Localization of non-linearly modeled autonomous mobile robots using out-of-sequence measurements.

PubMed

Besada-Portas, Eva; Lopez-Orozco, Jose A; Lanillos, Pablo; de la Cruz, Jesus M

2012-01-01

This paper presents a state of the art of the estimation algorithms dealing with Out-of-Sequence (OOS) measurements for non-linearly modeled systems. The state of the art includes a critical analysis of the algorithm properties that takes into account the applicability of these techniques to autonomous mobile robot navigation based on the fusion of the measurements provided, delayed and OOS, by multiple sensors. Besides, it shows a representative example of the use of one of the most computationally efficient approaches in the localization module of the control software of a real robot (which has non-linear dynamics, and linear and non-linear sensors) and compares its performance against other approaches. The simulated results obtained with the selected OOS algorithm shows the computational requirements that each sensor of the robot imposes to it. The real experiments show how the inclusion of the selected OOS algorithm in the control software lets the robot successfully navigate in spite of receiving many OOS measurements. Finally, the comparison highlights that not only is the selected OOS algorithm among the best performing ones of the comparison, but it also has the lowest computational and memory cost.

Improved Indentation Test for Measuring Nonlinear Elasticity

NASA Technical Reports Server (NTRS)

Eldridge, Jeffrey I.

2004-01-01

A cylindrical-punch indentation technique has been developed as a means of measuring the nonlinear elastic responses of materials -- more specifically, for measuring the moduli of elasticity of materials in cases in which these moduli vary with applied loads. This technique offers no advantage for characterizing materials that exhibit purely linear elastic responses (constant moduli of elasticity, independent of applied loads). However, the technique offers a significant advantage for characterizing such important materials as plasma-sprayed thermal-barrier coatings, which, in cyclic loading, exhibit nonlinear elasticity with hysteresis related to compaction and sliding within their microstructures.

Measuring of nonlinear properties of spatial light modulator with different wavelengths

NASA Astrophysics Data System (ADS)

Khalid, Farah G.; Younis Al-Dabagh, Samar; Ahmed, Sudad S.; Mahmood, Aseel I.; Al-Naimee, Kais

2018-05-01

The non-linear optical properties of Spatial Light Modulator(SLM) represented by Nonlinear Refractive Index (NLR) and nonlinear Absorption coefficient has been measured in this work using highly sensitive method known as Z-scan technique for different wavelengths (red and green). The capability to do instant measurements of different nonlinear optical parameters lead to consider these techniques as a one of the most desired and effective methods that could apply for different materials. The results showed that the NLR were in the same power for the different wavelengths while the nonlinear absorption is higher in case of green laser.

Field Measurement of the Acoustic Nonlinearity Parameter in Turbine Blades

NASA Technical Reports Server (NTRS)

Hinton, Yolanda L.; Na, Jeong K.; Yost, William T.; Kessel, Gregory L.

2000-01-01

Nonlinear acoustics techniques were used to measure fatigue in turbine blades in a power generation plant. The measurements were made in the field using a reference based measurement technique, and a reference sample previously measured in the laboratory. The acoustic nonlinearity parameter showed significant increase with fatigue in the blades, as indicated by service age and areas of increased stress. The technique shows promise for effectively measuring fatigue in field applications and predicting subsequent failures.

Nonlinear matching measure for the analysis of on-off type DNA microarray images

NASA Astrophysics Data System (ADS)

Kim, Jong D.; Park, Misun; Kim, Jongwon

2003-07-01

In this paper, we propose a new nonlinear matching measure for automatic analysis of the on-off type DNA microarray images in which the hybridized spots are detected by the template matching method. The targeting spots of HPV DNA chips are designed for genotyping the human papilloma virus(HPV). The proposed measure is obtained by binarythresholding over the whole template region and taking the number of white pixels inside the spotted area. This measure is evaluated in terms of the accuracy of the estimated marker location to show better performance than the normalized covariance.

From local to global measurements of nonclassical nonlinear elastic effects in geomaterials

DOE PAGES

Lott, Martin; Remillieux, Marcel C.; Le Bas, Pierre-Yves; ...

2016-09-07

Here, the equivalence between local and global measures of nonclassical nonlinear elasticity is established in a slender resonant bar. Nonlinear effects are first measured globally using nonlinear resonance ultrasound spectroscopy (NRUS), which monitors the relative shift of the resonance frequency as a function of the maximum dynamic strain in the sample. Subsequently, nonlinear effects are measured locally at various positions along the sample using dynamic acousto elasticity testing (DAET). Finally, after correcting analytically the DAET data for three-dimensional strain effects and integrating numerically these corrected data along the length of the sample, the NRUS global measures are retrieved almost exactly.

Measurement Model Nonlinearity in Estimation of Dynamical Systems

NASA Astrophysics Data System (ADS)

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

2012-06-01

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

Human middle-ear nonlinearity measurements using laser Doppler vibrometry

NASA Astrophysics Data System (ADS)

Gladiné, Kilian; Muyshondt, Pieter G. G.; Dirckx, Joris J. J.

2017-12-01

It has long been supposed that the middle-ear has near to perfect linear characteristics, and several attempts have been made to investigate this hypothesis. In conclusion, the middle-ear was regarded as a linear system at least up till sound pressure levels of 120 dB. Because of the linear relationship between Doppler shift of light and the vibration velocity of the object on which the light is reflected, laser Doppler vibrometry (LDV) is an intrinsically highly linear measurement technique. Therefore it allows straightforward detection of very small nonlinearities in a vibration response. In this paper, laser Doppler vibrometry and multisine stimulation are used to detect nonlinear distortions in the vibration response at the umbo of the tympanic membrane of seven human cadaver temporal bones. Nonlinear distortions were detected starting from sound pressure levels of 99 dB and measurements were performed up to 120 dB. These distortions can be subdivided into even degree (e.g. quadratic distortion tones) and odd degree nonlinear distortions (e.g. cubic distortion tones). We illustrate that with odd multisine stimulation the level of even and odd degree nonlinear distortions can be investigated separately. In conclusion, laser Doppler vibrometry is an adequate tool to detect nonlinear distortions in the middle-ear system and to quantify the level of such distortions even at 57 dB below the vibration response. The possibility to analyze even degree and odd degree nonlinear distortion levels separately can help in future work to pinpoint the source of the nonlinearity.

Nonlinear ultrasonic measurements with EMATs for detecting pre-cracking fatigue damage

NASA Astrophysics Data System (ADS)

Cobb, A.; Capps, M.; Duffer, C.; Feiger, J.; Robinson, K.; Hollingshaus, B.

2012-05-01

This paper describes an approach for measuring material degradation using nonlinear acoustics. The importance of this measurement is that prior efforts have shown that the degree of acoustic nonlinearity increases as a function of fatigue damage accumulation. By exploiting this physical mechanism, there is the potential to develop methods for measuring the remaining life of critical components. The challenge with existing approaches for measuring acoustic nonlinearity is that primarily they have only been shown to be successful in a laboratory setting. This paper presents a potential approach for field measurement of acoustic nonlinearity that utilizes Rayleigh waves generated from electromagnetic acoustic transducers (EMATs). Rayleigh waves have unique advantages because the sound propagates along the surface, allowing for application on complex engineering structures. EMATs were used in place of traditional piezoelectric transducers because the sound is generated directly in the metallic structure, eliminating the need for sound coupling fluids that are a source of variability. Custom EMATs were developed and nonlinearity measurements were performed on 410 stainless steel specimens that were subjected to a fatigue process. Some experiments showed an increase in the acoustic nonlinearity of up to 500% compared to the unfatigued value. Other experiments had too much scatter and did not show this relationship consistently due to unanticipated challenges in producing repeatable measurements. Lessons learned from the project effort will be presented to potentially improve the repeatability of the measurement approach. If the scatter can be reduced, this EMAT-based technique could result in a field deployable prognosis tool.

Epileptic seizure prediction by non-linear methods

DOEpatents

Hively, Lee M.; Clapp, Ned E.; Daw, C. Stuart; Lawkins, William F.

1999-01-01

Methods and apparatus for automatically predicting epileptic seizures monitor and analyze brain wave (EEG or MEG) signals. Steps include: acquiring the brain wave data from the patient; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis tools; obtaining time serial trends in the nonlinear measures; comparison of the trend to known seizure predictors; and providing notification that a seizure is forthcoming.

Synthesis of nonlinear frequency responses with experimentally extracted nonlinear modes

NASA Astrophysics Data System (ADS)

Peter, Simon; Scheel, Maren; Krack, Malte; Leine, Remco I.

2018-02-01

Determining frequency response curves is a common task in the vibration analysis of nonlinear systems. Measuring nonlinear frequency responses is often challenging and time consuming due to, e.g., coexisting stable or unstable vibration responses and structure-exciter-interaction. The aim of the current paper is to develop a method for the synthesis of nonlinear frequency responses near an isolated resonance, based on data that can be easily and automatically obtained experimentally. The proposed purely experimental approach relies on (a) a standard linear modal analysis carried out at low vibration levels and (b) a phase-controlled tracking of the backbone curve of the considered forced resonance. From (b), the natural frequency and vibrational deflection shape are directly obtained as a function of the vibration level. Moreover, a damping measure can be extracted by power considerations or from the linear modal analysis. In accordance with the single nonlinear mode assumption, the near-resonant frequency response can then be synthesized using this data. The method is applied to a benchmark structure consisting of a cantilevered beam attached to a leaf spring undergoing large deflections. The results are compared with direct measurements of the frequency response. The proposed approach is fast, robust and provides a good estimate for the frequency response. It is also found that direct frequency response measurement is less robust due to bifurcations and using a sine sweep excitation with a conventional force controller leads to underestimation of maximum vibration response.

Epileptic seizure prediction by non-linear methods

DOEpatents

Hively, L.M.; Clapp, N.E.; Day, C.S.; Lawkins, W.F.

1999-01-12

This research discloses methods and apparatus for automatically predicting epileptic seizures monitor and analyze brain wave (EEG or MEG) signals. Steps include: acquiring the brain wave data from the patient; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis tools; obtaining time serial trends in the nonlinear measures; comparison of the trend to known seizure predictors; and providing notification that a seizure is forthcoming. 76 figs.

Apparatus and method for epileptic seizure detection using non-linear techniques

DOEpatents

Hively, Lee M.; Clapp, Ned E.; Daw, C. Stuart; Lawkins, William F.

1998-01-01

Methods and apparatus for automatically detecting epileptic seizures by monitoring and analyzing brain wave (EEG or MEG) signals. Steps include: acquiring the brain wave data from the patient; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; determining that one or more trends in the nonlinear measures indicate a seizure, and providing notification of seizure occurrence.

Nonscanning Moiré deflectometry for measurement of nonlinear refractive index and absorption coefficient of liquids.

PubMed

Farahani, Shahrzad Shahrabi; Madanipour, Khosro; Koohian, Ata

2017-05-01

In this work, a nonscanning measurement technique is presented for determining the nonlinear refractive index and absorption coefficient of liquid media based on Moiré deflectometry. In the proposed method two lasers are used: a low power, wide beam as probe and a high power with specific wavelength as a pump. Interaction of the pump laser beam with the nonlinear sample changes the refractive index, which leads to change in convergence/divergence of the collimated incident probe laser beam. The induced deflection is monitored by Moiré deflectometry. If the pump laser has a Gaussian intensity profile, the refractive index profile of the sample is Gaussian, too. Measuring the deflection angle of the probe beam by Moiré fringes deflection, and by using the inverse Abel transform integral, the refractive index profile and nonlinear refractive index can be determined. This method is fast, easy, and insensitive to environmental noise and allows real-time measurement. Also, the refractive index profile of the interacted medium with pump laser can be achieved by this technique. As a liquid sample, a DCJ dye in water solution was studied. The value of nonlinear refractive index, n₂, and absorption coefficient, α, were obtained -2.54×10^-4  cm² w^-1 and 1.368  cm^-1, respectively.

Apparatus and method for epileptic seizure detection using non-linear techniques

DOEpatents

Hively, L.M.; Clapp, N.E.; Daw, C.S.; Lawkins, W.F.

1998-04-28

Methods and apparatus are disclosed for automatically detecting epileptic seizures by monitoring and analyzing brain wave (EEG or MEG) signals. Steps include: acquiring the brain wave data from the patient; digitizing the data; obtaining nonlinear measures of the data via chaotic time series analysis; obtaining time serial trends in the nonlinear measures; determining that one or more trends in the nonlinear measures indicate a seizure, and providing notification of seizure occurrence. 76 figs.

Quantum state matching of qubits via measurement-induced nonlinear transformations

NASA Astrophysics Data System (ADS)

Kálmán, Orsolya; Kiss, Tamás

2018-03-01

We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined with a postselection scheme conditioned on the measurement result obtained on one of the qubits of the pair. The resulting transformation is a deterministic, nonlinear, chaotic map in the Hilbert space. We derive a class of these transformations capable of orthogonalizing nonorthogonal qubit states after a few iterations. These nonlinear maps orthogonalize states which correspond to the two different convergence regions of the nonlinear map. Based on the analysis of the border (the so-called Julia set) between the two regions of convergence, we show that it is always possible to find a map capable of deciding whether an unknown state is within a neighborhood of fixed radius around a desired quantum state. We analyze which one- and two-qubit operations would physically realize the scheme. It is possible to find a single two-qubit unitary gate for each map or, alternatively, a universal special two-qubit gate together with single-qubit gates in order to carry out the task. We note that it is enough to have a single physical realization of the required gates due to the iterative nature of the scheme.

Cross-evidence for hypnotic susceptibility through nonlinear measures on EEGs of non-hypnotized subjects

NASA Astrophysics Data System (ADS)

Chiarucci, Riccardo; Madeo, Dario; Loffredo, Maria I.; Castellani, Eleonora; Santarcangelo, Enrica L.; Mocenni, Chiara

2014-07-01

Assessment of hypnotic susceptibility is usually obtained through the application of psychological instruments. A satisfying classification obtained through quantitative measures is still missing, although it would be very useful for both diagnostic and clinical purposes. Aiming at investigating the relationship between the cortical brain activity and the hypnotic susceptibility level, we propose the combined use of two methodologies - Recurrence Quantification Analysis and Detrended Fluctuation Analysis - both inherited from nonlinear dynamics. Indicators obtained through the application of these techniques to EEG signals of individuals in their ordinary state of consciousness allowed us to obtain a clear discrimination between subjects with high and low susceptibility to hypnosis. Finally a neural network approach was used to perform classification analysis.

Measurement of nonlinear refractive index and ionization rates in air using a wavefront sensor.

PubMed

Schwarz, Jens; Rambo, Patrick; Kimmel, Mark; Atherton, Briggs

2012-04-09

A wavefront sensor has been used to measure the Kerr nonlinear focal shift of a high intensity ultrashort pulse beam in a focusing beam geometry while accounting for the effects of plasma-defocusing. It is shown that plasma-defocusing plays a major role in the nonlinear focusing dynamics and that measurements of Kerr nonlinearity and ionization are coupled. Furthermore, this coupled effect leads to a novel way that measures the laser ionization rates in air under atmospheric conditions as well as Kerr nonlinearity. The measured nonlinear index n₂ compares well with values found in the literature and the measured ionization rates could be successfully benchmarked to the model developed by Perelomov, Popov, and Terentev (PPT model) [Sov. Phys. JETP 50, 1393 (1966)].

Femtosecond Z-scan measurements of the nonlinear refractive index of fused silica

NASA Astrophysics Data System (ADS)

Zhang, Lin; Shi, Zhendong; Ma, Hua; Ren, Huan; Yuan, Quan; Ma, Yurong; Feng, Xiaoxuan; Chen, Bo; Yang, Yi

2018-01-01

Z-scan technology is a popular experimental technique for determining the nonlinear refractive index of the material. However, it encounters a great difficulty in measuring the weak nonlinear material like fused silica which is about two orders of magnitude below the nonlinear refractive index of most of the materials studied with the nanosecond and picosecond Z-scan methods. In this case, the change of refractive index introduced by accumulation of thermal effects cannot be neglected. In order to have a reliable measurement of the nonlinear refractive index, a metrology bench based on the femtosecond Z-scan technology is developed. The intensity modulation component and the differential measurement system are applied to guarantee the accuracy of the measuring system. Based on the femtosecond Z-scan theory, the femtosecond laser Z-scan technique is performed on fused silica, and the nonlinear refractive index of Fused silica is determined to be 9.2039×10-14esu for 800nm, 37fs pulse duration at I0=50GW/cm2 with a good repeatability of 6.7%.

[Formula: see text]-Contraction in terms of measure of noncompactness with application for nonlinear integral equations.

PubMed

Nikbakhtsarvestani, Farzaneh; Vaezpour, S Mansour; Asadi, Mehdi

2017-01-01

In this paper, some new generalization of Darbo's fixed point theorem is proved by using a [Formula: see text]-contraction in terms of a measure of noncompactness. Our result extends to obtaining a common fixed point for a pair of compatible mappings. The paper contains an application for nonlinear integral equations as well.

Measurement of material nonlinearity using surface acoustic wave parametric interaction and laser ultrasonics.

PubMed

Stratoudaki, Theodosia; Ellwood, Robert; Sharples, Steve; Clark, Matthew; Somekh, Michael G; Collison, Ian J

2011-04-01

A dual frequency mixing technique has been developed for measuring velocity changes caused by material nonlinearity. The technique is based on the parametric interaction between two surface acoustic waves (SAWs): The low frequency pump SAW generated by a transducer and the high frequency probe SAW generated and detected using laser ultrasonics. The pump SAW stresses the material under the probe SAW. The stress (typically <5 MPa) is controlled by varying the timing between the pump and probe waves. The nonlinear interaction is measured as a phase modulation of the probe SAW and equated to a velocity change. The velocity-stress relationship is used as a measure of material nonlinearity. Experiments were conducted to observe the pump-probe interaction by changing the pump frequency and compare the nonlinear response of aluminum and fused silica. Experiments showed these two materials had opposite nonlinear responses, consistent with previously published data. The technique could be applied to life-time predictions of engineered components by measuring changes in nonlinear response caused by fatigue.

Nonlinear analysis and dynamic compensation of stylus scanning measurement with wide range

NASA Astrophysics Data System (ADS)

Hui, Heiyang; Liu, Xiaojun; Lu, Wenlong

2011-12-01

Surface topography is an important geometrical feature of a workpiece that influences its quality and functions such as friction, wearing, lubrication and sealing. Precision measurement of surface topography is fundamental for product quality characterizing and assurance. Stylus scanning technique is a widely used method for surface topography measurement, and it is also regarded as the international standard method for 2-D surface characterizing. Usually surface topography, including primary profile, waviness and roughness, can be measured precisely and efficiently by this method. However, by stylus scanning method to measure curved surface topography, the nonlinear error is unavoidable because of the difference of horizontal position of the actual measured point from given sampling point and the nonlinear transformation process from vertical displacement of the stylus tip to angle displacement of the stylus arm, and the error increases with the increasing of measuring range. In this paper, a wide range stylus scanning measurement system based on cylindrical grating interference principle is constructed, the originations of the nonlinear error are analyzed, the error model is established and a solution to decrease the nonlinear error is proposed, through which the error of the collected data is dynamically compensated.

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

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

Direct measurements of nonlinear absorption and refraction in solutions of phthalocyanines

NASA Technical Reports Server (NTRS)

Wei, T. H.; Hagan, D. J.; Sence, M. J.; Van Stryland, E. W.; Perry, J. W.; Coulter, D. R.

1992-01-01

Direct measurements are reported of the excited singlet-state absorption cross section and the associated nonlinear refractive cross section using picosecond pulses at 532 nm in solutions of phthalocyanine and naphthalocyanine dyes. By monitoring the transmittance and far-field spatial beam distortion for different pulsewidths in the picosecond regime, it is shown that both the nonlinear absorption and refraction are fluence (energy-per-unit-area) rather than irradiance dependent. Thus, excited-state absorption is the dominant nonlinear absorption process, and the observed nonlinear refraction is also due to real population excitation.

Study of third order nonlinearity of chalcogenide thin films using third harmonic generation measurements

NASA Astrophysics Data System (ADS)

Rani, Sunita; Mohan, Devendra; Kumar, Manish; Sanjay

2018-05-01

Third order nonlinear susceptibility of (GeSe3.5)100-xBix (x = 0, 10, 14) and ZnxSySe100-x-y (x = 2, y = 28; x = 4, y = 20; x = 6, y = 12; x = 8, y = 4) amorphous chalcogenide thin films prepared using thermal evaporation technique is estimated. The dielectric constant at incident and third harmonic wavelength is calculated using "PARAV" computer program. 1064 nm wavelength of Nd: YAG laser is incident on thin film and third harmonic signal at 355 nm wavelength alongwith fundamental light is obtained in reflection that is separated from 1064 nm using suitable optical filter. Reflected third harmonic signal is measured to trace the influence of Bi and Zn on third order nonlinear susceptibility and is found to increase with increase in Bi and Zn content in (GeSe3.5)100-xBix, and ZnxSySe100-x-y chalcogenide thin films respectively. The excellent optical nonlinear property shows the use of chalcogenide thin films in photonics for wavelength conversion and optical data processing.

Single shot, double differential spectral measurements of inverse Compton scattering in the nonlinear regime

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

Sakai, Y.; Gadjev, I.; Hoang, P.

Inverse Compton scattering (ICS) is a unique mechanism for producing fast pulses$-$picosecond and below$-$of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by thismore » source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K -edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.« less

Single shot, double differential spectral measurements of inverse Compton scattering in the nonlinear regime

DOE PAGES

Sakai, Y.; Gadjev, I.; Hoang, P.; ...

2017-06-05

Inverse Compton scattering (ICS) is a unique mechanism for producing fast pulses$-$picosecond and below$-$of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by thismore » source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K -edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.« less

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

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

Smith, Scott A; Catalfamo, Simone; Brake, Matthew R. W.

2017-01-01

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratiomore » variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.« less

Information measures in nonlinear experimental design

NASA Technical Reports Server (NTRS)

Niple, E.; Shaw, J. H.

1980-01-01

Some different approaches to the problem of designing experiments which estimate the parameters of nonlinear models are discussed. The assumption in these approaches that the information in a set of data can be represented by a scalar is criticized, and the nonscalar discrimination information is proposed as the proper measure to use. The two-step decay example in Box and Lucas (1959) is used to illustrate the main points of the discussion.

Modified method of simplest equation: Powerful tool for obtaining exact and approximate traveling-wave solutions of nonlinear PDEs

NASA Astrophysics Data System (ADS)

Vitanov, Nikolay K.

2011-03-01

We discuss the class of equations ∑i,j=0mAij(u){∂iu}/{∂ti}∂+∑k,l=0nBkl(u){∂ku}/{∂xk}∂=C(u) where Aij( u), Bkl( u) and C( u) are functions of u( x, t) as follows: (i) Aij, Bkl and C are polynomials of u; or (ii) Aij, Bkl and C can be reduced to polynomials of u by means of Taylor series for small values of u. For these two cases the above-mentioned class of equations consists of nonlinear PDEs with polynomial nonlinearities. We show that the modified method of simplest equation is powerful tool for obtaining exact traveling-wave solution of this class of equations. The balance equations for the sub-class of traveling-wave solutions of the investigated class of equations are obtained. We illustrate the method by obtaining exact traveling-wave solutions (i) of the Swift-Hohenberg equation and (ii) of the generalized Rayleigh equation for the cases when the extended tanh-equation or the equations of Bernoulli and Riccati are used as simplest equations.

Comparison of simulated and measured nonlinear ultrasound fields

NASA Astrophysics Data System (ADS)

Du, Yigang; Jensen, Henrik; Jensen, Jørgen Arendt

2011-03-01

In this paper results from a non-linear AS (angular spectrum) based ultrasound simulation program are compared to water-tank measurements. A circular concave transducer with a diameter of 1 inch (25.4 mm) is used as the emitting source. The measured pulses are first compared with the linear simulation program Field II, which will be used to generate the source for the AS simulation. The generated non-linear ultrasound field is measured by a hydrophone in the focal plane. The second harmonic component from the measurement is compared with the AS simulation, which is used to calculate both fundamental and second harmonic fields. The focused piston transducer with a center frequency of 5 MHz is excited by a waveform generator emitting a 6-cycle sine wave. The hydrophone is mounted in the focal plane 118 mm from the transducer. The point spread functions at the focal depth from Field II and measurements are illustrated. The FWHM (full width at half maximum) values are 1.96 mm for the measurement and 1.84 mm for the Field II simulation. The fundamental and second harmonic components of the experimental results are plotted compared with the AS simulations. The RMS (root mean square) errors of the AS simulations are 7.19% and 10.3% compared with the fundamental and second harmonic components of the measurements.

A method for measuring the nonlinear response in dielectric spectroscopy through third harmonics detection.

PubMed

Thibierge, C; L'Hôte, D; Ladieu, F; Tourbot, R

2008-10-01

We present a high sensitivity method allowing the measurement of the nonlinear dielectric susceptibility of an insulating material at finite frequency. It has been developed for the study of dynamic heterogeneities in supercooled liquids using dielectric spectroscopy at frequencies 0.05 Hz < or = f < or = 3x10(4) Hz. It relies on the measurement of the third harmonics component of the current flowing out of a capacitor. We first show that standard laboratory electronics (amplifiers and voltage sources) nonlinearities lead to limits on the third harmonics measurements that preclude reaching the level needed by our physical goal, a ratio of the third harmonics to the fundamental signal about 10(-7). We show that reaching such a sensitivity needs a method able to get rid of the nonlinear contributions both of the measuring device (lock-in amplifier) and of the excitation voltage source. A bridge using two sources fulfills only the first of these two requirements, but allows to measure the nonlinearities of the sources. Our final method is based on a bridge with two plane capacitors characterized by different dielectric layer thicknesses. It gets rid of the source and amplifier nonlinearities because in spite of a strong frequency dependence of the capacitor impedance, it is equilibrated at any frequency. We present the first measurements of the physical nonlinear response using our method. Two extensions of the method are suggested.

Direct measurement of nonlinear properties of bipartite quantum states.

PubMed

Bovino, Fabio Antonio; Castagnoli, Giuseppe; Ekert, Artur; Horodecki, Paweł; Alves, Carolina Moura; Sergienko, Alexander Vladimir

2005-12-09

Nonlinear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum-information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number of parameters that specify the state. Here we extract a nonlocal and a nonlinear quantity, namely, the Renyi entropy, from local measurements on two pairs of polarization-entangled photons. We also introduce a "phase marking" technique which allows the selection of uncorrupted outcomes even with nondeterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of nonlinear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-Clauser-Horne-Shimony-Holt inequalities.

Nonlinear refractive index measurements and self-action effects in Roselle-Hibiscus Sabdariffa solutions

NASA Astrophysics Data System (ADS)

Henari, F. Z.; Al-Saie, A.

2006-12-01

We report the observation of self-action phenomena, such as self-focusing, self-defocusing, self-phase modulation and beam fanning in Roselle-Hibiscus Sabdariffa solutions. This material is found to be a new type of natural nonlinear media, and the nonlinear reflective index coefficient has been determined using a Z-scan technique and by measuring the critical power for the self-trapping effect. Z-scan measurements show that this material has a large negative nonlinear refractive index, n 2 = 1 × 10-4 esu. A comparison between the experimental n 2 values and the calculated thermal value for n 2 suggests that the major contribution to nonlinear response is of thermal origin.

Neural net classification of REM sleep based on spectral measures as compared to nonlinear measures.

PubMed

Grözinger, M; Fell, J; Röschke, J

2001-11-01

In various studies the implementation of nonlinear and nonconventional measures has significantly improved EEG (electroencephalogram) analyses as compared to using conventional parameters alone. A neural network algorithm well approved in our laboratory for the automatic recognition of rapid eye movement (REM) sleep was investigated in this regard. Originally based on a broad range of spectral power inputs, we additionally supplied the nonlinear measures of the largest Lyapunov exponent and correlation dimension as well as the nonconventional stochastic measures of spectral entropy and entropy of amplitudes. No improvement in the detection of REM sleep could be achieved by the inclusion of the new measures. The accuracy of the classification was significantly worse, however, when supplied with these variables alone. In view of results demonstrating the efficiency of nonconventional measures in EEG analysis, the benefit appears to depend on the nature of the problem.

Stress measurement in thick plates using nonlinear ultrasonics

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

Abbasi, Zeynab, E-mail: zabbas5@uic.edu, E-mail: dozevin@uic.edu; Ozevin, Didem, E-mail: zabbas5@uic.edu, E-mail: dozevin@uic.edu

2015-03-31

In this paper the interaction between nonlinear ultrasonic characteristics and stress state of complex loaded thick steel plates using fundamental theory of nonlinear ultrasonics is investigated in order to measure the stress state at a given cross section. The measurement concept is based on phased array placement of ultrasonic transmitter-receiver to scan three angles of a given cross section using Rayleigh waves. The change in the ultrasonic data in thick steel plates is influenced by normal and shear stresses; therefore, three measurements are needed to solve the equations simultaneously. Different thickness plates are studied in order to understand the interactionmore » of Rayleigh wave penetration depth and shear stress. The purpose is that as the thickness becomes smaller, the shear stress becomes negligible at the angled measurement. For thicker cross section, shear stress becomes influential if the depth of penetration of Rayleigh wave is greater than the half of the thickness. The influences of plate thickness and ultrasonic frequency on the identification of stress tensor are numerically studied in 3D structural geometry and Murnaghan material model. The experimental component of this study includes uniaxial loading of the plate while measuring ultrasonic wave at three directions (perpendicular, parallel and angled to the loading direction). Instead of rotating transmitter-receiver pair for each test, a device capable of measuring the three angles is designed.« less

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

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

Perev, Kamen

2013-12-18

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

General implementation of arbitrary nonlinear quadrature phase gates

NASA Astrophysics Data System (ADS)

Marek, Petr; Filip, Radim; Ogawa, Hisashi; Sakaguchi, Atsushi; Takeda, Shuntaro; Yoshikawa, Jun-ichi; Furusawa, Akira

2018-02-01

We propose general methodology of deterministic single-mode quantum interaction nonlinearly modifying single quadrature variable of a continuous-variable system. The methodology is based on linear coupling of the system to ancillary systems subsequently measured by quadrature detectors. The nonlinear interaction is obtained by using the data from the quadrature detection for dynamical manipulation of the coupling parameters. This measurement-induced methodology enables direct realization of arbitrary nonlinear quadrature interactions without the need to construct them from the lowest-order gates. Such nonlinear interactions are crucial for more practical and efficient manipulation of continuous quadrature variables as well as qubits encoded in continuous-variable systems.

Nonlinear Poisson Equation for Heterogeneous Media

PubMed Central

Hu, Langhua; Wei, Guo-Wei

2012-01-01

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. PMID:22947937

Nonlinear Poisson equation for heterogeneous media.

PubMed

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.

Probe classification of on-off type DNA microarray images with a nonlinear matching measure

NASA Astrophysics Data System (ADS)

Ryu, Munho; Kim, Jong Dae; Min, Byoung Goo; Kim, Jongwon; Kim, Y. Y.

2006-01-01

We propose a nonlinear matching measure, called counting measure, as a signal detection measure that is defined as the number of on pixels in the spot area. It is applied to classify probes for an on-off type DNA microarray, where each probe spot is classified as hybridized or not. The counting measure also incorporates the maximum response search method, where the expected signal is obtained by taking the maximum among the measured responses of the various positions and sizes of the spot template. The counting measure was compared to existing signal detection measures such as the normalized covariance and the median for 2390 patient samples tested on the human papillomavirus (HPV) DNA chip. The counting measure performed the best regardless of whether or not the maximum response search method was used. The experimental results showed that the counting measure combined with the positional search was the most preferable.

Bilinear modeling and nonlinear estimation

NASA Technical Reports Server (NTRS)

Dwyer, Thomas A. W., III; Karray, Fakhreddine; Bennett, William H.

1989-01-01

New methods are illustrated for online nonlinear estimation applied to the lateral deflection of an elastic beam on board measurements of angular rates and angular accelerations. The development of the filter equations, together with practical issues of their numerical solution as developed from global linearization by nonlinear output injection are contrasted with the usual method of the extended Kalman filter (EKF). It is shown how nonlinear estimation due to gyroscopic coupling can be implemented as an adaptive covariance filter using off-the-shelf Kalman filter algorithms. The effect of the global linearization by nonlinear output injection is to introduce a change of coordinates in which only the process noise covariance is to be updated in online implementation. This is in contrast to the computational approach which arises in EKF methods arising by local linearization with respect to the current conditional mean. Processing refinements for nonlinear estimation based on optimal, nonlinear interpolation between observations are also highlighted. In these methods the extrapolation of the process dynamics between measurement updates is obtained by replacing a transition matrix with an operator spline that is optimized off-line from responses to selected test inputs.

Nonlinear viscoelastic characterization of polymer materials using a dynamic-mechanical methodology

NASA Technical Reports Server (NTRS)

Strganac, Thomas W.; Payne, Debbie Flowers; Biskup, Bruce A.; Letton, Alan

1995-01-01

Polymer materials retrieved from LDEF exhibit nonlinear constitutive behavior; thus the authors present a method to characterize nonlinear viscoelastic behavior using measurements from dynamic (oscillatory) mechanical tests. Frequency-derived measurements are transformed into time-domain properties providing the capability to predict long term material performance without a lengthy experimentation program. Results are presented for thin-film high-performance polymer materials used in the fabrication of high-altitude scientific balloons. Predictions based upon a linear test and analysis approach are shown to deteriorate for moderate to high stress levels expected for extended applications. Tests verify that nonlinear viscoelastic response is induced by large stresses. Hence, an approach is developed in which the stress-dependent behavior is examined in a manner analogous to modeling temperature-dependent behavior with time-temperature correspondence and superposition principles. The development leads to time-stress correspondence and superposition of measurements obtained through dynamic mechanical tests. Predictions of material behavior using measurements based upon linear and nonlinear approaches are compared with experimental results obtained from traditional creep tests. Excellent agreement is shown for the nonlinear model.

Nondestructive distributed measurement of supercontinuum generation along highly nonlinear optical fibers.

PubMed

Hontinfinde, Régis; Coulibaly, Saliya; Megret, Patrice; Taki, Majid; Wuilpart, Marc

2017-05-01

Supercontinuum generation (SCG) in optical fibers arises from the spectral broadening of an intense light, which results from the interplay of both linear and nonlinear optical effects. In this Letter, a nondestructive optical time domain reflectometry method is proposed for the first time, to the best of our knowledge, to measure the spatial (longitudinal) evolution of the SC induced along an optical fiber. The method was experimentally tested on highly nonlinear fibers. The experimental results are in a good agreement with the optical spectra measured at the fiber outputs.

Analysis and correction of gradient nonlinearity bias in ADC measurements

PubMed Central

Malyarenko, Dariya I.; Ross, Brian D.; Chenevert, Thomas L.

2013-01-01

Purpose Gradient nonlinearity of MRI systems leads to spatially-dependent b-values and consequently high non-uniformity errors (10–20%) in ADC measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. Methods All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Results Spatial dependence of nonlinearity correction terms accounts for the bulk (75–95%) of ADC bias for FA = 0.3–0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. Conclusions The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. PMID:23794533

Direct measurement of nonlinear dispersion relation for water surface waves

NASA Astrophysics Data System (ADS)

Magnus Arnesen Taklo, Tore; Trulsen, Karsten; Elias Krogstad, Harald; Gramstad, Odin; Nieto Borge, José Carlos; Jensen, Atle

2013-04-01

The linear dispersion relation for water surface waves is often taken for granted for the interpretation of wave measurements. High-resolution spatiotemporal measurements suitable for direct validation of the linear dispersion relation are on the other hand rarely available. While the imaging of the ocean surface with nautical radar does provide the desired spatiotemporal coverage, the interpretation of the radar images currently depends on the linear dispersion relation as a prerequisite, (Nieto Borge et al., 2004). Krogstad & Trulsen (2010) carried out numerical simulations with the nonlinear Schrödinger equation and its generalizations demonstrating that the nonlinear evolution of wave fields may render the linear dispersion relation inadequate for proper interpretation of observations, the reason being that the necessary domain of simultaneous coverage in space and time would allow significant nonlinear evolution. They found that components above the spectral peak can have larger phase and group velocities than anticipated by linear theory, and that the spectrum does not maintain a thin dispersion surface. We have run laboratory experiments and accurate numerical simulations designed to have sufficient resolution in space and time to deduce the dispersion relation directly. For a JONSWAP spectrum we find that the linear dispersion relation can be appropriate for the interpretation of spatiotemporal measurements. For a Gaussian spectrum with narrower bandwidth we find that the dynamic nonlinear evolution in space and time causes the directly measured dispersion relation to deviate from the linear dispersion surface in good agreement with our previous numerical predictions. This work has been supported by RCN grant 214556/F20. Krogstad, H. E. & Trulsen, K. (2010) Interpretations and observations of ocean wave spectra. Ocean Dynamics 60:973-991. Nieto Borge, J. C., Rodríguez, G., Hessner, K., Izquierdo, P. (2004) Inversion of marine radar images for surface wave

Measurement of picometre non-linearity in an optical grating encoder using x-ray interferometry

NASA Astrophysics Data System (ADS)

Yacoot, Andrew; Cross, Nigel

2003-01-01

X-ray interferometry has been used to characterize the non-linearity in an optical encoder displacement measuring system. Traceable measurements of the non-linearity have been made and an estimation of the uncertainty associated with the measurements is given. Cyclic errors with a magnitude of up to 50 pm and periodicity of the encoder system (128 nm) have been recorded.

Nonlinear system identification technique validation

NASA Astrophysics Data System (ADS)

Rudko, M.; Bussgang, J. J.

1982-01-01

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

Nonlinearity of resistive impurity effects on van der Pauw measurements

NASA Astrophysics Data System (ADS)

Koon, D. W.

2006-09-01

The dependence of van der Pauw resistivity measurements on local macroscopic inhomogeneities is shown to be nonlinear. A resistor grid network models a square laminar specimen, enabling the investigation of both positive and negative local perturbations in resistivity. The effect of inhomogeneity is measured both experimentally, for an 11×11 grid, and computationally, for both 11×11 and 101×101 grids. The maximum "shortlike" perturbation produces 3.1±0.2 times the effect predicted by the linear approximation, regardless of its position within the specimen, while all "openlike" perturbations produce a smaller effect than predicted. An empirical nonlinear correction for f(x ,y) is presented which provides excellent fit over the entire range of both positive and negative perturbations for the entire specimen.

Model updating strategy for structures with localised nonlinearities using frequency response measurements

NASA Astrophysics Data System (ADS)

Wang, Xing; Hill, Thomas L.; Neild, Simon A.; Shaw, Alexander D.; Haddad Khodaparast, Hamed; Friswell, Michael I.

2018-02-01

This paper proposes a model updating strategy for localised nonlinear structures. It utilises an initial finite-element (FE) model of the structure and primary harmonic response data taken from low and high amplitude excitations. The underlying linear part of the FE model is first updated using low-amplitude test data with established techniques. Then, using this linear FE model, the nonlinear elements are localised, characterised, and quantified with primary harmonic response data measured under stepped-sine or swept-sine excitations. Finally, the resulting model is validated by comparing the analytical predictions with both the measured responses used in the updating and with additional test data. The proposed strategy is applied to a clamped beam with a nonlinear mechanism and good agreements between the analytical predictions and measured responses are achieved. Discussions on issues of damping estimation and dealing with data from amplitude-varying force input in the updating process are also provided.

Raman gain and nonlinear optical absorption measurements in a low-loss silicon waveguide

NASA Astrophysics Data System (ADS)

Rong, Haisheng; Liu, Ansheng; Nicolaescu, Remus; Paniccia, Mario; Cohen, Oded; Hak, Dani

2004-09-01

We fabricated a low-loss (˜0.22dB/cm) rib waveguide (WG) in silicon-on-insulator with a small effective core area of ˜1.57μm2 and measured the stimulated Raman scattering gain in the WG. We obtained 2.3dB Raman gain in a 4.8-cm-long S-shaped WG using a 1455nm pump laser with a cw power of 0.9W measured before the WG. In addition, we observed nonlinear dependence of Raman gain and optical propagation loss as a function of the pump power. Our study shows that this mainly is due to two-photon absorption (TPA) induced free carrier absorption in the silicon WG. We experimentally determined the TPA induced free carrier lifetime of 25ns, which agrees well with our modeling.

Non-linear optical measurements using a scanned, Bessel beam

NASA Astrophysics Data System (ADS)

Collier, Bradley B.; Awasthi, Samir; Lieu, Deborah K.; Chan, James W.

2015-03-01

Oftentimes cells are removed from the body for disease diagnosis or cellular research. This typically requires fluorescent labeling followed by sorting with a flow cytometer; however, possible disruption of cellular function or even cell death due to the presence of the label can occur. This may be acceptable for ex vivo applications, but as cells are more frequently moving from the lab to the body, label-free methods of cell sorting are needed to eliminate these issues. This is especially true of the growing field of stem cell research where specialized cells are needed for treatments. Because differentiation processes are not completely efficient, cells must be sorted to eliminate any unwanted cells (i.e. un-differentiated or differentiated into an unwanted cell type). In order to perform label-free measurements, non-linear optics (NLO) have been increasingly utilized for single cell analysis because of their ability to not disrupt cellular function. An optical system was developed for the measurement of NLO in a microfluidic channel similar to a flow cytometer. In order to improve the excitation efficiency of NLO, a scanned Bessel beam was utilized to create a light-sheet across the channel. The system was tested by monitoring twophoton fluorescence from polystyrene microbeads of different sizes. Fluorescence intensity obtained from light-sheet measurements were significantly greater than measurements made using a static Gaussian beam. In addition, the increase in intensity from larger sized beads was more evident for the light-sheet system.

Nonlinear effects in the time measurement device based on surface acoustic wave filter excitation.

PubMed

Prochazka, Ivan; Panek, Petr

2009-07-01

A transversal surface acoustic wave filter has been used as a time interpolator in a time interval measurement device. We are presenting the experiments and results of an analysis of the nonlinear effects in such a time interpolator. The analysis shows that the nonlinear distortion in the time interpolator circuits causes a deterministic measurement error which can be understood as the time interpolation nonlinearity. The dependence of this error on time of the measured events can be expressed as a sparse Fourier series thus it usually oscillates very quickly in comparison to the clock period. The theoretical model is in good agreement with experiments carried out on an experimental two-channel timing system. Using highly linear amplifiers in the time interpolator and adjusting the filter excitation level to the optimum, we have achieved the interpolation nonlinearity below 0.2 ps. The overall single-shot precision of the experimental timing device is 0.9 ps rms in each channel.

Mutual information and phase dependencies: measures of reduced nonlinear cardiorespiratory interactions after myocardial infarction.

PubMed

Hoyer, Dirk; Leder, Uwe; Hoyer, Heike; Pompe, Bernd; Sommer, Michael; Zwiener, Ulrich

2002-01-01

The heart rate variability (HRV) is related to several mechanisms of the complex autonomic functioning such as respiratory heart rate modulation and phase dependencies between heart beat cycles and breathing cycles. The underlying processes are basically nonlinear. In order to understand and quantitatively assess those physiological interactions an adequate coupling analysis is necessary. We hypothesized that nonlinear measures of HRV and cardiorespiratory interdependencies are superior to the standard HRV measures in classifying patients after acute myocardial infarction. We introduced mutual information measures which provide access to nonlinear interdependencies as counterpart to the classically linear correlation analysis. The nonlinear statistical autodependencies of HRV were quantified by auto mutual information, the respiratory heart rate modulation by cardiorespiratory cross mutual information, respectively. The phase interdependencies between heart beat cycles and breathing cycles were assessed basing on the histograms of the frequency ratios of the instantaneous heart beat and respiratory cycles. Furthermore, the relative duration of phase synchronized intervals was acquired. We investigated 39 patients after acute myocardial infarction versus 24 controls. The discrimination of these groups was improved by cardiorespiratory cross mutual information measures and phase interdependencies measures in comparison to the linear standard HRV measures. This result was statistically confirmed by means of logistic regression models of particular variable subsets and their receiver operating characteristics.

Lateral resolution improvement in scanning nonlinear dielectric microscopy by measuring super-higher-order nonlinear dielectric constants

NASA Astrophysics Data System (ADS)

Chinone, N.; Yamasue, K.; Hiranaga, Y.; Honda, K.; Cho, Y.

