV completion of constrained multiplets in string theory.

Non-equilibrium condensation process in holographic superconductor with nonlinear electrodynamics

Energy Technology Data Exchange (ETDEWEB)

Liu, Yunqi; Gong, Yungui [School of Physics, Huazhong University of Science and Technology,Wuhan, Hubei 430074 (China); Wang, Bin [IFSA Collaborative Innovation Center, Department of Physics and Astronomy, Shanghai Jiao Tong University,Shanghai 200240 (China)

2016-02-17

We study the non-equilibrium condensation process in a holographic superconductor with nonlinear corrections to the U(1) gauge field. We start with an asymptotic Anti-de-Sitter(AdS) black hole against a complex scalar perturbation at the initial time, and solve the dynamics of the gravitational systems in the bulk. When the black hole temperature T is smaller than a critical value T{sub c}, the scalar perturbation grows exponentially till saturation, the final state of spacetime approaches to a hairy black hole. In the bulk theory, we find the clue of the influence of nonlinear corrections in the gauge filed on the process of the scalar field condensation. We show that the bulk dynamics in the non-equilibrium process is completely consistent with the observations on the boundary order parameter. Furthermore we examine the time evolution of horizons in the bulk non-equilibrium transformation process from the bald AdS black hole to the AdS hairy hole. Both the evolution of apparent and event horizons show that the original AdS black hole configuration requires more time to finish the transformation to become a hairy black hole if there is nonlinear correction to the electromagnetic field. We generalize our non-equilibrium discussions to the holographic entanglement entropy and find that the holographic entanglement entropy can give us further understanding of the influence of the nonlinearity in the gauge field on the scalar condensation.

A Weakly Nonlinear Model for Kelvin–Helmholtz Instability in Incompressible Fluids

International Nuclear Information System (INIS)

Li-Feng, Wang; Wen-Hua, Ye; Zheng-Feng, Fan; Chuang, Xue; Ying-Jun, Li

2009-01-01

A weakly nonlinear model is proposed for the Kelvin–Helmholtz instability in two-dimensional incompressible fluids by expanding the perturbation velocity potential to third order. The third-order harmonic generation effects of single-mode perturbation are analyzed, as well as the nonlinear correction to the exponential growth of the fundamental modulation. The weakly nonlinear results are supported by numerical simulations. Density and resonance effects exist in the development of mode coupling. (fundamental areas of phenomenology (including applications))

Differential Polarization Nonlinear Optical Microscopy with Adaptive Optics Controlled Multiplexed Beams

Directory of Open Access Journals (Sweden)

Virginijus Barzda

2013-09-01

Full Text Available Differential polarization nonlinear optical microscopy has the potential to become an indispensable tool for structural investigations of ordered biological assemblies and microcrystalline aggregates. Their microscopic organization can be probed through fast and sensitive measurements of nonlinear optical signal anisotropy, which can be achieved with microscopic spatial resolution by using time-multiplexed pulsed laser beams with perpendicular polarization orientations and photon-counting detection electronics for signal demultiplexing. In addition, deformable membrane mirrors can be used to correct for optical aberrations in the microscope and simultaneously optimize beam overlap using a genetic algorithm. The beam overlap can be achieved with better accuracy than diffraction limited point-spread function, which allows to perform polarization-resolved measurements on the pixel-by-pixel basis. We describe a newly developed differential polarization microscope and present applications of the differential microscopy technique for structural studies of collagen and cellulose. Both, second harmonic generation, and fluorescence-detected nonlinear absorption anisotropy are used in these investigations. It is shown that the orientation and structural properties of the fibers in biological tissue can be deduced and that the orientation of fluorescent molecules (Congo Red, which label the fibers, can be determined. Differential polarization microscopy sidesteps common issues such as photobleaching and sample movement. Due to tens of megahertz alternating polarization of excitation pulses fast data acquisition can be conveniently applied to measure changes in the nonlinear signal anisotropy in dynamically changing in vivo structures.

Analysis and Correction of Diffraction Effect on the B/A Measurement at High Frequencies

Science.gov (United States)

Zhang, Dong; Gong, Xiu-Fen; Liu, Xiao-Zhou; Kushibiki, Jun-ichi; Nishino, Hideo

2004-01-01

A numerical method is developed to analyse and to correct the diffraction effect in the measurement of acoustic nonlinearity parameter B/A at high frequencies. By using the KZK nonlinear equation and the superposition approach of Gaussian beams, an analytical model is derived to describe the second harmonic generation through multi-layer medium SiO2/liquid specimen/SiO2. Frequency dependence of the nonlinear characterization curve for water in 110-155 MHz is numerically and experimentally investigated. With the measured dip position and the new model, values of B/A for water are evaluated. The results show that the present method can effectively correct the diffraction effect in the measurement.

Nonlinear Regression with R

CERN Document Server

Ritz, Christian; Parmigiani, Giovanni

2009-01-01

R is a rapidly evolving lingua franca of graphical display and statistical analysis of experiments from the applied sciences. This book provides a coherent treatment of nonlinear regression with R by means of examples from a diversity of applied sciences such as biology, chemistry, engineering, medicine and toxicology.

Tunable Resonators for Nonlinear Modal Interactions

KAUST Repository

Ramini, Abdallah; Hajjaj, Amal Z.; Younis, Mohammad I.

2016-01-01

Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.

Tunable Resonators for Nonlinear Modal Interactions

KAUST Repository

Ramini, Abdallah

2016-10-04

Understanding the various mechanisms of nonlinear mode coupling in micro and nano resonators has become an imminent necessity for their successful implementation in practical applications. However, consistent, repeatable, and flexible experimental procedures to produce nonlinear mode coupling are lacking, and hence research into well-controlled experimental conditions is crucial. Here, we demonstrate well-controlled and repeatable experiments to study nonlinear mode coupling among micro and nano beam resonators. Such experimental approach can be applied to other micro and nano structures to help study their nonlinear interactions and exploit them for higher sensitive and less noisy responses. Using electrothermal tuning and electrostatic excitation, we demonstrate three different kinds of nonlinear interactions among the first and third bending modes of vibrations of slightly curved beams (arches): two-one internal resonance, three-one internal resonance, and mode veering (near crossing). The experimental procedure is repeatable, highly flexible, do not require special or precise fabrication, and is conducted in air and at room temperature. This approach can be applied to other micro and nano structures, which come naturally curved due to fabrication imperfections, such as CNTs, and hence lays the foundation to deeply investigate the nonlinear mode coupling in these structures in a consistent way.

Film thickness measurement based on nonlinear phase analysis using a Linnik microscopic white-light spectral interferometer.

Science.gov (United States)

Guo, Tong; Chen, Zhuo; Li, Minghui; Wu, Juhong; Fu, Xing; Hu, Xiaotang

2018-04-20

Based on white-light spectral interferometry and the Linnik microscopic interference configuration, the nonlinear phase components of the spectral interferometric signal were analyzed for film thickness measurement. The spectral interferometric signal was obtained using a Linnik microscopic white-light spectral interferometer, which includes the nonlinear phase components associated with the effective thickness, the nonlinear phase error caused by the double-objective lens, and the nonlinear phase of the thin film itself. To determine the influence of the effective thickness, a wavelength-correction method was proposed that converts the effective thickness into a constant value; the nonlinear phase caused by the effective thickness can then be determined and subtracted from the total nonlinear phase. A method for the extraction of the nonlinear phase error caused by the double-objective lens was also proposed. Accurate thickness measurement of a thin film can be achieved by fitting the nonlinear phase of the thin film after removal of the nonlinear phase caused by the effective thickness and by the nonlinear phase error caused by the double-objective lens. The experimental results demonstrated that both the wavelength-correction method and the extraction method for the nonlinear phase error caused by the double-objective lens improve the accuracy of film thickness measurements.

To Apply Microdosing or Not? Recommendations to Single Out Compounds with Non-Linear Pharmacokinetics

NARCIS (Netherlands)

Bosgra, S.; Vlaming, M.L.H.; Vaes, W.H.J.

2015-01-01

Non-linearities occur no more frequently between microdose and therapeutic dose studies than in therapeutic range ascending-dose studies. Most non-linearities are due to known saturable processes, and can be foreseen by integrating commonly available preclinical data. The guidance presented here may

Discrete- and finite-bandwidth-frequency distributions in nonlinear stability applications

Science.gov (United States)

Kuehl, Joseph J.

2017-02-01

A new "wave packet" formulation of the parabolized stability equations method is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening, and results in disturbance representation more consistent with the experiment than traditional formulations. A Mach 6 flared-cone example is presented.

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

Science.gov (United States)

Bache, Morten; Lavrinenko, Andrei V.

2017-09-01

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

Corrections to the rho-parameter due to a heavy Higgs particle

International Nuclear Information System (INIS)

Bij, J.J. van der.

1983-01-01

The main part of this thesis is concerned with the calculation of the two-loop contribution to the rho-parameter, i.e. the ratio of charged and neutral vector boson masses, due to a heavy Higgs particle. It involves the calculation of a large number of Feynman diagrams. The result is that a contribution growing like m 2 exists (m = Higgs mass), but it does not correspond to the poles at n=3 in the non-linear model. First the model is introduced, the precise definition of rho is given and the formal connection with the non-linear model is derived. Then the one-loop infinities are calculated. It is shown that no m 2 corrections are observable in one loop and the log m 2 correction to rho is calculated. Finally the two-loop correction to rho is calculated. (Auth.)

Ultrafast nonlinear optics

CERN Document Server

Leburn, Christopher; Reid, Derryck

2013-01-01

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

Corrections to the Eckhaus' stability criterion for one-dimensional stationary structures

Science.gov (United States)

Malomed, B. A.; Staroselsky, I. E.; Konstantinov, A. B.

1989-01-01

Two amendments to the well-known Eckhaus' stability criterion for small-amplitude non-linear structures generated by weak instability of a spatially uniform state of a non-equilibrium one-dimensional system against small perturbations with finite wavelengths are obtained. Firstly, we evaluate small corrections to the main Eckhaus' term which, on the contrary so that term, do not have a universal form. Comparison of those non-universal corrections with experimental or numerical results gives a possibility to select a more relevant form of an effective nonlinear evolution equation. In particular, the comparison with such results for convective rolls and Taylor vortices gives arguments in favor of the Swift-Hohenberg equation. Secondly, we derive an analog of the Eckhaus criterion for systems degenerate in the sense that in an expansion of their non-linear parts in powers of dynamical variables, the second and third degree terms are absent.

Applying a nonlinear, pitch-catch, ultrasonic technique for the detection of kissing bonds in friction stir welds.

Science.gov (United States)

Delrue, Steven; Tabatabaeipour, Morteza; Hettler, Jan; Van Den Abeele, Koen

2016-05-01

Friction stir welding (FSW) is a promising technology for the joining of aluminum alloys and other metallic admixtures that are hard to weld by conventional fusion welding. Although FSW generally provides better fatigue properties than traditional fusion welding methods, fatigue properties are still significantly lower than for the base material. Apart from voids, kissing bonds for instance, in the form of closed cracks propagating along the interface of the stirred and heat affected zone, are inherent features of the weld and can be considered as one of the main causes of a reduced fatigue life of FSW in comparison to the base material. The main problem with kissing bond defects in FSW, is that they currently are very difficult to detect using existing NDT methods. Besides, in most cases, the defects are not directly accessible from the exposed surface. Therefore, new techniques capable of detecting small kissing bond flaws need to be introduced. In the present paper, a novel and practical approach is introduced based on a nonlinear, single-sided, ultrasonic technique. The proposed inspection technique uses two single element transducers, with the first transducer transmitting an ultrasonic signal that focuses the ultrasonic waves at the bottom side of the sample where cracks are most likely to occur. The large amount of energy at the focus activates the kissing bond, resulting in the generation of nonlinear features in the wave propagation. These nonlinear features are then captured by the second transducer operating in pitch-catch mode, and are analyzed, using pulse inversion, to reveal the presence of a defect. The performance of the proposed nonlinear, pitch-catch technique, is first illustrated using a numerical study of an aluminum sample containing simple, vertically oriented, incipient cracks. Later, the proposed technique is also applied experimentally on a real-life friction stir welded butt joint containing a kissing bond flaw. Copyright © 2016

Theory and design of nonlinear metamaterials

Science.gov (United States)

Rose, Alec Daniel

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

Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

Science.gov (United States)

Zhu, Yanqui; Cohn, Stephen E.; Todling, Ricardo

1999-01-01

The Kalman filter is the optimal filter in the presence of known gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions. Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz model as well as more realistic models of the means and atmosphere. A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter situations to allow for correct update of the ensemble members. The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to be quite puzzling in that results state estimates are worse than for their filter analogue. In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use the Lorenz model to test and compare the behavior of a variety of implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Nonlinear quantum fluid equations for a finite temperature Fermi plasma

International Nuclear Information System (INIS)

Eliasson, Bengt; Shukla, Padma K

2008-01-01

Nonlinear quantum electron fluid equations are derived, taking into account the moments of the Wigner equation and by using the Fermi-Dirac equilibrium distribution for electrons with an arbitrary temperature. A simplified formalism with the assumptions of incompressibility of the distribution function is used to close the moments in velocity space. The nonlinear quantum diffraction effects into the fluid equations are incorporated. In the high-temperature limit, we retain the nonlinear fluid equations for a dense hot plasma and in the low-temperature limit, we retain the correct fluid equations for a fully degenerate plasma

The importance of non-linearities in modern proton synchrotrons

International Nuclear Information System (INIS)

Wilson, E.J.N.

1977-01-01

The paper outlines the physics and mathematics of non-linear field errors in the quide fields of accelerators, with particular reference to large accelerators such as the SPS. These non-linearities give rise to closed orbital distortions and non-linear resonances or stopbands. Both of these effects are briefly discussed and the use of resonances for slow beam extraction is also described. Another problem considered is that of chromaticity of the particle beam. The use of sextupoles to correct chromaticity and the Landau damping of beam instabilities using octupoles are also discussed. In the final section the application of Hamiltonian mechanics to non-linearities is demonstrated. The author concludes that the effect of non-linearities on particle dynamics may place a more severe limit on intensity and storage time in large rings than any other effect in transverse phase space. (B.D.)

Non-Linear Approximation of Bayesian Update

KAUST Repository

Litvinenko, Alexander

2016-01-01

We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

Non-Linear Approximation of Bayesian Update

KAUST Repository

Litvinenko, Alexander

2016-06-23

We develop a non-linear approximation of expensive Bayesian formula. This non-linear approximation is applied directly to Polynomial Chaos Coefficients. In this way, we avoid Monte Carlo sampling and sampling error. We can show that the famous Kalman Update formula is a particular case of this update.

Squeezing corrections to the Bloch equations

International Nuclear Information System (INIS)

Abundo, M.; Accardi, L.

1991-01-01

The general analysis of quantum noise shows that a squeezing noise can produce quadratic nonlinearities in the Langevin equations leading to the Bloch equations. These quadratic nonlinearities are governed by the imaginary part of the off-diagonal terms of the covariance of the noise (the squeezing terms) and imply a correction to the usual form of the Bloch equations. Here the case of spin-one nuclei subjected to squeezing noises of particular type is studied numerically. It is shown that the corrections to the Bloch equations, suggested by the theory, to the behaviour of the macroscopic nuclear polarization in a scale of times of the order of the relaxation time can be quite substantial. In the equilibrium regime, even if the qualitative behaviour of the system is the same (exponential decay), the numerical equilibrium values predicted by the theory are consistently different from those predicted by the usual Bloch equation. It is suggested that this difference might be used to test experimentally the observable effects of squeezing noises

A study of discrete nonlinear systems

International Nuclear Information System (INIS)

Dhillon, H.S.

2001-04-01

An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations

International Nuclear Information System (INIS)

Yomba, Emmanuel

2008-01-01

With the aid of symbolic computation, a generalized auxiliary equation method is proposed to construct more general exact solutions to two types of NLPDEs. First, we present new family of solutions to a nonlinear Klein-Gordon equation, by using this auxiliary equation method including a new first-order nonlinear ODE with six-degree nonlinear term proposed by Sirendaoreji. Then, we apply an indirect F-function method very close to the F-expansion method to solve the generalized Camassa-Holm equation with fully nonlinear dispersion and fully nonlinear convection C(l,n,p). Taking advantage of the new first-order nonlinear ODE with six degree nonlinear term, this indirect F-function method is used to map the solutions of C(l,n,p) equations to those of that nonlinear ODE. As a result, we can successfully obtain in a unified way, many exact solutions

International Conference on Applications in Nonlinear Dynamics

CERN Document Server

Longhini, Patrick; Palacios, Antonio

2017-01-01

This book presents collaborative research works carried out by experimentalists and theorists around the world in the field of nonlinear dynamical systems. It provides a forum for applications of nonlinear systems while solving practical problems in science and engineering. Topics include: Applied Nonlinear Optics, Sensor, Radar & Communication Signal Processing, Nano Devices, Nonlinear Biomedical Applications, Circuits & Systems, Coupled Nonlinear Oscillator, Precision Timing Devices, Networks, and other contemporary topics in the general field of Nonlinear Science. This book provides a comprehensive report of the various research projects presented at the International Conference on Applications in Nonlinear Dynamics (ICAND 2016) held in Denver, Colorado, 2016. It can be a valuable tool for scientists and engineering interested in connecting ideas and methods in nonlinear dynamics with actual design, fabrication and implementation of engineering applications or devices.

Nonlinearities Distribution Homotopy Perturbation Method Applied to Solve Nonlinear Problems: Thomas-Fermi Equation as a Case Study

Directory of Open Access Journals (Sweden)

U. Filobello-Nino

2015-01-01

Full Text Available We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM. Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results.

Nonlinear dynamics in biological systems

CERN Document Server

Carballido-Landeira, Jorge

2016-01-01

This book presents recent research results relating to applications of nonlinear dynamics, focusing specifically on four topics of wide interest: heart dynamics, DNA/RNA, cell mobility, and proteins. The book derives from the First BCAM Workshop on Nonlinear Dynamics in Biological Systems, held in June 2014 at the Basque Center of Applied Mathematics (BCAM). At this international meeting, researchers from different but complementary backgrounds, including molecular dynamics, physical chemistry, bio-informatics and biophysics, presented their most recent results and discussed the future direction of their studies using theoretical, mathematical modeling and experimental approaches. Such was the level of interest stimulated that the decision was taken to produce this publication, with the organizers of the event acting as editors. All of the contributing authors are researchers working on diverse biological problems that can be approached using nonlinear dynamics. The book will appeal especially to applied math...

Influence of heart rate in nonlinear HRV indices as a sampling rate effect evaluated on supine and standing

Directory of Open Access Journals (Sweden)

Juan Bolea

2016-11-01

Full Text Available The purpose of this study is to characterize and attenuate the influence of mean heart rate (HR on nonlinear heart rate variability (HRV indices (correlation dimension, sample and approximate entropy as a consequence of being the HR the intrinsic sampling rate of HRV signal. This influence can notably alter nonlinear HRV indices and lead to biased information regarding autonomic nervous system (ANS modulation.First, a simulation study was carried out to characterize the dependence of nonlinear HRV indices on HR assuming similar ANS modulation. Second, two HR-correction approaches were proposed: one based on regression formulas and another one based on interpolating RR time series. Finally, standard and HR-corrected HRV indices were studied in a body position change database.The simulation study showed the HR-dependence of non-linear indices as a sampling rate effect, as well as the ability of the proposed HR-corrections to attenuate mean HR influence. Analysis in a body position changes database shows that correlation dimension was reduced around 21% in median values in standing with respect to supine position (p < 0.05, concomitant with a 28% increase in mean HR (p < 0.05. After HR-correction, correlation dimension decreased around 18% in standing with respect to supine position, being the decrease still significant. Sample and approximate entropy showed similar trends.HR-corrected nonlinear HRV indices could represent an improvement in their applicability as markers of ANS modulation when mean HR changes.

Software Package for Optics Measurement and Correction in the LHC

CERN Document Server

Aiba, M; Tomas, R; Vanbavinckhove, G

2010-01-01

A software package has been developed for the LHC on-line optics measurement and correction. This package includes several different algorithms to measure phase advance, beta functions, dispersion, coupling parameters and even some non-linear terms. A Graphical User Interface provides visualization tools to compare measurements to model predictions, fit analytical formula, localize error sources and compute and send corrections to the hardware.

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

Science.gov (United States)

Farokhi, Hamed; Païdoussis, Michael P.; Misra, Arun K.

2018-04-01

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

Report from LHC MD 2158: IR-nonlinear studies

CERN Document Server

Maclean, Ewen Hamish; Cruz Alaniz, Emilia; Dalena, Barbara; Dilly, Joschua Werner; Fol, Elena; Giovannozzi, Massimo; Hofer, Michael; Malina, Lukas; Persson, Tobias Hakan Bjorn; Coello De Portugal - Martinez Vazquez, Jaime Maria; Skowronski, Piotr Krzysztof; Solfaroli Camillocci, Matteo; Tomas Garcia, Rogelio; Garcia-Tabares Valdivieso, Ana; Wegscheider, Andreas; CERN. Geneva. ATS Department

2018-01-01

For the first time the LHC is running for luminosity-production with local corrections for nonlinear errors in the ATLAS and CMS insertions. While a major step forward in LHC optics commissioning strategy (and one which has yielded clear operational benefits) considerable challenges remain to be overcome, both in regard to the optimization of LHC optics and in order to ensure successful commissioning of the High-Luminosity LHC. MD 2158 sought to follow up several aspects of the 2017 nonlinear optics commissioning which are not yet understood, and by enhancing sextupole and dodecapole sources in the ATLAS and CMS insertions explore the prospects for linear and nonlinear optics commissioning in the HL-LHC.

