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Academic literature on the topic 'Nonlinear'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2024

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Journal articles on the topic "Nonlinear"

1

TRUEBA, JOSÉ L., JOAQUÍN RAMS, and MIGUEL A. F. SANJUÁN. "ANALYTICAL ESTIMATES OF THE EFFECT OF NONLINEAR DAMPING IN SOME NONLINEAR OSCILLATORS." International Journal of Bifurcation and Chaos 10, no. 09 (September 2000): 2257–67. http://dx.doi.org/10.1142/s0218127400001419.

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This paper reports on the effect of nonlinear damping on certain nonlinear oscillators, where analytical estimates provided by the Melnikov theory are obtained. We assume general nonlinear damping terms proportional to the power of velocity. General and useful expressions for the nonlinearly damped Duffing oscillator and for the nonlinearly damped simple pendulum are computed. They provide the critical parameters in terms of the damping coefficient and damping exponent, that is, the power of the velocity, for which complicated behavior is expected. We also consider generalized nonlinear damped systems, which may contain several nonlinear damping terms. Using the idea of Melnikov equivalence, we show that the effect of nonlinear dissipation can be equivalent to a linearly damped nonlinear oscillator with a modified damping coefficient.

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Wang, Yunze, Yan Sheng, Shan Liu, Ruwei Zhao, Tianxiang Xu, Tiefeng Xu, Feng Chen, and Wieslaw Krolikowski. "Wavelength-dependent nonlinear wavefront shaping in 3D nonlinear photonic crystal." Chinese Optics Letters 22, no. 7 (2024): 071901. http://dx.doi.org/10.3788/col202422.071901.

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Kosek, Zdeněk. "Nonlinear boundary value problem for a system of nonlinear ordinary differential equations." Časopis pro pěstování matematiky 110, no. 2 (1985): 130–44. http://dx.doi.org/10.21136/cpm.1985.108595.

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Tejedor Sastre, María Teresa, and Christian Vanhille. "Nonlinear Maximization of the Sum-Frequency Component from Two Ultrasonic Signals in a Bubbly Liquid." Sensors 20, no. 1 (December 23, 2019): 113. http://dx.doi.org/10.3390/s20010113.

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Techniques based on ultrasound in nondestructive testing and medical imaging analyze the response of the source frequencies (linear theory) or the second-order frequencies such as higher harmonics, difference and sum frequencies (nonlinear theory). The low attenuation and high directivity of the difference-frequency component generated nonlinearly by parametric arrays are useful. Higher harmonics created directly from a single-frequency source and the sum-frequency component generated nonlinearly by parametric arrays are attractive because of their high spatial resolution and accuracy. The nonlinear response of bubbly liquids can be strong even at relatively low acoustic pressure amplitudes. Thus, these nonlinear frequencies can be generated easily in these media. Since the experimental study of such nonlinear waves in stable bubbly liquids is a very difficult task, in this work we use a numerical model developed previously to describe the nonlinear propagation of ultrasound interacting with nonlinearly oscillating bubbles in a liquid. This numerical model solves a differential system coupling a Rayleigh–Plesset equation and the wave equation. This paper performs an analysis of the generation of the sum-frequency component by nonlinear mixing of two signals of lower frequencies. It shows that the amplitude of this component can be maximized by taking into account the nonlinear resonance of the system. This effect is due to the softening of the medium when pressure amplitudes rise.

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Vatanshenas, Ali. "Nonlinear Analysis of Reinforced Concrete Shear Walls Using Nonlinear Layered Shell Approach." Nordic Concrete Research 65, no. 2 (December 1, 2021): 63–79. http://dx.doi.org/10.2478/ncr-2021-0014.

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Abstract This study discusses nonlinear modelling of a reinforced concrete wall utilizing the nonlinear layered shell approach. Rebar, unconfined and confined concrete behaviours are defined nonlinearly using proposed analytical models in the literature. Then, finite element model is validated using experimental results. It is shown that the nonlinear layered shell approach is capable of estimating wall response (i.e., stiffness, ultimate strength, and cracking pattern) with adequate accuracy and low computational effort. Modal analysis is conducted to evaluate the inherent characteristics of the wall to choose a logical loading pattern for the nonlinear static analysis. Moreover, pushover analysis’ outputs are interpreted comprehensibly from cracking of the concrete until reaching the rupture step by step.

