Phase Equilibrium and Crystal Growth Studies on AgGaSe2 and Related Nonlinear Optical Materials

DTIC Science & Technology

1989-09-01

identify by block number) IELD GROUP SUB-GROUP - "°Silver selenogallate, AgGaSe2, nonlinear optical materials, infrared materials, optical defects 19...materials has unique nonlinear infrared optical properties( 1-4 ) including high nonlinear coefficients, and the ability to be phase matched through a...have a milky appearance in thin section or when viewed with a commercial infrared image converter. Microscopic examination of AgGaSe2 in both reflected

The Nonlinear Jaynes-Cummings Model for the Multiphoton Transition

NASA Astrophysics Data System (ADS)

Liu, Xiao-Jing; Lu, Jing-Bin; Zhang, Si-Qi; Liu, Ji-Ping; Li, Hong; Liang, Yu; Ma, Ji; Weng, Yi-Jiao; Zhang, Qi-Rui; Liu, Han; Zhang, Xiao-Ru; Wu, Xiang-Yao

2018-01-01

With the nonlinear Jaynes-Cummings model, we have studied the atom and light field quantum entanglement of multiphoton transition in nonlinear medium, and researched the effect of the transition photon number N and the nonlinear coefficient χ on the quantum entanglement degrees. We have given the quantum entanglement degrees curves with time evolution, we find when the transition photon number N increases, the entanglement degrees oscillation get faster. When the nonlinear coefficient α > 0, the entanglement degrees oscillation get quickly, the nonlinear term is disadvantage of the atom and light field entanglement, and when the nonlinear coefficient α < 0, the entanglement degrees oscillation get slow, the nonlinear term is advantage of the atom and light field entanglement. These results will have been used in the quantum communication and quantum information.

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.

Determination of nonlinear nanomechanical resonator-qubit coupling coefficient in a hybrid quantum system.

PubMed

Geng, Qi; Zhu, Ka-Di

2016-07-10

We have theoretically investigated a hybrid system that is composed of a traditional optomechanical component and an additional charge qubit (Cooper pair box) that induces a new nonlinear interaction. It is shown that the peak in optomechanically induced transparency has been split by the new nonlinear interaction, and the width of the splitting is proportional to the coupling coefficient of this nonlinear interaction. This may give a way to measure the nanomechanical oscillator-qubit coupling coefficient in hybrid quantum systems.

The equivalent angle-of-attack method for estimating the nonlinear aerodynamic characteristics of missile wings and control surfaces

NASA Technical Reports Server (NTRS)

Hemsch, M. J.; Nielsen, J. N.

1982-01-01

A method has been developed for estimating the nonlinear aerodynamic characteristics of missile wing and control surfaces. The method is based on the following assumption: if a fin on a body has the same normal-force coefficient as a wing alone composed of two of the same fins joined together at their root chords, then the other force and moment coefficients of the fin and the wing alone are the same including the nonlinearities. The method can be used for deflected fins at arbitrary bank angles and at high angles of attack. In the paper, a full derivation of the method is given, its accuracy demonstrated and its use in extending missile data bases is shown.

Highly coherent octave-spanning supercontinuum generation in CS2-filled photonic crystal fiber with strong slow nonlinearity

NASA Astrophysics Data System (ADS)

Wang, Liyun; Yuan, Jinhui; Wang, Kuiru; Kang, Zhe; Sang, Xinzhu; Yu, Chongxiu; Yan, Binbin

2016-11-01

In this paper, the supercontinuum (SC) generation in a carbon disulfide (CS2)-filled photonic crystal fiber (PCF) with strong slow nonlinearity is investigated. When the PCF is pumped at 1.55 μm in the anomalous dispersion region, we obtain highly coherent SC spanning from 0.99 to 2.32 μm, at -40 dB level. Moreover, the influences of the slow nonlinearity, the input pulse width, the pulse peak power, the fiber length, and the temperature on the supercontinuum generation (SCG) are studied. The role of the slow nonlinearity in enhancing the coherence of SC is proved. To our best knowledge, this is the first demonstration on generating the octave-spanning SC with high coherence using the slow nonlinearity of CS2. CS2 is a material that has high nonlinearity coefficient and well transparency in infrared. What's more, the slow nonlinearity is very strong in this material.

Optical Quasi-Soliton Solutions for the Cubic-Quintic Nonlinear SCHRÖDINGER Equation with Variable Coefficients

NASA Astrophysics Data System (ADS)

Yang, Qin; Zhang, Jie-Fang

Optical quasi-soliton solutions for the cubic-quintic nonlinear Schrödinger equation (CQNLSE) with variable coefficients are considered. Based on the extended tanh-function method, we not only successfully obtained bright and dark quasi-soliton solutions, but also obtained the kink quasi-soliton solutions under certain parametric conditions. We conclude that the quasi-solitons induced by the combined effects of the group velocity dispersion (GVD) distribution, the nonlinearity distribution, higher-order nonlinearity distribution, and the amplification or absorption coefficient are quite different from those of the solitons induced only by the combined effects of the GVD, the nonlinearity distribution, and the amplification or absorption coefficient without considering the higher-order nonlinearity distribution (i.e. α(z)=0). Furthermore, we choose appropriate optical fiber parameters D(z) and R(z) to control the velocity of quasi-soliton and time shift, and discuss the evolution behavior of the special quasi-soliton.

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.

Nonlinear thermotics: nonlinearity enhancement and harmonic generation in thermal metasurfaces

NASA Astrophysics Data System (ADS)

Dai, Gaole; Shang, Jin; Wang, Ruizhe; Huang, Jiping

2018-03-01

We propose and investigate a class of structural surfaces (metasurfaces). We develop the perturbation theory and the effective medium theory to study the thermal properties of the metasurface. We report that the coefficient of temperature-dependent (nonlinear) item in thermal conductivity can be enhanced under certain conditions. Furthermore, the existence of nonlinear item helps to generate high-order harmonic frequencies of heat flux in the presence of a heat source with periodic temperature. This work paves a different way to control and manipulate the transfer of heat, and it also makes it possible to develop nonlinear thermotics in the light of nonlinear optics.

Exact traveling-wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional Schrödinger equation with polynomial nonlinearity of arbitrary order.

PubMed

Petrović, Nikola Z; Belić, Milivoj; Zhong, Wei-Ping

2011-02-01

We obtain exact traveling wave and spatiotemporal soliton solutions to the generalized (3+1)-dimensional nonlinear Schrödinger equation with variable coefficients and polynomial Kerr nonlinearity of an arbitrarily high order. Exact solutions, given in terms of Jacobi elliptic functions, are presented for the special cases of cubic-quintic and septic models. We demonstrate that the widely used method for finding exact solutions in terms of Jacobi elliptic functions is not applicable to the nonlinear Schrödinger equation with saturable nonlinearity. ©2011 American Physical Society

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.

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

PubMed

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

2016-02-22

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

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.

A recurrence network approach for the analysis of skin blood flow dynamics in response to loading pressure.

PubMed

Liao, Fuyuan; Jan, Yih-Kuen

2012-06-01

This paper presents a recurrence network approach for the analysis of skin blood flow dynamics in response to loading pressure. Recurrence is a fundamental property of many dynamical systems, which can be explored in phase spaces constructed from observational time series. A visualization tool of recurrence analysis called recurrence plot (RP) has been proved to be highly effective to detect transitions in the dynamics of the system. However, it was found that delay embedding can produce spurious structures in RPs. Network-based concepts have been applied for the analysis of nonlinear time series recently. We demonstrate that time series with different types of dynamics exhibit distinct global clustering coefficients and distributions of local clustering coefficients and that the global clustering coefficient is robust to the embedding parameters. We applied the approach to study skin blood flow oscillations (BFO) response to loading pressure. The results showed that global clustering coefficients of BFO significantly decreased in response to loading pressure (p<0.01). Moreover, surrogate tests indicated that such a decrease was associated with a loss of nonlinearity of BFO. Our results suggest that the recurrence network approach can practically quantify the nonlinear dynamics of BFO.

Role of annealing temperatures on structure polymorphism, linear and nonlinear optical properties of nanostructure lead dioxide thin films

NASA Astrophysics Data System (ADS)

Zeyada, H. M.; Makhlouf, M. M.

2016-04-01

The powder of as synthesized lead dioxide (PbO2) has polycrystalline structure β-PbO2 phase of tetragonal crystal system. It becomes nanocrystallites α-PbO2 phase with orthorhombic crystal system upon thermal deposition to form thin films. Annealing temperatures increase nanocrystallites size from 28 to 46 nm. The optical properties of α-PbO2 phase were calculated from absolute values of transmittance and reflectance at nearly normal incidence of light by spectrophotometer measurements. The refractive and extinction indices were determined and showed a response to annealing temperatures. The absorption coefficient of α-PbO2 films is >106 cm-1 in UV region of spectra. Analysis of the absorption coefficient spectra near optical edge showed indirect allowed transition. Annealing temperature decreases the value of indirect energy gap for α-PbO2 films. The dispersion parameters such as single oscillator energy, dispersion energy, dielectric constant at high frequency and lattice dielectric constant were calculated and its variations with annealing temperatures are reported. The nonlinear refractive index (n2), third-order nonlinear susceptibility (χ(3)) and nonlinear absorption coefficient (βc) were determined. It was found that χ(3), n2 and β increase with increasing photon energy and decrease with increasing annealing temperature. The pristine film of α-PbO2 has higher values of nonlinear optical constants than for annealed films; therefore it is suitable for applications in manufacturing nonlinear optical devices.

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.

Comparisons of linear and nonlinear pyramid schemes for signal and image processing

NASA Astrophysics Data System (ADS)

Morales, Aldo W.; Ko, Sung-Jea

1997-04-01

Linear filters banks are being used extensively in image and video applications. New research results in wavelet applications for compression and de-noising are constantly appearing in the technical literature. On the other hand, non-linear filter banks are also being used regularly in image pyramid algorithms. There are some inherent advantages in using non-linear filters instead of linear filters when non-Gaussian processes are present in images. However, a consistent way of comparing performance criteria between these two schemes has not been fully developed yet. In this paper a recently discovered tool, sample selection probabilities, is used to compare the behavior of linear and non-linear filters. In the conversion from weights of order statistics (OS) filters to coefficients of the impulse response is obtained through these probabilities. However, the reverse problem: the conversion from coefficients of the impulse response to the weights of OS filters is not yet fully understood. One of the reasons for this difficulty is the highly non-linear nature of the partitions and generating function used. In the present paper the problem is posed as an optimization of integer linear programming subject to constraints directly obtained from the coefficients of the impulse response. Although the technique to be presented in not completely refined, it certainly appears to be promising. Some results will be shown.

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.

Elliptical As2Se3 filled core ultra-high-nonlinearity and polarization-maintaining photonic crystal fiber with double hexagonal lattice cladding

NASA Astrophysics Data System (ADS)

Li, Feng; He, Menghui; Zhang, Xuedian; Chang, Min; Wu, Zhizheng; Liu, Zheng; Chen, Hua

2018-05-01

A high birefringence and ultra-high nonlinearity photonic crystal fiber (PCF) is proposed, which is composed of an elliptical As2Se3-doped core and an inner cladding with hexagonal lattice. Optical properties of the PCF are simulated by the full-vector finite element method. The simulation results show that the high birefringence of ∼0.33, ultra-high-nonlinearity coefficient of 300757 W-1km-1 and the low confinement loss can be achieved in the proposed PCF simultaneously at the wavelength of 1.55 μm. Furthermore, by comparison with the other two materials (80PbO•20Ga2O3, As2S3) filled in the core, the As2Se3-doped PCF is found to have the highest birefringence and nonlinearity due to its higher refractive index and nonlinear refractive index. The flattened dispersion feature, as well as the low confinement loss of the proposed PCF structure make it suitable as a wide range of applications, such as the coherent optical communications, polarization-maintaining and nonlinear optics, etc.

Effect of size and indium-composition on linear and nonlinear optical absorption of InGaN/GaN lens-shaped quantum dot

NASA Astrophysics Data System (ADS)

Ahmed, S. Jbara; Zulkafli, Othaman; M, A. Saeed

2016-05-01

Based on the Schrödinger equation for envelope function in the effective mass approximation, linear and nonlinear optical absorption coefficients in a multi-subband lens quantum dot are investigated. The effects of quantum dot size on the interband and intraband transitions energy are also analyzed. The finite element method is used to calculate the eigenvalues and eigenfunctions. Strain and In-mole-fraction effects are also studied, and the results reveal that with the decrease of the In-mole fraction, the amplitudes of linear and nonlinear absorption coefficients increase. The present computed results show that the absorption coefficients of transitions between the first excited states are stronger than those of the ground states. In addition, it has been found that the quantum dot size affects the amplitudes and peak positions of linear and nonlinear absorption coefficients while the incident optical intensity strongly affects the nonlinear absorption coefficients. Project supported by the Ministry of Higher Education and Scientific Research in Iraq, Ibnu Sina Institute and Physics Department of Universiti Teknologi Malaysia (UTM RUG Vote No. 06-H14).

Rogue waves for a discrete (2+1)-dimensional Ablowitz-Ladik equation in the nonlinear optics and Bose-Einstein condensation

NASA Astrophysics Data System (ADS)

Wu, Xiao-Yu; Tian, Bo; Chai, Han-Peng; Du, Zhong

2018-03-01

Under investigation in this paper is a discrete (2+1)-dimensional Ablowitz-Ladik equation, which is used to model the nonlinear waves in the nonlinear optics and Bose-Einstein condensation. Employing the Kadomtsev-Petviashvili hierarchy reduction, we obtain the rogue wave solutions in terms of the Gramian. We graphically study the first-, second- and third-order rogue waves with the influence of the focusing coefficient and coupling strength. When the value of the focusing coefficient increases, both the peak of the rogue wave and background decrease. When the value of the coupling strength increases, the rogue wave raises and decays in a shorter time. High-order rogue waves are exhibited as one single highest peak and some lower humps, and such lower humps are shown as the triangular and circular patterns.

Nonlinear absorption enhancement of AuNPs based polymer nanocomposites

NASA Astrophysics Data System (ADS)

Zulina, Natalia A.; Baranov, Mikhail A.; Kniazev, Kirill I.; Kaliabin, Viacheslav O.; Denisyuk, Igor Yu.; Achor, Susan U.; Sitnikova, Vera E.

2018-07-01

Au nanoparticles (AuNPs) based polymer nanocomposites with high nonlinear absorption coefficient were synthesized by UV-photocuring. AuNPs were synthesized by laser ablation method in liquid monomer isodecyl acrylate (IDA). In this research, two colloids with 70 nm and 20 nm nanoparticles average sizes were studied. Size control was performed with SEM and STEM. Prepared nanomaterials exhibit strong third-order nonlinear optical responses under CW laser irradiation at 532 nm, which was estimated by using z-scan technique performed with open aperture. It was found experimentally that nonlinear absorption β is almost twice higher for nanocomposites with smaller AuNPs.

Chalcogenide based rib waveguide for compact on-chip supercontinuum sources in mid-infrared domain

NASA Astrophysics Data System (ADS)

Saini, Than Singh; Tiwari, Umesh Kumar; Sinha, Ravindra Kumar

2017-08-01

We have designed and analysed a rib waveguide structure in recently reported Ga-Sb-S based highly nonlinear chalcogenide glass for nonlinear applications. The proposed waveguide structure possesses a very high nonlinear coefficient and can be used to generate broadband supercontinuum in mid-infrared domain. The reported design of the chalcogenide waveguide offers two zero dispersion values at 1800 nm and 2900 nm. Such rib waveguide structure is suitable to generate efficient supercontinuum generation ranging from 500 - 7400 μm. The reported waveguide can be used for the realization of the compact on-chip supercontinuum sources which are highly applicable in optical imaging, optical coherence tomography, food quality control, security and sensing.

Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable

ERIC Educational Resources Information Center

du Toit, Stephen H. C.; Cudeck, Robert

2009-01-01

A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…

Dielectric and varistor properties of rare-earth-doped ZnO and CaCu3Ti4O12 composite ceramics

NASA Astrophysics Data System (ADS)

Lu, Huafei; Lin, Yuanhua; Yuan, Jiancong; Nan, Cewen; Chen, Kexin

2013-02-01

To investigate the multi-functional ceramics with both high permittivity and large nonlinear coefficient, we have prepared rare-earth Tb-and-Co doped ZnO and TiO2-rich CaCu3Ti4O12 (TCCTO) powders by chemical co-precipitation and sol-gel methods respectively, and then obtained the TCCTO/ZnO composite ceramics, sintered at 1100°C for 3 h in air. Analyzing the composite ceramics of the microstructure and phase composition indicated that the composite ceramics were composed of the main phases of ZnO and CaCu3Ti4O12 (CCTO). Our results revealed that the TCCTO/ZnO composite ceramics showed both high dielectric and good nonlinear electrical behaviors. The composite ceramic of TCCTO: ZnO = 0.3 exhibited a high dielectric constant of 210(1 kHz) with a nonlinear coefficient of 11. The dielectric behavior of TCCTO/ZnO composite could be explained by the mixture rule. With the high dielectric permittivity and tunable varistor behaviors, the composite ceramics has a potential application for the higher voltage transportation devices.

Bilayered Hybrid Perovskite Ferroelectric with Giant Two-Photon Absorption.

PubMed

Li, Lina; Shang, Xiaoying; Wang, Sasa; Dong, Ningning; Ji, Chengmin; Chen, Xueyuan; Zhao, Sangen; Wang, Jun; Sun, Zhihua; Hong, Maochun; Luo, Junhua

2018-06-06

Perovskite ferroelectrics with prominent nonlinear optical absorption have attracted great attention in the field of photonics. However, they are traditionally dominated by inorganic oxides and exhibit relatively small nonlinear optical absorption coefficients, which hinder their further applications. Herein, we report a new organic-inorganic hybrid bilayered perovskite ferroelectric, (C 4 H 9 NH 3 ) 2 (NH 2 CHNH 2 )Pb 2 Br 7 (1), showing an above-room-temperature Curie temperature (∼322 K) and notable spontaneous polarization (∼3.8 μC cm -2 ). Significantly, the unique quantum-well structure of 1 results in intriguing two-photon absorption properties with a giant nonlinear optical absorption coefficient as high as 5.76 × 10 3 cm GW -1 , which is almost two-orders of magnitude larger than those of mostly traditional all-inorganic perovskite ferroelectrics. To our best knowledge, 1 is the first example of hybrid ferroelectrics with giant two-photon absorption coefficient. The mechanisms for ferroelectric and two-photon absorption are revealed. This work will shed light on the design of new ferroelectrics with two-photon absorption and promote their potentials in the photonic application.

Nonlinearity of the forward-backward correlation function in the model with string fusion

NASA Astrophysics Data System (ADS)

Vechernin, Vladimir

2017-12-01

The behavior of the forward-backward correlation functions and the corresponding correlation coefficients between multiplicities and transverse momenta of particles produced in high energy hadronic interactions is analyzed by analytical and MC calculations in the models with and without string fusion. The string fusion is taking into account in simplified form by introducing the lattice in the transverse plane. The results obtained with two alternative definitions of the forward-backward correlation coefficient are compared. It is shown that the nonlinearity of correlation functions increases with the width of observation windows, leading at small string density to a strong dependence of correlation coefficient value on the definition. The results of the modeling enable qualitatively to explain the experimentally observed features in the behavior of the correlation functions between multiplicities and mean transverse momenta at small and large multiplicities.

Soliton tunneling in the nonlinear Schrödinger equation with variable coefficients and an external harmonic potential.

PubMed

Zhong, Wei-Ping; Belić, Milivoj R

2010-05-01

We report on the nonlinear tunneling effects of spatial solitons of the generalized nonlinear Schrödinger equation with distributed coefficients in an external harmonic potential. By using the homogeneous balance principle and the F-expansion technique we find the spatial bright and dark soliton solutions. We then display tunneling effects of such solutions occurring under special conditions; specifically when the spatial solitons pass unchanged through the potential barriers and wells affected by special choices of the diffraction and/or the nonlinearity coefficients. Our results show that the solitons display tunneling effects not only when passing through the nonlinear potential barriers or wells but also when passing through the diffractive barriers or wells. During tunneling the solitons may also undergo a controllable compression.

Comprehensive analysis of the optical Kerr coefficient of graphene

DOE PAGES

Soh, Daniel B. S.; Hamerly, Ryan; Mabuchi, Hideo

2016-08-25

We present a comprehensive analysis of the nonlinear optical Kerr effect in graphene. We directly solve the S-matrix element to calculate the absorption rate, utilizing the Volkov-Keldysh-type crystal wave functions. We then convert to the nonlinear refractive index coefficients through the Kramers-Kronig relation. In this formalism, the source of Kerr nonlinearity is the interplay of optical fields that cooperatively drive the transition from valence to conduction band. This formalism makes it possible to identify and compute the rates of distinct nonlinear processes that contribute to the Kerr nonlinear refractive index coefficient. The four identified mechanisms are two-photon absorption, Raman transition,more » self-coupling, and quadratic ac Stark effect. As a result, we present a comparison of our theory with recent experimental and theoretical results.« less

Nonlinear-drifted Brownian motion with multiple hidden states for remaining useful life prediction of rechargeable batteries

NASA Astrophysics Data System (ADS)

Wang, Dong; Zhao, Yang; Yang, Fangfang; Tsui, Kwok-Leung

2017-09-01

Brownian motion with adaptive drift has attracted much attention in prognostics because its first hitting time is highly relevant to remaining useful life prediction and it follows the inverse Gaussian distribution. Besides linear degradation modeling, nonlinear-drifted Brownian motion has been developed to model nonlinear degradation. Moreover, the first hitting time distribution of the nonlinear-drifted Brownian motion has been approximated by time-space transformation. In the previous studies, the drift coefficient is the only hidden state used in state space modeling of the nonlinear-drifted Brownian motion. Besides the drift coefficient, parameters of a nonlinear function used in the nonlinear-drifted Brownian motion should be treated as additional hidden states of state space modeling to make the nonlinear-drifted Brownian motion more flexible. In this paper, a prognostic method based on nonlinear-drifted Brownian motion with multiple hidden states is proposed and then it is applied to predict remaining useful life of rechargeable batteries. 26 sets of rechargeable battery degradation samples are analyzed to validate the effectiveness of the proposed prognostic method. Moreover, some comparisons with a standard particle filter based prognostic method, a spherical cubature particle filter based prognostic method and two classic Bayesian prognostic methods are conducted to highlight the superiority of the proposed prognostic method. Results show that the proposed prognostic method has lower average prediction errors than the particle filter based prognostic methods and the classic Bayesian prognostic methods for battery remaining useful life prediction.

Self-Inversion of the Image of a Small-Scale Opaque Object in the Process of Focusing of the Illuminating Beam in an Absorbing Medium

NASA Astrophysics Data System (ADS)

Bubis, E. L.; Lozhrkarev, V. V.; Stepanov, A. N.; Smirnov, A. I.; Martynov, V. O.; Mal'shakova, O. A.; Silin, D. E.; Gusev, S. A.

2017-03-01

We describe the process of adaptive self-inversion of an image (nonlinear switching) of smallscale opaque object, when the amplitude-modulated laser beam, which illuminates it, is focused in a weakly absorbing medium. It is shown that, despite the nonlocal character of the process, which is due to thermal nonlinearity, the brightness-inverse image is characterized by acceptable quality and a high conversion coefficient. It is shown that the coefficient of conversion of the original image to the inverse one depends on the ratio of the object dimensions and the size of the illuminating beam, and decreases sharply for relatively large objects. The obtained experimental data agree with the numerical calculations. Inversion of the images of several model objects and microdefects in a nonlinear KDP crystal is demonstrated.

Coupled oscillators in identification of nonlinear damping of a real parametric pendulum

NASA Astrophysics Data System (ADS)

Olejnik, Paweł; Awrejcewicz, Jan

2018-01-01

A damped parametric pendulum with friction is identified twice by means of its precise and imprecise mathematical model. A laboratory test stand designed for experimental investigations of nonlinear effects determined by a viscous resistance and the stick-slip phenomenon serves as the model mechanical system. An influence of accurateness of mathematical modeling on the time variability of the nonlinear damping coefficient of the oscillator is proved. A free decay response of a precisely and imprecisely modeled physical pendulum is dependent on two different time-varying coefficients of damping. The coefficients of the analyzed parametric oscillator are identified with the use of a new semi-empirical method based on a coupled oscillators approach, utilizing the fractional order derivative of the discrete measurement series treated as an input to the numerical model. Results of application of the proposed method of identification of the nonlinear coefficients of the damped parametric oscillator have been illustrated and extensively discussed.

Theoretical investigation of intensity-dependent optical nonlinearity in graphene-aided D-microfiber

NASA Astrophysics Data System (ADS)

Shah, Manoj Kumar; Lu, Rongguo; Zhang, Yali; Ye, Shengwei; Zhang, Shangjian; Liu, Yong

2018-01-01

We theoretically investigate the intensity-dependent optical nonlinearity in graphene-aided D-microfiber, by tuning the chemical potential of graphene and varying radial distance and radii of the D-microfiber. Utilizing an interplay between graphene and the enhanced evanescent field of a guided mode in the waveguide of interest, the net utility of nonlinear coefficient is harnessed up to a very high value of 106 W-1m-1. Importantly, which is ∼ two orders of magnitude larger than in PMMA-graphene-PMMA waveguide. The highly dispersive nature of the waveguide, D ∼ 103 ps/nm-km, and large nonlinear figure-of-merit, FOMNL ∼ 1.29, have raised the possibilities of utilizing slow light structures to operate devices at few watts power level with microscale length. These studies have opened one window towards the next-generation all fiber-optic graphene nonlinear optical devices.

Periodic solutions for one dimensional wave equation with bounded nonlinearity

NASA Astrophysics Data System (ADS)

Ji, Shuguan

2018-05-01

This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.

Kurtosis Approach for Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation.

Substituent Dependence of Third-Order Optical Nonlinearity in Chalcone Derivatives

NASA Astrophysics Data System (ADS)

Kiran, Anthony John; Satheesh Rai, Nooji; Chandrasekharan, Keloth; Kalluraya, Balakrishna; Rotermund, Fabian

2008-08-01

The third-order nonlinear optical properties of derivatives of dibenzylideneacetone were investigated using the single beam z-scan technique at 532 nm. A strong dependence of third-order optical nonlinearity on electron donor and acceptor type of substituents was observed. An enhancement in χ(3)-value of one order of magnitude was achieved upon the substitution of strong electron donors compared to that of the molecule substituted with an electron acceptor. The magnitude of nonlinear refractive index of these chalcones is as high as of 10-11 esu. Their nonlinear optical coefficients are larger than those of widely used thiophene oligomers and trans-1-[p-(p-dimethylaminobenzyl-azo)-benzyl]-2-(N-methyl-4-pyridinium)-ethene iodide (DABA-PEI) organic compounds.

Numerical study of surface plasmon enhanced nonlinear absorption and refraction.

PubMed

Kohlgraf-Owens, Dana C; Kik, Pieter G

2008-07-07

Maxwell Garnett effective medium theory is used to study the influence of silver nanoparticle induced field enhancement on the nonlinear response of a Kerr-type nonlinear host. We show that the composite nonlinear absorption coefficient, beta(c), can be enhanced relative to the host nonlinear absorption coefficient near the surface plasmon resonance of silver nanoparticles. This enhancement is not due to a resonant enhancement of the host nonlinear absorption, but rather due to a phase shifted enhancement of the host nonlinear refractive response. The enhancement occurs at the expense of introducing linear absorption, alpha(c), which leads to an overall reduced figure of merit beta(c)/alpha(c) for nonlinear absorption. For thin (< 1 microm) composites, the use of surface plasmons is found to result in an increased nonlinear absorption response compared to that of the host material.

Linear and nonlinear trending and prediction for AVHRR time series data

NASA Technical Reports Server (NTRS)

Smid, J.; Volf, P.; Slama, M.; Palus, M.

1995-01-01

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse.

Nonlinear optical properties of TeO2-P2 O5- ZnO-LiNbO3 glass doped with Er3+ ions

NASA Astrophysics Data System (ADS)

Miedzinski, R.; Fuks-Janczarek, I.; El Sayed Said, Y.

2016-10-01

A series of lithium niobate LiNbO3 (LN) single crystals doped with Er3+ were grown under the same conditions by melt-quenching method. The distribution coefficients of rare-earth (RE) elements in the "crystal-melt" system of LN were determined at the beginning of the crystal growth. Their dependence on the dopant concentration in melt for 0.4 and 0.8 wt % was investigated. The procedure is applied to RE-doped lithium niobate (LiNbO3), a material of great interest for optoelectronic applications. We have obtained the real χR(3) and imaginary parts χI(3) of the third-order, nonlinear optical susceptibility to the nonlinear refractive index n2 and the nonlinear absorption coefficient β that are valid for absorbing systems. We show that nonlinear refractive or absorptive effects are the consequence of the interplay between the real and imaginary parts of the third-order susceptibilities of the materials. The method for measuring non-linear absorption coefficients and nonlinear refractive index based on well-known Z-scan is presented.

Traveling wave and soliton solutions of coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients.

PubMed

Zhong, Wei-Ping; Belić, Milivoj

2010-10-01

Exact traveling wave and soliton solutions, including the bright-bright and dark-dark soliton pairs, are found for the system of two coupled nonlinear Schrödinger equations with harmonic potential and variable coefficients, by employing the homogeneous balance principle and the F-expansion technique. A kind of shape-changing soliton collision is identified in the system. The collision is essentially elastic between the two solitons with opposite velocities. Our results demonstrate that the dynamics of solitons can be controlled by selecting the diffraction, nonlinearity, and gain coefficients.

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.

Effects of intermode nonlinearity and intramode nonlinearity on modulation instability in randomly birefringent two-mode optical fibers

NASA Astrophysics Data System (ADS)

Li, Jin Hua; Xu, Hui; Sun, Ting Ting; Pei, Shi Xin; Ren, Hai Dong

2018-05-01

We analyze in detail the effects of the intermode nonlinearity (IEMN) and intramode nonlinearity (IRMN) on modulation instability (MI) in randomly birefringent two-mode optical fibers (RB-TMFs). In the anomalous dispersion regime, the MI gain enhances significantly as the IEMN and IRMN coefficients increases. In the normal dispersion regime, MI can be generated without the differential mode group delay (DMGD) effect, as long as the IEMN coefficient between two distinct modes is above a critical value, or the IRMN coefficient inside a mode is below a critical value. This critical IEMN (IRMN) coefficient depends strongly on the given IRMN (IEMN) coefficient and DMGD for a given nonlinear RB-TMF structure, and is independent on the input total power, the power ratio distribution and the group velocity dispersion (GVD) ratio between the two modes. On the other hand, in contrast to the MI band arising from the pure effect of DMGD in the normal dispersion regime, where MI vanishes after a critical total power, the generated MI band under the combined effects of IEMN and IRMN without DMGD exists for any total power and enhances with the total power. The MI analysis is verified numerically by launching perturbed continuous waves (CWs) with wave propagation method.

Theory and Simulation of Self- and Mutual-Diffusion of Carrier Density and Temperature in Semiconductor Lasers

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.

2001-01-01

Carrier diffusion and thermal conduction play a fundamental role in the operation of high-power, broad-area semiconductor lasers. Restricted geometry, high pumping level and dynamic instability lead to inhomogeneous spatial distribution of plasma density, temperature, as well as light field, due to strong light-matter interaction. Thus, modeling and simulation of such optoelectronic devices rely on detailed descriptions of carrier dynamics and energy transport in the system. A self-consistent description of lasing and heating in large-aperture, inhomogeneous edge- or surface-emitting lasers (VCSELs) require coupled diffusion equations for carrier density and temperature. In this paper, we derive such equations from the Boltzmann transport equation for the carrier distributions. The derived self- and mutual-diffusion coefficients are in general nonlinear functions of carrier density and temperature including many-body interactions. We study the effects of many-body interactions on these coefficients, as well as the nonlinearity of these coefficients for large-area VCSELs. The effects of mutual diffusions on carrier and temperature distributions in gain-guided VCSELs will be also presented.

Thermal properties of borate crystals for high power optical parametric chirped-pulse amplification.

PubMed

Riedel, R; Rothhardt, J; Beil, K; Gronloh, B; Klenke, A; Höppner, H; Schulz, M; Teubner, U; Kränkel, C; Limpert, J; Tünnermann, A; Prandolini, M J; Tavella, F

2014-07-28

The potential of borate crystals, BBO, LBO and BiBO, for high average power scaling of optical parametric chirped-pulse amplifiers is investigated. Up-to-date measurements of the absorption coefficients at 515 nm and the thermal conductivities are presented. The measured absorption coefficients are a factor of 10-100 lower than reported by the literature for BBO and LBO. For BBO, a large variation of the absorption coefficients was found between crystals from different manufacturers. The linear and nonlinear absorption coefficients at 515 nm as well as thermal conductivities were determined for the first time for BiBO. Further, different crystal cooling methods are presented. In addition, the limits to power scaling of OPCPAs are discussed.

A novel structure photonic crystal fiber based on bismuth-oxide for optical parametric amplification

NASA Astrophysics Data System (ADS)

Jin, Cang; Yuan, Jinhui; Yu, Chongxiu

2010-11-01

The heavy metal oxide glasses containing bismuth such as bismuth sesquioxide show unique high refractive index. In addition, the bismuth-oxide based glass does not include toxic elements such as Pb, As, Se, Te, and exhibits well chemical, mechanical and thermal stability. Hence, it is used to fabricate high nonlinear fiber for nonlinear optical application. Although the bismuth-oxide based high nonlinear fiber can be fusion-spliced to conventional silica fibers and have above advantages, yet it suffers from large group velocity dispersion because of material chromatic dispersion which restricts its utility. In regard to this, the micro-structure was introduced to adjust the dispersion of bismuth-oxide high nonlinear fiber in the 1550nm wave-band. In this paper, a hexagonal solid-core micro-structure is developed to balance its dispersion and nonlinearity. Our simulation and calculation results show that the bismuth-oxide based photonic crystal fiber has near zero dispersion around 1550nm where the optical parametric amplification suitable wavelength is. Its dispersion slop in the communication wavelength range is also relatively flat. Moreover, both nonlinear coefficient and model filed distribution were simulated, respectively.

Solid-state reversible quadratic nonlinear optical molecular switch with an exceptionally large contrast.

PubMed

Sun, Zhihua; Luo, Junhua; Zhang, Shuquan; Ji, Chengmin; Zhou, Lei; Li, Shenhui; Deng, Feng; Hong, Maochun

2013-08-14

Exceptional nonlinear optical (NLO) switching behavior, including an extremely large contrast (on/off) of ∼35 and high NLO coefficients, is displayed by a solid-state reversible quadratic NLO switch. The favorable results, induced by very fast molecular motion and anionic ordering, provides impetus for the design of a novel second-harmonic-generation switch involving molecular motion. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

NASA Astrophysics Data System (ADS)

Pepi, John W.

2017-08-01

Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

Diffusion Coefficients of a Non-Linear Astrophysical Process: Luis Carrasco's Scientific (and other) Contributions

NASA Astrophysics Data System (ADS)

Aguilar, L. A.

2009-11-01

The Luis Carrasco phenomenon in Astrophysics is a widespread event that has appeared in many branches of theoretical and observational Astronomy, as well as in astronomical instrumentation. It is an ubiquitous and highly non-linear effect with multiple coupling constants. To understand it, it is necessary to dwell, not only into many areas of Astronomy, but of human culture and knowledge in general. Some authors believe that it is only through the ``many-worlds'' interpretation of Quantum Mechanics, that this effect can be understood. In this work, we will demonstrate its fractal nature, present a panoramic view of this global effect, and estimate its diffusion coefficients in the regular and irregular regimes. Connections with areas outside Astronomy will be shown.

Kurtosis Approach Nonlinear Blind Source Separation

NASA Technical Reports Server (NTRS)

Duong, Vu A.; Stubbemd, Allen R.

2005-01-01

In this paper, we introduce a new algorithm for blind source signal separation for post-nonlinear mixtures. The mixtures are assumed to be linearly mixed from unknown sources first and then distorted by memoryless nonlinear functions. The nonlinear functions are assumed to be smooth and can be approximated by polynomials. Both the coefficients of the unknown mixing matrix and the coefficients of the approximated polynomials are estimated by the gradient descent method conditional on the higher order statistical requirements. The results of simulation experiments presented in this paper demonstrate the validity and usefulness of our approach for nonlinear blind source signal separation Keywords: Independent Component Analysis, Kurtosis, Higher order statistics.

Laser Ablation of Poly(methylmethacrylate) Doped with Aromatic Compounds: Laser Intensity Dependence of Absorption Coefficient

NASA Astrophysics Data System (ADS)

Wang, Jun; Niino, Hiroyuki; Yabe, Akira

1999-02-01

We developed a novel method of obtaining an absorption coefficient which depends on the laser intensity, since a single-photon absorption coefficient of a polymer could not be applied to laser ablation. The relationship between the nonlinear absorption coefficient and the laser intensity was derived from experimental data of transmission and incident laser intensities. Using the nonlinear absorption coefficient of poly(methylmethacrylate) doped with benzil and pyrene, we succeeded in fitting the relationship of etch depth and laser intensity, obtained experimentally, and discussed the energy absorbed by the polymer at the threshold fluence.

Chi 3 dispersion in planar tantalum pentoxide waveguides in the telecommunications window.

PubMed

Chen, Ruiqi Y; Charlton, Martin D B; Lagoudakis, Pavlos G

2009-04-01

We report on the dispersion of the third-order nonlinear susceptibility (chi(3) or "Chi 3") in planar Ta2O5 waveguides in the telecommunications spectral window. We utilize the observation of third-harmonic generation under ultrashort pulsed excitation as a reference-free characterization method of chi(3) and obtain a large nonlinear coefficient, 2x10(-13) esu, at 1550 nm. Our observation of efficient third-harmonic generation in Ta2O5 waveguides in the telecoms window reveals the potential of this material system in high-speed integrated nonlinear optical switches.

Exact solutions for an oscillator with anti-symmetric quadratic nonlinearity

NASA Astrophysics Data System (ADS)

Beléndez, A.; Martínez, F. J.; Beléndez, T.; Pascual, C.; Alvarez, M. L.; Gimeno, E.; Arribas, E.

2018-04-01

Closed-form exact solutions for an oscillator with anti-symmetric quadratic nonlinearity are derived from the first integral of the nonlinear differential equation governing the behaviour of this oscillator. The mathematical model is an ordinary second order differential equation in which the sign of the quadratic nonlinear term changes. Two parameters characterize this oscillator: the coefficient of the linear term and the coefficient of the quadratic term. Not only the common case in which both coefficients are positive but also all possible combinations of positive and negative signs of these coefficients which provide periodic motions are considered, giving rise to four different cases. Three different periods and solutions are obtained, since the same result is valid in two of these cases. An interesting feature is that oscillatory motions whose equilibrium points are not at x = 0 are also considered. The periods are given in terms of an incomplete or complete elliptic integral of the first kind, and the exact solutions are expressed as functions including Jacobi elliptic cosine or sine functions.

Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

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

Cieplak, Agnieszka M.; Slosar, Anze

The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n-th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation overmore » mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. In conclusion, we find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.« less

Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

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

Cieplak, Agnieszka M.; Slosar, Anže, E-mail: acieplak@bnl.gov, E-mail: anze@bnl.gov

The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n -th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisationmore » over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. We find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.« less

Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

DOE PAGES

Cieplak, Agnieszka M.; Slosar, Anze

2017-10-12

The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n-th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation overmore » mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. In conclusion, we find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.« less

Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

NASA Astrophysics Data System (ADS)

Cieplak, Agnieszka M.; Slosar, Anže

2017-10-01

The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n-th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. We find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.

Reverse saturable absorption studies in polymerized indole - Effect of polymerization in the phenomenal enhancement of third order optical nonlinearity

NASA Astrophysics Data System (ADS)

Jayakrishnan, K.; Joseph, Antony; Bhattathiripad, Jayakrishnan; Ramesan, M. T.; Chandrasekharan, K.; Siji Narendran, N. K.

2016-04-01

We report our results on the identification of large order enhancement in nonlinear optical coefficients of polymerized indole and its comparative study with reference to its monomer counterpart. Indole monomer shows virtually little third order effects whereas its polymerized version exhibits phenomenal increase in its third order nonlinear optical parameters such as nonlinear refractive index and nonlinear absorption. Open aperture Z-scan trace of polyindole done with Q-switched Nd:YAG laser source (532 nm, 7 ns), shows β value as high as 89 cm/GW at a beam energy of 0.83 GW/cm2. Closed aperture Z-scan done at identical energies reveals nonlinear refractive index of the order of -3.55 × 10-17 m2/W. Band gap measurement of polyindole was done with UV-Vis absorption spectra and compared with that of Indole. FTIR spectra of the monomer and polymerized versions were recorded and relevant bond formations were confirmed from the characteristic peaks. Photo luminescent spectra were investigated to know the emission features of both molecules. Beam energy (I0) versus nonlinear absorption coefficient (β) plot indicates reverse saturable type of absorption behaviour in polyindole molecules. Degenerate Four Wave Mixing (DFWM) plot of polyindole reveals quite a cubic dependence between probe and phase conjugate signal and the resulting χ(3) is comparable with Z-scan results. Optical limiting efficiency of polyindole is comparable with certain derivatives of porphyrins, phthalocyanines and graphene oxides.

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients.

PubMed

Charalampidis, E G; Kevrekidis, P G; Frantzeskakis, D J; Malomed, B A

2016-08-01

We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multiring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multiring complexes into stable vortex-bright solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self- and cross-repulsive nonlinearities.

Nonlinear optical whispering gallery mode resonators

NASA Technical Reports Server (NTRS)

Ilchenko, Vladimir (Inventor); Matsko, Andrey B. (Inventor); Savchenkov, Anatoliy (Inventor); Maleki, Lutfollah (Inventor)

2005-01-01

Whispering gallery mode (WGM) optical resonators comprising nonlinear optical materials, where the nonlinear optical material of a WGM resonator includes a plurality of sectors within the optical resonator and nonlinear coefficients of two adjacent sectors are oppositely poled.

Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.

PubMed

Meair, Jonathan; Jacquod, Philippe

2013-02-27

We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance.

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

NASA Astrophysics Data System (ADS)

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

2007-12-01

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

Synthesis of nanocomposites based on carbon nanotube/smart copolymer with nonlinear optical properties

NASA Astrophysics Data System (ADS)

Sousani, Abbas; Motiei, Hamideh; Najafimoghadam, Peyman; Hasanzade, Reza

2017-05-01

In this study new nanocompoites based on polyglycidylmethacrylate grafted 4-[(4-methoxyphenyl) diazenyl] phenol (Azo-PGMA) and Carboxylicacid functionalized multi-walled carbon nanotubes (MWCNT-COOH) were prepared. The nanocomposites structure was characterized by FT-IR, TGA and SEM. The Z-scan technique was applied for measuring the nonlinear parameters of nanocomposites. The samples after solving in AWM solution (equal ratio of acetone, deionized water and methanol) were investigated by using closed aperture Z-scan technique and a diode-pumped laser at the line 532 nm. All the nonlinear refractive index of the samples at three concentrations of carbon nanotubes in three different intensities of the laser beam were investigated and the nonlinear optical response of them are compared under the same condition. Because of high order of nonlinear refractive coefficient and good nonlinearity, these compounds are suitable candidate for optical switching, optical limiting and electro-optical devices.

Nonlinear Spectral Singularity and Laser Output Intensity for the TE and TM Modes

NASA Astrophysics Data System (ADS)

Ghaemidizicheh, Hamed; Mostafazadeh, Ali

The nonlinear spectral singularity arising from a Kerr nonlinearity is explored in. This reference studies the effect of nonlinearity in Lasing condition and shows that Kerr nonlinearity with spectral singularity for a normally incident wave provides an explanation of lasing at gain coefficient g. Lasing occurs when it exceeds threshold gain g0. For oblique waves, Ref. looks at the behavior of threshold gain coefficient g0 which is given by the condition that there is a linear spectral singularity. We investigated imposing the condition of the existence of nonlinear spectral singularity in the TE / TM modes of a mirrorless slab of gain materials and studied the θ-dependence of intensity. Supported by TUBITAK Project No: 114F357 and by the Turkish Academy of Science (TUBA).

Prediction and Characterization of NaGaS2, A High Thermal Conductivity Mid-Infrared Nonlinear Optical Material for High-Power Laser Frequency Conversion.

PubMed

Hou, Dianwei; Nissimagoudar, Arun S; Bian, Qiang; Wu, Kui; Pan, Shilie; Li, Wu; Yang, Zhihua

2018-06-15

Infrared nonlinear optical (IR NLO) crystals are the major materials to widen the output range of solid-state lasers to mid- or far-infrared regions. The IR NLO crystals used in the middle IR region are still inadequate for high-power laser applications because of deleterious thermal effects (lensing and expansion), low laser-induced damage threshold, and two-photon absorption. Herein, the unbiased global minimum search method was used for the first time to search for IR NLO optical materials and ultimately found a new IR NLO material NaGaS 2 . It meets the stringent demands for IR NLO materials pumped by high-power laser with the highest thermal conductivity among common IR NLO materials able to avoid two-photon absorption, a classic nonlinear coefficient, and wide infrared transparency.

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system.

PubMed

Tao, S; Trzasko, J D; Gunter, J L; Weavers, P T; Shu, Y; Huston, J; Lee, S K; Tan, E T; Bernstein, M A

2017-01-21

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer's Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26 cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients.

Finite-time output feedback stabilization of high-order uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Jiang, Meng-Meng; Xie, Xue-Jun; Zhang, Kemei

2018-06-01

This paper studies the problem of finite-time output feedback stabilization for a class of high-order nonlinear systems with the unknown output function and control coefficients. Under the weaker assumption that output function is only continuous, by using homogeneous domination method together with adding a power integrator method, introducing a new analysis method, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee global finite-time stability of the closed-loop system.

Quantitative Analysis of Temperature Dependence of Raman shift of monolayer WS2

NASA Astrophysics Data System (ADS)

Huang, Xiaoting; Gao, Yang; Yang, Tianqi; Ren, Wencai; Cheng, Hui-Ming; Lai, Tianshu

2016-08-01

We report the temperature-dependent evolution of Raman spectra of monolayer WS2 directly CVD-grown on a gold foil and then transferred onto quartz substrates over a wide temperature range from 84 to 543 K. The nonlinear temperature dependence of Raman shifts for both and A1g modes has been observed. The first-order temperature coefficients of Raman shifts are obtained to be -0.0093 (cm-1/K) and -0.0122 (cm-1/K) for and A1g peaks, respectively. A physical model, including thermal expansion and three- and four-phonon anharmonic effects, is used quantitatively to analyze the observed nonlinear temperature dependence. Thermal expansion coefficient (TEC) of monolayer WS2 is extracted from the experimental data for the first time. It is found that thermal expansion coefficient of out-plane mode is larger than one of in-plane mode, and TECs of and A1g modes are temperature-dependent weakly and strongly, respectively. It is also found that the nonlinear temperature dependence of Raman shift of mode mainly originates from the anharmonic effect of three-phonon process, whereas one of A1g mode is mainly contributed by thermal expansion effect in high temperature region, revealing that thermal expansion effect cannot be ignored.

High Reynolds number analysis of flat plate and separated afterbody flow using non-linear turbulence models

NASA Technical Reports Server (NTRS)

Carlson, John R.

1996-01-01

The ability of the three-dimensional Navier-Stokes method, PAB3D, to simulate the effect of Reynolds number variation using non-linear explicit algebraic Reynolds stress turbulence modeling was assessed. Subsonic flat plate boundary-layer flow parameters such as normalized velocity distributions, local and average skin friction, and shape factor were compared with DNS calculations and classical theory at various local Reynolds numbers up to 180 million. Additionally, surface pressure coefficient distributions and integrated drag predictions on an axisymmetric nozzle afterbody were compared with experimental data from 10 to 130 million Reynolds number. The high Reynolds data was obtained from the NASA Langley 0.3m Transonic Cryogenic Tunnel. There was generally good agreement of surface static pressure coefficients between the CFD and measurement. The change in pressure coefficient distributions with varying Reynolds number was similar to the experimental data trends, though slightly over-predicting the effect. The computational sensitivity of viscous modeling and turbulence modeling are shown. Integrated afterbody pressure drag was typically slightly lower than the experimental data. The change in afterbody pressure drag with Reynolds number was small both experimentally and computationally, even though the shape of the distribution was somewhat modified with Reynolds number.

A new treatment for predicting the self-excited vibrations of nonlinear systems with frictional interfaces: The Constrained Harmonic Balance Method, with application to disc brake squeal

NASA Astrophysics Data System (ADS)

Coudeyras, N.; Sinou, J.-J.; Nacivet, S.

2009-01-01

Brake squeal noise is still an issue since it generates high warranty costs for the automotive industry and irritation for customers. Key parameters must be known in order to reduce it. Stability analysis is a common method of studying nonlinear phenomena and has been widely used by the scientific and the engineering communities for solving disc brake squeal problems. This type of analysis provides areas of stability versus instability for driven parameters, thereby making it possible to define design criteria. Nevertheless, this technique does not permit obtaining the vibrating state of the brake system and nonlinear methods have to be employed. Temporal integration is a well-known method for computing the dynamic solution but as it is time consuming, nonlinear methods such as the Harmonic Balance Method (HBM) are preferred. This paper presents a novel nonlinear method called the Constrained Harmonic Balance Method (CHBM) that works for nonlinear systems subject to flutter instability. An additional constraint-based condition is proposed that omits the static equilibrium point (i.e. the trivial static solution of the nonlinear problem that would be obtained by applying the classical HBM) and therefore focuses on predicting both the Fourier coefficients and the fundamental frequency of the stationary nonlinear system. The effectiveness of the proposed nonlinear approach is illustrated by an analysis of disc brake squeal. The brake system under consideration is a reduced finite element model of a pad and a disc. Both stability and nonlinear analyses are performed and the results are compared with a classical variable order solver integration algorithm. Therefore, the objectives of the following paper are to present not only an extension of the HBM (CHBM) but also to demonstrate an application to the specific problem of disc brake squeal with extensively parametric studies that investigate the effects of the friction coefficient, piston pressure, nonlinear stiffness and structural damping.

Simulation of Alfvén eigenmode bursts using a hybrid code for nonlinear magnetohydrodynamics and energetic particles

NASA Astrophysics Data System (ADS)

Todo, Y.; Berk, H. L.; Breizman, B. N.

2012-03-01

A hybrid simulation code for nonlinear magnetohydrodynamics (MHD) and energetic-particle dynamics has been extended to simulate recurrent bursts of Alfvén eigenmodes by implementing the energetic-particle source, collisions and losses. The Alfvén eigenmode bursts with synchronization of multiple modes and beam ion losses at each burst are successfully simulated with nonlinear MHD effects for the physics condition similar to a reduced simulation for a TFTR experiment (Wong et al 1991 Phys. Rev. Lett. 66 1874, Todo et al 2003 Phys. Plasmas 10 2888). It is demonstrated with a comparison between nonlinear MHD and linear MHD simulation results that the nonlinear MHD effects significantly reduce both the saturation amplitude of the Alfvén eigenmodes and the beam ion losses. Two types of time evolution are found depending on the MHD dissipation coefficients, namely viscosity, resistivity and diffusivity. The Alfvén eigenmode bursts take place for higher dissipation coefficients with roughly 10% drop in stored beam energy and the maximum amplitude of the dominant magnetic fluctuation harmonic δBm/n/B ~ 5 × 10-3 at the mode peak location inside the plasma. Quadratic dependence of beam ion loss rate on magnetic fluctuation amplitude is found for the bursting evolution in the nonlinear MHD simulation. For lower dissipation coefficients, the amplitude of the Alfvén eigenmodes is at steady levels δBm/n/B ~ 2 × 10-3 and the beam ion losses take place continuously. The beam ion pressure profiles are similar among the different dissipation coefficients, and the stored beam energy is higher for higher dissipation coefficients.

Coherent source interaction, third-order nonlinear response of synthesized PEG coated magnetite nanoparticles in polyethylene glycol and its application

NASA Astrophysics Data System (ADS)

Gopal, S. Veena; Chitrambalam, S.; Joe, I. Hubert

2018-01-01

Third-order nonlinear response of synthesized polyethylene glycol coated Fe3O4 nanoparticles dispersed in a suitable solvent, polyethylene glycol has been studied. The structural characterization of the synthesized magnetite nanoparticles were carried out. The linear optical property of the synthesized magnetite nanoparticles was investigated using UV-visible technique. Both closed and open aperture Z-scan techniques have been performed at 532 nm with pulse width 5 ns and repetition rate 10 Hz. It was found that polyethylene glycol coated magnetite exhibits reverse saturable absorption, with significant nonlinear absorption coefficient. Two-photon absorption intensity dependent positive nonlinear refraction coefficients indicate self focusing phenomena. Results show that higher concentration gives better nonlinear and optical limiting properties.

Formulation of the linear model from the nonlinear simulation for the F18 HARV

NASA Technical Reports Server (NTRS)

Hall, Charles E., Jr.

1991-01-01

The F-18 HARV is a modified F-18 Aircraft which is capable of flying in the post-stall regime in order to achieve superagility. The onset of aerodynamic stall, and continued into the post-stall region, is characterized by nonlinearities in the aerodynamic coefficients. These aerodynamic coefficients are not expressed as analytic functions, but rather in the form of tabular data. The nonlinearities in the aerodynamic coefficients yield a nonlinear model of the aircraft's dynamics. Nonlinear system theory has made many advances, but this area is not sufficiently developed to allow its application to this problem, since many of the theorems are existance theorems and that the systems are composed of analytic functions. Thus, the feedback matrices and the state estimators are obtained from linear system theory techniques. It is important, in order to obtain the correct feedback matrices and state estimators, that the linear description of the nonlinear flight dynamics be as accurate as possible. A nonlinear simulation is run under the Advanced Continuous Simulation Language (ACSL). The ACSL simulation uses FORTRAN subroutines to interface to the look-up tables for the aerodynamic data. ACSL has commands to form the linear representation for the system. Other aspects of this investigation are discussed.

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.

Space-dependent perfusion coefficient estimation in a 2D bioheat transfer problem

NASA Astrophysics Data System (ADS)

Bazán, Fermín S. V.; Bedin, Luciano; Borges, Leonardo S.

2017-05-01

In this work, a method for estimating the space-dependent perfusion coefficient parameter in a 2D bioheat transfer model is presented. In the method, the bioheat transfer model is transformed into a time-dependent semidiscrete system of ordinary differential equations involving perfusion coefficient values as parameters, and the estimation problem is solved through a nonlinear least squares technique. In particular, the bioheat problem is solved by the method of lines based on a highly accurate pseudospectral approach, and perfusion coefficient values are estimated by the regularized Gauss-Newton method coupled with a proper regularization parameter. The performance of the method on several test problems is illustrated numerically.

Robust check loss-based variable selection of high-dimensional single-index varying-coefficient model

NASA Astrophysics Data System (ADS)

Song, Yunquan; Lin, Lu; Jian, Ling

2016-07-01

Single-index varying-coefficient model is an important mathematical modeling method to model nonlinear phenomena in science and engineering. In this paper, we develop a variable selection method for high-dimensional single-index varying-coefficient models using a shrinkage idea. The proposed procedure can simultaneously select significant nonparametric components and parametric components. Under defined regularity conditions, with appropriate selection of tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Moreover, due to the robustness of the check loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion. Finally, the method is illustrated with numerical simulations.

The near optimality of the stabilizing control in a weakly nonlinear system with state-dependent coefficients

NASA Astrophysics Data System (ADS)

Dmitriev, Mikhail G.; Makarov, Dmitry A.

2016-08-01

We carried out analysis of near optimality of one computationally effective nonlinear stabilizing control built for weakly nonlinear systems with coefficients depending on the state and the formal small parameter. First investigation of that problem was made in [M. G. Dmitriev, and D. A. Makarov, "The suboptimality of stabilizing regulator in a quasi-linear system with state-depended coefficients," in 2016 International Siberian Conference on Control and Communications (SIBCON) Proceedings, National Research University, Moscow, 2016]. In this paper, another optimal control and gain matrix representations were used and theoretical results analogous to cited work above were obtained. Also as in the cited work above the form of quality criterion on which this close-loop control is optimal was constructed.

On new classes of solutions of nonlinear partial differential equations in the form of convergent special series

NASA Astrophysics Data System (ADS)

Filimonov, M. Yu.

2017-12-01

The method of special series with recursively calculated coefficients is used to solve nonlinear partial differential equations. The recurrence of finding the coefficients of the series is achieved due to a special choice of functions, in powers of which the solution is expanded in a series. We obtain a sequence of linear partial differential equations to find the coefficients of the series constructed. In many cases, one can deal with a sequence of linear ordinary differential equations. We construct classes of solutions in the form of convergent series for a certain class of nonlinear evolution equations. A new class of solutions of generalized Boussinesque equation with an arbitrary function in the form of a convergent series is constructed.

The effects of five-order nonlinear on the dynamics of dark solitons in optical fiber.

PubMed

He, Feng-Tao; Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce.