Adaptive regression for modeling nonlinear relationships

CERN Document Server

Knafl, George J

2016-01-01

This book presents methods for investigating whether relationships are linear or nonlinear and for adaptively fitting appropriate models when they are nonlinear. Data analysts will learn how to incorporate nonlinearity in one or more predictor variables into regression models for different types of outcome variables. Such nonlinear dependence is often not considered in applied research, yet nonlinear relationships are common and so need to be addressed. A standard linear analysis can produce misleading conclusions, while a nonlinear analysis can provide novel insights into data, not otherwise possible. A variety of examples of the benefits of modeling nonlinear relationships are presented throughout the book. Methods are covered using what are called fractional polynomials based on real-valued power transformations of primary predictor variables combined with model selection based on likelihood cross-validation. The book covers how to formulate and conduct such adaptive fractional polynomial modeling in the s...

Nonlinear oscillation system of mass with serial linear and nonlinear springs

DEFF Research Database (Denmark)

Seyedalizadeh Ganji,, S.R; Barari, Amin; Karimpour, S

2013-01-01

In this paper, two powerful methods called Max–Min and parameter expansion have been applied for the determination of the periodic solutions of the nonlinear free vibration of a conservative oscillator with inertia and static type cubic nonlinearities. It is found that these methods introduce two...... alternatives to overcome the difficulty of capturing the periodic behavior of the solution, as the most evident characteristic of oscillators. It can be clearly observed that approximate frequencies and periodic solutions are in excellent agreement with the exact ones. First approximation leads to high...

Nonlinear analysis of pupillary dynamics.

Science.gov (United States)

Onorati, Francesco; Mainardi, Luca Tommaso; Sirca, Fabiola; Russo, Vincenzo; Barbieri, Riccardo

2016-02-01

Pupil size reflects autonomic response to different environmental and behavioral stimuli, and its dynamics have been linked to other autonomic correlates such as cardiac and respiratory rhythms. The aim of this study is to assess the nonlinear characteristics of pupil size of 25 normal subjects who participated in a psychophysiological experimental protocol with four experimental conditions, namely “baseline”, “anger”, “joy”, and “sadness”. Nonlinear measures, such as sample entropy, correlation dimension, and largest Lyapunov exponent, were computed on reconstructed signals of spontaneous fluctuations of pupil dilation. Nonparametric statistical tests were performed on surrogate data to verify that the nonlinear measures are an intrinsic characteristic of the signals. We then developed and applied a piecewise linear regression model to detrended fluctuation analysis (DFA). Two joinpoints and three scaling intervals were identified: slope α0, at slow time scales, represents a persistent nonstationary long-range correlation, whereas α1 and α2, at middle and fast time scales, respectively, represent long-range power-law correlations, similarly to DFA applied to heart rate variability signals. Of the computed complexity measures, α0 showed statistically significant differences among experimental conditions (pnonlinear dynamics, (b) three well-defined and distinct long-memory processes exist at different time scales, and (c) autonomic stimulation is partially reflected in nonlinear dynamics. (c) autonomic stimulation is partially reflected in nonlinear dynamics.

Multiorder nonlinear diffraction in frequency doubling processes

DEFF Research Database (Denmark)

Saltiel, Solomon M.; Neshev, Dragomir N.; Krolikowski, Wieslaw

2009-01-01

We analyze experimentally light scattering from 2 nonlinear gratings and observe two types of second-harmonic frequency-scattering processes. The first process is identified as Raman–Nath type nonlinear diffraction that is explained by applying only transverse phase-matching conditions. The angular...... position of this type of diffraction is defined by the ratio of the second-harmonic wavelength and the grating period. In contrast, the second type of nonlinear scattering process is explained by the longitudinal phase matching only, being insensitive to the nonlinear grating...

Correction for polychromatic aberration in computed tomography images

International Nuclear Information System (INIS)

Naparstek, A.

1979-01-01

A method and apparatus for correcting a computed tomography image for polychromatic aberration caused by the non-linear interaction (i.e. the energy dependent attenuation characteristics) of different body constituents, such as bone and soft tissue, with a polychromatic X-ray beam are described in detail. An initial image is conventionally computed from path measurements made as source and detector assembly scan a body section. In the improvement, each image element of the initial computed image representing attenuation is recorded in a store and is compared with two thresholds, one representing bone and the other soft tissue. Depending on the element value relative to the thresholds, a proportion of the respective constituent is allocated to that element location and corresponding bone and soft tissue projections are determined and stored. An error projection generator calculates projections of polychromatic aberration errors in the raw image data from recalled bone and tissue projections using a multidimensional polynomial function which approximates the non-linear interaction involved. After filtering, these are supplied to an image reconstruction computer to compute image element correction values which are subtracted from raw image element values to provide a corrected reconstructed image for display. (author)

A simple approach to nonlinear oscillators

International Nuclear Information System (INIS)

Ren Zhongfu; He Jihuan

2009-01-01

A very simple and effective approach to nonlinear oscillators is suggested. Anyone with basic knowledge of advanced calculus can apply the method to finding approximately the amplitude-frequency relationship of a nonlinear oscillator. Some examples are given to illustrate its extremely simple solution procedure and an acceptable accuracy of the obtained solutions.

Detector correction in large container inspection systems

CERN Document Server

Kang Ke Jun; Chen Zhi Qiang

2002-01-01

In large container inspection systems, the image is constructed by parallel scanning with a one-dimensional detector array with a linac used as the X-ray source. The linear nonuniformity and nonlinearity of multiple detectors and the nonuniform intensity distribution of the X-ray sector beam result in horizontal striations in the scan image. This greatly impairs the image quality, so the image needs to be corrected. The correction parameters are determined experimentally by scaling the detector responses at multiple points with logarithm interpolation of the results. The horizontal striations are eliminated by modifying the original image data with the correction parameters. This method has proven to be effective and applicable in large container inspection systems

Nonlinear rheology of complex fluid-fluid interfaces

NARCIS (Netherlands)

Sagis, L.M.C.; Fischer, P.

2014-01-01

Fluid–fluid interfaces stabilized by proteins, protein aggregates, polymers, or colloidal particles, tend to have a complex microstructure. Their response to an applied deformation is often highly nonlinear, even at small deformation (rates). The nonlinearity of the response is a result of changes

Nonlinear dynamic range transformation in visual communication channels.

Science.gov (United States)

Alter-Gartenberg, R

1996-01-01

The article evaluates nonlinear dynamic range transformation in the context of the end-to-end continuous-input/discrete processing/continuous-display imaging process. Dynamic range transformation is required when we have the following: (i) the wide dynamic range encountered in nature is compressed into the relatively narrow dynamic range of the display, particularly for spatially varying irradiance (e.g., shadow); (ii) coarse quantization is expanded to the wider dynamic range of the display; and (iii) nonlinear tone scale transformation compensates for the correction in the camera amplifier.

SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS

KAUST Repository

Desmal, Abdulla

2015-07-29

A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.

Nonlinear Optics: Principles and Applications

DEFF Research Database (Denmark)

Rottwitt, Karsten; Tidemand-Lichtenberg, Peter

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

A solution of nonlinear equation for the gravity wave spectra from Adomian decomposition method: a first approach

Directory of Open Access Journals (Sweden)

Antonio Gledson Goulart

2013-12-01

Full Text Available In this paper, the equation for the gravity wave spectra in mean atmosphere is analytically solved without linearization by the Adomian decomposition method. As a consequence, the nonlinear nature of problem is preserved and the errors found in the results are only due to the parameterization. The results, with the parameterization applied in the simulations, indicate that the linear solution of the equation is a good approximation only for heights shorter than ten kilometers, because the linearization the equation leads to a solution that does not correctly describe the kinetic energy spectra.

Device Applications of Nonlinear Dynamics

CERN Document Server

Baglio, Salvatore

2006-01-01

This edited book is devoted specifically to the applications of complex nonlinear dynamic phenomena to real systems and device applications. While in the past decades there has been significant progress in the theory of nonlinear phenomena under an assortment of system boundary conditions and preparations, there exist comparatively few devices that actually take this rich behavior into account. "Device Applications of Nonlinear Dynamics" applies and exploits this knowledge to make devices which operate more efficiently and cheaply, while affording the promise of much better performance. Given the current explosion of ideas in areas as diverse as molecular motors, nonlinear filtering theory, noise-enhanced propagation, stochastic resonance and networked systems, the time is right to integrate the progress of complex systems research into real devices.

Geometry effect on energy transfer rate in a coupled-quantum-well structure: nonlinear regime

International Nuclear Information System (INIS)

Salavati-fard, T; Vazifehshenas, T

2014-01-01

We study theoretically the effect of geometry on the energy transfer rate at nonlinear regime in a coupled-quantum-well system using the balance equation approach. To investigate comparatively the effect of both symmetric and asymmetric geometry, different structures are considered. The random phase approximation dynamic dielectric function is employed to include the contributions from both quasiparticle and plasmon excitations. Also, the short-range exchange interaction is taken into account through the Hubbard approximation. Our numerical results show that the energy transfer rate increases by increasing the well thicknesses in symmetric structures. Furthermore, by increasing spatial asymmetry, the energy transfer rate decreases for the electron temperature range of interest. From numerical calculations, it is obtained that the nonlinear energy transfer rate is proportional to the square of electron drift velocity in all structures and also, found that the influence of Hubbard local field correction on the energy transfer rate gets weaker by increasing the strength of applied electric field. (paper)

Nonlinear single-spin spectrum analyzer.

Science.gov (United States)

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.

Retrieval of high-order susceptibilities of nonlinear metamaterials

International Nuclear Information System (INIS)

Wang Zhi-Yu; Qiu Jin-Peng; Chen Hua; Mo Jiong-Jiong; Yu Fa-Xin

2017-01-01

Active metamaterials embedded with nonlinear elements are able to exhibit strong nonlinearity in microwave regime. However, existing S -parameter based parameter retrieval approaches developed for linear metamaterials do not apply in nonlinear cases. In this paper, a retrieval algorithm of high-order susceptibilities for nonlinear metamaterials is derived. Experimental demonstration shows that, by measuring the power level of each harmonic while sweeping the incident power, high-order susceptibilities of a thin-layer nonlinear metamaterial can be effectively retrieved. The proposedapproach can be widely used in the research of active metamaterials. (paper)

Rapidly rotating pulsar radiation in vacuum nonlinear electrodynamics

Energy Technology Data Exchange (ETDEWEB)

Denisov, V.I.; Pimenov, A.B.; Sokolov, V.A. [Moscow State University, Physics Department, Moscow (Russian Federation); Denisova, I.P. [Moscow Aviation Institute (National Research University), Moscow (Russian Federation)

2016-11-15

In this paper we investigate the corrections of vacuum nonlinear electrodynamics on rapidly rotating pulsar radiation and spin-down in the perturbative QED approach (post-Maxwellian approximation). An analytical expression for the pulsar's radiation intensity has been obtained and analyzed. (orig.)

Nonlinear optomechanical measurement of mechanical motion

DEFF Research Database (Denmark)

Brawley, G.A.; Vanner, M R; Larsen, Peter Emil

2016-01-01

Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing with oth......Precision measurement of nonlinear observables is an important goal in all facets of quantum optics. This allows measurement-based non-classical state preparation, which has been applied to great success in various physical systems, and provides a route for quantum information processing...... with otherwise linear interactions. In cavity optomechanics much progress has been made using linear interactions and measurement, but observation of nonlinear mechanical degrees-of-freedom remains outstanding. Here we report the observation of displacement-squared thermal motion of a micro-mechanical resonator...... by exploiting the intrinsic nonlinearity of the radiation-pressure interaction. Using this measurement we generate bimodal mechanical states of motion with separations and feature sizes well below 100 pm. Future improvements to this approach will allow the preparation of quantum superposition states, which can...

Input saturation in nonlinear multivariable processes resolved by nonlinear decoupling

Directory of Open Access Journals (Sweden)

Jens G. Balchen

1995-04-01

Full Text Available A new method is presented for the resolution of the problem of input saturation in nonlinear multivariable process control by means of elementary nonlinear decoupling (END. Input saturation can have serious consequences particularly in multivariable control because it may lead to very undesirable system behaviour and quite often system instability. Many authors have searched for systematic techniques for designing multivariable control systems in which saturation may occur in any of the control variables (inputs, manipulated variables. No generally accepted method seems to have been presented so far which gives a solution in closed form. The method of elementary nonlinear decoupling (END can be applied directly to the case of saturation control variables by deriving as many control strategies as there are combinations of saturating control variables. The method is demonstrated by the multivariable control of a simulated Fluidized Catalytic Cracker (FCC with very convincing results.

Nonlinear Dot Plots.

Science.gov (United States)

Rodrigues, Nils; Weiskopf, Daniel

2018-01-01

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

Volterra Filtering for ADC Error Correction

Directory of Open Access Journals (Sweden)

J. Saliga

2001-09-01

Full Text Available Dynamic non-linearity of analog-to-digital converters (ADCcontributes significantly to the distortion of digitized signals. Thispaper introduces a new effective method for compensation such adistortion based on application of Volterra filtering. Considering ana-priori error model of ADC allows finding an efficient inverseVolterra model for error correction. Efficiency of proposed method isdemonstrated on experimental results.

A Novel Nonlinear Parameter Estimation Method of Soft Tissues

Directory of Open Access Journals (Sweden)

Qianqian Tong

2017-12-01

Full Text Available The elastic parameters of soft tissues are important for medical diagnosis and virtual surgery simulation. In this study, we propose a novel nonlinear parameter estimation method for soft tissues. Firstly, an in-house data acquisition platform was used to obtain external forces and their corresponding deformation values. To provide highly precise data for estimating nonlinear parameters, the measured forces were corrected using the constructed weighted combination forecasting model based on a support vector machine (WCFM_SVM. Secondly, a tetrahedral finite element parameter estimation model was established to describe the physical characteristics of soft tissues, using the substitution parameters of Young’s modulus and Poisson’s ratio to avoid solving complicated nonlinear problems. To improve the robustness of our model and avoid poor local minima, the initial parameters solved by a linear finite element model were introduced into the parameter estimation model. Finally, a self-adapting Levenberg–Marquardt (LM algorithm was presented, which is capable of adaptively adjusting iterative parameters to solve the established parameter estimation model. The maximum absolute error of our WCFM_SVM model was less than 0.03 Newton, resulting in more accurate forces in comparison with other correction models tested. The maximum absolute error between the calculated and measured nodal displacements was less than 1.5 mm, demonstrating that our nonlinear parameters are precise.

The chemistry and physics of nonlinear optical materials

International Nuclear Information System (INIS)

Velsko, S.P.; Eimerl, D.

1989-01-01

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

A nonlinear efficient layerwise finite element model for smart piezolaminated composites under strong applied electric field

International Nuclear Information System (INIS)

Kapuria, S; Yaqoob Yasin, M

2013-01-01

In this work, we present an electromechanically coupled efficient layerwise finite element model for the static response of piezoelectric laminated composite and sandwich plates, considering the nonlinear behavior of piezoelectric materials under strong electric field. The nonlinear model is developed consistently using a variational principle, considering a rotationally invariant second order nonlinear constitutive relationship, and full electromechanical coupling. In the piezoelectric layer, the electric potential is approximated to have a quadratic variation across the thickness, as observed from exact three dimensional solutions, and the equipotential condition of electroded piezoelectric surfaces is modeled using the novel concept of an electric node. The results predicted by the nonlinear model compare very well with the experimental data available in the literature. The effect of the piezoelectric nonlinearity on the static response and deflection/stress control is studied for piezoelectric bimorph as well as hybrid laminated plates with isotropic, angle-ply composite and sandwich substrates. For high electric fields, the difference between the nonlinear and linear predictions is large, and cannot be neglected. The error in the prediction of the smeared counterpart of the present theory with the same number of primary displacement unknowns is also examined. (paper)

q-Deformed nonlinear maps

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 64; Issue 3 ... Keywords. Nonlinear dynamics; logistic map; -deformation; Tsallis statistics. ... As a specific example, a -deformation procedure is applied to the logistic map. Compared ...

Nonlinear singular elliptic equations

International Nuclear Information System (INIS)

Dong Minh Duc.

1988-09-01

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

Nonlinear transport processes in tokamak plasmas. I. The collisional regimes

International Nuclear Information System (INIS)

Sonnino, Giorgio; Peeters, Philippe

2008-01-01

An application of the thermodynamic field theory (TFT) to transport processes in L-mode tokamak plasmas is presented. The nonlinear corrections to the linear ('Onsager') transport coefficients in the collisional regimes are derived. A quite encouraging result is the appearance of an asymmetry between the Pfirsch-Schlueter (P-S) ion and electron transport coefficients: the latter presents a nonlinear correction, which is absent for the ions, and makes the radial electron coefficients much larger than the former. Explicit calculations and comparisons between the neoclassical results and the TFT predictions for Joint European Torus (JET) plasmas are also reported. It is found that the nonlinear electron P-S transport coefficients exceed the values provided by neoclassical theory by a factor that may be of the order 10 2 . The nonlinear classical coefficients exceed the neoclassical ones by a factor that may be of order 2. For JET, the discrepancy between experimental and theoretical results for the electron losses is therefore significantly reduced by a factor 10 2 when the nonlinear contributions are duly taken into account but, there is still a factor of 10 2 to be explained. This is most likely due to turbulence. The expressions of the ion transport coefficients, determined by the neoclassical theory in these two regimes, remain unaltered. The low-collisional regimes, i.e., the plateau and the banana regimes, are analyzed in the second part of this work

An Excel Solver Exercise to Introduce Nonlinear Regression

Science.gov (United States)

Pinder, Jonathan P.

2013-01-01

Business students taking business analytics courses that have significant predictive modeling components, such as marketing research, data mining, forecasting, and advanced financial modeling, are introduced to nonlinear regression using application software that is a "black box" to the students. Thus, although correct models are…

A method to correct coordinate distortion in EBSD maps

International Nuclear Information System (INIS)

Zhang, Y.B.; Elbrønd, A.; Lin, F.X.

2014-01-01

Drift during electron backscatter diffraction mapping leads to coordinate distortions in resulting orientation maps, which affects, in some cases significantly, the accuracy of analysis. A method, thin plate spline, is introduced and tested to correct such coordinate distortions in the maps after the electron backscatter diffraction measurements. The accuracy of the correction as well as theoretical and practical aspects of using the thin plate spline method is discussed in detail. By comparing with other correction methods, it is shown that the thin plate spline method is most efficient to correct different local distortions in the electron backscatter diffraction maps. - Highlights: • A new method is suggested to correct nonlinear spatial distortion in EBSD maps. • The method corrects EBSD maps more precisely than presently available methods. • Errors less than 1–2 pixels are typically obtained. • Direct quantitative analysis of dynamic data are available after this correction

Nonlinear response time-dependent density functional theory combined with the effective fragment potential method

Energy Technology Data Exchange (ETDEWEB)

Zahariev, Federico; Gordon, Mark S., E-mail: mark@si.msg.chem.iastate.edu [Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)

2014-05-14

This work presents an extension of the linear response TDDFT/EFP method to the nonlinear-response regime together with the implementation of nonlinear-response TDDFT/EFP in the quantum-chemistry computer package GAMESS. Included in the new method is the ability to calculate the two-photon absorption cross section and to incorporate solvent effects via the EFP method. The nonlinear-response TDDFT/EFP method is able to make correct qualitative predictions for both gas phase values and aqueous solvent shifts of several important nonlinear properties.

Correction of SiPM temperature dependencies

International Nuclear Information System (INIS)

Kaplan, A.

2009-01-01

The performance of a high granular analogue hadronic calorimeter (AHCAL) using scintillator tiles with built-in Silicon Photomultiplier (SiPM) readout is reported. A muon beam is used for the minimum ionizing particle (MIP) based calibration of the single cells. The calibration chain including corrections for the non-linearity of the SiPM is presented. The voltage and temperature dependencies of the SiPM signal have been investigated using the versatile LED system of the AHCAL. Monitoring and correction methods are discussed. Measurements from the operation 2006 and 2007 at the CERN SPS test beam and data provided by the Institute for Theoretical and Experimental Physics (ITEP) in Moscow are compared.

Applying corrections to digitized data while digitizing magnetic chart

Digital Repository Service at National Institute of Oceanography (India)

Suresh, T.

data could be time consuming during online digitizing operation. Secondly, this could be more error prone if proper error detection and correction methods are not em- ployed. Here a simpler method is illustrated which has been used for digitizing...

Nonlinear vs. linear biasing in Trp-cage folding simulations

Energy Technology Data Exchange (ETDEWEB)

Spiwok, Vojtěch, E-mail: spiwokv@vscht.cz; Oborský, Pavel; Králová, Blanka [Department of Biochemistry and Microbiology, University of Chemistry and Technology, Prague, Technická 3, Prague 6 166 28 (Czech Republic); Pazúriková, Jana [Institute of Computer Science, Masaryk University, Botanická 554/68a, 602 00 Brno (Czech Republic); Křenek, Aleš [Institute of Computer Science, Masaryk University, Botanická 554/68a, 602 00 Brno (Czech Republic); Center CERIT-SC, Masaryk Univerzity, Šumavská 416/15, 602 00 Brno (Czech Republic)

2015-03-21

Biased simulations have great potential for the study of slow processes, including protein folding. Atomic motions in molecules are nonlinear, which suggests that simulations with enhanced sampling of collective motions traced by nonlinear dimensionality reduction methods may perform better than linear ones. In this study, we compare an unbiased folding simulation of the Trp-cage miniprotein with metadynamics simulations using both linear (principle component analysis) and nonlinear (Isomap) low dimensional embeddings as collective variables. Folding of the mini-protein was successfully simulated in 200 ns simulation with linear biasing and non-linear motion biasing. The folded state was correctly predicted as the free energy minimum in both simulations. We found that the advantage of linear motion biasing is that it can sample a larger conformational space, whereas the advantage of nonlinear motion biasing lies in slightly better resolution of the resulting free energy surface. In terms of sampling efficiency, both methods are comparable.

Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications

Science.gov (United States)

Pesaresi, L.; Salles, L.; Jones, A.; Green, J. S.; Schwingshackl, C. W.