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Kubáček, Lubomír. "Nonlinear error propagation law." Applications of Mathematics 41, no. 5 (1996): 329–45. http://dx.doi.org/10.21136/am.1996.134330.

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Knobloch, H. W. "Observability of nonlinear systems." Mathematica Bohemica 131, no. 4 (2006): 411–18. http://dx.doi.org/10.21136/mb.2006.133974.

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Gerasimchuk, V. S., I. V. Gerasimchuk, and N. I. Dranik. "Solutions of Nonlinear Schrodinger Equation with Two Potential Wells in Linear / Nonlinear Media." Zurnal matematiceskoj fiziki, analiza, geometrii 12, no. 2 (June 25, 2016): 168–76. http://dx.doi.org/10.15407/mag12.02.168.

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Wang, Meiqiao, and Wuquan Li. "Distributed adaptive control for nonlinear multi-agent systems with nonlinear parametric uncertainties." Mathematical Biosciences and Engineering 20, no. 7 (2023): 12908–22. http://dx.doi.org/10.3934/mbe.2023576.

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<abstract><p>This paper considers the distributed tracking control problem for a class of nonlinear multi-agent systems with nonlinearly parameterized control coefficients and inherent nonlinearities. The essential of multi-agent systems makes it difficult to directly generalize the existing works for single nonlinearly parameterized systems with uncontrollable unstable linearization to the case in this paper. To dominate the inherent nonlinearities and nonlinear parametric uncertainties, a powerful distributed adaptive tracking control is presented by combing the algebra graph theory with the distributed backstepping method, which guarantees that all the closed-loop system signals are global bounded while the range of the tracking error between the follower's output and the leader's output can be tuned arbitrarily small. Finally, a numerical example is provided to verify the validity of the developed methods.</p></abstract>

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Zhu, Yun-Peng, Z. Q. Lang, and Yu-Zhu Guo. "Nonlinear model standardization for the analysis and design of nonlinear systems with multiple equilibria." Nonlinear Dynamics 104, no. 3 (April 22, 2021): 2553–71. http://dx.doi.org/10.1007/s11071-021-06429-9.

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AbstractIn engineering practice, a nonlinear system stable about several equilibria is often studied by linearizing the system over a small range of operation around each of these equilibria, and allowing the study of the system using linear system methods. Theoretically, for operations beyond a small range but still within the stable regime of an equilibrium, the system behaves nonlinearly, and can be described and investigated using the Volterra series approach. However, there is still no available approach that can systematically transform the model of a nonlinear system into a form that can be studied over the whole stable regime about an equilibrium so as to facilitate the system study using the Volterra series approach. This transformation is, in the present study, referred to as nonlinear model standardization, which is the extension of the well-known concept of linearization to the nonlinear case. In this paper, a novel approach to nonlinear model standardization is proposed for nonlinear systems that can be described by a Nonlinear AutoRegressive model with eXogeneous input (NARX) or a nonlinear differential equation (NDE) model. The proposed approach is then used in three case studies covering the applications in nonlinear system analysis, nonlinear system design, and nonlinearity compensation, respectively, demonstrating the significance of the proposed nonlinear model standardization in a wide range of engineering practices.

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Dissertations / Theses on the topic "Nonlinear"

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Tretter, Christiane. "On l-nonlinear [lambda-nonlinear] boundary eigenvalue problems /." Berlin : Akad.-Verl, 1993. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=004392929&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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Meier, Joachim. "DISCRETE NONLINEAR WAVE PROPAGATION IN KERR NONLINEAR MEDIA." Doctoral diss., University of Central Florida, 2004. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/2900.