The Effects of Five-Order Nonlinear on the Dynamics of Dark Solitons in Optical Fiber

PubMed Central

Wang, Xiao-Lin; Duan, Zuo-Liang

2013-01-01

We study the influence of five-order nonlinear on the dynamic of dark soliton. Starting from the cubic-quintic nonlinear Schrodinger equation with the quadratic phase chirp term, by using a similarity transformation technique, we give the exact solution of dark soliton and calculate the precise expressions of dark soliton's width, amplitude, wave central position, and wave velocity which can describe the dynamic behavior of soliton's evolution. From two different kinds of quadratic phase chirps, we mainly analyze the effect on dark soliton's dynamics which different fiver-order nonlinear term generates. The results show the following two points with quintic nonlinearities coefficient increasing: (1) if the coefficients of the quadratic phase chirp term relate to the propagation distance, the solitary wave displays a periodic change and the soliton's width increases, while its amplitude and wave velocity reduce. (2) If the coefficients of the quadratic phase chirp term do not depend on propagation distance, the wave function only emerges in a fixed area. The soliton's width increases, while its amplitude and the wave velocity reduce. PMID:23818814

Nonlinear absorption in single LaF3 and MgF2 layers at 193 nm measured by surface sensitive laser induced deflection technique

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

Muehlig, Christian; Bublitz, Simon; Kufert, Siegfried

2009-12-10

We report nonlinear absorption data of LaF3 and MgF2 single layers at 193 nm. A highly surface sensitive measurement strategy of the laser induced deflection technique is introduced and applied to measure the absorption of highly transparent thin films independently of the substrate absorption. Linear absorptions k=({alpha}x{lambda})/4{pi} of 2x10{sup -4} and 8.5x10{sup -4} (LaF3) and 1.8x10{sup -4} and 6.9x10{sup -4} (MgF2) are found. Measured two photon absorption (TPA) coefficients are {beta}=1x10{sup -4} cm/W (LaF3), 1.8x10{sup -5}, and 5.8x10{sup -5} cm/W (MgF2). The TPA coefficients are several orders of magnitude higher than typical values for fluoride single crystals, which is likelymore » to result from sequential two step absorption processes.« less

Brownian motion with adaptive drift for remaining useful life prediction: Revisited

NASA Astrophysics Data System (ADS)

Wang, Dong; Tsui, Kwok-Leung

2018-01-01

Linear Brownian motion with constant drift is widely used in remaining useful life predictions because its first hitting time follows the inverse Gaussian distribution. State space modelling of linear Brownian motion was proposed to make the drift coefficient adaptive and incorporate on-line measurements into the first hitting time distribution. Here, the drift coefficient followed the Gaussian distribution, and it was iteratively estimated by using Kalman filtering once a new measurement was available. Then, to model nonlinear degradation, linear Brownian motion with adaptive drift was extended to nonlinear Brownian motion with adaptive drift. However, in previous studies, an underlying assumption used in the state space modelling was that in the update phase of Kalman filtering, the predicted drift coefficient at the current time exactly equalled the posterior drift coefficient estimated at the previous time, which caused a contradiction with the predicted drift coefficient evolution driven by an additive Gaussian process noise. In this paper, to alleviate such an underlying assumption, a new state space model is constructed. As a result, in the update phase of Kalman filtering, the predicted drift coefficient at the current time evolves from the posterior drift coefficient at the previous time. Moreover, the optimal Kalman filtering gain for iteratively estimating the posterior drift coefficient at any time is mathematically derived. A discussion that theoretically explains the main reasons why the constructed state space model can result in high remaining useful life prediction accuracies is provided. Finally, the proposed state space model and its associated Kalman filtering gain are applied to battery prognostics.

Rapid assessment of nonlinear optical propagation effects in dielectrics

PubMed Central

Hoyo, J. del; de la Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

2015-01-01

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process. PMID:25564243

Rapid assessment of nonlinear optical propagation effects in dielectrics.

PubMed

del Hoyo, J; de la Cruz, A Ruiz; Grace, E; Ferrer, A; Siegel, J; Pasquazi, A; Assanto, G; Solis, J

2015-01-07

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

Rapid assessment of nonlinear optical propagation effects in dielectrics

NASA Astrophysics Data System (ADS)

Hoyo, J. Del; de La Cruz, A. Ruiz; Grace, E.; Ferrer, A.; Siegel, J.; Pasquazi, A.; Assanto, G.; Solis, J.

2015-01-01

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear absorption under simplified conditions by employing a state-of-the art computationally efficient approach. By comparing with experimental results we can rapidly estimate the nonlinear refractive index and nonlinear absorption coefficients of the material. The validity of this approach has been tested in a variety of experiments where nonlinearities play a key role, like spatial soliton shaping or fs-laser waveguide writing. The approach provides excellent results for propagated power densities for which free carrier generation effects can be neglected. Above such a threshold, the peculiarities of the nonlinear propagation of elliptical beams enable acquiring an instantaneous picture of the deposition of energy inside the material realistic enough to estimate the effective nonlinear refractive index and nonlinear absorption coefficients that can be used for predicting the spatial distribution of energy deposition inside the material and controlling the beam in the writing process.

Modelling Nonlinear Dynamic Textures using Hybrid DWT-DCT and Kernel PCA with GPU

NASA Astrophysics Data System (ADS)

Ghadekar, Premanand Pralhad; Chopade, Nilkanth Bhikaji

2016-12-01

Most of the real-world dynamic textures are nonlinear, non-stationary, and irregular. Nonlinear motion also has some repetition of motion, but it exhibits high variation, stochasticity, and randomness. Hybrid DWT-DCT and Kernel Principal Component Analysis (KPCA) with YCbCr/YIQ colour coding using the Dynamic Texture Unit (DTU) approach is proposed to model a nonlinear dynamic texture, which provides better results than state-of-art methods in terms of PSNR, compression ratio, model coefficients, and model size. Dynamic texture is decomposed into DTUs as they help to extract temporal self-similarity. Hybrid DWT-DCT is used to extract spatial redundancy. YCbCr/YIQ colour encoding is performed to capture chromatic correlation. KPCA is applied to capture nonlinear motion. Further, the proposed algorithm is implemented on Graphics Processing Unit (GPU), which comprise of hundreds of small processors to decrease time complexity and to achieve parallelism.

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

PubMed

Basko, D M

2014-02-01

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

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

NASA Technical Reports Server (NTRS)

Muravyov, Alexander A.

1999-01-01

In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

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

A displacement-based approach for determining non-linear effects on pre-tensioned-cable cross-braced structures

NASA Astrophysics Data System (ADS)

Giaccu, Gian Felice; Caracoglia, Luca

2017-04-01

Pre-tensioned-cable bracing systems are widely employed in structural engineering to limit lateral deflections and stabilize structures. A suitable configuration of the pre-tensioned-cable bracing systems in a structure is an important issue since the internal force distribution, emerging from the interaction with the existing structure, significantly affects the structural dynamic behavior. The design, however, is often based on the intuition and the previous experience of the engineer. In recent years, the authors have been investigating the non-linear dynamic response of cable systems, installed on cable-stayed bridges, and in particular the so-called "cable-cross-tie systems" forming a cable network. The bracing cables (cross-ties) can exhibit slackening or snapping. Therefore, a non-linear unilateral model, combined with the taut-cable theory, is required to simulate the incipient slackening conditions in the stays. Capitalizing from this work on non-linear cable dynamics, this paper proposes a new approach to analyze, in laterally- braced truss structures, the unilateral effects and dynamic response accounting for the loss in the pre-tensioning force imparted to the bracing cables. This effect leads to non-linear vibration of the structure. In this preliminary study, the free vibrations of the structure are investigated by using the "Equivalent Linearization Method". A performance coefficient, a real positive number between 0.5 and 1.0, is defined and employed to monitor the relative reduction in the apparent stiffness of the braces during structural vibration, "mode by mode". It is shown that the system can exhibit alternate unilateral behavior of the cross-braces. A reduction of the performance coefficient close to fifty percent is observed in the braces when the initial pre-tensioning force is small. On the other hand the performance coefficient tends to one in the case of a high level of pre-stress. It is concluded that the performance coefficient may possibly be used as an indicator for the design of the braces since a suitable selection of the initial pre-tensioning force can avoid slackening in the braces.

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-trials repeatability and test-retest reliability with potential to quantify the effects of a wide variety of manual therapy techniques on the soft tissue elastic properties. Copyright © 2011 National University of Health Sciences. Published by Mosby, Inc. All rights reserved.

Cubication of Conservative Nonlinear Oscillators

ERIC Educational Resources Information Center

Belendez, Augusto; Alvarez, Mariela L.; Fernandez, Elena; Pascual, Immaculada

2009-01-01

A cubication procedure 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, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear…

Estimation of intrinsic and extrinsic capacitances of graphene self-switching diode using conformal mapping technique

NASA Astrophysics Data System (ADS)

Singh, Arun K.; Auton, Gregory; Hill, Ernie; Song, Aimin

2018-07-01

Due to a very high carrier concentration and low band gap, graphene based self-switching diodes do not demonstrate a very high rectification ratio. Despite that, it takes the advantage of graphene’s high carrier mobility and has been shown to work at very high microwave frequencies. However, the AC component of these devices is hidden in the very linear current–voltage characteristics. Here, we extract and quantitatively study the device capacitance that determines the device nonlinearity by implementing a conformal mapping technique. The estimated value of the nonlinear component or curvature coefficient from DC results based on Shichman–Hodges model predicts the rectified output voltage, which is in good agreement with the experimental RF results.

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.

Fourier Series and Elliptic Functions

ERIC Educational Resources Information Center

Fay, Temple H.

2003-01-01

Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…

Nonlinear optical properties of hybridized CdS/ZnS-PVP sols

NASA Astrophysics Data System (ADS)

Kulagina, A. S.; Evstropiev, S. K.; Khrebtov, A. I.

2017-11-01

Hybrid composites of CdS-core ZnS-shell nanoparticles embedded in polyvinylpyrrolidone (PVP) matrixes have been prepared and characterized. Cadmium sulfide (CdS) nanocrystals were grown in water-propanol-2 solutions containing high-molecular (Ms=1300000) polyvinylpyrrolidone (PVP) at room temperature using cadmium nitrate and sodium sulfide as the cadmium and sulfur sources, respectively. The CdS/ZnS-PVP suspensions have promising optical properties for nanocomposite films based on. Nonlinear optical properties of diluted CdS/ZnS sols were studied at 532 nm and 5 ns laser pulses by using the Z-scan technique. Dependence of the nonlinear-optical coefficients on the CdS weight has been obtained.

CW all optical self switching in nonlinear chalcogenide nano plasmonic directional coupler

NASA Astrophysics Data System (ADS)

Motamed-Jahromi, Leila; Hatami, Mohsen

2018-04-01

In this paper we obtain the coupling coefficient of plasmonic directional coupler (PDC) made up of two parallel monolayer waveguides filled with high nonlinear chalcogenide material for TM mode in continues wave (CW) regime. In addition, we assume each waveguides acts as a perturbation to other waveguide. Four nonlinear-coupled equations are derived. Transfer distances are numerically calculated and used for deriving length of all optical switch. The length of designed switch is in the range of 10-1000 μm, and the switching power is in the range of 1-100 W/m. Obtained values are suitable for designing all optical elements in the integrated optical circuits.

A Mathematica program for the approximate analytical solution to a nonlinear undamped Duffing equation by a new approximate approach

NASA Astrophysics Data System (ADS)

Wu, Dongmei; Wang, Zhongcheng

2006-03-01

According to Mickens [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563], the general HB (harmonic balance) method is an approximation to the convergent Fourier series representation of the periodic solution of a nonlinear oscillator and not an approximation to an expansion in terms of a small parameter. Consequently, for a nonlinear undamped Duffing equation with a driving force Bcos(ωx), to find a periodic solution when the fundamental frequency is identical to ω, the corresponding Fourier series can be written as y˜(x)=∑n=1m acos[(2n-1)ωx]. How to calculate the coefficients of the Fourier series efficiently with a computer program is still an open problem. For HB method, by substituting approximation y˜(x) into force equation, expanding the resulting expression into a trigonometric series, then letting the coefficients of the resulting lowest-order harmonic be zero, one can obtain approximate coefficients of approximation y˜(x) [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563]. But for nonlinear differential equations such as Duffing equation, it is very difficult to construct higher-order analytical approximations, because the HB method requires solving a set of algebraic equations for a large number of unknowns with very complex nonlinearities. To overcome the difficulty, forty years ago, Urabe derived a computational method for Duffing equation based on Galerkin procedure [M. Urabe, A. Reiter, Numerical computation of nonlinear forced oscillations by Galerkin's procedure, J. Math. Anal. Appl. 14 (1966) 107-140]. Dooren obtained an approximate solution of the Duffing oscillator with a special set of parameters by using Urabe's method [R. van Dooren, Stabilization of Cowell's classic finite difference method for numerical integration, J. Comput. Phys. 16 (1974) 186-192]. In this paper, in the frame of the general HB method, we present a new iteration algorithm to calculate the coefficients of the Fourier series. By using this new method, the iteration procedure starts with a(x)cos(ωx)+b(x)sin(ωx), and the accuracy may be improved gradually by determining new coefficients a,a,… will be produced automatically in an one-by-one manner. In all the stage of calculation, we need only to solve a cubic equation. Using this new algorithm, we develop a Mathematica program, which demonstrates following main advantages over the previous HB method: (1) it avoids solving a set of associate nonlinear equations; (2) it is easier to be implemented into a computer program, and produces a highly accurate solution with analytical expression efficiently. It is interesting to find that, generally, for a given set of parameters, a nonlinear Duffing equation can have three independent oscillation modes. For some sets of the parameters, it can have two modes with complex displacement and one with real displacement. But in some cases, it can have three modes, all of them having real displacement. Therefore, we can divide the parameters into two classes, according to the solution property: there is only one mode with real displacement and there are three modes with real displacement. This program should be useful to study the dynamically periodic behavior of a Duffing oscillator and can provide an approximate analytical solution with high-accuracy for testing the error behavior of newly developed numerical methods with a wide range of parameters. Program summaryTitle of program:AnalyDuffing.nb Catalogue identifier:ADWR_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADWR_v1_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Computer for which the program is designed and others on which it has been tested:the program has been designed for a microcomputer and been tested on the microcomputer. Computers:IBM PC Installations:the address(es) of your computer(s) Operating systems under which the program has been tested:Windows XP Programming language used:Software Mathematica 4.2, 5.0 and 5.1 No. of lines in distributed program, including test data, etc.:23 663 No. of bytes in distributed program, including test data, etc.:152 321 Distribution format:tar.gz Memory required to execute with typical data:51 712 Bytes No. of bits in a word: No. of processors used:1 Has the code been vectorized?:no Peripherals used:no Program Library subprograms used:no Nature of physical problem:To find an approximate solution with analytical expressions for the undamped nonlinear Duffing equation with periodic driving force when the fundamental frequency is identical to the driving force. Method of solution:In the frame of the general HB method, by using a new iteration algorithm to calculate the coefficients of the Fourier series, we can obtain an approximate analytical solution with high-accuracy efficiently. Restrictions on the complexity of the problem:For problems, which have a large driving frequency, the convergence may be a little slow, because more iterative times are needed. Typical running time:several seconds Unusual features of the program:For an undamped Duffing equation, it can provide all the solutions or the oscillation modes with real displacement for any interesting parameters, for the required accuracy, efficiently. The program can be used to study the dynamically periodic behavior of a nonlinear oscillator, and can provide a high-accurate approximate analytical solution for developing high-accurate numerical method.

Third-order nonlinear optical properties of methylammonium lead halide perovskite films

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

Johnson, Justin C.; Li, Zhen; Ndione, Paul F.

2016-01-01

We report third-order nonlinear coefficient values and decay time kinetics vs. halide composition (CH3NH3PbBr3 and CH3NH3PbBr2I), temperature, and excitation wavelength. The maximum values of the third-order nonlinear susceptibility X(3) (-1.6 x 10-6 esu) are similar to or larger than many common third-order materials. The source of the nonlinearity is shown to be primarily excitonic in the tribromide film by virtue of its strong enhancement near the exciton resonance. Nonresonant excitation reduces the nonlinearity significantly, as does increasing the temperature. Substitution of one I for one Br also reduces the nonlinearity by at least one order of magnitude, presumably due tomore » the lack of strong exciton resonance in the substituted form. The thin films are stable, highly homogenous (lacking significant light scattering), and simple and inexpensive to fabricate, making them potentially useful in a variety of optoelectronic applications in which wavelength selectivity is important.« less

Triple tailored nonlinear dispersion of dressed four- and six-wave mixing

NASA Astrophysics Data System (ADS)

Sun, Yanyong; Wang, Zhiguo; Zhang, Zhaoyang; Gu, Bingling; Wang, Kun; Yang, Gaoguo; Zhang, Yanpeng

2018-06-01

We investigate the spectral signals and spatial images of a probe transmission signal, four-wave mixing (FWM), and six-wave mixing (SWM) under double dressing effects in an inverted Y-type system. Especially, we get the triple tailored nonlinear dispersion (about 60 MHz) of the dressed FWM and SWM through the interaction between electromagnetically induced transparency (EIT) windows and the Kerr nonlinearity. Moreover, SWM and dressed FWM with narrow linewidth are obtained through the tailoring of the three EIT windows, which is much narrower than the EIT. In addition, we first elaborate the modulation effect from the self-Kerr coefficient of FWM on the spot. We also investigate the spatial characteristics (defocusing, shifting, and splitting) of FWM and SWM induced by tailored self-Kerr and cross-Kerr effects among the relative fields. Such spatial shifting, splitting induced by the tailored nonlinear dispersion can be used for a higher contrast and high speed switch as well as a high resolution router.

Nonlinear ARMA models for the D(st) index and their physical interpretation

NASA Technical Reports Server (NTRS)

Vassiliadis, D.; Klimas, A. J.; Baker, D. N.

1996-01-01

Time series models successfully reproduce or predict geomagnetic activity indices from solar wind parameters. A method is presented that converts a type of nonlinear filter, the nonlinear Autoregressive Moving Average (ARMA) model to the nonlinear damped oscillator physical model. The oscillator parameters, the growth and decay, the oscillation frequencies and the coupling strength to the input are derived from the filter coefficients. Mathematical methods are derived to obtain unique and consistent filter coefficients while keeping the prediction error low. These methods are applied to an oscillator model for the Dst geomagnetic index driven by the solar wind input. A data set is examined in two ways: the model parameters are calculated as averages over short time intervals, and a nonlinear ARMA model is calculated and the model parameters are derived as a function of the phase space.

Static and Dynamic Effects of Lateral Carrier Diffusion in Semiconductor Lasers

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Cheung, Samson H.; Ning, C. Z.; Biegel, Bryan A. (Technical Monitor)

2002-01-01

Electron and hole diffusions in the plane of semiconductor quantum wells play an important part in the static and dynamic operations of semiconductor lasers. It is well known that the value of diffusion coefficients affects the threshold pumping current of a semiconductor laser. At the same time, the strength of carrier diffusion process is expected to affect the modulation bandwidth of an AC-modulated laser. It is important not only to investigate the combined DC and AC effects due to carrier diffusion, but also to separate the AC effects from that of the combined effects in order to provide design insights for high speed modulation. In this presentation, we apply a hydrodynamic model developed by the present authors recently from the semiconductor Bloch equations. The model allows microscopic calculation of the lateral carrier diffusion coefficient, which is a nonlinear function of the carrier density and plasma temperature. We first studied combined AC and DC effects of lateral carrier diffusion by studying the bandwidth dependence on diffusion coefficient at a given DC current under small signal modulation. The results show an increase of modulation bandwidth with decrease in the diffusion coefficient. We simultaneously studied the effects of nonlinearity in the diffusion coefficient. To clearly identify how much of the bandwidth increase is a result of decrease in the threshold pumping current for smaller diffusion coefficient, thus an effective increase of DC pumping, we study the bandwidth dependence on diffusion coefficient at a given relative pumping. A detailed comparison of the two cases will be presented.

Nonlinear response in runoff magnitude to fluctuating rain patterns.

PubMed

Curtu, R; Fonley, M

2015-03-01

The runoff coefficient of a hillslope is a reliable measure for changes in the streamflow response at the river link outlet. A high runoff coefficient is a good indicator of the possibility of flash floods. Although the relationship between runoff coefficient and streamflow has been the subject of much study, the physical mechanisms affecting runoff coefficient including the dependence on precipitation pattern remain open topics for investigation. In this paper, we analyze a rainfall-runoff model at the hillslope scale as that hillslope is forced with different rain patterns: constant rain and fluctuating rain with different frequencies and amplitudes. When an oscillatory precipitation pattern is applied, although the same amount of water may enter the system, its response (measured by the runoff coefficient) will be maximum for a certain frequency of precipitation. The significant increase in runoff coefficient after a certain pattern of rainfall can be a potential explanation for the conditions preceding flash-floods.

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.

Study of nonlinear absorption properties of reduced graphene oxide by Z-scan technique

NASA Astrophysics Data System (ADS)

Sreeja, V. G.; Vinitha, G.; Reshmi, R.; Anila, E. I.; Jayaraj, M. K.

2017-05-01

Graphene has generated enormous research interest during the last decade due to its significant unique properties and wide applications in the field of optoelectronics and photonics. This research studied the structural and nonlinear absorption properties of reduced graphene oxide (rGO) synthesized by Modified Hummer's method. Structural and physiochemical properties of the rGO were explored with the help of Fourier transform infrared spectroscopy (FTIR) and Raman spectroscopy (Raman). Nonlinear absorption property in rGO, was investigated by open aperture Z-scan technique by using a continuous wave (CW) laser. The Z-scan results demonstrate saturable absorption property of rGO with a nonlinear absorption coefficient, β, of -2.62 × 10-4 cm/W, making it suitable for applications in Q switching, generation of ultra-fast high energy pulses in laser cavity and mode lockers.

Nonlinear optical studies on 1,3-disubstituent chalcones doped polymer films

NASA Astrophysics Data System (ADS)

Poornesh, P.; Shettigar, Seetharam; Umesh, G.; Manjunatha, K. B.; Prakash Kamath, K.; Sarojini, B. K.; Narayana, B.

2009-04-01

We report the measurements of the third-order nonlinear optical properties of recently synthesized and characterized two different 1,3-disubstituent chalcones doped PMMA films, with the prospective of reaching a good compromise between processability and high nonlinear optical properties. The measurements were done using nanosecond Z-scan at 532 nm. The Z-scan spectra reveal a large negative nonlinear refraction coefficient n2 of the order 10 -11 esu and the molecular two photon absorption cross section is 10 -46 cm 4 s/photon. The doped films exhibit good optical power limiting property under nanosecond regime and the two photon absorption (TPA) is the dominating process leading to the nonlinear behavior. The improvement in the nonlinear properties has been observed when methylenedioxy group is replaced by dimethoxy group due to increase in conjugation length. The observed nonlinear parameters of chalcone derivatives doped PMMA film is comparable with stilbazolieum derivatives, a well-known class of optical materials for photonics and biophotonics applications, which suggests that, these moieties have potential for the application of all-optical limiting and switching devices.

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system

PubMed Central

Tao, S; Trzasko, J D; Gunter, J L; Weavers, P T; Shu, Y; Huston, J; Lee, S K; Tan, E T; Bernstein, M A

2017-01-01

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer’s Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26-cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients. PMID:28033119

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 CE_c2 the nonlinearity can be described in the same way as in soft PZT. The results indicate that irreversible motion of (ferroelastic) non-180^o walls causes the nonlinearity of PZT and that the contribution of (non-ferroelastic) 180^o walls to the linear and nonlinear coefficients is negligibly small. The experimentally observed non-analytic scaling behavior is qualitatively inconsistent with the assumption that the nonlinearity is related to the anharmonicity of the domain wall potential. We suggest that the dynamics of the domain wall in a randomly pinned medium dominates the piezoelectric and dielectric nonlinearity at field strengths well below the limiting field necessary to depole the piezoceramic. The analysis of results obtained at different ceramic systems indicates that linear and nonlinear coefficients are not independent from each other. The observed relationship between linear and nonlinear properties leads us to the suggestion that another extrinsic contribution to the permittivity exists in PZT which may not be attributed to domain wall motion but related to the dielectric dispersion at microwave frequencies.

Chaos in high-dimensional dissipative dynamical systems

PubMed Central

Ispolatov, Iaroslav; Madhok, Vaibhav; Allende, Sebastian; Doebeli, Michael

2015-01-01

For dissipative dynamical systems described by a system of ordinary differential equations, we address the question of how the probability of chaotic dynamics increases with the dimensionality of the phase space. We find that for a system of d globally coupled ODE’s with quadratic and cubic non-linearities with randomly chosen coefficients and initial conditions, the probability of a trajectory to be chaotic increases universally from ~10−5 − 10−4 for d = 3 to essentially one for d ~ 50. In the limit of large d, the invariant measure of the dynamical systems exhibits universal scaling that depends on the degree of non-linearity, but not on the choice of coefficients, and the largest Lyapunov exponent converges to a universal scaling limit. Using statistical arguments, we provide analytical explanations for the observed scaling, universality, and for the probability of chaos. PMID:26224119

Optical response in a laser-driven quantum pseudodot system

NASA Astrophysics Data System (ADS)

Kilic, D. Gul; Sakiroglu, S.; Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sokmen, I.

2017-03-01

We investigate theoretically the intense laser-induced optical absorption coefficients and refractive index changes in a two-dimensional quantum pseudodot system under an uniform magnetic field. The effects of non-resonant, monochromatic intense laser field upon the system are treated within the framework of high-frequency Floquet approach in which the system is supposed to be governed by a laser-dressed potential. Linear and nonlinear absorption coefficients and relative changes in the refractive index are obtained by means of the compact-density matrix approach and iterative method. The results of numerical calculations for a typical GaAs quantum dot reveal that the optical response depends strongly on the magnitude of external magnetic field and characteristic parameters of the confinement potential. Moreover, we have demonstrated that the intense laser field modifies the confinement and thereby causes remarkable changes in the linear and nonlinear optical properties of the system.

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

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

Liberman, V.; Sworin, M.; Kingsborough, R. P.

2013-02-07

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

Development of side-chain NLO polymer materials with high electro-optic activity and long-term stability

NASA Astrophysics Data System (ADS)

Huang, Diyun; Parker, Timothy; Guan, Hann Wen; Cong, Shuxin; Jin, Danliang; Dinu, Raluca; Chen, Baoquan; Tolstedt, Don; Wolf, Nick; Condon, Stephen

2005-01-01

The electro-optic coefficient and long-term dipole alignment stability are two major factors in the development of high performance NLO materials for the application of high-speed EO devices. We have developed a high performance non-linear organic chromophore and incorporated it into a crosslinkable side-chain polyimide system. The polymer was synthesized through stepwise grafting of the crosslinker followed by the chromophore onto the polyimide backbone via esterification. Different chromophore loading levels were achieved by adjusting the crosslinker/chromophore feeding ratio. The polyimides films were contact-poled with second-harmonic generation monitoring. A large EO coefficient value was obtained and good long-term thermal stability at 85°C was observed.

Mechanics of the acoustic radiation force in tissue-like solids

NASA Astrophysics Data System (ADS)

Dontsov, Egor V.

The acoustic radiation force (ARF) is a phenomenon affiliated with the nonlinear effects of high-intensity wave propagation. It represents the mean momentum transfer from the sound wave to the medium, and allows for an effective computation of the mean motion (e.g. acoustic streaming in fluids) induced by a high-intensity sound wave. Nowadays, the high-intensity focused ultrasound is frequently used in medical diagnosis applications due to its ability to "push" inside the tissue with the radiation body force and facilitate the local quantification of tissue's viscoelastic properties. The main objectives of this study include: i) the theoretical investigation of the ARF in fluids and tissue-like solids generated respectively by the amplitude modulated plane wave and focused ultrasound; ii) computation of the nonlinear acoustic wave propagation when the amplitude of the focused ultrasound field is modulated by a low-frequency signal, and iii) modeling of the ARF-induced motion in tissue-like solids for the purpose of quantifying their nonlinear elasticity via the magnitude of the ARF. Regarding the first part, a comparison with the existing theory of the ARF reveals a number of key features that are brought to light by the new formulation, including the contributions to the ARF of ultrasound modulation and thermal expansion, as well as the precise role of constitutive nonlinearities in generating the sustained body force in tissue-like solids by a focused ultrasound beam. In the second part, the hybrid time-frequency domain algorithm for the numerical analysis of the nonlinear wave equation is proposed. The approach is validated by comparing the results to the finite-difference modeling in time domain. Regarding the third objective, the Fourier transform approach is used to compute the ARF-induced shear wave motion in tissue-mimicking phantoms. A comparison between the experiment (tests performed at the Mayo Clinic) and model permitted the estimation of a particular coefficient of nonlinear tissue elasticity from the amplitude of the ARF-generated shear waves. For completeness, the ARF estimates of this coefficient are verified via an established technique known as acoustoelasticity.

NLSCIDNT user's guide maximum likehood parameter identification computer program with nonlinear rotorcraft model

NASA Technical Reports Server (NTRS)

1979-01-01

A nonlinear, maximum likelihood, parameter identification computer program (NLSCIDNT) is described which evaluates rotorcraft stability and control coefficients from flight test data. The optimal estimates of the parameters (stability and control coefficients) are determined (identified) by minimizing the negative log likelihood cost function. The minimization technique is the Levenberg-Marquardt method, which behaves like the steepest descent method when it is far from the minimum and behaves like the modified Newton-Raphson method when it is nearer the minimum. Twenty-one states and 40 measurement variables are modeled, and any subset may be selected. States which are not integrated may be fixed at an input value, or time history data may be substituted for the state in the equations of motion. Any aerodynamic coefficient may be expressed as a nonlinear polynomial function of selected 'expansion variables'.

Fundamental aerodynamic characteristics of delta wings with leading-edge vortex flows

NASA Technical Reports Server (NTRS)

Wood, R. M.; Miller, D. S.

1985-01-01

An investigation of the aerodynamics of sharp leading-edge delta wings at supersonic speeds has been conducted. The supporting experimental data for this investigation were taken from published force, pressure, and flow-visualization data in which the Mach number normal to the wing leading edge is always less than 1.0. The individual upper- and lower-surface nonlinear characteristics for uncambered delta wings are determined and presented in three charts. The upper-surface data show that both the normal-force coefficient and minimum pressure coefficient increase nonlinearly with a decreasing slope with increasing angle of attack. The lower-surface normal-force coefficient was shown to be independent of Mach number and to increase nonlinearly, with an increasing slope, with increasing angle of attack. These charts are then used to define a wing-design space for sharp leading-edge delta wings.

Transverse effects in nonlinear optics: Toward the photon superfluid

NASA Astrophysics Data System (ADS)

McCormick, Colin Fraser

Nonlinear optics displays a wealth of transverse effects. These effects are particularly rich in the presence of an optical cavity. Many considerations suggest that in a Kerr nonlinear cavity a new state of light known as a "photon superfluid" can form, with strong analogies to atomic superfluids. The conditions for the formation of the photon superfluid include requirements on the cavity, input light fields and the nonlinear medium as well as various timescales. The most favorable candidate nonlinear medium for observing the photon super-fluid is an atomic vapor. With a strong and fast Kerr effect, atomic vapors also have the advantage of a Kerr coefficient that is tunable in both magnitude and sign. A series of z-scan experiments in far-detuned atomic rubidium vapor is reported, measuring the Kerr coefficient and determining its functional dependence on detuning to be that of a Doppler-broadened two-level model with adiabatic following of the electric field by the atom pseudomoment. Saturation effects are found to be important. Z-scan measurements for detunings within the Doppler profile are shown to agree well with numerical simulations based on the Doppler-broadened model. Agreement between absorptive and refractive non-linear coefficients is evidence of the Kramers-Kronig relations at work, even in this nonlinear system. The formation of the photon superfluid is discussed and the calculation of a new process, nearly collinear four-wave mixing, is presented. This process is essentially an inverse beam filamentation that is likely to be the underlying physical mechanism for transverse cooling and condensation of photons in a nonlinear optical cavity. Nearly collinear four-wave mixing may also be related to phenomena in general nonlinear physics, including modulation instability and Fermi-Pasta-Ulam recurrence.

Enhanced nonlinear optical properties of L-arginine stabilized gold nanoparticles embedded in PVP polymer

NASA Astrophysics Data System (ADS)

Sunatkari, A. L.; Talwatkar, S. S.; Tamgadge, Y. S.; Muley, G. G.

2018-05-01

Highly stable colloidal gold nanoparticles (GNPs) stabilised in l-arginine were synthesized and embedded in polyvinyl pyrrolidone (PVP) polymer matrix to fabricate thin films by spin coating method. Nonlinear optical response of GNP-PVP nanocomposite were investigated using single beam Z-scan technique using He-Ne laser beam in CW regime operated at 632.8 nm as an excitation source. The sign of nonlinear refractive index was found negative, which is of self-defocusing nature. The nonlinear optical parameters estimated for GNP-PVP nanocomposite and found values as large as n2≈(1.7 -3.1 ) ×10-4c m2W-1, β ≈(2.40 -4.69 ) ×10-5c m W-1 and χef f (3 )≈(2.30 -4.34 ) ×10-4e s u . The nonlinear refractive index, absorption coefficient and third order nonlinear susceptibility have found decreasing with the increase in the concentration of l-arginine. Localized surface plasmon resonance (LSPR) peaks show the blue shift. The average size of the GNPs is found reducing from 11 nm to 7.5 nm with the increase in the stabilizer concentration, as analysed by transmission electron microscopy. The XRD study reveals face-centred cubic (fcc) structure of GNPs. The huge nonlinearity is attributed to the thermo-optic phenomenon. The huge enhancement in third order nonlinear susceptibility and nonlinear refractive index indicates that this optical material possess a high potential for various optoelectronic devices applications.

Current and Future Constraints on Higgs Couplings in the Nonlinear Effective Theory

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

de Blas, Jorge; Eberhardt, Otto; Krause, Claudius

We perform a Bayesian statistical analysis of the constraints on the nonlinear Effective Theory given by the Higgs electroweak chiral Lagrangian. We obtain bounds on the effective coefficients entering in Higgs observables at the leading order, using all available Higgs-boson signal strengths from the LHC runs 1 and 2. Using a prior dependence study of the solutions, we discuss the results within the context of natural-sized Wilson coefficients. We further study the expected sensitivities to the different Wilson coefficients at various possible future colliders. Finally, we interpret our results in terms of some minimal composite Higgs models.

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

NASA Astrophysics Data System (ADS)

Rai, Buddhi; McGurn, Arthur R.

2015-02-01

Photonic crystal and split ring resonator (SRR) metamaterial waveguides with Kerr nonlinear dielectric impurities are studied. The transmission coefficients for two guided modes of different frequencies scattering from the Kerr impurities are computed. The systems are shown to exhibit multiple transmission coefficient solutions arising from the Kerr nonlinearity. Multiple transmission coefficients occur when different input intensities into a waveguide result in the same transmitted output intensities past its nonlinear impurities. (In the case of a single incident guided mode the multiplicity of transmission coefficients is known as optical bistability.) The analytical conditions under which the transmission coefficients are single and multiple valued are determined, and specific examples of both single and multiple valued transmission coefficient scattering are presented. Both photonic crystal and split ring resonator systems are studied as the Kerr nonlinearity enters the photonic crystal and SRR systems in different ways. This allows for an interesting comparison of the differences in behaviors of these two types of system which are described by distinctly different mathematical structures. Both the photonic crystal and SRR models used in the calculations are based on a difference equation approach to the system dynamics. The difference equation approach has been extensively employed in previous papers to model the basic properties of these systems. The paper is a continuation of work on the optical bistability of single guided modes interacting with Kerr impurities in photonic crystals originally considered by McGurn [Chaos 13, 754 (2003), 10.1063/1.1568691] and work on the resonant scattering from Kerr impurities in photonic crystal waveguides considered by McGurn [J. Phys.: Condens. Matter 16, S5243 (2004), 10.1088/0953-8984/16/44/021]. It generalizes this work making the extension to the more complex interaction of two guided modes at different frequencies. It extends the two guided mode treatment by McGurn [Organ. Electron. 8, 227 (2007), 10.1016/j.orgel.2006.06.008] which was limited to a special case of one of the photonic crystal systems considered here.

Heterogeneous integration of lithium niobate and silicon nitride waveguides for wafer-scale photonic integrated circuits on silicon.

PubMed

Chang, Lin; Pfeiffer, Martin H P; Volet, Nicolas; Zervas, Michael; Peters, Jon D; Manganelli, Costanza L; Stanton, Eric J; Li, Yifei; Kippenberg, Tobias J; Bowers, John E

2017-02-15

An ideal photonic integrated circuit for nonlinear photonic applications requires high optical nonlinearities and low loss. This work demonstrates a heterogeneous platform by bonding lithium niobate (LN) thin films onto a silicon nitride (Si₃N₄) waveguide layer on silicon. It not only provides large second- and third-order nonlinear coefficients, but also shows low propagation loss in both the Si₃N₄ and the LN-Si₃N₄ waveguides. The tapers enable low-loss-mode transitions between these two waveguides. This platform is essential for various on-chip applications, e.g., modulators, frequency conversions, and quantum communications.

Higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials

NASA Astrophysics Data System (ADS)

Liu, Lei; Tian, Bo; Wu, Xiao-Yu; Sun, Yan

2018-02-01

Under investigation in this paper is the higher-order rogue wave-like solutions for a nonautonomous nonlinear Schrödinger equation with external potentials which can be applied in the nonlinear optics, hydrodynamics, plasma physics and Bose-Einstein condensation. Based on the Kadomtsev-Petviashvili hierarchy reduction, we construct the Nth order rogue wave-like solutions in terms of the Gramian under the integrable constraint. With the help of the analytic and graphic analysis, we exhibit the first-, second- and third-order rogue wave-like solutions through the different dispersion, nonlinearity and linear potential coefficients. We find that only if the dispersion and nonlinearity coefficients are proportional to each other, heights of the background of those rogue waves maintain unchanged with time increasing. Due to the existence of complex parameters, such nonautonomous rogue waves in the higher-order cases have more complex features than those in the lower.

Two and four photon absorption and nonlinear refraction in undoped, chromium doped and copper doped ZnS quantum dots

NASA Astrophysics Data System (ADS)

Sharma, Dimple; Malik, B. P.; Gaur, Arun

2015-12-01

The ZnS quantum dots (QDs) with Cr and Cu doping were synthesized by chemical co-precipitation method. The nanostructures of the prepared undoped and doped ZnS QDs were characterized by UV-vis spectroscopy, Transmission electron microscopy (TEM) and X-ray diffraction (XRD). The sizes of QDs were found to be within 3-5 nm range. The nonlinear parameters viz. Two photon absorption coefficient (β2), nonlinear refractive index (n2), third order nonlinear susceptibility (χ3) at wavelength 532 nm and Four photon absorption coefficient (β4) at wavelength 1064 nm have been calculated by Z-scan technique using nanosecond Nd:YAG laser in undoped, Cr doped and Cu doped ZnS QDs. Higher values of nonlinear parameters for doped ZnS infer that they are potential material for the development of photonics devices and sensor protection applications.

Automatic weight determination in nonlinear model predictive control of wind turbines using swarm optimization technique

NASA Astrophysics Data System (ADS)

Tofighi, Elham; Mahdizadeh, Amin

2016-09-01

This paper addresses the problem of automatic tuning of weighting coefficients for the nonlinear model predictive control (NMPC) of wind turbines. The choice of weighting coefficients in NMPC is critical due to their explicit impact on efficiency of the wind turbine control. Classically, these weights are selected based on intuitive understanding of the system dynamics and control objectives. The empirical methods, however, may not yield optimal solutions especially when the number of parameters to be tuned and the nonlinearity of the system increase. In this paper, the problem of determining weighting coefficients for the cost function of the NMPC controller is formulated as a two-level optimization process in which the upper- level PSO-based optimization computes the weighting coefficients for the lower-level NMPC controller which generates control signals for the wind turbine. The proposed method is implemented to tune the weighting coefficients of a NMPC controller which drives the NREL 5-MW wind turbine. The results are compared with similar simulations for a manually tuned NMPC controller. Comparison verify the improved performance of the controller for weights computed with the PSO-based technique.

Oriented niobate ferroelectric thin films for electrical and optical devices

DOEpatents

Wessels, Bruce W.; Nystrom, Michael J.

2001-01-01

Sr.sub.x Ba.sub.1-x Nb.sub.2 O.sub.6, where x is greater than 0.25 and less than 0.75, and KNbO.sub.3 ferroelectric thin films metalorganic chemical vapor deposited on amorphous or cyrstalline substrate surfaces to provide a crystal axis of the film exhibiting a high dielectric susceptibility, electro-optic coefficient, and/or nonlinear optic coefficient oriented preferentially in a direction relative to a crystalline or amorphous substrate surface. Such films can be used in electronic, electro-optic, and frequency doubling components.

Dynamic Nonlinear Elastic Stability of Helicopter Rotor Blades in Hover and in Forward Flight

NASA Technical Reports Server (NTRS)

Friedmann, P.; Tong, P.

1972-01-01

Equations for large coupled flap-lag motion of hingeless elastic helicopter blades are consistently derived. Only torsionally-rigid blades excited by quasi-steady aerodynamic loads are considered. The nonlinear equations of motion in the time and space variables are reduced to a system of coupled nonlinear ordinary differential equations with periodic coefficients, using Galerkin's method for the space variables. The nonlinearities present in the equations are those arising from the inclusion of moderately large deflections in the inertia and aerodynamic loading terms. The resulting system of nonlinear equations has been solved, using an asymptotic expansion procedure in multiple time scales. The stability boundaries, amplitudes of nonlinear response, and conditions for existence of limit cycles are obtained analytically. Thus, the different roles played by the forcing function, parametric excitation, and nonlinear coupling in affecting the solution can be easily identified, and the basic physical mechanism of coupled flap-lag response becomes clear. The effect of forward flight is obtained with the requirement of trimmed flight at fixed values of the thrust coefficient.

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

NASA Astrophysics Data System (ADS)

Hasanov, Alemdar; Erdem, Arzu

2008-08-01

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

Natural laminar flow airfoil design considerations for winglets on low-speed airplanes

NASA Technical Reports Server (NTRS)

Vandam, C. P.

1984-01-01

Winglet airfoil section characteristics which significantly influence cruise performance and handling qualities of an airplane are discussed. A good winglet design requires an airfoil section with a low cruise drag coefficient, a high maximum lift coefficient, and a gradual and steady movement of the boundary layer transition location with angle of attack. The first design requirement provides a low crossover lift coefficient of airplane drag polars with winglets off and on. The other requirements prevent nonlinear changes in airplane lateral/directional stability and control characteristics. These requirements are considered in the design of a natural laminar flow airfoil section for winglet applications and chord Reynolds number of 1 to 4 million.

Theoretical transient analysis of a hearing aid feedback canceller with a saturation type nonlinearity in the direct path.

PubMed

Costa, Márcio Holsbach

2017-12-01

Feedback cancellation in a hearing aid is essential for achieving high maximum stable gain to compensate for the losses in severe to profound hearing impaired people. The performance of adaptive feedback cancellers has been studied by assuming that the feedback path can be modeled as a linear system. However, limited dynamic range, low-cost loudspeakers, and nonlinear power amplifiers may distort the hearing aid output signal. In this way, linear-based predictions of the canceller performance may lead to significant deviations from its actual behavior. This work presents a theoretical performance analysis of a Least Mean Square based shadow filter that is applied to set up the coefficients of a feedback canceller, which is subject to a static saturation type nonlinearity at the output of the direct path. Deterministic recursive equations are derived to predict the mean square feedback error and the mean coefficient vector evolution between updates of the feedback canceller. These models are defined as functions of the canceller parameters and input signal statistics. Comparisons with Monte Carlo simulations show the provided models are highly accurate under the considered assumptions. The developed models allow inferences about the potential impact of an overdriven loudspeaker over the transient performance of the direct method feedback canceller, serving as insightful tools for understanding the involved mechanisms. Copyright © 2017 Elsevier Ltd. All rights reserved.

Laterally azo-bridged h-shaped ferroelectric dimesogens for second-order nonlinear optics: ferroelectricity and second harmonic generation.

PubMed

Zhang, Yongqiang; Martinez-Perdiguero, Josu; Baumeister, Ute; Walker, Christopher; Etxebarria, Jesus; Prehm, Marko; Ortega, Josu; Tschierske, Carsten; O'Callaghan, Michael J; Harant, Adam; Handschy, Mark

2009-12-30

Two classes of laterally azo-bridged H-shaped ferroelectric liquid crystals (FLCs), incorporating azobenzene and disperse red 1 (DR-1) chromophores along the FLC polar axes, were synthesized and characterized by polarized light microscopy, differential scanning calorimetry, 2D X-ray diffraction analysis, and electro-optical investigations. They represent the first H-shaped FLC materials exhibiting the ground-state, thermodynamically stable enantiotropic SmC* phase, i.e., ground-state ferroelectricity. Second harmonic generation measurements of one compound incorporating a DR-1 chromophore at the incident wavelength of 1064 nm give a nonlinear coefficient of d(22) = 17 pm/V, the largest nonlinear optics coefficient reported to date for calamitic FLCs. This value enables viable applications of FLCs in nonlinear optics.

Nonlinear defect localized modes and composite gray and anti-gray solitons in one-dimensional waveguide arrays with dual-flip defects

NASA Astrophysics Data System (ADS)

Liu, Yan; Guan, Yefeng; Li, Hai; Luo, Zhihuan; Mai, Zhijie

2017-08-01

We study families of stationary nonlinear localized modes and composite gray and anti-gray solitons in a one-dimensional linear waveguide array with dual phase-flip nonlinear point defects. Unstaggered fundamental and dipole bright modes are studied when the defect nonlinearity is self-focusing. For the fundamental modes, symmetric and asymmetric nonlinear modes are found. Their stable areas are studied using different defect coefficients and their total power. For the nonlinear dipole modes, the stability conditions of this type of mode are also identified by different defect coefficients and the total power. When the defect nonlinearity is replaced by the self-defocusing one, staggered fundamental and dipole bright modes are created. Finally, if we replace the linear waveguide with a full nonlinear waveguide, a new type of gray and anti-gray solitons, which are constructed by a kink and anti-kink pair, can be supported by such dual phase-flip defects. In contrast to the usual gray and anti-gray solitons formed by a single kink, their backgrounds on either side of the gray hole or bright hump have the same phase.

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.

Integrable equations of the infinite nonlinear Schrödinger equation hierarchy with time variable coefficients.

PubMed

Kedziora, D J; Ankiewicz, A; Chowdury, A; Akhmediev, N

2015-10-01

We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions. These resulting wavefunctions are given in exact analytical form. We then show that the Lax pair and Darboux transformation formalisms still apply in this scheme when the coefficients in the hierarchy depend on the propagation variable (e.g., time). This extension thus allows for the construction of complicated solutions within a greatly diversified domain of generalised nonlinear systems.

Behavioral Modeling and Characterization of Nonlinear Operation in RF and Microwave Systems

DTIC Science & Technology

2005-01-01

the model further reinforces the intuition gained by employing this modeling technique. 84 Chapter 5 Remote Characterization of RF Devices 5.1...was used to extract the power series coefficients, 21 dBm. This further reinforces the conclusion that the nonlinear coefficients should be extracted...are becoming important. The fit of the odd-ordered model reinforces this hypothesis since the phase component of the fit roughly splits the

Approximate effective nonlinear coefficient of second-harmonic generation in KTiOPO(4).

PubMed

Asaumi, K

1993-10-20

A simplified approximate expression for the effective nonlinear coefficient of type-II second-harmonicgeneration in KTiOPO(4) was obtained by observing that the difference between the refractive indices n(x) and n(y) is 1 order of magnitude smaller than the difference between n(z) and n(y) (or n(x)). The agreement of this approximate equation with the true definition is good, with a maximum discrepancy of 4%.

New method to determine the refractive index and the absorption coefficient of organic nonlinear crystals in the ultra-wideband THz region.

PubMed

Ohno, Seigo; Miyamoto, Katsuhiko; Minamide, Hiroaki; Ito, Hiromasa

2010-08-02

A method for simultaneously measuring the refractive index and absorption coefficient of nonlinear optical crystals in the ultra-wideband terahertz (THz) region is described. This method is based on the analysis of a collinear difference frequency generation (DFG) process using a tunable, dual-wavelength, optical parametric oscillator. The refractive index and the absorption coefficient in the organic nonlinear crystal DAST were experimentally determined in the frequency range 2.5-26.2 THz by measuring the THz-wave output using DFG. The resultant refractive index in the x-direction was approximately 2.3, while the absorption spectrum was in good agreement with FT-IR measurements. The output of the DAST-DFG THz-wave source was optimized to the phase-matching condition using the measured refractive index spectrum in THz region, which resulted in an improvement in the output power of up to a factor of nine.

Estimation of Rotary Stability Derivatives at Subsonic and Transonic Speeds

NASA Technical Reports Server (NTRS)

Tobak, Murray; Lessing, Henry C.

1961-01-01

The first part of this paper pertains to the estimation of subsonic rotary stability derivatives of wings. The unsteady potential flow problem is solved by a superposition of steady flow solutions. Numerical results for the damping coefficients of triangular wings are presented as functions of aspect ratio and Mach number, and are compared with experimental results over the Mach number range 0 to 1. In the second part, experimental results are used. to point out a close correlation between the nonlinear variations with angle of attack of the static pitching-moment curve slope and the damping-in-pitch coefficient. The underlying basis for the correlation is found as a result of an analysis in which the indicial function concept and. the principle of super-position are adapted to apply to the nonlinear problem. The form of the result suggests a method of estimating nonlinear damping coefficients from results of static wind-tunnel measurements.

Ultrasonic Non Linearity Characterization of the Stainless Steel Wire Reinforced Aluminium Composite

NASA Astrophysics Data System (ADS)

Kim, C. S.; Park, T. S.; Park, I. K.; Hyun, C. Y.

2009-03-01

The effectiveness of the ultrasonic nonlinearity measurement for nearly closed cracks was demonstrated for hot pressing and extrusion of stainless steel 304 short wire reinforced aluminum composite. Aluminum based composites show considerable potential in the aerospace industry and the automotive industry due to their high specific strength and low thermal expansion coefficient. The ultrasonic nonlinearity (β/β0) increased with the volume fraction of SSF and aging heat treatment because of the generation of microvoids resulted from localized SSF and matrix precipitation. This study demonstrates the potential for characterization of reinforced composite materials fabricated by the powder metallurgy technique.

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.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

NASA Astrophysics Data System (ADS)

Lu, S. F.; Zhang, W.; Song, X. J.

2017-09-01

Using Reddy's high-order shear theory for laminated plates and Hamilton's principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom (DOF) nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics, including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

Families of stable solitons and excitations in the PT-symmetric nonlinear Schrödinger equations with position-dependent effective masses.

PubMed

Chen, Yong; Yan, Zhenya; Mihalache, Dumitru; Malomed, Boris A

2017-04-28

Since the parity-time-([Formula: see text]-) symmetric quantum mechanics was put forward, fundamental properties of some linear and nonlinear models with [Formula: see text]-symmetric potentials have been investigated. However, previous studies of [Formula: see text]-symmetric waves were limited to constant diffraction coefficients in the ambient medium. Here we address effects of variable diffraction coefficient on the beam dynamics in nonlinear media with generalized [Formula: see text]-symmetric Scarf-II potentials. The broken linear [Formula: see text] symmetry phase may enjoy a restoration with the growing diffraction parameter. Continuous families of one- and two-dimensional solitons are found to be stable. Particularly, some stable solitons are analytically found. The existence range and propagation dynamics of the solitons are identified. Transformation of the solitons by means of adiabatically varying parameters, and collisions between solitons are studied too. We also explore the evolution of constant-intensity waves in a model combining the variable diffraction coefficient and complex potentials with globally balanced gain and loss, which are more general than [Formula: see text]-symmetric ones, but feature similar properties. Our results may suggest new experiments for [Formula: see text]-symmetric nonlinear waves in nonlinear nonuniform optical media.

Dispersion in tidally averaged transport equation

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.

1992-01-01

A general governing inter-tidal transport equation for conservative solutes has been derived without invoking the weakly nonlinear approximation. The governing inter-tidal transport equation is a convection-dispersion equation in which the convective velocity is a mean Lagrangian residual current, and the inter-tidal dispersion coefficient is defined by a dispersion patch. When the weakly nonlinear condition is violated, the physical significance of the Stokes' drift, as used in tidal dynamics, becomes questionable. For nonlinear problems, analytical solutions for the mean Lagrangian residual current and for the inter-tidal dispersion coefficient do not exist, they must be determined numerically. A rectangular tidal inlet with a constriction is used in the first example. The solutions of the residual currents and the computed properties of the inter-tidal dispersion coefficient are used to illuminate the mechanisms of the inter-tidal transport processes. Then, the present formulation is tested in a geometrically complex tidal estuary – San Francisco Bay, California. The computed inter-tidal dispersion coefficients are in the range between 5×104 and 5×106 cm2/sec., which are consistent with the values reported in the literature

Modeling the variations of reflection coefficient of Earth's lower ionosphere using very low frequency radio wave data by artificial neural network

NASA Astrophysics Data System (ADS)

Ghanbari, Keyvan; Khakian Ghomi, Mehdi; Mohammadi, Mohammad; Marbouti, Marjan; Tan, Le Minh

2016-08-01

The ionized atmosphere lying from 50 to 600 km above surface, known as ionosphere, contains high amount of electrons and ions. Very Low Frequency (VLF) radio waves with frequencies between 3 and 30 kHz are reflected from the lower ionosphere specifically D-region. A lot of applications in long range communications and navigation systems have been inspired by this characteristic of ionosphere. There are several factors which affect the ionization rate in this region, such as: time of day (presence of sun in the sky), solar zenith angle (seasons) and solar activities. Due to nonlinear response of ionospheric reflection coefficient to these factors, finding an accurate relation between these parameters and reflection coefficient is an arduous task. In order to model these kinds of nonlinear functionalities, some numerical methods are employed. One of these methods is artificial neural network (ANN). In this paper, the VLF radio wave data of 4 sudden ionospheric disturbance (SID) stations are given to a multi-layer perceptron ANN in order to simulate the variations of reflection coefficient of D region ionosphere. After training, validation and testing the ANN, outputs of ANN and observed values are plotted together for 2 random cases of each station. By evaluating the results using 2 parameters of pearson correlation coefficient and root mean square error, a satisfying agreement was found between ANN outputs and real observed data.

CMOS-compatible 2-bit optical spectral quantization scheme using a silicon-nanocrystal-based horizontal slot waveguide

PubMed Central

Kang, Zhe; Yuan, Jinhui; Zhang, Xianting; Wu, Qiang; Sang, Xinzhu; Farrell, Gerald; Yu, Chongxiu; Li, Feng; Tam, Hwa Yaw; Wai, P. K. A.

2014-01-01

All-optical analog-to-digital converters based on the third-order nonlinear effects in silicon waveguide are a promising candidate to overcome the limitation of electronic devices and are suitable for photonic integration. In this paper, a 2-bit optical spectral quantization scheme for on-chip all-optical analog-to-digital conversion is proposed. The proposed scheme is realized by filtering the broadened and split spectrum induced by the self-phase modulation effect in a silicon horizontal slot waveguide filled with silicon-nanocrystal. Nonlinear coefficient as high as 8708 W−1/m is obtained because of the tight mode confinement of the horizontal slot waveguide and the high nonlinear refractive index of the silicon-nanocrystal, which provides the enhanced nonlinear interaction and accordingly low power threshold. The results show that a required input peak power level less than 0.4 W can be achieved, along with the 1.98-bit effective-number-of-bit and Gray code output. The proposed scheme can find important applications in on-chip all-optical digital signal processing systems. PMID:25417847

CMOS-compatible 2-bit optical spectral quantization scheme using a silicon-nanocrystal-based horizontal slot waveguide.

PubMed

Kang, Zhe; Yuan, Jinhui; Zhang, Xianting; Wu, Qiang; Sang, Xinzhu; Farrell, Gerald; Yu, Chongxiu; Li, Feng; Tam, Hwa Yaw; Wai, P K A

2014-11-24

All-optical analog-to-digital converters based on the third-order nonlinear effects in silicon waveguide are a promising candidate to overcome the limitation of electronic devices and are suitable for photonic integration. In this paper, a 2-bit optical spectral quantization scheme for on-chip all-optical analog-to-digital conversion is proposed. The proposed scheme is realized by filtering the broadened and split spectrum induced by the self-phase modulation effect in a silicon horizontal slot waveguide filled with silicon-nanocrystal. Nonlinear coefficient as high as 8708 W(-1)/m is obtained because of the tight mode confinement of the horizontal slot waveguide and the high nonlinear refractive index of the silicon-nanocrystal, which provides the enhanced nonlinear interaction and accordingly low power threshold. The results show that a required input peak power level less than 0.4 W can be achieved, along with the 1.98-bit effective-number-of-bit and Gray code output. The proposed scheme can find important applications in on-chip all-optical digital signal processing systems.

Lattice Boltzmann model for high-order nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

PubMed

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

2018-01-01

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

Unifying diffusion and seepage for nonlinear gas transport in multiscale porous media

NASA Astrophysics Data System (ADS)

Song, Hongqing; Wang, Yuhe; Wang, Jiulong; Li, Zhengyi

2016-09-01

We unify the diffusion and seepage process for nonlinear gas transport in multiscale porous media via a proposed new general transport equation. A coherent theoretical derivation indicates the wall-molecule and molecule-molecule collisions drive the Knudsen and collective diffusive fluxes, and constitute the system pressure across the porous media. A new terminology, nominal diffusion coefficient can summarize Knudsen and collective diffusion coefficients. Physical and numerical experiments show the support of the new formulation and provide approaches to obtain the diffusion coefficient and permeability simultaneously. This work has important implication for natural gas extraction and greenhouse gases sequestration in geological formations.