2017-02-01

Underplatform dampers (UPD) are commonly used in aircraft engines to mitigate the risk of high-cycle fatigue failure of turbine blades. The energy dissipated at the friction contact interface of the damper reduces the vibration amplitude significantly, and the couplings of the blades can also lead to significant shifts of the resonance frequencies of the bladed disk. The highly nonlinear behaviour of bladed discs constrained by UPDs requires an advanced modelling approach to ensure that the correct damper geometry is selected during the design of the turbine, and that no unexpected resonance frequencies and amplitudes will occur in operation. Approaches based on an explicit model of the damper in combination with multi-harmonic balance solvers have emerged as a promising way to predict the nonlinear behaviour of UPDs correctly, however rigorous experimental validations are required before approaches of this type can be used with confidence. In this study, a nonlinear analysis based on an updated explicit damper model having different levels of detail is performed, and the results are evaluated against a newly-developed UPD test rig. Detailed linear finite element models are used as input for the nonlinear analysis, allowing the inclusion of damper flexibility and inertia effects. The nonlinear friction interface between the blades and the damper is described with a dense grid of 3D friction contact elements which allow accurate capturing of the underlying nonlinear mechanism that drives the global nonlinear behaviour. The introduced explicit damper model showed a great dependence on the correct contact pressure distribution. The use of an accurate, measurement based, distribution, better matched the nonlinear dynamic behaviour of the test rig. Good agreement with the measured frequency response data could only be reached when the zero harmonic term (constant term) was included in the multi-harmonic expansion of the nonlinear problem, highlighting its importance

Analysis of nonlinear behavior of loudspeakers using the instantaneous frequency

DEFF Research Database (Denmark)

Huang, Hai; Jacobsen, Finn

2003-01-01

on the Fourier transform. In this work, a new method using the instantaneous frequency is introduced for describing and characterizing loudspeaker nonlinearities. First, numerical integration is applied to simulate the nonlinearities of loudspeakers caused by two nonlinear parameters, force factor and stiffness...

Ripple distribution for nonlinear fiber-optic channels.

Science.gov (United States)

Sorokina, Mariia; Sygletos, Stylianos; Turitsyn, Sergei

2017-02-06

We demonstrate data rates above the threshold imposed by nonlinearity on conventional optical signals by applying novel probability distribution, which we call ripple distribution, adapted to the properties of the fiber channel. Our results offer a new direction for signal coding, modulation and practical nonlinear distortions compensation algorithms.

Considering system non-linearity in transmission pricing

International Nuclear Information System (INIS)

Oloomi-Buygi, M.; Salehizadeh, M. Reza

2008-01-01

In this paper a new approach for transmission pricing is presented. The contribution of a contract on power flow of a transmission line is used as extent-of-use criterion for transmission pricing. In order to determine the contribution of each contract on power flow of each transmission line, first the contribution of each contract on each voltage angle is determined, which is called voltage angle decomposition. To this end, DC power flow is used to compute a primary solution for voltage angle decomposition. To consider the impacts of system non-linearity on voltage angle decomposition, a method is presented to determine the share of different terms of sine argument in sine value. Then the primary solution is corrected in different iterations of decoupled Newton-Raphson power flow using the presented sharing method. The presented approach is applied to a 4-bus test system and IEEE 30-bus test system and the results are analyzed. (author)

Analysis of the interplay of quantum phases and nonlinearity applied to dimers with anharmonic interactions

International Nuclear Information System (INIS)

Raghavan, S.

1997-06-01

We extend our analysis of the effects of the interplay of quantum phases and nonlinearity to address saturation effects in small quantum systems. We find that initial phases dramatically control the dependence of self-trapping on initial asymmetry of quasiparticle population and can compete or act with nonlinearity as well as saturation effects. We find that there is a minimum finite saturation value in order to obtain self-trapping that crucially depends on the initial quasiparticle phases and present a detailed phase-diagram in terms of the control parameters of the system: nonlinearity and saturation. (author). 14 refs, 3 figs

Non-linear dielectric monitoring of biological suspensions

International Nuclear Information System (INIS)

Treo, E F; Felice, C J

2007-01-01

Non-linear dielectric spectroscopy as a tool for in situ monitoring of enzyme assumes a non-linear behavior of the sample when a sinusoidal voltage is applied to it. Even many attempts have been made to improve the original experiments, all of them had limited success. In this paper we present upgrades made to a non-linear dielectric spectrometer developed and the results obtained when using different cells. We emphasized on the electrode surface, characterizing the grinding and polishing procedure. We found that the biological medium does not behave as expected, and the non-linear response is generated in the electrode-electrolyte interface. The electrochemistry of this interface can bias unpredictably the measured non-linear response

Nonlinear hyperbolic waves in multidimensions

CERN Document Server

Prasad, Phoolan

2001-01-01

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

Introduction to Nonlinear and Global Optimization

NARCIS (Netherlands)

Hendrix, E.M.T.; Tóth, B.

2010-01-01

This self-contained text provides a solid introduction to global and nonlinear optimization, providing students of mathematics and interdisciplinary sciences with a strong foundation in applied optimization techniques. The book offers a unique hands-on and critical approach to applied optimization

Filtering Non-Linear Transfer Functions on Surfaces.

Science.gov (United States)

Heitz, Eric; Nowrouzezahrai, Derek; Poulin, Pierre; Neyret, Fabrice

2014-07-01

Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view- and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view- and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few

A Simple FEM Formulation Applied to Nonlinear Problems of Impact with Thermomechanical Coupling

Directory of Open Access Journals (Sweden)

João Paulo de Barros Cavalcante

Full Text Available Abstract The thermal effects of problems involving deformable structures are essential to describe the behavior of materials in feasible terms. Verifying the transformation of mechanical energy into heat it is possible to predict the modifications of mechanical properties of materials due to its temperature changes. The current paper presents the numerical development of a finite element method suitable for nonlinear structures coupled with thermomechanical behavior; including impact problems. A simple and effective alternative formulation is presented, called FEM positional, to deal with the dynamic nonlinear systems. The developed numerical is based on the minimum potential energy written in terms of nodal positions instead of displacements. The effects of geometrical, material and thermal nonlinearities are considered. The thermodynamically consistent formulation is based on the laws of thermodynamics and the Helmholtz free-energy, used to describe the thermoelastic and the thermoplastic behaviors. The coupled thermomechanical model can result in secondary effects that cause redistributions of internal efforts, depending on the history of deformation and material properties. The numerical results of the proposed formulation are compared with examples found in the literature.

Mathematical modeling and applications in nonlinear dynamics

CERN Document Server

Merdan, Hüseyin

2016-01-01

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...

Grey-box state-space identification of nonlinear mechanical vibrations

Science.gov (United States)

Noël, J. P.; Schoukens, J.

2018-05-01

The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semi-physical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.

Correction of response defects in scintillation cameras by an on-line microcomputer

International Nuclear Information System (INIS)

Hadjeris, L.

1982-07-01

A fast microprocessor device has been developed, to allow removal of non-linearity and non-uniformity effects of gamma camera signals. It slips in between a commercial gamma camera and the associated data processing system. Camera signals are digitized by fast ADC and numerically processed in real time. Corrected data are given analogic to be taken into account by process device associated to the camera. The principle is first to correct energy spatial variations by using coefficients determinated during calibration by a uniform radioactive distribution source. Then non-linearity of X and Y signals are removed by translations of them. The displacement coefficient table is given from reference images of parallel line phantom [fr

Digital Communication Devices Based on Nonlinear Dynamics and Chaos

National Research Council Canada - National Science Library

Larson, Lawrence

2003-01-01

The final report of the ARO MURI "Digital Communications Based on Chaos and Nonlinear Dynamics" contains research results in the areas of chaos and nonlinear dynamics applied to wireless and optical communications...

Nonlinear singular perturbation problems of arbitrary real orders

International Nuclear Information System (INIS)

Bijura, Angelina M.

2003-10-01

Higher order asymptotic solutions of singularly perturbed nonlinear fractional integral and derivatives of order 1/2 are investigated. It is particularly shown that whilst certain asymptotic expansions are applied successfully to linear equations and particular nonlinear problems, the standard formal asymptotic expansion is appropriate for the general class of nonlinear equations. This theory is then generalised to the general equation (of order β, 0 < β < 1). (author)

Correction of spectral and temporal phases for ultra-intense lasers; Correction des phases spectrale et temporelle pour les lasers ultra-intenses

Energy Technology Data Exchange (ETDEWEB)

Salmon, E

2000-12-15

The discovery of new regimes of interaction between laser and matter requires to produce laser pulses presenting higher luminous flux density. The only solutions that allow us to reach important power (about ten peta-watts) imply the correction of non-linear effects before compressing the laser pulse so that we do not transfer the phase modulation to the amplitude modulation. The aim of this work is the correction of the spectral phase through the modulation of the temporal phase. The first chapter is dedicated to the review of the physical phenomena involved in the interaction of ultra-intense laser pulse with matter. The peta-watt laser operating on the LIL (integrated laser line), the prototype line of the Megajoule Laser, is described in the second chapter. The third chapter presents the method used and optimized for getting an absolute measurement of the spectral phase in our experimental configuration. The fourth chapter details the analogy existing between the spatial domain and the temporal domain particularly between diffraction and dispersion. This analogy has allowed us to benefit from the knowledge cumulated in the spatial domain, particularly the treatment of the aberrations and their impact on the focal spot and to use it in the temporal domain. The principle of the phase correction is exposed in the fifth chapter. We have formalized the correspondence of the phase modulation between temporal domain and the spectral domain for strongly stretched pulses. In this way a modulation of the temporal phase is turned into a modulation of the spectral phase. All the measurements concerning phases and modulation spectral phase correction are presented in the sixth chapter. In the last chapter we propose an extension of the temporal phase correction by correcting non-linear effects directly in the temporal phase. This correction will improve the performances of the peta-watt laser. Numerical simulations show that the temporal phase correction can lead to a

Quantitative evaluation of automated skull-stripping methods applied to contemporary and legacy images: effects of diagnosis, bias correction, and slice location

DEFF Research Database (Denmark)

Fennema-Notestine, Christine; Ozyurt, I Burak; Clark, Camellia P

2006-01-01

Extractor (BSE, Sandor and Leahy [1997] IEEE Trans Med Imag 16:41-54; Shattuck et al. [2001] Neuroimage 13:856-876) to manually stripped images. The methods were applied to uncorrected and bias-corrected datasets; Legacy and Contemporary T1-weighted image sets; and four diagnostic groups (depressed...... distances, and an Expectation-Maximization algorithm. Methods tended to perform better on contemporary datasets; bias correction did not significantly improve method performance. Mesial sections were most difficult for all methods. Although AD image sets were most difficult to strip, HWA and BSE were more...

Introduction to nonlinear finite element analysis

CERN Document Server

Kim, Nam-Ho

2015-01-01

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

Multi-frequency Defect Selective Imaging via Nonlinear Ultrasound

Science.gov (United States)

Solodov, Igor; Busse, Gerd

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

Solving Nonlinear Partial Differential Equations with Maple and Mathematica

CERN Document Server

Shingareva, Inna K

2011-01-01

The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple an

3D early embryogenesis image filtering by nonlinear partial differential equations.

Science.gov (United States)

Krivá, Z; Mikula, K; Peyriéras, N; Rizzi, B; Sarti, A; Stasová, O

2010-08-01

We present nonlinear diffusion equations, numerical schemes to solve them and their application for filtering 3D images obtained from laser scanning microscopy (LSM) of living zebrafish embryos, with a goal to identify the optimal filtering method and its parameters. In the large scale applications dealing with analysis of 3D+time embryogenesis images, an important objective is a correct detection of the number and position of cell nuclei yielding the spatio-temporal cell lineage tree of embryogenesis. The filtering is the first and necessary step of the image analysis chain and must lead to correct results, removing the noise, sharpening the nuclei edges and correcting the acquisition errors related to spuriously connected subregions. In this paper we study such properties for the regularized Perona-Malik model and for the generalized mean curvature flow equations in the level-set formulation. A comparison with other nonlinear diffusion filters, like tensor anisotropic diffusion and Beltrami flow, is also included. All numerical schemes are based on the same discretization principles, i.e. finite volume method in space and semi-implicit scheme in time, for solving nonlinear partial differential equations. These numerical schemes are unconditionally stable, fast and naturally parallelizable. The filtering results are evaluated and compared first using the Mean Hausdorff distance between a gold standard and different isosurfaces of original and filtered data. Then, the number of isosurface connected components in a region of interest (ROI) detected in original and after the filtering is compared with the corresponding correct number of nuclei in the gold standard. Such analysis proves the robustness and reliability of the edge preserving nonlinear diffusion filtering for this type of data and lead to finding the optimal filtering parameters for the studied models and numerical schemes. Further comparisons consist in ability of splitting the very close objects which

Systematic Error of Acoustic Particle Image Velocimetry and Its Correction

Directory of Open Access Journals (Sweden)

Mickiewicz Witold

2014-08-01

Full Text Available Particle Image Velocimetry is getting more and more often the method of choice not only for visualization of turbulent mass flows in fluid mechanics, but also in linear and non-linear acoustics for non-intrusive visualization of acoustic particle velocity. Particle Image Velocimetry with low sampling rate (about 15Hz can be applied to visualize the acoustic field using the acquisition synchronized to the excitation signal. Such phase-locked PIV technique is described and used in experiments presented in the paper. The main goal of research was to propose a model of PIV systematic error due to non-zero time interval between acquisitions of two images of the examined sound field seeded with tracer particles, what affects the measurement of complex acoustic signals. Usefulness of the presented model is confirmed experimentally. The correction procedure, based on the proposed model, applied to measurement data increases the accuracy of acoustic particle velocity field visualization and creates new possibilities in observation of sound fields excited with multi-tonal or band-limited noise signals.

Quantification of myocardial perfusion SPECT for the assessment of coronary artery disease: should we apply scatter correction?

International Nuclear Information System (INIS)

Hambye, A.S.; Vervaet, A.; Dobbeleir, A.

2002-01-01

Compared to other non invasive testings for CAD diagnosis, myocardial perfusion imaging (MPI) is considered as a very sensitive method which accuracy is however often dimmed by a certain lack of specificity, especially in patients with a small heart. With gated SPECT MPI, use of end-diastolic instead of summed images has been presented as an interesting approach for increasing specificity. Since scatter correction is reported to improve image contrast, it might potentially constitute another way to ameliorate MPI accuracy. We aimed at comparing the value of both approaches, either separate or combined, for CAD diagnosis. Methods. Hundred patients addressed for gated 99m-Tc sestamibi SPECT MPI were prospectively included (Group A). Thirty-five had an end-systolic volume <30ml by QGS-analysis (Group B). All had a coronary angiogram within 3 months of the MPI. Four polar maps (non-corrected and scatter-corrected summed, and non-corrected and scatter-corrected end-diastolic) were created to quantify the extent (EXT) and severity (TDS) of the perfusion defects if any. ROC-curve analysis was applied to define the optimal thresholds of EXT and TDS separating non-CAD from CAD-patients, using a 50%-stenosis on coronary angiogram as cutoff for disease positivity. Results. Significant CAD was present in 86 patients (25 in Group B). In Group A, assessment of EXT and TDS of perfusion defects on scatter-corrected summed images demonstrated the highest accuracy (76% for EXT; sens: 77%; spec: 71%, and 74% for TDS, sens: 73%, spec: 79%). Accuracy of EXT and TDS calculated from the other data sets was slightly but not significantly lower, especially because of a lower sensitivity. As a comparison, visual analysis was 90% accurate for the diagnosis of CAD (sens: 94%, spec: 64%). In group B, overall results were worse mainly due to a decreased sensitivity, with accuracies ranging between 51 and 63%. Again scatter-corrected summed data were the most accurate (EXT: 60%, TDS: 63%, visual

Correction Factors Applied to Finger Dosimetry: A Theoretical Assessment of Appropriate Values for Use in Handling Radiopharmaceuticals

International Nuclear Information System (INIS)

Sherbini, Sami; Ilas, Dan; Eckerman, Keith F.; DeCicco, Joseph

2011-01-01

United States Nuclear Regulatory Commission (USNRC) regulations limit the dose to the skin to 500 mSv per year. This is also the dose limit recommended by the International Commission on Radiological Protection (ICRP). The operational quantity recommended by ICRP for quantifying dose to the skin is the personal dose equivalent, Hp(0.07) and is identical to NRC's shallow dose equivalent, Hs, also measured at a skin depth of 7 mg cm 2. However, whereas ICRP recommends averaging the dose to the skin over an area of 1 cm2 regardless of the size of the exposed area of skin, USNRC requires the shallow dose equivalent to be averaged over 10 cm2. To monitor dose to the skin of the hands of workers handling radioactive materials and particularly in radiopharmaceutical manufacturing facilities, which is the focus of this work, workers are frequently required to wear finger ring dosimeters. The dosimeters monitor the dose at the location of the sensitive element, but this is not the dose required to show compliance (i.e., the dose averaged over the highest exposed contiguous 10 cm2 of skin). Therefore, it may be necessary to apply a correction factor that enables estimation of the required skin dose from the dosimeter reading. This work explored the effects of finger ring placement and of the geometry of the radioactive materials being handled by the worker on the relationship between the dosimeter reading and the desired average dose. A mathematical model of the hand was developed for this purpose that is capable of positioning the fingers in any desired grasping configuration, thereby realistically modeling manipulation of any object. The model was then used with the radiation transport code MCNP to calculate the dose distribution on the skin of the hand when handling a variety of radioactive vials and syringes, as well as the dose to the dosimeter element. Correction factors were calculated using the results of these calculations and examined for any patterns that may be

Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

Science.gov (United States)

Athanassoulis, Agissilaos

2018-03-01

We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

Nonlinear Binormal Flow of Vortex Filaments

Science.gov (United States)

Strong, Scott; Carr, Lincoln

2015-11-01

With the current advances in vortex imaging of Bose-Einstein condensates occurring at the Universities of Arizona, São Paulo and Cambridge, interest in vortex filament dynamics is experiencing a resurgence. Recent simulations, Salman (2013), depict dissipative mechanisms resulting from vortex ring emissions and Kelvin wave generation associated with vortex self-intersections. As the local induction approximation fails to capture reconnection events, it lacks a similar dissipative mechanism. On the other hand, Strong&Carr (2012) showed that the exact representation of the velocity field induced by a curved segment of vortex contains higher-order corrections expressed in powers of curvature. This nonlinear binormal flow can be transformed, Hasimoto (1972), into a fully nonlinear equation of Schrödinger type. Continued transformation, Madelung (1926), reveals that the filament's square curvature obeys a quasilinear scalar conservation law with source term. This implies a broader range of filament dynamics than is possible with the integrable linear binormal flow. In this talk we show the affect higher-order corrections have on filament dynamics and discuss physical scales for which they may be witnessed in future experiments. Partially supported by NSF.

Nonlinear transport of accelerator beam phase space

International Nuclear Information System (INIS)

Xie Xi; Xia Jiawen

1995-01-01

Based on the any order analytical solution of accelerator beam dynamics, the general theory for nonlinear transport of accelerator beam phase space is developed by inverse transformation method. The method is general by itself, and hence can also be applied to the nonlinear transport of various dynamic systems in physics, chemistry and biology

Fast pressure-correction method for incompressible Navier-Stokes equations in curvilinear coordinates

Science.gov (United States)

Aithal, Abhiram; Ferrante, Antonino

2017-11-01

In order to perform direct numerical simulations (DNS) of turbulent flows over curved surfaces and axisymmetric bodies, we have developed the numerical methodology to solve the incompressible Navier-Stokes (NS) equations in curvilinear coordinates for orthogonal meshes. The orthogonal meshes are generated by solving a coupled system of non-linear Poisson equations. The NS equations in orthogonal curvilinear coordinates are discretized in space on a staggered mesh using second-order central-difference scheme and are solved with an FFT-based pressure-correction method. The momentum equation is integrated in time using the second-order Adams-Bashforth scheme. The velocity field is advanced in time by applying the pressure correction to the approximate velocity such that it satisfies the divergence free condition. The novelty of the method stands in solving the variable coefficient Poisson equation for pressure using an FFT-based Poisson solver rather than the slower multigrid methods. We present the verification and validation results of the new numerical method and the DNS results of transitional flow over a curved axisymmetric body.

Volume fraction dependence of transient absorption signal and nonlinearities in metal nanocolloids

International Nuclear Information System (INIS)

Jayabalan, J; Singh, Asha; Khan, Salahuddin; Chari, Rama

2013-01-01

Electron–lattice thermalization dynamics in metal nanoparticles or in bulk metal is usually estimated by measuring the decay time of the change in transmission following an optical excitation. Such measurements can be performed in transient absorption geometry using a femtosecond laser. We find that for silver nanoplatelet/water colloids, the decay time of the transient absorption depends on the volume fraction of silver in water. By estimating the volume fraction dependence of nonlinearities in the same samples, we show that the variation in the measured decay time is due to pump-depletion effects present in the sample. The correct correction factor for taking into account pump-depletion effects in fifth- and higher-order nonlinearities is also presented. (paper)

Non-linear effects in the Snoek relaxation of Nb-O

International Nuclear Information System (INIS)

Hermida, E.B.; Povolo, F.

1996-01-01

Internal friction peaks measured as a function of temperature or frequency have been associated to non-linear processes only after studying how the amplitude of the applied stress affects the relaxation process. Here it is demonstrated that the partial derivative of the internal friction with respect to the frequency at constant temperature is a useful tool to determine that non-linear effects are involved. This analysis applied to actual data of the Snoek relaxation in Nb-O, reveals that at high interstitial contents non-linear effects appear. (orig.)

Nonlinear structural mechanics theory, dynamical phenomena and modeling

CERN Document Server

Lacarbonara, Walter

2013-01-01

Nonlinear Structural Mechanics: Theory, Dynamical Phenomena and Modeling offers a concise, coherent presentation of the theoretical framework of nonlinear structural mechanics, computational methods, applications, parametric investigations of nonlinear phenomena and their mechanical interpretation towards design. The theoretical and computational tools that enable the formulation, solution, and interpretation of nonlinear structures are presented in a systematic fashion so as to gradually attain an increasing level of complexity of structural behaviors, under the prevailing assumptions on the geometry of deformation, the constitutive aspects and the loading scenarios. Readers will find a treatment of the foundations of nonlinear structural mechanics towards advanced reduced models, unified with modern computational tools in the framework of the prominent nonlinear structural dynamic phenomena while tackling both the mathematical and applied sciences. Nonlinear Structural Mechanics: Theory, Dynamical Phenomena...