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Discrete optical systems are a subgroup of periodic structures in which the evolution of a continuous electromagnetic field can be described by a discrete model. In this model, the total field is the sum of localized, discrete modes. Weakly coupled arrays of single mode channel waveguides have been known to fall into this class of systems since the late 1960's. Nonlinear discrete optics has received a considerable amount of interest in the last few years, triggered by the experimental realization of discrete solitons in a Kerr nonlinear AlGaAs waveguide array by H. Eisenberg and coworkers in 1998. In this work a detailed experimental investigation of discrete nonlinear wave propagation and the interactions between beams, including discrete solitons, in discrete systems is reported for the case of a strong Kerr nonlinearity. The possibility to completely overcome "discrete" diffraction and create highly localized solitons, in a scalar or vector geometry, as well as the limiting factors in the formation of such nonlinear waves is discussed. The reversal of the sign of diffraction over a range of propagation angles leads to the stability of plane waves in a material with positive nonlinearity. This behavior can not be found in continuous self-focusing materials where plane waves are unstable against perturbations. The stability of plane waves in the anomalous diffraction region, even at highest powers, has been experimentally verified. The interaction of high power beams and discrete solitons in arrays has been studied in detail. Of particular interest is the experimental verification of a theoretically predicted unique, all optical switching scheme, based on the interaction of a so called "blocker" soliton with a second beam. This switching method has been experimentally realized for both the coherent and incoherent case. Limitations of such schemes due to nonlinear losses at the required high powers are shown.
Ph.D.
Other
Optics and Photonics
Optics

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Reynard, D. M. "Nonlinear estimation." Thesis, University of Newcastle Upon Tyne, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.336142.

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Stepanyan, Anush. "Nonlinear preservers." Doctoral thesis, Université Laval, 2016. http://hdl.handle.net/20.500.11794/26928.

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Dans cette thèse, nous sommes intéressés par des problèmes de préservation des applications non-linéaires entre deux algèbres de Banach complexes unitaires A et B. En général, ces problèmes demandent la caractérisation des applications φ : A → B non nécessairement linéaires, qui laissent invariant une propriété, une relation ou un sous-ensemble. Dans le Chapitre 3, la description des applications surjectives φ de B(X) sur B(Y), qui satisfont c(φ(S)±φ(T)) = c(S ± T), (S, T ∈ B(X)), est donnée, où c(·) représente soit le module minimal, ou le module de surjectivité ou le module maximal et B(X) (resp. B(Y)) dénote l’algèbre de tous les opérateurs linéaires et bornés sur X (resp. sur Y). Dans le Chapitre 4, une question similaire pour la conorme des opérateurs, est considérée. La caractérisation des applications bicontinues et bijectives φ deB(X) surB(Y), qui satisfont γ(φ(S ± φ(T)) = γ(S ± T), (S, T ∈ B(X)), est obtenue. Le Chapitre 5 est consacré à la description des applications surjectives φ1, φ2 d’une algèbre de Banach semisimple A sur une algèbre de Banach B avec un socle essentiel, qui satisfont σ(φ1(a)φ2(b)) = σ(ab), (a, b ∈ A). Aussi, la caractérisation des applications φ de A sur B, sous les mêmes hypothèses sur A et B, qui satisfont σ(φ(a)φ(b)φ(a)) = σ(aba), (a, b ∈ A), est donnée. Comme conséquences, nous incluons les résultats obtenus au cas des algèbres B(X) et B(Y).
In this thesis, we are interested in nonlinear preserver problems. In a general formulation, these demand the characterization of a map φ : A → B, which is not supposed to be linear and leaves a certain property, particular relation, or even a subset invariant, where A and B are complex Banach algebras with unit. In Chapter 3, the description of maps φ from B(X) onto B(Y) satisfying c(φ(S)±φ(T)) = c(S ± T), (S, T ∈ B(X)), is given, where c(·) stands either for the minimum modulus, or the surjectivity modulus, or the maximum modulus and B(X) (resp. B(Y)) denotes the algebra of all bounded linear operators on a Banach space X (resp. on Y). In Chapter 4, a similar question for the reduced minimum modulus of operators, is considered. The characterization of bijective bicontinuous maps φ from B(X) to B(Y) satisfying γ(φ(S ± φ(T)) = γ(S ± T), (S, T ∈ B(X)), is obtained. Chapter 5 is devoted to description of maps φ1, φ2 from a semisimple Banach algebra A onto a Banach algebra B with an essential socle, that satisfy σ(φ1(a)φ2(b)) = σ(ab), (a, b ∈ A). Also, the characterization of maps φ from A onto B, under the same assumptions on A and B, satisfying σ(φ(a)φ(b)φ(a)) = σ(aba), (a, b ∈ A), is given. The corollaries for algebras B(X) and B(Y), that follow immediately from the results, are included.

