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Sample records for order single nonlinear

  1. Third order nonlinear optical properties of a paratellurite single crystal

    Duclère, J.-R.; Hayakawa, T.; Roginskii, E. M.; Smirnov, M. B.; Mirgorodsky, A.; Couderc, V.; Masson, O.; Colas, M.; Noguera, O.; Rodriguez, V.; Thomas, P.

    2018-05-01

    The (a,b) plane angular dependence of the third-order nonlinear optical susceptibility, χ(3) , of a c-cut paratellurite (α-TeO2) single crystal was quantitatively evaluated here by the Z-scan technique, using a Ti:sapphire femtosecond laser operated at 800 nm. In particular, the mean value Re( ⟨χ(3)⟩a,b )(α-TeO2) of the optical tensor has been extracted from such experiments via a direct comparison with the data collected for a fused silica reference glass plate. A R e (⟨χ(3)⟩(a,b )(α-TeO2)):R e (χ(3))(SiO2 glass) ratio roughly equal to 49.1 is found, and our result compares thus very favourably with the unique experimental value (a ratio of ˜50) reported by Kim et al. [J. Am. Ceram. Soc. 76, 2486 (1993)] for a pure TeO2 glass. In addition, it is shown that the angular dependence of the phase modulation within the (a,b) plane can be fully understood in the light of the strong dextro-rotatory power known for TeO2 materials. Taking into account the optical activity, some analytical model serving to estimate the diagonal and non-diagonal components of the third order nonlinear susceptibility tensor has been thus developed. Finally, Re( χxxxx(3) ) and Re( χxxyy(3) ) values of 95.1 ×10-22 m 2/V2 and 42.0 ×10-22 m2/V2 , respectively, are then deduced for a paratellurite single crystal, considering fused silica as a reference.

  2. Single-photon blockade in a hybrid cavity-optomechanical system via third-order nonlinearity

    Sarma, Bijita; Sarma, Amarendra K.

    2018-04-01

    Photon statistics in a weakly driven optomechanical cavity, with Kerr-type nonlinearity, are analyzed both analytically and numerically. The single-photon blockade effect is demonstrated via calculations of the zero-time-delay second-order correlation function g (2)(0). The analytical results obtained by solving the Schrödinger equation are in complete conformity with the results obtained through numerical solution of the quantum master equation. A systematic study on the parameter regime for observing photon blockade in the weak coupling regime is reported. The parameter regime where the photon blockade is not realizable due to the combined effect of nonlinearities owing to the optomechanical coupling and the Kerr-effect is demonstrated. The experimental feasibility with state-of-the-art device parameters is discussed and it is observed that photon blockade could be generated at the telecommunication wavelength. An elaborate analysis of the thermal effects on photon antibunching is presented. The system is found to be robust against pure dephasing-induced decoherences and thermal phonon number fluctuations.

  3. Studies of Second Order Optical Nonlinearities of 4-Aminobenzophenone (ABP) Single Crystal Films

    Bhowmik, Achintya; Thakur, Mrinal

    1998-03-01

    Specific organic materials exhibit very high second order optical susceptibilities. Growth of single crystal films of these materials and characterization of nonlinear optical properties are necessary for implementation of device applications. We have grown large-area films ( 1 cm^2 area, 4 μm thick) of ABP by a modification of the shear method. Single crystal nature of the films was confirmed by polarized optical microscopy. X-ray diffraction analysis showed a [100] surface orientation. The absorption spectra revealed transparency from 390 nm to 1940 nm. Significant elements of the second order optical susceptibility tensor were measured by detailed SHG experiments using a Nd:YAG laser (1064 nm, 100 ps, 82 MHz). Second-harmonic power was measured using lock-in detection with carefully selected polarization conditions while the film was rotated about the propagation direction. Using LiNbØas the reference, d-coefficients of ABP were found to be d_23=7.2 pm/V and d_22=0.7 pm/V. Type-I and type-II phase-matching directions were identified on the film by analyzing the optical indicatrix surfaces at fundamental and second-harmonic frequencies.

  4. Femtosecond single-beam direct laser poling of stable and efficient second-order nonlinear optical properties in glass

    Papon, G.; Marquestaut, N.; Royon, A.; Canioni, L.; Petit, Y.; Dussauze, M.; Rodriguez, V.; Cardinal, T.

    2014-01-01

    We depict a new approach for the localized creation in three dimensions (3D) of a highly demanded nonlinear optical function for integrated optics, namely second harmonic generation. We report on the nonlinear optical characteristics induced by single-beam femtosecond direct laser writing in a tailored silver-containing phosphate glass. The original spatial distribution of the nonlinear pattern, composed of four lines after one single laser writing translation, is observed and modeled with success, demonstrating the electric field induced origin of the second harmonic generation. These efficient second-order nonlinear structures (with χ eff (2)  ∼ 0.6 pm V −1 ) with sub-micron scale are impressively stable under thermal constraint up to glass transition temperature, which makes them very promising for new photonic applications, especially when 3D nonlinear architectures are desired

  5. Synthesis, crystal structure, growth, optical and third order nonlinear optical studies of 8HQ2C5N single crystal - An efficient third-order nonlinear optical material

    Divya Bharathi, M.; Ahila, G.; Mohana, J. [Department of Physics, Presidency College, Chennai 600005 (India); Chakkaravarthi, G. [Department of Physics, CPCL Polytechnic College, Chennai 600068 (India); Anbalagan, G., E-mail: anbu24663@yahoo.co.in [Department of Nuclear Physics, University of Madras, Chennai 600025 (India)

    2017-05-01

    A neoteric organic third order nonlinear optical material 8-hydroxyquinolinium 2-chloro-5-nitrobenzoate dihydrate (8HQ2C5N) was grown by slow cooling technique using ethanol: water (1:1) mixed solvent. The calculated low value of average etch pit solidity (4.12 × 10{sup 3} cm{sup −2}) indicated that the title crystal contain less defects. From the single crystal X-ray diffraction data, it was endowed that 8HQ2C5N crystal belongs to the monoclinic system with centrosymmetric space group P2{sub 1}/c and the cell parameters values, a = 9.6546 (4) Ǻ, b = 7.1637(3) Ǻ, c = 24.3606 (12) Ǻ, α = γ = 90°, β = 92.458(2)° and volume = 1683.29(13) Ǻ{sup 3}. The FT-IR and FT-Raman spectrum were used to affirm the functional group of the title compound. The chemical structure of 8HQ2C5N was scrutinized by {sup 13}C and {sup 1}H NMR spectral analysis and thermal stability through the differential scanning calorimetry study. Using optical studies the lower cut-off wavelength and optical band gap of 8HQ2C5N were found to be 364 nm and 3.17 eV respectively. Using the single oscillator model suggested by Wemple – Didomenico, the oscillator energy (E{sub o}), the dispersion energy (E{sub d}) and static dielectric constant (ε{sub o}) were estimated. The third-order susceptibility were determined as Im χ{sup (3)} = 2.51 × 10{sup −5} esu and Re χ{sup (3)} = 4.46 × 10{sup −7} esu. The theoretical third-order nonlinear optical susceptibility χ{sup (3)} was calculated and the results were compared with experimental value. Photoluminescence spectrum of 8HQ2C5N crystal showed the yellow emission. The crystal had the single shot laser damage threshold of 5.562 GW/cm{sup 2}. Microhardness measurement showed that 8HQ2C5N belongs to a soft material category. - Highlights: • A new organic single crystals were grown and the crystal structure was reported. • Crystal possess, good transmittance, thermal and mechanical stability. • Single shot LDT value is found to be

  6. High-order modulation on a single discrete eigenvalue for optical communications based on nonlinear Fourier transform.

    Gui, Tao; Lu, Chao; Lau, Alan Pak Tao; Wai, P K A

    2017-08-21

    In this paper, we experimentally investigate high-order modulation over a single discrete eigenvalue under the nonlinear Fourier transform (NFT) framework and exploit all degrees of freedom for encoding information. For a fixed eigenvalue, we compare different 4 bit/symbol modulation formats on the spectral amplitude and show that a 2-ring 16-APSK constellation achieves optimal performance. We then study joint spectral phase, spectral magnitude and eigenvalue modulation and found that while modulation on the real part of the eigenvalue induces pulse timing drift and leads to neighboring pulse interactions and nonlinear inter-symbol interference (ISI), it is more bandwidth efficient than modulation on the imaginary part of the eigenvalue in practical settings. We propose a spectral amplitude scaling method to mitigate such nonlinear ISI and demonstrate a record 4 GBaud 16-APSK on the spectral amplitude plus 2-bit eigenvalue modulation (total 6 bit/symbol at 24 Gb/s) transmission over 1000 km.

  7. Synthesis, growth, crystal structure, optical and third order nonlinear optical properties of quinolinium derivative single crystal: PNQI

    Karthigha, S.; Krishnamoorthi, C.

    2018-03-01

    An organic quinolinium derivative nonlinear optical (NLO) crystal, 1-ethyl-2-[2-(4-nitro-phenyl)-vinyl]-quinolinium iodide (PNQI) was synthesized and successfully grown by slow evaporation solution growth technique. Formation of a crystalline compound was confirmed by single crystal X-ray diffraction. The quinolinium compound PNQI crystallizes in the triclinic crystal system with a centrosymmetric space group of P-1 symmetry. The molecular structure of PNQI was confirmed by 1H NMR and 13C NMR spectral studies. The thermal properties of the crystal have been investigated by thermogravimetric (TG) and differential scanning calorimetry (DSC) studies. The optical characteristics obtained from UV-Vis-NIR spectral data were described and the cut-off wavelength observed at 506 nm. The etching study was performed to analyse the growth features of PNQI single crystal. The third order NLO properties such as nonlinear refractive index (n2), nonlinear absorption coefficient (β) and nonlinear susceptibility (χ (3)) of the crystal were investigated using Z-scan technique at 632.8 nm of Hesbnd Ne laser.

  8. Growth and Characterization of Lithium Potassium Phthalate (LiKP) Single Crystals for Third Order Nonlinear Optical Applications

    Sivakumar, B.; Mohan, R. [Preidency College, Bangalore (India); Raj, S. Gokul [RR and Dr. SR Technical Univ., Avadi (India); Kumar, G. Ramesh [Anna Univ., Arni (India)

    2012-11-15

    Single crystals of lithium potassium phthalate (LiKP) were successfully grown from aqueous solution by solvent evaporation technique. The grown crystals were characterized by single crystal X-ray diffraction. The lithium potassium phthalate C{sub 16} H{sub 12} K Li{sub 3} O{sub 11} belongs to triclinic system with the following unit-cell dimensions at 298(2) K; a = 7.405(5) A; b = 9.878(5) A; c = 13.396(5) A; α = 71.778(5) .deg.; β = 87.300(5) .deg.; γ = 85.405(5) .deg.; having a space group P1. Mass spectrometric analysis provides the molecular weight of the compound and possible ways of fragmentations occurs in the compound. Thermal stability of the crystal was also studied by both simultaneous TGA/DTA analyses. The UV-Vis-NIR spectrum shows a good transparency in the whole of Visible and as well as in the near IR range. Third order nonlinear optical studies have also been studied by Z-scan technique. Nonlinear absorption and nonlinear refractive index were found out and the third order bulk susceptibility of compound was also estimated.

  9. Bulk crystal growth and their effective third order nonlinear optical properties of 2-(4-fluorobenzylidene) malononitrile (FBM) single crystal

    Priyadharshini, A.; Kalainathan, S.

    2018-04-01

    2-(4-fluorobenzylidene) malononitrile (FBM), an organic third order nonlinear (TONLO) single crystal with the dimensions of 32 × 7 × 11 mm3, has been successfully grown in acetone solution by slow evaporation technique at 35 °C. The crystal system (triclinic), space group (P-1) and crystalline purity of the titular crystal were measured by single crystal and powder X-ray diffraction, respectively. The molecular weight and the multiple functional groups of the FBM material were confirmed through the mass and FT-IR spectral analysis. UV-Vis-NIR spectral study enroles that the FBM crystal exhibits excellent transparency (83%) in the entire visible and near infra-red region with a wide bandgap 2.90 eV. The low dielectric constant (εr) value of FBM crystal is appreciable for microelectronics industry applications. Thermal stability and melting point (130.09 °C) were ascertained by TGA-DSC analysis. The laser-induced surface damage threshold (LDT) value of FBM specimen is found to be 2.14 GW/cm2, it is fairly good compared to other reported NLO crystals. The third - order nonlinear optical character of the FBM crystal was confirmed through the typical single beam Z-scan technique. All these finding authorized that the organic crystal of FBM is favorably suitable for NLO applications.

  10. Growth and physicochemical properties of second-order nonlinear optical 2-amino-5-chloropyridinium trichloroacetate single crystals

    Renugadevi, R.; Kesavasamy, R.

    2015-09-01

    The growth of organic nonlinear optical (NLO) crystal 2-amino-5-chloropyridinium trichloroacetate (2A5CPTCA) has been synthesized and single crystals have been grown from methanol solvent by slow evaporation technique. The grown crystals were subjected to various characterization analyses in order to find out the suitability for device fabrication. Single crystal X-ray diffraction analysis reveals that 2A5CPTCA crystallizes in monoclinic system with the space group Cc. The grown crystal was further characterized by Fourier transform infrared spectral analysis to find out the functional groups. The nuclear magnetic resonance spectroscopy is a research technique that exploits the magnetic properties of certain atomic nuclei. The optical transparency window in the visible and near-IR (200--1100 nm) regions was found to be good for NLO applications. Thermogravimetric analysis and differential thermal analysis were used to study its thermal properties. The powder second harmonic generation efficiency measurement with Nd:YAG laser (1064 nm) radiation shows that the highest value when compared with the standard potassium dihydrogen phosphate crystal.

  11. Dynamics of Nonlinear Excitation of the High-Order Mode in a Single-Mode Step-Index Optical Fiber

    Burdin, V.; Bourdine, A.

    2018-04-01

    This work is concerned with approximate model of higher-order mode nonlinear excitation in a singlemode silica optical fiber. We present some results of simulation for step-index optical fiber under femtosecond optical pulse launching, which confirm ability of relatively stable higher-order mode excitation in such singlemode optical fiber over sufficiently narrow range of launched optical power variation.

  12. Multifunctional Bi2ZnOB2O6 single crystals for second and third order nonlinear optical applications

    Iliopoulos, K.; Kasprowicz, D.; Majchrowski, A.; Michalski, E.; Gindre, D.; Sahraoui, B.

    2013-01-01

    Bi 2 ZnOB 2 O 6 nonlinear optical single crystals were grown by means of the Kyropoulos method from stoichiometric melt. The second and third harmonic generation (SHG/THG) of Bi 2 ZnOB 2 O 6 crystals were investigated by the SHG/THG Maker fringes technique. Moreover, SHG microscopy studies were carried out providing two-dimensional SHG images as a function of the incident laser polarization. The high nonlinear optical efficiency combined with the possibility to grow high quality crystals make Bi 2 ZnOB 2 O 6 an excellent candidate for photonic applications

  13. Growth and characterization of benzaldehyde 4-nitro phenyl hydrazone (BPH) single crystal: A proficient second order nonlinear optical material

    Saravanan, M.; Abraham Rajasekar, S.

    2016-04-01

    The crystals (benzaldehyde 4-nitro phenyl hydrazone (BPH)) appropriate for NLO appliance were grown by the slow cooling method. The solubility and metastable zone width measurement of BPH specimen was studied. The material crystallizes in the monoclinic crystal system with noncentrosymmetric space group of Cc. The optical precision in the whole visible region was found to be excellent for non-linear optical claim. Excellence of the grown crystal is ascertained by the HRXRD and etching studies. Laser Damage Threshold and Photoluminescence studies designate that the grown crystal contains less imperfection. The mechanical behaviour of BPH sample at different temperatures was investigated to determine the hardness stability of the grown specimen. The piezoelectric temperament and the relative Second Harmonic Generation (for diverse particle sizes) of the material were also studied. The dielectric studies were executed at varied temperatures and frequencies to investigate the electrical properties. Photoconductivity measurement enumerates consummate of inducing dipoles due to strong incident radiation and also divulge the nonlinear behaviour of the material. The third order nonlinear optical properties of BPH crystals were deliberate by Z-scan method.

  14. Crucial role of molecular planarity on the second order nonlinear optical property of pyridine based chalcone single crystals

    Menezes, Anthoni Praveen; Jayarama, A.; Ng, Seik Weng

    2015-05-01

    An efficient nonlinear optical material 2E-3-(4-bromophenyl)-1-(pyridin-3-yl) prop-2-en-1-one (BPP) was synthesized and single crystals were grown using slow evaporation solution growth technique at room temperature. Grown crystal had prismatic morphology and its structure was confirmed by various spectroscopic studies, elemental analysis, and single crystal X-ray diffraction (XRD) technique. The single crystal XRD of the crystal showed that BPP crystallizes in monoclinic system with noncentrosymmetric space group P21 and the cell parameters are a = 5.6428(7) Å, b = 3.8637(6) Å, c = 26.411(2) Å, β = 97.568(11) deg and v = 575.82(12) Å3. The UV-Visible spectrum reveals that the crystal is optically transparent and has high optical energy band gap of 3.1 eV. The powder second harmonic generation efficiency (SHG) of BPP is 6.8 times that of KDP. From thermal analysis it is found that the crystal melts at 139 °C and decomposes at 264 °C. High optical transparency down to blue region, higher powder SHG efficiency and better thermal stability than that of urea makes this chalcone derivative a promising candidate for SHG applications. Furthermore, effect of molecular planarity on SHG efficiency and role of pyridine ring adjacent to carbonyl group in forming noncentrosymmetric crystal systems of chalcone family is also discussed.

  15. Studies on the growth aspects, structural, thermal, dielectric and third order nonlinear optical properties of solution grown 4-methylpyridinium p-nitrophenolate single crystal

    Devi, S. Reena; Kalaiyarasi, S.; Zahid, I. MD.; Kumar, R. Mohan

    2016-11-01

    An ionic organic optical crystal of 4-methylpyridinium p-nitrophenolate was grown from methanol by slow evaporation method at ambient temperature. Powder and single crystal X-ray diffraction studies revealed the crystal system and its crystalline perfection. The rocking curve recorded from HRXRD study confirmed the crystal quality. FTIR spectral analysis confirmed the functional groups present in the title compound. UV-visible spectral study revealed the optical window and band gap of grown crystal. The thermal, electrical and surface laser damage threshold properties of harvested crystal were examined by using TGA/DTA, LCR/Impedance Analyzer and Nd:YAG laser system respectively. The third order nonlinear optical property of grown crystal was elucidated by Z-scan technique.

  16. Second-order nonlinearity induced transparency.

    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.

  17. Synthesis, optical, experimental and theoretical investigation of third order nonlinear optical properties of 8-hydroxyquinolinium 2-carboxy-6-nitrophthalate monohydrate single crystal

    Bharathi, M. Divya; Bhuvaneswari, R.; Srividya, J.; Vinitha, G.; Prithiviraajan, R. N.; Anbalagan, G.

    2018-02-01

    Single crystals of 8-hydroxyquinolinium 2-carboxy-6-nitrophthalate monohydrate (8HQNP) were obtained from slow evaporation solution growth method using methanol-water (1:1) as a solvent. Powder X-ray diffraction was utilized to compute the unit cell parameters and dislocation density of 8HQNP crystal. The crystalline perfection of the as-grown crystal was investigated by high-resolution X-ray diffraction at room temperature. The molecular structure was analyzed by identifying the functional groups from FT-IR and FT-Raman spectra. The cut-off wavelength and the corresponding optical band gap obtained from an optical spectrum were 376 nm and 3.29 eV respectively. The dispersion nature of refractive index was investigated by the single-oscillator Wemple and Di-Domenico model. Red emission was observed in the photoluminescence spectrum when excited with 376 nm. The low birefringence and high laser damage threshold (8.538 GW/cm2) values dictate the suitability of the crystal for optical devices. Z-scan studies revealed the third order nonlinear absorption coefficient (β) and refractive index (n2) of the 8HQNP crystal. The theoretical value of third order nonlinear susceptibility obtained from density function theory is good accordance with the experimental value. The frontier molecular orbital energy gap decreases with increasing external electric field in different directions which attributed to the enhancement of the second hyperpolarizability. The grown title crystal is thermally stable up to 102 °C which was identified using thermal analysis. Mechanical strength of 8HQNP was estimated by using Vicker's microhardness studies.

  18. Discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities

    Khare, A.; Rasmussen, Kim Ø; Salerno, M.

    2006-01-01

    -Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.......A class of discrete nonlinear Schrodinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrodinger equation and the Ablowitz...

  19. 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

    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.

  20. Expert system for accelerator single-freedom nonlinear components

    Wang Sheng; Xie Xi; Liu Chunliang

    1995-01-01

    An expert system by Arity Prolog is developed for accelerator single-freedom nonlinear components. It automatically yields any order approximate analytical solutions for various accelerator single-freedom nonlinear components. As an example, the eighth order approximate analytical solution is derived by this expert system for a general accelerator single-freedom nonlinear component, showing that the design of the expert system is successful

  1. On nonlinear reduced order modeling

    Abdel-Khalik, Hany S.

    2011-01-01

    When applied to a model that receives n input parameters and predicts m output responses, a reduced order model estimates the variations in the m outputs of the original model resulting from variations in its n inputs. While direct execution of the forward model could provide these variations, reduced order modeling plays an indispensable role for most real-world complex models. This follows because the solutions of complex models are expensive in terms of required computational overhead, thus rendering their repeated execution computationally infeasible. To overcome this problem, reduced order modeling determines a relationship (often referred to as a surrogate model) between the input and output variations that is much cheaper to evaluate than the original model. While it is desirable to seek highly accurate surrogates, the computational overhead becomes quickly intractable especially for high dimensional model, n ≫ 10. In this manuscript, we demonstrate a novel reduced order modeling method for building a surrogate model that employs only 'local first-order' derivatives and a new tensor-free expansion to efficiently identify all the important features of the original model to reach a predetermined level of accuracy. This is achieved via a hybrid approach in which local first-order derivatives (i.e., gradient) of a pseudo response (a pseudo response represents a random linear combination of original model’s responses) are randomly sampled utilizing a tensor-free expansion around some reference point, with the resulting gradient information aggregated in a subspace (denoted by the active subspace) of dimension much less than the dimension of the input parameters space. The active subspace is then sampled employing the state-of-the-art techniques for global sampling methods. The proposed method hybridizes the use of global sampling methods for uncertainty quantification and local variational methods for sensitivity analysis. In a similar manner to

  2. Nonlinear dynamics of fractional order Duffing system

    Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian

    2015-01-01

    In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.

  3. Nonlinear Single Spin Spectrum Analayzer

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

    2014-05-01

    Qubits are excellent probes of their environment. When operating in the linear regime, they can be used as linear spectrum analyzers of the noise processes surrounding them. These methods fail for strong non-Gaussian noise where the qubit response is no longer linear. Here we solve the problem of nonlinear spectral analysis, required for strongly coupled environments. Our non-perturbative analytic model shows a nonlinear signal dependence on noise power, resulting in a spectral resolution beyond the Fourier limit as well as frequency mixing. We developed a noise characterization scheme adapted to this non-linearity. We then applied it using a single trapped 88Sr+ ion as the a sensitive probe of strong, non-Gaussian, discrete magnetic field noise. With this method, we attained a ten fold improvement over the standard Fourier limit. Finally, we experimentally compared the performance of equidistant vs. Uhrig modulation schemes for spectral analysis. Phys. Rev. Lett. 110, 110503 (2013), Synopsis at http://physics.aps.org/synopsis-for/10.1103/PhysRevLett.110.110503 Current position: National Institute of Standards and Tehcnology, Boulder, CO.

  4. Nonlinear elliptic equations of the second order

    Han, Qing

    2016-01-01

    Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...

  5. Single-shot measurement of nonlinear absorption and nonlinear refraction.

    Jayabalan, J; Singh, Asha; Oak, Shrikant M

    2006-06-01

    A single-shot method for measurement of nonlinear optical absorption and refraction is described and analyzed. A spatial intensity variation of an elliptical Gaussian beam in conjugation with an array detector is the key element of this method. The advantages of this single-shot technique were demonstrated by measuring the two-photon absorption and free-carrier absorption in GaAs as well as the nonlinear refractive index of CS2 using a modified optical Kerr setup.

  6. High-order nonlinear susceptibilities of He

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

    1996-01-01

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

  7. Single-ion nonlinear mechanical oscillator

    Akerman, N.; Kotler, S.; Glickman, Y.; Dallal, Y.; Keselman, A.; Ozeri, R.

    2010-01-01

    We study the steady-state motion of a single trapped ion oscillator driven to the nonlinear regime. Damping is achieved via Doppler laser cooling. The ion motion is found to be well described by the Duffing oscillator model with an additional nonlinear damping term. We demonstrate here the unique ability of tuning both the linear as well as the nonlinear damping coefficients by controlling the laser-cooling parameters. Our observations pave the way for the investigation of nonlinear dynamics on the quantum-to-classical interface as well as mechanical noise squeezing in laser-cooling dynamics.

  8. Higher-order modulation instability in nonlinear fiber optics.

    Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry

    2011-12-16

    We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. © 2011 American Physical Society

  9. Nonlinear spectroscopic studies of interfacial molecular ordering

    Superfine, R.

    1991-07-01

    The second order nonlinear optical processes of second harmonic generation and sum frequency generation are powerful new probes of surfaces. They possess unusual surface sensitivity due to the symmetry properties of the nonlinear susceptibility. In particular, infrared-visible sum frequency generation (SFG) can obtain the vibrational spectrum of sub-monolayer coverages of molecules. In this thesis, we explore the unique information that can be obtained from SFG. We take advantage of the sensitivity of SFG to the conformation of alkane chains to study the interaction between adsorbed liquid crystal molecules and surfactant treated surfaces. The sign of the SFG susceptibility depends on the sign of the molecular polarizability and the orientation, up or down, of the molecule. We experimentally determine the sign of the susceptibility and use it to determine the absolute orientation to obtain the sign of the molecular polarizability and show that this quantity contains important information about the dynamics of molecular charge distributions. Finally, we study the vibrational spectra and the molecular orientation at the pure liquid/vapor interface of methanol and water and present the most detailed evidence yet obtained for the structure of the pure water surface. 32 refs., 4 figs., 2 tabs

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

    Singh, Vijender, E-mail: chahal-gju@rediffmail.com [Department of Applied Science, N.C. College of Engineering, Israna, Panipat-132107, Haryana (India); Aghamkar, Praveen, E-mail: p-aghamkar@yahoo.co.in [Department of Physics, Chaudhary Devi Lal University, Sirsa-125055, Haryana (India)

    2015-08-28

    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 be 9.64 × 10{sup −7} cm/W, 8.55 × 10{sup −12} cm{sup 2}/W and 5.48 × 10{sup −10} esu, respectively.

  11. Nonlinear single-spin spectrum analyzer.

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

    2013-03-15

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

  12. Nonlinear singular perturbation problems of arbitrary real orders

    Bijura, Angelina M.

    2003-10-01

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

  13. Retrieval of high-order susceptibilities of nonlinear metamaterials

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

    2017-01-01

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

  14. Exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres

    Liu Chunping

    2005-01-01

    First, by using the generally projective Riccati equation method, many kinds of exact solutions for the higher-order nonlinear Schoerdinger equation in nonlinear optical fibres are obtained in a unified way. Then, some relations among these solutions are revealed

  15. Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

    Tieshan He

    2011-01-01

    Full Text Available This paper is concerned with the existence of nontrivial periodic solutions and positive periodic solutions to a nonlinear second-order difference equation. Under some conditions concerning the first positive eigenvalue of the linear equation corresponding to the nonlinear second-order equation, we establish the existence results by using the topological degree and fixed point index theories.

  16. Exact solutions to two higher order nonlinear Schroedinger equations

    Xu Liping; Zhang Jinliang

    2007-01-01

    Using the homogeneous balance principle and F-expansion method, the exact solutions to two higher order nonlinear Schroedinger equations which describe the propagation of femtosecond pulses in nonlinear fibres are obtained with the aid of a set of subsidiary higher order ordinary differential equations (sub-equations for short)

  17. Deterministic nonlinear phase gates induced by a single qubit

    Park, Kimin; Marek, Petr; Filip, Radim

    2018-05-01

    We propose deterministic realizations of nonlinear phase gates by repeating a finite sequence of non-commuting Rabi interactions between a harmonic oscillator and only a single two-level ancillary qubit. We show explicitly that the key nonclassical features of the ideal cubic phase gate and the quartic phase gate are generated in the harmonic oscillator faithfully by our method. We numerically analyzed the performance of our scheme under realistic imperfections of the oscillator and the two-level system. The methodology is extended further to higher-order nonlinear phase gates. This theoretical proposal completes the set of operations required for continuous-variable quantum computation.

  18. Second-order nonlinear optical metamaterials: ABC-type nanolaminates

    Alloatti, L.; Kieninger, C.; Lauermann, M.; Köhnle, K.; Froelich, A.; Wegener, M.; Frenzel, T.; Freude, W.; Leuthold, J.; Koos, C.

    2015-01-01

    We demonstrate a concept for second-order nonlinear metamaterials that can be obtained from non-metallic centrosymmetric constituents with inherently low optical absorption. The concept is based on iterative atomic-layer deposition of three different materials, A = Al 2 O 3 , B = TiO 2 , and C = HfO 2 . The centrosymmetry of the resulting ABC stack is broken since the ABC and the inverted CBA sequences are not equivalent—a necessary condition for non-zero second-order nonlinearity. In our experiments, we find that the bulk second-order nonlinear susceptibility depends on the density of interfaces, leading to a nonlinear susceptibility of 0.26 pm/V at a wavelength of 800 nm. ABC-type nanolaminates can be deposited on virtually any substrate and offer a promising route towards engineering of second-order optical nonlinearities at both infrared and visible wavelengths

  19. Nonlinear partial differential equations of second order

    Dong, Guangchang

    1991-01-01

    This book addresses a class of equations central to many areas of mathematics and its applications. Although there is no routine way of solving nonlinear partial differential equations, effective approaches that apply to a wide variety of problems are available. This book addresses a general approach that consists of the following: Choose an appropriate function space, define a family of mappings, prove this family has a fixed point, and study various properties of the solution. The author emphasizes the derivation of various estimates, including a priori estimates. By focusing on a particular approach that has proven useful in solving a broad range of equations, this book makes a useful contribution to the literature.

  20. Order and chaos in polarized nonlinear optics

    Holm, D.D.

    1990-01-01

    Methods for investigating temporal complexity in Hamiltonian systems are applied to the dynamics of a polarized optical laser beam propagating as a travelling wave in a medium with cubically nonlinear polarizability (i.e., a Kerr medium). The theory of Hamiltonian systems with symmetry is used to study the geometry of phase space for the optical problem, transforming from C 2 to S 2 x (J,θ), where (J,θ) is a symplectic action-angle pair. The bifurcations of the phase portraits of the Hamiltonian motion on S 2 are classified and shown graphically. These bifurcations create various saddle connections on S 2 as either J (the beam intensity), or the optical parameters of the medium are varied. After this bifurcation analysis, the Melnikov method is used to demonstrate analytically that the saddle connections break and intersect transversely in a Poincare map under spatially periodic perturbations of the optical parameters of the medium. These transverse intersections in the Poincare map imply intermittent polarization switching with extreme sensitivity to initial conditions characterized by a Smale horseshoe construction for the travelling waves of a polarized optical laser pulse. The resulting chaotic behavior in the form of sensitive dependence on initial conditions may have implications for the control and predictability of nonlinear optical polarization switching in birefringent media. 19 refs., 2 figs., 1 tab

  1. Discrete second order trajectory generator with nonlinear constraints

    Morselli, R.; Zanasi, R.; Stramigioli, Stefano

    2005-01-01

    A discrete second order trajectory generator for motion control systems is presented. The considered generator is a nonlinear system which receives as input a raw reference signal and provides as output a smooth reference signal satisfying nonlinear constraints on the output derivatives as UM-(x) ≤

  2. Fourth Order Nonlinear Intensity and the corresponding Refractive ...

    Nonlinear effects occur whenever the optical fields associated with one or more intense light such as from laser beams propagating in a crystal are large enough to produce polarization fields. This paper describes how the fourth order nonlinear intensity and the corresponding effective refractive index that is intensity ...

  3. Solution of continuous nonlinear PDEs through order completion

    Oberguggenberger, MB

    1994-01-01

    This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.

  4. Microscopic cascading of second-order molecular nonlinearity: New design principles for enhancing third-order nonlinearity.

    Baev, Alexander; Autschbach, Jochen; Boyd, Robert W; Prasad, Paras N

    2010-04-12

    Herein, we develop a phenomenological model for microscopic cascading and substantiate it with ab initio calculations. It is shown that the concept of local microscopic cascading of a second-order nonlinearity can lead to a third-order nonlinearity, without introducing any new loss mechanisms that could limit the usefulness of our approach. This approach provides a new molecular design protocol, in which the current great successes achieved in producing molecules with extremely large second-order nonlinearity can be used in a supra molecular organization in a preferred orientation to generate very large third-order response magnitudes. The results of density functional calculations for a well-known second-order molecule, (para)nitroaniline, show that a head-to-tail dimer configuration exhibits enhanced third-order nonlinearity, in agreement with the phenomenological model which suggests that such an arrangement will produce cascading due to local field effects.

  5. Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation

    Ren Ji; Ruan Hangyu

    2008-01-01

    We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained

  6. Oscillation criteria for fourth-order nonlinear delay dynamic equations

    Yunsong Qi

    2013-03-01

    Full Text Available We obtain criteria for the oscillation of all solutions to a fourth-order nonlinear delay dynamic equation on a time scale that is unbounded from above. The results obtained are illustrated with examples

  7. Oscillation criteria for third order delay nonlinear differential equations

    E. M. Elabbasy

    2012-01-01

    via comparison with some first differential equations whose oscillatory characters are known. Our results generalize and improve some known results for oscillation of third order nonlinear differential equations. Some examples are given to illustrate the main results.

  8. Higher-order techniques for some problems of nonlinear control

    Sarychev Andrey V.

    2002-01-01

    Full Text Available A natural first step when dealing with a nonlinear problem is an application of some version of linearization principle. This includes the well known linearization principles for controllability, observability and stability and also first-order optimality conditions such as Lagrange multipliers rule or Pontryagin's maximum principle. In many interesting and important problems of nonlinear control the linearization principle fails to provide a solution. In the present paper we provide some examples of how higher-order methods of differential geometric control theory can be used for the study nonlinear control systems in such cases. The presentation includes: nonlinear systems with impulsive and distribution-like inputs; second-order optimality conditions for bang–bang extremals of optimal control problems; methods of high-order averaging for studying stability and stabilization of time-variant control systems.

  9. Synthesis, characterization and third-order nonlinear optical ...

    2016-09-20

    Sep 20, 2016 ... the past, several strategies have been evolved to enhance the third-order nonlinear ..... retical fit using the formulation given in ref. [22]. Fit param- ..... Acknowledgement. The corresponding author acknowledges the financial.

  10. Stability Analysis of Fractional-Order Nonlinear Systems with Delay

    Yu Wang

    2014-01-01

    Full Text Available Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.

  11. Investigation of odd-order nonlinear susceptibilities in atomic vapors

    Yan, Yaqi [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Teaching and Research Section of Maths and Physics, Guangzhou Commanding Academy of Chinese People’s Armed Police Force, Guangzhou, 510440 (China); Wu, Zhenkun; Si, Jinhai; Yan, Lihe; Zhang, Yiqi; Yuan, Chenzhi; Sun, Jia [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China); Zhang, Yanpeng, E-mail: ypzhang@mail.xjtu.edu.cn [Key Laboratory for Physical Electronics and Devices of the Ministry of Education, Xi’an Jiaotong University, Xi’an 710049 (China); Shaanxi Key Laboratory of Information Photonic Technique, Xi’an Jiaotong University, Xi’an 710049 (China)

    2013-06-15

    We theoretically deduce the macroscopic symmetry constraints for arbitrary odd-order nonlinear susceptibilities in homogeneous media including atomic vapors for the first time. After theoretically calculating the expressions using a semiclassical method, we demonstrate that the expressions for third- and fifth-order nonlinear susceptibilities for undressed and dressed four- and six-wave mixing (FWM and SWM) in atomic vapors satisfy the macroscopic symmetry constraints. We experimentally demonstrate consistence between the macroscopic symmetry constraints and the semiclassical expressions for atomic vapors by observing polarization control of FWM and SWM processes. The experimental results are in reasonable agreement with our theoretical calculations. -- Highlights: •The macroscopic symmetry constraints are deduced for homogeneous media including atomic vapors. •We demonstrate that odd-order nonlinear susceptibilities satisfy the constraints. •We experimentally demonstrate the deduction in part.

  12. Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

    Jia Li-Xin; Dai Hao; Hui Meng

    2010-01-01

    This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method

  13. Nonlinear Phenomena in the Single-Mode Dynamics in an AFM Cantilever Beam

    Ruzziconi, Laura; Lenci, Stefano; Younis, Mohammad I.

    2016-01-01

    This study deals with the nonlinear dynamics arising in an atomic force microscope cantilever beam. After analyzing the static behavior, a single degree of freedom Galerkin reduced order model is introduced, which describes the overall scenario

  14. Riccati-parameter solutions of nonlinear second-order ODEs

    Reyes, M A; Rosu, H C

    2008-01-01

    It has been proven by Rosu and Cornejo-Perez (Rosu and Cornejo-Perez 2005 Phys. Rev. E 71 046607, Cornejo-Perez and Rosu 2005 Prog. Theor. Phys. 114 533) that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions is easy to obtain if the proposed factorization has a particular form, which happily turns out to be the case in many problems of physical interest. The method that we exemplify with a few explicitly solved cases consists in using the general solution of the Riccati equation, which contributes with one parameter to this class of parametric solutions. For these nonlinear cases, the Riccati parameter serves as a 'growth' parameter from the trivial null solution up to the particular solution found through the factorization procedure

  15. Nonlinear noninteger order circuits and systems an introduction

    Arena, P; Fortuna, L; Porto, D

    2001-01-01

    In this book, the reader will find a theoretical introduction to noninteger order systems, as well as several applications showing their features and peculiarities. The main definitions and results of research on noninteger order systems and modelling of physical noninteger phenomena are reported together with problems of their approximation. Control applications, noninteger order CNNs and circuit realizations of noninteger order systems are also presented.The book is intended for students and researchers involved in the simulation and control of nonlinear noninteger order systems, with partic

  16. Nonlinear second order evolution inclusions with noncoercive viscosity term

    Papageorgiou, Nikolaos S.; Rădulescu, Vicenţiu D.; Repovš, Dušan D.

    2018-04-01

    In this paper we deal with a second order nonlinear evolution inclusion, with a nonmonotone, noncoercive viscosity term. Using a parabolic regularization (approximation) of the problem and a priori bounds that permit passing to the limit, we prove that the problem has a solution.

  17. Oscillation criteria for first-order forced nonlinear difference equations

    Grace Said R; Agarwal Ravi P; Smith Tim

    2006-01-01

    Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form Δx(n)+q1(n)xμ(n+1) = q2(n)xλ(n+1)+e(n), where λ, μ are the ratios of positive odd integers 0 <μ < 1 and λ > 1, are established.

  18. New Efficient Fourth Order Method for Solving Nonlinear Equations

    Farooq Ahmad

    2013-12-01

    Full Text Available In a paper [Appl. Math. Comput., 188 (2 (2007 1587--1591], authors have suggested and analyzed a method for solving nonlinear equations. In the present work, we modified this method by using the finite difference scheme, which has a quintic convergence. We have compared this modified Halley method with some other iterative of fifth-orders convergence methods, which shows that this new method having convergence of fourth order, is efficient.

  19. Higher-Order Spectrum in Understanding Nonlinearity in EEG Rhythms

    Cauchy Pradhan

    2012-01-01

    Full Text Available The fundamental nature of the brain's electrical activities recorded as electroencephalogram (EEG remains unknown. Linear stochastic models and spectral estimates are the most common methods for the analysis of EEG because of their robustness, simplicity of interpretation, and apparent association with rhythmic behavioral patterns in nature. In this paper, we extend the use of higher-order spectrum in order to indicate the hidden characteristics of EEG signals that simply do not arise from random processes. The higher-order spectrum is an extension Fourier spectrum that uses higher moments for spectral estimates. This essentially nullifies all Gaussian random effects, therefore, can reveal non-Gaussian and nonlinear characteristics in the complex patterns of EEG time series. The paper demonstrates the distinguishing features of bispectral analysis for chaotic systems, filtered noises, and normal background EEG activity. The bispectrum analysis detects nonlinear interactions; however, it does not quantify the coupling strength. The squared bicoherence in the nonredundant region has been estimated to demonstrate nonlinear coupling. The bicoherence values are minimal for white Gaussian noises (WGNs and filtered noises. Higher bicoherence values in chaotic time series and normal background EEG activities are indicative of nonlinear coupling in these systems. The paper shows utility of bispectral methods as an analytical tool in understanding neural process underlying human EEG patterns.

  20. Embedded solitons in the third-order nonlinear Schroedinger equation

    Pal, Debabrata; Ali, Sk Golam; Talukdar, B

    2008-01-01

    We work with a sech trial function with space-dependent soliton parameters and envisage a variational study for the nonlinear Schoedinger (NLS) equation in the presence of third-order dispersion. We demonstrate that the variational equations for pulse evolution in this NLS equation provide a natural basis to derive a potential model which can account for the existence of a continuous family of embedded solitons supported by the third-order NLS equation. Each member of the family is parameterized by the propagation velocity and co-efficient of the third-order dispersion

  1. Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

    Taher S. Hassan

    2016-01-01

    Full Text Available We will consider the higher order functional dynamic equations with mixed nonlinearities of the form xnt+∑j=0Npjtϕγjxφjt=0, on an above-unbounded time scale T, where n≥2, xi(t≔ri(tϕαixi-1Δ(t,  i=1,…,n-1,   with  x0=x,  ϕβ(u≔uβsgn⁡u, and α[i,j]≔αi⋯αj. The function φi:T→T is a rd-continuous function such that limt→∞φi(t=∞ for j=0,1,…,N. The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.

  2. Ultrafast third-order nonlinearity of silver nanospheres and nanodiscs

    Jayabalan, J; Singh, Asha; Chari, Rama; Oak, Shrikant M [Ultrafast Studies Section, Laser Physics Application Division, Raja Ramanna Centre for Advanced Technology, Indore-452013 (India)

    2007-08-08

    We have measured and compared the absolute values of nonlinear susceptibility of colloidal solutions containing silver nanospheres and nanodiscs at their respective plasmon peaks using a femtosecond laser. The nonlinear process responsible for the laser-induced grating formation in the sample is determined to be of third order. The ratio between the third-order susceptibility (|{chi}{sup (3)}|) and the linear absorption coefficient ({alpha}) of the nanodiscs at 590 nm is three times than that of the similar ratio for nanospheres at 398 nm. Using a randomly oriented ellipsoidal model, we have shown that the increase in |{chi}{sup (3)}|/{alpha} for a nanodisc at 590 nm can be attributed to the change in the field enhancement factor with shape.

  3. Ultrafast third-order nonlinearity of silver nanospheres and nanodiscs

    Jayabalan, J; Singh, Asha; Chari, Rama; Oak, Shrikant M

    2007-01-01

    We have measured and compared the absolute values of nonlinear susceptibility of colloidal solutions containing silver nanospheres and nanodiscs at their respective plasmon peaks using a femtosecond laser. The nonlinear process responsible for the laser-induced grating formation in the sample is determined to be of third order. The ratio between the third-order susceptibility (|χ (3) |) and the linear absorption coefficient (α) of the nanodiscs at 590 nm is three times than that of the similar ratio for nanospheres at 398 nm. Using a randomly oriented ellipsoidal model, we have shown that the increase in |χ (3) |/α for a nanodisc at 590 nm can be attributed to the change in the field enhancement factor with shape

  4. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

    N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem

    2015-01-01

    This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

  5. Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems

    N'Doye, Ibrahima

    2015-07-01

    This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.

  6. Surface plasmon enhanced third-order optical nonlinearity of Ag nanocomposite film

    Singh, Vijender [Department of Applied Science, N.C. College of Engineering, Israna, Panipat 132107, Haryana (India); Aghamkar, Praveen, E-mail: p-aghamkar@yahoo.in [Department of Physics, Chaudhary Devi Lal University, Sirsa 125055, Haryana (India)

    2014-03-17

    We obtain a large third-order optical nonlinearity (χ{sup (3)} ≈ 10{sup −10}esu) of silver nanoparticles dispersed in polyvinyl alcohol/tetraethyl orthosilicate matrix using single beam z-scan technique at 532 nm by Q-switched Nd:YAG laser. We have shown that mechanisms responsible for third-order optical nonlinearity of Ag nanocomposite film are reverse saturable absorption (RSA) and self-defocusing in the purlieu of surface plasmon resonance (SPR). Optical band-gap and width of SPR band of Ag nanocomposite film decrease with increasing silver concentration, which leads to enhancement of local electric field and hence third-order optical nonlinearity. Optical limiting, due to RSA has also been demonstrated at 532 nm.

  7. Surface plasmon enhanced third-order optical nonlinearity of Ag nanocomposite film

    Singh, Vijender; Aghamkar, Praveen

    2014-01-01

    We obtain a large third-order optical nonlinearity (χ (3)  ≈ 10 −10 esu) of silver nanoparticles dispersed in polyvinyl alcohol/tetraethyl orthosilicate matrix using single beam z-scan technique at 532 nm by Q-switched Nd:YAG laser. We have shown that mechanisms responsible for third-order optical nonlinearity of Ag nanocomposite film are reverse saturable absorption (RSA) and self-defocusing in the purlieu of surface plasmon resonance (SPR). Optical band-gap and width of SPR band of Ag nanocomposite film decrease with increasing silver concentration, which leads to enhancement of local electric field and hence third-order optical nonlinearity. Optical limiting, due to RSA has also been demonstrated at 532 nm

  8. Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation

    Petráš, Ivo

    2011-01-01

    "Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...