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

Science.gov (United States)

Buttrill, Carey S.

1989-01-01

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding

KAUST Repository

Desmal, Abdulla; Bagci, Hakan

2015-01-01

A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.

Sparse electromagnetic imaging using nonlinear iterative shrinkage thresholding

KAUST Repository

Desmal, Abdulla

2015-04-13

A sparse nonlinear electromagnetic imaging scheme is proposed for reconstructing dielectric contrast of investigation domains from measured fields. The proposed approach constructs the optimization problem by introducing the sparsity constraint to the data misfit between the scattered fields expressed as a nonlinear function of the contrast and the measured fields and solves it using the nonlinear iterative shrinkage thresholding algorithm. The thresholding is applied to the result of every nonlinear Landweber iteration to enforce the sparsity constraint. Numerical results demonstrate the accuracy and efficiency of the proposed method in reconstructing sparse dielectric profiles.

FEEDBACK LINEARISATION APPLIED ON A HYDRAULIC

DEFF Research Database (Denmark)

Andersen, Torben Ole; Hansen, Michael Rygaard; Pedersen, Henrik C.

2005-01-01

is on developing and applying several different feedback linearisation (FL) controllers to the individual servo actuators in a hydraulically driven servo robot to evaluate and compare their possiblities and limitations. This is done based on both simulation and experimental results.......Generally most hydraulic systems are intrensically non-linear, why applying linear control techniques typically results in conservatively dimensioned controllers to obtain stable performance. Non-linear control techniques have the potential of overcoming these problems, and in this paper the focus...

Operator quantum error-correcting subsystems for self-correcting quantum memories

International Nuclear Information System (INIS)

Bacon, Dave

2006-01-01

The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general notion of quantum error correction known as operator quantum error correction. In standard quantum error-correcting codes, one requires the ability to apply a procedure which exactly reverses on the error-correcting subspace any correctable error. In contrast, for operator error-correcting subsystems, the correction procedure need not undo the error which has occurred, but instead one must perform corrections only modulo the subsystem structure. This does not lead to codes which differ from subspace codes, but does lead to recovery routines which explicitly make use of the subsystem structure. Here we present two examples of such operator error-correcting subsystems. These examples are motivated by simple spatially local Hamiltonians on square and cubic lattices. In three dimensions we provide evidence, in the form a simple mean field theory, that our Hamiltonian gives rise to a system which is self-correcting. Such a system will be a natural high-temperature quantum memory, robust to noise without external intervening quantum error-correction procedures

Estimation of dynamic reactivity using an H∞ optimal filter with a nonlinear term

International Nuclear Information System (INIS)

Suzuki, Katsuo; Watanabe, Koiti

1996-01-01

A method of nonlinear filtering is applied to the problem of estimating the dynamic reactivity of a nonlinear reactor system. The nonlinear filtering algorithm developed is a simple modification of a linear H ∞ optimal filter with a nonlinear feedback loop added. The linear filter is designed on the basis of a linearized dynamical system model that consists of linearized point reactor kinetic equations and a reactivity state equation driven by a fictitious signal. The latter is artificially introduced to deal with the reactivity as a state variable. The results of the computer simulation show that the nonlinear filtering algorithm can be applied to estimate the dynamic reactivity of the nonlinear reactor system, even under relatively large reactivity disturbances

Identification of Nonlinear Dynamic Systems Possessing Some Non-linearities

Directory of Open Access Journals (Sweden)

Y. N. Pavlov

2015-01-01

Full Text Available The subject of this work is the problem of identification of nonlinear dynamic systems based on the experimental data obtained by applying test signals to the system. The goal is to determinate coefficients of differential equations of systems by experimental frequency hodographs and separate similar, but different, in essence, forces: dissipative forces with the square of the first derivative in the motion equations and dissipative force from the action of dry friction. There was a proposal to use the harmonic linearization method to approximate each of the nonlinearity of "quadratic friction" and "dry friction" by linear friction with the appropriate harmonic linearization coefficient.Assume that a frequency transfer function of the identified system has a known form. Assume as well that there are disturbances while obtaining frequency characteristics of the realworld system. As a result, the points of experimentally obtained hodograph move randomly. Searching for solution of the identification problem was in the hodograph class, specified by the system model, which has the form of the frequency transfer function the same as the form of the frequency transfer function of the system identified. Minimizing a proximity criterion (measure of the experimentally obtained system hodograph and the system hodograph model for all the experimental points described and previously published by one of the authors allowed searching for the unknown coefficients of the frequenc ransfer function of the system model. The paper shows the possibility to identify a nonlinear dynamic system with multiple nonlinearities, obtained on the experimental samples of the frequency system hodograph. The proposed algorithm allows to select the nonlinearity of the type "quadratic friction" and "dry friction", i.e. also in the case where the nonlinearity is dependent on the same dynamic parameter, in particular, on the derivative of the system output value. For the dynamic

Non-Linear Fibres for Widely Tunable Femtosecond Fibre Lasers

DEFF Research Database (Denmark)

Pedersen, Martin Erland Vestergaard

and numerically. For the intermodal four-wave mixing experiment an alternative version of the Generalised Non-Linear Schrödinger Equation is derived, which includes the correct dispersion of the transverse field. It is observed that the alternative version of the Generalised Non-Linear Schrödinger Equation......, as opposed to the commonly used version, is able to reproduce the intermodal four-wave mixing experiment. The relation between the intramodal self-phase modulation and the intramodal Raman effect is determined from experimental measurements on a number of step-index fibres. The Raman fraction is found...

Nonlinear optical effects in pure and N-doped semiconductors

International Nuclear Information System (INIS)

Donlagic, N.S.

2000-01-01

Over the last decades, the nonlinear optical properties of condensed matter systems have been an attractive and fruitful field of research. While the linear response functions of solids provide information about the elementary excitations of the systems, nonlinear optical experiments give insight into the dynamics of the fundamental many-body processes which are initiated by the external excitations. Stimulated by the experimental results, new theoretical concepts and methods have been developed in order to relate the observed phenomena to the microscopic properties of the investigated materials. The present work deals with the study of the nonlinear dynamics of the optical interband polarization in pure and n-doped semiconductors.In the first part of the thesis, the relaxation behavior of optically excited electron-hole pairs in a one-dimensional semiconductor, which are coupled to longitudinal optical phonons with an initial lattice temperature T>0, is studied with the help of quantum kinetic equations. Apart from Hartree-Fock-like Coulomb contributions, these equations contain additional Coulomb terms, the so-called vertex corrections, by which the influence of the electron-electron interaction on the electron-phonon scattering processes is taken into account. The numerical studies indicate that the vertex corrections are essential for a correct description of the excitonic dynamics.In the second part of the thesis, the attention is shifted to the characteristics of the optical response of a one-dimensional n-doped two-band semiconductor whose conduction band has been linearized with respect to the two Fermi points. Due to the linearization it is possible to calculate the linear and nonlinear response functions of the interacting electron system exactly. These response functions are then used in order to determine the linear absorption spectrum and the time-integrated signal of a degenerated four-wave-mixing experiment. It is shown that the well-known features

Analytical Solutions to Non-linear Mechanical Oscillation Problems

DEFF Research Database (Denmark)

Kaliji, H. D.; Ghadimi, M.; Barari, Amin

2011-01-01

In this paper, the Max-Min Method is utilized for solving the nonlinear oscillation problems. The proposed approach is applied to three systems with complex nonlinear terms in their motion equations. By means of this method, the dynamic behavior of oscillation systems can be easily approximated u...

Analytical construction of peaked solutions for the nonlinear ...

African Journals Online (AJOL)

These results demonstrate the existence of peaked pulses propagating through a pair plasma. The algebraic decay rate of the pulses are determined analytically, as well. The method discussed here can be applied to approximate solutions to similar nonlinear partial differential equations of nonlinear Schrödinger type.

Overlapping Schwarz for Nonlinear Problems. An Element Agglomeration Nonlinear Additive Schwarz Preconditioned Newton Method for Unstructured Finite Element Problems

Energy Technology Data Exchange (ETDEWEB)

Cai, X C; Marcinkowski, L; Vassilevski, P S

2005-02-10

This paper extends previous results on nonlinear Schwarz preconditioning ([4]) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The non-local finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in [8]. Then, the algebraic construction from [9] of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. Numerical illustration is also provided.

Real-Time Implementation of Nonlinear Optical Processing Functions.

Science.gov (United States)

1986-09-30

information capacity) with the nonlinear error correction properties of associative neural nets such as the Hopfield model. Analogies between holography...symnolic ma.Ip’:ation Th.e error correcting -apart" :ty of non" ;n-ar associative merTtnies is necessary for s’uch structu-res Experimerta. results... geometrica snapes in contact ’A,.n a c-:’:ser ’Figure 51a’ ., and a spher:cal 4:verg.ng reference -eam Upion :"um’latlon of t -" c-’gram by the object beam

Nonlinear physics with Maple for scientists and engineers

CERN Document Server

Enns, Richard H

1997-01-01

Philosophy of the Text This text has been designed to be an introductory survey of the basic concepts and applied mathematical methods of nonlinear science. Students in engineer­ ing, physics, chemistry, mathematics, computing science, and biology should be able to successfully use this text. In an effort to provide the students with a cutting edge approach to one of the most dynamic, often subtle, complex, and still rapidly evolving, areas of modern research-nonlinear physics-we have made extensive use of the symbolic, numeric, and plotting capabilities of Maple V Release 4 applied to examples from these disciplines. No prior knowledge of Maple or computer programming is assumed, the reader being gently introduced to Maple as an auxiliary tool as the concepts of nonlinear science are developed. The diskette which accompanies the text gives a wide variety of illustrative nonlinear examples solved with Maple. An accompanying laboratory manual of experimental activities keyed to the text allows the student the...

Recent topics in non-linear partial differential equations 4

CERN Document Server

Mimura, M

1989-01-01

This fourth volume concerns the theory and applications of nonlinear PDEs in mathematical physics, reaction-diffusion theory, biomathematics, and in other applied sciences. Twelve papers present recent work in analysis, computational analysis of nonlinear PDEs and their applications.

Projection-reduction method applied to deriving non-linear optical conductivity for an electron-impurity system

Directory of Open Access Journals (Sweden)

Nam Lyong Kang

2013-07-01

Full Text Available The projection-reduction method introduced by the present authors is known to give a validated theory for optical transitions in the systems of electrons interacting with phonons. In this work, using this method, we derive the linear and first order nonlinear optical conductivites for an electron-impurity system and examine whether the expressions faithfully satisfy the quantum mechanical philosophy, in the same way as for the electron-phonon systems. The result shows that the Fermi distribution function for electrons, energy denominators, and electron-impurity coupling factors are contained properly in organized manners along with absorption of photons for each electron transition process in the final expressions. Furthermore, the result is shown to be represented properly by schematic diagrams, as in the formulation of electron-phonon interaction. Therefore, in conclusion, we claim that this method can be applied in modeling optical transitions of electrons interacting with both impurities and phonons.

Universality in an information-theoretic motivated nonlinear Schrodinger equation

International Nuclear Information System (INIS)

Parwani, R; Tabia, G

2007-01-01

Using perturbative methods, we analyse a nonlinear generalization of Schrodinger's equation that had previously been obtained through information-theoretic arguments. We obtain analytical expressions for the leading correction, in terms of the nonlinearity scale, to the energy eigenvalues of the linear Schrodinger equation in the presence of an external potential and observe some generic features. In one space dimension these are (i) for nodeless ground states, the energy shifts are subleading in the nonlinearity parameter compared to the shifts for the excited states; (ii) the shifts for the excited states are due predominantly to contribution from the nodes of the unperturbed wavefunctions, and (iii) the energy shifts for excited states are positive for small values of a regulating parameter and negative at large values, vanishing at a universal critical value that is not manifest in the equation. Some of these features hold true for higher dimensional problems. We also study two exactly solved nonlinear Schrodinger equations so as to contrast our observations. Finally, we comment on the possible significance of our results if the nonlinearity is physically realized

The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

Science.gov (United States)

Zhu, Yanqiu; Cohn, Stephen E.; Todling, Ricardo

1999-01-01

The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Nonlinear bleaching, absorption, and scattering of 532-nm-irradiated plasmonic nanoparticles

International Nuclear Information System (INIS)

Liberman, V.; Sworin, M.; Kingsborough, R. P.; Geurtsen, G. P.; Rothschild, M.

2013-01-01

Single-pulse irradiation of Au and Ag suspensions of nanospheres and nanodisks with 532-nm 4-ns pulses has identified complex optical nonlinearities while minimizing material damage. For all materials tested, we observe competition between saturable absorption (SA) and reverse SA (RSA), with RSA behavior dominating for intensities above ∼50 MW/cm 2 . Due to reduced laser damage in single-pulse experiments, the observed intrinsic nonlinear absorption coefficients are the highest reported to date for Au nanoparticles. We find size dependence to the nonlinear absorption enhancement for Au nanoparticles, peaking in magnitude for 80-nm nanospheres and falling off at larger sizes. The nonlinear absorption coefficients for Au and Ag spheres are comparable in magnitude. On the other hand, the nonlinear absorption for Ag disks, when corrected for volume fraction, is several times higher. These trends in nonlinear absorption are correlated to local electric field enhancement through quasi-static mean-field theory. Through variable size aperture measurements, we also separate nonlinear scattering from nonlinear absorption. For all materials tested, we find that nonlinear scattering is highly directional and that its magnitude is comparable to that of nonlinear absorption. These results indicate methods to improve the efficacy of plasmonic nanoparticles as optical limiters in pulsed laser systems.

An analytical nonlinear magnetoelectric coupling model of laminated composites under combined pre-stress and magnetic bias loadings

International Nuclear Information System (INIS)

Zhou, Hao-Miao; Qu, Shao-Xing; Ou, Xiao-Wei; Xiao, Ying; Wu, Hua-Ping

2013-01-01

Based on the equivalent circuit method, this paper adopts the nonlinear magnetostrictive constitutive relations to establish an analytical nonlinear magnetoelectric coefficient model for magnetostrictive/piezoelectric/magnetostrictive laminated magnetoelectric composites. When the pre-stress is set to zero in the model, the predicted results of the magnetoelectric coefficient coincide well with the available experimental results both qualitatively and quantitatively. Using the model, we can qualitatively predict the influence of the pre-stress, magnetic bias fields and the volume fraction of the magnetostrictive material on the magnetoelectric coefficient. The predicted results show that the influences of the pre-stress on the magnetoelectric coefficient, which varies with the magnetic bias field, before and after reaching the magnetoelectric coefficient maximum, are opposite. That is, the influence of the pre-stress on curves of the magnetoelectric coefficient reverses when the magnetoelectric coefficient reaches its maximum. Therefore, the correct setting of the pre-stress can lower the applied magnetic bias field and improve the magnetoelectric coefficient. The established nonlinear magnetoelectric effect model can provide a theoretical basis for regulating the magnetoelectric coefficient by the pre-stress and magnetic bias field and make it possible to design high-precision miniature magnetoelectric devices. (paper)

Exact solutions for nonlinear variants of Kadomtsev–Petviashvili (n,n ...

Indian Academy of Sciences (India)

2013-12-05

Dec 5, 2013 ... 1Department of Engineering Sciences, Faculty of Technology and Engineering, ... mathematics, for a nonlinear partial differential equation (PDE), .... The functional variable method definitely can be applied to nonlinear PDEs.

On the Limitations of Variational Bias Correction

Science.gov (United States)

Moradi, Isaac; Mccarty, Will; Gelaro, Ronald

2018-01-01

Satellite radiances are the largest dataset assimilated into Numerical Weather Prediction (NWP) models, however the data are subject to errors and uncertainties that need to be accounted for before assimilating into the NWP models. Variational bias correction uses the time series of observation minus background to estimate the observations bias. This technique does not distinguish between the background error, forward operator error, and observations error so that all these errors are summed up together and counted as observation error. We identify some sources of observations errors (e.g., antenna emissivity, non-linearity in the calibration, and antenna pattern) and show the limitations of variational bias corrections on estimating these errors.

An approximate method for nonlinear diffusion applied to enzyme inactivation during drying

NARCIS (Netherlands)

Liou, J.K.

1982-01-01

An approximate model was developed for nonlinear diffusion with a power-function variation of the diffusion coefficient with concentration. This model may serve for the computation of desorption times and concentration profiles in non-shrinking or shrinking slabs, cylinders or spheres, under

Numerical Treatment of Fixed Point Applied to the Nonlinear Fredholm Integral Equation

Directory of Open Access Journals (Sweden)

Berenguer MI

2009-01-01

Full Text Available The authors present a method of numerical approximation of the fixed point of an operator, specifically the integral one associated with a nonlinear Fredholm integral equation, that uses strongly the properties of a classical Schauder basis in the Banach space .

The anisotropic Kerr nonlinear refractive index of the beta-barium borate (β-BaB₂O₄) nonlinear crystal

DEFF Research Database (Denmark)

Bache, Morten; Guo, Hairun; Zhou, Binbin

2013-01-01

We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (β-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant χ(3) cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments in the literat...... a complete list that we propose as reference of the four major cubic tensor components in BBO. We finally discuss the impact of using the cubic anisotropic response in ultrafast cascading experiments in BBO.......We study the anisotropic nature of the Kerr nonlinear response in a beta-barium borate (β-BaB2O4, BBO) nonlinear crystal. The focus is on determining the relevant χ(3) cubic tensor components that affect interaction of type I cascaded second-harmonic generation. Various experiments...... in the literature are analyzed and we correct the data from some of the experiments for contributions from cascading as well as for updated material parameters. We also perform an additional experimental measurement of the Kerr nonlinear tensor component responsible for self-phase modulation in cascading, and we...

Advanced in Nonlinear Optics and Laser Research and Development

International Nuclear Information System (INIS)

Jackel, S.; Kotler, Z; Lavi, R.; Sternklar, S.

1996-01-01

The Nonlinear Optics Group (NLOG) at Soreq NRC is engaged in the development of fundamental and applied technology in the related fields of nonlinear optics and laser development. Our work in nonlinear optics started with the goal of improving laser performance. These efforts were successful and opened the way for R and D in nonlinear optics for other applications. Today we use nonlinear optics to enable continuous tunability of lasers, control the path of light beams, modulate a light signal rapidly, provide optical data storage, and supply new means of microscopically probing biological and inorganic samples. Technology maturation and interaction with users will show which aspects of nonlinear optics will make the most impact

Exact travelling wave solutions for some important nonlinear

Indian Academy of Sciences (India)

The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...

Radiative corrections due to a heavy Higgs-particle

International Nuclear Information System (INIS)

Van der Bij, J.J.

1984-01-01

The leading two-loop corrections to the rho parameter and to the vectorboson masses was calculated in the limit of large Higgs-mass. The corrections appear to be too small to be measured, of the order of a few tenths of a percent. For rho perturbation theory breaks down for a Higgs-mass of 11 TeV and larger, for the vectorboson mass this happens for a Higgs-mass of a 4 TeV or larger. There is no direct correspondence between these results and the poles at n=3 in the gauged non-linear σ-model

Nonlinear Control of Heartbeat Models

Directory of Open Access Journals (Sweden)

Witt Thanom

2011-02-01

Full Text Available This paper presents a novel application of nonlinear control theory to heartbeat models. Existing heartbeat models are investigated and modified by incorporating the control input as a pacemaker to provide the control channel. A nonlinear feedback linearization technique is applied to force the output of the systems to generate artificial electrocardiogram (ECG signal using discrete data as the reference inputs. The synthetic ECG may serve as a flexible signal source to assess the effectiveness of a diagnostic ECG signal-processing device.

Describing pediatric dysphonia with nonlinear dynamic parameters

Science.gov (United States)

Meredith, Morgan L.; Theis, Shannon M.; McMurray, J. Scott; Zhang, Yu; Jiang, Jack J.

2008-01-01

Objective Nonlinear dynamic analysis has emerged as a reliable and objective tool for assessing voice disorders. However, it has only been tested on adult populations. In the present study, nonlinear dynamic analysis was applied to normal and dysphonic pediatric populations with the goal of collecting normative data. Jitter analysis was also applied in order to compare nonlinear dynamic and perturbation measures. This study’s findings will be useful in creating standards for the use of nonlinear dynamic analysis as a tool to describe dysphonia in the pediatric population. Methods The study included 38 pediatric subjects (23 children with dysphonia and 15 without). Recordings of sustained vowels were obtained from each subject and underwent nonlinear dynamic analysis and percent jitter analysis. The resulting correlation dimension (D2) and percent jitter values were compared across the two groups using t-tests set at a significance level of p = 0.05. Results It was shown that D2 values covary with the presence of pathology in children. D2 values were significantly higher in dysphonic children than in normal children (p = 0.002). Standard deviations indicated a higher level of variation in normal children’s D2 values than in dysphonic children’s D2 values. Jitter analysis showed markedly higher percent jitter in dysphonic children than in normal children (p = 0.025) and large standard deviations for both groups. Conclusion This study indicates that nonlinear dynamic analysis could be a viable tool for the detection and assessment of dysphonia in children. Further investigations and more normative data are needed to create standards for using nonlinear dynamic parameters for the clinical evaluation of pediatric dysphonia. PMID:18947887

Extreme Nonlinear Optics An Introduction

CERN Document Server

Wegener, Martin

2005-01-01

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

Lattice Boltzmann model for high-order nonlinear partial differential equations.