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Xie, (Lily) Hong 1965. "Contaminant transport coupled with nonlinear biodegradation and nonlinear sorption." Diss., The University of Arizona, 1996. http://hdl.handle.net/10150/290676.

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A coupled process one-dimensional model with two-region transport, two-domain nonlinear sorption, and nonlinear biodegradation is formulated in this research. A numerical code is developed for this complex system with two sets of initial/boundary conditions. The second order upwind method is used to solve PDEs of the system, and the Adam-Bashforth three step method is used to solve ODEs of the system. By nondimensionalizing the governing equations for transport and nonlinear biodegradation, we show that biodegradation is controlled by three characteristic combined factors: the effective maximum specific growth rate, the relative half-saturation constant, and the relative substrate-utilization coefficient. A diagram with type curves was constructed based on the three characteristic factors to show the conditions under which complete and incomplete biodegradation is observed, and the conditions for which the linear, first-order approximation is valid for representing biodegradation. Analytical and numerical approaches were used to study the effect of substrate boundary concentration on biodegradation in a coupled-process system. For a system with fixed biotic and abiotic properties, substrate input concentration could be positively or negatively correlated to the magnitude of substrate degradation, depending on the time scale of the process. The relative scale of substrate concentration and its half-saturation constant is very important for the success and efficiency of bioremediation. It is found that bioremediation can be more efficient for higher concentration contaminant under certain conditions. The impact of biodegradation on solute transport with linear or nonlinear, equilibrium sorption was studied by using moments analysis. Computation results show that linear biodegradation has no impact on spatial moments of transport with linear instantaneous sorption. Conversely, it has an impact when sorption is nonlinear, since nonlinear sorption is enhanced by biodegradation. Nonlinear biodegradation causes preferential non-uniform substrate degradation and, therefore, affects spatial moments of transport with linear or nonlinear sorption. The oxygen constraint decreases the degree of nonlinear biodegradation and increases the degree of preferential degradation, thus it also impacts spatial moments of transport with linear or nonlinear sorption.

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Savvidis, Petros. "Nonlinear control : an LPV nonlinear predictive generalised minimum variance perspective." Thesis, University of Strathclyde, 2017. http://digitool.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=27947.

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This thesis describes new developments in nonlinear controllers for industrial applications. It first introduces the Nonlinear Generalised Minimum Variance (NGMV) control algorithm, for Linear Parameter Varying systems (LPV). This combines the benefits of the basic NGMV algorithm in dealing with nonlinearities, where a black box input model can be used, and adds an option to also approximate a nonlinear system with an LPV output subsystem. The models can therefore represent LPV systems and characteristics including saturation, discontinuities and time-varying dynamics. The next major contribution is in the nonlinear predictive control algorithms proposed that are also using the LPV model structure. The simplest is the Nonlinear Generalized Predictive Control (NGPC) algorithm that relates to the best known model predictive control law for linear systems. The final predictive control solution is one that may be specialized to either the NGMV or NGPC cases and is therefore the most general. This is referred to as a Nonlinear Predictive Generalized Minimum Variance Controller (NPGMV). When the algorithms use only the LPV structure to approximate the nonlinear system the solutions are particularly simple in unconstrained and constrained versions, and are relatively light computationally for implementation. Three representative industrial design examples have been chosen to validate the algorithms for different Bandwidth (BW) and nonlinear characteristics. All three examples were based on real application problems with company interest. In the first example (small BW) the basic state-space and LPV versions of the algorithm are used for the auto-manoeuvring and dynamic positioning of marine vessel. In this application the parameter variations were representative of wave disturbance changes with sea state, rather than due to approximating nonlinear behaviour. Actuator constraints were considered in the design. In the second industrial example (medium BW) the LPV-NPGMV was implemented for controlling the blade pitch and generator torque of a 5MW offshore wind turbine. The main objective here was to maintain the power produced at the rated value which requires compensation against wind disturbances, so that wind speed is the varying parameter. The LPV-NPGMV controller produced here used a parameterised system model involving the wind speed so that the controller performance changed with wind conditions. Actuator constraints were included and statistical performance assessed. The third example (fast BW) explores the stabilisation of a 2-axis gyroscopic electro-optical turret used in surveillance applications. This application was designed and employed on a real system. Because of the limitations imposed by BW requirements and the memory of the digital controller, only the basic state-space version of the algorithm was possible to implement. The main objective in this problem was to improve the tracking performance around the NADIR singularity point (a discontinuity) in the trajectory. In all three examples the NGMV controllers showed notable improvement in comparison to the baseline controllers without the need for scheduled gains or re-configuration when moving across different operating points.