  9. Second order optical nonlinearity in silicon by symmetry breaking

    Cazzanelli, Massimo, E-mail: massimo.cazzanelli@unitn.it [Laboratorio IdEA, Dipartimento di Fisica, Università di Trento, via Sommarive, 14 Povo (Trento) (Italy); Schilling, Joerg, E-mail: joerg.schilling@physik.uni-halle.de [Centre for Innovation Competence SiLi-nano, Martin-Luther-University Halle-Wittenberg, Karl-Freiherr-von-Fritsch Str. 3, 06120 Halle (Germany)

    2016-03-15

    Although silicon does not possess a dipolar bulk second order nonlinear susceptibility due to its centro-symmetric crystal structure, in recent years several attempts were undertaken to create such a property in silicon. This review presents the different sources of a second order susceptibility (χ{sup (2)}) in silicon and the connected second order nonlinear effects which were investigated up to now. After an introduction, a theoretical overview discusses the second order nonlinearity in general and distinguishes between the dipolar contribution—which is usually dominating in non-centrosymmetric structures—and the quadrupolar contribution, which even exists in centro-symmetric materials. Afterwards, the classic work on second harmonic generation from silicon surfaces in reflection measurements is reviewed. Due to the abrupt symmetry breaking at surfaces and interfaces locally a dipolar second order susceptibility appears, resulting in, e.g., second harmonic generation. Since the bulk contribution is usually small, the study of this second harmonic signal allows a sensitive observation of the surface/interface conditions. The impact of covering films, strain, electric fields, and defect states at the interfaces was already investigated in this way. With the advent of silicon photonics and the search for ever faster electrooptic modulators, the interest turned to the creation of a dipolar bulk χ{sup (2)} in silicon. These efforts have been focussing on several experiments applying an inhomogeneous strain to the silicon lattice to break its centro-symmetry. Recent results suggesting the impact of electric fields which are exerted from fixed charges in adjacent covering layers are also included. After a subsequent summary on “competing” concepts using not Si but Si-related materials, the paper will end with some final conclusions, suggesting possible future research direction in this dynamically developing field.

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

    Azarnavid, Babak; Parand, Kourosh; Abbasbandy, Saeid

    2018-06-01

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

  11. Single Particle Linear and Nonlinear Dynamics

    Cai, Y

    2004-06-25

    I will give a comprehensive review of existing particle tracking tools to assess long-term particle stability for small and large accelerators in the presence of realistic magnetic imperfections and machine misalignments. The emphasis will be on the tracking and analysis tools based upon the differential algebra, Lie operator, and ''polymorphism''. Using these tools, a uniform linear and non-linear analysis will be outlined as an application of the normal form.

  12. Single Particle Linear and Nonlinear Dynamics

    Cai, Y

    2004-01-01

    I will give a comprehensive review of existing particle tracking tools to assess long-term particle stability for small and large accelerators in the presence of realistic magnetic imperfections and machine misalignments. The emphasis will be on the tracking and analysis tools based upon the differential algebra, Lie operator, and ''polymorphism''. Using these tools, a uniform linear and non-linear analysis will be outlined as an application of the normal form

  13. Ablation and optical third-order nonlinearities in Ag nanoparticles

    Carlos Torres-Torres

    2010-11-01

    Full Text Available Carlos Torres-Torres1, Néstor Peréa-López2, Jorge Alejandro Reyes-Esqueda3, Luis Rodríguez-Fernández3, Alejandro Crespo-Sosa3, Juan Carlos Cheang-Wong3, Alicia Oliver31Section of Graduate Studies and Research, School of Mechanical and Electrical Engineering, National Polytechnic Institute, Zacatenco, Distrito Federal, Mexico; 2Laboratory for Nanoscience and Nanotechnology Research and Advanced Materials Department, IPICYT, Camino a la Presa San Jose, San Luis Potosi, Mexico; 3Instituto de Física, Universidad Nacional Autónoma de México, A.P. 20-364, México, D.F. 01000, MéxicoAbstract: The optical damage associated with high intensity laser excitation of silver nanoparticles (NPs was studied. In order to investigate the mechanisms of optical nonlinearity of a nanocomposite and their relation with its ablation threshold, a high-purity silica sample implanted with Ag ions was exposed to different nanosecond and picosecond laser irradiations. The magnitude and sign of picosecond refractive and absorptive nonlinearities were measured near and far from the surface plasmon resonance (SPR of the Ag NPs with a self-diffraction technique. Saturable optical absorption and electronic polarization related to self-focusing were identified. Linear absorption is the main process involved in nanosecond laser ablation, but nonlinearities are important for ultrashort picosecond pulses when the absorptive process become significantly dependent on the irradiance. We estimated that near the resonance, picosecond intraband transitions allow an expanded distribution of energy among the NPs, in comparison to the energy distribution resulting in a case of far from resonance, when the most important absorption takes place in silica. We measured important differences in the ablation threshold and we estimated that the high selectiveness of the SPR of Ag NPs as well as their corresponding optical nonlinearities can be strongly significant for laser

  14. Dynamical Properties in a Fourth-Order Nonlinear Difference Equation

    Xianyi Li; Yunxin Chen

    2010-01-01

    The rule of trajectory structure for fourth-order nonlinear difference equation xn+1=(xan−2+xn−3)/(xan−2xn−3+1), n=0,1,2,…, where a∈[0,1) and the initial values x−3,x−2,x−1,x0∈[0,∞), is described clearly out in this paper. Mainly, the lengths of positive and negative semicycles of its nontrivial solutions are found to occur periodically with prime period 15. The rule is 4+,3−,1+,2−,2+,1−,1+, 1&#x...

  15. Nonlinear dynamics of single-helicity neoclassical MHD tearing instabilities

    Spong, D.A.; Shaing, K.C.; Carreras, B.A.; Callen, J.D.; Garcia, L.

    1988-10-01

    Neoclassical magnetohydrodynamic (MHD) effects can significantly alter the nonlinear evolution of resistive tearing instabilities. This is studied numerically by using a flux-surface-averaged set of evolution equations that includes the lowest-order neoclassical MHD effects. The new terms in the equations are fluctuating bootstrap current, neoclassical modification of the resistivity, and neoclassical damping of the vorticity. Single-helicity tearing modes are studied in a cylindrical model over a range of neoclassical viscosities (μ/sub e//ν/sup e/) and values of the Δ' parameter of tearing mode theory. Increasing the neoclassical viscosity leads to increased growth rate and saturated island width as predicted analytically. The larger island width is caused by the fluctuating bootstrap current contribution in Ohm's law. The Δ' parameter no longer solely determines the island width, and finite-width saturated islands may be obtained even when Δ' is negative. The importance of the bootstrap current (/approximately/∂/rho///partial derivative/psi/) in the nonlinear dynamics leads us to examine the sensitivity of the results with respect to different models for the density evolution. 11 refs., 8 figs

  16. Nonlinear ultrasonic fatigue crack detection using a single piezoelectric transducer

    An, Yun-Kyu; Lee, Dong Jun

    2016-04-01

    This paper proposes a new nonlinear ultrasonic technique for fatigue crack detection using a single piezoelectric transducer (PZT). The proposed technique identifies a fatigue crack using linear (α) and nonlinear (β) parameters obtained from only a single PZT mounted on a target structure. Based on the different physical characteristics of α and β, a fatigue crack-induced feature is able to be effectively isolated from the inherent nonlinearity of a target structure and data acquisition system. The proposed technique requires much simpler test setup and less processing costs than the existing nonlinear ultrasonic techniques, but fast and powerful. To validate the proposed technique, a real fatigue crack is created in an aluminum plate, and then false positive and negative tests are carried out under varying temperature conditions. The experimental results reveal that the fatigue crack is successfully detected, and no positive false alarm is indicated.

  17. Existence of solutions to second-order nonlinear coupled systems with nonlinear coupled boundary conditions

    Imran Talib

    2015-12-01

    Full Text Available In this article, study the existence of solutions for the second-order nonlinear coupled system of ordinary differential equations $$\\displaylines{ u''(t=f(t,v(t,\\quad t\\in [0,1],\\cr v''(t=g(t,u(t,\\quad t\\in [0,1], }$$ with nonlinear coupled boundary conditions $$\\displaylines{ \\phi(u(0,v(0,u(1,v(1,u'(0,v'(0=(0,0, \\cr \\psi(u(0,v(0,u(1,v(1,u'(1,v'(1=(0,0, }$$ where $f,g:[0,1]\\times \\mathbb{R}\\to \\mathbb{R}$ and $\\phi,\\psi:\\mathbb{R}^6\\to \\mathbb{R}^2$ are continuous functions. Our main tools are coupled lower and upper solutions, Arzela-Ascoli theorem, and Schauder's fixed point theorem.

  18. Third-order nonlinear optical properties of ADP crystal

    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.

  19. Any order approximate analytical solution of the nonlinear Volterra's integral equation for accelerator dynamic systems

    Liu Chunliang; Xie Xi; Chen Yinbao

    1991-01-01

    The universal nonlinear dynamic system equation is equivalent to its nonlinear Volterra's integral equation, and any order approximate analytical solution of the nonlinear Volterra's integral equation is obtained by exact analytical method, thus giving another derivation procedure as well as another computation algorithm for the solution of the universal nonlinear dynamic system equation

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

    Xiao Yafeng; Xue Haili; Zhang Hongqing

    2011-01-01

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

  1. Evaluation of third order nonlinear optical parameters of CdS/PVA nanocomposite

    Sharma, Mamta; Tripathi, S. K.

    2015-01-01

    CdS nanoparticles dispersed in PVA are prepared by Chemical method at room temperature. The nonlinear optical parameters such as nonlinear absorption (β), nonlinear refractive index (n 2 ) and nonlinear susceptibility (χ 3 ) are calculated for this sample by using Z-scan technique. CdS/PVA samples show the two photon absorption mechanism. The third order nonlinear susceptibility is calculated from n 2 and β and is found to be of the order of 10 −7 – 10 −8 m 2 /V 2 . The larger value of third order nonlinear susceptibility is due to dielectric and quantum confinement effect

  2. Engineering high-order nonlinear dissipation for quantum superconducting circuits

    Mundhada, S. O.; Grimm, A.; Touzard, S.; Shankar, S.; Minev, Z. K.; Vool, U.; Mirrahimi, M.; Devoret, M. H.

    Engineering nonlinear driven-dissipative processes is essential for quantum control. In the case of a harmonic oscillator, nonlinear dissipation can stabilize a decoherence-free manifold, leading to protected quantum information encoding. One possible approach to implement such nonlinear interactions is to combine the nonlinearities provided by Josephson circuits with parametric pump drives. However, it is usually hard to achieve strong nonlinearities while avoiding undesired couplings. Here we propose a scheme to engineer a four-photon drive and dissipation in a harmonic oscillator by cascading experimentally demonstrated two-photon processes. We also report experimental progress towards realization of such a scheme. Work supported by: ARO, ONR, AFOSR and YINQE.

  3. Dynamic Flight Simulation Utilizing High Fidelity CFD-Based Nonlinear Reduced Order Model, Phase I

    National Aeronautics and Space Administration — The overall technical objective of the Phase I effort is to develop a nonlinear aeroelastic solver utilizing the FUN3D generated nonlinear aerodynamic Reduced Order...

  4. Multi-order nonlinear diffraction in second harmonic generation

    Saltiel, S. M.; Neshev, D.; Krolikowski, Wieslaw

    We analyze the emission patterns in the process of second harmonic (SH) generation in χ(2) nonlinear gratings and identify for the first time, to the best of our knowledge, the evidence of Raman-Nath type nonlinear diffraction in frequency doubling processes.......We analyze the emission patterns in the process of second harmonic (SH) generation in χ(2) nonlinear gratings and identify for the first time, to the best of our knowledge, the evidence of Raman-Nath type nonlinear diffraction in frequency doubling processes....

  5. Single-nary philosophy for non-linear study of mechanics of materials

    Tran, C.

    2005-01-01

    Non-linear study of mechanics of materials is formulated in this paper as a problem of meta-intelligent system analysis. Non-linearity will be singled out as an important concept for understanding of high-order complex systems. Through single-nary thinking, which will be represented in this work, we introduce a modification of Aristotelian philosophy using modal logic and multi-valued logic (these logics we call 'high-order' logic). Next, non-linear cause - effect relations are expressed through non-additive measures and multiple-information aggregation principles based on fuzzy integration. The study of real time behaviors, required experiences and intuition, will be realized using truth measures (non-additive measures) and a procedure for information processing in intelligence levels. (author)

  6. Evaluation of polymer based third order nonlinear integrated optics devices

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

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

  7. Pressure tunable cascaded third order nonlinearity and temporal pulse switching

    Eilenberger, Falk; Bache, Morten; Minardi, Stefano

    2013-01-01

    Effects based on the χ(3)-nonlinearity are arguably the most commonly discussed nonlinear interactions in photonics. In the description of pulse propagation, however, the generation of the third harmonic (TH) is commonly neglected, because it is strongly phase mismatched in most materials...

  8. Second-Order Nonlinear Optical Dendrimers and Dendronized Hyperbranched Polymers.

    Tang, Runli; Li, Zhen

    2017-01-01

    Second-order nonlinear optical (NLO) dendrimers with a special topological structure were regarded as the most promising candidates for practical applications in the field of optoelectronic materials. Dendronized hyperbranched polymers (DHPs), a new type of polymers with dendritic structures, proposed and named by us recently, demonstrated interesting properties and some advantages over other polymers. Some of our work concerning these two types of polymers are presented herein, especially focusing on the design idea and structure-property relationship. To enhance their comprehensive NLO performance, dendrimers were designed and synthesized by adjusting their isolation mode, increasing the number of the dendritic generation, modifying their topological structure, introducing isolation chromophores, and utilizing the Ar-Ar F self-assembly effect. To make full use of the advantages of both the structural integrity of dendrimers and the convenient one-pot synthesis of hyperbranched polymers, DHPs were explored by utilizing low-generation dendrons as big monomers to construct hyperbranched polymers. These selected works could provide valuable information to deeply understand the relationship between the structure and properties of functional polymers with dendritic structures, but not only limited to the NLO ones, and might contribute much to the further development of functional polymers with rational design. © 2017 The Chemical Society of Japan & Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

  9. Nonlinear characterization of a single-axis acoustic levitator

    Andrade, Marco A. B.; Ramos, Tiago S.; Okina, Fábio T. A.; Adamowski, Julio C.

    2014-01-01

    The nonlinear behavior of a 20.3 kHz single-axis acoustic levitator formed by a Langevin transducer with a concave radiating surface and a concave reflector is experimentally investigated. In this study, a laser Doppler vibrometer is applied to measure the nonlinear sound field in the air gap between the transducer and the reflector. Additionally, an electronic balance is used in the measurement of the acoustic radiation force on the reflector as a function of the distance between the transducer and the reflector. The experimental results show some effects that cannot be described by the linear acoustic theory, such as the jump phenomenon, harmonic generation, and the hysteresis effect. The influence of these nonlinear effects on the acoustic levitation of small particles is discussed

  10. Nonlinear characterization of a single-axis acoustic levitator

    Andrade, Marco A. B. [Institute of Physics, University of São Paulo, São Paulo (Brazil); Ramos, Tiago S.; Okina, Fábio T. A.; Adamowski, Julio C. [Department of Mechatronics and Mechanical Systems Engineering, Escola Politécnica, University of São Paulo, São Paulo (Brazil)

    2014-04-15

    The nonlinear behavior of a 20.3 kHz single-axis acoustic levitator formed by a Langevin transducer with a concave radiating surface and a concave reflector is experimentally investigated. In this study, a laser Doppler vibrometer is applied to measure the nonlinear sound field in the air gap between the transducer and the reflector. Additionally, an electronic balance is used in the measurement of the acoustic radiation force on the reflector as a function of the distance between the transducer and the reflector. The experimental results show some effects that cannot be described by the linear acoustic theory, such as the jump phenomenon, harmonic generation, and the hysteresis effect. The influence of these nonlinear effects on the acoustic levitation of small particles is discussed.

  11. Nonlinear characterization of a single-axis acoustic levitator.

    Andrade, Marco A B; Ramos, Tiago S; Okina, Fábio T A; Adamowski, Julio C

    2014-04-01

    The nonlinear behavior of a 20.3 kHz single-axis acoustic levitator formed by a Langevin transducer with a concave radiating surface and a concave reflector is experimentally investigated. In this study, a laser Doppler vibrometer is applied to measure the nonlinear sound field in the air gap between the transducer and the reflector. Additionally, an electronic balance is used in the measurement of the acoustic radiation force on the reflector as a function of the distance between the transducer and the reflector. The experimental results show some effects that cannot be described by the linear acoustic theory, such as the jump phenomenon, harmonic generation, and the hysteresis effect. The influence of these nonlinear effects on the acoustic levitation of small particles is discussed.

  12. Photonic single nonlinear-delay dynamical node for information processing

    Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel

    2012-06-01

    An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.

  13. Syntheses, structures and third-order non-linear optical properties of homometal clusters containing molybdenum

    Li Yong; Lu Jing; Cui Xiaobing; Xu Jiqing; Li Kechang; Sun Huaying; Li Guanghua; Pan Lingyun; Yang Qingxin

    2005-01-01

    Both the homometal cluster [P(ph 4 )] 2 [Mo 2 O 2 (μ-S) 2 (S 2 ) 2 ] (1) and [Mo 2 O 2 (μ-S) 2 (Et 2 dtc) 2 ] (2) (Et 2 dtc=diethyl-dithiocarbamate) were successfully synthesized by low-temperature solid-state reactions. X-ray single-crystal diffraction studies suggest that compound (1) is a dinuclear anion cluster, and compound (2) is a dinuclear neutral cluster. The two compounds were characterized by elemental analyses, IR spectra and UV-Vis spectra. The third-order non-linear optical (NLO) properties of the clusters were also investigated and all exhibited nice non-linear absorption and self-defocusing performance with moduli of the hyperpolarizabilities 5.145x10 -30 esu for (1) and 5.428x10 -30 esu for (2)

  14. Stability analysis of embedded solitons in the generalized third-order nonlinear Schroedinger equation

    Pelinovsky, Dmitry E.; Yang Jianke

    2005-01-01

    We study the generalized third-order nonlinear Schroedinger (NLS) equation which admits a one-parameter family of single-hump embedded solitons. Analyzing the spectrum of the linearization operator near the embedded soliton, we show that there exists a resonance pole in the left half-plane of the spectral parameter, which explains linear stability, rather than nonlinear semistability, of embedded solitons. Using exponentially weighted spaces, we approximate the resonance pole both analytically and numerically. We confirm in a near-integrable asymptotic limit that the resonance pole gives precisely the linear decay rate of parameters of the embedded soliton. Using conserved quantities, we qualitatively characterize the stable dynamics of embedded solitons

  15. Weak and Strong Order of Convergence of a Semidiscrete Scheme for the Stochastic Nonlinear Schrodinger Equation

    Bouard, Anne de; Debussche, Arnaud

    2006-01-01

    In this article we analyze the error of a semidiscrete scheme for the stochastic nonlinear Schrodinger equation with power nonlinearity. We consider supercritical or subcritical nonlinearity and the equation can be either focusing or defocusing. Allowing sufficient spatial regularity we prove that the numerical scheme has strong order 1/2 in general and order 1 if the noise is additive. Furthermore, we also prove that the weak order is always 1

  16. Nonlinear evolution of single spike in Richtmyer-Meshkov instability

    Fukuda, Y.; Nishihara, K.; Wouchuk, J.G.

    2000-01-01

    Nonlinear evolution of single spike structure and vortex in the Richtmyer-Meshkov instability is investigated with the use of a two-dimensional hydrodynamic code. It is shown that singularity appears in the vorticity left by transmitted and reflected shocks at a corrugated interface. This singularity results in opposite sign of vorticity along the interface that causes double spiral structure of the spike. (authors)

  17. Order-disorder transitions in time-discrete mean field systems with memory: a novel approach via nonlinear autoregressive models

    Frank, T D; Mongkolsakulvong, S

    2015-01-01

    In a previous study strongly nonlinear autoregressive (SNAR) models have been introduced as a generalization of the widely-used time-discrete autoregressive models that are known to apply both to Markov and non-Markovian systems. In contrast to conventional autoregressive models, SNAR models depend on process mean values. So far, only linear dependences have been studied. We consider the case in which process mean values can have a nonlinear impact on the processes under consideration. It is shown that such models describe Markov and non-Markovian many-body systems with mean field forces that exhibit a nonlinear impact on single subsystems. We exemplify that such nonlinear dependences can describe order-disorder phase transitions of time-discrete Markovian and non-Markovian many-body systems. The relevant order parameter equations are derived and issues of stability and stationarity are studied. (paper)

  18. Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR

    Dong Zhang

    2017-03-01

    Full Text Available This article presents a new fractional-order sliding mode control (FOSMC strategy based on a linear-quadratic regulator (LQR for a class of uncertain nonlinear systems. First, input/output feedback linearization is used to linearize the nonlinear system and decouple tracking error dynamics. Second, LQR is designed to ensure that the tracking error dynamics converges to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding surface is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, the global stability of the closed-loop control system is analytically proved using Lyapunov stability theory. Finally, a typical single-input single-output system and a typical multi-input multi-output system are simulated to illustrate the effectiveness and advantages of the proposed control strategy. The results of the simulation indicate that the proposed control strategy exhibits excellent performance and robustness with system uncertainties. Compared to conventional integer-order sliding mode control, the high-frequency chattering of the control input is drastically depressed.

  19. The third order nonlinear susceptibility of InAs at infrared region

    Musayev, M.A.

    2008-01-01

    Nonlinear susceptibilities of the third order and coefficient of nonlinear absorption in InAs n-type with a different degree of a doping have been measured. The values of the third order nonlinear susceptibilities have derived from these measurements essentially exceed the values calculated on the basis of model featuring nonlinear susceptibility of electrons, being in conduction-band nonparabolicity. It has been shown that the observable discrepancy has been eliminated, if in calculation a dissipation of energy of electrons has been considered. Growth of efficiency at four-wave mixingin narrow-gap semiconductors has been restricted to nonlinear absorption of interacting waves

  20. Single nano-hole as a new effective nonlinear element for third-harmonic generation

    Melentiev, P N; Konstantinova, T V; Afanasiev, A E; Balykin, V I; Kuzin, A A; Baturin, A S; Tausenev, A V; Konyaschenko, A V

    2013-01-01

    In this letter, we report on a particularly strong optical nonlinearity at the nanometer scale in aluminum. A strong optical nonlinearity of the third order was demonstrated on a single nanoslit. Single nanoslits of different aspect ratio were excited by a laser pulse (120 fs) at the wavelength 1.5 μm, leading predominantly to third-harmonic generation (THG). It has been shown that strong surface plasmon resonance in a nanoslit allows the realization of an effective nanolocalized source of third-harmonic radiation. We show also that a nanoslit in a metal film has a significant advantage in nonlinear processes over its Babinet complementary nanostructure (nanorod): the effective abstraction of heat in a film with a slit makes it possible to use much higher laser radiation intensities. (letter)

  1. Single nano-hole as a new effective nonlinear element for third-harmonic generation

    Melentiev, P. N.; Konstantinova, T. V.; Afanasiev, A. E.; Kuzin, A. A.; Baturin, A. S.; Tausenev, A. V.; Konyaschenko, A. V.; Balykin, V. I.

    2013-07-01

    In this letter, we report on a particularly strong optical nonlinearity at the nanometer scale in aluminum. A strong optical nonlinearity of the third order was demonstrated on a single nanoslit. Single nanoslits of different aspect ratio were excited by a laser pulse (120 fs) at the wavelength 1.5 μm, leading predominantly to third-harmonic generation (THG). It has been shown that strong surface plasmon resonance in a nanoslit allows the realization of an effective nanolocalized source of third-harmonic radiation. We show also that a nanoslit in a metal film has a significant advantage in nonlinear processes over its Babinet complementary nanostructure (nanorod): the effective abstraction of heat in a film with a slit makes it possible to use much higher laser radiation intensities.

  2. Second-order nonlinear optical microscopy of spider silk

    Zhao, Yue; Hien, Khuat Thi Thu; Mizutani, Goro; Rutt, Harvey N.

    2017-06-01

    Asymmetric β-sheet protein structures in spider silk should induce nonlinear optical interaction such as second harmonic generation (SHG) which is experimentally observed for a radial line and dragline spider silk using an imaging femtosecond laser SHG microscope. By comparing different spider silks, we found that the SHG signal correlates with the existence of the protein β-sheets. Measurements of the polarization dependence of SHG from the dragline indicated that the β-sheet has a nonlinear response depending on the direction of the incident electric field. We propose a model of what orientation the β-sheet takes in spider silk.

  3. The Volterra's integral equation theory for accelerator single-freedom nonlinear components

    Wang Sheng; Xie Xi

    1996-01-01

    The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed

  4. Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order

    Pradeep, R Gladwin; Chandrasekar, V K; Senthilvelan, M; Lakshmanan, M

    2011-01-01

    In this paper, we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use of the Lie point symmetries of the linear ODEs and the nonlocal connection to deduce the nonlocal symmetries of the corresponding nonlinear ODEs. Using these nonlocal symmetries, we obtain reduction transformations and reduced equations to specific examples. We find that the reduced equations can be explicitly integrated to deduce the general solutions for these cases. We also extend this procedure to coupled higher order nonlinear ODEs with specific reference to second-order nonlinear ODEs. (paper)

  5. Computational studies of third-order nonlinear optical properties of ...

    Anuj Kumar

    2017-06-20

    Jun 20, 2017 ... Department of Physics, Jaypee University of Engineering and Technology, Raghogarh,. Guna 473 226, India. ∗ ... properties and other molecular properties of the organic nonlinear optical crystal 2-aminopyridinium p- toluenesulphonate ... nal processing, optical limiting, optical logic gates, laser radiation ...

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

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

    2018-03-01

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

  7. ON THE INSTABILITY OF SOLUTIONS TO A NONLINEAR VECTOR DIFFERENTIAL EQUATION OF FOURTH ORDER

    2011-01-01

    This paper presents a new result related to the instability of the zero solution to a nonlinear vector differential equation of fourth order.Our result includes and improves an instability result in the previous literature,which is related to the instability of the zero solution to a nonlinear scalar differential equation of fourth order.

  8. Single-order laser high harmonics in XUV for ultrafast photoelectron spectroscopy of molecular wavepacket dynamics

    Mizuho Fushitani

    2016-11-01

    Full Text Available We present applications of extreme ultraviolet (XUV single-order laser harmonics to gas-phase ultrafast photoelectron spectroscopy. Ultrashort XUV pulses at 80 nm are obtained as the 5th order harmonics of the fundamental laser at 400 nm by using Xe or Kr as the nonlinear medium and separated from other harmonic orders by using an indium foil. The single-order laser harmonics is applied for real-time probing of vibrational wavepacket dynamics of I2 molecules in the bound and dissociating low-lying electronic states and electronic-vibrational wavepacket dynamics of highly excited Rydberg N2 molecules.

  9. Single-order laser high harmonics in XUV for ultrafast photoelectron spectroscopy of molecular wavepacket dynamics.

    Fushitani, Mizuho; Hishikawa, Akiyoshi

    2016-11-01

    We present applications of extreme ultraviolet (XUV) single-order laser harmonics to gas-phase ultrafast photoelectron spectroscopy. Ultrashort XUV pulses at 80 nm are obtained as the 5th order harmonics of the fundamental laser at 400 nm by using Xe or Kr as the nonlinear medium and separated from other harmonic orders by using an indium foil. The single-order laser harmonics is applied for real-time probing of vibrational wavepacket dynamics of I 2 molecules in the bound and dissociating low-lying electronic states and electronic-vibrational wavepacket dynamics of highly excited Rydberg N 2 molecules.

  10. Evaluation of third order nonlinear optical parameters of CdS/PVA nanocomposite

    Sharma, Mamta [Department of Physics, Center of Advanced Study in Physics, Panjab University, Chandigarh-160014 (India); Department of Applied Sciences (Physics), UIET, Panjab University, Chandigarh-160014 (India); Tripathi, S. K., E-mail: surya@pu.ac.in, E-mail: surya-tr@yahoo.com [Department of Physics, Center of Advanced Study in Physics, Panjab University, Chandigarh-160014 (India)

    2015-06-24

    CdS nanoparticles dispersed in PVA are prepared by Chemical method at room temperature. The nonlinear optical parameters such as nonlinear absorption (β), nonlinear refractive index (n{sub 2}) and nonlinear susceptibility (χ{sup 3}) are calculated for this sample by using Z-scan technique. CdS/PVA samples show the two photon absorption mechanism. The third order nonlinear susceptibility is calculated from n{sub 2} and β and is found to be of the order of 10{sup −7} – 10{sup −8} m{sup 2}/V{sup 2}. The larger value of third order nonlinear susceptibility is due to dielectric and quantum confinement effect.

  11. Nonlinear polarization effects in a birefringent single mode optical fiber

    Ishiekwene, G.C.; Mensah, S.Y.; Brown, C.S.

    2001-04-01

    The nonlinear polarization effects in a birefringent single mode optical fiber is studied using Jacobi elliptic functions. We find that the polarization state of the propagating beam depends on the initial polarization as well as the intensity of the input light in a complicated way. The Stokes polarization parameters are either periodic or aperiodic depending on the value of the Jacobian modulus. Our calculations suggest that the effective beat length of the fiber can become infinite at a higher critical value of the input power when polarization dependent losses are considered. (author)

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

    Engsig-Karup, Allan Peter; Bingham, Harry B.; Lindberg, Ole

    2009-01-01

    The flexible-order, finite difference based fully nonlinear potential flow model described in [H.B. Bingham, H. Zhang, On the accuracy of finite difference solutions for nonlinear water waves, J. Eng. Math. 58 (2007) 211-228] is extended to three dimensions (3D). In order to obtain an optimal......, robustness and energy conservation are presented together with demonstrations of grid independent iteration count and optimal scaling of the solution effort. Calculations are made for 3D nonlinear wave problems for steep nonlinear waves and a shoaling problem which show good agreement with experimental...

  13. Nonlinear dynamics of an electrically actuated imperfect microbeam resonator: Experimental investigation and reduced-order modeling

    Ruzziconi, Laura

    2013-06-10

    We present a study of the dynamic behavior of a microelectromechanical systems (MEMS) device consisting of an imperfect clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. Our objective is to develop a theoretical analysis, which is able to describe and predict all the main relevant aspects of the experimental response. Extensive experimental investigation is conducted, where the main imperfections coming from microfabrication are detected, the first four experimental natural frequencies are identified and the nonlinear dynamics are explored at increasing values of electrodynamic excitation, in a neighborhood of the first symmetric resonance. Several backward and forward frequency sweeps are acquired. The nonlinear behavior is highlighted, which includes ranges of multistability, where the nonresonant and the resonant branch coexist, and intervals where superharmonic resonances are clearly visible. Numerical simulations are performed. Initially, two single mode reduced-order models are considered. One is generated via the Galerkin technique, and the other one via the combined use of the Ritz method and the Padé approximation. Both of them are able to provide a satisfactory agreement with the experimental data. This occurs not only at low values of electrodynamic excitation, but also at higher ones. Their computational efficiency is discussed in detail, since this is an essential aspect for systematic local and global simulations. Finally, the theoretical analysis is further improved and a two-degree-of-freedom reduced-order model is developed, which is also capable of capturing the measured second symmetric superharmonic resonance. Despite the apparent simplicity, it is shown that all the proposed reduced-order models are able to describe the experimental complex nonlinear dynamics of the device accurately and properly, which validates the proposed theoretical approach. © 2013 IOP Publishing Ltd.

  14. Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

    Gottlieb, Sigal

    2015-04-10

    High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge-Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge-Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge-Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may still be worthwhile to use methods with higher nonlinear order.

  15. Visual aftereffects and sensory nonlinearities from a single statistical framework

    Laparra, Valero; Malo, Jesús

    2015-01-01

    When adapted to a particular scenery our senses may fool us: colors are misinterpreted, certain spatial patterns seem to fade out, and static objects appear to move in reverse. A mere empirical description of the mechanisms tuned to color, texture, and motion may tell us where these visual illusions come from. However, such empirical models of gain control do not explain why these mechanisms work in this apparently dysfunctional manner. Current normative explanations of aftereffects based on scene statistics derive gain changes by (1) invoking decorrelation and linear manifold matching/equalization, or (2) using nonlinear divisive normalization obtained from parametric scene models. These principled approaches have different drawbacks: the first is not compatible with the known saturation nonlinearities in the sensors and it cannot fully accomplish information maximization due to its linear nature. In the second, gain change is almost determined a priori by the assumed parametric image model linked to divisive normalization. In this study we show that both the response changes that lead to aftereffects and the nonlinear behavior can be simultaneously derived from a single statistical framework: the Sequential Principal Curves Analysis (SPCA). As opposed to mechanistic models, SPCA is not intended to describe how physiological sensors work, but it is focused on explaining why they behave as they do. Nonparametric SPCA has two key advantages as a normative model of adaptation: (i) it is better than linear techniques as it is a flexible equalization that can be tuned for more sensible criteria other than plain decorrelation (either full information maximization or error minimization); and (ii) it makes no a priori functional assumption regarding the nonlinearity, so the saturations emerge directly from the scene data and the goal (and not from the assumed function). It turns out that the optimal responses derived from these more sensible criteria and SPCA are

  16. Cascading second-order nonlinear processes in a lithium niobate-on-insulator microdisk.

    Liu, Shijie; Zheng, Yuanlin; Chen, Xianfeng

    2017-09-15

    Whispering-gallery-mode (WGM) microcavities are very important in both fundamental science and practical applications, among which on-chip second-order nonlinear microresonators play an important role in integrated photonic functionalities. Here we demonstrate resonant second-harmonic generation (SHG) and cascaded third-harmonic generation (THG) in a lithium niobate-on-insulator (LNOI) microdisk resonator. Efficient SHG in the visible range was obtained with only several mW input powers at telecom wavelengths. THG was also observed through a cascading process, which reveals simultaneous phase matching and strong mode coupling in the resonator. Cascading of second-order nonlinear processes gives rise to an effectively large third-order nonlinearity, which makes on-chip second-order nonlinear microresonators a promising frequency converter for integrated nonlinear photonics.

  17. The second-order decomposition model of nonlinear irregular waves

    Yang, Zhi Wen; Bingham, Harry B.; Li, Jin Xuan

    2013-01-01

    into the first- and the second-order super-harmonic as well as the second-order sub-harmonic components by transferring them into an identical Fourier frequency-space and using a Newton-Raphson iteration method. In order to evaluate the present model, a variety of monochromatic waves and the second...

  18. Report of the working group on single-particle nonlinear dynamics

    Bazzani, A.; Bongini, L.; Corbett, J.; Dome, G.; Fedorova, A.; Freguglia, P.; Ng, K.; Ohmi, K.; Owen, H.; Papaphilippou, Y.; Robin, D.; Safranek, J.; Scandale, W.; Terebilo, A.; Turchetti, G.; Todesco, E.; Warnock, R.; Zeitlin, M.

    1999-01-01

    The Working Group on single-particle nonlinear dynamics has developed a set of tools to study nonlinear dynamics in a particle accelerator. The design of rings with large dynamic apertures is still far from automatic. The Working Group has concluded that nonlinear single-particle dynamics limits the performance of accelerators. (AIP) copyright 1999 American Institute of Physics

  19. Nonlinear magnetohydrodynamics simulation using high-order finite elements

    Plimpton, Steven James; Schnack, D.D.; Tarditi, A.; Chu, M.S.; Gianakon, T.A.; Kruger, S.E.; Nebel, R.A.; Barnes, D.C.; Sovinec, C.R.; Glasser, A.H.

    2005-01-01

    A conforming representation composed of 2D finite elements and finite Fourier series is applied to 3D nonlinear non-ideal magnetohydrodynamics using a semi-implicit time-advance. The self-adjoint semi-implicit operator and variational approach to spatial discretization are synergistic and enable simulation in the extremely stiff conditions found in high temperature plasmas without sacrificing the geometric flexibility needed for modeling laboratory experiments. Growth rates for resistive tearing modes with experimentally relevant Lundquist number are computed accurately with time-steps that are large with respect to the global Alfven time and moderate spatial resolution when the finite elements have basis functions of polynomial degree (p) two or larger. An error diffusion method controls the generation of magnetic divergence error. Convergence studies show that this approach is effective for continuous basis functions with p (ge) 2, where the number of test functions for the divergence control terms is less than the number of degrees of freedom in the expansion for vector fields. Anisotropic thermal conduction at realistic ratios of parallel to perpendicular conductivity (x(parallel)/x(perpendicular)) is computed accurately with p (ge) 3 without mesh alignment. A simulation of tearing-mode evolution for a shaped toroidal tokamak equilibrium demonstrates the effectiveness of the algorithm in nonlinear conditions, and its results are used to verify the accuracy of the numerical anisotropic thermal conduction in 3D magnetic topologies.

  20. Nonlinear Growth Models as Measurement Models: A Second-Order Growth Curve Model for Measuring Potential.

    McNeish, Daniel; Dumas, Denis

    2017-01-01

    Recent methodological work has highlighted the promise of nonlinear growth models for addressing substantive questions in the behavioral sciences. In this article, we outline a second-order nonlinear growth model in order to measure a critical notion in development and education: potential. Here, potential is conceptualized as having three components-ability, capacity, and availability-where ability is the amount of skill a student is estimated to have at a given timepoint, capacity is the maximum amount of ability a student is predicted to be able to develop asymptotically, and availability is the difference between capacity and ability at any particular timepoint. We argue that single timepoint measures are typically insufficient for discerning information about potential, and we therefore describe a general framework that incorporates a growth model into the measurement model to capture these three components. Then, we provide an illustrative example using the public-use Early Childhood Longitudinal Study-Kindergarten data set using a Michaelis-Menten growth function (reparameterized from its common application in biochemistry) to demonstrate our proposed model as applied to measuring potential within an educational context. The advantage of this approach compared to currently utilized methods is discussed as are future directions and limitations.

  1. On nonlinear differential equation with exact solutions having various pole orders

    Kudryashov, N.A.

    2015-01-01

    We consider a nonlinear ordinary differential equation having solutions with various movable pole order on the complex plane. We show that the pole order of exact solution is determined by values of parameters of the equation. Exact solutions in the form of the solitary waves for the second order nonlinear differential equation are found taking into account the method of the logistic function. Exact solutions of differential equations are discussed and analyzed

  2. Giant fifth-order nonlinearity via tunneling induced quantum interference in triple quantum dots

    Si-Cong Tian

    2015-02-01

    Full Text Available Schemes for giant fifth-order nonlinearity via tunneling in both linear and triangular triple quantum dots are proposed. In both configurations, the real part of the fifth-order nonlinearity can be greatly enhanced, and simultaneously the absorption is suppressed. The analytical expression and the dressed states of the system show that the two tunnelings between the neighboring quantum dots can induce quantum interference, resulting in the giant higher-order nonlinearity. The scheme proposed here may have important applications in quantum information processing at low light level.

  3. Stabilization of solutions to higher-order nonlinear Schrodinger equation with localized damping

    Eleni Bisognin

    2007-01-01

    Full Text Available We study the stabilization of solutions to higher-order nonlinear Schrodinger equations in a bounded interval under the effect of a localized damping mechanism. We use multiplier techniques to obtain exponential decay in time of the solutions of the linear and nonlinear equations.

  4. Analytical Solutions to Nonlinear Conservative Oscillator with Fifth-Order Nonlinearity

    Sfahania, M. G.; Ganji, S. S.; Barari, Amin

    2010-01-01

    This paper describes analytical and numerical methods to analyze the steady state periodic response of an oscillator with symmetric elastic and inertia nonlinearity. A new implementation of the homotopy perturbation method (HPM) and an ancient Chinese method called the max-min approach are presen...

  5. Expanded porphyrins as third order non-linear optical materials ...

    WINTEC

    function correlations ... An understanding of the structure–function corre- lations of these expanded porphyrins is an important first step for ... where χ (2) and χ (3) are the quadratic χ (2) (first- order) and χ (3) cubic (second-order) susceptibilities.

  6. Graphical user interface for input output characterization of single variable and multivariable highly nonlinear systems

    Shahrukh Adnan Khan M. D.

    2017-01-01

    Full Text Available This paper presents a Graphical User Interface (GUI software utility for the input/output characterization of single variable and multivariable nonlinear systems by obtaining the sinusoidal input describing function (SIDF of the plant. The software utility is developed on MATLAB R2011a environment. The developed GUI holds no restriction on the nonlinearity type, arrangement and system order; provided that output(s of the system is obtainable either though simulation or experiments. An insight to the GUI and its features are presented in this paper and example problems from both single variable and multivariable cases are demonstrated. The formulation of input/output behavior of the system is discussed and the nucleus of the MATLAB command underlying the user interface has been outlined. Some of the industries that would benefit from this software utility includes but not limited to aerospace, defense technology, robotics and automotive.

  7. Nonlinear absorption and receptivity of the third order in InAs infrared region

    Musayev, M.A.

    2005-01-01

    Nonlinear absorption and receptivity of the third order and coefficient nonlinear absorption in InAs n-type with different degree of alloying was measured. Obtained score considerably exceed sense, calculated on the basis of the models describing nonlinear receptivity of electrons, situated in the nonparabolic area of conductivity. It was shown that, observable deviations withdraw; if in the calculation apply energy dissipation of electrons. Growth of the efficiency under four-wave interaction in low-energy-gap semiconductors confines nonlinear absorption of interacting waves

  8. On nonlinear control design for autonomous chaotic systems of integer and fractional orders

    Ahmad, Wajdi M.; Harb, Ahmad M.

    2003-01-01

    In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations

  9. Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models.

    Shah, A A; Xing, W W; Triantafyllidis, V

    2017-04-01

    In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

  10. EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY

    2010-01-01

    This paper is concerned with nonlinear second order neutral stochastic differential equations with delay in a Hilbert space. Sufficient conditions for the existence of solution to the system are obtained by Picard iterations.

  11. ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

    2008-01-01

    In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.

  12. Stability and square integrability of solutions of nonlinear fourth order differential equations

    Moussadek Remili

    2016-05-01

    Full Text Available The aim of the present paper is to establish a new result, which guarantees the asymptotic stability of zero solution and square integrability of solutions and their derivatives to nonlinear differential equations of fourth order.

  13. Dynamical Tangles in Third-Order Oscillator with Single Jump Function

    Jiří Petržela

    2014-01-01

    Full Text Available This contribution brings a deep and detailed study of the dynamical behavior associated with nonlinear oscillator described by a single third-order differential equation with scalar jump nonlinearity. The relative primitive geometry of the vector field allows making an exhaustive numerical analysis of its possible solutions, visualizations of the invariant manifolds, and basins of attraction as well as proving the existence of chaotic motion by using the concept of both Shilnikov theorems. The aim of this paper is also to complete, carry out and link the previous works on simple Newtonian dynamics, and answer the question how individual types of the phenomenon evolve with time via understandable notes.

  14. Further results on global state feedback stabilization of nonlinear high-order feedforward systems.

    Xie, Xue-Jun; Zhang, Xing-Hui

    2014-03-01

    In this paper, by introducing a combined method of sign function, homogeneous domination and adding a power integrator, and overcoming several troublesome obstacles in the design and analysis, the problem of state feedback control for a class of nonlinear high-order feedforward systems with the nonlinearity's order being relaxed to an interval rather than a fixed point is solved. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

  15. State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation

    Junhai Luo

    2014-01-01

    Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.

  16. Progress Toward Single-Photon-Level Nonlinear Optics in Crystalline Microcavities

    Kowligy, Abijith S.

    Over the last two decades, the emergence of quantum information science has uncovered many practical applications in areas such as communications, imaging, and sensing where harnessing quantum features of Nature provides tremendous benefits over existing methods exploiting classical physical phenomena. In this effort, one of the frontiers of research has been to identify and utilize quantum phenomena that are not susceptible to environmental and parasitic noise processes. Quantum photonics has been at the forefront of these studies because it allows room-temperature access to its inherently quantum-mechanical features, and allows leveraging the mature telecommunication industry. Accompanying the weak environmental influence, however, are also weak optical nonlinearities. Efficient nonlinear optical interactions are indispensible for many of the existing protocols for quantum optical computation and communication, e.g. high-fidelity entangling quantum logic gates rely on large nonlinear responses at the one- or few-photon-level. While this has been addressed to a great extent by interfacing photons with single quantum emitters and cold atomic gases, scalability has remained elusive. In this work, we identify the macroscopic second-order nonlinear polarization as a robust platform to address this challenge, and utilize the recent advances in the burgeoning field of optical microcavities to enhance this nonlinear response. In particular, we show theoretically that by using the quantum Zeno effect, low-noise, single-photon-level optical nonlinearities can be realized in lithium niobate whispering-gallery-mode microcavities, and present experimental progress toward this goal. Using the measured strength of the second-order nonlinear response in lithium niobate, we modeled the nonlinear system in the strong coupling regime using the Schrodinger picture framework and theoretically demonstrated that the single-photon-level operation can be observed for cavity lifetimes in

  17. Investigation of the spatial distribution of second-order nonlinearity in thermally poled optical fibers.

    An, Honglin; Fleming, Simon

    2005-05-02

    The spatial distribution of second-order nonlinearity in thermally poled optical fibers was characterized by second-harmonic microscopy. The second-order nonlinearity was found to be confined to a thin layer close to the anode surface and progressed further into the silica as the poling time increased. Position uncertainty of the anode metal wire was observed to have an effect, as the nonlinear layers were found not always symmetrically located around the nearest points between the anode and cathode. Optical microscopy results were obtained on etched poled fiber cross-sections and compared with those from second-harmonic microscopy.

  18. Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

    Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)

    2013-09-02

    We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.

  19. Third-order nonlinear differential operators preserving invariant subspaces of maximal dimension

    Qu Gai-Zhu; Zhang Shun-Li; Li Yao-Long

    2014-01-01

    In this paper, third-order nonlinear differential operators are studied. It is shown that they are quadratic forms when they preserve invariant subspaces of maximal dimension. A complete description of third-order quadratic operators with constant coefficients is obtained. One example is given to derive special solutions for evolution equations with third-order quadratic operators. (general)

  20. Traveling wave solutions for two nonlinear evolution equations with nonlinear terms of any order

    Feng Qing-Hua; Zhang Yao-Ming; Meng Fan-Wei

    2011-01-01

    In this paper, based on the known first integral method and the Riccati sub-ordinary differential equation (ODE) method, we try to seek the exact solutions of the general Gardner equation and the general Benjamin—Bona—Mahoney equation. As a result, some traveling wave solutions for the two nonlinear equations are established successfully. Also we make a comparison between the two methods. It turns out that the Riccati sub-ODE method is more effective than the first integral method in handling the proposed problems, and more general solutions are constructed by the Riccati sub-ODE method. (general)

  1. Ultra-fast dynamics in the nonlinear optical response of silver nanoprism ordered arrays.

    Sánchez-Esquivel, Héctor; Raygoza-Sanchez, Karen Y; Rangel-Rojo, Raúl; Kalinic, Boris; Michieli, Niccolò; Cesca, Tiziana; Mattei, Giovanni

    2018-03-15

    In this work we present the study of the ultra-fast dynamics of the nonlinear optical response of a honeycomb array of silver triangular nanoprisms, performed using a femtosecond pulsed laser tuned with the dipolar surface plasmon resonance of the nanoarray. Nonlinear absorption and refraction, and their time-dependence, were explored using the z-scan and time-resolved excite-probe techniques. Nonlinear absorption is shown to change sign with the input irradiance and the behavior was explained on the basis of a three-level model. The response time was determined to be in the picosecond regime. A technique based on a variable frequency chopper was also used in order to discriminate the thermal and electronic contributions to the nonlinearity, which were found to have opposite signs. All these findings propel the investigated nanoprism arrays as good candidates for applications in advanced ultra-fast nonlinear nanophotonic devices.