Reduced basis technique for evaluating the sensitivity coefficients of the nonlinear tire response

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Tanner, John A.; Peters, Jeanne M.

1992-01-01

An efficient reduced-basis technique is proposed for calculating the sensitivity of nonlinear tire response to variations in the design variables. The tire is modeled using a 2-D, moderate rotation, laminated anisotropic shell theory, including the effects of variation in material and geometric parameters. The vector of structural response and its first-order and second-order sensitivity coefficients are each expressed as a linear combination of a small number of basis vectors. The effectiveness of the basis vectors used in approximating the sensitivity coefficients is demonstrated by a numerical example involving the Space Shuttle nose-gear tire, which is subjected to uniform inflation pressure.

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.

Dark solitons for a variable-coefficient higher-order nonlinear Schrödinger equation in the inhomogeneous optical fiber

NASA Astrophysics Data System (ADS)

Sun, Yan; Tian, Bo; Wu, Xiao-Yu; Liu, Lei; Yuan, Yu-Qiang

2017-04-01

Under investigation in this paper is a variable-coefficient higher-order nonlinear Schrödinger equation, which has certain applications in the inhomogeneous optical fiber communication. Through the Hirota method, bilinear forms, dark one- and two-soliton solutions for such an equation are obtained. We graphically study the solitons with d1(z), d2(z) and d3(z), which represent the variable coefficients of the group-velocity dispersion, third-order dispersion and fourth-order dispersion, respectively. With the different choices of the variable coefficients, we obtain the parabolic, periodic and V-shaped dark solitons. Head-on and overtaking collisions are depicted via the dark two soliton solutions. Velocities of the dark solitons are linearly related to d1(z), d2(z) and d3(z), respectively, while the amplitudes of the dark solitons are not related to such variable coefficients.

Khokhlov Zabolotskaya Kuznetsov type equation: nonlinear acoustics in heterogeneous media

NASA Astrophysics Data System (ADS)

Kostin, Ilya; Panasenko, Grigory

2006-04-01

The KZK type equation introduced in this Note differs from the traditional form of the KZK model known in acoustics by the assumptions on the nonlinear term. For this modified form, a global existence and uniqueness result is established for the case of non-constant coefficients. Afterwards the asymptotic behaviour of the solution of the KZK type equation with rapidly oscillating coefficients is studied. To cite this article: I. Kostin, G. Panasenko, C. R. Mecanique 334 (2006).

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.

How to characterize the nonlinear amplifier?

NASA Technical Reports Server (NTRS)

Kallistratova, Dmitri Kouznetsov; Cotera, Carlos Flores

1994-01-01

The conception of the amplification of the coherent field is formulated. The definition of the coefficient of the amplification as the relation between the mean value of the field at the output to the value at the input and the definition of the noise as the difference between the number of photons in the output mode and square of the modulus of the mean value of the output amplitude are considered. Using a simple example it is shown that by these definitions the noise of the nonlinear amplifier may be less than the noise of the ideal linear amplifier of the same amplification coefficient. Proposals to search another definition of basic parameters of the nonlinear amplifiers are discussed. This definition should enable us to formulate the universal fundamental lower limit of the noise which should be valid for linear quantum amplifiers as for nonlinear ones.

Study of parameter of nonlinearity in 2-chloroethanol with 2-dimethylethanolamine/2-diethylethanolamine at different temperatures

NASA Astrophysics Data System (ADS)

Awasthi, Anjali; Awasthi, Aashees

2017-06-01

The acoustic non-linearity parameter (B/A) for binary mixtures of 2-chloroethanol with 2-dimethylethanolamine (2-DMAE) and 2-diethylethanolamine (2-DEAE) are evaluated using Tong Dong, Beyer and Beyer-Tong Dong coefficients at varying concentrations and temperatures ranging from 293.15 to 313.15 K. The nonlinearity parameter is used to calculate various molecular properties such as internal pressure, cohesive energy density, Van der waals' constant, distance of closest approach, diffusion coefficient and rotational correlation time. Additionally, the intermediate quantities like temperature and pressure derivatives of sound velocity and phase shift parameter as a function of temperature are also deduced. The extent of intermolecular interactions, anharmonicity and structural configuration of the binaries under investigation are discussed in terms of excess non-linearity parameter (B/A)E.

Cross Linked Metal Particles for Low Noise Bolometer Materials

DTIC Science & Technology

2016-12-12

Our results indicate that the CLMPs can simultaneously have a high temperature coefficient of resistivity and a low noise, and therefore have a...indicate that the CLMPs can simultaneously have a high temperature co- efficient of resistivity and a low noise, and therefore have a great potential...current as a function of the inverse of applied bias for CLMP films at different temperatures. It is seen that the I-V curves are highly nonlinear as 7 0

Structural characterization and optical constants of CuIn3Se5 vacuum and air annealed thin films

NASA Astrophysics Data System (ADS)

Segmane, N. E. H.; Abdelkader, D.; Amara, A.; Drici, A.; Akkari, F. Chaffar; Khemiri, N.; Bououdina, M.; Kanzari, M.; Bernède, J. C.

2018-01-01

Milled powder of ordered defect compound (ODC) CuIn3Se5 phase was successfully synthesized via milling process. Thin films of CuIn3Se5 were deposited onto glass substrates at room temperature by thermal evaporation technique. The obtained layers were annealed in vacuum and air atmosphere. The structural and compositional properties of the powder were analyzed using X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). Powder XRD characterization, Rietveld analysis and chemical bounding confirm the tetragonal ordered defect compound phase formation with lattice constants a = 5.732 Å and c = 11.575 Å. Thin films were characterized by XRD, atomic force microscopy (AFM) and UV/Vis spectroscopy. Transmittance (T) and reflectance (R) spectra were measured in the spectral range of 300-1800 nm. The absorption coefficient α exhibits high values in the visible range and reaches a value of 105 cm-1. The band gap energy Eg of the annealed thin films is estimated to be approximately 1.75 eV. The refractive index n was estimated from transmittance data using Swanepoel's method. The refractive indices of the films as a function of wavelengths can be fitted with Cauchy dispersion equation. The oscillator energy E0, dispersion energy Ed, zero frequency refractive index n0, high frequency dielectric constant ε∞ and the carrier concentration per effective mass N/m∗ values were determined from the analysis of the experimental data using Wemple-DiDomenico and Spitzer-Fan models. We exploited the refractive index dispersion for the determination of the magneto-optical constant V, which characterizes the Faraday rotation. The nonlinear optical parameters namely nonlinear susceptibility χ(3), nonlinear refractive index and nonlinear absorption coefficient β are investigated for the first time for CuIn3Se5 material.

A new nonlinear conjugate gradient coefficient under strong Wolfe-Powell line search

NASA Astrophysics Data System (ADS)

Mohamed, Nur Syarafina; Mamat, Mustafa; Rivaie, Mohd

2017-08-01

A nonlinear conjugate gradient method (CG) plays an important role in solving a large-scale unconstrained optimization problem. This method is widely used due to its simplicity. The method is known to possess sufficient descend condition and global convergence properties. In this paper, a new nonlinear of CG coefficient βk is presented by employing the Strong Wolfe-Powell inexact line search. The new βk performance is tested based on number of iterations and central processing unit (CPU) time by using MATLAB software with Intel Core i7-3470 CPU processor. Numerical experimental results show that the new βk converge rapidly compared to other classical CG method.

Spiraling elliptic Laguerre-Gaussian soliton in isotropic nonlocal competing cubic-quintic nonlinear media

NASA Astrophysics Data System (ADS)

Wang, Qing; Li, JingZhen; Xie, WeiXin

2018-06-01

This paper introduce a kind of spiraling elliptic Laguerre-Gaussian (SELG) soliton which has complicated structures in its profile and phase, and find that it can be formed in nonlocal cubic, quantic and competing cubic-quintic nonlinear media, respectively. The different-order SELG solitons with the same ellipticity have the same rotation period, cross-term phase coefficient, critical power and different critical orbital angular momentums (OAM). However, with the increase of ellipticity, the rotation period, cross-term phase coefficient, critical power and OAM are all increased. In particular, there are bistable SELG solitons stemmed by the competing effect between self-focusing cubic and self-defocusing quintic nonlinearities.

Nonlinear Dynamics of Silicon Nanowire Resonator Considering Nonlocal Effect.

PubMed

Jin, Leisheng; Li, Lijie

2017-12-01

In this work, nonlinear dynamics of silicon nanowire resonator considering nonlocal effect has been investigated. For the first time, dynamical parameters (e.g., resonant frequency, Duffing coefficient, and the damping ratio) that directly influence the nonlinear dynamics of the nanostructure have been derived. Subsequently, by calculating their response with the varied nonlocal coefficient, it is unveiled that the nonlocal effect makes more obvious impacts at the starting range (from zero to a small value), while the impact of nonlocal effect becomes weaker when the nonlocal term reaches to a certain threshold value. Furthermore, to characterize the role played by nonlocal effect in exerting influence on nonlinear behaviors such as bifurcation and chaos (typical phenomena in nonlinear dynamics of nanoscale devices), we have calculated the Lyapunov exponents and bifurcation diagram with and without nonlocal effect, and results shows the nonlocal effect causes the most significant effect as the device is at resonance. This work advances the development of nanowire resonators that are working beyond linear regime.

Coefficient Alpha and Reliability of Scale Scores

ERIC Educational Resources Information Center

Almehrizi, Rashid S.

2013-01-01

The majority of large-scale assessments develop various score scales that are either linear or nonlinear transformations of raw scores for better interpretations and uses of assessment results. The current formula for coefficient alpha (a; the commonly used reliability coefficient) only provides internal consistency reliability estimates of raw…

SPM of nonlinear surface plasmon waveguides

NASA Astrophysics Data System (ADS)

Li, Yuee; Zhang, Xiaoping

2008-10-01

Pulse propagation equation of nonlinear dispersion surface plasmon waveguide is educed strictly from wave equation. The nonlinear coefficient is defined and then used to assess and compare the nonlinear characteristic of three popular 1-D surface plasmon waveguides: the single metal-dielectric interface, the metal slab bounded by dielectric and the dielectric slab bounded by metal. SPM (self-phase modulation) of the typical surface plasmon waveguide is predicted and discussed.

Practical estimate of gradient nonlinearity for implementation of apparent diffusion coefficient bias correction.

PubMed

Malkyarenko, Dariya I; Chenevert, Thomas L

2014-12-01

To describe an efficient procedure to empirically characterize gradient nonlinearity and correct for the corresponding apparent diffusion coefficient (ADC) bias on a clinical magnetic resonance imaging (MRI) scanner. Spatial nonlinearity scalars for individual gradient coils along superior and right directions were estimated via diffusion measurements of an isotropicic e-water phantom. Digital nonlinearity model from an independent scanner, described in the literature, was rescaled by system-specific scalars to approximate 3D bias correction maps. Correction efficacy was assessed by comparison to unbiased ADC values measured at isocenter. Empirically estimated nonlinearity scalars were confirmed by geometric distortion measurements of a regular grid phantom. The applied nonlinearity correction for arbitrarily oriented diffusion gradients reduced ADC bias from 20% down to 2% at clinically relevant offsets both for isotropic and anisotropic media. Identical performance was achieved using either corrected diffusion-weighted imaging (DWI) intensities or corrected b-values for each direction in brain and ice-water. Direction-average trace image correction was adequate only for isotropic medium. Empiric scalar adjustment of an independent gradient nonlinearity model adequately described DWI bias for a clinical scanner. Observed efficiency of implemented ADC bias correction quantitatively agreed with previous theoretical predictions and numerical simulations. The described procedure provides an independent benchmark for nonlinearity bias correction of clinical MRI scanners.

Oriented niobate ferroelectric thin films for electrical and optical devices and method of making such films

DOEpatents

Wessels, B.W.; Nystrom, M.J.

1998-05-19

Sr{sub x}Ba{sub 1{minus}x}Nb{sub 2}O{sub 6}, where x is greater than 0.25 and less than 0.75, and KNbO{sub 3} ferroelectric thin films metalorganic chemical vapor deposited on amorphous or crystalline substrate surfaces to provide a crystal axis of the film exhibiting a high dielectric susceptibility, electro-optic coefficient, and/or nonlinear optic coefficient oriented preferentially in a direction relative to a crystalline or amorphous substrate surface are disclosed. Such films can be used in electronic, electro-optic, and frequency doubling components. 8 figs.

Oriented niobate ferroelectric thin films for electrical and optical devices and method of making such films

DOEpatents

Wessels, Bruce W.; Nystrom, Michael J.

1998-01-01

Sr.sub.x Ba.sub.1-x Nb.sub.2 O.sub.6, where x is greater than 0.25 and less than 0.75, and KNbO.sub.3 ferroelectric thin films metalorganic chemical vapor deposited on amorphous or crystalline substrate surfaces to provide a crystal axis of the film exhibiting a high dielectric susceptibility, electro-optic coefficient, and/or nonlinear optic coefficient oriented preferentially in a direction relative to a crystalline or amorphous substrate surface. Such films can be used in electronic, electro-optic, and frequency doubling components.

BRIEF COMMUNICATIONS: Q switching of a resonator by the metal-semiconductor phase transition

NASA Astrophysics Data System (ADS)

Bugaev, A. A.; Zakharchenya, Boris P.; Chudnovskiĭ, F. A.

1981-12-01

An experimental study was made of Q switching in a resonator by a mirror with a nonlinear reflection coefficient. This mirror was an interference reflecting structure containing a vanadium oxide film capable of undergoing a metal-semiconductor transition. The nonlinearity of the reflection coefficient was due to initiation of this phase transition by laser radiation. A determination was made of the parameters of a giant radiation pulse obtained using such a passive switch with a vanadium oxide film.

Octupolar molecules for nonlinear optics: from molecular design to crystals and films with large second-harmonic generation.

PubMed

Jeong, Mi-Yun; Cho, Bong Rae

2015-02-01

We summarize the nonlinear optical (NLO) properties of octupolar molecules, crystals, and films developed in our laboratory. We present the design strategy, structure-property relationship, and second-order NLO properties of 1,3,5-trinitro- and 1,3,5-tricyano-2,4,6-tris(p-diethylaminostyryl)benzene (TTB) derivatives, TTB crystals, and films prepared by free-casting TTB in poly(methyl methacrylate) (PMMA). The first hyperpolarizability of TTB was fivefold larger than that of the dipolar analogue. Moreover, the TTB crystal showed unprecedentedly large second-harmonic generation (SHG). While TTB crystal films (20 wt% TTB/PMMA) on various substrates showed appreciable SHG values, the cylinder film exhibited much larger SHG values and large electro-optic (EO) coefficients. The large SHG values and EO coefficients, as well as the high thermal stability of the cylinder film, will make it a potential candidate for NLO device applications. Copyright © 2014 The Chemical Society of Japan and Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

General multicomponent Yajima-Oikawa system: Painlevé analysis, soliton solutions, and energy-sharing collisions.

PubMed

Kanna, T; Sakkaravarthi, K; Tamilselvan, K

2013-12-01

We consider the multicomponent Yajima-Oikawa (YO) system and show that the two-component YO system can be derived in a physical setting of a three-coupled nonlinear Schrödinger (3-CNLS) type system by the asymptotic reduction method. The derivation is further generalized to the multicomponent case. This set of equations describes the dynamics of nonlinear resonant interaction between a one-dimensional long wave and multiple short waves. The Painlevé analysis of the general multicomponent YO system shows that the underlying set of evolution equations is integrable for arbitrary nonlinearity coefficients which will result in three different sets of equations corresponding to positive, negative, and mixed nonlinearity coefficients. We obtain the general bright N-soliton solution of the multicomponent YO system in the Gram determinant form by using Hirota's bilinearization method and explicitly analyze the one- and two-soliton solutions of the multicomponent YO system for the above mentioned three choices of nonlinearity coefficients. We also point out that the 3-CNLS system admits special asymptotic solitons of bright, dark, anti-dark, and gray types, when the long-wave-short-wave resonance takes place. The short-wave component solitons undergo two types of energy-sharing collisions. Specifically, in the two-component YO system, we demonstrate that two types of energy-sharing collisions-(i) energy switching with opposite nature for a particular soliton in two components and (ii) similar kind of energy switching for a given soliton in both components-result for two different choices of nonlinearity coefficients. The solitons appearing in the long-wave component always exhibit elastic collision whereas those of short-wave components exhibit standard elastic collisions only for a specific choice of parameters. We have also investigated the collision dynamics of asymptotic solitons in the original 3-CNLS system. For completeness, we explore the three-soliton interaction and demonstrate the pairwise nature of collisions and unravel the fascinating state restoration property.

Interpreting spectral unmixing coefficients: From spectral weights to mass fractions

NASA Astrophysics Data System (ADS)

Grumpe, Arne; Mengewein, Natascha; Rommel, Daniela; Mall, Urs; Wöhler, Christian

2018-01-01

It is well known that many common planetary minerals exhibit prominent absorption features. Consequently, the analysis of spectral reflectance measurements has become a major tool of remote sensing. Quantifying the mineral abundances, however, is not a trivial task. The interaction between the incident light rays and particulate surfaces, e.g., the lunar regolith, leads to a non-linear relationship between the reflectance spectra of the pure minerals, the so-called ;endmembers;, and the surface's reflectance spectrum. It is, however, possible to transform the non-linear reflectance mixture into a linear mixture of single-scattering albedos of the Hapke model. The abundances obtained by inverting the linear single-scattering albedo mixture may be interpreted as volume fractions which are weighted by the endmember's extinction coefficient. Commonly, identical extinction coefficients are assumed throughout all endmembers and the obtained volume fractions are converted to mass fractions using either measured or assumed densities. In theory, the proposed method may cover different grain sizes if each grain size range of a mineral is treated as a distinct endmember. Here, we present a method to transform the mixing coefficients to mass fractions for arbitrary combinations of extinction coefficients and densities. The required parameters are computed from reflectance measurements of well defined endmember mixtures. Consequently, additional measurements, e.g., the endmember density, are no longer required. We evaluate the method based on laboratory measurements and various results presented in the literature, respectively. It is shown that the procedure transforms the mixing coefficients to mass fractions yielding an accuracy comparable to carefully calibrated laboratory measurements without additional knowledge. For our laboratory measurements, the square root of the mean squared error is less than 4.82 wt%. In addition, the method corrects for systematic effects originating from mixtures of endmembers showing a highly varying albedo, e.g., plagioclase and pyroxene.

Solving intuitionistic fuzzy multi-objective nonlinear programming problem

NASA Astrophysics Data System (ADS)

Anuradha, D.; Sobana, V. E.

2017-11-01

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

Stochastic Resonance and Safe Basin of Single-Walled Carbon Nanotubes with Strongly Nonlinear Stiffness under Random Magnetic Field.

PubMed

Xu, Jia; Li, Chao; Li, Yiran; Lim, Chee Wah; Zhu, Zhiwen

2018-05-04

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of the microstructure is considered based on Eringen’s differential constitutive model. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases.

Physicochemical and Nonlinear Optical Properties of Novel Environmentally Benign Heterocyclic Azomethine Dyes: Experimental and Theoretical Studies

PubMed Central

Afzal, S. M.; Razvi, M. A. N.; Khan, Salman A.; Osman, Osman I.; Bakry, Ahmed H.; Asiri, Abdullah M.

2016-01-01

Novel heterocyclic azomethine dyes were prepared by the reaction of anthracene-9-carbaldehyde with different heterocyclic amines under microwave irradiation. Structures of the azomethine dyes were confirmed by the elemental analysis, mass spectrometry and several spectroscopic techniques. We studied absorbance and fluorescence spectra of the azomethine dyes in various solvents. They are found to be good absorbers and emitters. We also report photophysical properties like, extinction coefficient, oscillator strength, stokes shift and transition dipole moment. This reflects physicochemical behaviors of synthesized dyes. In addition, their intramolecular charge transfer and nonlinear optical properties, supported by natural bond orbital technique, were also studied computationally by density functional theory. The negative nonlinear refractive index and nonlinear absorption coefficient were measured for these dyes using the closed and open aperture Z-scan technique with a continuous wave helium-neon laser. These are found to vary linearly with solution concentration. PMID:27631371

The estimation of nonlinearity in problems of the building of initial confidence regions for small bodies motion. (Russian Title: Оценивание нелинейности в задачах построения начальных доверительных областей движения малых тел)

NASA Astrophysics Data System (ADS)

Syusina, O. M.; Chernitsov, A. M.; Tamarov, V. A.

2011-07-01

Simple and mathematically rigorous methods for calculating of nonlinearity coefficients are proposed. These coefficients allow us to make classification for the least squares problem as strongly or weakly nonlinear one. The advices are given on how to reduce a concrete estimation problem to weakly nonlinear one where a more efficient linear approach can be used.

Renormalization group estimates of transport coefficients in the advection of a passive scalar by incompressible turbulence

NASA Technical Reports Server (NTRS)

Zhou, YE; Vahala, George

1993-01-01

The advection of a passive scalar by incompressible turbulence is considered using recursive renormalization group procedures in the differential sub grid shell thickness limit. It is shown explicitly that the higher order nonlinearities induced by the recursive renormalization group procedure preserve Galilean invariance. Differential equations, valid for the entire resolvable wave number k range, are determined for the eddy viscosity and eddy diffusivity coefficients, and it is shown that higher order nonlinearities do not contribute as k goes to 0, but have an essential role as k goes to k(sub c) the cutoff wave number separating the resolvable scales from the sub grid scales. The recursive renormalization transport coefficients and the associated eddy Prandtl number are in good agreement with the k-dependent transport coefficients derived from closure theories and experiments.

Effect of the concentration of magnetic grains on the linear-optical-absorption coefficient of ferrofluid-doped lyotropic mesophases: deviation from the Beer-Lambert law.

PubMed

Cuppo, F L S; Gómez, S L; Figueiredo Neto, A M

2004-04-01

In this paper is reported a systematic experimental study of the linear-optical-absorption coefficient of ferrofluid-doped isotropic lyotropic mixtures as a function of the magnetic-grains concentration. The linear optical absorption of ferrolyomesophases increases in a nonlinear manner with the concentration of magnetic grains, deviating from the usual Beer-Lambert law. This behavior is associated to the presence of correlated micelles in the mixture which favors the formation of small-scale aggregates of magnetic grains (dimers), which have a higher absorption coefficient with respect to that of isolated grains. We propose that the indirect heating of the micelles via the ferrofluid grains (hyperthermia) could account for this nonlinear increase of the linear-optical-absorption coefficient as a function of the grains concentration.

Equivalent circuit model of converse magnetoelectric effect for the tri-layer magnetoelectric laminates with thermal and stress loadings

NASA Astrophysics Data System (ADS)

Zhou, Hao-Miao; Li, Meng-Han; Liu, Hui; Cui, Xiao-Le

2015-12-01

For the converse magnetoelectric coupling effect of the piezoelectric/magnetostrictive/piezoelectric tri-layer symmetric magnetoelectric laminates, based on the nonlinear thermo-magneto-mechanical constitutive equations of the giant magnetostrictive materials and the thermo-electro-mechanical constitutive equations of the piezoelectric materials, according to Newton's second law and the magnetic circuit theorem, an equivalent circuit is established. Then an expression of the converse magnetoelectric coefficient describing nonlinear thermo-magneto-electro-mechanical coupling is established. The curve of the nonlinear converse magnetoelectric coefficient versus the bias magnetic field, is predicted effectively by the expression, and the predictions are in good agreement with the experimental result both qualitatively and quantitatively. Furthermore, the model can predict the complex influences of the bias magnetic field, the stress and the ambient temperature on the converse magnetoelectric coefficient. It can be found from these predictions that the converse magnetoelectric coefficient decreases with the increasing temperature and increases with the increasing tensile stress. Under the common effect of the ambient temperature and the stress, it is also found that the converse magnetoelectric coefficient changes sharply with the ambient temperature when the tensile stress is applied on the laminates, but it has a good stability of temperature when a large compressive stress is applied. Therefore, this work contributes to the researches on the giant converse magnetoelectric coefficient and the designs of magnetoelectric devices based on the converse magnetoelectric coupling.

Enhancing Security of Double Random Phase Encoding Based on Random S-Box

NASA Astrophysics Data System (ADS)

Girija, R.; Singh, Hukum

2018-06-01

In this paper, we propose a novel asymmetric cryptosystem for double random phase encoding (DRPE) using random S-Box. While utilising S-Box separately is not reliable and DRPE does not support non-linearity, so, our system unites the effectiveness of S-Box with an asymmetric system of DRPE (through Fourier transform). The uniqueness of proposed cryptosystem lies on employing high sensitivity dynamic S-Box for our DRPE system. The randomness and scalability achieved due to applied technique is an additional feature of the proposed solution. The firmness of random S-Box is investigated in terms of performance parameters such as non-linearity, strict avalanche criterion, bit independence criterion, linear and differential approximation probabilities etc. S-Boxes convey nonlinearity to cryptosystems which is a significant parameter and very essential for DRPE. The strength of proposed cryptosystem has been analysed using various parameters such as MSE, PSNR, correlation coefficient analysis, noise analysis, SVD analysis, etc. Experimental results are conferred in detail to exhibit proposed cryptosystem is highly secure.

Mixed higher-order flow harmonics and nonlinear response coefficients in PbPb collisions at 2.76 and 5.02 TeV with CMS

NASA Astrophysics Data System (ADS)

Tuo, Shengquan; CMS Collaboration

2017-11-01

The mixed higher-order flow harmonics and nonlinear response coefficients of charged particles are presented as a function of pT and centrality in PbPb collisions at √{sNN} = 2.76 TeV and 5.02 TeV with the CMS detector. The results are obtained using the scalar product method, and cover a pT range from 0.3 GeV/c to 8.0 GeV/c, pseudorapidity | η | < 2.4, and a centrality range of 0-60%. The mixed harmonic results at 5.02 TeV are compared to the matching higher-order flow harmonics from two-particle correlations, which measure vn values with respect to the n-th order event plane. It is observed that the nonlinear response coefficients of the odd harmonics are larger than the even harmonics ones. The results are compared with hydrodynamic predictions using different shear viscosity to entropy density ratios and different initial conditions.

Investigation of a Nonlinear Control System

NASA Technical Reports Server (NTRS)

Flugge-Lotz, I; Taylor, C F; Lindberg, H E

1958-01-01

A discontinuous variation of coefficients of the differential equation describing the linear control system before nonlinear elements are added is studied in detail. The nonlinear feedback is applied to a second-order system. Simulation techniques are used to study performance of the nonlinear control system and to compare it with the linear system for a wide variety of inputs. A detailed quantitative study of the influence of relay delays and of a transport delay is presented.

Linear and Non-Linear Piezoresistance Coefficients in Cubic Semiconductors. I. Theoretical Formulations

NASA Astrophysics Data System (ADS)

Durand, S.; Tellier, C. R.

1996-02-01

This paper constitutes the first part of a work devoted to applications of piezoresistance effects in germanium and silicon semiconductors. In this part, emphasis is placed on a formal explanation of non-linear effects. We propose a brief phenomenological description based on the multi-valleys model of semiconductors before to adopt a macroscopic tensorial model from which general analytical expressions for primed non-linear piezoresistance coefficients are derived. Graphical representations of linear and non-linear piezoresistance coefficients allows us to characterize the influence of the two angles of cut and of directions of alignment. The second part will primarily deal with specific applications for piezoresistive sensors. Cette publication constitue la première partie d'un travail consacré aux applications des effets piézorésistifs dans les semiconducteurs germanium et silicium. Cette partie traite essentiellement de la modélisation des effets non-linéaires. Après une description phénoménologique à partir du modèle de bande des semiconducteurs nous développons un modèle tensoriel macroscopique et nous proposons des équations générales analytiques exprimant les coefficients piézorésistifs non-linéaires dans des repères tournés. Des représentations graphiques des variations des coefficients piézorésistifs linéaires et non-linéaires permettent une pré-caractérisation de l'influence des angles de coupes et des directions d'alignement avant l'étude d'applications spécifiques qui feront l'objet de la deuxième partie.

Experimental investigation of material nonlinearity using the Rayleigh surface waves excited and detected by angle beam wedge transducers.

PubMed

Zhang, Shuzeng; Li, Xiongbing; Jeong, Hyunjo; Hu, Hongwei

2018-05-12

Angle beam wedge transducers are widely used in nonlinear Rayleigh wave experiments as they can generate Rayleigh wave easily and produce high intensity nonlinear waves for detection. When such a transducer is used, the spurious harmonics (source nonlinearity) and wave diffraction may occur and will affect the measurement results, so it is essential to fully understand its acoustic nature. This paper experimentally investigates the nonlinear Rayleigh wave beam fields generated and received by angle beam wedge transducers, in which the theoretical predictions are based on the acoustic model developed previously for angle beam wedge transducers [S. Zhang, et al., Wave Motion, 67, 141-159, (2016)]. The source of the spurious harmonics is fully characterized by scrutinizing the nonlinear Rayleigh wave behavior in various materials with different driving voltages. Furthermore, it is shown that the attenuation coefficients for both fundamental and second harmonic Rayleigh waves can be extracted by comparing the measurements with the predictions when the experiments are conducted at many locations along the propagation path. A technique is developed to evaluate the material nonlinearity by making appropriate corrections for source nonlinearity, diffraction and attenuation. The nonlinear parameters of three aluminum alloy specimens - Al 2024, Al 6061 and Al 7075 - are measured, and the results indicate that the measurement results can be significantly improved using the proposed method. Copyright © 2018. Published by Elsevier B.V.

Bootstrap evaluation of a young Douglas-fir height growth model for the Pacific Northwest

Treesearch

Nicholas R. Vaughn; Eric C. Turnblom; Martin W. Ritchie

2010-01-01

We evaluated the stability of a complex regression model developed to predict the annual height growth of young Douglas-fir. This model is highly nonlinear and is fit in an iterative manner for annual growth coefficients from data with multiple periodic remeasurement intervals. The traditional methods for such a sensitivity analysis either involve laborious math or...

Second-order nonlinear optical properties of composite material of an azo-chromophore with a tricyanodiphenyl acceptor in a poly(styrene-co-methyl methacrylate) matrix

NASA Astrophysics Data System (ADS)

Shelkovnikov, Vladimir; Selivanova, Galina; Lyubas, Gleb; Korotaev, Sergey; Shundrina, Inna; Tretyakov, Evgeny; Zueva, Ekaterina; Plekhanov, Alexander; Mikerin, Sergey; Simanchuk, Andrey

2017-07-01

The composite material of new synthesized 4-((4-(N,N-n-dibutylamino) phenyl)diazenyl)-biphenyl-2,3,4-tricarbonitrile (GAS dye) in commercial poly(styrene-co-methyl methacrylate) (PSMMA) was prepared, poled and its nonlinear optical properties compared with DR1 dye were studied. High thermal stability of the composite material was revealed, and the maximal concentration of the chromophore was found to reach ∼20 wt%. The dipole moment, polarizability tensor, and first hyperpolarizability tensor of the investigated dyes were calculated by within the framework of the coupled perturbed density functional theory. A nanosecond second-harmonic generation Maker fringes technique was used which is capable of providing the magnitude of the second-order nonlinearity of optical materials at a wavelength of 1064 nm. For the tested GAS-PSMMA composite material, maximal coefficient d33 was found to be 50 pm/V. The nonlinear optical response, which was achieved here, shows possible usefulness of the GAS dye as a component for molecular design of nonlinear-optical materials with advanced characteristics.

Modeling the High Speed Research Cycle 2B Longitudinal Aerodynamic Database Using Multivariate Orthogonal Functions

NASA Technical Reports Server (NTRS)

Morelli, E. A.; Proffitt, M. S.

1999-01-01

The data for longitudinal non-dimensional, aerodynamic coefficients in the High Speed Research Cycle 2B aerodynamic database were modeled using polynomial expressions identified with an orthogonal function modeling technique. The discrepancy between the tabular aerodynamic data and the polynomial models was tested and shown to be less than 15 percent for drag, lift, and pitching moment coefficients over the entire flight envelope. Most of this discrepancy was traced to smoothing local measurement noise and to the omission of mass case 5 data in the modeling process. A simulation check case showed that the polynomial models provided a compact and accurate representation of the nonlinear aerodynamic dependencies contained in the HSR Cycle 2B tabular aerodynamic database.

The effect of excitation intensity variation and silver nanoparticle codoping on nonlinear optical properties of mixed tellurite and zinc oxide glass doped with Nd2O3 studied through ultrafast z-scan spectroscopy

NASA Astrophysics Data System (ADS)

Moreira, L.; Falci, R. F.; Darabian, H.; Anjos, V.; Bell, M. J. V.; Kassab, L. R. P.; Bordon, C. D. S.; Doualan, J. L.; Camy, P.; Moncorgé, R.

2018-05-01

The research on Nd3+ doped new solid-state laser hosts with specific thermo-mechanical and optical properties is very active. Nd3+ doped tellurite glasses are suitable for these applications. They have high linear and nonlinear refraction index, wide transmittance range. The TeO2-ZnO (TZO) glass considered in the present work combines all those features and the nonlinear optical properties can be used for the development of Kerr-lens mode-locked sub picosecond lasers. Recently the laser performance of Nd3+ doped TZO glass and was reported and laser slope efficiency of 21% was observed. We investigate how the intensity variation and the silver nanoparticles codoping affects the nonlinear optical properties of Nd3+ doped TZO glasses. Intensity dependent nonlinear refraction indices coefficients at 750, 800 and 850 nm were observed. The nonlinear optical features were obtained through ultrafast single beam z-scan technique with excitations at 750, 800 and 850 nm and are up to two orders of magnitude higher than those reported in the literature.

Investigation on the growth, spectral, lifetime, mechanical analysis and third-order nonlinear optical studies of L-methionine admixtured D-mandelic acid single crystal: A promising material for nonlinear optical applications

NASA Astrophysics Data System (ADS)

Jayaprakash, P.; Sangeetha, P.; Kumari, C. Rathika Thaya; Caroline, M. Lydia

2017-08-01

A nonlinear optical bulk single crystal of L-methionine admixtured D-mandelic acid (LMDMA) has been grown by slow solvent evaporation technique using water as solvent at ambient temperature. The crystallized LMDMA single crystal subjected to single crystal X-ray diffraction study confirmed monoclinic system with the acentric space group P21. The FTIR analysis gives information about the modes of vibration in the various functional groups present in LMDMA. The UV-visible spectral analysis assessed the optical quality and linear optical properties such as extinction coefficient, reflectance, refractive index and from which optical conductivity and electric susceptibility were also evaluated. The frequency doubling efficiency was observed using Kurtz Perry powder technique. A multiple shot laser was utilized to evaluate the laser damage threshold energy of the crystal. Discrete thermodynamic properties were carried out by TG-DTA studies. The hardness, Meyer's index, yield strength, elastic stiffness constant, Knoop hardness, fracture toughness and brittleness index were analyzed using Vickers microhardness tester. Layer growth pattern and the surface defect were examined by chemical etching studies using optical microscope. Fluorescence emission spectrum was recorded and lifetime was also studied. The electric field response of crystal was investigated from the dielectric studies at various temperatures at different frequencies. The third-order nonlinear optical response in LMDMA has been investigated using Z-scan technique with He-Ne laser at 632.8 nm and nonlinear parameters such as refractive index (n2), absorption coefficient (β) and susceptibility (χ3) investigated extensively for they are in optical phase conjucation, high-speed optical switches and optical dielectric devices.

Nonlinear optical and microscopic analysis of Cu2+ doped zinc thiourea chloride (ZTC) monocrystal

NASA Astrophysics Data System (ADS)

Ramteke, S. P.; Anis, Mohd; Pandian, M. S.; Kalainathan, S.; Baig, M. I.; Ramasamy, P.; Muley, G. G.

2018-02-01

Organometallic crystals offer considerable nonlinear response therefore, present article focuses on bulk growth and investigation of Cu2+ ion doped zinc thiourea chloride (ZTC) crystal to explore its technological impetus for laser assisted nonlinear optical (NLO) device applications. The Cu2+ ion doped ZTC bulk single crystal of dimension 03 × 2.4 × 0.4 cm3 has been grown from pH controlled aqueous solution by employing slow solvent evaporation technique. The structural analysis has been performed by means of single crystal X-ray diffraction technique. The doping of Cu2+ ion in ZTC crystal matrix has been confirmed by means of energy dispersive spectroscopic (EDS) technique. The origin of nonlinear optical properties in Cu2+ ion doped ZTC crystal has been studied by employing the Kurtz-Perry test and Z-scan analysis. The remarkable enhancement in second harmonic generation (SHG) efficiency of Cu2+ ion doped ZTC crystal with reference to ZTC crystal has been determined. The He-Ne laser assisted Z-scan analysis has been performed to determine the third order nonlinear optical (TONLO) nature of grown crystal. The TONLO parameters such as susceptibility, absorption coefficient, refractive index and figure of merit of Cu-ZTC crystal have been evaluated using the Z-scan transmittance data. The laser damage threshold of grown crystal to high intensity of Nd:YAG laser is found to be 706.2 MW/cm2. The hardness number, work hardening index, yield strength and elastic stiffness coefficient of grown crystal has been investigated under microhardness study. The etching study has been carried out to determine the growth likelihood, nature of etch pits and surface quality of grown crystal.

Study of critical behavior in concrete during curing by application of dynamic linear and nonlinear means.

PubMed

Lacouture, Jean-Christoph; Johnson, Paul A; Cohen-Tenoudji, Frederic

2003-03-01

The monitoring of both linear and nonlinear elastic properties of a high performance concrete during curing is presented by application of compressional and shear waves. To follow the linear elastic behavior, both compressional and shear waves are used in wide band pulse echo mode. Through the value of the complex reflection coefficient between the cell material (Lucite) and the concrete within the cell, the elastic moduli are calculated. Simultaneously, the transmission of a continuous compressional sine wave at progressively increasing drive levels permits us to calculate the nonlinear properties by extracting the harmonics amplitudes of the signal. Information regarding the chemical evolution of the concrete based upon the reaction of hydration of cement is obtained by monitoring the temperature inside the sample. These different types of measurements are linked together to interpret the critical behavior.

Sensor fault detection and isolation system for a condensation process.

PubMed

Castro, M A López; Escobar, R F; Torres, L; Aguilar, J F Gómez; Hernández, J A; Olivares-Peregrino, V H

2016-11-01

This article presents the design of a sensor Fault Detection and Isolation (FDI) system for a condensation process based on a nonlinear model. The condenser is modeled by dynamic and thermodynamic equations. For this work, the dynamic equations are described by three pairs of differential equations which represent the energy balance between the fluids. The thermodynamic equations consist in algebraic heat transfer equations and empirical equations, that allow for the estimation of heat transfer coefficients. The FDI system consists of a bank of two nonlinear high-gain observers, in order to detect, estimate and to isolate the fault in any of both outlet temperature sensors. The main contributions of this work were the experimental validation of the condenser nonlinear model and the FDI system. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear graphene plasmonics

PubMed Central

2017-01-01

The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications. PMID:29118665

Nonlinear graphene plasmonics

NASA Astrophysics Data System (ADS)

Ooi, Kelvin J. A.; Tan, Dawn T. H.

2017-10-01

The rapid development of graphene has opened up exciting new fields in graphene plasmonics and nonlinear optics. Graphene's unique two-dimensional band structure provides extraordinary linear and nonlinear optical properties, which have led to extreme optical confinement in graphene plasmonics and ultrahigh nonlinear optical coefficients, respectively. The synergy between graphene's linear and nonlinear optical properties gave rise to nonlinear graphene plasmonics, which greatly augments graphene-based nonlinear device performance beyond a billion-fold. This nascent field of research will eventually find far-reaching revolutionary technological applications that require device miniaturization, low power consumption and a broad range of operating wavelengths approaching the far-infrared, such as optical computing, medical instrumentation and security applications.

Mode matching in multiresonant plasmonic nanoantennas for enhanced second harmonic generation

NASA Astrophysics Data System (ADS)

Celebrano, Michele; Wu, Xiaofei; Baselli, Milena; Großmann, Swen; Biagioni, Paolo; Locatelli, Andrea; de Angelis, Costantino; Cerullo, Giulio; Osellame, Roberto; Hecht, Bert; Duò, Lamberto; Ciccacci, Franco; Finazzi, Marco

2015-05-01

Boosting nonlinear frequency conversion in extremely confined volumes remains a challenge in nano-optics research, but can enable applications in nanomedicine, photocatalysis and background-free biosensing. To obtain brighter nonlinear nanoscale sources, approaches that enhance the electromagnetic field intensity and counter the lack of phase matching in nanoplasmonic systems are often employed. However, the high degree of symmetry in the crystalline structure of plasmonic materials (metals in particular) and in nanoantenna designs strongly quenches second harmonic generation. Here, we describe doubly-resonant single-crystalline gold nanostructures with no axial symmetry displaying spatial mode overlap at both the excitation and second harmonic wavelengths. The combination of these features allows the attainment of a nonlinear coefficient for second harmonic generation of ˜5 × 10-10 W-1, enabling a second harmonic photon yield higher than 3 × 106 photons per second. Theoretical estimations point toward the use of our nonlinear plasmonic nanoantennas as efficient platforms for label-free molecular sensing.

High sensitive nonlinear modulation magnetoelectric magnetic sensors with a magnetostrictive metglas structure based on bell-shaped geometry

NASA Astrophysics Data System (ADS)

Ma, Jiashuai; Jiao, Jie; Fang, Cong; Zhao, Xiangyong; Luo, Haosu

2016-05-01

In this paper both linear and nonlinear magnetoelectric (ME) effects have been investigated intensively. In order to obtain magnetic amplification, we fabricated 3 multi-push-pull mode magnetoelectric laminated composites metglas/PMNT/metglas based on dumbbell-shaped metglas. The linear magnetoelectric charge coefficient is enhanced to 2600 pC/Oe at 2 Hz based on dumbbell-shaped metglas and it increases as the end-flange width of the dumbbell-shaped metglas increases at 2 Hz, respectively. Based on these 3 ME composites, we establish an active mode nonlinear modulation system for ME magnetic sensor, the sensitivity of which are enhanced to 80, 100 and 102 pT / √ Hz at 1 Hz for the composites with the end-flange width 20, 15 and 10 mm, respectively, via nonlinear ME　modulation method. Strain distribution simulations illustrate the theoretically accurate amplification of the dumbbell-shaped geometry. The center strains of 3 dumbbell-shaped metglas decrease as the width of end-flanges decreases

How Artificial Should the Treatment of a Plasma's Viscosity Be?

NASA Astrophysics Data System (ADS)

Whitney, K. G.; Velikovich, A. L.; Thornhill, J. W.; Davis, J.

1999-11-01

Electron viscosity dominates over ion viscosity and is important in describing the generation of shock fronts in highly ionizable plasmas. The sizes of shock front jumps in electron and ion temperature are determined from the magnitudes of the heat flow vector and pressure tensor, which, in turn, acquire non-negligible nonlinear contributions from the temperature and density gradients when these gradients are large. Thus, a consistent treatment of steep gradient formation in plasmas must come from investigations that include the effects of these nonlinear contributions to heat and momentum transport. Coefficients for each of five nonlinear contributions to the pressure tensor for an (r,z) Z-pinch geometry are presented and discussed in this talk. Hydrodynamic code calculations generally are not designed to provide a testbed for directly evaluating the kinetic energy dissipation that occurs at shock fronts; therefore, the strength of these nonlinear pressure tensor terms will be estimated by post-processing a Z-pinch hydrodynamics calculation and a steady-state planar shock wave calculation.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

NASA Astrophysics Data System (ADS)

Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.

2017-08-01

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.

Bilinear forms and soliton solutions for a fourth-order variable-coefficient nonlinear Schrödinger equation in an inhomogeneous Heisenberg ferromagnetic spin chain or an alpha helical protein

NASA Astrophysics Data System (ADS)

Yang, Jin-Wei; Gao, Yi-Tian; Wang, Qi-Min; Su, Chuan-Qi; Feng, Yu-Jie; Yu, Xin

2016-01-01

In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation is studied, which might describe a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain with the octuple-dipole interaction or an alpha helical protein with higher-order excitations and interactions under continuum approximation. With the aid of auxiliary function, we derive the bilinear forms and corresponding constraints on the variable coefficients. Via the symbolic computation, we obtain the Lax pair, infinitely many conservation laws, one-, two- and three-soliton solutions. We discuss the influence of the variable coefficients on the solitons. With different choices of the variable coefficients, we obtain the parabolic, cubic, and periodic solitons, respectively. We analyse the head-on and overtaking interactions between/among the two and three solitons. Interactions between a bound state and a single soliton are displayed with different choices of variable coefficients. We also derive the quasi-periodic formulae for the three cases of the bound states.

Size-dependent geometrically nonlinear free vibration analysis of fractional viscoelastic nanobeams based on the nonlocal elasticity theory

NASA Astrophysics Data System (ADS)

Ansari, R.; Faraji Oskouie, M.; Gholami, R.

2016-01-01

In recent decades, mathematical modeling and engineering applications of fractional-order calculus have been extensively utilized to provide efficient simulation tools in the field of solid mechanics. In this paper, a nonlinear fractional nonlocal Euler-Bernoulli beam model is established using the concept of fractional derivative and nonlocal elasticity theory to investigate the size-dependent geometrically nonlinear free vibration of fractional viscoelastic nanobeams. The non-classical fractional integro-differential Euler-Bernoulli beam model contains the nonlocal parameter, viscoelasticity coefficient and order of the fractional derivative to interpret the size effect, viscoelastic material and fractional behavior in the nanoscale fractional viscoelastic structures, respectively. In the solution procedure, the Galerkin method is employed to reduce the fractional integro-partial differential governing equation to a fractional ordinary differential equation in the time domain. Afterwards, the predictor-corrector method is used to solve the nonlinear fractional time-dependent equation. Finally, the influences of nonlocal parameter, order of fractional derivative and viscoelasticity coefficient on the nonlinear time response of fractional viscoelastic nanobeams are discussed in detail. Moreover, comparisons are made between the time responses of linear and nonlinear models.

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.

Third-order optical nonlinearity studies of bilayer Au/Ag metallic films

NASA Astrophysics Data System (ADS)

Mezher, M. H.; Chong, W. Y.; Zakaria, R.

2016-05-01

This paper presents nonlinear optical studies of bilayer metallic films of gold (Au) and silver (Ag) on glass substrate prepared using electron beam evaporation. The preparation of Au and Ag nanoparticles (NPs) on the substrate involved the use of electron beam deposition, then thermal annealing at 600 °C and 270 °C, respectively, to produce a randomly distributed layer of Au and a layer of Ag NPs. Observation of field-effect scanning electron microscope images indicated the size of the NPs. Details of the optical properties related to peak absorption of surface plasmon resonance of the nanoparticle were revealed by use of UV-Vis spectroscopy. The Z-scan technique was used to measure the nonlinear absorption and nonlinear refraction of the fabricated NP layers. The third-order nonlinear refractive index coefficients for Au and Ag are (-9.34 and  -1.61)  ×  10-11 cm2 W-1 given lower n 2, in comparison with bilayer (Au and Ag) NPs at  -1.24  ×  10-10 cm2 W-1. The results show bilayer NPs have higher refractive index coefficients thus enhance the nonlinearity effects.

Acoustic characterization of a nonlinear vibroacoustic absorber at low frequencies and high sound levels

NASA Astrophysics Data System (ADS)

Chauvin, A.; Monteil, M.; Bellizzi, S.; Côte, R.; Herzog, Ph.; Pachebat, M.

2018-03-01

A nonlinear vibroacoustic absorber (Nonlinear Energy Sink: NES), involving a clamped thin membrane made in Latex, is assessed in the acoustic domain. This NES is here considered as an one-port acoustic system, analyzed at low frequencies and for increasing excitation levels. This dynamic and frequency range requires a suitable experimental technique, which is presented first. It involves a specific impedance tube able to deal with samples of sufficient size, and reaching high sound levels with a guaranteed linear response thank's to a specific acoustic source. The identification method presented here requires a single pressure measurement, and is calibrated from a set of known acoustic loads. The NES reflection coefficient is then estimated at increasing source levels, showing its strong level dependency. This is presented as a mean to understand energy dissipation. The results of the experimental tests are first compared to a nonlinear viscoelastic model of the membrane absorber. In a second step, a family of one degree of freedom models, treated as equivalent Helmholtz resonators is identified from the measurements, allowing a parametric description of the NES behavior over a wide range of levels.

Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1998-01-01

Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.

Detection and Classification of Whale Acoustic Signals

NASA Astrophysics Data System (ADS)

Xian, Yin

This dissertation focuses on two vital challenges in relation to whale acoustic signals: detection and classification. In detection, we evaluated the influence of the uncertain ocean environment on the spectrogram-based detector, and derived the likelihood ratio of the proposed Short Time Fourier Transform detector. Experimental results showed that the proposed detector outperforms detectors based on the spectrogram. The proposed detector is more sensitive to environmental changes because it includes phase information. In classification, our focus is on finding a robust and sparse representation of whale vocalizations. Because whale vocalizations can be modeled as polynomial phase signals, we can represent the whale calls by their polynomial phase coefficients. In this dissertation, we used the Weyl transform to capture chirp rate information, and used a two dimensional feature set to represent whale vocalizations globally. Experimental results showed that our Weyl feature set outperforms chirplet coefficients and MFCC (Mel Frequency Cepstral Coefficients) when applied to our collected data. Since whale vocalizations can be represented by polynomial phase coefficients, it is plausible that the signals lie on a manifold parameterized by these coefficients. We also studied the intrinsic structure of high dimensional whale data by exploiting its geometry. Experimental results showed that nonlinear mappings such as Laplacian Eigenmap and ISOMAP outperform linear mappings such as PCA and MDS, suggesting that the whale acoustic data is nonlinear. We also explored deep learning algorithms on whale acoustic data. We built each layer as convolutions with either a PCA filter bank (PCANet) or a DCT filter bank (DCTNet). With the DCT filter bank, each layer has different a time-frequency scale representation, and from this, one can extract different physical information. Experimental results showed that our PCANet and DCTNet achieve high classification rate on the whale vocalization data set. The word error rate of the DCTNet feature is similar to the MFSC in speech recognition tasks, suggesting that the convolutional network is able to reveal acoustic content of speech signals.

Multispectral medical image fusion in Contourlet domain for computer based diagnosis of Alzheimer's disease.

PubMed

Bhateja, Vikrant; Moin, Aisha; Srivastava, Anuja; Bao, Le Nguyen; Lay-Ekuakille, Aimé; Le, Dac-Nhuong

2016-07-01

Computer based diagnosis of Alzheimer's disease can be performed by dint of the analysis of the functional and structural changes in the brain. Multispectral image fusion deliberates upon fusion of the complementary information while discarding the surplus information to achieve a solitary image which encloses both spatial and spectral details. This paper presents a Non-Sub-sampled Contourlet Transform (NSCT) based multispectral image fusion model for computer-aided diagnosis of Alzheimer's disease. The proposed fusion methodology involves color transformation of the input multispectral image. The multispectral image in YIQ color space is decomposed using NSCT followed by dimensionality reduction using modified Principal Component Analysis algorithm on the low frequency coefficients. Further, the high frequency coefficients are enhanced using non-linear enhancement function. Two different fusion rules are then applied to the low-pass and high-pass sub-bands: Phase congruency is applied to low frequency coefficients and a combination of directive contrast and normalized Shannon entropy is applied to high frequency coefficients. The superiority of the fusion response is depicted by the comparisons made with the other state-of-the-art fusion approaches (in terms of various fusion metrics).

Multispectral medical image fusion in Contourlet domain for computer based diagnosis of Alzheimer’s disease

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

Bhateja, Vikrant, E-mail: bhateja.vikrant@gmail.com, E-mail: nhuongld@hus.edu.vn; Moin, Aisha; Srivastava, Anuja

Computer based diagnosis of Alzheimer’s disease can be performed by dint of the analysis of the functional and structural changes in the brain. Multispectral image fusion deliberates upon fusion of the complementary information while discarding the surplus information to achieve a solitary image which encloses both spatial and spectral details. This paper presents a Non-Sub-sampled Contourlet Transform (NSCT) based multispectral image fusion model for computer-aided diagnosis of Alzheimer’s disease. The proposed fusion methodology involves color transformation of the input multispectral image. The multispectral image in YIQ color space is decomposed using NSCT followed by dimensionality reduction using modified Principal Componentmore » Analysis algorithm on the low frequency coefficients. Further, the high frequency coefficients are enhanced using non-linear enhancement function. Two different fusion rules are then applied to the low-pass and high-pass sub-bands: Phase congruency is applied to low frequency coefficients and a combination of directive contrast and normalized Shannon entropy is applied to high frequency coefficients. The superiority of the fusion response is depicted by the comparisons made with the other state-of-the-art fusion approaches (in terms of various fusion metrics).« less

Consistent nonlinear deterministic and stochastic evolution equations for deep to shallow water wave shoaling

NASA Astrophysics Data System (ADS)

Vrecica, Teodor; Toledo, Yaron

2015-04-01

One-dimensional deterministic and stochastic evolution equations are derived for the dispersive nonlinear waves while taking dissipation of energy into account. The deterministic nonlinear evolution equations are formulated using operational calculus by following the approach of Bredmose et al. (2005). Their formulation is extended to include the linear and nonlinear effects of wave dissipation due to friction and breaking. The resulting equation set describes the linear evolution of the velocity potential for each wave harmonic coupled by quadratic nonlinear terms. These terms describe the nonlinear interactions between triads of waves, which represent the leading-order nonlinear effects in the near-shore region. The equations are translated to the amplitudes of the surface elevation by using the approach of Agnon and Sheremet (1997) with the correction of Eldeberky and Madsen (1999). The only current possibility for calculating the surface gravity wave field over large domains is by using stochastic wave evolution models. Hence, the above deterministic model is formulated as a stochastic one using the method of Agnon and Sheremet (1997) with two types of stochastic closure relations (Benney and Saffman's, 1966, and Hollway's, 1980). These formulations cannot be applied to the common wave forecasting models without further manipulation, as they include a non-local wave shoaling coefficients (i.e., ones that require integration along the wave rays). Therefore, a localization method was applied (see Stiassnie and Drimer, 2006, and Toledo and Agnon, 2012). This process essentially extracts the local terms that constitute the mean nonlinear energy transfer while discarding the remaining oscillatory terms, which transfer energy back and forth. One of the main findings of this work is the understanding that the approximated non-local coefficients behave in two essentially different manners. In intermediate water depths these coefficients indeed consist of rapidly oscillating terms, but as the water depth becomes shallow they change to an exponential growth (or decay) behavior. Hence, the formerly used localization technique cannot be justified for the shallow water region. A new formulation is devised for the localization in shallow water, it approximates the nonlinear non-local shoaling coefficient in shallow water and matches it to the one fitting to the intermediate water region. This allows the model behavior to be consistent from deep water to intermediate depths and up to the shallow water regime. Various simulations of the model were performed for the cases of intermediate, and shallow water, overall the model was found to give good results in both shallow and intermediate water depths. The essential difference between the shallow and intermediate nonlinear shoaling physics is explained via the dominating class III Bragg resonances phenomenon. By inspecting the resonance conditions and the nature of the dispersion relation, it is shown that unlike in the intermediate water regime, in shallow water depths the formation of resonant interactions is possible without taking into account bottom components. References Agnon, Y. & Sheremet, A. 1997 Stochastic nonlinear shoaling of directional spectra. J. Fluid Mech. 345, 79-99. Benney, D. J. & Saffman, P. G. 1966 Nonlinear interactions of random waves. Proc. R. Soc. Lond. A 289, 301-321. Bredmose, H., Agnon, Y., Madsen, P.A. & Schaffer, H.A. 2005 Wave transformation models with exact second-order transfer. European J. of Mech. - B/Fluids 24 (6), 659-682. Eldeberky, Y. & Madsen, P. A. 1999 Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves. Coastal Engineering 38, 1-24. Kaihatu, J. M. & Kirby, J. T. 1995 Nonlinear transformation of waves in infinite water depth. Phys. Fluids 8, 175-188. Holloway, G. 1980 Oceanic internal waves are not weak waves. J. Phys. Oceanogr. 10, 906-914. Stiassnie, M. & Drimer, N. 2006 Prediction of long forcing waves for harbor agitation studies. J. of waterways, port, coastal and ocean engineering 132(3), 166-171. Toledo, Y. & Agnon, Y. 2012 Stochastic evolution equations with localized nonlinear shoaling coefficients. European J. of Mech. - B/Fluids 34, 13-18.