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Grün, Alexander. "Nonlinear pulse compression." Doctoral thesis, Universitat Politècnica de Catalunya, 2014. http://hdl.handle.net/10803/284879.

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In this thesis I investigate two methods for generating ultrashort laser pulses in spectral regions which are ordinarily difficult to achieve by the existing techniques. These pulses are specially attractive in the study of ultrafast (few femtosecond) atomic and molecular dynamics. The first involves Optical Parametric Amplification (OPA) mediated by four-wave-mixing in gas and supports the generation of ultrashort pulses in the Near-InfraRed (NIR) to the Mid-InfraRed (MIR) spectral region. By combining pulses at a centre wavelength of 800 nm and their second harmonic in an argon-filled hollow-core fibre, we demonstrate near-infrared pulses, peaked at 1.4 µm, with 5 µJ energy and 45 fs duration at the fibre output. The four-wave-mixing process involved in the OPA is expected to lead carrier-envelope phase stable pulses which is of great importance for applications in extreme nonlinear optics. These NIR to MIR pulses can be used directly for nonlinear light-matter interactions making use of its long-wavelength characteristics. The second method allows the compression of intense femtosecond pulses in the ultraviolet (UV) region by sum-frequency mixing two bandwidth limited NIR pulses in a noncollinear phasematching geometry under particular conditions of group-velocity mismatch. Specifically, the crystal has to be chosen such that the group velocities of the NIR pump pulses, v1 and v2 , and of the sum-frequency generated pulse, vSF, meet the following condition, v1 < vSF < v2. In case of strong energy exchange and an appropriate pre-delay between the pump waves, the leading edge of the faster pump pulse and the trailing edge of the slower one are depleted. This way the temporal overlap region of the pump pulses remains narrow resulting in the shortening of the upconverted pulse. The noncollinear beam geometry allows to control the relative group velocities while maintaining the phasematching condition. To ensure parallel wavefronts inside the crystal and that the sum-frequency generated pulses emerge untilted, pre-compensation of the NIR pulse-front tilts is essential. I show that these pulse-front tilts can be achieved using a very compact setup based on transmission gratings and a more complex setup based on prisms combined with telescopes. UV pulses as short as 32 fs (25 fs) have been generated by noncollinear nonlinear pulse compression in a type II phasematching BBO crystal, starting with NIR pulses of 74 fs (46 fs) duration. This is of interest, because there is no crystal that can be used for nonlinear pulse compression at wavelengths near 800 nm in a collinear geometry. Compared to state-of-the-art compression techniques based on self-phase modulation, pulse compression by sum-frequency generation is free of aperture limitation, and thus scalable in energy. Such femtosecond pulses in the visible and in the ultraviolet are strongly desired for studying ultrafast dynamics of a variety of (bio)molecular systems.
En esta tesis he investigado dos métodos para generar pulsos láser ultracortos en regiones espectrales que son típicamente difíciles de lograr con las técnicas existentes. Estos pulsos son especialmente atractivos en el estudio de la dinámica ultrarrápida (pocos femtosegundos) en átomos y moléculas. La primera técnica implica Amplificación Paramétrica Óptica (OPA) mediante mezcla de cuatro ondas en fase gaseosa y soporta la generación de pulsos ultracortos desde el Infrarrojo-Cercano (NIR) hasta la región espectral del Infrarrojo-Medio (MIR). Mediante la combinación de pulsos centrados a una longitud de onda de 800 nm y su segundo armónico en una fibra hueca rellena