  2. Linear and ultrafast nonlinear plasmonics of single nano-objects

    Crut, Aurélien; Maioli, Paolo; Vallée, Fabrice; Del Fatti, Natalia

    2017-03-01

    Single-particle optical investigations have greatly improved our understanding of the fundamental properties of nano-objects, avoiding the spurious inhomogeneous effects that affect ensemble experiments. Correlation with high-resolution imaging techniques providing morphological information (e.g. electron microscopy) allows a quantitative interpretation of the optical measurements by means of analytical models and numerical simulations. In this topical review, we first briefly recall the principles underlying some of the most commonly used single-particle optical techniques: near-field, dark-field, spatial modulation and photothermal microscopies/spectroscopies. We then focus on the quantitative investigation of the surface plasmon resonance (SPR) of metallic nano-objects using linear and ultrafast optical techniques. While measured SPR positions and spectral areas are found in good agreement with predictions based on Maxwell’s equations, SPR widths are strongly influenced by quantum confinement (or, from a classical standpoint, surface-induced electron scattering) and, for small nano-objects, cannot be reproduced using the dielectric functions of bulk materials. Linear measurements on single nano-objects (silver nanospheres and gold nanorods) allow a quantification of the size and geometry dependences of these effects in confined metals. Addressing the ultrafast response of an individual nano-object is also a powerful tool to elucidate the physical mechanisms at the origin of their optical nonlinearities, and their electronic, vibrational and thermal relaxation processes. Experimental investigations of the dynamical response of gold nanorods are shown to be quantitatively modeled in terms of modifications of the metal dielectric function enhanced by plasmonic effects. Ultrafast spectroscopy can also be exploited to unveil hidden physical properties of more complex nanosystems. In this context, two-color femtosecond pump-probe experiments performed on individual

  3. Signatures of nonlinearity in single cell noise-induced oscillations.

    Thomas, Philipp; Straube, Arthur V; Timmer, Jens; Fleck, Christian; Grima, Ramon

    2013-10-21

    A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power spectrum which measures the dependence of the oscillatory signal's power with frequency. In this paper we derive an approximate closed-form expression for the power spectrum of any monostable biochemical system close to a Hopf bifurcation, where noise-induced oscillations are most pronounced. Unlike the commonly used linear noise approximation which is valid in the macroscopic limit of large volumes, our theory is valid over a wide range of volumes and hence affords a more suitable description of single cell noise-induced oscillations. Our theory predicts that the spectra have three universal features: (i) a dominant peak at some frequency, (ii) a smaller peak at twice the frequency of the dominant peak and (iii) a peak at zero frequency. Of these, the linear noise approximation predicts only the first feature while the remaining two stem from the combination of intrinsic noise and nonlinearity in the law of mass action. The theoretical expressions are shown to accurately match the power spectra determined from stochastic simulations of mitotic and circadian oscillators. Furthermore it is shown how recently acquired single cell rhythmic fibroblast data displays all the features predicted by our theory and that the experimental spectrum is well described by our theory but not by the conventional linear noise approximation. © 2013 Elsevier Ltd. All rights reserved.

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

    Kimiagar, Salimeh; Abrinaei, Fahimeh

    2018-05-01

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

  5. Participation of the Third Order Optical Nonlinearities in Nanostructured Silver Doped Zinc Oxide Thin Solid Films

    C. Torres-Torres

    2012-01-01

    Full Text Available We report the transmittance modulation of optical signals in a nanocomposite integrated by two different silver doped zinc oxide thin solid films. An ultrasonic spray pyrolysis approach was employed for the preparation of the samples. Measurements of the third-order nonlinear optical response at a nonresonant 532 nm wavelength of excitation were performed using a vectorial two-wave mixing. It seems that the separated contribution of the optical nonlinearity associated with each film noticeable differs in the resulting nonlinear effects with respect to the additive response exhibited by the bilayer system. An enhancement of the optical Kerr nonlinearity is predicted for prime number arrays of the studied nanoclusters in a two-wave interaction. We consider that the nanostructured morphology of the thin solid films originates a strong modification of the third-order optical phenomena exhibited by multilayer films based on zinc oxide.

  6. Chaos control of third-order phase-locked loops using backstepping nonlinear controller

    Harb, Ahmad M.; Harb, Bassam A.

    2004-01-01

    Previous study showed that a third-order phase-locked loop (PLL) with sinusoidal phase detector characteristics experienced a Hopf bifurcation point as well as chaotic behavior. As a result, this behavior drives the PLL to the out-of-lock (unstable) state. The analysis was based on a modern nonlinear theory such as bifurcation and chaos. The main goal of this paper is to control this chaotic behavior. A nonlinear controller based on the theory of backstepping is designed. The study showed the effectiveness of the designed nonlinear controller in controlling the undesirable unstable behavior and pulling the PLL back to the in-lock state

  7. The second order extended Kalman filter and Markov nonlinear filter for data processing in interferometric systems

    Ermolaev, P; Volynsky, M

    2014-01-01

    Recurrent stochastic data processing algorithms using representation of interferometric signal as output of a dynamic system, which state is described by vector of parameters, in some cases are more effective, compared with conventional algorithms. Interferometric signals depend on phase nonlinearly. Consequently it is expedient to apply algorithms of nonlinear stochastic filtering, such as Kalman type filters. An application of the second order extended Kalman filter and Markov nonlinear filter that allows to minimize estimation error is described. Experimental results of signals processing are illustrated. Comparison of the algorithms is presented and discussed.

  8. Ordered macro-microporous metal-organic framework single crystals

    Shen, Kui; Zhang, Lei; Chen, Xiaodong; Liu, Lingmei; Zhang, Daliang; Han, Yu; Chen, Junying; Long, Jilan; Luque, Rafael; Li, Yingwei; Chen, Banglin

    2018-01-01

    We constructed highly oriented and ordered macropores within metal-organic framework (MOF) single crystals, opening up the area of three-dimensional–ordered macro-microporous materials (that is, materials containing both macro- and micropores) in single-crystalline form. Our methodology relies on the strong shaping effects of a polystyrene nanosphere monolith template and a double-solvent–induced heterogeneous nucleation approach. This process synergistically enabled the in situ growth of MOFs within ordered voids, rendering a single crystal with oriented and ordered macro-microporous structure. The improved mass diffusion properties of such hierarchical frameworks, together with their robust single-crystalline nature, endow them with superior catalytic activity and recyclability for bulky-molecule reactions, as compared with conventional, polycrystalline hollow, and disordered macroporous ZIF-8.

  9. Ordered macro-microporous metal-organic framework single crystals

    Shen, Kui

    2018-01-16

    We constructed highly oriented and ordered macropores within metal-organic framework (MOF) single crystals, opening up the area of three-dimensional-ordered macro-microporous materials (that is, materials containing both macro- and micropores) in single-crystalline form. Our methodology relies on the strong shaping effects of a polystyrene nanosphere monolith template and a double-solvent-induced heterogeneous nucleation approach. This process synergistically enabled the in situ growth of MOFs within ordered voids, rendering a single crystal with oriented and ordered macro-microporous structure. The improved mass diffusion properties of such hierarchical frameworks, together with their robust single-crystalline nature, endow them with superior catalytic activity and recyclability for bulky-molecule reactions, as compared with conventional, polycrystalline hollow, and disordered macroporous ZIF-8.

  10. Ordered macro-microporous metal-organic framework single crystals

    Shen, Kui; Zhang, Lei; Chen, Xiaodong; Liu, Lingmei; Zhang, Daliang; Han, Yu; Chen, Junying; Long, Jilan; Luque, Rafael; Li, Yingwei; Chen, Banglin

    2018-01-01

    We constructed highly oriented and ordered macropores within metal-organic framework (MOF) single crystals, opening up the area of three-dimensional-ordered macro-microporous materials (that is, materials containing both macro- and micropores) in single-crystalline form. Our methodology relies on the strong shaping effects of a polystyrene nanosphere monolith template and a double-solvent-induced heterogeneous nucleation approach. This process synergistically enabled the in situ growth of MOFs within ordered voids, rendering a single crystal with oriented and ordered macro-microporous structure. The improved mass diffusion properties of such hierarchical frameworks, together with their robust single-crystalline nature, endow them with superior catalytic activity and recyclability for bulky-molecule reactions, as compared with conventional, polycrystalline hollow, and disordered macroporous ZIF-8.

  11. Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations

    Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng

    2004-01-01

    Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair

  12. Fermat collocation method for the solutions of nonlinear system of second order boundary value problems

    Salih Yalcinbas

    2016-01-01

    Full Text Available In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of second order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results.

  13. Analysis of an Nth-order nonlinear differential-delay equation

    Vallée, Réal; Marriott, Christopher

    1989-01-01

    The problem of a nonlinear dynamical system with delay and an overall response time which is distributed among N individual components is analyzed. Such a system can generally be modeled by an Nth-order nonlinear differential delay equation. A linear-stability analysis as well as a numerical simulation of that equation are performed and a comparison is made with the experimental results. Finally, a parallel is established between the first-order differential equation with delay and the Nth-order differential equation without delay.

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

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

    2014-01-01

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

  15. Alkali-Responsive Absorption Spectra and Third-Order Optical Nonlinearities of Imino Squaramides

    Li Zhong-Yu; Xu Song; Zhou Xin-Yu; Zhang Fu-Shi

    2012-01-01

    Third-order optical nonlinearities and dynamic responses of two imino squaramides under neutral and base conditions were studied using the femtosecond degenerate four-wave mixing technique at 800 nm. Ultrafast optical responses have been observed and the magnitude of the second-order hyperpolarizabilities of the squaramides has been measured to be as large as 10 −31 esu. The absorption spectra, color of solution, and third-order optical nonlinearities of two imino squaramides change with the addition of sodium hydroxide. The γ value under the base condition for each dye is approximately 1.25 times larger than that under neutral conditions. (fundamental areas of phenomenology(including applications))

  16. Periodic solutions of certain third order nonlinear differential systems with delay

    Tejumola, H.O.; Afuwape, A.U.

    1990-12-01

    This paper investigates the existence of 2π-periodic solutions of systems of third-order nonlinear differential equations, with delay, under varied assumptions. The results obtained extend earlier works of Tejumola and generalize to third order systems those of Conti, Iannacci and Nkashama as well as DePascale and Iannacci and Iannacci and Nkashama. 16 refs

  17. On realization of nonlinear systems described by higher-order differential equations

    van der Schaft, Arjan

    1987-01-01

    We consider systems of smooth nonlinear differential and algebraic equations in which some of the variables are distinguished as “external variables.” The realization problem is to replace the higher-order implicit differential equations by first-order explicit differential equations and the

  18. On existence of soliton solutions of arbitrary-order system of nonlinear Schrodinger equations

    Zhestkov, S.V.

    2003-01-01

    The soliton solutions are constructed for the system of arbitrary-order coupled nonlinear Schrodinger equations . The necessary and sufficient conditions of existence of these solutions are obtained. It is shown that the maximum number of solitons in nondegenerate case is 4L, where L is order of the system. (author)

  19. Large optical second-order nonlinearity of poled WO3-TeO2 glass.

    Tanaka, K; Narazaki, A; Hirao, K

    2000-02-15

    Second-harmonic generation, one of the second-order nonlinear optical properties of thermally and electrically poled WO>(3)-TeO>(2) glasses, has been examined. We poled glass samples with two thicknesses (0.60 and 0.86 mm) at various temperatures to explore the effects of external electric field strength and poling temperature on second-order nonlinearity. The dependence of second-harmonic intensity on the poling temperature is maximum at a specific poling temperature. A second-order nonlinear susceptibility of 2.1 pm/V was attained for the 0.60-mm-thick glass poled at 250 degrees C. This value is fairly large compared with those for poled silica and tellurite glasses reported thus far. We speculate that the large third-order nonlinear susceptibility of WO>(3)- TeO>(2) glasses gives rise to the large second-order nonlinearity by means of a X((2)) = 3X((3)) E(dc) process.

  20. Cheap arbitrary high order methods for single integrand SDEs

    Debrabant, Kristian; Kværnø, Anne

    2017-01-01

    For a particular class of Stratonovich SDE problems, here denoted as single integrand SDEs, we prove that by applying a deterministic Runge-Kutta method of order $p_d$ we obtain methods converging in the mean-square and weak sense with order $\\lfloor p_d/2\\rfloor$. The reason is that the B-series...

  1. Explicit formulation of second and third order optical nonlinearity in the FDTD framework

    Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

    2018-01-01

    The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

  2. The third-order nonlinear optical susceptibility of C{sub 60}-derived nanotubes

    Xiangang, Wan [Nanjing Univ. (China). National Lab. of Solid State Microstructures; [Center for Advanced Studies in Science and Technology of Microstructures, Nanjing (China); Jinming, Dong [Nanjing Univ. (China). National Lab. of Solid State Microstructures; [Center for Advanced Studies in Science and Technology of Microstructures, Nanjing (China); Jie, Jiang [Nanjing Univ., JS (China). Dept. of Physics; Xing, D Y [Nanjing Univ., JS (China). Dept. of Physics

    1997-02-01

    Using the extended Su-Schrieffer-Heeger (SSH) model and the sum-over-state (SOS) method, we have calculated the third-order nonlinear polarizability {gamma} and its dispersion spectra for C{sub 60}-derived nanotubes, which is one of the narrowest tubes. Our numerical calculations indicate that both symmetry and size of the nanotubes have great effect on the third-order nonlinear polarizability {gamma} spectra. We find that with increasing size, both static {gamma} values and dynamical response peak values increase. When the atom number of the C{sub 60}-derived nanotubes is 140, the static {gamma} value is about 65 times larger than that of C{sub 60}, and the highest peak value of {gamma} (at 3{omega} = 3.52 eV) is about three orders larger than that of C{sub 60}. So, C{sub 60}-derived nanotubes may become a kind of good nonlinear optical materials. (orig.)

  3. Spectral dependence of third-order nonlinear optical properties in InN

    Ahn, H.; Lee, M.-T.; Chang, Y.-M.

    2014-01-01

    We report on the nonlinear optical properties of InN measured in a wide near-infrared spectral range with the femtosecond Z-scan technique. The above-bandgap nonlinear absorption in InN is found to originate from the saturation of absorption by the band-state-filling and its cross-section increases drastically near the bandgap energy. With below-bandgap excitation, the nonlinear absorption undergoes a transition from saturation absorption (SA) to reverse-SA (RSA), attributed to the competition between SA of band-tail states and two-photon-related RSA. The measured large nonlinear refractive index of the order of 10 −10 cm 2 /W indicates InN as a potential material for all-optical switching and related applications

  4. Third-order nonlinear optical studies of anthraquinone dyes using a CW He–Ne laser

    Pramodini, S; Poornesh, P

    2014-01-01

    We present investigations on the third-order optical nonlinearity and optical power limiting of anthraquinone dyes. Z-scan measurements were performed using a continuous wave He–Ne laser at 633 nm wavelength as an excitation source. The nonlinear refraction studies exhibited self-defocusing behavior of the dyes. The nonlinear absorption in the dyes was dominated by a reverse saturable absorption process. Self-diffraction ring patterns were observed due to the change in refractive index and thermal lensing. Increase of the electron donating ability of the substituents resulted in enhanced values of the nonlinear optical parameters, establishing the structure–property relationship. The optical limiting study revealed that the dyes possess a lower limiting threshold and clamping level which is very important for eye and sensor protection. Hence, the dyes investigated here emerge as promising candidates for future opto-electronic and photonic device applications such as optical power limiters. (paper)

  5. Third-order nonlinear optical studies of anthraquinone dyes using a CW He-Ne laser

    Pramodini, S.; Poornesh, P.

    2014-05-01

    We present investigations on the third-order optical nonlinearity and optical power limiting of anthraquinone dyes. Z-scan measurements were performed using a continuous wave He-Ne laser at 633 nm wavelength as an excitation source. The nonlinear refraction studies exhibited self-defocusing behavior of the dyes. The nonlinear absorption in the dyes was dominated by a reverse saturable absorption process. Self-diffraction ring patterns were observed due to the change in refractive index and thermal lensing. Increase of the electron donating ability of the substituents resulted in enhanced values of the nonlinear optical parameters, establishing the structure-property relationship. The optical limiting study revealed that the dyes possess a lower limiting threshold and clamping level which is very important for eye and sensor protection. Hence, the dyes investigated here emerge as promising candidates for future opto-electronic and photonic device applications such as optical power limiters.

  6. Order and chaos in the nonlinear response of driven nuclear spin systems

    Brun, E; Derighetti, B; Holzner, R; Ravani, M [Zurich Univ. (Switzerland). Inst. fuer Physik

    1984-01-01

    The authors report on observations of ordered and chaotic behavior of a nonlinear system of strongly polarized nuclear spins inside the tuning coil of an NMR detector. The combined system: spins plus LC-circuit, may act as a nonlinear bistable absorber or a spin-flip laser, depending on the sign of the nuclear spin polarization. For the NMR laser experimental evidence is presented for limit-cycle behavior, sequences of bifurcations which lead to chaos, intermittency, multistability, and pronounced hysteresis effects. The experimental facts are compared with computer solutions of appropriate Bloch equations for the macroscopic order parameters.

  7. Large third-order optical nonlinearity of silver colloids in silica glasses synthesized by ion implantation

    Ghosh, Binita; Chakraborty, Purushottam

    2011-01-01

    Silver ion implantations in fused silica glasses have been made to synthesize silver nanocluster-glass composites and a combination of 'Anti-Resonant Interferometric Nonlinear Spectroscopy (ARINS)' and 'Z-scan' techniques has been employed for the measurement of the third-order optical susceptibility of these nanocomposites. The ARINS technique utilizes the dressing of two unequal-intensity counter-propagating pulsed optical beams with differential nonlinear phases, which occurs upon traversing the sample. This difference in phase manifests itself in the intensity-dependent transmission, measurement of which enables us to extract the values of nonlinear refractive index (η 2 ) and nonlinear absorption coefficient (β), finally yielding the real and imaginary parts of the third-order dielectric susceptibility (χ (3) ). The real and imaginary parts of χ (3) are obtained in the orders of 10 -10 e.s.u for silver nanocluster-glass composites. The present value of χ (3) , to our knowledge, is extremely accurate and much more reliable compared to the values previously obtained by other workers for similar silver-glass nanocomposites using only Z-scan technique. Optical nonlinearity has been explained to be due to two-photon absorption in the present nanocomposite glasses and is essentially of electronic origin.

  8. A novel nonlinear adaptive filter using a pipelined second-order Volterra recurrent neural network.

    Zhao, Haiquan; Zhang, Jiashu

    2009-12-01

    To enhance the performance and overcome the heavy computational complexity of recurrent neural networks (RNN), a novel nonlinear adaptive filter based on a pipelined second-order Volterra recurrent neural network (PSOVRNN) is proposed in this paper. A modified real-time recurrent learning (RTRL) algorithm of the proposed filter is derived in much more detail. The PSOVRNN comprises of a number of simple small-scale second-order Volterra recurrent neural network (SOVRNN) modules. In contrast to the standard RNN, these modules of a PSOVRNN can be performed simultaneously in a pipelined parallelism fashion, which can lead to a significant improvement in its total computational efficiency. Moreover, since each module of the PSOVRNN is a SOVRNN in which nonlinearity is introduced by the recursive second-order Volterra (RSOV) expansion, its performance can be further improved. Computer simulations have demonstrated that the PSOVRNN performs better than the pipelined recurrent neural network (PRNN) and RNN for nonlinear colored signals prediction and nonlinear channel equalization. However, the superiority of the PSOVRNN over the PRNN is at the cost of increasing computational complexity due to the introduced nonlinear expansion of each module.

  9. Theoretical analysis of open aperture reflection Z-scan on materials with high-order optical nonlinearities

    Petris, Adrian I.; Vlad, Valentin I.

    2010-03-01

    We present a theoretical analysis of open aperture reflection Z-scan in nonlinear media with third-, fifth-, and higher-order nonlinearities. A general analytical expression for the normalized reflectance when third-, fifth- and higher-order optical nonlinearities are excited is derived and its consequences on RZ-scan in media with high-order nonlinearities are discussed. We show that by performing RZ-scan experiments at different incident intensities it is possible to put in evidence the excitation of different order nonlinearities in the medium. Their contributions to the overall nonlinear response can be discriminated by using formulas derived by us. A RZ-scan numerical simulation using these formulas and data taken from literature, measured by another method for the third-, fifth-, and seventh-order nonlinear refractive indices of As 2 S 3 chalcogenide glass, is performed. (author)

  10. Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

    Gao, Peng

    2018-04-01

    This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

  11. Averaging Principle for the Higher Order Nonlinear Schrödinger Equation with a Random Fast Oscillation

    Gao, Peng

    2018-06-01

    This work concerns the problem associated with averaging principle for a higher order nonlinear Schrödinger equation perturbed by a oscillating term arising as the solution of a stochastic reaction-diffusion equation evolving with respect to the fast time. This model can be translated into a multiscale stochastic partial differential equations. Stochastic averaging principle is a powerful tool for studying qualitative analysis of stochastic dynamical systems with different time-scales. To be more precise, under suitable conditions, we prove that there is a limit process in which the fast varying process is averaged out and the limit process which takes the form of the higher order nonlinear Schrödinger equation is an average with respect to the stationary measure of the fast varying process. Finally, by using the Khasminskii technique we can obtain the rate of strong convergence for the slow component towards the solution of the averaged equation, and as a consequence, the system can be reduced to a single higher order nonlinear Schrödinger equation with a modified coefficient.

  12. Output Feedback Distributed Containment Control for High-Order Nonlinear Multiagent Systems.

    Li, Yafeng; Hua, Changchun; Wu, Shuangshuang; Guan, Xinping

    2017-01-31

    In this paper, we study the problem of output feedback distributed containment control for a class of high-order nonlinear multiagent systems under a fixed undirected graph and a fixed directed graph, respectively. Only the output signals of the systems can be measured. The novel reduced order dynamic gain observer is constructed to estimate the unmeasured state variables of the system with the less conservative condition on nonlinear terms than traditional Lipschitz one. Via the backstepping method, output feedback distributed nonlinear controllers for the followers are designed. By means of the novel first virtual controllers, we separate the estimated state variables of different agents from each other. Consequently, the designed controllers show independence on the estimated state variables of neighbors except outputs information, and the dynamics of each agent can be greatly different, which make the design method have a wider class of applications. Finally, a numerical simulation is presented to illustrate the effectiveness of the proposed method.

  13. European Workshop on High Order Nonlinear Numerical Schemes for Evolutionary PDEs

    Beaugendre, Héloïse; Congedo, Pietro; Dobrzynski, Cécile; Perrier, Vincent; Ricchiuto, Mario

    2014-01-01

    This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.

  14. High-order optical nonlinearities in nanocomposite films dispersed with semiconductor quantum dots at high concentrations

    Tomita, Yasuo; Matsushima, Shun-suke; Yamagami, Ryu-ichi; Jinzenji, Taka-aki; Sakuma, Shohei; Liu, Xiangming; Izuishi, Takuya; Shen, Qing

    2017-01-01

    We describe the nonlinear optical properties of inorganic-organic nanocomposite films in which semiconductor CdSe quantum dots as high as 6.8 vol.% are dispersed. Open/closed Z-scan measurements, degenerate multi-wave mixing and femtosecond pump-probe/transient grating measurements are conducted. It is shown that the observed fifth-order optical nonlinearity has the cascaded third-order contribution that becomes prominent at high concentrations of CdSe QDs. It is also shown that there are picosecond-scale intensity-dependent and nanosecond-scale intensity-independent decay components in absorptive and refractive nonlinearities. The former is caused by the Auger process, while the latter comes from the electron-hole recombination process. (paper)

  15. Nonlinear and Nonsymmetric Single-Molecule Electronic Properties Towards Molecular Information Processing.

    Tamaki, Takashi; Ogawa, Takuji

    2017-09-05

    This review highlights molecular design for nonlinear and nonsymmetric single-molecule electronic properties such as rectification, negative differential resistance, and switching, which are important components of future single-molecule information processing devices. Perspectives on integrated "molecular circuits" are also provided. Nonlinear and nonsymmetric single-molecule electronics can be designed by utilizing (1) asymmetric molecular cores, (2) asymmetric anchoring groups, (3) an asymmetric junction environment, and (4) asymmetric electrode materials. This review mainly focuses on the design of molecular cores.

  16. Third-order nonlinear optical response of Ag-CdSe/PVA hybrid nanocomposite

    Tripathi, S.K.; Kaur, Ramneek; Kaur, Jaspreet; Sharma, Mamta [Panjab University, Department of Physics, Center of Advanced Study in Physics, Chandigarh (India)

    2015-09-15

    Hybrid nanocomposites of II-VI semiconductor nanoparticles are gaining great interest in nonlinear optoelectronic devices. Present work includes the characterization of CdSe polymer nanocomposite prepared by chemical in situ technique. From X-ray diffraction, the hexagonal wurtzite structure of nanoparticles has been confirmed with spherical morphology from transmission electron microscopy. Ag-CdSe hybrid polymer nanocomposite has been prepared chemically at different Ag concentrations. The presence of Ag in hybrid nanocomposite has been confirmed with energy-dispersive X-ray spectroscopy. The effect of varying Ag concentration on the linear and nonlinear optical properties of the nanocomposites has been studied. In linear optical parameters, the linear absorption coefficient, refractive index, extinction coefficient and optical conductivity have been calculated. The third-order nonlinear optical properties have been observed with open- and closed-aperture Z-scan technique. The large nonlinear refractive index ∝10{sup -5} cm{sup 2}/W with self-focusing behaviour is due to the combined effect of quantum confinement and thermo-optical effects. The enhanced nonlinearity with increasing Ag content is due to the surface plasmon resonance, which enhances the local electric field near the nanoparticle surface. Thus, Ag-CdSe hybrid polymer nanocomposite has favourable nonlinear optical properties for various optoelectronic applications. (orig.)

  17. Third-order nonlinear optical response of Ag-CdSe/PVA hybrid nanocomposite

    Tripathi, S.K.; Kaur, Ramneek; Kaur, Jaspreet; Sharma, Mamta

    2015-01-01

    Hybrid nanocomposites of II-VI semiconductor nanoparticles are gaining great interest in nonlinear optoelectronic devices. Present work includes the characterization of CdSe polymer nanocomposite prepared by chemical in situ technique. From X-ray diffraction, the hexagonal wurtzite structure of nanoparticles has been confirmed with spherical morphology from transmission electron microscopy. Ag-CdSe hybrid polymer nanocomposite has been prepared chemically at different Ag concentrations. The presence of Ag in hybrid nanocomposite has been confirmed with energy-dispersive X-ray spectroscopy. The effect of varying Ag concentration on the linear and nonlinear optical properties of the nanocomposites has been studied. In linear optical parameters, the linear absorption coefficient, refractive index, extinction coefficient and optical conductivity have been calculated. The third-order nonlinear optical properties have been observed with open- and closed-aperture Z-scan technique. The large nonlinear refractive index ∝10 -5 cm 2 /W with self-focusing behaviour is due to the combined effect of quantum confinement and thermo-optical effects. The enhanced nonlinearity with increasing Ag content is due to the surface plasmon resonance, which enhances the local electric field near the nanoparticle surface. Thus, Ag-CdSe hybrid polymer nanocomposite has favourable nonlinear optical properties for various optoelectronic applications. (orig.)

  18. Testing for one Generalized Linear Single Order Parameter

    Ellegaard, Niels Langager; Christensen, Tage Emil; Dyre, Jeppe

    We examine a linear single order parameter model for thermoviscoelastic relaxation in viscous liquids, allowing for a distribution of relaxation times. In this model the relaxation of volume and entalpy is completely described by the relaxation of one internal order parameter. In contrast to prior...... work the order parameter may be chosen to have a non-exponential relaxation. The model predictions contradict the general consensus of the properties of viscous liquids in two ways: (i) The model predicts that following a linear isobaric temperature step, the normalized volume and entalpy relaxation...... responses or extrapolate from measurements of a glassy state away from equilibrium. Starting from a master equation description of inherent dynamics, we calculate the complex thermodynamic response functions. We device a way of testing for the generalized single order parameter model by measuring 3 complex...

  19. Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time-delay

    Zhang, Kemei; Zhao, Cong-Ran; Xie, Xue-Jun

    2015-12-01

    This paper considers the problem of output feedback stabilisation for stochastic high-order feedforward nonlinear systems with time-varying delay. By using the homogeneous domination theory and solving several troublesome obstacles in the design and analysis, an output feedback controller is constructed to drive the closed-loop system globally asymptotically stable in probability.

  20. Non-linear second-order periodic systems with non-smooth potential

    In this paper we study second order non-linear periodic systems driven by the ordinary vector -Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth conditions on ...

  1. Non-linear second-order periodic systems with non-smooth potential

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Abstract. In this paper we study second order non-linear periodic systems driven by the ordinary vector p-Laplacian with a non-smooth, locally Lipschitz potential function. Our approach is variational and it is based on the non-smooth critical point theory. We prove existence and multiplicity results under general growth ...

  2. Existence of solutions for nonlinear mixed type integrodifferential equation of second order

    Haribhau Laxman Tidke

    2010-04-01

    Full Text Available In this paper, we investigate the existence of solutions for nonlinear mixed Volterra-Fredholm integrodifferential equation of second order with nonlocal conditions in Banach spaces. Our analysis is based on Leray-Schauder alternative, rely on a priori bounds of solutions and the inequality established by B. G. Pachpatte.

  3. Compound waves in a higher order nonlinear model of thermoviscous fluids

    Rønne Rasmussen, Anders; Sørensen, Mads Peter; Gaididei, Yuri B.

    2016-01-01

    A generalized traveling wave ansatz is used to investigate compound shock waves in a higher order nonlinear model of a thermoviscous fluid. The fluid velocity potential is written as a traveling wave plus a linear function of space and time. The latter offers the possibility of predicting...

  4. Second-Order Consensus for Multiagent Systems With Directed Topologies and Nonlinear Dynamics

    Yu, Wenwu; Chen, Guanrong; Cao, Ming; Kurths, Juergen; Kurths, Jürgen

    This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position and velocity consensus terms with a time-varying asymptotic velocity. To describe the system's ability for reaching consensus, a

  5. The focal boundary value problem for strongly singular higher-order nonlinear functional-differential equations

    Mukhigulashvili, Sulkhan; Půža, B.

    2015-01-01

    Roč. 2015, January (2015), s. 17 ISSN 1687-2770 Institutional support: RVO:67985840 Keywords : higher order nonlinear functional-differential equations * two-point right-focal boundary value problem * strong singularity Subject RIV: BA - General Mathematics Impact factor: 0.642, year: 2015 http://link.springer.com/article/10.1186%2Fs13661-014-0277-1

  6. Multiple periodic solutions for a class of second-order nonlinear neutral delay equations

    2006-01-01

    Full Text Available By means of a variational structure and Z 2 -group index theory, we obtain multiple periodic solutions to a class of second-order nonlinear neutral delay equations of the form0, au>0$"> x ″ ( t − τ + λ ( t f ( t , x ( t , x ( t − τ , x ( t − 2 τ = x ( t , λ ( t > 0 , τ > 0 .

  7. High-order finite difference solution for 3D nonlinear wave-structure interaction

    Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter

    2010-01-01

    This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme O...

  8. Khater method for nonlinear Sharma Tasso-Olever (STO) equation of fractional order

    Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Khan, Umar; Ahmed, Naveed

    In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations of fractional order. Number of solutions provided by this method is greater than other traditional methods. Exact solutions of nonlinear fractional order Sharma Tasso-Olever (STO) equation are expressed in terms of kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative and Fractional complex transform have been used for compatibility with fractional order sense. Solutions have been graphically simulated for understanding the physical aspects and importance of the method. A comparative discussion between our established results and the results obtained by existing ones is also presented. Our results clearly reveal that the proposed method is an effective, powerful and straightforward technique to work out new solutions of various types of differential equations of non-integer order in the fields of applied sciences and engineering.

  9. Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems

    Ge Zhengming; Chang Chingming; Chen Yensheng

    2006-01-01

    Anti-control of chaos of single time scale brushless dc motors (BLDCM) and chaos synchronization of different order systems are studied in this paper. By addition of an external nonlinear term, we can obtain anti-control of chaos. Then, by addition of the coupling terms, by the use of Lyapunov stability theorem and by the linearization of the error dynamics, chaos synchronization between a third-order BLDCM and a second-order Duffing system are presented

  10. A mixed-order nonlinear diffusion compressed sensing MR image reconstruction.

    Joy, Ajin; Paul, Joseph Suresh

    2018-03-07

    Avoid formation of staircase artifacts in nonlinear diffusion-based MR image reconstruction without compromising computational speed. Whereas second-order diffusion encourages the evolution of pixel neighborhood with uniform intensities, fourth-order diffusion considers smooth region to be not necessarily a uniform intensity region but also a planar region. Therefore, a controlled application of fourth-order diffusivity function is used to encourage second-order diffusion to reconstruct the smooth regions of the image as a plane rather than a group of blocks, while not being strong enough to introduce the undesirable speckle effect. Proposed method is compared with second- and fourth-order nonlinear diffusion reconstruction, total variation (TV), total generalized variation, and higher degree TV using in vivo data sets for different undersampling levels with application to dictionary learning-based reconstruction. It is observed that the proposed technique preserves sharp boundaries in the image while preventing the formation of staircase artifacts in the regions of smoothly varying pixel intensities. It also shows reduced error measures compared with second-order nonlinear diffusion reconstruction or TV and converges faster than TV-based methods. Because nonlinear diffusion is known to be an effective alternative to TV for edge-preserving reconstruction, the crucial aspect of staircase artifact removal is addressed. Reconstruction is found to be stable for the experimentally determined range of fourth-order regularization parameter, and therefore not does not introduce a parameter search. Hence, the computational simplicity of second-order diffusion is retained. © 2018 International Society for Magnetic Resonance in Medicine.

  11. Dispersion of the resonant second order nonlinearity in 2D semiconductors probed by femtosecond continuum pulses

    Mohammad Mokim

    2017-10-01

    Full Text Available We demonstrate an effective microspectroscopy technique by tracing the dispersion of second order nonlinear susceptibility (χ(2 in a monolayer tungsten diselenide (WSe2. The χ(2 dispersion obtained with better than 3 meV photon energy resolution showed peak value being within 6.3-8.4×10-19 m2/V range. We estimate the fundamental bandgap to be at 2.2 eV. Sub-structure in the χ(2 dispersion reveals a contribution to the nonlinearity due to exciton transitions with exciton binding energy estimated to be at 0.7 eV.

  12. Computation of Nonlinear Backscattering Using a High-Order Numerical Method

    Fibich, G.; Ilan, B.; Tsynkov, S.

    2001-01-01

    The nonlinear Schrodinger equation (NLS) is the standard model for propagation of intense laser beams in Kerr media. The NLS is derived from the nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. In this study we use a fourth-order finite-difference method supplemented by special two-way artificial boundary conditions (ABCs) to solve the NLH as a boundary value problem. Our numerical methodology allows for a direct comparison of the NLH and NLS models and for an accurate quantitative assessment of the backscattered signal.

  13. Symmetry of the complete second-order nonlinear conductivity tensor for an unmagnetized relativistic turbulent plasma

    Brandt, H.E.

    1983-01-01

    A new exact symmetry is proved for the complete second-order nonlinear conductivity tensor of an unmagnetized relativistic turbulent plasma. The symmetry is not limited to principal parts. If Cerenkov resonance is ignored, the new symmetry reduces to the well-known symmetry related to the Manley--Rowe relations, crossing symmetry, and nondissipation of the principal part of the nonlinear current. Also, a new utilitarian representation for the complete tensor is obtained in which all derivatives are removed and the pole structure is clearly exhibited

  14. Computation of nonlinear water waves with a high-order Boussinesq model

    Fuhrman, David R.; Madsen, Per A.; Bingham, Harry

    2005-01-01

    Computational highlights from a recently developed high-order Boussinesq model are shown. The model is capable of treating fully nonlinear waves (up to the breaking point) out to dimensionless depths of (wavenumber times depth) kh \\approx 25. Cases considered include the study of short......-crested waves in shallow/deep water, resulting in hexagonal/rectangular surface patterns; crescent waves, resulting from unstable perturbations of plane progressive waves; and highly-nonlinear wave-structure interactions. The emphasis is on physically demanding problems, and in eachcase qualitative and (when...

  15. Exact solitary wave solution for higher order nonlinear Schrodinger equation using He's variational iteration method

    Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet

    2017-11-01

    In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.

  16. Nonlinear Parameter-Varying AeroServoElastic Reduced Order Model for Aerostructural Sensing and Control, Phase I

    National Aeronautics and Space Administration — The overall goal of the project is to develop reliable reduced order modeling technologies to automatically generate nonlinear, parameter-varying (PV),...

  17. Single shot trajectory design for region-specific imaging using linear and nonlinear magnetic encoding fields.

    Layton, Kelvin J; Gallichan, Daniel; Testud, Frederik; Cocosco, Chris A; Welz, Anna M; Barmet, Christoph; Pruessmann, Klaas P; Hennig, Jürgen; Zaitsev, Maxim

    2013-09-01

    It has recently been demonstrated that nonlinear encoding fields result in a spatially varying resolution. This work develops an automated procedure to design single-shot trajectories that create a local resolution improvement in a region of interest. The technique is based on the design of optimized local k-space trajectories and can be applied to arbitrary hardware configurations that employ any number of linear and nonlinear encoding fields. The trajectories designed in this work are tested with the currently available hardware setup consisting of three standard linear gradients and two quadrupolar encoding fields generated from a custom-built gradient insert. A field camera is used to measure the actual encoding trajectories up to third-order terms, enabling accurate reconstructions of these demanding single-shot trajectories, although the eddy current and concomitant field terms of the gradient insert have not been completely characterized. The local resolution improvement is demonstrated in phantom and in vivo experiments. Copyright © 2012 Wiley Periodicals, Inc.

  18. Third-order nonlinear optical response of colloidal gold nanoparticles prepared by sputtering deposition

    Castro, Hemerson P. S.; Alencar, Márcio A. R. C.; Hickmann, Jandir M. [Optics and Materials Group–OPTMA, Universidade Federal de Alagoas, CAIXA POSTAL 2051, 57061-970 Maceió (Brazil); Wender, Heberton [Brazilian Synchrotron National Laboratory (LNLS), CNPEM, Rua Giuseppe Máximo Scolfaro 10.000, 13083-970 Campinas (Brazil); Department of Physics, Universidade Federal do Mato Grosso do Sul, 79070-900, Campo Grande (Brazil); Teixeira, Sergio R. [Institute of Physics, Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre (Brazil); Dupont, Jairton [Laboratory of Molecular Catalysis, Institute of Chemistry, Universidade Federal do Rio Grande do Sul, 91501-970, Porto Alegre (Brazil)

    2013-11-14

    The nonlinear optical responses of gold nanoparticles dispersed in castor oil produced by sputtering deposition were investigated, using the thermally managed Z-scan technique. Particles with spherical shape and 2.6 nm of average diameter were obtained and characterized by transmission electron microscopy and small angle X-ray scattering. This colloid was highly stable, without the presence of chemical impurities, neither stabilizers. It was observed that this system presents a large refractive third-order nonlinear response and a negligible nonlinear absorption. Moreover, the evaluation of the all-optical switching figures of merit demonstrated that the colloidal nanoparticles prepared by sputtering deposition have a good potential for the development of ultrafast photonic devices.

  19. An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

    Xu, Tiantian

    2014-08-17

    Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools that typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. We plot and compare the expanded form of the electrostatic force to the exact form and found that at least twenty terms are needed to capture accurately the strong nonlinear form of the force over the full range of motion. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. We found that the use of the new expanded form of the electrostatic force enables avoiding the cumbersome evaluation of the spatial integrals involving the electrostatic force during the modal projection procedure in the Galerkin method, which needs to be done at every time step. Hence, the new method proves to be much more efficient computationally.

  20. Existence and Uniqueness of Solutions for Coupled Systems of Higher-Order Nonlinear Fractional Differential Equations

    Ahmad Bashir

    2010-01-01

    Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.

  1. Single-step digital backpropagation for nonlinearity mitigation

    Secondini, Marco; Rommel, Simon; Meloni, Gianluca

    2015-01-01

    Nonlinearity mitigation based on the enhanced split-step Fourier method (ESSFM) for the implementation of low-complexity digital backpropagation (DBP) is investigated and experimentally demonstrated. After reviewing the main computational aspects of DBP and of the conventional split-step Fourier...... in the computational complexity, power consumption, and latency with respect to a simple feed-forward equalizer for bulk dispersion compensation....

  2. Nonlinear digital out-of-plane waveguide coupler based on nonlinear scattering of a single graphene layer

    Asadi, Reza; Ouyang, Zhengbiao

    2018-03-01

    A new mechanism for out-of-plane coupling into a waveguide is presented and numerically studied based on nonlinear scattering of a single nano-scale Graphene layer inside the waveguide. In this mechanism, the refractive index nonlinearity of Graphene and nonhomogeneous light intensity distribution occurred due to the interference between the out-of-plane incident pump light and the waveguide mode provide a virtual grating inside the waveguide, coupling the out-of-plane pump light into the waveguide. It has been shown that the coupling efficiency has two distinct values with high contrast around a threshold pump intensity, providing suitable condition for digital optical applications. The structure operates at a resonance mode due to band edge effect, which enhances the nonlinearity and decreases the required threshold intensity.

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

    Feng-Tao He

    2013-01-01

    Full Text Available 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.

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

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

    2009-01-01

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

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

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

    2009-04-01

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

  6. Polarized dependence of nonlinear susceptibility in a single layer graphene system in infrared region

    Solookinejad, G., E-mail: ghsolooki@gmail.com

    2016-09-15

    In this study, the linear and nonlinear susceptibility of a single-layer graphene nanostructure driven by a weak probe light and an elliptical polarized coupling field is discussed theoretically. The Landau levels of graphene can be separated in infrared or terahertz regions under the strong magnetic field. Therefore, by using the density matrix formalism in quantum optic, the linear and nonlinear susceptibility of the medium can be derived. It is demonstrated that by adjusting the elliptical parameter, one can manipulate the linear and nonlinear absorption as well as Kerr nonlinearity of the medium. It is realized that the enhanced Kerr nonlinearity can be possible with zero linear absorption and nonlinear amplification at some values of elliptical parameter. Our results may be having potential applications in quantum information science based on Nano scales devices.

  7. Magnetic order of Nd5Pb3 single crystals

    Yan, J.-Q.; Ochi, M.; Cao, H. B.; Saparov, B.; Cheng, J.-G.; Uwatoko, Y.; Arita, R.; Sales, B. C.; Mandrus, D. G.

    2018-04-01

    We report millimeter-sized Nd5Pb3 single crystals grown out of a Nd-Co flux. We experimentally study the magnetic order of Nd5Pb3 single crystals by measuring the anisotropic magnetic properties, electrical resistivity under high pressure up to 8 GPa, specific heat, and neutron single crystal diffraction. Two successive magnetic orders are observed at T N1  =  44 K and T N2  =  8 K. The magnetic cells can be described with a propagation vector k=(0.5, 0, 0) . Cooling below T N1, Nd1 and Nd3 order forming ferromagnetic stripes along the b-axis, and the ferromagnetic stripes are coupled antiferromagnetically along the a-axis for the k=(0.5, 0, 0) magnetic domain. Cooling below T N2, Nd2 orders antiferromagnetically to nearby Nd3 ions. All ordered moments align along the crystallographic c-axis. The magnetic order at T N1 is accompanied by a quick drop of electrical resistivity upon cooling and a lambda-type anomaly in the temperature dependence of specific heat. At T N2, no anomaly was observed in electrical resistivity but there is a weak feature in specific heat. The resistivity measurements under hydrostatic pressures up to 8 GPa suggest a possible phase transition around 6 GPa. Our first-principles band structure calculations show that Nd5Pb3 has the same electronic structure as does Y5Si3 which has been reported to be a one-dimensional electride with anionic electrons that do not belong to any atom. Our study suggests that R 5Pb3 (R  =  rare earth) can be a materials playground for the study of magnetic electrides. This deserves further study after experimental confirmation of the presence of anionic electrons.

  8. Oscillation criteria for third order nonlinear delay differential equations with damping

    Said R. Grace

    2015-01-01

    Full Text Available This note is concerned with the oscillation of third order nonlinear delay differential equations of the form \\[\\label{*} \\left( r_{2}(t\\left( r_{1}(ty^{\\prime}(t\\right^{\\prime}\\right^{\\prime}+p(ty^{\\prime}(t+q(tf(y(g(t=0.\\tag{\\(\\ast\\}\\] In the papers [A. Tiryaki, M. F. Aktas, Oscillation criteria of a certain class of third order nonlinear delay differential equations with damping, J. Math. Anal. Appl. 325 (2007, 54-68] and [M. F. Aktas, A. Tiryaki, A. Zafer, Oscillation criteria for third order nonlinear functional differential equations, Applied Math. Letters 23 (2010, 756-762], the authors established some sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates or converges to zero, provided that the second order equation \\[\\left( r_{2}(tz^{\\prime }(t\\right^{\\prime}+\\left(p(t/r_{1}(t\\right z(t=0\\tag{\\(\\ast\\ast\\}\\] is nonoscillatory. Here, we shall improve and unify the results given in the above mentioned papers and present some new sufficient conditions which insure that any solution of equation (\\(\\ast\\ oscillates if equation (\\(\\ast\\ast\\ is nonoscillatory. We also establish results for the oscillation of equation (\\(\\ast\\ when equation (\\(\\ast\\ast\\ is oscillatory.

  9. Single-order-parameter description of glass-forming liquids

    Ellegaard, Niels Langager; Christensen, Tage Emil; Christiansen, Peder Voetmann

    2007-01-01

    Thermoviscoelastic linear-response functions are calculated from the master equation describing viscous liquid inherent dynamics. From the imaginary parts of the frequency-dependent isobaric specific heat, isothermal compressibility, and isobaric thermal expansion coefficient, we define a "linear...... dynamic Prigogine-Defay ratio" with the property that if this ratio is unity at one frequency, then it is unity at all frequencies. This happens if and only if there is a single-order-parameter description of the thermoviscoelastic linear responses via an order parameter which may be nonexponential...