Distance correlation methods for discovering associations in large astrophysical databases

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

Martínez-Gómez, Elizabeth; Richards, Mercedes T.; Richards, Donald St. P., E-mail: elizabeth.martinez@itam.mx, E-mail: mrichards@astro.psu.edu, E-mail: richards@stat.psu.edu

2014-01-20

High-dimensional, large-sample astrophysical databases of galaxy clusters, such as the Chandra Deep Field South COMBO-17 database, provide measurements on many variables for thousands of galaxies and a range of redshifts. Current understanding of galaxy formation and evolution rests sensitively on relationships between different astrophysical variables; hence an ability to detect and verify associations or correlations between variables is important in astrophysical research. In this paper, we apply a recently defined statistical measure called the distance correlation coefficient, which can be used to identify new associations and correlations between astrophysical variables. The distance correlation coefficient applies to variables of any dimension,more » can be used to determine smaller sets of variables that provide equivalent astrophysical information, is zero only when variables are independent, and is capable of detecting nonlinear associations that are undetectable by the classical Pearson correlation coefficient. Hence, the distance correlation coefficient provides more information than the Pearson coefficient. We analyze numerous pairs of variables in the COMBO-17 database with the distance correlation method and with the maximal information coefficient. We show that the Pearson coefficient can be estimated with higher accuracy from the corresponding distance correlation coefficient than from the maximal information coefficient. For given values of the Pearson coefficient, the distance correlation method has a greater ability than the maximal information coefficient to resolve astrophysical data into highly concentrated horseshoe- or V-shapes, which enhances classification and pattern identification. These results are observed over a range of redshifts beyond the local universe and for galaxies from elliptical to spiral.« less

Third-order Nonlinear Optical Properties of Metallodielectric Stacks

DTIC Science & Technology

2011-07-01

developed by Sheik- Bahae et al [7] a (Gaussian) laser beam is focused in free space; a sample is positioned along the propagation (Z) axis of the laser...transmittance and reflectance coefficients are defined for any angle of incidence as 22 0 ||,|| cos cos rRt n n T i tt    ; (2) i  and t are...nonlinear coefficient,    4 2 2 i n  , has a complex value. The longitudinal component of the Poynting vector was used in Eq. (11). The Kerr

Laser ablation of PMMA doped with benzyl

NASA Astrophysics Data System (ADS)

Wang, Jun; Niino, Hiroyuki; Yabe, Akira

1998-08-01

KrF-laser ablation of poly(methylmethacrylate) (PMMA) doped with benzil was studied from the viewpoint of nonlinear absorption of the PMMA film during the laser irradiation. After measuring the relationship between the transmission and incident laser intensity, we developed a novel method to obtain absorption coefficient depending on laser intensity. Using the nonlinear absorption coefficient of PMMA doped with benzil, we succeeded in fitting the relationship of etch depth and laser intensity. The dependence of concentration of benzil in PMMA film and the difference between benzil and pyrene were also discussed.

In situ SHG monitoring of dipolar orientation and relaxation in Disperse Red type/derivative urethane-urea copolymer

NASA Astrophysics Data System (ADS)

Samoc, A.; Holland, A.; Tsuchimori, M.; Watanabe, O.; Samoc, M.; Luther-Davies, B.; Kolev, V. Z.

2005-09-01

We investigated linear optical and second-order nonlinear optical (NLO) properties of films of urethane-urea copolymer (UU2) functionalised with a high concentration of an azobenzene chromophore. The polymer films on ITO-coated substrate were corona poled to induce a noncentrosymmetric organization of chromophore dipoles and data on the second harmonic generated with the laser beam (the fundamental wavelength 1053 nm, 6 ps/pulse, 20 Hz repetition rate) was acquired as a function of time and temperature. Second harmonic generation (SHG) was used to monitor in situ the polar alignment and relaxation of orientation of the side-chain Disperse Red-like chromophore molecules in the films poled at room temperature and high above the glass transition temperature (Tg 140-150oC). The deff coefficient was determined from the Maker-fringe method and corrected for absorption. A strong second harmonic effect with a fast relaxation was observed in "cold" (room temperature) poling experiments. A large second-order resonantly enhanced optical nonlinearity (d33 of the order of 200 pm/V) was obtained in high temperature poling. A strong and stable nonlinearity has persisted for years after the films were high-temperature poled.

Prediction of Unsteady Aerodynamic Coefficients at High Angles of Attack

NASA Technical Reports Server (NTRS)

Pamadi, Bandu N.; Murphy, Patrick C.; Klein, Vladislav; Brandon, Jay M.

2001-01-01

The nonlinear indicial response method is used to model the unsteady aerodynamic coefficients in the low speed longitudinal oscillatory wind tunnel test data of the 0.1 scale model of the F-16XL aircraft. Exponential functions are used to approximate the deficiency function in the indicial response. Using one set of oscillatory wind tunnel data and parameter identification method, the unknown parameters in the exponential functions are estimated. The genetic algorithm is used as a least square minimizing algorithm. The assumed model structures and parameter estimates are validated by comparing the predictions with other sets of available oscillatory wind tunnel test data.

Determination of piezo-optic coefficients of crystals by means of four-point bending.

PubMed

Krupych, Oleg; Savaryn, Viktoriya; Krupych, Andriy; Klymiv, Ivan; Vlokh, Rostyslav

2013-06-10

A technique developed recently for determining piezo-optic coefficients (POCs) of isotropic optical media, which represents a combination of digital imaging laser interferometry and a classical four-point bending method, is generalized and applied to a single-crystalline anisotropic material. The peculiarities of measuring procedures and data processing for the case of optically uniaxial crystals are described in detail. The capabilities of the technique are tested on the example of canonical nonlinear optical crystal LiNbO3. The high precision achieved in determination of the POCs for isotropic and anisotropic materials testifies that the technique should be both versatile and reliable.

Generalized Correlation Coefficient for Non-Parametric Analysis of Microarray Time-Course Data.

PubMed

Tan, Qihua; Thomassen, Mads; Burton, Mark; Mose, Kristian Fredløv; Andersen, Klaus Ejner; Hjelmborg, Jacob; Kruse, Torben

2017-06-06

Modeling complex time-course patterns is a challenging issue in microarray study due to complex gene expression patterns in response to the time-course experiment. We introduce the generalized correlation coefficient and propose a combinatory approach for detecting, testing and clustering the heterogeneous time-course gene expression patterns. Application of the method identified nonlinear time-course patterns in high agreement with parametric analysis. We conclude that the non-parametric nature in the generalized correlation analysis could be an useful and efficient tool for analyzing microarray time-course data and for exploring the complex relationships in the omics data for studying their association with disease and health.

Nonlinear unbiased minimum-variance filter for Mars entry autonomous navigation under large uncertainties and unknown measurement bias.

PubMed

Xiao, Mengli; Zhang, Yongbo; Fu, Huimin; Wang, Zhihua

2018-05-01

High-precision navigation algorithm is essential for the future Mars pinpoint landing mission. The unknown inputs caused by large uncertainties of atmospheric density and aerodynamic coefficients as well as unknown measurement biases may cause large estimation errors of conventional Kalman filters. This paper proposes a derivative-free version of nonlinear unbiased minimum variance filter for Mars entry navigation. This filter has been designed to solve this problem by estimating the state and unknown measurement biases simultaneously with derivative-free character, leading to a high-precision algorithm for the Mars entry navigation. IMU/radio beacons integrated navigation is introduced in the simulation, and the result shows that with or without radio blackout, our proposed filter could achieve an accurate state estimation, much better than the conventional unscented Kalman filter, showing the ability of high-precision Mars entry navigation algorithm. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Mid-infrared high birefringence As2Se3-based PCF with large nonlinearity and distinctive dispersion by using asymmetric elliptical air hole cladding

NASA Astrophysics Data System (ADS)

Hui, Zhanqiang; Yang, Min; Zhang, Youkun; Zhang, Meizhi

2018-01-01

A novel high birefringence As2Se3-based hexagonal lattice photonic crystal fiber (PCF) is proposed. In the structure, a central defect core and three kinds of elliptical air holes with different major axes length and ellipticity are introduced in the cladding. The finite difference time domain (FDTD) method with perfectly matched layer (PML) absorption boundary conditions are used to simulate the guided modes of the designed PCF. The properties of this PCF are investigated in detail including the birefringence, beat length, dispersion, nonlinearity and polarization mode dispersion in the 2-5 μm mid-infrared range. The results show that for the optimized structure parameters of Λ = 1.6μm, a = 0.4μm, b = 0.1μm, a1 = 0.6μm, b1 = 0.04μm, a2 = 0.8μm, b2 = 0.06μm, the high birefringence of 0.1192 and beat length of 41.93 μm are obtained. The maximum nonlinearity coefficient of 10,050 w-1km-1 and 15,200 w-1km-1 for x- and y-polarization modes are achieved. The distinctive dispersion is analyzed, which is all-normal in x-polarization direction while it has two zero dispersion points at 3.18 μm and 3.65 μm in y-polarization direction. The designed PCF with high birefringence, large nonlinearity and distinctive dispersion will be beneficial for mid-infrared fiber sensing, mid-infrared spectroscopy and nonlinear optics applications.

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.

Estimation of delays and other parameters in nonlinear functional differential equations

NASA Technical Reports Server (NTRS)

Banks, H. T.; Lamm, P. K. D.

1983-01-01

A spline-based approximation scheme for nonlinear nonautonomous delay differential equations is discussed. Convergence results (using dissipative type estimates on the underlying nonlinear operators) are given in the context of parameter estimation problems which include estimation of multiple delays and initial data as well as the usual coefficient-type parameters. A brief summary of some of the related numerical findings is also given.

Effect of asymmetrical transfer coefficients of a non-polarizing beam splitter on the nonlinear error of the polarization interferometer

NASA Astrophysics Data System (ADS)

Zhao, Chen-Guang; Tan, Jiu-Bin; Liu, Tao

2010-09-01

The mechanism of a non-polarizing beam splitter (NPBS) with asymmetrical transfer coefficients causing the rotation of polarization direction is explained in principle, and the measurement nonlinear error caused by NPBS is analyzed based on Jones matrix theory. Theoretical calculations show that the nonlinear error changes periodically, and the error period and peak values increase with the deviation between transmissivities of p-polarization and s-polarization states. When the transmissivity of p-polarization is 53% and that of s-polarization is 48%, the maximum error reaches 2.7 nm. The imperfection of NPBS is one of the main error sources in simultaneous phase-shifting polarization interferometer, and its influence can not be neglected in the nanoscale ultra-precision measurement.

Comparison of linear and non-linear models for the adsorption of fluoride onto geo-material: limonite.

PubMed

Sahin, Rubina; Tapadia, Kavita

2015-01-01

The three widely used isotherms Langmuir, Freundlich and Temkin were examined in an experiment using fluoride (F⁻) ion adsorption on a geo-material (limonite) at four different temperatures by linear and non-linear models. Comparison of linear and non-linear regression models were given in selecting the optimum isotherm for the experimental results. The coefficient of determination, r², was used to select the best theoretical isotherm. The four Langmuir linear equations (1, 2, 3, and 4) are discussed. Langmuir isotherm parameters obtained from the four Langmuir linear equations using the linear model differed but they were the same when using the nonlinear model. Langmuir-2 isotherm is one of the linear forms, and it had the highest coefficient of determination (r² = 0.99) compared to the other Langmuir linear equations (1, 3 and 4) in linear form, whereas, for non-linear, Langmuir-4 fitted best among all the isotherms because it had the highest coefficient of determination (r² = 0.99). The results showed that the non-linear model may be a better way to obtain the parameters. In the present work, the thermodynamic parameters show that the absorption of fluoride onto limonite is both spontaneous (ΔG < 0) and endothermic (ΔH > 0). Scanning electron microscope and X-ray diffraction images also confirm the adsorption of F⁻ ion onto limonite. The isotherm and kinetic study reveals that limonite can be used as an adsorbent for fluoride removal. In future we can develop new technology for fluoride removal in large scale by using limonite which is cost-effective, eco-friendly and is easily available in the study area.

Influence of sintering time on switching of the femtosecond nonlinear optical properties of CuNb2O6

NASA Astrophysics Data System (ADS)

Priyadarshani, N.; Sabari Girisun, T. C.; Venugopal Rao, S.

2017-04-01

Transition of mixed phases (monoclinic and orthorhombic) to pure orthorhombic phase was achieved during the synthesis process of CuNb2O6 by varying the sintering time. The suppression of monoclinic phase and dominant formation of orthorhombic CuNb2O6 was confirmed from the XRD and FTIR data analysis. FESEM studies demonstrated that due to increase in sintering time, coarsening process initiated the grain growth and trapping of pores leading to pore-free structures. The nonlinear optical (NLO) properties of mixed and pure copper niobate were studied by the Z-scan technique using near-infrared (800 nm, ∼150 fs, 80 MHz) laser excitation. Mixed phases exhibited saturable absorption and self-defocusing behaviour while pure orthorhombic demonstrated reverse saturable absorption and self-focusing process. The switching of nonlinearity along with increase in NLO coefficient of O-CuNb2O6 was attributed to the decreased metal-oxygen bond length and pore free structure. The increase in nonlinear absorption coefficient with input irradiance suggests the occurrence of effective 3 PA (2 PA followed by ESA) process. The magnitudes of nonlinear absorption coefficient (2.14 × 10-23m3/W2) and nonlinear refractive index (6.0 × 0-17 m2/W) of O-CuNb2O6 were found to be higher than well-known NLO materials. Orthorhombic CuNb2O6 exhibited optical limiting action with low limiting threshold of 38.26 μJ/cm2 and favouring NLO properties suggesting that the material to be an entrant candidate for safety devices against ultrashort pulsed lasers.

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

Minissale, S.; Yerci, S.; Dal Negro, L.

We investigate the nonlinear optical properties of Si-rich silicon oxide (SRO) and Si-rich silicon nitride (SRN) samples as a function of silicon content, annealing temperature, and excitation wavelength. Using the Z-scan technique, we measure the non-linear refractive index n{sub 2} and the nonlinear absorption coefficient {beta} for a large number of samples fabricated by reactive co-sputtering. Moreover, we characterize the nonlinear optical parameters of SRN in the broad spectral region 1100-1500 nm and show the strongest nonlinearity at 1500 nm. These results demonstrate the potential of the SRN matrix for the engineering of compact devices with enhanced Kerr nonlinearities formore » silicon photonics applications.« less

ECG compression using Slantlet and lifting wavelet transform with and without normalisation

NASA Astrophysics Data System (ADS)

Aggarwal, Vibha; Singh Patterh, Manjeet

2013-05-01

This article analyses the performance of: (i) linear transform: Slantlet transform (SLT), (ii) nonlinear transform: lifting wavelet transform (LWT) and (iii) nonlinear transform (LWT) with normalisation for electrocardiogram (ECG) compression. First, an ECG signal is transformed using linear transform and nonlinear transform. The transformed coefficients (TC) are then thresholded using bisection algorithm in order to match the predefined user-specified percentage root mean square difference (UPRD) within the tolerance. Then, the binary look up table is made to store the position map for zero and nonzero coefficients (NZCs). The NZCs are quantised by Max-Lloyd quantiser followed by Arithmetic coding. The look up table is encoded by Huffman coding. The results show that the LWT gives the best result as compared to SLT evaluated in this article. This transform is then considered to evaluate the effect of normalisation before thresholding. In case of normalisation, the TC is normalised by dividing the TC by ? (where ? is number of samples) to reduce the range of TC. The normalised coefficients (NC) are then thresholded. After that the procedure is same as in case of coefficients without normalisation. The results show that the compression ratio (CR) in case of LWT with normalisation is improved as compared to that without normalisation.

Crystal growth of organics for nonlinear optical applications

NASA Technical Reports Server (NTRS)

Singh, N. B.; Mazelsky, R.

1993-01-01

The crystal growth and characterization of organic and inorganic nonlinear optical materials were extensively studied. For example, inorganic crystals such as thallium arsenic selenide were studied in our laboratory for several years and crystals in sizes over 2.5 cm in diameter are available. Organic crystals are suitable for the ultraviolet and near infrared region, but are relatively less developed than their inorganic counterparts. Very high values of the second harmonic conversion efficiency and the electro-optic coefficient were reported for organic compounds. Single crystals of a binary organic alloy based on m.NA and CNA were grown and higher second harmonic conversion efficiency than the values reported for m.NA were observed.

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

Adjusted adaptive Lasso for covariate model-building in nonlinear mixed-effect pharmacokinetic models.

PubMed

Haem, Elham; Harling, Kajsa; Ayatollahi, Seyyed Mohammad Taghi; Zare, Najaf; Karlsson, Mats O

2017-02-01

One important aim in population pharmacokinetics (PK) and pharmacodynamics is identification and quantification of the relationships between the parameters and covariates. Lasso has been suggested as a technique for simultaneous estimation and covariate selection. In linear regression, it has been shown that Lasso possesses no oracle properties, which means it asymptotically performs as though the true underlying model was given in advance. Adaptive Lasso (ALasso) with appropriate initial weights is claimed to possess oracle properties; however, it can lead to poor predictive performance when there is multicollinearity between covariates. This simulation study implemented a new version of ALasso, called adjusted ALasso (AALasso), to take into account the ratio of the standard error of the maximum likelihood (ML) estimator to the ML coefficient as the initial weight in ALasso to deal with multicollinearity in non-linear mixed-effect models. The performance of AALasso was compared with that of ALasso and Lasso. PK data was simulated in four set-ups from a one-compartment bolus input model. Covariates were created by sampling from a multivariate standard normal distribution with no, low (0.2), moderate (0.5) or high (0.7) correlation. The true covariates influenced only clearance at different magnitudes. AALasso, ALasso and Lasso were compared in terms of mean absolute prediction error and error of the estimated covariate coefficient. The results show that AALasso performed better in small data sets, even in those in which a high correlation existed between covariates. This makes AALasso a promising method for covariate selection in nonlinear mixed-effect models.

Characterization of second and third order optical nonlinearities of ZnO sputtered films

NASA Astrophysics Data System (ADS)

Larciprete, M. C.; Haertle, D.; Belardini, A.; Bertolotti, M.; Sarto, F.; Günter, P.

2006-03-01

We measured the second and third order optical nonlinearity of zinc oxide, grown on glass substrates by the ion beam sputtering technique. Second and third harmonic generation measurements were performed by means of the rotational Maker fringes technique for different polarization configurations, thus allowing the determination of all non-zero components of the second order susceptibility at three different fundamental beam wavelengths, i.e., 1064 nm, 1542 nm and 1907 nm. The dispersion of the nonlinear optical coefficients has been evaluated, while the nonlinear optical coefficients were found to range between 0.9 pm/V and 0.16 pm/V for d33, 0.53 pm/V and 0.08 pm/V for |d15|, 0.31 and 0.08 pm/V for |d31|, with increasing wavelength. Finally, one third order susceptibility, χijkl (3), has been determined by third harmonic generation measurements at a fundamental wavelength λ=1907 nm and a value for χ3333 (3) of 185×10-20 m2/V2 has been found.

Growth and characterization of a third order nonlinear optical single crystal: Ethylenediamine-4-nitrophenolate monohydrate

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

Dhanalakshmi, B.; Ponnusamy, S., E-mail: suruponnus@gmail.com; Muthamizhchelvan, C.

2015-10-15

Highlights: • EDA4NPH crystal possesses negative nonlinear refractive index. • The crystal exhibits high third-order NLO susceptibility. • Wide transparency of the crystal makes it suitable for NLO applications. • Dielectric studies substantiate the suitability for electro-optic applications. • The crystal possesses suitable mechanical strength for device fabrication. - Abstract: Bulk crystals of the charge-transfer complex, ethylenediamine-4-nitrophenolate monohydrate, were grown by slow solvent evaporation method from aqueous solution at room temperature. The X-ray diffraction measurements showed that the crystal belongs to centrosymmetric space group C2/c of monoclinic system. The functional groups in the complex were identified using FTIR, FTRaman andmore » FTNMR analyses. The Z-scan measurements revealed the negative nonlinear refractive index of the crystal. The nonlinear absorption coefficient and third order nonlinear optical susceptibility calculated from the measurements were −3.5823 × 10{sup −3} cm/W and 2.3762 × 10{sup −6} esu respectively. The crystal was shown to be highly transparent above 366 nm by UV–vis spectroscopy and a yellow fluorescence was observed from PL spectrum. The TG–DTA and DSC analyses showed that the crystal is thermally stable up to 117.4 °C. The crystals were characterized by dielectric, etching and microhardness studies.« less

Bright-dark soliton solutions for the (2+1)-dimensional variable-coefficient coupled nonlinear Schrödinger system in a graded-index waveguide

NASA Astrophysics Data System (ADS)

Yuan, Yu-Qiang; Tian, Bo; Xie, Xi-Yang; Chai, Jun; Liu, Lei

2017-04-01

Under investigation in this paper is the (2+1)-dimensional coupled nonlinear Schrödinger (NLS) system with variable coefficients, which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. Through a similarity transformation, we convert that system into a set of the integrable defocusing (1+1)-dimensional coupled NLS equations, and subsequently construct the bright-dark soliton solutions for the original system which are converted from the ones of the latter set. With the graphic analysis, we discuss the soliton propagation and collision with r(t), which is related to the nonlinear, profile and gain/loss coefficients. When r(t) is a constant, one soliton propagates with the amplitude, width and velocity unvaried, while velocity and width of the one soliton can be affected, and two solitons possess the elastic collision; When r(t) is a linear function, velocity and width of the one soliton varies with t increasing, and collision of the two solitons is altered. Besides, bound-state solitons are seen.

A Generic Nonlinear Aerodynamic Model for Aircraft

NASA Technical Reports Server (NTRS)

Grauer, Jared A.; Morelli, Eugene A.

2014-01-01

A generic model of the aerodynamic coefficients was developed using wind tunnel databases for eight different aircraft and multivariate orthogonal functions. For each database and each coefficient, models were determined using polynomials expanded about the state and control variables, and an othgonalization procedure. A predicted squared-error criterion was used to automatically select the model terms. Modeling terms picked in at least half of the analyses, which totalled 45 terms, were retained to form the generic nonlinear aerodynamic (GNA) model. Least squares was then used to estimate the model parameters and associated uncertainty that best fit the GNA model to each database. Nonlinear flight simulations were used to demonstrate that the GNA model produces accurate trim solutions, local behavior (modal frequencies and damping ratios), and global dynamic behavior (91% accurate state histories and 80% accurate aerodynamic coefficient histories) under large-amplitude excitation. This compact aerodynamics model can be used to decrease on-board memory storage requirements, quickly change conceptual aircraft models, provide smooth analytical functions for control and optimization applications, and facilitate real-time parametric system identification.

An inherent curvature-compensated voltage reference using non-linearity of gate coupling coefficient

NASA Astrophysics Data System (ADS)

Hande, Vinayak; Shojaei Baghini, Maryam

2015-08-01

A novel current-mode voltage reference circuit which is capable of generating sub-1 V output voltage is presented. The proposed architecture exhibits the inherent curvature compensation ability. The curvature compensation is achieved by utilizing the non-linear behavior of gate coupling coefficient to compensate non-linear temperature dependence of base-emitter voltage. We have also utilized the developments in CMOS process to reduce power and area consumption. The proposed voltage reference is analyzed theoretically and compared with other existing methods. The circuit is designed and simulated in 180 nm mixed-mode CMOS UMC technology which gives a reference level of 246 mV. The minimum required supply voltage is 1 V with maximum current drawn of 9.24 μA. A temperature coefficient of 9 ppm/°C is achieved over -25 to 125 °C temperature range. The reference voltage varies by ±11 mV across process corners. The reference circuit shows the line sensitivity of 0.9 mV/V with area consumption of 100 × 110 μm2

Electro-Optic Beam Steering Using Non-Linear Organic Materials

DTIC Science & Technology

1993-08-01

York (SUNY), Buffalo, for potential application to the Hughes electro - optic beam deflector device. Evaluations include electro - optic coefficient...response time, transmission, and resistivity. Electro - optic coefficient measurements were made at 633 nm using a simple reflection technique. The

Fast and accurate modeling of nonlinear pulse propagation in graded-index multimode fibers.

PubMed

Conforti, Matteo; Mas Arabi, Carlos; Mussot, Arnaud; Kudlinski, Alexandre

2017-10-01

We develop a model for the description of nonlinear pulse propagation in multimode optical fibers with a parabolic refractive index profile. It consists of a 1+1D generalized nonlinear Schrödinger equation with a periodic nonlinear coefficient, which can be solved in an extremely fast and efficient way. The model is able to quantitatively reproduce recently observed phenomena like geometric parametric instability and broadband dispersive wave emission. We envisage that our equation will represent a valuable tool for the study of spatiotemporal nonlinear dynamics in the growing field of multimode fiber optics.

Integrability and solitons for the higher-order nonlinear Schrödinger equation with space-dependent coefficients in an optical fiber

NASA Astrophysics Data System (ADS)

Su, Jing-Jing; Gao, Yi-Tian

2018-03-01

Under investigation in this paper is a higher-order nonlinear Schrödinger equation with space-dependent coefficients, related to an optical fiber. Based on the self-similarity transformation and Hirota method, related to the integrability, the N-th-order bright and dark soliton solutions are derived under certain constraints. It is revealed that the velocities and trajectories of the solitons are both affected by the coefficient of the sixth-order dispersion term while the amplitudes of the solitons are determined by the gain function. Amplitudes increase when the gain function is positive and decrease when the gain function is negative. Furthermore, we find that the intensities of dark solitons are presented as a superposition of the solitons and stationary waves.

A Numerical Study of Coupled Non-Linear Equations of Thermo-Viscous Fluid Flow in Cylindrical Geometry

NASA Astrophysics Data System (ADS)

Pothanna, N.; Aparna, P.; Gorla, R. S. R.

2017-12-01

In this paper we present numerical solutions to coupled non-linear governing equations of thermo-viscous fluid flow in cylindrical geometry using MATHEMATICA software solver. The numerical results are presented in terms of velocity, temperature and pressure distribution for various values of the material parameters such as the thermo-mechanical stress coefficient, thermal conductivity coefficient, Reiner Rivlin cross viscosity coefficient and the Prandtl number in the form of tables and graphs. Also, the solutions to governing equations for slow steady motion of a fluid have been obtained numerically and compared with the existing analytical results and are found to be in excellent agreement. The results of the present study will hopefully enable a better understanding applications of the flow under consideration.

Linear and nonlinear magneto-optical properties of an off-center single dopant in a spherical core/shell quantum dot

NASA Astrophysics Data System (ADS)

Feddi, E.; Talbi, A.; Mora-Ramos, M. E.; El Haouari, M.; Dujardin, F.; Duque, C. A.

2017-11-01

Using the effective mass approximation and a variational procedure, we have investigated the nonlinear optical absorption coefficient and the relative refractive index changes associated to a single dopant confined in core/shell quantum dots considering the influences of the core/shell dimensions, externally applied magnetic field, and dielectric mismatch. The results show that the optical absorption coefficient and the coefficients of relative refractive index change depend strongly on the core/shell sizes and they are blue shifted when the spatial confinement increases so this effect is magnified by higher structural dimensions. Additionally, it is obtained that both studied optical properties are sensitive to the dielectric environment in such a way that their amplitudes are very affected by the local field corrections.

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.

Fe induced optical limiting properties of Zn1-xFexS nanospheres

NASA Astrophysics Data System (ADS)

Vineeshkumar, T. V.; Raj, D. Rithesh; Prasanth, S.; Unnikrishnan, N. V.; Mahadevan Pillai, V. P.; Sudarasanakumar, C.

2018-02-01

Zn1-xFexS (x = 0.00, 0.01, 0.03, 0.05) nanospheres were synthesized by polyethylene glycol assisted hydrothermal method. XRD studies revealed that samples of all concentrations exhibited cubic structure with crystallite grain size 7-9 nm. TEM and SEM show the formation of nanospheres by dense aggregation of smaller particles. Increasing Zn/Fe ratio tune the band gap from 3.4 to 3.2 eV and also quenches the green luminescence. FTIR spectra reveal the presence of capping agent, intensity variation and shifting of LO and TO phonon modes confirm the presence of Fe ions. Nonlinear optical properties were measured using open and closed aperture z-scan techniques, employing frequency doubled 532 nm pumping sources which indicated reverse saturable absorption (RSA) process. The nonlinear optical coefficients are obtained by two photon absorption (2PA). Composition dependent nonlinear optical coefficients ;β;, nonlinear refractive index, third order susceptibility and optical limiting threshold were estimated. The sample shows good nonlinear absorption and enhancement of optical limiting behavior with increasing Fe volume fraction. Contribution of RSA on optical nonlinearity of Zn1-xFexS nanospheres are also investigated using three different input energies. Zn1-xFexS with comparatively small limiting threshold value is a promising candidate for optical power limiting applications.

Advanced Statistical Analyses to Reduce Inconsistency of Bond Strength Data.

PubMed

Minamino, T; Mine, A; Shintani, A; Higashi, M; Kawaguchi-Uemura, A; Kabetani, T; Hagino, R; Imai, D; Tajiri, Y; Matsumoto, M; Yatani, H

2017-11-01

This study was designed to clarify the interrelationship of factors that affect the value of microtensile bond strength (µTBS), focusing on nondestructive testing by which information of the specimens can be stored and quantified. µTBS test specimens were prepared from 10 noncarious human molars. Six factors of µTBS test specimens were evaluated: presence of voids at the interface, X-ray absorption coefficient of resin, X-ray absorption coefficient of dentin, length of dentin part, size of adhesion area, and individual differences of teeth. All specimens were observed nondestructively by optical coherence tomography and micro-computed tomography before µTBS testing. After µTBS testing, the effect of these factors on µTBS data was analyzed by the general linear model, linear mixed effects regression model, and nonlinear regression model with 95% confidence intervals. By the general linear model, a significant difference in individual differences of teeth was observed ( P < 0.001). A significantly positive correlation was shown between µTBS and length of dentin part ( P < 0.001); however, there was no significant nonlinearity ( P = 0.157). Moreover, a significantly negative correlation was observed between µTBS and size of adhesion area ( P = 0.001), with significant nonlinearity ( P = 0.014). No correlation was observed between µTBS and X-ray absorption coefficient of resin ( P = 0.147), and there was no significant nonlinearity ( P = 0.089). Additionally, a significantly positive correlation was observed between µTBS and X-ray absorption coefficient of dentin ( P = 0.022), with significant nonlinearity ( P = 0.036). A significant difference was also observed between the presence and absence of voids by linear mixed effects regression analysis. Our results showed correlations between various parameters of tooth specimens and µTBS data. To evaluate the performance of the adhesive more precisely, the effect of tooth variability and a method to reduce variation in bond strength values should also be considered.

Finite element analysis of hysteresis effects in piezoelectric transducers

NASA Astrophysics Data System (ADS)

Simkovics, Reinhard; Landes, Hermann; Kaltenbacher, Manfred; Hoffelner, Johann; Lerch, Reinhard

2000-06-01

The design of ultrasonic transducers for high power applications, e.g. in medical therapy or production engineering, asks for effective computer aided design tools to analyze the occurring nonlinear effects. In this paper the finite-element-boundary-element package CAPA is presented that allows to model different types of electromechanical sensors and actuators. These transducers are based on various physical coupling effects, such as piezoelectricity or magneto- mechanical interactions. Their computer modeling requires the numerical solution of a multifield problem, such as coupled electric-mechanical fields or magnetic-mechanical fields as well as coupled mechanical-acoustic fields. With the reported software environment we are able to compute the dynamic behavior of electromechanical sensors and actuators by taking into account geometric nonlinearities, nonlinear wave propagation and ferroelectric as well as magnetic material nonlinearities. After a short introduction to the basic theory of the numerical calculation schemes, two practical examples will demonstrate the applicability of the numerical simulation tool. As a first example an ultrasonic thickness mode transducer consisting of a piezoceramic material used for high power ultrasound production is examined. Due to ferroelectric hysteresis, higher order harmonics can be detected in the actuators input current. Also in case of electrical and mechanical prestressing a resonance frequency shift occurs, caused by ferroelectric hysteresis and nonlinear dependencies of the material coefficients on electric field and mechanical stresses. As a second example, a power ultrasound transducer used in HIFU-therapy (high intensity focused ultrasound) is presented. Due to the compressibility and losses in the propagating fluid a nonlinear shock wave generation can be observed. For both examples a good agreement between numerical simulation and experimental data has been achieved.

Sorption of polycyclic aromatic hydrocarbons to polystyrene nanoplastic.

PubMed

Liu, Lijing; Fokkink, Remco; Koelmans, Albert A

2016-07-01

Microplastic has become an emerging contaminant of global concern. Bulk plastic can degrade to form smaller particles down to the nanoscale (<100 nm), which are referred to as nanoplastics. Because of their high surface area, nanoplastic may bind hydrophobic chemicals very effectively, increasing their hazard when such nanoplastics are taken up by biota. The present study reports distribution coefficients for sorption of polycyclic aromatic hydrocarbons (PAHs) to 70 nm polystyrene in freshwater, and PAH adsorption isotherms spanning environmentally realistic aqueous concentrations of 10(-5)  μg/L to 1 μg/L. Nanopolystyrene aggregate state was assessed using dynamic light scattering. The adsorption isotherms were nonlinear, and the distribution coefficients at the lower ends of the isotherms were very high, with values up to 10(9) L/kg. The high and nonlinear sorption was explained from π-π interactions between the planar PAHs and the surface of the aromatic polymer polystyrene and was higher than for micrometer-sized polystyrene. Reduction of nanopolystyrene aggregate sizes had no significant effect on sorption, which suggests that the PAHs could reach the sorption sites on the pristine nanoparticles regardless of the aggregation state. Pre-extraction of the nanopolystyrene with C18 polydimethylsiloxane decreased sorption of PAHs, which could be explained by removal of the most hydrophobic fraction of the nanopolystyrene. Environ Toxicol Chem 2016;35:1650-1655. © 2015 SETAC. © 2015 SETAC.

Reliability of heart rate measures during walking before and after running maximal efforts.

PubMed

Boullosa, D A; Barros, E S; del Rosso, S; Nakamura, F Y; Leicht, A S

2014-11-01

Previous studies on HR recovery (HRR) measures have utilized the supine and the seated postures. However, the most common recovery mode in sport and clinical settings after running exercise is active walking. The aim of the current study was to examine the reliability of HR measures during walking (4 km · h(-1)) before and following a maximal test. Twelve endurance athletes performed an incremental running test on 2 days separated by 48 h. Absolute (coefficient of variation, CV, %) and relative [Intraclass correlation coefficient, (ICC)] reliability of time domain and non-linear measures of HR variability (HRV) from 3 min recordings, and HRR parameters over 5 min were assessed. Moderate to very high reliability was identified for most HRV indices with short-term components of time domain and non-linear HRV measures demonstrating the greatest reliability before (CV: 12-22%; ICC: 0.73-0.92) and after exercise (CV: 14-32%; ICC: 0.78-0.91). Most HRR indices and parameters of HRR kinetics demonstrated high to very high reliability with HR values at a given point and the asymptotic value of HR being the most reliable (CV: 2.5-10.6%; ICC: 0.81-0.97). These findings demonstrate these measures as reliable tools for the assessment of autonomic control of HR during walking before and after maximal efforts. © Georg Thieme Verlag KG Stuttgart · New York.

Inversion of Robin coefficient by a spectral stochastic finite element approach

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

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Effect of nonideal square-law detection on static calibration in noise-injection radiometers

NASA Technical Reports Server (NTRS)

Hearn, C. P.

1984-01-01

The effect of nonideal square-law detection on the static calibration for a class of Dicke radiometers is examined. It is shown that fourth-order curvature in the detection characteristic adds a nonlinear term to the linear calibration relationship normally ascribed to noise-injection, balanced Dicke radiometers. The minimum error, based on an optimum straight-line fit to the calibration curve, is derived in terms of the power series coefficients describing the input-output characteristics of the detector. These coefficients can be determined by simple measurements, and detection nonlinearity is, therefore, quantitatively related to radiometric measurement error.

Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing

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

Wang, J. F.; Ma, Q. M.; Song, T.

The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusionmore » coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.« less

An oscillating wave energy converter with nonlinear snap-through Power-Take-Off systems in regular waves

NASA Astrophysics Data System (ADS)

Zhang, Xian-tao; Yang, Jian-min; Xiao, Long-fei

2016-07-01

Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off (PTO) system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.

High Energy Laser Beam Propagation in the Atmosphere: The Integral Invariants of the Nonlinear Parabolic Equation and the Method of Moments

NASA Technical Reports Server (NTRS)

Manning, Robert M.

2012-01-01

The method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for high-energy propagation through the Earth s atmosphere. These expressions are augmented with the integral invariants of the corresponding nonlinear parabolic equation that describes the electric field of high-energy laser beam to propagation to yield universal equations for the aforementioned quantities; the beam deflection is a linear function of the propagation distance whereas the beam broadening is a quadratic function of distance. The coefficients of these expressions are then derived from a thin screen approximation solution of the nonlinear parabolic equation to give corresponding analytical expressions for a target located outside the Earth s atmospheric layer. These equations, which are graphically presented for a host of propagation scenarios, as well as the thin screen model, are easily amenable to the phase expansions of the wave front for the specification and design of adaptive optics algorithms to correct for the inherent phase aberrations. This work finds application in, for example, the analysis of beamed energy propulsion for space-based vehicles.

Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model

NASA Astrophysics Data System (ADS)

Sinou, J.-J.; Thouverez, F.; Jezequel, L.

2003-08-01

This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.

A non-linear regression method for CT brain perfusion analysis

NASA Astrophysics Data System (ADS)

Bennink, E.; Oosterbroek, J.; Viergever, M. A.; Velthuis, B. K.; de Jong, H. W. A. M.

2015-03-01

CT perfusion (CTP) imaging allows for rapid diagnosis of ischemic stroke. Generation of perfusion maps from CTP data usually involves deconvolution algorithms providing estimates for the impulse response function in the tissue. We propose the use of a fast non-linear regression (NLR) method that we postulate has similar performance to the current academic state-of-art method (bSVD), but that has some important advantages, including the estimation of vascular permeability, improved robustness to tracer-delay, and very few tuning parameters, that are all important in stroke assessment. The aim of this study is to evaluate the fast NLR method against bSVD and a commercial clinical state-of-art method. The three methods were tested against a published digital perfusion phantom earlier used to illustrate the superiority of bSVD. In addition, the NLR and clinical methods were also tested against bSVD on 20 clinical scans. Pearson correlation coefficients were calculated for each of the tested methods. All three methods showed high correlation coefficients (>0.9) with the ground truth in the phantom. With respect to the clinical scans, the NLR perfusion maps showed higher correlation with bSVD than the perfusion maps from the clinical method. Furthermore, the perfusion maps showed that the fast NLR estimates are robust to tracer-delay. In conclusion, the proposed fast NLR method provides a simple and flexible way of estimating perfusion parameters from CT perfusion scans, with high correlation coefficients. This suggests that it could be a better alternative to the current clinical and academic state-of-art methods.

Image-based gradient non-linearity characterization to determine higher-order spherical harmonic coefficients for improved spatial position accuracy in magnetic resonance imaging.

PubMed

Weavers, Paul T; Tao, Shengzhen; Trzasko, Joshua D; Shu, Yunhong; Tryggestad, Erik J; Gunter, Jeffrey L; McGee, Kiaran P; Litwiller, Daniel V; Hwang, Ken-Pin; Bernstein, Matt A

2017-05-01

Spatial position accuracy in magnetic resonance imaging (MRI) is an important concern for a variety of applications, including radiation therapy planning, surgical planning, and longitudinal studies of morphologic changes to study neurodegenerative diseases. Spatial accuracy is strongly influenced by gradient linearity. This work presents a method for characterizing the gradient non-linearity fields on a per-system basis, and using this information to provide improved and higher-order (9th vs. 5th) spherical harmonic coefficients for better spatial accuracy in MRI. A large fiducial phantom containing 5229 water-filled spheres in a grid pattern is scanned with the MR system, and the positions all the fiducials are measured and compared to the corresponding ground truth fiducial positions as reported from a computed tomography (CT) scan of the object. Systematic errors from off-resonance (i.e., B0) effects are minimized with the use of increased receiver bandwidth (±125kHz) and two acquisitions with reversed readout gradient polarity. The spherical harmonic coefficients are estimated using an iterative process, and can be subsequently used to correct for gradient non-linearity. Test-retest stability was assessed with five repeated measurements on a single scanner, and cross-scanner variation on four different, identically-configured 3T wide-bore systems. A decrease in the root-mean-square error (RMSE) over a 50cm diameter spherical volume from 1.80mm to 0.77mm is reported here in the case of replacing the vendor's standard 5th order spherical harmonic coefficients with custom fitted 9th order coefficients, and from 1.5mm to 1mm by extending custom fitted 5th order correction to the 9th order. Minimum RMSE varied between scanners, but was stable with repeated measurements in the same scanner. The results suggest that the proposed methods may be used on a per-system basis to more accurately calibrate MR gradient non-linearity coefficients when compared to vendor standard corrections. Copyright © 2016 Elsevier Inc. All rights reserved.

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.

Dispersion of Sound in Dilute Suspensions with Nonlinear Particle Relaxation

NASA Technical Reports Server (NTRS)

Kandula, Max

2010-01-01

The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of Omega(Tau)(sub d), where Omega is the circular frequency, and Tau(sub d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction

Solution of a Nonlinear Heat Conduction Equation for a Curvilinear Region with Dirichlet Conditions by the Fast-Expansion Method

NASA Astrophysics Data System (ADS)

Chernyshov, A. D.

2018-05-01

The analytical solution of the nonlinear heat conduction problem for a curvilinear region is obtained with the use of the fast-expansion method together with the method of extension of boundaries and pointwise technique of computing Fourier coefficients.

Observations of the R reflector and sediment interface reflection at the Shallow Water '06 Central Site.

PubMed

Choi, Jee Woong; Dahl, Peter H; Goff, John A

2008-09-01

Acoustic bottom-interacting measurements from the Shallow Water '06 experiment experiment (frequency range 1-20 kHz) are presented. These are co-located with coring and stratigraphic studies showing a thin (approximately 20 cm) higher sound speed layer overlaying a thicker (approximately 20 m) lower sound speed layer ending at a high-impedance reflector (R reflector). Reflections from the R reflector and analysis of the bottom reflection coefficient magnitude for the upper two sediment layers confirm both these features. Geoacoustic parameters are estimated, dispersion effects addressed, and forward modeling using the parabolic wave equation undertaken. The reflection coefficient measurements suggest a nonlinear attenuation law for the thin layer of sandy sediments.

Linear, non-linear and thermal properties of single crystal of LHMHCl

NASA Astrophysics Data System (ADS)

Kulshrestha, Shobha; Shrivastava, A. K.

2018-05-01

The single crystal of amino acid of L-histidine monohydrochloride was grown by slow evaporation technique at room temperature. High optical quality and appropriate size of crystals were grown under optimized growth conditions. The grown crystals were transparent. Crystals are characterized with different characterizations such as Solubility test, UV-Visible, optical band gap (Eg). With the help of optical data to be calculate absorption coefficient (α), extinction coefficient (k), refractive index (n), dielectric constant (ɛ). These optical constants are shows favorable conditions for photonics devices. Second harmonic generation (NLO) test show the green light emission which is confirm that crystal have properties for laser application. Thermal stability of grown crystal is confirmed by TG/DTA.

Investigation of heat and mass transfer under the influence of variable diffusion coefficient and thermal conductivity

NASA Astrophysics Data System (ADS)

Mohyud Din, S. T.; Zubair, T.; Usman, M.; Hamid, M.; Rafiq, M.; Mohsin, S.

2018-04-01

This study is devoted to analyze the influence of variable diffusion coefficient and variable thermal conductivity on heat and mass transfer in Casson fluid flow. The behavior of concentration and temperature profiles in the presence of Joule heating and viscous dissipation is also studied. The dimensionless conversation laws with suitable BCs are solved via Modified Gegenbauer Wavelets Method (MGWM). It has been observed that increase in Casson fluid parameter (β ) and parameter ɛ enhances the Nusselt number. Moreover, Nusselt number of Newtonian fluid is less than that of the Casson fluid. The phenomenon of mass transport can be increased by solute of variable diffusion coefficient rather than solute of constant diffusion coefficient. A detailed analysis of results is appropriately highlighted. The obtained results, error estimates, and convergence analysis reconfirm the credibility of proposed algorithm. It is concluded that MGWM is an appropriate tool to tackle nonlinear physical models and hence may be extended to some other nonlinear problems of diversified physical nature also.

QR code-based non-linear image encryption using Shearlet transform and spiral phase transform

NASA Astrophysics Data System (ADS)

Kumar, Ravi; Bhaduri, Basanta; Hennelly, Bryan

2018-02-01

In this paper, we propose a new quick response (QR) code-based non-linear technique for image encryption using Shearlet transform (ST) and spiral phase transform. The input image is first converted into a QR code and then scrambled using the Arnold transform. The scrambled image is then decomposed into five coefficients using the ST and the first Shearlet coefficient, C1 is interchanged with a security key before performing the inverse ST. The output after inverse ST is then modulated with a random phase mask and further spiral phase transformed to get the final encrypted image. The first coefficient, C1 is used as a private key for decryption. The sensitivity of the security keys is analysed in terms of correlation coefficient and peak signal-to noise ratio. The robustness of the scheme is also checked against various attacks such as noise, occlusion and special attacks. Numerical simulation results are shown in support of the proposed technique and an optoelectronic set-up for encryption is also proposed.

Exact Solutions of Atmospheric (2+1)-Dimensional Nonlinear Incompressible Non-hydrostatic Boussinesq Equations

NASA Astrophysics Data System (ADS)

Liu, Ping; Wang, Ya-Xiong; Ren, Bo; Li, Jin-Hua

2016-12-01

Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. Supported by the National Natural Science Foundation of China under Grant Nos. 11305031 and 11305106, and Training Programme Foundation for Outstanding Young Teachers in Higher Education Institutions of Guangdong Province under Grant No. Yq2013205

From non-linear magnetoacoustics and spin reorientation transition to magnetoelectric micro/nano-systems

NASA Astrophysics Data System (ADS)

Tiercelin, Nicolas; Preobrazhensky, Vladimir; BouMatar, Olivier; Talbi, Abdelkrim; Giordano, Stefano; Dusch, Yannick; Klimov, Alexey; Mathurin, Théo.; Elmazria, Omar; Hehn, Michel; Pernod, Philippe

2017-09-01

The interaction of a strongly nonlinear spin system with a crystalline lattice through magnetoelastic coupling results in significant modifications of the acoustic properties of magnetic materials, especially in the vicinity of magnetic instabilities associated with the spin-reorientation transition (SRT). The magnetoelastic coupling transfers the critical properties of the magnetic subsystem to the elastic one, which leads to a strong decrease of the sound velocity in the vicinity of the SRT, and allows a large control over acoustic nonlinearities. The general principles of the non-linear magneto-acoustics (NMA) will be introduced and illustrated in `bulk' applications such as acoustic wave phase conjugation, multi-phonon coupling, explosive instability of magneto-elastic vibrations, etc. The concept of the SRT coupled to magnetoelastic interaction has been transferred into nanostructured magnetoelastic multilayers with uni-axial anisotropy. The high sensitivity and the non-linear properties have been demonstrated in cantilever type actuators, and phenomena such as magneto-mechanical RF demodulation have been observed. The combination of the magnetic layers with piezoelectric materials also led to stress-mediated magnetoelectric (ME) composites with high ME coefficients, thanks to the SRT. The magnetoacoustic effects of the SRT have also been studied for surface acoustic waves propagating in the magnetoelastic layers and found to be promising for highly sensitive magnetic field sensors working at room temperature. On the other hand, mechanical stress is a very efficient way to control the magnetic subsystem. The principle of a very energy efficient stress-mediated magnetoelectric writing and reading in a magnetic memory is described.

Nonlinear optical and light emission studies of special organic molecules and crystals

NASA Astrophysics Data System (ADS)

Bhowmik, Achintya K.

The nonlinear optical properties and light emission characteristics of some special organic molecules and crystals have been studied in detail. The second-order nonlinear optical effects were measured in the single- crystal films of the materials. The crystallographic orientations of the films were determined using x-ray diffraction measurements. The second-order susceptibility tensor elements of 4-aminobenzophenone (ABP) and 8- (4'-acetylphenyl)-1,4-dioxa-8- azaspiro[4.5]decane (APDA) films were measured using polarization selective second-harmonic generation experiments. The d-coefficients of ABP are: d 23 = 7.3 +/- 0.4 pm/V and d22 = 0.73 +/- 0.04 pm/V, while those of APDA are: d33 = 54 +/- 6 pm/V and d15 = 18 +/- 3 pm/V at 1064 nm. Phase-matched propagation directions were identified on the films. The application of these films in measuring ultra-short laser pulse-width was demonstrated. Polarized optical absorption and photo- luminescence were measured in 4'- dimethylamino-N-methyl-4-stilbazolium tosylate (DAST). The electro-optic properties of single- crystal films of DAST and styryl pyridinium cyanine dye (SPCD) were studied over a broad range of wavelengths. The measured r-coefficients are the largest reported in any material. Thin-film electro-optic modulators were demonstrated using these films which have insignificant insertion and propagation losses compared to the traditional waveguide based devices. The response was observed to be flat over the measured frequency range (2 kHz-100 MHz), which indicates the origin of the electro-optic effect to be predominantly electronic. Thus these materials have significant potential for applications in high-speed optical signal processing. Spectral broadening of femtosecond laser pulses in poly- [2,4 hexadiyne-1,6 diol-bis-(p-toluene sulfonate)] (PTS) single-crystals due to self-phase modulation was studied. The magnitudes of the nonlinear refractive index were determined over the wavelength range of 720-1064 nm. The two-photon absorption spectrum, determined from nonlinear transmission measurements, was observed to have no discernible influence on the dispersion of the nonlinear index at these wavelengths. Highly efficient spectrally narrowed emission has been observed for the first time in strongly dipolar organic salts based on the stilbazolium chromophore. An unusually high conversion efficiency (40%) with a low excitation threshold (<1 μJ) has been observed despite a very low photoluminescence efficiency (~0.3%). The results are explained in terms of cooperative emission upon short-pulse optical excitation. These materials have a wide range of potential applications in photonics, including frequency conversion, high-speed electro-optic modulation, sensors, and novel laser-like light sources.

Spectroscopic line parameters of 12CH4 for atmospheric composition retrievals in the 4300-4500 cm-1 region

NASA Astrophysics Data System (ADS)

Hashemi, R.; Predoi-Cross, A.; Nikitin, A. V.; Tyuterev, Vl. G.; Sung, K.; Smith, M. A. H.; Malathy Devi, V.

2017-01-01

Due to the importance of methane as a trace atmospheric gas and a greenhouse gas, we have carried out a precise line-shape study to obtain the CH4-CH4 and CH4-air half-width coefficients, CH4-CH4 and CH4-air shift coefficients and off-diagonal relaxation matrix element coefficients for methane transitions in the spectral range known as the "methane Octad". In addition, the associated temperature dependences of these coefficients have been measured in the 4300-4500 cm-1 region of the Octad. The high signal to noise ratio spectra of pure methane and of dilute mixtures of methane in dry air with high resolution have been recorded at temperatures from 148 K to room temperature using the Bruker IFS 125 HR Fourier transform spectrometer (FTS) at the Jet Propulsion Laboratory, Pasadena, California. The analysis of spectra was done using a multispectrum non-linear least-squares curve fitting technique. Theoretical calculations have been performed and the results are compared with the previously published line positions, intensities and with the line parameters available in the GEISA and HITRAN2012 databases.

Characterizing the Lyman-alpha forest flux probability distribution function using Legendre polynomials

NASA Astrophysics Data System (ADS)

Cieplak, Agnieszka; Slosar, Anze

2017-01-01

The Lyman-alpha forest has become a powerful cosmological probe of the underlying matter distribution at high redshift. It is a highly non-linear field with much information present beyond the two-point statistics of the power spectrum. The flux probability distribution function (PDF) in particular has been used as a successful probe of small-scale physics. In addition to the cosmological evolution however, it is also sensitive to pixel noise, spectrum resolution, and continuum fitting, all of which lead to possible biased estimators. Here we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over the binned PDF as is commonly done. Since the n-th coefficient can be expressed as a linear combination of the first n moments of the field, this allows for the coefficients to be measured in the presence of noise and allows for a clear route towards marginalization over the mean flux. In addition, we use hydrodynamic cosmological simulations to demonstrate that in the presence of noise, a finite number of these coefficients are well measured with a very sharp transition into noise dominance. This compresses the information into a finite small number of well-measured quantities.

Characterizing the Lyman-alpha forest flux probability distribution function using Legendre polynomials

NASA Astrophysics Data System (ADS)

Cieplak, Agnieszka; Slosar, Anze

2018-01-01

The Lyman-alpha forest has become a powerful cosmological probe at intermediate redshift. It is a highly non-linear field with much information present beyond the power spectrum. The flux probability flux distribution (PDF) in particular has been a successful probe of small scale physics. However, it is also sensitive to pixel noise, spectrum resolution, and continuum fitting, all of which lead to possible biased estimators. Here we argue that measuring the coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. Since the n-th Legendre coefficient can be expressed as a linear combination of the first n moments of the field, this allows for the coefficients to be measured in the presence of noise and allows for a clear route towards marginalization over the mean flux. Additionally, in the presence of noise, a finite number of these coefficients are well measured with a very sharp transition into noise dominance. This compresses the information into a small amount of well-measured quantities. Finally, we find that measuring fewer quasars with high signal-to-noise produces a higher amount of recoverable information.

Highly efficient flexible piezoelectric nanogenerator and femtosecond two-photon absorption properties of nonlinear lithium niobate nanowires

NASA Astrophysics Data System (ADS)

Gupta, Manoj Kumar; Aneesh, Janardhanakurup; Yadav, Rajesh; Adarsh, K. V.; Kim, Sang-Woo

2017-05-01

We present a high performance flexible piezoelectric nanogenerator (NG) device based on the hydrothermally grown lead-free piezoelectric lithium niobate (LiNbO3) nanowires (NWs) for scavenging mechanical energies. The non-linear optical coefficient and optical limiting properties of LiNbO3 were analyzed using femtosecond laser pulse assisted two photon absorption techniques for the first time. Further, a flexible hybrid type NG using a composite structure of the polydimethylsiloxane polymer and LiNbO3 NWs was fabricated, and their piezoelectric output signals were measured. A large output voltage of ˜4.0 V and a recordable large current density of about 1.5 μA cm-2 were obtained under the cyclic compressive force of 1 kgf. A subsequent UV-Vis analysis of the as-prepared sample provides a remarkable increase in the optical band gap (UV absorption cut-off, ˜251 nm) due to the nanoscale size effect. The high piezoelectric output voltage and current are discussed in terms of large band gap, significant nonlinear optical response, and electric dipole alignments under poling effects. Such high performance and unique optical properties of LiNbO3 show its great potential towards various next generation smart electronic applications and self-powered optoelectronic devices.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Characteristics of solitary waves, quasiperiodic solutions, homoclinic breather solutions and rogue waves in the generalized variable-coefficient forced Kadomtsev-Petviashvili equation

NASA Astrophysics Data System (ADS)

Yan, Xue-Wei; Tian, Shou-Fu; Dong, Min-Jie; Zou, Li

2017-12-01

In this paper, the generalized variable-coefficient forced Kadomtsev-Petviashvili (gvcfKP) equation is investigated, which can be used to characterize the water waves of long wavelength relating to nonlinear restoring forces. Using a dependent variable transformation and combining the Bell’s polynomials, we accurately derive the bilinear expression for the gvcfKP equation. By virtue of bilinear expression, its solitary waves are computed in a very direct method. By using the Riemann theta function, we derive the quasiperiodic solutions for the equation under some limitation factors. Besides, an effective way can be used to calculate its homoclinic breather waves and rogue waves, respectively, by using an extended homoclinic test function. We hope that our results can help enrich the dynamical behavior of the nonlinear wave equations with variable-coefficient.

Third-order nonlinear optical properties of phthalocyanines in solution and in polystyrene films

NASA Astrophysics Data System (ADS)

Reeves, Roger J.; Powell, Richard C.; Chang, Young H.; Ford, Warren T.; Zhu, Weiming

1996-01-01

Degenerate four-wave mixing (DFWM) measurements of third-order nonlinear optical (NLO) coefficients of metal-free, Cu, Pt, Pb and Bi octa(2-ethylhexyloxy) phthalocyanines (MPc's) were done with 20 ps duration laser pulses under resonant conditions at 532 nm in polystyrene films and under nonresonant conditions at 1064 nm in chloroform solutions. The NLO coefficients ξxxxx(3) show saturation with increasing incident intensity and no strong dependence on the central metal atom of the MPc below the saturation intensity. Optical delays of the probe-pulse up to 3 ns show an acoustic phonon response in both the polystyrene films and the chloroform solutions. An intensity-dependent absorption coefficient was measured by a pump/probe experiment and used in a simple model to qualitatively account for the saturation of ξ(3) measured by DFWM.

Estimation of diffusion coefficients from voltammetric signals by support vector and gaussian process regression

PubMed Central

2014-01-01

Background Support vector regression (SVR) and Gaussian process regression (GPR) were used for the analysis of electroanalytical experimental data to estimate diffusion coefficients. Results For simulated cyclic voltammograms based on the EC, Eqr, and EqrC mechanisms these regression algorithms in combination with nonlinear kernel/covariance functions yielded diffusion coefficients with higher accuracy as compared to the standard approach of calculating diffusion coefficients relying on the Nicholson-Shain equation. The level of accuracy achieved by SVR and GPR is virtually independent of the rate constants governing the respective reaction steps. Further, the reduction of high-dimensional voltammetric signals by manual selection of typical voltammetric peak features decreased the performance of both regression algorithms compared to a reduction by downsampling or principal component analysis. After training on simulated data sets, diffusion coefficients were estimated by the regression algorithms for experimental data comprising voltammetric signals for three organometallic complexes. Conclusions Estimated diffusion coefficients closely matched the values determined by the parameter fitting method, but reduced the required computational time considerably for one of the reaction mechanisms. The automated processing of voltammograms according to the regression algorithms yields better results than the conventional analysis of peak-related data. PMID:24987463

Analysis of structural and optical properties of annealed fullerene thin films

NASA Astrophysics Data System (ADS)

El-Nahass, M. M.; Ali, H. A. M.; Gadallah, A.-S.; Atta Khedr, M.; Afify, H. A.