2012-11-01

Scanning nonlinear dielectric microscopy (SNDM) can be used to visualize polarization distributions in ferroelectric materials and dopant profiles in semiconductor devices. Without using a special sharp tip, we achieved an improved lateral resolution in SNDM through the measurement of super-higher-order nonlinearity up to the fourth order. We observed a multidomain single crystal congruent LiTaO3 (CLT) sample, and a cross section of a metal-oxide-semiconductor (MOS) field-effect-transistor (FET). The imaged domain boundaries of the CLT were narrower in the super-higher-order images than in the conventional image. Compared to the conventional method, the super-higher-order method resolved the more detailed structure of the MOSFET.

Response phase mapping of nonlinear joint dynamics using continuous scanning LDV measurement method

NASA Astrophysics Data System (ADS)

Di Maio, D.; Bozzo, A.; Peyret, Nicolas

2016-06-01

This study aims to present a novel work aimed at locating discrete nonlinearities in mechanical assemblies. The long term objective is to develop a new metric for detecting and locating nonlinearities using Scanning LDV systems (SLDV). This new metric will help to improve the modal updating, or validation, of mechanical assemblies presenting discrete and sparse nonlinearities. It is well established that SLDV systems can scan vibrating structures with high density of measurement points and produc e highly defined Operational Deflection Shapes (ODSs). This paper will present some insights on how to use response phase mapping for locating nonlinearities of a bolted flange. This type of structure presents two types of nonlinearities, which are geometr ical and frictional joints. The interest is focussed on the frictional joints and, therefore, the ability to locate which joint s are responsible for nonlinearity is seen highly valuable for the model validation activities.

Nonlinear acoustic measurements ahead of a notch during fatigue

NASA Astrophysics Data System (ADS)

Martin, R. W.; Mooers, R. D.; Hutson, A. L.; Sathish, S.; Blodgett, M. P.

2013-01-01

This paper presents measurements of relative nonlinear acoustic parameter (βrel), ahead of a notch in Al 7075-T651 dog bone samples, subjected to fatigue. It is compared with crack growth measurements on the same samples. Measurements performed on two samples subjected to identical fatigue conditions that failed at vastly different number of fatigue cycles are described. The βrel measurement for both samples as a function of fatigue cycles was fit a Boltzmann curve. The role of changing βrel ahead of a notch is explored as a possible approach for remain life evaluation.

Effects of geometric nonlinearity in an adhered microbeam for measuring the work of adhesion

NASA Astrophysics Data System (ADS)

Fang, Wenqiang; Mok, Joyce; Kesari, Haneesh

2018-03-01

Design against adhesion in microelectromechanical devices is predicated on the ability to quantify this phenomenon in microsystems. Previous research related the work of adhesion for an adhered microbeam to the beam's unadhered length, and as such, interferometric techniques were developed to measure that length. We propose a new vibration-based technique that can be easily implemented with existing atomic force microscopy tools or similar metrology systems. To make such a technique feasible, we analysed a model of the adhered microbeam using the nonlinear beam theory put forth by Woinowsky-Krieger. We found a new relation between the work of adhesion and the unadhered length; this relation is more accurate than the one by Mastrangelo & Hsu (Mastrangelo & Hsu 1993 J. Microelectromech. S., 2, 44-55. (doi:10.1109/84.232594)) which is commonly used. Then, we derived a closed-form approximate relationship between the microbeam's natural frequency and its unadhered length. Results obtained from this analytical formulation are in good agreement with numerical results from three-dimensional nonlinear finite-element analysis.

Assessment of precipitation in alloy steel using nonlinear Rayleigh surface waves

NASA Astrophysics Data System (ADS)

Thiele, Sebastian; Matlack, Kathryn H.; Kim, Jin-Yeon; Qu, Jianmin; Wall, James J.; Jacobs, Laurence J.

2014-02-01

Nonlinear ultrasonic waves have shown to be sensitive to various microstructural changes in metals including coherent precipitates; these precipitates introduce a strain field in the lattice structure. The thermal aging of certain alloy steels leads to the formation of coherent precipitates, which pin dislocations and contribute to the generation of a second harmonic component. A precipitate hardenable material namely 17-4 PH stainless steel is thermally treated in this research to obtain different precipitation stages, and then the influence of precipitates on the acoustic nonlinearity parameter is assessed. Conclusions about the microstrucutural changes in the material are drawn based on the results from a nonlinear Rayleigh surface wave measurement and complementary thermo-electric power, hardness and ultrasonic velocity measurements. The results show that the nonlinear parameter is sensitive to coherent precipitates in the material and moreover that precipitation characteristics can be characterized based on the obtained experimental data.

THREE-POINT PHASE CORRELATIONS: A NEW MEASURE OF NONLINEAR LARGE-SCALE STRUCTURE

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

Wolstenhulme, Richard; Bonvin, Camille; Obreschkow, Danail

2015-05-10

We derive an analytical expression for a novel large-scale structure observable: the line correlation function. The line correlation function, which is constructed from the three-point correlation function of the phase of the density field, is a robust statistical measure allowing the extraction of information in the nonlinear and non-Gaussian regime. We show that, in perturbation theory, the line correlation is sensitive to the coupling kernel F{sub 2}, which governs the nonlinear gravitational evolution of the density field. We compare our analytical expression with results from numerical simulations and find a 1σ agreement for separations r ≳ 30 h{sup −1} Mpc.more » Fitting formulae for the power spectrum and the nonlinear coupling kernel at small scales allow us to extend our prediction into the strongly nonlinear regime, where we find a 1σ agreement with the simulations for r ≳ 2 h{sup −1} Mpc. We discuss the advantages of the line correlation relative to standard statistical measures like the bispectrum. Unlike the latter, the line correlation is independent of the bias, in the regime where the bias is local and linear. Furthermore, the variance of the line correlation is independent of the Gaussian variance on the modulus of the density field. This suggests that the line correlation can probe more precisely the nonlinear regime of gravity, with less contamination from the power spectrum variance.« less

Nonlinearity response correction in phase-shifting deflectometry

NASA Astrophysics Data System (ADS)

Nguyen, Manh The; Kang, Pilseong; Ghim, Young-Sik; Rhee, Hyug-Gyo

2018-04-01

Owing to the nonlinearity response of digital devices such as screens and cameras in phase-shifting deflectometry, non-sinusoidal phase-shifted fringe patterns are generated and additional measurement errors are introduced. In this paper, a new deflectometry technique is described for overcoming these problems using a pre-distorted pattern combined with an advanced iterative algorithm. The experiment results show that this method can reconstruct the 3D surface map of a sample without fringe print-through caused by the nonlinearity response of digital devices. The proposed technique is verified by measuring the surface height variations in a deformable mirror and comparing them with the measurement result obtained using a coordinate measuring machine. The difference between the two measurement results is estimated to be less than 13 µm.

Measurement of nonlinear normal modes using multi-harmonic stepped force appropriation and free decay

NASA Astrophysics Data System (ADS)

Ehrhardt, David A.; Allen, Matthew S.

2016-08-01

Nonlinear Normal Modes (NNMs) offer tremendous insight into the dynamic behavior of a nonlinear system, extending many concepts that are familiar in linear modal analysis. Hence there is interest in developing methods to experimentally and numerically determine a system's NNMs for model updating or simply to characterize its dynamic response. Previous experimental work has shown that a mono-harmonic excitation can be used to isolate a system's dynamic response in the neighborhood of a NNM along the main backbones of a system. This work shows that a multi-harmonic excitation is needed to isolate a NNM when well separated linear modes of a structure couple to produce an internal resonance. It is shown that one can tune the multiple harmonics of the input excitation using a plot of the input force versus the response velocity until the area enclosed by the force-velocity curve is minimized. Once an appropriated NNM is measured, one can increase the force level and retune the frequency to obtain a NNM at a higher amplitude or remove the excitation and measure the structure's decay down a NNM backbone. This work explores both methods using simulations and measurements of a nominally-flat clamped-clamped beam excited at a single point with a magnetic force. Numerical simulations are used to validate the method in a well defined environment and to provide comparison with the experimentally measured NNMs. The experimental results seem to produce a good estimate of two NNMs along their backbone and part of an internal resonance branch. Full-field measurements are then used to further explore the couplings between the underlying linear modes along the identified NNMs.

Analysis of Nonlinear Dynamics by Square Matrix Method

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

Yu, Li Hua

The nonlinear dynamics of a system with periodic structure can be analyzed using a square matrix. In this paper, we show that because the special property of the square matrix constructed for nonlinear dynamics, we can reduce the dimension of the matrix from the original large number for high order calculation to low dimension in the first step of the analysis. Then a stable Jordan decomposition is obtained with much lower dimension. The transformation to Jordan form provides an excellent action-angle approximation to the solution of the nonlinear dynamics, in good agreement with trajectories and tune obtained from tracking. Andmore » more importantly, the deviation from constancy of the new action-angle variable provides a measure of the stability of the phase space trajectories and their tunes. Thus the square matrix provides a novel method to optimize the nonlinear dynamic system. The method is illustrated by many examples of comparison between theory and numerical simulation. Finally, in particular, we show that the square matrix method can be used for optimization to reduce the nonlinearity of a system.« less

Finite-time H∞ filtering for non-linear stochastic systems

NASA Astrophysics Data System (ADS)

Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

2016-09-01

This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

Nonlinear refraction properties of nickel oxide thin films at 800 nm

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

Melo, Ronaldo P. Jr. de; Silva, Blenio J. P. da; Santos, Francisco Eroni P. dos

2009-11-01

Measurements of the nonlinear refractive index, n{sub 2}, of nickel oxide films prepared by controlled oxidation of nickel films deposited on substrates of soda-lime glass are reported. The structure and morphology of the samples were characterized by scanning electron microscopy, atomic force microscopy, and x-ray diffractometry. Samples of excellent optical quality were prepared. The nonlinear measurements were performed using the thermally managed eclipse Z-scan technique at 800 nm. A large value of n{sub 2}approx =10{sup -12} cm{sup 2}/W and negligible nonlinear absorption were obtained.

Novel approach of wavelet analysis for nonlinear ultrasonic measurements and fatigue assessment of jet engine components

NASA Astrophysics Data System (ADS)

Bunget, Gheorghe; Tilmon, Brevin; Yee, Andrew; Stewart, Dylan; Rogers, James; Webster, Matthew; Farinholt, Kevin; Friedersdorf, Fritz; Pepi, Marc; Ghoshal, Anindya

2018-04-01

Widespread damage in aging aircraft is becoming an increasing concern as both civil and military fleet operators are extending the service lifetime of their aircraft. Metallic components undergoing variable cyclic loadings eventually fatigue and form dislocations as precursors to ultimate failure. In order to characterize the progression of fatigue damage precursors (DP), the acoustic nonlinearity parameter is measured as the primary indicator. However, using proven standard ultrasonic technology for nonlinear measurements presents limitations for settings outside of the laboratory environment. This paper presents an approach for ultrasonic inspection through automated immersion scanning of hot section engine components where mature ultrasonic technology is used during periodic inspections. Nonlinear ultrasonic measurements were analyzed using wavelet analysis to extract multiple harmonics from the received signals. Measurements indicated strong correlations of nonlinearity coefficients and levels of fatigue in aluminum and Ni-based superalloys. This novel wavelet cross-correlation (WCC) algorithm is a potential technique to scan for fatigue damage precursors and identify critical locations for remaining life prediction.

Objective Dysphonia Quantification in Vocal Fold Paralysis: Comparing Nonlinear with Classical Measures

PubMed Central

Little, Max A.; Costello, Declan A. E.; Harries, Meredydd L.

2010-01-01

Summary Clinical acoustic voice-recording analysis is usually performed using classical perturbation measures, including jitter, shimmer, and noise-to-harmonic ratios (NHRs). However, restrictive mathematical limitations of these measures prevent analysis for severely dysphonic voices. Previous studies of alternative nonlinear random measures addressed wide varieties of vocal pathologies. Here, we analyze a single vocal pathology cohort, testing the performance of these alternative measures alongside classical measures. We present voice analysis pre- and postoperatively in 17 patients with unilateral vocal fold paralysis (UVFP). The patients underwent standard medialization thyroplasty surgery, and the voices were analyzed using jitter, shimmer, NHR, nonlinear recurrence period density entropy (RPDE), detrended fluctuation analysis (DFA), and correlation dimension. In addition, we similarly analyzed 11 healthy controls. Systematizing the preanalysis editing of the recordings, we found that the novel measures were more stable and, hence, reliable than the classical measures on healthy controls. RPDE and jitter are sensitive to improvements pre- to postoperation. Shimmer, NHR, and DFA showed no significant change (P > 0.05). All measures detect statistically significant and clinically important differences between controls and patients, both treated and untreated (P < 0.001, area under curve [AUC] > 0.7). Pre- to postoperation grade, roughness, breathiness, asthenia, and strain (GRBAS) ratings show statistically significant and clinically important improvement in overall dysphonia grade (G) (AUC = 0.946, P < 0.001). Recalculating AUCs from other study data, we compare these results in terms of clinical importance. We conclude that, when preanalysis editing is systematized, nonlinear random measures may be useful for monitoring UVFP-treatment effectiveness, and there may be applications to other forms of dysphonia. PMID:19900790

All-fiber wavelength-tunable picosecond nonlinear reflectivity measurement setup for characterization of semiconductor saturable absorber mirrors

NASA Astrophysics Data System (ADS)

Viskontas, K.; Rusteika, N.

2016-09-01

Semiconductor saturable absorber mirror (SESAM) is the key component for many passively mode-locked ultrafast laser sources. Particular set of nonlinear parameters is required to achieve self-starting mode-locking or avoid undesirable q-switch mode-locking for the ultra-short pulse laser. In this paper, we introduce a novel all-fiber wavelength-tunable picosecond pulse duration setup for the measurement of nonlinear properties of saturable absorber mirrors at around 1 μm center wavelength. The main advantage of an all-fiber configuration is the simplicity of measuring the fiber-integrated or fiber-pigtailed saturable absorbers. A tunable picosecond fiber laser enables to investigate the nonlinear parameters at different wavelengths in ultrafast regime. To verify the capability of the setup, nonlinear parameters for different SESAMs with low and high modulation depth were measured. In the operating wavelength range 1020-1074 nm, <1% absolute nonlinear reflectivity accuracy was demonstrated. Achieved fluence range was from 100 nJ/cm2 to 2 mJ/cm2 with corresponding intensity from 10 kW/cm2 to 300 MW/cm2.

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

PubMed

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.

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

NASA Astrophysics Data System (ADS)

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.

Analysis and correction of gradient nonlinearity bias in apparent diffusion coefficient measurements.

PubMed

Malyarenko, Dariya I; Ross, Brian D; Chenevert, Thomas L

2014-03-01

Gradient nonlinearity of MRI systems leads to spatially dependent b-values and consequently high non-uniformity errors (10-20%) in apparent diffusion coefficient (ADC) measurements over clinically relevant field-of-views. This work seeks practical correction procedure that effectively reduces observed ADC bias for media of arbitrary anisotropy in the fewest measurements. All-inclusive bias analysis considers spatial and time-domain cross-terms for diffusion and imaging gradients. The proposed correction is based on rotation of the gradient nonlinearity tensor into the diffusion gradient frame where spatial bias of b-matrix can be approximated by its Euclidean norm. Correction efficiency of the proposed procedure is numerically evaluated for a range of model diffusion tensor anisotropies and orientations. Spatial dependence of nonlinearity correction terms accounts for the bulk (75-95%) of ADC bias for FA = 0.3-0.9. Residual ADC non-uniformity errors are amplified for anisotropic diffusion. This approximation obviates need for full diffusion tensor measurement and diagonalization to derive a corrected ADC. Practical scenarios are outlined for implementation of the correction on clinical MRI systems. The proposed simplified correction algorithm appears sufficient to control ADC non-uniformity errors in clinical studies using three orthogonal diffusion measurements. The most efficient reduction of ADC bias for anisotropic medium is achieved with non-lab-based diffusion gradients. Copyright © 2013 Wiley Periodicals, Inc.

Nonlinear refraction at the absorption edge in InAs.

PubMed

Poole, C D; Garmire, E

1984-08-01

The results of measurements of nonlinear refraction at the absorption edge in InAs between 68 and 90 K taken with an HF laser are compared with those of a band-gap resonant model in which the contribution of the light-hole band is included and found to account for more than 40% of the observed nonlinear refraction. A generalized expression for the nonlinear index is derived by using the complete Fermi-Dirac distribution function. Good agreement between theory and experiment is obtained, with no free parameters.

Nonlocal nonlinear refraction in Hibiscus sabdariffa with large phase shifts.

PubMed

Ramírez-Martínez, D; Alvarado-Méndez, E; Trejo-Durán, M; Vázquez-Guevara, M A

2014-10-20

In this work we present a study of nonlinear optical properties in organic materials (hibiscus sabdariffa). Our results demonstrate that the medium exhibits a highly nonlocal nonlinear response. We show preliminary numerical results of the transmittance as nonlocal response by considering, simultaneously, the nonlinear absorption and refraction in media. Numerical results are accord to measurement obtained by Z- scan technique where we observe large phase shifts. We also analyze the far field diffraction ring patterns of the sample.

Examining the Error of Mis-Specifying Nonlinear Confounding Effect With Application on Accelerometer-Measured Physical Activity.

PubMed

Lee, Paul H

2017-06-01

Some confounders are nonlinearly associated with dependent variables, but they are often adjusted using a linear term. The purpose of this study was to examine the error of mis-specifying the nonlinear confounding effect. We carried out a simulation study to investigate the effect of adjusting for a nonlinear confounder in the estimation of a causal relationship between the exposure and outcome in 3 ways: using a linear term, binning into 5 equal-size categories, or using a restricted cubic spline of the confounder. Continuous, binary, and survival outcomes were simulated. We examined the confounder across varying measurement error. In addition, we performed a real data analysis examining the 3 strategies to handle the nonlinear effects of accelerometer-measured physical activity in the National Health and Nutrition Examination Survey 2003-2006 data. The mis-specification of a nonlinear confounder had little impact on causal effect estimation for continuous outcomes. For binary and survival outcomes, this mis-specification introduced bias, which could be eliminated using spline adjustment only when there is small measurement error of the confounder. Real data analysis showed that the associations between high blood pressure, high cholesterol, and diabetes and mortality adjusted for physical activity with restricted cubic spline were about 3% to 11% larger than their counterparts adjusted with a linear term. For continuous outcomes, confounders with nonlinear effects can be adjusting with a linear term. Spline adjustment should be used for binary and survival outcomes on confounders with small measurement error.

Field measurements of the linear and nonlinear shear moduli of cemented alluvium using dynamically loaded surface footings

NASA Astrophysics Data System (ADS)

Park, Kwangsoo

In this dissertation, a research effort aimed at development and implementation of a direct field test method to evaluate the linear and nonlinear shear modulus of soil is presented. The field method utilizes a surface footing that is dynamically loaded horizontally. The test procedure involves applying static and dynamic loads to the surface footing and measuring the soil response beneath the loaded area using embedded geophones. A wide range in dynamic loads under a constant static load permits measurements of linear and nonlinear shear wave propagation from which shear moduli and associated shearing strains are evaluated. Shear wave velocities in the linear and nonlinear strain ranges are calculated from time delays in waveforms monitored by geophone pairs. Shear moduli are then obtained using the shear wave velocities and the mass density of a soil. Shear strains are determined using particle displacements calculated from particle velocities measured at the geophones by assuming a linear variation between geophone pairs. The field test method was validated by conducting an initial field experiment at sandy site in Austin, Texas. Then, field experiments were performed on cemented alluvium, a complex, hard-to-sample material. Three separate locations at Yucca Mountain, Nevada were tested. The tests successfully measured: (1) the effect of confining pressure on shear and compression moduli in the linear strain range and (2) the effect of strain on shear moduli at various states of stress in the field. The field measurements were first compared with empirical relationships for uncemented gravel. This comparison showed that the alluvium was clearly cemented. The field measurements were then compared to other independent measurements including laboratory resonant column tests and field seismic tests using the spectral-analysis-of-surface-waves method. The results from the field tests were generally in good agreement with the other independent test results, indicating

Geometrically nonlinear analysis of adhesively bonded joints

NASA Technical Reports Server (NTRS)

Dattaguru, B.; Everett, R. A., Jr.; Whitcomb, J. D.; Johnson, W. S.

1982-01-01

A geometrically nonlinear finite element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode 1, crack opening, and mode 2, inplane shear, strain-energy-release rates. The ratio of the mode 1 to mode 2 strain-energy-relase rates (G1/G2) was found to be strongly affected by he adhesive modulus and the adherend thickness. The ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode 1 strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements.

A computational procedure to analyze metal matrix laminates with nonlinear lamination residual strains

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Sullivan, T. L.

1974-01-01

An approximate computational procedure is described for the analysis of angleplied laminates with residual nonlinear strains. The procedure consists of a combination of linear composite mechanics and incremental linear laminate theory. The procedure accounts for initial nonlinear strains, unloading, and in-situ matrix orthotropic nonlinear behavior. The results obtained in applying the procedure to boron/aluminum angleplied laminates show that this is a convenient means to accurately predict the initial tangent properties of angleplied laminates in which the matrix has been strained nonlinearly by the lamination residual stresses. The procedure predicted initial tangent properties results which were in good agreement with measured data obtained from boron/aluminum angleplied laminates.

Simulation and measurement of nonlinear behavior in a high-power test cell.

PubMed

Harvey, Gerald; Gachagan, Anthony

2011-04-01

High-power ultrasound has many diverse uses in process applications in industries ranging from food to pharmaceutical. Because cavitation is frequently a desirable effect within many high-power, low-frequency systems, these systems are commonly expected to feature highly nonlinear acoustic propagation because of the high input levels employed. This generation of harmonics significantly alters the field profile compared with that of a linear system, making accurate field modeling difficult. However, when the short propagation distances involved are considered, it is not unreasonable to assume that these systems may remain largely linear until the onset of cavitation, in terms of classical acoustic propagation. The purpose of this paper is to investigate the possible nonlinear effects within such systems before the onset of cavitation. A theoretical description of nonlinear propagation will be presented and the merits of common analytical models will be discussed. Following this, a numerical model of nonlinearity will be outlined and the advantages it presents for representing nonlinear effects in bounded fields will be discussed. Next, the driving equipment and transducers will be evaluated for linearity to disengage any effects from those formed in the transmission load. Finally, the linearity of the system will be measured using an acoustic hydrophone and compared with finite element analysis to confirm that nonlinear effects are not prevalent in such systems at the onset of cavitation. © 2011 IEEE

Inducing in situ, nonlinear soil response applying an active source

USGS Publications Warehouse

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.

Accounting For Nonlinearity In A Microwave Radiometer

NASA Technical Reports Server (NTRS)

Stelzried, Charles T.

1991-01-01

Simple mathematical technique found to account adequately for nonlinear component of response of microwave radiometer. Five prescribed temperatures measured to obtain quadratic calibration curve. Temperature assumed to vary quadratically with reading. Concept not limited to radiometric application; applicable to other measuring systems in which relationships between quantities to be determined and readings of instruments differ slightly from linearity.

Using compressive measurement to obtain images at ultra low-light-level

NASA Astrophysics Data System (ADS)

Ke, Jun; Wei, Ping

2013-08-01

In this paper, a compressive imaging architecture is used for ultra low-light-level imaging. In such a system, features, instead of object pixels, are imaged onto a photocathode, and then magnified by an image intensifier. By doing so, system measurement SNR is increased significantly. Therefore, the new system can image objects at ultra low-ligh-level, while a conventional system has difficulty. PCA projection is used to collect feature measurements in this work. Linear Wiener operator and nonlinear method based on FoE model are used to reconstruct objects. Root mean square error (RMSE) is used to quantify system reconstruction quality.

The Applicability of Nonlinear Systems Dynamics Chaos Measures to Cardiovascular Physiology Variables

NASA Technical Reports Server (NTRS)

Hooker, John C.

1991-01-01

Three measures of nonlinear chaos (fractal dimension, Approximate Entropy (ApEn), and Lyapunov exponents) were studied as potential measures of cardiovascular condition. It is suggested that these measures have potential in the assessment of cardiovascular condition in environments of normal cardiovascular stress (normal gravity on the Earth surface), cardiovascular deconditioning (microgravity of space), and increased cardiovascular stress (lower body negative pressure (LBNP) treatments).

Nonlinear fractional waves at elastic interfaces

NASA Astrophysics Data System (ADS)

Kappler, Julian; Shrivastava, Shamit; Schneider, Matthias F.; Netz, Roland R.

2017-11-01

We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface.

Controllability in nonlinear systems

NASA Technical Reports Server (NTRS)

Hirschorn, R. M.

1975-01-01

An explicit expression for the reachable set is obtained for a class of nonlinear systems. This class is described by a chain condition on the Lie algebra of vector fields associated with each nonlinear system. These ideas are used to obtain a generalization of a controllability result for linear systems in the case where multiplicative controls are present.

Nonlinear Acoustical Assessment of Precipitate Nucleation

NASA Technical Reports Server (NTRS)

Cantrell, John H.; Yost, William T.

2004-01-01

The purpose of the present work is to show that measurements of the acoustic nonlinearity parameter in heat treatable alloys as a function of heat treatment time can provide quantitative information about the kinetics of precipitate nucleation and growth in such alloys. Generally, information on the kinetics of phase transformations is obtained from time-sequenced electron microscopical examination and differential scanning microcalorimetry. The present nonlinear acoustical assessment of precipitation kinetics is based on the development of a multiparameter analytical model of the effects on the nonlinearity parameter of precipitate nucleation and growth in the alloy system. A nonlinear curve fit of the model equation to the experimental data is then used to extract the kinetic parameters related to the nucleation and growth of the targeted precipitate. The analytical model and curve fit is applied to the assessment of S' precipitation in aluminum alloy 2024 during artificial aging from the T4 to the T6 temper.

Measuring Ultrasonic Backscatter in the Presence of Nonlinear Propagation

NASA Astrophysics Data System (ADS)

Stiles, Timothy; Guerrero, Quinton

2011-11-01

A goal of medical ultrasound is the formation of quantitative ultrasound images in which contrast is determined by acoustic or physical properties of tissue rather than relative echo amplitude. Such images could greatly enhance early detection of many diseases, including breast cancer and liver cirrhosis. Accurate determination of the ultrasonic backscatter coefficient from patients remains a difficult task. One reason for this difficulty is the inherent nonlinear propagation of ultrasound at high intensities used for medical imaging. The backscatter coefficient from several tissue-mimicking samples were measured using the planar reflector method. In this method, the power spectrum from a sample is compared to the power spectrum of an optically flat sample of quartz. The results should be independent of incident pressure amplitude. Results demonstrate that backscatter coefficients can vary by more than an order of magnitude when ultrasound pressure varies from 0.1 MPa to 1.5 MPa at 5.0 MHz. A new method that incorporates nonlinear propagation is proposed to explain these discrepancies.

Generalised observer design for dissipative Lipschitz nonlinear systems in the presence of measurement noise

NASA Astrophysics Data System (ADS)

Vijayaraghavan, Krishna

2014-11-01

This paper presents two novel observer concepts. First, it develops a globally exponentially stable nonlinear observer for noise-free dissipative nonlinear systems. Second, for a dissipative nonlinear system with measurement noise, the paper develops an observer to guarantee a desired performance, namely an upper limit on the ratio of the square of the weighted L2 norm of the error to the square of the weighted L2 norm of the measurement noise. The necessary and sufficient conditions for both observers are reformulated as algebraic Riccati equations (AREs) so that standard solvers can be utilised. In addition, the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the ARE (and hence the observer design problem) has a solution. The use of the methodology developed in this paper is demonstrated through illustrative examples. In literature, there is no previous observer for dissipative system that provides both necessary and sufficient conditions. Results for noisy system either rely on linearising the system about state trajectory (requiring initial estimates to be close to the actual states) or are for specialised systems that cannot be extended to dissipative systems.

Broadband attenuation and nonlinear propagation in biological fluids: an experimental facility and measurements.

PubMed

Verma, Prashant K; Humphrey, Victor F; Duck, Francis A

2005-12-01

The design and construction of a versatile experimental facility for making measurements of the frequency-dependence of attenuation coefficient (over the range 1 MHz to 25 MHz) and nonlinear propagation in samples of biological fluids is described. The main feature of the facility is the ability to perform all of the measurements on the same sample of fluid within a short period of time and under temperature control. In particular, the facility allows the axial development of nonlinear waveform distortion to be measured with a wideband bilaminar polyvinylidene difluoride membrane hydrophone to study nonlinear propagation in biological fluids. The system uses a variable length bellows to contain the fluid, with transparent Mylar end-windows to couple the acoustic field into the fluid. Example results for the frequency-dependence of attenuation of Dow Corning 200/350 silicone fluid, used as a standard fluid, are presented and shown to be in good agreement with alternative measurements. Measurements of finite amplitude propagation in amniotic fluid, urine and 4.5% human albumin solutions at physiological temperature (37 degrees C) are presented and compared with theoretical predictions using existing models. The measurements were made using a 2.25-MHz single-element transducer coupled to a polymethyl methacrylate lens with a focal amplitude gain of 12 in water. The transducer was driven with an eight-cycle tone burst at source pressures up to 0.137 MPa. In general, given an accurate knowledge of the medium parameters and source conditions, the agreement with theoretical prediction is good for the first five harmonics.

Optical measurement of the weak non-linearity in the eardrum vibration response to auditory stimuli

NASA Astrophysics Data System (ADS)

Aerts, Johan

The mammalian hearing organ consists of the external ear (auricle and ear canal) followed by the middle ear (eardrum and ossicles) and the inner ear (cochlea). Its function is to convert the incoming sound waves and convert them into nerve pulses which are processed in the final stage by the brain. The main task of the external and middle ear is to concentrate the incoming sound waves on a smaller surface to reduce the loss that would normally occur in transmission from air to inner ear fluid. In the past it has been shown that this is a linear process, thus without serious distortions, for sound waves going up to pressures of 130 dB SPL (˜90 Pa). However, at large pressure changes up to several kPa, the middle ear movement clearly shows non-linear behaviour. Thus, it is possible that some small non-linear distortions are also present in the middle ear vibration at lower sound pressures. In this thesis a sensitive measurement set-up is presented to detect this weak non-linear behaviour. Essentially, this set-up consists of a loud-speaker which excites the middle ear, and the resulting vibration is measured with an heterodyne vibrometer. The use of specially designed acoustic excitation signals (odd random phase multisines) enables the separation of the linear and non-linear response. The application of this technique on the middle ear demonstrates that there are already non-linear distortions present in the vibration of the middle ear at a sound pressure of 93 dB SPL. This non-linear component also grows strongly with increasing sound pressure. Knowledge of this non-linear component can contribute to the improvement of modern hearing aids, which operate at higher sound pressures where the non-linearities could distort the signal considerably. It is also important to know the contribution of middle ear non-linearity to otoacoustic emissions. This are non-linearities caused by the active feedback amplifier in the inner ear, and can be detected in the external and

Numerical Calculation and Measurement of Nonlinear Acoustic Fields in Ultrasound Diagnosis

NASA Astrophysics Data System (ADS)

Kawagishi, Tetsuya; Saito, Shigemi; Mine, Yoshitaka

2002-05-01

In order to develop a tool for designing on the ultrasonic probe and its peripheral devices for tissue-harmonic-imaging systems, a study is carried out to compare the calculation and observation results of nonlinear acoustic fields for a diagnostic ultrasound system. The pulsed ultrasound with a center frequency of 2.5 MHz is emanated from a weakly focusing sector probe with a 6.5 mm aperture radius and a 50 mm focal length into an agar phantom with an attenuation coefficient of about 0.6 dB/cm/MHz or 1.2 dB/cm/MHz. The nonlinear acoustic field is measured using a needle-type hydrophone. The calculation is based on the Khokhlov-Zabolotskaya-Kuznetsov(KZK) equation which is modified so that the frequency dependence of the attenuation coefficient is the same as that in biological tissue. This equation is numerically solved with the implicit backward method employing the iterative method. The measured and calculated amplitude spectra show good agreement with each other.

Measurements on a guitar string as an example of a physical nonlinear driven oscillator

NASA Astrophysics Data System (ADS)

Carlà, Marcello; Straulino, Samuele

2017-08-01

An experimental study is described to characterize the oscillation of a guitar string around resonance. A periodic force was applied to the string, generated by the electromagnetic interaction between an alternating current flowing in the string and a magnetic field. The oscillation was studied by measuring the voltage induced in the string itself, which is proportional to the velocity. Accurate quantitative data were obtained for the velocity, both modulus and phase, with a time resolution of 3 ms, corresponding to the oscillation period. The measuring instrument was a personal computer with its sound card and an electronic amplifier, both used to generate the excitation current and record the velocity signal, while performing the required frequency sweep. The study covered an excitation force range more than two and half decades wide (51 dB). The experimental results showed very good agreement with the theoretical behavior of a Duffing oscillator with nonlinear damping over about two decades.

The nonlinear effect of resistive inhomogeneities on van der Pauw measurements

NASA Astrophysics Data System (ADS)

Koon, Daniel W.

2005-03-01

The resistive weighting function [D. W. Koon and C. J. Knickerbocker, Rev. Sci. Instrum. 63, 207 (1992)] quantifies the effect of small local inhomogeneities on van der Pauw resistivity measurements, but assumes such effects to be linear. This talk will describe deviations from linearity for a square van der Pauw geometry, modeled using a 5 x 5 grid network of discrete resistors and introducing both positive and negative perturbations to local resistors, covering nearly two orders of magnitude in -δρ/ρ or -δσ/σ. While there is a relatively modest quadratic nonlinearity for inhomogeneities of decreasing conductivity, the nonlinear term for inhomogeneities of decreasing resistivity is approximately cubic and can exceed the linear term.

A measurement fusion method for nonlinear system identification using a cooperative learning algorithm.

PubMed

Xia, Youshen; Kamel, Mohamed S

2007-06-01

Identification of a general nonlinear noisy system viewed as an estimation of a predictor function is studied in this article. A measurement fusion method for the predictor function estimate is proposed. In the proposed scheme, observed data are first fused by using an optimal fusion technique, and then the optimal fused data are incorporated in a nonlinear function estimator based on a robust least squares support vector machine (LS-SVM). A cooperative learning algorithm is proposed to implement the proposed measurement fusion method. Compared with related identification methods, the proposed method can minimize both the approximation error and the noise error. The performance analysis shows that the proposed optimal measurement fusion function estimate has a smaller mean square error than the LS-SVM function estimate. Moreover, the proposed cooperative learning algorithm can converge globally to the optimal measurement fusion function estimate. Finally, the proposed measurement fusion method is applied to ARMA signal and spatial temporal signal modeling. Experimental results show that the proposed measurement fusion method can provide a more accurate model.

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

Nonlinear Ultrasonic Measurements in Nuclear Reactor Environments

NASA Astrophysics Data System (ADS)

Reinhardt, Brian T.

Several Department of Energy Office of Nuclear Energy (DOE-NE) programs, such as the Fuel Cycle Research and Development (FCRD), Advanced Reactor Concepts (ARC), Light Water Reactor Sustainability, and Next Generation Nuclear Power Plants (NGNP), are investigating new fuels, materials, and inspection paradigms for advanced and existing reactors. A key objective of such programs is to understand the performance of these fuels and materials during irradiation. In DOE-NE's FCRD program, ultrasonic based technology was identified as a key approach that should be pursued to obtain the high-fidelity, high-accuracy data required to characterize the behavior and performance of new candidate fuels and structural materials during irradiation testing. The radiation, high temperatures, and pressure can limit the available tools and characterization methods. In this thesis, two ultrasonic characterization techniques will be explored. The first, finite amplitude wave propagation has been demonstrated to be sensitive to microstructural material property changes. It is a strong candidate to determine fuel evolution; however, it has not been demonstrated for in-situ reactor applications. In this thesis, finite amplitude wave propagation will be used to measure the microstructural evolution in Al-6061. This is the first demonstration of finite amplitude wave propagation at temperatures in excess of 200 °C and during an irradiation test. Second, a method based on contact nonlinear acoustic theory will be developed to identify compressed cracks. Compressed cracks are typically transparent to ultrasonic wave propagation; however, by measuring harmonic content developed during finite amplitude wave propagation, it is shown that even compressed cracks can be characterized. Lastly, piezoelectric transducers capable of making these measurements are developed. Specifically, three piezoelectric sensors (Bismuth Titanate, Aluminum Nitride, and Zinc Oxide) are tested in the Massachusetts

Characterization of Infrastructure Materials using Nonlinear Ultrasonics

NASA Astrophysics Data System (ADS)

Liu, Minghe

In order to improve the safety, reliability, cost, and performance of civil and mechanical structures/components, it is necessary to develop techniques that are capable of characterizing and quantifying the amount of distributed damage in engineering materials before any detectable discontinuities (cracks, delaminations, voids, etc.) appear. In this dissertation, novel nonlinear ultrasonic NDE methods are developed and applied to characterize cumulative damage such as fatigue damage in metallic materials and degradation of cement-based materials due to chemical reactions. First, nonlinear Rayleigh surface waves are used to measure the near-surface residual stresses in shot-peened aluminum alloy (AA 7075) samples. Results show that the nonlinear Rayleigh wave is very sensitive to near-surface residual stresses, and has the potential to quantitatively detect them. Second, a novel two-wave mixing method is theoretically developed and numerically verified. This method is then successfully applied to detect the fatigue damage in aluminum alloy (AA 6061) samples subjected to monotonic compression. In addition to its high sensitivity to fatigue damage, this collinear wave mixing method allows the measurement over a specific region of interest in the specimen, and this capability makes it possible to obtain spatial distribution of fatigue damage through the thickness direction of the sample by simply timing the transducers. Third, the nonlinear wave mixing method is used to characterize the degradation of cement-based materials caused by alkali-silica reaction (ASR). It is found that the nonlinear ultrasonic method is sensitive to detect ASR damage at very early stage, and has the potential to identify the different damage stages. Finally, a micromechanics-based chemo-mechanical model is developed which relates the acoustic nonlinearity parameter to ASR damage. This model provides a way to quantitatively predict the changes in the acoustic nonlinearity parameter due to ASR

Nonlinear optical measurements of conducting copolymers of aniline under CW laser excitation

NASA Astrophysics Data System (ADS)

Pramodini, S.; Poornesh, P.

2015-08-01

Synthesis and measurements of third-order optical nonlinearity and optical limiting of conducting copolymers of aniline are presented. Single beam z-scan technique was employed for the nonlinear optical studies. Continuous wave He-Ne laser operating at 633 nm was used as the source of excitation. Copolymer samples exhibited reverse saturable absorption (RSA) process. The nonlinear refraction studies depict that the copolymers exhibit self-defocusing property. The estimated values of βeff, n2 and χ(3) were found to be of the order of 10-2 cm/W, 10-5 esu and 10-7 esu respectively. Self-diffraction rings were observed due to refractive index change when exposed to the laser beam. A good optical limiting and clamping of power of ∼0.9 mW and ∼0.05 mW was observed. Therefore, copolymers of aniline emerge as a potential candidate for photonic device applications.

Obtaining high-energy responses of nonlinear piezoelectric energy harvester by voltage impulse perturbations

NASA Astrophysics Data System (ADS)

Lan, Chunbo; Tang, Lihua; Qin, Weiyang

2017-07-01

Nonlinear energy harvesters have attracted wide research attentions to achieve broadband performances in recent years. Nonlinear structures have multiple solutions in certain frequency region that contains high-energy and low-energy orbits. It is effectively the frequency region of capturing a high-energy orbit that determines the broadband performance. Thus, maintaining large-amplitude high-energy-orbit oscillations is highly desired. In this paper, a voltage impulse perturbation approach based on negative resistance is applied to trigger high-energy-orbit responses of piezoelectric nonlinear energy harvesters. First, the mechanism of the voltage impulse perturbation and the implementation of the synthetic negative resistance circuit are discussed in detail. Subsequently, numerical simulation and experiment are conducted and the results demonstrate that the high-energy-orbit oscillations can be triggered by the voltage impulse perturbation method for both monostable and bistable configurations given various scenarios. It is revealed that the perturbation levels required to trigger and maintain high-energy-orbit oscillations are different for various excitation frequencies in the region where multiple solutions exist. The higher gain in voltage output when high-energy-orbit oscillations are captured is accompanied with the demand of a higher voltage impulse perturbation level.

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

NASA Astrophysics Data System (ADS)

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

2010-04-01

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

NASA Astrophysics Data System (ADS)

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.

Z-scan theory for nonlocal nonlinear media with simultaneous nonlinear refraction and nonlinear absorption.

PubMed

Rashidian Vaziri, Mohammad Reza

2013-07-10

In this paper, the Z-scan theory for nonlocal nonlinear media has been further developed when nonlinear absorption and nonlinear refraction appear simultaneously. To this end, the nonlinear photoinduced phase shift between the impinging and outgoing Gaussian beams from a nonlocal nonlinear sample has been generalized. It is shown that this kind of phase shift will reduce correctly to its known counterpart for the case of pure refractive nonlinearity. Using this generalized form of phase shift, the basic formulas for closed- and open-aperture beam transmittances in the far field have been provided, and a simple procedure for interpreting the Z-scan results has been proposed. In this procedure, by separately performing open- and closed-aperture Z-scan experiments and using the represented relations for the far-field transmittances, one can measure the nonlinear absorption coefficient and nonlinear index of refraction as well as the order of nonlocality. Theoretically, it is shown that when the absorptive nonlinearity is present in addition to the refractive nonlinearity, the sample nonlocal response can noticeably suppress the peak and enhance the valley of the Z-scan closed-aperture transmittance curves, which is due to the nonlocal action's ability to change the beam transverse dimensions.

Peak intensity measurement of relativistic lasers via nonlinear Thomson scattering.

PubMed

Har-Shemesh, Omri; Di Piazza, Antonino

2012-04-15

The measurement of peak laser intensities exceeding 10(20) W/cm(2) is in general a very challenging task. We suggest a simple method to accurately measure such high intensities up to about 10(23) W/cm(2), by colliding a beam of ultrarelativistic electrons with the laser pulse. The method exploits the high directionality of the radiation emitted by ultrarelativistic electrons via nonlinear Thomson scattering. Initial electron energies well within the reach of laser wake-field accelerators are required, allowing in principle for an all-optical setup. Accuracies of the order of 10% are theoretically envisaged. © 2012 Optical Society of America

Third-order optical nonlinearity of N-doped graphene oxide nanocomposites at different GO ratios

NASA Astrophysics Data System (ADS)

Kimiagar, Salimeh; Abrinaei, Fahimeh

2018-05-01

In the present work, the influence of GO ratios on the structural, linear and nonlinear optical properties of nitrogen-doped graphene oxide nanocomposites (N-GO NCs) has been studied. N-GO NCs were synthesized by hydrothermal method. The XRD, FTIR, SEM, and TEM results confirmed the reduction of GO by nitrogen doping. The energy band gaps of N-GO NCs calculated from UV-Vis analyzed by using Tauc plot. To obtain further insight into potential optical changes in the N-GO NCs by increasing GO contents, Z-scan analysis was performed with nanosecond Nd-YAG laser at 532 nm. The nonlinear absorption coefficient, β, and nonlinear refractive index, n2, for N-GO NCs at the laser intensity of 113 MW/cm were measured and an increase was observed in both parameters after addition of nitrogen to GO. The third-order nonlinear optical susceptibilities of N-GO NCs were measured in the order of 10-9 esu. The results showed that N-GO NCs have negative nonlinearity which can be controlled by GO contents to obtain the highest values for nonlinear optical parameters. The nonlinear optical results not only imply that N-GO NCs can serve as an important material in the advancing of optoelectronics but also open new possibilities for the design of new graphene-based materials by variation of N and GO ratios as well as manufacturing conditions.

Stiffness optimization of non-linear elastic structures

DOE PAGES

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

2017-11-13

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Stiffness optimization of non-linear elastic structures

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

Wallin, Mathias; Ivarsson, Niklas; Tortorelli, Daniel

Our paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. And for the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed bymore » using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. We formulate a well-posed topology optimization problem by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.« less

Localization and identification of structural nonlinearities using cascaded optimization and neural networks

NASA Astrophysics Data System (ADS)

Koyuncu, A.; Cigeroglu, E.; Özgüven, H. N.

2017-10-01

In this study, a new approach is proposed for identification of structural nonlinearities by employing cascaded optimization and neural networks. Linear finite element model of the system and frequency response functions measured at arbitrary locations of the system are used in this approach. Using the finite element model, a training data set is created, which appropriately spans the possible nonlinear configurations space of the system. A classification neural network trained on these data sets then localizes and determines the types of all nonlinearities associated with the nonlinear degrees of freedom in the system. A new training data set spanning the parametric space associated with the determined nonlinearities is created to facilitate parametric identification. Utilizing this data set, initially, a feed forward regression neural network is trained, which parametrically identifies the classified nonlinearities. Then, the results obtained are further improved by carrying out an optimization which uses network identified values as starting points. Unlike identification methods available in literature, the proposed approach does not require data collection from the degrees of freedoms where nonlinear elements are attached, and furthermore, it is sufficiently accurate even in the presence of measurement noise. The application of the proposed approach is demonstrated on an example system with nonlinear elements and on a real life experimental setup with a local nonlinearity.