  10. Third-order nonlinear optical properties of the poly(methyl methacrylate)-phenothiazinium dye hybrid thin films

    Sun, Ru; Lu, Yue-Ting; Yan, Bao-Long; Lu, Jian-Mei; Wu, Xing-Zhi; Song, Ying-Lin; Ge, Jian-Feng

    2014-01-01

    The third-order nonlinear optical properties of poly(methyl methacrylate) films doped with charge flowable 3,7-di(piperidinyl)phenothiazin-5-ium chloride, which tested by Z-scan method with nanosecond laser beam at 532 nm, are reported. Large third-order nonlinear optical susceptibilities (up to 10 −7 esu) and high second hyperpolarizabilities (up to 10 −27 esu) are found. The third-order nonlinear absorptions change from reverse saturated absorptions to saturated absorptions with different percentage of the phenothiazinium dye in the poly(methyl methacrylate) films, which can be explained by the accumulation phenomenon of the phenothiazinium. The results suggest that the phenothiazinium salt is a promising material for third order non-linear applications. - Highlights: • Phenothiazinium containing optical films • Strong third-order nonlinear optical (NLO) absorption • Large third-order NLO susceptibilities

  11. On Single-Valued Neutrosophic Entropy of order α

    Harish Garg, Nancy

    2016-12-01

    Full Text Available Entropy is one of the measures which is used for measuring the fuzziness of the set. In this article, we have presented an entropy measure of order α under the single-valued neutrosophic set environment by considering the pair of their membership functions as well as the hesitation degree between them. Based on this measure, some of its desirable properties have been proposed and validated by taking an example of structure linguistic variable.

  12. Validation of a RANS transition model using a high-order weighted compact nonlinear scheme

    Tu, GuoHua; Deng, XiaoGang; Mao, MeiLiang

    2013-04-01

    A modified transition model is given based on the shear stress transport (SST) turbulence model and an intermittency transport equation. The energy gradient term in the original model is replaced by flow strain rate to saving computational costs. The model employs local variables only, and then it can be conveniently implemented in modern computational fluid dynamics codes. The fifth-order weighted compact nonlinear scheme and the fourth-order staggered scheme are applied to discrete the governing equations for the purpose of minimizing discretization errors, so as to mitigate the confusion between numerical errors and transition model errors. The high-order package is compared with a second-order TVD method on simulating the transitional flow of a flat plate. Numerical results indicate that the high-order package give better grid convergence property than that of the second-order method. Validation of the transition model is performed for transitional flows ranging from low speed to hypersonic speed.

  13. Efficient Model Order Reduction for the Dynamics of Nonlinear Multilayer Sheet Structures with Trial Vector Derivatives

    Wolfgang Witteveen

    2014-01-01

    Full Text Available The mechanical response of multilayer sheet structures, such as leaf springs or car bodies, is largely determined by the nonlinear contact and friction forces between the sheets involved. Conventional computational approaches based on classical reduction techniques or the direct finite element approach have an inefficient balance between computational time and accuracy. In the present contribution, the method of trial vector derivatives is applied and extended in order to obtain a-priori trial vectors for the model reduction which are suitable for determining the nonlinearities in the joints of the reduced system. Findings show that the result quality in terms of displacements and contact forces is comparable to the direct finite element method but the computational effort is extremely low due to the model order reduction. Two numerical studies are presented to underline the method’s accuracy and efficiency. In conclusion, this approach is discussed with respect to the existing body of literature.

  14. Assessing first-order emulator inference for physical parameters in nonlinear mechanistic models

    Hooten, Mevin B.; Leeds, William B.; Fiechter, Jerome; Wikle, Christopher K.

    2011-01-01

    We present an approach for estimating physical parameters in nonlinear models that relies on an approximation to the mechanistic model itself for computational efficiency. The proposed methodology is validated and applied in two different modeling scenarios: (a) Simulation and (b) lower trophic level ocean ecosystem model. The approach we develop relies on the ability to predict right singular vectors (resulting from a decomposition of computer model experimental output) based on the computer model input and an experimental set of parameters. Critically, we model the right singular vectors in terms of the model parameters via a nonlinear statistical model. Specifically, we focus our attention on first-order models of these right singular vectors rather than the second-order (covariance) structure.

  15. CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

    Roldan, Omar, E-mail: oaroldan@if.ufrj.br [Instituto de Física, Universidade Federal do Rio de Janeiro, 21941-972, Rio de Janeiro, RJ (Brazil)

    2017-08-01

    We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instance, facilitate the search for primordial non-Gaussianity in future works. It also disentangles the non-linear ISW from other effects. Finally, we provide a method which can iteratively be used to obtain the lensing solution at the desired order.

  16. CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

    Roldan, Omar

    2017-01-01

    We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instance, facilitate the search for primordial non-Gaussianity in future works. It also disentangles the non-linear ISW from other effects. Finally, we provide a method which can iteratively be used to obtain the lensing solution at the desired order.

  17. Order Selection for General Expression of Nonlinear Autoregressive Model Based on Multivariate Stepwise Regression

    Shi, Jinfei; Zhu, Songqing; Chen, Ruwen

    2017-12-01

    An order selection method based on multiple stepwise regressions is proposed for General Expression of Nonlinear Autoregressive model which converts the model order problem into the variable selection of multiple linear regression equation. The partial autocorrelation function is adopted to define the linear term in GNAR model. The result is set as the initial model, and then the nonlinear terms are introduced gradually. Statistics are chosen to study the improvements of both the new introduced and originally existed variables for the model characteristics, which are adopted to determine the model variables to retain or eliminate. So the optimal model is obtained through data fitting effect measurement or significance test. The simulation and classic time-series data experiment results show that the method proposed is simple, reliable and can be applied to practical engineering.

  18. Third-order nonlinearity of Er3+-doped lead phosphate glass

    Santos, C. C. [Universidade Federal do Ceara, Ceara, Brazil; Guedes Da Silva, Ilde [ORNL; Siqueira, J. P. [Instituto de Física de São Carlos, Universidade de São Paulo, Brazil; Misoguti, L. [Instituto de Física de São Carlos, Universidade de São Paulo, Brazil; Zilio, S. C. [Instituto de Física de São Carlos, Universidade de São Paulo, Brazil; Boatner, Lynn A [ORNL

    2010-01-01

    The third-order optical susceptibility and dispersion of the linear refractive index of Er3+-doped lead phosphate glass were measured in the wavelength range between 400 and 1940 nm by using the spectrally resolved femtosecond Maker fringes technique. The nonlinear refractive index obtained from the third-order susceptibility was found to be five times higher than that of silica, indicating that Er3+-doped lead phosphate glass is a potential candidate to be used as the base component for the fabrication of photonic devices. For comparison purposes, the Z-scan technique was also employed to obtain the values of the nonlinear refractive index of E-doped lead phosphate glass at several wavelengths, and the values obtained using the two techniques agree to within 15%.

  19. Zeolite Y Films as Ideal Platform for Evaluation of Third-Order Nonlinear Optical Quantum Dots

    Hyun Sung Kim

    2016-01-01

    Full Text Available Zeolites are ideal host material for generation and stabilization of regular ultrasmall quantum dots (QDs array with the size below 1.5 nm. Quantum dots (QDs with high density and extinction absorption coefficient have been expected to give high level of third-order nonlinear optical (3rd-NLO and to have great potential applications in optoelectronics. In this paper, we carried out a systematic elucidation of the third-order nonlinear optical response of various types of QDs including PbSe, PbS, CdSe, CdS, ZnSe, ZnS, Ag2Se, and Ag2S by manipulation of QDs into zeolites Y pores. In this respect, we could demonstrate that the zeolite offers an ideal platform for capability comparison 3rd-NLO response of various types of QDs with high sensitivities.

  20. Emergence of complex space-temporal order in nonlinear field theories

    Gleiser, Marcelo

    2006-01-01

    We investigate the emergence of time-dependent nonperturbative configurations during the evolution of nonlinear scalar field models with symmetric and asymmetric double-well potentials. Complex space-temporal behavior emerges as the system seeks to establish equipartition after a fast quench. We show that fast quenches may dramatically modify the decay rate of metastable states in first order phase transitions. We discuss possible applications in condensed matter systems and in inflationary cosmology. (author)

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

    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.

  2. Multivariate Padé Approximation for Solving Nonlinear Partial Differential Equations of Fractional Order

    Veyis Turut

    2013-01-01

    Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.

  3. CMB anisotropies at all orders: the non-linear Sachs-Wolfe formula

    Roldan, Omar

    2017-01-01

    We obtain the non-linear generalization of the Sachs-Wolfe + integrated Sachs-Wolfe (ISW) formula describing the CMB temperature anisotropies. Our formula is valid at all orders in perturbation theory, is also valid in all gauges and includes scalar, vector and tensor modes. A direct consequence of our results is that the maps of the logarithmic temperature anisotropies are much cleaner than the usual CMB maps, because they automatically remove many secondary anisotropies. This can for instan...

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

    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.

  5. Jacobian projection reduced-order models for dynamic systems with contact nonlinearities

    Gastaldi, Chiara; Zucca, Stefano; Epureanu, Bogdan I.

    2018-02-01

    In structural dynamics, the prediction of the response of systems with localized nonlinearities, such as friction dampers, is of particular interest. This task becomes especially cumbersome when high-resolution finite element models are used. While state-of-the-art techniques such as Craig-Bampton component mode synthesis are employed to generate reduced order models, the interface (nonlinear) degrees of freedom must still be solved in-full. For this reason, a new generation of specialized techniques capable of reducing linear and nonlinear degrees of freedom alike is emerging. This paper proposes a new technique that exploits spatial correlations in the dynamics to compute a reduction basis. The basis is composed of a set of vectors obtained using the Jacobian of partial derivatives of the contact forces with respect to nodal displacements. These basis vectors correspond to specifically chosen boundary conditions at the contacts over one cycle of vibration. The technique is shown to be effective in the reduction of several models studied using multiple harmonics with a coupled static solution. In addition, this paper addresses another challenge common to all reduction techniques: it presents and validates a novel a posteriori error estimate capable of evaluating the quality of the reduced-order solution without involving a comparison with the full-order solution.

  6. Polyharmonic boundary value problems positivity preserving and nonlinear higher order elliptic equations in bounded domains

    Gazzola, Filippo; Sweers, Guido

    2010-01-01

    This monograph covers higher order linear and nonlinear elliptic boundary value problems in bounded domains, mainly with the biharmonic or poly-harmonic operator as leading principal part. Underlying models and, in particular, the role of different boundary conditions are explained in detail. As for linear problems, after a brief summary of the existence theory and Lp and Schauder estimates, the focus is on positivity or - since, in contrast to second order equations, a general form of a comparison principle does not exist - on “near positivity.” The required kernel estimates are also presented in detail. As for nonlinear problems, several techniques well-known from second order equations cannot be utilized and have to be replaced by new and different methods. Subcritical, critical and supercritical nonlinearities are discussed and various existence and nonexistence results are proved. The interplay with the positivity topic from the first part is emphasized and, moreover, a far-reaching Gidas-Ni-Nirenbe...

  7. On the physical contributions to the third-order nonlinear optical response in plasmonic nanocomposites

    Fernández-Hernández, Roberto Carlos; Gleason-Villagran, Roberto; Rodríguez-Fernández, Luis; Crespo-Sosa, Alejandro; Cheang-Wong, Juan Carlos; López-Suárez, Alejandra; Oliver, Alicia; Reyes-Esqueda, Jorge Alejandro; Torres-Torres, Carlos; Rangel-Rojo, Raúl

    2012-01-01

    Au and Ag isotropic and anisotropic nanocomposites were prepared using the ion implantation technique. Their optical properties were studied at several wavelengths in the optical range 300–800 nm, across their plasmon resonances. The linear regime was characterized by measuring the absorption spectrum and the third-order nonlinear regime by means of the Z-scan technique using a tunable picosecond pulsed laser system (26 ps). Open-aperture Z-scan traces show a superposition of different optical nonlinear absorption (NLA) processes in the whole range studied. We associate these phenomena with the excitation of inter- and intra-band electronic transitions, which contribute with a positive sign to NLA, and to the formation of hot-electrons, which contribute with opposite sign to NLA. Closed-aperture traces for measuring nonlinear refraction (NLR) show different signs for Au and Ag samples, and a change of sign in Au is found when purely inter-band transitions are excited. In this work, for the appropriate wavelength, it is worth remarking on the free-electron response to the exciting light and its strong contribution to the nonlinear optical properties for low (intra-band) and high (hot-electrons) irradiances. (paper)

  8. Static aeroelastic analysis including geometric nonlinearities based on reduced order model

    Changchuan Xie

    2017-04-01

    Full Text Available This paper describes a method proposed for modeling large deflection of aircraft in nonlinear aeroelastic analysis by developing reduced order model (ROM. The method is applied for solving the static aeroelastic and static aeroelastic trim problems of flexible aircraft containing geometric nonlinearities; meanwhile, the non-planar effects of aerodynamics and follower force effect have been considered. ROMs are computational inexpensive mathematical representations compared to traditional nonlinear finite element method (FEM especially in aeroelastic solutions. The approach for structure modeling presented here is on the basis of combined modal/finite element (MFE method that characterizes the stiffness nonlinearities and we apply that structure modeling method as ROM to aeroelastic analysis. Moreover, the non-planar aerodynamic force is computed by the non-planar vortex lattice method (VLM. Structure and aerodynamics can be coupled with the surface spline method. The results show that both of the static aeroelastic analysis and trim analysis of aircraft based on structure ROM can achieve a good agreement compared to analysis based on the FEM and experimental result.

  9. An Efficient Higher-Order Quasilinearization Method for Solving Nonlinear BVPs

    Eman S. Alaidarous

    2013-01-01

    Full Text Available In this research paper, we present higher-order quasilinearization methods for the boundary value problems as well as coupled boundary value problems. The construction of higher-order convergent methods depends on a decomposition method which is different from Adomain decomposition method (Motsa and Sibanda, 2013. The reported method is very general and can be extended to desired order of convergence for highly nonlinear differential equations and also computationally superior to proposed iterative method based on Adomain decomposition because our proposed iterative scheme avoids the calculations of Adomain polynomials and achieves the same computational order of convergence as authors have claimed in Motsa and Sibanda, 2013. In order to check the validity and computational performance, the constructed iterative schemes are also successfully applied to bifurcation problems to calculate the values of critical parameters. The numerical performance is also tested for one-dimension Bratu and Frank-Kamenetzkii equations.

  10. Simulation of nonlinear wave run-up with a high-order Boussinesq model

    Fuhrman, David R.; Madsen, Per A.

    2008-01-01

    This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions....... As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions...... cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability...

  11. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

    Calatroni, Luca

    2013-08-01

    We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

  12. Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

    Bin Wang

    2016-01-01

    Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.

  13. High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains

    Fisher, Travis C.; Carpenter, Mark H.

    2013-01-01

    Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.

  14. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

    Calatroni, Luca; Dü ring, Bertram; Schö nlieb, Carola-Bibiane

    2013-01-01

    We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

  15. Internal crisis in a second-order non-linear non-autonomous electronic oscillator

    Stavrinides, S.G.; Deliolanis, N.C.; Miliou, A.N.; Laopoulos, Th.; Anagnostopoulos, A.N.

    2008-01-01

    The internal crisis of a second-order non-linear non-autonomous chaotic electronic circuit is studied. The phase portraits consist of two interacting sub-attractors, a chaotic and a periodic one. Maximal Lyapunov exponents were calculated, for both the periodic and the chaotic waveforms, in order to confirm their nature. Transitions between the chaotic and the periodic sub-attractors become more frequent by increasing the circuit driving frequency. The frequency distribution of the corresponding laminar lengths and their average values indicate that an internal crisis takes place in this circuit, manifested in the intermittent behaviour of the corresponding orbits

  16. Higher order terms of the nonlinear forces in plasmas with collisions at laser interaction

    Kentwell, G.W.; Hora, H.

    1980-01-01

    The evaluation of the general expression of the nonlinear force of laser-plasma interaction showed discrepancies depending on the assumptions of the phase and collisions in the expressions used for E and H. While the first order terms of the derivations are remaining unchanged, new third order terms are found for the case of perpendicular incidence without collisions. With collisions, the additional non-pondermotive terms are derived to be more general than known before. It is then possible to evaluate the forces for oblique incidence with collisions and find an absorption caused force in the plane of the plasma surface. (author)

  17. Reduced-order modeling of piezoelectric energy harvesters with nonlinear circuits under complex conditions

    Xiang, Hong-Jun; Zhang, Zhi-Wei; Shi, Zhi-Fei; Li, Hong

    2018-04-01

    A fully coupled modeling approach is developed for piezoelectric energy harvesters in this work based on the use of available robust finite element packages and efficient reducing order modeling techniques. At first, the harvester is modeled using finite element packages. The dynamic equilibrium equations of harvesters are rebuilt by extracting system matrices from the finite element model using built-in commands without any additional tools. A Krylov subspace-based scheme is then applied to obtain a reduced-order model for improving simulation efficiency but preserving the key features of harvesters. Co-simulation of the reduced-order model with nonlinear energy harvesting circuits is achieved in a system level. Several examples in both cases of harmonic response and transient response analysis are conducted to validate the present approach. The proposed approach allows to improve the simulation efficiency by several orders of magnitude. Moreover, the parameters used in the equivalent circuit model can be conveniently obtained by the proposed eigenvector-based model order reduction technique. More importantly, this work establishes a methodology for modeling of piezoelectric energy harvesters with any complicated mechanical geometries and nonlinear circuits. The input load may be more complex also. The method can be employed by harvester designers to optimal mechanical structures or by circuit designers to develop novel energy harvesting circuits.

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

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

    2018-05-01

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

  19. Axion as a Cold Dark Matter Candidate: Proof to Fully Nonlinear Order

    Noh, Hyerim [Center for Large Telescope, Korea Astronomy and Space Science Institute, Daejon (Korea, Republic of); Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu (Korea, Republic of); Park, Chan-Gyung [Division of Science Education and Institute of Fusion Science, Chonbuk National University, Jeonju (Korea, Republic of)

    2017-09-01

    We present proof of the axion as a cold dark matter (CDM) candidate to the fully nonlinear order perturbations based on Einstein’s gravity. We consider the axion as a coherently oscillating massive classical scalar field without interaction. We present the fully nonlinear and exact, except for ignoring the transverse-tracefree tensor-type perturbation, hydrodynamic equations for an axion fluid in Einstein’s gravity. We show that the axion has the characteristic pressure and anisotropic stress; the latter starts to appear from the second-order perturbation. But these terms do not directly affect the hydrodynamic equations in our axion treatment. Instead, what behaves as the effective pressure term in relativistic hydrodynamic equations is the perturbed lapse function and the relativistic result coincides exactly with the one known in the previous non-relativistic studies. The effective pressure term leads to a Jeans scale that is of the solar-system scale for conventional axion mass. As the fully nonlinear and relativistic hydrodynamic equations for an axion fluid coincide exactly with the ones of a zero-pressure fluid in the super-Jeans scale, we have proved the CDM nature of such an axion in that scale.

  20. Higher-Order Approximations of Motion of a Nonlinear Oscillator Using the Parameter Expansion Technique

    Ganji, S. S.; Domairry, G.; Davodi, A. G.; Babazadeh, H.; Seyedalizadeh Ganji, S. H.

    The main objective of this paper is to apply the parameter expansion technique (a modified Lindstedt-Poincaré method) to calculate the first, second, and third-order approximations of motion of a nonlinear oscillator arising in rigid rod rocking back. The dynamics and frequency of motion of this nonlinear mechanical system are analyzed. A meticulous attention is carried out to the study of the introduced nonlinearity effects on the amplitudes of the oscillatory states and on the bifurcation structures. We examine the synchronization and the frequency of systems using both the strong and special method. Numerical simulations and computer's answers confirm and complement the results obtained by the analytical approach. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. The solutions of this method are compared with the exact ones in order to validate the approach, and assess the accuracy of the solutions. In particular, APL-PM works well for the whole range of oscillation amplitudes and excellent agreement of the approximate frequency with the exact one has been demonstrated. The approximate period derived here is accurate and close to the exact solution. This method has a distinguished feature which makes it simple to use, and also it agrees with the exact solutions for various parameters.

  1. Third order nonlinear optical properties and optical limiting behavior of alkali metal complexes of p-nitrophenol

    Thangaraj, M.; Vinitha, G.; Sabari Girisun, T. C.; Anandan, P.; Ravi, G.

    2015-10-01

    Optical nonlinearity of metal complexes of p-nitrophenolate (M=Li, Na and K) in ethanol is studied by using a continuous wave (cw) diode pumped Nd:YAG laser (532 nm, 50 mW). The predominant mechanism of observed nonlinearity is thermal in origin. The nonlinear refractive index and the nonlinear absorption coefficient of the samples were found to be in the order of 10-8 cm2/W and 10-3 cm/W respectively. Magnitude of third-order optical parameters varies according to the choice of alkali metal chosen for metal complex formation of p-nitrophenolate. The third-order nonlinear susceptibility was found to be in the order of 10-6 esu. The observed saturable absorption and the self-defocusing effect were used to demonstrate the optical limiting action at 532 nm by using the same cw laser beam.

  2. Adaptive fuzzy wavelet network control of second order multi-agent systems with unknown nonlinear dynamics.

    Taheri, Mehdi; Sheikholeslam, Farid; Najafi, Majddedin; Zekri, Maryam

    2017-07-01

    In this paper, consensus problem is considered for second order multi-agent systems with unknown nonlinear dynamics under undirected graphs. A novel distributed control strategy is suggested for leaderless systems based on adaptive fuzzy wavelet networks. Adaptive fuzzy wavelet networks are employed to compensate for the effect of unknown nonlinear dynamics. Moreover, the proposed method is developed for leader following systems and leader following systems with state time delays. Lyapunov functions are applied to prove uniformly ultimately bounded stability of closed loop systems and to obtain adaptive laws. Three simulation examples are presented to illustrate the effectiveness of the proposed control algorithms. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  3. Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique

    Omar Abu Arqub

    2014-01-01

    Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.

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

    El Beltagy, Mohamed

    2016-01-06

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

  5. Uncertainty analysis of nonlinear systems employing the first-order reliability method

    Choi, Chan Kyu; Yoo, Hong Hee

    2012-01-01

    In most mechanical systems, properties of the system elements have uncertainties due to several reasons. For example, mass, stiffness coefficient of a spring, damping coefficient of a damper or friction coefficients have uncertain characteristics. The uncertain characteristics of the elements have a direct effect on the system performance uncertainty. It is very important to estimate the performance uncertainty since the performance uncertainty is directly related to manufacturing yield and consumer satisfaction. Due to this reason, the performance uncertainty should be estimated accurately and considered in the system design. In this paper, performance measures are defined for nonlinear vibration systems and the performance measure uncertainties are estimated employing the first order reliability method (FORM). It was found that the FORM could provide good results in spite of the system nonlinear characteristics. Comparing to the results obtained by Monte Carlo Simulation (MCS), the accuracy of the uncertainty analysis results obtained by the FORM is validated

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

    El Beltagy, Mohamed

    2016-01-01

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

  7. A framework for simulating ultrasound imaging based on first order nonlinear pressure–velocity relations

    Du, Yigang; Fan, Rui; Li, Yong

    2016-01-01

    An ultrasound imaging framework modeled with the first order nonlinear pressure–velocity relations (NPVR) based simulation and implemented by a half-time staggered solution and pseudospectral method is presented in this paper. The framework is capable of simulating linear and nonlinear ultrasound...... propagation and reflections in a heterogeneous medium with different sound speeds and densities. It can be initialized with arbitrary focus, excitation and apodization for multiple individual channels in both 2D and 3D spatial fields. The simulated channel data can be generated using this framework......, and ultrasound image can be obtained by beamforming the simulated channel data. Various results simulated by different algorithms are illustrated for comparisons. The root mean square (RMS) errors for each compared pulses are calculated. The linear propagation is validated by an angular spectrum approach (ASA...

  8. Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators

    Talukdar, Abdul Hafiz

    2011-05-01

    Exceptional behaviours of Memristor are illustrated in Memristor based second order (Wien oscillator) and third order (phase shift oscillator) oscillator systems in this Thesis. Conventional concepts about sustained oscillation have been argued by demonstrating the possibility of sustained oscillation with oscillating resistance and dynamic poles. Mathematical models are also proposed for analysis and simulations have been presented to support the surprising characteristics of the Memristor based oscillator systems. This thesis also describes a comparative study among the Wien family oscillators with one Memristor. In case of phase shift oscillator, one Memristor and three Memristors systems are illustrated and compared to generalize the nonlinear dynamics observed for both 2nd order and 3rd order system. Detail explanations are provided with analytical models to simplify the unconventional properties of Memristor based oscillatory systems.

  9. Third-order nonlinear optical properties of thin sputtered gold films

    Xenogiannopoulou, E.; Aloukos, P.; Couris, S.; Kaminska, E.; Piotrowska, A.; Dynowska, E.

    2007-07-01

    Au films of thickness ranging between 5 and 52 nm were prepared by sputtering on quartz substrates and their third-order nonlinear optical response was investigated by Optical Kerr effect (OKE) and Z-scan techniques using 532 nm, 35 ps laser pulses. All prepared films were characterized by XRD, AFM and UV-VIS-NIR spectrophotometry while their third-order susceptibility χ(3) was measured and found to be of the order of 10 -9 esu. The real and imaginary parts of the third-order susceptibility were found in very good agreement with experimental results and theoretical predictions reported by Smith et al. [D.D. Smith, Y. Yoon, R.W. Boyd, Y.K. Cambell, L.A. Baker, R.M. Crooks, M. George, J. Appl. Phys. 86 (1999) 6200].

  10. Growth and characterization of nonlinear optical single crystals: bis ...

    Administrator

    molecules have received great attention for NLO applica- tions. However ... Figure 3. Single crystals of bis(cyclohexylammonium) terephthalate (crystal a) and cyclohexylammo- .... from ground state to higher energy states.17 Optical window ...

  11. "E pluribus unum" or How to Derive Single-equation Descriptions for Output-quantities in Nonlinear Circuits using Differential Algebra

    Gerbracht, Eberhard H. -A.

    2008-01-01

    In this paper we describe by a number of examples how to deduce one single characterizing higher order differential equation for output quantities of an analog circuit. In the linear case, we apply basic "symbolic" methods from linear algebra to the system of differential equations which is used to model the analog circuit. For nonlinear circuits and their corresponding nonlinear differential equations, we show how to employ computer algebra tools implemented in Maple, which are based on diff...

  12. On-demand single-photon state generation via nonlinear absorption

    Hong Tao; Jack, Michael W.; Yamashita, Makoto

    2004-01-01

    We propose a method for producing on-demand single-photon states based on collision-induced exchanges of photons and unbalanced linear absorption between two single-mode light fields. These two effects result in an effective nonlinear absorption of photons in one of the modes, which can lead to single-photon states. A quantum nonlinear attenuator based on such a mechanism can absorb photons in a normal input light pulse and terminate the absorption at a single-photon state. Because the output light pulses containing single photons preserve the properties of the input pulses, we expect this method to be a means for building a highly controllable single-photon source

  13. ℋ- adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

    Ndoye, Ibrahima; Voos, Holger; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed

    2014-01-01

    In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown

  14. Second order nonlinear optical properties of zinc oxide films deposited by low temperature dual ion beam sputtering

    Larciprete, M.C.; Passeri, D.; Michelotti, F.; Paoloni, S.; Sibilia, C.; Bertolotti, M.; Belardini, A.; Sarto, F.; Somma, F.; Lo Mastro, S.

    2005-01-01

    We investigated second order optical nonlinearity of zinc oxide thin films, grown on glass substrates by the dual ion beam sputtering technique under different deposition conditions. Linear optical characterization of the films was carried out by spectrophotometric optical transmittance and reflectance measurements, giving the complex refractive index dispersion. Resistivity of the films was determined using the four-point probe sheet resistance method. Second harmonic generation measurements were performed by means of the Maker fringes technique where the fundamental beam was originated by nanosecond laser at λ=1064 nm. We found a relatively high nonlinear optical response, and evidence of a dependence of the nonlinear coefficient on the deposition parameters for each sample. Moreover, the crystalline properties of the films were investigated by x-ray diffraction measurements and correlation with second order nonlinearity were analyzed. Finally, we investigated the influence of the oxygen flow rate during the deposition process on both the second order nonlinearity and the structural properties of the samples

  15. Coherent excitonic nonlinearity versus inhomogeneous broadening in single quantum wells

    Langbein, Wolfgang Werner; Borri, Paola; Hvam, Jørn Märcher

    1998-01-01

    The coherent response of excitons in semiconductor nanostructures, as measured in four wave mixing (FWM) experiments, depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs-AlGaAs single quantum wells (SQW) of 4 nm to 25 nm well width. Two main mechanisms...

  16. Signatures of nonlinearity in single cell noise-induced oscillations

    Thomas, P.; Straube, A.V.; Timmer, J.; Fleck, C.; Grima, R.

    2013-01-01

    A class of theoretical models seeks to explain rhythmic single cell data by postulating that they are generated by intrinsic noise in biochemical systems whose deterministic models exhibit only damped oscillations. The main features of such noise-induced oscillations are quantified by the power

  17. Distributed robust adaptive control of high order nonlinear multi agent systems.

    Hashemi, Mahnaz; Shahgholian, Ghazanfar

    2018-03-01

    In this paper, a robust adaptive neural network based controller is presented for multi agent high order nonlinear systems with unknown nonlinear functions, unknown control gains and unknown actuator failures. At first, Neural Network (NN) is used to approximate the nonlinear uncertainty terms derived from the controller design procedure for the followers. Then, a novel distributed robust adaptive controller is developed by combining the backstepping method and the Dynamic Surface Control (DSC) approach. The proposed controllers are distributed in the sense that the designed controller for each follower agent only requires relative state information between itself and its neighbors. By using the Young's inequality, only few parameters need to be tuned regardless of NN nodes number. Accordingly, the problems of dimensionality curse and explosion of complexity are counteracted, simultaneously. New adaptive laws are designed by choosing the appropriate Lyapunov-Krasovskii functionals. The proposed approach proves the boundedness of all the closed-loop signals in addition to the convergence of the distributed tracking errors to a small neighborhood of the origin. Simulation results indicate that the proposed controller is effective and robust. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  18. Photo-physics of third-order nonlinear optical processes in organic dyes

    Delysse, Stephane

    1997-01-01

    We study some aspects of the nonlinear picosecond photo-physics in organic dyes using Kerr ellipsometry. The aim is to establish link between the photo-physics and nonlinear optics in these compounds. First, we study coherent processes directly linked to the third-order susceptibility. Thus, we measure two-photon absorption spectra of large internal charge transfer dyes. We take into account all coupling between three electronic states which can interfere to explain the particular response of some stilbene dyes. On the second hand, we expose a more photophysical approach to determine the S 1 → S n transition energies and moments using the measurement of excited state absorption cross sections. These results allow the prediction of the susceptibilities relevant to alternative nonlinear optical methods. Nevertheless, the stationary approach hides the complex relaxation processes which can take place in organic dyes. As an illustration, we study the formation and disappearance of a TICT (Twisted intramolecular charge transfer) in a pyrylium salt in solvents of increasing viscosity. (author) [fr

  19. Nonsingular Terminal Sliding Mode Control of Uncertain Second-Order Nonlinear Systems

    Minh-Duc Tran

    2015-01-01

    Full Text Available This paper presents a high-performance nonsingular terminal sliding mode control method for uncertain second-order nonlinear systems. First, a nonsingular terminal sliding mode surface is introduced to eliminate the singularity problem that exists in conventional terminal sliding mode control. By using this method, the system not only can guarantee that the tracking errors reach the reference value in a finite time with high-precision tracking performance but also can overcome the complex-value and the restrictions of the exponent (the exponent should be fractional number with an odd numerator and an odd denominator in traditional terminal sliding mode. Then, in order to eliminate the chattering phenomenon, a super-twisting higher-order nonsingular terminal sliding mode control method is proposed. The stability of the closed-loop system is established using the Lyapunov theory. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.

  20. LOO: a low-order nonlinear transport scheme for acceleration of method of characteristics

    Li, Lulu; Smith, Kord; Forget, Benoit; Ferrer, Rodolfo

    2015-01-01

    This paper presents a new physics-based multi-grid nonlinear acceleration method: the low-order operator method, or LOO. LOO uses a coarse space-angle multi-group method of characteristics (MOC) neutron transport calculation to accelerate the fine space-angle MOC calculation. LOO is designed to capture more angular effects than diffusion-based acceleration methods through a transport-based low-order solver. LOO differs from existing transport-based acceleration schemes in that it emphasizes simplified coarse space-angle characteristics and preserves physics in quadrant phase-space. The details of the method, including the restriction step, the low-order iterative solver and the prolongation step are discussed in this work. LOO shows comparable convergence behavior to coarse mesh finite difference on several two-dimensional benchmark problems while not requiring any under-relaxation, making it a robust acceleration scheme. (author)

  1. Conservative fourth-order time integration of non-linear dynamic systems

    Krenk, Steen

    2015-01-01

    An energy conserving time integration algorithm with fourth-order accuracy is developed for dynamic systems with nonlinear stiffness. The discrete formulation is derived by integrating the differential state-space equations of motion over the integration time increment, and then evaluating...... the resulting time integrals of the inertia and stiffness terms via integration by parts. This process introduces the time derivatives of the state space variables, and these are then substituted from the original state-space differential equations. The resulting discrete form of the state-space equations...... is a direct fourth-order accurate representation of the original differential equations. This fourth-order form is energy conserving for systems with force potential in the form of a quartic polynomial in the displacement components. Energy conservation for a force potential of general form is obtained...

  2. Highly efficient single-pass sum frequency generation by cascaded nonlinear crystals

    Hansen, Anders Kragh; Andersen, Peter E.; Jensen, Ole Bjarlin

    2015-01-01

    , despite differences in the phase relations of the involved fields. An unprecedented 5.5 W of continuous-wave diffraction-limited green light is generated from the single-pass sum frequency mixing of two diode lasers in two periodically poled nonlinear crystals (conversion efficiency 50%). The technique......The cascading of nonlinear crystals has been established as a simple method to greatly increase the conversion efficiency of single-pass second-harmonic generation compared to a single-crystal scheme. Here, we show for the first time that the technique can be extended to sum frequency generation...... is generally applicable and can be applied to any combination of fundamental wavelengths and nonlinear crystals....

  3. Third-order perturbations of a zero-pressure cosmological medium: Pure general relativistic nonlinear effects

    Hwang, Jai-chan; Noh, Hyerim

    2005-01-01

    We consider a general relativistic zero-pressure irrotational cosmological medium perturbed to the third order. We assume a flat Friedmann background but include the cosmological constant. We ignore the rotational perturbation which decays in expanding phase. In our previous studies we discovered that, to the second-order perturbation, except for the gravitational wave contributions, the relativistic equations coincide exactly with the previously known Newtonian ones. Since the Newtonian second-order equations are fully nonlinear, any nonvanishing third- and higher-order terms in the relativistic analyses are supposed to be pure relativistic corrections. In this work, we derive such correction terms appearing in the third order. Continuing our success in the second-order perturbations, we take the comoving gauge. We discover that the third-order correction terms are of φ v order higher than the second-order terms where φ v is a gauge-invariant combination related to the three-space curvature perturbation in the comoving gauge; compared with the Newtonian potential, we have δΦ∼(3/5)φ v to the linear order. Therefore, the pure general relativistic effects are of φ v order higher than the Newtonian ones. The corrections terms are independent of the horizon scale and depend only on the linear-order gravitational potential (curvature) perturbation strength. From the temperature anisotropy of cosmic microwave background, we have (δT/T)∼(1/3)δΦ∼(1/5)φ v ∼10 -5 . Therefore, our present result reinforces our previous important practical implication that near the current era one can use the large-scale Newtonian numerical simulation more reliably even as the simulation scale approaches near (and goes beyond) the horizon

  4. The fourth-order non-linear sigma models and asymptotic freedom in four dimensions

    Buchbinder, I.L.; Ketov, S.V.

    1991-01-01

    Starting with the most general Lagrangian of the fourth-order non-linear sigma model in four space-time dimensions, we calculate the one-loop, on-shell ultra-violet-divergent part of the effective action. The formalism is based on the background field method and the generalised Schwinger-De Witt technique. The multiplicatively renormalisable case is investigated in some detail. The renormalisation group equations are obtained, and the conditions for a realisation of asymptotic freedom are considered. (orig.)

  5. Sturm-Picone type theorems for second-order nonlinear differential equations

    Aydin Tiryaki

    2014-06-01

    Full Text Available The aim of this article is to give Sturm-Picone type theorems for the pair of second-order nonlinear differential equations $$\\displaylines{ (p_1(t|x'|^{\\alpha-1}x''+q_1(tf_1(x=0 \\cr (p_2(t|y'|^{\\alpha-1}y''+q_2(tf_2(y=0,\\quad t_1

  6. Nonlinear optics in the LP(02) higher-order mode of a fiber.

    Chen, Y; Chen, Z; Wadsworth, W J; Birks, T A

    2013-07-29

    The distinct disperion properties of higher-order modes in optical fibers permit the nonlinear generation of radiation deeper into the ultraviolet than is possible with the fundamental mode. This is exploited using adiabatic, broadband mode convertors to couple light efficiently from an input fundamental mode and also to return the generated light to an output fundamental mode over a broad spectral range. For example, we generate visible and UV supercontinuum light in the LP(02) mode of a photonic crystal fiber from sub-ns pulses with a wavelength of 532 nm.

  7. Temporal mode selectivity by frequency conversion in second-order nonlinear optical waveguides

    Reddy, D. V.; Raymer, M. G.; McKinstrie, C. J.

    2013-01-01

    in a transparent optical network using temporally orthogonal waveforms to encode different channels. We model the process using coupled-mode equations appropriate for wave mixing in a uniform second-order nonlinear optical medium pumped by a strong laser pulse. We find Green functions describing the process...... in this optimal regime. We also find an operating regime in which high-efficiency frequency conversion without temporal-shape selectivity can be achieved while preserving the shapes of a wide class of input pulses. The results are applicable to both classical and quantum frequency conversion....

  8. A higher-order nonlinear Schrödinger equation with variable coefficients

    Carvajal, X.; Linares, F.

    2003-01-01

    We study the initial value problem (IVP) associated to a higher-order nonlinear Schrödinger equation with variable coefficients. Under some regularity on its coefficients we establish local well-posedness for the IVP for data in $H^s(\\mathbb R)$, $s\\ge1/4$, improving previous results [22]. The main ingredient in our proof is an estimate of the maximal function associated to the linear solution similar to the sharp one obtained for linear solutions of the Schrödinger and K...

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

    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.

  10. Generalized effective potential in nonlinear theories of the 4-th order

    Ananikyan, N.S.; Savvidy, G.K.

    1980-01-01

    By means of the Legendre transformations in the framework of nonlinear theories of the 4-th order a generalized effective potential GITA(phi, G, H, S) is constructed. It depends on PHI, a possible expectation value of the quantum field; on G, H, possible expectation values of the 2- a.nd 3-point connected Green functions and on S= a possible expectation value of the classical action. The expansion for the functional GITA(phi, G, H, S) is obtained, which is similar to the loop expansion for the effective action GITA(phi)

  11. Experimental study of the third-order nonlinearity of atomic and molecular gases using 10-μm laser pulses

    Pigeon, J. J.; Tochitsky, S. Ya.; Welch, E. C.; Joshi, C.

    2018-04-01

    We present measurements of the third-order optical nonlinearity of Kr, Xe, N2, O2, and air at a wavelength near 10 µm by using four-wave mixing of ˜15 -GW /c m2 , 200-ps (full width at half maximum) C O2 laser pulses. Measurements in molecular gases resulted in an asymmetric four-wave mixing spectrum indicating that the nonlinear response is strongly affected by the delayed, rotational contribution to the effective nonlinear refractive index. Within the uncertainty of our measurements, we have found that the long-wavelength nonlinear refractive indices of these gases are consistent with measurements performed in the near IR.

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

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

    2018-04-01

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

  13. Low-order longitudinal modes of single-component plasmas

    Tinkle, M.D.; Greaves, R.G.; Surko, C.M.

    1995-01-01

    The low-order modes of spheroidal, pure electron plasmas have been studied experimentally, both in a cylindrical electrode structure and in a quadrupole trap. Comparison is made between measurements of mode frequencies, recent analytical theories, and numerical simulations. Effects considered include trap anharmonicity, image charges, and temperature. Quantitative agreement is obtained between the predictions and these measurements for spheroidal plasmas in the quadrupole trap. In many experiments on single-component plasmas, including antimatter plasmas, the standard diagnostic techniques used to measure the density and temperature are not appropriate. A new method is presented for determining the size, shape, average density, and temperature of a plasma confined in a Penning trap from measurements of the mode frequencies. copyright 1995 American Institute of Physics

  14. Nonlinear convergence active vibration absorber for single and multiple frequency vibration control

    Wang, Xi; Yang, Bintang; Guo, Shufeng; Zhao, Wenqiang

    2017-12-01

    This paper presents a nonlinear convergence algorithm for active dynamic undamped vibration absorber (ADUVA). The damping of absorber is ignored in this algorithm to strengthen the vibration suppressing effect and simplify the algorithm at the same time. The simulation and experimental results indicate that this nonlinear convergence ADUVA can help significantly suppress vibration caused by excitation of both single and multiple frequency. The proposed nonlinear algorithm is composed of equivalent dynamic modeling equations and frequency estimator. Both the single and multiple frequency ADUVA are mathematically imitated by the same mechanical structure with a mass body and a voice coil motor (VCM). The nonlinear convergence estimator is applied to simultaneously satisfy the requirements of fast convergence rate and small steady state frequency error, which are incompatible for linear convergence estimator. The convergence of the nonlinear algorithm is mathematically proofed, and its non-divergent characteristic is theoretically guaranteed. The vibration suppressing experiments demonstrate that the nonlinear ADUVA can accelerate the convergence rate of vibration suppressing and achieve more decrement of oscillation attenuation than the linear ADUVA.

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

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

    2016-09-15

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

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

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

    2016-09-01

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

  17. Application of power series to the solution of the boundary value problem for a second order nonlinear differential equation

    Semenova, V.N.

    2016-01-01

    A boundary value problem for a nonlinear second order differential equation has been considered. A numerical method has been proposed to solve this problem using power series. Results of numerical experiments have been presented in the paper [ru

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

    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.

  19. A novel algebraic procedure for solving non-linear evolution equations of higher order

    Huber, Alfred

    2007-01-01

    We report here a systematic approach that can easily be used for solving non-linear partial differential equations (nPDE), especially of higher order. We restrict the analysis to the so called evolution equations describing any wave propagation. The proposed new algebraic approach leads us to traveling wave solutions and moreover, new class of solution can be obtained. The crucial step of our method is the basic assumption that the solutions satisfy an ordinary differential equation (ODE) of first order that can be easily integrated. The validity and reliability of the method is tested by its application to some non-linear evolution equations. The important aspect of this paper however is the fact that we are able to calculate distinctive class of solutions which cannot be found in the current literature. In other words, using this new algebraic method the solution manifold is augmented to new class of solution functions. Simultaneously we would like to stress the necessity of such sophisticated methods since a general theory of nPDE does not exist. Otherwise, for practical use the algebraic construction of new class of solutions is of fundamental interest

  20. DISPL-1, 2. Order Nonlinear Partial Differential Equation System Solution for Kinetics Diffusion Problems

    Leaf, G.K.; Minkoff, M.

    1982-01-01

    1 - Description of problem or function: DISPL1 is a software package for solving second-order nonlinear systems of partial differential equations including parabolic, elliptic, hyperbolic, and some mixed types. The package is designed primarily for chemical kinetics- diffusion problems, although not limited to these problems. Fairly general nonlinear boundary conditions are allowed as well as inter- face conditions for problems in an inhomogeneous medium. The spatial domain is one- or two-dimensional with rectangular Cartesian, cylindrical, or spherical (in one dimension only) geometry. 2 - Method of solution: The numerical method is based on the use of Galerkin's procedure combined with the use of B-Splines (C.W.R. de-Boor's B-spline package) to generate a system of ordinary differential equations. These equations are solved by a sophisticated ODE software package which is a modified version of Hindmarsh's GEAR package, NESC Abstract 592. 3 - Restrictions on the complexity of the problem: The spatial domain must be rectangular with sides parallel to the coordinate geometry. Cross derivative terms are not permitted in the PDE. The order of the B-Splines is at most 12. Other parameters such as the number of mesh points in each coordinate direction, the number of PDE's etc. are set in a macro table used by the MORTRAn2 preprocessor in generating the object code

  1. Higher order analytical approximate solutions to the nonlinear pendulum by He's homotopy method

    Belendez, A; Pascual, C; Alvarez, M L; Mendez, D I; Yebra, M S; Hernandez, A

    2009-01-01

    A modified He's homotopy perturbation method is used to calculate the periodic solutions of a nonlinear pendulum. The method has been modified by truncating the infinite series corresponding to the first-order approximate solution and substituting a finite number of terms in the second-order linear differential equation. As can be seen, the modified homotopy perturbation method works very well for high values of the initial amplitude. Excellent agreement of the analytical approximate period with the exact period has been demonstrated not only for small but also for large amplitudes A (the relative error is less than 1% for A < 152 deg.). Comparison of the result obtained using this method with the exact ones reveals that this modified method is very effective and convenient.

  2. A non-linear reduced order methodology applicable to boiling water reactor stability analysis

    Prill, Dennis Paul

    2013-01-01

    Thermal-hydraulic coupling between power, flow rate and density, intensified by neutronics feedback are the main drivers of boiling water reactor (BWR) stability behavior. High-power low-flow conditions in connection with unfavorable power distributions can lead the BWR system into unstable regions where power oscillations can be triggered. This important threat to operational safety requires careful analysis for proper understanding. Analyzing an exhaustive parameter space of the non-linear BWR system becomes feasible with methodologies based on reduced order models (ROMs), saving computational cost and improving the physical understanding. Presently within reactor dynamics, no general and automatic prediction of high-dimensional ROMs based on detailed BWR models are available. In this thesis a systematic self-contained model order reduction (MOR) technique is derived which is applicable for several classes of dynamical problems, and in particular to BWRs of any degree of details. Expert knowledge can be given by operational, experimental or numerical transient data and is transfered into an optimal basis function representation. The methodology is mostly automated and provides the framework for the reduction of various different systems of any level of complexity. Only little effort is necessary to attain a reduced version within this self-written code which is based on coupling of sophisticated commercial software. The methodology reduces a complex system in a grid-free manner to a small system able to capture even non-linear dynamics. It is based on an optimal choice of basis functions given by the so-called proper orthogonal decomposition (POD). Required steps to achieve reliable and numerical stable ROM are given by a distinct calibration road-map. In validation and verification steps, a wide spectrum of representative test examples is systematically studied regarding a later BWR application. The first example is non-linear and has a dispersive character

  3. Validity testing of third-order nonlinear models for synchronous generators

    Arjona, M.A. [Division de Estudios de Posgrado e Investigacion, Instituto Tecnologico de La Laguna Torreon, Coah. (Mexico); Escarela-Perez, R. [Universidad Autonoma Metropolitana - Azcapotzalco, Departamento de Energia, Av. San Pablo 180, Col. Reynosa, C.P. 02200 (Mexico); Espinosa-Perez, G. [Division de Estudios Posgrado de la Facultad de Ingenieria Universidad Nacional Autonoma de Mexico (Mexico); Alvarez-Ramirez, J. [Universidad Autonoma Metropolitana -Iztapalapa, Division de Ciencias Basicas e Ingenieria (Mexico)

    2009-06-15

    Third-order nonlinear models are commonly used in control theory for the analysis of the stability of both open-loop and closed-loop synchronous machines. However, the ability of these models to describe the electrical machine dynamics has not been tested experimentally. This work focuses on this issue by addressing the parameters identification problem for third-order models for synchronous generators. For a third-order model describing the dynamics of power angle {delta}, rotor speed {omega} and quadrature axis transient EMF E{sub q}{sup '}, it is shown that the parameters cannot be identified because of the effects of the unknown initial condition of E{sub q}{sup '}. To avoid this situation, a model that incorporates the measured electrical power dynamics is considered, showing that state measurements guarantee the identification of the model parameters. Data obtained from a 7 kVA lab-scale synchronous generator and from a 150 MVA finite-element simulation were used to show that, at least for the worked examples, the estimated parameters display only moderate variations over the operating region. This suggests that third-order models can suffice to describe the main dynamical features of synchronous generators, and that third-order models can be used to design and tune power system stabilizers and voltage regulators. (author)

  4. Run-up on a body in waves and current. Fully nonlinear and finite-order calculations

    Büchmann, Bjarne; Ferrant, P.; Skourup, J.