2015-08-01

Fullerene thin films were thermally deposited onto different substrates. The films annealed at 523 K for 10 h. X-ray diffraction technique was used to examine the structure of the films. The morphology of films was examined by field emission scanning electron microscopy. Fourier transform infrared spectra were recorded in wavenumber range 400-2000 cm-1. The optical characteristics were analyzed using UV- Vis-NIR spectrophotometric measurements in the spectral range 200-2500 nm. The refractive index and extinction coefficient were determined. Some dispersion parameters were calculated such as single oscillator energy, dispersion energy, dielectric constant at high frequency and lattice dielectric constant. As well as, the nonlinear optical susceptibility χ(3) and nonlinear refractive index n2 were determined.

Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping

NASA Astrophysics Data System (ADS)

Smith, Timothy; Pantano, Carlos

2017-11-01

We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.

Absolute linearity measurements on a gold-black-coated deuterated L-alanine-doped triglycine sulfate pyroelectric detector.

PubMed

Theocharous, E

2008-07-20

The nonlinearity characteristics of a commercially available deuterated L-alanine-doped triglycine sulfate (DLATGS) pyroelectric detector were experimentally investigated at high levels of illumination using the National Physical Laboratory detector linearity characterization facility. The detector was shown to exhibit a superlinear response at high levels of illumination. Moreover, the linearity factor was shown to depend on the area of the spot on the detector active area being illuminated, i.e., the incident irradiance. Possible reasons for the observed behavior are proposed and discussed. The temperature coefficient of the response of the DLATGS pyroelectric detector was measured and found to be higher than +2.5% degrees C(-1). This large and positive temperature coefficient of response is the most likely cause of the superlinear behavior of the DLATGS pyroelectric detector.

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

High pressure ferroelastic phase transition in SrTiO3

NASA Astrophysics Data System (ADS)

Salje, E. K. H.; Guennou, M.; Bouvier, P.; Carpenter, M. A.; Kreisel, J.

2011-07-01

High pressure measurements of the ferroelastic phase transition of SrTiO3 (Guennou et al 2010 Phys. Rev. B 81 054115) showed a linear pressure dependence of the transition temperature between the cubic and tetragonal phase. Furthermore, the pressure induced transition becomes second order while the temperature dependent transition is near a tricritical point. The phase transition mechanism is characterized by the elongation and tilt of the TiO6 octahedra in the tetragonal phase, which leads to strongly nonlinear couplings between the structural order parameter, the volume strain and the applied pressure. The phase diagram is derived from the Clausius-Clapeyron relationship and is directly related to a pressure dependent Landau potential. The nonlinearities of the pressure dependent strains lead to an increase of the fourth order Landau coefficient with increasing pressure and, hence, to a tricritical-second order crossover. This behaviour is reminiscent of the doping related crossover in isostructural KMnF3.

Nonlinear evolution of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities

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

Dimonte, G

Scaled experiments on the nonlinear evolution of the Rayleigh- Taylor (RT) and Richtmyer-Meshkov (RM) instabilities are described under a variety, of conditions that occur in nature. At high Reynolds number, the mixing layer grows self-similarly - {alpha}{sub i}Agt{sup 2} for a constant acceleration (g), and as a power law t{sup {theta}{sub i}} for impulsive accelerations U{delta}(t) at low and high Mach numbers. The growth coefficients {alpha}{sub i} and {theta}{sub i} exponents are measured over a comprehensive range of Atwood numbers A. The RT instability is also investigated with Non- Newtonian materials which are independently characterized. A critical wavelength and amplitudemore » for instability is observed associated with the shear modulus and tensile yield of the material. The results are applicable from supernova explosions to geophysical flows subject to these hydrodynamic instabilities.« less

Highly efficient broadband terahertz generation from ultrashort laser filamentation in liquids.

PubMed

Dey, Indranuj; Jana, Kamalesh; Fedorov, Vladimir Yu; Koulouklidis, Anastasios D; Mondal, Angana; Shaikh, Moniruzzaman; Sarkar, Deep; Lad, Amit D; Tzortzakis, Stelios; Couairon, Arnaud; Kumar, G Ravindra

2017-10-30

Generation and application of energetic, broadband terahertz pulses (bandwidth ~0.1-50 THz) is an active and contemporary area of research. The main thrust is toward the development of efficient sources with minimum complexities-a true table-top setup. In this work, we demonstrate the generation of terahertz radiation via ultrashort pulse induced filamentation in liquids-a counterintuitive observation due to their large absorption coefficient in the terahertz regime. The generated terahertz energy is more than an order of magnitude higher than that obtained from the two-color filamentation of air (the most standard table-top technique). Such high terahertz energies would generate electric fields of the order of MV cm -1 , which opens the doors for various nonlinear terahertz spectroscopic applications. The counterintuitive phenomenon has been explained via the solution of nonlinear pulse propagation equation in the liquid medium.

Diagnostic-Photographic Determination of Drag/Lift/Torque Coefficients of High Speed Rigid Body in Water Column

DTIC Science & Technology

2008-01-01

various physical processes such as supercavitation and bubbles. A diagnostic- photographic method is developed in this study to determine the drag...nonlinear dynamics, body and multi-phase fluid interaction, supercavitation , and instability theory. The technical application of the hydrodynamics of...uV U ω= = − ×V e e e ei i , (29) where Eq.(9) is used. For a supercavitation area, a correction factor may be

Noise Estimation in Electroencephalogram Signal by Using Volterra Series Coefficients

PubMed Central

Hassani, Malihe; Karami, Mohammad Reza

2015-01-01

The Volterra model is widely used for nonlinearity identification in practical applications. In this paper, we employed Volterra model to find the nonlinearity relation between electroencephalogram (EEG) signal and the noise that is a novel approach to estimate noise in EEG signal. We show that by employing this method. We can considerably improve the signal to noise ratio by the ratio of at least 1.54. An important issue in implementing Volterra model is its computation complexity, especially when the degree of nonlinearity is increased. Hence, in many applications it is urgent to reduce the complexity of computation. In this paper, we use the property of EEG signal and propose a new and good approximation of delayed input signal to its adjacent samples in order to reduce the computation of finding Volterra series coefficients. The computation complexity is reduced by the ratio of at least 1/3 when the filter memory is 3. PMID:26284176

On the conditions for the onset of nonlinear chirping structures in NSTX

NASA Astrophysics Data System (ADS)

Duarte, Vinicius; Podesta, Mario; Berk, Herbert; Gorelenkov, Nikolai

2015-11-01

The nonlinear dynamics of phase space structures is a topic of interest in tokamak physics in connection with fast ion loss mechanisms. The onset of phase-space holes and clumps has been theoretically shown to be associated with an explosive solution of an integro-differential, nonlocal cubic equation that governs the early mode amplitude evolution in the weakly nonlinear regime. The existence and stability of the solutions of the cubic equation have been theoretically studied as a function of Fokker-Planck coefficients for the idealized case of a single resonant point of a localized mode. From realistic computations of NSTX mode structures and resonant surfaces, we calculate effective pitch angle scattering and slowing-down (drag) collisional coefficients and analyze NSTX discharges for different cases with respect to chirping experimental observation. Those results are confronted to the theory that predicts the parameters region that allow for chirping to take place.

Investigation of third-order nonlinear and optical power limiting properties of terphenyl derivatives

NASA Astrophysics Data System (ADS)

Kamath, Laxminarayana; Manjunatha, K. B.; Shettigar, Seetharam; Umesh, G.; Narayana, B.; Samshuddin, S.; Sarojini, B. K.

2014-03-01

A series of new chalcones containing terphenyl as a core and with different functional groups has been successfully synthesized by Claisen-Schmidt condensation method in search of new nonlinear optical (NLO) materials. Molecular structural characterization for the compounds was achieved by FTIR and single crystal X-ray diffraction. The third-order NLO absorption and refraction coefficients were simultaneously determined by Z-scan technique. The measurements were performed at 532 nm with 7 ns laser pulses using a Nd:YAG laser in solution form. The Z-scan experiments reveal that the compounds exhibit strong nonlinear refraction coefficient of the order 10-11 esu and the molecular two photon absorption cross section is 10-46 cm4 s/photon. The results also show that the structures of the compounds have great impact on NLO properties. The compounds show optical power limiting behavior due to two-photon absorption (TPA).

Mechanical-magnetic-electric coupled behaviors for stress-driven Terfenol-D energy harvester

NASA Astrophysics Data System (ADS)

Cao, Shuying; Zheng, Jiaju; Wang, Bowen; Pan, Ruzheng; Zhao, Ran; Weng, Ling; Sun, Ying; Liu, Chengcheng

2017-05-01

The stress-driven Terfernol-D energy harvester exhibits the nonlinear mechanical-magnetic-electric coupled (MMEC) behaviors and the eddy current effects. To analyze and design the device, it is necessary to establish an accurate model of the device. Based on the effective magnetic field expression, the constitutive equations with eddy currents and variable coefficients, and the dynamic equations, a nonlinear dynamic MMEC model for the device is founded. Comparisons between the measured and calculated results show that the model can describe the nonlinear coupled curves of magnetization versus stress and strain versus stress under different bias fields, and can provide the reasonable data trends of piezomagnetic coefficients, Young's modulus and relative permeability for Terfenol-D. Moreover, the calculated power results show that the model can determine the optimal bias conditions, optimal resistance, suitable proof mass, suitable slices for the maximum energy extraction of the device under broad stress amplitude and broad frequency.

Wiener Chaos and Nonlinear Filtering

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

Lototsky, S.V.

2006-11-15

The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the Cameron-Martin version of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated by the observation process. The coefficients in the expansion depend only on the deterministic dynamics of the state and observation processes. For real-time applications, computing the coefficients in advance improves the performance of the algorithms in comparison with most other existing methods of nonlinear filtering. Themore » paper summarizes the main existing results about these Wiener chaos algorithms and resolves some open questions concerning the convergence of the algorithms in the noise-correlated setting. The presentation includes the necessary background on the Wiener chaos and optimal nonlinear filtering.« less

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.

Two-photon absorption in SiO{sub 2}- and (SiO{sub 2} + GeO{sub 2})-based fibres at a wavelength of 349 nm

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

Chunaev, D S; Karasik, A Ya

2014-06-30

The nonlinear two-photon light absorption coefficients have been measured in an optical fibre with a quartz glass (SiO{sub 2}) core and in a fibre with a germanosilicate glass (SiO{sub 2} + GeO{sub 2}) core. The two-photon absorption coefficient β measured at a wavelength of 349 nm in the (SiO{sub 2} + GeO{sub 2})-based fibre (13.7 cm TW{sup -1}) multiply exceeds that for the pure quartz glass optical fibre (0.54 cm TW{sup -1}). (nonlinear optical phenomena)

Dark Soliton Solutions of Space-Time Fractional Sharma-Tasso-Olver and Potential Kadomtsev-Petviashvili Equations

NASA Astrophysics Data System (ADS)

Guner, Ozkan; Korkmaz, Alper; Bekir, Ahmet

2017-02-01

Dark soliton solutions for space-time fractional Sharma-Tasso-Olver and space-time fractional potential Kadomtsev-Petviashvili equations are determined by using the properties of modified Riemann-Liouville derivative and fractional complex transform. After reducing both equations to nonlinear ODEs with constant coefficients, the \\tanh ansatz is substituted into the resultant nonlinear ODEs. The coefficients of the solutions in the ansatz are calculated by algebraic computer computations. Two different solutions are obtained for the Sharma-Tasso-Olver equation as only one solution for the potential Kadomtsev-Petviashvili equation. The solution profiles are demonstrated in 3D plots in finite domains of time and space.

NONLINEAR OPTICAL PHENOMENA: Self-reflection in a system of excitons and biexcitons in semiconductors

NASA Astrophysics Data System (ADS)

Khadzhi, P. I.; Lyakhomskaya, K. D.

1999-10-01

The characteristic features of the self-reflection of a powerful electromagnetic wave in a system of coherent excitons and biexcitons in semiconductors were investigated as one of the manifestations of the nonlinear optical skin effect. It was found that a monotonically decreasing standing wave with an exponentially falling spatial tail is formed in the surface region of a semiconductor. Under the influence of the field of a powerful pulse, an optically homogeneous medium is converted into one with distributed feedback. The appearance of spatially separated narrow peaks of the refractive index, extinction coefficient, and reflection coefficient is predicted.

Some optical properties of KTP, LiIO3, and LiNbO3

NASA Technical Reports Server (NTRS)

Gettemy, Donald J.; Harker, William C.; Lindholm, Glenn; Barnes, Norman P.

1988-01-01

Measurements of the absorption coefficient for KTP, LiIO3, and LiNbO3 are discussed. The variation of the refractive index with temperature has been measured for KTP and LiIO3. It is necessary to know both the absorption coefficient beta and the variation in the indexes of refraction with temperature change dn/dT to determine the average power limit of a nonlinear interaction. With the dn/dT information, it is also possible to estimate the temperature half width of any nonlinear interaction by calculating the variation of the phase-matching condition with temperature.

Ventilatory Patterning in a Mouse Model of Stroke

PubMed Central

Koo, Brian B; Strohl, Kingman P; Gillombardo, Carl B; Jacono, Frank J

2010-01-01

Cheyne-Stokes respiration (CSR) is a breathing pattern characterized by waxing and waning of breath volume and frequency, and is often recognized following stroke, when causal pathways are often obscure. We used an animal model to address the hypothesis that cerebral infarction is a mechanism for producing breathing instability. Fourteen male A/J mice underwent either stroke (n=7) or sham (n=7) procedure. Ventilation was measured using whole body plethysmography. Respiratory rate (RR), tidal volume (VT) and minute ventilation (Ve) mean values and coefficient of variation were computed for ventilation and oscillatory behavior. In addition, the ventilatory data were computationally fit to models to quantify autocorrelation, mutual information, sample entropy and a nonlinear complexity index. At the same time post procedure, stroke when compared to sham animal breathing consisted of a lower RR and autocorrelation, higher coefficient of variation for VT and higher coefficient of variation for Ve. Mutual information and the nonlinear complexity index were higher in breathing following stroke which also demonstrated a waxing/waning pattern. The absence of stroke in the sham animals was verified anatomically. We conclude that ventilatory pattern following cerebral infarction demonstrated increased variability with increased nonlinear patterning and a waxing/waning pattern, consistent with CSR. PMID:20472101

Standard electrode potential, Tafel equation, and the solvation thermodynamics.

PubMed

Matyushov, Dmitry V

2009-06-21

Equilibrium in the electronic subsystem across the solution-metal interface is considered to connect the standard electrode potential to the statistics of localized electronic states in solution. We argue that a correct derivation of the Nernst equation for the electrode potential requires a careful separation of the relevant time scales. An equation for the standard metal potential is derived linking it to the thermodynamics of solvation. The Anderson-Newns model for electronic delocalization between the solution and the electrode is combined with a bilinear model of solute-solvent coupling introducing nonlinear solvation into the theory of heterogeneous electron transfer. We therefore are capable of addressing the question of how nonlinear solvation affects electrochemical observables. The transfer coefficient of electrode kinetics is shown to be equal to the derivative of the free energy, or generalized force, required to shift the unoccupied electronic level in the bulk. The transfer coefficient thus directly quantifies the extent of nonlinear solvation of the redox couple. The current model allows the transfer coefficient to deviate from the value of 0.5 of the linear solvation models at zero electrode overpotential. The electrode current curves become asymmetric in respect to the change in the sign of the electrode overpotential.

Donor impurity-related linear and nonlinear intraband optical absorption coefficients in quantum ring: effects of applied electric field and hydrostatic pressure

PubMed Central

2012-01-01

The linear and nonlinear intraband optical absorption coefficients in GaAs three-dimensional single quantum rings are investigated. Taking into account the combined effects of hydrostatic pressure and electric field, applied along the growth direction of the heterostructure, the energies of the ground and first excited states of a donor impurity have been found using the effective mass approximation and a variational method. The energies of these states are examined as functions of the dimensions of the structure, electric field, and hydrostatic pressure. We have also investigated the dependencies of the linear, nonlinear, and total optical absorption coefficients as a function of incident photon energy for several configurations of the system. It is found that the variation of distinct sizes of the structure leads to either a redshift and/or a blueshift of the resonant peaks of the intraband optical spectrum. In addition, we have found that the application of an electric field leads to a redshift, whereas the influence of hydrostatic pressure leads to a blueshift (in the case of on-ring-center donor impurity position) of the resonant peaks of the intraband optical spectrum. PMID:23021497

Nonlinear shear wave interaction at a frictional interface: energy dissipation and generation of harmonics.

PubMed

Meziane, A; Norris, A N; Shuvalov, A L

2011-10-01

Analytical and numerical modeling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by remote normal compression. A shear wave, either time harmonic or a narrow band pulse, is incident normal to the interface and propagates through the contact. Two friction laws are considered and the influence on interface behavior is investigated: Coulomb's law with a constant friction coefficient and a slip-weakening friction law which involves static and dynamic friction coefficients. The relationship between the nonlinear harmonics and the dissipated energy, and the dependence on the contact dynamics (friction law, sliding, and tangential stress) and on the normal contact stress are examined in detail. The analytical and numerical results indicate universal type laws for the amplitude of the higher harmonics and for the dissipated energy, properly non-dimensionalized in terms of the pre-stress, the friction coefficient and the incident amplitude. The results suggest that measurements of higher harmonics can be used to quantify friction and dissipation effects of a sliding interface. © 2011 Acoustical Society of America

REVIEWS OF TOPICAL PROBLEMS: Particle kinetics in highly turbulent plasmas (renormalization and self-consistent field methods)

NASA Astrophysics Data System (ADS)

Bykov, Andrei M.; Toptygin, Igor'N.

1993-11-01

This review presents methods available for calculating transport coefficients for impurity particles in plasmas with strong long-wave MHD-type velocity and magnetic-field fluctuations, and random ensembles of strong shock fronts. The renormalization of the coefficients of the mean-field equation of turbulent dynamo theory is also considered. Particular attention is devoted to the renormalization method developed by the authors in which the renormalized transport coefficients are calculated from a nonlinear transcendental equation (or a set of such equations) and are expressed in the form of explicit functions of pair correlation tensors describing turbulence. Numerical calculations are reproduced for different turbulence spectra. Spatial transport in a magnetic field and particle acceleration by strong turbulence are investigated. The theory can be used in a wide range of practical problems in plasma physics, atmospheric physics, ocean physics, astrophysics, cosmic-ray physics, and so on.

Influence of Ga doping ratio on the saturable absorption mechanism in Ga doped ZnO thin solid films processed by sol-gel spin coating technique

NASA Astrophysics Data System (ADS)

Sandeep, K. M.; Bhat, Shreesha; Dharmaprakash, S. M.; Byrappa, K.

2017-03-01

In the present study, the nonlinear optical properties of sol-gel spin coated gallium doped zinc oxide (GZO) thin solid films are explored with nanosecond laser pulses using the z-scan technique. The higher doping ratios of Ga result in a large redshift of the energy gap (0.38 eV) due to the existence of enhanced grain boundary defects in GZO films. A positive nonlinear absorption coefficient is observed in undoped 1 at.wt.% GZO and 2 at.wt.% GZO films, and a negative nonlinear absorption coefficient in 3 at.wt.% GZO film. Fewer defects in undoped 1% GZO and 2% GZO films resulted in reverse saturable absorption (RSA), whereas a saturable absorption (SA) mechanism is observed in 3% GZO films and is attributed to the enhanced defect concentration in the band structure of GZO. However, all the films showed a self-defocusing mechanism, derived by a closed aperture z-scan technique. The present work sheds light on the defect mechanism involved in the observed nonlinear properties of GZO films.

Nonlinear absorption of Sb-based phase change materials due to the weakening of the resonant bond

NASA Astrophysics Data System (ADS)

Liu, Shuang; Wei, Jingsong; Gan, Fuxi

2012-03-01

The current study proposes a model based on the weakening of the resonant bond to explore the giant optical nonlinear saturable absorption of Sb-based phase change materials. In order to analyze the weakening of resonant bond effectively, we take the Sb2Te3 as an example. First-principle calculations show that both the Born effective charge and optical dielectric constant of crystalline Sb2Te3 in the 300 K to 500 K temperature range monotonically decrease with the temperature, indicating a weakening of the resonant bond. This weakening induces a decline in the absorption coefficient at a rate of 103 m-1 K-1, which results in a nonlinear saturable absorption coefficient in the order of 10-2 m/W. The nonlinear absorption characteristics of the crystalline Sb, Sb7Te3, and Sb2Te3 thin films at 405 nm laser wavelength are measured via z-scan technique using nanosecond laser pulses to validate the above-proposed model. The experimental results are in good agreement with theoretical prediction.

Investigation on thermally-induced optical nonlinearity of alcohols

NASA Astrophysics Data System (ADS)

Zhang, Qian; Cheng, Xuemei; He, Bo; Ren, Zhaoyu; Zhang, Ying; Chen, Haowei; Bai, Jintao

2018-06-01

In this work, we studied the thermally-induced optical nonlinearity of alcohols by analyzing the far-filed diffraction rings patterns, which are generated when the alcohols are illuminated by a laser beam resonant to their overtones. We deduced the nonlinear refractive index coefficient n2 generated by thermal nonlinear optical effect to be - (20.53 ± 00.03) ×10-8cm2 /W , which is much higher than that of Kerr effect (7.7 ×10-16cm2 /W). The results also demonstrated that the thermally-induced optical nonlinearity increased with the laser power and sample concentration increasing. The notable nonlinearity suggests that thermal effect has potentials in many applications such as optical spatial modulation, and trapping and guiding of atoms.

Self-Broadening and Self-Shift Coefficients in the Fundamental Band of 12C 16O

NASA Technical Reports Server (NTRS)

Devi, Malathy V.; Benner, D. Chris; Smith, Mary Ann H.; Rinsland, Curtis P.

1998-01-01

High quality and precise measurements of self-broadened and self-shift coefficients in the fundamental band of C-12O-16 were made using spectra recorded at room temperature with the high-resolution (0.0027 cm(exp -1)) McMath-Pierce Fourier transform spectrometer located at the National Solar Observatory on Kitt Peak, Arizona. The spectral region under investigation (2008-2247 cm(exp -1)) contains the P(31) to R(31) transitions. The data were obtained using a high-purity natural isotopic sample ofcarbon monoxide and two absorption cells with pathlengths of 4.08 and 9.98 cm, respectively. Various pressures of CO were used, ranging between 0.25 and 201.2 Torr. The results were obtained by analyzing five spectra simultaneously, using a multispectrum nonlinear least-squares fitting technique. The self-broadened coefficients ranged from 0.0426(2) cm(exp -1) atm(exp -1) at 296 K to 0.0924(2) cm(exp -1) atm(exp -1) at 296 K, while the pressure-induced shift coefficients varied between -0.0042(3) cm(exp -1) atm(exp -1) at 296 K and +0.0005(l) cm(exp -1) atm(exp -1) at 296 K. The value in parentheses is the estimated uncertainty in units of the last digit. The self-broadened coefficients of lines with same values of m in the P and R branches agree close to within experimental uncertainties while the self-shift coefficients showed considerable variation within and between the two branches. The mean value of the ratios of P branch to R branch self-broadened coefficients was found to be 1.01 with a standard deviation of + or - 0.01. Comparisons of the results with other published data were made.

Design considerations for multi component molecular-polymeric nonlinear optical materials

NASA Astrophysics Data System (ADS)

Singer, K. D.; Kuzyk, M. G.; Fang, T.; Holland, W. R.; Cahill, P. A.

1990-08-01

We review our work on multi component polymeric nonlinear optical materials. These materials consist of nonlinear optical molecules incorporated in a polymeric host. A cross-linked triazine polymer incorporating a dicyanovinyl terminated azo dye was found to be relatively stable at 85 deg and possess an electro-optic coefficient of 11pm/V. We have also observed the zero dispersion condition in a new anomalous dispersion dye for phase matched second harmonic generation, and expect efficient conversion to the blue. A squarylium dye, ISQ, has been found to possess a large third order nonlinearity, and may display two-level behavior.

Description of a computer program and numerical techniques for developing linear perturbation models from nonlinear systems simulations

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1978-01-01

A numerical technique was developed which generates linear perturbation models from nonlinear aircraft vehicle simulations. The technique is very general and can be applied to simulations of any system that is described by nonlinear differential equations. The computer program used to generate these models is discussed, with emphasis placed on generation of the Jacobian matrices, calculation of the coefficients needed for solving the perturbation model, and generation of the solution of the linear differential equations. An example application of the technique to a nonlinear model of the NASA terminal configured vehicle is included.

A multiphase non-linear mixed effects model: An application to spirometry after lung transplantation.

PubMed

Rajeswaran, Jeevanantham; Blackstone, Eugene H

2017-02-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time-varying coefficients.

Asymptotically exact parabolic solutions of the generalized nonlinear Schrödinger equation with varying parameters

NASA Astrophysics Data System (ADS)

Kruglov, Vladimir I.; Harvey, John D.

2006-12-01

We present exact asymptotic similariton solutions of the generalized nonlinear Schrödinger equation (NLSE) with gain or loss terms for a normal-dispersion fiber amplifier with dispersion, nonlinearity, and gain profiles that depend on the propagation distance. Our treatment is based on the mapping of the NLSE with varying parameters to the NLSE with constant dispersion and nonlinearity coefficients and an arbitrary varying gain function. We formulate an effective procedure that leads directly, under appropriate conditions, to a wide range of exact asymptotic similariton solutions of NLSE demonstrating self-similar propagating regimes with linear chirp.

Vapor deposition and characterization of supramolecular assemblies for integrated nonlinear optics

NASA Astrophysics Data System (ADS)

Esembeson, Bweh

Very recently, some organic molecules have been developed that are very compact and have exceptionally high molecular polarizabilities which approach the fundamental quantum limit. Supramolecular assemblies created from such highly nonlinear molecules could find applications in integrated nonlinear optics such as all-optical signal processing, electro-optic modulators and frequency conversion. In this work, we have constructed a versatile vacuum deposition system for the creation of organic thin films from these molecules that can be sublimated without decomposition. We have used deposition temperatures of the order of 100--200°C in a high vacuum of 10-6--10 -7 Torrs. While some molecules showed a tendency to form polycrystalline films, others led to very high optical quality films, with a roughness of less than 10 nm over tens of micrometers and no grains detected down to a size of 2 nm, as seen in Atomic Force and Scanning Electron Microscopy studies. The best material we developed has a linear refractive index of 1.8 +/- 0.1 at 1.5 mum and an off-resonant third order susceptibility, chi (3), measured through Degenerate Four Wave Mixing, of 2 +/- 1 x 10-19 m2V-2 at 1.5 mum, a value three orders of magnitude larger than fused silica. This vapor deposited thin film may represent one of the best materials demonstrated to date whereby a large third order susceptibility, high optical quality, and simplicity of fabrication and integration are in perfect harmony for integrated nonlinear optical applications. We have used this novel organic material to create a hybrid organic/silicon-on-insulator waveguide that showed a record high nonlinearity coefficient of 10 5 W-1m-1 and has been used as an all-optical switch for demultiplexing a 120 Gbit/s data stream to 10 Gbit/s on a 6 mm long device.

Do large rate coefficients for ion-polar neutral reactions have a serious effect on chemical models of dense clouds?

NASA Technical Reports Server (NTRS)

Herbst, E.; Leung, C. M.

1986-01-01

In order to incorporate large ion-polar neutral rate coefficients into existing gas phase reaction networks, it is necessary to utilize simplified theoretical treatments because of the significant number of rate coefficients needed. The authors have used two simple theoretical treatments: the locked dipole approach of Moran and Hamill for linear polar neutrals and the trajectory scaling approach of Su and Chesnavich for nonlinear polar neutrals. The former approach is suitable for linear species because in the interstellar medium these are rotationally relaxed to a large extent and the incoming charged reactants can lock their dipoles into the lowest energy configuration. The latter approach is a better approximation for nonlinear neutral species, in which rotational relaxation is normally less severe and the incoming charged reactants are not as effective at locking the dipoles. The treatments are in reasonable agreement with more detailed long range theories and predict an inverse square root dependence on kinetic temperature for the rate coefficient. Compared with the locked dipole method, the trajectory scaling approach results in rate coefficients smaller by a factor of approximately 2.5.

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.

Gamma ray interaction studies of organic nonlinear optical materials in the energy range 122 keV-1330 keV

NASA Astrophysics Data System (ADS)

Awasarmol, V. V.; Gaikwad, D. K.; Raut, S. D.; Pawar, P. P.

The mass attenuation coefficients (μm) for organic nonlinear optical materials measured at 122-1330 keV photon energies were investigated on the basis of mixture rule and compared with obtained values of WinXCOM program. It is observed that there is a good agreement between theoretical and experimental values of the samples. All samples were irradiated with six radioactive sources such as 57Co, 133Ba, 22Na, 137Cs, 54Mn and 60Co using transmission arrangement. Effective atomic and electron numbers or electron densities (Zeff and Neff), molar extinction coefficient (ε), mass energy absorption coefficient (μen/ρ) and effective atomic energy absorption cross section (σa,en) were determined experimentally and theoretically using the obtained μm values for investigated samples and graphs have been plotted. The graph shows that the variation of all samples decreases with increasing photon energy.

Internal friction between fluid particles of MHD tangent hyperbolic fluid with heat generation: Using coefficients improved by Cash and Karp

NASA Astrophysics Data System (ADS)

Salahuddin, T.; Khan, Imad; Malik, M. Y.; Khan, Mair; Hussain, Arif; Awais, Muhammad

2017-05-01

The present work examines the internal resistance between fluid particles of tangent hyperbolic fluid flow due to a non-linear stretching sheet with heat generation. Using similarity transformations, the governing system of partial differential equations is transformed into a coupled non-linear ordinary differential system with variable coefficients. Unlike the current analytical works on the flow problems in the literature, the main concern here is to numerically work out and find the solution by using Runge-Kutta-Fehlberg coefficients improved by Cash and Karp (Naseer et al., Alexandria Eng. J. 53, 747 (2014)). To determine the relevant physical features of numerous mechanisms acting on the deliberated problem, it is sufficient to have the velocity profile and temperature field and also the drag force and heat transfer rate all as given in the current paper.

Breather management in the derivative nonlinear Schrödinger equation with variable coefficients

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

Zhong, Wei-Ping, E-mail: zhongwp6@126.com; Texas A&M University at Qatar, P.O. Box 23874 Doha; Belić, Milivoj

2015-04-15

We investigate breather solutions of the generalized derivative nonlinear Schrödinger (DNLS) equation with variable coefficients, which is used in the description of femtosecond optical pulses in inhomogeneous media. The solutions are constructed by means of the similarity transformation, which reduces a particular form of the generalized DNLS equation into the standard one, with constant coefficients. Examples of bright and dark breathers of different orders, that ride on finite backgrounds and may be related to rogue waves, are presented. - Highlights: • Exact solutions of a generalized derivative NLS equation are obtained. • The solutions are produced by means of amore » transformation to the usual integrable equation. • The validity of the solutions is verified by comparing them to numerical counterparts. • Stability of the solutions is checked by means of direct simulations. • The model applies to the propagation of ultrashort pulses in optical media.« less

A sub-cc nonlinear piezoelectric energy harvester for powering leadless pacemakers

PubMed Central

Ansari, MH; Karami, M Amin

2018-01-01

A miniature nonlinear piezoelectric energy harvester is developed to power state of the art leadless cardiac pacemakers from cardiac motions. The energy harvester is integrated in the leadless pacemaker and is connected to the myocardium. The energy harvester converts myocardial motions to electricity to power leadless pacemakers. The energy is stored in a battery or supercapacitor and is used for pacing. The device is composed of a bimorph piezoelectric beam confined in a gray iron frame. The system is assembled at high temperature and operated at the body temperature. The mismatch in the coefficients of thermal expansion of the beam and the frame causes the beam to buckle in body temperature. This intentional buckling makes the beam unstable and improves the power production and robustness of the device. Having high natural frequency is a major problem in microelectromechanical systems energy harvesters. Considering the small size of the energy harvester, 0.5 cm3, the natural frequency is expected to be high. In our design, the natural frequency is lowered significantly using a buckled beam and a proof mass. Since the beam is buckled, the design is bistable and nonlinear, which could increase the output power. In this article, the device is analytically modeled, and the natural frequencies and mode shapes of the energy harvester are analytically derived. The terms corresponding to geometric nonlinearities are included in the electromechanical coupled governing equations. The simulations show that the device generates sufficient electricity to power leadless pacemakers. PMID:29674842

The development and validation of a numerical integration method for non-linear viscoelastic modeling

PubMed Central

Ramo, Nicole L.; Puttlitz, Christian M.

2018-01-01

Compelling evidence that many biological soft tissues display both strain- and time-dependent behavior has led to the development of fully non-linear viscoelastic modeling techniques to represent the tissue’s mechanical response under dynamic conditions. Since the current stress state of a viscoelastic material is dependent on all previous loading events, numerical analyses are complicated by the requirement of computing and storing the stress at each step throughout the load history. This requirement quickly becomes computationally expensive, and in some cases intractable, for finite element models. Therefore, we have developed a strain-dependent numerical integration approach for capturing non-linear viscoelasticity that enables calculation of the current stress from a strain-dependent history state variable stored from the preceding time step only, which improves both fitting efficiency and computational tractability. This methodology was validated based on its ability to recover non-linear viscoelastic coefficients from simulated stress-relaxation (six strain levels) and dynamic cyclic (three frequencies) experimental stress-strain data. The model successfully fit each data set with average errors in recovered coefficients of 0.3% for stress-relaxation fits and 0.1% for cyclic. The results support the use of the presented methodology to develop linear or non-linear viscoelastic models from stress-relaxation or cyclic experimental data of biological soft tissues. PMID:29293558

Model reduction and frequency residuals for a robust estimation of nonlinearities in subspace identification

NASA Astrophysics Data System (ADS)

De Filippis, G.; Noël, J. P.; Kerschen, G.; Soria, L.; Stephan, C.

2017-09-01

The introduction of the frequency-domain nonlinear subspace identification (FNSI) method in 2013 constitutes one in a series of recent attempts toward developing a realistic, first-generation framework applicable to complex structures. If this method showed promising capabilities when applied to academic structures, it is still confronted with a number of limitations which needs to be addressed. In particular, the removal of nonphysical poles in the identified nonlinear models is a distinct challenge. In the present paper, it is proposed as a first contribution to operate directly on the identified state-space matrices to carry out spurious pole removal. A modal-space decomposition of the state and output matrices is examined to discriminate genuine from numerical poles, prior to estimating the extended input and feedthrough matrices. The final state-space model thus contains physical information only and naturally leads to nonlinear coefficients free of spurious variations. Besides spurious variations due to nonphysical poles, vibration modes lying outside the frequency band of interest may also produce drifts of the nonlinear coefficients. The second contribution of the paper is to include residual terms, accounting for the existence of these modes. The proposed improved FNSI methodology is validated numerically and experimentally using a full-scale structure, the Morane-Saulnier Paris aircraft.

A constitutive model for the warp-weft coupled non-linear behavior of knitted biomedical textiles.

PubMed

Yeoman, Mark S; Reddy, Daya; Bowles, Hellmut C; Bezuidenhout, Deon; Zilla, Peter; Franz, Thomas

2010-11-01

Knitted textiles have been used in medical applications due to their high flexibility and low tendency to fray. Their mechanics have, however, received limited attention. A constitutive model for soft tissue using a strain energy function was extended, by including shear and increasing the number and order of coefficients, to represent the non-linear warp-weft coupled mechanics of coarse textile knits under uniaxial tension. The constitutive relationship was implemented in a commercial finite element package. The model and its implementation were verified and validated for uniaxial tension and simple shear using patch tests and physical test data of uniaxial tensile tests of four very different knitted fabric structures. A genetic algorithm with step-wise increase in resolution and linear reduction in range of the search space was developed for the optimization of the fabric model coefficients. The numerically predicted stress-strain curves exhibited non-linear stiffening characteristic for fabrics. For three fabrics, the predicted mechanics correlated well with physical data, at least in one principal direction (warp or weft), and moderately in the other direction. The model exhibited limitations in approximating the linear elastic behavior of the fourth fabric. With proposals to address this limitation and to incorporate time-dependent changes in the fabric mechanics associated with tissue ingrowth, the constitutive model offers a tool for the design of tissue regenerative knit textile implants. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Sorption of metolachlor and atrazine in fly ash amended soils: comparison of optimized isotherm models.

PubMed

Ghosh, Rakesh K; Singh, Neera

2012-01-01

Adsorption of metolachlor and atrazine was studied in the fly ash (Inderprastha and Badarpur)- amended Inceptisol and Alfisol soils using batch method. Results indicated that sorption of both the herbicides in soil+fly ash mixtures was highly nonlinear and sorption decreased with a higher herbicide concentration in the solution. Also, nonlinearity increased with an increase in the level of fly ash amendment from 0-5%. Three two-parameter monolayer isotherms viz. Langmuir, Temkin, Jovanovic and one imperical Freundlich models were used to fit the experimental data. Data analysis and comparison revealed that the Temkin and the Freundlich isotherms were best-suited to explain the sorption results and the observed and the calculated adsorption coefficient values showed less variability. The study suggested that sorption mechanism of metolachlor and atrazine involved the physical association at the sorbate surface and the nonlinearity in the sorption at higher pesticide or fly ash concentration was due to a decrease in the heat of adsorption and higher binding energy.

Third-order nonlinear optical properties of ADP crystal

NASA Astrophysics Data System (ADS)

Wang, Mengxia; Wang, Zhengping; Chai, Xiangxu; Sun, Yuxiang; Sui, Tingting; Sun, Xun; Xu, Xinguang

2018-05-01

By using the Z-scan method, we investigated the third-order nonlinear optical (NLO) properties of ADP crystal at different wavelengths (355, 532, and 1064 nm) and different orientations ([001], [100], [110], I and II). The experimental data were fitted by NLO theory, to give out the two photon absorption (TPA) coefficient β 2 and the nonlinear refractive index n 2. When the light source changed from a 40 ps, 1064 nm fundamental laser to a 30 ps, 355 nm third-harmonic-generation (THG) laser, the β 2 value increased about 5 times (0.2 × 10‑2 → 1 × 10‑2 cm GW‑1), and the n 2 value increased about 1.5 times (1.5 × 10‑16 → 2.2 × 10‑16 cm2 W‑1). Among all of the orientations, the [110] sample exhibits the smallest β 2, and the second smallest n 2. It indicates that this orientation and its surroundings will be the preferred directions for high-power laser applications of ADP crystal.

Efficient Global Aerodynamic Modeling from Flight Data

NASA Technical Reports Server (NTRS)

Morelli, Eugene A.

2012-01-01

A method for identifying global aerodynamic models from flight data in an efficient manner is explained and demonstrated. A novel experiment design technique was used to obtain dynamic flight data over a range of flight conditions with a single flight maneuver. Multivariate polynomials and polynomial splines were used with orthogonalization techniques and statistical modeling metrics to synthesize global nonlinear aerodynamic models directly and completely from flight data alone. Simulation data and flight data from a subscale twin-engine jet transport aircraft were used to demonstrate the techniques. Results showed that global multivariate nonlinear aerodynamic dependencies could be accurately identified using flight data from a single maneuver. Flight-derived global aerodynamic model structures, model parameter estimates, and associated uncertainties were provided for all six nondimensional force and moment coefficients for the test aircraft. These models were combined with a propulsion model identified from engine ground test data to produce a high-fidelity nonlinear flight simulation very efficiently. Prediction testing using a multi-axis maneuver showed that the identified global model accurately predicted aircraft responses.

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

NASA Astrophysics Data System (ADS)

Cai, Jun; Wang, Kuaishe; Shi, Jiamin; Wang, Wen; Liu, Yingying

2018-01-01

Constitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress-strain data from isothermal hot compression tests, in a wide range of temperature of 1,023 1,273 K, and strain rate range of 0.001 10 s-1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

Linear and nonlinear optical characteristics of Te nanoparticles-doped germanate glasses

NASA Astrophysics Data System (ADS)

Xu, Zhousu; Guo, Qiangbing; Liu, Chang; Ma, Zhijun; Liu, Xiaofeng; Qiu, Jianrong

2016-10-01

Te nanoparticles (NPs)-doped GeO2-MgO-B2O3-Al2O3-TeO2 glasses were prepared by the conventional melt-quenching method. Based on X-ray photoelectron spectroscopy, Raman spectroscopy and transmission electron microscope observation, the coloration of the glass at high TeO2 concentration is ascribed to the precipitation of elemental Te NPs with a size of 5-10 nm in the germanate glass. Optical absorption spectra and nonlinear optical (NLO) properties of the glass samples were analyzed by UV-3600 spectrophotometry and Z-scan technique, respectively. The nonlinear absorption coefficient ( β) and the imaginary part of the third-order NLO susceptibility (Im χ (3)) were estimated to be 1.74 cm/GW and 1.142 × 10-12 esu for laser power of 95 μW, respectively. Due to the excellent NLO properties, the Te NPs-doped germanate glasses may have potential applications for ultrafast optical switch and photonics.

User Selection Criteria of Airspace Designs in Flexible Airspace Management

NASA Technical Reports Server (NTRS)

Lee, Hwasoo E.; Lee, Paul U.; Jung, Jaewoo; Lai, Chok Fung

2011-01-01

A method for identifying global aerodynamic models from flight data in an efficient manner is explained and demonstrated. A novel experiment design technique was used to obtain dynamic flight data over a range of flight conditions with a single flight maneuver. Multivariate polynomials and polynomial splines were used with orthogonalization techniques and statistical modeling metrics to synthesize global nonlinear aerodynamic models directly and completely from flight data alone. Simulation data and flight data from a subscale twin-engine jet transport aircraft were used to demonstrate the techniques. Results showed that global multivariate nonlinear aerodynamic dependencies could be accurately identified using flight data from a single maneuver. Flight-derived global aerodynamic model structures, model parameter estimates, and associated uncertainties were provided for all six nondimensional force and moment coefficients for the test aircraft. These models were combined with a propulsion model identified from engine ground test data to produce a high-fidelity nonlinear flight simulation very efficiently. Prediction testing using a multi-axis maneuver showed that the identified global model accurately predicted aircraft responses.

The linear -- non-linear frontier for the Goldstone Higgs

DOE PAGES

Gavela, M. B.; Kanshin, K.; Machado, P. A. N.; ...

2016-12-01

The minimalmore » $SO(5)/SO(4)$ sigma model is used as a template for the ultraviolet completion of scenarios in which the Higgs particle is a low-energy remnant of some high-energy dynamics, enjoying a (pseudo) Nambu-Goldstone boson ancestry. Varying the $$\\sigma$$ mass allows to sweep from the perturbative regime to the customary non-linear implementations. The low-energy benchmark effective non-linear Lagrangian for bosons and fermions is obtained, determining as well the operator coefficients including linear corrections. At first order in the latter, three effective bosonic operators emerge which are independent of the explicit soft breaking assumed. The Higgs couplings to vector bosons and fermions turn out to be quite universal: the linear corrections are proportional to the explicit symmetry breaking parameters. Furthermore, we define an effective Yukawa operator which allows a simple parametrization and comparison of different heavy fermion ultraviolet completions. In addition, one particular fermionic completion is explored in detail, obtaining the corresponding leading low-energy fermionic operators.« less

Performance of thermal deposition and mass flux condition on bioconvection nanoparticles containing gyrotactic microorganisms

NASA Astrophysics Data System (ADS)

Iqbal, Z.; Ahmad, Bilal

2017-11-01

This is an attempt to investigate the influence of thermal radiation on the movement of motile gyrotactic microorganisms submerged in a water-based nanofluid flow over a nonlinear stretching sheet. The mathematical modeling of this physical problem leads to a system of nonlinear coupled partial differential equations. The problem is tackled by converting nonlinear partial differential equations into the system of highly nonlinear ordinary differential equations. The resulting nonlinear equations of momentum, energy, concentration of nanoparticles and motile gyrotactic microorganisms along with the mass flux condition are solved numerically by means of a shooting algorithm. The effects of the involved physical parameters of interest are discussed graphically. The values of the skin friction coefficient, Nusselt number, Sherwood number and local density number of motile microorganisms are tabulated for detailed analysis on the flow pattern at the stretching surface. It is concluded that the nanofluid temperature is an increasing function of the thermal radiation and the Biot number parameter. An opposite trend is observed for the local Nusselt number. The association with the preceding results in limiting sense is shown as well. A tremendous agreement of the current study in a restrictive manner is achieved as well. In addition, flow configurations through stream functions are presented and deliberated significantly.

Nonlinear closures for scale separation in supersonic magnetohydrodynamic turbulence

NASA Astrophysics Data System (ADS)

Grete, Philipp; Vlaykov, Dimitar G.; Schmidt, Wolfram; Schleicher, Dominik R. G.; Federrath, Christoph

2015-02-01

Turbulence in compressible plasma plays a key role in many areas of astrophysics and engineering. The extreme plasma parameters in these environments, e.g. high Reynolds numbers, supersonic and super-Alfvenic flows, however, make direct numerical simulations computationally intractable even for the simplest treatment—magnetohydrodynamics (MHD). To overcome this problem one can use subgrid-scale (SGS) closures—models for the influence of unresolved, subgrid-scales on the resolved ones. In this work we propose and validate a set of constant coefficient closures for the resolved, compressible, ideal MHD equations. The SGS energies are modeled by Smagorinsky-like equilibrium closures. The turbulent stresses and the electromotive force (EMF) are described by expressions that are nonlinear in terms of large scale velocity and magnetic field gradients. To verify the closures we conduct a priori tests over 137 simulation snapshots from two different codes with varying ratios of thermal to magnetic pressure ({{β }p}=0.25,1,2.5,5,25) and sonic Mach numbers ({{M}s}=2,2.5,4). Furthermore, we make a comparison to traditional, phenomenological eddy-viscosity and α -β -γ closures. We find only mediocre performance of the kinetic eddy-viscosity and α -β -γ closures, and that the magnetic eddy-viscosity closure is poorly correlated with the simulation data. Moreover, three of five coefficients of the traditional closures exhibit a significant spread in values. In contrast, our new closures demonstrate consistently high correlations and constant coefficient values over time and over the wide range of parameters tested. Important aspects in compressible MHD turbulence such as the bi-directional energy cascade, turbulent magnetic pressure and proper alignment of the EMF are well described by our new closures.

Modulation of localized solutions in a system of two coupled nonlinear Schrödinger equations.

PubMed

Cardoso, W B; Avelar, A T; Bazeia, D

2012-08-01

In this work we study localized solutions of a system of two coupled nonlinear Schrödinger equations, with the linear (potential) and nonlinear coefficients engendering spatial and temporal dependencies. Similarity transformations are used to convert the nonautonomous coupled equations into autonomous ones and we use the trial orbit method to help us solving them, presenting solutions in a general way. Numerical experiments are then used to verify the stability of the localized solutions.

Bistability in mushroom-type metamaterials

NASA Astrophysics Data System (ADS)

Fernandes, David E.; Silveirinha, Mário G.

2017-07-01

Here, we study the electromagnetic response of asymmetric mushroom-type metamaterials loaded with nonlinear elements. It is shown that near a Fano resonance, these structures may have a strong tunable, bistable, and switchable response and enable giant nonlinear effects. By using an effective medium theory and full wave simulations, it is proven that the nonlinear elements may allow the reflection and transmission coefficients to follow hysteresis loops, and to switch the metamaterial between "go" and "no-go" states similar to an ideal electromagnetic switch.

Large-eddy simulation of laminar-turbulent breakdown at high speeds with dynamic subgrid-scale modeling

NASA Technical Reports Server (NTRS)

El-Hady, Nabil M.

1993-01-01

The laminar-turbulent breakdown of a boundary-layer flow along a hollow cylinder at Mach 4.5 is investigated with large-eddy simulation. The subgrid scales are modeled dynamically, where the model coefficients are determined from the local resolved field. The behavior of the dynamic-model coefficients is investigated through both an a priori test with direct numerical simulation data for the same case and a complete large-eddy simulation. Both formulations proposed by Germano et al. and Lilly are used for the determination of unique coefficients for the dynamic model and their results are compared and assessed. The behavior and the energy cascade of the subgrid-scale field structure are investigated at various stages of the transition process. The investigations are able to duplicate a high-speed transition phenomenon observed in experiments and explained only recently by the direct numerical simulations of Pruett and Zang, which is the appearance of 'rope-like' waves. The nonlinear evolution and breakdown of the laminar boundary layer and the structure of the flow field during the transition process were also investigated.

A new cellular automata model of traffic flow with negative exponential weighted look-ahead potential

NASA Astrophysics Data System (ADS)

Ma, Xiao; Zheng, Wei-Fan; Jiang, Bao-Shan; Zhang, Ji-Ye

2016-10-01

With the development of traffic systems, some issues such as traffic jams become more and more serious. Efficient traffic flow theory is needed to guide the overall controlling, organizing and management of traffic systems. On the basis of the cellular automata model and the traffic flow model with look-ahead potential, a new cellular automata traffic flow model with negative exponential weighted look-ahead potential is presented in this paper. By introducing the negative exponential weighting coefficient into the look-ahead potential and endowing the potential of vehicles closer to the driver with a greater coefficient, the modeling process is more suitable for the driver’s random decision-making process which is based on the traffic environment that the driver is facing. The fundamental diagrams for different weighting parameters are obtained by using numerical simulations which show that the negative exponential weighting coefficient has an obvious effect on high density traffic flux. The complex high density non-linear traffic behavior is also reproduced by numerical simulations. Project supported by the National Natural Science Foundation of China (Grant Nos. 11572264, 11172247, 11402214, and 61373009).

Development and characterization of a tissue-mimicking material for high-intensity focused ultrasound.

PubMed

King, Randy L; Liu, Yunbo; Maruvada, Subha; Herman, Bruce A; Wear, Keith A; Harris, Gerald R

2011-07-01

A tissue-mimicking material (TMM) for the acoustic and thermal characterization of high-intensity focused ultrasound (HIFU) devices has been developed. The material is a high-temperature hydrogel matrix (gellan gum) combined with different sizes of aluminum oxide particles and other chemicals. The ultrasonic properties (attenuation coefficient, speed of sound, acoustical impedance, and the thermal conductivity and diffusivity) were characterized as a function of temperature from 20 to 70°C. The backscatter coefficient and nonlinearity parameter B/A were measured at room temperature. Importantly, the attenuation coefficient has essentially linear frequency dependence, as is the case for most mammalian tissues at 37°C. The mean value is 0.64f(0.95) dB·cm(-1) at 20°C, based on measurements from 2 to 8 MHz. Most of the other relevant physical parameters are also close to the reported values, although backscatter signals are low compared with typical human soft tissues. Repeatable and consistent temperature elevations of 40°C were produced under 20-s HIFU exposures in the TMM. This TMM is appropriate for developing standardized dosimetry techniques, validating numerical models, and determining the safety and efficacy of HIFU devices.

Dust Acoustic Solitary Waves in Dusty Plasma with Trapped Electrons Having Different Temperature Nonthermal Ions

NASA Astrophysics Data System (ADS)

Deka, Manoj Kr.

2016-12-01

In this report, a detailed investigation on the study of dust acoustics solitary waves solution with negatively dust charge fluctuation in dusty plasma corresponding to lower and higher temperature nonthermal ions with trapped electrons is presented. We consider temporal variation of dust charge as a source of dissipation term to derive the lower order modified Kadomtsev-Petviashvili equation by using the reductive perturbation technique. Solitary wave solution is obtained with the help of sech method in presence of trapped electrons and low (and high) temperature nonthermal ions. Both nonthermality of ions and trapped state of the electrons are found to have an imperative control on the nonlinear coefficient, dissipative coefficient as well as height of the wave potential.

Prediction of Battery Life and Behavior from Analysis of Voltage Data

NASA Technical Reports Server (NTRS)

Mcdermott, P. P.

1984-01-01

A method for simulating charge and discharge characteristics of secondary batteries is discussed. The analysis utilizes a nonlinear regression technique where empirical data is computer fitted with a five coefficient nonlinear equation. The equations for charge and discharge voltage are identical except for a change of sign before the second and third terms.

Alignment of large image series using cubic B-splines tessellation: application to transmission electron microscopy data.

PubMed

Dauguet, Julien; Bock, Davi; Reid, R Clay; Warfield, Simon K

2007-01-01

3D reconstruction from serial 2D microscopy images depends on non-linear alignment of serial sections. For some structures, such as the neuronal circuitry of the brain, very large images at very high resolution are necessary to permit reconstruction. These very large images prevent the direct use of classical registration methods. We propose in this work a method to deal with the non-linear alignment of arbitrarily large 2D images using the finite support properties of cubic B-splines. After initial affine alignment, each large image is split into a grid of smaller overlapping sub-images, which are individually registered using cubic B-splines transformations. Inside the overlapping regions between neighboring sub-images, the coefficients of the knots controlling the B-splines deformations are blended, to create a virtual large grid of knots for the whole image. The sub-images are resampled individually, using the new coefficients, and assembled together into a final large aligned image. We evaluated the method on a series of large transmission electron microscopy images and our results indicate significant improvements compared to both manual and affine alignment.

Nonlinear guiding of picosecond CO2 laser pulses in atmosphere(Conference Presentation)

NASA Astrophysics Data System (ADS)

Tochitsky, Sergei

2017-05-01

During the last 20 years much attention has been given to the study of propagation of short intense laser pulses for which the peak power exceeds the critical power of self-focusing, Pcr. For a laser power P < Pcr, a dynamic equilibrium between the Kerr self-focusing, diffraction and defocusing caused by laser-ionized plasma result in the production of a high intensity laser filament in air within which a variety of nonlinear optical phenomena are observed. However, research in the 0.8-1 μm range so far has shown a fundamental limitation of guided energy to a few mJ transported within an 100 μm single channel. A long-wavelength, 0 10 μm CO2 laser is a promising candidate for nonlinear guiding because expected high Pcr values according to the modeling should allow for the increase of energy (and therefore power) in a self-guided beam from mJ (GW) to few Joules (TW). During the last decade a significant progress has been achieved in amplification of picosecond pulses to terawatt and recently to <10 TW power level at UCLA and ATF BNL. Such powerful 10 μm lasers open possibility for nonlinear propagation studies in an atmospheric window with high transmission. As a natural first step in a our program on picosecond CO2 laser filamentation, we have made first measurements of Kerr coefficients of air and air constituents around 10 μm. We also undertook direct measurements of n2 of air by analyzing nonlinear self-focusing in air using a 3 ps, 600 GW pulses of the BNL CO2 laser.

Polarization-selective three-photon absorption and subsequent photoluminescence in CsPbBr3 single crystal at room temperature

NASA Astrophysics Data System (ADS)

Clark, D. J.; Stoumpos, C. C.; Saouma, F. O.; Kanatzidis, M. G.; Jang, J. I.

2016-05-01

We report on highly polarization-selective three-photon absorption (3PA) in a Bridgman-grown single crystal of CsPbBr3 oriented along the (112) direction, which is an inorganic counterpart to emerging organic-inorganic hybrid halide perovskites for solar-cell and optoelectronic applications. The crystal exhibits strong photoluminescence (PL) at room temperature as a direct consequence of 3PA of fundamental radiation. Interestingly, 3PA disappears when the input polarization is parallel to the (-110 ) direction. This 3PA effect is strongest when orthogonal to (-110 ) and the corresponding 3PA coefficient was measured to be γ =0.14 ±0.03 cm3/GW2 under picosecond-pulse excitation at the fundamental wavelength of λ =1200 nm. The laser-induced damage threshold was also determined to be about 20 GW/cm2 at the same wavelength. Based on relative PL intensities upon λ tuning over the entire 3PA range (1100 -1700 nm), we determined the nonlinear optical dispersion of the 3PA coefficient for CsPbBr3, which is consistent with a theoretical prediction. Experimentally observed significant polarization dependence of γ was explained by relevant selection rules. The perovskite is potentially important for nonlinear optical applications owing to its highly efficient 3PA-induced PL response with a sharp on/off ratio by active polarization control.