Demonstration of Nonlinearity Bias in the Measurement of the Apparent Diffusion Coefficient in Multicenter Trials

PubMed Central

Malyarenko, Dariya; Newitt, David; Wilmes, Lisa; Tudorica, Alina; Helmer, Karl G.; Arlinghaus, Lori R.; Jacobs, Michael A.; Jajamovich, Guido; Taouli, Bachir; Yankeelov, Thomas E.; Huang, Wei; Chenevert, Thomas L.

2015-01-01

Purpose Characterize system-specific bias across common magnetic resonance imaging (MRI) platforms for quantitative diffusion measurements in multicenter trials. Methods Diffusion weighted imaging (DWI) was performed on an ice-water phantom along the superior-inferior (SI) and right-left (RL) orientations spanning ±150 mm. The same scanning protocol was implemented on 14 MRI systems at seven imaging centers. The bias was estimated as a deviation of measured from known apparent diffusion coefficient (ADC) along individual DWI directions. The relative contributions of gradient nonlinearity, shim errors, imaging gradients and eddy currents were assessed independently. The observed bias errors were compared to numerical models. Results The measured systematic ADC errors scaled quadratically with offset from isocenter, and ranged between −55% (SI) and 25% (RL). Nonlinearity bias was dependent on system design and diffusion gradient direction. Consistent with numerical models, minor ADC errors (±5%) due to shim, imaging and eddy currents were mitigated by double echo DWI and image co-registration of individual gradient directions. Conclusion The analysis confirms gradient nonlinearity as a major source of spatial DW bias and variability in off-center ADC measurements across MRI platforms, with minor contributions from shim, imaging gradients and eddy currents. The developed protocol enables empiric description of systematic bias in multicenter quantitative DWI studies. PMID:25940607

Demonstration of nonlinearity bias in the measurement of the apparent diffusion coefficient in multicenter trials.

PubMed

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

2016-03-01

Characterize system-specific bias across common magnetic resonance imaging (MRI) platforms for quantitative diffusion measurements in multicenter trials. Diffusion weighted imaging (DWI) was performed on an ice-water phantom along the superior-inferior (SI) and right-left (RL) orientations spanning ± 150 mm. The same scanning protocol was implemented on 14 MRI systems at seven imaging centers. The bias was estimated as a deviation of measured from known apparent diffusion coefficient (ADC) along individual DWI directions. The relative contributions of gradient nonlinearity, shim errors, imaging gradients, and eddy currents were assessed independently. The observed bias errors were compared with numerical models. The measured systematic ADC errors scaled quadratically with offset from isocenter, and ranged between -55% (SI) and 25% (RL). Nonlinearity bias was dependent on system design and diffusion gradient direction. Consistent with numerical models, minor ADC errors (± 5%) due to shim, imaging and eddy currents were mitigated by double echo DWI and image coregistration of individual gradient directions. The analysis confirms gradient nonlinearity as a major source of spatial DW bias and variability in off-center ADC measurements across MRI platforms, with minor contributions from shim, imaging gradients and eddy currents. The developed protocol enables empiric description of systematic bias in multicenter quantitative DWI studies. © 2015 Wiley Periodicals, Inc.

A problem in non-linear Diophantine approximation

NASA Astrophysics Data System (ADS)

Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon

2018-05-01

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

Integrability and correspondence of classical and quantum non-linear three-mode systems

NASA Astrophysics Data System (ADS)

Odzijewicz, A.; Wawreniuk, E.

2018-04-01

The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the quantum system are constructed. We find the explicit formulas for the reproducing measure for these states. Examples of some applications of the obtained results in non-linear quantum optics are presented.

H∞ filter design for nonlinear systems with quantised measurements in finite frequency domain

NASA Astrophysics Data System (ADS)

El Hellani, D.; El Hajjaji, A.; Ceschi, R.

2017-04-01

This paper deals with the problem of finite frequency (FF) H∞ full-order fuzzy filter design for nonlinear discrete-time systems with quantised measurements, described by Takagi-Sugeno models. The measured signals are assumed to be quantised with a logarithmic quantiser. Using a fuzzy-basis-dependent Lyapunov function, the finite frequency ℓ2 gain definition, the generalised S-procedure, and Finsler's lemma, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H∞ attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. With the aid of Finsler's lemma, a large number of slack variables are introduced to the design conditions, which provides extra degrees of freedom in optimising the guaranteed H∞ performance. This directly leads to performance improvement and reduction of conservatism. Finally, we give a simulation example to demonstrate the efficiency of the proposed design method, and we show that a lower H∞ attenuation level can be obtained by our developed approach in comparison with another result in the literature.

Nonlinear digital signal processing in mental health: characterization of major depression using instantaneous entropy measures of heartbeat dynamics.

PubMed

Valenza, Gaetano; Garcia, Ronald G; Citi, Luca; Scilingo, Enzo P; Tomaz, Carlos A; Barbieri, Riccardo

2015-01-01

Nonlinear digital signal processing methods that address system complexity have provided useful computational tools for helping in the diagnosis and treatment of a wide range of pathologies. More specifically, nonlinear measures have been successful in characterizing patients with mental disorders such as Major Depression (MD). In this study, we propose the use of instantaneous measures of entropy, namely the inhomogeneous point-process approximate entropy (ipApEn) and the inhomogeneous point-process sample entropy (ipSampEn), to describe a novel characterization of MD patients undergoing affective elicitation. Because these measures are built within a nonlinear point-process model, they allow for the assessment of complexity in cardiovascular dynamics at each moment in time. Heartbeat dynamics were characterized from 48 healthy controls and 48 patients with MD while emotionally elicited through either neutral or arousing audiovisual stimuli. Experimental results coming from the arousing tasks show that ipApEn measures are able to instantaneously track heartbeat complexity as well as discern between healthy subjects and MD patients. Conversely, standard heart rate variability (HRV) analysis performed in both time and frequency domains did not show any statistical significance. We conclude that measures of entropy based on nonlinear point-process models might contribute to devising useful computational tools for care in mental health.

Femtosecond Kerr index of cyclic olefin co/polymers for THz nonlinear optics

NASA Astrophysics Data System (ADS)

Noskovicova, E.; Lorenc, D.; Slusna, L.; Velic, D.

2016-10-01

The second-order nonlinear refractive index n2 (Kerr index) of cyclic olefin copolymer (TOPAS) and cyclic olefin polymers (ZEONEX, ZEONOR) was determined at the wavelength of 800 nm within this work. Bulk samples of ZEONEX, ZEONOR and TOPAS were measured using the single-beam Z-scan technique and the values of their nonlinear refractive index were determined to be approximately 2 × 10-20 m2W-1 for all cases. The obtained values of n2 play a vital role for ultrafast pulse evolution and corresponding phenomena such as nonlinear spectral transformation.

Gold nanoparticles on the surface of soda-lime glass: morphological, linear and nonlinear optical characterization.

PubMed

Romani, E C; Vitoreti, Douglas; Gouvêa, Paula M P; Caldas, P G; Prioli, R; Paciornik, S; Fokine, Michael; Braga, Arthur M B; Gomes, Anderson S L; Carvalho, Isabel C S

2012-02-27

Materials presenting high optical nonlinearity, such as materials containing metal nanoparticles (NPs), can be used in various applications in photonics. This motivated the research presented in this paper, where morphological, linear and nonlinear optical characteristics of gold NPs on the surface of bulk soda-lime glass substrates were investigated as a function of nanoparticle height. The NPs were obtained by annealing gold (Au) thin films previously deposited on the substrates. Pixel intensity histogram fitting on Atomic Force Microscopy (AFM) images was performed to obtain the thickness of the deposited film. Image analysis was employed to obtain the statistical distribution of the average height of the NPs. In addition, absorbance spectra of the samples before and after annealing were measured. Finally, the nonlinear refractive index (n2) and the nonlinear absorption index (α2) at 800 nm were obtained before and after annealing by using the thermally managed eclipse Z-scan (TM-EZ) technique with a Ti:Sapphire laser (150 fs pulses). Results show that both n2 and α2 at this wavelength change signs after the annealing and that the samples presented a high nonlinear refractive index.

Mapping the nonlinear optical susceptibility by noncollinear second-harmonic generation.

PubMed

Larciprete, M C; Bovino, F A; Giardina, M; Belardini, A; Centini, M; Sibilia, C; Bertolotti, M; Passaseo, A; Tasco, V

2009-07-15

We present a method, based on noncollinear second-harmonic generation, to evaluate the nonzero elements of the nonlinear optical susceptibility. At a fixed incidence angle, the generated signal is investigated by varying the polarization state of both fundamental beams. The resulting polarization charts allows us to verify if Kleinman's symmetry rules can be applied to a given material or to retrieve the absolute value of the nonlinear optical tensor terms, from a reference measurement. Experimental measurements obtained from gallium nitride layers are reported. The proposed method does not require an angular scan and thus is useful when the generated signal is strongly affected by sample rotation.

Nonlinear Acoustics.

DTIC Science & Technology

1984-09-01

1, 1983-November 30, 1984 3 I. ANNUAL SUMMARY REPORT A. Nonlinear Properties of the Fluoroperovskites (Cubic Symmnetry) In addition to measurement of...the nonlinear properties of the fluoroperovskites CsCdF3 and KZnF 3 at room temperature published last year [N. A. Breazeale, J. Philip, A

Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation

NASA Astrophysics Data System (ADS)

Peter, Simon; Leine, Remco I.

2017-11-01

Phase resonance testing is one method for the experimental extraction of nonlinear normal modes. This paper proposes a novel method for nonlinear phase resonance testing. Firstly, the issue of appropriate excitation is approached on the basis of excitation power considerations. Therefore, power quantities known from nonlinear systems theory in electrical engineering are transferred to nonlinear structural dynamics applications. A new power-based nonlinear mode indicator function is derived, which is generally applicable, reliable and easy to implement in experiments. Secondly, the tuning of the excitation phase is automated by the use of a Phase-Locked-Loop controller. This method provides a very user-friendly and fast way for obtaining the backbone curve. Furthermore, the method allows to exploit specific advantages of phase control such as the robustness for lightly damped systems and the stabilization of unstable branches of the frequency response. The reduced tuning time for the excitation makes the commonly used free-decay measurements for the extraction of backbone curves unnecessary. Instead, steady-state measurements for every point of the curve are obtained. In conjunction with the new mode indicator function, the correlation of every measured point with the associated nonlinear normal mode of the underlying conservative system can be evaluated. Moreover, it is shown that the analysis of the excitation power helps to locate sources of inaccuracies in the force appropriation process. The method is illustrated by a numerical example and its functionality in experiments is demonstrated on a benchmark beam structure.

Nonlinearity characterization of temperature sensing systems for integrated circuit testing by intermodulation products monitoring.

PubMed

Altet, J; Mateo, D; Perpiñà, X; Grauby, S; Dilhaire, S; Jordà, X

2011-09-01

This work presents an alternative characterization strategy to quantify the nonlinear behavior of temperature sensing systems. The proposed approach relies on measuring the temperature under thermal sinusoidal steady state and observing the intermodulation products that are generated within the sensing system itself due to its nonlinear temperature-output voltage characteristics. From such intermodulation products, second-order interception points can be calculated as a figure of merit of the measuring system nonlinear behavior. In this scenario, the present work first shows a theoretical analysis. Second, it reports the experimental results obtained with three thermal sensing techniques used in integrated circuits. © 2011 American Institute of Physics

Low-amplitude non-linear volume vibrations of single microbubbles measured with an "acoustical camera".

PubMed

Renaud, Guillaume; Bosch, Johan G; Van Der Steen, Antonius F W; De Jong, Nico

2014-06-01

Contrast-enhanced ultrasound imaging is based on the detection of non-linear vibrational responses of a contrast agent after its intravenous administration. Improving contrast-enhanced images requires an accurate understanding of the vibrational response to ultrasound of the lipid-coated gas microbubbles that constitute most ultrasound contrast agents. Variations in the volume of microbubbles provide the most efficient radiation of ultrasound and, therefore, are the most important bubble vibrations for medical diagnostic ultrasound imaging. We developed an "acoustical camera" that measures the dynamic volume change of individual microbubbles when excited by a pressure wave. In the work described here, the technique was applied to the characterization of low-amplitude non-linear behaviors of BR14 microbubbles (Bracco Research, Geneva, Switzerland). The amplitude dependence of the resonance frequency and the damping, the prevalence of efficient subharmonic and ultraharmonic vibrations and the amplitude dependence of the response at the fundamental frequency and at the second harmonic frequency were investigated. Because of the large number of measurements, we provide a statistical characterization of the low-amplitude non-linear properties of the contrast agent. Copyright © 2014 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.

Characterization of Non-Linearized Spacecraft Relative Motion using Nonlinear Normal Modes

DTIC Science & Technology

2016-04-20

10 5.1 Results for Four Models with Different Nonlinearities ..................................................11 5.2 Effects of...Force Research Laboratory or the U.S. Government. 1.0 SUMMARY In this report, the effects of incorporating nonlinearities in sequential relative orbit...exactly. Huxel and Bishop [1] discussed the effects of using both inertial range measurements from tracking stations and relative range measurements

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

NASA Astrophysics Data System (ADS)

Geng, Xianguo; Liu, Huan

2018-04-01

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

Inverse Modelling to Obtain Head Movement Controller Signal

NASA Technical Reports Server (NTRS)

Kim, W. S.; Lee, S. H.; Hannaford, B.; Stark, L.

1984-01-01

Experimentally obtained dynamics of time-optimal, horizontal head rotations have previously been simulated by a sixth order, nonlinear model driven by rectangular control signals. Electromyography (EMG) recordings have spects which differ in detail from the theoretical rectangular pulsed control signal. Control signals for time-optimal as well as sub-optimal horizontal head rotations were obtained by means of an inverse modelling procedures. With experimentally measured dynamical data serving as the input, this procedure inverts the model to produce the neurological control signals driving muscles and plant. The relationships between these controller signals, and EMG records should contribute to the understanding of the neurological control of movements.

Nonlinear optical switching and optical limiting in colloidal CdSe quantum dots investigated by nanosecond Z-scan measurement

NASA Astrophysics Data System (ADS)

Valligatla, Sreeramulu; Haldar, Krishna Kanta; Patra, Amitava; Desai, Narayana Rao

2016-10-01

The semiconductor nanocrystals are found to be promising class of third order nonlinear optical materials because of quantum confinement effects. Here, we highlight the nonlinear optical switching and optical limiting of cadmium selenide (CdSe) quantum dots (QDs) using nanosecond Z-scan measurement. The intensity dependent nonlinear absorption and nonlinear refraction of CdSe QDs were investigated by applying the Z-scan technique with 532 nm, nanosecond laser pulses. At lower intensities, the nonlinear process is dominated by saturable absorption (SA) and it is changed to reverse saturable absorption (RSA) at higher intensities. The SA behaviour is attributed to the ground state bleaching and the RSA is ascribed to free carrier absorption (FCA) of CdSe QDs. The nonlinear optical switching behaviour and reverse saturable absorption makes CdSe QDs are good candidate for all-optical device and optical limiting applications.

Linear and Nonlinear Thinking: A Multidimensional Model and Measure

ERIC Educational Resources Information Center

Groves, Kevin S.; Vance, Charles M.

2015-01-01

Building upon previously developed and more general dual-process models, this paper provides empirical support for a multidimensional thinking style construct comprised of linear thinking and multiple dimensions of nonlinear thinking. A self-report assessment instrument (Linear/Nonlinear Thinking Style Profile; LNTSP) is presented and…

A Feasibility Study of Nonlinear Spectroscopic Measurement of Magnetic Nanoparticles Targeted to Cancer Cells.

PubMed

Ficko, Bradley W; NDong, Christian; Giacometti, Paolo; Griswold, Karl E; Diamond, Solomon G

2017-05-01

Magnetic nanoparticles (MNPs) are an emerging platform for targeted diagnostics in cancer. An important component needed for translation of MNPs is the detection and quantification of targeted MNPs bound to tumor cells. This study explores the feasibility of a multifrequency nonlinear magnetic spectroscopic method that uses excitation and pickup coils and is capable of discriminating between quantities of bound and unbound MNPs in 0.5 ml samples of KB and Igrov human cancer cell lines. The method is tested over a range of five concentrations of MNPs from 0 to 80 μg/ml and five concentrations of cells from 50 to 400 000 count per ml. A linear model applied to the magnetic spectroscopy data was able to simultaneously measure bound and unbound MNPs with agreement between the model-fit and lab assay measurements (p < 0.001). The detectable iron of the presented method to bound and unbound MNPs was < 2 μg in a 0.5 ml sample. The linear model parameters used to determine the quantities of bound and unbound nanoparticles in KB cells were also used to measure the bound and unbound MNP in the Igrov cell line and vice versa. Nonlinear spectroscopic measurement of MNPs may be a useful method for studying targeted MNPs in oncology. Determining the quantity of bound and unbound MNP in an unknown sample using a linear model represents an exciting opportunity to translate multifrequency nonlinear spectroscopy methods to in vivo applications where MNPs could be targeted to cancer cells.

Exploring the nonlinear regime of light-matter interaction using electronic spins in diamond

NASA Astrophysics Data System (ADS)

Alfasi, Nir; Masis, Sergei; Winik, Roni; Farfurnik, Demitry; Shtempluck, Oleg; Bar-Gill, Nir; Buks, Eyal

2018-06-01

The coupling between defects in diamond and a superconducting microwave resonator is studied in the nonlinear regime. Both negatively charged nitrogen-vacancy and P1 defects are explored. The measured cavity mode response exhibits strong nonlinearity near a spin resonance. Data is compared with theoretical predictions and a good agreement is obtained in a wide range of externally controlled parameters. The nonlinear effect under study in the current paper is expected to play a role in any cavity-based magnetic resonance imaging technique and to impose a fundamental limit upon its sensitivity.

Development of attenuation and diffraction corrections for linear and nonlinear Rayleigh surface waves radiating from a uniform line source

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

Jeong, Hyunjo, E-mail: hjjeong@wku.ac.kr; Cho, Sungjong; Zhang, Shuzeng

2016-04-15

In recent studies with nonlinear Rayleigh surface waves, harmonic generation measurements have been successfully employed to characterize material damage and microstructural changes, and found to be sensitive to early stages of damage process. A nonlinearity parameter of Rayleigh surface waves was derived and frequently measured to quantify the level of damage. The accurate measurement of the nonlinearity parameter generally requires making corrections for beam diffraction and medium attenuation. These effects are not generally known for nonlinear Rayleigh waves, and therefore not properly considered in most of previous studies. In this paper, the nonlinearity parameter for a Rayleigh surface wave ismore » defined from the plane wave displacement solutions. We explicitly define the attenuation and diffraction corrections for fundamental and second harmonic Rayleigh wave beams radiated from a uniform line source. Attenuation corrections are obtained from the quasilinear theory of plane Rayleigh wave equations. To obtain closed-form expressions for diffraction corrections, multi-Gaussian beam (MGB) models are employed to represent the integral solutions derived from the quasilinear theory of the full two-dimensional wave equation without parabolic approximation. Diffraction corrections are presented for a couple of transmitter-receiver geometries, and the effects of making attenuation and diffraction corrections are examined through the simulation of nonlinearity parameter determination in a solid sample.« less

Effect of initial strain and material nonlinearity on the nonlinear static and dynamic response of graphene sheets

NASA Astrophysics Data System (ADS)

Singh, Sandeep; Patel, B. P.

2018-06-01

Computationally efficient multiscale modelling based on Cauchy-Born rule in conjunction with finite element method is employed to study static and dynamic characteristics of graphene sheets, with/without considering initial strain, involving Green-Lagrange geometric and material nonlinearities. The strain energy density function at continuum level is established by coupling the deformation at continuum level to that at atomic level through Cauchy-Born rule. The atomic interactions between carbon atoms are modelled through Tersoff-Brenner potential. The governing equation of motion obtained using Hamilton's principle is solved through standard Newton-Raphson method for nonlinear static response and Newmark's time integration technique to obtain nonlinear transient response characteristics. Effect of initial strain on the linear free vibration frequencies, nonlinear static and dynamic response characteristics is investigated in detail. The present multiscale modelling based results are found to be in good agreement with those obtained through molecular mechanics simulation. Two different types of boundary constraints generally used in MM simulation are explored in detail and few interesting findings are brought out. The effect of initial strain is found to be greater in linear response when compared to that in nonlinear response.

Third-order nonlinear optical properties of organic azo dyes by using strength of nonlinearity parameter and Z-scan technique

NASA Astrophysics Data System (ADS)

Motiei, H.; Jafari, A.; Naderali, R.

2017-02-01

In this paper, two chemically synthesized organic azo dyes, 2-(2,5-Dichloro-phenyazo)-5,5-dimethyl-cyclohexane-1,3-dione (azo dye (i)) and 5,5-Dimethyl-2-tolylazo-cyclohexane-1,3-dione (azo dye (ii)), have been studied from optical Kerr nonlinearity point of view. These materials were characterized by Ultraviolet-visible spectroscopy. Experiments were performed using a continous wave diode-pumped laser at 532 nm wavelength in three intensities of the laser beam. Nonlinear absorption (β), refractive index (n2) and third-order susceptibility (χ (3)) of dyes, were calculated. Nonlinear absorption coefficient of dyes have been calculated from two methods; 1) using theoretical fits and experimental data in the Z-scan technique, 2) using the strength of nonlinearity curves. The values of β obtained from both of the methods were approximately the same. The results demonstrated that azo dye (ii) displays better nonlinearity and has a lower two-photon absorption threshold than azo dye (i). Calculated parameter related to strength of nonlinearity for azo dye (ii) was higher than azo dye (i), It may be due to presence of methyl in azo dye (ii) instead of chlorine in azo dye (i). Furthermore, The measured values of third order susceptibility of azo dyes were from the order of 10-9 esu . These azo dyes can be suitable candidate for optical switching devices.

A spline-based non-linear diffeomorphism for multimodal prostate registration.

PubMed

Mitra, Jhimli; Kato, Zoltan; Martí, Robert; Oliver, Arnau; Lladó, Xavier; Sidibé, Désiré; Ghose, Soumya; Vilanova, Joan C; Comet, Josep; Meriaudeau, Fabrice

2012-08-01

This paper presents a novel method for non-rigid registration of transrectal ultrasound and magnetic resonance prostate images based on a non-linear regularized framework of point correspondences obtained from a statistical measure of shape-contexts. The segmented prostate shapes are represented by shape-contexts and the Bhattacharyya distance between the shape representations is used to find the point correspondences between the 2D fixed and moving images. The registration method involves parametric estimation of the non-linear diffeomorphism between the multimodal images and has its basis in solving a set of non-linear equations of thin-plate splines. The solution is obtained as the least-squares solution of an over-determined system of non-linear equations constructed by integrating a set of non-linear functions over the fixed and moving images. However, this may not result in clinically acceptable transformations of the anatomical targets. Therefore, the regularized bending energy of the thin-plate splines along with the localization error of established correspondences should be included in the system of equations. The registration accuracies of the proposed method are evaluated in 20 pairs of prostate mid-gland ultrasound and magnetic resonance images. The results obtained in terms of Dice similarity coefficient show an average of 0.980±0.004, average 95% Hausdorff distance of 1.63±0.48 mm and mean target registration and target localization errors of 1.60±1.17 mm and 0.15±0.12 mm respectively. Copyright © 2012 Elsevier B.V. All rights reserved.

Large electronic third-order optical nonlinearities of cyanine dyes measured by resonant femtosecond degenerate four-wave mixing

NASA Astrophysics Data System (ADS)

Kasatani, Kazuo

2003-01-01

Third-order optical nonlinearities of several cyanine dyes were measured under resonant conditions by the femtosecond degenerate four-wave mixing (DFWM) technique. Temporal profiles of the DFWM signal were measured with a time resolution of 0.3 ps, and were found to consist of at least two components, the coherent instantaneous nonlinear response and the delayed response with a decay time constant of several hundred picoseconds. The latter can be attributed to molecular rotational relaxation of these dyes. The values of electronic component of the optical nonlinear susceptibility, χ e xxxx (3), for these dyes were ≈2×10 -12 esu at the very low concentration of 1×10 -5 mol dm -3. The electronic component of molecular hyperpolarizability, γe, was calculated to be ≈1×10 -28 esu for each dye.

General job stress: a unidimensional measure and its non-linear relations with outcome variables.

PubMed

Yankelevich, Maya; Broadfoot, Alison; Gillespie, Jennifer Z; Gillespie, Michael A; Guidroz, Ashley

2012-04-01

This article aims to examine the non-linear relations between a general measure of job stress [Stress in General (SIG)] and two outcome variables: intentions to quit and job satisfaction. In so doing, we also re-examine the factor structure of the SIG and determine that, as a two-factor scale, it obscures non-linear relations with outcomes. Thus, in this research, we not only test for non-linear relations between stress and outcome variables but also present an updated version of the SIG scale. Using two distinct samples of working adults (sample 1, N = 589; sample 2, N = 4322), results indicate that a more parsimonious eight-item SIG has better model-data fit than the 15-item two-factor SIG and that the eight-item SIG has non-linear relations with job satisfaction and intentions to quit. Specifically, the revised SIG has an inverted curvilinear J-shaped relation with job satisfaction such that job satisfaction drops precipitously after a certain level of stress; the SIG has a J-shaped curvilinear relation with intentions to quit such that turnover intentions increase exponentially after a certain level of stress. Copyright © 2011 John Wiley & Sons, Ltd.

Unraveling complex nonlinear elastic behaviors in rocks using dynamic acousto-elasticity

NASA Astrophysics Data System (ADS)

Riviere, J.; Guyer, R.; Renaud, G.; TenCate, J. A.; Johnson, P. A.

2012-12-01

In comparison with standard nonlinear ultrasonic methods like frequency mixing or resonance based measurements that allow one to extract average, bulk variations of modulus and attenuation versus strain level, dynamic acousto-elasticity (DAE) allows to obtain the elastic behavior over the entire dynamic cycle, detailing the full nonlinear behavior under tension and compression, including hysteresis and memory effects. This method consists of exciting a sample in Bulk-mode resonance at strains of 10-7 to 10-5 and simultaneously probing with a sequence of high frequency, low amplitude pulses. Time of flight and amplitudes of these pulses, respectively related to nonlinear elastic and dissipative parameters, can be plotted versus vibration strain level. Despite complex nonlinear signatures obtained for most rocks, it can be shown that for low strain amplitude (< 10-6), the nonlinear classical theory issued from a Taylor decomposition can explain the harmonic content. For higher strain, harmonic content becomes richer and the material exhibits more hysteretic behaviors, i.e. strain rate dependencies. Such observations have been made in the past (e.g., Pasqualini et al., JGR 2007), but not with the extreme detail of elasticity provided by DAE. Previous quasi-static measurements made in Berea sandstone (Claytor et al, GRL 2009), show that the hysteretic behavior disappears when the protocol is performed at a very low strain-rate (static limit). Therefore, future work will aim at linking quasi-static and dynamic observations, i.e. the frequency or strain-rate dependence, in order to understand underlying physical phenomena.

Nonlinear optical properties of semiconductor nanocrystals

NASA Astrophysics Data System (ADS)

Ricard, Gianpiero Banfi Vittorio Degiorgio Daniel

1998-05-01

This review is devoted to the description of recent experimental results concerning the nonlinear optical properties of semiconductor-doped glasses SDGs with particular emphasis on the regime in which the energy of the incident photon is smaller than the energy gap. A considerable theoretical and experimental effort has been devoted in the last 10years to the fundamental aspects of quantumconfined structures, which have properties somewhat intermediate between the bulk crystals and atoms or molecules. From this point of view, SDGs represent an easily available test system, and optical techniques have been a major diagnostic tool. Luminescence and absorption spectroscopy were extensively used to characterize the electronic states. The experiments aimed at the measurement of the real and imaginary parts of the third-order optical susceptibility of SDGs below the bandgap are described in some detail, and the results obtained with different techniques are compared. Besides the intrinsic fast nonlinearity due to bound electrons, SDGs may present a larger but much slower nonlinearity due to the free carriers generated by two-photon absorption. This implies that experiments have to be properly designed for separation of the two effects. In this article we stress the importance of a detailed structural characterization of the samples. Knowledge of the volume fraction occupied by the nanocrystals is necessary in order to derive from the experimental data the intrinsic nonlinearity and to compare it with the bulk nonlinearity. We discuss recent experiments in which the dependence of the intrinsic nonlinearity on the crystal size is derived by performing, on the samples, measurements of the real part and imaginary part of the nonlinear optical susceptibility and measurements of crystal size and volume fraction. Structural characterization is of interest also for a better understanding of the physical processes underlying the growth of crystallites in SDGs. The average size of

Nonlinear ultrasonic pulsed measurements and applications to metal processing and fatigue

NASA Astrophysics Data System (ADS)

Yost, William T.; Cantrell, John H.; Na, Jeong K.

2001-04-01

Nonlinear ultrasonics research at NASA-Langley Research Center emphasizes development of experimental techniques and modeling, with applications to metal fatigue and metals processing. This review work includes a summary of results from our recent efforts in technique refinement, modeling of fatigue related microstructure contributions, and measurements on fatigued turbine blades. Also presented are data on 17-4PH and 410-Cb stainless steels. The results are in good agreement with the models.

Nonlinear coupling of flow harmonics: Hexagonal flow and beyond

NASA Astrophysics Data System (ADS)

Giacalone, Giuliano; Yan, Li; Ollitrault, Jean-Yves

2018-05-01

Higher Fourier harmonics of anisotropic flow (v4 and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one and allows us to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at s =2.76 TeV, we perform an application of our formalism to hexagonal flow, v6, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient χ624, which couples v6 to v2 and v4. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, and higher order moments recently analyzed by the ALICE Collaboration. The value of χ624 extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher order harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of v7 and v8.

Third-Order Optical Nonlinearities of Squarylium Dyes with Benzothiazole Donor Groups Measured Using the Picosecond Z-Scan Technique

NASA Astrophysics Data System (ADS)

Li, Zhong-Yu; Xu, Song; Chen, Zi-Hui; Zhang, Fu-Shi; Kasatani, Kazuo

2011-08-01

Third-order optical nonlinearities of two squarylium dyes with benzothiazole donor groups (BSQ1 and BSQ2) in chloroform solution are measured by a picosecond Z-scan technique at 532 nm. It is found that the two compounds show the saturation absorption and nonlinear self-focus refraction effect. The molecular second hyperpolarizabilities are calculated to be 7.46 × 10-31 esu and 5.01 × 10-30 esu for BSQ1 and BSQ2, respectively. The large optical nonlinearities of squarylium dyes can be attributed to their rigid and intramolecular charge transfer structure. The difference in γ values is attributed to the chloro group of benzene rings of BSQ2 and the one-photon resonance effect. It is found that the third-order nonlinear susceptibilities of two squarylium dyes are mainly determined by the real parts of χ(3), and the large optical nonlinearities of studied squarylium dyes can be attributed to the nonlinear refraction.

A nonlinear propagation model-based phase calibration technique for membrane hydrophones.

PubMed

Cooling, Martin P; Humphrey, Victor F

2008-01-01

A technique for the phase calibration of membrane hydrophones in the frequency range up to 80 MHz is described. This is achieved by comparing measurements and numerical simulation of a nonlinearly distorted test field. The field prediction is obtained using a finite-difference model that solves the nonlinear Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation in the frequency domain. The measurements are made in the far field of a 3.5 MHz focusing circular transducer in which it is demonstrated that, for the high drive level used, spatial averaging effects due to the hydrophone's finite-receive area are negligible. The method provides a phase calibration of the hydrophone under test without the need for a device serving as a phase response reference, but it requires prior knowledge of the amplitude sensitivity at the fundamental frequency. The technique is demonstrated using a 50-microm thick bilaminar membrane hydrophone, for which the results obtained show functional agreement with predictions of a hydrophone response model. Further validation of the results is obtained by application of the response to the measurement of the high amplitude waveforms generated by a modern biomedical ultrasonic imaging system. It is demonstrated that full deconvolution of the calculated complex frequency response of a nonideal hydrophone results in physically realistic measurements of the transmitted waveforms.

Critical Evaluation of Kinetic Method Measurements: Possible Origins of Nonlinear Effects

NASA Astrophysics Data System (ADS)

Bourgoin-Voillard, Sandrine; Afonso, Carlos; Lesage, Denis; Zins, Emilie-Laure; Tabet, Jean-Claude; Armentrout, P. B.

2013-03-01

The kinetic method is a widely used approach for the determination of thermochemical data such as proton affinities (PA) and gas-phase acidities ( ΔH° acid ). These data are easily obtained from decompositions of noncovalent heterodimers if care is taken in the choice of the method, references used, and experimental conditions. Previously, several papers have focused on theoretical considerations concerning the nature of the references. Few investigations have been devoted to conditions required to validate the quality of the experimental results. In the present work, we are interested in rationalizing the origin of nonlinear effects that can be obtained with the kinetic method. It is shown that such deviations result from intrinsic properties of the systems investigated but can also be enhanced by artifacts resulting from experimental issues. Overall, it is shown that orthogonal distance regression (ODR) analysis of kinetic method data provides the optimum way of acquiring accurate thermodynamic information.

Kinetic effects on Alfven wave nonlinearity. II - The modified nonlinear wave equation

NASA Technical Reports Server (NTRS)

Spangler, Steven R.

1990-01-01

A previously developed Vlasov theory is used here to study the role of resonant particle and other kinetic effects on Alfven wave nonlinearity. A hybrid fluid-Vlasov equation approach is used to obtain a modified version of the derivative nonlinear Schroedinger equation. The differences between a scalar model for the plasma pressure and a tensor model are discussed. The susceptibilty of the modified nonlinear wave equation to modulational instability is studied. The modulational instability normally associated with the derivative nonlinear Schroedinger equation will, under most circumstances, be restricted to left circularly polarized waves. The nonlocal term in the modified nonlinear wave equation engenders a new modulational instability that is independent of beta and the sense of circular polarization. This new instability may explain the occurrence of wave packet steepening for all values of the plasma beta in the vicinity of the earth's bow shock.

Nonlinear derating of high-intensity focused ultrasound beams using Gaussian modal sums.

PubMed

Dibaji, Seyed Ahmad Reza; Banerjee, Rupak K; Soneson, Joshua E; Myers, Matthew R

2013-11-01

A method is introduced for using measurements made in water of the nonlinear acoustic pressure field produced by a high-intensity focused ultrasound transducer to compute the acoustic pressure and temperature rise in a tissue medium. The acoustic pressure harmonics generated by nonlinear propagation are represented as a sum of modes having a Gaussian functional dependence in the radial direction. While the method is derived in the context of Gaussian beams, final results are applicable to general transducer profiles. The focal acoustic pressure is obtained by solving an evolution equation in the axial variable. The nonlinear term in the evolution equation for tissue is modeled using modal amplitudes measured in water and suitably reduced using a combination of "source derating" (experiments in water performed at a lower source acoustic pressure than in tissue) and "endpoint derating" (amplitudes reduced at the target location). Numerical experiments showed that, with proper combinations of source derating and endpoint derating, direct simulations of acoustic pressure and temperature in tissue could be reproduced by derating within 5% error. Advantages of the derating approach presented include applicability over a wide range of gains, ease of computation (a single numerical quadrature is required), and readily obtained temperature estimates from the water measurements.

Sediment transport under wave groups: Relative importance between nonlinear waveshape and nonlinear boundary layer streaming

USGS Publications Warehouse

Yu, X.; Hsu, T.-J.; Hanes, D.M.

2010-01-01

Sediment transport under nonlinear waves in a predominately sheet flow condition is investigated using a two-phase model. Specifically, we study the relative importance between the nonlinear waveshape and nonlinear boundary layer streaming on cross-shore sand transport. Terms in the governing equations because of the nonlinear boundary layer process are included in this one-dimensional vertical (1DV) model by simplifying the two-dimensional vertical (2DV) ensemble-averaged two-phase equations with the assumption that waves propagate without changing their form. The model is first driven by measured time series of near-bed flow velocity because of a wave group during the SISTEX99 large wave flume experiment and validated with the measured sand concentration in the sheet flow layer. Additional studies are then carried out by including and excluding the nonlinear boundary layer terms. It is found that for the grain diameter (0.24 mm) and high-velocity skewness wave condition considered here, nonlinear waveshape (e.g., skewness) is the dominant mechanism causing net onshore transport and nonlinear boundary layer streaming effect only causes an additional 36% onshore transport. However, for conditions of relatively low-wave skewness and a stronger offshore directed current, nonlinear boundary layer streaming plays a more critical role in determining the net transport. Numerical experiments further suggest that the nonlinear boundary layer streaming effect becomes increasingly important for finer grain. When the numerical model is driven by measured near-bed flow velocity in a more realistic surf zone setting, model results suggest nonlinear boundary layer processes may nearly double the onshore transport purely because of nonlinear waveshape. Copyright 2010 by the American Geophysical Union.

Nonlinear propagation of phase-conjugate focused sound beams in water

NASA Astrophysics Data System (ADS)

Brysev, A. P.; Krutyansky, L. M.; Preobrazhensky, V. L.; Pyl'nov, Yu. V.; Cunningham, K. B.; Hamilton, M. F.

2000-07-01

Nonlinear propagation of phase-conjugate, focused, ultrasound beams is studied. Measurements are presented of harmonic amplitudes along the axis and in the focal plane of the conjugate beam, and of the waveform and spectrum at the focus. A maximum peak pressure of 3.9 MPa was recorded in the conjugate beam. The measurements are compared with simulations based on the KZK equation, and satisfactory agreement is obtained.

Measurement of Nonlinear Coefficients of Crystals at Terahertz Frequencies via High Field THz at the FELIX FEL

DTIC Science & Technology

2017-04-02

field terahertz, felix free electron laser, nonlinear crystal coefficients, EOARD 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR 18...the Felix free electron laser. Measurements of these properties, which are crucial for designing of efficient nonlinear optical frequency...Currently, only free electron lasers are the source that can readily meet those requirements in the THz range, see Fig 2. Fig. 2 Power and tunability of the

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

NASA Astrophysics Data System (ADS)

Thenozhi, Suresh; Tang, Yu

2018-01-01

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

Linear and non-linear bias: predictions versus measurements

NASA Astrophysics Data System (ADS)

Hoffmann, K.; Bel, J.; Gaztañaga, E.

2017-02-01

We study the linear and non-linear bias parameters which determine the mapping between the distributions of galaxies and the full matter density fields, comparing different measurements and predictions. Associating galaxies with dark matter haloes in the Marenostrum Institut de Ciències de l'Espai (MICE) Grand Challenge N-body simulation, we directly measure the bias parameters by comparing the smoothed density fluctuations of haloes and matter in the same region at different positions as a function of smoothing scale. Alternatively, we measure the bias parameters by matching the probability distributions of halo and matter density fluctuations, which can be applied to observations. These direct bias measurements are compared to corresponding measurements from two-point and different third-order correlations, as well as predictions from the peak-background model, which we presented in previous papers using the same data. We find an overall variation of the linear bias measurements and predictions of ˜5 per cent with respect to results from two-point correlations for different halo samples with masses between ˜1012and1015 h-1 M⊙ at the redshifts z = 0.0 and 0.5. Variations between the second- and third-order bias parameters from the different methods show larger variations, but with consistent trends in mass and redshift. The various bias measurements reveal a tight relation between the linear and the quadratic bias parameters, which is consistent with results from the literature based on simulations with different cosmologies. Such a universal relation might improve constraints on cosmological models, derived from second-order clustering statistics at small scales or higher order clustering statistics.

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

NASA Astrophysics Data System (ADS)

Yildiz, Nihat; San, Sait Eren; Köysal, Oğuz

2010-09-01

In this paper, two complementary objectives related to optical transmission spectra of nematic liquid crystals (NLCs) were achieved. First, at room temperature, for both pure and dye (DR9) doped E7 NLCs, the 10-250 W halogen lamp transmission spectra (wavelength 400-1200 nm) were measured at various bias voltages. Second, because the measured spectra were inherently highly nonlinear, it was difficult to construct explicit empirical physical formulas (EPFs) to employ as transmittance functions. To avoid this difficulty, layered feedforward neural networks (LFNNs) were used to construct explicit EPFs for these theoretically unknown nonlinear NLC transmittance functions. As we theoretically showed in a previous work, a LFNN, as an excellent nonlinear function approximator, is highly relevant to EPF construction. The LFNN-EPFs efficiently and consistently estimated both the measured and yet-to-be-measured nonlinear transmittance response values. The experimentally obtained doping ratio dependencies and applied bias voltage responses of transmittance were also confirmed by LFFN-EPFs. This clearly indicates that physical laws embedded in the physical data can be faithfully extracted by the suitable LFNNs. The extraordinary success achieved with LFNN here suggests two potential applications. First, although not attempted here, these LFNN-EPFs, by such mathematical operations as derivation, integration, minimization etc., can be used to obtain further transmittance related functions of NLCs. Second, for a given NLC response function, whose theoretical nonlinear functional form is yet unknown, a suitable experimental data based LFNN-EPF can be constructed to predict the yet-to-be-measured values.

Solutions of the cylindrical nonlinear Maxwell equations.

PubMed

Xiong, Hao; Si, Liu-Gang; Ding, Chunling; Lü, Xin-You; Yang, Xiaoxue; Wu, Ying

2012-01-01

Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical nonlinear Maxwell equations and presents an interesting connection between the exact solutions for different cylindrical nonlinear Maxwell equations. We also provide some examples and discussion to show the application of the results we obtained. Our results provide the basis for solving complex systems of nonlinearity and inhomogeneity with simple systems.

Nonlinear reflection of a spherically divergent N-wave from a plane surface: Optical interferometry measurements in air

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

Karzova, M., E-mail: masha@acs366.phys.msu.ru; Physics Faculty, Moscow State University, Leninskie Gory, 119991 Moscow; Yuldashev, P.

2015-10-28

Mach stem is a well-known structure typically observed in the process of strong (acoustic Mach numbers greater than 0.4) step-shock waves reflection from a rigid boundary. However, this phenomenon has been much less studied for weak shocks in nonlinear acoustic fields where Mach numbers are in the range from 0.001 to 0.01 and pressure waveforms have more complicated waveforms than step shocks. The goal of this work was to demonstrate experimentally how nonlinear reflection occurs in air for very weak spherically divergent acoustic spark-generated pulses resembling an N-wave. Measurements of reflection patterns were performed using a Mach-Zehnder interferometer. A thinmore » laser beam with sub-millimeter cross-section was used to obtain the time resolution of 0.4 µs, which is 6 times higher than the time resolution of the condenser microphones. Pressure waveforms were reconstructed using the inverse Abel transform applied to the phase of the signal measured by the interferometer. The Mach stem formation was observed experimentally as a result of collision of the incident and reflected shock pulses. It was shown that irregular reflection of the pulse occurred in a dynamic way and the length of the Mach stem increased linearly while the pulse propagated along the surface. Since the front shock of the spark-generated pulse was steeper than the rear shock, irregular type of reflection was observed only for the front shock of the pulse while the rear shock reflection occurred in a regular regime.« less

Solving Nonlinear Coupled Differential Equations

NASA Technical Reports Server (NTRS)

Mitchell, L.; David, J.

1986-01-01

Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

Linearization of Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

Belendez, A.; Alvarez, M. L.; Fernandez, E.; Pascual, I.

2009-01-01

A linearization method of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force which allows us to obtain a frequency-amplitude relation which is valid not only for small but also for large amplitudes and, sometimes, for…

Non-linear optical measurement of the twist elastic constant in thermotropic and DNA lyotropic chiral nematics.

PubMed

Lucchetti, Liana; Fraccia, Tommaso P; Ciciulla, Fabrizio; Bellini, Tommaso

2017-07-10

Throughout the whole history of liquid crystals science, the balancing of intrinsic elasticity with coupling to external forces has been the key strategy for most application and investigation. While the coupling of the optical field to the nematic director is at the base of a wealth of thoroughly described optical effects, a significant variety of geometries and materials have not been considered yet. Here we show that by adopting a simple cell geometry and measuring the optically induced birefringence, we can readily extract the twist elastic coefficient K 22 of thermotropic and lyotropic chiral nematics (N*). The value of K 22 we obtain for chiral doped 5CB thermotropic N* well matches those reported in the literature. With this same strategy, we could determine for the first time K 22 of the N* phase of concentrated aqueous solutions of DNA oligomers, bypassing the limitations that so far prevented measuring the elastic constants of this class of liquid crystalline materials. The present study also enlightens the significant nonlinear optical response of DNA liquid crystals.