de argón, hemos demostrado a la salida de la fibra la generación de pulsos en el NIR, centrados a 1.4 µm, con 5 µJ de energía y 45 fs de duración. Se espera que el proceso de mezcla de cuatro ondas involucrado en el OPA lleve a pulsos con fase de la envolvente de la portadora estables, ya que es de gran importancia para aplicaciones en óptica extrema no lineal. Estos pulsos desde el NIR hasta el MIR se pueden utilizar directamente en interacciones no-lineales materia-radiación, haciendo uso de sus características de longitud de onda largas. El segundo método permite la compresión de pulsos intensos de femtosegundos en la región del ultravioleta (UV) mediante la mezcla de suma de frecuencias de dos pulsos en el NIR limitados en el ancho de banda en una geometría de ajuste de fases no-colineal bajo condiciones particulares de discrepancia de velocidades de grupo. Específicamente, el cristal debe ser elegido de tal manera que las velocidades de grupo de los pulsos de bombeo del NIR, v1 y v2, y la del pulso suma-de-frecuencias generado, vSF, cumplan la siguiente condición, v1 < vSF < v2. En el caso de un fuerte intercambio de energía y un pre-retardo adecuado entre las ondas de bombeo, el borde delantero del pulso de bombeo más rápido y el borde trasero del más lento se agotan. De esta manera la región de solapamiento temporal de los impulsos de bombeo permanece estrecha, resultando en el acortamiento del impulso generado. La geometría de haces no-colineales permite controlar las velocidades de grupo relativas mientras mantiene la condición de ajuste de fase. Para asegurar frentes de onda paralelos dentro del cristal y que los pulsos generados por suma de frecuencias se generen sin inclinación, es esencial la pre-compensación de la inclinación de los frente de onda de los pulsos NIR. En esta tesis se muestra que estas inclinaciones de los frentes de onda se pueden lograr utilizando una configuración muy compacta basada en rejillas de transmisión y una configuración más compleja basada en prismas combinados con telescopios. Pulsos en el UV tan cortos como 32 fs (25 fs) se han generado mediante compresión de pulsos no-lineal no-colineal en un cristal BBO de ajuste de fase tipo II, comenzando con pulsos en el NIR de 74 fs (46 fs) de duración. El interés de este método radica en la inexistencia de cristales que se puedan utilizar para la compresión de impulsos no-lineal a longitudes de onda entorno a 800 nm en una geometría colineal. En comparación con las técnicas de última generación de compresión basadas en la automodulación de fase, la compresión de pulsos por suma de frecuencias esta libre de restricciones en la apertura de los pulsos, y por lo tanto es expandible en energía. Tales pulsos de femtosegundos en el visible y en el ultravioleta son fuertemente deseados en el estudio de dinámica ultrarrápida de una gran variedad de sistemas (bio)moleculares.

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Ungan, Cahit Ugur. "Nonlinear Image Restoration." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/2/12606796/index.pdf.

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This thesis analyzes the process of deblurring of degraded images generated by space-variant nonlinear image systems with Gaussian observation noise. The restoration of blurred images is performed by using two methods
a modified version of the Optimum Decoding Based Smoothing Algorithm and the Bootstrap Filter Algorithm which is a version of Particle Filtering methods. A computer software called MATLAB is used for performing the simulations of image estimation. The results of some simulations for various observation and image models are presented.

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9

Thompson, Peter Anthony. "Nonlinear optical materials." Thesis, Cranfield University, 1994. http://dspace.lib.cranfield.ac.uk/handle/1826/4162.