The effect of external magnetic field on the bremsstrahlung nonlinear absorption mechanism in the interaction of high intensity short laser pulse with collisional underdense plasma

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

Sedaghat, M.; Ettehadi-Abari, M.; Shokri, B., E-mail: b-shokri@sbu.ac.ir

2015-03-15

Laser absorption in the interaction between ultra-intense femtosecond laser and solid density plasma is studied theoretically here in the intensity range Iλ{sup 2}≃10{sup 14}−10{sup 16}Wcm{sup −2}μm{sup 2}. The collisional effect is found to be significant when the incident laser intensity is less than 10{sup 16}Wcm{sup −2}μm{sup 2}. In the current work, the propagation of a high frequency electromagnetic wave, for underdense collisional plasma in the presence of an external magnetic field is investigated. It is shown that, by considering the effect of the ponderomotive force in collisional magnetized plasmas, the increase of laser pulse intensity leads to steepening of themore » electron density profile and the electron bunches of plasma makes narrower. Moreover, it is found that the wavelength of electric and magnetic fields oscillations increases by increasing the external magnetic field and the density distribution of electrons also grows in comparison with the unmagnetized collisional plasma. Furthermore, the spatial damping rate of laser energy and the nonlinear bremsstrahlung absorption coefficient are obtained in the collisional regime of magnetized plasma. The other remarkable result is that by increasing the external magnetic field in this case, the absorption coefficient increases strongly.« less

Photorefractive Nonlinear Optics

DTIC Science & Technology

1991-01-15

conjugate interferometer for the measurement of thin film thickness, refractive index and absorption coefficients. Also, we have investigated...conjugate interferometer for the measurement of thin film thickness, refractive index and absorption coefficients. Also, we have investigated...interaction by considering the refractive index grating as a linear superposition of the gratings from each of the frequency components of the

Dynamic modification of optical nonlinearities related to femtosecond laser filamentation in gases

NASA Astrophysics Data System (ADS)

Romanov (1, 3), Dmitri; Tarazkar (2, 3), Maryam; Levis (2, 3), Robert

2017-04-01

During and immediately after the passing of a filamenting laser pulse through a gas-phase medium, the nonlinear optical characteristics of the emerging filament-wake channel undergo substantial transient modification, which stems from ionization and electronic excitation of constituent atoms/molecules. We calculate the related hyperpolarizability coefficients of individual ions, and we develop a theoretical model of filament channel evolution applicable to atmospheric-pressure and high-pressure gases. The evolution is mediated by energetic free-electron gas that results from the strong-field ionization and gains considerable energy via inverse Bremsstrahlung process. The ensuing impact ionization and excitation of the residual neutral atoms/molecules proceeds inhomogeneously both inside the channel and on its surface, being strongly influenced by the thermal conduction of the electron gas. The model shows critical importance of channel-surface effects, especially as regards the effective electron temperature. The calculated spatial-temporal evolution patterns ultimately determine the transient modifications of linear and nonlinear optical properties of filament wake channels. Medium-specific estimates are made for atmospheric- and high-pressure argon, as well as for molecular nitrogen gas. Support of Defense Threat Reduction Agency (Grant No. HDTRA1-12-1-0014) is gratefully acknowledged.

Flow and Heat Transfer in a Newtonian Nanoliquid due to a Curved Stretching Sheet

NASA Astrophysics Data System (ADS)

Siddheshwar, Pradeep Ganapathi; Nerolu, Meenakshi; Pažanin, Igor

2017-08-01

Flow of a Newtonian nanoliquid due to a curved stretching sheet and heat transfer in it is studied. The governing nonlinear partial differential equations are reduced to nonlinear ordinary differential equations with variable coefficients by using a similarity transformation. The flow characteristics are studied using plots of flow velocity components and the skin-friction coefficient as a function of suction-injection parameter, curvature, and volume fraction. Prescribed surface temperature and prescribed surface heat flux are considered for studying the temperature distribution in the flow. The thermophysical properties of 20 nanoliquids are considered in the investigation by modeling them through the use of phenomenological laws and mixture theory. The results of the corresponding problem involving a plane stretching sheet is obtained as a particular case of those obtained in the present paper. Skin friction coefficient and Nusselt number are evaluated and it is observed that skin friction coefficient decreases with concentration of nanoparticles in the absence as well as presence of suction where as Nusselt number increases with increase in concentration of nanoparticles in a dilute range.

Optical Nonlinearities in Semiconductors for Limiting.

NASA Astrophysics Data System (ADS)

Wu, Yuan-Yen

I have conducted detailed experimental and theoretical studies of the nonlinear optical properties of semiconductor materials useful for optical limiting. I have constructed optical limiters utilizing two-photon absorption along with photogenerated carrier defocusing as well as the bound electronic nonlinearity using the semiconducting material ZnSe. I have optimized the focusing geometry to achieve a large dynamic range while maintaining a low limiting energy for the device. The ZnSe monolithic optical limiter has achieved a limiting energy as low as 13 nJ (corresponding to 300W peak power) and a dynamic range as large as 10 ^5 at 532 nm using psec pulses. Theoretical analysis showed that the ZnSe device has a broad-band response covering the wavelength range from 550 nm to 800 nm. Moreover, I found that existing theoretical models (e.g. the Auston model and the band-resonant model using Boltzmann statistics) adequately describe the photo-generated carriers refractive nonlinearity in ZnSe. Material nonlinear optical parameters, such as the two-photon absorption coefficient beta _2 = 5.5 cm/GW, the refraction per unit carrier density sigma_{rm n} = -0.8cdot 10^ {-21}cm^3 and the bound electronic refraction n_2 = -4cdot 10^{ -11}esu, have been measured via time-integrated beam distortion experiments in the near field. A numerical code has been written to simulate the beam distortion in order to extract the previously mentioned material parameters. In addition, I have performed time-resolved distortion measurements that provide an intuitive picture of the carrier generation process via two-photon absorption. I also characterized the optical nonlinearities in a ZnSe Fabry-Perot thin film structure (an interference filter). I concluded that the nonlinear absorption alone in the thin film is insufficient to build an effective optical limiter, as it did not show a net change in refraction using psec pulses. An innovative numerical program was developed to simulate the nonlinear beam propagation inside the Fabry-Perot structure. For comparison, pump-probe experiments were performed using both thin film and bulk ZnSe. The results showed relatively long carrier lifetimes (>300 psec) in both samples. A numerical code was written to fit the pump-probe experimental results. The fitting yielded that carrier lifetimes (recombination through traps), radiative decay rate, two-photon absorption coefficient as well as the free carrier absorption coefficient for ZnSe bulk material.

Enhanced diffusion on oscillating surfaces through synchronization

NASA Astrophysics Data System (ADS)

Wang, Jin; Cao, Wei; Ma, Ming; Zheng, Quanshui

2018-02-01

The diffusion of molecules and clusters under nanoscale confinement or absorbed on surfaces is the key controlling factor in dynamical processes such as transport, chemical reaction, or filtration. Enhancing diffusion could benefit these processes by increasing their transport efficiency. Using a nonlinear Langevin equation with an extensive number of simulations, we find a large enhancement in diffusion through surface oscillation. For helium confined in a narrow carbon nanotube, the diffusion enhancement is estimated to be over three orders of magnitude. A synchronization mechanism between the kinetics of the particles and the oscillating surface is revealed. Interestingly, a highly nonlinear negative correlation between diffusion coefficient and temperature is predicted based on this mechanism, and further validated by simulations. Our results provide a general and efficient method for enhancing diffusion, especially at low temperatures.

Quantum treatment of field propagation in a fiber near the zero dispersion wavelength

NASA Astrophysics Data System (ADS)

Safaei, A.; Bassi, A.; Bolorizadeh, M. A.

2018-05-01

In this report, we present a quantum theory describing the propagation of the electromagnetic radiation in a fiber in the presence of the third order dispersion coefficient. We obtained the quantum photon-polariton field, hence, we provide herein a coupled set of operator forms for the corresponding nonlinear Schrödinger equations when the third order dispersion coefficient is included. Coupled stochastic nonlinear Schrödinger equations were obtained by applying a positive P-representation that governs the propagation and interaction of quantum solitons in the presence of the third-order dispersion term. Finally, to reduce the fluctuations near solitons in the first approximation, we developed coupled stochastic linear equations.

Dark-dark solitons for a coupled variable-coefficient higher-order nonlinear Schrödinger system in an inhomogeneous optical fiber

NASA Astrophysics Data System (ADS)

Li, Ming-Zhen; Tian, Bo; Qu, Qi-Xing; Chai, Han-Peng; Liu, Lei; Du, Zhong

2017-12-01

In this paper, under investigation is a coupled variable-coefficient higher-order nonlinear Schrödinger system, which describes the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the Lax pair and binary Darboux transformation, we present the nondegenerate N-dark-dark soliton solutions. With the graphical simulation, soliton propagation and interaction are discussed with the group velocity dispersion and fourth-order dispersion effects, which affect the velocity but have no effect on the amplitude. Linear, parabolic and periodic one dark-dark solitons are displayed. Interactions between the two solitons are presented as well, which are all elastic.

Sound Propagation in Gas-Vapor-Droplet Suspensions with Evaporation and Nonlinear Particle Relaxation

NASA Technical Reports Server (NTRS)

Kandula, Max

2012-01-01

The Sound attenuation and dispersion in saturated gas-vapor-droplet mixture in the presence of evaporation has been investigated theoretically. The theory is based on an extension of the work of Davidson to accommodate the effects of nonlinear particle relaxation processes of mass, momentum and energy transfer on sound attenuation and dispersion. The results indicate the existence of a spectral broadening effect in the attenuation coefficient (scaled with respect to the peak value) with a decrease in droplet mass concentration. It is further shown that for large values of the droplet concentration the scaled attenuation coefficient is characterized by a universal spectrum independent of droplet mass concentration.

Thermal expansion behavior study of Co nanowire array with in situ x-ray diffraction and x-ray absorption fine structure techniques

NASA Astrophysics Data System (ADS)

Mo, Guang; Cai, Quan; Jiang, Longsheng; Wang, Wei; Zhang, Kunhao; Cheng, Weidong; Xing, Xueqing; Chen, Zhongjun; Wu, Zhonghua

2008-10-01

In situ x-ray diffraction and x-ray absorption fine structure techniques were used to study the structural change of ordered Co nanowire array with temperature. The results show that the Co nanowires are polycrystalline with hexagonal close packed structure without phase change up until 700 °C. A nonlinear thermal expansion behavior has been found and can be well described by a quadratic equation with the first-order thermal expansion coefficient of 4.3×10-6/°C and the second-order thermal expansion coefficient of 5.9×10-9/°C. The mechanism of this nonlinear thermal expansion behavior is discussed.

Internal rotor friction instability

NASA Technical Reports Server (NTRS)

Walton, J.; Artiles, A.; Lund, J.; Dill, J.; Zorzi, E.

1990-01-01

The analytical developments and experimental investigations performed in assessing the effect of internal friction on rotor systems dynamic performance are documented. Analytical component models for axial splines, Curvic splines, and interference fit joints commonly found in modern high speed turbomachinery were developed. Rotor systems operating above a bending critical speed were shown to exhibit unstable subsynchronous vibrations at the first natural frequency. The effect of speed, bearing stiffness, joint stiffness, external damping, torque, and coefficient of friction, was evaluated. Testing included material coefficient of friction evaluations, component joint quantity and form of damping determinations, and rotordynamic stability assessments. Under conditions similar to those in the SSME turbopumps, material interfaces experienced a coefficient of friction of approx. 0.2 for lubricated and 0.8 for unlubricated conditions. The damping observed in the component joints displayed nearly linear behavior with increasing amplitude. Thus, the measured damping, as a function of amplitude, is not represented by either linear or Coulomb friction damper models. Rotordynamic testing of an axial spline joint under 5000 in.-lb of static torque, demonstrated the presence of an extremely severe instability when the rotor was operated above its first flexible natural frequency. The presence of this instability was predicted by nonlinear rotordynamic time-transient analysis using the nonlinear component model developed under this program. Corresponding rotordynamic testing of a shaft with an interference fit joint demonstrated the presence of subsynchronous vibrations at the first natural frequency. While subsynchronous vibrations were observed, they were bounded and significantly lower in amplitude than the synchronous vibrations.

Damage Characterization and Real-Time Health Monitoring of Aerospace Materials Using Innovative NDE Tools

NASA Astrophysics Data System (ADS)

Matikas, Theodore E.

2010-07-01

The objective of this work is to characterize the damage and monitor in real-time aging structural components used in aerospace applications by means of advanced nondestructive evaluation techniques. Two novel experimental methodologies are used in this study, based on ultrasonic microscopy and nonlinear acoustics. It is demonstrated in this work that ultrasonic microscopy can be successfully utilized for local elastic property measurement, crack-size determination as well as for interfacial damage evaluation in high-temperature materials, such as metal matrix composites. Nonlinear acoustics enables real-time monitoring of material degradation in aerospace structures. When a sinusoidal ultrasonic wave of a given frequency and of sufficient amplitude is introduced into a nonharmonic solid, the fundamental wave distorts as it propagates, and therefore the second and higher harmonics of the fundamental frequency are generated. Measurements of the amplitude of these harmonics provide information on the coefficient of second- and higher-order terms of the stress-strain relation for a nonlinear solid. It is shown in this article that the material bulk nonlinear parameter for metallic alloy samples at different fatigue levels exhibits large changes compared to linear ultrasonic parameters, such as velocity and attenuation.

Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation

NASA Astrophysics Data System (ADS)

Popescu, Mihaela; Shyy, Wei; Garbey, Marc

2005-12-01

In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.

A Multiphase Non-Linear Mixed Effects Model: An Application to Spirometry after Lung Transplantation

PubMed Central

Rajeswaran, Jeevanantham; Blackstone, Eugene H.

2014-01-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time varying coefficients. PMID:24919830

Theoretical and Analog Studies of the Effects of Nonlinear Stability Derivatives on the Longitudinal Motions of an Aircraft in Response to Step Control Deflections and to the Influence of Proportional Automatic Control

NASA Technical Reports Server (NTRS)

Curfman, Howard J , Jr

1955-01-01

Through theoretical and analog results the effects of two nonlinear stability derivatives on the longitudinal motions of an aircraft have been investigated. Nonlinear functions of pitching-moment and lift coefficients with angle of attack were considered. Analog results of aircraft motions in response to step elevator deflections and to the action of the proportional control systems are presented. The occurrence of continuous hunting oscillations was predicted and demonstrated for the attitude stabilization system with proportional control for certain nonlinear pitching-moment variations and autopilot adjustments.

Determination of the major groups of phytoplankton pigments from the absorption spectra of total particulate matter

NASA Technical Reports Server (NTRS)

Hoepffner, Nicolas; Sathyendranath, Shubha

1993-01-01

The contributions of detrital particles and phytoplankton to total light absorption are retrieved by nonlinear regression on the absorption spectra of total particles from various oceanic regions. The model used explains more than 96% of the variance in the observed particle absorption spectra. The resulting absorption spectra of phytoplankton are then decomposed into several Gaussian bands reflecting absorption by phytoplankton pigments. Such a decomposition, combined with high-performance liquid chromatography data on phytoplankton pigment concentrations, allows the computation of specific absorption coefficients for chlorophylls a, b, and c and carotenoids. The spectral values of these in vivo absorption coefficients are then discussed, considering the effects of secondary pigments which were not measured quantitatively. We show that these coefficients can be used to reconstruct the absorption spectra of phytoplankton at various locations and depths. Discrepancies that do occur at some stations are explained in terms of particle size effect. These coefficients can be used to determine the concentrations of phytoplankton pigments in the water, given the absorption spectrum of total particles.

Simulation program of nonlinearities applied to telecommunication systems

NASA Technical Reports Server (NTRS)

Thomas, C.

1979-01-01

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

Two-photon interband absorption coefficients in tungstate and molybdate crystals

NASA Astrophysics Data System (ADS)

Lukanin, V. I.; Karasik, A. Ya.

2015-02-01

Two-photon absorption (TPA) coefficients were measured in tungstate and molybdate crystals - BaWO4, KGW, CaMoO4, BaMoO4, CaWO4, PbWO4 and ZnWO4 upon different orientations of excitation polarization with respect to the crystallographic axes. Trains of 25 ps pulses with variable radiation intensities of third (349 nm) harmonics of passively mode-locked 1047 nm Nd:YLF laser were used for interband two-photon excitation of the crystals. It was suggested that in the case, when 349 nm radiation pumping energy exceeds the bandgap width (hν>Eg), the nonlinear excitation process can be considered as two-step absorption. The interband two-photon absorption in all the studied crystals induces the following one-photon absorption from the exited states, which affects the nonlinear process dynamics and leads to a hysteresis in the dependence of the transmission on the excitation intensity. This fact was taken into account under analysis of the experimental dependences of the reciprocal transmission on the excitation intensity. Laser excitation in the transparency region of the crystals caused stimulated Raman scattering (SRS) not for all the crystals studied. The measured nonlinear coefficients allowed us to explain the suppression of SRS in crystals as a result of competition between the SRS and TPA.

The analysis of harmonic generation coefficients in the ablative Rayleigh-Taylor instability

NASA Astrophysics Data System (ADS)

Lu, Yan; Fan, Zhengfeng; Lu, Xinpei; Ye, Wenhua; Zou, Changlin; Zhang, Ziyun; Zhang, Wen

2017-10-01

In this research, we use the numerical simulation method to investigate the generation coefficients of the first three harmonics and the zeroth harmonic in the Ablative Rayleigh-Taylor Instability. It is shown that the interface shifts to the low temperature side during the ablation process. In consideration of the third-order perturbation theory, the first three harmonic amplitudes of the weakly nonlinear regime are calculated and then the harmonic generation coefficients are obtained by curve fitting. The simulation results show that the harmonic generation coefficients changed with time and wavelength. Using the higher-order perturbation theory, we find that more and more harmonics are generated in the later weakly nonlinear stage, which is caused by the negative feedback of the later higher harmonics. Furthermore, extending the third-order theory to the fifth-order theory, we find that the second and the third harmonics coefficients linearly depend on the wavelength, while the feedback coefficients are almost constant. Further analysis also shows that when the fifth-order theory is considered, the normalized effective amplitudes of second and third harmonics can reach about 25%-40%, which are only 15%-25% in the frame of the previous third-order theory. Therefore, the third order perturbation theory is needed to be modified by the higher-order theory when ηL reaches about 20% of the perturbation wavelength.

Tuning the nonlinear optical absorption of reduced graphene oxide by chemical reduction.

PubMed

Shi, Hongfei; Wang, Can; Sun, Zhipei; Zhou, Yueliang; Jin, Kuijuan; Redfern, Simon A T; Yang, Guozhen

2014-08-11

Reduced graphene oxides with varying degrees of reduction have been produced by hydrazine reduction of graphene oxide. The linear and nonlinear optical properties of both graphene oxide as well as the reduced graphene oxides have been measured by single beam Z-scan measurement in the picosecond region. The results reveal both saturable absorption and two-photon absorption, strongly dependent on the intensity of the pump pulse: saturable absorption occurs at lower pump pulse intensity (~1.5 GW/cm2 saturation intensity) whereas two-photon absorption dominates at higher intensities (≥5.7 GW/cm2). Intriguingly, we find that the two-photon absorption coefficient (from 1.5 cm/GW to 4.5cm/GW) and the saturation intensity (from 1 GW/cm2 to 2 GW/cm2) vary with chemical reduction, which is ascribed to the varying concentrations of sp2 domains and sp2 clusters in the reduced graphene oxides. Our results not only provide an insight into the evolution of the nonlinear optical coefficient in reduced graphene oxide, but also suggest that chemical engineering techniques may usefully be applied to tune the nonlinear optical properties of various nano-materials, including atomically thick graphene sheets.

Testing of next-generation nonlinear calibration based non-uniformity correction techniques using SWIR devices

NASA Astrophysics Data System (ADS)

Lovejoy, McKenna R.; Wickert, Mark A.

2017-05-01

A known problem with infrared imaging devices is their non-uniformity. This non-uniformity is the result of dark current, amplifier mismatch as well as the individual photo response of the detectors. To improve performance, non-uniformity correction (NUC) techniques are applied. Standard calibration techniques use linear, or piecewise linear models to approximate the non-uniform gain and off set characteristics as well as the nonlinear response. Piecewise linear models perform better than the one and two-point models, but in many cases require storing an unmanageable number of correction coefficients. Most nonlinear NUC algorithms use a second order polynomial to improve performance and allow for a minimal number of stored coefficients. However, advances in technology now make higher order polynomial NUC algorithms feasible. This study comprehensively tests higher order polynomial NUC algorithms targeted at short wave infrared (SWIR) imagers. Using data collected from actual SWIR cameras, the nonlinear techniques and corresponding performance metrics are compared with current linear methods including the standard one and two-point algorithms. Machine learning, including principal component analysis, is explored for identifying and replacing bad pixels. The data sets are analyzed and the impact of hardware implementation is discussed. Average floating point results show 30% less non-uniformity, in post-corrected data, when using a third order polynomial correction algorithm rather than a second order algorithm. To maximize overall performance, a trade off analysis on polynomial order and coefficient precision is performed. Comprehensive testing, across multiple data sets, provides next generation model validation and performance benchmarks for higher order polynomial NUC methods.

Rogue waves and unbounded solutions of the NLSE

NASA Astrophysics Data System (ADS)

Lechuga, Antonio

2017-04-01

Since the pioneering work of Zakharov has been generally admitted that rogue waves can be studied in the framework of the Nonlinear Schrödinger Equation (NLSE). Many researchers, Akhmediev, Peregrine, Matveev among others gave different solutions to this equation that, in some way, could be linked to rogue waves and also to its more important characteristic: its unexpectedness. Janssen (2003, 2004), Onorato (2004, 2006) and Waseda (2006) linked the coefficient of the nonlinear term of the Schrödinger equation with the Benjamin-Feir index (BFI) that, we know, is a measure of the modulational instability of the waves. From this point of view the value of this coefficient of the NLSE could be known from statistics. Thus the relationship between sea states and the mechanism of generation of rogue waves could be found out. Following the well-known Lie group theory researchers have been studying the Lie point symmetries of the NLSE: the scaling transformations, Galilean transformations and phase transformations. Basically these transformations turn the NLSE into a nonlinear ordinary differential equation called Duffing equation (also called eikonal equation). There are different ways to do this, but in most of them the independent variable that could be seen as a space variable is a kind of moving frame with the time incorporated in this way. The main aim of this work is to classify solutions of the Duffing equation (periodic and nonperiodic waves and also bounded and unbounded waves) bearing in mind that the coefficient of the nonlinear term in the NLSE is left unaltered in the process of the transformation.

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.

Dynamics of vector dark solitons propagation and tunneling effect in the variable coefficient coupled nonlinear Schrödinger equation.

PubMed

Musammil, N M; Porsezian, K; Subha, P A; Nithyanandan, K

2017-02-01

We investigate the dynamics of vector dark solitons propagation using variable coefficient coupled nonlinear Schrödinger (Vc-CNLS) equation. The dark soliton propagation and evolution dynamics in the inhomogeneous system are studied analytically by employing the Hirota bilinear method. It is apparent from our asymptotic analysis that the collision between the dark solitons is elastic in nature. The various inhomogeneous effects on the evolution and interaction between dark solitons are explored, with a particular emphasis on nonlinear tunneling. It is found that the tunneling of the soliton depends on a condition related to the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or a valley, thus retaining its shape after tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well. Thus, a comprehensive study of dark soliton pulse evolution and propagation dynamics in Vc-CNLS equation is presented in the paper.

Frequency-degenerate phase-sensitive optical parametric amplification based on four-wave mixing in graphene–silicon slot waveguide

NASA Astrophysics Data System (ADS)

Li, Zhen; Liu, Hongjun; Huang, Nan; Wang, Zhaolu; Han, Jing

2018-06-01

The phase-sensitive amplification process of a hybrid graphene–silicon (HyGS) slot waveguide with trilayers of graphene is investigated in this paper. Numerical simulation shows that a relatively high extinction ratio (42 dB) is achieved, because of the ultrahigh nonlinear coefficients, with a waveguide length of only 680 µm. In addition, the graphene layer provides the possibility of modulating the phase status and gain of the output signal. This study is expected to be highly beneficial to applications such as integrated optics and graphene-related active optical devices.

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.

Relationship of crop radiance to alfalfa agronomic values

NASA Technical Reports Server (NTRS)

Tucker, C. J.; Elgin, J. H., Jr.; Mcmurtrey, J. E., III

1980-01-01

Red and photographic infrared spectral data of alfalfa were collected at the time of the third and fourth cuttings using a hand-held radiometer for the earlier alfalfa cutting. Significant linear and non-linear correlation coefficients were found between the spectral variables and plant height, biomass, forage water content, and estimated canopy cover. For the alfalfa of the later cutting, which had experienced a period of severe drought stress which limited growth, the spectral variables were found to be highly correlated with the estimated drought scores.

A Nonlinear Finite Element Framework for Viscoelastic Beams Based on the High-Order Reddy Beam Theory

DTIC Science & Technology

2012-06-09

employed theories are the Euler-Bernoulli beam theory (EBT) and the Timoshenko beam theory ( TBT ). The major deficiency associated with the EBT is failure to...account for defor- mations associated with shearing. The TBT relaxes the normality assumption of the EBT and admits a constant state of shear strain...on a given cross-section. As a result, the TBT necessitates the use of shear correction coefficients in order to accurately predict transverse

Second order sliding mode control for a quadrotor UAV.

PubMed

Zheng, En-Hui; Xiong, Jing-Jing; Luo, Ji-Liang

2014-07-01

A method based on second order sliding mode control (2-SMC) is proposed to design controllers for a small quadrotor UAV. For the switching sliding manifold design, the selection of the coefficients of the switching sliding manifold is in general a sophisticated issue because the coefficients are nonlinear. In this work, in order to perform the position and attitude tracking control of the quadrotor perfectly, the dynamical model of the quadrotor is divided into two subsystems, i.e., a fully actuated subsystem and an underactuated subsystem. For the former, a sliding manifold is defined by combining the position and velocity tracking errors of one state variable, i.e., the sliding manifold has two coefficients. For the latter, a sliding manifold is constructed via a linear combination of position and velocity tracking errors of two state variables, i.e., the sliding manifold has four coefficients. In order to further obtain the nonlinear coefficients of the sliding manifold, Hurwitz stability analysis is used to the solving process. In addition, the flight controllers are derived by using Lyapunov theory, which guarantees that all system state trajectories reach and stay on the sliding surfaces. Extensive simulation results are given to illustrate the effectiveness of the proposed control method. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Vibration measurement with nonlinear converter in the presence of noise

NASA Astrophysics Data System (ADS)

Mozuras, Almantas

2017-10-01

Conventional vibration measurement methods use the linear properties of physical converters. These methods are strongly influenced by nonlinear distortions, because ideal linear converters are not available. Practically, any converter can be considered as a linear one, when an output signal is very small. However, the influence of noise increases significantly and signal-to-noise ratio decreases at lower signals. When the output signal is increasing, the nonlinear distortions are also augmenting. If the wide spectrum vibration is measured, conventional methods face a harmonic distortion as well as intermodulation effects. Purpose of this research is to develop a measurement method of wide spectrum vibration by using a converter described by a nonlinear function of type f(x), where x =x(t) denotes the dependence of coordinate x on time t due to the vibration. Parameter x(t) describing the vibration is expressed as Fourier series. The spectral components of the converter output f(x(t)) are determined by using Fourier transform. The obtained system of nonlinear equations is solved using the least squares technique that permits to find x(t) in the presence of noise. This method allows one to carry out the absolute or relative vibration measurements. High resistance to noise is typical for the absolute vibration measurement, but it is necessary to know the Taylor expansion coefficients of the function f(x). If the Taylor expansion is not known, the relative measurement of vibration parameters is also possible, but with lower resistance to noise. This method allows one to eliminate the influence of nonlinear distortions to the measurement results, and consequently to eliminate harmonic distortion and intermodulation effects. The use of nonlinear properties of the converter for measurement gives some advantages related to an increased frequency range of the output signal (consequently increasing the number of equations) that allows one to decrease the noise influence on the measurement results. The greater is the nonlinearity the lower is noise. This method enables the use of the converters that are normally not suitable due to the high nonlinearity.

Spectral Line Parameters Including Temperature Dependences of Self- and Air-Broadening in the 2 (left arrow) 0 Band of CO at 2.3 micrometers

NASA Technical Reports Server (NTRS)

Devi, V. Malathy; Benner, D. Chris; Smith, M. A. H.; Mantz, A. W.; Sung, K.; Brown, L. R.; Predoi-Cross, A.

2012-01-01

Temperature dependences of pressure-broadened half-width and pressure-induced shift coefficients along with accurate positions and intensities have been determined for transitions in the 2<--0 band of C-12 O-16 from analyzing high-resolution and high signal-to-noise spectra recorded with two different Fourier transform spectrometers. A total of 28 spectra, 16 self-broadened and 12 air-broadened, recorded using high- purity (greater than or equal to 99.5% C-12-enriched) CO samples and CO diluted with dry air(research grade) at different temperatures and pressures, were analyzed simultaneously to maximize the accuracy of the retrieved parameters. The sample temperatures ranged from 150 to 298K and the total pressures varied between 5 and 700 Torr. A multispectrum nonlinear least squares spectrum fitting technique was used to adjust the rovibrational constants (G, B, D, etc.) and intensity parameters (including Herman-Wallis coefficients), rather than determining individual line positions and intensities. Self-and air-broadened Lorentz half-width coefficients, their temperature dependence exponents, self- and air-pressure-induced shift coefficients, their temperature dependences, self- and air-line mixing coefficients, their temperature dependences and speed dependence have been retrieved from the analysis. Speed-dependent line shapes with line mixing employing off-diagonal relaxation matrix element formalism were needed to minimize the fit residuals. This study presents a precise and complete set of spectral line parameters that consistently reproduce the spectrum of carbon monoxide over terrestrial atmospheric conditions.

The third-order optical nonlinearities of Ge-Ga-Sb(In)-S chalcogenide glasses

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

Guo, Haitao, E-mail: guoht_001@opt.ac.cn; Chen, Hongyan; Hou, Chaoqi

2011-05-15

Research highlights: {yields} It is firstly demonstrated that the nonlinear refractive index n{sub 2} is dependent on the covalency of bonds in chalcogenide glass. {yields} Homopolar metallic bonds in chalcogenide glass have positive contribution to large nonlinear refractive index n{sub 2} also. {yields} The 80GeS{sub 2}.20Sb{sub 2}S{sub 3} glass would be expected to be used in the all-optical switches working at 1330 nm and 1550 nm telecommunication wavelengths. -- Abstract: The third-order optical nonlinearities of 80GeS{sub 2}.(20 - x)Ga{sub 2}S{sub 3}.xY{sub 2}S{sub 3} (x = 0, 5, 10, 15, 20 and Y = Sb or In) chalcogenide glasses were investigatedmore » utilizing the Z-scan method at the wavelength of 800 nm and their linear optical properties and structure were also studied. By analyzing the compositional dependences and possible influencing factors including the linear refractive index, the concentration of lone electron pairs, the optical bandgap and the amount of weak covalent/homopolar bonds, it indicates that the electronic contribution in weak heteropolar covalent and homopolar metallic bonds is responsible for large nonlinear refractive index n{sub 2} in the chalcogenide glasses. These chalcogenide glasses have characteristics of environmentally friendship, wide transparency in the visible region, high nonlinear refractive index n{sub 2} and low nonlinear absorption coefficient {beta}, and would be expected to be used in the all-optical switches working at 1330 nm and 1550 nm telecommunication wavelengths.« less

Generalized nonlinear Schrödinger equation for dispersive susceptibility and permeability: application to negative index materials.

PubMed

Scalora, Michael; Syrchin, Maxim S; Akozbek, Neset; Poliakov, Evgeni Y; D'Aguanno, Giuseppe; Mattiucci, Nadia; Bloemer, Mark J; Zheltikov, Aleksei M

2005-07-01

A new generalized nonlinear Schrödinger equation describing the propagation of ultrashort pulses in bulk media exhibiting frequency dependent dielectric susceptibility and magnetic permeability is derived and used to characterize wave propagation in a negative index material. The equation has new features that are distinct from ordinary materials (mu=1): the linear and nonlinear coefficients can be tailored through the linear properties of the medium to attain any combination of signs unachievable in ordinary matter, with significant potential to realize a wide class of solitary waves.

Prediction of jump phenomena in rotationally-coupled maneuvers of aircraft, including nonlinear aerodynamic effects

NASA Technical Reports Server (NTRS)

Young, J. W.; Schy, A. A.; Johnson, K. G.

1977-01-01

An analytical method has been developed for predicting critical control inputs for which nonlinear rotational coupling may cause sudden jumps in aircraft response. The analysis includes the effect of aerodynamics which are nonlinear in angle of attack. The method involves the simultaneous solution of two polynomials in roll rate, whose coefficients are functions of angle of attack and the control inputs. Results obtained using this procedure are compared with calculated time histories to verify the validity of the method for predicting jump-like instabilities.

Crystal growth, piezoelectric, non-linear optical and mechanical properties of lithium hydrogen oxalate monohydrate single crystal

NASA Astrophysics Data System (ADS)

Chandran, Senthilkumar; Paulraj, Rajesh; Ramasamy, P.

2017-05-01

Semi-organic lithium hydrogen oxalate monohydrate non-linear optical single crystals have been grown by slow evaporation solution growth technique at 35 °C. Single crystal X-ray diffraction study showed that the grown crystal belongs to the triclinic system with space group P1. The mechanical strength decreases with increasing load. The piezoelectric coefficient is found to be 1.41 pC/N. The nonlinear optical property was measured using Kurtz Perry powder technique and SHG efficiency was almost equal to that of KDP.

Realization of non-linear coherent states by photonic lattices

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

Dehdashti, Shahram, E-mail: shdehdashti@zju.edu.cn; Li, Rujiang; Chen, Hongsheng, E-mail: hansomchen@zju.edu.cn

2015-06-15

In this paper, first, by introducing Holstein-Primakoff representation of α-deformed algebra, we achieve the associated non-linear coherent states, including su(2) and su(1, 1) coherent states. Second, by using waveguide lattices with specific coupling coefficients between neighbouring channels, we generate these non-linear coherent states. In the case of positive values of α, we indicate that the Hilbert size space is finite; therefore, we construct this coherent state with finite channels of waveguide lattices. Finally, we study the field distribution behaviours of these coherent states, by using Mandel Q parameter.

Continuous-wave to pulse regimes for a family of passively mode-locked lasers with saturable nonlinearity

NASA Astrophysics Data System (ADS)

Dikandé, Alain M.; Voma Titafan, J.; Essimbi, B. Z.

2017-10-01

The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg-Landau equation with a general m:n saturable nonlinearity (i.e {I}m/{(1+{{Γ }}I)}n, where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple (m, n), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.

State, Parameter, and Unknown Input Estimation Problems in Active Automotive Safety Applications

NASA Astrophysics Data System (ADS)

Phanomchoeng, Gridsada

A variety of driver assistance systems such as traction control, electronic stability control (ESC), rollover prevention and lane departure avoidance systems are being developed by automotive manufacturers to reduce driver burden, partially automate normal driving operations, and reduce accidents. The effectiveness of these driver assistance systems can be significant enhanced if the real-time values of several vehicle parameters and state variables, namely tire-road friction coefficient, slip angle, roll angle, and rollover index, can be known. Since there are no inexpensive sensors available to measure these variables, it is necessary to estimate them. However, due to the significant nonlinear dynamics in a vehicle, due to unknown and changing plant parameters, and due to the presence of unknown input disturbances, the design of estimation algorithms for this application is challenging. This dissertation develops a new approach to observer design for nonlinear systems in which the nonlinearity has a globally (or locally) bounded Jacobian. The developed approach utilizes a modified version of the mean value theorem to express the nonlinearity in the estimation error dynamics as a convex combination of known matrices with time varying coefficients. The observer gains are then obtained by solving linear matrix inequalities (LMIs). A number of illustrative examples are presented to show that the developed approach is less conservative and more useful than the standard Lipschitz assumption based nonlinear observer. The developed nonlinear observer is utilized for estimation of slip angle, longitudinal vehicle velocity, and vehicle roll angle. In order to predict and prevent vehicle rollovers in tripped situations, it is necessary to estimate the vertical tire forces in the presence of unknown road disturbance inputs. An approach to estimate unknown disturbance inputs in nonlinear systems using dynamic model inversion and a modified version of the mean value theorem is presented. The developed theory is used to estimate vertical tire forces and predict tripped rollovers in situations involving road bumps, potholes, and lateral unknown force inputs. To estimate the tire-road friction coefficients at each individual tire of the vehicle, algorithms to estimate longitudinal forces and slip ratios at each tire are proposed. Subsequently, tire-road friction coefficients are obtained using recursive least squares parameter estimators that exploit the relationship between longitudinal force and slip ratio at each tire. The developed approaches are evaluated through simulations with industry standard software, CARSIM, with experimental tests on a Volvo XC90 sport utility vehicle and with experimental tests on a 1/8th scaled vehicle. The simulation and experimental results show that the developed approaches can reliably estimate the vehicle parameters and state variables needed for effective ESC and rollover prevention applications.

Nonlinear response and avalanche behavior in metallic glasses

NASA Astrophysics Data System (ADS)

Riechers, B.; Samwer, K.

2017-08-01

The response to different stress amplitudes at temperatures below the glass transition temperature is analyzed by mechanical oscillatory excitation of Pd40Ni40P20 metallic glass samples in single cantilever bending geometry. While low amplitude oscillatory excitations are commonly used in mechanical spectroscopy to probe the relaxation spectrum, in this work the response to comparably high amplitudes is investigated. The strain response of the material is well below the critical yield stress even for highest stress amplitudes, implying the expectation of a linear relation between stress and strain according to Hooke's Law. However, a deviation from the linear behavior is evident, which is analyzed in terms of temperature dependence and influence of the applied stress amplitude by two different approaches of evaluation. The nonlinear approach is based on a nonlinear expansion of the stress-strain-relation, assuming an intrinsic nonlinear character of the shear or elastic modulus. The degree of nonlinearity is extracted by a period-by-period Fourier-analysis and connected to nonlinear coefficients, describing the intensity of nonlinearity at the fundamental and higher harmonic frequencies. The characteristic timescale to adapt to a significant change in stress amplitude in terms of a recovery timescale to a steady state value is connected to the structural relaxation time of the material, suggesting a connection between the observed nonlinearity and primary relaxation processes. The second approach of evaluation is termed the incremental analysis and relates the observed response behavior to avalanches, which occur due to the activation and correlation of local microstructural rearrangements. These rearrangements are connected with shear transformation zones and correspond to localized plastic events, which are superimposed on the linear response behavior of the material.

Influence of electrode width of interdigital transducer on third-order nonlinearity of surface acoustic wave devices on 42°YX-LiTaO3 substrate

NASA Astrophysics Data System (ADS)

Nakagawa, Ryo; Hashimoto, Ken-ya

2018-07-01

In this paper, we discuss the influence of the electrode width of an interdigital transducer on the third-order nonlinearity of surface acoustic wave (SAW) devices. First, an estimation technique of third-order nonlinear signals based on the linear finite element method is proposed, and the variation of nonlinear signal level with electrode width is estimated. Then, several one-port SAW resonators with different electrode widths are fabricated, and measured nonlinear signal levels are compared with simulation. As predicted by the numerical simulation, nonlinear signal levels became large with electrode width. However, harmonics takes a minimum at a certain electrode width. This tendency disagrees with the simulation. The variation of nonlinear coefficients is evaluated by numerical fitting for the measured data using the nonlinear signal simulator proposed by the authors. As the result, it is concluded that the generation mechanism is not limited to the acoustic strain in electrodes.

Nanosecond nonlinear optical and optical limiting properties of hollow gold nanocages

NASA Astrophysics Data System (ADS)

Zheng, Chan; Huang, Jiaxin; Lei, Li; Chen, Wenzhe; Wang, Haiyan; Li, Wei

2018-01-01

Gold nanocages (NCs) were prepared using the galvanic replacement reaction. Transmission electron microscopy images confirmed the porous morphology and completely hollow interior of the gold NCs. The nanosecond nonlinear optical and optical limiting (OL) properties of the NCs were characterized using the open-aperture Z-scan technique with 8-ns laser pulses at 532 nm. The gold NCs exhibited intensity-dependent transformation from saturable absorption to reverse-saturable absorption. The nonlinear absorption coefficient and saturable energy of the NCs were 5 × 10- 12 m/W and 2.5 × 1010 W/m2, respectively. Meanwhile, the gold NCs were found to display strong OL properties towards nanosecond laser pulses. The OL threshold of the gold NCs was lower than that of solid gold nanoparticles and comparable with that of a carbon nanotube suspension. Input fluence and angle-dependent scattering measurements indicated that nonlinear scattering plays an important role in the OL behavior of the gold nanostructures at high laser excitation. The improved OL response in gold NCs was discussed from the viewpoint of structural characteristic. The ultrathin and highly porous walls of the gold NCs can effectively transfer the photon-induced heat to the surrounding solvent, resulting in enhanced OL properties compared with those of solid gold nanoparticles. The intensity-dependent transformation from saturable absorption to reverse-saturable absorption and excellent OL response indicate that the smart gold NCs with ultrathin and highly porous walls can be considered as potential candidate in pulse shaping, passive mode locking, and eye protection against powerful lasers.

A Computational and Experimental Study of Nonlinear Aspects of Induced Drag

NASA Technical Reports Server (NTRS)

Smith, Stephen C.

1996-01-01

Despite the 80-year history of classical wing theory, considerable research has recently been directed toward planform and wake effects on induced drag. Nonlinear interactions between the trailing wake and the wing offer the possibility of reducing drag. The nonlinear effect of compressibility on induced drag characteristics may also influence wing design. This thesis deals with the prediction of these nonlinear aspects of induced drag and ways to exploit them. A potential benefit of only a few percent of the drag represents a large fuel savings for the world's commercial transport fleet. Computational methods must be applied carefully to obtain accurate induced drag predictions. Trefftz-plane drag integration is far more reliable than surface pressure integration, but is very sensitive to the accuracy of the force-free wake model. The practical use of Trefftz plane drag integration was extended to transonic flow with the Tranair full-potential code. The induced drag characteristics of a typical transport wing were studied with Tranair, a full-potential method, and A502, a high-order linear panel method to investigate changes in lift distribution and span efficiency due to compressibility. Modeling the force-free wake is a nonlinear problem, even when the flow governing equation is linear. A novel method was developed for computing the force-free wake shape. This hybrid wake-relaxation scheme couples the well-behaved nature of the discrete vortex wake with viscous-core modeling and the high-accuracy velocity prediction of the high-order panel method. The hybrid scheme produced converged wake shapes that allowed accurate Trefftz-plane integration. An unusual split-tip wing concept was studied for exploiting nonlinear wake interaction to reduced induced drag. This design exhibits significant nonlinear interactions between the wing and wake that produced a 12% reduction in induced drag compared to an equivalent elliptical wing at a lift coefficient of 0.7. The performance of the split-tip wing was also investigated by wing tunnel experiments. Induced drag was determined from force measurements by subtracting the estimated viscous drag, and from an analytical drag-decomposition method using a wake survey. The experimental results confirm the computational prediction.

Efficient particle acceleration in shocks

NASA Astrophysics Data System (ADS)

Heavens, A. F.

1984-10-01

A self-consistent non-linear theory of acceleration of particles by shock waves is developed, using an extension of the two-fluid hydrodynamical model by Drury and Völk. The transport of the accelerated particles is governed by a diffusion coefficient which is initially assumed to be independent of particle momentum, to obtain exact solutions for the spectrum. It is found that steady-state shock structures with high acceleration efficiency are only possible for shocks with Mach numbers less than about 12. A more realistic diffusion coefficient is then considered, and this maximum Mach number is reduced to about 6. The efficiency of the acceleration process determines the relative importance of the non-relativistic and relativistic particles in the distribution of accelerated particles, and this determines the effective specific heat ratio.

Soliton and periodic solutions for time-dependent coefficient non-linear equation

NASA Astrophysics Data System (ADS)

Guner, Ozkan

2016-01-01

In this article, we establish exact solutions for the generalized (3+1)-dimensional variable coefficient Kadomtsev-Petviashvili (GVCKP) equation. Using solitary wave ansatz in terms of ? functions and the modified sine-cosine method, we find exact analytical bright soliton solutions and exact periodic solutions for the considered model. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients. The effectiveness and reliability of the method are shown by its application to the GVCKP equation.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

A nonlinear Fokker-Planck equation approach for interacting systems: Anomalous diffusion and Tsallis statistics

NASA Astrophysics Data System (ADS)

Marin, D.; Ribeiro, M. A.; Ribeiro, H. V.; Lenzi, E. K.

2018-07-01

We investigate the solutions for a set of coupled nonlinear Fokker-Planck equations coupled by the diffusion coefficient in presence of external forces. The coupling by the diffusion coefficient implies that the diffusion of each species is influenced by the other and vice versa due to this term, which represents an interaction among them. The solutions for the stationary case are given in terms of the Tsallis distributions, when arbitrary external forces are considered. We also use the Tsallis distributions to obtain a time dependent solution for a linear external force. The results obtained from this analysis show a rich class of behavior related to anomalous diffusion, which can be characterized by compact or long-tailed distributions.

Time domain simulation of the response of geometrically nonlinear panels subjected to random loading

NASA Technical Reports Server (NTRS)

Moyer, E. Thomas, Jr.

1988-01-01

The response of composite panels subjected to random pressure loads large enough to cause geometrically nonlinear responses is studied. A time domain simulation is employed to solve the equations of motion. An adaptive time stepping algorithm is employed to minimize intermittent transients. A modified algorithm for the prediction of response spectral density is presented which predicts smooth spectral peaks for discrete time histories. Results are presented for a number of input pressure levels and damping coefficients. Response distributions are calculated and compared with the analytical solution of the Fokker-Planck equations. RMS response is reported as a function of input pressure level and damping coefficient. Spectral densities are calculated for a number of examples.

Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks.

PubMed

Subramaniyam, Narayan Puthanmadam; Hyttinen, Jari

2015-02-01

Recently Andrezejak et al. combined the randomness and nonlinear independence test with iterative amplitude adjusted Fourier transform (iAAFT) surrogates to distinguish between the dynamics of seizure-free intracranial electroencephalographic (EEG) signals recorded from epileptogenic (focal) and nonepileptogenic (nonfocal) brain areas of epileptic patients. However, stationarity is a part of the null hypothesis for iAAFT surrogates and thus nonstationarity can violate the null hypothesis. In this work we first propose the application of the randomness and nonlinear independence test based on recurrence network measures to distinguish between the dynamics of focal and nonfocal EEG signals. Furthermore, we combine these tests with both iAAFT and truncated Fourier transform (TFT) surrogate methods, which also preserves the nonstationarity of the original data in the surrogates along with its linear structure. Our results indicate that focal EEG signals exhibit an increased degree of structural complexity and interdependency compared to nonfocal EEG signals. In general, we find higher rejections for randomness and nonlinear independence tests for focal EEG signals compared to nonfocal EEG signals. In particular, the univariate recurrence network measures, the average clustering coefficient C and assortativity R, and the bivariate recurrence network measure, the average cross-clustering coefficient C(cross), can successfully distinguish between the focal and nonfocal EEG signals, even when the analysis is restricted to nonstationary signals, irrespective of the type of surrogates used. On the other hand, we find that the univariate recurrence network measures, the average path length L, and the average betweenness centrality BC fail to distinguish between the focal and nonfocal EEG signals when iAAFT surrogates are used. However, these two measures can distinguish between focal and nonfocal EEG signals when TFT surrogates are used for nonstationary signals. We also report an improvement in the performance of nonlinear prediction error N and nonlinear interdependence measure L used by Andrezejak et al., when TFT surrogates are used for nonstationary EEG signals. We also find that the outcome of the nonlinear independence test based on the average cross-clustering coefficient C(cross) is independent of the outcome of the randomness test based on the average clustering coefficient C. Thus, the univariate and bivariate recurrence network measures provide independent information regarding the dynamics of the focal and nonfocal EEG signals. In conclusion, recurrence network analysis combined with nonstationary surrogates can be applied to derive reliable biomarkers to distinguish between epileptogenic and nonepileptogenic brain areas using EEG signals.

Dynamics of intracranial electroencephalographic recordings from epilepsy patients using univariate and bivariate recurrence networks

NASA Astrophysics Data System (ADS)

Subramaniyam, Narayan Puthanmadam; Hyttinen, Jari

2015-02-01

Recently Andrezejak et al. combined the randomness and nonlinear independence test with iterative amplitude adjusted Fourier transform (iAAFT) surrogates to distinguish between the dynamics of seizure-free intracranial electroencephalographic (EEG) signals recorded from epileptogenic (focal) and nonepileptogenic (nonfocal) brain areas of epileptic patients. However, stationarity is a part of the null hypothesis for iAAFT surrogates and thus nonstationarity can violate the null hypothesis. In this work we first propose the application of the randomness and nonlinear independence test based on recurrence network measures to distinguish between the dynamics of focal and nonfocal EEG signals. Furthermore, we combine these tests with both iAAFT and truncated Fourier transform (TFT) surrogate methods, which also preserves the nonstationarity of the original data in the surrogates along with its linear structure. Our results indicate that focal EEG signals exhibit an increased degree of structural complexity and interdependency compared to nonfocal EEG signals. In general, we find higher rejections for randomness and nonlinear independence tests for focal EEG signals compared to nonfocal EEG signals. In particular, the univariate recurrence network measures, the average clustering coefficient C and assortativity R , and the bivariate recurrence network measure, the average cross-clustering coefficient Ccross, can successfully distinguish between the focal and nonfocal EEG signals, even when the analysis is restricted to nonstationary signals, irrespective of the type of surrogates used. On the other hand, we find that the univariate recurrence network measures, the average path length L , and the average betweenness centrality BC fail to distinguish between the focal and nonfocal EEG signals when iAAFT surrogates are used. However, these two measures can distinguish between focal and nonfocal EEG signals when TFT surrogates are used for nonstationary signals. We also report an improvement in the performance of nonlinear prediction error N and nonlinear interdependence measure L used by Andrezejak et al., when TFT surrogates are used for nonstationary EEG signals. We also find that the outcome of the nonlinear independence test based on the average cross-clustering coefficient Ccross is independent of the outcome of the randomness test based on the average clustering coefficient C . Thus, the univariate and bivariate recurrence network measures provide independent information regarding the dynamics of the focal and nonfocal EEG signals. In conclusion, recurrence network analysis combined with nonstationary surrogates can be applied to derive reliable biomarkers to distinguish between epileptogenic and nonepileptogenic brain areas using EEG signals.

A 2.87 ppm/°C 65 nm CMOS bandgap reference with nonlinearity compensation

NASA Astrophysics Data System (ADS)

Xingyuan, Tong; Zhangming, Zhu; Yintang, Yang

2011-09-01

Based on the review and analysis of two recently reported low temperature coefficient (TC) bandgap voltage references (BGRs), a new temperature compensation technique is presented. With the double-end piecewise nonlinearity correction method, the logarithm cancellation technique and the mixed-mode output topology, a BGR with high-temperature stability is realised based on 65 nm CMOS low-leakage process. The post-simulation results using Spectre show that this BGR produces an output voltage of about 953 mV with 2.5 V supply voltage, and the output voltage varies by only 0.16 mV from -40°C to 125°C. This low TC BGR has been used in a 65 nm CMOS touch screen controller, and the measurement shows that the output voltage of this BGR is about 949 mV varying by 0.44 mV from -40°C to 125°C. The TC of this BGR is about 2.87 ppm/°C, meeting the requirement of high-precision SoC application.

Nonlinear Simulation of the Tooth Enamel Spectrum for EPR Dosimetry

NASA Astrophysics Data System (ADS)

Kirillov, V. A.; Dubovsky, S. V.

2016-07-01

Software was developed where initial EPR spectra of tooth enamel were deconvoluted based on nonlinear simulation, line shapes and signal amplitudes in the model initial spectrum were calculated, the regression coefficient was evaluated, and individual spectra were summed. Software validation demonstrated that doses calculated using it agreed excellently with the applied radiation doses and the doses reconstructed by the method of additive doses.

Metabolic control analysis using transient metabolite concentrations. Determination of metabolite concentration control coefficients.

PubMed Central

Delgado, J; Liao, J C

1992-01-01

The methodology previously developed for determining the Flux Control Coefficients [Delgado & Liao (1992) Biochem. J. 282, 919-927] is extended to the calculation of metabolite Concentration Control Coefficients. It is shown that the transient metabolite concentrations are related by a few algebraic equations, attributed to mass balance, stoichiometric constraints, quasi-equilibrium or quasi-steady states, and kinetic regulations. The coefficients in these relations can be estimated using linear regression, and can be used to calculate the Control Coefficients. The theoretical basis and two examples are discussed. Although the methodology is derived based on the linear approximation of enzyme kinetics, it yields reasonably good estimates of the Control Coefficients for systems with non-linear kinetics. PMID:1497632

Giant thermo-optical relaxation oscillations in millimeter-size whispering gallery mode disk resonators.

PubMed

Diallo, Souleymane; Lin, Guoping; Chembo, Yanne K

2015-08-15

In this Letter, we show that giant thermo-optical oscillations can be triggered in millimeter (mm)-size whispering gallery mode (WGM) disk resonators when they are pumped by a resonant continuous-wave laser. Our resonator is an ultrahigh-Q barium fluoride cavity that features a positive thermo-optic coefficient and a negative thermo-elastic coefficient. We demonstrate for the first time, to our knowledge, that the complex interplay between these two thermic coefficients and the intrinsic Kerr nonlinearity yields very sharp slow-fast relaxation oscillations with a slow timescale that can be exceptionally large, typically of the order of 1 s. We use a time-domain model to gain understanding into this instability, and we find that both the experimental and theoretical results are in excellent agreement. The understanding of these thermal effects is an essential requirement for every WGM-related application and our study demonstrates that even in the case of mm-size resonators, such effects can still be accurately analyzed using nonlinear time-domain models.

Time-dependent transport of energetic particles in magnetic turbulence: computer simulations versus analytical theory

NASA Astrophysics Data System (ADS)

Arendt, V.; Shalchi, A.

2018-06-01

We explore numerically the transport of energetic particles in a turbulent magnetic field configuration. A test-particle code is employed to compute running diffusion coefficients as well as particle distribution functions in the different directions of space. Our numerical findings are compared with models commonly used in diffusion theory such as Gaussian distribution functions and solutions of the cosmic ray Fokker-Planck equation. Furthermore, we compare the running diffusion coefficients across the mean magnetic field with solutions obtained from the time-dependent version of the unified non-linear transport theory. In most cases we find that particle distribution functions are indeed of Gaussian form as long as a two-component turbulence model is employed. For turbulence setups with reduced dimensionality, however, the Gaussian distribution can no longer be obtained. It is also shown that the unified non-linear transport theory agrees with simulated perpendicular diffusion coefficients as long as the pure two-dimensional model is excluded.

Linear and Nonlinear Optical Properties of Spherical Quantum Dots: Effects of Hydrogenic Impurity and Conduction Band Non-Parabolicity

NASA Astrophysics Data System (ADS)

Rezaei, G.; Vaseghi, B.; Doostimotlagh, N. A.

2012-03-01

Simultaneous effects of an on-center hydrogenic impurity and band edge non-parabolicity on intersubband optical absorption coefficients and refractive index changes of a typical GaAs/AlxGa1-x As spherical quantum dot are theoretically investigated, using the Luttinger—Kohn effective mass equation. So, electronic structure and optical properties of the system are studied by means of the matrix diagonalization technique and compact density matrix approach, respectively. Finally, effects of an impurity, band edge non-parabolicity, incident light intensity and the dot size on the linear, the third-order nonlinear and the total optical absorption coefficients and refractive index changes are investigated. Our results indicate that, the magnitudes of these optical quantities increase and their peaks shift to higher energies as the influences of the impurity and the band edge non-parabolicity are considered. Moreover, incident light intensity and the dot size have considerable effects on the optical absorption coefficients and refractive index changes.

Nonlinear optical properties of Nd3+-Li+ co-doped ZnS-PVP thin films

NASA Astrophysics Data System (ADS)

Talwatkar, S. S.; Sunatkari, A. L.; Tamgadge, Y. S.; Muley, G. G.

2018-04-01

The nonlinear optical properties of Nd3+-Li+ co-doped ZnS-PVP nanocomposite were studied using a continuous wave (CW) He-Ne laser (λ = 632.8 nm)by z-scan technique. The nonlinear refractive index (n2), absorption coefficient (β) and third order nonlinear susceptibility (χ(3)) of PVP thin films embedded with Nd3+-Li+ co-doped ZnS NPs was found in the order of 10-7 cm2/W, 10-6 cm/W and 10-7 esu respectively. The nonlinearity found increasing with Nd3+-Li+ co-dopant concentration. Based on the results, it is proposed that this material is a new class of luminescent material suitable in optoelectronics devices application, especially in light-emitting devices, electroluminescent devices, display devices, etc.

Bright-dark and dark-dark solitons in coupled nonlinear Schrödinger equation with P T -symmetric potentials

NASA Astrophysics Data System (ADS)

Nath, Debraj; Gao, Yali; Babu Mareeswaran, R.; Kanna, T.; Roy, Barnana

2017-12-01

We explore different nonlinear coherent structures, namely, bright-dark (BD) and dark-dark (DD) solitons in a coupled nonlinear Schrödinger/Gross-Pitaevskii equation with defocusing/repulsive nonlinearity coefficients featuring parity-time ( P T )-symmetric potentials. Especially, for two choices of P T -symmetric potentials, we obtain the exact solutions for BD and DD solitons. We perform the linear stability analysis of the obtained coherent structures. The results of this linear stability analysis are well corroborated by direct numerical simulation incorporating small random noise. It has been found that there exists a parameter regime which can support stable BD and DD solitons.

Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems

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

D'Aguanno, G.; Mattiucci, N.; C. M. Bowden Facility, Building 7804, RDECOM, Redstone Arsenal, Alabama 35898

2010-01-15

We have investigated and experimentally demonstrated the applicability of the Bloch vector for one-dimensional, nonlinear, finite, dissipative systems. The case studied is the second harmonic generation from metallodielectric multilayer filters. In particular, we have applied the Bloch vector analysis to Ag/Ta{sub 2}O{sub 5} thin-film multilayer samples and shown the importance of the phase matching calculated through the Bloch vector. The nonlinear coefficients extracted from experimental results are consistent with previous studies. Nowadays, metal-based nanostructures play a fundamental role in nonlinear nanophotonics and nanoplasmonics. Our results clearly suggest that even in these forefront fields the Bloch vector continues to play anmore » essential role.« less

System Identification for Nonlinear Control Using Neural Networks

NASA Technical Reports Server (NTRS)

Stengel, Robert F.; Linse, Dennis J.

1990-01-01

An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique.