Amplitude-dependent internal friction, hysteretic nonlinearity, and nonlinear oscillations in a magnesite resonator.

PubMed

Nazarov, V E; Kolpakov, A B; Radostin, A V

2012-07-01

The results of experimental and theoretical studies of low-frequency nonlinear acoustics phenomena (amplitude-dependent loss, resonance frequency shifts, and a generation of second and third harmonics) in a magnesite rod resonator are presented. Acceleration and velocity oscillograms of vibrations of the free boundary of the resonator caused by harmonic excitations were measured and analyzed. A theoretical description of the observed amplitude dependences was carried out within the framework of the phenomenological state equations that contain either of the two types of hysteretic nonlinearity (elastic and inelastic). The type of hysteresis and parameters of acoustic nonlinearity of magnesite were established from comparing the experimental measurements with the theoretical dependences. The values of the parameters were anomalously high even when compared to those of other strongly nonlinear polycrystalline materials such as granite, marble, limestone, sandstone, etc.

Measurement of nonlinear optical refraction of composite material based on sapphire with silver by Kerr-lens autocorrelation method.

PubMed

Yu, Xiang-xiang; Wang, Yu-hua

2014-01-13

Silver nanoparticles synthesized in a synthetic sapphire matrix were fabricated by ion implantation using the metal vapor vacuum arc ion source. The optical absorption spectrum of the Ag: Al2O3 composite material has been measured. The analysis of the supercontinuum spectrum displayed the nonlinear refractive property of this kind of sample. Nonlinear optical refraction index was identified at 800 nm excitation using the Kerr-lens autocorrelation (KLAC) technique. The spectrum showed that the material possessed self-defocusing property (n(2) = -1.1 × 10(-15) cm(2)W). The mechanism of nonlinear refraction has been discussed.

NONLINEAR AND FIBER OPTICS: Influence of nonlinearity of the parameters of guided modes in fiber waveguides

NASA Astrophysics Data System (ADS)

Goncharenko, I. A.

1990-04-01

The shift formula method is used to obtain analytic expressions which provide estimates of the influence of nonlinearity on the parameters of fiber waveguide modes. Depending on the sign of the nonlinear susceptibility of the waveguide core, the nonlinearity can improve or impair (right down to complete loss) the waveguiding properties of fibers. The optical power at which a fiber loses its guiding properties is constant far from the cutoff, but rises steeply near the critical cutoff frequency. The nonlinearity can be used to vary the zero dispersion wavelength and the range of single-mode operation of a fiber waveguide.

TEPC measurements obtained on the Mir space station.

PubMed

Bottollier-Depois, J F; Siegrist, M; Petrov, V M; Shurshakov, V V; Bengin, V; Koslova, S B

2002-10-01

Measurements of the radiation environment inside the Mir space station were performed with a tissue equivalent proportional counter (TEPC) during the Antares mission in 1992, and over a long period following it. Interesting results concerning radiation measurements show (a) the South Atlantic Anomaly crossing, (b) the increase of radiation near the poles, and (c) the effects of solar particle events (the most important one occurring in early November 1992). This data also provides information about the dose and the quality factor of the radiation to which the cosmonauts were exposed during different missions. These data are compared with measurements obtained using a solid state detector. c2002 Elsevier Science Ltd. All rights reserved.

Experimental Observation of Bohr's Nonlinear Fluidic Surface Oscillation.

PubMed

Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon

2016-01-25

Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η(2) for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr's hydrodynamic theory.

Non-Linear Structural Dynamics Characterization using a Scanning Laser Vibrometer

NASA Technical Reports Server (NTRS)

Pai, P. F.; Lee, S.-Y.

2003-01-01

This paper presents the use of a scanning laser vibrometer and a signal decomposition method to characterize non-linear dynamics of highly flexible structures. A Polytec PI PSV-200 scanning laser vibrometer is used to measure transverse velocities of points on a structure subjected to a harmonic excitation. Velocity profiles at different times are constructed using the measured velocities, and then each velocity profile is decomposed using the first four linear mode shapes and a least-squares curve-fitting method. From the variations of the obtained modal \\ielocities with time we search for possible non-linear phenomena. A cantilevered titanium alloy beam subjected to harmonic base-excitations around the second. third, and fourth natural frequencies are examined in detail. Influences of the fixture mass. gravity. mass centers of mode shapes. and non-linearities are evaluated. Geometrically exact equations governing the planar, harmonic large-amplitude vibrations of beams are solved for operational deflection shapes using the multiple shooting method. Experimental results show the existence of 1:3 and 1:2:3 external and internal resonances. energy transfer from high-frequency modes to the first mode. and amplitude- and phase- modulation among several modes. Moreover, the existence of non-linear normal modes is found to be questionable.

Quantitative thickness measurement of polarity-inverted piezoelectric thin-film layer by scanning nonlinear dielectric microscopy

NASA Astrophysics Data System (ADS)

Odagawa, Hiroyuki; Terada, Koshiro; Tanaka, Yohei; Nishikawa, Hiroaki; Yanagitani, Takahiko; Cho, Yasuo

2017-10-01

A quantitative measurement method for a polarity-inverted layer in ferroelectric or piezoelectric thin film is proposed. It is performed nondestructively by scanning nonlinear dielectric microscopy (SNDM). In SNDM, linear and nonlinear dielectric constants are measured using a probe that converts the variation of capacitance related to these constants into the variation of electrical oscillation frequency. In this paper, we describe a principle for determining the layer thickness and some calculation results of the output signal, which are related to the radius of the probe tip and the thickness of the inverted layer. Moreover, we derive an equation that represents the relationship between the output signal and the oscillation frequency of the probe and explain how to determine the thickness from the measured frequency. Experimental results in Sc-doped AlN piezoelectric thin films that have a polarity-inverted layer with a thickness of 1.5 µm fabricated by radio frequency magnetron sputtering showed a fairly good value of 1.38 µm for the thickness of the polarity-inverted layer.

Nonlinear mathematical modeling and sensitivity analysis of hydraulic drive unit

NASA Astrophysics Data System (ADS)

Kong, Xiangdong; Yu, Bin; Quan, Lingxiao; Ba, Kaixian; Wu, Liujie

2015-09-01

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Measurement of the Nonlinearity of Heat-Flux Sensors Employing a CO_2 laser

NASA Astrophysics Data System (ADS)

van der Ham, E. W. M.; Beer, C. M.; Ballico, M. J.

2018-01-01

Heat-flux sensors are widely used in industry to test building products and designs for resistance to bushfire, to test the flammability of textiles and in numerous applications such as concentrated solar collectors. In Australia, such detectors are currently calibrated by the National Measurement Institute Australia (NMIA) at low flux levels of 20 W \\cdot m^{-2}. Estimates of the uncertainty arising from nonlinearity at industrial levels (e.g. 50 kW \\cdot m^{-2} for bushfire testing) rely on literature information. NMIA has developed a facility to characterize the linearity response of these heat-flux sensors up to 110 kW \\cdot m^{-2} using a low-power CO_2 laser and a chopped quartz tungsten-halogen lamp. The facility was validated by comparison with the conventional flux-addition method, and used to characterize several Schmidt-Boelter-type sensors. A significant nonlinear response was found, ranging from (3.2 ± 0.9)% at 40 kW \\cdot m^{-2} to more than 8 % at 100 kW \\cdot m^{-2}. Additional measurements confirm that this is not attributable to convection effects, but due to the temperature dependence of the sensor's responsivity.

Simple nonlinearity evaluation and modeling of low-noise amplifiers with application to radio astronomy receivers.

PubMed

Casas, F J; Pascual, J P; de la Fuente, M L; Artal, E; Portilla, J

2010-07-01

This paper describes a comparative nonlinear analysis of low-noise amplifiers (LNAs) under different stimuli for use in astronomical applications. Wide-band Gaussian-noise input signals, together with the high values of gain required, make that figures of merit, such as the 1 dB compression (1 dBc) point of amplifiers, become crucial in the design process of radiometric receivers in order to guarantee the linearity in their nominal operation. The typical method to obtain the 1 dBc point is by using single-tone excitation signals to get the nonlinear amplitude to amplitude (AM-AM) characteristic but, as will be shown in the paper, in radiometers, the nature of the wide-band Gaussian-noise excitation signals makes the amplifiers present higher nonlinearity than when using single tone excitation signals. Therefore, in order to analyze the suitability of the LNA's nominal operation, the 1 dBc point has to be obtained, but using realistic excitation signals. In this work, an analytical study of compression effects in amplifiers due to excitation signals composed of several tones is reported. Moreover, LNA nonlinear characteristics, as AM-AM, total distortion, and power to distortion ratio, have been obtained by simulation and measurement with wide-band Gaussian-noise excitation signals. This kind of signal can be considered as a limit case of a multitone signal, when the number of tones is very high. The work is illustrated by means of the extraction of realistic nonlinear characteristics, through simulation and measurement, of a 31 GHz back-end module LNA used in the radiometer of the QUIJOTE (Q U I JOint TEnerife) CMB experiment.

Direct measurements of multi-photon induced nonlinear lattice dynamics in semiconductors via time-resolved x-ray scattering.

PubMed

Williams, G Jackson; Lee, Sooheyong; Walko, Donald A; Watson, Michael A; Jo, Wonhuyk; Lee, Dong Ryeol; Landahl, Eric C

2016-12-22

Nonlinear optical phenomena in semiconductors present several fundamental problems in modern optics that are of great importance for the development of optoelectronic devices. In particular, the details of photo-induced lattice dynamics at early time-scales prior to carrier recombination remain poorly understood. We demonstrate the first integrated measurements of both optical and structural, material-dependent quantities while also inferring the bulk impulsive strain profile by using high spatial-resolution time-resolved x-ray scattering (TRXS) on bulk crystalline gallium arsenide. Our findings reveal distinctive laser-fluence dependent crystal lattice responses, which are not described by previous TRXS experiments or models. The initial linear expansion of the crystal upon laser excitation stagnates at a laser fluence corresponding to the saturation of the free carrier density before resuming expansion in a third regime at higher fluences where two-photon absorption becomes dominant. Our interpretations of the lattice dynamics as nonlinear optical effects are confirmed by numerical simulations and by additional measurements in an n-type semiconductor that allows higher-order nonlinear optical processes to be directly observed as modulations of x-ray diffraction lineshapes.

Nonlinearity and Scaling Behavior in Lead Zirconate Titanate Piezoceramic

NASA Astrophysics Data System (ADS)

Mueller, V.

1998-03-01

The results of a comprehensive study of the nonlinear dielectric and electromechanical response of lead zirconate titanate (PZT) piezoceramics are presented. The piezoelectric strain of a series of donor doped (soft PZT) and acceptor doped (hard PZT) polycrystalline systems was measured under quasistatic (nonresonant) conditions. The measuring field was applied both parallel and perpendicular to the poling direction of the ceramic in order to investigate the influence of different symmetry conditions. Dielectric properties were studied in addition to the electromechanical measurements which enables us to compare piezoelectric and dielectric nonlinearities. Due to the different level and type of dopants, the piezoceramics examined differ significantly with regard to its Curie temperature (190^o Cnonlinearity of dielectric and piezoelectric properties is qualitatively the same but more pronounced if the measuring field is applied perpendicular to the poling direction. In soft PZT, two different effective thresholds for the onset of nonlinearity of dielectric and piezoelectric coefficients are found at electric ac-fields E_c1≈ 100V/cm and E_c2 ≈ 1V/cm, respectively. Both are characterized by non-analytic scaling behavior \\chi (E_ac) = \\chi_lin+ A[(E-E_c)/E_c]^φ above the respective threshold. The values of the effective exponent φ are apparently independent of the particular ceramic system which indicates a universal behavior of soft PZT. Hard PZT exhibits a less pronounced nonlinearity and a threshold E_c2≈ 1000V/cm at higher field level than soft PZT. The low field behavior of hard PZT seems to be related to a gradual depinning of ferroelectric domain walls with individual depinning threshold whereas in large fields E>E_c2 the

A computer program to obtain time-correlated gust loads for nonlinear aircraft using the matched-filter-based method

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Pototzky, Anthony S.; Perry, Boyd, III

1994-01-01

NASA Langley Research Center has, for several years, conducted research in the area of time-correlated gust loads for linear and nonlinear aircraft. The results of this work led NASA to recommend that the Matched-Filter-Based One-Dimensional Search Method be used for gust load analyses of nonlinear aircraft. This manual describes this method, describes a FORTRAN code which performs this method, and presents example calculations for a sample nonlinear aircraft model. The name of the code is MFD1DS (Matched-Filter-Based One-Dimensional Search). The program source code, the example aircraft equations of motion, a sample input file, and a sample program output are all listed in the appendices.

Quantitative evaluation method for nonlinear characteristics of piezoelectric transducers under high stress with complex nonlinear elastic constant

NASA Astrophysics Data System (ADS)

Miyake, Susumu; Kasashima, Takashi; Yamazaki, Masato; Okimura, Yasuyuki; Nagata, Hajime; Hosaka, Hiroshi; Morita, Takeshi

2018-07-01

The high power properties of piezoelectric transducers were evaluated considering a complex nonlinear elastic constant. The piezoelectric LCR equivalent circuit with nonlinear circuit parameters was utilized to measure them. The deformed admittance curve of piezoelectric transducers was measured under a high stress and the complex nonlinear elastic constant was calculated by curve fitting. Transducers with various piezoelectric materials, Pb(Zr,Ti)O3, (K,Na)NbO3, and Ba(Zr,Ti)O3–(Ba,Ca)TiO3, were investigated by the proposed method. The measured complex nonlinear elastic constant strongly depends on the linear elastic and piezoelectric constants. This relationship indicates that piezoelectric high power properties can be controlled by modifying the linear elastic and piezoelectric constants.

Guided wave methods and apparatus for nonlinear frequency generation

DOEpatents

Durfee, III, Charles G.; Rundquist, Andrew; Kapteyn, Henry C.; Murnane, Margaret M.

2000-01-01

Methods and apparatus are disclosed for the nonlinear generation of sum and difference frequencies of electromagnetic radiation propagating in a nonlinear material. A waveguide having a waveguide cavity contains the nonlinear material. Phase matching of the nonlinear generation is obtained by adjusting a waveguide propagation constant, the refractive index of the nonlinear material, or the waveguide mode in which the radiation propagates. Phase matching can be achieved even in isotropic nonlinear materials. A short-wavelength radiation source uses phase-matched nonlinear generation in a waveguide to produce high harmonics of a pulsed laser.

Z-scan theoretical and experimental studies for accurate measurements of the nonlinear refractive index and absorption of optical glasses near damage threshold

NASA Astrophysics Data System (ADS)

Olivier, Thomas; Billard, Franck; Akhouayri, Hassan

2004-06-01

Self-focusing is one of the dramatic phenomena that may occur during the propagation of a high power laser beam in a nonlinear material. This phenomenon leads to a degradation of the wave front and may also lead to a photoinduced damage of the material. Realistic simulations of the propagation of high power laser beams require an accurate knowledge of the nonlinear refractive index γ. In the particular case of fused silica and in the nanosecond regime, it seems that electronic mechanisms as well as electrostriction and thermal effects can lead to a significant refractive index variation. Compared to the different methods used to measure this parmeter, the Z-scan method is simple, offers a good sensitivity and may give absolute measurements if the incident beam is accurately studied. However, this method requires a very good knowledge of the incident beam and of its propagation inside a nonlinear sample. We used a split-step propagation algorithm to simlate Z-scan curves for arbitrary beam shape, sample thickness and nonlinear phase shift. According to our simulations and a rigorous analysis of the Z-scan measured signal, it appears that some abusive approximations lead to very important errors. Thus, by reducing possible errors on the interpretation of Z-scan experimental studies, we performed accurate measurements of the nonlinear refractive index of fused silica that show the significant contribution of nanosecond mechanisms.

High frequency measures of OHC nonlinear capacitance (NLC) and their significance: Why measures stray away from predictions

NASA Astrophysics Data System (ADS)

Santos-Sacchi, Joseph

2018-05-01

Measures of membrane capacitance (Cm) can be used to assess important characteristics of voltage-dependent membrane proteins (e.g., channels and transporters). In particular, a protein's time-dependent voltage-sensor charge movement is equivalently represented as a frequency-dependent component of Cm, telling much about the kinetics of the protein's conformational behavior. Recently, we have explored the frequency dependence of OHC voltage-dependent capacitance (aka nonlinear capacitance, NLC) to query rates of conformational switching within prestin (SLC26a5), the cell's lateral membrane molecular motor 1. Following removal of confounding stray capacitance effects, high frequency Cm measures using wide-band stimuli accurately reveal unexpected low pass behavior in prestin's molecular motions.

Performance of linear and nonlinear texture measures in 2D and 3D for monitoring architectural changes in osteoporosis using computer-generated models of trabecular bone

NASA Astrophysics Data System (ADS)

Boehm, Holger F.; Link, Thomas M.; Monetti, Roberto A.; Mueller, Dirk; Rummeny, Ernst J.; Raeth, Christoph W.

2005-04-01

Osteoporosis is a metabolic bone disease leading to de-mineralization and increased risk of fracture. The two major factors that determine the biomechanical competence of bone are the degree of mineralization and the micro-architectural integrity. Today, modern imaging modalities (high resolution MRI, micro-CT) are capable of depicting structural details of trabecular bone tissue. From the image data, structural properties obtained by quantitative measures are analysed with respect to the presence of osteoporotic fractures of the spine (in-vivo) or correlated with biomechanical strength as derived from destructive testing (in-vitro). Fairly well established are linear structural measures in 2D that are originally adopted from standard histo-morphometry. Recently, non-linear techniques in 2D and 3D based on the scaling index method (SIM), the standard Hough transform (SHT), and the Minkowski Functionals (MF) have been introduced, which show excellent performance in predicting bone strength and fracture risk. However, little is known about the performance of the various parameters with respect to monitoring structural changes due to progression of osteoporosis or as a result of medical treatment. In this contribution, we generate models of trabecular bone with pre-defined structural properties which are exposed to simulated osteoclastic activity. We apply linear and non-linear texture measures to the models and analyse their performance with respect to detecting architectural changes. This study demonstrates, that the texture measures are capable of monitoring structural changes of complex model data. The diagnostic potential varies for the different parameters and is found to depend on the topological composition of the model and initial "bone density". In our models, non-linear texture measures tend to react more sensitively to small structural changes than linear measures. Best performance is observed for the 3rd and 4th Minkowski Functionals and for the scaling

Design of a nonlinear torsional vibration absorber

NASA Astrophysics Data System (ADS)

Tahir, Ammaar Bin

Tuned mass dampers (TMD) utilizing linear spring mechanisms to mitigate destructive vibrations are commonly used in practice. A TMD is usually tuned for a specific resonant frequency or an operating frequency of a system. Recently, nonlinear vibration absorbers attracted attention of researchers due to some potential advantages they possess over the TMDs. The nonlinear vibration absorber, or the nonlinear energy sink (NES), has an advantage of being effective over a broad range of excitation frequencies, which makes it more suitable for systems with several resonant frequencies, or for a system with varying excitation frequency. Vibration dissipation mechanism in an NES is passive and ensures that there is no energy backflow to the primary system. In this study, an experimental setup of a rotational system has been designed for validation of the concept of nonlinear torsional vibration absorber with geometrically induced cubic stiffness nonlinearity. Dimensions of the primary system have been optimized so as to get the first natural frequency of the system to be fairly low. This was done in order to excite the dynamic system for torsional vibration response by the available motor. Experiments have been performed to obtain the modal parameters of the system. Based on the obtained modal parameters, the design optimization of the nonlinear torsional vibration absorber was carried out using an equivalent 2-DOF modal model. The optimality criterion was chosen to be maximization of energy dissipation in the nonlinear absorber attached to the equivalent 2-DOF system. The optimized design parameters of the nonlinear absorber were tested on the original 5-DOF system numerically. A comparison was made between the performance of linear and nonlinear absorbers using the numerical models. The comparison showed the superiority of the nonlinear absorber over its linear counterpart for the given set of primary system parameters as the vibration energy dissipation in the former is

Nonlinear extraordinary wave in dense plasma

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

Krasovitskiy, V. B., E-mail: krasovit@mail.ru; Turikov, V. A.

2013-10-15

Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. Themore » possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.« less

How to obtain traceability on optical radiation measurements?

NASA Astrophysics Data System (ADS)

Matamoros García, Carlos H.

2006-02-01

Traceability to national standards provides confidence in measurements results, granting a guaranty when carrying out governmental rules and when demonstrating conformity with quality requirements such as ISO 9000 or ISO/IEC 17025 (and the Mexican equivalent standards). The appropriate traceability contributes with confidence of the quality of products or services. This paper presents different ways to obtain traceability in Mexico for the optical radiation measurements, mentioning some applications, and highlighting the necessity of having traceability to the appropriate units of the SI. Additionally it present the national standards maintained by Centro Nacional de Metrologia (CENAM), the national metrology institute in Mexico, that give the technical support to Mexican measurements in this field and the international recognition that the personal of the Optics and Radiometry Division had gained in 10 years of development.

Z-scan measurements using femtosecond continuum generation

NASA Astrophysics Data System (ADS)

de Boni, Leonardo; Andrade, Acácio A.; Misoguti, Lino; Mendonça, Cléber R.; Zilio, Sérgio Carlos

2004-08-01

We present a single beam Z-scan technique using an intense, broadband, white-light continuum (WLC) beam for the direct measurement of nonlinear absorption spectra. In order to demonstrate the validity of our technique, we compared the results of tetraaniline and Sudan 3 solutions obtained with WLC and conventional single wavelength light sources. Both approaches lead to the same nonlinear spectrum, indicating that the association of the Z-scan technique and the WLC source results in an useful method for the measurement of nonlinear spectra of both absorbing (saturable absorption or reverse saturable absorption) and transparent (two-photon absorption) samples.

High Resolution Measurements of Nonlinear Internal Waves and Mixing on the Washington Continental Shelf

DTIC Science & Technology

2015-09-30

hour tidally -resolving transects showing the generation conditions leading to wave formation 6. Nine synthetic aperture images collected during...High resolution measurements of nonlinear internal waves and mixing on the Washington continental...email: jmickett@apl.washington.edu Grant Number: N00014-13-1-0390 LONG-TERM GOALS We are interested in the general problems of internal waves and

An experimental study of nonlinear dynamic system identification

NASA Technical Reports Server (NTRS)

Stry, Greselda I.; Mook, D. Joseph

1990-01-01

A technique for robust identification of nonlinear dynamic systems is developed and illustrated using both simulations and analog experiments. The technique is based on the Minimum Model Error optimal estimation approach. A detailed literature review is included in which fundamental differences between the current approach and previous work is described. The most significant feature of the current work is the ability to identify nonlinear dynamic systems without prior assumptions regarding the form of the nonlinearities, in constrast to existing nonlinear identification approaches which usually require detailed assumptions of the nonlinearities. The example illustrations indicate that the method is robust with respect to prior ignorance of the model, and with respect to measurement noise, measurement frequency, and measurement record length.

Scalar discrete nonlinear multipoint boundary value problems

NASA Astrophysics Data System (ADS)

Rodriguez, Jesus; Taylor, Padraic

2007-06-01

In this paper we provide sufficient conditions for the existence of solutions to scalar discrete nonlinear multipoint boundary value problems. By allowing more general boundary conditions and by imposing less restrictions on the nonlinearities, we obtain results that extend previous work in the area of discrete boundary value problems [Debra L. Etheridge, Jesus Rodriguez, Periodic solutions of nonlinear discrete-time systems, Appl. Anal. 62 (1996) 119-137; Debra L. Etheridge, Jesus Rodriguez, Scalar discrete nonlinear two-point boundary value problems, J. Difference Equ. Appl. 4 (1998) 127-144].

Design and nonlinear modeling of a sensitive sensor for the measurement of flow in mice.

PubMed

Bou Jawde, Samer; Smith, Bradford J; Sonnenberg, Adam; Bates, Jason H T; Suki, Bela

2018-06-07

While many studies rely on flow and pressure measurements in small animal models of respiratory disease, such measurements can however be inaccurate and difficult to obtain. Thus, the goal of this study was to design and implement an easy to manufacture and accurate sensor capable of monitoring flow. We designed and 3-D printed a flowmeter and utilized parametric (resistance and inertance) and nonparametric (polynomial and Volterra series) system identification to characterize the device. The sensor was tested in a closed system for apparent flow using the common mode rejection ratio (CMRR). The sensor properly measured tidal volumes and respiratory rates in spontaneously breathing mice. The device was used to evaluate a ventilator's ability to deliver a prescribed volume before and after lung injury. The parametric and polynomial models provided a reasonable prediction of the independently measured flow (Coefficient of determination (Cv)=0.9591 and 0.9147 respectively), but the Volterra series of the 1st, 2nd, and 3rd order with a memory of six time points provided better fits (Cv=0.9775, 0.9787, and 0.9954, respectively). At and below the mouse breathing frequency (1-5 Hz), CMRR was higher than 40 dB. Following lung injury, the sensor revealed a significant drop in delivered tidal volume. We demonstrate that the application of nonparametric nonlinear Volterra series modeling in combination with 3-D printing technology allows the inexpensive and rapid fabrication of an accurate flow sensor for continuously measuring small flows in various physiological conditions. © 2018 Institute of Physics and Engineering in Medicine.

Multi-linear model set design based on the nonlinearity measure and H-gap metric.

PubMed

Shaghaghi, Davood; Fatehi, Alireza; Khaki-Sedigh, Ali

2017-05-01

This paper proposes a model bank selection method for a large class of nonlinear systems with wide operating ranges. In particular, nonlinearity measure and H-gap metric are used to provide an effective algorithm to design a model bank for the system. Then, the proposed model bank is accompanied with model predictive controllers to design a high performance advanced process controller. The advantage of this method is the reduction of excessive switch between models and also decrement of the computational complexity in the controller bank that can lead to performance improvement of the control system. The effectiveness of the method is verified by simulations as well as experimental studies on a pH neutralization laboratory apparatus which confirms the efficiency of the proposed algorithm. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Effect of Nozzle Nonlinearities upon Nonlinear Stability of Liquid Propellant Rocket Motors

NASA Technical Reports Server (NTRS)

Padmanabhan, M. S.; Powell, E. A.; Zinn, B. T.

1975-01-01

A three dimensional, nonlinear nozzle admittance relation is developed by solving the wave equation describing finite amplitude oscillatory flow inside the subsonic portion of a choked, slowly convergent axisymmetric nozzle. This nonlinear nozzle admittance relation is then used as a boundary condition in the analysis of nonlinear combustion instability in a cylindrical liquid rocket combustor. In both nozzle and chamber analyses solutions are obtained using the Galerkin method with a series expansion consisting of the first tangential, second tangential, and first radial modes. Using Crocco's time lag model to describe the distributed unsteady combustion process, combustion instability calculations are presented for different values of the following parameters: (1) time lag, (2) interaction index, (3) steady-state Mach number at the nozzle entrance, and (4) chamber length-to-diameter ratio. In each case, limit cycle pressure amplitudes and waveforms are shown for both linear and nonlinear nozzle admittance conditions. These results show that when the amplitudes of the second tangential and first radial modes are considerably smaller than the amplitude of the first tangential mode the inclusion of nozzle nonlinearities has no significant effect on the limiting amplitude and pressure waveforms.

Towards homoscedastic nonlinear cointegration for structural health monitoring

NASA Astrophysics Data System (ADS)

Zolna, Konrad; Dao, Phong B.; Staszewski, Wieslaw J.; Barszcz, Tomasz

2016-06-01

The paper presents the homoscedastic nonlinear cointegration. The method leads to stable variances in nonlinear cointegration residuals. The adapted Breusch-Pagan test procedure is developed to test for the presence of heteroscedasticity (or homoscedasticity) in the cointegration residuals obtained from the nonlinear cointegration analysis. Three different time series - i.e. one with a nonlinear quadratic deterministic trend, simulated vibration data and experimental wind turbine data - are used to illustrate the application of the proposed method. The proposed approach can be used for effective removal of nonlinear trends from various types of data and for reliable structural damage detection based on data that are corrupted by environmental and/or operational nonlinear trends.

Nonlinear laminate analysis for metal matrix fiber composites

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Sinclair, J. H.

1981-01-01

A nonlinear laminate analysis is described for predicting the mechanical behavior (stress-strain relationships) of angleplied laminates in which the matrix is strained nonlinearly by both the residual stress and the mechanical load and in which additional nonlinearities are induced due to progressive fiber fractures and ply relative rotations. The nonlinear laminate analysis (NLA) is based on linear composite mechanics and a piece wise linear laminate analysis to handle the nonlinear responses. Results obtained by using this nonlinear analysis on boron fiber/aluminum matrix angleplied laminates agree well with experimental data. The results shown illustrate the in situ ply stress-strain behavior and synergistic strength enhancement.

Experimental Investigation of the Acoustic Nonlinear Behavior in Granular Polymer Bonded Explosives with Progressive Fatigue Damage

PubMed Central

Yang, Zhanfeng; Tian, Yong; Li, Weibin; Zhou, Haiqiang; Zhang, Weibin; Li, Jingming

2017-01-01

The measurement of acoustic nonlinear response is known as a promising technique to characterize material micro-damages. In this paper, nonlinear ultrasonic approach is used to characterize the evolution of fatigue induced micro-cracks in polymer bonded explosives. The variations of acoustic nonlinearity with respect to fatigue cycles in the specimens are obtained in this investigation. The present results show a significant increase of acoustic nonlinearity with respect to fatigue cycles. The experimental observation of the correlation between the acoustic nonlinearity and fatigue cycles in carbon/epoxy laminates, verifies that an acoustic nonlinear response can be used to evaluate the progressive fatigue damage in the granular polymer bonded explosives. The sensitivity comparison of nonlinear and linear parameters of ultrasonic waves in the specimens shows that nonlinear acoustic parameters are more promising indicators to fatigue induced micro-damage than linear ones. The feasibility study of the micro-damage assessment of polymer bonded explosives by nonlinear ultrasonic technique in this work can be applied to damage identification, material degradation monitoring, and lifetime prediction of the explosive parts. PMID:28773017

Experimental Investigation of the Acoustic Nonlinear Behavior in Granular Polymer Bonded Explosives with Progressive Fatigue Damage.

PubMed

Yang, Zhanfeng; Tian, Yong; Li, Weibin; Zhou, Haiqiang; Zhang, Weibin; Li, Jingming

2017-06-16

The measurement of acoustic nonlinear response is known as a promising technique to characterize material micro-damages. In this paper, nonlinear ultrasonic approach is used to characterize the evolution of fatigue induced micro-cracks in polymer bonded explosives. The variations of acoustic nonlinearity with respect to fatigue cycles in the specimens are obtained in this investigation. The present results show a significant increase of acoustic nonlinearity with respect to fatigue cycles. The experimental observation of the correlation between the acoustic nonlinearity and fatigue cycles in carbon/epoxy laminates, verifies that an acoustic nonlinear response can be used to evaluate the progressive fatigue damage in the granular polymer bonded explosives. The sensitivity comparison of nonlinear and linear parameters of ultrasonic waves in the specimens shows that nonlinear acoustic parameters are more promising indicators to fatigue induced micro-damage than linear ones. The feasibility study of the micro-damage assessment of polymer bonded explosives by nonlinear ultrasonic technique in this work can be applied to damage identification, material degradation monitoring, and lifetime prediction of the explosive parts.

Linear versus non-linear measures of temporal variability in finger tapping and their relation to performance on open- versus closed-loop motor tasks: comparing standard deviations to Lyapunov exponents.

PubMed

Christman, Stephen D; Weaver, Ryan

2008-05-01

The nature of temporal variability during speeded finger tapping was examined using linear (standard deviation) and non-linear (Lyapunov exponent) measures. Experiment 1 found that right hand tapping was characterised by lower amounts of both linear and non-linear measures of variability than left hand tapping, and that linear and non-linear measures of variability were often negatively correlated with one another. Experiment 2 found that increased non-linear variability was associated with relatively enhanced performance on a closed-loop motor task (mirror tracing) and relatively impaired performance on an open-loop motor task (pointing in a dark room), especially for left hand performance. The potential uses and significance of measures of non-linear variability are discussed.

Theory and design of nonlinear metamaterials

NASA Astrophysics Data System (ADS)

Rose, Alec Daniel

and oscillators. By applying this set of tools and knowledge to microwave metamaterials, I experimentally confirm several novel nonlinear phenomena. Most notably, I construct a backward wave nonlinear medium from varactor-loaded split ring resonators loaded in a rectangular waveguide, capable of generating second-harmonic opposite to conventional nonlinear materials with a conversion efficiency as high as 1.5%. In addition, I confirm nonlinear magnetoelectric coupling in two dual gap varactor-loaded split ring resonator metamaterials through measurement of the amplitude and phase of the second-harmonic generated in the forward and backward directions from a thin slab. I then use the presence of simultaneous nonlinearities in such metamaterials to observe nonlinear interference, manifest as unidirectional difference frequency generation with contrasts of 6 and 12 dB in the forward and backward directions, respectively. Finally, I apply these principles and intuition to several plasmonic platforms with the goal of achieving similar enhancements and configurations at optical frequencies. Using the example of fluorescence enhancement in optical patch antennas, I develop a semi-classical numerical model for the calculation of field-induced enhancements to both excitation and spontaneous emission rates of an embedded fluorophore, showing qualitative agreement with experimental results, with enhancement factors of more than 30,000. Throughout these series of works, I emphasize the indispensability of effective design and retrieval tools in understanding and optimizing both metamaterials and plasmonic systems. Ultimately, when weighed against the disadvantages in fabrication and optical losses, the results presented here provide a context for the application of nonlinear metamaterials within three distinct areas where a competitive advantage over conventional materials might be obtained: fundamental science demonstrations, linear and nonlinear anisotropy engineering, and

Absolute and relative nonlinear optical coefficients of KDP, KD(asterisk)P, BaB2O4, LiIO3, MgO:LiNbO3, and KTP measured by phase-matched second-harmonic generation

NASA Technical Reports Server (NTRS)

Eckardt, Robert C.; Byer, Robert L.; Masuda, Hisashi; Fan, Yuan Xuan

1990-01-01

Both absolute and relative nonlinear optical coefficients of six nonlinear materials measured by second-harmonic generation are discussed. A single-mode, injection-seeded, Q-switched Nd:YAG laser with spatially filtered output was used to generate the 1.064-micron fundamental radiation. The following results were obtained: d36(KDP) = 0.38 pm/V, d36(KD/asterisk/P) = 0.37 pm/V, (parallel)d22(BaB2O4)(parallel) = 2.2 pm/V, d31(LiIO3) = -4.1 pm/V, d31(5 percentMgO:MgO LiNbO3) = -4.7 pm/V, and d(eff)(KTP) = 3.2 pm/V. The accuracy of these measurements is estimated to be better than 10 percent.

Experimental Observation of Bohr’s Nonlinear Fluidic Surface Oscillation

PubMed Central

Moon, Songky; Shin, Younghoon; Kwak, Hojeong; Yang, Juhee; Lee, Sang-Bum; Kim, Soyun; An, Kyungwon

2016-01-01

Niels Bohr in the early stage of his career developed a nonlinear theory of fluidic surface oscillation in order to study surface tension of liquids. His theory includes the nonlinear interaction between multipolar surface oscillation modes, surpassing the linear theory of Rayleigh and Lamb. It predicts a specific normalized magnitude of 0.416η2 for an octapolar component, nonlinearly induced by a quadrupolar one with a magnitude of η much less than unity. No experimental confirmation on this prediction has been reported. Nonetheless, accurate determination of multipolar components is important as in optical fiber spinning, film blowing and recently in optofluidic microcavities for ray and wave chaos studies and photonics applications. Here, we report experimental verification of his theory. By using optical forward diffraction, we measured the cross-sectional boundary profiles at extreme positions of a surface-oscillating liquid column ejected from a deformed microscopic orifice. We obtained a coefficient of 0.42 ± 0.08 consistently under various experimental conditions. We also measured the resonance mode spectrum of a two-dimensional cavity formed by the cross-sectional segment of the liquid jet. The observed spectra agree well with wave calculations assuming a coefficient of 0.414 ± 0.011. Our measurements establish the first experimental observation of Bohr’s hydrodynamic theory. PMID:26803911

Nonlinear analysis and performance evaluation of the Annular Suspension and Pointing System (ASPS)

NASA Technical Reports Server (NTRS)

Joshi, S. M.

1978-01-01

The Annular Suspension and Pointing System (ASPS) can provide high accurate fine pointing for a variety of solar-, stellar-, and Earth-viewing scientific instruments during space shuttle orbital missions. In this report, a detailed nonlinear mathematical model is developed for the ASPS/Space Shuttle system. The equations are augmented with nonlinear models of components such as magnetic actuators and gimbal torquers. Control systems and payload attitude state estimators are designed in order to obtain satisfactory pointing performance, and statistical pointing performance is predicted in the presence of measurement noise and disturbances.

Nonlinear analysis of pupillary dynamics.

PubMed

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 (p<0.001). Our results suggest that (a) pupil size at constant light condition is characterized by nonlinear 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.

Direct measurements of multi-photon induced nonlinear lattice dynamics in semiconductors via time-resolved x-ray scattering

DOE PAGES

Williams, G. Jackson; Lee, Sooheyong; Walko, Donald A.; ...

2016-12-22

Nonlinear optical phenomena in semiconductors present several fundamental problems in modern optics that are of great importance for the development of optoelectronic devices. In particular, the details of photo-induced lattice dynamics at early time-scales prior to carrier recombination remain poorly understood. We demonstrate the first integrated measurements of both optical and structural, material-dependent quantities while also inferring the bulk impulsive strain profile by using high spatial-resolution time-resolved x-ray scattering (TRXS) on bulk crystalline gallium arsenide. Our findings reveal distinctive laser-fluence dependent crystal lattice responses, which are not described by previous TRXS experiments or models. The initial linear expansion of themore » crystal upon laser excitation stagnates at a laser fluence corresponding to the saturation of the free carrier density before resuming expansion in a third regime at higher fluences where two-photon absorption becomes dominant. Our interpretations of the lattice dynamics as nonlinear optical effects are confirmed by numerical simulations and by additional measurements in an n-type semiconductor that allows higher-order nonlinear optical processes to be directly observed as modulations of x-ray diffraction lineshapes.« less

Direct measurements of multi-photon induced nonlinear lattice dynamics in semiconductors via time-resolved x-ray scattering

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

Williams, G. Jackson; Lee, Sooheyong; Walko, Donald A.

Nonlinear optical phenomena in semiconductors present several fundamental problems in modern optics that are of great importance for the development of optoelectronic devices. In particular, the details of photo-induced lattice dynamics at early time-scales prior to carrier recombination remain poorly understood. We demonstrate the first integrated measurements of both optical and structural, material-dependent quantities while also inferring the bulk impulsive strain profile by using high spatial-resolution time-resolved x-ray scattering (TRXS) on bulk crystalline gallium arsenide. Our findings reveal distinctive laser-fluence dependent crystal lattice responses, which are not described by previous TRXS experiments or models. The initial linear expansion of themore » crystal upon laser excitation stagnates at a laser fluence corresponding to the saturation of the free carrier density before resuming expansion in a third regime at higher fluences where two-photon absorption becomes dominant. Our interpretations of the lattice dynamics as nonlinear optical effects are confirmed by numerical simulations and by additional measurements in an n-type semiconductor that allows higher-order nonlinear optical processes to be directly observed as modulations of x-ray diffraction lineshapes.« less

On Least Squares Fitting Nonlinear Submodels.

ERIC Educational Resources Information Center

Bechtel, Gordon G.

Three simplifying conditions are given for obtaining least squares (LS) estimates for a nonlinear submodel of a linear model. If these are satisfied, and if the subset of nonlinear parameters may be LS fit to the corresponding LS estimates of the linear model, then one attains the desired LS estimates for the entire submodel. Two illustrative…

Vowel selection and its effects on perturbation and nonlinear dynamic measures.

PubMed

Maccallum, Julia K; Zhang, Yu; Jiang, Jack J

2011-01-01

Acoustic analysis of voice is typically conducted on recordings of sustained vowel phonation. This study applied perturbation and nonlinear dynamic analyses to the vowels /a/, /i/, and /u/ in order to determine vowel selection effects on analysis. Forty subjects (20 males and 20 females) with normal voices participated in recording. Traditional parameters of fundamental frequency, signal-to-noise ratio, percent jitter, and percent shimmer were calculated for the signals using CSpeech. Nonlinear dynamic parameters of correlation dimension and second-order entropy were also calculated. Perturbation analysis results were largely incongruous in this study and in previous research. Fundamental frequency results corroborated previous work, indicating higher fundamental frequency for /i/ and /u/ and lower fundamental frequency for /a/. Signal-to-noise ratio results showed that /i/ and /u/ have greater harmonic levels than /a/. Results of nonlinear dynamic analysis suggested that more complex activity may be evident in /a/ than in /i/ or /u/. Percent jitter and percent shimmer may not be useful for description of acoustic differences between vowels. Fundamental frequency, signal-to-noise ratio, and nonlinear dynamic parameters may be applied to characterize /a/ as having lower frequency, higher noise, and greater nonlinear components than /i/ and /u/. Copyright © 2010 S. Karger AG, Basel.

Nonlinear acoustic techniques for landmine detection.

PubMed

Korman, Murray S; Sabatier, James M

2004-12-01

Measurements of the top surface vibration of a buried (inert) VS 2.2 anti-tank plastic landmine reveal significant resonances in the frequency range between 80 and 650 Hz. Resonances from measurements of the normal component of the acoustically induced soil surface particle velocity (due to sufficient acoustic-to-seismic coupling) have been used in detection schemes. Since the interface between the top plate and the soil responds nonlinearly to pressure fluctuations, characteristics of landmines, the soil, and the interface are rich in nonlinear physics and allow for a method of buried landmine detection not previously exploited. Tuning curve experiments (revealing "softening" and a back-bone curve linear in particle velocity amplitude versus frequency) help characterize the nonlinear resonant behavior of the soil-landmine oscillator. The results appear to exhibit the characteristics of nonlinear mesoscopic elastic behavior, which is explored. When two primary waves f1 and f2 drive the soil over the mine near resonance, a rich spectrum of nonlinearly generated tones is measured with a geophone on the surface over the buried landmine in agreement with Donskoy [SPIE Proc. 3392, 221-217 (1998); 3710, 239-246 (1999)]. In profiling, particular nonlinear tonals can improve the contrast ratio compared to using either primary tone in the spectrum.

A simple nonlinear element model

NASA Astrophysics Data System (ADS)

Mikhailov, S. G.; Rudenko, O. V.

2017-05-01

We study experimentally the behavior of a nonlinear element, a light plate pressed to the opening in the cavity of an acoustic resonator. Measurements of field oscillations inside and outside the cavity have shown that for large amplitudes, they become essentially anharmonic. The time dependences of displacement of the plate with increasing amplitude of the exciting voltage demonstrates a gradual change in the shape of vibrations from harmonic to half-period oscillation. A constant component appears in the cavity: rarefaction or outflow of the medium through the orifice. We construct a theory for nonlinear oscillations of a plate taking into account its different elastic reactions to compression and rarefaction with allowance for monopole radiation by the small-wave-size plate or radiation of a plane wave by the plate. We calculate the amplitudes of the harmonics and solve the problem of low-frequency stationary noise acting on the plate. We obtain expressions for the correlation function and mean power at the output given a normal random process at the input.

Enhanced energy transport owing to nonlinear interface interaction

PubMed Central

Su, Ruixia; Yuan, Zongqiang; Wang, Jun; Zheng, Zhigang

2016-01-01

It is generally expected that the interface coupling leads to the suppression of thermal transport through coupled nanostructures due to the additional interface phonon-phonon scattering. However, recent experiments demonstrated that the interface van der Waals interactions can significantly enhance the thermal transfer of bonding boron nanoribbons compared to a single freestanding nanoribbon. To obtain a more in-depth understanding on the important role of the nonlinear interface coupling in the heat transports, in the present paper, we explore the effect of nonlinearity in the interface interaction on the phonon transport by studying the coupled one-dimensional (1D) Frenkel-Kontorova lattices. It is found that the thermal conductivity increases with increasing interface nonlinear intensity for weak inter-chain nonlinearity. By developing the effective phonon theory of coupled systems, we calculate the dependence of heat conductivity on interfacial nonlinearity in weak inter-chain couplings regime which is qualitatively in good agreement with the result obtained from molecular dynamics simulations. Moreover, we demonstrate that, with increasing interface nonlinear intensity, the system dimensionless nonlinearity strength is reduced, which in turn gives rise to the enhancement of thermal conductivity. Our results pave the way for manipulating the energy transport through coupled nanostructures for future emerging applications. PMID:26787363

On the origin of nonlinear elasticity in disparate rocks

DOE PAGES

Riviere, Jacques Vincent; Shokouhi, Parisa; Guyer, Robert A.; ...