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂_{t}ϕ+∑_{k=1}^{m}α_{k}∂_{x}^{k}Π_{k}(ϕ)=0 (1≤k≤m≤6), α_{k} are constant coefficients, Π_{k}(ϕ) are some known differential functions of ϕ. As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K(n,n)-Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009)1672-179910.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009)PHYADX0378-437110.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Lattice Boltzmann model for high-order nonlinear partial differential equations

Science.gov (United States)

Chai, Zhenhua; He, Nanzhong; Guo, Zhaoli; Shi, Baochang

2018-01-01

In this paper, a general lattice Boltzmann (LB) model is proposed for the high-order nonlinear partial differential equation with the form ∂tϕ +∑k=1mαk∂xkΠk(ϕ ) =0 (1 ≤k ≤m ≤6 ), αk are constant coefficients, Πk(ϕ ) are some known differential functions of ϕ . As some special cases of the high-order nonlinear partial differential equation, the classical (m)KdV equation, KdV-Burgers equation, K (n ,n ) -Burgers equation, Kuramoto-Sivashinsky equation, and Kawahara equation can be solved by the present LB model. Compared to the available LB models, the most distinct characteristic of the present model is to introduce some suitable auxiliary moments such that the correct moments of equilibrium distribution function can be achieved. In addition, we also conducted a detailed Chapman-Enskog analysis, and found that the high-order nonlinear partial differential equation can be correctly recovered from the proposed LB model. Finally, a large number of simulations are performed, and it is found that the numerical results agree with the analytical solutions, and usually the present model is also more accurate than the existing LB models [H. Lai and C. Ma, Sci. China Ser. G 52, 1053 (2009), 10.1007/s11433-009-0149-3; H. Lai and C. Ma, Phys. A (Amsterdam) 388, 1405 (2009), 10.1016/j.physa.2009.01.005] for high-order nonlinear partial differential equations.

Current interactions from the one-form sector of nonlinear higher-spin equations

Science.gov (United States)

Gelfond, O. A.; Vasiliev, M. A.

2018-06-01

The form of higher-spin current interactions in the sector of one-forms is derived from the nonlinear higher-spin equations in AdS4. Quadratic corrections to higher-spin equations are shown to be independent of the phase of the parameter η = exp ⁡ iφ in the full nonlinear higher-spin equations. The current deformation resulting from the nonlinear higher-spin equations is represented in the canonical form with the minimal number of space-time derivatives. The non-zero spin-dependent coupling constants of the resulting currents are determined in terms of the higher-spin coupling constant η η bar . Our results confirm the conjecture that (anti-)self-dual nonlinear higher-spin equations result from the full system at (η = 0) η bar = 0.

Voltage-Induced Nonlinear Conduction Properties of Epoxy Resin/Micron-Silver Particles Composites

Science.gov (United States)

Qu, Zhaoming; Lu, Pin; Yuan, Yang; Wang, Qingguo

2018-01-01

The nonlinear conduction properties of epoxy resin (ER)/micron-silver particles (MP) composites were investigated. Under sufficient high intensity applied constant voltage, the obvious nonlinear conduction properties of the samples with volume fraction 25% were found. With increments in the voltage, the conductive switching effect was observed. The nonlinear conduction mechanism of the ER/MP composites under high applied voltages could be attributed to the electrical current conducted via discrete paths of conductive particles induced by the electric field. The test results show that the ER/MP composites with nonlinear conduction properties are of great potential application in electromagnetic protection of electron devices and systems.

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

Science.gov (United States)

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.

Nonlinear Radon Transform Using Zernike Moment for Shape Analysis

Directory of Open Access Journals (Sweden)

Ziping Ma

2013-01-01

Full Text Available We extend the linear Radon transform to a nonlinear space and propose a method by applying the nonlinear Radon transform to Zernike moments to extract shape descriptors. These descriptors are obtained by computing Zernike moment on the radial and angular coordinates of the pattern image's nonlinear Radon matrix. Theoretical and experimental results validate the effectiveness and the robustness of the method. The experimental results show the performance of the proposed method in the case of nonlinear space equals or outperforms that in the case of linear Radon.

A novel method to produce nonlinear empirical physical formulas for experimental nonlinear electro-optical responses of doped nematic liquid crystals: Feedforward neural network approach

Energy Technology Data Exchange (ETDEWEB)

Yildiz, Nihat, E-mail: nyildiz@cumhuriyet.edu.t [Cumhuriyet University, Faculty of Science and Literature, Department of Physics, 58140 Sivas (Turkey); San, Sait Eren; Okutan, Mustafa [Department of Physics, Gebze Institute of Technology, P.O. Box 141, Gebze 41400, Kocaeli (Turkey); Kaya, Hueseyin [Cumhuriyet University, Faculty of Science and Literature, Department of Physics, 58140 Sivas (Turkey)

2010-04-15

Among other significant obstacles, inherent nonlinearity in experimental physical response data poses severe difficulty in empirical physical formula (EPF) construction. In this paper, we applied a novel method (namely layered feedforward neural network (LFNN) approach) to produce explicit nonlinear EPFs for experimental nonlinear electro-optical responses of doped nematic liquid crystals (NLCs). Our motivation was that, as we showed in a previous theoretical work, an appropriate LFNN, due to its exceptional nonlinear function approximation capabilities, is highly relevant to EPF construction. Therefore, in this paper, we obtained excellently produced LFNN approximation functions as our desired EPFs for above-mentioned highly nonlinear response data of NLCs. In other words, by using suitable LFNNs, we successfully fitted the experimentally measured response and predicted the new (yet-to-be measured) response data. The experimental data (response versus input) were diffraction and dielectric properties versus bias voltage; and they were all taken from our previous experimental work. We conclude that in general, LFNN can be applied to construct various types of EPFs for the corresponding various nonlinear physical perturbation (thermal, electronic, molecular, electric, optical, etc.) data of doped NLCs.

A novel method to produce nonlinear empirical physical formulas for experimental nonlinear electro-optical responses of doped nematic liquid crystals: Feedforward neural network approach

International Nuclear Information System (INIS)

Yildiz, Nihat; San, Sait Eren; Okutan, Mustafa; Kaya, Hueseyin

2010-01-01

Among other significant obstacles, inherent nonlinearity in experimental physical response data poses severe difficulty in empirical physical formula (EPF) construction. In this paper, we applied a novel method (namely layered feedforward neural network (LFNN) approach) to produce explicit nonlinear EPFs for experimental nonlinear electro-optical responses of doped nematic liquid crystals (NLCs). Our motivation was that, as we showed in a previous theoretical work, an appropriate LFNN, due to its exceptional nonlinear function approximation capabilities, is highly relevant to EPF construction. Therefore, in this paper, we obtained excellently produced LFNN approximation functions as our desired EPFs for above-mentioned highly nonlinear response data of NLCs. In other words, by using suitable LFNNs, we successfully fitted the experimentally measured response and predicted the new (yet-to-be measured) response data. The experimental data (response versus input) were diffraction and dielectric properties versus bias voltage; and they were all taken from our previous experimental work. We conclude that in general, LFNN can be applied to construct various types of EPFs for the corresponding various nonlinear physical perturbation (thermal, electronic, molecular, electric, optical, etc.) data of doped NLCs.

Nonlinear Schrodinger equation: A testing ground for the quantization of nonlinear waves

International Nuclear Information System (INIS)

Klein, A.; Krejs, F.

1976-01-01

Quantization of the nonlinear Schrodinger equation is carried out by the method due to Kerman and Klein. A viable procedure is inferred from the quantum interpretation of the classical (soliton) solution. The ground-state energy for a system with n particles is calculated to an accuracy which includes the first quantum correction to the semiclassical result. It is demonstrated that the exact answer can be obtained systematically only at the next level of approximation. For the calculation of the first quantum correction, the quantum theory of the stability of periodic orbits in field theory is developed and discussed. Since one is dealing with a finite many-body problem, the field theory can be written so that no infinite terms are encountered, but the Hamiltonian can also be artificially rearranged so as to destory this feature. For learning purposes the calculations are carried out with the various alternatives, and our methods prove capable of providing a uniform final result

Reduced Order Extended Luenberger Observer Based Sensorless Vector Control Fed by Matrix Converter with Non-linearity Modeling

DEFF Research Database (Denmark)

Lee, Kyo-Beum; Blaabjerg, Frede

2004-01-01

This paper presents a new sensorless vector control system for high performance induction motor drives fed by a matrix converter with non-linearity compensation. The nonlinear voltage distortion that is caused by commutation delay and on-state voltage drop in switching device is corrected by a new...

Nonlinear self-precession and wavenumber shift of electromagnetic waves under resonance and of Alfven waves in plasmas

International Nuclear Information System (INIS)

Bhattacharyya, B.; Chakraborty, B.

1979-01-01

Nonlinear corrections of a left and a right circularly polarized electromagnetic wave of the same frequency, propagating in the direction of a static and uniform magnetic field in a cold and collisionally damped two-component plasma, have been evaluated. The nonlinearly correct dispersion relation, self-generating nonlinear precessional rotation of the polarization ellipse of the wave and the shift in a wave parameter depend on linear combinations of products of the amplitude components taken two at a time and hence on the energies of the waves. Both in the low frequency resonance (that is when the ion cyclotron frequency equals the wave frequency) and in the high frequency resonance (that is when the electron cyclotron frequency equals the wave frequency), the self-precessional rate and wavenumber shift are found to be large and so have the possibility of detection in laboratory experiments. Moreover, for the limit leading to Alfven waves, these nonlinear effects have been found to have some interesting and significant properties. (Auth.)

Analysis of Instantaneous Linear, Nonlinear and Complex Cardiovascular Dynamics from Videophotoplethysmography.

Science.gov (United States)

Valenza, Gaetano; Iozzia, Luca; Cerina, Luca; Mainardi, Luca; Barbieri, Riccardo

2018-05-01

There is a fast growing interest in the use of non-contact devices for health and performance assessment in humans. In particular, the use of non-contact videophotoplethysmography (vPPG) has been recently demonstrated as a feasible way to extract cardiovascular information. Nevertheless, proper validation of vPPG-derived heartbeat dynamics is still missing. We aim to an in-depth validation of time-varying, linear and nonlinear/complex dynamics of the pulse rate variability extracted from vPPG. We apply inhomogeneous pointprocess nonlinear models to assess instantaneous measures defined in the time, frequency, and bispectral domains as estimated through vPPG and standard ECG. Instantaneous complexity measures, such as the instantaneous Lyapunov exponents and the recently defined inhomogeneous point-process approximate and sample entropy, were estimated as well. Video recordings were processed using our recently proposed method based on zerophase principal component analysis. Experimental data were gathered from 60 young healthy subjects (age: 24±3 years) undergoing postural changes (rest-to-stand maneuver). Group averaged results show that there is an overall agreement between linear and nonlinear/complexity indices computed from ECG and vPPG during resting state conditions. However, important differences are found, particularly in the bispectral and complexity domains, in recordings where the subjects has been instructed to stand up. Although significant differences exist between cardiovascular estimates from vPPG and ECG, it is very promising that instantaneous sympathovagal changes, as well as time-varying complex dynamics, were correctly identified, especially during resting state. In addition to a further improvement of the video signal quality, more research is advocated towards a more precise estimation of cardiovascular dynamics by a comprehensive nonlinear/complex paradigm specifically tailored to the non-contact quantification. Schattauer GmbH.

Parameter Scaling in Non-Linear Microwave Tomography

DEFF Research Database (Denmark)

Jensen, Peter Damsgaard; Rubæk, Tonny; Talcoth, Oskar

2012-01-01

Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when the imag......Non-linear microwave tomographic imaging of the breast is a challenging computational problem. The breast is heterogeneous and contains several high-contrast and lossy regions, resulting in large differences in the measured signal levels. This implies that special care must be taken when...... the imaging problem is formulated. Under such conditions, microwave imaging systems will most often be considerably more sensitive to changes in the electromagnetic properties in certain regions of the breast. The result is that the parameters might not be reconstructed correctly in the less sensitive regions...... introduced as a measure of the sensitivity. The scaling of the parameters is shown to improve performance of the microwave imaging system when applied to reconstruction of images from 2-D simulated data and measurement data....

Sensitivity theory for general non-linear algebraic equations with constraints

International Nuclear Information System (INIS)

Oblow, E.M.

1977-04-01

Sensitivity theory has been developed to a high state of sophistication for applications involving solutions of the linear Boltzmann equation or approximations to it. The success of this theory in the field of radiation transport has prompted study of possible extensions of the method to more general systems of non-linear equations. Initial work in the U.S. and in Europe on the reactor fuel cycle shows that the sensitivity methodology works equally well for those non-linear problems studied to date. The general non-linear theory for algebraic equations is summarized and applied to a class of problems whose solutions are characterized by constrained extrema. Such equations form the basis of much work on energy systems modelling and the econometrics of power production and distribution. It is valuable to have a sensitivity theory available for these problem areas since it is difficult to repeatedly solve complex non-linear equations to find out the effects of alternative input assumptions or the uncertainties associated with predictions of system behavior. The sensitivity theory for a linear system of algebraic equations with constraints which can be solved using linear programming techniques is discussed. The role of the constraints in simplifying the problem so that sensitivity methodology can be applied is highlighted. The general non-linear method is summarized and applied to a non-linear programming problem in particular. Conclusions are drawn in about the applicability of the method for practical problems

The non-linear Perron-Frobenius theorem : Perturbations and aggregation

NARCIS (Netherlands)

Dietzenbacher, E

The dominant eigenvalue and the corresponding eigenvector (or Perron vector) of a non-linear eigensystem are considered. We discuss the effects upon these, of perturbations and of aggregation of the underlying mapping. The results are applied to study the sensivity of the outputs in a non-linear

Computational investigation of nonlinear microwave tomography on anatomically realistic breast phantoms

DEFF Research Database (Denmark)

Jensen, P. D.; Rubæk, Tonny; Mohr, J. J.

2013-01-01

The performance of a nonlinear microwave tomography algorithm is tested using simulated data from anatomically realistic breast phantoms. These tests include several different anatomically correct breast models from the University of Wisconsin-Madison repository with and without tumors inserted....

Nonlinear Local Bending Response and Bulging Factors for Longitudinal and Circumferential Cracks in Pressurized Cylindrical Shells

Science.gov (United States)

Young, Richard D.; Rose, Cheryl A.; Starnes, James H., Jr.

2000-01-01

Results of a geometrically nonlinear finite element parametric study to determine curvature correction factors or bulging factors that account for increased stresses due to curvature for longitudinal and circumferential cracks in unstiffened pressurized cylindrical shells are presented. Geometric parameters varied in the study include the shell radius, the shell wall thickness, and the crack length. The major results are presented in the form of contour plots of the bulging factor as a function of two nondimensional parameters: the shell curvature parameter, lambda, which is a function of the shell geometry, Poisson's ratio, and the crack length; and a loading parameter, eta, which is a function of the shell geometry, material properties, and the applied internal pressure. These plots identify the ranges of the shell curvature and loading parameters for which the effects of geometric nonlinearity are significant. Simple empirical expressions for the bulging factor are then derived from the numerical results and shown to predict accurately the nonlinear response of shells with longitudinal and circumferential cracks. The numerical results are also compared with analytical solutions based on linear shallow shell theory for thin shells, and with some other semi-empirical solutions from the literature, and limitations on the use of these other expressions are suggested.

Asymmetric GaAs n-type double δ-doped quantum wells as a source of intersubband-related nonlinear optical response: Effects of an applied electric field

International Nuclear Information System (INIS)

Rodríguez-Magdaleno, K.A.; Martínez-Orozco, J.C.; Rodríguez-Vargas, I.; Mora-Ramos, M.E.; Duque, C.A.

2014-01-01

In this work, the conduction band electron states and the associated intersubband-related linear and nonlinear optical absorption coefficient and relative refractive index change are calculated for an asymmetric double n-type δ-doped quantum well in a GaAs-matrix. The effects of an external applied static electric field are included. Values of the two-dimensional impurities density (N 2d ) of each single δ-doped quantum well are taken to vary within the range of 1.0×10 12 to 7.0×10 12 cm −2 , consistent with the experimental data growth regime. The optical responses are reported as a function of the δ-doped impurities density and the applied electric field. It is shown that single electron states and the related optical quantities are significantly affected by the structural asymmetry of the double δ-doped quantum well system. In addition, a brief comparison with the free-carrier-related optical response is presented. -- Highlights: • Nonlinear optics in asymmetric double n-type δ-doped quantum well in a GaAs-matrix. • The system is considered under external applied electric field in growth direction. • The 2D impurity density is consistent with the experimental data growth regime. • The optical quantities are significantly affected by the structural asymmetry of the system

Asymmetric GaAs n-type double δ-doped quantum wells as a source of intersubband-related nonlinear optical response: Effects of an applied electric field

Energy Technology Data Exchange (ETDEWEB)

Rodríguez-Magdaleno, K.A.; Martínez-Orozco, J.C.; Rodríguez-Vargas, I. [Unidad Académica de Física, Universidad Autónoma de Zacatecas, Calz. Solidaridad Esq. Paseo a La Bufa S/N. C.P. 98060 Zacatecas (Mexico); Mora-Ramos, M.E. [Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad 1001, CP 62209 Cuernavaca, Morelos (Mexico); Física Teórica y Aplicada, Escuela de Ingeniería de Antioquia, AA 7516 Medellín (Colombia); Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia); Duque, C.A., E-mail: cduque@fisica.udea.edu.co [Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín (Colombia)

2014-03-15

In this work, the conduction band electron states and the associated intersubband-related linear and nonlinear optical absorption coefficient and relative refractive index change are calculated for an asymmetric double n-type δ-doped quantum well in a GaAs-matrix. The effects of an external applied static electric field are included. Values of the two-dimensional impurities density (N{sub 2d}) of each single δ-doped quantum well are taken to vary within the range of 1.0×10{sup 12} to 7.0×10{sup 12} cm{sup −2}, consistent with the experimental data growth regime. The optical responses are reported as a function of the δ-doped impurities density and the applied electric field. It is shown that single electron states and the related optical quantities are significantly affected by the structural asymmetry of the double δ-doped quantum well system. In addition, a brief comparison with the free-carrier-related optical response is presented. -- Highlights: • Nonlinear optics in asymmetric double n-type δ-doped quantum well in a GaAs-matrix. • The system is considered under external applied electric field in growth direction. • The 2D impurity density is consistent with the experimental data growth regime. • The optical quantities are significantly affected by the structural asymmetry of the system.

Multi-symplectic Runge-Kutta methods for nonlinear Dirac equations

International Nuclear Information System (INIS)

Hong Jialin; Li Chun

2006-01-01

In this paper, we consider the multi-symplectic Runge-Kutta (MSRK) methods applied to the nonlinear Dirac equation in relativistic quantum physics, based on a discovery of the multi-symplecticity of the equation. In particular, the conservation of energy, momentum and charge under MSRK discretizations is investigated by means of numerical experiments and numerical comparisons with non-MSRK methods. Numerical experiments presented reveal that MSRK methods applied to the nonlinear Dirac equation preserve exactly conservation laws of charge and momentum, and conserve the energy conservation in the corresponding numerical accuracy to the method utilized. It is verified numerically that MSRK methods are stable and convergent with respect to the conservation laws of energy, momentum and charge, and MSRK methods preserve not only the inner geometric structure of the equation, but also some crucial conservative properties in quantum physics. A remarkable advantage of MSRK methods applied to the nonlinear Dirac equation is the precise preservation of charge conservation law

An efficient and accurate method for calculating nonlinear diffraction beam fields

Energy Technology Data Exchange (ETDEWEB)

Jeong, Hyun Jo; Cho, Sung Jong; Nam, Ki Woong; Lee, Jang Hyun [Division of Mechanical and Automotive Engineering, Wonkwang University, Iksan (Korea, Republic of)

2016-04-15

This study develops an efficient and accurate method for calculating nonlinear diffraction beam fields propagating in fluids or solids. The Westervelt equation and quasilinear theory, from which the integral solutions for the fundamental and second harmonics can be obtained, are first considered. A computationally efficient method is then developed using a multi-Gaussian beam (MGB) model that easily separates the diffraction effects from the plane wave solution. The MGB models provide accurate beam fields when compared with the integral solutions for a number of transmitter-receiver geometries. These models can also serve as fast, powerful modeling tools for many nonlinear acoustics applications, especially in making diffraction corrections for the nonlinearity parameter determination, because of their computational efficiency and accuracy.

Measurement of nonlinear mode coupling of tearing fluctuations

International Nuclear Information System (INIS)

Assadi, S.; Prager, S.C.; Sidikman, K.L.

1992-03-01

Three-wave nonlinear coupling of spatial Fourier modes is measured in the MST reversed field pinch by applying bi-spectral analysis to magnetic fluctuations measured at the plasma edge at 64 toroidal locations and 16 poloidal locations, permitting observation of coupling over 8 polodial modes and 32 toroidal modes. Comparison to bi-spectra predicted by MHD computation indicates reasonably good agreement. However, during the crash phase of the sawtooth oscillation the nonlinear coupling is strongly enhanced, concomittant with a broadened (presumably nonlinearly generated) k-spectrum

Applying non-linear dynamics to atrial appendage flow data to understand and characterize atrial arrhythmia

International Nuclear Information System (INIS)

Chandra, S.; Grimm, R.A.; Katz, R.; Thomas, J.D.