    2001-01-01

    Run-up on a large fixed body in waves and current have been calculated using both a fully nonlinear time-domain boundary element model and a finite-order time-domain boundary element model, the latter being correct to second order in the wave steepness and to first-order in the current strength...

  5. Summary report of the group on single-particle nonlinear dynamics

    Axinescu, S.; Bartolini, R.; Bazzani, A.

    1996-10-01

    This report summarizes the research on single-particle nonlinear beam dynamics. It discusses the following topics: analytical and semi-analytical tools; early prediction of the dynamic aperture; how the results are commonly presented; Is the mechanism of the dynamic aperture understand; ripple effects; and beam-beam effects

  6. Non-critically phase-matched second harmonic generation and third order nonlinearity in organic crystal glucuronic acid γ-lactone

    Saripalli, Ravi Kiran; Katturi, Naga Krishnakanth; Soma, Venugopal Rao; Bhat, H. L.; Elizabeth, Suja

    2017-12-01

    The linear, second order, and third order nonlinear optical properties of glucuronic acid γ-lactone single crystals were investigated. The optic axes and principal dielectric axes were identified through optical conoscopy and the principal refractive indices were obtained using the Brewster's angle method. Conic sections were observed which is perceived to be due to spontaneous non-collinear phase matching. The direction of collinear phase matching was determined and the deff evaluated in this direction was 0.71 pm/V. Open and closed aperture Z-scan measurements with femtosecond pulses revealed high third order nonlinearity in the form of self-defocusing, two-photon absorption, as well as saturable absorption.

  7. Studies on third-order optical nonlinearity and power limiting of conducting polymers using the z-scan technique for nonlinear optical applications

    Pramodini, S.; Sudhakar, Y. N.; SelvaKumar, M.; Poornesh, P.

    2014-04-01

    We present the synthesis and characterization of third-order optical nonlinearity and optical limiting of the conducting polymers poly (aniline-co-o-anisidine) and poly (aniline-co-pyrrole). Nonlinear optical studies were carried out by employing the z-scan technique using a He-Ne laser operating in continuous wave mode at 633 nm. The copolymers exhibited a reverse saturable absorption process and self-defocusing properties under the experimental conditions. The estimated values of βeff, n2 and χ(3) were found to be of the order of 10-2 cm W-1, 10-5 esu and 10-7 esu respectively. Self-diffraction rings were observed due to refractive index change when exposed to the laser beam. The copolymers possess a lower limiting threshold and clamping level, which is essential to a great extent for power limiting devices. Therefore, copolymers of aniline emerge as a potential candidate for nonlinear optical device applications.

  8. Physical origin of third order non-linear optical response of porphyrin nanorods

    Mongwaketsi, N.; Khamlich, S.; Pranaitis, M.; Sahraoui, B.; Khammar, F.; Garab, G.; Sparrow, R.; Maaza, M.

    2012-01-01

    The non-linear optical properties of porphyrin nanorods were studied using Z-scan, Second and Third harmonic generation techniques. We investigated in details the heteroaggregate behaviour formation of [H 4 TPPS 4 ] 2- and [SnTPyP] 2+ mixture by means of the UV-VIS spectroscopy and aggregates structure and morphology by transmission electron microscopy. The porphyrin nanorods under investigation were synthesized by self assembly and molecular recognition method. They have been optimized in view of future application in the construction of the light harvesting system. The focus of this study was geared towards understanding the influence of the type of solvent used on these porphyrins nanorods using spectroscopic and microscopic techniques. Highlights: ► We synthesized porphyrin nanorods by self assembly and molecular recognition method. ► TEM images confirmed solid cylindrical shapes. ► UV-VIS spectroscopy showed the decrease in the absorbance peaks of the precursors. ► The enhanced third-order nonlinearities were observed.

  9. Passive impedance-based second-order sliding mode control for non-linear teleoperators

    Luis G García-Valdovinos

    2017-02-01

    Full Text Available Bilateral teleoperation systems have attracted significant attention in the last decade mainly because of technological advancements in both the communication channel and computers performance. In addition, non-linear multi-degree-of-freedom bilateral teleoperators along with state observers have become an open research area. In this article, a model-free exact differentiator is used to estimate the full state along with a chattering-free second-order sliding mode controller to guarantee a robust impedance tracking under both constant and an unknown time delay of non-linear multi-degree-of-freedom robots. The robustness of the proposed controller is improved by introducing a change of coordinates in terms of a new nominal reference similar to that used in adaptive control theory. Experimental results that validate the predicted behaviour are presented and discussed using a Phantom Premium 1.0 as the master robot and a Catalyst-5 virtual model as the slave robot. The dynamics of the Catalyst-5 system is solved online.

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

    Crass, Jonathan; King, David; Mackay, Craig

    2013-12-01

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

  11. Distributed Consensus Tracking for Second-Order Nonlinear Multiagent Systems with a Specified Reference State

    Guoguang Wen

    2014-01-01

    Full Text Available This paper mainly addresses the distributed consensus tracking problem for second-order nonlinear multiagent systems with a specified reference trajectory. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position and velocity information of its neighbors. The consensus reference is taken as a virtual leader, whose output is only its position and velocity information that is available to only a subset of a group of followers. To achieve consensus tracking, a class of nonsmooth control protocols is proposed which reply on the relative information among the neighboring agents. Then some corresponding sufficient conditions are derived. It is shown that if the communication graph associated with the virtual leader and followers is connected at each time instant, the consensus can be achieved at least globally exponentially with the proposed protocol. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Finally, numerical examples are presented to illustrate the theoretical analysis.

  12. Robust and adaptive techniques for numerical simulation of nonlinear partial differential equations of fractional order

    Owolabi, Kolade M.

    2017-03-01

    In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE) on a finite but large spatial domain x ∈ [0, L], x = x(x , y , z) and t ∈ [0, T] are considered. Also in this work, the standard reaction-diffusion system with boundary conditions is generalized by replacing the second-order spatial derivatives with Riemann-Liouville space-fractional derivatives of order α, for 0 Fourier spectral method is introduced as a better alternative to existing low order schemes for the integration of fractional in space reaction-diffusion problems in conjunction with an adaptive exponential time differencing method, and solve a range of one-, two- and three-components SFORDE numerically to obtain patterns in one- and two-dimensions with a straight forward extension to three spatial dimensions in a sub-diffusive (0 reaction-diffusion case. With application to models in biology and physics, different spatiotemporal dynamics are observed and displayed.

  13. Vectorial control of nonlinear emission via chiral butterfly nanoantennas: generation of pure high order nonlinear vortex beams.

    Lesina, Antonino Cala'; Berini, Pierre; Ramunno, Lora

    2017-02-06

    We report on a chiral gap-nanostructure, which we term a "butterfly nanoantenna," that offers full vectorial control over nonlinear emission. The field enhancement in its gap occurs for only one circular polarization but for every incident linear polarization. As the polarization, phase and amplitude of the linear field in the gap are highly controlled, the linear field can drive nonlinear emitters within the gap, which behave as an idealized Huygens source. A general framework is thereby proposed wherein the butterfly nanoantennas can be arranged in a metasurface, and the nonlinear Huygens sources exploited to produce a highly structured far-field optical beam. Nonlinearity allows us to shape the light at shorter wavelengths, not accessible by linear plasmonics, and resulting in high purity beams. The chirality of the butterfly allows us to create orbital angular momentum states using a linearly polarized excitation. A third harmonic Laguerre-Gauss beam carrying an optical orbital angular momentum of 41 is demonstrated as an example, through large-scale simulations on a high-performance computing platform of the full plasmonic metasurface with an area large enough to contain up to 3600 nanoantennas.

  14. Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type. Part II

    Akira Shirai

    2015-01-01

    Full Text Available In this paper, we study the following nonlinear first order partial differential equation: \\[f(t,x,u,\\partial_t u,\\partial_x u=0\\quad\\text{with}\\quad u(0,x\\equiv 0.\\] The purpose of this paper is to determine the estimate of Gevrey order under the condition that the equation is singular of a totally characteristic type. The Gevrey order is indicated by the rate of divergence of a formal power series. This paper is a continuation of the previous papers [Convergence of formal solutions of singular first order nonlinear partial differential equations of totally characteristic type, Funkcial. Ekvac. 45 (2002, 187-208] and [Maillet type theorem for singular first order nonlinear partial differential equations of totally characteristic type, Surikaiseki Kenkyujo Kokyuroku, Kyoto University 1431 (2005, 94-106]. Especially the last-mentioned paper is regarded as part I of this paper.

  15. Dynamic Flight Simulation Utilizing High Fidelity CFD-Based Nonlinear Reduced Order Model, Phase II

    National Aeronautics and Space Administration — The Nonlinear Dynamic Flight Simulation (NL-DFS) system will be developed in the Phase II project by combining the classical nonlinear rigid-body flight dynamics...

  16. 1/N-expansion of the non-linear σ-model: The first three orders

    Flyvbjerg, H.; Varsted, S.

    1990-01-01

    The two-point function of the O(N)-symmetric non-linear σ-model is expanded in 1/N, keeping terms of three leading orders. The mass gap and the magnetic susceptibility are obtained from the two-point function. They are evaluated on square lattices for N=3 and N=4. The systematic errors of the 1/N-series truncated after the first, second, or third term are found by using recent high precision Monte Carlo results as bench marks. For all three truncations, we find systematic errors which are smaller than the expected magnitude of neglected terms, both for the mass gap and for the susceptibility. This result is uniform in the inverse coupling β, and valid for N as small as 3. We conclude that the 1/N-series approach the exact results as rapidly as one could ever hope for. (orig.)

  17. Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

    El-Beltagy, Mohamed A.; Al-Mulla, Noah

    2014-01-01

    Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

  18. Higher-order Solution of Stochastic Diffusion equation with Nonlinear Losses Using WHEP technique

    El-Beltagy, Mohamed A.

    2014-01-06

    Using Wiener-Hermite expansion with perturbation (WHEP) technique in the solution of the stochastic partial differential equations (SPDEs) has the advantage of converting the problem to a system of deterministic equations that can be solved efficiently using the standard deterministic numerical methods [1]. The Wiener-Hermite expansion is the only known expansion that handles the white/colored noise exactly. The main statistics, such as the mean, covariance, and higher order statistical moments, can be calculated by simple formulae involving only the deterministic Wiener-Hermite coefficients. In this poster, the WHEP technique is used to solve the 2D diffusion equation with nonlinear losses and excited with white noise. The solution will be obtained numerically and will be validated and compared with the analytical solution that can be obtained from any symbolic mathematics package such as Mathematica.

  19. Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay

    Zhonghai Guo

    2012-01-01

    Full Text Available We study the following second order mixed nonlinear impulsive differential equations with delay (r(tΦα(x′(t′+p0(tΦα(x(t+∑i=1npi(tΦβi(x(t-σ=e(t, t≥t0, t≠τk,x(τk+=akx(τk, x'(τk+=bkx'(τk, k=1,2,…, where Φ*(u=|u|*-1u, σ is a nonnegative constant, {τk} denotes the impulsive moments sequence, and τk+1-τk>σ. Some sufficient conditions for the interval oscillation criteria of the equations are obtained. The results obtained generalize and improve earlier ones. Two examples are considered to illustrate the main results.

  20. Toward a scalable flexible-order model for 3D nonlinear water waves

    Engsig-Karup, Allan Peter; Ducrozet, Guillaume; Bingham, Harry B.

    For marine and coastal applications, current work are directed toward the development of a scalable numerical 3D model for fully nonlinear potential water waves over arbitrary depths. The model is high-order accurate, robust and efficient for large-scale problems, and support will be included...... for flexibility in the description of structures by the use of curvilinear boundary-fitted meshes. The mathematical equations for potential waves in the physical domain is transformed through $\\sigma$-mapping(s) to a time-invariant boundary-fitted domain which then becomes a basis for an efficient solution...... strategy on a time-invariant mesh. The 3D numerical model is based on a finite difference method as in the original works \\cite{LiFleming1997,BinghamZhang2007}. Full details and other aspects of an improved 3D solution can be found in \\cite{EBL08}. The new and improved approach for three...

  1. A third-order asymptotic solution of nonlinear standing water waves in Lagrangian coordinates

    Yang-Yih, Chen; Hung-Chu, Hsu

    2009-01-01

    Asymptotic solutions up to third-order which describe irrotational finite amplitude standing waves are derived in Lagrangian coordinates. The analytical Lagrangian solution that is uniformly valid for large times satisfies the irrotational condition and the pressure p = 0 at the free surface, which is in contrast with the Eulerian solution existing under a residual pressure at the free surface due to Taylor's series expansion. In the third-order Lagrangian approximation, the explicit parametric equation and the Lagrangian wave frequency of water particles could be obtained. In particular, the Lagrangian mean level of a particle motion that is a function of vertical label is found as a part of the solution which is different from that in an Eulerian description. The dynamic properties of nonlinear standing waves in water of a finite depth, including particle trajectory, surface profile and wave pressure are investigated. It is also shown that the Lagrangian solution is superior to an Eulerian solution of the same order for describing the wave shape and the kinematics above the mean water level. (general)

  2. Creating large second-order optical nonlinearity in optical waveguides written by femtosecond laser pulses in boro-aluminosilicate glass

    An, Hong-Lin; Arriola, Alexander; Gross, Simon; Fuerbach, Alexander; Withford, Michael J.; Fleming, Simon

    2014-01-01

    The thermal poling technique was applied to optical waveguides embedded in a commercial boro-aluminosilicate glass, resulting in high levels of induced second-order optical nonlinearity. The waveguides were fabricated using the femtosecond laser direct-write technique, and thermally poled samples were characterized with second harmonic optical microscopy to reveal the distribution profile of the induced nonlinearity. It was found that, in contrast to fused silica, the presence of waveguides in boro-aluminosilicate glass led to an enhancement of the creation of the second-order nonlinearity, which is larger in the laser written waveguiding regions when compared to the un-modified substrate. The magnitude of the nonlinear coefficient d33 achieved in the core of the laser-written waveguides, up to 0.2 pm/V, was comparable to that in thermally poled fused silica, enabling the realization of compact integrated electro-optic devices in boro-aluminosilicate glasses.

  3. Stochastic Parameter Estimation of Non-Linear Systems Using Only Higher Order Spectra of the Measured Response

    Vasta, M.; Roberts, J. B.

    1998-06-01

    Methods for using fourth order spectral quantities to estimate the unknown parameters in non-linear, randomly excited dynamic systems are developed. Attention is focused on the case where only the response is measurable and the excitation is unmeasurable and known only in terms of a stochastic process model. The approach is illustrated through application to a non-linear oscillator with both non-linear damping and stiffness and with excitation modelled as a stationary Gaussian white noise process. The methods have applications in studies of the response of structures to random environmental loads, such as wind and ocean wave forces.

  4. Nonlinear Phenomena in the Single-Mode Dynamics in an AFM Cantilever Beam

    Ruzziconi, Laura

    2016-12-05

    This study deals with the nonlinear dynamics arising in an atomic force microscope cantilever beam. After analyzing the static behavior, a single degree of freedom Galerkin reduced order model is introduced, which describes the overall scenario of the structure response in a neighborhood of the primary resonance. Extensive numerical simulations are performed when both the forcing amplitude and frequency are varied, ranging from low up to elevated excitations. The coexistence of competing attractors with different characteristics is analyzed. Both the non-resonant and the resonant behavior are observed, as well as ranges of inevitable escape. Versatility of behavior is highlighted, which may be attractive in applications. Special attention is devoted to the effects of the tip-sample separation distance, since this aspect is of fundamental importance to understand the operation of an AFM. We explore the metamorphoses of the multistability region when the tip-sample separation distance is varied. To have a complete description of the AFM response, comprehensive behavior charts are introduced to detect the theoretical boundaries of appearance and disappearance of the main attractors. Also, extensive numerical simulations investigate the AFM response when both the forcing amplitude and the tip-sample separation distance are considered as control parameters. The main features are analyzed in detail and the obtained results are interpreted in terms of oscillations of the cantilever-tip ensemble. However, we note that all the aforementioned results represent the limit when disturbances are absent, which never occurs in practice. Here comes the importance of overcoming local investigations and exploring dynamics from a global perspective, by introducing dynamical integrity concepts. To extend the AFM results to the practical case where disturbances exist, we develop a dynamical integrity analysis. After performing a systematic basin of attraction analysis, integrity

  5. Nonlinear free vibration of single walled Carbone NanoTubes conveying fluid

    Azrar A.

    2014-04-01

    Full Text Available Nonlinear free vibration of single-walled carbon nanotubes (CNTs conveying fluid are modeled and numerically simulated based on von Kármán geometric nonlinearity and Eringen’s nonlocal elasticity theory. The CNTs are modelled as nanobeams where the effects of transverse shear deformation and rotary inertia are considered within the framework of Timoshenko beam theory. The governing equations and boundary conditions are derived using the Hamilton’s principle and the nonlinear equation of motion is solved by the Galerkin’s method. The small scale parameter and the fluid-tube interaction effects on the dynamic behaviours of the CNT-fluid system as well as the instabilities induced by the fluid-velocity can be investigated. The critical fluid-velocity and frequency-amplitude relationships as well as the flutter and divergence instability types and the associated time responses are obtained based on the presented methodological approach.

  6. Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion

    Xian-Qiong, Zhong; An-Ping, Xiang

    2010-01-01

    Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the case of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity. (classical areas of phenomenology)

  7. Optimal Decision-Making in Fuzzy Economic Order Quantity (EOQ Model under Restricted Space: A Non-Linear Programming Approach

    M. Pattnaik

    2013-08-01

    Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.

  8. Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay

    Xia Huang

    2013-01-01

    Full Text Available A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.

  9. Light-induced second-order nonlinear optical properties of molecular materials

    Fiorini, Celine

    1995-01-01

    We present a theoretical and experimental study of all-optical orientation. The work focusses more particularly on the realization of poled polymers for quadratic nonlinear optics. It is shown that the coherent superposition of two beams at fundamental and second harmonic frequencies results in the breaking of the former centro-symmetry of the material. The source is a Neodymium-YAG laser delivering 25 ps pulses at 1064 nm. The incident second-harmonic beam is obtained by frequency doubling in a KDP crystal. Using a phase conjugation configuration based on six-wave mixing interactions, we have Investigated in detail the mechanism of photo-induced second-harmonic generation in initially centrosymmetric materials. It is shown that the light-induced non-centro-symmetry is due to an orientational hole burning of the molecules. The process involves interference effects between one and two photon absorptions. Experiments are performed in various solutions of an azo-dye molecule (Disperse Red One). The possibility of inducing quasi-permanent second-order susceptibility in a PMMA polymer matrix doped with the azo-dye molecule of Disperse Red One is also demonstrated. The method of all-optical poling consists in a seeding type process with alternate writing and probing phases. Permanent orientation of the molecules can be described in terms of photo-isomerization processes. It leads to a poling of the molecules with a spatial modulation which is phase-matched for frequency doubling. Relevant parameters leading to an efficient polarisation of the sample are identified. A theoretical modelling of the different phenomena observed is proposed. Last part of the study is devoted to an enlarged study of the potentialities offered by this dual-frequency holography technique: orientation of octupolar molecules, polarisation of highly transparent materials. We also show that the new techniques developed during this work can also reveal to be complementary methods for nonlinear

  10. Stability of a nonlinear second order equation under parametric bounded noise excitation

    Wiebe, Richard; Xie, Wei-Chau

    2016-01-01

    The motivation for the following work is a structural column under dynamic axial loads with both deterministic (harmonic transmitted forces from the surrounding structure) and random (wind and/or earthquake) loading components. The bounded noise used herein is a sinusoid with an argument composed of a random (Wiener) process deviation about a mean frequency. By this approach, a noise parameter may be used to investigate the behavior through the spectrum from simple harmonic forcing, to a bounded random process with very little harmonic content. The stability of both the trivial and non-trivial stationary solutions of an axially-loaded column (which is modeled as a second order nonlinear equation) under parametric bounded noise excitation is investigated by use of Lyapunov exponents. Specifically the effect of noise magnitude, amplitude of the forcing, and damping on stability of a column is investigated. First order averaging is employed to obtain analytical approximations of the Lyapunov exponents of the trivial solution. For the non-trivial stationary solution however, the Lyapunov exponents are obtained via Monte Carlo simulation as the stability equations become analytically intractable. (paper)

  11. Mechano-optic logic gate controlled by third-order nonlinear optical properties in a rotating ZnO:Au thin film

    Carrillo-Delgado, C; Torres-Torres, C; García-Merino, J A; García-Gil, C I; Khomenko, A V; Trejo-Valdez, M; Martínez-Gutiérrez, H; Torres-Martínez, R

    2016-01-01

    Measurements of the third-order nonlinear optical properties exhibited by a ZnO thin solid film deposited on a SnO 2 substrate are presented. The samples were prepared by a spray pyrolysis processing route. Scanning electron microscopy analysis and UV–Vis spectroscopy studies were carried out. The picosecond response at 1064 nm was explored by the z-scan technique. A large optical Kerr effect with two-photon absorption was obtained. The inhibition of the nonlinear optical absorption together with a noticeable enhancement in the optical Kerr effect in the sample was achieved by the incorporation of Au nanoparticles into the ZnO film. Additionally, a two-wave mixing configuration at 532 nm was performed and an optical Kerr effect was identified as the main cause of the nanosecond third-order optical nonlinearity. The relaxation time of the photothermal response of the sample was estimated to be about 1 s when the sample was excited by nanosecond single-shots. The rotation of the sample during the nanosecond two-wave mixing experiments was analyzed. It was stated that a non-monotonic relation between rotating frequency and pulse repetition rate governs the thermal contribution to the nonlinear refractive index exhibited by a rotating film. Potential applications for switching photothermal interactions in rotating samples can be contemplated. A rotary logic system dependent on Kerr transmittance in a two-wave mixing experiment was proposed. (paper)

  12. Analytical results for a conditional phase shift between single-photon pulses in a nonlocal nonlinear medium

    Viswanathan, Balakrishnan; Gea-Banacloche, Julio

    2018-03-01

    It has been suggested that second-order nonlinearities could be used for quantum logic at the single-photon level. Specifically, successive two-photon processes in principle could accomplish the phase shift (conditioned on the presence of two photons in the low-frequency modes) |011 〉→i |100 〉→-|011 〉 . We have analyzed a recent scheme proposed by Xia et al. [Phys. Rev. Lett. 116, 023601 (2016)], 10.1103/PhysRevLett.116.023601 to induce such a conditional phase shift between two single-photon pulses propagating at different speeds through a nonlinear medium with a nonlocal response. We present here an analytical solution for the most general case, i.e., for an arbitrary response function, initial state, and pulse velocity, which supports their numerical observation that a π phase shift with unit fidelity is possible, in principle, in an appropriate limit. We also discuss why this is possible in this system, despite the theoretical objections to the possibility of conditional phase shifts on single photons that were raised some time ago by Shapiro [Phys. Rev. A 73, 062305 (2006)], 10.1103/PhysRevA.73.062305 and by Gea-Banacloche [Phys. Rev. A 81, 043823 (2010)], 10.1103/PhysRevA.81.043823 one of us.

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

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

    2017-01-01

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

  14. Support-Vector-Machine-Based Reduced-Order Model for Limit Cycle Oscillation Prediction of Nonlinear Aeroelastic System

    Gang Chen

    2012-01-01

    Full Text Available It is not easy for the system identification-based reduced-order model (ROM and even eigenmode based reduced-order model to predict the limit cycle oscillation generated by the nonlinear unsteady aerodynamics. Most of these traditional ROMs are sensitive to the flow parameter variation. In order to deal with this problem, a support vector machine- (SVM- based ROM was investigated and the general construction framework was proposed. The two-DOF aeroelastic system for the NACA 64A010 airfoil in transonic flow was then demonstrated for the new SVM-based ROM. The simulation results show that the new ROM can capture the LCO behavior of the nonlinear aeroelastic system with good accuracy and high efficiency. The robustness and computational efficiency of the SVM-based ROM would provide a promising tool for real-time flight simulation including nonlinear aeroelastic effects.

  15. Two (multi point nonlinear Lyapunov systems associated with an n th order nonlinear system of differential equations – existence and uniqueness

    Murty K. N.

    2000-01-01

    Full Text Available This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with an n th order nonlinear Lyapunov system. A variation of parameters formula is developed and used as a tool to obtain existence and uniqueness. We discuss solution of the second order problem by the ADI method and develop a fixed point method to find the general solution of the n th order Lyapunov system. The results of Barnett (SIAM J. Appl. Anal. 24(1, 1973 are a particular case.

  16. Self-Similar Nanocavity Design with Ultrasmall Mode Volume for Single-Photon Nonlinearities

    Choi, Hyeongrak; Heuck, Mikkel; Englund, Dirk R.

    2017-01-01

    We propose a photonic crystal nanocavity design with self-similar electromagnetic boundary conditions, achieving ultrasmall mode volume (V-eff). The electric energy density of a cavity mode can be maximized in the air or dielectric region, depending on the choice of boundary conditions. We illust...... at the single-photon level. These features open new directions in cavity quantum electrodynamics, spectroscopy, and quantum nonlinear optics....

  17. ONIOM Investigation of the Second-Order Nonlinear Optical Responses of Fluorescent Proteins.

    de Wergifosse, Marc; Botek, Edith; De Meulenaere, Evelien; Clays, Koen; Champagne, Benoît

    2018-05-17

    The first hyperpolarizability (β) of six fluorescent proteins (FPs), namely, enhanced green fluorescent protein, enhanced yellow fluorescent protein, SHardonnay, ZsYellow, DsRed, and mCherry, has been calculated to unravel the structure-property relationships on their second-order nonlinear optical properties, owing to their potential for multidimensional biomedical imaging. The ONIOM scheme has been employed and several of its refinements have been addressed to incorporate efficiently the effects of the microenvironment on the nonlinear optical responses of the FP chromophore that is embedded in a protective β-barrel protein cage. In the ONIOM scheme, the system is decomposed into several layers (here two) treated at different levels of approximation (method1/method2), from the most elaborated method (method1) for its core (called the high layer) to the most approximate one (method2) for the outer surrounding (called the low layer). We observe that a small high layer can already account for the variations of β as a function of the nature of the FP, provided the low layer is treated at an ab initio level to describe properly the effects of key H-bonds. Then, for semiquantitative reproduction of the experimental values obtained from hyper-Rayleigh scattering experiments, it is necessary to incorporate electron correlation as described at the second-order Møller-Plesset perturbation theory (MP2) level as well as implicit solvent effects accounted for using the polarizable continuum model (PCM). This led us to define the MP2/6-31+G(d):HF/6-31+G(d)/IEFPCM scheme as an efficient ONIOM approach and the MP2/6-31+G(d):HF/6-31G(d)/IEFPCM as a better compromise between accuracy and computational needs. Using these methods, we demonstrate that many parameters play a role on the β response of FPs, including the length of the π-conjugated segment, the variation of the bond length alternation, and the presence of π-stacking interactions. Then, noticing the small diversity

  18. Efficient Estimation of Extreme Non-linear Roll Motions using the First-order Reliability Method (FORM)

    Jensen, Jørgen Juncher

    2007-01-01

    In on-board decision support systems efficient procedures are needed for real-time estimation of the maximum ship responses to be expected within the next few hours, given on-line information on the sea state and user defined ranges of possible headings and speeds. For linear responses standard...... frequency domain methods can be applied. To non-linear responses like the roll motion, standard methods like direct time domain simulations are not feasible due to the required computational time. However, the statistical distribution of non-linear ship responses can be estimated very accurately using...... the first-order reliability method (FORM), well-known from structural reliability problems. To illustrate the proposed procedure, the roll motion is modelled by a simplified non-linear procedure taking into account non-linear hydrodynamic damping, time-varying restoring and wave excitation moments...

  19. Single-pulse CARS based multimodal nonlinear optical microscope for bioimaging.

    Kumar, Sunil; Kamali, Tschackad; Levitte, Jonathan M; Katz, Ori; Hermann, Boris; Werkmeister, Rene; Považay, Boris; Drexler, Wolfgang; Unterhuber, Angelika; Silberberg, Yaron

    2015-05-18

    Noninvasive label-free imaging of biological systems raises demand not only for high-speed three-dimensional prescreening of morphology over a wide-field of view but also it seeks to extract the microscopic functional and molecular details within. Capitalizing on the unique advantages brought out by different nonlinear optical effects, a multimodal nonlinear optical microscope can be a powerful tool for bioimaging. Bringing together the intensity-dependent contrast mechanisms via second harmonic generation, third harmonic generation and four-wave mixing for structural-sensitive imaging, and single-beam/single-pulse coherent anti-Stokes Raman scattering technique for chemical sensitive imaging in the finger-print region, we have developed a simple and nearly alignment-free multimodal nonlinear optical microscope that is based on a single wide-band Ti:Sapphire femtosecond pulse laser source. Successful imaging tests have been realized on two exemplary biological samples, a canine femur bone and collagen fibrils harvested from a rat tail. Since the ultra-broad band-width femtosecond laser is a suitable source for performing high-resolution optical coherence tomography, a wide-field optical coherence tomography arm can be easily incorporated into the presented multimodal microscope making it a versatile optical imaging tool for noninvasive label-free bioimaging.

  20. Dynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation

    Karpman, V.I.; Juul Rasmussen, J.; Shagalov, A.G.

    2001-01-01

    The dynamics of soliton and quasisoliton solutions of the cubic third-order nonlinear Schrodinger equation is studied. Regular solitons exist due to a balance between the nonlinear terms and (linear) third-order dispersion; they are not important at small alpha (3) (alpha (3) is the coefficient...... in the third derivative term) and vanish at alpha3 -->0. The most essential, at small alpha (3), is a quasisoliton emitting resonant radiation (resonantly radiating soliton). Its relationship with the other (steady) quasisoliton, called embedded soliton, is studied analytically and also in numerical...

  1. The role of dendritic non-linearities in single neuron computation

    Boris Gutkin

    2014-05-01

    Full Text Available Experiment has demonstrated that summation of excitatory post-synaptic protientials (EPSPs in dendrites is non-linear. The sum of multiple EPSPs can be larger than their arithmetic sum, a superlinear summation due to the opening of voltage-gated channels and similar to somatic spiking. The so-called dendritic spike. The sum of multiple of EPSPs can also be smaller than their arithmetic sum, because the synaptic current necessarily saturates at some point. While these observations are well-explained by biophysical models the impact of dendritic spikes on computation remains a matter of debate. One reason is that dendritic spikes may fail to make the neuron spike; similarly, dendritic saturations are sometime presented as a glitch which should be corrected by dendritic spikes. We will provide solid arguments against this claim and show that dendritic saturations as well as dendritic spikes enhance single neuron computation, even when they cannot directly make the neuron fire. To explore the computational impact of dendritic spikes and saturations, we are using a binary neuron model in conjunction with Boolean algebra. We demonstrate using these tools that a single dendritic non-linearity, either spiking or saturating, combined with somatic non-linearity, enables a neuron to compute linearly non-separable Boolean functions (lnBfs. These functions are impossible to compute when summation is linear and the exclusive OR is a famous example of lnBfs. Importantly, the implementation of these functions does not require the dendritic non-linearity to make the neuron spike. Next, We show that reduced and realistic biophysical models of the neuron are capable of computing lnBfs. Within these models and contrary to the binary model, the dendritic and somatic non-linearity are tightly coupled. Yet we show that these neuron models are capable of linearly non-separable computations.

  2. Single Polygon Counting on Cayley Tree of Order 3

    Pah, Chin Hee

    2010-07-01

    We showed that one form of generalized Catalan numbers is the solution to the problem of finding different connected component with finite vertices containing a fixed root for the semi-infinite Cayley tree of order 3. We give the formula for the full graph, Cayley tree of order 3 which is derived from the generalized Catalan numbers. Using ratios of Gamma functions, two upper bounds are given for problem defined on semi-infinite Cayley tree of order 3 as well as the full graph.

  3. Crystal growth and characterization of a semiorganic nonlinear optical single crystal of gamma glycine

    Prakash, J. Thomas Joseph; Kumararaman, S.

    2008-01-01

    Gamma glycine has been successfully synthesized by taking glycine and potassium chloride and single crystals have been grown by solvent evaporation method for the first time. The grown single crystals have been analyzed with XRD, Fourier transform infrared (FTIR), and thermo gravimetric and differential thermal analyses (TG/DTA) measurements. Its mechanical behavior has been assessed by Vickers microhardness measurements. Its nonlinear optical property has been tested by Kurtz powder technique. Its optical behavior was examined by UV-vis., and found that the crystal is transparent in the region between 240 and 1200 nm. Hence, it may be very much useful for the second harmonic generation (SHG) applications

  4. Dye molecules as single-photon sources and large optical nonlinearities on a chip

    Hwang, J; Hinds, E A

    2011-01-01

    We point out that individual organic dye molecules, deposited close to optical waveguides on a photonic chip, can act as single-photon sources. A thin silicon nitride strip waveguide is expected to collect 28% of the photons from a single dibenzoterrylene molecule. These molecules can also provide large, localized optical nonlinearities, which are enough to discriminate between one photon or two through a differential phase shift of 2 0 per photon. This new atom-photon interface may be used as a resource for processing quantum information.

  5. Growth and characterization of nonlinear optical single crystal: Nicotinic L-tartaric

    Sheelarani, V.; Shanthi, J., E-mail: shanthinelson@gmail.com [Department of Physics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore-641043 (India)

    2015-06-24

    Nonlinear optical single crystals were grown from Nicotinic and L-Tartaric acid by slow evaporation technique at room temperature. Structure of the grown crystal was confirmed by single crystal X-ray diffraction studies, The crystallinity of the Nicotinic L-Tartaric (NLT) crystals was confirmed from the powder XRD pattern. The transparent range and cut off wavelength of the grown crystal was studied by the UV–Vis spectroscopic analysis.The thermal stability of the crystal was studied by TG-DTA. The second harmonic generation (SHG) efficiency of NLT was confirmed by Kurtz Perry technique.

  6. Modulation stability and optical soliton solutions of nonlinear Schrödinger equation with higher order dispersion and nonlinear terms and its applications

    Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

    2017-12-01

    In optical fibers, the higher order non-linear Schrödinger equation (NLSE) with cubic quintic nonlinearity describes the propagation of extremely short pulses. We constructed bright and dark solitons, solitary wave and periodic solitary wave solutions of generalized higher order NLSE in cubic quintic non Kerr medium by applying proposed modified extended mapping method. These obtained solutions have key applications in physics and mathematics. Moreover, we have also presented the formation conditions on solitary wave parameters in which dark and bright solitons can exist for this media. We also gave graphically the movement of constructed solitary wave and soliton solutions, that helps to realize the physical phenomena's of this model. The stability of the model in normal dispersion and anomalous regime is discussed by using the modulation instability analysis, which confirms that all constructed solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method.

  7. Linear and nonlinear Stability analysis for finite difference discretizations of higher order Boussinesq equations

    Fuhrmann, David R.; Bingham, Harry B.; Madsen, Per A.

    2004-01-01

    of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water nonlinearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into into the numerical behavior of this rather complicated system of nonlinear PDEs....

  8. Transparent Higher Order Sliding Mode Control for Nonlinear Master-Slave Systems without Velocity Measurement

    Luis G. Garcia-Valdovinos

    2015-04-01

    Full Text Available Transparency has been a major objective in bilateral teleoperation systems, even in the absence of time delay induced by the communication channel, since a high degree of transparency would allow humans to drive the remote teleoperator as if he or she were directly interacting with the remote environment, with the remote teleoperator as a physical and sensorial extension of the operator. When fast convergence of position and force tracking errors are ensured by the control system, then complete transparency is obtained, which would ideally guarantee humans to be tightly kinaesthetically coupled. In this paper a model-free Cartesian second order sliding mode (SOSM PD control scheme for nonlinear master-slave systems is presented. The proposed scheme does not rely on velocity measurements and attains very fast convergence of position trajectories, with bounded tracking of force trajectories, rendering a high degree of transparency with lesser knowledge of the system. The degree of transparency can easily be improved by tuning a feedback gain in the force loop. A unique energy storage function is introduced; such that a similar Cartesian-based controller is implemented in the master and slave sides. The resulting properties of the Cartesian control structure allows the human operator to input directly Cartesian variables, which makes clearer the kinaesthetic coupling, thus the proposed controller becomes a suitable candidate for practical implementation. The performance of the proposed scheme is evaluated in a semi-experimental setup.

  9. Nonlinear fractional differential equations and inclusions of arbitrary order and multi-strip boundary conditions

    Bashir Ahmad

    2012-06-01

    Full Text Available We study boundary value problems of nonlinear fractional differential equations and inclusions of order $q in (m-1, m]$, $m ge 2$ with multi-strip boundary conditions. Multi-strip boundary conditions may be regarded as the generalization of multi-point boundary conditions. Our problem is new in the sense that we consider a nonlocal strip condition of the form: $$ x(1=sum_{i=1}^{n-2}alpha_i int^{eta_i}_{zeta_i} x(sds, $$ which can be viewed as an extension of a multi-point nonlocal boundary condition: $$ x(1=sum_{i=1}^{n-2}alpha_i x(eta_i. $$ In fact, the strip condition corresponds to a continuous distribution of the values of the unknown function on arbitrary finite segments $(zeta_i,eta_i$ of the interval $[0,1]$ and the effect of these strips is accumulated at $x=1$. Such problems occur in the applied fields such as wave propagation and geophysics. Some new existence and uniqueness results are obtained by using a variety of fixed point theorems. Some illustrative examples are also discussed.

  10. Non-linear phenomena in electronic systems consisting of coupled single-electron oscillators

    Kikombo, Andrew Kilinga; Hirose, Tetsuya; Asai, Tetsuya; Amemiya, Yoshihito

    2008-01-01

    This paper describes non-linear dynamics of electronic systems consisting of single-electron oscillators. A single-electron oscillator is a circuit made up of a tunneling junction and a resistor, and produces simple relaxation oscillation. Coupled with another, single electron oscillators exhibit complex behavior described by a combination of continuous differential equations and discrete difference equations. Computer simulation shows that a double-oscillator system consisting of two coupled oscillators produces multi-periodic oscillation with a single attractor, and that a quadruple-oscillator system consisting of four oscillators also produces multi-periodic oscillation but has a number of possible attractors and takes one of them determined by initial conditions

  11. A modified stochastic averaging method on single-degree-of-freedom strongly nonlinear stochastic vibrations

    Ge, Gen; Li, ZePeng

    2016-01-01

    A modified stochastic averaging method on single-degree-of-freedom (SDOF) oscillators under white noise excitations with strongly nonlinearity was proposed. Considering the existing approach dealing with strongly nonlinear SDOFs derived by Zhu and Huang [14, 15] is quite time consuming in calculating the drift coefficient and diffusion coefficients and the expressions of them are considerable long, the so-called He's energy balance method was applied to overcome the minor defect of the Zhu and Huang's method. The modified method can offer more concise approximate expressions of the drift and diffusion coefficients without weakening the accuracy of predicting the responses of the systems too much by giving an averaged frequency beforehand. Three examples, a cubic and quadratic nonlinearity coexisting oscillator, a quadratic nonlinear oscillator under external white noise excitations and an externally excited Duffing–Rayleigh oscillator, were given to illustrate the approach we proposed. The three examples were excited by the Gaussian white noise and the Gaussian colored noise separately. The stationary responses of probability density of amplitudes and energy, together with joint probability density of displacement and velocity are studied to verify the presented approach. The reliability of the systems were also investigated to offer further support. Digital simulations were carried out and the output of that are coincide with the theoretical approximations well.

  12. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Shahid Hasnain

    2017-07-01

    Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  13. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

    2017-07-01

    This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  14. Importance of the alignment of polar π conjugated molecules inside carbon nanotubes in determining second-order non-linear optical properties.

    Yumura, Takashi; Yamamoto, Wataru

    2017-09-20

    We employed density functional theory (DFT) calculations with dispersion corrections to investigate energetically preferred alignments of certain p,p'-dimethylaminonitrostilbene (DANS) molecules inside an armchair (m,m) carbon nanotube (n × DANS@(m,m)), where the number of inner molecules (n) is no greater than 3. Here, three types of alignments of DANS are considered: a linear alignment in a parallel fashion and stacking alignments in parallel and antiparallel fashions. According to DFT calculations, a threshold tube diameter for containing DANS molecules in linear or stacking alignments was found to be approximately 1.0 nm. Nanotubes with diameters smaller than 1.0 nm result in the selective formation of linearly aligned DANS molecules due to strong confinement effects within the nanotubes. By contrast, larger diameter nanotubes allow DANS molecules to align in a stacking and linear fashion. The type of alignment adopted by the DANS molecules inside a nanotube is responsible for their second-order non-linear optical properties represented by their static hyperpolarizability (β 0 values). In fact, we computed β 0 values of DANS assemblies taken from optimized n × DANS@(m,m) structures, and their values were compared with those of a single DANS molecule. DFT calculations showed that β 0 values of DANS molecules depend on their alignment, which decrease in the following order: linear alignment > parallel stacking alignment > antiparallel stacking alignment. In particular, a linear alignment has a β 0 value more significant than that of the same number of isolated molecules. Therefore, the linear alignment of DANS molecules, which is only allowed inside smaller diameter nanotubes, can strongly enhance their second-order non-linear optical properties. Since the nanotube confinement determines the alignment of DANS molecules, a restricted nanospace can be utilized to control their second-order non-linear optical properties. These DFT findings can assist in the

  15. Optimal explicit strong stability preserving Runge–Kutta methods with high linear order and optimal nonlinear order

    Gottlieb, Sigal; Grant, Zachary; Higgs, Daniel

    2015-01-01

    High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search

  16. ℋ- adaptive observer design and parameter identification for a class of nonlinear fractional-order systems

    Ndoye, Ibrahima

    2014-12-01

    In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown parameters are also adapted to their values. Sufficient conditions for the stability of the adaptive observer error dynamics are derived in terms of linear matrix inequalities. Simulation results for chaotic Lorenz systems with unknown parameters in the presence of external perturbations are given to illustrate the effectiveness of our proposed approach. © 2014 IEEE.

  17. Uniqueness of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations

    Tran Duc Van

    1994-01-01

    The notion of global quasi-classical solutions of the Cauchy problems for first-order nonlinear partial differential equations is presented, some uniqueness theorems and a stability result are established by the method based on the theory of differential inclusions. In particular, the answer to an open problem of S.N. Kruzhkov is given. (author). 10 refs, 1 fig

  18. A HIGH ORDER SOLUTION OF THREE DIMENSIONAL TIME DEPENDENT NONLINEAR CONVECTIVE-DIFFUSIVE PROBLEM USING MODIFIED VARIATIONAL ITERATION METHOD

    Pratibha Joshi

    2014-12-01

    Full Text Available In this paper, we have achieved high order solution of a three dimensional nonlinear diffusive-convective problem using modified variational iteration method. The efficiency of this approach has been shown by solving two examples. All computational work has been performed in MATHEMATICA.

  19. Application of He’s Variational Iteration Method to Nonlinear Helmholtz Equation and Fifth-Order KDV Equation

    Miansari, Mo; Miansari, Me; Barari, Amin

    2009-01-01

    In this article, He’s variational iteration method (VIM), is implemented to solve the linear Helmholtz partial differential equation and some nonlinear fifth-order Korteweg-de Vries (FKdV) partial differential equations with specified initial conditions. The initial approximations can be freely c...

  20. On the Asymptotic Properties of Nonlinear Third-Order Neutral Delay Differential Equations with Distributed Deviating Arguments

    Youliang Fu

    2016-01-01

    Full Text Available This paper is concerned with the asymptotic properties of solutions to a third-order nonlinear neutral delay differential equation with distributed deviating arguments. Several new theorems are obtained which ensure that every solution to this equation either is oscillatory or tends to zero. Two illustrative examples are included.

  1. The behavior of steady quasisolitons near the limit cases of third-order nonlinear Schrödinger equation

    Karpman, V.I.; Shagalov, A.G.; Juul Rasmussen, J.

    2002-01-01

    The behavior of steady quasisoliton solutions to the extended third-order nonlinear Schrodinger (NLS) equation is studied in two cases: (i) when the coefficients in the equation approach the Hirota conditions, and (ii) near the limit of the regular NLS equation. (C) 2002 Published by Elsevier...

  2. Nonlinear evolution of single spike structure and vortex in Richtmeyer-Meshkov instability

    Fukuda, Yuko O.; Nishihara, Katsunobu; Okamoto, Masayo; Nagatomo, Hideo; Matsuoka, Chihiro; Ishizaki, Ryuichi; Sakagami, Hitoshi

    1999-01-01

    Nonlinear evolution of single spike structure and vortex in the Richtmyer-Meshkov instability is investigated for two dimensional case, and axial symmetric and non axial symmetric cases with the use of a three-dimensional hydrodynamic code. It is shown that singularity appears in the vorticity left by transmitted and reflected shocks at a corrugated interface. This singularity results in opposite sign of vorticity along the interface that causes double spiral structure of the spike. Difference of nonlinear growth rate and double spiral structure among three cases is also discussed by visualization of simulation data. In a case that there is no slip-off of initial spike axis, vorticity ring is relatively stable, but phase rotation occurs. (author)

  3. Studies on third-order optical nonlinearity and power limiting of conducting polymers using the z-scan technique for nonlinear optical applications

    Pramodini, S; Poornesh, P; Sudhakar, Y N; SelvaKumar, M

    2014-01-01

    We present the synthesis and characterization of third-order optical nonlinearity and optical limiting of the conducting polymers poly (aniline-co-o-anisidine) and poly (aniline-co-pyrrole). Nonlinear optical studies were carried out by employing the z-scan technique using a He–Ne laser operating in continuous wave mode at 633 nm. The copolymers exhibited a reverse saturable absorption process and self-defocusing properties under the experimental conditions. The estimated values of β eff , n 2 and χ (3) were found to be of the order of 10 −2  cm W −1 , 10 -5  esu and 10 −7  esu respectively. Self-diffraction rings were observed due to refractive index change when exposed to the laser beam. The copolymers possess a lower limiting threshold and clamping level, which is essential to a great extent for power limiting devices. Therefore, copolymers of aniline emerge as a potential candidate for nonlinear optical device applications. (paper)

  4. ℋ∞ Adaptive observer for nonlinear fractional-order systems

    Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed; Voos, Holger

    2016-01-01

    inequalities (LMIs) by using an indirect Lyapunov method.The proposed ℋ∞ adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü

  5. Stabilization of the higher order nonlinear Schrödinger equation with ...

    18

    self-steepening and delayed nonlinear response effect arising from stimulated Raman s- cattering ... The method is a power series expansion of the solution along this direction. ..... The proof of Theorem 1.1 is motivated by [12, 13]. Proof.