2015-03-31

Dynamic acousto-elastic (DAE) studies are performed on a set of 6 rock samples (four sandstones, one soapstone, and one granite). From these studies, at 20 strain levels 10 -7 < ϵ < 10 -5, four measures characterizing the nonlinear elastic response of each sample are found. Additionally, each sample is tested with nonlinear resonant ultrasonic spectroscopy (NRUS) and a fth measure of nonlinear elastic response is found. The ve measures of the nonlinear elastic response of the samples (approximately 3 x 6 x 20 x 5 numbers as each measurement is repeated 3 times) are subjected to careful analysis usingmore » model independent statistical methods, principal component analysis and fuzzy clustering. This analysis reveals di erences among the samples and di erences among the nonlinear measures. Four of the nonlinear measures are sensing much the same physical mechanism in the samples. The fth is seeing something di erent. This is the case for all samples. Although the same physical mechanisms (two) are operating in all samples there are distinctive features in the way the physical mechanisms present themselves from sample to sample. This suggests classi cation of the samples into two groups. The numbers in this study and the classi cation of the measures/samples constitute an empirical characterization of rock nonlinear elastic properties that can serve as a valuable testing ground for physically based theories that relate rock nonlinear elastic properties to microscopic elastic features.« less

Nonlinear Viscoelastic Characterization of the Porcine Spinal Cord

PubMed Central

Shetye, Snehal; Troyer, Kevin; Streijger, Femke; Lee, Jae H. T.; Kwon, Brian K.; Cripton, Peter; Puttlitz, Christian M.

2014-01-01

Although quasi-static and quasi-linear viscoelastic properties of the spinal cord have been reported previously, there are no published studies that have investigated the fully (strain-dependent) nonlinear viscoelastic properties of the spinal cord. In this study, stress relaxation experiments and dynamic cycling were performed on six fresh porcine lumbar cord specimens to examine their viscoelastic mechanical properties. The stress relaxation data were fitted to a modified superposition formulation and a novel finite ramp time correction technique was applied. The parameters obtained from this fitting methodology were used to predict the average dynamic cyclic viscoelastic behavior of the porcine cord. The data indicate that the porcine spinal cord exhibited fully nonlinear viscoelastic behavior. The average weighted RMSE for a Heaviside ramp fit was 2.8kPa, which was significantly greater (p < 0.001) than that of the nonlinear (comprehensive viscoelastic characterization (CVC) method) fit (0.365kPa). Further, the nonlinear mechanical parameters obtained were able to accurately predict the dynamic behavior, thus exemplifying the reliability of the obtained nonlinear parameters. These parameters will be important for future studies investigating various damage mechanisms of the spinal cord and studies developing high resolution finite elements models of the spine. PMID:24211612

Change detection in the dynamics of an intracellular protein synthesis model using nonlinear Kalman filtering.

PubMed

Rigatos, Gerasimos G; Rigatou, Efthymia G; Djida, Jean Daniel

2015-10-01

A method for early diagnosis of parametric changes in intracellular protein synthesis models (e.g. the p53 protein - mdm2 inhibitor model) is developed with the use of a nonlinear Kalman Filtering approach (Derivative-free nonlinear Kalman Filter) and of statistical change detection methods. The intracellular protein synthesis dynamic model is described by a set of coupled nonlinear differential equations. It is shown that such a dynamical system satisfies differential flatness properties and this allows to transform it, through a change of variables (diffeomorphism), to the so-called linear canonical form. For the linearized equivalent of the dynamical system, state estimation can be performed using the Kalman Filter recursion. Moreover, by applying an inverse transformation based on the previous diffeomorphism it becomes also possible to obtain estimates of the state variables of the initial nonlinear model. By comparing the output of the Kalman Filter (which is assumed to correspond to the undistorted dynamical model) with measurements obtained from the monitored protein synthesis system, a sequence of differences (residuals) is obtained. The statistical processing of the residuals with the use of x2 change detection tests, can provide indication within specific confidence intervals about parametric changes in the considered biological system and consequently indications about the appearance of specific diseases (e.g. malignancies).

Nonlinear guided wave propagation in prestressed plates.

PubMed

Pau, Annamaria; Lanza di Scalea, Francesco

2015-03-01

The measurement of stress in a structure presents considerable interest in many fields of engineering. In this paper, the diagnostic potential of nonlinear elastic guided waves in a prestressed plate is investigated. To do so, an analytical model is formulated accounting for different aspects involved in the phenomenon. The fact that the initial strains can be finite is considered using the Green Lagrange strain tensor, and initial and final configurations are not merged, as it would be assumed in the infinitesimal strain theory. Moreover, an appropriate third-order expression of the strain energy of the hyperelastic body is adopted to account for the material nonlinearities. The model obtained enables to investigate both the linearized case, which gives the variation of phase and group velocity as a function of the initial stress, and the nonlinear case, involving second-harmonic generation as a function of the initial state of stress. The analysis is limited to Rayleigh-Lamb waves propagating in a plate. Three cases of initial prestress are considered, including prestress in the direction of the wave propagation, prestress orthogonal to the direction of wave propagation, and plane isotropic stress.

Second-order nonlinearity induced transparency.

PubMed

Zhou, Y H; Zhang, S S; Shen, H Z; Yi, X X

2017-04-01

In analogy to electromagnetically induced transparency, optomechanically induced transparency was proposed recently in [Science330, 1520 (2010)SCIEAS0036-807510.1126/science.1195596]. In this Letter, we demonstrate another form of induced transparency enabled by second-order nonlinearity. A practical application of the second-order nonlinearity induced transparency is to measure the second-order nonlinear coefficient. Our scheme might find applications in quantum optics and quantum information processing.

Effects of Inertial and Geometric Nonlinearities in the Simulation of Flexible Aircraft Dynamics

NASA Astrophysics Data System (ADS)

Bun Tse, Bosco Chun

This thesis examines the relative importance of the inertial and geometric nonlinearities in modelling the dynamics of a flexible aircraft. Inertial nonlinearities are derived by employing an exact definition of the velocity distribution and lead to coupling between the rigid body and elastic motions. The geometric nonlinearities are obtained by applying nonlinear theory of elasticity to the deformations. Peters' finite state unsteady aerodynamic model is used to evaluate the aerodynamic forces. Three approximate models obtained by excluding certain combinations of nonlinear terms are compared with that of the complete dynamics equations to obtain an indication of which terms are required for an accurate representation of the flexible aircraft behavior. A generic business jet model is used for the analysis. The results indicate that the nonlinear terms have a significant effect for more flexible aircraft, especially the geometric nonlinearities which leads to increased damping in the dynamics.

Controllable optical rogue waves via nonlinearity management.

PubMed

Yang, Zhengping; Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi

2018-03-19

Using a similarity transformation, we obtain analytical solutions to a class of nonlinear Schrödinger (NLS) equations with variable coefficients in inhomogeneous Kerr media, which are related to the optical rogue waves of the standard NLS equation. We discuss the dynamics of such optical rogue waves via nonlinearity management, i.e., by selecting the appropriate nonlinearity coefficients and integration constants, and presenting the solutions. In addition, we investigate higher-order rogue waves by suitably adjusting the nonlinearity coefficient and the rogue wave parameters, which could help in realizing complex but controllable optical rogue waves in properly engineered fibers and other photonic materials.

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

NASA Astrophysics Data System (ADS)

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.

A Weighted Measurement Fusion Particle Filter for Nonlinear Multisensory Systems Based on Gauss–Hermite Approximation

PubMed Central

Li, Yun

2017-01-01

We addressed the fusion estimation problem for nonlinear multisensory systems. Based on the Gauss–Hermite approximation and weighted least square criterion, an augmented high-dimension measurement from all sensors was compressed into a lower dimension. By combining the low-dimension measurement function with the particle filter (PF), a weighted measurement fusion PF (WMF-PF) is presented. The accuracy of WMF-PF appears good and has a lower computational cost when compared to centralized fusion PF (CF-PF). An example is given to show the effectiveness of the proposed algorithms. PMID:28956862

Multi-frequency Defect Selective Imaging via Nonlinear Ultrasound

NASA Astrophysics Data System (ADS)

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.

How to characterize a nonlinear elastic material? A review on nonlinear constitutive parameters in isotropic finite elasticity

PubMed Central

2017-01-01

The mechanical response of a homogeneous isotropic linearly elastic material can be fully characterized by two physical constants, the Young’s modulus and the Poisson’s ratio, which can be derived by simple tensile experiments. Any other linear elastic parameter can be obtained from these two constants. By contrast, the physical responses of nonlinear elastic materials are generally described by parameters which are scalar functions of the deformation, and their particular choice is not always clear. Here, we review in a unified theoretical framework several nonlinear constitutive parameters, including the stretch modulus, the shear modulus and the Poisson function, that are defined for homogeneous isotropic hyperelastic materials and are measurable under axial or shear experimental tests. These parameters represent changes in the material properties as the deformation progresses, and can be identified with their linear equivalent when the deformations are small. Universal relations between certain of these parameters are further established, and then used to quantify nonlinear elastic responses in several hyperelastic models for rubber, soft tissue and foams. The general parameters identified here can also be viewed as a flexible basis for coupling elastic responses in multi-scale processes, where an open challenge is the transfer of meaningful information between scales. PMID:29225507

Measurement of the optical nonlinearities of water, ethanol and tetrahydrofuran (THF) at 355 nm

NASA Astrophysics Data System (ADS)

Wang, Hongzhen; Ciret, Charles; Godet, Jean-Luc; Cassagne, Christophe; Boudebs, Georges

2018-06-01

The nonlinear (NL) responses of liquid water, ethanol and tetrahydrofuran (THF) are investigated at 355 nm using a Nd:YAG laser delivering pulses of 10 ps. The experiments are performed using the D4σ method combined with the Z-scan technique. Third-order NL refractive indices are determined, as well as the two-photon absorption coefficient and the critical self-focus power. The NL refractive indices are found to be constant for intensity up to 150 GW/cm2 for the three considered solvents, revealing no higher order nonlinearities. Water appears to be a better solvent than ethanol and THF in the UV domain because of its lower NL index and absence of NL absorption. We expect the present study to be useful for NL index measurements in solutions and for numerous future fundamental interest or potential applications.

Nonlinear optical inves

NASA Astrophysics Data System (ADS)

Zidan, M. D.; Arfan, A.; Allahham, A.

2017-03-01

Z-scan technique was used to investigate the nonlinear optical properties of Quinine and 1-(carboxymethyl)-6-methoxy-4-(3-(3-vinylpiperidin-4-yl) propanoyl) quinolin-1-ium chloride (Quinotoxine) salts. The two salts were characterized using UV-visible, FTIR and NMR measurements. The characterization spectra confirm the expected molecular structure of the prepared ;Quinotoxine ; salt. The z-scan measurements were performed with a CW Diode laser at 635 nm wavelength and 26 mW power. The nonlinear absorption coefficient (β), nonlinear refractive index (n2), the ground-state absorption cross sections (σg), the excited-state absorption cross sections (σex) and thermo-optic coefficient of the samples were determined. Our results reveal that the σex is higher than the σg indicating that the reverse saturable absorption (RSA) is the dominating mechanism for the observed absorption nonlinearities. The results suggest that this material should be considered as a promising candidate for future optical devices applications.

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

NASA Astrophysics Data System (ADS)

Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

2018-06-01

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

Nonlinear Schrödinger equations with single power nonlinearity and harmonic potential

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Theoretical Issues of Validity in the Measurement of Aided Speech Reception Threshold in Noise for Comparing Nonlinear Hearing Aid Systems.

PubMed

Naylor, Graham

2016-07-01

Adaptive Speech Reception Threshold in noise (SRTn) measurements are often used to make comparisons between alternative hearing aid (HA) systems. Such measurements usually do not constrain the signal-to-noise ratio (SNR) at which testing takes place. Meanwhile, HA systems increasingly include nonlinear features that operate differently in different SNRs, and listeners differ in their inherent SNR requirements. To show that SRTn measurements, as commonly used in comparisons of alternative HA systems, suffer from threats to their validity, to illustrate these threats with examples of potentially invalid conclusions in the research literature, and to propose ways to tackle these threats. An examination of the nature of SRTn measurements in the context of test theory, modern nonlinear HAs, and listener diversity. Examples from the audiological research literature were used to estimate typical interparticipant variation in SRTn and to illustrate cases where validity may have been compromised. There can be no doubt that SRTn measurements, when used to compare nonlinear HA systems, in principle, suffer from threats to their internal and external/ecological validity. Interactions between HA nonlinearities and SNR, and interparticipant differences in inherent SNR requirements, can act to generate misleading results. In addition, SRTn may lie at an SNR outside the range for which the HA system is designed or expected to operate in. Although the extent of invalid conclusions in the literature is difficult to evaluate, examples of studies were nevertheless identified where the risk of each form of invalidity is significant. Reliable data on ecological SNRs is becoming available, so that ecological validity can be assessed. Methodological developments that can reduce the risk of invalid conclusions include variations on the SRTn measurement procedure itself, manipulations of stimulus or scoring conditions to place SRTn in an ecologically relevant range, and design and analysis

Kerr nonlinearity and nonlinear absorption coefficient in a four-level M-model cylindrical quantum dot under the phenomenon of electromagnetically induced transparency

NASA Astrophysics Data System (ADS)

Behroozian, B.; Askari, H. R.

2018-07-01

The Kerr nonlinearity and the nonlinear absorption coefficient in a four-level M-model of a GaAs cylindrical quantum dot (QD) with parabolic potential under electromagnetically induced transparency are investigated. By solving the density matrix equations in the steady-state, the third order susceptibility is obtained. Then, by using the real and imaginary parts of third order susceptibility, the Kerr nonlinearity and the nonlinear absorption coefficient, respectively, for this system are computed. The effects of the radius and height of the cylindrical QD are then investigated. In addition, the effects of the control laser fields on the Kerr nonlinearity and the nonlinear absorption coefficient are investigated.

Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays

NASA Astrophysics Data System (ADS)

Ma, Li-Yuan; Ji, Jia-Liang; Xu, Zong-Wei; Zhu, Zuo-Nong

2018-03-01

We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term. Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964).

The non-linear power spectrum of the Lyman alpha forest

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

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

2015-12-01

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

The determination of third order linear models from a seventh order nonlinear jet engine model

NASA Technical Reports Server (NTRS)

Lalonde, Rick J.; Hartley, Tom T.; De Abreu-Garcia, J. Alex

1989-01-01

Results are presented that demonstrate how good reduced-order models can be obtained directly by recursive parameter identification using input/output (I/O) data of high-order nonlinear systems. Three different methods of obtaining a third-order linear model from a seventh-order nonlinear turbojet engine model are compared. The first method is to obtain a linear model from the original model and then reduce the linear model by standard reduction techniques such as residualization and balancing. The second method is to identify directly a third-order linear model by recursive least-squares parameter estimation using I/O data of the original model. The third method is to obtain a reduced-order model from the original model and then linearize the reduced model. Frequency responses are used as the performance measure to evaluate the reduced models. The reduced-order models along with their Bode plots are presented for comparison purposes.

Twistacene contained molecule for optical nonlinearity: Excited-state based negative refraction and optical limiting

NASA Astrophysics Data System (ADS)

Wu, Xingzhi; Xiao, Jinchong; Sun, Ru; Jia, Jidong; Yang, Junyi; Ao, Guanghong; Shi, Guang; Wang, Yuxiao; Zhang, Xueru; Song, Yinglin

2018-06-01

Spindle-type molecules containing twisted acenes (PyBTA-1 &PyBTA-2) are designed, synthesized characterized. Picosecond Z-scan experiments under 532 nm show reverse saturable absorption and negative nonlinear refraction, indicating large third-order optical nonlinearity in PyBTA-1. The mechanism of the optical nonlinearity is investigated and the results show that the nonlinear absorption and refraction in PyBTA-1 originates from a charge transfer (CT) state. Furthermore, relatively long lifetime and absorptive cross section of the CT state are measured. Based on the excited state absorption in PyBTA-1, strong optical limiting with ∼0.3 J/cm2 thresholds are obtained when excited by picoseconds and nanoseconds pulses. The findings on nonlinear optics suggest PyBTA-1 a promising material of all optical modulation and laser protection, which enrich the potential applications of these spindle-type molecules. Comparing to the previously reported spindle-type molecules with analogous structures, the introduction of ICT in PyBTA-1 &PyBTA-2 dramatically decreases the two-photon absorption while enhances the nonlinear refraction. The results could be used to selectively tailor the optical nonlinearity in such kind of compounds.

Optimal perturbations for nonlinear systems using graph-based optimal transport

NASA Astrophysics Data System (ADS)

Grover, Piyush; Elamvazhuthi, Karthik

2018-06-01

We formulate and solve a class of finite-time transport and mixing problems in the set-oriented framework. The aim is to obtain optimal discrete-time perturbations in nonlinear dynamical systems to transport a specified initial measure on the phase space to a final measure in finite time. The measure is propagated under system dynamics in between the perturbations via the associated transfer operator. Each perturbation is described by a deterministic map in the measure space that implements a version of Monge-Kantorovich optimal transport with quadratic cost. Hence, the optimal solution minimizes a sum of quadratic costs on phase space transport due to the perturbations applied at specified times. The action of the transport map is approximated by a continuous pseudo-time flow on a graph, resulting in a tractable convex optimization problem. This problem is solved via state-of-the-art solvers to global optimality. We apply this algorithm to a problem of transport between measures supported on two disjoint almost-invariant sets in a chaotic fluid system, and to a finite-time optimal mixing problem by choosing the final measure to be uniform. In both cases, the optimal perturbations are found to exploit the phase space structures, such as lobe dynamics, leading to efficient global transport. As the time-horizon of the problem is increased, the optimal perturbations become increasingly localized. Hence, by combining the transfer operator approach with ideas from the theory of optimal mass transportation, we obtain a discrete-time graph-based algorithm for optimal transport and mixing in nonlinear systems.

Non-linear vibrations of sandwich viscoelastic shells

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Modified harmonic balance method for the solution of nonlinear jerk equations

NASA Astrophysics Data System (ADS)

Rahman, M. Saifur; Hasan, A. S. M. Z.

2018-03-01

In this paper, a second approximate solution of nonlinear jerk equations (third order differential equation) can be obtained by using modified harmonic balance method. The method is simpler and easier to carry out the solution of nonlinear differential equations due to less number of nonlinear equations are required to solve than the classical harmonic balance method. The results obtained from this method are compared with those obtained from the other existing analytical methods that are available in the literature and the numerical method. The solution shows a good agreement with the numerical solution as well as the analytical methods of the available literature.

Nonlinear and quantum optics near nanoparticles

NASA Astrophysics Data System (ADS)

Dhayal, Suman

We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. We have also studied the modifications of the electromagnetic fields in a collection of nanoparticles due to strong near field nonlinear interactions using the generalized Mie theory for the case of many particles applicable in photovoltaics (PV). We also consider quantum coherence phenomena such as modification of dark states, stimulated Raman adiabatic passage (STIRAP), optical pumping in 4-level atoms near nanoparticles by using rotating wave approximation to describe the Hamiltonian of the atomic system. We also considered the behavior of atomic and the averaged atomic polarization in 7-level atoms near nanoparticles. This could be used as a prototype to study

Stationary states of extended nonlinear Schrödinger equation with a source

NASA Astrophysics Data System (ADS)

Borich, M. A.; Smagin, V. V.; Tankeev, A. P.

2007-02-01

Structure of nonlinear stationary states of the extended nonlinear Schrödinger equation (ENSE) with a source has been analyzed with allowance for both third-order and nonlinearity dispersion. A new class of particular solutions (solitary waves) of the ENSe has been obtained. The scenario of the destruction of these states under the effect of an external perturbation has been investigated analytically and numerically. The results obtained can be used to interpret experimental data on the weakly nonlinear dynamics of the magnetostatic envelope in heterophase ferromagnet-insulator-metal, metal-insulator-ferromagnet-insulator-metal, and other similar structures and upon the simulation of nonlinear processes in optical systems.

Nonlinear Gyro-Landau-Fluid Equations

NASA Astrophysics Data System (ADS)

Raskolnikov, I.; Mattor, Nathan; Parker, Scott E.

1996-11-01

We present fluid equations which describe the effects of both linear and nonlinear Landau damping (wave-particle-wave effects). These are derived using a recently developed analytical method similar to renormalization group theory. (Scott E. Parker and Daniele Carati, Phys. Rev. Lett. 75), 441 (1995). In this technique, the phase space structure inherent in Landau damping is treated analytically by building a ``renormalized collisionality'' onto a bare collisionality (which may be taken as vanishingly small). Here we apply this technique to the nonlinear ion gyrokinetic equation in slab geometry, obtaining nonlinear fluid equations for density, parallel momentum and heat. Wave-particle resonances are described by two functions appearing in the heat equation: a renormalized ``collisionality'' and a renormalized nonlinear coupling coeffient. It will be shown that these new equations may correct a deficiency in existing gyrofluid equations, (G. W. Hammett and F. W. Perkins, Phys. Rev. Lett. 64,) 3019 (1990). which can severely underestimate the strength of nonlinear interaction in regimes where linear resonance is strong. (N. Mattor, Phys. Fluids B 4,) 3952 (1992).

Stabilization of domain walls between traveling waves by nonlinear mode coupling in Taylor-Couette flow.

PubMed

Heise, M; Hoffmann, Ch; Abshagen, J; Pinter, A; Pfister, G; Lücke, M

2008-02-15

We present a new mechanism that allows the stable existence of domain walls between oppositely traveling waves in pattern-forming systems far from onset. It involves a nonlinear mode coupling that results directly from the nonlinearities in the underlying momentum balance. Our work provides the first observation and explanation of such strongly nonlinearly driven domain walls that separate structured states by a phase generating or annihilating defect. Furthermore, the influence of a symmetry breaking externally imposed flow on the wave domains and the domain walls is studied. The results are obtained for vortex waves in the Taylor-Couette system by combining numerical simulations of the full Navier-Stokes equations and experimental measurements.

Nonlinear ultrasonic wave modulation for online fatigue crack detection

NASA Astrophysics Data System (ADS)

Sohn, Hoon; Lim, Hyung Jin; DeSimio, Martin P.; Brown, Kevin; Derriso, Mark

2014-02-01

This study presents a fatigue crack detection technique using nonlinear ultrasonic wave modulation. Ultrasonic waves at two distinctive driving frequencies are generated and corresponding ultrasonic responses are measured using permanently installed lead zirconate titanate (PZT) transducers with a potential for continuous monitoring. Here, the input signal at the lower driving frequency is often referred to as a 'pumping' signal, and the higher frequency input is referred to as a 'probing' signal. The presence of a system nonlinearity, such as a crack formation, can provide a mechanism for nonlinear wave modulation, and create spectral sidebands around the frequency of the probing signal. A signal processing technique combining linear response subtraction (LRS) and synchronous demodulation (SD) is developed specifically to extract the crack-induced spectral sidebands. The proposed crack detection method is successfully applied to identify actual fatigue cracks grown in metallic plate and complex fitting-lug specimens. Finally, the effect of pumping and probing frequencies on the amplitude of the first spectral sideband is investigated using the first sideband spectrogram (FSS) obtained by sweeping both pumping and probing signals over specified frequency ranges.

Nonlinear dynamics and numerical uncertainties in CFD

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching, approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with spurious behavior observed in CFD computations.

Nonlinear acoustics in cicada mating calls enhance sound propagation.

PubMed

Hughes, Derke R; Nuttall, Albert H; Katz, Richard A; Carter, G Clifford

2009-02-01

An analysis of cicada mating calls, measured in field experiments, indicates that the very high levels of acoustic energy radiated by this relatively small insect are mainly attributed to the nonlinear characteristics of the signal. The cicada emits one of the loudest sounds in all of the insect population with a sound production system occupying a physical space typically less than 3 cc. The sounds made by tymbals are amplified by the hollow abdomen, functioning as a tuned resonator, but models of the signal based solely on linear techniques do not fully account for a sound radiation capability that is so disproportionate to the insect's size. The nonlinear behavior of the cicada signal is demonstrated by combining the mutual information and surrogate data techniques; the results obtained indicate decorrelation when the phase-randomized and non-phase-randomized data separate. The Volterra expansion technique is used to fit the nonlinearity in the insect's call. The second-order Volterra estimate provides further evidence that the cicada mating calls are dominated by nonlinear characteristics and also suggests that the medium contributes to the cicada's efficient sound propagation. Application of the same principles has the potential to improve radiated sound levels for sonar applications.

Nonlinear dielectric effects in liquids: a guided tour

NASA Astrophysics Data System (ADS)

Richert, Ranko

2017-09-01

Dielectric relaxation measurements probe how the polarization of a material responds to the application of an external electric field, providing information on structure and dynamics of the sample. In the limit of small fields and thus linear response, such experiments reveal the properties of the material in the same thermodynamic state it would have in the absence of the external field. At sufficiently high fields, reversible changes in enthalpy and entropy of the system occur even at constant temperature, and these will in turn alter the polarization responses. The resulting nonlinear dielectric effects feature field induced suppressions (saturation) and enhancements (chemical effect) of the amplitudes, as well as time constant shifts towards faster (energy absorption) and slower (entropy reduction) dynamics. This review focuses on the effects of high electric fields that are reversible and observed at constant temperature for single component glass-forming liquids. The experimental challenges involved in nonlinear dielectric experiments, the approaches to separating and identifying the different sources of nonlinear behavior, and the current understanding of how high electric fields affect dielectric materials will be discussed. Covering studies from Debye’s initial approach to the present state-of-the-art, it will be emphasized what insight can be gained from the nonlinear responses that are not available from dielectric relaxation results obtained in the linear regime.

Nonlinear photoacoustic spectroscopy of hemoglobin.

PubMed

Danielli, Amos; Maslov, Konstantin; Favazza, Christopher P; Xia, Jun; Wang, Lihong V

2015-05-18

As light intensity increases in photoacoustic imaging, the saturation of optical absorption and the temperature dependence of the thermal expansion coefficient result in a measurable nonlinear dependence of the photoacoustic (PA) signal on the excitation pulse fluence. Here, under controlled conditions, we investigate the intensity-dependent photoacoustic signals from oxygenated and deoxygenated hemoglobin at varied optical wavelengths and molecular concentrations. The wavelength and concentration dependencies of the nonlinear PA spectrum are found to be significantly greater in oxygenated hemoglobin than in deoxygenated hemoglobin. These effects are further influenced by the hemoglobin concentration. These nonlinear phenomena provide insights into applications of photoacoustics, such as measurements of average inter-molecular distances on a nm scale or with a tuned selection of wavelengths, a more accurate quantitative PA tomography.

Cosmological constraints from the CFHTLenS shear measurements using a new, accurate, and flexible way of predicting non-linear mass clustering

NASA Astrophysics Data System (ADS)

Angulo, Raul E.; Hilbert, Stefan

2015-03-01

We explore the cosmological constraints from cosmic shear using a new way of modelling the non-linear matter correlation functions. The new formalism extends the method of Angulo & White, which manipulates outputs of N-body simulations to represent the 3D non-linear mass distribution in different cosmological scenarios. We show that predictions from our approach for shear two-point correlations at 1-300 arcmin separations are accurate at the ˜10 per cent level, even for extreme changes in cosmology. For moderate changes, with target cosmologies similar to that preferred by analyses of recent Planck data, the accuracy is close to ˜5 per cent. We combine this approach with a Monte Carlo Markov chain sampler to explore constraints on a Λ cold dark matter model from the shear correlation functions measured in the Canada-France-Hawaii Telescope Lensing Survey (CFHTLenS). We obtain constraints on the parameter combination σ8(Ωm/0.27)0.6 = 0.801 ± 0.028. Combined with results from cosmic microwave background data, we obtain marginalized constraints on σ8 = 0.81 ± 0.01 and Ωm = 0.29 ± 0.01. These results are statistically compatible with previous analyses, which supports the validity of our approach. We discuss the advantages of our method and the potential it offers, including a path to model in detail (i) the effects of baryons, (ii) high-order shear correlation functions, and (iii) galaxy-galaxy lensing, among others, in future high-precision cosmological analyses.

An Efficient Numerical Approach for Nonlinear Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Otten, Dustin; Vedula, Prakash

2009-03-01

Fokker-Planck equations which are nonlinear with respect to their probability densities that occur in many nonequilibrium systems relevant to mean field interaction models, plasmas, classical fermions and bosons can be challenging to solve numerically. To address some underlying challenges in obtaining numerical solutions, we propose a quadrature based moment method for efficient and accurate determination of transient (and stationary) solutions of nonlinear Fokker-Planck equations. In this approach the distribution function is represented as a collection of Dirac delta functions with corresponding quadrature weights and locations, that are in turn determined from constraints based on evolution of generalized moments. Properties of the distribution function can be obtained by solution of transport equations for quadrature weights and locations. We will apply this computational approach to study a wide range of problems, including the Desai-Zwanzig Model (for nonlinear muscular contraction) and multivariate nonlinear Fokker-Planck equations describing classical fermions and bosons, and will also demonstrate good agreement with results obtained from Monte Carlo and other standard numerical methods.

Optimal Energy Measurement in Nonlinear Systems: An Application of Differential Geometry

NASA Technical Reports Server (NTRS)

Fixsen, Dale J.; Moseley, S. H.; Gerrits, T.; Lita, A.; Nam, S. W.

2014-01-01

Design of TES microcalorimeters requires a tradeoff between resolution and dynamic range. Often, experimenters will require linearity for the highest energy signals, which requires additional heat capacity be added to the detector. This results in a reduction of low energy resolution in the detector. We derive and demonstrate an algorithm that allows operation far into the nonlinear regime with little loss in spectral resolution. We use a least squares optimal filter that varies with photon energy to accommodate the nonlinearity of the detector and the non-stationarity of the noise. The fitting process we use can be seen as an application of differential geometry. This recognition provides a set of well-developed tools to extend our work to more complex situations. The proper calibration of a nonlinear microcalorimeter requires a source with densely spaced narrow lines. A pulsed laser multi-photon source is used here, and is seen to be a powerful tool for allowing us to develop practical systems with significant detector nonlinearity. The combination of our analysis techniques and the multi-photon laser source create a powerful tool for increasing the performance of future TES microcalorimeters.

Numerical modelling of nonlinear full-wave acoustic propagation

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

Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx

2015-10-28

The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on amore » GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.« less

Localized spatially nonlinear matter waves in atomic-molecular Bose-Einstein condensates with space-modulated nonlinearity

PubMed Central

Yao, Yu-Qin; Li, Ji; Han, Wei; Wang, Deng-Shan; Liu, Wu-Ming

2016-01-01

The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number n, and the numbers of the density packets for each quantum state depend on both the principal quantum number n and the secondary quantum number l. When the coupling is not zero, the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number n, only depend on the secondary quantum number l. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number n, while the stability of the rational solutions depends on the chemical potential and Raman detuning. PMID:27403634

Nonlinear photothermal mid-infrared spectroscopy

NASA Astrophysics Data System (ADS)

Totachawattana, Atcha; Erramilli, Shyamsunder; Sander, Michelle Y.

2016-10-01

Mid-infrared photothermal spectroscopy is a pump-probe technique for label-free and non-destructive sample characterization by targeting intrinsic vibrational modes. In this method, the mid-infrared pump beam excites a temperature-induced change in the refractive index of the sample. This laser-induced change in the refractive index is measured by a near-infrared probe laser using lock-in detection. At increased pump powers, emerging nonlinear phenomena not previously demonstrated in other mid-infrared techniques are observed. Nonlinear study of a 6 μm-thick 4-Octyl-4'-Cyanobiphenyl (8CB) liquid crystal sample is conducted by targeting the C=C stretching band at 1606 cm-1. At high pump powers, nonlinear signal enhancement and multiple pitchfork bifurcations of the spectral features are observed. An explanation of the nonlinear peak splitting is provided by the formation of bubbles in the sample at high pump powers. The discontinuous refractive index across the bubble interface results in a decrease in the forward scatter of the probe beam. This effect can be recorded as a bifurcation of the absorption peak in the photothermal spectrum. These nonlinear effects are not present in direct measurements of the mid-infrared beam. Evolution of the nonlinear photothermal spectrum of 8CB liquid crystal with increasing pump power shows enhancement of the absorption peak at 1606 cm-1. Multiple pitchfork bifurcations and spectral narrowing of the photothermal spectrum are demonstrated. This novel nonlinear regime presents potential for improved spectral resolution as well as a new regime for sample characterization in mid-infrared photothermal spectroscopy.

NR-code: Nonlinear reconstruction code

NASA Astrophysics Data System (ADS)

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 identification of the total baroreflex arc: higher-order nonlinearity

PubMed Central

Moslehpour, Mohsen; Kawada, Toru; Sunagawa, Kenji; Sugimachi, Masaru

2016-01-01

The total baroreflex arc is the open-loop system relating carotid sinus pressure (CSP) to arterial pressure (AP). The nonlinear dynamics of this system were recently characterized. First, Gaussian white noise CSP stimulation was employed in open-loop conditions in normotensive and hypertensive rats with sectioned vagal and aortic depressor nerves. Nonparametric system identification was then applied to measured CSP and AP to establish a second-order nonlinear Uryson model. The aim in this study was to assess the importance of higher-order nonlinear dynamics via development and evaluation of a third-order nonlinear model of the total arc using the same experimental data. Third-order Volterra and Uryson models were developed by employing nonparametric and parametric identification methods. The R2 values between the AP predicted by the best third-order Volterra model and measured AP in response to Gaussian white noise CSP not utilized in developing the model were 0.69 ± 0.03 and 0.70 ± 0.03 for normotensive and hypertensive rats, respectively. The analogous R2 values for the best third-order Uryson model were 0.71 ± 0.03 and 0.73 ± 0.03. These R2 values were not statistically different from the corresponding values for the previously established second-order Uryson model, which were both 0.71 ± 0.03 (P > 0.1). Furthermore, none of the third-order models predicted well-known nonlinear behaviors including thresholding and saturation better than the second-order Uryson model. Additional experiments suggested that the unexplained AP variance was partly due to higher brain center activity. In conclusion, the second-order Uryson model sufficed to represent the sympathetically mediated total arc under the employed experimental conditions. PMID:27629885

Lipschitz regularity results for nonlinear strictly elliptic equations and applications

NASA Astrophysics Data System (ADS)

Ley, Olivier; Nguyen, Vinh Duc

2017-10-01

Most of Lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic growth power in gradient, one usually uses weak Bernstein-type arguments which require regularity and/or convex-type assumptions on the gradient nonlinearity. In this article, we obtain new Lipschitz regularity results for a large class of nonlinear strictly elliptic equations with possibly arbitrary growth power of the Hamiltonian with respect to the gradient variable using some ideas coming from Ishii-Lions' method. We use these bounds to solve an ergodic problem and to study the regularity and the large time behavior of the solution of the evolution equation.

Modeling nonlinearities in MEMS oscillators.

PubMed

Agrawal, Deepak K; Woodhouse, Jim; Seshia, Ashwin A

2013-08-01

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude-frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier- based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases.

Some Aspects of Nonlinear Dynamics and CFD

NASA Technical Reports Server (NTRS)

Yee, Helen C.; Merriam, Marshal (Technical Monitor)

1996-01-01

The application of nonlinear dynamics to improve the understanding of numerical uncertainties in computational fluid dynamics (CFD) is reviewed. Elementary examples in the use of dynamics to explain the nonlinear phenomena and spurious behavior that occur in numerics are given. The role of dynamics in the understanding of long time behavior of numerical integrations and the nonlinear stability, convergence, and reliability of using time-marching approaches for obtaining steady-state numerical solutions in CFD is explained. The study is complemented with examples of spurious behavior observed in CFD computations.

Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity

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

Lebedev, M. E., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Alfimov, G. L., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Malomed, Boris A., E-mail: malomed@post.tau.ac.il

We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate thatmore » one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.« less

Practical nonlinear method for detection of respiratory and cardiac dysfunction in human subjects

NASA Astrophysics Data System (ADS)

Katz, Richard A.; Lawee, Michael S.; Newman, Anthony K.; Weiss, J. Woodrow; Chandra, Shalabh; Grimm, Richard A.; Thomas, James D.

1995-12-01

This research applies novel nonlinear signal detection techniques in studies of human subjects with respiratory and cardiac diseases. One of the studies concerns a breathing disorder during sleep, a disease called Obstructive Sleep Apnea (OSA). In a second study we investigate a disease of the heart, Atrial Fibrillation (AF). The former study involves nonlinear processing of the time sequences of sleep apnea recordings (cardio-respirograms) collected from patients with known obstructive sleep apnea, and from a normal control. In the latter study, we apply similar nonlinear metrics to Doppler flow measurements obtained by transesophageal echocardiography (TEE). One of our metrics, the 'chaotic radius' is used for tracking the position of points in phase space relative to some reference position. A second metric, the 'differential radius' provides a measure of the separation rate of contiguous (evolving) points in phase space. A third metric, the 'chaotic frequency' gives angular position of the phase space orbit as a function of time. All are useful for identifying change of physiologic condition that is not always apparent using conventional methods.

Naturally stable Sagnac–Michelson nonlinear interferometer

DOE PAGES

Lukens, Joseph M.; Peters, Nicholas A.; Pooser, Raphael C.

2016-11-16

Interferometers measure a wide variety of dynamic processes by converting a phase change into an intensity change. Nonlinear interferometers, making use of nonlinear media in lieu of beamsplitters, promise substantial improvement in the quest to reach the ultimate sensitivity limits. Here we demonstrate a new nonlinear interferometer utilizing a single parametric amplifier for mode mixing conceptually, a nonlinear version of the conventional Michelson interferometer with its arms collapsed together. We observe up to 99.9% interference visibility and find evidence for noise reduction based on phase-sensitive gain. As a result, our configuration utilizes fewer components than previous demonstrations and requires nomore » active stabilization, offering new capabilities for practical nonlinear interferometric-based sensors.« less

Nonlinear propagation of electromagnetic waves in negative-refraction-index composite materials.

PubMed

Kourakis, I; Shukla, P K

2005-07-01

We investigate the nonlinear propagation of electromagnetic waves in left-handed materials. For this purpose, we consider a set of coupled nonlinear Schrödinger (CNLS) equations, which govern the dynamics of coupled electric and magnetic field envelopes. The CNLS equations are used to obtain a nonlinear dispersion, which depicts the modulational stability profile of the coupled plane-wave solutions in left-handed materials. An exact (in)stability criterion for modulational interactions is derived, and analytical expressions for the instability growth rate are obtained.

Nonlinear photoacoustic spectroscopy of hemoglobin

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

Danielli, Amos; Maslov, Konstantin; Favazza, Christopher P.

2015-05-18

As light intensity increases in photoacoustic imaging, the saturation of optical absorption and the temperature dependence of the thermal expansion coefficient result in a measurable nonlinear dependence of the photoacoustic (PA) signal on the excitation pulse fluence. Here, under controlled conditions, we investigate the intensity-dependent photoacoustic signals from oxygenated and deoxygenated hemoglobin at varied optical wavelengths and molecular concentrations. The wavelength and concentration dependencies of the nonlinear PA spectrum are found to be significantly greater in oxygenated hemoglobin than in deoxygenated hemoglobin. These effects are further influenced by the hemoglobin concentration. These nonlinear phenomena provide insights into applications of photoacoustics,more » such as measurements of average inter-molecular distances on a nm scale or with a tuned selection of wavelengths, a more accurate quantitative PA tomography.« less

Nonlinear photoacoustic spectroscopy of hemoglobin

PubMed Central

Danielli, Amos; Maslov, Konstantin; Favazza, Christopher P.; Xia, Jun; Wang, Lihong V.

2015-01-01

As light intensity increases in photoacoustic imaging, the saturation of optical absorption and the temperature dependence of the thermal expansion coefficient result in a measurable nonlinear dependence of the photoacoustic (PA) signal on the excitation pulse fluence. Here, under controlled conditions, we investigate the intensity-dependent photoacoustic signals from oxygenated and deoxygenated hemoglobin at varied optical wavelengths and molecular concentrations. The wavelength and concentration dependencies of the nonlinear PA spectrum are found to be significantly greater in oxygenated hemoglobin than in deoxygenated hemoglobin. These effects are further influenced by the hemoglobin concentration. These nonlinear phenomena provide insights into applications of photoacoustics, such as measurements of average inter-molecular distances on a nm scale or with a tuned selection of wavelengths, a more accurate quantitative PA tomography. PMID:26045627

Third-order optical nonlinearities of sol-gel silica coating films containing metal porphyrin derivatives measured by resonant femtosecond degenerate four-wave mixing technique

NASA Astrophysics Data System (ADS)

Kasatani, Kazuo; Okamoto, Hiroaki; Takenaka, Shunsuke

2003-11-01

Third-order optical nonlinearities of sol-gel silica coating films containing metal porphyrin derivatives were measured under resonant conditions by the femtosecond degenerate four-wave mixing (DFWM) technique. Temporal profiles of the DFWM signal were measured with a time resolution of 0.3 ps, and were found to consist of two components, the coherent instantaneous nonlinear response and the delayed response with a decay time constant of several to several hundred ps. The latter can be attributed to population grating of an excited state, and contribution of slow component was very little for a zinc porphyrin derivative. The values of electronic component of the optical nonlinear susceptibility, χ(3) xxxx, for these films were ca. 2 x 10-10 esu.

Nonlinear response of unidirectional boron/aluminum

NASA Technical Reports Server (NTRS)

Pindera, M.-J.; Herakovich, C. T.; Becker, W.; Aboudi, J.

1990-01-01

Experimental results obtained for unidirectional boron/aluminum subjected to combined loading using off-axis tension, compression and Iosipescu shear specimens are correlated with a nonlinear micromechanics model. It is illustrated that the nonlinear response in the principal material directions is markedly influenced by the different loading modes and different ratios of the applied stress components. The observed nonlinear response under pure and combined loading is discussed in terms of initial yielding, subsequent hardening, stress-interaction effects and unloading-reloading characteristics. The micromechanics model is based on the concept of a repeating unit cell representative of the composite-at-large and employs the unified theory of Bodner and Partom to model the inelastic response of the matrix. It is shown that the employed micromechanics model is sufficiently general to predict the observed nonlinear response of unidirectional boron/aluminum with good accuracy.

Nonlinear spectral singularities for confined nonlinearities.

PubMed

Mostafazadeh, Ali

2013-06-28

We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrödinger operators involving a confined nonlinearity. The presence of the nonlinearity does not break the parity-reflection symmetry of spectral singularities but makes them amplitude dependent. Nonlinear spectral singularities are, therefore, associated with a resonance effect that produces amplified waves with a specific amplitude-wavelength profile. We explore the consequences of this phenomenon for a complex δ-function potential that is subject to a general confined nonlinearity.

Nonlinearity in rock - Evidence from earth tides

NASA Technical Reports Server (NTRS)

Agnew, D. C.

1981-01-01

The earth is sinusoidally stressed by tidal forces; if the stress-strain relation for rock is nonlinear, energy should appear in an earth tide record at frequencies which are multiples of those of the larger tidal lines. An examination of the signals to be expected for different nonlinear deformation laws shows that for a nonlinear response without dissipation, the largest anomalous signal should occur at twice the forcing frequency, whereas for nonlinear laws involving dissipation (cusped hysteresis loops) the anomalous signal will be greatest at three times this frequency. The size of the signal in the dissipative case depends on the amount by which dissipation affects the particular response being measured. For measurements of strain tides this depends on whether dissipation is assumed to be present throughout the earth or localized around the point of measurement. An analysis of 5.7 years of strain tide records from Pinon Flat, California, shows a small signal at twice the frequency of the largest (M2) tide.