1996-01-01

The aim of this study was to better understand and characterize left atrial appendage flow in atrial fibrillation. Atrial fibrillation and flutter are the most common cardiac arrhythmias affecting 15% of the older population. The pulsed Doppler velocity profile data was recorded from the left atrial appendage of patients using transesophageal echocardiography. The data was analyzed using Fourier analysis and nonlinear dynamical tools. Fourier analysis showed that appendage mechanical frequency (f f ) for patients in sinus rhythm was always lower (around1 Hz) than that in atrial fibrillation (5-8 Hz). Among patients with atrial fibrillation spectral power below f f was significantly different suggesting variability within this group of patients. Results that suggested the presence of nonlinear dynamics were: a) the existence of two arbitrary peak frequencies f 1 , f 2 , and other peak frequencies as linear combinations thereof (mf 1 ±nf 2 ), and b) the similarity between the spectrum of patient data and that obtained using the Lorenz equation. Nonlinear analysis tools, including Phase plots and differential radial plots, were also generated from the velocity data using a delay of 10. In the phase plots, some patients displayed a torus-like structure, while others had a more random-like pattern. In the differential radial plots, the first set of patients (with torus-like phase plots) showed fewer values crossing an arbitrary threshold of 10 than did the second set (8 vs. 27 in one typical example). The outcome of cardioversion was different for these two set of patients. Fourier analysis helped to: differentiate between sinus rhythm and atrial fibrillation, understand the characteristics of the wide range of atrial fibrillation patients, and provide hints that atrial fibrillation could be a nonlinear process. Nonlinear dynamical tools helped to further characterize and sub-classify atrial fibrillation

Multiphase Weakly Nonlinear Geometric Optics for Schrödinger Equations

KAUST Repository

Carles, Ré mi; Dumas, Eric; Sparber, Christof

2010-01-01

We describe and rigorously justify the nonlinear interaction of highly oscillatory waves in nonlinear Schrödinger equations, posed on Euclidean space or on the torus. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading order amplitude of the solution, but does not alter the rapid oscillations. We consider initial states which are superpositions of slowly modulated plane waves, and use the framework of Wiener algebras. A detailed analysis of the corresponding nonlinear wave mixing phenomena is given, including a geometric interpretation of the resonance structure for cubic nonlinearities. As an application, we recover and extend some instability results for the nonlinear Schrödinger equation on the torus in negative order Sobolev spaces. © 2010 Society for Industrial and Applied Mathematics.

Nonlinear observer design for a nonlinear string/cable FEM model using contraction theory

DEFF Research Database (Denmark)

Turkyilmaz, Yilmaz; Jouffroy, Jerome; Egeland, Olav

model is presented in the form of partial differential equations (PDE). Galerkin's method is then applied to obtain a set of ordinary differential equations such that the cable model is approximated by a FEM model. Based on the FEM model, a nonlinear observer is designed to estimate the cable...

Field of view extension and truncation correction for MR-based human attenuation correction in simultaneous MR/PET imaging

International Nuclear Information System (INIS)

Blumhagen, Jan O.; Ladebeck, Ralf; Fenchel, Matthias; Braun, Harald; Quick, Harald H.; Faul, David; Scheffler, Klaus

2014-01-01

Purpose: In quantitative PET imaging, it is critical to accurately measure and compensate for the attenuation of the photons absorbed in the tissue. While in PET/CT the linear attenuation coefficients can be easily determined from a low-dose CT-based transmission scan, in whole-body MR/PET the computation of the linear attenuation coefficients is based on the MR data. However, a constraint of the MR-based attenuation correction (AC) is the MR-inherent field-of-view (FoV) limitation due to static magnetic field (B 0 ) inhomogeneities and gradient nonlinearities. Therefore, the MR-based human AC map may be truncated or geometrically distorted toward the edges of the FoV and, consequently, the PET reconstruction with MR-based AC may be biased. This is especially of impact laterally where the patient arms rest beside the body and are not fully considered. Methods: A method is proposed to extend the MR FoV by determining an optimal readout gradient field which locally compensates B 0 inhomogeneities and gradient nonlinearities. This technique was used to reduce truncation in AC maps of 12 patients, and the impact on the PET quantification was analyzed and compared to truncated data without applying the FoV extension and additionally to an established approach of PET-based FoV extension. Results: The truncation artifacts in the MR-based AC maps were successfully reduced in all patients, and the mean body volume was thereby increased by 5.4%. In some cases large patient-dependent changes in SUV of up to 30% were observed in individual lesions when compared to the standard truncated attenuation map. Conclusions: The proposed technique successfully extends the MR FoV in MR-based attenuation correction and shows an improvement of PET quantification in whole-body MR/PET hybrid imaging. In comparison to the PET-based completion of the truncated body contour, the proposed method is also applicable to specialized PET tracers with little uptake in the arms and might reduce the

Exact travelling wave solutions for some important nonlinear ...

Indian Academy of Sciences (India)

The study of nonlinear partial differential equations is an active area of research in applied mathematics, theoretical physics and engineering fields. In particular ... In [16–18], the author applied this method to construct the exact solutions of.

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

Science.gov (United States)

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

2018-06-01

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

A practical procedure to improve the accuracy of radiochromic film dosimetry. A integration with a correction method of uniformity correction and a red/blue correction method

International Nuclear Information System (INIS)

Uehara, Ryuzo; Tachibana, Hidenobu; Ito, Yasushi; Yoshino, Shinichi; Matsubayashi, Fumiyasu; Sato, Tomoharu

2013-01-01

It has been reported that the light scattering could worsen the accuracy of dose distribution measurement using a radiochromic film. The purpose of this study was to investigate the accuracy of two different films, EDR2 and EBT2, as film dosimetry tools. The effectiveness of a correction method for the non-uniformity caused from EBT2 film and the light scattering was also evaluated. In addition the efficacy of this correction method integrated with the red/blue correction method was assessed. EDR2 and EBT2 films were read using a flatbed charge-coupled device scanner (EPSON 10000 G). Dose differences on the axis perpendicular to the scanner lamp movement axis were within 1% with EDR2, but exceeded 3% (Maximum: +8%) with EBT2. The non-uniformity correction method, after a single film exposure, was applied to the readout of the films. A corrected dose distribution data was subsequently created. The correction method showed more than 10%-better pass ratios in dose difference evaluation than when the correction method was not applied. The red/blue correction method resulted in 5%-improvement compared with the standard procedure that employed red color only. The correction method with EBT2 proved to be able to rapidly correct non-uniformity, and has potential for routine clinical intensity modulated radiation therapy (IMRT) dose verification if the accuracy of EBT2 is required to be similar to that of EDR2. The use of red/blue correction method may improve the accuracy, but we recommend we should use the red/blue correction method carefully and understand the characteristics of EBT2 for red color only and the red/blue correction method. (author)

[A practical procedure to improve the accuracy of radiochromic film dosimetry: a integration with a correction method of uniformity correction and a red/blue correction method].

Science.gov (United States)

Uehara, Ryuzo; Tachibana, Hidenobu; Ito, Yasushi; Yoshino, Shinichi; Matsubayashi, Fumiyasu; Sato, Tomoharu

2013-06-01

It has been reported that the light scattering could worsen the accuracy of dose distribution measurement using a radiochromic film. The purpose of this study was to investigate the accuracy of two different films, EDR2 and EBT2, as film dosimetry tools. The effectiveness of a correction method for the non-uniformity caused from EBT2 film and the light scattering was also evaluated. In addition the efficacy of this correction method integrated with the red/blue correction method was assessed. EDR2 and EBT2 films were read using a flatbed charge-coupled device scanner (EPSON 10000G). Dose differences on the axis perpendicular to the scanner lamp movement axis were within 1% with EDR2, but exceeded 3% (Maximum: +8%) with EBT2. The non-uniformity correction method, after a single film exposure, was applied to the readout of the films. A corrected dose distribution data was subsequently created. The correction method showed more than 10%-better pass ratios in dose difference evaluation than when the correction method was not applied. The red/blue correction method resulted in 5%-improvement compared with the standard procedure that employed red color only. The correction method with EBT2 proved to be able to rapidly correct non-uniformity, and has potential for routine clinical IMRT dose verification if the accuracy of EBT2 is required to be similar to that of EDR2. The use of red/blue correction method may improve the accuracy, but we recommend we should use the red/blue correction method carefully and understand the characteristics of EBT2 for red color only and the red/blue correction method.

Bound-Electron Nonlinearity Beyond the Ionization Threshold

Science.gov (United States)

Wahlstrand, J. K.; Zahedpour, S.; Bahl, A.; Kolesik, M.; Milchberg, H. M.

2018-05-01

We present absolute space- and time-resolved measurements of the ultrafast laser-driven nonlinear polarizability in argon, krypton, xenon, nitrogen, and oxygen up to ionization fractions of a few percent. These measurements enable determination of the strongly nonperturbative bound-electron nonlinear polarizability well beyond the ionization threshold, where it is found to remain approximately quadratic in the laser field, a result normally expected at much lower intensities where perturbation theory applies.

Nonlinear Deformable-body Dynamics

CERN Document Server

Luo, Albert C J

2010-01-01

"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...

Nonlinear PI control of chaotic systems using singular perturbation theory

International Nuclear Information System (INIS)

Wang Jiang; Wang Jing; Li Huiyan

2005-01-01

In this paper, we develop the nonlinear PI controllers for a class of chaotic systems based on singular perturbation theory. The original system is decomposed into two reduced order systems, to which the nonlinear uncertain terms belongs. In order to alleviate the deterioration of these nonlinear uncertainties, the nonlinear PI controllers are applied to each subsystem and combined to construct the composite controller for the full order system. The effectiveness and feasibility of the proposed control scheme is demonstrated through numerical simulations on the chaotic Chua's circuit

The nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores

International Nuclear Information System (INIS)

Yu-Lin, Feng; Xiao-Zhou, Liu; Jie-Hui, Liu; Li, Ma

2009-01-01

Based on an equivalent medium approach, this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation, sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of micropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore, multiple scattering has been taken into account, which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%

Dynamical generation of gauge bosons of hidden local symmetries in nonlinear sigma models

International Nuclear Information System (INIS)

Koegerler, R.; Lucha, W.; Neufeld, H.; Stremnitzer, H.

1988-01-01

We demonstrate how quantum corrections generate a kinetic term for the (at tree-level non-propagating) gauge fields of hidden local symmetries in nonlinear sigma models in four space-time dimensions. (orig.)

Use of bias correction techniques to improve seasonal forecasts for reservoirs - A case-study in northwestern Mediterranean.

Science.gov (United States)

Marcos, Raül; Llasat, Ma Carmen; Quintana-Seguí, Pere; Turco, Marco

2018-01-01

In this paper, we have compared different bias correction methodologies to assess whether they could be advantageous for improving the performance of a seasonal prediction model for volume anomalies in the Boadella reservoir (northwestern Mediterranean). The bias correction adjustments have been applied on precipitation and temperature from the European Centre for Middle-range Weather Forecasting System 4 (S4). We have used three bias correction strategies: two linear (mean bias correction, BC, and linear regression, LR) and one non-linear (Model Output Statistics analogs, MOS-analog). The results have been compared with climatology and persistence. The volume-anomaly model is a previously computed Multiple Linear Regression that ingests precipitation, temperature and in-flow anomaly data to simulate monthly volume anomalies. The potential utility for end-users has been assessed using economic value curve areas. We have studied the S4 hindcast period 1981-2010 for each month of the year and up to seven months ahead considering an ensemble of 15 members. We have shown that the MOS-analog and LR bias corrections can improve the original S4. The application to volume anomalies points towards the possibility to introduce bias correction methods as a tool to improve water resource seasonal forecasts in an end-user context of climate services. Particularly, the MOS-analog approach gives generally better results than the other approaches in late autumn and early winter. Copyright © 2017 Elsevier B.V. All rights reserved.

High-order nonlinear susceptibilities of He

International Nuclear Information System (INIS)

Liu, W.C.; Clark, C.W.

1996-01-01

High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. The authors have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s, within the framework of Rayleigh=Schroedinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Ponte and Shakeshaft, and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used; the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals

Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.

Science.gov (United States)

Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G

2016-12-02

We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.

Manipulating acoustic wave reflection by a nonlinear elastic metasurface

Science.gov (United States)

Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent

2018-03-01

The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.

Using Recursive Regression to Explore Nonlinear Relationships and Interactions: A Tutorial Applied to a Multicultural Education Study

Directory of Open Access Journals (Sweden)

Kenneth David Strang

2009-03-01

Full Text Available This paper discusses how a seldom-used statistical procedure, recursive regression (RR, can numerically and graphically illustrate data-driven nonlinear relationships and interaction of variables. This routine falls into the family of exploratory techniques, yet a few interesting features make it a valuable compliment to factor analysis and multiple linear regression for method triangulation. By comparison, nonlinear cluster analysis also generates graphical dendrograms to visually depict relationships, but RR (as implemented here uses multiple combinations of nominal and interval predictors regressed on a categorical or ratio dependent variable. In similar fashion, multidimensional scaling, multiple discriminant analysis and conjoint analysis are constrained at best to predicting an ordinal dependent variable (as currently implemented in popular software. A flexible capability of RR (again as implemented here is the transformation of factor data (for substituting codes. One powerful RR feature is the ability to treat missing data as a theoretically important predictor value (useful for survey questions that respondents do not wish to answer. For practitioners, the paper summarizes how this technique fits within the generally-accepted statistical methods. Popular software such as SPSS, SAS or LISREL can be used, while sample data can be imported in common formats including ASCII text, comma delimited, Excel XLS, and SPSS SAV. A tutorial approach is applied here using RR in LISREL. The tutorial leverages a partial sample from a study that used recursive regression to predict grades from international student learning styles. Some tutorial portions are technical, to improve the ambiguous RR literature.

Nonlinear differential equations

Energy Technology Data Exchange (ETDEWEB)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

Nonlinear differential equations

International Nuclear Information System (INIS)

Dresner, L.

1988-01-01

This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

Genetic algorithm for chromaticity correction in diffraction limited storage rings

Directory of Open Access Journals (Sweden)

M. P. Ehrlichman

2016-04-01

Full Text Available A multiobjective genetic algorithm is developed for optimizing nonlinearities in diffraction limited storage rings. This algorithm determines sextupole and octupole strengths for chromaticity correction that deliver optimized dynamic aperture and beam lifetime. The algorithm makes use of dominance constraints to breed desirable properties into the early generations. The momentum aperture is optimized indirectly by constraining the chromatic tune footprint and optimizing the off-energy dynamic aperture. The result is an effective and computationally efficient technique for correcting chromaticity in a storage ring while maintaining optimal dynamic aperture and beam lifetime.

Non-linear variation of the beta function with momentum

International Nuclear Information System (INIS)

Parzen, G.

1983-07-01

A theory is presented for computing the non-linear dependence of the β-functions on momentum. Results are found for the quadratic term. The results of the theory are compared with computed results. A procedure is proposed for computing the strengths of the sextupole correctors to correct the dependence of the β-function on momentum

OCOPTR, Minimization of Nonlinear Function, Variable Metric Method, Derivative Calculation. DRVOCR, Minimization of Nonlinear Function, Variable Metric Method, Derivative Calculation

International Nuclear Information System (INIS)

Nazareth, J. L.

1979-01-01

1 - Description of problem or function: OCOPTR and DRVOCR are computer programs designed to find minima of non-linear differentiable functions f: R n →R with n dimensional domains. OCOPTR requires that the user only provide function values (i.e. it is a derivative-free routine). DRVOCR requires the user to supply both function and gradient information. 2 - Method of solution: OCOPTR and DRVOCR use the variable metric (or quasi-Newton) method of Davidon (1975). For OCOPTR, the derivatives are estimated by finite differences along a suitable set of linearly independent directions. For DRVOCR, the derivatives are user- supplied. Some features of the codes are the storage of the approximation to the inverse Hessian matrix in lower trapezoidal factored form and the use of an optimally-conditioned updating method. Linear equality constraints are permitted subject to the initial Hessian factor being chosen correctly. 3 - Restrictions on the complexity of the problem: The functions to which the routine is applied are assumed to be differentiable. The routine also requires (n 2 /2) + 0(n) storage locations where n is the problem dimension

Time series with tailored nonlinearities

Science.gov (United States)

Räth, C.; Laut, I.

2015-10-01

It is demonstrated how to generate time series with tailored nonlinearities by inducing well-defined constraints on the Fourier phases. Correlations between the phase information of adjacent phases and (static and dynamic) measures of nonlinearities are established and their origin is explained. By applying a set of simple constraints on the phases of an originally linear and uncorrelated Gaussian time series, the observed scaling behavior of the intensity distribution of empirical time series can be reproduced. The power law character of the intensity distributions being typical for, e.g., turbulence and financial data can thus be explained in terms of phase correlations.

Nonlinear harmonic generation and proposed experimental verification in SASE FELs

CERN Document Server

Freund, H P; Milton, S V

2000-01-01

Recently, a 3D, polychromatic, nonlinear simulation code was developed to study the growth of nonlinear harmonics in self-amplified spontaneous emission (SASE) free-electron lasers (FELs). The simulation was applied to the parameters for each stage of the Advanced Photon Source (APS) SASE FEL, intended for operation in the visible, UV, and short UV wavelength regimes, respectively, to study the presence of nonlinear harmonic generation. Significant nonlinear harmonic growth is seen. Here, a discussion of the code development, the APS SASE FEL, the simulations and results, and, finally, the proposed experimental procedure for verification of such nonlinear harmonic generation at the APS SASE FEL will be given.

Long-Term Aging Diagnosis of Rotor Steel Using Acoustic Nonlinearity

Energy Technology Data Exchange (ETDEWEB)

Kim, Chung Seok; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of); Park, Ik Keun; Hyun, Chang Yong [Seoul National University of Science and Tecnology, Seoul (Korea, Republic of)

2011-12-15

The long-term aging of ferritic 2.25CrMo steel was characterized using the acoustic nonlinear effect in order to apply to diagnose the degradation behavior of structural materials. We measured the acoustic nonlinearity parameter for each thermally aged specimen by the higher harmonic-generation technique. The acoustic nonlinearity parameter increased with aging time due to equilibrium M6C carbide precipitation, and has a favorable linear relation with Rockwell hardness. This study suggests that acoustic nonlinearity testing may be applicable to diagnostics on strength degradation in rotor steels.

Applications of Nonlinear Dynamics Model and Design of Complex Systems

CERN Document Server

In, Visarath; Palacios, Antonio

2009-01-01

This edited book is aimed at interdisciplinary, device-oriented, applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. Examples include: complex networks of magnetic sensor systems, coupled nano-mechanical oscillators, nano-detectors, microscale devices, stochastic resonance in multi-dimensional chaotic systems, biosensors, and stochastic signal quantization. "applications of nonlinear dynamics: model and design of complex systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems.

Evaluation of polymer based third order nonlinear integrated optics devices

NARCIS (Netherlands)

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

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

Polaron effects on the linear and the nonlinear optical absorption coefficients and refractive index changes in cylindrical quantum dots with applied magnetic field

International Nuclear Information System (INIS)

Wu Qingjie; Guo Kangxian; Liu Guanghui; Wu Jinghe

2013-01-01

Polaron effects on the linear and the nonlinear optical absorption coefficients and refractive index changes in cylindrical quantum dots with the radial parabolic potential and the z-direction linear potential with applied magnetic field are theoretically investigated. The optical absorption coefficients and refractive index changes are presented by using the compact-density-matrix approach and iterative method. Numerical calculations are presented for GaAs/AlGaAs. It is found that taking into account the electron-LO-phonon interaction, not only are the linear, the nonlinear and the total optical absorption coefficients and refractive index changes enhanced, but also the total optical absorption coefficients are more sensitive to the incident optical intensity. It is also found that no matter whether the electron-LO-phonon interaction is considered or not, the absorption coefficients and refractive index changes above are strongly dependent on the radial frequency, the magnetic field and the linear potential coefficient.

Large-time asymptotic behaviour of solutions of non-linear Sobolev-type equations

International Nuclear Information System (INIS)

Kaikina, Elena I; Naumkin, Pavel I; Shishmarev, Il'ya A

2009-01-01

The large-time asymptotic behaviour of solutions of the Cauchy problem is investigated for a non-linear Sobolev-type equation with dissipation. For small initial data the approach taken is based on a detailed analysis of the Green's function of the linear problem and the use of the contraction mapping method. The case of large initial data is also closely considered. In the supercritical case the asymptotic formulae are quasi-linear. The asymptotic behaviour of solutions of a non-linear Sobolev-type equation with a critical non-linearity of the non-convective kind differs by a logarithmic correction term from the behaviour of solutions of the corresponding linear equation. For a critical convective non-linearity, as well as for a subcritical non-convective non-linearity it is proved that the leading term of the asymptotic expression for large times is a self-similar solution. For Sobolev equations with convective non-linearity the asymptotic behaviour of solutions in the subcritical case is the product of a rarefaction wave and a shock wave. Bibliography: 84 titles.

The AOLI Non-Linear Curvature Wavefront Sensor: High sensitivity reconstruction for low-order AO

Science.gov (United States)

Crass, Jonathan; King, David; Mackay, Craig

2013-12-01

Many adaptive optics (AO) systems in use today require bright reference objects to determine the effects of atmospheric distortions on incoming wavefronts. This requirement is because Shack Hartmann wavefront sensors (SHWFS) distribute incoming light from reference objects into a large number of sub-apertures. Bright natural reference objects occur infrequently across the sky leading to the use of laser guide stars which add complexity to wavefront measurement systems. The non-linear curvature wavefront sensor as described by Guyon et al. has been shown to offer a significant increase in sensitivity when compared to a SHWFS. This facilitates much greater sky coverage using natural guide stars alone. This paper describes the current status of the non-linear curvature wavefront sensor being developed as part of an adaptive optics system for the Adaptive Optics Lucky Imager (AOLI) project. The sensor comprises two photon-counting EMCCD detectors from E2V Technologies, recording intensity at four near-pupil planes. These images are used with a reconstruction algorithm to determine the phase correction to be applied by an ALPAO 241-element deformable mirror. The overall system is intended to provide low-order correction for a Lucky Imaging based multi CCD imaging camera. We present the current optical design of the instrument including methods to minimise inherent optical effects, principally chromaticity. Wavefront reconstruction methods are discussed and strategies for their optimisation to run at the required real-time speeds are introduced. Finally, we discuss laboratory work with a demonstrator setup of the system.