  6. Unbounded Perturbations of Nonlinear Second-Order Difference Equations at Resonance

    Ma Ruyun

    2007-01-01

    Full Text Available We study the existence of solutions of nonlinear discrete boundary value problems , , , where is the first eigenvalue of the linear problem , , , satisfies some “asymptotic nonuniform” resonance conditions, and for .

  7. An Efficient Reduced-Order Model for the Nonlinear Dynamics of Carbon Nanotubes

    Xu, Tiantian; Younis, Mohammad I.

    2014-01-01

    Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction

  8. PD/PID controller tuning based on model approximations: Model reduction of some unstable and higher order nonlinear models

    Christer Dalen

    2017-10-01

    Full Text Available A model reduction technique based on optimization theory is presented, where a possible higher order system/model is approximated with an unstable DIPTD model by using only step response data. The DIPTD model is used to tune PD/PID controllers for the underlying possible higher order system. Numerous examples are used to illustrate the theory, i.e. both linear and nonlinear models. The Pareto Optimal controller is used as a reference controller.

  9. Maximal intensity higher-order Akhmediev breathers of the nonlinear Schrödinger equation and their systematic generation

    Chin, Siu A., E-mail: chin@physics.tamu.edu [Department of Physics and Astronomy, Texas A& M University, College Station, TX 77843 (United States); Ashour, Omar A. [Department of Physics and Astronomy, Texas A& M University, College Station, TX 77843 (United States); Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Nikolić, Stanko N. [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar); Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade (Serbia); Belić, Milivoj R. [Science Program, Texas A& M University at Qatar, P.O. Box 23874 Doha (Qatar)

    2016-10-23

    It is well known that Akhmediev breathers of the nonlinear cubic Schrödinger equation can be superposed nonlinearly via the Darboux transformation to yield breathers of higher order. Surprisingly, we find that the peak height of each Akhmediev breather only adds linearly to form the peak height of the final breather. Using this peak-height formula, we show that at any given periodicity, there exists a unique high-order breather of maximal intensity. Moreover, these high-order breathers form a continuous hierarchy, growing in intensity with increasing periodicity. For any such higher-order breather, a simple initial wave function can be extracted from the Darboux transformation to dynamically generate that breather from the nonlinear Schrödinger equation. - Highlights: • Proved an analytical formula for the peak-height of an nth-order Akhmediev breather. • Constructed nth-order Akhmediev breathers of maximal peak intensity. • Extracted initial wave functions that can be used experimentally to produce these maximal breathers in optical fibers.

  10. Large third-order optical nonlinearity in vertically oriented mesoporous silica thin films embedded with Ag nanoparticles

    Tan, Min; Liu, Qiming, E-mail: qmliu@whu.edu.cn [Wuhan University, Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, School of Physics and Technology (China)

    2016-12-15

    Taking advantage of the channel confinement of mesoporous films to prevent the agglomeration of Ag nanoparticles to achieve large third-order optical nonlinearity in amorphous materials, Ag-loaded composite mesoporous silica film was prepared by the electrochemical deposition method on ITO substrate. Ag ions were firstly transported into the channels of mesoporous film by the diffusion and binding force of channels, which were reduced to nanoparticles by applying suitable voltage. The existence and uniform distribution of Ag nanoparticles ranging in 1–10 nm in the mesoporous silica thin films were exhibited by UV spectrophotometer, X-ray powder diffraction (XRD), transmission electron microscopy (TEM), and X-ray photoelectron spectroscopy (XPS) measurements. The third-order optical nonlinearity induced by Ag nanoparticles was studied by the Z-scan technique. Due to the local field surface plasmon resonance, the maximum third-order nonlinear optical susceptibility of Ag-loaded composite mesoporous silica film is 1.53×10{sup −10} esu, which is 1000 times larger than that of the Ag-contained chalcogenide glasses which showed large nonlinearity in amorphous materials.

  11. Third-order nonlinear optical properties of GeSe2-Ga2Se3-PbI2 glasses

    Tang Gao; Liu Cunming; Luo Lan; Chen Wei

    2010-01-01

    The third-order nonlinear optical (NLO) properties of new selenium-based GeSe 2 -Ga 2 Se 3 -PbI 2 glasses have been measured using the optical Kerr effect (OKE) technique, with picosecond and femtosecond laser pulses. The 0.70GeSe 2 -0.15Ga 2 Se 3 -0.15PbI 2 glass has the largest third-order optical nonlinear susceptibility in GeSe 2 -Ga 2 Se 3 -PbI 2 glass system with χ (3) of 5.28x10 12 esu. In addition, the response time of glasses is sub-picosecond, which is predominantly associated with electron cloud. Local structure of the glasses has been identified by using Raman studies, while the origins of the observed nonlinear optical response are discussed. The [Ge(Ga)Se 4 ] tetrahedral and lone-pair electrons from highly polarizable Pb atom in glasses play an important role in enhanced NLO response. These results as well as their good chemical stability indicate that GeSe 2 -Ga 2 Se 3 -PbI 2 glasses are promising materials for photonic applications of third-order nonlinear optical signal processing.

  12. Role of third-order dispersion in chirped Airy pulse propagation in single-mode fibers

    Cai, Wangyang; Wang, Lei; Wen, Shuangchun

    2018-04-01

    The dynamic propagation of the initial chirped Airy pulse in single-mode fibers is studied numerically, special attention being paid to the role of the third-order dispersion (TOD). It is shown that for the positive TOD, the Airy pulse experiences inversion irrespective of the sign of initial chirp. The role of TOD in the dynamic propagation of the initial chirped Airy pulse depends on the combined sign of the group-velocity dispersion (GVD) and the initial chirp. If the GVD and chirp have the opposite signs, the chirped Airy pulse compresses first and passes through a breakdown area, then reconstructs a new Airy pattern with opposite acceleration, with the breakdown area becoming small and the main peak of the new Airy pattern becoming asymmetric with an oscillatory structure due to the positive TOD. If the GVD and chirp have the same signs, the finite-energy Airy pulse compresses to a focal point and then inverses its acceleration, in the case of positive TOD, the distance to the focal point becoming smaller. At zero-dispersion point, the finite-energy Airy pulse inverses to the opposite acceleration at a focal point, with the tight-focusing effect being reduced by initial chirp. Under the effect of negative TOD, the initial chirped Airy pulse disperses and the lobes split. In addition, in the anomalous dispersion region, for strong nonlinearity, the initial chirped Airy pulse splits and enters a soliton shedding regime.

  13. A study of single multiplicative neuron model with nonlinear filters for hourly wind speed prediction

    Wu, Xuedong; Zhu, Zhiyu; Su, Xunliang; Fan, Shaosheng; Du, Zhaoping; Chang, Yanchao; Zeng, Qingjun

    2015-01-01

    Wind speed prediction is one important methods to guarantee the wind energy integrated into the whole power system smoothly. However, wind power has a non–schedulable nature due to the strong stochastic nature and dynamic uncertainty nature of wind speed. Therefore, wind speed prediction is an indispensable requirement for power system operators. Two new approaches for hourly wind speed prediction are developed in this study by integrating the single multiplicative neuron model and the iterated nonlinear filters for updating the wind speed sequence accurately. In the presented methods, a nonlinear state–space model is first formed based on the single multiplicative neuron model and then the iterated nonlinear filters are employed to perform dynamic state estimation on wind speed sequence with stochastic uncertainty. The suggested approaches are demonstrated using three cases wind speed data and are compared with autoregressive moving average, artificial neural network, kernel ridge regression based residual active learning and single multiplicative neuron model methods. Three types of prediction errors, mean absolute error improvement ratio and running time are employed for different models’ performance comparison. Comparison results from Tables 1–3 indicate that the presented strategies have much better performance for hourly wind speed prediction than other technologies. - Highlights: • Developed two novel hybrid modeling methods for hourly wind speed prediction. • Uncertainty and fluctuations of wind speed can be better explained by novel methods. • Proposed strategies have online adaptive learning ability. • Proposed approaches have shown better performance compared with existed approaches. • Comparison and analysis of two proposed novel models for three cases are provided

  14. Communication: atomic force detection of single-molecule nonlinear optical vibrational spectroscopy.

    Saurabh, Prasoon; Mukamel, Shaul

    2014-04-28

    Atomic Force Microscopy (AFM) allows for a highly sensitive detection of spectroscopic signals. This has been first demonstrated for NMR of a single molecule and recently extended to stimulated Raman in the optical regime. We theoretically investigate the use of optical forces to detect time and frequency domain nonlinear optical signals. We show that, with proper phase matching, the AFM-detected signals closely resemble coherent heterodyne-detected signals. Applications are made to AFM-detected and heterodyne-detected vibrational resonances in Coherent Anti-Stokes Raman Spectroscopy (χ((3))) and sum or difference frequency generation (χ((2))).

  15. Development of nonperturbative nonlinear optics models including effects of high order nonlinearities and of free electron plasma: Maxwell–Schrödinger equations coupled with evolution equations for polarization effects, and the SFA-like nonlinear optics model

    Lorin, E; Bandrauk, A D; Lytova, M; Memarian, A

    2015-01-01

    This paper is dedicated to the exploration of non-conventional nonlinear optics models for intense and short electromagnetic fields propagating in a gas. When an intense field interacts with a gas, usual nonlinear optics models, such as cubic nonlinear Maxwell, wave and Schrödinger equations, derived by perturbation theory may become inaccurate or even irrelevant. As a consequence, and to include in particular the effect of free electrons generated by laser–molecule interaction, several heuristic models, such as UPPE, HOKE models, etc, coupled with Drude-like models [1, 2], were derived. The goal of this paper is to present alternative approaches based on non-heuristic principles. This work is in particular motivated by the on-going debate in the filamentation community, about the effect of high order nonlinearities versus plasma effects due to free electrons, in pulse defocusing occurring in laser filaments [3–9]. The motivation of our work goes beyond filamentation modeling, and is more generally related to the interaction of any external intense and (short) pulse with a gas. In this paper, two different strategies are developed. The first one is based on the derivation of an evolution equation on the polarization, in order to determine the response of the medium (polarization) subject to a short and intense electromagnetic field. Then, we derive a combined semi-heuristic model, based on Lewenstein’s strong field approximation model and the usual perturbative modeling in nonlinear optics. The proposed model allows for inclusion of high order nonlinearities as well as free electron plasma effects. (paper)

  16. ℋ∞ Adaptive observer for nonlinear fractional-order systems

    Ndoye, Ibrahima

    2016-06-23

    In this paper, an adaptive observer is proposed for the joint estimation of states and parameters of a fractional nonlinear system with external perturbations. The convergence of the proposed observer is derived in terms of linear matrix inequalities (LMIs) by using an indirect Lyapunov method.The proposed ℋ∞ adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü\\'s systems. © 2016 John Wiley & Sons, Ltd.

  17. Traveling solitary wave solutions to evolution equations with nonlinear terms of any order

    Feng Zhaosheng

    2003-01-01

    Many physical phenomena in one- or higher-dimensional space can be described by nonlinear evolution equations, which can be reduced to ordinary differential equations such as the Lienard equation. Thus, to study those ordinary differential equations is of significance not only in mathematics itself, but also in physics. In this paper, a kind of explicit exact solutions to the Lienard equation is obtained. The applications of the solutions to the nonlinear RR-equation and the compound KdV-type equation are presented, which extend the results obtained in the previous literature

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

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

    2015-09-01

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

  19. Interacting wave fronts and rarefaction waves in a second order model of nonlinear thermoviscous fluids : Interacting fronts and rarefaction waves

    Rasmussen, Anders Rønne; Sørensen, Mads Peter; Gaididei, Yuri Borisovich

    2011-01-01

    A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hami...... is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation. © 2010 Springer Science+Business Media B.V.......A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves...... the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions...

  20. The mixed BVP for second order nonlinear ordinary differential equation at resonance

    Mukhigulashvili, Sulkhan

    2017-01-01

    Roč. 290, 2-3 (2017), s. 393-400 ISSN 0025-584X Institutional support: RVO:67985840 Keywords : mixed problem at resonance * nonlinear ordinary differencial equation Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.742, year: 2016

  1. Higher order criterion for the nonexistence of formal first integral for nonlinear systems

    Zhiguo Xu

    2017-11-01

    Full Text Available The main purpose of this article is to find a criterion for the nonexistence of formal first integrals for nonlinear systems under general resonance. An algorithm illustrates an application to a class of generalized Lokta-Volterra systems. Our result generalize the classical Poincare's nonintegrability theorem and the existing results in the literature.

  2. New Chiral Bis-Dipolar 6,6'-Disubstituted-Binaphthol Derivatives for Second-Order Nonlinear Optics

    Deussen, Heinz-Josef; Boutton, Carlo; Thorup, Niels

    1998-01-01

    (S)everal chiral molecules with C-2 symmetry derived from two geometries of the binaphthol (BN) system substituted with different accepters have been synthesized in order to study the possibility of producing noncentrosymmetric crystals formed from these chiral structures. All the molecules possess...... cancel out exactly despite the noncentrosymmetry. The crystal structure of racemic 9,14-dicyanodinaphtho[2,1-d:1',2'-f][1,3]-dioxepin (2b) was found to be centrosymmetric. The new compounds were investigated for second-harmonic generation (including BN derivatives reported earlier) by the Kurtz......-Perry powder test to evaluate the second-order nonlinear optical (NLO) properties of polycrystalline samples. Although chirality ensures noncentrosymmetric crystals, only modest (approximate to 2-methyl-4-nitroaniline) or no nonlinearities were observed in the powder test, For a representative selection...

  3. A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives

    Duan Jun-Sheng

    2017-12-01

    Full Text Available We conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative. For each of the two vibration systems, we consider the stiffness contribution factor and damping contribution factor of the term of fractional derivatives, the amplitude and the phase difference for the response. The effects of driving frequency on these response quantities are discussed. Also the influences of the order α of the fractional derivative and the parameter γ parameterizing the weight function in the distributed-order derivative are analyzed. Two cases display similar response behaviors, but the stiffness contribution factor and damping contribution factor of the distributed-order derivative are almost monotonic change with the parameter γ, not exactly like the case of single fractional-order derivative for the order α. The case of the distributed-order derivative provides us more options for the weight function and parameters.

  4. On the Painleve integrability, periodic wave solutions and soliton solutions of generalized coupled higher-order nonlinear Schroedinger equations

    Xu Guiqiong; Li Zhibin

    2005-01-01

    It is proven that generalized coupled higher-order nonlinear Schroedinger equations possess the Painleve property for two particular choices of parameters, using the Weiss-Tabor-Carnevale method and Kruskal's simplification. Abundant families of periodic wave solutions are obtained by using the Jacobi elliptic function expansion method with the assistance of symbolic manipulation system, Maple. It is also shown that these solutions exactly degenerate to bright soliton, dark soliton and mixed dark and bright soliton solutions with physical interests

  5. Nonlinear perturbations of differential operators with nontrivial kernel and applications to third order periodic boundary value problems

    Afuwape, A.U.; Omari, P.

    1987-11-01

    This paper deals with the solvability of the nonlinear operator equations in normed spaces Lx=EGx+f, where L is a linear map with possible nontrivial kernel. Applications are given to the existence of periodic solutions for the third order scalar differential equation x'''+ax''+bx'+cx+g(t,x)=p(t), under various conditions on the interaction of g(t,x)/x with spectral configurations of a, b and c. (author). 48 refs

  6. High-order nonlinear optical processes in ablated carbon-containing materials: Recent approaches in development of the nonlinear spectroscopy using harmonic generation in the extreme ultraviolet range

    Ganeev, R. A.

    2017-08-01

    The nonlinear spectroscopy using harmonic generation in the extreme ultraviolet range became a versatile tool for the analysis of the optical, structural and morphological properties of matter. The carbon-contained materials have shown the advanced properties among other studied species, which allowed both the definition of the role of structural properties on the nonlinear optical response and the analysis of the fundamental features of carbon as the attractive material for generation of coherent short-wavelength radiation. We review the studies of the high-order harmonic generation by focusing ultrashort pulses into the plasmas produced during laser ablation of various organic compounds. We discuss the role of ionic transitions of ablated carbon-containing molecules on the harmonic yield. We also show the similarities and distinctions of the harmonic and plasma spectra of organic compounds and graphite. We discuss the studies of the generation of harmonics up to the 27th order (λ = 29.9 nm) of 806 nm radiation in the boron carbide plasma and analyze the advantages and disadvantages of this target compared with the ingredients comprising B4C (solid boron and graphite) by comparing plasma emission and harmonic spectra from three species. We also show that the coincidence of harmonic and plasma emission wavelengths in most cases does not cause the enhancement or decrease of the conversion efficiency of this harmonic.

  7. Investigation of inorganic nonlinear optical potassium penta borate tetra hydrate (PPBTH) single crystals grown by slow evaporation method

    Arivuselvi, R.; Babu, P. Ramesh

    2018-03-01

    Borates family crystals were plays vital role in the field of non linear optics (NLO) due to needs of wide range of applications. In this report, NLO crystals (potassium penta borate tetra hydrate (KB5H8O12) are grown by slow evaporation method at room temperature (28° C) and studied their physical properties. The harvested single crystals are transparent with the dimension of 12 × 10 × 6 mm3 and colourless. X-ray diffraction of single crystals reveals that the grown crystal belongs to orthorhombic system with non-centrosymmetric space group Pba2. All the absorbed functional groups are present in the order of inorganic compounds expect 1688 cm-1 because of water (Osbnd H sbnd O blending) molecule present in the pristine. Crystals show transparent in the entire visible region with 5.9 eV optical band gap and also it shows excellence in both second and third order nonlinear optical properties. Crystals can withstand upto 154 °C without any phase changes which is observed using thermal (TGA/DTA) analysis.

  8. Nonlinear Optical Properties of XPh4 (X = B-, C, N+, P+): A New Class of Molecules with a Negative Third-Order Polarizability

    Gieseking, Rebecca L.

    2015-06-22

    Organic π-conjugated materials have been widely used for a variety of nonlinear optical (NLO) applications. Molecules with negative real components Re(γ) of the third-order polarizability, which leads to nonlinear refraction in macroscopic systems, have important benefits for several NLO applications. However, few organic systems studied to date have negative Re(γ) in the long wavelength limit, and all inorganic materials show positive nonlinear refraction in this limit. Here, we introduce a new class of molecules of the form X(C6H5)4, where X = B-, C, N+, and P+, that have negative Re(γ). The molecular mechanism for the NLO properties in these systems is very different from those in typical linear conjugated systems: these systems have a band of excited states involving single-electron excitations within the π-system, several of which have significant coupling to the ground state. Thus, Re(γ) cannot be understood in terms of a simplified essential-state model and must be analyzed in the context of the full sum-over-states expression. Although Re(γ) is significantly smaller than that of other commonly-studied NLO chromophores, the introduction of a new molecular architecture offering the potential for a negative Re(γ) introduces new avenues of molecular design for NLO applications.

  9. Nonlinear Optical Properties of XPh4 (X = B-, C, N+, P+): A New Class of Molecules with a Negative Third-Order Polarizability

    Gieseking, Rebecca L.; Ensley, Trenton R.; Hu, Honghua; Hagan, David J.; Risko, Chad; Van Stryland, Eric W.; Bredas, Jean-Luc

    2015-01-01

    Organic π-conjugated materials have been widely used for a variety of nonlinear optical (NLO) applications. Molecules with negative real components Re(γ) of the third-order polarizability, which leads to nonlinear refraction in macroscopic systems, have important benefits for several NLO applications. However, few organic systems studied to date have negative Re(γ) in the long wavelength limit, and all inorganic materials show positive nonlinear refraction in this limit. Here, we introduce a new class of molecules of the form X(C6H5)4, where X = B-, C, N+, and P+, that have negative Re(γ). The molecular mechanism for the NLO properties in these systems is very different from those in typical linear conjugated systems: these systems have a band of excited states involving single-electron excitations within the π-system, several of which have significant coupling to the ground state. Thus, Re(γ) cannot be understood in terms of a simplified essential-state model and must be analyzed in the context of the full sum-over-states expression. Although Re(γ) is significantly smaller than that of other commonly-studied NLO chromophores, the introduction of a new molecular architecture offering the potential for a negative Re(γ) introduces new avenues of molecular design for NLO applications.

  10. Efficient nonlinear registration of 3D images using high order co-ordinate transfer functions.

    Barber, D C

    1999-01-01

    There is an increasing interest in image registration for a variety of medical imaging applications. Image registration is achieved through the use of a co-ordinate transfer function (CTF) which maps voxels in one image to voxels in the other image, including in the general case changes in mapped voxel intensity. If images of the same subject are to be registered the co-ordinate transfer function needs to implement a spatial transformation consisting of a displacement and a rigid rotation. In order to achieve registration a common approach is to choose a suitable quality-of-registration measure and devise a method for the efficient generation of the parameters of the CTF which minimize this measure. For registration of images from different subjects more complex transforms are required. In general function minimization is too slow to allow the use of CTFs with more than a small number of parameters. However, provided the images are from the same modality and the CTF can be expanded in terms of an appropriate set of basis functions this paper will show how relatively complex CTFs can be used for registration. The use of increasingly complex CTFs to minimize the within group standard deviation of a set of normal single photon emission tomography brain images is used to demonstrate the improved registration of images from different subjects using CTFs of increasing complexity.

  11. Growth, structural, thermal, dielectric and nonlinear optical properties of potassium hexachloro cadmate (IV) a novel single crystal

    Umarani, P.; Jagannathan, K.

    2018-02-01

    The Potassium hexachloro cadmate (IV) (PHC) single crystal was grown from the aqueous of the solution by a controlled evaporation method. Single crystal XRD solved the structure. FTIR is used to identify the functional groups of grown crystal. The UV-Vis-NIR spectrometer was used to find out the UV cut off region and to calculate the optical band gap of the Potassium hexachloro cadmate (IV) single crystal. The EDAX spectrum has been used to identify the compounds present in title compound. The TG-DTA profile shows the thermal stability of the grown crystal of Potassium hexachloro cadmate (IV). The Vicker's hardness measurement was used to calculate the material hardness of the title compound. The dielectric loss and constant varied with frequencies and activation energy is also calculated. The solid state parameters like plasma energy, Penn gap, Fermi energy, electronic polarizability using Penn analysis and Clausius-Mossotti equation were also calculated for the title compound. The Z-scan technique is used to calculate the third order nonlinear susceptibility of a real and imaginary part.

  12. Third-order optical nonlinearities in bulk and fs-laser inscribed waveguides in strengthened alkali aluminosilcate glass

    Almeida, Gustavo F. B.; Almeida, Juliana M. P.; Martins, Renato J.; De Boni, Leonardo; Arnold, Craig B.; Mendonca, Cleber R.

    2018-01-01

    The development of advanced photonics devices requires materials with large optical nonlinearities, fast response times and high optical transparency, while at the same time allowing for the micro/nano-processing needed for integrated photonics. In this context, glasses have been receiving considerable attention given their relevant optical properties which can be specifically tailored by compositional control. Corning Gorilla® Glass (strengthened alkali aluminosilicate glass) is well-known for its use as a protective screen in mobile devices, and has attracted interest as a potential candidate for optical devices. Therefore, it is crucial not only to expand the knowledge on the fabrication of waveguides in Gorilla Glass under different regimes, but also to determine its nonlinear optical response, both using fs-laser pulses. Thus, this paper reports, for the first time, characterization of the third-order optical nonlinearities of Gorilla Glass, as well as linear and nonlinear characterization of waveguide written with femtosecond pulses under the low repetition rate regime (1 kHz).

  13. Solving nonlinear, High-order partial differential equations using a high-performance isogeometric analysis framework

    Cortes, Adriano Mauricio; Vignal, Philippe; Sarmiento, Adel; Garcí a, Daniel O.; Collier, Nathan; Dalcin, Lisandro; Calo, Victor M.

    2014-01-01

    In this paper we present PetIGA, a high-performance implementation of Isogeometric Analysis built on top of PETSc. We show its use in solving nonlinear and time-dependent problems, such as phase-field models, by taking advantage of the high-continuity of the basis functions granted by the isogeometric framework. In this work, we focus on the Cahn-Hilliard equation and the phase-field crystal equation.

  14. On periodic bounded and unbounded solutions of second order nonlinear ordinary differential equations

    Lomtatidze, Alexander

    2017-01-01

    Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2017-0009/gmj-2017-0009.xml

  15. Wave propagation in ordered, disordered, and nonlinear photonic band gap materials

    Lidorikis, Elefterios [Iowa State Univ., Ames, IA (United States)

    1999-12-10

    Photonic band gap materials are artificial dielectric structures that give the promise of molding and controlling the flow of optical light the same way semiconductors mold and control the electric current flow. In this dissertation the author studied two areas of photonic band gap materials. The first area is focused on the properties of one-dimensional PBG materials doped with Kerr-type nonlinear material, while, the second area is focused on the mechanisms responsible for the gap formation as well as other properties of two-dimensional PBG materials. He first studied, in Chapter 2, the general adequacy of an approximate structure model in which the nonlinearity is assumed to be concentrated in equally-spaced very thin layers, or 6-functions, while the rest of the space is linear. This model had been used before, but its range of validity and the physical reasons for its limitations were not quite clear yet. He performed an extensive examination of many aspects of the model's nonlinear response and comparison against more realistic models with finite-width nonlinear layers, and found that the d-function model is quite adequate, capturing the essential features in the transmission characteristics. The author found one exception, coming from the deficiency of processing a rigid bottom band edge, i.e. the upper edge of the gaps is always independent of the refraction index contrast. This causes the model to miss-predict that there are no soliton solutions for a positive Kerr-coefficient, something known to be untrue.

  16. On periodic bounded and unbounded solutions of second order nonlinear ordinary differential equations

    Lomtatidze, Alexander

    2017-01-01

    Roč. 24, č. 2 (2017), s. 241-263 ISSN 1072-947X Institutional support: RVO:67985840 Keywords : nonlinear ordinary differential equations * periodic boundary value problem * solvability Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.290, year: 2016 https://www.degruyter.com/view/j/gmj.2017.24.issue-2/gmj-2017-0009/gmj-2017-0009. xml

  17. Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions

    Weiguo Rui

    2014-01-01

    Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.

  18. Construction of a single/multiple wavelength RZ optical pulse source at 40 GHz by use of wavelength conversion in a high-nonlinearity DSF-NOLM

    Yu, Jianjun; Yujun, Qian; Jeppesen, Palle

    2001-01-01

    A single or multiple wavelength RZ optical pulse source at 40 GHz is successfully obtained by using wavelength conversion in a nonlinear optical loop mirror consisting of high nonlinearity-dispersion shifted fiber.......A single or multiple wavelength RZ optical pulse source at 40 GHz is successfully obtained by using wavelength conversion in a nonlinear optical loop mirror consisting of high nonlinearity-dispersion shifted fiber....

  19. Nonlinear optical susceptibilities in the diffusion modified AlxGa1-xN/GaN single quantum well

    Das, T.; Panda, S.; Panda, B. K.

    2018-05-01

    Under thermal treatment of the post growth AlGaN/GaN single quantum well, the diffusion of Al and Ga atoms across the interface is expected to form the diffusion modified quantum well with diffusion length as a quantitative parameter for diffusion. The modification of confining potential and position-dependent effective mass in the quantum well due to diffusion is calculated taking the Fick's law. The built-in electric field which arises from spontaneous and piezoelectric polarizations in the wurtzite structure is included in the effective mass equation. The electronic states are calculated from the effective mass equation using the finite difference method for several diffusion lengths. Since the effective well width decreases with increasing diffusion length, the energy levels increase with it. The intersubband energy spacing in the conduction band decreases with diffusion length due to built-in electric field and reduction of effective well width. The linear susceptibility for first-order and the nonlinear second-order and third-order susceptibilities are calculated using the compact density matrix approach taking only two levels. The calculated susceptibilities are red shifted with increase in diffusion lengths due to decrease in intersubband energy spacing.

  20. Nonlinear Dynamic Model of Power Plants with Single-Phase Coolant Reactors

    Vollmer, H.

    1968-12-01

    The traditional way of developing dynamic models for a specific nuclear power plant and for specific purpose seems rather uneconomical, as much of the information often can not be utilized if the plant design or the required accuracy of the calculation is desired to be changed. It is therefore suggested that the model development may be made more systematic, general and flexible by - applying the 'box of bricks' system, where the main components of a nuclear power plant are treated separately and combined afterwards according to a given flow scheme, - a dynamic determination of the components which is as general as possible without taking into account those details which have a minor influence on the overall dynamics, - providing approximations of the more rigorous solution sufficient to meet the user s requirements on accuracy, - proper use of computers. A dynamic model for single-phase coolant reactor plants is established along these lines. By separation of the nonlinear and linear parts of the system, application of Laplace transformation and proper approximations, and the use of a hybrid computer it seems possible to determine the (nonlinear) dynamic behaviour of such a plant for perturbations which are not so large that phase changes of physical parameters occur, e. g. fuel does not melt. The model is applied to a steam cooled fast reactor power plant

  1. Nonlinear Dynamic Model of Power Plants with Single-Phase Coolant Reactors

    Vollmer, H

    1968-12-15

    The traditional way of developing dynamic models for a specific nuclear power plant and for specific purpose seems rather uneconomical, as much of the information often can not be utilized if the plant design or the required accuracy of the calculation is desired to be changed. It is therefore suggested that the model development may be made more systematic, general and flexible by - applying the 'box of bricks' system, where the main components of a nuclear power plant are treated separately and combined afterwards according to a given flow scheme, - a dynamic determination of the components which is as general as possible without taking into account those details which have a minor influence on the overall dynamics, - providing approximations of the more rigorous solution sufficient to meet the user s requirements on accuracy, - proper use of computers. A dynamic model for single-phase coolant reactor plants is established along these lines. By separation of the nonlinear and linear parts of the system, application of Laplace transformation and proper approximations, and the use of a hybrid computer it seems possible to determine the (nonlinear) dynamic behaviour of such a plant for perturbations which are not so large that phase changes of physical parameters occur, e. g. fuel does not melt. The model is applied to a steam cooled fast reactor power plant.

  2. Piezoelectric Field Enhanced Second-Order Nonlinear Optical Susceptibilities in Wurtzite GaN/AlGaN Quantum Wells

    Liu, Ansheng; Chuang, S.-L.; Ning, C. Z.; Woo, Alex (Technical Monitor)

    1999-01-01

    Second-order nonlinear optical processes including second-harmonic generation, optical rectification, and difference-frequency generation associated with intersubband transitions in wurtzite GaN/AlGaN quantum well (QW) are investigated theoretically. Taking into account the strain-induced piezoelectric (PZ) effects, we solve the electronic structure of the QW from coupled effective-mass Schrodinger equation and Poisson equation including the exchange-correlation effect under the local-density approximation. We show that the large PZ field in the QW breaks the symmetry of the confinement potential profile and leads to large second-order susceptibilities. We also show that the interband optical pump-induced electron-hole plasma results in an enhancement in the maximum value of the nonlinear coefficients and a redshift of the peak position in the nonlinear optical spectrum. By use of the difference-frequency generation, THz radiation can be generated from a GaN/Al(0.75)Ga(0.25)N with a pump laser of 1.55 micron.

  3. A novel condition for stable nonlinear sampled-data models using higher-order discretized approximations with zero dynamics.

    Zeng, Cheng; Liang, Shan; Xiang, Shuwen

    2017-05-01

    Continuous-time systems are usually modelled by the form of ordinary differential equations arising from physical laws. However, the use of these models in practice and utilizing, analyzing or transmitting these data from such systems must first invariably be discretized. More importantly, for digital control of a continuous-time nonlinear system, a good sampled-data model is required. This paper investigates the new consistency condition which is weaker than the previous similar results presented. Moreover, given the stability of the high-order approximate model with stable zero dynamics, the novel condition presented stabilizes the exact sampled-data model of the nonlinear system for sufficiently small sampling periods. An insightful interpretation of the obtained results can be made in terms of the stable sampling zero dynamics, and the new consistency condition is surprisingly associated with the relative degree of the nonlinear continuous-time system. Our controller design, based on the higher-order approximate discretized model, extends the existing methods which mainly deal with the Euler approximation. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  4. Rogue wave train generation in a metamaterial induced by cubic-quintic nonlinearities and second-order dispersion

    Essama, Bedel Giscard Onana; Atangana, Jacques; Frederick, Biya Motto; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Kofane, Timoleon Crepin

    2014-09-01

    We investigate the behavior of the electromagnetic wave that propagates in a metamaterial for negative index regime. Second-order dispersion and cubic-quintic nonlinearities are taken into account. The behavior obtained for negative index regime is compared to that observed for absorption regime. The collective coordinates technique is used to characterize the light pulse intensity profile at some frequency ranges. Five frequency ranges have been pointed out. The perfect combination of second-order dispersion and cubic nonlinearity leads to a robust soliton at each frequency range for negative index regime. The soliton peak power progressively decreases for absorption regime. Further, this peak power also decreases with frequency. We show that absorption regime can induce rogue wave trains generation at a specific frequency range. However, this rogue wave trains generation is maintained when the quintic nonlinearity comes into play for negative index regime and amplified for absorption regime at a specific frequency range. It clearly appears that rogue wave behavior strongly depends on the frequency and the regime considered. Furthermore, the stability conditions of the electromagnetic wave have also been discussed at frequency ranges considered for both negative index and absorption regimes.

  5. Nonlinear dynamics and chaos in a fractional-order financial system

    Chen Weiching

    2008-01-01

    This study examines the two most attractive characteristics, memory and chaos, in simulations of financial systems. A fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The fractional-order financial system displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in fractional-order financial systems with orders less than 3. In this study, the lowest order at which this system yielded chaos was 2.35. Period doubling and intermittency routes to chaos in the fractional-order financial system were found

  6. Adaptive nonlinear control of single-phase to three-phase UPS system

    Kissaoui M.

    2014-01-01

    Full Text Available This work deals with the problems of uninterruptible power supplies (UPS based on the single-phase to three-phase converters built in two stages: an input bridge rectifier and an output three phase inverter. The two blocks are joined by a continuous intermediate bus. The objective of control is threefold: i power factor correction “PFC”, ii generating a symmetrical three-phase system at the output even if the load is unknown, iii regulating the DC bus voltage. The synthesis of controllers has been reached by two nonlinear techniques that are the sliding mode and adaptive backstepping control. The performances of regulators have been validated by numerical simulation in MATLAB / SIMULINK.

  7. Single-particle And Collective Effects Of Cubic Nonlinearity In The Beam Dynamics Of Proton Synchrotrons

    Tran Hy, J

    1998-01-01

    This thesis describes some new studies of the effects of cubic nonlinearities arising from image-charge forces and octupole magnets on the transverse beam dynamics of proton synchrotrons and storage rings, and also a study of the damping of coherent oscillations using a feed-back damper. In the latter case, various corrective algorithms were modeled using linear one-turn maps. Kicks of fixed amplitude but appropriate sign were shown to provide linear damping and no coherent tune shift, though the rate predicted analytically was somewhat higher than that observed in simulations. This algorithm gave much faster damping (for equal power) than conventional proportional kicks, which damp exponentially. Two single-particle effects of the image-change force were investigated: distortion of the momentum dispersion function and amplitude dependence of the betatron tunes (resulting in tune spread). The former is calculated using transfer maps and the method of undetermined coefficients, the latter by solving the cubic ...

  8. Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability

    Yan, R.; Aluie, H.; Betti, R.; Sanz, J.; Liu, B.; Frank, A.

    2016-01-01

    The nonlinear evolution of the single-mode ablative Rayleigh-Taylor instability is studied in three dimensions. As the mode wavelength approaches the cutoff of the linear spectrum (short-wavelength modes), it is found that the three-dimensional (3D) terminal bubble velocity greatly exceeds both the two-dimensional (2D) value and the classical 3D bubble velocity. Unlike in 2D, the 3D short-wavelength bubble velocity does not saturate. The growing 3D bubble acceleration is driven by the unbounded accumulation of vorticity inside the bubble. The vorticity is transferred by mass ablation from the Rayleigh-Taylor spikes to the ablated plasma filling the bubble volume

  9. Probabilistically cloning two single-photon states using weak cross-Kerr nonlinearities

    Zhang, Wen; Rui, Pinshu; Zhang, Ziyun; Yang, Qun

    2014-01-01

    By using quantum nondemolition detectors (QNDs) based on weak cross-Kerr nonlinearities, we propose an experimental scheme for achieving 1→2 probabilistic quantum cloning (PQC) of a single-photon state, secretly choosing from a two-state set. In our scheme, after a QND is performed on the to-be-cloned photon and the assistant photon, a single-photon projection measurement is performed by a polarization beam splitter (PBS) and two single-photon trigger detectors (SPTDs). The measurement is to judge whether the PQC should be continued. If the cloning fails, a cutoff is carried out and some operations are omitted. This makes our scheme economical. If the PQC is continued according to the measurement result, two more QNDs and some unitary operations are performed on the to-be-cloned photon and the cloning photon to achieve the PQC in a nearly deterministic way. Our experimental scheme for PQC is feasible for future technology. Furthermore, the quantum logic network of our PQC scheme is presented. In comparison with similar networks, our PQC network is simpler and more economical. (paper)

  10. Nonlinear Dynamics of Memristor Based 2nd and 3rd Order Oscillators

    Talukdar, Abdul Hafiz

    2011-01-01

    Exceptional behaviours of Memristor are illustrated in Memristor based second order (Wien oscillator) and third order (phase shift oscillator) oscillator systems in this Thesis. Conventional concepts about sustained oscillation have been argued

  11. Stochastic change detection in uncertain nonlinear systems using reduced-order models: classification

    Yun, Hae-Bum; Masri, Sami F

    2009-01-01

    A reliable structural health monitoring methodology (SHM) is proposed to detect relatively small changes in uncertain nonlinear systems. A total of 4000 physical tests were performed using a complex nonlinear magneto-rheological (MR) damper. With the effective (or 'genuine') changes and uncertainties in the system characteristics of the semi-active MR damper, which were precisely controlled with known means and standard deviation of the input current, the tested MR damper was identified with the restoring force method (RFM), a non-parametric system identification method involving two-dimensional orthogonal polynomials. Using the identified RFM coefficients, both supervised and unsupervised pattern recognition techniques (including support vector classification and k-means clustering) were employed to detect system changes in the MR damper. The classification results showed that the identified coefficients with orthogonal basis function can be used as reliable indicators for detecting (small) changes, interpreting the physical meaning of the detected changes without a priori knowledge of the monitored system and quantifying the uncertainty bounds of the detected changes. The classification errors were analyzed using the standard detection theory to evaluate the performance of the developed SHM methodology. An optimal classifier design procedure was also proposed and evaluated to minimize type II (or 'missed') errors

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

    Hesthaven, J. S.; Ubbiali, S.

    2018-06-01

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

  13. Microstructure evolution to reach the single variant in an ordered Fe–55at.%Pd alloy

    Farjami, Sahar; Fukuda, Takashi; Kakeshita, Tomoyuki

    2013-01-01

    Highlights: ► We confirmed formation of the single variant in Fe–55at.%Pd by XRD measurement and TEM observation. ► The size of each ordered domain is about 2 nm at the early stage of ordering. ► High density of antiphase boundaries has been observed after formation of the single variant. -- Abstract: Recently, we reported single variant formation in an Fe–55at.%Pd is certainly realized from a disordered fcc-phase to an ordered L1 0 -phase by heat-treatment under magnetic field. In the present study, we have investigated microstructure evolution during the process of the single variant formation by an X-ray diffraction and an electron microscopy observation. As a result, followings are obtained: size of the ordered particles at the early stage of ordering is about 2 nm and the nucleation ratio of preferable variant, whose easy axis lies in the field direction, is higher than that of other variants. Each of the ordered preferable variant grows by consuming the order variants and finally come together to become a single variant. Based on the observation, a model is proposed for the single variant formation of the ordered L1 0 -phase under magnetic field

  14. Single-step emulation of nonlinear fiber-optic link with gaussian mixture model

    Borkowski, Robert; Doberstein, Andy; Haisch, Hansjörg

    2015-01-01

    We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission.......We use a fast and low-complexity statistical signal processing method to emulate nonlinear noise in fiber links. The proposed emulation technique stands in good agreement with the numerical NLSE simulation for 32 Gbaud DP-16QAM nonlinear transmission....

  15. An economic order quantity model with nonlinear holding cost, partial backlogging and ramp-type demand

    San-José, Luis A.; Sicilia, Joaquín; González-de-la-Rosa, Manuel; Febles-Acosta, Jaime

    2018-07-01

    In this article, a deterministic inventory model with a ramp-type demand depending on price and time is developed. The cumulative holding cost is assumed to be a nonlinear function of time. Shortages are allowed and are partially backlogged. Thus, the fraction of backlogged demand depends on the waiting time and on the stock-out period. The aim is to maximize the total profit per unit time. To do this, a procedure that determines the economic lot size, the optimal inventory cycle and the maximum profit is presented. The inventory system studied here extends diverse inventory models proposed in the literature. Finally, some numerical examples are provided to illustrate the theoretical results previously propounded.

  16. Nonlinear model order reduction for flexible multibody dynamics: a modal derivatives approach

    Wu, Long, E-mail: L.Wu-1@tudelft.nl [Delft University of Technology, Faculty of Mechanical, Maritime and Materials Engineering (Netherlands); Tiso, Paolo, E-mail: ptiso@ethz.ch [ETH Zürich, Institute for Mechanical Systems (Switzerland)

    2016-04-15

    An effective reduction technique is presented for flexible multibody systems, for which the elastic deflection could not be considered small. We consider here the planar beam systems undergoing large elastic rotations, in the floating frame description. The proposed method enriches the classical linear reduction basis with modal derivatives stemming from the derivative of the eigenvalue problem. Furthermore, the Craig–Bampton method is applied to couple the different reduced components. Based on the linear projection, the configuration-dependent internal force can be expressed as cubic polynomials in the reduced coordinates. Coefficients of these polynomials can be precomputed for efficient runtime evaluation. The numerical results show that the modal derivatives are essential for the correct approximation of the nonlinear elastic deflection with respect to the body reference. The proposed reduction method constitutes a natural and effective extension of the classical linear modal reduction in the floating frame.

  17. Analytical study of nonlinear phase shift through stimulated Brillouin scattering in single mode fiber with the pump power recycling technique

    Al-Asadi, H A; Mahdi, M A; Bakar, A A A; Adikan, F R Mahamd

    2011-01-01

    We present a theoretical study of nonlinear phase shift through stimulated Brillouin scattering in single mode optical fiber. Analytical expressions describing the nonlinear phase shift for the pump and Stokes waves in the pump power recycling technique have been derived. The dependence of the nonlinear phase shift on the optical fiber length, the reflectivity of the optical mirror and the frequency detuning coefficient have been analyzed for different input pump power values. We found that with the recycling pump technique, the nonlinear phase shift due to stimulated Brillouin scattering reduced to less than 0.1 rad for 5 km optical fiber length and 0.65 reflectivity of the optical mirror, respectively, at an input pump power equal to 30 mW

  18. Attitude Control of a Single Tilt Tri-Rotor UAV System: Dynamic Modeling and Each Channel's Nonlinear Controllers Design

    Juing-Shian Chiou

    2013-01-01

    Full Text Available This paper has implemented nonlinear control strategy for the single tilt tri-rotor aerial robot. Based on Newton-Euler’s laws, the linear and nonlinear mathematical models of tri-rotor UAVs are obtained. A numerical analysis using Newton-Raphson method is chosen for finding hovering equilibrium point. Back-stepping nonlinear controller design is based on constructing Lyapunov candidate function for closed-loop system. By imitating the linguistic logic of human thought, fuzzy logic controllers (FLCs are designed based on control rules and membership functions, which are much less rigid than the calculations computers generally perform. Effectiveness of the controllers design scheme is shown through nonlinear simulation model on each channel.

  19. Imperfection Sensitivity of Nonlinear Vibration of Curved Single-Walled Carbon Nanotubes Based on Nonlocal Timoshenko Beam Theory

    Iman Eshraghi

    2016-09-01

    Full Text Available Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive governing equations of motion. Spatial discretization of governing equations and associated boundary conditions is performed using differential quadrature (DQ method and the corresponding nonlinear eigenvalue problem is iteratively solved. Effects of amplitude and location of the geometric imperfection, and the nonlocal small-scale parameter on the nonlinear frequency for various boundary conditions are investigated. The results show that the geometric imperfection and non-locality play a significant role in the nonlinear vibration characteristics of curved SWCNTs.

  20. Second-order kinetic model for the sorption of cadmium onto tree fern: a comparison of linear and non-linear methods.

    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.

  1. Third-order-accurate numerical methods for efficient, large time-step solutions of mixed linear and nonlinear problems

    Cobb, J.W.

    1995-02-01

    There is an increasing need for more accurate numerical methods for large-scale nonlinear magneto-fluid turbulence calculations. These methods should not only increase the current state of the art in terms of accuracy, but should also continue to optimize other desired properties such as simplicity, minimized computation, minimized memory requirements, and robust stability. This includes the ability to stably solve stiff problems with long time-steps. This work discusses a general methodology for deriving higher-order numerical methods. It also discusses how the selection of various choices can affect the desired properties. The explicit discussion focuses on third-order Runge-Kutta methods, including general solutions and five examples. The study investigates the linear numerical analysis of these methods, including their accuracy, general stability, and stiff stability. Additional appendices discuss linear multistep methods, discuss directions for further work, and exhibit numerical analysis results for some other commonly used lower-order methods.

  2. Decentralized adaptive neural control for high-order interconnected stochastic nonlinear time-delay systems with unknown system dynamics.