Nonlinear effective permittivity of field grading composite dielectrics

NASA Astrophysics Data System (ADS)

Yang, Xiao; Zhao, Xiaolei; Li, Qi; Hu, Jun; He, Jinliang

2018-02-01

Field grading composite dielectrics with good nonlinear electrical properties can function as smart materials for electrical field control in a high-voltage apparatus. Besides the well-documented nonlinear conducting behavior, the field-dependent effective permittivity of field grading composites were also reported; however, in-depth research on the mechanism and influencing factors of this nonlinear permittivity are absent. This paper theoretically discusses the origin of the nonlinear effective permittivity, and the mechanism is illustrated through the waveform analysis of the nonlinear response of ZnO microvaristor/silicone rubber composites under a pure AC field. The field-dependent effective permittivity and loss property of the ZnO composites are measured by a dielectric spectrometer in both DC and AC fields under different frequencies. Through comparison of measurement results and theoretical models, the influence of the filler concentration, frequency, and time domain characteristics of the applied field on the nonlinear permittivity of the field grading composites are well explained. This paper provides insight into the nonlinear permittivity of field grading composites, and will be helpful for further tuning the performance of field grading composites.

Moderately nonlinear ultrasound propagation in blood-mimicking fluid.

PubMed

Kharin, Nikolay A; Vince, D Geoffrey

2004-04-01

In medical diagnostic ultrasound (US), higher than-in-water nonlinearity of body fluids and tissue usually does not produce strong nonlinearly distorted waves because of the high absorption. The relative influence of absorption and nonlinearity can be characterized by the Gol'dberg number Gamma. There are two limiting cases in nonlinear acoustics: weak waves (Gamma < 1) or strong waves (Gamma > 1). However, at diagnostic frequencies in tissue and body fluids, the nonlinear effects and effects of absorption more likely are comparable (Gol'dberg number Gamma approximately 1). The aim of this work was to study the nonlinear propagation of a moderately nonlinear US second harmonic signal in a blood-mimicking fluid. Quasilinear solutions to the KZK equation are presented, assuming radiation from a flat and geometrically focused circular Gaussian source. The solutions are expressed in a new simplified closed form and are in very good agreement with those of previous studies measuring and modeling Gaussian beams. The solutions also show good agreement with the measurements of the beams produced by commercially available transducers, even without special Gaussian shading.

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

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

Conductivity of higher dimensional holographic superconductors with nonlinear electrodynamics

NASA Astrophysics Data System (ADS)

Sheykhi, Ahmad; Hashemi Asl, Doa; Dehyadegari, Amin

2018-06-01

We investigate analytically as well as numerically the properties of s-wave holographic superconductors in d-dimensional spacetime and in the presence of Logarithmic nonlinear electrodynamics. We study three aspects of this kind of superconductors. First, we obtain, by employing analytical Sturm-Liouville method as well as numerical shooting method, the relation between critical temperature and charge density, ρ, and disclose the effects of both nonlinear parameter b and the dimensions of spacetime, d, on the critical temperature Tc. We find that in each dimension, Tc /ρ 1 / (d - 2) decreases with increasing the nonlinear parameter b while it increases with increasing the dimension of spacetime for a fixed value of b. Then, we calculate the condensation value and critical exponent of the system analytically and numerically and observe that in each dimension, the dimensionless condensation get larger with increasing the nonlinear parameter b. Besides, for a fixed value of b, it increases with increasing the spacetime dimension. We confirm that the results obtained from our analytical method are in agreement with the results obtained from numerical shooting method. This fact further supports the correctness of our analytical method. Finally, we explore the holographic conductivity of this system and find out that the superconducting gap increases with increasing either the nonlinear parameter or the spacetime dimension.

Heterodyne interferometer with subatomic periodic nonlinearity.

PubMed

Wu, C M; Lawall, J; Deslattes, R D

1999-07-01

A new, to our knowledge, heterodyne interferometer for differential displacement measurements is presented. It is, in principle, free of periodic nonlinearity. A pair of spatially separated light beams with different frequencies is produced by two acousto-optic modulators, avoiding the main source of periodic nonlinearity in traditional heterodyne interferometers that are based on a Zeeman split laser. In addition, laser beams of the same frequency are used in the measurement and the reference arms, giving the interferometer theoretically perfect immunity from common-mode displacement. We experimentally demonstrated a residual level of periodic nonlinearity of less than 20 pm in amplitude. The remaining periodic error is attributed to unbalanced ghost reflections that drift slowly with time.

A computer-aided approach to nonlinear control systhesis

NASA Technical Reports Server (NTRS)

Wie, Bong; Anthony, Tobin

1988-01-01

The major objective of this project is to develop a computer-aided approach to nonlinear stability analysis and nonlinear control system design. This goal is to be obtained by refining the describing function method as a synthesis tool for nonlinear control design. The interim report outlines the approach by this study to meet these goals including an introduction to the INteractive Controls Analysis (INCA) program which was instrumental in meeting these study objectives. A single-input describing function (SIDF) design methodology was developed in this study; coupled with the software constructed in this study, the results of this project provide a comprehensive tool for design and integration of nonlinear control systems.

A mechano-acoustic indentor system for in vivo measurement of nonlinear elastic properties of soft tissue.

PubMed

Koo, Terry K; Cohen, Jeffrey H; Zheng, Yongping

2011-11-01

Soft tissue exhibits nonlinear stress-strain behavior under compression. Characterizing its nonlinear elasticity may aid detection, diagnosis, and treatment of soft tissue abnormality. The purposes of this study were to develop a rate-controlled Mechano-Acoustic Indentor System and a corresponding finite element optimization method to extract nonlinear elastic parameters of soft tissue and evaluate its test-retest reliability. An indentor system using a linear actuator to drive a force-sensitive probe with a tip-mounted ultrasound transducer was developed. Twenty independent sites at the upper lateral quadrant of the buttock from 11 asymptomatic subjects (7 men and 4 women from a chiropractic college) were indented at 6% per second for 3 sessions, each consisting of 5 trials. Tissue thickness, force at 25% deformation, and area under the load-deformation curve from 0% to 25% deformation were calculated. Optimized hyperelastic parameters of the soft tissue were calculated with a finite element model using a first-order Ogden material model. Load-deformation response on a standardized block was then simulated, and the corresponding area and force parameters were calculated. Between-trials repeatability and test-retest reliability of each parameter were evaluated using coefficients of variation and intraclass correlation coefficients, respectively. Load-deformation responses were highly reproducible under repeated measurements. Coefficients of variation of tissue thickness, area under the load-deformation curve from 0% to 25% deformation, and force at 25% deformation averaged 0.51%, 2.31%, and 2.23%, respectively. Intraclass correlation coefficients ranged between 0.959 and 0.999, indicating excellent test-retest reliability. The automated Mechano-Acoustic Indentor System and its corresponding optimization technique offers a viable technology to make in vivo measurement of the nonlinear elastic properties of soft tissue. This technology showed excellent between

Ultrahigh precision nonlinear reflectivity measurement system for saturable absorber mirrors with self-referenced fluence characterization.

PubMed

Orsila, Lasse; Härkönen, Antti; Hyyti, Janne; Guina, Mircea; Steinmeyer, Günter

2014-08-01

Measurement of nonlinear optical reflectivity of saturable absorber devices is discussed. A setup is described that enables absolute accuracy of reflectivity measurements better than 0.3%. A repeatability within 0.02% is shown for saturable absorbers with few-percent modulation depth. The setup incorporates an in situ knife-edge characterization of beam diameters, making absolute reflectivity estimations and determination of saturation fluences significantly more reliable. Additionally, several measures are discussed to substantially improve the reliability of the reflectivity measurements. At its core, the scheme exploits the limits of state-of-the-art digital lock-in technology but also greatly benefits from a fiber-based master-oscillator power-amplifier source, the use of an integrating sphere, and simultaneous comparison with a linear reflectivity standard.

Isotope shift, nonlinearity of King plots, and the search for new particles

NASA Astrophysics Data System (ADS)

Flambaum, V. V.; Geddes, A. J.; Viatkina, A. V.

2018-03-01

We derive a mean-field relativistic formula for the isotope shift of an electronic energy level for arbitrary angular momentum; we then use it to predict the spectra of superheavy metastable neutron-rich isotopes belonging to the hypothetical island of stability. Our results may be applied to the search for superheavy atoms in astrophysical spectra using the known values of the transition frequencies for the neutron-deficient isotopes produced in the laboratory. An example of a relevant astrophysical system may be the spectra of the Przybylski's star where superheavy elements up to Z =99 have been possibly identified. In addition, it has been recently suggested to use the measurements of King plot nonlinearity in a search for hypothetical new light bosons. On the other hand, one can find the nonlinear corrections to the King plot arising already in the standard model framework. We investigate contributions to the nonlinearity arising from relativistic effects in the isotope field shift, the nuclear polarizability, and many-body effects. It is found that the nuclear polarizability contribution can lead to the significant deviation of the King plot from linearity. Therefore, the measurements of the nonlinearity of King plots may be applied to obtain the nuclear polarizability change between individual isotopes. We then proceed with providing a rough analytical estimate of the nonlinearity arising solely from the effect of a hypothetical scalar boson. Our predictions give theoretical limitations on the sensitivity of the search for new interactions and should help to identify the most suitable atoms for corresponding experiments.

Aircraft and ground vehicle friction measurements obtained under winter runway conditions

NASA Technical Reports Server (NTRS)

Yager, Thomas J.

1989-01-01

Tests with specially instrumented NASA B-737 and B-727 aircraft together with several different ground friction measuring devices have been conducted for a variety of runway surface types and wetness conditions. This effort is part of the Joint FAA/NASA Aircraft/Ground Vehicle Runway Friction Program aimed at obtaining a better understanding of aircraft ground handling performance under adverse weather conditions, and defining relationships between aircraft and ground vehicle tire friction measurements. Aircraft braking performance on dry, wet, snow-, and ice-covered runway conditions is discussed together with ground vehicle friction data obtained under similar runway conditions. For the wet, compacted snow- and ice-covered runway conditions, the relationship between ground vehicles and aircraft friction data is identified. The influence of major test parameters on friction measurements such as speed, test tire characteristics, and surface contaminant-type are discussed. The test results indicate that use of properly maintained and calibrated ground vehicles for monitoring runway friction conditions should be encouraged particularly under adverse weather conditions.

Ultrafast nonlinear spectrometer for material characterization

NASA Astrophysics Data System (ADS)

Negres, Raluca Aurelia

2001-11-01

This work describes the use of a broadband spectral source for nonlinear spectroscopy to characterize various materials with potential applications in confocal microscopy, biological sample markers, optical limiting devices and optical switches. The goal is to study the spectrum of nonlinear absorption and the dispersion of nonlinear refraction as well as the dynamics of the nonlinearities by means of femtosecond excite-probe experiments. The principle is quite simple: if a sample is under the influence of a strong fs excitation pulse and a probe pulse beam is incident at the same time, or shortly after (within the decay time of the nonlinearity), then the probe pulse will sense the nonlinearity induced by the excitation. If the probe pulse is broadband, a femtosecond white-light continuum (WLC) in our case, we can monitor the nonlinearity induced over the entire continuum spectrum in one laser ``shot''. The use of femtosecond laser pulses to generate WLC will provide femtosecond time resolution for time-resolved spectroscopy. We built the nonlinear spectrometer and allowed for many degrees of flexibility in terms of choice of wavelengths for pump and probe beams and a dual detection system to cover both visible and infrared spectral ranges. We have the possibility of performing broad band spectral measurements using a spectrometer or selected narrow bandwidth probes incident on Si or Ge photodiodes, for improved S/N ratios. The intrinsic properties of the continuum probe demand a careful characterization of its spatial and temporal profile. Knowledge of the dispersion of the index of refraction in various optical elements, including the sample itself, is also required for a correct analysis of the transient absorption raw data, especially for short time-scale dynamics of nonlinear processes. We tested the system using well-characterized semiconductor samples, and the results came out in excellent agreement with those from previous picosecond Z-scan measurements

Dynamics of cochlear nonlinearity: Automatic gain control or instantaneous damping?

PubMed

Altoè, Alessandro; Charaziak, Karolina K; Shera, Christopher A

2017-12-01

Measurements of basilar-membrane (BM) motion show that the compressive nonlinearity of cochlear mechanical responses is not an instantaneous phenomenon. For this reason, the cochlear amplifier has been thought to incorporate an automatic gain control (AGC) mechanism characterized by a finite reaction time. This paper studies the effect of instantaneous nonlinear damping on the responses of oscillatory systems. The principal results are that (i) instantaneous nonlinear damping produces a noninstantaneous gain control that differs markedly from typical AGC strategies; (ii) the kinetics of compressive nonlinearity implied by the finite reaction time of an AGC system appear inconsistent with the nonlinear dynamics measured on the gerbil basilar membrane; and (iii) conversely, those nonlinear dynamics can be reproduced using an harmonic oscillator with instantaneous nonlinear damping. Furthermore, existing cochlear models that include instantaneous gain-control mechanisms capture the principal kinetics of BM nonlinearity. Thus, an AGC system with finite reaction time appears neither necessary nor sufficient to explain nonlinear gain control in the cochlea.

Nonlinear dielectric spectroscopy of propylene carbonate derivatives

NASA Astrophysics Data System (ADS)

Casalini, R.; Roland, C. M.

2018-04-01

Nonlinear dielectric measurements were carried out on two strongly polar liquids, 4-vinyl-1,3-dioxolan-2-one (VPC) and 4-ethyl-1,3-dioxolan-2-one (EPC), having chemical structures differing from propylene carbonate (PC) only by the presence of a pendant group. Despite their polarity, the compounds are all non-associated, "simple" liquids. From the linear component of the dielectric response, the α relaxation peak breadth was found to be invariant at a fixed value of the relaxation time, τα. From spectra from the nonlinear component, the number of dynamically correlated molecules was determined; it was also constant at fixed τα. Thus, two manifestations of dynamic heterogeneity depend only on the time constant for structural reorientation. More broadly, the cooperativity of molecular motions for non-associated glass-forming materials is connected to (i.e., reciprocally governs) the time scale. The equation of state for the two liquids was also obtained from density measurements made over a broad range of pressures and temperatures. Using these data, it was determined that the relaxation times of both liquids conform to density scaling. The effect of density, relative to thermal effects, on the α relaxation increases going from PC < VPC < EPC.

Structural stability of nonlinear population dynamics.

PubMed

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Structural stability of nonlinear population dynamics

NASA Astrophysics Data System (ADS)

Cenci, Simone; Saavedra, Serguei

2018-01-01

In population dynamics, the concept of structural stability has been used to quantify the tolerance of a system to environmental perturbations. Yet, measuring the structural stability of nonlinear dynamical systems remains a challenging task. Focusing on the classic Lotka-Volterra dynamics, because of the linearity of the functional response, it has been possible to measure the conditions compatible with a structurally stable system. However, the functional response of biological communities is not always well approximated by deterministic linear functions. Thus, it is unclear the extent to which this linear approach can be generalized to other population dynamics models. Here, we show that the same approach used to investigate the classic Lotka-Volterra dynamics, which is called the structural approach, can be applied to a much larger class of nonlinear models. This class covers a large number of nonlinear functional responses that have been intensively investigated both theoretically and experimentally. We also investigate the applicability of the structural approach to stochastic dynamical systems and we provide a measure of structural stability for finite populations. Overall, we show that the structural approach can provide reliable and tractable information about the qualitative behavior of many nonlinear dynamical systems.

Determination of nonlinear optical properties by time resolved Z-scan in Nd-doped phosphate glass

NASA Astrophysics Data System (ADS)

de Souza, J. M.; de Lima, W. J.; Pilla, V.; Andrade, A. A.; Dantas, N. O.; Messias, D. N.

2017-02-01

In this work, we have used a Ti3+:Safira laser tuned at 803nm to performed time-resolved measurements using the Z-scan technique to characterize the nonlinear optical properties of phosphate glasses. The glass matrices, labeled PAN (P2O5-Al2O3-Na2CO3) and PANK (P2O5-Al2O3- Na2O-K2O), were doped with increasing Nd3+ concentration, ranging from 0.5 to 5 wt%. For both systems, we have seen that the optical nonlinearity has a linear dependence with the doping ion concentration. Therefore, we propose a new approach to obtain the parameters Δα and Δσ. All results obtained are in good agreement with others found in the literature.

Inverting Monotonic Nonlinearities by Entropy Maximization

PubMed Central

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

2016-01-01

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

Inverting Monotonic Nonlinearities by Entropy Maximization.

PubMed

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

2016-01-01

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

Estimating linear-nonlinear models using Renyi divergences.

PubMed

Kouh, Minjoon; Sharpee, Tatyana O

2009-01-01

This article compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramer-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data.

Autofocus and fusion using nonlinear correlation

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

Cabazos-Marín, Alma Rocío; Álvarez-Borrego, Josué, E-mail: josue@cicese.mx; Coronel-Beltrán, Ángel

2014-10-06

In this work a new algorithm is proposed for auto focusing and images fusion captured by microscope's CCD. The proposed algorithm for auto focusing implements the spiral scanning of each image in the stack f(x, y){sub w} to define the V{sub w} vector. The spectrum of the vector FV{sub w} is calculated by fast Fourier transform. The best in-focus image is determined by a focus measure that is obtained by the FV{sub 1} nonlinear correlation vector, of the reference image, with each other FV{sub W} images in the stack. In addition, fusion is performed with a subset of selected imagesmore » f(x, y){sub SBF} like the images with best focus measurement. Fusion creates a new improved image f(x, y){sub F} with the selection of pixels of higher intensity.« less

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

NASA Astrophysics Data System (ADS)

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.

Hypersonic entry vehicle state estimation using nonlinearity-based adaptive cubature Kalman filters

NASA Astrophysics Data System (ADS)

Sun, Tao; Xin, Ming

2017-05-01

Guidance, navigation, and control of a hypersonic vehicle landing on the Mars rely on precise state feedback information, which is obtained from state estimation. The high uncertainty and nonlinearity of the entry dynamics make the estimation a very challenging problem. In this paper, a new adaptive cubature Kalman filter is proposed for state trajectory estimation of a hypersonic entry vehicle. This new adaptive estimation strategy is based on the measure of nonlinearity of the stochastic system. According to the severity of nonlinearity along the trajectory, the high degree cubature rule or the conventional third degree cubature rule is adaptively used in the cubature Kalman filter. This strategy has the benefit of attaining higher estimation accuracy only when necessary without causing excessive computation load. The simulation results demonstrate that the proposed adaptive filter exhibits better performance than the conventional third-degree cubature Kalman filter while maintaining the same performance as the uniform high degree cubature Kalman filter but with lower computation complexity.

Vacuum nonlinear electrodynamic polarization effects in hard emission of pulsars and magnetars

NASA Astrophysics Data System (ADS)

Denisov, V. I.; Sokolov, V. A.; Svertilov, S. I.

2017-09-01

The nonlinear electrodynamics influence of pulsar magnetic field on the electromagnetic pulse polarization is discussed from the point of observation interpretation. The calculations of pulsar magnetic field impact on the electromagnetic pulse polarization are made in such a way to make it easier to interpret these effects in space experiments. The law of hard emission pulse propagation in the pulsar magnetic field according to the vacuum (nonlinear electrodynamics is obtained. It has been shown, that due to the birefringence in the vacuum the front part of any hard emission pulse coming from a pulsar should be linearly polarized and the rest of pulse can have arbitrary polarization. The observational possibilities of vacuum birefringence are discussed. In this paper we give the estimations of detector parameters such as effective area, exposure time and necessity of polarization measurements with high accuracy. The combination of large area and extremely long exposure time gives the good opportunity to search the fine polarization effects like vacuum nonlinear electrodynamics birefringence.

Linear and nonlinear ARMA model parameter estimation using an artificial neural network

NASA Technical Reports Server (NTRS)

Chon, K. H.; Cohen, R. J.

1997-01-01

This paper addresses parametric system identification of linear and nonlinear dynamic systems by analysis of the input and output signals. Specifically, we investigate the relationship between estimation of the system using a feedforward neural network model and estimation of the system by use of linear and nonlinear autoregressive moving-average (ARMA) models. By utilizing a neural network model incorporating a polynomial activation function, we show the equivalence of the artificial neural network to the linear and nonlinear ARMA models. We compare the parameterization of the estimated system using the neural network and ARMA approaches by utilizing data generated by means of computer simulations. Specifically, we show that the parameters of a simulated ARMA system can be obtained from the neural network analysis of the simulated data or by conventional least squares ARMA analysis. The feasibility of applying neural networks with polynomial activation functions to the analysis of experimental data is explored by application to measurements of heart rate (HR) and instantaneous lung volume (ILV) fluctuations.

A thermodynamic approach to nonlinear ultrasonics for material state awareness and prognosis

NASA Astrophysics Data System (ADS)

Chillara, Vamshi Krishna

2017-11-01

We develop a thermodynamic framework for modeling nonlinear ultrasonic damage sensing and prognosis in materials undergoing progressive damage. The framework is based on the internal variable approach and relies on the construction of a pseudo-elastic strain energy function that captures the energetics associated with the damage progression. The pseudo-elastic strain energy function is composed of two energy functions—one that describes how a material stores energy in an elastic fashion and the other describes how material dissipates energy or stores it in an inelastic fashion. Experimental motivation for the choice of the above two functionals is discussed and some specific choices pertaining to damage progression during fatigue and creep are presented. The thermodynamic framework is employed to model the nonlinear response of material undergoing stress relaxation and creep-like degradation. For each of the above cases, evolution of the nonlinearity parameter with damage as well as with macroscopic measurables like accumulated plastic strain is obtained.

Super-rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations.

PubMed

Slunyaev, A; Pelinovsky, E; Sergeeva, A; Chabchoub, A; Hoffmann, N; Onorato, M; Akhmediev, N

2013-07-01

The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.

Cumulants of heat transfer across nonlinear quantum systems

NASA Astrophysics Data System (ADS)

Li, Huanan; Agarwalla, Bijay Kumar; Li, Baowen; Wang, Jian-Sheng

2013-12-01

We consider thermal conduction across a general nonlinear phononic junction. Based on two-time observation protocol and the nonequilibrium Green's function method, heat transfer in steady-state regimes is studied, and practical formulas for the calculation of the cumulant generating function are obtained. As an application, the general formalism is used to study anharmonic effects on fluctuation of steady-state heat transfer across a single-site junction with a quartic nonlinear on-site pinning potential. An explicit nonlinear modification to the cumulant generating function exact up to the first order is given, in which the Gallavotti-Cohen fluctuation symmetry is found still valid. Numerically a self-consistent procedure is introduced, which works well for strong nonlinearity.

Nanopore Current Oscillations: Nonlinear Dynamics on the Nanoscale.

PubMed

Hyland, Brittany; Siwy, Zuzanna S; Martens, Craig C

2015-05-21

In this Letter, we describe theoretical modeling of an experimentally realized nanoscale system that exhibits the general universal behavior of a nonlinear dynamical system. In particular, we consider the description of voltage-induced current fluctuations through a single nanopore from the perspective of nonlinear dynamics. We briefly review the experimental system and its behavior observed and then present a simple phenomenological nonlinear model that reproduces the qualitative behavior of the experimental data. The model consists of a two-dimensional deterministic nonlinear bistable oscillator experiencing both dissipation and random noise. The multidimensionality of the model and the interplay between deterministic and stochastic forces are both required to obtain a qualitatively accurate description of the physical system.

Improved nonlinear plasmonic slot waveguide: a full study

NASA Astrophysics Data System (ADS)

Elsawy, Mahmoud M. R.; Nazabal, Virginie; Chauvet, Mathieu; Renversez, Gilles

2016-04-01

We present a full study of an improved nonlinear plasmonic slot waveguides (NPSWs) in which buffer linear dielectric layers are added between the Kerr type nonlinear dielectric core and the two semi-infinite metal regions. Our approach computes the stationary solutions using the fixed power algorithm, in which for a given structure the wave power is an input parameter and the outputs are the propagation constant and the corresponding field components. For TM polarized waves, the inclusion of these supplementary layers have two consequences. First, they reduced the overall losses. Secondly, they modify the types of solutions that propagate in the NPSWs adding new profiles enlarging the possibilities offered by these nonlinear waveguides. In addition to the symmetric linear plasmonic profile obtained in the simple plasmonic structure with linear core such that its effective index is above the linear core refractive index, we obtained a new field profile which is more localized in the core with an effective index below the core linear refractive index. In the nonlinear case, if the effective index of the symmetric linear mode is above the core linear refractive index, the mode field profiles now exhibit a spatial transition from a plasmonic type profile to a solitonic type one. Our structure also provides longer propagation length due to the decrease of the losses compared to the simple nonlinear slot waveguide and exhibits, for well-chosen refractive index or thickness of the buffer layer, a spatial transition of its main modes that can be controlled by the power. We provide a full phase diagram of the TM wave operating regimes of these improved NPSWs. The stability of the main TM modes is then demonstrated numerically using the FDTD. We also demonstrate the existence of TE waves for both linear and nonlinear cases (for some configurations) in which the maximum intensity is located in the middle of the waveguide. We indicate the bifurcation of the nonlinear

Neoclassical transport including collisional nonlinearity.

PubMed

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.

Shoaling of nonlinear internal waves in Massachusetts Bay

USGS Publications Warehouse

Scotti, A.; Beardsley, R.C.; Butman, B.; Pineda, J.

2008-01-01

The shoaling of the nonlinear internal tide in Massachusetts Bay is studied with a fully nonlinear and nonhydrostatic model. The results are compared with current and temperature observations obtained during the August 1998 Massachusetts Bay Internal Wave Experiment and observations from a shorter experiment which took place in September 2001. The model shows how the approaching nonlinear undular bore interacts strongly with a shoaling bottom, offshore of where KdV theory predicts polarity switching should occur. It is shown that the shoaling process is dominated by nonlinearity, and the model results are interpreted with the aid of a two-layer nonlinear but hydrostatic model. After interacting with the shoaling bottom, the undular bore emerges on the shallow shelf inshore of the 30-m isobath as a nonlinear internal tide with a range of possible shapes, all of which are found in the available observational record. Copyright 2008 by the American Geophysical Union.

A theoretical and experimental investigation of nonlinear propagation of ultrasound through tissue mimicking media

NASA Astrophysics Data System (ADS)

Rielly, Matthew Robert

An existing numerical model (known as the Bergen code) is used to investigate finite amplitude ultrasound propagation through multiple layers of tissue-like media. This model uses a finite difference method to solve the nonlinear parabolic KZK wave equation. The code is modified to include an arbitrary frequency dependence of absorption and transmission effects for wave propagation across a plane interface at normal incidence. In addition the code is adapted to calculate the total intensity loss associated with the absorption of the fundamental and nonlinearly generated harmonics. Measurements are also taken of the axial nonlinear pressure field generated from a circular focused, 2.25 MHz source, through single and multiple layered tissue mimicking fluids, for source pressures in the range from 13 kPa to 310 kPa. Two tissue mimicking fluids are developed to provide acoustic properties similar to amniotic fluid and a typical soft tissue. The values of the nonlinearity parameter, sound velocity and frequency dependence of attenuation for both fluids are presented, and the measurement procedures employed to obtain these characteristics are described in detail. These acoustic parameters, together with the measured source conditions are used as input to the numerical model, allowing the experimental conditions to be simulated. Extensive comparisons are made between the model's predictions and the axial pressure field measurements. Results are presented in the frequency domain showing the fundamental and three subsequent harmonic amplitudes on axis, as a function of axial distance. These show that significant nonlinear distortion can occur through media with characteristics typical of tissue. Time domain waveform comparisons are also made. An excellent agreement is found between theory and experiment indicating that the model can be used to predict nonlinear ultrasound propagation through multiple layers of tissue-like media. The numerical code is also used to model the

Nonlinear oscillator with power-form elastic-term: Fourier series expansion of the exact solution

NASA Astrophysics Data System (ADS)

Beléndez, Augusto; Francés, Jorge; Beléndez, Tarsicio; Bleda, Sergio; Pascual, Carolina; Arribas, Enrique

2015-05-01

A family of conservative, truly nonlinear, oscillators with integer or non-integer order nonlinearity is considered. These oscillators have only one odd power-form elastic-term and exact expressions for their period and solution were found in terms of Gamma functions and a cosine-Ateb function, respectively. Only for a few values of the order of nonlinearity, is it possible to obtain the periodic solution in terms of more common functions. However, for this family of conservative truly nonlinear oscillators we show in this paper that it is possible to obtain the Fourier series expansion of the exact solution, even though this exact solution is unknown. The coefficients of the Fourier series expansion of the exact solution are obtained as an integral expression in which a regularized incomplete Beta function appears. These coefficients are a function of the order of nonlinearity only and are computed numerically. One application of this technique is to compare the amplitudes for the different harmonics of the solution obtained using approximate methods with the exact ones computed numerically as shown in this paper. As an example, the approximate amplitudes obtained via a modified Ritz method are compared with the exact ones computed numerically.

Block distributions on the lunar surface: A comparison between measurements obtained from surface and orbital photography

NASA Technical Reports Server (NTRS)

Cintala, Mark J.; Mcbride, Kathleen M.

1995-01-01

Among the hazards that must be negotiated by lunar-landing spacecraft are blocks on the surface of the Moon. Unfortunately, few data exist that can be used to evaluate the threat posed by such blocks to landing spacecraft. Perhaps the best information is that obtained from Surveyor photographs, but those data do not extend to the dimensions of the large blocks that would pose the greatest hazards. Block distributions in the vicinities of the Surveyor 1, 3, 6, and 7 sites have been determined from Lunar Orbiter photography and are presented here. Only large (i.e., greater than or equal to 2.5 m) blocks are measurable in these pictures, resulting in a size gap between the Surveyor and Lunar Orbiter distributions. Nevertheless, the orbital data are self-consistent, a claim supported by the similarity in behavior between the subsets of data from the Surveyor 1, 3, and 6 sites and by the good agreement in position (if not slopes) between the data obtained from the Surveyor 3 photography and those derived from the Lunar Orbiter photographs. Confidence in the results is also justified by the well-behaved distribution of large blocks at the surveyor site. Comparisons between the Surveyor distributions and those derived from the orbital photography permit these observations: (1) in all cases but that for Surveyor 3, the density of large blocks is overestimated by extrapolation of the Surveyor-derived trends; (2) the slopes of the Surveyor-derived distributions are consistently lower than those determined for the large blocks; and (3) these apparent disagreements could be mitigated if the overall shapes of the cumulative lunar block populations were nonlinear, allowing for different slopes over different size intervals. The relatively large gaps between the Surveyor-derived and Orbiter-derived data sets, however, do not permit a determination of those shapes.

Development and field application of a nonlinear ultrasonic modulation technique for fatigue crack detection without reference data from an intact condition

NASA Astrophysics Data System (ADS)

Lim, Hyung Jin; Kim, Yongtak; Koo, Gunhee; Yang, Suyoung; Sohn, Hoon; Bae, In-hwan; Jang, Jeong-Hwan

2016-09-01

In this study, a fatigue crack detection technique, which detects a fatigue crack without relying on any reference data obtained from the intact condition of a target structure, is developed using nonlinear ultrasonic modulation and applied to a real bridge structure. Using two wafer-type lead zirconate titanate (PZT) transducers, ultrasonic excitations at two distinctive frequencies are applied to a target inspection spot and the corresponding ultrasonic response is measured by another PZT transducer. Then, the nonlinear modulation components produced by a breathing-crack are extracted from the measured ultrasonic response, and a statistical classifier, which can determine if the nonlinear modulation components are statistically significant in comparison with the background noise level, is proposed. The effectiveness of the proposed fatigue crack detection technique is experimentally validated using the data obtained from aluminum plates and aircraft fitting-lug specimens under varying temperature and loading conditions, and through a field testing of Yeongjong Grand Bridge in South Korea. The uniqueness of this study lies in that (1) detection of a micro fatigue crack with less than 1 μm width and fatigue cracks in the range of 10-20 μm in width using nonlinear ultrasonic modulation, (2) automated detection of fatigue crack formation without using reference data obtained from an intact condition, (3) reliable and robust diagnosis under varying temperature and loading conditions, (4) application of a local fatigue crack detection technique to online monitoring of a real bridge.

Robust Nonlinear Neural Codes

NASA Astrophysics Data System (ADS)

Yang, Qianli; Pitkow, Xaq

2015-03-01

Most interesting natural sensory stimuli are encoded in the brain in a form that can only be decoded nonlinearly. But despite being a core function of the brain, nonlinear population codes are rarely studied and poorly understood. Interestingly, the few existing models of nonlinear codes are inconsistent with known architectural features of the brain. In particular, these codes have information content that scales with the size of the cortical population, even if that violates the data processing inequality by exceeding the amount of information entering the sensory system. Here we provide a valid theory of nonlinear population codes by generalizing recent work on information-limiting correlations in linear population codes. Although these generalized, nonlinear information-limiting correlations bound the performance of any decoder, they also make decoding more robust to suboptimal computation, allowing many suboptimal decoders to achieve nearly the same efficiency as an optimal decoder. Although these correlations are extremely difficult to measure directly, particularly for nonlinear codes, we provide a simple, practical test by which one can use choice-related activity in small populations of neurons to determine whether decoding is suboptimal or optimal and limited by correlated noise. We conclude by describing an example computation in the vestibular system where this theory applies. QY and XP was supported by a grant from the McNair foundation.

Homogenized description and retrieval method of nonlinear metasurfaces

NASA Astrophysics Data System (ADS)

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

Nonlinear optical response in narrow graphene nanoribbons

NASA Astrophysics Data System (ADS)

Karimi, Farhad; Knezevic, Irena

We present an iterative method to calculate the nonlinear optical response of armchair graphene nanoribbons (aGNRs) and zigzag graphene nanoribbons (zGNRs) while including the effects of dissipation. In contrast to methods that calculate the nonlinear response in the ballistic (dissipation-free) regime, here we obtain the nonlinear response of an electronic system to an external electromagnetic field while interacting with a dissipative environment (to second order). We use a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations, and we solve the master equation iteratively to obtain the higher-order response functions. We employ the SCF-MMEF to calculate the nonlinear conductance and susceptibility, as well as to calculate the dependence of the plasmon dispersion and plasmon propagation length on the intensity of the electromagnetic field in GNRs. The electron scattering mechanisms included in this work are scattering with intrinsic phonons, ionized impurities, surface optical phonons, and line-edge roughness. Unlike in wide GNRs, where ionized-impurity scattering dominates dissipation, in ultra-narrow nanoribbons on polar substrates optical-phonon scattering and ionized-impurity scattering are equally prominent. Support by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0008712.

Single-point nonlinearity indicators for the propagation of high-amplitude acoustic signals

NASA Astrophysics Data System (ADS)

Falco, Lauren E.

. Both single-frequency signals and band-limited noise were used as sources, and waveforms were recorded at all four propagation distances. The second set of data was obtained at the model-scale jet facility at the University of Mississippi's National Center for Physical Acoustics. A computer controlled microphone boom was constructed to hold an array of six microphones. The array was rotated about the presumed location of the acoustic source center (4 jet diameters downstream of the nozzle exit), and two stationary microphones were mounted on the walls. Measurements were made for several jet conditions; data presented here represent Mach 0.85 and Mach 2 conditions. Application of the four candidate nonlinearity indicators to the experimental data reveals that each indicator has advantages and disadvantages. Qneg/Qpos does not detect the presence of shocks as postulated, but it does conform to expectations in the shock-free region and support the use of Qpos as an indicator. The main advantage of Qpos/p3rms is that it can be used for band-limited measurements. Increased indicator values are seen for signals with higher source frequencies and amplitudes that are expected to undergo stronger nonlinear evolution. However, no physical meaning can yet be derived from the numerical value of the indicator. The spectral Gol'dberg number Gammas is the most promising of the candidate quantities. It has the ability to indicate the direction of nonlinear energy transfer as well as provide a comparison between the strengths of linear and nonlinear effects. These attributes allow it to be used to qualitatively predict the evolution of a spectrum. The coherence indicator gammaQ also specifies the direction of nonlinear energy transfer, but its numerical value holds less meaning. However, it is bounded between -1 and 1, so values near zero denote very weak or no nonlinearity, and values near -1 or 1 denote strong nonlinearity. Further, because it is bounded, it does not become unstable

Measurement of the third order non-linearity of gold-graphene hybrid nanocomposite for near-infrared wavelengths

NASA Astrophysics Data System (ADS)

Syed, Salmaan R.; Lim, Guh-Hwan; Lim, Byungkwon; Chon, James W. M.

2016-04-01

We present measurements of nonlinear refraction (NLR) and nonlinear absorption (NLA) of single crystalline gold nanosheets (single crystalline-GNSs) and sputter coated polycrystalline thin gold metal film hybridized with multilayer grapheme (MLG) using Z-Scan technique for near-infrared wavelengths (NIR) ranging from 700 nm to 900 nm. Single crystalline GNSs of 20 nm thickness were prepared through chemical synthesis. MLG was found to have few monolayers of graphene, usually between 1-7 layers with an average of 4 monolayer thickness. The composite of GNSs and MLG was prepared by drop casting GNSs on MLG. Z-Scan experimental was carried out using Ti:sapphire femtosecond pulsed laser (700 nm - 900 nm wavelength, 115-130 fs pulse width and 0.82 MHz-82 MHz repetition rate). Intensity dependence on open aperture Z-scan was studied in detail for all materials. The NLA of polycrystalline thin gold metal film was found to be fractionally higher than that of single crystalline-GNSs. This is thought to be due to field enhancement around of gold islands formed on polycrystalline thin gold metal film during sputtering process. At higher repetition rates NLA phenomenon is diminished due to the temperature accumulation effect. As the repetition rate decreases the nonlinear effect is enhanced. On the other hand MLG exhibited saturable absorption (NSA) . Z-Scan results for single crystalline and poly crystalline gold-MLG nanocomposite exhibit NSA characteristics. The measured NSA coefficient `α' was found to be approximately ≍1.7×10-5-4.5×10-5 cmW-1 which is lower than that of MLG, clearly demonstrating the effect of hybridization.

A nonlinear analysis of the transport Barkhausen-like noise measured in (Bi,Pb)2Sr2Ca2Cu3O10+δ superconductors

NASA Astrophysics Data System (ADS)

García-Fornaris, I.; Millán, H.; Jardim, R. F.; Govea-Alcaide, E.

2013-06-01

We investigated the transport Barkhausen-like noise (TBN) by using nonlinear time series analysis. TBN signals were measured in (Bi,Pb)2Sr2Ca2Cu3O10+δ ceramic samples subjected to different uniaxial compacting pressures (UCP). These samples display similar intragranular properties but different intergranular features. We found positive Lyapunov exponents in all samples, λm≥0.062, indicating the nonlinear dynamics of the experimental TBN signals. It was also observed higher values of the embedding dimension, m >9, and the Kaplan-Yorke dimension, DKY>2.9. Between samples, the behavior of λm and DKY with increasing excitation current is quite different. Such a behavior is explained in terms of changes in the microstructure associated with the UCP. In addition, determinism tests indicated that the TBN masked determinist components, as inferred by |k →| values larger than 0.70 in most of the cases. Evidence on the existence of empirical attractors by reconstructing the phase spaces has been also found. All obtained results are useful indicators of the interplay between the uniaxial compacting pressure, differences in the microstructure of the samples, and the TBN signal dynamics.

Broadband Energy Harvester Using Non-linear Polymer Spring and Electromagnetic/Triboelectric Hybrid Mechanism

PubMed Central

Gupta, Rahul Kumar; Shi, Qiongfeng; Dhakar, Lokesh; Wang, Tao; Heng, Chun Huat; Lee, Chengkuo

2017-01-01

Over the years, several approaches have been devised to widen the operating bandwidth, but most of them can only be triggered at high accelerations. In this work, we investigate a broadband energy harvester based on combination of non-linear stiffening effect and multimodal energy harvesting to obtain high bandwidth over wide range of accelerations (0.1 g–2.0 g). In order to achieve broadband behavior, a polymer based spring exhibiting multimodal energy harvesting is used. Besides, non-linear stiffening effect is introduced by using mechanical stoppers. At low accelerations (<0.5 g), the nearby mode frequencies of polymer spring contribute to broadening characteristics, while proof mass engages with mechanical stoppers to introduce broadening by non-linear stiffening at higher accelerations. The electromagnetic mechanism is employed in this design to enhance its output at low accelerations when triboelectric output is negligible. Our device displays bandwidth of 40 Hz even at low acceleration of 0.1 g and it is increased up to 68 Hz at 2 g. When non-linear stiffening is used along with multimodal energy-harvesting, the obtained bandwidth increases from 23 Hz to 68 Hz with percentage increment of 295% at 1.8 g. Further, we have demonstrated the triboelectric output measured as acceleration sensing signals in terms of voltage and current sensitivity of 4.7 Vg−1 and 19.7 nAg−1, respectively. PMID:28120924

Broadband Energy Harvester Using Non-linear Polymer Spring and Electromagnetic/Triboelectric Hybrid Mechanism

NASA Astrophysics Data System (ADS)

Gupta, Rahul Kumar; Shi, Qiongfeng; Dhakar, Lokesh; Wang, Tao; Heng, Chun Huat; Lee, Chengkuo

2017-01-01

Over the years, several approaches have been devised to widen the operating bandwidth, but most of them can only be triggered at high accelerations. In this work, we investigate a broadband energy harvester based on combination of non-linear stiffening effect and multimodal energy harvesting to obtain high bandwidth over wide range of accelerations (0.1 g-2.0 g). In order to achieve broadband behavior, a polymer based spring exhibiting multimodal energy harvesting is used. Besides, non-linear stiffening effect is introduced by using mechanical stoppers. At low accelerations (<0.5 g), the nearby mode frequencies of polymer spring contribute to broadening characteristics, while proof mass engages with mechanical stoppers to introduce broadening by non-linear stiffening at higher accelerations. The electromagnetic mechanism is employed in this design to enhance its output at low accelerations when triboelectric output is negligible. Our device displays bandwidth of 40 Hz even at low acceleration of 0.1 g and it is increased up to 68 Hz at 2 g. When non-linear stiffening is used along with multimodal energy-harvesting, the obtained bandwidth increases from 23 Hz to 68 Hz with percentage increment of 295% at 1.8 g. Further, we have demonstrated the triboelectric output measured as acceleration sensing signals in terms of voltage and current sensitivity of 4.7 Vg-1 and 19.7 nAg-1, respectively.

Determination of power system component parameters using nonlinear dead beat estimation method

NASA Astrophysics Data System (ADS)

Kolluru, Lakshmi

Power systems are considered the most complex man-made wonders in existence today. In order to effectively supply the ever increasing demands of the consumers, power systems are required to remain stable at all times. Stability and monitoring of these complex systems are achieved by strategically placed computerized control centers. State and parameter estimation is an integral part of these facilities, as they deal with identifying the unknown states and/or parameters of the systems. Advancements in measurement technologies and the introduction of phasor measurement units (PMU) provide detailed and dynamic information of all measurements. Accurate availability of dynamic measurements provides engineers the opportunity to expand and explore various possibilities in power system dynamic analysis/control. This thesis discusses the development of a parameter determination algorithm for nonlinear power systems, using dynamic data obtained from local measurements. The proposed algorithm was developed by observing the dead beat estimator used in state space estimation of linear systems. The dead beat estimator is considered to be very effective as it is capable of obtaining the required results in a fixed number of steps. The number of steps required is related to the order of the system and the number of parameters to be estimated. The proposed algorithm uses the idea of dead beat estimator and nonlinear finite difference methods to create an algorithm which is user friendly and can determine the parameters fairly accurately and effectively. The proposed algorithm is based on a deterministic approach, which uses dynamic data and mathematical models of power system components to determine the unknown parameters. The effectiveness of the algorithm is tested by implementing it to identify the unknown parameters of a synchronous machine. MATLAB environment is used to create three test cases for dynamic analysis of the system with assumed known parameters. Faults are

Shake, Rattle, and Roll: Nonlinear Dynamics in Mechanical Engineering

NASA Astrophysics Data System (ADS)

Shaw, Steven

1997-03-01

This presentation will focus on three mechanical engineering applications in which methods from nonlinear dynamics have been applied with success. Each topic will be briefly surveyed by outlining the development of a mathematical model, providing a description of the analysis tools employed, and showing the main results obtained. The applications are: vibration reduction in internal combustion engines, impact dynamics of mechanical components, and the dynamics of ship capsize. The first topic demonstrates a novel arrangement of dynamic absorbers that can be used for attenuating torsional vibrations in rotating machinery. The operation of this device takes advantage of a purely nonlinear system response that results from a period doubling bifurcation. This configuration is more effective than existing absorbers and it cannot be imagined by using naive extensions of linear vibration theory. The second topic deals with the dynamics of mechanical systems in which components make intermittent contact with each another. Such dynamics are often the source of undesirable noise and wear in machinery and can be extremely complicated. Results obtained from simple predictive models and some application areas will be presented for these impacting systems. The final topic deals with the gross motions of seagoing vessels and their stability against capsize. Existing safety regulations for ship stability are based on purely static measures, whereas capsize is an inherently nonlinear dynamic event. An overview will be given that considers some basic modeling issues, dynamic analysis techniques (based on the concept of chaotic phase-space transport), and the resulting predictive tools that have been developed for this class of problems.