Nonlinear analysis of pre-stressed concrete containment vessel (PCCV) using the damage plasticity model

Energy Technology Data Exchange (ETDEWEB)

Shokoohfar, Ahmad; Rahai, Alireza, E-mail: rahai@aut.ac.ir

2016-03-15

Highlights: • This paper describes nonlinear analyses of a 1:4 scale model of a (PCCV). • Coupled temp-disp. analysis and concrete damage plasticity are considered. • Temperature has limited effects on correct failure mode estimation. • Higher pre-stressing forces have limited effects on ultimate radial displacements. • Anchorage details of liner plates leads to prediction of correct failure mode. - Abstract: This paper describes the nonlinear analyses of a 1:4 scale model of a pre-stressed concrete containment vessel (PCCV). The analyses are performed under pressure and high temperature effects with considering anchorage details of liner plate. The temperature-time history of the model test is considered as an input boundary condition in the coupled temp-displacement analysis. The constitutive model developed by Chang and Mander (1994) is adopted in the model as the basis for the concrete stress–strain relation. To trace the crack pattern of the PCCV concrete faces, the concrete damage plasticity model is applied. This study includes the results of the thermal and mechanical behaviors of the PCCV subject to temperature loading and internal pressure at the same time. The test results are compared with the analysis results. The analysis results show that the temperature has little impact on the ultimate pressure capacity of the PCCV. To simulate the exact failure mode of the PCCV, the anchorage details of the liner plates around openings should be maintained in the analytical models. Also the failure mode of the PCCV structure hasn’t influenced by hoop tendons pre-stressing force variations.

The application of He's exp-function method to a nonlinear differential-difference equation

International Nuclear Information System (INIS)

Dai Chaoqing; Cen Xu; Wu Shengsheng

2009-01-01

This paper applies He's exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear partial differential equations (NPDEs) or coupled nonlinear partial differential equations (CNPDEs), to a nonlinear differential-difference equation, and some new travelling wave solutions are obtained.

A new automated assessment method for contrast-detail images by applying support vector machine and its robustness to nonlinear image processing.

Science.gov (United States)

Takei, Takaaki; Ikeda, Mitsuru; Imai, Kuniharu; Yamauchi-Kawaura, Chiyo; Kato, Katsuhiko; Isoda, Haruo

2013-09-01

The automated contrast-detail (C-D) analysis methods developed so-far cannot be expected to work well on images processed with nonlinear methods, such as noise reduction methods. Therefore, we have devised a new automated C-D analysis method by applying support vector machine (SVM), and tested for its robustness to nonlinear image processing. We acquired the CDRAD (a commercially available C-D test object) images at a tube voltage of 120 kV and a milliampere-second product (mAs) of 0.5-5.0. A partial diffusion equation based technique was used as noise reduction method. Three radiologists and three university students participated in the observer performance study. The training data for our SVM method was the classification data scored by the one radiologist for the CDRAD images acquired at 1.6 and 3.2 mAs and their noise-reduced images. We also compared the performance of our SVM method with the CDRAD Analyser algorithm. The mean C-D diagrams (that is a plot of the mean of the smallest visible hole diameter vs. hole depth) obtained from our devised SVM method agreed well with the ones averaged across the six human observers for both original and noise-reduced CDRAD images, whereas the mean C-D diagrams from the CDRAD Analyser algorithm disagreed with the ones from the human observers for both original and noise-reduced CDRAD images. In conclusion, our proposed SVM method for C-D analysis will work well for the images processed with the non-linear noise reduction method as well as for the original radiographic images.

Nonlinear rock behavior and its implications on deeper-level platinum mining

CSIR Research Space (South Africa)

Watson, BP

2008-10-01

Full Text Available Uniaxial tests performed on core from instrumented sites at Amandelbult 1 shaft, Impala 10 shaft and Union Section Spud-shaft showed a nonlinear elastic relationship between applied load and induced deformation. This nonlinear behaviour does...

Simplified Methods Applied to Nonlinear Motion of Spar Platforms

Energy Technology Data Exchange (ETDEWEB)

Haslum, Herbjoern Alf

2000-07-01

Simplified methods for prediction of motion response of spar platforms are presented. The methods are based on first and second order potential theory. Nonlinear drag loads and the effect of the pumping motion in a moon-pool are also considered. Large amplitude pitch motions coupled to extreme amplitude heave motions may arise when spar platforms are exposed to long period swell. The phenomenon is investigated theoretically and explained as a Mathieu instability. It is caused by nonlinear coupling effects between heave, surge, and pitch. It is shown that for a critical wave period, the envelope of the heave motion makes the pitch motion unstable. For the same wave period, a higher order pitch/heave coupling excites resonant heave response. This mutual interaction largely amplifies both the pitch and the heave response. As a result, the pitch/heave instability revealed in this work is more critical than the previously well known Mathieu's instability in pitch which occurs if the wave period (or the natural heave period) is half the natural pitch period. The Mathieu instability is demonstrated both by numerical simulations with a newly developed calculation tool and in model experiments. In order to learn more about the conditions for this instability to occur and also how it may be controlled, different damping configurations (heave damping disks and pitch/surge damping fins) are evaluated both in model experiments and by numerical simulations. With increased drag damping, larger wave amplitudes and more time are needed to trigger the instability. The pitch/heave instability is a low probability of occurrence phenomenon. Extreme wave periods are needed for the instability to be triggered, about 20 seconds for a typical 200m draft spar. However, it may be important to consider the phenomenon in design since the pitch/heave instability is very critical. It is also seen that when classical spar platforms (constant cylindrical cross section and about 200m draft

Analytical treatment of the nonlinear electron cloud effect and the combined effects with beam-beam and space charge nonlinear forces in storage rings

International Nuclear Information System (INIS)

Gao Jie

2009-01-01

In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC II. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations. (author)

Nonlinear Elasticity

Science.gov (United States)

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

2001-05-01

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

Development of the Heated Length Correction Factor

International Nuclear Information System (INIS)

Park, Ho-Young; Kim, Kang-Hoon; Nahm, Kee-Yil; Jung, Yil-Sup; Park, Eung-Jun

2008-01-01

The Critical Heat Flux (CHF) on a nuclear fuel is defined by the function of flow channel geometry and flow condition. According to the selection of the explanatory variable, there are three hypotheses to explain CHF at uniformly heated vertical rod (inlet condition hypothesis, exit condition hypothesis, local condition hypothesis). For inlet condition hypothesis, CHF is characterized by function of system pressure, rod diameter, rod length, mass flow and inlet subcooling. For exit condition hypothesis, exit quality substitutes for inlet subcooling. Generally the heated length effect on CHF in exit condition hypothesis is smaller than that of other variables. Heated length is usually excluded in local condition hypothesis to describe the CHF with only local fluid conditions. Most of commercial plants currently use the empirical CHF correlation based on local condition hypothesis. Empirical CHF correlation is developed by the method of fitting the selected sensitive local variables to CHF test data using the multiple non-linear regression. Because this kind of method can not explain physical meaning, it is difficult to reflect the proper effect of complex geometry. So the recent CHF correlation development strategy of nuclear fuel vendor is making the basic CHF correlation which consists of basic flow variables (local fluid conditions) at first, and then the geometrical correction factors are compensated additionally. Because the functional forms of correction factors are determined from the independent test data which represent the corresponding geometry separately, it can be applied to other CHF correlation directly only with minor coefficient modification

Homogenized description and retrieval method of nonlinear metasurfaces

Science.gov (United States)

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

2018-03-01

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

PSB Chromaticity Correction in both Planes

CERN Document Server

Bartosik, Hannes; CERN. Geneva. ATS Department

2017-01-01

In view of the LHC injector upgrade program (LIU[1]), all LHC pre-accelerators and in particular the CERN Booster (PSB) are being reviewed for potential lattice optics and equipment optimizations. The option to correct the chromaticity in both planes would be very helpful for a better control of the beam in the presence of both non-linearities and space charge. Moreover, one could reduce decoherence phenomena that otherwise limit the usefulness of resonance measurement techniques based on a turn-by-turn BPM system.

A New Numerical Technique for Solving Systems Of Nonlinear Fractional Partial Differential Equations

Directory of Open Access Journals (Sweden)

Mountassir Hamdi Cherif

2017-11-01

Full Text Available In this paper, we apply an efficient method called the Aboodh decomposition method to solve systems of nonlinear fractional partial differential equations. This method is a combined form of Aboodh transform with Adomian decomposition method. The theoretical analysis of this investigated for systems of nonlinear fractional partial differential equations is calculated in the explicit form of a power series with easily computable terms. Some examples are given to shows that this method is very efficient and accurate. This method can be applied to solve others nonlinear systems problems.

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

African Journals Online (AJOL)

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

Optimization for nonlinear inverse problem

International Nuclear Information System (INIS)

Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.

2007-06-01

The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)

Extrinsic contribution to the non-linearity in a PZT disc

Energy Technology Data Exchange (ETDEWEB)

Perez, Rafel [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Albareda, Alfons [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Garcia, Jose E [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Tiana, Jordi [Departament de Fisica Aplicada, Universitat Politecnica de Catalunya, Jordi Girona 1-3, Campus Nord, 08034 Barcelona (Spain); Ringgaard, Erling [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark); Wolny, Wanda W [Ferroperm Piezoceramics A/S, Hejreskovvej 18, DK-3490 Kvistgaard (Denmark)

2004-10-07

Non-linear increases in elastic, piezoelectric (direct and reverse) and dielectric coefficients have been measured under a high electrical field or under high mechanical stress. The permittivity and reverse piezoelectric coefficient can be measured by applying a high voltage at a low frequency, while the elastic compliance and direct piezoelectric coefficient can be measured at the first radial resonance frequency in order to apply a high stress. The non-linear behaviour has been analysed at the radial resonance of a disc. In all the materials tested, the results show that there is a close relation between the non-linear increments of the different coefficients. An empirical model has been proposed in order to describe and understand these relations. It is assumed that either the strain or the electrical displacement is produced by intrinsic and extrinsic processes, but only the latter, which consist mainly in the motion of domain walls, contribute to the non-linearity. The model enables us to find the domain wall contribution to elastic, piezoelectric and dielectric non-linearities, and allows us to compare the amplitudes of the fields and stresses that produce the same displacement of domain walls.

Real-Time Corrected Traffic Correlation Model for Traffic Flow Forecasting

Directory of Open Access Journals (Sweden)

Hua-pu Lu

2015-01-01

Full Text Available This paper focuses on the problems of short-term traffic flow forecasting. The main goal is to put forward traffic correlation model and real-time correction algorithm for traffic flow forecasting. Traffic correlation model is established based on the temporal-spatial-historical correlation characteristic of traffic big data. In order to simplify the traffic correlation model, this paper presents correction coefficients optimization algorithm. Considering multistate characteristic of traffic big data, a dynamic part is added to traffic correlation model. Real-time correction algorithm based on Fuzzy Neural Network is presented to overcome the nonlinear mapping problems. A case study based on a real-world road network in Beijing, China, is implemented to test the efficiency and applicability of the proposed modeling methods.

Empirical investigation of purchasing power parity for Turkey: Evidence from recent nonlinear unit root tests

Directory of Open Access Journals (Sweden)

Dilem Yıldırım

2017-06-01

Full Text Available This study explores the empirical validity of the purchasing power parity (PPP hypothesis between Turkey and its four major trading partners, the European Union, Russia, China and the US. Accounting for the nonlinear nature of real exchange rates, we employ a battery of recently developed nonlinear unit root tests. Our empirical results reveal that nonlinear unit root tests deliver stronger evidence in favour of the PPP hypothesis when compared to the conventional unit root tests only if nonlinearities in real exchange rates are correctly specified. Furthermore, it emerges from our findings that the real exchange rates of the countries having a free trade agreement are more likely to behave as linear stationary processes.

Non-linear realizations of supersymmetry with off-shell central charges

International Nuclear Information System (INIS)

Santos Filho, P.B.; Oliveira Rivelles, V. de.

1985-01-01

A new class of non-linear realizations of the extended supersymmetry algebra with central charges is presented. They were obtained by applying the technique of dimensional reduction by Legendre transformation to a non-linear realization without central charges in one higher dimension. As a result an off-shell central charge is obtained. The non-linear lagrangian is the same as is the case of vanishing central charge. On-shell the central charge vanishes so this non-linear realization differs from that without central charges only off-shell. It is worked in two dimensions and its extension to higher dimensions is discussed. (Author) [pt

A non-linear kinematic hardening function

International Nuclear Information System (INIS)

Ottosen, N.S.

1977-05-01

Based on the classical theory of plasticity, and accepting the von Mises criterion as the initial yield criterion, a non-linear kinematic hardening function applicable both to Melan-Prager's and to Ziegler's hardening rule is proposed. This non-linear hardening function is determined by means of the uniaxial stress-strain curve, and any such curve is applicable. The proposed hardening function considers the problem of general reversed loading, and a smooth change in the behaviour from one plastic state to another nearlying plastic state is obtained. A review of both the kinematic hardening theory and the corresponding non-linear hardening assumptions is given, and it is shown that material behaviour is identical whether Melan-Prager's or Ziegler's hardening rule is applied, provided that the von Mises yield criterion is adopted. (author)

Forecasting with nonlinear time series models

DEFF Research Database (Denmark)

Kock, Anders Bredahl; Teräsvirta, Timo

In this paper, nonlinear models are restricted to mean nonlinear parametric models. Several such models popular in time series econo- metrics are presented and some of their properties discussed. This in- cludes two models based on universal approximators: the Kolmogorov- Gabor polynomial model...... applied to economic fore- casting problems, is briefly highlighted. A number of large published studies comparing macroeconomic forecasts obtained using different time series models are discussed, and the paper also contains a small simulation study comparing recursive and direct forecasts in a partic...... and two versions of a simple artificial neural network model. Techniques for generating multi-period forecasts from nonlinear models recursively are considered, and the direct (non-recursive) method for this purpose is mentioned as well. Forecasting with com- plex dynamic systems, albeit less frequently...

Development of non-linear TWB parts

Energy Technology Data Exchange (ETDEWEB)

Lee, J.; Yoon, C.S.; Lim, J.D. [Hyundai Motor Company and Kia Motors Corp. (Korea). Advanced Technology Center; Park, H.C. [Hyundai Hysco (Korea). Technical Research Lab.

2005-07-01

New manufacturing methods have applied for automotive parts to reduce total weight of car, resulting in improvement of fuel efficiency. TWB technique is applied to auto body parts, especially door inner, side inner and outer panel, and center floor panel to accomplish this goal. We applied non-linear (circular welded) TWB to shock absorber housing (to reduce total weight of shock absorber housing assembly). Welding line and shape of blank were determined by FEM analysis. High formability steel sheet and 440MPa grade high strength steel sheet were laser welded and press formed to final shock absorber housing (S/ABS HSG) panel and assembled with other sub parts. As a result, more than 10% of total weight of shock absorber housing assembly could be reduced compared with the mass of same part manufactured by conventional method. Also circular welding technique made it possible to design optimum welding line of TWB part. This paper is about result of FEM analysis and development procedure of non-linear TWB part (shock absorber housing assembly). (orig.)

Corrected Integral Shape Averaging Applied to Obstructive Sleep Apnea Detection from the Electrocardiogram

Directory of Open Access Journals (Sweden)

C. O'Brien

2007-01-01

Full Text Available We present a technique called corrected integral shape averaging (CISA for quantifying shape and shape differences in a set of signals. CISA can be used to account for signal differences which are purely due to affine time warping (jitter and dilation/compression, and hence provide access to intrinsic shape fluctuations. CISA can also be used to define a distance between shapes which has useful mathematical properties; a mean shape signal for a set of signals can be defined, which minimizes the sum of squared shape distances of the set from the mean. The CISA procedure also allows joint estimation of the affine time parameters. Numerical simulations are presented to support the algorithm for obtaining the CISA mean and parameters. Since CISA provides a well-defined shape distance, it can be used in shape clustering applications based on distance measures such as k-means. We present an application in which CISA shape clustering is applied to P-waves extracted from the electrocardiogram of subjects suffering from sleep apnea. The resulting shape clustering distinguishes ECG segments recorded during apnea from those recorded during normal breathing with a sensitivity of 81% and specificity of 84%.

Nonlinear time reversal signal processing techniques applied to acousto-mechanical imaging of complex materials

Czech Academy of Sciences Publication Activity Database

Dos Santos, S.; Dvořáková, Zuzana; Caliez, M.; Převorovský, Zdeněk

2015-01-01

Roč. 138, č. 3 (2015) ISSN 0001-4966 Institutional support: RVO:61388998 Keywords : acousto-mechanical characterization of skin aging * nonlinear elastic wave spectroscopy (NEWS) * PM-space statistical approach Subject RIV: BI - Acoustics

A Semi-Analytical Approach for the Response of Nonlinear Conservative Systems

DEFF Research Database (Denmark)

Kimiaeifar, Amin; Barari, Amin; Fooladi, M

2011-01-01

This work applies Parameter expanding method (PEM) as a powerful analytical technique in order to obtain the exact solution of nonlinear problems in the classical dynamics. Lagrange method is employed to derive the governing equations. The nonlinear governing equations are solved analytically by ...

A normal form approach to the theory of nonlinear betatronic motion

International Nuclear Information System (INIS)

Bazzani, A.; Todesco, E.; Turchetti, G.; Servizi, G.

1994-01-01

The betatronic motion of a particle in a circular accelerator is analysed using the transfer map description of the magnetic lattice. In the linear case the transfer matrix approach is shown to be equivalent to the Courant-Snyder theory: In the normal coordinates' representation the transfer matrix is a pure rotation. When the nonlinear effects due to the multipolar components of the magnetic field are taken into account, a similar procedure is used: a nonlinear change of coordinates provides a normal form representation of the map, which exhibits explicit symmetry properties depending on the absence or presence of resonance relations among the linear tunes. The use of normal forms is illustrated in the simplest but significant model of a cell with a sextupolar nonlinearity which is described by the quadratic Henon map. After recalling the basic theoretical results in Hamiltonian dynamics, we show how the normal forms describe the different topological structures of phase space such as KAM tori, chains of islands and chaotic regions; a critical comparison with the usual perturbation theory for Hamilton equations is given. The normal form theory is applied to compute the tune shift and deformation of the orbits for the lattices of the SPS and LHC accelerators, and scaling laws are obtained. Finally, the correction procedure of the multipolar errors of the LHC, based on the analytic minimization of the tune shift computed via the normal forms, is described and the results for a model of the LHC are presented. This application, relevant for the lattice design, focuses on the advantages of normal forms with respect to tracking when parametric dependences have to be explored. (orig.)

An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator–prey system

Directory of Open Access Journals (Sweden)

Md. Nur Alam

2016-06-01

Full Text Available In this article, we apply the exp(-Φ(ξ-expansion method to construct many families of exact solutions of nonlinear evolution equations (NLEEs via the nonlinear diffusive predator–prey system and the Bogoyavlenskii equations. These equations can be transformed to nonlinear ordinary differential equations. As a result, some new exact solutions are obtained through the hyperbolic function, the trigonometric function, the exponential functions and the rational forms. If the parameters take specific values, then the solitary waves are derived from the traveling waves. Also, we draw 2D and 3D graphics of exact solutions for the special diffusive predator–prey system and the Bogoyavlenskii equations by the help of programming language Maple.

Convex models and probabilistic approach of nonlinear fatigue failure

International Nuclear Information System (INIS)

Qiu Zhiping; Lin Qiang; Wang Xiaojun

2008-01-01

This paper is concerned with the nonlinear fatigue failure problem with uncertainties in the structural systems. In the present study, in order to solve the nonlinear problem by convex models, the theory of ellipsoidal algebra with the help of the thought of interval analysis is applied. In terms of the inclusion monotonic property of ellipsoidal functions, the nonlinear fatigue failure problem with uncertainties can be solved. A numerical example of 25-bar truss structures is given to illustrate the efficiency of the presented method in comparison with the probabilistic approach

Nonlinear structural damage detection using support vector machines

Science.gov (United States)

Xiao, Li; Qu, Wenzhong

2012-04-01

An actual structure including connections and interfaces may exist nonlinear. Because of many complicated problems about nonlinear structural health monitoring (SHM), relatively little progress have been made in this aspect. Statistical pattern recognition techniques have been demonstrated to be competitive with other methods when applied to real engineering datasets. When a structure existing 'breathing' cracks that open and close under operational loading may cause a linear structural system to respond to its operational and environmental loads in a nonlinear manner nonlinear. In this paper, a vibration-based structural health monitoring when the structure exists cracks is investigated with autoregressive support vector machine (AR-SVM). Vibration experiments are carried out with a model frame. Time-series data in different cases such as: initial linear structure; linear structure with mass changed; nonlinear structure; nonlinear structure with mass changed are acquired.AR model of acceleration time-series is established, and different kernel function types and corresponding parameters are chosen and compared, which can more accurate, more effectively locate the damage. Different cases damaged states and different damage positions have been recognized successfully. AR-SVM method for the insufficient training samples is proved to be practical and efficient on structure nonlinear damage detection.

Correcting Mortality for Loss to Follow-Up: A Nomogram Applied to Antiretroviral Treatment Programmes in Sub-Saharan Africa

Science.gov (United States)

Egger, Matthias; Spycher, Ben D.; Sidle, John; Weigel, Ralf; Geng, Elvin H.; Fox, Matthew P.; MacPhail, Patrick; van Cutsem, Gilles; Messou, Eugène; Wood, Robin; Nash, Denis; Pascoe, Margaret; Dickinson, Diana; Etard, Jean-François; McIntyre, James A.; Brinkhof, Martin W. G.

2011-01-01

Background The World Health Organization estimates that in sub-Saharan Africa about 4 million HIV-infected patients had started antiretroviral therapy (ART) by the end of 2008. Loss of patients to follow-up and care is an important problem for treatment programmes in this region. As mortality is high in these patients compared to patients remaining in care, ART programmes with high rates of loss to follow-up may substantially underestimate mortality of all patients starting ART. Methods and Findings We developed a nomogram to correct mortality estimates for loss to follow-up, based on the fact that mortality of all patients starting ART in a treatment programme is a weighted average of mortality among patients lost to follow-up and patients remaining in care. The nomogram gives a correction factor based on the percentage of patients lost to follow-up at a given point in time, and the estimated ratio of mortality between patients lost and not lost to follow-up. The mortality observed among patients retained in care is then multiplied by the correction factor to obtain an estimate of programme-level mortality that takes all deaths into account. A web calculator directly calculates the corrected, programme-level mortality with 95% confidence intervals (CIs). We applied the method to 11 ART programmes in sub-Saharan Africa. Patients retained in care had a mortality at 1 year of 1.4% to 12.0%; loss to follow-up ranged from 2.8% to 28.7%; and the correction factor from 1.2 to 8.0. The absolute difference between uncorrected and corrected mortality at 1 year ranged from 1.6% to 9.8%, and was above 5% in four programmes. The largest difference in mortality was in a programme with 28.7% of patients lost to follow-up at 1 year. Conclusions The amount of bias in mortality estimates can be large in ART programmes with substantial loss to follow-up. Programmes should routinely report mortality among patients retained in care and the proportion of patients lost. A simple

A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

Science.gov (United States)

Benhammouda, Brahim

2016-01-01

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

Constructing networks from a dynamical system perspective for multivariate nonlinear time series.