    Si, Wenjie; Dong, Xunde; Yang, Feifei

    2018-03-01

    This paper is concerned with the problem of decentralized adaptive backstepping state-feedback control for uncertain high-order large-scale stochastic nonlinear time-delay systems. For the control design of high-order large-scale nonlinear systems, only one adaptive parameter is constructed to overcome the over-parameterization, and neural networks are employed to cope with the difficulties raised by completely unknown system dynamics and stochastic disturbances. And then, the appropriate Lyapunov-Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown unmatched time-delay interactions of high-order large-scale systems for the first time. At last, on the basis of Lyapunov stability theory, the decentralized adaptive neural controller was developed, and it decreases the number of learning parameters. The actual controller can be designed so as to ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges in the small neighborhood of zero. The simulation example is used to further show the validity of the design method. Copyright © 2018 Elsevier Ltd. All rights reserved.

  3. Global output feedback control for a class of high-order feedforward nonlinear systems with input delay.

    Zha, Wenting; Zhai, Junyong; Fei, Shumin

    2013-07-01

    This paper investigates the problem of output feedback stabilization for a class of high-order feedforward nonlinear systems with time-varying input delay. First, a scaling gain is introduced into the system under a set of coordinate transformations. Then, the authors construct an observer and controller to make the nominal system globally asymptotically stable. Based on homogeneous domination approach and Lyapunov-Krasovskii functional, it is shown that the closed-loop system can be rendered globally asymptotically stable by the scaling gain. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.

  4. A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

    Castro-Ramírez, Joel, E-mail: ingcastro.7@gmail.com [Universidad Politécnica de Tlaxcala Av. Universidad Politecnica de Tlaxcala No.1, San Pedro Xalcaltzinco, Tepeyanco, Tlaxcala, C.P. 90180 (Mexico); Martínez-Guerra, Rafael, E-mail: rguerra@ctrl.cinvestav.mx [Departamento de Control Automático CINVESTAV-IPN, A.P. 14-740, D.F., México C.P. 07360 (Mexico); Cruz-Victoria, Juan Crescenciano, E-mail: juancrescenciano.cruz@uptlax.edu.mx [Universidad Politécnica de Tlaxcala Av. Universidad Politécnica de Tlaxcala No.1, San Pedro Xalcaltzinco, Tepeyanco, Tlaxcala, C.P. 90180 (Mexico)

    2015-10-15

    This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system.

  5. Numerical Simulation of Freak Waves Based on the Four-Order Nonlinear Schr(o)dinger Equation

    ZHANG Yun-qiu; ZHANG Ning-chuan; PEI Yu-guo

    2007-01-01

    A numerical wave model based on the modified four-order nonlinear Schrodinger (NLS) equation in deep water is developed to simulate freak waves. A standard split-step, pseudo-spectral method is used to solve NLS equation. The validation of the model is firstly verified, and then the simulation of freak waves is performed by changing sideband conditions. Results show that freak waves entirely consistent with the definition in the evolution of wave trains are obtained. The possible occurrence mechanism of freak waves is discussed and the relevant characteristics are also analyzed.

  6. Contribution of Higher-Order Dispersion to Nonlinear Electron-Acoustic Solitary Waves in a Relativistic Electron Beam Plasma System

    Zahran, M.A.; El-Shewy, E.K.

    2008-01-01

    The nonlinear properties of solitary wave structures are reported in an unmagnetized collisionless plasma comprising of cold relativistic electron fluid, Maxwellian hot electrons, relativistic electron beam, and stationary ions. The Korteweg--de Vries (KdV) equation has been derived using a reductive perturbation theory. As the wave amplitude increases, the width and velocity of the soliton deviate from the prediction of the KdV equation i.e. the breakdown of the KdV approximation. On the other hand, to overcome this weakness we extend our analysis to obtain the KdV equation with fifth-order dispersion term. The solution of the resulting equation has been obtained

  7. A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

    Castro-Ramírez, Joel; Martínez-Guerra, Rafael; Cruz-Victoria, Juan Crescenciano

    2015-01-01

    This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system

  8. The Nonlinear Behavior of Vibrational Conveyers with Single-Mass Crank-and-Rod Exciters

    G. Füsun Alışverişçi

    2012-01-01

    Full Text Available The single-mass, crank-and-rod exciters vibrational conveyers have a trough supported on elastic stands which are rigidly fastened to the trough and a supporting frame. The trough is oscillated by a common crank drive. This vibration causes the load to move forward and upward. The moving loads jump periodically and move forward with relatively small vibration. The movement is strictly related to vibrational parameters. This is applicable in laboratory conditions in the industry which accommodate a few grams of loads, up to those that accommodate tons of loading capacity. In this study I explore the transitional behavior across resonance, during the starting of a single degree of freedom vibratory system excited by crank-and-rod. A loaded vibratory conveyor is more safe to start than an empty one. Vibrational conveyers with cubic nonlinear spring and ideal vibration exciter have been analyzed analytically for primary and secondary resonance by the Method of Multiple Scales, and numerically. The approximate analytical results obtained in this study have been compared with the numerical results and have been found to be well matched.

  9. Non-linear effects and thermoelectric efficiency of quantum dot-based single-electron transistors.

    Talbo, Vincent; Saint-Martin, Jérôme; Retailleau, Sylvie; Dollfus, Philippe

    2017-11-01

    By means of advanced numerical simulation, the thermoelectric properties of a Si-quantum dot-based single-electron transistor operating in sequential tunneling regime are investigated in terms of figure of merit, efficiency and power. By taking into account the phonon-induced collisional broadening of energy levels in the quantum dot, both heat and electrical currents are computed in a voltage range beyond the linear response. Using our homemade code consisting in a 3D Poisson-Schrödinger solver and the resolution of the Master equation, the Seebeck coefficient at low bias voltage appears to be material independent and nearly independent on the level broadening, which makes this device promising for metrology applications as a nanoscale standard of Seebeck coefficient. Besides, at higher voltage bias, the non-linear characteristics of the heat current are shown to be related to the multi-level effects. Finally, when considering only the electronic contribution to the thermal conductance, the single-electron transistor operating in generator regime is shown to exhibit very good efficiency at maximum power.

  10. Fractional-Order Control of a Nonlinear Time-Delay System: Case Study in Oxygen Regulation in the Heart-Lung Machine

    S. J. Sadati

    2012-01-01

    Full Text Available A fractional-order controller will be proposed to regulate the inlet oxygen into the heart-lung machine. An analytical approach will be explained to satisfy some requirements together with practical implementation of some restrictions for the first time. Primarily a nonlinear single-input single-output (SISO time-delay model which was obtained previously in the literature is introduced for the oxygen generation process in the heart-lung machine system and we will complete it by adding some new states to control it. Thereafter, the system is linearized using the state feedback linearization approach to find a third-order time-delay dynamics. Consequently classical PID and fractional order controllers are gained to assess the quality of the proposed technique. A set of optimal parameters of those controllers are achieved through the genetic algorithm optimization procedure through minimizing a cost function. Our design method focuses on minimizing some famous performance criterions such as IAE, ISE, and ITSE. In the genetic algorithm, the controller parameters are chosen as a random population. The best relevant values are achieved by reducing the cost function. A time-domain simulation signifies the performance of controller with respect to a traditional optimized PID controller.

  11. High-order Finite Difference Solution of Euler Equations for Nonlinear Water Waves

    Christiansen, Torben Robert Bilgrav; Bingham, Harry B.; Engsig-Karup, Allan Peter

    2012-01-01

    is discretized using arbitrary-order finite difference schemes on a staggered grid with one optional stretching in each coordinate direction. The momentum equations and kinematic free surface condition are integrated in time using the classic fourth-order Runge-Kutta scheme. Mass conservation is satisfied...

  12. A single-vendor and a single-buyer integrated inventory model with ordering cost reduction dependent on lead time

    Vijayashree, M.; Uthayakumar, R.

    2017-09-01

    Lead time is one of the major limits that affect planning at every stage of the supply chain system. In this paper, we study a continuous review inventory model. This paper investigates the ordering cost reductions are dependent on lead time. This study addressed two-echelon supply chain problem consisting of a single vendor and a single buyer. The main contribution of this study is that the integrated total cost of the single vendor and the single buyer integrated system is analyzed by adopting two different (linear and logarithmic) types ordering cost reductions act dependent on lead time. In both cases, we develop effective solution procedures for finding the optimal solution and then illustrative numerical examples are given to illustrate the results. The solution procedure is to determine the optimal solutions of order quantity, ordering cost, lead time and the number of deliveries from the single vendor and the single buyer in one production run, so that the integrated total cost incurred has the minimum value. Ordering cost reduction is the main aspect of the proposed model. A numerical example is given to validate the model. Numerical example solved by using Matlab software. The mathematical model is solved analytically by minimizing the integrated total cost. Furthermore, the sensitivity analysis is included and the numerical examples are given to illustrate the results. The results obtained in this paper are illustrated with the help of numerical examples. The sensitivity of the proposed model has been checked with respect to the various major parameters of the system. Results reveal that the proposed integrated inventory model is more applicable for the supply chain manufacturing system. For each case, an algorithm procedure of finding the optimal solution is developed. Finally, the graphical representation is presented to illustrate the proposed model and also include the computer flowchart in each model.

  13. Fourth-order perturbative extension of the single-double excitation coupled-cluster method

    Derevianko, Andrei; Emmons, Erik D.

    2002-01-01

    Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wave function. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulas are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e., contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed

  14. Estimates on the minimal period for periodic solutions of nonlinear second order Hamiltonian systems

    Yiming Long.

    1994-11-01

    In this paper, we prove a sharper estimate on the minimal period for periodic solutions of autonomous second order Hamiltonian systems under precisely Rabinowitz' superquadratic condition. (author). 20 refs, 1 fig

  15. Waves, conservation laws and symmetries of a third-order nonlinear ...

    order is under consideration. Important properties concerning advanced character such like conservation laws and the equation of continuity are given. Characteristic wave properties such like dispersion relations and both the group and phase ...

  16. Structural characterizations, Hirshfeld surface analyses, and third-order nonlinear optical properties of two novel chalcone derivatives

    Maidur, Shivaraj R.; Jahagirdar, Jitendra R.; Patil, Parutagouda Shankaragouda; Chia, Tze Shyang; Quah, Ching Kheng

    2018-01-01

    We report synthesis, characterizations, structure-property relationships, and third-order nonlinear optical studies for two new chalcone derivatives, (2E)-1-(anthracen-9-yl)-3-(4-bromophenyl)prop-2-en-1-one (Br-ANC) and (2E)-1-(anthracen-9-yl)-3-(4-chlorophenyl)prop-2-en-1-one (Cl-ANC). These derivatives were crystallized in the centrosymmetric monoclinic P21/c crystal structure. The intermolecular interactions of both the crystals were visualized by Hirshfeld surface analyses (HSA). The crystals are thermally stable up to their melting points (180.82 and 191.16 °C for Cl-ANC and Br-ANC, respectively). The geometry optimizations, FT-IR spectra, 1H and 13C NMR spectra, electronic absorption spectra, electronic transitions, and HOMO-LUMO energy gaps were studied by Density Functional Theory (DFT) at B3LYP/6-311+G(d, p) level. The theoretical results provide excellent agreement with experimental findings. The electric dipole moments, static polarizabilities, molecular electrostatic potentials (MEP) and global chemical reactivity descriptors (GCRD) were also theoretically computed. The materials exhibited good nonlinear absorption (NLA), nonlinear refraction (NLR) and optical limiting (OL) behavior under diode-pumped solid-state (DPSS) continuous wave (CW) laser excitation (532 nm and 200 mW). The NLO parameters such as NLA coefficient (β∼10-5 cmW-1), NLR index (n2∼10-10 cm2 W-1) and third-order NLO susceptibilities (χ(3) ∼10-7 esu) were measured. Further, we estimated one-photon and two-photon figures of merit, which satisfy the demands (W > 1 and T < 1) for all-optical switching. Thus, the present chalcone derivatives with anthracene moiety are potential materials for OL and optical switching applications.

  17. Fractional order nonlinear variable speed and current regulation of a permanent magnet synchronous generator wind turbine system

    Anitha Karthikeyan

    2018-03-01

    Full Text Available In this paper we derived the fractional order model of the Permanent Magnet Synchronous Generator (PMSG from its integer model. The PMSG was employing a shaft sensor for the speed sensing and control. But this sensor would increase the hardware complexity as well as the cost of the system. Hence we have developed a Fractional order Nonlinear adaptive control method for speed and current tracking of the PMSG. The objective of an adaptive controller is to first define a virtual control state and force it to become a stabilizing function in accordance with a corresponding error dynamics. In order to study the Lyapunov exponents of the fractional order controller, we proposed a new method which would remove the complexity of finding the sign of the Lyapunov first derivative. The Fractional order control scheme is implemented in LabVIEW for simulation results. The simulation results indicated that the estimated rotor position and speed correspond to their actual values well. Keywords: Chaos suppression, Fractional order systems, Permanent magnet synchronous generator, Speed and current control, Lyapunov stability

  18. Nonlinear image encryption using a fully phase nonzero-order joint transform correlator in the Gyrator domain

    Vilardy, Juan M.; Millán, María S.; Pérez-Cabré, Elisabet

    2017-02-01

    A novel nonlinear image encryption scheme based on a fully phase nonzero-order joint transform correlator architecture (JTC) in the Gyrator domain (GD) is proposed. In this encryption scheme, the two non-overlapping data distributions of the input plane of the JTC are fully encoded in phase and this input plane is transformed using the Gyrator transform (GT); the intensity distribution captured in the GD represents a new definition of the joint Gyrator power distribution (JGPD). The JGPD is modified by two nonlinear operations with the purpose of retrieving the encrypted image, with enhancement of the decrypted signal quality and improvement of the overall security. There are three keys used in the encryption scheme, two random phase masks and the rotation angle of the GT, which are all necessary for a proper decryption. Decryption is highly sensitivity to changes of the rotation angle of the GT as well as to little changes in other parameters or keys. The proposed encryption scheme in the GD still preserves the shift-invariance properties originated in the JTC-based encryption in the Fourier domain. The proposed encryption scheme is more resistant to brute force attacks, chosen-plaintext attacks, known-plaintext attacks, and ciphertext-only attacks, as they have been introduced in the cryptanalysis of the JTC-based encryption system. Numerical results are presented and discussed in order to verify and analyze the feasibility and validity of the novel encryption-decryption scheme.

  19. Energy-momentum conserving higher-order time integration of nonlinear dynamics of finite elastic fiber-reinforced continua

    Erler, Norbert; Groß, Michael

    2015-05-01

    Since many years the relevance of fibre-reinforced polymers is steadily increasing in fields of engineering, especially in aircraft and automotive industry. Due to the high strength in fibre direction, but the possibility of lightweight construction, these composites replace more and more traditional materials as metals. Fibre-reinforced polymers are often manufactured from glass or carbon fibres as attachment parts or from steel or nylon cord as force transmission parts. Attachment parts are mostly subjected to small strains, but force transmission parts usually suffer large deformations in at least one direction. Here, a geometrically nonlinear formulation is necessary. Typical examples are helicopter rotor blades, where the fibres have the function to stabilize the structure in order to counteract large centrifugal forces. For long-run analyses of rotor blade deformations, we have to apply numerically stable time integrators for anisotropic materials. This paper presents higher-order accurate and numerically stable time stepping schemes for nonlinear elastic fibre-reinforced continua with anisotropic stress behaviour.

  20. Third-order nonlinearities and structural features in Langmuir-Blodgett films of 1-benzyl-9-hydrofullerene-60

    Shihong Ma; Liying Liu; Xingze Lu

    1995-01-01

    Third-order nonlinear susceptibilities χ xxxx (3) (-3ω; ω, ω, ω) have been deduced by measuring third-harmonic generation in Langmuir-Blodgett (LB) films of 1-benzyl-9-hydrofullerene-60 (C 60 -Be). The structural features of the condensed layer at the air-water interface and LB films of the C 60 -Be were investigated by small angle x-ray diffraction (SAXD) and optical measurements. The third-order nonlinear susceptibilities (χ (3) ) were obtained by measuring the THG intensities in LB films of C 60 -Be and comparing with that of CS 2 used as the reference. The value of χ xxxx (3) (2.1 x 10 -11 esu) was deduced at a 65 nm thick films. The χ (3) is attributed to a three-photon near resonance at the energy level of 29410 cm -1 . A new-type of two-chain amphiphilic molecule 1,10-bistearyl-4,6,13, 15-tetra-18-nitrogencrown-6 (NC) was used as insert material to construct mixed C 60 -Be/NC LB films. Our π-A, UV-visible absorption and SAXD measurements showed that the structural improvement in the mixed C 60 -Be/NC LB films was realized by insertion of the C 60 -Be molecules between the two hydrophobic chains of the NC molecules

  1. A high-order relaxation method with projective integration for solving nonlinear systems of hyperbolic conservation laws

    Lafitte, Pauline; Melis, Ward; Samaey, Giovanni

    2017-07-01

    We present a general, high-order, fully explicit relaxation scheme which can be applied to any system of nonlinear hyperbolic conservation laws in multiple dimensions. The scheme consists of two steps. In a first (relaxation) step, the nonlinear hyperbolic conservation law is approximated by a kinetic equation with stiff BGK source term. Then, this kinetic equation is integrated in time using a projective integration method. After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge-Kutta method of arbitrary order. We show that, with an appropriate choice of inner step size, the time step restriction on the outer time step is similar to the CFL condition for the hyperbolic conservation law. Moreover, the number of inner time steps is also independent of the stiffness of the BGK source term. We discuss stability and consistency, and illustrate with numerical results (linear advection, Burgers' equation and the shallow water and Euler equations) in one and two spatial dimensions.

  2. Full 3D modelling of pulse propagation enables efficient nonlinear frequency conversion with low energy laser pulses in a single-element tripler

    Kardaś, Tomasz M.; Nejbauer, Michał; Wnuk, Paweł; Resan, Bojan; Radzewicz, Czesław; Wasylczyk, Piotr

    2017-02-01

    Although new optical materials continue to open up access to more and more wavelength bands where femtosecond laser pulses can be generated, light frequency conversion techniques are still indispensable in filling the gaps on the ultrafast spectral scale. With high repetition rate, low pulse energy laser sources (oscillators) tight focusing is necessary for a robust wave mixing and the efficiency of broadband nonlinear conversion is limited by diffraction as well as spatial and temporal walk-off. Here we demonstrate a miniature third harmonic generator (tripler) with conversion efficiency exceeding 30%, producing 246 fs UV pulses via cascaded second order processes within a single laser beam focus. Designing this highly efficient and ultra compact frequency converter was made possible by full 3-dimentional modelling of propagation of tightly focused, broadband light fields in nonlinear and birefringent media.

  3. A Model-Free Diagnostic for Single-Peakedness of Item Responses Using Ordered Conditional Means

    Polak, Marike; De Rooij, Mark; Heiser, Willem J.

    2012-01-01

    In this article we propose a model-free diagnostic for single-peakedness (unimodality) of item responses. Presuming a unidimensional unfolding scale and a given item ordering, we approximate item response functions of all items based on ordered conditional means (OCM). The proposed OCM methodology is based on Thurstone & Chave's (1929) "criterion…

  4. A partitioned model order reduction approach to rationalise computational expenses in nonlinear fracture mechanics

    Kerfriden, P.; Goury, O.; Rabczuk, T.; Bordas, S.P.A.

    2013-01-01

    We propose in this paper a reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No a priori knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture. PMID:23750055

  5. The second-order interference of two independent single-mode He-Ne lasers

    Liu, Jianbin; Le, Mingnan; Bai, Bin; Wang, Wentao; Chen, Hui; Zhou, Yu; Li, Fu-li; Xu, Zhuo

    2015-09-01

    The second-order spatial and temporal interference patterns with two independent single-mode continuous-wave He-Ne lasers are observed when these two lasers are incident to two adjacent input ports of a 1:1 non-polarizing beam splitter, respectively. Two-photon interference based on the superposition principle in Feynman's path integral theory is employed to interpret the experimental results. The conditions to observe the second-order interference pattern with two independent single-mode continuous-wave lasers are discussed. It is concluded that frequency stability is important to observe the second-order interference pattern with two independent light beams.

  6. The nonlocal boundary value problems for strongly singular higher-order nonlinear functional-differential equations

    Mukhigulashvili, Sulkhan

    -, č. 35 (2015), s. 23-50 ISSN 1126-8042 Institutional support: RVO:67985840 Keywords : higher order functional differential equations * Dirichlet boundary value problem * strong singularity Subject RIV: BA - General Mathematics http://ijpam.uniud.it/online_issue/201535/03-Mukhigulashvili.pdf

  7. Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay.

    Korkmaz, Erdal

    2017-01-01

    In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

  8. Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay

    Erdal Korkmaz

    2017-06-01

    Full Text Available Abstract In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov’s second method. The results obtained essentially improve, include and complement the results in the literature.

  9. Explicit fourth-order stiffness representation in non-linear dynamics

    Krenk, Steen

    2013-01-01

    global form of the effective internal force is presented, in which it is represented by its algebraic mean value plus a higher order term in the form of the product of the increment of the tangent stiffness matrix at the interval end-points and the corresponding displacement increment. This explicit...

  10. Mechanism of linear and nonlinear optical properties of bis-thiourea cadmium chloride single crystal

    Yang, J.T.; Luo, S.J.; Yi, L.; Laref, A.

    2013-01-01

    Within the generalized gradient approximation (GGA), a calculation of the electronic structure of a semiorganic crystal named bis-thiourea cadmium chloride (BTCC) was performed, then the linear and nonlinear optical responses were obtained over a wide energy range, using a scissor energy of 1.30 eV, and our results are in good agreement with the experiments. The accurate full-potential projected augmented wave (FP-PAW) method was used. The prominent spectrum of the second harmonic generation (SHG) was successfully correlated with the dielectric function in terms of single- and double-photon resonances. Both the virtual electron (VE) and virtual hole (VH) processes make contributions to the SHG of BTCC crystal, and the VH process is enhanced by the Cd-centered tetrahedron. The SHG effect of the semiorganic material is attributed to the charge transfer (CT). The CT model for the semiorganic crystal is named as “M-Π O ⋯X”. “M” is a metal atom providing electrons, “Π O ” is a π-conjugated covalent of an organic molecule, and “X” is a high electronegativity atom. The CT across the BTCC molecule is along a π-electron conjugation covalence bond, and the delocalized electrons of sulfur provide an excellent bridge. The strong “pull” effect for the CT is due to the intramolecular hydrogen bonds provided by the chlorine with the high electron affinity.

  11. A novel control framework for nonlinear time-delayed dual-master/single-slave teleoperation.

    Ghorbanian, A; Rezaei, S M; Khoogar, A R; Zareinejad, M; Baghestan, K

    2013-03-01

    A novel trilateral control architecture for the Dual-master/Single-slave teleoperation is proposed in this paper. This framework has been used in surgical training and rehabilitation applications. In this structure, the slave motion has been controlled by weighted summation of signals transmitted by the operator referring to task control authority through the dominance factors. The nonlinear dynamics for telemanipulators are considered which were considered as disregarded issues in previous studies of this field. Bounded variable time-delay has been considered which affects the transmitted signals in the communication channels. Two types of controllers have been offered and an appropriate stability analysis for each controller has been demonstrated. The first controller includes Proportional with dissipative gains (P+d). The second one contains Proportional and Derivative with dissipative gains (PD+d). In both cases, the stability of the trilateral control framework is preserved by choosing appropriate controller's gains. It is shown that these controllers attempt to coordinate the positions of telemanipulators in the free motion condition. The stability of the Dual-master/Single-slave teleoperation has been proved by an appropriate Lyapunov like function and the stability conditions have been studied. In addition the proposed PD+d control architecture is modified for trilateral teleoperation with internet communication between telemanipulators that caused such communication complications as packet loss, data duplication and swapping. A number of experiments have been conducted with various levels of dominance factor to validate the effectiveness of the new control architecture. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

  12. Analytical and Numerical solutions of a nonlinear alcoholism model via variable-order fractional differential equations

    Gómez-Aguilar, J. F.

    2018-03-01

    In this paper, we analyze an alcoholism model which involves the impact of Twitter via Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives with constant- and variable-order. Two fractional mathematical models are considered, with and without delay. Special solutions using an iterative scheme via Laplace and Sumudu transform were obtained. We studied the uniqueness and existence of the solutions employing the fixed point postulate. The generalized model with variable-order was solved numerically via the Adams method and the Adams-Bashforth-Moulton scheme. Stability and convergence of the numerical solutions were presented in details. Numerical examples of the approximate solutions are provided to show that the numerical methods are computationally efficient. Therefore, by including both the fractional derivatives and finite time delays in the alcoholism model studied, we believe that we have established a more complete and more realistic indicator of alcoholism model and affect the spread of the drinking.

  13. A single network adaptive critic (SNAC) architecture for optimal control synthesis for a class of nonlinear systems.

    Padhi, Radhakant; Unnikrishnan, Nishant; Wang, Xiaohua; Balakrishnan, S N

    2006-12-01

    Even though dynamic programming offers an optimal control solution in a state feedback form, the method is overwhelmed by computational and storage requirements. Approximate dynamic programming implemented with an Adaptive Critic (AC) neural network structure has evolved as a powerful alternative technique that obviates the need for excessive computations and storage requirements in solving optimal control problems. In this paper, an improvement to the AC architecture, called the "Single Network Adaptive Critic (SNAC)" is presented. This approach is applicable to a wide class of nonlinear systems where the optimal control (stationary) equation can be explicitly expressed in terms of the state and costate variables. The selection of this terminology is guided by the fact that it eliminates the use of one neural network (namely the action network) that is part of a typical dual network AC setup. As a consequence, the SNAC architecture offers three potential advantages: a simpler architecture, lesser computational load and elimination of the approximation error associated with the eliminated network. In order to demonstrate these benefits and the control synthesis technique using SNAC, two problems have been solved with the AC and SNAC approaches and their computational performances are compared. One of these problems is a real-life Micro-Electro-Mechanical-system (MEMS) problem, which demonstrates that the SNAC technique is applicable to complex engineering systems.

  14. Output-Feedback Nonlinear Adaptive Control Strategy of the Single-Phase Grid-Connected Photovoltaic System

    Abdelmajid Abouloifa

    2018-01-01

    Full Text Available This paper addresses the problem of controlling the single-phase grid connected to the photovoltaic system through a full bridge inverter with LCL-filter. The control aims are threefold: (i imposing the voltage in the output of PV panel to track a reference provided by the MPPT block; (ii regulating the DC-link voltage to guarantee the power exchange between the source and AC grid; (iii ensuring a satisfactory power factor correction (PFC. The problem is dealt with using a cascade nonlinear adaptive controller that is developed making use of sliding-mode technique and observers in order to estimate the state variables and grid parameters, by measuring only the grid current, PV voltage, and the DC bus voltage. The control problem addressed by this work involves several difficulties, including the uncertainty of some parameters of the system and the numerous state variables are inaccessible to measurements. The results are confirmed by simulation under MATLAB∖Simulink∖SimPowerSystems, which show that the proposed regulator is robust with respect to climate changes.

  15. Single-Wire Electric-Field Coupling Power Transmission Using Nonlinear Parity-Time-Symmetric Model with Coupled-Mode Theory

    Xujian Shu

    2018-03-01

    Full Text Available The output power and transmission efficiency of the traditional single-wire electric-field coupling power transmission (ECPT system will drop sharply with the increase of the distance between transmitter and receiver, thus, in order to solve the above problem, in this paper, a new nonlinear parity-time (PT-symmetric model for single-wire ECPT system based on coupled-mode theory (CMT is proposed. The proposed model for single-wire ECPT system not only achieves constant output power but also obtains a high constant transmission efficiency against variable distance, and the steady-state characteristics of the single-wire ECPT system are analyzed. Based on the theoretical analysis and circuit simulation, it shows that the transmission efficiency with constant output power remains 60% over a transmission distance of approximately 34 m without the need for any tuning. Furthermore, the application of a nonlinear PT-symmetric circuit based on CMT enables robust electric power transfer to moving devices or vehicles.

  16. Laterally Loaded Single Pile Response Considering the Influence of Suction and Non-Linear Behaviour of Reinforced Concrete Sections

    Stefano Stacul

    2017-12-01

    Full Text Available A hybrid BEM-p-y curves approach was developed for the single pile analysis with free/fixed head restraint conditions. The method considers the soil non-linear behaviour by means of p-y curves in series to a multi-layered elastic half-space. The non-linearity of reinforced concrete pile sections, also considering the influence of tension-stiffening, has been considered. The model reproduces the influence of suction by increasing the stress state and hence the stiffness of shallow soil-layers. Suction is modeled using the Modified-Kovacs model. The hybrid BEM-py curves method was validated by comparing results from data of 22 load tests on single piles. In addition, a detailed comparison is presented between measured and computed data on a large-diameter reinforced concrete bored single pile.

  17. High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water

    Madsen, Per A.; Fuhrman, David R.

    2010-01-01

    In this work, we start with a review of the development of Boussinesq theory for water waves covering the period from 1872 to date. Previous reviews have been given by Dingemans,1 Kirby,2,3 and Madsen & Schäffer.4 Next, we present our most recent high-order Boussinesq-type formulation valid for f...... from an undular sea bed; (8) Run-up of non-breaking solitary waves on a beach; and (9) Tsunami generation from submerged landslides....

  18. Suppression and nonlinear excitation of parasitic modes in second harmonic gyrotrons operating in a very high order mode

    Nusinovich, Gregory S.; Pu, Ruifeng; Granatstein, Victor L.

    2015-01-01

    In recent years, there was an active development of high-power, sub-terahertz (sub-THz) gyrotrons for numerous applications. For example, a 0.67 THz gyrotron delivering more than 200 kW with about 20% efficiency was developed. This record high efficiency was achieved because the gyrotron operated in a high-order TE 31,8 -mode with the power of ohmic losses less than 10% of the power of outgoing radiation. That gyrotron operated at the fundamental cyclotron resonance, and a high magnetic field of about 27 T was created by a pulse solenoid. For numerous applications, it is beneficial to use gyrotrons at cyclotron harmonics which can operate in available cryomagnets with fields not exceeding 15 T. However, typically, the gyrotron operation at harmonics faces severe competition from parasitic modes at the fundamental resonance. In the present paper, we consider a similar 0.67 THz gyrotron designed for operation in the same TE 31,8 -mode, but at the second harmonic. We focus on two nonlinear effects typical for interaction between the fundamental and second harmonic modes, viz., the mode suppression and the nonlinear excitation of the mode at the fundamental harmonic by the second harmonic oscillations. Our study includes both the analytical theory and numerical simulations performed with the self-consistent code MAGY. The simulations show that stable second harmonic operation in the TE 31,8 mode is possible with only modest sacrifice of efficiency and power

  19. A new fourth-order Fourier-Bessel split-step method for the extended nonlinear Schroedinger equation

    Nash, Patrick L.

    2008-01-01

    Fourier split-step techniques are often used to compute soliton-like numerical solutions of the nonlinear Schroedinger equation. Here, a new fourth-order implementation of the Fourier split-step algorithm is described for problems possessing azimuthal symmetry in 3 + 1-dimensions. This implementation is based, in part, on a finite difference approximation Δ perpendicular FDA of 1/r (∂)/(∂r) r(∂)/(∂r) that possesses an associated exact unitary representation of e i/2λΔ perpendicular FDA . The matrix elements of this unitary matrix are given by special functions known as the associated Bessel functions. Hence the attribute Fourier-Bessel for the method. The Fourier-Bessel algorithm is shown to be unitary and unconditionally stable. The Fourier-Bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium. This numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction, and labeled by the cylindrical coordinate z. These profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times, and provide evidence for a physical effect that may be loosely termed normal mode condensation. Normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts, which may occur as a result of short, intense irradiation of a medium

  20. Preparation and third-order nonlinear optical property of poly(urethane-imide containing dispersed red chromophore

    2008-11-01

    Full Text Available A novel poly(urethane-imide (PUI containing dispersed red chromophore was synthesized. The PUI was characterized by FT-IR, UV-Vis, DSC and TGA. The results of DSC and TGA indicated that the PUI exhibited high thermal stability up to its glass-transition temperature (Tg of 196°C and 5% heat weight loss temperature of 229°C. According to UV-Vis spectrum and working curve, the maximum molar absorption coefficient and absorption wavelength were measured. They were used to calculate the third-order nonlinear optical coefficient χ(3. At the same time, the chromophore density of PUI, nonlinear refractive index coefficient and molecular hyperpolarizability of PUI were obtained. The fluorescence spectra of PUI and model compound DR-19 were determined at excitation wavelength 300 nm. The electron donor and acceptor in polymer formed the exciplex through the transfer of the electric charges. The results show that the poly(urethane-imide is a promising candidate for application in optical devices.

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

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

    2015-01-01

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

  2. Strongly increasing solutions of cyclic systems of second order differential equations with power-type nonlinearities

    Jaroslav Jaroš

    2015-01-01

    Full Text Available We consider \\(n\\-dimensional cyclic systems of second order differential equations \\[(p_i(t|x_{i}'|^{\\alpha_i -1}x_{i}'' = q_{i}(t|x_{i+1}|^{\\beta_i-1}x_{i+1},\\] \\[\\quad i = 1,\\ldots,n, \\quad (x_{n+1} = x_1 \\tag{\\(\\ast\\}\\] under the assumption that the positive constants \\(\\alpha_i\\ and \\(\\beta_i\\ satisfy \\(\\alpha_1{\\ldots}\\alpha_n \\gt \\beta_1{\\ldots}\\beta_n\\ and \\(p_i(t\\ and \\(q_i(t\\ are regularly varying functions, and analyze positive strongly increasing solutions of system (\\(\\ast\\ in the framework of regular variation. We show that the situation for the existence of regularly varying solutions of positive indices for (\\(\\ast\\ can be characterized completely, and moreover that the asymptotic behavior of such solutions is governed by the unique formula describing their order of growth precisely. We give examples demonstrating that the main results for (\\(\\ast\\ can be applied to some classes of partial differential equations with radial symmetry to acquire accurate information about the existence and the asymptotic behavior of their radial positive strongly increasing solutions.

  3. Intensity-dependent nonlinear optical properties in a modulation-doped single quantum well

    Ungan, F.

    2011-01-01

    In the present work, the changes in the intersubband optical absorption coefficients and the refractive index in a modulation-doped quantum well have been investigated theoretically. Within the envelope function approach and the effective mass approximation, the electronic structure of the quantum well is calculated from the self-consistent numerical solution of the coupled Schroedinger-Poisson equations. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The numerical results GaAs/Al x Ga 1-x As are presented for typical modulation-doped quantum well system. The linear, third-order nonlinear and total absorption and refractive index changes depending on the doping concentration are investigated as a function of the incident optical intensity and structure parameters, such as quantum well width and stoichiometric ratio. The results show that the doping concentration, the structure parameters and the incident optical intensity have a great effect on the optical characteristics of these structures. - Highlights: → The doping concentration has a great effect on the optical characteristics of these structures. → The structure parameters have a great effect on the optical properties of these structures. → The total absorption coefficients reduced as the incident optical intensity increases. → The RICs reduced as the incident optical intensity increases.

  4. Linear and non-linear energy barriers in systems of interacting single-domain ferromagnetic particles

    Petrila, Iulian; Bodale, Ilie; Rotarescu, Cristian; Stancu, Alexandru

    2011-01-01

    A comparative analysis between linear and non-linear energy barriers used for modeling statistical thermally-excited ferromagnetic systems is presented. The linear energy barrier is obtained by new symmetry considerations about the anisotropy energy and the link with the non-linear energy barrier is also presented. For a relevant analysis we compare the effects of linear and non-linear energy barriers implemented in two different models: Preisach-Neel and Ising-Metropolis. The differences between energy barriers which are reflected in different coercive field dependence of the temperature are also presented. -- Highlights: → The linear energy barrier is obtained from symmetry considerations. → The linear and non-linear energy barriers are calibrated and implemented in Preisach-Neel and Ising-Metropolis models. → The temperature and time effects of the linear and non-linear energy barriers are analyzed.

  5. Ordered array of CoPc-vacancies filled with single-molecule rotors

    Xie, Zheng-Bo; Wang, Ya-Li; Tao, Min-Long; Sun, Kai; Tu, Yu-Bing; Yuan, Hong-Kuan; Wang, Jun-Zhong

    2018-05-01

    We report the highly ordered array of CoPc-vacancies and the single-molecule rotors inside the vacancies. When CoPc molecules are deposited on Cd(0001) at low-temperature, three types of molecular vacancies appeared randomly in the CoPc monolayer. Annealing the sample to higher temperature leads to the spontaneous phase separation and self-organized arrangement of the vacancies. Highly ordered arrays of two-molecule vacancies and single-molecule vacancies have been obtained. In particular, there is a rotating CoPc molecule inside each single-molecule vacancy, which constitutes the array of single-molecule rotors. These results provide a new routine to fabricate the nano-machines on a large scale.

  6. Near resonant and nonresonant third-order optical nonlinearities of colloidal InP/ZnS quantum dots

    Wang, Y.; Yang, X.; He, T. C.; Gao, Y.; Demir, H. V.; Sun, X. W.; Sun, H. D.

    2013-01-01

    We have investigated the third-order optical nonlinearities of high-quality colloidal InP/ZnS core-shell quantum dots (QDs) using Z-scan technique with femtosecond pulses. The two-photon absorption cross-sections as high as 6.2 × 103 GM are observed at 800 nm (non-resonant regime) in InP/ZnS QDs with diameter of 2.8 nm, which is even larger than those of CdSe, CdS, and CdTe QDs at similar sizes. Furthermore, both of the 2.2 nm and 2.8 nm-sized InP/ZnS QDs exhibit strong saturable absorption in near resonant regime, which is attributed to large exciton Bohr radius in this material. These results strongly suggest the promising potential of InP/ZnS QDs for widespread applications, especially in two-photon excited bio-imaging and saturable absorbing.

  7. Second-order interference of two independent and tunable single-mode continuous-wave lasers

    Liu Jianbin; Chen Hui; Zheng Huaibin; Xu Zhuo; Wei Dong; Zhou Yu; Gao Hong; Li Fu-Li

    2016-01-01

    The second-order temporal interference of two independent single-mode continuous-wave lasers is discussed by employing two-photon interference in Feynman’s path integral theory. It is concluded that whether the second-order temporal interference pattern can or cannot be retrieved via two-photon coincidence counting rate is dependent on the resolution time of the detection system and the frequency difference between these two lasers. Two identical and tunable single-mode continuous-wave diode lasers are employed to verify the predictions. These studies are helpful to understand the physics of two-photon interference with photons of different spectra. (paper)

  8. A reduced-order vortex model of three-dimensional unsteady non-linear aerodynamics

    Eldredge, Jeff D.

    2014-11-01

    Rapid, large-amplitude maneuvers of low aspect ratio wings are inherent to biologically-inspired flight. These give rise to unsteady phenomena associated with the interactions among the coherent structures shed from wing edges. The objective of this work is to distill these phenomena into a low-order physics-based dynamical model. The model is based on interconnected vortex loops, composed of linear segments between a small number of vertices. Thus, the dynamics of the fluid are reduced to tracking the evolution of the vertices, whose motions are determined from the velocity field induced by the loops and wing motion. The feature that distinguishes this method from previous treatments is that the vortex loops, analogous to point vortices in our two-dimensional model, have time-varying strength. That is, the flux of vorticity from the wing is concentrated in the constituent segments. Chains of interconnected loops can be shed from any edge of the wing. The evolution equation for the loop vertices is based on the impulse matching principle developed in previous work. We demonstrate the model in various maneuvers, including impulse starts of low aspect ratio wings, oscillatory pitching, etc., and compare with experimental results and high-fidelity simulations where applicable. This work was supported by AFOSR under Award FA9550-11-1-0098.

  9. Unbounded oscillation of higher-order nonlinear delay dynamic equations of neutral type with oscillating coefficients

    Başak Karpuz

    2009-05-01

    where $n\\in[2,\\infty_{\\mathbb{Z}}$, $t_{0}\\in\\mathbb{T}$, $\\sup\\{\\mathbb{T}\\}=\\infty$, $A\\in\\rm{C_{rd}}([t_{0},\\infty_{\\mathbb{T}},\\mathbb{R}$ is allowed to alternate in sign infinitely many times, $B\\in\\rm{C_{rd}}([t_{0},\\infty_{\\mathbb{T}},\\mathbb{R}^{+}$, $F\\in\\rm{C_{rd}}(\\mathbb{R},\\mathbb{R}$ is nondecreasing, and $\\alpha,\\beta\\in\\rm{C_{rd}}([t_{0},\\infty_{\\mathbb{T}},\\mathbb{T}$ are unbounded increasing functions satisfying $\\alpha(t,\\beta(t\\leq t$ for all sufficiently large $t$. We give change of order formula for double(iterated integrals to prove our main result. Some simple examples are given to illustrate the applicability of our results too. In the literature, almost all of the results for \\eqref{asbeq1} with $\\mathbb{T}=\\mathbb{R}$ and $\\mathbb{T}=\\mathbb{Z}$ hold for bounded solutions. Our results are new and not stated in the literature even for the particular cases $\\mathbb{T}=\\mathbb{R}$ and/or $\\mathbb{T}=\\mathbb{Z}$.

  10. A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations

    Christlieb, Andrew J.; Feng, Xiao; Seal, David C.; Tang, Qi

    2016-07-01

    We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23], where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax-Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton-Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8], but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free

  11. Fast and high-order numerical algorithms for the solution of multidimensional nonlinear fractional Ginzburg-Landau equation

    Mohebbi, Akbar

    2018-02-01

    In this paper we propose two fast and accurate numerical methods for the solution of multidimensional space fractional Ginzburg-Landau equation (FGLE). In the presented methods, to avoid solving a nonlinear system of algebraic equations and to increase the accuracy and efficiency of method, we split the complex problem into simpler sub-problems using the split-step idea. For a homogeneous FGLE, we propose a method which has fourth-order of accuracy in time component and spectral accuracy in space variable and for nonhomogeneous one, we introduce another scheme based on the Crank-Nicolson approach which has second-order of accuracy in time variable. Due to using the Fourier spectral method for fractional Laplacian operator, the resulting schemes are fully diagonal and easy to code. Numerical results are reported in terms of accuracy, computational order and CPU time to demonstrate the accuracy and efficiency of the proposed methods and to compare the results with the analytical solutions. The results show that the present methods are accurate and require low CPU time. It is illustrated that the numerical results are in good agreement with the theoretical ones.

  12. Calculations on the Nonlinear Second—Order Optical Polarizabilities for Series of Donor—C60 Molecules

    刘孝娟; 封继康; 任爱民

    2003-01-01

    The equilibrium geometries and UV-visible spectra of a series of donor-C60 molecules were obtained by means of the AM1 and INDO/CI method,on the basis of accurate geometric and electronic structures.The nonlinear second-order optical polarizabilities were calculated using the method INDO/SDCI combined with the Sum-Over-States(SOS) expression.The calculatedβ(λ=1.34μm) values are 28.81,48.56,57.33,66.99,70.85,85.84,and 142.14(×10-30 esu) for the molecules A,B,C,D,E,F and G,respectively.The frontier orbitals were plot for the representative molecules in order to exhibit the intramolecular charge transfer.The results indicate the introduction of thienylethylene can enhance the NLO response and the dimethylaniline-substituted dithienyl-ethylene-C60 (molecule G) possesses the largest NLO second-order optical polarizability.The large β values can be attributed to the charge transfer between the substituents and C60,as well as within the three-dimensional conjugated sphere of C60.

  13. Green synthesis and third-order nonlinear optical properties of 6-(9H-carbazol-9-yl) hexyl acetate

    Chen, Baili; Geng, Feng; Luo, Xuan; Zhong, Quanjie; Zhang, Qingjun; Fang, Yu; Huang, Chuanqun; Yang, Ruizhuang; Shao, Ting; Chen, Shufan

    2016-10-01

    An extremely simple and green approach for the synthesis of photoelectric material 6-(9H-carbazol-9-yl) hexy-acetate (CHA) has been described in detail. The molecular structure of CHA was identified with Fourier transform infrared (FT-IR) spectra and 1H Nuclear Magnetic Resonance (1H NMR) spectroscopy. The optical absorption of CHA was recorded using ultraviolet-visible (UV-vis) spectrum. Notably, the reaction was accomplished in water medium instead of traditional toxic solvents (e.g., benzene and chloroform). The yield of CHA is up to 99%, which is increased by 13% compared with the traditional method. The approach developed by us makes it possible to achieve commercial production of CHA. Moreover, the thermal stability of CHA was studied with thermogravimetric (TG) and derivative thermogravimetric (DTG) method. The third-order nonlinear optical (NLO) properties of CHAn (obtained by new method) and CHAt (obtained by traditional method) have been studied by a Z-scan technique at 440 nm. The thermal decomposition temperature is above 200 °C. The third-order NLO of CHAn and CHAt are the same. The third-order NLO susceptibility χ (3) and two photon Figures of Merit (FOMs) of CHA are 1.58 × 10-8 (esu) and 4.55, respectively. The results reveal that CHA may be a promising candidate for all-optical switching application.

  14. Diagnostic study of the roughness surface effect of zirconium on the third-order nonlinear-optical properties of thin films based on zinc oxide nanomaterials

    Bahedi, K.; Addou, M.; El Jouad, M.; Sofiani, Z.; Alaoui Lamrani, M.; El Habbani, T.; Fellahi, N.; Bayoud, S.; Dghoughi, L.; Sahraoui, B.; Essaidi, Z.

    2009-01-01

    Zinc oxide (ZnO) and zirconium doped zinc oxide (ZnO:Zr) thin films were deposited by reactive chemical pulverization spray pyrolysis technique on heated glass substrates at 500 deg. C using zinc and zirconium chlorides as precursors. Effects of zirconium doping agent and surface roughness on the nonlinear optical properties were investigated in detail using atomic force microscopy (AFM) and third harmonic generation (THG) technique. The best value of nonlinear optical susceptibility χ (3) was obtained from the doped films with less roughness. A strong third order nonlinear optical susceptibility χ (3) = 20.12 x 10 -12 (esu) of the studied films was found for the 3% doped sample.

  15. Approximate Forward Difference Equations for the Lower Order Non-Stationary Statistics of Geometrically Non-Linear Systems subject to Random Excitation

    Köylüoglu, H. U.; Nielsen, Søren R. K.; Cakmak, A. S.

    Geometrically non-linear multi-degree-of-freedom (MDOF) systems subject to random excitation are considered. New semi-analytical approximate forward difference equations for the lower order non-stationary statistical moments of the response are derived from the stochastic differential equations...... of motion, and, the accuracy of these equations is numerically investigated. For stationary excitations, the proposed method computes the stationary statistical moments of the response from the solution of non-linear algebraic equations....

  16. First-order aerodynamic and aeroelastic behavior of a single-blade installation setup

    Gaunaa, Mac; Bergami, Leonardo; Guntur, Srinivas

    2014-01-01

    the first-order aerodynamic and aeroelastic behavior of a single blade installation system, where the blade is grabbed by a yoke, which is lifted by the crane and stabilized by two taglines. A simple engineering model is formulated to describe the aerodynamic forcing on the blade subject to turbulent wind...