Vector matter waves in two-component Bose-Einstein condensates with spatially modulated nonlinearities

NASA Astrophysics Data System (ADS)

Xu, Si-Liu; He, Jun-Rong; Xue, Li; Belić, Milivoj R.

2018-02-01

We demonstrate three-dimensional (3D) vector solitary waves in the coupled (3 + 1)-D nonlinear Gross-Pitaevskii equations with variable nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing novel localized solutions that depend on three modal numbers, l, m, and n. Using the similarity transformation (ST) method in 3D, vector solitary waves are built with the help of a combination of harmonic and trapping potentials, including multipole solutions and necklace rings. In general, the solutions found are stable for low values of the modal numbers; for values larger than 2, the solutions are found to be unstable. Variable nonlinearity allows the utilization of soliton management methods.

Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

PubMed

Ho, Yuh-Shan

2006-01-01

A comparison was made of the linear least-squares method and a trial-and-error non-linear method of the widely used pseudo-second-order kinetic model for the sorption of cadmium onto ground-up tree fern. Four pseudo-second-order kinetic linear equations are discussed. Kinetic parameters obtained from the four kinetic linear equations using the linear method differed but they were the same when using the non-linear method. A type 1 pseudo-second-order linear kinetic model has the highest coefficient of determination. Results show that the non-linear method may be a better way to obtain the desired parameters.

The application of water coupled nonlinear ultrasonics to quantify the dislocation density in aluminum 1100

NASA Astrophysics Data System (ADS)

Mostavi, Amir; Tehrani, N.; Kamali, N.; Ozevin, D.; Chi, S. W.; Indacochea, J. E.

2017-02-01

This article investigates water coupled nonlinear ultrasonic method to measure the dislocation density in aluminum 1100 specimens. The different levels of dislocation densities are introduced to the samples by applying different levels of plastic strains by tensile loading. The ultrasonic testing includes 2.25 MHz transducer as transmitter and 5.0 MHz transducer as receiver in an immersion tank. The results of immersion experiments are compared with oil-coupled experiments. While water has significant nonlinearity within itself, the immersion ultrasound results agree with the literature of oil coupled ultrasound results of the specimens that the nonlinearity coefficient increases with the increase of dislocation density in aluminum.

Discontinuous Galerkin method with Gaussian artificial viscosity on graphical processing units for nonlinear acoustics

NASA Astrophysics Data System (ADS)

Tripathi, Bharat B.; Marchiano, Régis; Baskar, Sambandam; Coulouvrat, François

2015-10-01

Propagation of acoustical shock waves in complex geometry is a topic of interest in the field of nonlinear acoustics. For instance, simulation of Buzz Saw Noice requires the treatment of shock waves generated by the turbofan through the engines of aeroplanes with complex geometries and wall liners. Nevertheless, from a numerical point of view it remains a challenge. The two main hurdles are to take into account the complex geometry of the domain and to deal with the spurious oscillations (Gibbs phenomenon) near the discontinuities. In this work, first we derive the conservative hyperbolic system of nonlinear acoustics (up to quadratic nonlinear terms) using the fundamental equations of fluid dynamics. Then, we propose to adapt the classical nodal discontinuous Galerkin method to develop a high fidelity solver for nonlinear acoustics. The discontinuous Galerkin method is a hybrid of finite element and finite volume method and is very versatile to handle complex geometry. In order to obtain better performance, the method is parallelized on Graphical Processing Units. Like other numerical methods, discontinuous Galerkin method suffers with the problem of Gibbs phenomenon near the shock, which is a numerical artifact. Among the various ways to manage these spurious oscillations, we choose the method of parabolic regularization. Although, the introduction of artificial viscosity into the system is a popular way of managing shocks, we propose a new approach of introducing smooth artificial viscosity locally in each element, wherever needed. Firstly, a shock sensor using the linear coefficients of the spectral solution is used to locate the position of the discontinuities. Then, a viscosity coefficient depending on the shock sensor is introduced into the hyperbolic system of equations, only in the elements near the shock. The viscosity is applied as a two-dimensional Gaussian patch with its shape parameters depending on the element dimensions, referred here as Element Centered Smooth Artificial Viscosity. Using this numerical solver, various numerical experiments are presented for one and two-dimensional test cases in homogeneous and quiescent medium. This work is funded by CEFIPRA (Indo-French Centre for the Promotion of Advance Research) and partially aided by EGIDE (Campus France).

Fatigue crack detection by nonlinear spectral correlation with a wideband input

NASA Astrophysics Data System (ADS)

Liu, Peipei; Sohn, Hoon

2017-04-01

Due to crack-induced nonlinearity, ultrasonic wave can distort, create accompanying harmonics, multiply waves of different frequencies, and, under resonance conditions, change resonance frequencies as a function of driving amplitude. All these nonlinear ultrasonic features have been widely studied and proved capable of detecting fatigue crack at its very early stage. However, in noisy environment, the nonlinear features might be drown in the noise, therefore it is difficult to extract those features using a conventional spectral density function. In this study, nonlinear spectral correlation is defined as a new nonlinear feature, which considers not only nonlinear modulations in ultrasonic waves but also spectral correlation between the nonlinear modulations. The proposed nonlinear feature is associated with the following two advantages: (1) stationary noise in the ultrasonic waves has little effect on nonlinear spectral correlation; and (2) the contrast of nonlinear spectral correlation between damage and intact conditions can be enhanced simply by using a wideband input. To validate the proposed nonlinear feature, micro fatigue cracks are introduced to aluminum plates by repeated tensile loading, and the experiment is conducted using surface-mounted piezoelectric transducers for ultrasonic wave generation and measurement. The experimental results confirm that the nonlinear spectral correlation can successfully detect fatigue crack with a higher sensitivity than the classical nonlinear coefficient.

Development of stock correlation networks using mutual information and financial big data.

PubMed

Guo, Xue; Zhang, Hu; Tian, Tianhai

2018-01-01

Stock correlation networks use stock price data to explore the relationship between different stocks listed in the stock market. Currently this relationship is dominantly measured by the Pearson correlation coefficient. However, financial data suggest that nonlinear relationships may exist in the stock prices of different shares. To address this issue, this work uses mutual information to characterize the nonlinear relationship between stocks. Using 280 stocks traded at the Shanghai Stocks Exchange in China during the period of 2014-2016, we first compare the effectiveness of the correlation coefficient and mutual information for measuring stock relationships. Based on these two measures, we then develop two stock networks using the Minimum Spanning Tree method and study the topological properties of these networks, including degree, path length and the power-law distribution. The relationship network based on mutual information has a better distribution of the degree and larger value of the power-law distribution than those using the correlation coefficient. Numerical results show that mutual information is a more effective approach than the correlation coefficient to measure the stock relationship in a stock market that may undergo large fluctuations of stock prices.

Breathers and rogue waves in a Heisenberg ferromagnetic spin chain or an alpha helical protein

NASA Astrophysics Data System (ADS)

Yang, Jin-Wei; Gao, Yi-Tian; Su, Chuan-Qi; Wang, Qi-Min; Lan, Zhong-Zhou

2017-07-01

In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation for a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain or an alpha helical protein has been investigated. Breathers and rogue waves are constructed via the Darboux transformation and generalized Darboux transformation, respectively. Results of the breathers and rogue waves are presented: (1) The first- and second-order Akhmediev breathers and Kuznetsov-Ma solitons are presented with different values of variable coefficients which are related to the energy transfer or higher-order excitations and interactions in the helical protein, or related to the spin excitations resulting from the lowest order continuum approximation and octupole-dipole interaction in a Heisenberg ferromagnetic spin chain, and the nonlinear periodic breathers resulting from the Akhmediev breathers are studied as well; (2) For the first- and second-order rogue waves, we find that they can be split into many similar components when the variable coefficients are polynomial functions of time; (3) Rogue waves can also be split when the variable coefficients are hyperbolic secant functions of time, but the profile of each component in such a case is different.

Development of stock correlation networks using mutual information and financial big data

PubMed Central

Guo, Xue; Zhang, Hu

2018-01-01

Stock correlation networks use stock price data to explore the relationship between different stocks listed in the stock market. Currently this relationship is dominantly measured by the Pearson correlation coefficient. However, financial data suggest that nonlinear relationships may exist in the stock prices of different shares. To address this issue, this work uses mutual information to characterize the nonlinear relationship between stocks. Using 280 stocks traded at the Shanghai Stocks Exchange in China during the period of 2014-2016, we first compare the effectiveness of the correlation coefficient and mutual information for measuring stock relationships. Based on these two measures, we then develop two stock networks using the Minimum Spanning Tree method and study the topological properties of these networks, including degree, path length and the power-law distribution. The relationship network based on mutual information has a better distribution of the degree and larger value of the power-law distribution than those using the correlation coefficient. Numerical results show that mutual information is a more effective approach than the correlation coefficient to measure the stock relationship in a stock market that may undergo large fluctuations of stock prices. PMID:29668715

Global Nonlinear Analysis of Piezoelectric Energy Harvesting from Ambient and Aeroelastic Vibrations

NASA Astrophysics Data System (ADS)

Abdelkefi, Abdessattar

Converting vibrations to a usable form of energy has been the topic of many recent investigations. The ultimate goal is to convert ambient or aeroelastic vibrations to operate low-power consumption devices, such as microelectromechanical systems, heath monitoring sensors, wireless sensors or replacing small batteries that have a finite life span or would require hard and expensive maintenance. The transduction mechanisms used for transforming vibrations to electric power include: electromagnetic, electrostatic, and piezoelectric mechanisms. Because it can be used to harvest energy over a wide range of frequencies and because of its ease of application, the piezoelectric option has attracted significant interest. In this work, we investigate the performance of different types of piezoelectric energy harvesters. The objective is to design and enhance the performance of these harvesters. To this end, distributed-parameter and phenomenological models of these harvesters are developed. Global analysis of these models is then performed using modern methods of nonlinear dynamics. In the first part of this Dissertation, global nonlinear distributed-parameter models for piezoelectric energy harvesters under direct and parametric excitations are developed. The method of multiple scales is then used to derive nonlinear forms of the governing equations and associated boundary conditions, which are used to evaluate their performance and determine the effects of the nonlinear piezoelectric coefficients on their behavior in terms of softening or hardening. In the second part, we assess the influence of the linear and nonlinear parameters on the dynamic behavior of a wing-based piezoaeroelastic energy harvester. The system is composed of a rigid airfoil that is constrained to pitch and plunge and supported by linear and nonlinear torsional and flexural springs with a piezoelectric coupling attached to the plunge degree of freedom. Linear analysis is performed to determine the effects of the linear spring coefficients and electrical load resistance on the flutter speed. Then, the normal form of the Hopf bifurcation ( utter) is derived to characterize the type of instability and determine the effects of the aerodynamic nonlinearities and the nonlinear coefficients of the springs on the system's stability near the bifurcation. This is useful to characterize the effects of different parameters on the system's output and ensure that subcritical or "catastrophic" bifurcation does not take place. Both linear and nonlinear analyses are then used to design and enhance the performance of these harvesters. In the last part, the concept of energy harvesting from vortex-induced vibrations of a circular cylinder is investigated. The power levels that can be generated from these vibrations and the variations of these levels with the freestream velocity are determined. A mathematical model that accounts for the coupled lift force, cylinder motion and generated voltage is presented. Linear analysis of the electromechanical model is performed to determine the effects of the electrical load resistance on the natural frequency of the rigid cylinder and the onset of the synchronization region. The impacts of the nonlinearities on the cylinder's response and energy harvesting are then investigated.

Blind identification of nonlinear models with non-Gaussian inputs

NASA Astrophysics Data System (ADS)

Prakriya, Shankar; Pasupathy, Subbarayan; Hatzinakos, Dimitrios

1995-12-01

Some methods are proposed for the blind identification of finite-order discrete-time nonlinear models with non-Gaussian circular inputs. The nonlinear models consist of two finite memory linear time invariant (LTI) filters separated by a zero-memory nonlinearity (ZMNL) of the polynomial type (the LTI-ZMNL-LTI models). The linear subsystems are allowed to be of non-minimum phase (NMP). The methods base their estimates of the impulse responses on slices of the N plus 1th order polyspectra of the output sequence. It is shown that the identification of LTI-ZMNL systems requires only a 1-D moment or polyspectral slice. The coefficients of the ZMNL are not estimated, and need not be known. The order of the nonlinearity can, in theory, be estimated from the received signal. These methods possess several noise and interference suppression characteristics, and have applications in modeling nonlinearly amplified QAM/QPSK signals in digital satellite and microwave communications.

Tuning the nonlinear response of (6,5)-enriched single-wall carbon nanotubes dispersions

NASA Astrophysics Data System (ADS)

Aréstegui, O. S.; Silva, E. C. O.; Baggio, A. L.; Gontijo, R. N.; Hickmann, J. M.; Fantini, C.; Alencar, M. A. R. C.; Fonseca, E. J. S.

2017-04-01

Ultrafast nonlinear optical properties of (6,5)-enriched single-wall carbon nanotubes (SWCNTs) dispersions are investigated using the thermally managed Z-scan technique. As the (6,5) SWCNTs presented a strong resonance in the range of 895-1048 nm, the nonlinear refractive index (n2) and the absorption coefficients (β) measurements were performed tuning the laser exactly around absorption peak of the (6,5) SWCNTs. It is observed that the nonlinear response is very sensitive to the wavelength and the spectral behavior of n2 is strongly correlated to the tubes one-photon absorption band, presenting also a peak when the laser photon energy is near the tube resonance energy. This result suggests that a suitable selection of nanotubes types may provide optimized nonlinear optical responses in distinct regions of the electromagnetic spectrum. Analysis of the figures of merit indicated that this material is promising for ultrafast nonlinear optical applications under near infrared excitation.

Pulsed laser induced optical nonlinearities in undoped, copper doped and chromium doped CdS quantum dots

NASA Astrophysics Data System (ADS)

Sharma, Dimple; Malik, B. P.; Gaur, Arun

2015-04-01

Quantum dots (QDs) of CdS, Cu doped and Cr doped CdS were synthesized through chemical co- precipitation method. The synthesized QDs have been characterized by x-ray diffraction, ultraviolet visible absorption spectroscopy. The diameters of QDs were calculated using Debye-Scherrer’s formula and Brus equation. They are found to be in 3.5-3.8 nm range. The nonlinear properties has been studied by the open and closed aperture Z-scan technique using frequency double Nd:YAG laser. The nonlinear refractive index (n2), nonlinear absorption coefficient (β), third order nonlinear susceptibilities (χ3) of QDs has been calculated. It has been found that the values of nonlinear parameters are higher for doped QDs than undoped CdS QDs. Hence they can be regarded as potential material for the development of optoelectronics and photonics devices.

Third-order nonlinear optical properties of acid green 25 dye by Z-scan method

NASA Astrophysics Data System (ADS)

Jeyaram, S.; Geethakrishnan, T.

2017-03-01

Third-order nonlinear optical (NLO) properties of aqueous solutions of an anthraquinone dye (Acid green 25 dye, color index: 61570) have been studied by Z-scan method with a 5 mW continuous wave (CW) diode laser operating at 635 nm. The nonlinear refractive index (n2) and the absorption coefficient (β) have been evaluated respectively from the closed and open aperture Z-scan data and the values of these parameters are found to increase with increase in concentration of the dye solution. The negative sign of the observed nonlinear refractive index (n2) indicates that the aqueous solution of acid green 25 dye exhibits self-defocusing type optical nonlinearity. The mechanism of the observed nonlinear absorption (NLA) and nonlinear refraction (NLR) is attributed respectively to reverse saturable absorption (RSA) and thermal nonlinear effects. The magnitudes of n2 and β are found to be of the order of 10-7 cm2/W and 10-3 cm/W respectively. With these experimental results, the authors suggest that acid green 25 dye may have potential applications in nonlinear optics.

Controlling the stability of nonlinear optical modes via electromagnetically induced transparency

NASA Astrophysics Data System (ADS)

Zhang, Kun; Liang, Yi-zeng; Lin, Ji; Li, Hui-jun

2018-02-01

We propose a scheme to generate and stabilize the high-dimensional spatial solitons via electromagnetically induced transparency (EIT). The system we consider is a resonant atomic ensemble having Λ configuration. We illustrate that under EIT conditions the equation satisfied by the probe field envelope is reduced to a saturable nonlinear Schrödinger equation with the trapping potential, provided by a far-detuned laser field and a random magnetic field. We present high-dimensional soliton solutions exhibiting many interesting characteristics, including diversity (i.e., many different types of soliton solutions can be found, including bright, ring multipole bright, ring multipole defect mode, multiring bright, multiring defect mode, and vortices solitons), the phase transition between bright soliton and higher-order defect modes (i.e., the phase transition can be realized by controlling the nonlinear coefficient or the intensity of the trapping potential), and stability (i.e., various solitons can be stabilized by the Gaussian potential provided by the far detuned laser field, or the random potential provided by the magnetic field). We also find that some solitons are the extension of the linear eigenmode, whereas others entirely derive from the role of nonlinearity. Compared with previous studies, we not only show the diverse soliton solutions in the same system but also find the boundary of the phase transition for the type of solitons. In addition, we present the possibility of using the random potential to stabilize various solitons and vortices.

On modelling the pressure-strain correlations in wall bounded flows

NASA Technical Reports Server (NTRS)

Peltier, L. J.; Biringen, S.

1990-01-01

Turbulence models for the pressure-strain term of the Reynolds-stress equations in the vicinity of a moving wall are evaluated for a high Reynolds number flow using decaying grid turbulence as a model problem. The data of Thomas and Hancock are used as a base for evaluating the different turbulence models. In particular, the Rotta model for return-to-isotropy is evaluated both in its inclusion into the Reynolds-stress equation model and in comparison to a nonlinear model advanced by Sarkar and Speziale. Further, models for the wall correction to the transfer term advanced by Launder et al., Shir, and Shih and Lumley are compared. Initial data using the decaying grid turbulence experiment as a base suggests that the coefficients proposed for these models are high perhaps by as much as an order of magnitude. The Shih and Lumley model which satisfies realizability constraints, in particular, seems to hold promise in adequately modeling the Reynolds stress components of this flow. Extensions of this work are to include testing the homogeneous transfer model by Shih and Lumley and the testing of the wall transfer models using their proposed coefficients and the coefficients chosen from this work in a flow with mean shear component.

Bio-inspired ``jigsaw''-like interlocking sutures: Modeling, optimization, 3D printing and testing

NASA Astrophysics Data System (ADS)

Malik, I. A.; Mirkhalaf, M.; Barthelat, F.

2017-05-01

Structural biological materials such as bone, teeth or mollusk shells draw their remarkable performance from a sophisticated interplay of architectures and weak interfaces. Pushed to the extreme, this concept leads to sutured materials, which contain thin lines with complex geometries. Sutured materials are prominent in nature, and have recently served as bioinspiration for toughened ceramics and glasses. Sutures can generate large deformations, toughness and damping in otherwise all brittle systems and materials. In this study we examine the design and optimization of sutures with a jigsaw puzzle-like geometry, focusing on the non-linear traction behavior generated by the frictional pullout of the jigsaw tabs. We present analytical models which accurately predict the entire pullout response. Pullout strength and energy absorption increase with higher interlocking angles and for higher coefficients of friction, but the associated high stresses in the solid may fracture the tabs. Systematic optimization reveals a counter-intuitive result: the best pullout performance is achieved with interfaces with low coefficient of friction and high interlocking angle. We finally use 3D printing and mechanical testing to verify the accuracy of the models and of the optimization. The models and guidelines we present here can be extended to other types of geometries and sutured materials subjected to other loading/boundary conditions. The nonlinear responses of sutures are particularly attractive to augment the properties and functionalities of inherently brittle materials such as ceramics and glasses.

Two-Photon Absorption in Organometallic Bromide Perovskites.

PubMed

Walters, Grant; Sutherland, Brandon R; Hoogland, Sjoerd; Shi, Dong; Comin, Riccardo; Sellan, Daniel P; Bakr, Osman M; Sargent, Edward H

2015-09-22

Organometallic trihalide perovskites are solution-processed semiconductors that have made great strides in third-generation thin film light-harvesting and light-emitting optoelectronic devices. Recently, it has been demonstrated that large, high-purity single crystals of these perovskites can be synthesized from the solution phase. These crystals' large dimensions, clean bandgap, and solid-state order have provided us with a suitable medium to observe and quantify two-photon absorption in perovskites. When CH3NH3PbBr3 single crystals are pumped with intense 800 nm light, we observe band-to-band photoluminescence at 572 nm, indicative of two-photon absorption. We report the nonlinear absorption coefficient of CH3NH3PbBr3 perovskites to be 8.6 cm GW(-1) at 800 nm, comparable to epitaxial single-crystal semiconductors of similar bandgap. We have leveraged this nonlinear process to electrically autocorrelate a 100 fs pulsed laser using a two-photon perovskite photodetector. This work demonstrates the viability of organometallic trihalide perovskites as a convenient and low-cost nonlinear absorber for applications in ultrafast photonics.

Reliability of recurrence quantification analysis measures of the center of pressure during standing in individuals with musculoskeletal disorders.

PubMed

Mazaheri, Masood; Negahban, Hossein; Salavati, Mahyar; Sanjari, Mohammad Ali; Parnianpour, Mohamad

2010-09-01

Although the application of nonlinear tools including recurrence quantification analysis (RQA) has increasingly grown in the recent years especially in balance-disordered populations, there have been few studies which determine their measurement properties. Therefore, a methodological study was performed to estimate the intersession and intrasession reliability of some dynamic features provided by RQA for nonlinear analysis of center of pressure (COP) signals recorded during quiet standing in a sample of patients with musculoskeletal disorders (MSDs) including low back pain (LBP), anterior cruciate ligament (ACL) injury and functional ankle instability (FAI). The subjects completed postural measurements with three levels of difficulty (rigid surface-eyes open, rigid surface-eyes closed, and foam surface-eyes closed). Four RQA measures (% recurrence, % determinism, entropy, and trend) were extracted from the recurrence plot. Relative reliability of these measures was assessed using intraclass correlation coefficient and absolute reliability using standard error of measurement and coefficient of variation. % Determinism and entropy were the most reliable features of RQA for the both intersession and intrasession reliability measures. High level of reliability of % determinism and entropy in this preliminary investigation may show their clinical promise for discriminative and evaluative purposes of balance performance. 2010 IPEM. Published by Elsevier Ltd. All rights reserved.

On shifted Jacobi spectral method for high-order multi-point boundary value problems

NASA Astrophysics Data System (ADS)

Doha, E. H.; Bhrawy, A. H.; Hafez, R. M.

2012-10-01

This paper reports a spectral tau method for numerically solving multi-point boundary value problems (BVPs) of linear high-order ordinary differential equations. The construction of the shifted Jacobi tau approximation is based on conventional differentiation. This use of differentiation allows the imposition of the governing equation at the whole set of grid points and the straight forward implementation of multiple boundary conditions. Extension of the tau method for high-order multi-point BVPs with variable coefficients is treated using the shifted Jacobi Gauss-Lobatto quadrature. Shifted Jacobi collocation method is developed for solving nonlinear high-order multi-point BVPs. The performance of the proposed methods is investigated by considering several examples. Accurate results and high convergence rates are achieved.

Estimation of real-time runway surface contamination using flight data recorder parameters

NASA Astrophysics Data System (ADS)

Curry, Donovan

Within this research effort, the development of an analytic process for friction coefficient estimation is presented. Under static equilibrium, the sum of forces and moments acting on the aircraft, in the aircraft body coordinate system, while on the ground at any instant is equal to zero. Under this premise the longitudinal, lateral and normal forces due to landing are calculated along with the individual deceleration components existent when an aircraft comes to a rest during ground roll. In order to validate this hypothesis a six degree of freedom aircraft model had to be created and landing tests had to be simulated on different surfaces. The simulated aircraft model includes a high fidelity aerodynamic model, thrust model, landing gear model, friction model and antiskid model. Three main surfaces were defined in the friction model; dry, wet and snow/ice. Only the parameters recorded by an FDR are used directly from the aircraft model all others are estimated or known a priori. The estimation of unknown parameters is also presented in the research effort. With all needed parameters a comparison and validation with simulated and estimated data, under different runway conditions, is performed. Finally, this report presents results of a sensitivity analysis in order to provide a measure of reliability of the analytic estimation process. Linear and non-linear sensitivity analysis has been performed in order to quantify the level of uncertainty implicit in modeling estimated parameters and how they can affect the calculation of the instantaneous coefficient of friction. Using the approach of force and moment equilibrium about the CG at landing to reconstruct the instantaneous coefficient of friction appears to be a reasonably accurate estimate when compared to the simulated friction coefficient. This is also true when the FDR and estimated parameters are introduced to white noise and when crosswind is introduced to the simulation. After the linear analysis the results show the minimum frequency at which the algorithm still provides moderately accurate data is at 2Hz. In addition, the linear analysis shows that with estimated parameters increased and decreased up to 25% at random, high priority parameters have to be accurate to within at least +/-5% to have an effect of less than 1% change in the average coefficient of friction. Non-linear analysis results show that the algorithm can be considered reasonably accurate for all simulated cases when inaccuracies in the estimated parameters vary randomly and simultaneously up to +/-27%. At worst-case the maximum percentage change in average coefficient of friction is less than 10% for all surfaces.

A statistical methodology for estimating transport parameters: Theory and applications to one-dimensional advectivec-dispersive systems

USGS Publications Warehouse

Wagner, Brian J.; Gorelick, Steven M.

1986-01-01

A simulation nonlinear multiple-regression methodology for estimating parameters that characterize the transport of contaminants is developed and demonstrated. Finite difference contaminant transport simulation is combined with a nonlinear weighted least squares multiple-regression procedure. The technique provides optimal parameter estimates and gives statistics for assessing the reliability of these estimates under certain general assumptions about the distributions of the random measurement errors. Monte Carlo analysis is used to estimate parameter reliability for a hypothetical homogeneous soil column for which concentration data contain large random measurement errors. The value of data collected spatially versus data collected temporally was investigated for estimation of velocity, dispersion coefficient, effective porosity, first-order decay rate, and zero-order production. The use of spatial data gave estimates that were 2–3 times more reliable than estimates based on temporal data for all parameters except velocity. Comparison of estimated linear and nonlinear confidence intervals based upon Monte Carlo analysis showed that the linear approximation is poor for dispersion coefficient and zero-order production coefficient when data are collected over time. In addition, examples demonstrate transport parameter estimation for two real one-dimensional systems. First, the longitudinal dispersivity and effective porosity of an unsaturated soil are estimated using laboratory column data. We compare the reliability of estimates based upon data from individual laboratory experiments versus estimates based upon pooled data from several experiments. Second, the simulation nonlinear regression procedure is extended to include an additional governing equation that describes delayed storage during contaminant transport. The model is applied to analyze the trends, variability, and interrelationship of parameters in a mourtain stream in northern California.

Role of orbital filling on nonlinear ionic Raman scattering in perovskite titanates

NASA Astrophysics Data System (ADS)

Gu, Mingqiang; Rondinelli, James M.

2017-01-01

The linear and nonlinear phononic interactions between an optically excited infrared (IR) or hyper-Raman mode and a driven Raman mode are computed for the d0 (CaTiO3) and d1 (LaTiO3) titanates within a first-principles density functional framework. We calculate the potential energy surface expanded in terms of the Ag or B1 g mode amplitudes coupled to the Au or the B3 u mode and determine the coupling coefficients for these multimode interactions. We find that the linear-quadratic coupling dominates the anharmonicities over the quadratic-quadratic interaction in the perovskite titanates. The IR and Raman modes both modify the electronic structure with the former being more significant but occurring on a different time scale; furthermore, the coupled-mode interactions lead to sizable perturbations to the valence bandwidth (˜100 meV ) and band gap (˜50 meV). By comparing the coupling coefficients of undoped CaTiO3 and LaTiO3 to those for electron-doped (CaTiO3) and hole-doped (LaTiO3) titanates, we isolate the role of orbital filling in the nonlinear coupling process. We find that with increasing occupancy of the d manifold, the linear-quadratic interaction decreases by approximately 30% with minor changes induced by the cation chemistry (that mainly affect the phonon mode frequencies) or by electron correlation. We identify the importance of the Ti-O bond stiffness, which depends on the orbital filling, in governing the lattice anharmonicitiy. This microscopic understanding can be used to increase the nonlinear coupling coefficient to facilitate more facile access of nonequilibrium structures and properties through ionic Raman scattering processes.

Physical uniqueness of higher-order Korteweg-de Vries theory for continuously stratified fluids without background shear

NASA Astrophysics Data System (ADS)

Shimizu, Kenji

2017-10-01

The 2nd-order Korteweg-de Vries (KdV) equation and the Gardner (or extended KdV) equation are often used to investigate internal solitary waves, commonly observed in oceans and lakes. However, application of these KdV-type equations for continuously stratified fluids to geophysical problems is hindered by nonuniqueness of the higher-order coefficients and the associated correction functions to the wave fields. This study proposes to reduce arbitrariness of the higher-order KdV theory by considering its uniqueness in the following three physical senses: (i) consistency of the nonlinear higher-order coefficients and correction functions with the corresponding phase speeds, (ii) wavenumber-independence of the vertically integrated available potential energy, and (iii) its positive definiteness. The spectral (or generalized Fourier) approach based on vertical modes in the isopycnal coordinate is shown to enable an alternative derivation of the 2nd-order KdV equation, without encountering nonuniqueness. Comparison with previous theories shows that Parseval's theorem naturally yields a unique set of special conditions for (ii) and (iii). Hydrostatic fully nonlinear solutions, derived by combining the spectral approach and simple-wave analysis, reveal that both proposed and previous 2nd-order theories satisfy (i), provided that consistent definitions are used for the wave amplitude and the nonlinear correction. This condition reduces the arbitrariness when higher-order KdV-type theories are compared with observations or numerical simulations. The coefficients and correction functions that satisfy (i)-(iii) are given by explicit formulae to 2nd order and by algebraic recurrence relationships to arbitrary order for hydrostatic fully nonlinear and linear fully nonhydrostatic effects.

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

Nonlinear Waves In A Stenosed Elastic Tube Filled With Viscous Fluid: Forced Perturbed Korteweg-De Vries Equation

NASA Astrophysics Data System (ADS)

Gaik*, Tay Kim; Demiray, Hilmi; Tiong, Ong Chee

In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the pro pagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By intro ducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the small-ness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.

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.

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

PubMed Central

Allagui, Anis; Freeborn, Todd J.; Elwakil, Ahmed S.; Maundy, Brent J.

2016-01-01

The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal SsC behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance Rs in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (Rs, Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical RsC model. We validate our formulae with the experimental measurements of different EDLCs. PMID:27934904

Ultrashort dark solitons interactions and nonlinear tunneling in the modified nonlinear Schrödinger equation with variable coefficient

NASA Astrophysics Data System (ADS)

Musammil, N. M.; Porsezian, K.; Nithyanandan, K.; Subha, P. A.; Tchofo Dinda, P.

2017-09-01

We present the study of the dark soliton dynamics in an inhomogeneous fiber by means of a variable coefficient modified nonlinear Schrödinger equation (Vc-MNLSE) with distributed dispersion, self-phase modulation, self-steepening and linear gain/loss. The ultrashort dark soliton pulse evolution and interaction is studied by using the Hirota bilinear (HB) method. In particular, we give much insight into the effect of self-steepening (SS) on the dark soliton dynamics. The study reveals a shock wave formation, as a major effect of SS. Numerically, we study the dark soliton propagation in the continuous wave background, and the stability of the soliton solution is tested in the presence of photon noise. The elastic collision behaviors of the dark solitons are discussed by the asymptotic analysis. On the other hand, considering the nonlinear tunneling of dark soliton through barrier/well, we find that the tunneling of the dark soliton depends on the height of the barrier and the amplitude of the soliton. The intensity of the tunneling soliton either forms a peak or valley and retains its shape after the tunneling. For the case of exponential background, the soliton tends to compress after tunneling through the barrier/well.

Two Photon Absorption And Refraction in Bulk of the Semiconducting Materials

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

Kumari, Vinay; Department of Physics, DCRUST Murthal, Haryana; Kumar, Vinod

2011-10-20

Fast electronic detection systems have opened up a number of new fields like nonlinear optics, optical communication, coherent optics, optical bistability, two/four wave mixing. The interest in this field has been stimulated by the importance of multiphoton processes in many fundamental aspects of physics. It has proved to be an invaluable tool for determining the optical and electronic properties of the solids because of the fact that one gets the information about the bulk of the material rather than the surface one. In this paper we report, the measurement of the nonlinear absorption and refraction from the band gap tomore » half-band gap region of bulk of semiconductors in the direct and indirect band gap crystals with nanosecond laser. The measured theoretical calculated values of two-photon absorption coefficients ({beta}) and nonlinear refraction n{sub 2}({omega}) of direct band gap crystal match the earlier reported theoretical predictions. By making use of these theoretical calculated values, we have estimated {beta} and n{sub 2}({omega}) in the case of indirect band gap crystals. Low value of absorption coefficient in case of indirect band gap crystals have been attributed to phonon assisted transition while reduction in nonlinear refraction is due to the rise in saturation taking place in the absorption.« less

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry

NASA Astrophysics Data System (ADS)

Allagui, Anis; Freeborn, Todd J.; Elwakil, Ahmed S.; Maundy, Brent J.

2016-12-01

The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal SsC behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance Rs in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (Rs, Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical RsC model. We validate our formulae with the experimental measurements of different EDLCs.

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

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

Incomplete data based parameter identification of nonlinear and time-variant oscillators with fractional derivative elements

NASA Astrophysics Data System (ADS)

Kougioumtzoglou, Ioannis A.; dos Santos, Ketson R. M.; Comerford, Liam

2017-09-01

Various system identification techniques exist in the literature that can handle non-stationary measured time-histories, or cases of incomplete data, or address systems following a fractional calculus modeling. However, there are not many (if any) techniques that can address all three aforementioned challenges simultaneously in a consistent manner. In this paper, a novel multiple-input/single-output (MISO) system identification technique is developed for parameter identification of nonlinear and time-variant oscillators with fractional derivative terms subject to incomplete non-stationary data. The technique utilizes a representation of the nonlinear restoring forces as a set of parallel linear sub-systems. In this regard, the oscillator is transformed into an equivalent MISO system in the wavelet domain. Next, a recently developed L1-norm minimization procedure based on compressive sensing theory is applied for determining the wavelet coefficients of the available incomplete non-stationary input-output (excitation-response) data. Finally, these wavelet coefficients are utilized to determine appropriately defined time- and frequency-dependent wavelet based frequency response functions and related oscillator parameters. Several linear and nonlinear time-variant systems with fractional derivative elements are used as numerical examples to demonstrate the reliability of the technique even in cases of noise corrupted and incomplete data.

Surface plasmon resonance and nonlinear optical behavior of pulsed laser-deposited semitransparent nanostructured copper thin films

NASA Astrophysics Data System (ADS)

Kesarwani, Rahul; Khare, Alika

2018-06-01

In this paper, surface plasmon resonance (SPR) and nonlinear optical properties of semitransparent nanostructured copper thin films fabricated on the glass substrate at 400 °C by pulsed laser deposition technique are reported. The thickness, linear absorption coefficient and linear refractive index of the films were measured by spectroscopic ellipsometer. The average particle size as measured via atomic force microscope was in the range of 12.84-26.02 nm for the deposition time ranging from 5 to 10 min, respectively. X-ray diffraction spectra revealed the formation of Cu (111) and Cu (200) planes. All these thin films exhibited broad SPR peak. The third-order optical nonlinearity of all the samples was investigated via modified z-scan technique using cw laser at a wavelength of 632.8 nm. The open aperture z-scan spectra of Cu thin film deposited for 5 min duration exhibited reverse saturation absorption whereas all the other samples displayed saturation absorption behavior. The nonlinear refractive index coefficient of these films showed a positive sign having the magnitude of the order of 10- 4 cm/W. The real and imaginary parts of susceptibilities were also calculated from the z-scan data and found to be of the order of 10- 6 esu.

Optical and dielectric studies of KH2PO4 crystal influenced by organic ligand of citric acid and L-valine: A single crystal growth and comparative study

NASA Astrophysics Data System (ADS)

Anis, Mohd; Hakeem, D. A.; Muley, G. G.

In the present study pure, citric acid (CA) and L-valine (LV) doped potassium dihydrogen phosphate (KDP) crystals have been grown with the aim to investigate the nonlinear optical applications facilitated by UV-visible, third order nonlinear optical (TONLO) and dielectric properties. The structural parameters of grown crystals have been confirmed by single crystal X-ray diffraction analysis. The enhancement in optical transparency of KDP crystal due to addition of CA and LV has been examined within 200-900 nm by means of UV-visible spectral analysis. In addition, the transmittance data have been used to evaluate the effect of dopants on reflectance, refractive index and extinction coefficient of grown crystals in the visible region. The Z-scan analysis has been performed at 632.8 nm to identify the nature of photoinduced nonlinear refraction and nonlinear absorption in doped KDP crystals. The influence of π-bonded ligand of dopant CA and LV on TONLO susceptibility (χ3), refractive index (n2) and absorption coefficient (β) of KDP crystals has been evaluated to discuss laser assisted device applications. The decrease in dielectric constant and dielectric loss of KDP crystal due to addition of CA and LV has been explored using the temperature dependent dielectric studies.

Reevaluation of Performance of Electric Double-layer Capacitors from Constant-current Charge/Discharge and Cyclic Voltammetry.

PubMed

Allagui, Anis; Freeborn, Todd J; Elwakil, Ahmed S; Maundy, Brent J

2016-12-09

The electric characteristics of electric-double layer capacitors (EDLCs) are determined by their capacitance which is usually measured in the time domain from constant-current charging/discharging and cyclic voltammetry tests, and from the frequency domain using nonlinear least-squares fitting of spectral impedance. The time-voltage and current-voltage profiles from the first two techniques are commonly treated by assuming ideal R s C behavior in spite of the nonlinear response of the device, which in turn provides inaccurate values for its characteristic metrics [corrected]. In this paper we revisit the calculation of capacitance, power and energy of EDLCs from the time domain constant-current step response and linear voltage waveform, under the assumption that the device behaves as an equivalent fractional-order circuit consisting of a resistance R s in series with a constant phase element (CPE(Q, α), with Q being a pseudocapacitance and α a dispersion coefficient). In particular, we show with the derived (R s , Q, α)-based expressions, that the corresponding nonlinear effects in voltage-time and current-voltage can be encompassed through nonlinear terms function of the coefficient α, which is not possible with the classical R s C model. We validate our formulae with the experimental measurements of different EDLCs.

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.

Strongly localized dark modes in binary discrete media with cubic-quintic nonlinearity within the anti-continuum limit

NASA Astrophysics Data System (ADS)

Taib, L. Abdul; Hadi, M. S. Abdul; Umarov, B. A.

2017-12-01

The existence of dark strongly localized modes of binary discrete media with cubic-quintic nonlinearity is numerically demonstrated by solving the relevant discrete nonlinear Schrödinger equations. In the model, the coupling coefficients between adjacent sites are set to be relatively small representing the anti-continuum limit. In addition, approximated analytical solutions for vectorial solitons with various topologies are derived. Stability analysis of the localized states was performed using the standard linearized eigenfrequency problem. The prediction from the stability analysis are furthermore verified by direct numerical integrations.

Nonlinear optical characterization of ZnS thin film synthesized by chemical spray pyrolysis method

NASA Astrophysics Data System (ADS)

G, Sreeja V.; V, Sabitha P.; Anila, E. I.; R, Reshmi; John, Manu Punnan; Radhakrishnan, P.

2014-10-01

ZnS thin film was prepared by Chemical Spray Pyrolysis (CSP) method. The sample was characterized by X-ray diffraction method and Z scan technique. XRD pattern showed that ZnS thin film has hexagonal structure with an average size of about 5.6nm. The nonlinear optical properties of ZnS thin film was studied by open aperture Z-Scan technique using Q-switched Nd-Yag Laser at 532nm. The Z-scan plot showed that the investigated ZnS thin film has saturable absorption behavior. The nonlinear absorption coefficient and saturation intensity were also estimated.

Cavity equations for a positive- or negative-refraction-index material with electric and magnetic nonlinearities.

PubMed

Mártin, Daniel A; Hoyuelos, Miguel

2009-11-01

We study evolution equations for electric and magnetic field amplitudes in a ring cavity with plane mirrors. The cavity is filled with a positive or negative-refraction-index material with third-order effective electric and magnetic nonlinearities. Two coupled nonlinear equations for the electric and magnetic amplitudes are obtained. We prove that the description can be reduced to one Lugiato-Lefever equation with generalized coefficients. A stability analysis of the homogeneous solution, complemented with numerical integration, shows that any combination of the parameters should correspond to one of three characteristic behaviors.

Approximating the nonlinear density dependence of electron transport coefficients and scattering rates across the gas-liquid interface

NASA Astrophysics Data System (ADS)

Garland, N. A.; Boyle, G. J.; Cocks, D. G.; White, R. D.

2018-02-01

This study reviews the neutral density dependence of electron transport in gases and liquids and develops a method to determine the nonlinear medium density dependence of electron transport coefficients and scattering rates required for modeling transport in the vicinity of gas-liquid interfaces. The method has its foundations in Blanc’s law for gas-mixtures and adapts the theory of Garland et al (2017 Plasma Sources Sci. Technol. 26) to extract electron transport data across the gas-liquid transition region using known data from the gas and liquid phases only. The method is systematically benchmarked against multi-term Boltzmann equation solutions for Percus-Yevick model liquids. Application to atomic liquids highlights the utility and accuracy of the derived method.

Linear and nonlinear magneto-optical properties of monolayer phosphorene

NASA Astrophysics Data System (ADS)

Nguyen, Chuong V.; Ngoc Hieu, Nguyen; Duque, C. A.; Quoc Khoa, Doan; Van Hieu, Nguyen; Van Tung, Luong; Vinh Phuc, Huynh

2017-01-01

We theoretically study the magneto-optical properties of monolayer phosphorene under a perpendicular magnetic field. We evaluate linear, third-order nonlinear, and total absorption coefficients and relative refractive index changes as functions of the photon energy and the magnetic field, and show that they are strongly influenced by the magnetic field. The magneto-optical absorption coefficients and relative refractive index changes appear in two different regimes: the microwave to THz and the visible frequency. The amplitude of intra-band transition peaks is larger than that of the inter-band transitions. The resonant peaks are blue-shifted with the magnetic field. Our results demonstrate the potential of monolayer phosphorene as a new two-dimensional material for applications in nano-electronic and optical devices as a promising alternative to graphene.

On some nonlinear effects in ultrasonic fields

PubMed

Tjotta

2000-03-01

Nonlinear effects associated with intense sound fields in fluids are considered theoretically. Special attention is directed to the study of higher effects that cannot be described within the standard propagation models of nonlinear acoustics (the KZK and Burgers equations). The analysis is based on the fundamental equations of motion for a thermoviscous fluid, for which thermal equations of state exist. Model equations are derived and used to analyze nonlinear sources for generation of flow and heat, and other changes in the ambient state of the fluid. Fluctuations in the coefficients of viscosity and thermal conductivity caused by the sound field, are accounted for. Also considered are nonlinear effects induced in the fluid by flexural vibrations. The intensity and absorption of finite amplitude sound waves are calculated, and related to the sources for generation of higher order effects.

Numerical solution of the generalized, dissipative KdV-RLW-Rosenau equation with a compact method

NASA Astrophysics Data System (ADS)

Apolinar-Fernández, Alejandro; Ramos, J. I.

2018-07-01

The nonlinear dynamics of the one-dimensional, generalized Korteweg-de Vries-regularized-long wave-Rosenau (KdV-RLW-Rosenau) equation with second- and fourth-order dissipative terms subject to initial Gaussian conditions is analyzed numerically by means of three-point, fourth-order accurate, compact finite differences for the discretization of the spatial derivatives and a trapezoidal method for time integration. By means of a Fourier analysis and global integration techniques, it is shown that the signs of both the fourth-order dissipative and the mixed fifth-order derivative terms must be negative. It is also shown that an increase of either the linear drift or the nonlinear convection coefficients results in an increase of the steepness, amplitude and speed of the right-propagating wave, whereas the speed and amplitude of the wave decrease as the power of the nonlinearity is increased, if the amplitude of the initial Gaussian condition is equal to or less than one. It is also shown that the wave amplitude and speed decrease and the curvature of the wave's trajectory increases as the coefficients of the second- and fourth-order dissipative terms are increased, while an increase of the RLW coefficient was found to decrease both the damping and the phase velocity, and generate oscillations behind the wave. For some values of the coefficients of both the fourth-order dissipative and the Rosenau terms, it has been found that localized dispersion shock waves may form in the leading part of the right-propagating wave, and that the formation of a train of solitary waves that result from the breakup of the initial Gaussian conditions only occurs in the absence of both Rosenau's, Kortweg-de Vries's and second- and fourth-order dissipative terms, and for some values of the amplitude and width of the initial condition and the RLW coefficient. It is also shown that negative values of the KdV term result in steeper, larger amplitude and faster waves and a train of oscillations behind the wave, whereas positive values of that coefficient may result in negative phase and group velocities, no wave breakup and oscillations ahead of the right-propagating wave.

Vibrational Properties of High- Superconductors Levitated Above a Bipolar Permanent Magnetic Guideway

NASA Astrophysics Data System (ADS)

Liu, Lu; Wang, Jiasu

2014-05-01

A bipolar permanent magnetic guideway (PMG) has a unique magnetic field distribution profile which may introduce a better levitation performance and stability to the high- superconducting (HTS) maglev system. The dynamic vibration properties of multiple YBCO bulks arranged into different arrays positioned above a bipolar PMG and free to levitate were investigated. The acceleration and resonance frequencies were experimentally measured, and the stiffness and damping coefficients were evaluated for dynamic stability. Results indicate that the levitation stiffness is closely related to the field-cooling-height and sample positioning. The damping ratio was found to be low and nonlinear for the Halbach bipolar HTS-PMG system.

Effect of antimony (Sb) addition on the linear and non-linear optical properties of amorphous Ge-Te-Sb thin films

NASA Astrophysics Data System (ADS)

Kumar, P.; Kaur, J.; Tripathi, S. K.; Sharma, I.

2017-12-01

Non-crystalline thin films of Ge20Te80-xSbx (x = 0, 2, 4, 6, 10) systems were deposited on glass substrate using thermal evaporation technique. The optical coefficients were accurately determined by transmission spectra using Swanepoel envelope method in the spectral region of 400-1600 nm. The refractive index was found to increase from 2.38 to 2.62 with the corresponding increase in Sb content over the entire spectral range. The dispersion of refractive index was discussed in terms of the single oscillator Wemple-DiDomenico model. Tauc relation for the allowed indirect transition showed decrease in optical band gap. To explore non-linearity, the spectral dependence of third order susceptibility of a-Ge-Te-Sb thin films was evaluated from change of index of refraction using Miller's rule. Susceptibility values were found to enhance rapidly from 10-13 to 10-12 (esu), with the red shift in the absorption edge. Non-linear refractive index was calculated by Fourier and Snitzer formula. The values were of the order of 10-12 esu. At telecommunication wavelength, these non-linear refractive index values showed three orders higher than that of silica glass. Dielectric constant and optical conductivity were also reported. The prepared Sb doped thin films on glass substrate with observed improved functional properties have a noble prospect in the application of nonlinear optical devices and might be used for a high speed communication fiber. Non-linear parameters showed good agreement with the values given in the literature.

Effect of marine derived deoxyribonucleic acid on nonlinear optical properties of PicoGreen dye

NASA Astrophysics Data System (ADS)

Pradeep, C.; Mathew, S.; Nithyaja, B.; Radhakrishnan, P.; Nampoori, V. P. N.

2013-06-01

We have investigated the effect of DNA on nonlinear absorption of PicoGreen dye using single beam open aperture Z-scan technique in nanosecond regime. We observed reverse saturable absorption at 532 nm for PicoGreen without DNA. In the presence of DNA, the sample begins to behave like saturable absorbers and this effect increased as the concentration of DNA was increased. The dye-intercalated DNA showed SA characteristics near the focus but exhibited RSA characteristics at the focus. Theoretical analysis has been performed using a two-photon absorption model based on nonlinear absorption coefficient and saturation intensity. Such tailoring of optical nonlinear absorption in PicoGreen makes it a potential candidate for photonic application.

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

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.

Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion

NASA Astrophysics Data System (ADS)

Sikora, Roman; Markiewicz, Przemysław; Pabjańczyk, Wiesława

2018-04-01

The power systems usually include a number of nonlinear receivers. Nonlinear receivers are the source of disturbances generated to the power system in the form of higher harmonics. The level of these disturbances describes the total harmonic distortion coefficient THD. Its value depends on many factors. One of them are the deformation and change in RMS value of supply voltage. A modern LED luminaire is a nonlinear receiver as well. The paper presents the results of the analysis of the influence of change in RMS value of supply voltage and the level of dimming of the tested luminaire on the value of the current THD. The analysis was made using a mathematical model based on multivariable polynomial fitting.

Parameter and Structure Inference for Nonlinear Dynamical Systems

NASA Technical Reports Server (NTRS)

Morris, Robin D.; Smelyanskiy, Vadim N.; Millonas, Mark

2006-01-01

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

Dark-bright solitons in coupled nonlinear Schrödinger equations with unequal dispersion coefficients.

PubMed

Charalampidis, E G; Kevrekidis, P G; Frantzeskakis, D J; Malomed, B A

2015-01-01

We study a two-component nonlinear Schrödinger system with equal, repulsive cubic interactions and different dispersion coefficients in the two components. We consider states that have a dark solitary wave in one component. Treating it as a frozen one, we explore the possibility of the formation of bright-solitonic structures in the other component. We identify bifurcation points at which such states emerge in the bright component in the linear limit and explore their continuation into the nonlinear regime. An additional analytically tractable limit is found to be that of vanishing dispersion of the bright component. We numerically identify regimes of potential stability, not only of the single-peak ground state (the dark-bright soliton), but also of excited states with one or more zero crossings in the bright component. When the states are identified as unstable, direct numerical simulations are used to investigate the outcome of the instability development. Although our principal focus is on the homogeneous setting, we also briefly touch upon the counterintuitive impact of the potential presence of a parabolic trap on the states of interest.

Synthesis, Spectrofluorometric Studies, Micellization and non Linear Optical Properties of Blue Emitting Quinoline (AMQC) Dye.

PubMed

Afzal, S M; Asiri, Abdullah M; Razvi, M A N; Bakry, Ahmed H; Khan, Salman A; Zayed, Mohie E M

2016-03-01

Blue emitting 2-amino-4-(3, 4, 5-tri methoxyphenyl)-9-methoxy-5,6 dihydrobenzo[f]isoquinoline-1-carbonitrile (AMQC) dye was synthesized by one-pot multicomponent reactions (MCRs) of 3,4,5-trimethoxybenzaldehyd, malononitrile, 6-methoxy-1,2,3,4-tetrahydro-naphthalin-1-one and ammonium acetate. Results obtained from spectroscopic and elemental analysis of synthesized AMQC was in good agreement with their chemical structures. Fluorescence polarity study demonstrated that AMQC was sensitive to the polarity of the microenvironment provided by different solvents. In addition, spectroscopic and physicochemical parameters, including electronic absorption, excitation coefficient, stokes shift, oscillator strength, transition dipole moment and fluorescence quantum yield were investigated in order to explore the analytical potential of AMQC. Dye undergoes solubilization in different micelles and may be used as a quencher and a probe to determine the critical micelle concentration (CMC) of SDS and CTAB. Nonlinear optical parameters of AMQC dye shows relatively lower nonlinear refractive index and nonlinear absorption coefficient at the power levels. Variation of n2 with concentration is linear in the concentration range used in the present study.

Effect of homogenous-heterogeneous reactions on MHD Prandtl fluid flow over a stretching sheet

NASA Astrophysics Data System (ADS)

Khan, Imad; Malik, M. Y.; Hussain, Arif; Salahuddin, T.

An analysis is performed to explore the effects of homogenous-heterogeneous reactions on two-dimensional flow of Prandtl fluid over a stretching sheet. In present analysis, we used the developed model of homogeneous-heterogeneous reactions in boundary layer flow. The mathematical configuration of presented flow phenomenon yields the nonlinear partial differential equations. Using scaling transformations, the governing partial differential equations (momentum equation and homogenous-heterogeneous reactions equations) are transformed into non-linear ordinary differential equations (ODE's). Then, resulting non-linear ODE's are solved by computational scheme known as shooting method. The quantitative and qualitative manners of concerned physical quantities (velocity, concentration and drag force coefficient) are examined under prescribed physical constrained through figures and tables. It is observed that velocity profile enhances verses fluid parameters α and β while Hartmann number reduced it. The homogeneous and heterogeneous reactions parameters have reverse effects on concentration profile. Concentration profile shows retarding behavior for large values of Schmidt number. Skin fraction coefficient enhances with increment in Hartmann number H and fluid parameter α .

Analysis of Composite Panels Subjected to Thermo-Mechanical Loads

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Peters, Jeanne M.

1999-01-01

The results of a detailed study of the effect of cutout on the nonlinear response of curved unstiffened panels are presented. The panels are subjected to combined temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order, shear deformation, Sanders-Budiansky-type shell theory with the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, as well as in the material properties of the individual layers. Numerical results are presented for cylindrical panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities as well as their sensitivity to changes in the various panel, layer, and micromechanical parameters.

Growth and nonlinear optical characterization of organic single crystal films

NASA Astrophysics Data System (ADS)

Zhou, Ligui

1997-12-01

Organic single crystal films are important for various future applications in photonics and integrated optics. The conventional method for inorganic crystal growth is not suitable for organic materials, and the high temperature melting method is not good for most organic materials due to decomposition problems. We developed a new method-modified shear method-to grow large area organic single crystal thin films which have exceptional nonlinear optical properties and high quality surfaces. Several organic materials (NPP, PNP and DAST) were synthesized and purified before the thin film crystal growth. Organic single crystal thin films were grown from saturated organic solutions using modified shear method. The area of single crystal films were about 1.5 cm2 for PNP, 1 cm2 for NPP and 5 mm2 for DAST. The thickness of the thin films which could be controlled by the applied pressure ranged from 1μm to 10 μm. The single crystal thin films of organic materials were characterized by polarized microscopy, x-ray diffraction, polarized UV-Visible and polarized micro-FTIR spectroscopy. Polarized microscopy showed uniform birefringence and complete extinction with the rotation of the single crystal thin films under crossed- polarization, which indicated high quality single crystals with no scattering. The surface orientation of single crystal thin films was characterized by x-ray diffraction. The molecular orientation within the crystal was further studied by the polarized UV-Visible and Polarized micro-FTIR techniques combined with the x-ray and polarized microscopy results. A Nd:YAG laser with 35 picosecond pulses at 1064nm wavelength was employed to perform the nonlinear optical characterization of the organic single crystal thin films. Two measurement techniques were used to study the crystal films: second harmonic generation (SHG) and electro-optic (EO) effect. SHG results showed that the nonlinear optical coefficient of NPP was 18 times that of LiNbO3, a standard inorganic crystal material, and the nonlinear optical coefficient of PNP was 11 times that of LiNbO3. Electro-optic measurements showed that r11 = 65 pm/V for NPP and r12 = 350 pm/V for DAST. EO modulation effect was also observed using Fabry-Perot interferometry. Waveguide devices are very important for integrated optics. But the fabrication of waveguide devices on the organic single crystal thin films was difficult due to the solubility of the film in common organic solvents. A modified photolithographic technique was employed to make channel waveguides and poly(vinyl alcohol) (PVA) was used as a protective layer in the fabrication of the waveguides. Waveguides with dimensions about 7/mum x 1μm x 1mm were obtained.

Arrhythmia recognition and classification using combined linear and nonlinear features of ECG signals.

PubMed

Elhaj, Fatin A; Salim, Naomie; Harris, Arief R; Swee, Tan Tian; Ahmed, Taqwa

2016-04-01

Arrhythmia is a cardiac condition caused by abnormal electrical activity of the heart, and an electrocardiogram (ECG) is the non-invasive method used to detect arrhythmias or heart abnormalities. Due to the presence of noise, the non-stationary nature of the ECG signal (i.e. the changing morphology of the ECG signal with respect to time) and the irregularity of the heartbeat, physicians face difficulties in the diagnosis of arrhythmias. The computer-aided analysis of ECG results assists physicians to detect cardiovascular diseases. The development of many existing arrhythmia systems has depended on the findings from linear experiments on ECG data which achieve high performance on noise-free data. However, nonlinear experiments characterize the ECG signal more effectively sense, extract hidden information in the ECG signal, and achieve good performance under noisy conditions. This paper investigates the representation ability of linear and nonlinear features and proposes a combination of such features in order to improve the classification of ECG data. In this study, five types of beat classes of arrhythmia as recommended by the Association for Advancement of Medical Instrumentation are analyzed: non-ectopic beats (N), supra-ventricular ectopic beats (S), ventricular ectopic beats (V), fusion beats (F) and unclassifiable and paced beats (U). The characterization ability of nonlinear features such as high order statistics and cumulants and nonlinear feature reduction methods such as independent component analysis are combined with linear features, namely, the principal component analysis of discrete wavelet transform coefficients. The features are tested for their ability to differentiate different classes of data using different classifiers, namely, the support vector machine and neural network methods with tenfold cross-validation. Our proposed method is able to classify the N, S, V, F and U arrhythmia classes with high accuracy (98.91%) using a combined support vector machine and radial basis function method. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Nonlinear effects on composite laminate thermal expansion

NASA Technical Reports Server (NTRS)

Hashin, Z.; Rosen, B. W.; Pipes, R. B.