Science.gov (United States)

Nakamura, Tomomichi; Tanizawa, Toshihiro; Small, Michael

2016-03-01

We describe a method for constructing networks for multivariate nonlinear time series. We approach the interaction between the various scalar time series from a deterministic dynamical system perspective and provide a generic and algorithmic test for whether the interaction between two measured time series is statistically significant. The method can be applied even when the data exhibit no obvious qualitative similarity: a situation in which the naive method utilizing the cross correlation function directly cannot correctly identify connectivity. To establish the connectivity between nodes we apply the previously proposed small-shuffle surrogate (SSS) method, which can investigate whether there are correlation structures in short-term variabilities (irregular fluctuations) between two data sets from the viewpoint of deterministic dynamical systems. The procedure to construct networks based on this idea is composed of three steps: (i) each time series is considered as a basic node of a network, (ii) the SSS method is applied to verify the connectivity between each pair of time series taken from the whole multivariate time series, and (iii) the pair of nodes is connected with an undirected edge when the null hypothesis cannot be rejected. The network constructed by the proposed method indicates the intrinsic (essential) connectivity of the elements included in the system or the underlying (assumed) system. The method is demonstrated for numerical data sets generated by known systems and applied to several experimental time series.

Fermat's principle and nonlinear traveltime tomography

International Nuclear Information System (INIS)

Berryman, J.G.; Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012)

1989-01-01

Fermat's principle shows that a definite convex set of feasible slowness models, depending only on the traveltime data, exists for the fully nonlinear traveltime inversion problem. In a new iterative reconstruction algorithm, the minimum number of nonfeasible ray paths is used as a figure of merit to determine the optimum size of the model correction at each step. The numerical results show that the new algorithm is robust, stable, and produces very good reconstructions even for high contrast materials where standard methods tend to diverge

Nonlinear excitations in biomolecules

International Nuclear Information System (INIS)

Peyrard, M.

1995-01-01

The aim of the workshop entitled ''Nonlinear Excitations in Biomolecules'' is to attempt to bridge the gap between the physicists and biologists communities which is mainly due to language and cultural barriers. The progress of nonlinear science in the last few decades which have shown that the combination of nonlinearity, which characterize most biological phenomena, and cooperative effects in a system having a large number of degrees of freedom, can give rise to coherent excitations with remarkable properties. New concepts, such as solitons nd nonlinear energy localisation have become familiar to physicists and applied mathematicians. It is thus tempting to make an analogy between these coherent excitations and the exceptional stability of some biological processes, such as for instance DNA transcription, which require the coordination of many events in the ever changing environment of a cell. Physicists are now invoking nonlinear excitations to describe and explain many bio-molecular processes while biologists often doubt that the seemingly infinite variety of phenomena that they are attempting to classify can be reduced to such simple concepts. A large part of the meeting is devoted to tutorial lectures rather than to latest research results. The book provides a pedagogical introduction to the two topics forming the backbone of the meeting: the theory of nonlinear excitations and solitons, and their application in biology; and the structure and function of biomolecules, as well as energy and charge transport in biophysics. In order to emphasize the link between physics and biology, the volume is not divided along these two topics but according to biological subjects. Each chapter starts with a short introduction attempting to help the reader to find his way among the contributions and point out the connection between them. 23 lectures over the 32 presented have been selected and refers to quantum properties of macro-molecules. (J.S.)

Transverse Field Dispersion in the Generalized Nonlinear Schrödinger Equation: Four Wave Mixing in a Higher Order Mode Fiber

DEFF Research Database (Denmark)

Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris

2013-01-01

An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...

Nonlinear propagation analysis of few-optical-cycle pulses for subfemtosecond compression and carrier envelope phase effect

International Nuclear Information System (INIS)

Mizuta, Yo; Nagasawa, Minoru; Ohtani, Morimasa; Yamashita, Mikio

2005-01-01

A numerical approach called Fourier direct method (FDM) is applied to nonlinear propagation of optical pulses with the central wavelength 800 nm, the width 2.67-12.00 fs, and the peak power 25-6870 kW in a fused-silica fiber. Bidirectional propagation, delayed Raman response, nonlinear dispersion (self-steepening, core dispersion), as well as correct linear dispersion are incorporated into 'bidirectional propagation equations' which are derived directly from Maxwell's equations. These equations are solved for forward and backward waves, instead of the electric-field envelope as in the nonlinear Schroedinger equation (NLSE). They are integrated as multidimensional simultaneous evolution equations evolved in space. We investigate, both theoretically and numerically, the validity and the limitation of assumptions and approximations used for deriving the NLSE. Also, the accuracy and the efficiency of the FDM are compared quantitatively with those of the finite-difference time-domain numerical approach. The time-domain size 500 fs and the number of grid points in time 2048 are chosen to investigate numerically intensity spectra, spectral phases, and temporal electric-field profiles up to the propagation distance 1.0 mm. On the intensity spectrum of a few-optical-cycle pulses, the self-steepening, core dispersion, and the delayed Raman response appear as dominant, middle, and slight effects, respectively. The delayed Raman response and the core dispersion reduce the effective nonlinearity. Correct linear dispersion is important since it affects the intensity spectrum sensitively. For the compression of femtosecond optical pulses by the complete phase compensation, the shortness and the pulse quality of compressed pulses are remarkably improved by the intense initial peak power rather than by the short initial pulse width or by the propagation distance longer than 0.1 mm. They will be compressed as short as 0.3 fs below the damage threshold of fused-silica fiber 6 MW. It

Transition from weak to strong measurements by nonlinear quantum feedback control

International Nuclear Information System (INIS)

Zhang Jing; Liu Yuxi; Wu Rebing; Li Chunwen; Tarn, Tzyh-Jong

2010-01-01

We find that feedback control may induce 'pseudo'-nonlinear dynamics in a damped harmonic oscillator, whose centroid trajectory in the phase space behaves like a classical nonlinear system. Thus, similar to nonlinear amplifiers (e.g., rf-driven Josephson junctions), feedback control on the harmonic oscillator can induce nonlinear bifurcation, which can be used to amplify small signals and further to measure quantum states of qubits. Using the cavity QED and the circuit QED systems as examples, we show how to apply our method to measuring the states of two-level atoms and superconducting charge qubits.

Bifurcation of positive solutions to scalar reaction-diffusion equations with nonlinear boundary condition

Science.gov (United States)

Liu, Ping; Shi, Junping

2018-01-01

The bifurcation of non-trivial steady state solutions of a scalar reaction-diffusion equation with nonlinear boundary conditions is considered using several new abstract bifurcation theorems. The existence and stability of positive steady state solutions are proved using a unified approach. The general results are applied to a Laplace equation with nonlinear boundary condition and bistable nonlinearity, and an elliptic equation with superlinear nonlinearity and sublinear boundary conditions.

A new automated assessment method for contrast–detail images by applying support vector machine and its robustness to nonlinear image processing

International Nuclear Information System (INIS)

Takei, Takaaki; Ikeda, Mitsuru; Imai, Kumiharu; Yamauchi-Kawaura, Chiyo; Kato, Katsuhiko; Isoda, Haruo

2013-01-01

The automated contrast–detail (C–D) analysis methods developed so-far cannot be expected to work well on images processed with nonlinear methods, such as noise reduction methods. Therefore, we have devised a new automated C–D analysis method by applying support vector machine (SVM), and tested for its robustness to nonlinear image processing. We acquired the CDRAD (a commercially available C–D test object) images at a tube voltage of 120 kV and a milliampere-second product (mAs) of 0.5–5.0. A partial diffusion equation based technique was used as noise reduction method. Three radiologists and three university students participated in the observer performance study. The training data for our SVM method was the classification data scored by the one radiologist for the CDRAD images acquired at 1.6 and 3.2 mAs and their noise-reduced images. We also compared the performance of our SVM method with the CDRAD Analyser algorithm. The mean C–D diagrams (that is a plot of the mean of the smallest visible hole diameter vs. hole depth) obtained from our devised SVM method agreed well with the ones averaged across the six human observers for both original and noise-reduced CDRAD images, whereas the mean C–D diagrams from the CDRAD Analyser algorithm disagreed with the ones from the human observers for both original and noise-reduced CDRAD images. In conclusion, our proposed SVM method for C–D analysis will work well for the images processed with the non-linear noise reduction method as well as for the original radiographic images.

Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks

Science.gov (United States)

Sebastian, Resmi; Sitharam, T. G.

2018-01-01

Rocks are generally regarded as linearly elastic even though the manifestations of nonlinearity are prominent. The variations of elastic constants with varying strain levels and stress conditions, disagreement between static and dynamic moduli, etc., are some of the examples of nonlinear elasticity in rocks. The grain-to-grain contact, presence of pores and joints along with other compliant features induce the nonlinear behavior in rocks. The nonlinear elastic behavior of rocks is demonstrated through resonant column tests and numerical simulations in this paper. Resonant column tests on intact and jointed gypsum samples across varying strain levels have been performed in laboratory and using numerical simulations. The paper shows the application of resonant column apparatus to obtain the wave velocities of stiff samples at various strain levels under long wavelength condition, after performing checks and incorporating corrections to the obtained resonant frequencies. The numerical simulation and validation of the resonant column tests using distinct element method are presented. The stiffness reductions of testing samples under torsional and flexural vibrations with increasing strain levels have been analyzed. The nonlinear elastic behavior of rocks is reflected in the results, which is enhanced by the presence of joints. The significance of joint orientation and influence of joint spacing during wave propagation have also been assessed and presented using the numerical simulations. It has been found that rock joints also exhibit nonlinear behavior within the elastic limit.

The Importance of Nonlinear Transformations Use in Medical Data Analysis.

Science.gov (United States)

Shachar, Netta; Mitelpunkt, Alexis; Kozlovski, Tal; Galili, Tal; Frostig, Tzviel; Brill, Barak; Marcus-Kalish, Mira; Benjamini, Yoav

2018-05-11

The accumulation of data and its accessibility through easier-to-use platforms will allow data scientists and practitioners who are less sophisticated data analysts to get answers by using big data for many purposes in multiple ways. Data scientists working with medical data are aware of the importance of preprocessing, yet in many cases, the potential benefits of using nonlinear transformations is overlooked. Our aim is to present a semi-automated approach of symmetry-aiming transformations tailored for medical data analysis and its advantages. We describe 10 commonly encountered data types used in the medical field and the relevant transformations for each data type. Data from the Alzheimer's Disease Neuroimaging Initiative study, Parkinson's disease hospital cohort, and disease-simulating data were used to demonstrate the approach and its benefits. Symmetry-targeted monotone transformations were applied, and the advantages gained in variance, stability, linearity, and clustering are demonstrated. An open source application implementing the described methods was developed. Both linearity of relationships and increase of stability of variability improved after applying proper nonlinear transformation. Clustering simulated nonsymmetric data gave low agreement to the generating clusters (Rand value=0.681), while capturing the original structure after applying nonlinear transformation to symmetry (Rand value=0.986). This work presents the use of nonlinear transformations for medical data and the importance of their semi-automated choice. Using the described approach, the data analyst increases the ability to create simpler, more robust and translational models, thereby facilitating the interpretation and implementation of the analysis by medical practitioners. Applying nonlinear transformations as part of the preprocessing is essential to the quality and interpretability of results. ©Netta Shachar, Alexis Mitelpunkt, Tal Kozlovski, Tal Galili, Tzviel Frostig, Barak

Linear and nonlinear response matrix and its application to the SIS18 synchrotron

International Nuclear Information System (INIS)

Parfenova, Angelina

2008-01-01

This Thesis is dedicated to the numerical as well as the experimental study of beam dynamics in circular accelerators. The experimental part was undertaken in the SIS18 synchrotron. The detailed description of the experiments contained in this work can be considered as a starting point for future experiments and machine development. The work has the following structure. In Chapter 2 an overview of the GSI and FAIR accelerator facilities, and a general description of the SIS18 instrumentation related to the study of this work are given. The expected SIS18 performance in view of the upgrade program for FAIR project are outlined. The main beam dynamics issues connected with the purpose of this work are discussed. Chapter 3 is devoted to the study of linear beam dynamics in the SIS18. The resonance beam loss measurements were carried out with residual gas profile monitor in the SIS18 (Chapter 4). In the frame of this work a novel technique 'nonlinear tune response matrix method' to identify strengths, polarities and locations of nonlinear errors in circular accelerators is developed (Chapter 5). In the method the feed down effect of the nonlinear components at level of linear tune response to the closed-orbit change is explored. The closed-orbit change is introduced by varying correction steerers. The tune values are retrieved from the spectrum of coherent betatron oscillations excited by a fast kick. The theoretical background, the robustness of the method and numerical examples for the SIS18 using numerical library MICROMAP are presented. The technique to measure lattice nonlinearities was experimentally validated in the SIS18 where two normal as well as two skew sextupolar errors of the order of natural errors were reconstructed with a tolerant precision. It was shown how this technique can be applied to reconstruct sextupolar nonlinear errors in the complete machine. In Chapter 6 the main results and the conclusions of this work are outlined. (orig.)

The Nonlinear Effects of Pion-Quark Coupling in the Cloudy Bag Model

OpenAIRE

Yasuhiko, FUTAMI; Satoru, AKIYAMA; Department of Physics, Faculty of Science and Technology Science University of Tokyo; Department of Physics, Faculty of Science and Technology Science University of Tokyo

1990-01-01

The nonlinear pion-quark interaction in the Cloudy Bag Model is investigated. The Hamiltonian is normal-ordered. The vacuum expectation value of pion field squared is evaluated by introducting some cutoff momentum for the virtual pions.We then calculate g_A, including other corrections.

The nonlinear effects of pion-quark coupling in the Cloudy Bag Model

International Nuclear Information System (INIS)

Futami, Yasuhiko; Akiyama, Satoru

1990-01-01

The nonlinear pion-quark interaction in the Cloudy Bag Model is investigated. The Hamiltonian is normal-ordered. The vacuum expectation value of pion field squared is evaluated by introducing some cutoff momentum for the virtual pions. We then calculate g A , including other corrections. (author)

Non-linear neutron star oscillations viewed as deviations from an equilibrium state

International Nuclear Information System (INIS)

Sperhake, U

2002-01-01

A numerical technique is presented which facilitates the evolution of non-linear neutron star oscillations with a high accuracy essentially independent of the oscillation amplitude. We apply this technique to radial neutron star oscillations in a Lagrangian formulation and demonstrate the superior performance of the new scheme compared with 'conventional' techniques. The key feature of our approach is to describe the evolution in terms of deviations from an equilibrium configuration. In contrast to standard perturbation analysis we keep all higher order terms in the evolution equations and thus obtain a fully non-linear description. The advantage of our scheme lies in the elimination of background terms from the equations and the associated numerical errors. The improvements thus achieved will be particularly significant in the study of mildly non-linear effects where the amplitude of the dynamic signal is small compared with the equilibrium values but large enough to warrant non-linear effects. We apply the new technique to the study of non-linear coupling of Eigenmodes and non-linear effects in the oscillations of marginally stable neutron stars. We find non-linear effects in low amplitude oscillations to be particularly pronounced in the range of modes with vanishing frequency which typically mark the onset of instability. (author)

Reed-Solomon error-correction as a software patch mechanism.

Energy Technology Data Exchange (ETDEWEB)

Pendley, Kevin D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2013-11-01

This report explores how error-correction data generated by a Reed-Solomon code may be used as a mechanism to apply changes to an existing installed codebase. Using the Reed-Solomon code to generate error-correction data for a changed or updated codebase will allow the error-correction data to be applied to an existing codebase to both validate and introduce changes or updates from some upstream source to the existing installed codebase.

Multiple Δt strategy for particle image velocimetry (PIV) error correction, applied to a hot propulsive jet

Science.gov (United States)

Nogueira, J.; Lecuona, A.; Nauri, S.; Legrand, M.; Rodríguez, P. A.

2009-07-01

PIV (particle image velocimetry) is a measurement technique with growing application to the study of complex flows with relevance to industry. This work is focused on the assessment of some significant PIV measurement errors. In particular, procedures are proposed for estimating, and sometimes correcting, errors coming from the sensor geometry and performance, namely peak-locking and contemporary CCD camera read-out errors. Although the procedures are of general application to PIV, they are applied to a particular real case, giving an example of the methodology steps and the improvement in results that can be obtained. This real case corresponds to an ensemble of hot high-speed coaxial jets, representative of the civil transport aircraft propulsion system using turbofan engines. Errors of ~0.1 pixels displacements have been assessed. This means 10% of the measured magnitude at many points. These results allow the uncertainty interval associated with the measurement to be provided and, under some circumstances, the correction of some of the bias components of the errors. The detection of conditions where the peak-locking error has a period of 2 pixels instead of the classical 1 pixel has been made possible using these procedures. In addition to the increased worth of the measurement, the uncertainty assessment is of interest for the validation of CFD codes.

Nonlinear Elliptic Differential Equations with Multivalued Nonlinearities

Indian Academy of Sciences (India)

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

Fuchs indices and the first integrals of nonlinear differential equations

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.

2005-01-01

New method of finding the first integrals of nonlinear differential equations in polynomial form is presented. Basic idea of our approach is to use the scaling of solution of nonlinear differential equation and to find the dimensions of arbitrary constants in the Laurent expansion of the general solution. These dimensions allows us to obtain the scalings of members for the first integrals of nonlinear differential equations. Taking the polynomials with unknown coefficients into account we present the algorithm of finding the first integrals of nonlinear differential equations in the polynomial form. Our method is applied to look for the first integrals of eight nonlinear ordinary differential equations of the fourth order. The general solution of one of the fourth order ordinary differential equations is given

Nonlinear charge transport in bipolar semiconductors due to electron heating

International Nuclear Information System (INIS)

Molina-Valdovinos, S.; Gurevich, Yu.G.

2016-01-01

It is known that when strong electric field is applied to a semiconductor sample, the current voltage characteristic deviates from the linear response. In this letter, we propose a new point of view of nonlinearity in semiconductors which is associated with the electron temperature dependence on the recombination rate. The heating of the charge carriers breaks the balance between generation and recombination, giving rise to nonequilibrium charge carriers concentration and nonlinearity. - Highlights: • A new mechanism of nonlinearity of current-voltage characteristic (CVC) is proposed. • The hot electron temperature violates the equilibrium between electrons and holes. • This violation gives rise to nonequilibrium concentration of electrons and holes. • This leads to nonlinear CVC (along with the heating nonlinearity).

Nonlinear charge transport in bipolar semiconductors due to electron heating

Energy Technology Data Exchange (ETDEWEB)

Molina-Valdovinos, S., E-mail: sergiom@fisica.uaz.edu.mx [Universidad Autónoma de Zacatecas, Unidad Académica de Física, Calzada Solidaridad esq. Paseo, La Bufa s/n, CP 98060, Zacatecas, Zac, México (Mexico); Gurevich, Yu.G. [Centro de Investigación y de Estudios Avanzados del IPN, Departamento de Física, Av. IPN 2508, México D.F., CP 07360, México (Mexico)

2016-05-27

It is known that when strong electric field is applied to a semiconductor sample, the current voltage characteristic deviates from the linear response. In this letter, we propose a new point of view of nonlinearity in semiconductors which is associated with the electron temperature dependence on the recombination rate. The heating of the charge carriers breaks the balance between generation and recombination, giving rise to nonequilibrium charge carriers concentration and nonlinearity. - Highlights: • A new mechanism of nonlinearity of current-voltage characteristic (CVC) is proposed. • The hot electron temperature violates the equilibrium between electrons and holes. • This violation gives rise to nonequilibrium concentration of electrons and holes. • This leads to nonlinear CVC (along with the heating nonlinearity).

New organic materials for optics: optical storage and nonlinear optics

International Nuclear Information System (INIS)

Gan, F.

1996-01-01

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

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

International Nuclear Information System (INIS)

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

2011-01-01

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

Stability of Nonlinear Neutral Stochastic Functional Differential Equations

Directory of Open Access Journals (Sweden)

Minggao Xue

2010-01-01

Full Text Available Neutral stochastic functional differential equations (NSFDEs have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper is to remove the linear growth condition and establish a Khasminskii-type test for nonlinear NSFDEs. New criteria not only cover a wide class of highly nonlinear NSFDEs but they can also be verified much more easily than the classical criteria. Finally, several examples are given to illustrate main results.

Perturbation analysis of nonlinear matrix population models

Directory of Open Access Journals (Sweden)

Hal Caswell

2008-03-01

Full Text Available Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models, feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios, age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.

Stochastic development regression on non-linear manifolds

DEFF Research Database (Denmark)

Kühnel, Line; Sommer, Stefan Horst

2017-01-01

We introduce a regression model for data on non-linear manifolds. The model describes the relation between a set of manifold valued observations, such as shapes of anatomical objects, and Euclidean explanatory variables. The approach is based on stochastic development of Euclidean diffusion...... processes to the manifold. Defining the data distribution as the transition distribution of the mapped stochastic process, parameters of the model, the non-linear analogue of design matrix and intercept, are found via maximum likelihood. The model is intrinsically related to the geometry encoded...... in the connection of the manifold. We propose an estimation procedure which applies the Laplace approximation of the likelihood function. A simulation study of the performance of the model is performed and the model is applied to a real dataset of Corpus Callosum shapes....