Determination of Magnetic Parameters of Maghemite (γ-Fe2O3) Core-Shell Nanoparticles from Nonlinear Magnetic Susceptibility Measurements

NASA Astrophysics Data System (ADS)

Syvorotka, Ihor I.; Pavlyk, Lyubomyr P.; Ubizskii, Sergii B.; Buryy, Oleg A.; Savytskyy, Hrygoriy V.; Mitina, Nataliya Y.; Zaichenko, Oleksandr S.

2017-04-01

Method of determining of magnetic moment and size from measurements of dependence of the nonlinear magnetic susceptibility upon magnetic field is proposed, substantiated and tested for superparamagnetic nanoparticles (SPNP) of the "magnetic core-polymer shell" type which are widely used in biomedical technologies. The model of the induction response of the SPNP ensemble on the combined action of the magnetic harmonic excitation field and permanent bias field is built, and the analysis of possible ways to determine the magnetic moment and size of the nanoparticles as well as the parameters of the distribution of these variables is performed. Experimental verification of the proposed method was implemented on samples of SPNP with maghemite core in dry form as well as in colloidal systems. The results have been compared with the data obtained by other methods. Advantages of the proposed method are analyzed and discussed, particularly in terms of its suitability for routine express testing of SPNP for biomedical technology.

Bound-Electron Nonlinearity Beyond the Ionization Threshold.

PubMed

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

2018-05-04

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.

Bound-Electron Nonlinearity Beyond the Ionization Threshold

NASA Astrophysics Data System (ADS)

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.

On measurement of the acoustic nonlinearity parameter using the finite amplitude insertion substitution (FAIS) technique

NASA Astrophysics Data System (ADS)

Zeqiri, Bajram; Cook, Ashley; Rétat, Lise; Civale, John; ter Haar, Gail

2015-04-01

The acoustic nonlinearity parameter, B/A, is an important parameter which defines the way a propagating finite amplitude acoustic wave progressively distorts when travelling through any medium. One measurement technique used to determine its value is the finite amplitude insertion substitution (FAIS) method which has been applied to a range of liquid, tissue and tissue-like media. Importantly, in terms of the achievable measurement uncertainties, it is a relative technique. This paper presents a detailed study of the method, employing a number of novel features. The first of these is the use of a large area membrane hydrophone (30 mm aperture) which is used to record the plane-wave component of the acoustic field. This reduces the influence of diffraction on measurements, enabling studies to be carried out within the transducer near-field, with the interrogating transducer, test cell and detector positioned close to one another, an attribute which assists in controlling errors arising from nonlinear distortion in any intervening water path. The second feature is the development of a model which estimates the influence of finite-amplitude distortion as the acoustic wave travels from the rear surface of the test cell to the detector. It is demonstrated that this can lead to a significant systematic error in B/A measurement whose magnitude and direction depends on the acoustic property contrast between the test material and the water-filled equivalent cell. Good qualitative agreement between the model and experiment is reported. B/A measurements are reported undertaken at (20 ± 0.5) °C for two fluids commonly employed as reference materials within the technical literature: Corn Oil and Ethylene Glycol. Samples of an IEC standardised agar-based tissue-mimicking material were also measured. A systematic assessment of measurement uncertainties is presented giving expanded uncertainties in the range ±7% to ±14%, expressed at a confidence level close to 95

Localization of Stable and Chaotic Nonpropagating Structures in Nonlinear Mesoscopic Lattices.

NASA Astrophysics Data System (ADS)

Greenfield, Alan Barry

Recent developments in the study of non-linear localized states, especially non-propagating ones, are outlined. Theoretical models of linear and nonlinear states in a lattice of coupled pendulums and related systems are reviewed. Particular attention is paid to those states which can be described by the Nonlinear Schrodinger equation as well as states where two modes can coexist and states exhibiting chaos. Measurement of localized stable and chaotic states in a 35 site physical pendulum lattice is reported. Various measurement techniques that were used are explained. States that were measured include the tanh profile or kink soliton, and the corresponding uniform state in the wavelength 2 mode, a similar soliton and uniform state in the wavelength 4 mode, a domain wall between the wavelength 2 and 4 modes and a domain wall between a chaotic state and the wavelength 2 mode. Amplitude profiles were measured for the stable kink and domain wall states and smooth curves were obtained by dividing the kink states by the corresponding uniform states. Return maps were measured for two sites in the chaotic domain wall. Simulation of a chaotic domain wall in a 50 site numerical lattice is reported. This system has the advantage that its parameters can be modified much more easily than those of the physical lattice. An attempt is made at quantifying the level of chaos as a function of lattice site with fractal dimension calculations on return maps embedded in a three dimensional space. The drive plane of the chaotic domain wall is mapped out in the drive amplitude - drive frequency plane. Transitions to various stable and quasiperiodic domain walls are noted.

Grey-box state-space identification of nonlinear mechanical vibrations

NASA Astrophysics Data System (ADS)

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.

Nonlinear wave chaos: statistics of second harmonic fields.

PubMed

Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M

2017-10-01

Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.

Nonlinear structural joint model updating based on instantaneous characteristics of dynamic responses

NASA Astrophysics Data System (ADS)

Wang, Zuo-Cai; Xin, Yu; Ren, Wei-Xin

2016-08-01

This paper proposes a new nonlinear joint model updating method for shear type structures based on the instantaneous characteristics of the decomposed structural dynamic responses. To obtain an accurate representation of a nonlinear system's dynamics, the nonlinear joint model is described as the nonlinear spring element with bilinear stiffness. The instantaneous frequencies and amplitudes of the decomposed mono-component are first extracted by the analytical mode decomposition (AMD) method. Then, an objective function based on the residuals of the instantaneous frequencies and amplitudes between the experimental structure and the nonlinear model is created for the nonlinear joint model updating. The optimal values of the nonlinear joint model parameters are obtained by minimizing the objective function using the simulated annealing global optimization method. To validate the effectiveness of the proposed method, a single-story shear type structure subjected to earthquake and harmonic excitations is simulated as a numerical example. Then, a beam structure with multiple local nonlinear elements subjected to earthquake excitation is also simulated. The nonlinear beam structure is updated based on the global and local model using the proposed method. The results show that the proposed local nonlinear model updating method is more effective for structures with multiple local nonlinear elements. Finally, the proposed method is verified by the shake table test of a real high voltage switch structure. The accuracy of the proposed method is quantified both in numerical and experimental applications using the defined error indices. Both the numerical and experimental results have shown that the proposed method can effectively update the nonlinear joint model.

Fully Nonlinear Modeling and Analysis of Precision Membranes

NASA Technical Reports Server (NTRS)

Pai, P. Frank; Young, Leyland G.

2003-01-01

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

Nonlinear programming extensions to rational function approximations of unsteady aerodynamics

NASA Technical Reports Server (NTRS)

Tiffany, Sherwood H.; Adams, William M., Jr.

1987-01-01

This paper deals with approximating unsteady generalized aerodynamic forces in the equations of motion of a flexible aircraft. Two methods of formulating these approximations are extended to include both the same flexibility in constraining them and the same methodology in optimizing nonlinear parameters as another currently used 'extended least-squares' method. Optimal selection of 'nonlinear' parameters is made in each of the three methods by use of the same nonlinear (nongradient) optimizer. The objective of the nonlinear optimization is to obtain rational approximations to the unsteady aerodynamics whose state-space realization is of lower order than that required when no optimization of the nonlinear terms is performed. The free 'linear' parameters are determined using least-squares matrix techniques on a Lagrange multiplier formulation of an objective function which incorporates selected linear equality constraints. State-space mathematical models resulting from the different approaches are described, and results are presented which show comparative evaluations from application of each of the extended methods to a numerical example. The results obtained for the example problem show a significant (up to 63 percent) reduction in the number of differential equations used to represent the unsteady aerodynamic forces in linear time-invariant equations of motion as compared to a conventional method in which nonlinear terms are not optimized.

Modulational instability and discrete breathers in a nonlinear helicoidal lattice model

NASA Astrophysics Data System (ADS)

Ding, Jinmin; Wu, Tianle; Chang, Xia; Tang, Bing

2018-06-01

We investigate the problem on the discrete modulation instability of plane waves and discrete breather modes in a nonlinear helicoidal lattice model, which is described by a discrete nonlinear Schrödinger equation with the first-, second-, and third-neighbor coupling. By means of the linear stability analysis, we present an analytical expression of the instability growth rate and identify the regions of modulational instability of plane waves. It is shown that the introduction of the third-neighbor coupling will affect the shape of the areas of modulational instability significantly. Based on the results obtained by the modulational instability analysis, we predict the existence conditions for the stationary breather modes. Otherwise, by making use of the semidiscrete multiple-scale method, we obtain analytical solutions of discrete breather modes and analyze their properties for different types of nonlinearities. Our results show that the discrete breathers obtained are stable for a long time only when the system exhibits the repulsive nonlinearity. In addition, it is found that the existence of the stable bright discrete breather closely relates to the presence of the third-neighbor coupling.

Measurement of attenuation coefficients of the fundamental and second harmonic waves in water

NASA Astrophysics Data System (ADS)

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

2016-02-01

Attenuation corrections in nonlinear acoustics play an important role in the study of nonlinear fluids, biomedical imaging, or solid material characterization. The measurement of attenuation coefficients in a nonlinear regime is not easy because they depend on the source pressure and requires accurate diffraction corrections. In this work, the attenuation coefficients of the fundamental and second harmonic waves which come from the absorption of water are measured in nonlinear ultrasonic experiments. Based on the quasilinear theory of the KZK equation, the nonlinear sound field equations are derived and the diffraction correction terms are extracted. The measured sound pressure amplitudes are adjusted first for diffraction corrections in order to reduce the impact on the measurement of attenuation coefficients from diffractions. The attenuation coefficients of the fundamental and second harmonics are calculated precisely from a nonlinear least squares curve-fitting process of the experiment data. The results show that attenuation coefficients in a nonlinear condition depend on both frequency and source pressure, which are much different from a linear regime. In a relatively lower drive pressure, the attenuation coefficients increase linearly with frequency. However, they present the characteristic of nonlinear growth in a high drive pressure. As the diffraction corrections are obtained based on the quasilinear theory, it is important to use an appropriate source pressure for accurate attenuation measurements.

Condition assessment of nonlinear processes

DOEpatents

Hively, Lee M.; Gailey, Paul C.; Protopopescu, Vladimir A.

2002-01-01

There is presented a reliable technique for measuring condition change in nonlinear data such as brain waves. The nonlinear data is filtered and discretized into windowed data sets. The system dynamics within each data set is represented by a sequence of connected phase-space points, and for each data set a distribution function is derived. New metrics are introduced that evaluate the distance between distribution functions. The metrics are properly renormalized to provide robust and sensitive relative measures of condition change. As an example, these measures can be used on EEG data, to provide timely discrimination between normal, preseizure, seizure, and post-seizure states in epileptic patients. Apparatus utilizing hardware or software to perform the method and provide an indicative output is also disclosed.

White light Z-scan measurements of ultrafast optical nonlinearity in reduced graphene oxide nanosheets in the 400–700 nm region

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

Perumbilavil, Sreekanth; Sankar, Pranitha; Priya Rose, T.

Wavelength dispersion of optical power limiting is an important factor to be considered while designing potential optical limiters for laser safety applications. We report the observation of broadband, ultrafast optical limiting in reduced graphene oxide (rGO), measured by a single open aperture Z-scan using a white light continuum (WLC) source. WLC Z-scan is fast when the nonlinearity is to be measured over broad wavelength ranges, and it obviates the need for an ultrafast tunable laser making it cost-economic compared to conventional Z-scan. The nonlinearity arises from nondegenerate two-photon absorption, owing mostly to the crystallinity and extended π conjugation of rGO.

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

PubMed

Petrov, E Yu; Kudrin, A V

2010-05-14

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

Nonlinear Terahertz Absorption of Graphene Plasmons.

PubMed

Jadidi, Mohammad M; König-Otto, Jacob C; Winnerl, Stephan; Sushkov, Andrei B; Drew, H Dennis; Murphy, Thomas E; Mittendorff, Martin

2016-04-13

Subwavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, subwavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanoribbons. We employ a terahertz pump-terahertz probe technique at the plasmon frequency and observe a strong saturation of plasmon absorption followed by a 10 ps relaxation time. The observed nonlinearity is enhanced by 2 orders of magnitude compared to unpatterned graphene with no plasmon resonance. We further present a thermal model for the nonlinear plasmonic absorption that supports the experimental results. The model shows that the observed strong linearity is caused by an unexpected red shift of plasmon resonance together with a broadening and weakening of the resonance caused by the transient increase in electron temperature. The model further predicts that even greater resonant enhancement of the nonlinear response can be expected in high-mobility graphene, suggesting that nonlinear graphene plasmonic devices could be promising candidates for nonlinear optical processing.

Using waveform information in nonlinear data assimilation

NASA Astrophysics Data System (ADS)

Rey, Daniel; Eldridge, Michael; Morone, Uriel; Abarbanel, Henry D. I.; Parlitz, Ulrich; Schumann-Bischoff, Jan

2014-12-01

Information in measurements of a nonlinear dynamical system can be transferred to a quantitative model of the observed system to establish its fixed parameters and unobserved state variables. After this learning period is complete, one may predict the model response to new forces and, when successful, these predictions will match additional observations. This adjustment process encounters problems when the model is nonlinear and chaotic because dynamical instability impedes the transfer of information from the data to the model when the number of measurements at each observation time is insufficient. We discuss the use of information in the waveform of the data, realized through a time delayed collection of measurements, to provide additional stability and accuracy to this search procedure. Several examples are explored, including a few familiar nonlinear dynamical systems and small networks of Colpitts oscillators.

Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems.

PubMed

Mei, Jie; Ren, Wei; Li, Bing; Ma, Guangfu

2015-09-01

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

Ultrasound coefficient of nonlinearity imaging.

PubMed

van Sloun, Ruud; Demi, Libertario; Shan, Caifeng; Mischi, Massimo

2015-07-01

Imaging the acoustical coefficient of nonlinearity, β, is of interest in several healthcare interventional applications. It is an important feature that can be used for discriminating tissues. In this paper, we propose a nonlinearity characterization method with the goal of locally estimating the coefficient of nonlinearity. The proposed method is based on a 1-D solution of the nonlinear lossy Westerfelt equation, thereby deriving a local relation between β and the pressure wave field. Based on several assumptions, a β imaging method is then presented that is based on the ratio between the harmonic and fundamental fields, thereby reducing the effect of spatial amplitude variations of the speckle pattern. By testing the method on simulated ultrasound pressure fields and an in vitro B-mode ultrasound acquisition, we show that the designed algorithm is able to estimate the coefficient of nonlinearity, and that the tissue types of interest are well discriminable. The proposed imaging method provides a new approach to β estimation, not requiring a special measurement setup or transducer, that seems particularly promising for in vivo imaging.

Nonlinear viscosity in brane-world cosmology with a Gauss–Bonnet term

NASA Astrophysics Data System (ADS)

Debnath, P. S.; Beesham, A.; Paul, B. C.

2018-06-01

Cosmological solutions are obtained with nonlinear bulk viscous cosmological fluid in the Randall–Sundrum type II (RS) brane-world model with or without Gauss–Bonnet (GB) terms. To describe such a viscous fluid, we consider the nonlinear transport equation which may be used far from equilibrium during inflation or reheating. Cosmological models are explored for both (i) power law and (ii) exponential evolution of the early universe in the presence of an imperfect fluid described by the non-linear Israel and Stewart theory (nIS). We obtain analytic solutions and the complex field equations are also analyzed numerically to study the evolution of the universe. The stability analysis of the equilibrium points of the dynamical system associated with the evolution of the nonlinear bulk viscous fluid in the RS Brane in the presence (or absence) of a GB term are also studied.

Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

PubMed

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

2018-01-01

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

Graphene-clad tapered fiber: effective nonlinearity and propagation losses.

PubMed

Gorbach, A V; Marini, A; Skryabin, D V

2013-12-15

We derive a pulse propagation equation for a graphene-clad optical fiber, treating the optical response of the graphene and nonlinearity of the dielectric fiber core as perturbations in asymptotic expansion of Maxwell equations. We analyze the effective nonlinear and attenuation coefficients due to the graphene layer. Based on the recent experimental measurements of the nonlinear graphene conductivity, we predict considerable enhancement of the effective nonlinearity for subwavelength fiber core diameters.

Evaluation of a physically based quasi-linear and a conceptually based nonlinear Muskingum methods

NASA Astrophysics Data System (ADS)

Perumal, Muthiah; Tayfur, Gokmen; Rao, C. Madhusudana; Gurarslan, Gurhan

2017-03-01

Two variants of the Muskingum flood routing method formulated for accounting nonlinearity of the channel routing process are investigated in this study. These variant methods are: (1) The three-parameter conceptual Nonlinear Muskingum (NLM) method advocated by Gillin 1978, and (2) The Variable Parameter McCarthy-Muskingum (VPMM) method recently proposed by Perumal and Price in 2013. The VPMM method does not require rigorous calibration and validation procedures as required in the case of NLM method due to established relationships of its parameters with flow and channel characteristics based on hydrodynamic principles. The parameters of the conceptual nonlinear storage equation used in the NLM method were calibrated using the Artificial Intelligence Application (AIA) techniques, such as the Genetic Algorithm (GA), the Differential Evolution (DE), the Particle Swarm Optimization (PSO) and the Harmony Search (HS). The calibration was carried out on a given set of hypothetical flood events obtained by routing a given inflow hydrograph in a set of 40 km length prismatic channel reaches using the Saint-Venant (SV) equations. The validation of the calibrated NLM method was investigated using a different set of hypothetical flood hydrographs obtained in the same set of channel reaches used for calibration studies. Both the sets of solutions obtained in the calibration and validation cases using the NLM method were compared with the corresponding solutions of the VPMM method based on some pertinent evaluation measures. The results of the study reveal that the physically based VPMM method is capable of accounting for nonlinear characteristics of flood wave movement better than the conceptually based NLM method which requires the use of tedious calibration and validation procedures.

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

Nonlinear random response prediction using MSC/NASTRAN

NASA Technical Reports Server (NTRS)

Robinson, J. H.; Chiang, C. K.; Rizzi, S. A.

1993-01-01

An equivalent linearization technique was incorporated into MSC/NASTRAN to predict the nonlinear random response of structures by means of Direct Matrix Abstract Programming (DMAP) modifications and inclusion of the nonlinear differential stiffness module inside the iteration loop. An iterative process was used to determine the rms displacements. Numerical results obtained for validation on simple plates and beams are in good agreement with existing solutions in both the linear and linearized regions. The versatility of the implementation will enable the analyst to determine the nonlinear random responses for complex structures under combined loads. The thermo-acoustic response of a hexagonal thermal protection system panel is used to highlight some of the features of the program.

Estimating linear-nonlinear models using Rényi divergences

PubMed Central

Kouh, Minjoon; Sharpee, Tatyana O.

2009-01-01

This paper compares a family of methods for characterizing neural feature selectivity using natural stimuli in the framework of the linear-nonlinear model. In this model, the spike probability depends in a nonlinear way on a small number of stimulus dimensions. The relevant stimulus dimensions can be found by optimizing a Rényi divergence that quantifies a change in the stimulus distribution associated with the arrival of single spikes. Generally, good reconstructions can be obtained based on optimization of Rényi divergence of any order, even in the limit of small numbers of spikes. However, the smallest error is obtained when the Rényi divergence of order 1 is optimized. This type of optimization is equivalent to information maximization, and is shown to saturate the Cramér-Rao bound describing the smallest error allowed for any unbiased method. We also discuss conditions under which information maximization provides a convenient way to perform maximum likelihood estimation of linear-nonlinear models from neural data. PMID:19568981

Resonant Column Tests and Nonlinear Elasticity in Simulated Rocks

NASA Astrophysics Data System (ADS)

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 Effect of Detector Nonlinearity on WFIRST PSF Profiles for Weak Gravitational Lensing Measurements

NASA Astrophysics Data System (ADS)

Plazas, A. A.; Shapiro, C.; Kannawadi, A.; Mandelbaum, R.; Rhodes, J.; Smith, R.

2016-10-01

Weak gravitational lensing (WL) is one of the most powerful techniques to learn about the dark sector of the universe. To extract the WL signal from astronomical observations, galaxy shapes must be measured and corrected for the point-spread function (PSF) of the imaging system with extreme accuracy. Future WL missions—such as NASA’s Wide-Field Infrared Survey Telescope (WFIRST)—will use a family of hybrid near-infrared complementary metal-oxide-semiconductor detectors (HAWAII-4RG) that are untested for accurate WL measurements. Like all image sensors, these devices are subject to conversion gain nonlinearities (voltage response to collected photo-charge) that bias the shape and size of bright objects such as reference stars that are used in PSF determination. We study this type of detector nonlinearity (NL) and show how to derive requirements on it from WFIRST PSF size and ellipticity requirements. We simulate the PSF optical profiles expected for WFIRST and measure the fractional error in the PSF size (ΔR/R) and the absolute error in the PSF ellipticity (Δe) as a function of star magnitude and the NL model. For our nominal NL model (a quadratic correction), we find that, uncalibrated, NL can induce an error of ΔR/R = 1 × 10-2 and Δe 2 = 1.75 × 10-3 in the H158 bandpass for the brightest unsaturated stars in WFIRST. In addition, our simulations show that to limit the bias of ΔR/R and Δe in the H158 band to ˜10% of the estimated WFIRST error budget, the quadratic NL model parameter β must be calibrated to ˜1% and ˜2.4%, respectively. We present a fitting formula that can be used to estimate WFIRST detector NL requirements once a true PSF error budget is established.

Ultrathin Nonlinear Metasurface for Optical Image Encoding.

PubMed

Walter, Felicitas; Li, Guixin; Meier, Cedrik; Zhang, Shuang; Zentgraf, Thomas

2017-05-10

Security of optical information is of great importance in modern society. Many cryptography techniques based on classical and quantum optics have been widely explored in the linear optical regime. Nonlinear optical encryption in which encoding and decoding involve nonlinear frequency conversions represents a new strategy for securing optical information. Here, we demonstrate that an ultrathin nonlinear photonic metasurface, consisting of meta-atoms with 3-fold rotational symmetry, can be used to hide optical images under illumination with a fundamental wave. However, the hidden image can be read out from second harmonic generation (SHG) waves. This is achieved by controlling the destructive and constructive interferences of SHG waves from two neighboring meta-atoms. In addition, we apply this concept to obtain gray scale SHG imaging. Nonlinear metasurfaces based on space variant optical interference open new avenues for multilevel image encryption, anticounterfeiting, and background free image reconstruction.

Nonlinear acoustics in biomedical ultrasound

NASA Astrophysics Data System (ADS)

Cleveland, Robin O.

2015-10-01

Ultrasound is widely used to image inside the body; it is also used therapeutically to treat certain medical conditions. In both imaging and therapy applications the amplitudes employed in biomedical ultrasound are often high enough that nonlinear acoustic effects are present in the propagation: the effects have the potential to be advantageous in some scenarios but a hindrance in others. In the case of ultrasound imaging the nonlinearity produces higher harmonics that result in images of greater quality. However, nonlinear effects interfere with the imaging of ultrasound contrast agents (typically micron sized bubbles with a strong nonlinear response of their own) and nonlinear effects also result in complications when derating of pressure measurements in water to in situ values in tissue. High intensity focused ultrasound (HIFU) is emerging as a non-invasive therapeutic modality which can result in thermal ablation of tissue. For thermal ablation, the extra effective attenuation resulting from nonlinear effects can result in enhanced heating of tissue if shock formation occurs in the target region for ablation - a highly desirable effect. However, if nonlinearity is too strong it can also result in undesired near-field heating and reduced ablation in the target region. The disruption of tissue (histotripsy) and fragmentation of kidney stones (lithotripsy) exploits shock waves to produce mechanically based effects, with minimal heating present. In these scenarios it is necessary for the waves to be of sufficient amplitude that a shock exists when the waveform reaches the target region. This talk will discuss how underlying nonlinear phenomenon act in all the diagnostic and therapeutic applications described above.

Analytical Model of the Nonlinear Dynamics of Cantilever Tip-Sample Surface Interactions for Various Acoustic-Atomic Force Microscopies

NASA Technical Reports Server (NTRS)

Cantrell, John H., Jr.; Cantrell, Sean A.

2008-01-01

A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.

Nonlinear aspects of acoustic radiation force in biomedical applications

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

Ostrovsky, Lev, E-mail: Lev.A.Ostrovsky@noaa.gov; Tsyuryupa, Sergey; Sarvazyan, Armen, E-mail: armen@artannlabs.com

In the past decade acoustic radiation force (ARF) became a powerful tool in numerous biomedical applications. ARF from a focused ultrasound beam acts as a virtual “finger” for remote probing of internal anatomical structures and obtaining diagnostic information. This presentation deals with generation of shear waves by nonlinear focused beams. Albeit the ARF has intrinsically nonlinear origin, in most cases the primary ultrasonic wave was considered in the linear approximation. In this presentation, we consider the effects of nonlinearly distorted beams on generation of shear waves by such beams.

Nonlinear aspects of acoustic radiation force in biomedical applications

NASA Astrophysics Data System (ADS)

Ostrovsky, Lev; Tsyuryupa, Sergey; Sarvazyan, Armen

2015-10-01

In the past decade acoustic radiation force (ARF) became a powerful tool in numerous biomedical applications. ARF from a focused ultrasound beam acts as a virtual "finger" for remote probing of internal anatomical structures and obtaining diagnostic information. This presentation deals with generation of shear waves by nonlinear focused beams. Albeit the ARF has intrinsically nonlinear origin, in most cases the primary ultrasonic wave was considered in the linear approximation. In this presentation, we consider the effects of nonlinearly distorted beams on generation of shear waves by such beams.

Nonlinear Wave Chaos and the Random Coupling Model

NASA Astrophysics Data System (ADS)

Zhou, Min; Ott, Edward; Antonsen, Thomas M.; Anlage, Steven

The Random Coupling Model (RCM) has been shown to successfully predict the statistical properties of linear wave chaotic cavities in the highly over-moded regime. It is of interest to extend the RCM to strongly nonlinear systems. To introduce nonlinearity, an active nonlinear circuit is connected to two ports of the wave chaotic 1/4-bowtie cavity. The active nonlinear circuit consists of a frequency multiplier, an amplifier and several passive filters. It acts to double the input frequency in the range from 3.5 GHz to 5 GHz, and operates for microwaves going in only one direction. Measurements are taken between two additional ports of the cavity and we measure the statistics of the second harmonic voltage over an ensemble of realizations of the scattering system. We developed an RCM-based model of this system as two chaotic cavities coupled by means of a nonlinear transfer function. The harmonics received at the output are predicted to be the product of three statistical quantities that describe the three elements correspondingly. Statistical results from simulation, RCM-based modeling, and direct experimental measurements will be compared. ONR under Grant No. N000141512134, AFOSR under COE Grant FA9550-15-1-0171,0 and the Maryland Center for Nanophysics and Advanced Materials.

Nonlinear ultrasonics for material state awareness

NASA Astrophysics Data System (ADS)

Jacobs, L. J.

2014-02-01

Predictive health monitoring of structural components will require the development of advanced sensing techniques capable of providing quantitative information on the damage state of structural materials. By focusing on nonlinear acoustic techniques, it is possible to measure absolute, strength based material parameters that can then be coupled with uncertainty models to enable accurate and quantitative life prediction. Starting at the material level, this review will present current research that involves a combination of sensing techniques and physics-based models to characterize damage in metallic materials. In metals, these nonlinear ultrasonic measurements can sense material state, before the formation of micro- and macro-cracks. Typically, cracks of a measurable size appear quite late in a component's total life, while the material's integrity in terms of toughness and strength gradually decreases due to the microplasticity (dislocations) and associated change in the material's microstructure. This review focuses on second harmonic generation techniques. Since these nonlinear acoustic techniques are acoustic wave based, component interrogation can be performed with bulk, surface and guided waves using the same underlying material physics; these nonlinear ultrasonic techniques provide results which are independent of the wave type used. Recent physics-based models consider the evolution of damage due to dislocations, slip bands, interstitials, and precipitates in the lattice structure, which can lead to localized damage.

Mathematical Techniques for Nonlinear System Theory.

DTIC Science & Technology

1981-09-01

This report deals with research results obtained in the following areas: (1) Finite-dimensional linear system theory by algebraic methods--linear...Infinite-dimensional linear systems--realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory --basic properties of

Nonlinear response and bistability of driven ion acoustic waves

NASA Astrophysics Data System (ADS)

Akbari-Moghanjoughi, M.

2017-08-01

The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.

From Nothing to Something II: Nonlinear Systems via Consistent Correlated Bang

NASA Astrophysics Data System (ADS)

Lou, Sen-Yue

2017-06-01

Chinese ancient sage Laozi said everything comes from \\emph{\\bf \\em "nothing"}. \\rm In the first letter (Chin. Phys. Lett. 30 (2013) 080202), infinitely many discrete integrable systems have been obtained from "nothing" via simple principles (Dao). In this second letter, a new idea, the consistent correlated bang, is introduced to obtain nonlinear dynamic systems including some integrable ones such as the continuous nonlinear Schr\\"odinger equation (NLS), the (potential) Korteweg de Vries (KdV) equation, the (potential) Kadomtsev-Petviashvili (KP) equation and the sine-Gordon (sG) equation. These nonlinear systems are derived from nothing via suitable "Dao", the shifted parity, the charge conjugate, the delayed time reversal, the shifted exchange, the shifted-parity-rotation and so on.

Nonlinear Dynamics of the Nearshore Boundary Layer of a Large Lake (Lake Geneva)

NASA Astrophysics Data System (ADS)

Cimatoribus, Andrea A.; Lemmin, U.; Bouffard, D.; Barry, D. A.

2018-02-01

We examine nearshore and pelagic current variability in Lake Geneva, a large and deep lake in western Europe, using observations from several measurement locations and a three-dimensional numerical model for the period 2014-2016. Linear internal seiche modes excited by wind forcing clearly appear as peaks in the energy spectra for measurements in offshore locations. In contrast, spectra from the nearshore data, where currents interact with the lake bed, reveal a negligible contribution of internal seiches to the total kinetic energy. A similar contrast is seen in the spectra obtained from the numerical model at the same locations. Comparing the contribution of the different terms in the vertically averaged momentum equation from the modeling results shows that the nonlinear advective term dominates in the nearshore boundary layer. Its contribution decays with distance from shore. The width of this nearshore boundary layer, which may extend for several kilometers, seems to be mainly determined by local topography. Both field measurements and modeling results indicate that nonlinear dynamics are of primary importance in the nearshore boundary layer.

Growth and characterization of new nonlinear optical 1-phenyl-3-(4-dimethylamino phenyl) prop-2-en-1-one (PDAC) single crystals

NASA Astrophysics Data System (ADS)

Ravindraswami, K.; Janardhana, K.; Gowda, Jayaprakash; Moolya, B. Narayana

2018-04-01

Non linear optical 1-phenyl-3-(4-dimethylamino phenyl) prop-2-en-1-one (PDAC) was synthesized using Claisen - Schmidt condensation method and studied for optical nonlinearity with an emphasis on structure-property relationship. The structural confirmation studies were carried out using 1H-NMR, FT-IR and single crystal XRD techniques. The nonlinear absorption and nonlinear refraction parameters in z-scan with nano second laser pulses were obtained by measuring the profile of propagated beam through the samples. The real and imaginary parts of third-order bulk susceptibility χ(3) were evaluated. Thermo gravimetric analysis is carried out to investigate the thermal stability.

A comprehensive study of the delay vector variance method for quantification of nonlinearity in dynamical systems

PubMed Central

Mandic, D. P.; Ryan, K.; Basu, B.; Pakrashi, V.

2016-01-01

Although vibration monitoring is a popular method to monitor and assess dynamic structures, quantification of linearity or nonlinearity of the dynamic responses remains a challenging problem. We investigate the delay vector variance (DVV) method in this regard in a comprehensive manner to establish the degree to which a change in signal nonlinearity can be related to system nonlinearity and how a change in system parameters affects the nonlinearity in the dynamic response of the system. A wide range of theoretical situations are considered in this regard using a single degree of freedom (SDOF) system to obtain numerical benchmarks. A number of experiments are then carried out using a physical SDOF model in the laboratory. Finally, a composite wind turbine blade is tested for different excitations and the dynamic responses are measured at a number of points to extend the investigation to continuum structures. The dynamic responses were measured using accelerometers, strain gauges and a Laser Doppler vibrometer. This comprehensive study creates a numerical and experimental benchmark for structurally dynamical systems where output-only information is typically available, especially in the context of DVV. The study also allows for comparative analysis between different systems driven by the similar input. PMID:26909175

Vacuum nonlinear electrodynamic polarization effects in hard emission of pulsars and magnetars

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

Denisov, V.I.; Sokolov, V.A.; Svertilov, S.I., E-mail: vid.msu@yandex.ru, E-mail: sokolov.sev@inbox.ru, E-mail: sis@coronas.ru

The nonlinear electrodynamics influence of pulsar magnetic field on the electromagnetic pulse polarization is discussed from the point of observation interpretation. The calculations of pulsar magnetic field impact on the electromagnetic pulse polarization are made in such a way to make it easier to interpret these effects in space experiments. The law of hard emission pulse propagation in the pulsar magnetic field according to the vacuum (nonlinear electrodynamics is obtained. It has been shown, that due to the birefringence in the vacuum the front part of any hard emission pulse coming from a pulsar should be linearly polarized and themore » rest of pulse can have arbitrary polarization. The observational possibilities of vacuum birefringence are discussed. In this paper we give the estimations of detector parameters such as effective area, exposure time and necessity of polarization measurements with high accuracy. The combination of large area and extremely long exposure time gives the good opportunity to search the fine polarization effects like vacuum nonlinear electrodynamics birefringence.« less

A Nonlinearity Mitigation Method for a Broadband RF Front-End in a Sensor Based on Best Delay Searching

PubMed Central

Zhao, Wen; Ma, Hong; Zhang, Hua; Jin, Jiang; Dai, Gang; Hu, Lin

2017-01-01

The cognitive radio wireless sensor network (CR-WSN) is experiencing more and more attention for its capacity to automatically extract broadband instantaneous radio environment information. Obtaining sufficient linearity and spurious-free dynamic range (SFDR) is a significant premise of guaranteeing sensing performance which, however, usually suffers from the nonlinear distortion coming from the broadband radio frequency (RF) front-end in the sensor node. Moreover, unlike other existing methods, the joint effect of non-constant group delay distortion and nonlinear distortion is discussed, and its corresponding solution is provided in this paper. After that, the nonlinearity mitigation architecture based on best delay searching is proposed. Finally, verification experiments, both on simulation signals and signals from real-world measurement, are conducted and discussed. The achieved results demonstrate that with best delay searching, nonlinear distortion can be alleviated significantly and, in this way, spectrum sensing performance is more reliable and accurate. PMID:28956860

Nonlinear Wave Mixing Technique for Nondestructive Assessment of Infrastructure Materials

NASA Astrophysics Data System (ADS)

Ju, Taeho

mixing technique is adapted to develop an NDE technique for characterizing thermal aging of adhesive joints. To this end, a nonlinear spring model is used to simulate the effect of the adhesive layer. Based on this nonlinear spring model, analytical expressions of the resonant wave generated by the adhesive layers is obtained through an asymptotic analysis when the adhesive layer thickness is much smaller than the pertinent wavelength. The solutions are expressed in terms of the properties of the adhesive layer. The nonlinear spring model shows a good agreement with the finite layer model solutions in the limit of a small thickness to wavelength ratio. Third, to demonstrate the effectiveness of this newly developed technique, measurements are conducted on adhesive joint samples made of two aluminum adherends bonded together by a polymer adhesive tape. The samples are aged in a thermal chamber to induce thermal ageing degradation in the adhesive layer. Using the developed wave-mixing technique in conjunction with the nonlinear spring model, we show that the thermal aging damage of the adhesive layer can be quantified from only one side of the sample. Finally, by mixing two L-waves, we develop a mixing technique to nondestructively evaluate the damage induced by alkali-silica reaction (ASR) in concrete. Experimental measurements are conducted on concrete prism samples that contain reactive aggregates and have been subjected to different ASR conditioning. This new technique takes into consideration of the significant attenuation caused by ASR-induced microcracks and scattering by the aggregates. The measurement results show that the ANLP has a much greater sensitivity to ASR damage than other parameters such as attenuation and wave speed. More remarkably, it is also found that the measured acoustic nonlinearity parameter is well-correlated with the reduction of the compressive strength induced by ASR damage. Thus, ANLP can be used to nondestructively track ASR damage in

Empirical method to measure stochasticity and multifractality in nonlinear time series

NASA Astrophysics Data System (ADS)

Lin, Chih-Hao; Chang, Chia-Seng; Li, Sai-Ping

2013-12-01

An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the stochasticity of different time series can be compared. The local volatility of the time series under study can be constructed using this algorithm, and the multifractal structure of the time series can be analyzed by using this local volatility. As an example, we employ this method to analyze financial time series from different stock markets. The result shows that while developed markets evolve very much like an Ito process, the emergent markets are far from efficient. Differences about the multifractal structures and leverage effects between developed and emergent markets are discussed. The algorithm used here can be applied in a similar fashion to study time series of other complex systems.

Nonlinear optical investigation of the Tris(2‧,2-bipyridyl)iron(II) tetrafluoroborate using z-scan technique

NASA Astrophysics Data System (ADS)

Zidan, M. D.; Al-Ktaifani, M. M.; Allahham, A.

2017-05-01

Z-scan measurements were performed with a CW diode laser at 635 nm to investigate the nonlinear optical properties of Tris(2‧,2-bipyridyl)iron(II) tetrafluoroborate in ethanol at two concentrations. Theoretical fit was carried out to evaluate the nonlinear absorption coefficient (β) and the negative nonlinear refractive index (n2) for the studied complex. Furthermore, the ground-state absorption cross sections (σg), the excited-state absorption cross sections (σex) and thermo-optic coefficient were also estimated. The investigations show large NLO response, which is predominantly associated with substantial conjugation between the aromatic ring π-electron system and d-electron set metal center. The obtained results give a strong indication that Tris(2‧,2-bipyridyl)iron(II) tetrafluoroborate have a potential application in optical domain.

Electronegative nonlinear oscillating modes in plasmas

NASA Astrophysics Data System (ADS)

Panguetna, Chérif Souleman; Tabi, Conrad Bertrand; Kofané, Timoléon Crépin

2018-02-01

The emergence of nonlinear modulated waves is addressed in an unmagnetized electronegative plasma made of Boltzmann electrons, Boltzmann negative ions and cold mobile positive ions. The reductive perturbation method is used to reduce the dynamics of the whole system to a cubic nonlinear Schrödinger equation, whose the nonlinear and dispersion coefficients, P and Q, are function of the negative ion parameters, namely the negative ion concentration ratio (α) and the electron-to-negative ion temperature ratio (σn). It is observed that these parameters importantly affect the formation of modulated ion-acoustic waves, either as exact solutions or via the activation of modulational instability. Especially, the theory of modulational instability is used to show the correlation between the parametric analysis and the formation of modulated solitons, obtained here as bright envelopes and kink-wave solitons.

Dynamic modeling of moment wheel assemblies with nonlinear rolling bearing supports

NASA Astrophysics Data System (ADS)

Wang, Hong; Han, Qinkai; Luo, Ruizhi; Qing, Tao

2017-10-01

Moment wheel assemblies (MWA) have been widely used in spacecraft attitude control and large angle slewing maneuvers over the years. Understanding and controlling vibration of MWAs is a crucial factor to achieving the desired level of payload performance. Dynamic modeling of a MWA with nonlinear rolling bearing supports is conducted. An improved load distribution analysis is proposed to more accurately obtain the contact deformations and angles between the rolling balls and raceways. Then, the bearing restoring forces are then obtained through iteratively solving the load distribution equations at every time step. The effects of preload condition, surface waviness, Hertz contact and elastohydrodynamic lubrication could all be reflected in the nonlinear bearing forces. Considering the mass imbalances of the flywheel, flexibility of supporting structures and rolling bearing nonlinearity, the dynamic model of a typical MWA is established based upon the energy theorem. Dynamic tests are conducted to verify the nonlinear dynamic model. The influences of flywheel mass eccentricity and inner/outer waviness amplitudes on the dynamic responses are discussed in detail. The obtained results would be useful for the design and vibration control of the MWA system.

Entropy production and nonlinear Fokker-Planck equations.

PubMed

Casas, G A; Nobre, F D; Curado, E M F

2012-12-01

The entropy time rate of systems described by nonlinear Fokker-Planck equations--which are directly related to generalized entropic forms--is analyzed. Both entropy production, associated with irreversible processes, and entropy flux from the system to its surroundings are studied. Some examples of known generalized entropic forms are considered, and particularly, the flux and production of the Boltzmann-Gibbs entropy, obtained from the linear Fokker-Planck equation, are recovered as particular cases. Since nonlinear Fokker-Planck equations are appropriate for the dynamical behavior of several physical phenomena in nature, like many within the realm of complex systems, the present analysis should be applicable to irreversible processes in a large class of nonlinear systems, such as those described by Tsallis and Kaniadakis entropies.

Comparison between Measurements Obtained with three Different Perineometers

PubMed Central

Barbosa, Patrícia Brentegani; Franco, Maíra Menezes; de Oliveira Souza, Flaviane; Antônio, Flávia Ignácio; Montezuma, Thaís; Ferreira, Cristine Homsi Jorge

2009-01-01

OBJECTIVE: To analyze the results obtained in the evaluation of intra-vaginal pressure using three different brands of perineometers in nulliparous volunteers. MATERIALS AND METHODS: Twenty nulliparous women with no anatomical alterations and/or dysfunction of the pelvic floor were enrolled in our study. All the women had the ability to voluntarily contract their PFM (Pelvic Floor Muscles), as assessed by digital palpation. The intra-vaginal pressure was assessed using three different brands of perineometer (Neurodyn Evolution™, SensuPower™ and Peritron™). Each volunteer was evaluated on three alternate days by a single examiner using a single brand of perineometer on each day. In the assessment, the volunteers were required to pull (contract) their PFM in and up as strongly as possible 3 times and to sustain the contraction for 5 seconds, with an interval of 30 seconds between each pull. For the statistical analysis, a concordance correlation coefficient was used to compare the values that were obtained with each brand of perineometer. RESULTS: A moderate concordance (0.51) was found between the results from the Peritron™ and Neurodyn™ perineometers, a fair concordance (0.21) between the Peritron™ and SensuPower™ brands and a poor concordance (0.19) between the Neurodyn™ and SensuPower™ brands. CONCLUSION: The concordance of the measurements of the intra-vaginal pressure ranged from poor to moderate, suggesting that perineometers of different brands generate different results. PMID:19578656

Absolute second order nonlinear susceptibility of Pt nanowire arrays on MgO faceted substrates with various cross-sectional shapes

NASA Astrophysics Data System (ADS)

Ogata, Yoichi; Mizutani, Goro

2013-08-01

We have measured optical second harmonic generation (SHG) intensity from three types of Pt nanowires with 7 nm widths of elliptical and boomerang cross-sectional shapes and with 2 nm width elliptical cross-sectional shapes on the MgO faceted templates. From the SHG intensities, we calculated the absolute value of the nonlinear susceptibility χ(2) integrated in the direction of the wire-layer thickness. The tentatively obtained bulk χ(2)B of the wire layer was very large, approaching the value of the well-known nonlinear optical material BaTiO3.

Measurement of ultrafast optical Kerr effect of Ge-Sb-Se chalcogenide slab waveguides by the beam self-trapping technique

NASA Astrophysics Data System (ADS)

Kuriakose, Tintu; Baudet, Emeline; Halenkovič, Tomáš; Elsawy, Mahmoud M. R.; Němec, Petr; Nazabal, Virginie; Renversez, Gilles; Chauvet, Mathieu

2017-11-01

We present a reliable and original experimental technique based on the analysis of beam self-trapping to measure ultrafast optical nonlinearities in planar waveguides. The technique is applied to the characterization of Ge-Sb-Se chalcogenide films that allow Kerr induced self-focusing and soliton formation. Linear and nonlinear optical constants of three different chalcogenide waveguides are studied at 1200 and 1550 nm in femtosecond regime. Waveguide propagation loss and two photon absorption coefficients are determined by transmission analysis. Beam broadening and narrowing results are compared with simulations of the nonlinear Schrödinger equation solved by BPM method to deduce the Kerr n2 coefficients. Kerr optical nonlinearities obtained by our original technique compare favorably with the values obtained by Z-scan technique. Nonlinear refractive index as high as (69 ± 11) × 10-18m2 / W is measured in Ge12.5Sb25Se62.5 at 1200 nm with low nonlinear absorption and low propagation losses which reveals the great characteristics of our waveguides for ultrafast all optical switching and integrated photonic devices.

Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium

PubMed Central

Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying

2015-01-01

A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066

Nonlinear tunneling of optical soliton in 3 coupled NLS equation with symbolic computation

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

Mani Rajan, M.S., E-mail: senthilmanirajanofc@gmail.com; Mahalingam, A.; Uthayakumar, A.

We investigated the soliton solution for N coupled nonlinear Schrödinger (CNLS) equations. These equations are coupled due to the cross-phase-modulation (CPM). Lax pair of this system is obtained via the Ablowitz–Kaup–Newell–Segur (AKNS) scheme and the corresponding Darboux transformation is constructed to derive the soliton solution. One and two soliton solutions are generated. Using two soliton solutions of 3 CNLS equation, nonlinear tunneling of soliton for both with and without exponential background has been discussed. Finally cascade compression of optical soliton through multi-nonlinear barrier has been discussed. The obtained results may have promising applications in all-optical devices based on optical solitons,more » study of soliton propagation in birefringence fiber systems and optical soliton with distributed dispersion and nonlinearity management. -- Highlights: •We consider the nonlinear tunneling of soliton in birefringence fiber. •3-coupled NLS (CNLS) equation with variable coefficients is considered. •Two soliton solutions are obtained via Darboux transformation using constructed Lax pair. •Soliton tunneling through dispersion barrier and well are investigated. •Finally, cascade compression of soliton has been achieved.« less

A non-collinear mixing technique to measure the acoustic nonlinearity parameter of adhesive bond

NASA Astrophysics Data System (ADS)

Ju, Taeho; Achenbach, Jan. D.; Jacobs, Laurence J.; Qu, Jianmin

2018-04-01

In this work, we employed a wave mixing technique with an incident longitudinal wave and a shear wave to measure the Acoustic Nonlinearity Parameter (ANLP) of adhesive bonds. An adhesive transfer tape (F-9473PC) was used as an adhesive material: two aluminum plates are bonded together by the tape. To achieve a high signal to noise ratio, the optimal interaction angle and frequency ratio between the two incident waves were carefully selected so resonance occurs primarily in the adhesive layer, which somewhat suppressed the resonance in the aluminum plates. One of the most significant features of this method is that the measurements need only one-side access to the sample being measured. To demonstrate the effectiveness of the proposed technique, the adhesively bonded aluminum sample was placed in a temperature-controlled chamber for thermal aging. The ANLP of the thermally aged sample was compared with that of a freshly made adhesive sample. The results show that the ANLP increases with aging time and temperature.

Studies on third-order nonlinear optical properties of chalcone derivatives in polymer host

NASA Astrophysics Data System (ADS)

Shettigar, Seetharam; Umesh, G.; Chandrasekharan, K.; Sarojini, B. K.; Narayana, B.

2008-04-01

In this paper we present the experimental study of the third-order nonlinear optical properties of two chalcone derivatives, viz., 1-(4-methoxyphenyl)-3-(4-butyloxyphenyl)-prop-2-en-1-one and 1-(4-methoxyphenyl)-3-(4-propyloxyphenyl)-prop-2-en-1-one in PMMA host, with the prospective of reaching a compromise between good processability and high nonlinear optical properties. The nonlinear optical properties have been investigated by Z-scan technique using 7 ns laser pulses at 532 nm. The nonlinear refractive index, nonlinear absorption coefficient, magnitude of third-order susceptibility and the coupling factor have been determined. The values obtained are of the order of 10 -14 cm 2/W, 1 cm/GW, 10 -13 esu and 0.2, respectively. The molecular second hyperpolarizability for the chalcone derivatives in polymer is of the order of 10 -31 esu. Different guest/host concentrations have also been studied. The results suggest that the nonlinear properties of the chalcones have been improved when they are used as dopants in polymer matrix. The nonlinear parameters obtained are comparable with the reported values of II-VI compound semiconductors. Hence, these chalcons are a promising class of nonlinear optical dopant materials for optical device applications.

Nonlinear refraction and two-photon absorption in dense 2Bi{sub 2}O{sub 3}-B{sub 2}O{sub 3} glasses

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

Paramesh, Gadige; Varma, K. B. R.

2012-06-05

High density transparent glasses (7.86 g/cc) were fabricated in the 2Bi{sub 2}O{sub 3}-B{sub 2}O{sub 3} (BBO) system. Optical band gap of the obtained glasses was found to be 2.6eV. The refractive index measured for these glasses was 2.25{+-}0.05 at {lambda}=543 nm. Nonlinear refraction and absorption studies were carried out on the BBO glasses using z-scan technique at {lambda}=532 nm of 10 ns pulse width. The nonlinear refractive index obtained was n{sub 2}=12.1x10{sup -14} cm{sup 2}/W and nonlinear absorption coefficient was {beta}=15.2 cm/GW. The n{sub 2} and {beta} values of the BBO glasses were large compared to the other reported highmore » index bismuth based oxide glass systems in the literature. These were attributed to the high density, high linear refractive index, low band gap and two photon absorption associated with these glasses. The electronic origin of large nonlinearities was discussed based on bond-orbital theory.« less

K-means-clustering-based fiber nonlinearity equalization techniques for 64-QAM coherent optical communication system.

PubMed

Zhang, Junfeng; Chen, Wei; Gao, Mingyi; Shen, Gangxiang

2017-10-30

In this work, we proposed two k-means-clustering-based algorithms to mitigate the fiber nonlinearity for 64-quadrature amplitude modulation (64-QAM) signal, the training-sequence assisted k-means algorithm and the blind k-means algorithm. We experimentally demonstrated the proposed k-means-clustering-based fiber nonlinearity mitigation techniques in 75-Gb/s 64-QAM coherent optical communication system. The proposed algorithms have reduced clustering complexity and low data redundancy and they are able to quickly find appropriate initial centroids and select correctly the centroids of the clusters to obtain the global optimal solutions for large k value. We measured the bit-error-ratio (BER) performance of 64-QAM signal with different launched powers into the 50-km single mode fiber and the proposed techniques can greatly mitigate the signal impairments caused by the amplified spontaneous emission noise and the fiber Kerr nonlinearity and improve the BER performance.

Nonlinear cavity optomechanics with nanomechanical thermal fluctuations

PubMed Central

Leijssen, Rick; La Gala, Giada R.; Freisem, Lars; Muhonen, Juha T.; Verhagen, Ewold

2017-01-01

Although the interaction between light and motion in cavity optomechanical systems is inherently nonlinear, experimental demonstrations to date have allowed a linearized description in all except highly driven cases. Here, we demonstrate a nanoscale optomechanical system in which the interaction between light and motion is so large (single-photon cooperativity C0≈103) that thermal motion induces optical frequency fluctuations larger than the intrinsic optical linewidth. The system thereby operates in a fully nonlinear regime, which pronouncedly impacts the optical response, displacement measurement and radiation pressure backaction. Specifically, we measure an apparent optical linewidth that is dominated by thermo-mechanically induced frequency fluctuations over a wide temperature range, and show that in this regime thermal displacement measurements cannot be described by conventional analytical models. We perform a proof-of-concept demonstration of exploiting the nonlinearity to conduct sensitive quadratic readout of nanomechanical displacement. Finally, we explore how backaction in this regime affects the mechanical fluctuation spectra. PMID:28685755

Nonlinear parity readout with a microwave photodetector

NASA Astrophysics Data System (ADS)

Schöndorf, M.; Wilhelm, F. K.

2018-04-01

Robust high-fidelity parity measurement is an important operation in many applications of quantum computing. In this work we show how in a circuit QED architecture, one can measure parity in a single shot at very high contrast by taking advantage of the nonlinear behavior of a strongly driven microwave cavity coupled to one or multiple qubits. We work in a nonlinear dispersive regime treated in an exact dispersive transformation. We show that appropriate tuning of experimental parameters leads to very high contrast in the cavity and therefore to a high-efficiency parity readout with a microwave photon counter or another amplitude detector. These tuning conditions are based on nonlinearity and are hence more robust than previously described linear tuning schemes. In the first part of the paper we show in detail how to achieve this for two-qubit parity measurements and extend this to N qubits in the second part of the paper. We also study the quantum nondemolition character of the protocol.

Z-scan: A simple technique for determination of third-order optical nonlinearity

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

Singh, Vijender, E-mail: chahal-gju@rediffmail.com; Aghamkar, Praveen, E-mail: p-aghamkar@yahoo.co.in

Z-scan is a simple experimental technique to measure intensity dependent nonlinear susceptibilities of third-order nonlinear optical materials. This technique is used to measure the sign and magnitude of both real and imaginary part of the third order nonlinear susceptibility (χ{sup (3)}) of nonlinear optical materials. In this paper, we investigate third-order nonlinear optical properties of Ag-polymer composite film by using single beam z-scan technique with Q-switched, frequency doubled Nd: YAG laser (λ=532 nm) at 5 ns pulse. The values of nonlinear absorption coefficient (β), nonlinear refractive index (n{sub 2}) and third-order nonlinear optical susceptibility (χ{sup (3)}) of permethylazine were found to bemore » 9.64 × 10{sup −7} cm/W, 8.55 × 10{sup −12} cm{sup 2}/W and 5.48 × 10{sup −10} esu, respectively.« less

Development of ultrasound transducer diffractive field theory for nonlinear propagation-based imaging

NASA Astrophysics Data System (ADS)

Kharin, Nikolay A.

2000-04-01

In nonlinear ultrasound imaging the images are formed using the second harmonic energy generated due to the nonlinear nature of finite amplitude propagation. This propagation can be modeled using the KZK wave equation. This paper presents further development of nonlinear diffractive field theory based on the KZK equation and its solution by means of the slowly changing profile method for moderate nonlinearity. The analytical expression for amplitudes and phases of sum frequency wave are obtained in addition to the second harmonic wave. Also, the analytical expression for the relative curvature of the wave fronts of fundamental and second harmonic signals are derived. The media with different nonlinear properties and absorption coefficients were investigated to characterize the diffractive field of the transducer at medical frequencies. All expressions demonstrate good agreement with experimental results. The expressions are novel and provide an easy way for prediction of amplitude and phase structure of nonlinearly distorted field of a transducer. The sum frequency signal technique could be implemented as well as second harmonic technique to improve the quality of biomedical images. The results obtained are of importance for medical diagnostic ultrasound equipment design.

Mode-locking peculiarities in an all-fiber erbium-doped ring ultrashort pulse laser with a highly-nonlinear resonator

NASA Astrophysics Data System (ADS)

Dvoretskiy, Dmitriy A.; Sazonkin, Stanislav G.; Kudelin, Igor S.; Orekhov, Ilya O.; Pnev, Alexey B.; Karasik, Valeriy E.; Denisov, Lev K.

2017-12-01

Today ultrashort pulse (USP) fiber lasers are in great demand in a frequency metrology field, THz pulse spectroscopy, optical communication, quantum optics application, etc. Therefore mode-locked (ML) fiber lasers have been extensively investigated over the last decade due the number of scientific, medical and industrial applications. It should be noted, that USP fiber lasers can be treated as an ideal platform to expand future applications due to the complex ML nonlinear dynamics in a laser resonator. Up to now a series of novel ML regimes have been investigated e.g. self-similar pulses, noise-like pulses, multi-bound solitons and soliton rain generation. Recently, we have used a highly nonlinear germanosilicate fiber (with germanium oxides concentration in the core 50 mol. %) inside the resonator for more reliable and robust launching of passive mode-locking based on the nonlinear polarization evolution effect in fibers. In this work we have measured promising and stable ML regimes such as stretched pulses, soliton rain and multi-bound solitons formed in a highly-nonlinear ring laser and obtained by intracavity group velocity dispersion (GVD) variation in slightly negative region. As a result, we have obtained the low noise ultrashort pulse generation with duration < 250 fs (more than 20 bound pulses when obtained multi-bound soliton generation with intertemporal width 5 ps) at a repetition rate 11.3 MHz (with signal-to-noise ratio at fundamental frequency > 59 dB) and relative intensity noise <-101 dBc / Hz.

Nonlinear Association Between Cerebrospinal Fluid and Florbetapir F-18 β-Amyloid Measures Across the Spectrum of Alzheimer Disease.

PubMed

Toledo, Jon B; Bjerke, Maria; Da, Xiao; Landau, Susan M; Foster, Norman L; Jagust, William; Jack, Clifford; Weiner, Michael; Davatzikos, Christos; Shaw, Leslie M; Trojanowski, John Q

2015-05-01

Cerebrospinal fluid (CSF) and positron emission tomographic (PET) amyloid biomarkers have been proposed for the detection of Alzheimer disease (AD) pathology in living patients and for the tracking of longitudinal changes, but the relation between biomarkers needs further study. To determine the association between CSF and PET amyloid biomarkers (cross-sectional and longitudinal measures) and compare the cutoffs for these measures. Longitudinal clinical cohort study from 2005 to 2014 including 820 participants with at least 1 florbetapir F-18 (hereafter referred to as simply florbetapir)-PET scan and at least 1 CSF β-amyloid 1-42 (Aβ1-42) sample obtained within 30 days of each other (501 participants had a second PET scan after 2 years, including 150 participants with CSF Aβ1-42 measurements). Data were obtained from the Alzheimer's Disease Neuroimaging Initiative database. Four different PET scans processing pipelines from 2 different laboratories were compared. The PET cutoff values were established using a mixture-modeling approach, and different mathematical models were applied to define the association between CSF and PET amyloid measures. The values of the CSF Aβ1-42 samples and florbetapir-PET scans showed a nonlinear association (R2 = 0.48-0.66), with the strongest association for values in the middle range. The presence of a larger dynamic range of florbetapir-PET scan values in the higher range compared with the CSF Aβ1-42 plateau explained the differences in correlation with cognition (R2 = 0.36 and R2 = 0.25, respectively). The APOE genotype significantly modified the association between both biomarkers. The PET cutoff values derived from an unsupervised classifier converged with previous PET cutoff values and the established CSF Aβ1-42 cutoff levels. There was no association between longitudinal Aβ1-42 levels and standardized uptake value ratios during follow-up. The association between both biomarkers is limited to a middle range of values, is

Structuring in complex plasma for nonlinearly screened dust particles

NASA Astrophysics Data System (ADS)

Tsytovich, Vadim; Gusein-zade, Namik

2014-03-01

An explanation is proposed for the recently discovered effect of spontaneous dusty plasma structuring (and the appearance of compact dust structures) under conditions of nonlinear dust screening. Physical processes are considered that make homogenous dusty plasma universally unstable and lead to the appearance of structures. It is shown for the first time that the efficiency of structuring increases substantially in the presence of plasma flows caused by the charging of nonlinearly screened dust grains. General results are obtained for arbitrary nonlinear screening, and special attention is paid to the model of nonlinear screening often used since 1964. The growth rate of structuring instability is derived. It is shown that, in the case of nonlinear screening, the structuring has a threshold determined by the friction of grains against the neutral gas. The theoretically obtained threshold agrees with recent experimental observations. The dispersion relation for dusty plasma structuring is shown to be similar to the dispersion relation for gravitational instability with an effective gravitational constant. The effective dust attraction caused by this instability is shown to be collective, and the dependence of the effective gravitational constant on the dust-to-ion density ratio is found explicitly for the first time. It is demonstrated that the proposed method of calculation of dust attraction by using the effective gravitational constant is the most efficient and straightforward. Understanding of the role of nonlinear screening gives deeper physical grounds for the theoretical interpretation of the observed phenomenon of dust crystal formation in complex plasmas.

Non-reciprocity in nonlinear elastodynamics

NASA Astrophysics Data System (ADS)

Blanchard, Antoine; Sapsis, Themistoklis P.; Vakakis, Alexander F.

2018-01-01

Reciprocity is a fundamental property of linear time-invariant (LTI) acoustic waveguides governed by self-adjoint operators with symmetric Green's functions. The break of reciprocity in LTI elastodynamics is only possible through the break of time reversal symmetry on the micro-level, and this can be achieved by imposing external biases, adding nonlinearities or allowing for time-varying system properties. We present a Volterra-series based asymptotic analysis for studying spatial non-reciprocity in a class of one-dimensional (1D), time-invariant elastic systems with weak stiffness nonlinearities. We show that nonlinearity is neither necessary nor sufficient for breaking reciprocity in this class of systems; rather, it depends on the boundary conditions, the symmetries of the governing linear and nonlinear operators, and the choice of the spatial points where the non-reciprocity criterion is tested. Extension of the analysis to higher dimensions and time-varying systems is straightforward from a mathematical point of view (but not in terms of new non-reciprocal physical phenomena), whereas the connection of non-reciprocity and time irreversibility can be studied as well. Finally, we show that suitably defined non-reciprocity measures enable optimization, and can provide physical understanding of the nonlinear effects in the dynamics, enabling one to establish regimes of "maximum nonlinearity." We highlight the theoretical developments by means of a numerical example.

Application of the Homotopy Perturbation Method to the Nonlinear Pendulum

ERIC Educational Resources Information Center

Belendez, A.; Hernandez, A.; Belendez, T.; Marquez, A.

2007-01-01

The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as…

Hazardous Continuation Backward in Time in Nonlinear Parabolic Equations, and an Experiment in Deblurring Nonlinearly Blurred Imagery

PubMed Central

Carasso, Alfred S

2013-01-01

Identifying sources of ground water pollution, and deblurring nanoscale imagery as well as astronomical galaxy images, are two important applications involving numerical computation of parabolic equations backward in time. Surprisingly, very little is known about backward continuation in nonlinear parabolic equations. In this paper, an iterative procedure originating in spectroscopy in the 1930’s, is adapted into a useful tool for solving a wide class of 2D nonlinear backward parabolic equations. In addition, previously unsuspected difficulties are uncovered that may preclude useful backward continuation in parabolic equations deviating too strongly from the linear, autonomous, self adjoint, canonical model. This paper explores backward continuation in selected 2D nonlinear equations, by creating fictitious blurred images obtained by using several sharp images as initial data in these equations, and capturing the corresponding solutions at some positive time T. Successful backward continuation from t=T to t = 0, would recover the original sharp image. Visual recognition provides meaningful evaluation of the degree of success or failure in the reconstructed solutions. Instructive examples are developed, illustrating the unexpected influence of certain types of nonlinearities. Visually and statistically indistinguishable blurred images are presented, with vastly different deblurring results. These examples indicate that how an image is nonlinearly blurred is critical, in addition to the amount of blur. The equations studied represent nonlinear generalizations of Brownian motion, and the blurred images may be interpreted as visually expressing the results of novel stochastic processes. PMID:26401430

Hazardous Continuation Backward in Time in Nonlinear Parabolic Equations, and an Experiment in Deblurring Nonlinearly Blurred Imagery.

PubMed

Carasso, Alfred S

2013-01-01

Identifying sources of ground water pollution, and deblurring nanoscale imagery as well as astronomical galaxy images, are two important applications involving numerical computation of parabolic equations backward in time. Surprisingly, very little is known about backward continuation in nonlinear parabolic equations. In this paper, an iterative procedure originating in spectroscopy in the 1930's, is adapted into a useful tool for solving a wide class of 2D nonlinear backward parabolic equations. In addition, previously unsuspected difficulties are uncovered that may preclude useful backward continuation in parabolic equations deviating too strongly from the linear, autonomous, self adjoint, canonical model. This paper explores backward continuation in selected 2D nonlinear equations, by creating fictitious blurred images obtained by using several sharp images as initial data in these equations, and capturing the corresponding solutions at some positive time T. Successful backward continuation from t=T to t = 0, would recover the original sharp image. Visual recognition provides meaningful evaluation of the degree of success or failure in the reconstructed solutions. Instructive examples are developed, illustrating the unexpected influence of certain types of nonlinearities. Visually and statistically indistinguishable blurred images are presented, with vastly different deblurring results. These examples indicate that how an image is nonlinearly blurred is critical, in addition to the amount of blur. The equations studied represent nonlinear generalizations of Brownian motion, and the blurred images may be interpreted as visually expressing the results of novel stochastic processes.

Column Chromatography To Obtain Organic Cation Sorption Isotherms.

PubMed

Jolin, William C; Sullivan, James; Vasudevan, Dharni; MacKay, Allison A

2016-08-02

Column chromatography was evaluated as a method to obtain organic cation sorption isotherms for environmental solids while using the peak skewness to identify the linear range of the sorption isotherm. Custom packed HPLC columns and standard batch sorption techniques were used to intercompare sorption isotherms and solid-water sorption coefficients (Kd) for four organic cations (benzylamine, 2,4-dichlorobenzylamine, phenyltrimethylammonium, oxytetracycline) with two aluminosilicate clay minerals and one soil. A comparison of Freundlich isotherm parameters revealed isotherm linearity or nonlinearity was not significantly different between column chromatography and traditional batch experiments. Importantly, skewness (a metric of eluting peak symmetry) analysis of eluting peaks can establish isotherm linearity, thereby enabling a less labor intensive means to generate the extensive data sets of linear Kd values required for the development of predictive sorption models. Our findings clearly show that column chromatography can reproduce sorption measures from conventional batch experiments with the benefit of lower labor-intensity, faster analysis times, and allow for consistent sorption measures across laboratories with distinct chromatography instrumentation.

Nonlinear transport theory in the metal with tunnel barrier

NASA Astrophysics Data System (ADS)

Zubov, E. E.

2018-02-01

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

Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities.

PubMed

Yan, Zhenya; Konotop, V V

2009-09-01

It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrödinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In the suggested reduction the original coordinates in the (1+3) space are mapped into a set of one-parametric coordinate surfaces, whose parameter plays the role of the coordinate of the one-dimensional equation. We describe the algorithm of finding solutions and concentrate on power (linear and nonlinear) potentials presenting a number of case examples. Generalizations of the method are also discussed.

Nonlinear Analytical Modeling of Interfacial Phenomenon and Nano-Size Microstructural Features to Better Correlate Nde Electronic Property Measurements to Material State

NASA Astrophysics Data System (ADS)

Roubidoux, J. A.; Jackson, J. E.; Lasseigne, A. N.; Mishra, B.; Olson, D. L.

2010-02-01

This paper correlates nonlinear material properties to nondestructive electronic measurements by using wave analysis techniques (e.g. Perturbation Methods) and incorporating higher-order phenomena. The correlations suggest that nondestructive electronic property measurements and practices can be used to assess thin films, surface layers, and other advanced materials that exhibit modified behaviors based on their space-charged interfacial behavior.

Wiener sliding-mode control for artificial pancreas: a new nonlinear approach to glucose regulation.

PubMed

Abu-Rmileh, Amjad; Garcia-Gabin, Winston

2012-08-01

Type 1 diabetic patients need insulin therapy to keep their blood glucose close to normal. In this paper an attempt is made to show how nonlinear control-oriented model may be used to improve the performance of closed-loop control of blood glucose in diabetic patients. The nonlinear Wiener model is used as a novel modeling approach to be applied to the glucose control problem. The identified Wiener model is used in the design of a robust nonlinear sliding mode control strategy. Two configurations of the nonlinear controller are tested and compared to a controller designed with a linear model. The controllers are designed in a Smith predictor structure to reduce the effect of system time delay. To improve the meal compensation features, the controllers are provided with a simple feedforward controller to inject an insulin bolus at meal time. Different simulation scenarios have been used to evaluate the proposed controllers. The obtained results show that the new approach outperforms the linear control scheme, and regulates the glucose level within safe limits in the presence of measurement and modeling errors, meal uncertainty and patient variations. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Linear and Nonlinear Viscoelastic Modeling of Aorta and Carotid Pressure-Area Dynamics under in vivo and ex vivo Conditions

PubMed Central

Valdez-Jasso, Daniela; Bia, Daniel; Zócalo, Yanina; Armentano, Ricardo L.; Haider, Mansoor A.; Olufsen, Mette S.

2013-01-01

A better understanding of the biomechanical properties of the arterial wall provides important insight into arterial vascular biology under normal (healthy) and pathological conditions. This insight has potential to improve tracking of disease progression and to aid in vascular graft design and implementation. In this study, we use linear and nonlinear viscoelastic models to predict biomechanical properties of the thoracic descending aorta and the carotid artery under ex vivo and in vivo conditions in ovine and human arteries. Models analyzed include a four-parameter (linear) Kelvin viscoelastic model and two five-parameter nonlinear viscoelastic models (an arctangent and a sigmoid model) that relate changes in arterial blood pressure to the vessel cross-sectional area (via estimation of vessel strain). These models were developed using the framework of Quasilinear Viscoelasticity (QLV) theory and were validated using measurements from the thoracic descending aorta and the carotid artery obtained from human and ovine arteries. In vivo measurements were obtained from ten ovine aortas and ten human carotid arteries. Ex vivo measurements (from both locations) were made in eleven male Merino sheep. Biomechanical properties were obtained through constrained estimation of model parameters. To further investigate the parameter estimates we computed standard errors and confidence intervals and we used analysis of variance to compare results within and between groups. Overall, our results indicate that optimal model selection depends on the arterial type. Results showed that for the thoracic descending aorta (under both experimental conditions) the best predictions were obtained with the nonlinear sigmoid model, while under healthy physiological pressure loading the carotid arteries nonlinear stiffening with increasing pressure is negligible, and consequently, the linear (Kelvin) viscoelastic model better describes the pressure-area dynamics in this vessel. Results

On solutions of the fifth-order dispersive equations with porous medium type non-linearity

NASA Astrophysics Data System (ADS)

Kocak, Huseyin; Pinar, Zehra

2018-07-01

In this work, we focus on obtaining the exact solutions of the fifth-order semi-linear and non-linear dispersive partial differential equations, which have the second-order diffusion-like (porous-type) non-linearity. The proposed equations were not studied in the literature in the sense of the exact solutions. We reveal solutions of the proposed equations using the classical Riccati equations method. The obtained exact solutions, which can play a key role to simulate non-linear waves in the medium with dispersion and diffusion, are illustrated and discussed in details.

Weakly nonlinear behavior of a plate thickness-mode piezoelectric transformer.

PubMed

Yang, Jiashi; Chen, Ziguang; Hu, Yuantai; Jiang, Shunong; Guo, Shaohua

2007-04-01

We analyzed the weakly nonlinear behavior of a plate thickness-shear mode piezoelectric transformer near resonance. An approximate analytical solution was obtained. Numerical results based on the analytical solution are presented. It is shown that on one side of the resonant frequency the input-output relation becomes nonlinear, and on the other side the output voltage experiences jumps.

Ultra-large nonlinear parameter in graphene-silicon waveguide structures.

PubMed

Donnelly, Christine; Tan, Dawn T H

2014-09-22

Mono-layer graphene integrated with optical waveguides is studied for the purpose of maximizing E-field interaction with the graphene layer, for the generation of ultra-large nonlinear parameters. It is shown that the common approach used to minimize the waveguide effective modal area does not accurately predict the configuration with the maximum nonlinear parameter. Both photonic and plasmonic waveguide configurations and graphene integration techniques realizable with today's fabrication tools are studied. Importantly, nonlinear parameters exceeding 10(4) W(-1)/m, two orders of magnitude larger than that in silicon on insulator waveguides without graphene, are obtained for the quasi-TE mode in silicon waveguides incorporating mono-layer graphene in the evanescent part of the optical field. Dielectric loaded surface plasmon polariton waveguides incorporating mono-layer graphene are observed to generate nonlinear parameters as large as 10(5) W(-1)/m, three orders of magnitude larger than that in silicon on insulator waveguides without graphene. The ultra-large nonlinear parameters make such waveguides promising platforms for nonlinear integrated optics at ultra-low powers, and for previously unobserved nonlinear optical effects to be studied in a waveguide platform.

Ultrasonic characterization of the nonlinear elastic properties of unidirectional graphite/epoxy composites

NASA Technical Reports Server (NTRS)

Prosser, William H.

1987-01-01

The theoretical treatment of linear and nonlinear elasticity in a unidirectionally fiber reinforced composite as well as measurements for a unidirectional graphite/epoxy composite (T300/5208) are presented. Linear elastic properties were measured by both ultrasonic and strain gage measurements. The nonlinear properties were determined by measuring changes in ultrasonic natural phase velocity with a pulsed phase locked loop interferometer as a function of stress and temperature. These measurements provide the basis for further investigations into the relationship between nonlinear elastic properties and other important properties such as strength and fiber-matrix interfacial stength in graphite/epoxy composites.

Optical rogue waves generation in a nonlinear metamaterial

NASA Astrophysics Data System (ADS)

Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin

2014-11-01

We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.

Nonlinear aerodynamics of two-dimensional airfoils in severe maneuver

NASA Technical Reports Server (NTRS)

Scott, Matthew T.; Mccune, James E.

1988-01-01

This paper presents a nonlinear theory of forces and moment acting on a two-dimensional airfoil in unsteady potential flow. Results are obtained for cases of both large and small amplitude motion. The analysis, which is based on an extension of Wagner's integral equation to the nonlinear regime, takes full advantage of the trailing wake's tendency to deform under local velocities. Interactive computational results are presented that show examples of wake-induced lift and moment augmentation on the order of 20 percent of quasi-static values. The expandability and flexibility of the present computational method are noted, as well as the relative speed with which solutions are obtained.

Examining the Error of Mis-Specifying Nonlinear Confounding Effect with Application on Accelerometer-Measured Physical Activity

ERIC Educational Resources Information Center

Lee, Paul H.

2017-01-01

Purpose: Some confounders are nonlinearly associated with dependent variables, but they are often adjusted using a linear term. The purpose of this study was to examine the error of mis-specifying the nonlinear confounding effect. Methods: We carried out a simulation study to investigate the effect of adjusting for a nonlinear confounder in the…

Nonlinear friction model for servo press simulation

NASA Astrophysics Data System (ADS)

Ma, Ninshu; Sugitomo, Nobuhiko; Kyuno, Takunori; Tamura, Shintaro; Naka, Tetsuo

2013-12-01

The friction coefficient was measured under an idealized condition for a pulse servo motion. The measured friction coefficient and its changing with both sliding distance and a pulse motion showed that the friction resistance can be reduced due to the re-lubrication during unloading process of the pulse servo motion. Based on the measured friction coefficient and its changes with sliding distance and re-lubrication of oil, a nonlinear friction model was developed. Using the newly developed the nonlinear friction model, a deep draw simulation was performed and the formability was evaluated. The results were compared with experimental ones and the effectiveness was verified.

Thermodynamic potentials in anisotropic and nonlinear dielectrics

NASA Astrophysics Data System (ADS)

Parravicini, Jacopo

2018-07-01

The variation of total energy, entropy, Helmoltz free energy due to the application of a static electric field is calculated and discussed, under suitable conditions, in the case of a dielectric with either anisotropic or nonlinear response. The proposed approach starts from Fröhlich's theory of dielectric thermodynamics and, by analyzing its assumptions, provides a method to generalize it. The obtained relationships can be employed for describing the thermodynamics of different classes of dielectric materials, also in experimental investigations. Specifically, the anisotropy and nonlinearity conditions are considered and relative examples are indicated and discussed.

Nonlinear Motion Tracking by Deep Learning Architecture

NASA Astrophysics Data System (ADS)

Verma, Arnav; Samaiya, Devesh; Gupta, Karunesh K.

2018-03-01

In the world of Artificial Intelligence, object motion tracking is one of the major problems. The extensive research is being carried out to track people in crowd. This paper presents a unique technique for nonlinear motion tracking in the absence of prior knowledge of nature of nonlinear path that the object being tracked may follow. We achieve this by first obtaining the centroid of the object and then using the centroid as the current example for a recurrent neural network trained using real-time recurrent learning. We have tweaked the standard algorithm slightly and have accumulated the gradient for few previous iterations instead of using just the current iteration as is the norm. We show that for a single object, such a recurrent neural network is highly capable of approximating the nonlinearity of its path.

Study on Nonlinear Lateral Parameter Bifurcation Characteristic of Soft Footbridge

NASA Astrophysics Data System (ADS)

Chen, Zhou; Deng, De-Yuan; Yan, Quan-Sheng; Lu, Jin-Zhong; Lu, Jian-Xin

2018-03-01

With the trend of large span in the development of footbridge, its nonlinear characteristic is more and more obvious. Bifurcation has a great influence on the nonstationary trivial solution and its boundary stability of nonlinear vibration. Based on the Millennium Bridge in London, this paper deduces its nonlinear transverse vibration equation. Also, the method of Galerkin and multi-scale method is used to obtain the judgment condition of nonstationary trivial stability. Based on the bifurcation theory, the influence of nonlinear behavior on nontrivial solution as well as its stability is studied in the paper under two situations, a 1 ‑ σ bifurcation and a 1 ‑ ζ2 bifurcation of parameter plane respectively.

Exact traveling wave solutions for system of nonlinear evolution equations.

PubMed

Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H

2016-01-01

In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.

Aeroelastic Response of Nonlinear Wing Section By Functional Series Technique

NASA Technical Reports Server (NTRS)

Marzocca, Piergiovanni; Librescu, Liviu; Silva, Walter A.

2000-01-01

This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indicial functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Aeroelastic Response of Nonlinear Wing Section by Functional Series Technique

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Marzocca, Piergiovanni

2001-01-01

This paper addresses the problem of the determination of the subcritical aeroelastic response and flutter instability of nonlinear two-dimensional lifting surfaces in an incompressible flow-field via indicial functions and Volterra series approach. The related aeroelastic governing equations are based upon the inclusion of structural and damping nonlinearities in plunging and pitching, of the linear unsteady aerodynamics and consideration of an arbitrary time-dependent external pressure pulse. Unsteady aeroelastic nonlinear kernels are determined, and based on these, frequency and time histories of the subcritical aeroelastic response are obtained, and in this context the influence of the considered nonlinearities is emphasized. Conclusions and results displaying the implications of the considered effects are supplied.

Tissue-engineered articular cartilage exhibits tension-compression nonlinearity reminiscent of the native cartilage.

PubMed

Kelly, Terri-Ann N; Roach, Brendan L; Weidner, Zachary D; Mackenzie-Smith, Charles R; O'Connell, Grace D; Lima, Eric G; Stoker, Aaron M; Cook, James L; Ateshian, Gerard A; Hung, Clark T

2013-07-26

The tensile modulus of articular cartilage is much larger than its compressive modulus. This tension-compression nonlinearity enhances interstitial fluid pressurization and decreases the frictional coefficient. The current set of studies examines the tensile and compressive properties of cylindrical chondrocyte-seeded agarose constructs over different developmental stages through a novel method that combines osmotic loading, video microscopy, and uniaxial unconfined compression testing. This method was previously used to examine tension-compression nonlinearity in native cartilage. Engineered cartilage, cultured under free-swelling (FS) or dynamically loaded (DL) conditions, was tested in unconfined compression in hypertonic and hypotonic salt solutions. The apparent equilibrium modulus decreased with increasing salt concentration, indicating that increasing the bath solution osmolarity shielded the fixed charges within the tissue, shifting the measured moduli along the tension-compression curve and revealing the intrinsic properties of the tissue. With this method, we were able to measure the tensile (401±83kPa for FS and 678±473kPa for DL) and compressive (161±33kPa for FS and 348±203kPa for DL) moduli of the same engineered cartilage specimens. These moduli are comparable to values obtained from traditional methods, validating this technique for measuring the tensile and compressive properties of hydrogel-based constructs. This study shows that engineered cartilage exhibits tension-compression nonlinearity reminiscent of the native tissue, and that dynamic deformational loading can yield significantly higher tensile properties. Copyright © 2013 Elsevier Ltd. All rights reserved.

Modeling of Nonlinear Beat Signals of TAE's

NASA Astrophysics Data System (ADS)

Zhang, Bo; Berk, Herbert; Breizman, Boris; Zheng, Linjin

2012-03-01

Experiments on Alcator C-Mod reveal Toroidal Alfven Eigenmodes (TAE) together with signals at various beat frequencies, including those at twice the mode frequency. The beat frequencies are sidebands driven by quadratic nonlinear terms in the MHD equations. These nonlinear sidebands have not yet been quantified by any existing codes. We extend the AEGIS code to capture nonlinear effects by treating the nonlinear terms as a driving source in the linear MHD solver. Our goal is to compute the spatial structure of the sidebands for realistic geometry and q-profile, which can be directly compared with experiment in order to interpret the phase contrast imaging diagnostic measurements and to enable the quantitative determination of the Alfven wave amplitude in the plasma core

Nonlinear optical studies of curcumin metal derivatives with cw laser

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

Henari, F. Z., E-mail: fzhenari@rcsi-mub.com; Cassidy, S.

2015-03-30

We report on measurements of the nonlinear refractive index and nonlinear absorption coefficients for curcumin and curcumin metal complexes of boron, copper, and iron at different wavelengths using the Z-scan technique. These materials are found to be novel nonlinear media. It was found that the addition of metals slightly influences its nonlinearity. These materials show a large negative nonlinear refractive index of the order of 10{sup −7} cm{sup 2}/W and negative nonlinear absorption of the order of 10{sup −6} cm/W. The origin of the nonlinearity was investigated by comparison of the formalism that is known as the Gaussian decomposition modelmore » with the thermal lens model. The optical limiting behavior based on the nonlinear refractive index was also investigated.« less

Toward a Nonlinear Acoustic Analogy: Turbulence as a Source of Sound and Nonlinear Propagation

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2015-01-01

An acoustic analogy is proposed that directly includes nonlinear propagation effects. We examine the Lighthill acoustic analogy and replace the Green's function of the wave equation with numerical solutions of the generalized Burgers' equation. This is justified mathematically by using similar arguments that are the basis of the solution of the Lighthill acoustic analogy. This approach is superior to alternatives because propagation is accounted for directly from the source to the far-field observer instead of from an arbitrary intermediate point. Validation of a numerical solver for the generalized Burgers' equation is performed by comparing solutions with the Blackstock bridging function and measurement data. Most importantly, the mathematical relationship between the Navier- Stokes equations, the acoustic analogy that describes the source, and canonical nonlinear propagation equations is shown. Example predictions are presented for nonlinear propagation of jet mixing noise at the sideline angle

Toward a Nonlinear Acoustic Analogy: Turbulence as a Source of Sound and Nonlinear Propagation

NASA Technical Reports Server (NTRS)

Miller, Steven A. E.

2015-01-01

An acoustic analogy is proposed that directly includes nonlinear propagation effects. We examine the Lighthill acoustic analogy and replace the Green's function of the wave equation with numerical solutions of the generalized Burgers' equation. This is justified mathematically by using similar arguments that are the basis of the solution of the Lighthill acoustic analogy. This approach is superior to alternatives because propagation is accounted for directly from the source to the far-field observer instead of from an arbitrary intermediate point. Validation of a numerical solver for the generalized Burgers' equation is performed by comparing solutions with the Blackstock bridging function and measurement data. Most importantly, the mathematical relationship between the Navier-Stokes equations, the acoustic analogy that describes the source, and canonical nonlinear propagation equations is shown. Example predictions are presented for nonlinear propagation of jet mixing noise at the sideline angle.

Correntropy-based partial directed coherence for testing multivariate Granger causality in nonlinear processes

NASA Astrophysics Data System (ADS)

Kannan, Rohit; Tangirala, Arun K.

2014-06-01

Identification of directional influences in multivariate systems is of prime importance in several applications of engineering and sciences such as plant topology reconstruction, fault detection and diagnosis, and neurosciences. A spectrum of related directionality measures, ranging from linear measures such as partial directed coherence (PDC) to nonlinear measures such as transfer entropy, have emerged over the past two decades. The PDC-based technique is simple and effective, but being a linear directionality measure has limited applicability. On the other hand, transfer entropy, despite being a robust nonlinear measure, is computationally intensive and practically implementable only for bivariate processes. The objective of this work is to develop a nonlinear directionality measure, termed as KPDC, that possesses the simplicity of PDC but is still applicable to nonlinear processes. The technique is founded on a nonlinear measure called correntropy, a recently proposed generalized correlation measure. The proposed method is equivalent to constructing PDC in a kernel space where the PDC is estimated using a vector autoregressive model built on correntropy. A consistent estimator of the KPDC is developed and important theoretical results are established. A permutation scheme combined with the sequential Bonferroni procedure is proposed for testing hypothesis on absence of causality. It is demonstrated through several case studies that the proposed methodology effectively detects Granger causality in nonlinear processes.

Nonlinear ultrasonic imaging with X wave

NASA Astrophysics Data System (ADS)

Du, Hongwei; Lu, Wei; Feng, Huanqing

2009-10-01

X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.

Nonlinear damping model for flexible structures. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Zang, Weijian

1990-01-01

The study of nonlinear damping problem of flexible structures is addressed. Both passive and active damping, both finite dimensional and infinite dimensional models are studied. In the first part, the spectral density and the correlation function of a single DOF nonlinear damping model is investigated. A formula for the spectral density is established with O(Gamma(sub 2)) accuracy based upon Fokker-Planck technique and perturbation. The spectral density depends upon certain first order statistics which could be obtained if the stationary density is known. A method is proposed to find the approximate stationary density explicitly. In the second part, the spectral density of a multi-DOF nonlinear damping model is investigated. In the third part, energy type nonlinear damping model in an infinite dimensional setting is studied.

Modulational-instability-induced supercontinuum generation with saturable nonlinear response

NASA Astrophysics Data System (ADS)

Raja, R. Vasantha Jayakantha; Porsezian, K.; Nithyanandan, K.

2010-07-01

We theoretically investigate the supercontinuum generation (SCG) on the basis of modulational instability (MI) in liquid-core photonic crystal fibers (LCPCF) with CS2-filled central core. The effect of saturable nonlinearity of LCPCF on SCG in the femtosecond regime is studied using an appropriately modified nonlinear Schrödinger equation. We also compare the MI induced spectral broadening with SCG obtained by soliton fission. To analyze the quality of the pulse broadening, we study the coherence of the SC pulse numerically. It is evident from the numerical simulation that the response of the saturable nonlinearity suppresses the broadening of the pulse. We also observe that the MI induced SCG in the presence of saturable nonlinearity degrades the coherence of the SCG pulse when compared to unsaturated medium.

Modulational-instability-induced supercontinuum generation with saturable nonlinear response

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

Raja, R. Vasantha Jayakantha; Porsezian, K.; Nithyanandan, K.

2010-07-15

We theoretically investigate the supercontinuum generation (SCG) on the basis of modulational instability (MI) in liquid-core photonic crystal fibers (LCPCF) with CS{sub 2}-filled central core. The effect of saturable nonlinearity of LCPCF on SCG in the femtosecond regime is studied using an appropriately modified nonlinear Schroedinger equation. We also compare the MI induced spectral broadening with SCG obtained by soliton fission. To analyze the quality of the pulse broadening, we study the coherence of the SC pulse numerically. It is evident from the numerical simulation that the response of the saturable nonlinearity suppresses the broadening of the pulse. We alsomore » observe that the MI induced SCG in the presence of saturable nonlinearity degrades the coherence of the SCG pulse when compared to unsaturated medium.« less

Nonlinear dynamic analysis of traveling wave-type ultrasonic motors.

PubMed

Nakagawa, Yosuke; Saito, Akira; Maeno, Takashi

2008-03-01

In this paper, nonlinear dynamic response of a traveling wave-type ultrasonic motor was investigated. In particular, understanding the transient dynamics of a bar-type ultrasonic motor, such as starting up and stopping, is of primary interest. First, the transient response of the bar-type ultrasonic motor at starting up and stopping was measured using a laser Doppler velocimeter, and its driving characteristics are discussed in detail. The motor is shown to possess amplitude-dependent nonlinearity that greatly influences the transient dynamics of the motor. Second, a dynamical model of the motor was constructed as a second-order nonlinear oscillator, which represents the dynamics of the piezoelectric ceramic, stator, and rotor. The model features nonlinearities caused by the frictional interface between the stator and the rotor, and cubic nonlinearity in the dynamics of the stator. Coulomb's friction model was employed for the interface model, and a stick-slip phenomenon is considered. Lastly, it was shown that the model is capable of representing the transient dynamics of the motor accurately. The critical parameters in the model were identified from measured results, and numerical simulations were conducted using the model with the identified parameters. Good agreement between the results of measurements and numerical simulations is observed.