1979-01-01

Analyses of Graphite/Polyimide laminates shown that the thermomechanical strains cannot be separated into mechanical strain and free thermal expansion strain. Elastic properties and thermal expansion coefficients of unidirectional Graphite/Polyimide specimens were measured as a function of temperature to provide inputs for the analysis. The + or - 45 degrees symmetric Graphite/Polyimide laminates were tested to obtain free thermal expansion coefficients and thermal expansion coefficients under various uniaxial loads. The experimental results demonstrated the effects predicted by the analysis, namely dependence of thermal expansion coefficients on load, and anisotropy of thermal expansion under load. The significance of time dependence on thermal expansion was demonstrated by comparison of measured laminate free expansion coefficients with and without 15 day delay at intermediate temperature.

Relationship of red and photographic infrared spectral radiances to alfalfa biomass, forage water content, percentage canopy cover, and severity of drought stress

NASA Technical Reports Server (NTRS)

Tucker, C. J.; Elgin, J. H., Jr.; Mcmurtrey, J. E., III

1979-01-01

Red and photographic infrared spectral data were collected using a handheld radiometer for two cuttings of alfalfa. Significant linear and non-linear correlation coefficients were found between the spectral variables and plant height, biomass, forage water content, and estimated canopy cover for the earlier alfalfa cutting. The alfalfa of later cutting experienced a period of severe drought stress which limited growth. The spectral variables were found to be highly correlated with the estimated drought scores for this alfalfa cutting.

Hybrid Upwinding for Two-Phase Flow in Heterogeneous Porous Media with Buoyancy and Capillarity

NASA Astrophysics Data System (ADS)

Hamon, F. P.; Mallison, B.; Tchelepi, H.

2016-12-01

In subsurface flow simulation, efficient discretization schemes for the partial differential equations governing multiphase flow and transport are critical. For highly heterogeneous porous media, the temporal discretization of choice is often the unconditionally stable fully implicit (backward-Euler) method. In this scheme, the simultaneous update of all the degrees of freedom requires solving large algebraic nonlinear systems at each time step using Newton's method. This is computationally expensive, especially in the presence of strong capillary effects driven by abrupt changes in porosity and permeability between different rock types. Therefore, discretization schemes that reduce the simulation cost by improving the nonlinear convergence rate are highly desirable. To speed up nonlinear convergence, we present an efficient fully implicit finite-volume scheme for immiscible two-phase flow in the presence of strong capillary forces. In this scheme, the discrete viscous, buoyancy, and capillary spatial terms are evaluated separately based on physical considerations. We build on previous work on Implicit Hybrid Upwinding (IHU) by using the upstream saturations with respect to the total velocity to compute the relative permeabilities in the viscous term, and by determining the directionality of the buoyancy term based on the phase density differences. The capillary numerical flux is decomposed into a rock- and geometry-dependent transmissibility factor, a nonlinear capillary diffusion coefficient, and an approximation of the saturation gradient. Combining the viscous, buoyancy, and capillary terms, we obtain a numerical flux that is consistent, bounded, differentiable, and monotone for homogeneous one-dimensional flow. The proposed scheme also accounts for spatially discontinuous capillary pressure functions. Specifically, at the interface between two rock types, the numerical scheme accurately honors the entry pressure condition by solving a local nonlinear problem to compute the numerical flux. Heterogeneous numerical tests demonstrate that this extended IHU scheme is non-oscillatory and convergent upon refinement. They also illustrate the superior accuracy and nonlinear convergence rate of the IHU scheme compared with the standard phase-based upstream weighting approach.

Axisymmetric Powell-Eyring fluid flow over a stretching sheet with a convective boundary condition and suction effects

NASA Astrophysics Data System (ADS)

Nasir, Nor Ain Azeany Mohd; Ishak, Anuar; Pop, Ioan

2018-04-01

In this paper, the heat and mass transfer of an axisymmetric Powell-Eyring fluid flow over a stretching sheet with a convective boundary condition and suction effects are investigated. An appropriate similarity transformation is used to reduce the highly non-linear partial differential equation into second and third order non-linear ordinary differential equations. Numerical solutions of the reduced governing equations are computed numerically by utilizing the MATLAB's built-in boundary value problem solver, bvp4c. The physical significance of various parameters such as Biot number, fluid parameters and Prandtl number on the velocity and temperature evolution profiles are illustrated graphically. The effects of these governing parameters on the skin friction coefficient and the local Nusselt number are also displayed graphically. It is noticed that the Powell-Eyring fluid parameter gives significant influence on the rates of heat and mass transfer of the fluid.

Fabrication of micromachined ceramic thin-film-type pressure sensors for overpressure tolerance and its characteristics

NASA Astrophysics Data System (ADS)

Chung, Gwiy-Sang; Kim, Jae-Min

2004-04-01

This paper describes the fabrication process and characteristics of ceramic thin-film pressure sensors based on Ta-N strain gauges for harsh environment applications. The Ta-N thin-film strain gauges are sputter-deposited on a thermally oxidized micromachined Si diaphragm with buried cavities for overpressure tolerance. The proposed device takes advantage of the good mechanical properties of single-crystalline Si as a diaphragm fabricated by SDB and electrochemical etch-stop technology, and in order to extend the temperature range, it has relatively higher resistance, stability and gauge factor of Ta-N thin-films more than other gauges. The fabricated pressure sensor presents a low temperature coefficient of resistance, high-sensitivity, low nonlinearity and excellent temperature stability. The sensitivity is 1.21-1.097 mV/V×kgf/cm2 in temperature ranges of 25-200°C and a maximum non-linearity is 0.43 %FS.

Supersonic, nonlinear, attached-flow wing design for high lift with experimental validation

NASA Technical Reports Server (NTRS)

Pittman, J. L.; Miller, D. S.; Mason, W. H.

1984-01-01

Results of the experimental validation are presented for the three dimensional cambered wing which was designed to achieve attached supercritical cross flow for lifting conditions typical of supersonic maneuver. The design point was a lift coefficient of 0.4 at Mach 1.62 and 12 deg angle of attack. Results from the nonlinear full potential method are presented to show the validity of the design process along with results from linear theory codes. Longitudinal force and moment data and static pressure data were obtained in the Langley Unitary Plan Wind Tunnel at Mach numbers of 1.58, 1.62, 1.66, 1.70, and 2.00 over an angle of attack range of 0 to 14 deg at a Reynolds number of 2.0 x 10 to the 6th power per foot. Oil flow photographs of the upper surface were obtained at M = 1.62 for alpha approx. = 8, 10, 12, and 14 deg.

Enhancement of two photon absorption with Ni doping in the dilute magnetic semiconductor ZnO crystalline nanorods

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

Rana, Amit Kumar; Kumar, Yogendra; Arjunan, M.S.

2015-12-07

In this letter, we have investigated the third-order optical nonlinearities of high-quality Ni doped ZnO nanorods crystallized in wurtzite lattice, prepared by the wet chemical method. In our experiments, we found that the two photon absorption coefficient (β) increases by as much as 14 times, i.e., 7.6 ± 0.4 to 112 ± 6 cm/GW, when the Ni doping is increased from 0% to 10%. The substantial enhancement in β is discussed in terms of the bandgap scaling and Ni doping. Furthermore, we also show that the optical bandgap measured by UV-Vis and photoluminescence spectroscopies, continuously redshift with increasing Ni doping concentration.more » We envision that the strong nonlinear optical properties together with their dilute magnetic effects, they form an important class of materials for potential applications in magneto-optical and integrated optical chips.« less

Determining Spacecraft Reaction Wheel Friction Parameters

NASA Technical Reports Server (NTRS)

Sarani, Siamak

2009-01-01

Software was developed to characterize the drag in each of the Cassini spacecraft's Reaction Wheel Assemblies (RWAs) to determine the RWA friction parameters. This tool measures the drag torque of RWAs for not only the high spin rates (greater than 250 RPM), but also the low spin rates (less than 250 RPM) where there is a lack of an elastohydrodynamic boundary layer in the bearings. RWA rate and drag torque profiles as functions of time are collected via telemetry once every 4 seconds and once every 8 seconds, respectively. Intermediate processing steps single-out the coast-down regions. A nonlinear model for the drag torque as a function of RWA spin rate is incorporated in order to characterize the low spin rate regime. The tool then uses a nonlinear parameter optimization algorithm based on the Nelder-Mead simplex method to determine the viscous coefficient, the Dahl friction, and the two parameters that account for the low spin-rate behavior.

Individual muscle segmentation in MR images: A 3D propagation through 2D non-linear registration approaches.

PubMed

Ogier, Augustin; Sdika, Michael; Foure, Alexandre; Le Troter, Arnaud; Bendahan, David

2017-07-01

Manual and automated segmentation of individual muscles in magnetic resonance images have been recognized as challenging given the high variability of shapes between muscles and subjects and the discontinuity or lack of visible boundaries between muscles. In the present study, we proposed an original algorithm allowing a semi-automatic transversal propagation of manually-drawn masks. Our strategy was based on several ascending and descending non-linear registration approaches which is similar to the estimation of a Lagrangian trajectory applied to manual masks. Using several manually-segmented slices, we have evaluated our algorithm on the four muscles of the quadriceps femoris group. We mainly showed that our 3D propagated segmentation was very accurate with an averaged Dice similarity coefficient value higher than 0.91 for the minimal manual input of only two manually-segmented slices.

Enhancement of two photon absorption with Ni doping in the dilute magnetic semiconductor ZnO crystalline nanorods

NASA Astrophysics Data System (ADS)

Rana, Amit Kumar; J, Aneesh; Kumar, Yogendra; M. S, Arjunan; Adarsh, K. V.; Sen, Somaditya; Shirage, Parasharam M.

2015-12-01

In this letter, we have investigated the third-order optical nonlinearities of high-quality Ni doped ZnO nanorods crystallized in wurtzite lattice, prepared by the wet chemical method. In our experiments, we found that the two photon absorption coefficient (β) increases by as much as 14 times, i.e., 7.6 ± 0.4 to 112 ± 6 cm/GW, when the Ni doping is increased from 0% to 10%. The substantial enhancement in β is discussed in terms of the bandgap scaling and Ni doping. Furthermore, we also show that the optical bandgap measured by UV-Vis and photoluminescence spectroscopies, continuously redshift with increasing Ni doping concentration. We envision that the strong nonlinear optical properties together with their dilute magnetic effects, they form an important class of materials for potential applications in magneto-optical and integrated optical chips.

Coupled rotor and fuselage equations of motion

NASA Technical Reports Server (NTRS)

Warmbrodt, W.

1979-01-01

The governing equations of motion of a helicopter rotor coupled to a rigid body fuselage are derived. A consistent formulation is used to derive nonlinear periodic coefficient equations of motion which are used to study coupled rotor/fuselage dynamics in forward flight. Rotor/fuselage coupling is documented and the importance of an ordering scheme in deriving nonlinear equations of motion is reviewed. The nature of the final equations and the use of multiblade coordinates are discussed.

Modulation stability analysis of exact multidimensional solutions to the generalized nonlinear Schrödinger equation and the Gross-Pitaevskii equation using a variational approach.

PubMed

Petrović, Nikola Z; Aleksić, Najdan B; Belić, Milivoj

2015-04-20

We analyze the modulation stability of spatiotemporal solitary and traveling wave solutions to the multidimensional nonlinear Schrödinger equation and the Gross-Pitaevskii equation with variable coefficients that were obtained using Jacobi elliptic functions. For all the solutions we obtain either unconditional stability, or a conditional stability that can be furnished through the use of dispersion management.

Study Of Pre-Shaped Membrane Mirrors And Electrostatic Mirrors With Nonlinear-Optical Correction

DTIC Science & Technology

2002-01-01

mirrors have been manufactured of glass-like material Zerodur with very low coefficient of linear expansion. They have a more light cellular construction...primary and flat secondary mirrors are both segmented ones. In the case of the primary mirror made of traditional materials such as Zerodur or fused...FINAL REPORT ISTC Project #2103p “Study of Pre-Shaped Membrane Mirrors and Electrostatic Mirrors with Nonlinear-Optical Correction” Manager

Three dimensional rotating flow of Powell-Eyring nanofluid with non-Fourier's heat flux and non-Fick's mass flux theory

NASA Astrophysics Data System (ADS)

Ibrahim, Wubshet

2018-03-01

This article numerically examines three dimensional boundary layer flow of a rotating Powell-Eyring nanofluid. In modeling heat transfer processes, non-Fourier heat flux theory and for mass transfer non-Fick's mass flux theory are employed. This theory is recently re-initiated and it becomes the active research area to resolves some drawback associated with the famous Fourier heat flux and mass flux theory. The mathematical model of the flow problem is a system of non-linear partial differential equations which are obtained using the boundary layer analysis. The non-linear partial differential equations have been transformed into non-linear high order ordinary differential equations using similarity transformation. Employing bvp4c algorithm from matlab software routine, the numerical solution of the transformed ordinary differential equations is obtained. The governing equations are constrained by parameters such as rotation parameter λ , the non-Newtonian parameter N, dimensionless thermal relaxation and concentration relaxation parameters δt and δc . The impacts of these parameters have been discussed thoroughly and illustrated using graphs and tables. The findings show that thermal relaxation time δt reduces the thermal and concentration boundary layer thickness. Further, the results reveal that the rotational parameter λ has the effect of decreasing the velocity boundary layer thickness in both x and y directions. Further examination pinpoints that the skin friction coefficient along x-axis is an increasing and skin friction coefficient along y-axis is a decreasing function of rotation parameter λ . Furthermore, the non-Newtonian fluid parameter N has the characteristic of reducing the amount of local Nusselt numbers -f″ (0) and -g″ (0) both in x and y -directions.

Scaling and characterisation of a 2-DoF velocity amplified electromagnetic vibration energy harvester

NASA Astrophysics Data System (ADS)

O’Donoghue, D.; Frizzell, R.; Punch, J.

2018-07-01

Vibration energy harvesters (VEHs) offer an alternative to batteries for the autonomous operation of low-power electronics. Understanding the influence of scaling on VEHs is of great importance in the design of reduced scale harvesters. The nonlinear harvesters investigated here employ velocity amplification, a technique used to increase velocity through impacts, to improve the power output of multiple-degree-of-freedom VEHs, compared to linear resonators. Such harvesters, employing electromagnetic induction, are referred to as velocity amplified electromagnetic generators (VAEGs), with gains in power achieved by increasing the relative velocity between the magnet and coil in the transducer. The influence of scaling on a nonlinear 2-DoF VAEG is presented. Due to the increased complexity of VAEGs, compared to linear systems, linear scaling theory cannot be directly applied to VAEGs. Therefore, a detailed nonlinear scaling method is utilised. Experimental and numerical methods are employed. This nonlinear scaling method can be used for analysing the scaling behaviour of all nonlinear electromagnetic VEHs. It is demonstrated that the electromagnetic coupling coefficient degrades more rapidly with scale for systems with larger displacement amplitudes, meaning that systems operating at low frequencies will scale poorly compared to those operating at higher frequencies. The load power of the 2-DoF VAEG is predicted to scale as {P}L\\propto {s}5.51 (s = volume1/3), suggesting that achieving high power densities in a VAEG with low device volume is extremely challenging.

Systematic Computation of Nonlinear Cellular and Molecular Dynamics with Low-Power CytoMimetic Circuits: A Simulation Study

PubMed Central

Papadimitriou, Konstantinos I.; Stan, Guy-Bart V.; Drakakis, Emmanuel M.

2013-01-01

This paper presents a novel method for the systematic implementation of low-power microelectronic circuits aimed at computing nonlinear cellular and molecular dynamics. The method proposed is based on the Nonlinear Bernoulli Cell Formalism (NBCF), an advanced mathematical framework stemming from the Bernoulli Cell Formalism (BCF) originally exploited for the modular synthesis and analysis of linear, time-invariant, high dynamic range, logarithmic filters. Our approach identifies and exploits the striking similarities existing between the NBCF and coupled nonlinear ordinary differential equations (ODEs) typically appearing in models of naturally encountered biochemical systems. The resulting continuous-time, continuous-value, low-power CytoMimetic electronic circuits succeed in simulating fast and with good accuracy cellular and molecular dynamics. The application of the method is illustrated by synthesising for the first time microelectronic CytoMimetic topologies which simulate successfully: 1) a nonlinear intracellular calcium oscillations model for several Hill coefficient values and 2) a gene-protein regulatory system model. The dynamic behaviours generated by the proposed CytoMimetic circuits are compared and found to be in very good agreement with their biological counterparts. The circuits exploit the exponential law codifying the low-power subthreshold operation regime and have been simulated with realistic parameters from a commercially available CMOS process. They occupy an area of a fraction of a square-millimetre, while consuming between 1 and 12 microwatts of power. Simulations of fabrication-related variability results are also presented. PMID:23393550

Analysis of globally connected active rotators with excitatory and inhibitory connections using the Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Kanamaru, Takashi; Sekine, Masatoshi

2003-03-01

The globally connected active rotators with excitatory and inhibitory connections are analyzed using the nonlinear Fokker-Planck equation. The bifurcation diagram of the system is obtained numerically, and both periodic solutions and chaotic solutions are found. By observing the interspike interval, the coefficient of variance, and the correlation coefficient of the system, the relationship of our model to the biological data is discussed.

Photon interaction study of organic nonlinear optical materials in the energy range 122-1330 keV

NASA Astrophysics Data System (ADS)

Awasarmol, Vishal V.; Gaikwad, Dhammajyot K.; Raut, Siddheshwar D.; Pawar, Pravina P.

2017-01-01

In the present study, the mass attenuation coefficient (μm) of six organic nonlinear optical materials has been calculated in the energy range 122-1330 keV and compared with the obtained values from the WinXCOM program. It is found that there is a good agreement between theoretical and experimental values (<3%). The linear attenuation coefficients (μ) total atomic cross section (σt, a), and total electronic cross section (σt, el) have also been calculated from the obtained μm values and their variations with photon energy have been plotted. From the present work, it is observed that the variation of obtained values of μm, μ, σt, a, and σt, el strongly depends on the photon energy and decreases or increases due to chemical composition and density of the sample. All the samples have been studied extensively using transmission method with a view to utilize the material for radiation dosimetry. Investigated samples are good material for radiation dosimetry due their low effective atomic number. The mass attenuation coefficient (μm), linear attenuation coefficients (μ), total atomic cross section (σt, a), total electronic cross section (σt, el), effective atomic numbers (Zeff), molar extinction coefficient (ε), mass energy absorption coefficient (μen/ρ) and effective atomic energy absorption cross section (σa, en) of all sample materials have been carried out and transmission curves have been plotted. The transmission curve shows that the variation of all sample materials decreases with increasing photon energy.

Ultra-fast pulse propagation in nonlinear graphene/silicon ridge waveguide

NASA Astrophysics Data System (ADS)

Liu, Ken; Zhang, Jian Fa; Xu, Wei; Zhu, Zhi Hong; Guo, Chu Cai; Li, Xiu Jian; Qin, Shi Qiao

2015-11-01

We report the femtosecond laser propagation in a hybrid graphene/silicon ridge waveguide with demonstration of the ultra-large Kerr coefficient of graphene. We also fabricated a slot-like graphene/silicon ridge waveguide which can enhance its effective Kerr coefficient 1.5 times compared with the graphene/silicon ridge waveguide. Both transverse-electric-like (TE-like) mode and transverse-magnetic-like (TM-like) mode are experimentally measured and numerically analyzed. The results show nonlinearity dependence on mode polarization not in graphene/silicon ridge waveguide but in slot-like graphene/silicon ridge waveguide. Great spectral broadening was observed due to self-phase modulation (SPM) after propagation in the hybrid waveguide with length of 2 mm. Power dependence property of the slot-like hybrid waveguide is also measured and numerically analyzed. The results also confirm the effective Kerr coefficient estimation of the hybrid structures. Spectral blue shift of the output pulse was observed in the slot-like graphene/silicon ridge waveguide. One possible explanation is that the blue shift was caused by the ultra-fast free carrier effect with the optical absorption of the doped graphene. This interesting effect can be used for soliton compression in femtosecond region. We also discussed the broadband anomalous dispersion of the Kerr coefficient of graphene.

[Study of blending method for the extracts of herbal plants].

PubMed

Liu, Yongsuo; Cao, Min; Chen, Yuying; Hu, Yuzhu; Wang, Yiming; Luo, Guoan

2006-03-01

The irregularity in herbal plant composition is influenced by multiple factors. As for quality control of traditional Chinese medicine, the most critical challenge is to ensure the dosage content uniformity. This content uniformity can be improved by blending different batches of the extracts of herbal plants. Nonlinear least-squares regression was used to calculate the blending coefficient, which means no great absolute differences allowed for all ingredients. For traditional Chinese medicines, even relatively smaller differences could present to be very important for all the ingredients. The auto-scaling pretreatment was used prior to the calculation of the blending coefficients. The pretreatment buffered the characteristics of individual data for the ingredients in different batches, so an improved auto-scaling pretreatment method was proposed. With the improved auto-scaling pretreatment, the relative. differences decreased after blending different batches of extracts of herbal plants according to the reference samples. And the content uniformity control of the specific ingredients could be achieved by the error control coefficient. In the studies for the extracts of fructus gardeniae, the relative differences of all the ingredients is less than 3% after blending different batches of the extracts. The results showed that nonlinear least-squares regression can be used to calculate the blending coefficient of the herbal plant extracts.

Linear and non-linear flow mode in Pb-Pb collisions at √{sNN} = 2.76 TeV

NASA Astrophysics Data System (ADS)

Acharya, S.; Adamová, D.; Adolfsson, J.; Aggarwal, M. M.; Aglieri Rinella, G.; Agnello, M.; Agrawal, N.; Ahammed, Z.; Ahmad, N.; Ahn, S. U.; Aiola, S.; Akindinov, A.; Alam, S. N.; Alba, J. L. B.; Albuquerque, D. S. D.; Aleksandrov, D.; Alessandro, B.; Alfaro Molina, R.; Alici, A.; Alkin, A.; Alme, J.; Alt, T.; Altenkamper, L.; Altsybeev, I.; Alves Garcia Prado, C.; An, M.; Andrei, C.; Andreou, D.; Andrews, H. A.; Andronic, A.; Anguelov, V.; Anson, C.; Antičić, T.; Antinori, F.; Antonioli, P.; Anwar, R.; Aphecetche, L.; Appelshäuser, H.; Arcelli, S.; Arnaldi, R.; Arnold, O. W.; Arsene, I. C.; Arslandok, M.; Audurier, B.; Augustinus, A.; Averbeck, R.; Azmi, M. D.; Badalà, A.; Baek, Y. W.; Bagnasco, S.; Bailhache, R.; Bala, R.; Baldisseri, A.; Ball, M.; Baral, R. C.; Barbano, A. M.; Barbera, R.; Barile, F.; Barioglio, L.; Barnaföldi, G. G.; Barnby, L. S.; Barret, V.; Bartalini, P.; Barth, K.; Bartsch, E.; Basile, M.; Bastid, N.; Basu, S.; Bathen, B.; Batigne, G.; Batista Camejo, A.; Batyunya, B.; Batzing, P. C.; Bearden, I. G.; Beck, H.; Bedda, C.; Behera, N. K.; Belikov, I.; Bellini, F.; Bello Martinez, H.; Bellwied, R.; Beltran, L. G. E.; Belyaev, V.; Bencedi, G.; Beole, S.; Bercuci, A.; Berdnikov, Y.; Berenyi, D.; Bertens, R. A.; Berzano, D.; Betev, L.; Bhasin, A.; Bhat, I. R.; Bhati, A. K.; Bhattacharjee, B.; Bhom, J.; Bianchi, L.; Bianchi, N.; Bianchin, C.; Bielčík, J.; Bielčíková, J.; Bilandzic, A.; Biro, G.; Biswas, R.; Biswas, S.; Blair, J. T.; Blau, D.; Blume, C.; Boca, G.; Bock, F.; Bogdanov, A.; Boldizsár, L.; Bombara, M.; Bonomi, G.; Bonora, M.; Book, J.; Borel, H.; Borissov, A.; Borri, M.; Botta, E.; Bourjau, C.; Braun-Munzinger, P.; Bregant, M.; Broker, T. A.; Browning, T. A.; Broz, M.; Brucken, E. J.; Bruna, E.; Bruno, G. E.; Budnikov, D.; Buesching, H.; Bufalino, S.; Buhler, P.; Buncic, P.; Busch, O.; Buthelezi, Z.; Butt, J. B.; Buxton, J. T.; Cabala, J.; Caffarri, D.; Caines, H.; Caliva, A.; Calvo Villar, E.; Camerini, P.; Capon, A. A.; Carena, F.; Carena, W.; Carnesecchi, F.; Castillo Castellanos, J.; Castro, A. J.; Casula, E. A. R.; Ceballos Sanchez, C.; Cerello, P.; Chandra, S.; Chang, B.; Chapeland, S.; Chartier, M.; Charvet, J. L.; Chattopadhyay, S.; Chattopadhyay, S.; Chauvin, A.; Cherney, M.; Cheshkov, C.; Cheynis, B.; Chibante Barroso, V.; Chinellato, D. D.; Cho, S.; Chochula, P.; Choi, K.; Chojnacki, M.; Choudhury, S.; Chowdhury, T.; Christakoglou, P.; Christensen, C. H.; Christiansen, P.; Chujo, T.; Chung, S. U.; Cicalo, C.; Cifarelli, L.; Cindolo, F.; Cleymans, J.; Colamaria, F.; Colella, D.; Collu, A.; Colocci, M.; Concas, M.; Conesa Balbastre, G.; Conesa Del Valle, Z.; Connors, M. E.; Contreras, J. G.; Cormier, T. M.; Corrales Morales, Y.; Cortés Maldonado, I.; Cortese, P.; Cosentino, M. R.; Costa, F.; Costanza, S.; Crkovská, J.; Crochet, P.; Cuautle, E.; Cunqueiro, L.; Dahms, T.; Dainese, A.; Danisch, M. C.; Danu, A.; Das, D.; Das, I.; Das, S.; Dash, A.; Dash, S.; de, S.; de Caro, A.; de Cataldo, G.; de Conti, C.; de Cuveland, J.; de Falco, A.; de Gruttola, D.; De Marco, N.; de Pasquale, S.; de Souza, R. D.; Degenhardt, H. F.; Deisting, A.; Deloff, A.; Deplano, C.; Dhankher, P.; di Bari, D.; di Mauro, A.; di Nezza, P.; di Ruzza, B.; Diaz Corchero, M. A.; Dietel, T.; Dillenseger, P.; Divià, R.; Djuvsland, Ø.; Dobrin, A.; Domenicis Gimenez, D.; Dönigus, B.; Dordic, O.; Doremalen, L. V. V.; Drozhzhova, T.; Dubey, A. K.; Dubla, A.; Ducroux, L.; Duggal, A. K.; Dupieux, P.; Ehlers, R. J.; Elia, D.; Endress, E.; Engel, H.; Epple, E.; Erazmus, B.; Erhardt, F.; Espagnon, B.; Esumi, S.; Eulisse, G.; Eum, J.; Evans, D.; Evdokimov, S.; Fabbietti, L.; Faivre, J.; Fantoni, A.; Fasel, M.; Feldkamp, L.; Feliciello, A.; Feofilov, G.; Ferencei, J.; Fernández Téllez, A.; Ferreiro, E. G.; Ferretti, A.; Festanti, A.; Feuillard, V. J. G.; Figiel, J.; Figueredo, M. A. S.; Filchagin, S.; Finogeev, D.; Fionda, F. M.; Fiore, E. M.; Floris, M.; Foertsch, S.; Foka, P.; Fokin, S.; Fragiacomo, E.; Francescon, A.; Francisco, A.; Frankenfeld, U.; Fronze, G. G.; Fuchs, U.; Furget, C.; Furs, A.; Fusco Girard, M.; Gaardhøje, J. J.; Gagliardi, M.; Gago, A. M.; Gajdosova, K.; Gallio, M.; Galvan, C. D.; Ganoti, P.; Gao, C.; Garabatos, C.; Garcia-Solis, E.; Garg, K.; Garg, P.; Gargiulo, C.; Gasik, P.; Gauger, E. F.; Gay Ducati, M. B.; Germain, M.; Ghosh, J.; Ghosh, P.; Ghosh, S. K.; Gianotti, P.; Giubellino, P.; Giubilato, P.; Gladysz-Dziadus, E.; Glässel, P.; Goméz Coral, D. M.; Gomez Ramirez, A.; Gonzalez, A. S.; Gonzalez, V.; González-Zamora, P.; Gorbunov, S.; Görlich, L.; Gotovac, S.; Grabski, V.; Graczykowski, L. K.; Graham, K. L.; Greiner, L.; Grelli, A.; Grigoras, C.; Grigoriev, V.; Grigoryan, A.; Grigoryan, S.; Grion, N.; Gronefeld, J. M.; Grosa, F.; Grosse-Oetringhaus, J. F.; Grosso, R.; Gruber, L.; Guber, F.; Guernane, R.; Guerzoni, B.; Gulbrandsen, K.; Gunji, T.; Gupta, A.; Gupta, R.; Guzman, I. B.; Haake, R.; Hadjidakis, C.; Hamagaki, H.; Hamar, G.; Hamon, J. C.; Harris, J. W.; Harton, A.; Hassan, H.; Hatzifotiadou, D.; Hayashi, S.; Heckel, S. T.; Hellbär, E.; Helstrup, H.; Herghelegiu, A.; Herrera Corral, G.; Herrmann, F.; Hess, B. A.; Hetland, K. F.; Hillemanns, H.; Hills, C.; Hippolyte, B.; Hladky, J.; Hohlweger, B.; Horak, D.; Hornung, S.; Hosokawa, R.; Hristov, P.; Hughes, C.; Humanic, T. J.; Hussain, N.; Hussain, T.; Hutter, D.; Hwang, D. S.; Iga Buitron, S. A.; Ilkaev, R.; Inaba, M.; Ippolitov, M.; Irfan, M.; Isakov, V.; Ivanov, M.; Ivanov, V.; Izucheev, V.; Jacak, B.; Jacazio, N.; Jacobs, P. M.; Jadhav, M. B.; Jadlovska, S.; Jadlovsky, J.; Jaelani, S.; Jahnke, C.; Jakubowska, M. J.; Janik, M. A.; Jayarathna, P. H. S. Y.; Jena, C.; Jena, S.; Jercic, M.; Jimenez Bustamante, R. T.; Jones, P. G.; Jusko, A.; Kalinak, P.; Kalweit, A.; Kang, J. H.; Kaplin, V.; Kar, S.; Karasu Uysal, A.; Karavichev, O.; Karavicheva, T.; Karayan, L.; Karpechev, E.; Kebschull, U.; Keidel, R.; Keijdener, D. L. D.; Keil, M.; Ketzer, B.; Khabanova, Z.; Khan, P.; Khan, S. A.; Khanzadeev, A.; Kharlov, Y.; Khatun, A.; Khuntia, A.; Kielbowicz, M. M.; Kileng, B.; Kim, D.; Kim, D. W.; Kim, D. J.; Kim, H.; Kim, J. S.; Kim, J.; Kim, M.; Kim, M.; Kim, S.; Kim, T.; Kirsch, S.; Kisel, I.; Kiselev, S.; Kisiel, A.; Kiss, G.; Klay, J. L.; Klein, C.; Klein, J.; Klein-Bösing, C.; Klewin, S.; Kluge, A.; Knichel, M. L.; Knospe, A. G.; Kobdaj, C.; Kofarago, M.; Kollegger, T.; Kolojvari, A.; Kondratiev, V.; Kondratyeva, N.; Kondratyuk, E.; Konevskikh, A.; Konyushikhin, M.; Kopcik, M.; Kour, M.; Kouzinopoulos, C.; Kovalenko, O.; Kovalenko, V.; Kowalski, M.; Koyithatta Meethaleveedu, G.; Králik, I.; Kravčáková, A.; Krivda, M.; Krizek, F.; Kryshen, E.; Krzewicki, M.; Kubera, A. M.; Kučera, V.; Kuhn, C.; Kuijer, P. G.; Kumar, A.; Kumar, J.; Kumar, L.; Kumar, S.; Kundu, S.; Kurashvili, P.; Kurepin, A.; Kurepin, A. B.; Kuryakin, A.; Kushpil, S.; Kweon, M. J.; Kwon, Y.; La Pointe, S. L.; La Rocca, P.; Lagana Fernandes, C.; Lai, Y. S.; Lakomov, I.; Langoy, R.; Lapidus, K.; Lara, C.; Lardeux, A.; Lattuca, A.; Laudi, E.; Lavicka, R.; Lazaridis, L.; Lea, R.; Leardini, L.; Lee, S.; Lehas, F.; Lehner, S.; Lehrbach, J.; Lemmon, R. C.; Lenti, V.; Leogrande, E.; León Monzón, I.; Lévai, P.; Li, S.; Li, X.; Lien, J.; Lietava, R.; Lim, B.; Lindal, S.; Lindenstruth, V.; Lindsay, S. W.; Lippmann, C.; Lisa, M. A.; Litichevskyi, V.; Ljunggren, H. M.; Llope, W. J.; Lodato, D. F.; Loenne, P. I.; Loginov, V.; Loizides, C.; Loncar, P.; Lopez, X.; López Torres, E.; Lowe, A.; Luettig, P.; Lunardon, M.; Luparello, G.; Lupi, M.; Lutz, T. H.; Maevskaya, A.; Mager, M.; Mahajan, S.; Mahmood, S. M.; Maire, A.; Majka, R. D.; Malaev, M.; Malinina, L.; Mal'Kevich, D.; Malzacher, P.; Mamonov, A.; Manko, V.; Manso, F.; Manzari, V.; Mao, Y.; Marchisone, M.; Mareš, J.; Margagliotti, G. V.; Margotti, A.; Margutti, J.; Marín, A.; Markert, C.; Marquard, M.; Martin, N. A.; Martinengo, P.; Martinez, J. A. L.; Martínez, M. I.; Martínez García, G.; Martinez Pedreira, M.; Mas, A.; Masciocchi, S.; Masera, M.; Masoni, A.; Masson, E.; Mastroserio, A.; Mathis, A. M.; Matyja, A.; Mayer, C.; Mazer, J.; Mazzilli, M.; Mazzoni, M. A.; Meddi, F.; Melikyan, Y.; Menchaca-Rocha, A.; Meninno, E.; Mercado Pérez, J.; Meres, M.; Mhlanga, S.; Miake, Y.; Mieskolainen, M. M.; Mihaylov, D.; Mihaylov, D. L.; Mikhaylov, K.; Milano, L.; Milosevic, J.; Mischke, A.; Mishra, A. N.; Miśkowiec, D.; Mitra, J.; Mitu, C. M.; Mohammadi, N.; Mohanty, B.; Mohisin Khan, M.; Montes, E.; Moreira de Godoy, D. A.; Moreno, L. A. P.; Moretto, S.; Morreale, A.; Morsch, A.; Muccifora, V.; Mudnic, E.; Mühlheim, D.; Muhuri, S.; Mukherjee, M.; Mulligan, J. D.; Munhoz, M. G.; Münning, K.; Munzer, R. H.; Murakami, H.; Murray, S.; Musa, L.; Musinsky, J.; Myers, C. J.; Myrcha, J. W.; Naik, B.; Nair, R.; Nandi, B. K.; Nania, R.; Nappi, E.; Narayan, A.; Naru, M. U.; Natal da Luz, H.; Nattrass, C.; Navarro, S. R.; Nayak, K.; Nayak, R.; Nayak, T. K.; Nazarenko, S.; Nedosekin, A.; Negrao de Oliveira, R. A.; Nellen, L.; Nesbo, S. V.; Ng, F.; Nicassio, M.; Niculescu, M.; Niedziela, J.; Nielsen, B. S.; Nikolaev, S.; Nikulin, S.; Nikulin, V.; Nobuhiro, A.; Noferini, F.; Nomokonov, P.; Nooren, G.; Noris, J. C. C.; Norman, J.; Nyanin, A.; Nystrand, J.; Oeschler, H.; Oh, S.; Ohlson, A.; Okubo, T.; Olah, L.; Oleniacz, J.; Oliveira da Silva, A. C.; Oliver, M. H.; Onderwaater, J.; Oppedisano, C.; Orava, R.; Oravec, M.; Ortiz Velasquez, A.; Oskarsson, A.; Otwinowski, J.; Oyama, K.; Pachmayer, Y.; Pacik, V.; Pagano, D.; Pagano, P.; Paić, G.; Palni, P.; Pan, J.; Pandey, A. K.; Panebianco, S.; Papikyan, V.; Pappalardo, G. S.; Pareek, P.; Park, J.; Parmar, S.; Passfeld, A.; Pathak, S. P.; Paticchio, V.; Patra, R. N.; Paul, B.; Pei, H.; Peitzmann, T.; Peng, X.; Pereira, L. G.; Pereira da Costa, H.; Peresunko, D.; Perez Lezama, E.; Peskov, V.; Pestov, Y.; Petráček, V.; Petrov, V.; Petrovici, M.; Petta, C.; Pezzi, R. P.; Piano, S.; Pikna, M.; Pillot, P.; Pimentel, L. O. D. L.; Pinazza, O.; Pinsky, L.; Piyarathna, D. B.; Płoskoń, M.; Planinic, M.; Pliquett, F.; Pluta, J.; Pochybova, S.; Podesta-Lerma, P. L. M.; Poghosyan, M. G.; Polichtchouk, B.; Poljak, N.; Poonsawat, W.; Pop, A.; Poppenborg, H.; Porteboeuf-Houssais, S.; Porter, J.; Pozdniakov, V.; Prasad, S. K.; Preghenella, R.; Prino, F.; Pruneau, C. A.; Pshenichnov, I.; Puccio, M.; Puddu, G.; Pujahari, P.; Punin, V.; Putschke, J.; Rachevski, A.; Raha, S.; Rajput, S.; Rak, J.; Rakotozafindrabe, A.; Ramello, L.; Rami, F.; Rana, D. B.; Raniwala, R.; Raniwala, S.; Räsänen, S. S.; Rascanu, B. T.; Rathee, D.; Ratza, V.; Ravasenga, I.; Read, K. F.; Redlich, K.; Rehman, A.; Reichelt, P.; Reidt, F.; Ren, X.; Renfordt, R.; Reolon, A. R.; Reshetin, A.; Reygers, K.; Riabov, V.; Ricci, R. A.; Richert, T.; Richter, M.; Riedler, P.; Riegler, W.; Riggi, F.; Ristea, C.; Rodríguez Cahuantzi, M.; Røed, K.; Rogochaya, E.; Rohr, D.; Röhrich, D.; Rokita, P. S.; Ronchetti, F.; Rosas, E. D.; Rosnet, P.; Rossi, A.; Rotondi, A.; Roukoutakis, F.; Roy, A.; Roy, C.; Roy, P.; Rubio Montero, A. J.; Rueda, O. V.; Rui, R.; Russo, R.; Rustamov, A.; Ryabinkin, E.; Ryabov, Y.; Rybicki, A.; Saarinen, S.; Sadhu, S.; Sadovsky, S.; Šafařík, K.; Saha, S. K.; Sahlmuller, B.; Sahoo, B.; Sahoo, P.; Sahoo, R.; Sahoo, S.; Sahu, P. K.; Saini, J.; Sakai, S.; Saleh, M. A.; Salzwedel, J.; Sambyal, S.; Samsonov, V.; Sandoval, A.; Sarkar, D.; Sarkar, N.; Sarma, P.; Sas, M. H. P.; Scapparone, E.; Scarlassara, F.; Scharenberg, R. P.; Scheid, H. S.; Schiaua, C.; Schicker, R.; Schmidt, C.; Schmidt, H. R.; Schmidt, M. O.; Schmidt, M.; Schuchmann, S.; Schukraft, J.; Schutz, Y.; Schwarz, K.; Schweda, K.; Scioli, G.; Scomparin, E.; Scott, R.; Šefčík, M.; Seger, J. E.; Sekiguchi, Y.; Sekihata, D.; Selyuzhenkov, I.; Senosi, K.; Senyukov, S.; Serradilla, E.; Sett, P.; Sevcenco, A.; Shabanov, A.; Shabetai, A.; Shahoyan, R.; Shaikh, W.; Shangaraev, A.; Sharma, A.; Sharma, A.; Sharma, M.; Sharma, M.; Sharma, N.; Sheikh, A. I.; Shigaki, K.; Shou, Q.; Shtejer, K.; Sibiriak, Y.; Siddhanta, S.; Sielewicz, K. M.; Siemiarczuk, T.; Silvermyr, D.; Silvestre, C.; Simatovic, G.; Simonetti, G.; Singaraju, R.; Singh, R.; Singhal, V.; Sinha, T.; Sitar, B.; Sitta, M.; Skaali, T. B.; Slupecki, M.; Smirnov, N.; Snellings, R. J. M.; Snellman, T. W.; Song, J.; Song, M.; Soramel, F.; Sorensen, S.; Sozzi, F.; Spiriti, E.; Sputowska, I.; Srivastava, B. K.; Stachel, J.; Stan, I.; Stankus, P.; Stenlund, E.; Stocco, D.; Strmen, P.; Suaide, A. A. P.; Sugitate, T.; Suire, C.; Suleymanov, M.; Suljic, M.; Sultanov, R.; Šumbera, M.; Sumowidagdo, S.; Suzuki, K.; Swain, S.; Szabo, A.; Szarka, I.; Szczepankiewicz, A.; Tabassam, U.; Takahashi, J.; Tambave, G. J.; Tanaka, N.; Tarhini, M.; Tariq, M.; Tarzila, M. G.; Tauro, A.; Tejeda Muñoz, G.; Telesca, A.; Terasaki, K.; Terrevoli, C.; Teyssier, B.; Thakur, D.; Thakur, S.; Thomas, D.; Tieulent, R.; Tikhonov, A.; Timmins, A. R.; Toia, A.; Tripathy, S.; Trogolo, S.; Trombetta, G.; Tropp, L.; Trubnikov, V.; Trzaska, W. H.; Trzeciak, B. A.; Tsuji, T.; Tumkin, A.; Turrisi, R.; Tveter, T. S.; Ullaland, K.; Umaka, E. N.; Uras, A.; Usai, G. L.; Utrobicic, A.; Vala, M.; van der Maarel, J.; van Hoorne, J. W.; van Leeuwen, M.; Vanat, T.; Vande Vyvre, P.; Varga, D.; Vargas, A.; Vargyas, M.; Varma, R.; Vasileiou, M.; Vasiliev, A.; Vauthier, A.; Vázquez Doce, O.; Vechernin, V.; Veen, A. M.; Velure, A.; Vercellin, E.; Vergara Limón, S.; Vernet, R.; Vértesi, R.; Vickovic, L.; Vigolo, S.; Viinikainen, J.; Vilakazi, Z.; Villalobos Baillie, O.; Villatoro Tello, A.; Vinogradov, A.; Vinogradov, L.; Virgili, T.; Vislavicius, V.; Vodopyanov, A.; Völkl, M. A.; Voloshin, K.; Voloshin, S. A.; Volpe, G.; von Haller, B.; Vorobyev, I.; Voscek, D.; Vranic, D.; Vrláková, J.; Wagner, B.; Wagner, J.; Wang, H.; Wang, M.; Watanabe, D.; Watanabe, Y.; Weber, M.; Weber, S. G.; Weiser, D. F.; Wenzel, S. C.; Wessels, J. P.; Westerhoff, U.; Whitehead, A. M.; Wiechula, J.; Wikne, J.; Wilk, G.; Wilkinson, J.; Willems, G. A.; Williams, M. C. S.; Willsher, E.; Windelband, B.; Witt, W. E.; Yalcin, S.; Yamakawa, K.; Yang, P.; Yano, S.; Yin, Z.; Yokoyama, H.; Yoo, I.-K.; Yoon, J. H.; Yurchenko, V.; Zaccolo, V.; Zaman, A.; Zampolli, C.; Zanoli, H. J. C.; Zardoshti, N.; Zarochentsev, A.; Závada, P.; Zaviyalov, N.; Zbroszczyk, H.; Zhalov, M.; Zhang, H.; Zhang, X.; Zhang, Y.; Zhang, C.; Zhang, Z.; Zhao, C.; Zhigareva, N.; Zhou, D.; Zhou, Y.; Zhou, Z.; Zhu, H.; Zhu, J.; Zhu, X.; Zichichi, A.; Zimmermann, A.; Zimmermann, M. B.; Zinovjev, G.; Zmeskal, J.; Zou, S.; Alice Collaboration

2017-10-01

The second and the third order anisotropic flow, V2 and V3, are mostly determined by the corresponding initial spatial anisotropy coefficients, ε2 and ε3, in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, Vn (n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow Vn for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider. The measurements are done for particles in the pseudorapidity range | η | < 0.8 and the transverse momentum range 0.2

Ring-shaped active mode-locked tunable laser using quantum-dot semiconductor optical amplifier

NASA Astrophysics Data System (ADS)

Zhang, Mingxiao; Wang, Yongjun; Liu, Xinyu

2018-03-01

In this paper, a lot of simulations has been done for ring-shaped active mode-locked lasers with quantum-dot semiconductor optical amplifier (QD-SOA). Based on the simulation model of QD-SOA, we discussed about the influence towards mode-locked waveform frequency and pulse caused by QD-SOA maximum mode peak gain, active layer loss coefficient, bias current, incident light pulse, fiber nonlinear coefficient. In the meantime, we also take the tunable performance of the laser into consideration. Results showed QD-SOA a better performance than original semiconductor optical amplifier (SOA) in recovery time, line width, and nonlinear coefficients, which makes it possible to output a locked-mode impulse that has a higher impulse power, narrower impulse width as well as the phase is more easily controlled. After a lot of simulations, this laser can realize a 20GHz better locked-mode output pulse after 200 loops, where the power is above 17.5mW, impulse width is less than 2.7ps, moreover, the tunable wavelength range is between 1540nm-1580nm.

Influence of image charge effect on impurity-related optical absorption coefficients and refractive index changes in a spherical quantum dot

NASA Astrophysics Data System (ADS)

Vartanian, A. L.; Asatryan, A. L.; Vardanyan, L. A.

2017-03-01

We have investigated the influence of an image charge effect (ICE) on the energies of the ground and first few excited states of a hydrogen-like impurity in a spherical quantum dot (QD) in the presence of an external electric field. The oscillator strengths of transitions from the 1 s -like state to excited states of 2px and 2pz symmetries are calculated as the functions of the strengths of the confinement potential and the electric field. Also, we have studied the effect of image charges on linear and third-order nonlinear optical absorption coefficients and refractive index changes (RICs). The results show that image charges lead to the decrease of energies for all the hydrogen-like states, to the significant enhancement of the oscillator strengths of transitions between the impurity states, and to comparatively large blue shifts in linear, nonlinear, and total absorption coefficients and refractive index changes. Our results indicate that the total optical characteristics can be controlled by the strength of the confinement and the electric field.

Modulated amplitude waves in collisionally inhomogeneous Bose Einstein condensates

NASA Astrophysics Data System (ADS)

Porter, Mason A.; Kevrekidis, P. G.; Malomed, Boris A.; Frantzeskakis, D. J.

2007-05-01

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length a subjected to a spatially periodic modulation, a=a(x)=a(x+L). This “collisionally inhomogeneous” BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of x. We transform this equation into a GP equation with a constant coefficient and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that “on-site” solutions, whose maxima correspond to maxima of a(x), are more robust and likely to be observed than their “off-site” counterparts.

Linear and non-linear flow mode in Pb–Pb collisions at s NN = 2.76  TeV

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

Acharya, S.; Adamová, D.; Adolfsson, J.

The second and the third order anisotropic flow, V 2 and V 3, are mostly determined by the corresponding initial spatial anisotropy coefficients, and , in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, V n (n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow V n for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider.more » The measurements are done for particles in the pseudorapidity range |η| < 0.8 and the transverse momentum range 0.2 < p T < 5.0 GeV/c as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system.« less

Linear and non-linear flow mode in Pb–Pb collisions at s NN = 2.76  TeV

DOE PAGES

Acharya, S.; Adamová, D.; Adolfsson, J.; ...

2017-08-04

The second and the third order anisotropic flow, V 2 and V 3, are mostly determined by the corresponding initial spatial anisotropy coefficients, and , in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, V n (n > 3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow V n for n = 4, 5, 6 with the ALICE detector at the Large Hadron Collider.more » The measurements are done for particles in the pseudorapidity range |η| < 0.8 and the transverse momentum range 0.2 < p T < 5.0 GeV/c as a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system.« less

Nonlinear Landau damping in the ionosphere

NASA Technical Reports Server (NTRS)

Kiwamoto, Y.; Benson, R. F.

1978-01-01

A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.

Nonlinear modeling and dynamic analysis of a hydro-turbine governing system in the process of sudden load increase transient

NASA Astrophysics Data System (ADS)

Li, Huanhuan; Chen, Diyi; Zhang, Hao; Wang, Feifei; Ba, Duoduo

2016-12-01

In order to study the nonlinear dynamic behaviors of a hydro-turbine governing system in the process of sudden load increase transient, we establish a novel nonlinear dynamic model of the hydro-turbine governing system which considers the elastic water-hammer model of the penstock and the second-order model of the generator. The six nonlinear dynamic transfer coefficients of the hydro-turbine are innovatively proposed by utilizing internal characteristics and analyzing the change laws of the characteristic parameters of the hydro-turbine governing system. Moreover, from the point of view of engineering, the nonlinear dynamic behaviors of the above system are exhaustively investigated based on bifurcation diagrams and time waveforms. More importantly, all of the above analyses supply theoretical basis for allowing a hydropower station to maintain a stable operation in the process of sudden load increase transient.

Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

PubMed

Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

2018-02-01

In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

Formulation of the aeroelastic stability and response problem of coupled rotor/support systems

NASA Technical Reports Server (NTRS)

Warmbrodt, W.; Friedmann, P.

1979-01-01

The consistent formulation of the governing nonlinear equations of motion for a coupled rotor/support system is presented. Rotor/support coupling is clearly documented by enforcing dynamic equilibrium between the rotor and the moving flexible support. The nonlinear periodic coefficient equations of motion are applicable to both coupled rotor/fuselage aeroelastic problems of helicopters in hover or forward flight and coupled rotor/tower dynamics of a large horizontal axis wind turbine (HAWT). Finally, the equations of motion are used to study the influence of flexible supports and nonlinear terms on rotor aeroelastic stability and response of a large two-bladed HAWT.

Adaptive wavelet collocation methods for initial value boundary problems of nonlinear PDE's

NASA Technical Reports Server (NTRS)

Cai, Wei; Wang, Jian-Zhong

1993-01-01

We have designed a cubic spline wavelet decomposition for the Sobolev space H(sup 2)(sub 0)(I) where I is a bounded interval. Based on a special 'point-wise orthogonality' of the wavelet basis functions, a fast Discrete Wavelet Transform (DWT) is constructed. This DWT transform will map discrete samples of a function to its wavelet expansion coefficients in O(N log N) operations. Using this transform, we propose a collocation method for the initial value boundary problem of nonlinear PDE's. Then, we test the efficiency of the DWT transform and apply the collocation method to solve linear and nonlinear PDE's.

Criterion for evaluating the predictive ability of nonlinear regression models without cross-validation.

PubMed

Kaneko, Hiromasa; Funatsu, Kimito

2013-09-23

We propose predictive performance criteria for nonlinear regression models without cross-validation. The proposed criteria are the determination coefficient and the root-mean-square error for the midpoints between k-nearest-neighbor data points. These criteria can be used to evaluate predictive ability after the regression models are updated, whereas cross-validation cannot be performed in such a situation. The proposed method is effective and helpful in handling big data when cross-validation cannot be applied. By analyzing data from numerical simulations and quantitative structural relationships, we confirm that the proposed criteria enable the predictive ability of the nonlinear regression models to be appropriately quantified.

Microscopic nonlinear relativistic quantum theory of absorption of powerful x-ray radiation in plasma.

PubMed

Avetissian, H K; Ghazaryan, A G; Matevosyan, H H; Mkrtchian, G F

2015-10-01

The microscopic quantum theory of plasma nonlinear interaction with the coherent shortwave electromagnetic radiation of arbitrary intensity is developed. The Liouville-von Neumann equation for the density matrix is solved analytically considering a wave field exactly and a scattering potential of plasma ions as a perturbation. With the help of this solution we calculate the nonlinear inverse-bremsstrahlung absorption rate for a grand canonical ensemble of electrons. The latter is studied in Maxwellian, as well as in degenerate quantum plasma for x-ray lasers at superhigh intensities and it is shown that one can achieve the efficient absorption coefficient in these cases.

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2002-01-01

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Second-order rogue wave breathers in the nonlinear Schrödinger equation with quadratic potential modulated by a spatially-varying diffraction coefficient.

PubMed

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

2015-02-09

Nonlinear Schrödinger equation with simple quadratic potential modulated by a spatially-varying diffraction coefficient is investigated theoretically. Second-order rogue wave breather solutions of the model are constructed by using the similarity transformation. A modal quantum number is introduced, useful for classifying and controlling the solutions. From the solutions obtained, the behavior of second order Kuznetsov-Ma breathers (KMBs), Akhmediev breathers (ABs), and Peregrine solitons is analyzed in particular, by selecting different modulation frequencies and quantum modal parameter. We show how to generate interesting second order breathers and related hybrid rogue waves. The emergence of true rogue waves - single giant waves that are generated in the interaction of KMBs, ABs, and Peregrine solitons - is explicitly displayed in our analytical solutions.

Weakly Nonlinear Model with Exact Coefficients for the Fluttering and Spiraling Motion of Buoyancy-Driven Bodies

NASA Astrophysics Data System (ADS)

Tchoufag, Joël; Fabre, David; Magnaudet, Jacques

2015-09-01

Gravity- or buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Here, using a weakly nonlinear expansion of the full set of governing equations, we present a new generic reduced-order model based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (e.g., fluttering or spiraling) and characteristics (e.g., frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.

A weakly nonlinear model with exact coefficients for the fluttering and spiraling motions of buoyancy-driven bodies

NASA Astrophysics Data System (ADS)

Magnaudet, Jacques; Tchoufag, Joel; Fabre, David

2015-11-01

Gravity/buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Using a weakly nonlinear expansion of the full set of governing equations, we derive a new generic reduced-order model of this class of phenomena based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (eg. fluttering or spiraling) and characteristics (eg. frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.

Matter-wave solitons in nonlinear optical lattices

NASA Astrophysics Data System (ADS)

Sakaguchi, Hidetsugu; Malomed, Boris A.

2005-10-01

We introduce a dynamical model of a Bose-Einstein condensate based on the one-dimensional (1D) Gross-Pitaevskii equation (GPE) with a nonlinear optical lattice (NOL), which is represented by the cubic term whose coefficient is periodically modulated in the coordinate. The model describes a situation when the atomic scattering length is spatially modulated, via the optically controlled Feshbach resonance, in an optical lattice created by interference of two laser beams. Relatively narrow solitons supported by the NOL are predicted by means of the variational approximation (VA), and an averaging method is applied to broad solitons. A different feature is a minimum norm (number of atoms), N=Nmin , necessary for the existence of solitons. The VA predicts Nmin very accurately. Numerical results are chiefly presented for the NOL with the zero spatial average value of the nonlinearity coefficient. Solitons with values of the amplitude A larger than at N=Nmin are stable. Unstable solitons with smaller, but not too small, A rearrange themselves into persistent breathers. For still smaller A , the soliton slowly decays into radiation without forming a breather. Broad solitons with very small A are practically stable, as their decay is extremely slow. These broad solitons may freely move across the lattice, featuring quasielastic collisions. Narrow solitons, which are strongly pinned to the NOL, can easily form stable complexes. Finally, the weakly unstable low-amplitude solitons are stabilized if a cubic term with a constant coefficient, corresponding to weak attraction, is included in the GPE.

Diffusion in different models of active Brownian motion

NASA Astrophysics Data System (ADS)

Lindner, B.; Nicola, E. M.

2008-04-01

Active Brownian particles (ABP) have served as phenomenological models of self-propelled motion in biology. We study the effective diffusion coefficient of two one-dimensional ABP models (simplified depot model and Rayleigh-Helmholtz model) differing in their nonlinear friction functions. Depending on the choice of the friction function the diffusion coefficient does or does not attain a minimum as a function of noise intensity. We furthermore discuss the case of an additional bias breaking the left-right symmetry of the system. We show that this bias induces a drift and that it generally reduces the diffusion coefficient. For a finite range of values of the bias, both models can exhibit a maximum in the diffusion coefficient vs. noise intensity.

Nonlinear equations of dynamics for spinning paraboloidal antennas

NASA Technical Reports Server (NTRS)

Utku, S.; Shoemaker, W. L.; Salama, M.

1983-01-01

The nonlinear strain-displacement and velocity-displacement relations of spinning imperfect rotational paraboloidal thin shell antennas are derived for nonaxisymmetrical deformations. Using these relations with the admissible trial functions in the principle functional of dynamics, the nonlinear equations of stress inducing motion are expressed in the form of a set of quasi-linear ordinary differential equations of the undetermined functions by means of the Rayleigh-Ritz procedure. These equations include all nonlinear terms up to and including the third degree. Explicit expressions are given for the coefficient matrices appearing in these equations. Both translational and rotational off-sets of the axis of revolution (and also the apex point of the paraboloid) with respect to the spin axis are considered. Although the material of the antenna is assumed linearly elastic, it can be anisotropic.