  17. Single jet photoproduction at HERA in next-to-leading order QCD

    Kramer, G.; Salesch, S.G.

    1993-01-01

    We present results for next- to-leading order calculations of single jet inclusive cross sections by resolved photons in ep-collisions at HERA. The dependence on the jet recombination cut and on the choice of the renormalization and factorization scales is studied in detail. (orig.). 5 figs

  18. Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials.

    Chen, Yong; Yan, Zhenya

    2016-03-22

    Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.

  19. Types of defect ordering in undoped and lanthanum-doped Bi2201 single crystals

    Martovitsky, V. P.

    2006-01-01

    Undoped and lanthanum-doped Bi2201 single crystals having a perfect average structure have been comparatively studied by x-ray diffraction. The undoped Bi2201 single crystals exhibit very narrow satellite reflections; their half-width is five to six times smaller than that of Bi2212 single crystals grown by the same technique. This narrowness indicates three-dimensional defect ordering in the former crystals. The lanthanumdoped Bi2201 single crystals with x = 0.7 and T c = 8-10 K exhibit very broad satellite reflections consisting of two systems (modulations) misoriented with respect to each other. The modulation-vector components of these two modulations are found to be q 1 = 0.237b* + 0.277c* and q 2 = 0.238b* + 0.037c*. The single crystals having a perfect average structure and a homogeneous average distribution of doping lanthanum consist of 70-to 80-A-thick layers that alternate along the c axis and have two different types of modulated superlattice. The crystals having a less perfect average structure also consist of alternating layers, but they have different lanthanum concentrations. The low value of T c in the undoped Bi2201 single crystals (9.5 K) correlates with three-dimensional defect ordering in them, and an increase in T c to 33 K upon lanthanum doping can be related to a thin-layer structure of these crystals and to partial substitution of lanthanum for the bismuth positions

  20. Using Directional Diffusion Coefficients for Nonlinear Diffusion Acceleration of the First Order SN Equations in Near-Void Regions

    Schunert, Sebastian; Hammer, Hans; Lou, Jijie; Wang, Yaqi; Ortensi, Javier; Gleicher, Frederick; Baker, Benjamin; DeHart, Mark; Martineau, Richard

    2016-11-01

    The common definition of the diffusion coeffcient as the inverse of three times the transport cross section is not compat- ible with voids. Morel introduced a non-local tensor diffusion coeffcient that remains finite in voids[1]. It can be obtained by solving an auxiliary transport problem without scattering or fission. Larsen and Trahan successfully applied this diffusion coeffcient for enhancing the accuracy of diffusion solutions of very high temperature reactor (VHTR) problems that feature large, optically thin channels in the z-direction [2]. It is demonstrated that a significant reduction of error can be achieved in particular in the optically thin region. Along the same line of thought, non-local diffusion tensors are applied modeling the TREAT reactor confirming the findings of Larsen and Trahan [3]. Previous work of the authors have introduced a flexible Nonlinear-Diffusion Acceleration (NDA) method for the first order S N equations discretized with the discontinuous finite element method (DFEM), [4], [5], [6]. This NDA method uses a scalar diffusion coeffcient in the low-order system that is obtained as the flux weighted average of the inverse transport cross section. Hence, it su?ers from very large and potentially unbounded diffusion coeffcients in the low order problem. However, it was noted that the choice of the diffusion coeffcient does not influence consistency of the method at convergence and hence the di?usion coeffcient is essentially a free parameter. The choice of the di?usion coeffcient does, however, affect the convergence behavior of the nonlinear di?usion iterations. Within this work we use Morel’s non-local di?usion coef- ficient in the aforementioned NDA formulation in lieu of the flux weighted inverse of three times the transport cross section. The goal of this paper is to demonstrate that significant en- hancement of the spectral properties of NDA can be achieved in near void regions. For testing the spectral properties of the NDA

  1. Persistent Charge-Density-Wave Order in Single-Layer TaSe2.

    Ryu, Hyejin; Chen, Yi; Kim, Heejung; Tsai, Hsin-Zon; Tang, Shujie; Jiang, Juan; Liou, Franklin; Kahn, Salman; Jia, Caihong; Omrani, Arash A; Shim, Ji Hoon; Hussain, Zahid; Shen, Zhi-Xun; Kim, Kyoo; Min, Byung Il; Hwang, Choongyu; Crommie, Michael F; Mo, Sung-Kwan

    2018-02-14

    We present the electronic characterization of single-layer 1H-TaSe 2 grown by molecular beam epitaxy using a combined angle-resolved photoemission spectroscopy, scanning tunneling microscopy/spectroscopy, and density functional theory calculations. We demonstrate that 3 × 3 charge-density-wave (CDW) order persists despite distinct changes in the low energy electronic structure highlighted by the reduction in the number of bands crossing the Fermi energy and the corresponding modification of Fermi surface topology. Enhanced spin-orbit coupling and lattice distortion in the single-layer play a crucial role in the formation of CDW order. Our findings provide a deeper understanding of the nature of CDW order in the two-dimensional limit.

  2. Derivation and solution of a time-dependent, nonlinear, Schrodinger-like equation for the superconductivity order parameter

    Esrick, M.A.

    1981-01-01

    A time-dependent, nonlinear, Schrodinger-like equation for the superconductivity order parameter is derived from the Gor'kov equations. Three types of traveling wave solutions of the equation are discussed. The phases and amplitudes of these solutions propagate at different speeds. The first type of solution has an amplitude that propagates as a soliton and it is suggested that this solution might correspond to the recently observed propagating collective modes of the order parameter. The amplitude of the second type of solution propagates as a periodic disturbance in space and time. It is suggested that this type of solution might explain the recently observed multiple values of the superconductor energy gap as well as the spatially inhomogenous superconducting state. The third type of solution, which is of a more general character, might provide some insight into non-periodic, inhomogeneous states occuring in superconductors. It is also proposed that quasiparticle injection and microwave irradiation might generate soliton-like disturbances in superconductors

  3. NLSEmagic: Nonlinear Schrödinger equation multi-dimensional Matlab-based GPU-accelerated integrators using compact high-order schemes

    Caplan, R. M.

    2013-04-01

    We present a simple to use, yet powerful code package called NLSEmagic to numerically integrate the nonlinear Schrödinger equation in one, two, and three dimensions. NLSEmagic is a high-order finite-difference code package which utilizes graphic processing unit (GPU) parallel architectures. The codes running on the GPU are many times faster than their serial counterparts, and are much cheaper to run than on standard parallel clusters. The codes are developed with usability and portability in mind, and therefore are written to interface with MATLAB utilizing custom GPU-enabled C codes with the MEX-compiler interface. The packages are freely distributed, including user manuals and set-up files. Catalogue identifier: AEOJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOJ_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 124453 No. of bytes in distributed program, including test data, etc.: 4728604 Distribution format: tar.gz Programming language: C, CUDA, MATLAB. Computer: PC, MAC. Operating system: Windows, MacOS, Linux. Has the code been vectorized or parallelized?: Yes. Number of processors used: Single CPU, number of GPU processors dependent on chosen GPU card (max is currently 3072 cores on GeForce GTX 690). Supplementary material: Setup guide, Installation guide. RAM: Highly dependent on dimensionality and grid size. For typical medium-large problem size in three dimensions, 4GB is sufficient. Keywords: Nonlinear Schröodinger Equation, GPU, high-order finite difference, Bose-Einstien condensates. Classification: 4.3, 7.7. Nature of problem: Integrate solutions of the time-dependent one-, two-, and three-dimensional cubic nonlinear Schrödinger equation. Solution method: The integrators utilize a fully-explicit fourth-order Runge-Kutta scheme in time

  4. Single particle train ordering in microchannel based on inertial and vortex effects

    Fan, Liang-Liang; Yan, Qing; Zhe, Jiang; Zhao, Liang

    2018-06-01

    A new microfluidic device for microparticle focusing and ordering in a single particle train is reported. The particle focusing and ordering are based on inertial and vortex effects in a microchannel with a series of suddenly contracted and widely expanded structures on one side. In the suddenly contracted regions, particles located near the contracted structures are subjected to a strong wall-effect lift force and momentum-change-induced inertial force due to the highly curved trajectory, migrating to the straight wall. A horizontal vortex is generated downstream of the contracted structure, which prevents the particle from getting close to the wall. In the widely expanded regions, the streamline is curved and no vortex is generated. The shear-gradient lift force and the momentum-change-induced inertial force are dominant for particle lateral migration, driving particles towards the wall of the expanded structures. Eventually, particles are focused and ordered in a single particle train by the combination effects of the inertial forces and the vortex. In comparison with other single-stream particle focusing methods, this device requires no sheath flow, is easy for fabrication and operation, and can work over a wide range of Reynolds numbers from 19.1–142.9. The highly ordered particle chain could be potentially utilized in a variety of lab-chip applications, including micro-flow cytometer, imaging and droplet-based cell entrapment.

  5. Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion

    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.

  6. Multivariable polynomial fitting of controlled single-phase nonlinear load of input current total harmonic distortion

    Sikora Roman

    2018-04-01

    Full Text Available 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.

  7. FRF decoupling of nonlinear systems

    Kalaycıoğlu, Taner; Özgüven, H. Nevzat

    2018-03-01

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

  8. Breakdown of the single-exchange approximation in third-order symmetry-adapted perturbation theory.

    Lao, Ka Un; Herbert, John M

    2012-03-22

    We report third-order symmetry-adapted perturbation theory (SAPT) calculations for several dimers whose intermolecular interactions are dominated by induction. We demonstrate that the single-exchange approximation (SEA) employed to derive the third-order exchange-induction correction (E(exch-ind)((30))) fails to quench the attractive nature of the third-order induction (E(ind)((30))), leading to one-dimensional potential curves that become attractive rather than repulsive at short intermolecular separations. A scaling equation for (E(exch-ind)((30))), based on an exact formula for the first-order exchange correction, is introduced to approximate exchange effects beyond the SEA, and qualitatively correct potential energy curves that include third-order induction are thereby obtained. For induction-dominated systems, our results indicate that a "hybrid" SAPT approach, in which a dimer Hartree-Fock calculation is performed in order to obtain a correction for higher-order induction, is necessary not only to obtain quantitative binding energies but also to obtain qualitatively correct potential energy surfaces. These results underscore the need to develop higher-order exchange-induction formulas that go beyond the SEA. © 2012 American Chemical Society

  9. Analytic theory of alternate multilayer gratings operating in single-order regime.

    Yang, Xiaowei; Kozhevnikov, Igor V; Huang, Qiushi; Wang, Hongchang; Hand, Matthew; Sawhney, Kawal; Wang, Zhanshan

    2017-07-10

    Using the coupled wave approach (CWA), we introduce the analytical theory for alternate multilayer grating (AMG) operating in the single-order regime, in which only one diffraction order is excited. Differing from previous study analogizing AMG to crystals, we conclude that symmetrical structure, or equal thickness of the two multilayer materials, is not the optimal design for AMG and may result in significant reduction in diffraction efficiency. The peculiarities of AMG compared with other multilayer gratings are analyzed. An influence of multilayer structure materials on diffraction efficiency is considered. The validity conditions of analytical theory are also discussed.

  10. Highly ordered uniform single-crystal Bi nanowires: fabrication and characterization

    Bisrat, Y; Luo, Z P; Davis, D; Lagoudas, D

    2007-01-01

    A mechanical pressure injection technique has been used to fabricate uniform bismuth (Bi) nanowires in the pores of an anodic aluminum oxide (AAO) template. The AAO template was prepared from general purity aluminum by a two-step anodization followed by heat treatment to achieve highly ordered nanochannels. The nanowires were then fabricated by an injection technique whereby the molten Bi was injected into the AAO template using a hydraulic pressure method. The Bi nanowires prepared by this method were found to be dense and continuous with uniform diameter throughout the length. Electron diffraction experiments using the transmission electron microscope on cross-sectional and free-standing longitudinal Bi nanowires showed that the majority of the individual nanowires were single crystalline, with preferred orientation of growth along the [011] zone axis of the pseudo-cubic structure. The work presented here provides an inexpensive and effective way of fabricating highly ordered single-crystalline Bi nanowires, with uniform size distributions

  11. Single attosecond pulse from terahertz-assisted high-order harmonic generation

    Balogh, Emeric; Kovacs, Katalin; Dombi, Peter; Fulop, Jozsef A.; Farkas, Gyozo; Hebling, Janos; Tosa, Valer; Varju, Katalin

    2011-08-01

    High-order harmonic generation by few-cycle 800 nm laser pulses in neon gas in the presence of a strong terahertz (THz) field is investigated numerically with propagation effects taken into account. Our calculations show that the combination of THz fields with up to 12 fs laser pulses can be an effective gating technique to generate single attosecond pulses. We show that in the presence of the strong THz field only a single attosecond burst can be phase matched, whereas radiation emitted during other half cycles disappears during propagation. The cutoff is extended and a wide supercontinuum appears in the near-field spectra, extending the available spectral width for isolated attosecond pulse generation from 23 to 93 eV. We demonstrate that phase-matching effects are responsible for the generation of isolated attosecond pulses, even in conditions when single-atom response yields an attosecond pulse train.

  12. Single attosecond pulse from terahertz-assisted high-order harmonic generation

    Balogh, Emeric; Kovacs, Katalin; Dombi, Peter; Farkas, Gyozo; Fulop, Jozsef A.; Hebling, Janos; Tosa, Valer; Varju, Katalin

    2011-01-01

    High-order harmonic generation by few-cycle 800 nm laser pulses in neon gas in the presence of a strong terahertz (THz) field is investigated numerically with propagation effects taken into account. Our calculations show that the combination of THz fields with up to 12 fs laser pulses can be an effective gating technique to generate single attosecond pulses. We show that in the presence of the strong THz field only a single attosecond burst can be phase matched, whereas radiation emitted during other half cycles disappears during propagation. The cutoff is extended and a wide supercontinuum appears in the near-field spectra, extending the available spectral width for isolated attosecond pulse generation from 23 to 93 eV. We demonstrate that phase-matching effects are responsible for the generation of isolated attosecond pulses, even in conditions when single-atom response yields an attosecond pulse train.

  13. Single attosecond pulse from terahertz-assisted high-order harmonic generation

    Balogh, Emeric [Department of Optics and Quantum Electronics, University of Szeged, H-6701 Szeged (Hungary); Kovacs, Katalin [Department of Optics and Quantum Electronics, University of Szeged, H-6701 Szeged (Hungary); National Institute for R and D of Isotopic and Molecular Technologies, RO-400293 Cluj-Napoca (Romania); Dombi, Peter; Farkas, Gyozo [Research Institute for Solid State Physics and Optics, H-1525 Budapest (Hungary); Fulop, Jozsef A.; Hebling, Janos [Department of Experimental Physics, University of Pecs, H-7624 Pecs (Hungary); Tosa, Valer [National Institute for R and D of Isotopic and Molecular Technologies, RO-400293 Cluj-Napoca (Romania); Varju, Katalin [HAS Research Group on Laser Physics, University of Szeged, H-6701 Szeged (Hungary)

    2011-08-15

    High-order harmonic generation by few-cycle 800 nm laser pulses in neon gas in the presence of a strong terahertz (THz) field is investigated numerically with propagation effects taken into account. Our calculations show that the combination of THz fields with up to 12 fs laser pulses can be an effective gating technique to generate single attosecond pulses. We show that in the presence of the strong THz field only a single attosecond burst can be phase matched, whereas radiation emitted during other half cycles disappears during propagation. The cutoff is extended and a wide supercontinuum appears in the near-field spectra, extending the available spectral width for isolated attosecond pulse generation from 23 to 93 eV. We demonstrate that phase-matching effects are responsible for the generation of isolated attosecond pulses, even in conditions when single-atom response yields an attosecond pulse train.

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

    Lee, Kyo-Beum; Blaabjerg, Frede

    2004-01-01

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

  15. Linear and non-linear stability analysis for finite difference discretizations of high-order Boussinesq equations

    Fuhrman, David R.; Bingham, Harry B.; Madsen, Per A.

    2004-01-01

    of rotational and irrotational formulations in two horizontal dimensions provides evidence that the irrotational formulation has significantly better stability properties when the deep-water non-linearity is high, particularly on refined grids. Computation of matrix pseudospectra shows that the system is only...... insight into the numerical behaviour of this rather complicated system of non-linear PDEs....

  16. Deuteron NMR resolved mesogen vs. crosslinker molecular order and reorientational exchange in liquid single crystal elastomers

    Milavec, J.; Domenici, V.; Zupančič, B.; Rešetič, A.; Bubnov, Alexej; Zalar, B.

    2016-01-01

    Roč. 18, č. 5 (2016), s. 4071-4077 ISSN 1463-9076 R&D Projects: GA ČR GA15-02843S; GA MŠk(CZ) LD14007 Grant - others:EU - ICT(XE) COST Action IC1208 Institutional support: RVO:68378271 Keywords : liquid single crystal elastomer * NMR * liquid crystal * molecular order * monomers Subject RIV: JJ - Other Materials Impact factor: 4.123, year: 2016

  17. Growth and dielectric, mechanical, thermal and etching studies of an organic nonlinear optical L-arginine trifluoroacetate (LATF) single crystal

    Arjunan, S.; Mohan Kumar, R.; Mohan, R.; Jayavel, R.

    2008-01-01

    L-arginine trifluoroacetate, an organic nonlinear optical material, has been synthesized from aqueous solution. Bulk single crystal of dimension 57 mm x 5 mm x 3 mm has been grown by temperature lowering technique. Powder X-ray diffraction studies confirmed the monoclinic structure of the grown L-arginine trifluoroacetate crystal. Linear optical property of the grown crystal has been studied by UV-vis spectrum. Dielectric response of the L-arginine trifluoroacetate crystal was analysed for different frequencies and temperatures in detail. Microhardness study on the sample reveals that the crystal possesses relatively higher hardness compared to many organic crystals. Thermal analyses confirmed that the L-arginine trifluoroacetate material is thermally stable upto 212 deg. C. The etching studies have been performed to assess the perfection of the L-arginine trifluoroacetate crystal. Kurtz powder second harmonic generation test confirms the nonlinear optical properties of the as-grown L-arginine trifluoroacetate crystal

  18. Ultrafast carrier dynamics and third-order nonlinear optical properties of AgInS2/ZnS nanocrystals

    Yu, Kuai; Yang, Yang; Wang, Junzhong; Tang, Xiaosheng; Xu, Qing-Hua; Wang, Guo Ping

    2018-06-01

    Broad photoluminescence (PL) emission, a large Stokes shift and extremely long-lived radiative lifetimes are the characteristics of ternary I–III–VI semiconductor nanocrystals (NCs), such as CuInS2 and AgInS2. However, the lack of understanding regarding the intriguing PL mechanisms and photo-carrier dynamics limits their further applications. Here, AgInS2 and AgInS2/ZnS NCs were chemically synthesized and their carrier dynamics were studied by time-resolved PL spectroscopy. The results demonstrated that the surface defect state, which contributed dominantly to the non-radiative decay processes, was effectively passivated through ZnS alloying. Femtosecond transient absorption spectroscopy was also used to investigate the carrier dynamics, revealing the electron storage at the surface state and donor state. Furthermore, the two photon absorption properties of AgInS2 and AgInS2/ZnS NCs were measured using an open-aperture Z-scan technique. The improved third-order nonlinear susceptibility {χ }(3) of AgInS2 through ZnS alloying demonstrates potential application in two photon PL biological imaging.

  19. Nonlinear optics at the single-photon level inside a hollow core fiber

    Hofferberth, Sebastian; Peyronel, Thibault; Liang, Qiyu

    2011-01-01

    Cold atoms inside a hollow core fiber provide an unique system for studying optical nonlinearities at the few-photon level. Confinement of both atoms and photons inside the fiber core to a diameter of just a few wavelengths results in high electric field intensity per photon and large optical...

  20. The AOLI low-order non-linear curvature wavefront sensor: laboratory and on-sky results

    Crass, Jonathan; King, David; MacKay, Craig

    2014-08-01

    Many adaptive optics (AO) systems in use today require the use of bright reference objects to determine the effects of atmospheric distortions. Typically these systems use Shack-Hartmann Wavefront sensors (SHWFS) to distribute incoming light from a reference object between a large number of sub-apertures. Guyon et al. evaluated the sensitivity of several different wavefront sensing techniques and proposed the non-linear Curvature Wavefront Sensor (nlCWFS) offering improved sensitivity across a range of orders of distortion. On large ground-based telescopes this can provide nearly 100% sky coverage using natural guide stars. We present work being undertaken on the nlCWFS development for the Adaptive Optics Lucky Imager (AOLI) project. The wavefront sensor is being developed as part of a low-order adaptive optics system for use in a dedicated instrument providing an AO corrected beam to a Lucky Imaging based science detector. The nlCWFS provides a total of four reference images on two photon-counting EMCCDs for use in the wavefront reconstruction process. We present results from both laboratory work using a calibration system and the first on-sky data obtained with the nlCWFS at the 4.2 metre William Herschel Telescope, La Palma. In addition, we describe the updated optical design of the wavefront sensor, strategies for minimising intrinsic effects and methods to maximise sensitivity using photon-counting detectors. We discuss on-going work to develop the high speed reconstruction algorithm required for the nlCWFS technique. This includes strategies to implement the technique on graphics processing units (GPUs) and to minimise computing overheads to obtain a prior for a rapid convergence of the wavefront reconstruction. Finally we evaluate the sensitivity of the wavefront sensor based upon both data and low-photon count strategies.

  1. A single dose of oxytocin nasal spray improves higher-order social cognition in schizophrenia.

    Guastella, Adam J; Ward, Philip B; Hickie, Ian B; Shahrestani, Sara; Hodge, Marie Antoinette Redoblado; Scott, Elizabeth M; Langdon, Robyn

    2015-11-01

    Schizophrenia is associated with significant impairments in both higher and lower order social cognitive performance and these impairments contribute to poor social functioning. People with schizophrenia report poor social functioning to be one of their greatest unmet treatment needs. Recent studies have suggested the potential of oxytocin as such a treatment, but mixed results render it uncertain what aspects of social cognition are improved by oxytocin and, subsequently, how oxytocin might best be applied as a therapeutic. The aim of this study was to determine whether a single dose of oxytocin improved higher-order and lower-order social cognition performance for patients with schizophrenia across a well-established battery of social cognition tests. Twenty-one male patients received both a single dose of oxytocin nasal spray (24IU) and a placebo, two weeks apart in a randomized within-subjects placebo controlled design. Following each administration, participants completed the social cognition tasks, as well as a test of general neurocognition. Results revealed that oxytocin particularly enhanced performance on higher order social cognition tasks, with no effects on general neurocognition. Results for individual tasks showed most improvement on tests measuring appreciation of indirect hints and recognition of social faux pas. These results suggest that oxytocin, if combined to enhance social cognition learning, may be beneficial when targeted at higher order social cognition domains. This study also suggests that these higher order tasks, which assess social cognitive processing in a social communication context, may provide useful markers of response to oxytocin in schizophrenia. Copyright © 2015 Elsevier B.V. All rights reserved.

  2. Third-order nonlinear optical properties of 1,3-bis(3,4-dimethoxyphenyl) prop-2-en-1-one under femtosecond laser pulses

    Maidur, Shivaraj R.; Patil, Parutagouda Shankaragouda; Rao, S. Venugopal

    2018-04-01

    In this paper, we present the third-order nonlinear optical (NLO) studies of 1,3-bis(3,4-dimethoxyphenyl)prop-2-en-1-one (abbreviated as VDMC). The chalcone was synthesized by Claisen-Schmidt condensation method. The third-order nonlinear optical properties were evaluated using standard, well-known Z-scan technique under femtosecond laser regime (150 fs, 900 nm) with two different laser repetition rates 500 Hz and 80 MHz. Open aperture studies showed that the molecule possess two photon absorption with the coefficients in the order 10-9 cmW-1. The closed aperture studies have resulted the negative nonlinear refraction with the coefficients in the order 10-14 cm2W-1. The two-photon absorption cross sections were estimated. Optical limiting properties have been studied and the limiting threshold values were found to be in the range 0.86-2.3 mJ/cm2, which suggests that VDMC has better applications in the field of nonlinear optics.

  3. Nonlinear optics

    Bloembergen, Nicolaas

    1996-01-01

    Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe

  4. Electrocatalytic oxidation of alcohols on single gold particles in highly ordered SiO2 cavities

    Li, Na; Zhou, Qun; Tian, Shu; Zhao, Hong; Li, Xiaowei; Adkins, Jason; Gu, Zhuomin; Zhao, Lili; Zheng, Junwei

    2013-01-01

    In the present work, we report a new and simple approach for preparing a highly ordered Au (1 1 1) nanoparticle (NP) array in SiO 2 cavities on indium-doped tin oxide (ITO) electrodes. We fabricated a SiO 2 cavity array on the surface of an ITO electrode using highly ordered self-assembly of polystyrene spheres as a template. Gold NPs were electrodeposited at the bottom of the SiO 2 cavities, and single gold NPs dominated with (1 1 1) facets were generated in each cavity by annealing the electrode at a high temperature. Such (1 1 1) facets were the predominate trait of the single gold particle which exhibited considerable electrocatalytic activity toward oxidation of methanol, ethanol, and glycerol. This has been attributed to the formation of incipient hydrous oxides at unusually low potential on the specific (1 1 1) facet of the gold particles. Moreover, each cavity of the SiO 2 possibly behaves as an independent electrochemical cell in which the methanol molecules are trapped; this produces an environment advantageous to catalyzing electrooxidation. The oxidation of methanol on the electrodes is a mixed control mechanism (both by diffusion and electrode kinetics). This strategy both provided an approach to study electrochemical reactions on a single particle in a microenvironment and may supply a way to construct alcohols sensors

  5. Effect of higher order nonlinearity, directionality and finite water depth on wave statistics: Comparison of field data and numerical simulations

    Fernández, Leandro; Monbaliu, Jaak; Onorato, Miguel; Toffoli, Alessandro

    2014-05-01

    This research is focused on the study of nonlinear evolution of irregular wave fields in water of arbitrary depth by comparing field measurements and numerical simulations.It is now well accepted that modulational instability, known as one of the main mechanisms for the formation of rogue waves, induces strong departures from Gaussian statistics. However, whereas non-Gaussian properties are remarkable when wave fields follow one direction of propagation over an infinite water depth, wave statistics only weakly deviate from Gaussianity when waves spread over a range of different directions. Over finite water depth, furthermore, wave instability attenuates overall and eventually vanishes for relative water depths as low as kh=1.36 (where k is the wavenumber of the dominant waves and h the water depth). Recent experimental results, nonetheless, seem to indicate that oblique perturbations are capable of triggering and sustaining modulational instability even if khthe aim of this research is to understand whether the combined effect of directionality and finite water depth has a significant effect on wave statistics and particularly on the occurrence of extremes. For this purpose, numerical experiments have been performed solving the Euler equation of motion with the Higher Order Spectral Method (HOSM) and compared with data of short crested wave fields for different sea states observed at the Lake George (Australia). A comparative analysis of the statistical properties (i.e. density function of the surface elevation and its statistical moments skewness and kurtosis) between simulations and in-situ data provides a confrontation between the numerical developments and real observations in field conditions.

  6. Linear and nonlinear auditory response properties of interneurons in a high-order avian vocal motor nucleus during wakefulness.

    Raksin, Jonathan N; Glaze, Christopher M; Smith, Sarah; Schmidt, Marc F

    2012-04-01

    Motor-related forebrain areas in higher vertebrates also show responses to passively presented sensory stimuli. However, sensory tuning properties in these areas, especially during wakefulness, and their relation to perception, are poorly understood. In the avian song system, HVC (proper name) is a vocal-motor structure with auditory responses well defined under anesthesia but poorly characterized during wakefulness. We used a large set of stimuli including the bird's own song (BOS) and many conspecific songs (CON) to characterize auditory tuning properties in putative interneurons (HVC(IN)) during wakefulness. Our findings suggest that HVC contains a diversity of responses that vary in overall excitability to auditory stimuli, as well as bias in spike rate increases to BOS over CON. We used statistical tests to classify cells in order to further probe auditory responses, yielding one-third of neurons that were either unresponsive or suppressed and two-thirds with excitatory responses to one or more stimuli. A subset of excitatory neurons were tuned exclusively to BOS and showed very low linearity as measured by spectrotemporal receptive field analysis (STRF). The remaining excitatory neurons responded well to CON stimuli, although many cells still expressed a bias toward BOS. These findings suggest the concurrent presence of a nonlinear and a linear component to responses in HVC, even within the same neuron. These characteristics are consistent with perceptual deficits in distinguishing BOS from CON stimuli following lesions of HVC and other song nuclei and suggest mirror neuronlike qualities in which "self" (here BOS) is used as a referent to judge "other" (here CON).

  7. Third-order nonlinear optical properties of open-shell supermolecular systems composed of acetylene linked phenalenyl radicals.

    Nakano, Masayoshi; Kishi, Ryohei; Yoneda, Kyohei; Inoue, Yudai; Inui, Tomoya; Shigeta, Yasuteru; Kubo, Takashi; Champagne, Benoît

    2011-08-11

    The third-order nonlinear optical (NLO) properties, at the molecular level, the static second hyperpolarizabilities, γ, of supermolecular systems composed of phenalenyl and pyrene rings linked by acetylene units are investigated by employing the long-range corrected spin-unrestricted density functional theory, LC-UBLYP, method. The phenalenyl based superethylene, superallyl, and superbutadiene in their lowest spin states have intermediate diradical characters and exhibit larger γ values than the closed-shell pyrene based superpolyene systems. The introduction of a positive charge into the phenalenyl based superallyl radical changes the sign of γ and enhances its amplitude by a factor of 35. Although such sign inversion is also observed in the allyl radical and cation systems in their ground state equilibrium geometries, the relative amplitude of γ is much different, that is, |γ(regular allyl cation)/γ(regular allyl radical)| = 0.61 versus |γ(phenalenyl based superallyl cation)/γ(phenalenyl based superallyl radical)| = 35. In contrast, the model ethylene, allyl radical/cation, and butadiene systems with stretched carbon-carbon bond lengths (2.0 Å), having intermediate diradical characters, exhibit similar γ features to those of the phenalenyl based superpolyene systems. This exemplifies that the size dependence of γ as well as its sign change by introducing a positive charge on the phenalenyl based superpolyene systems originate from their intermediate diradical characters. In addition, the change from the lowest to the highest π-electron spin states significantly reduces the γ amplitudes of the neutral phenalenyl based superpolyene systems. For phenalenyl based superallyl cation, the sign inversion of γ (from negative to positive) is observed upon switching between the singlet and triplet states, which is predicted to be associated with a modification of the balance between the positive and negative contributions to γ. The present study paves the way

  8. Stability analysis solutions and optical solitons in extended nonlinear Schrödinger equation with higher-order odd and even terms

    Peng, Wei-Qi; Tian, Shou-Fu; Zou, Li; Zhang, Tian-Tian

    2018-01-01

    In this paper, the extended nonlinear Schrödinger equation with higher-order odd (third order) and even (fourth order) terms is investigated, whose particular cases are the Hirota equation, the Sasa-Satsuma equation and Lakshmanan-Porsezian-Daniel equation by selecting some specific values on the parameters of higher-order terms. We first study the stability analysis of the equation. Then, using the ansatz method, we derive its bright, dark solitons and some constraint conditions which can guarantee the existence of solitons. Moreover, the Ricatti equation extension method is employed to derive some exact singular solutions. The outstanding characteristics of these solitons are analyzed via several diverting graphics.

  9. Bulk monocrystal growth, optical, dielectric, third order nonlinear, thermal and mechanical studies on HCl added L-alanine: An organic NLO material

    Shkir, Mohd, E-mail: shkirphysics@gmail.com [Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Physics Department, Faculty of Science, King Khalid University, Abha (Saudi Arabia); Yahia, I.S., E-mail: dr_isyahia@yahoo.com [Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Physics Department, Faculty of Science, King Khalid University, Abha (Saudi Arabia); Nano-Science & Semiconductor Labs, Physics Department, Faculty of Education, Ain Shams University, Roxy, Cairo (Egypt); Al-Qahtani, A.M.A. [Advanced Functional Materials & Optoelectronic Laboratory (AFMOL), Physics Department, Faculty of Science, King Khalid University, Abha (Saudi Arabia)

    2016-12-01

    In the current work, good quality bulk size (∼32 mm × 23 mm × 10 mm) single crystals of HCl added L-alanine with well-defined morphology are successfully grown using slow evaporation technique. Crystal structure and other structural parameters were evaluated from X-ray diffraction data. Vibrational assessment of the grown crystal was done by FT-Raman analysis. The presence of chlorine and good quality of the grown crystal was confirmed by SEM/EDX analysis. Solid state UV–Vis–NIR diffused reflectance was measured and direct and indirect optical band gap was calculated using Kubelka-Munk relation and found to be 5.64 and 5 eV respectively. Dielectric measurement was carried out in high frequency range. Third order nonlinear optical susceptibility value was found to be enhanced from 1.91 × 10{sup −6} (pure) to 8.6 × 10{sup −6} esu (LAHCl). Good thermal stability of grown crystals was confirmed from DSC analysis. The enhancement in mechanical strength and crystalline perfection was also observed. - Highlights: • Bulk size (32 mm × 23 mm × 10 mm), good crystalline perfection HCl added L-alanine monocrystal is grown. • The shift in X-ray diffraction and vibrational peaks confirms the interaction of HCl. • The high optical transparency and band gap confirms its application in optoelectronic devices. • Third order NLO properties are found to be enhanced in HCl added L-alanine crystals. • The mechanical strength of the grown crystals is found to be enhanced due HCl addition.

  10. Symmetric and arbitrarily high-order Birkhoff-Hermite time integrators and their long-time behaviour for solving nonlinear Klein-Gordon equations

    Liu, Changying; Iserles, Arieh; Wu, Xinyuan

    2018-03-01

    The Klein-Gordon equation with nonlinear potential occurs in a wide range of application areas in science and engineering. Its computation represents a major challenge. The main theme of this paper is the construction of symmetric and arbitrarily high-order time integrators for the nonlinear Klein-Gordon equation by integrating Birkhoff-Hermite interpolation polynomials. To this end, under the assumption of periodic boundary conditions, we begin with the formulation of the nonlinear Klein-Gordon equation as an abstract second-order ordinary differential equation (ODE) and its operator-variation-of-constants formula. We then derive a symmetric and arbitrarily high-order Birkhoff-Hermite time integration formula for the nonlinear abstract ODE. Accordingly, the stability, convergence and long-time behaviour are rigorously analysed once the spatial differential operator is approximated by an appropriate positive semi-definite matrix, subject to suitable temporal and spatial smoothness. A remarkable characteristic of this new approach is that the requirement of temporal smoothness is reduced compared with the traditional numerical methods for PDEs in the literature. Numerical results demonstrate the advantage and efficiency of our time integrators in comparison with the existing numerical approaches.

  11. Single-Molecule Kinetics Reveal Cation-Promoted DNA Duplex Formation Through Ordering of Single-Stranded Helices

    Dupuis, Nicholas F.; Holmstrom, Erik D.; Nesbitt, David J.

    2013-01-01

    In this work, the kinetics of short, fully complementary oligonucleotides are investigated at the single-molecule level. Constructs 6–9 bp in length exhibit single exponential kinetics over 2 orders of magnitude time for both forward (kon, association) and reverse (koff, dissociation) processes. Bimolecular rate constants for association are weakly sensitive to the number of basepairs in the duplex, with a 2.5-fold increase between 9 bp (k′on = 2.1(1) × 106 M−1 s−1) and 6 bp (k′on = 5.0(1) × 106 M−1 s−1) sequences. In sharp contrast, however, dissociation rate constants prove to be exponentially sensitive to sequence length, varying by nearly 600-fold over the same 9 bp (koff = 0.024 s−1) to 6 bp (koff = 14 s−1) range. The 8 bp sequence is explored in more detail, and the NaCl dependence of kon and koff is measured. Interestingly, konincreases by >40-fold (kon = 0.10(1) s−1 to 4.0(4) s−1 between [NaCl] = 25 mM and 1 M), whereas in contrast, koffdecreases by fourfold (0.72(3) s−1 to 0.17(7) s−1) over the same range of conditions. Thus, the equilibrium constant (Keq) increases by ≈160, largely due to changes in the association rate, kon. Finally, temperature-dependent measurements reveal that increased [NaCl] reduces the overall exothermicity (ΔΔH° > 0) of duplex formation, albeit by an amount smaller than the reduction in entropic penalty (−TΔΔS° duplex formation. PMID:23931323

  12. Variable-coefficient higher-order nonlinear Schroedinger model in optical fibers: Variable-coefficient bilinear form, Baecklund transformation, brightons and symbolic computation

    Tian Bo; Gao Yitian; Zhu Hongwu

    2007-01-01

    Symbolically investigated in this Letter is a variable-coefficient higher-order nonlinear Schroedinger (vcHNLS) model for ultrafast signal-routing, fiber laser systems and optical communication systems with distributed dispersion and nonlinearity management. Of physical and optical interests, with bilinear method extend, the vcHNLS model is transformed into a variable-coefficient bilinear form, and then an auto-Baecklund transformation is constructed. Constraints on coefficient functions are analyzed. Potentially observable with future optical-fiber experiments, variable-coefficient brightons are illustrated. Relevant properties and features are discussed as well. Baecklund transformation and other results of this Letter will be of certain value to the studies on inhomogeneous fiber media, core of dispersion-managed brightons, fiber amplifiers, laser systems and optical communication links with distributed dispersion and nonlinearity management

  13. Diagnostic study of the roughness surface effect of zirconium on the third-order nonlinear-optical properties of thin films based on zinc oxide nanomaterials

    Bahedi, K., E-mail: bahedikhadija@yahoo.com [Laboratoire Optoelectronique et Physico-chimie des Materiaux Universite Ibn Tofail, Faculte des Sciences BP 133 Kenitra 14000, Maroc (Morocco); Addou, M.; El Jouad, M.; Sofiani, Z.; Alaoui Lamrani, M.; El Habbani, T.; Fellahi, N.; Bayoud, S.; Dghoughi, L. [Laboratoire Optoelectronique et Physico-chimie des Materiaux Universite Ibn Tofail, Faculte des Sciences BP 133 Kenitra 14000, Maroc (Morocco); Sahraoui, B.; Essaidi, Z. [Laboratoire POMA, UMR CNRS 6136, Universite d' Angers 2, Bd Lavoisier, 49045 France (France)

    2009-02-01

    Zinc oxide (ZnO) and zirconium doped zinc oxide (ZnO:Zr) thin films were deposited by reactive chemical pulverization spray pyrolysis technique on heated glass substrates at 500 deg. C using zinc and zirconium chlorides as precursors. Effects of zirconium doping agent and surface roughness on the nonlinear optical properties were investigated in detail using atomic force microscopy (AFM) and third harmonic generation (THG) technique. The best value of nonlinear optical susceptibility {chi}{sup (3)} was obtained from the doped films with less roughness. A strong third order nonlinear optical susceptibility {chi}{sup (3)} = 20.12 x 10{sup -12} (esu) of the studied films was found for the 3% doped sample.

  14. Distributed Adaptive Neural Network Output Tracking of Leader-Following High-Order Stochastic Nonlinear Multiagent Systems With Unknown Dead-Zone Input.

    Hua, Changchun; Zhang, Liuliu; Guan, Xinping

    2017-01-01

    This paper studies the problem of distributed output tracking consensus control for a class of high-order stochastic nonlinear multiagent systems with unknown nonlinear dead-zone under a directed graph topology. The adaptive neural networks are used to approximate the unknown nonlinear functions and a new inequality is used to deal with the completely unknown dead-zone input. Then, we design the controllers based on backstepping method and the dynamic surface control technique. It is strictly proved that the resulting closed-loop system is stable in probability in the sense of semiglobally uniform ultimate boundedness and the tracking errors between the leader and the followers approach to a small residual set based on Lyapunov stability theory. Finally, two simulation examples are presented to show the effectiveness and the advantages of the proposed techniques.

  15. Modulation stability and dispersive optical soliton solutions of higher order nonlinear Schrödinger equation and its applications in mono-mode optical fibers

    Arshad, Muhammad; Seadawy, Aly R.; Lu, Dianchen

    2018-01-01

    In mono-mode optical fibers, the higher order non-linear Schrödinger equation (NLSE) describes the propagation of enormously short light pulses. We constructed optical solitons and, solitary wave solutions of higher order NLSE mono-mode optical fibers via employing modified extended mapping method which has important applications in Mathematics and physics. Furthermore, the formation conditions are also given on parameters in which optical bright and dark solitons can exist for this media. The moment of the obtained solutions are also given graphically, that helps to realize the physical phenomena's of this model. The modulation instability analysis is utilized to discuss the model stability, which verifies that all obtained solutions are exact and stable. Many other such types of models arising in applied sciences can also be solved by this reliable, powerful and effective method. The method can also be functional to other sorts of higher order nonlinear problems in contemporary areas of research.

  16. Estimation of Joule heating and its role in nonlinear electrical response of Tb0.5Sr0.5MnO3 single crystal

    Nhalil, Hariharan; Elizabeth, Suja

    2016-12-01

    Highly non-linear I-V characteristics and apparent colossal electro-resistance were observed in non-charge ordered manganite Tb0.5Sr0.5MnO3 single crystal in low temperature transport measurements. Significant changes were noticed in top surface temperature of the sample as compared to its base while passing current at low temperature. By analyzing these variations, we realize that the change in surface temperature (ΔTsur) is too small to have caused by the strong negative differential resistance. A more accurate estimation of change in the sample temperature was made by back-calculating the sample temperature from the temperature variation of resistance (R-T) data (ΔTcal), which was found to be higher than ΔTsur. This result indicates that there are large thermal gradients across the sample. The experimentally derived ΔTcal is validated with the help of a simple theoretical model and estimation of Joule heating. Pulse measurements realize substantial reduction in Joule heating. With decrease in sample thickness, Joule heating effect is found to be reduced. Our studies reveal that Joule heating plays a major role in the nonlinear electrical response of Tb0.5Sr0.5MnO3. By careful management of the duty cycle and pulse current I-V measurements, Joule heating can be mitigated to a large extent.

  17. Carbon nanotubes as electromechanical resonators : Single-electron tunneling, nonlinearity, and high-bandwidth readout

    Meerwaldt, H.B.

    2013-01-01

    A carbon nanotube (CNT) is a remarkable material and can be thought of as a single-atom thick cylinder of carbon atoms capped of with a semisphere. This is called a single-walled CNT and, depending on how the cylinder is rolled up, CNTs are either semiconducting or metallic. A CNT is made into a

  18. Laser direct-write of single microbeads into spatially-ordered patterns

    Phamduy, Theresa B; Schiele, Nathan R; Corr, David T; Chrisey, Douglas B; Raof, Nurazhani Abdul; Xie Yubing; Yan Zijie; Huang Yong

    2012-01-01

    Fabrication of heterogeneous microbead patterns on a bead-by-bead basis promotes new opportunities for sensors, lab-on-a-chip technology and cell-culturing systems within the context of customizable constructs. Laser direct-write (LDW) was utilized to target and deposit solid polystyrene and stem cell-laden alginate hydrogel beads into computer-programmed patterns. We successfully demonstrated single-bead printing resolution and fabricated spatially-ordered patterns of microbeads. The probability of successful microbead transfer from the ribbon surface increased from 0 to 80% with decreasing diameter of 600 to 45 µm, respectively. Direct-written microbeads retained spatial pattern registry, even after 10 min of ultrasonication treatment. SEM imaging confirmed immobilization of microbeads. Viability of cells encapsulated in transferred hydrogel microbeads achieved 37 ± 11% immediately after the transfer process, whereas randomly-patterned pipetted control beads achieved a viability of 51 ± 25%. Individual placement of >10 µm diameter microbeads onto planar surfaces has previously been unattainable. We have demonstrated LDW as a valuable tool for the patterning of single, micrometer-diameter beads into spatially-ordered patterns. (paper)

  19. Spiro-OMeTAD single crystals: Remarkably enhanced charge-carrier transport via mesoscale ordering

    Shi, Dong

    2016-04-15

    We report the crystal structure and hole-transport mechanism in spiro-OMeTAD [2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenyl-amine)9,9′-spirobifluorene], the dominant hole-transporting material in perovskite and solid-state dye-sensitized solar cells. Despite spiro-OMeTAD’s paramount role in such devices, its crystal structure was unknown because of highly disordered solution-processed films; the hole-transport pathways remained ill-defined and the charge carrier mobilities were low, posing a major bottleneck for advancing cell efficiencies. We devised an antisolvent crystallization strategy to grow single crystals of spiro-OMeTAD, which allowed us to experimentally elucidate its molecular packing and transport properties. Electronic structure calculations enabled us to map spiro-OMeTAD’s intermolecular charge-hopping pathways. Promisingly, single-crystal mobilities were found to exceed their thin-film counterparts by three orders of magnitude. Our findings underscore mesoscale ordering as a key strategy to achieving breakthroughs in hole-transport material engineering of solar cells.

  20. Analysis of second order harmonic distortion due to transmitter non-linearity and chromatic and modal dispersion of optical OFDM SSB modulated signals in SMF-MMF fiber links

    Patel, Dhananjay; Singh, Vinay Kumar; Dalal, U. D.

    2017-01-01

    Single mode fibers (SMF) are typically used in Wide Area Networks (WAN), Metropolitan Area Networks (MAN) and also find applications in Radio over Fiber (RoF) architectures supporting data transmission in Fiber to the Home (FTTH), Remote Antenna Units (RAUs), in-building networks etc. Multi-mode fibers (MMFs) with low cost, ease of installation and low maintenance are predominantly (85-90%) deployed in-building networks providing data access in local area networks (LANs). The transmission of millimeter wave signals through the SMF in WAN and MAN, along with the reuse of MMF in-building networks will not levy fiber reinstallation cost. The transmission of the millimeter waves experiences signal impairments due to the transmitter non-linearity and modal dispersion of the MMF. The MMF exhibiting large modal dispersion limits the bandwidth-length product of the fiber. The second and higher-order harmonics present in the optical signal fall within the system bandwidth. This causes degradation in the received signal and an unwanted radiation of power at the RAU. The power of these harmonics is proportional to the non-linearity of the transmitter and the modal dispersion of the MMF and should be maintained below the standard values as per the international norms. In this paper, a mathematical model is developed for Second-order Harmonic Distortion (HD2) generated due to non-linearity of the transmitter and chromatic-modal dispersion of the SMF-MMF optic link. This is also verified using a software simulation. The model consists of a Mach Zehnder Modulator (MZM) that generates two m-QAM OFDM Single Sideband (SSB) signals based on phase shift of the hybrid coupler (90° and 120°). Our results show that the SSB signal with 120° hybrid coupler has suppresses the higher-order harmonics and makes the system more robust against the HD2 in the SMF-MMF optic link.