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Twenty different materials have been successfully deposited as Langmuir- Blodgett monolayer films. All exhibit second harmonic generation (SHG) when irradiated with laser light at 1064 nm. E-1-docosyl-4-{2-(4-dimethylami nophenyl)ethenyl}quinolinium bromide (C22H45QHBr) and E-1-docosyl-4-{2-(4-dimethy laminonaphthyl)ethenyl}quinolinium bromide (C22H45QNBr) have been deposited separately as multilayer films. They form Y-type structures when deposition is alternated with the material N-docosyl-4- methylquinolinium bromide. The nonlinear responses are quadratic up to 20 and 10 bilayers respectively and the response from the thick films is only 2 orders less than that produced by a Y-cut quartz plate. Similar results were obtained with C22H45QHBr when interleaved with 4,4'-dioctadecyl-3,5,3', 5'- tetra me thyldipyrrylmethenehydrobromide. Ellipsometry studies of the 10 bilayer film of C H45QNBr indicate that the structure is interdigitated. This explains the stability of the film which gave the same SH response up to 6 months after deposition. A 10 bilayer films has also been fabricated using E-1- docosyl-4-{2-(4-{2-(4-dimethylaminophenyl)ethenyl}benzyl)ethenyl}pyridinium bromide (C22H45PBHBr) alternated with E-1-docosy1-4-{2-(4-methylphenyl)ethenyl}pyridinium bromide (C22H45PT). E-1-octadecyl-4-{2-(4-methyloxyphenyl)ethenyl}pyridinium iodide and E-1- methyl-4-{2-(4-octadecyloxyphenyl)ethenyl}pyridinium iodide have been fabricated into monolayer films that are transparent at 1064 and 532 nm, therefore resonant enhancement does not contribute to their nonlinear response which is attributed solely to charge transfer in the molecule. Mixed solutions of E-1-octadecyl-4-{2-(4-methyloxyphenyl)ethenyl}pyridinium iodide and sodium octadecylsulphate (C1SH37OSO3 Na+) have been deposited as very stable monolayers. The nonlinear response from the mixed film offers a significant improvement upon the performance of the film containing pure hemicyanine. Novel zwitterionic materials have been fabricated as LB monolayers that also exhibit SHG.

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Murray, Nicholas Durante. "Nonlinear PID controller." Thesis, This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-03242009-040653/.

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Books on the topic "Nonlinear"

1

Gaeta, Giuseppe. Nonlinear Symmetries and Nonlinear Equations. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1018-1.

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Gaeta, Giuseppe. Nonlinear symmetries and nonlinear equations. Dordrecht: Kluwer Academic Publishers, 1994.

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Gaeta, Giuseppe. Nonlinear symmetries and nonlinear equations. Dordrecht: Kluwer Academic, 1994.

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Gaeta, Giuseppe. Nonlinear Symmetries and Nonlinear Equations. Dordrecht: Springer Netherlands, 1994.

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Fertis, Demeter G. Nonlinear mechanics. 2nd ed. Boca Raton: CRC Press, 1999.

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Sauter, E. G. Nonlinear optics. New York: Wiley, 1996.

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Galatzer-Levy, Robert M. Nonlinear Psychoanalysis. Abingdon, Oxon; New York, NY: Routledge, 2017. | Series: Psychoanalysis in a new key book series; 36: Routledge, 2017. http://dx.doi.org/10.4324/9781315266473.

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Biskamp, D. Nonlinear magnetohydrodynamics. Cambridge [England]: Cambridge University Press, 1993.

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Datseris, George, and Ulrich Parlitz. Nonlinear Dynamics. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-91032-7.

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Aragón, Francisco J., Miguel A. Goberna, Marco A. López, and Margarita M. L. Rodríguez. Nonlinear Optimization. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11184-7.

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Book chapters on the topic "Nonlinear"

1

Weik, Martin H. "nonlinear." In Computer Science and Communications Dictionary, 1107. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/1-4020-0613-6_12427.

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Breazeale, Mack A. "How Nonlinear Can Nonlinear Be?" In Review of Progress in Quantitative Nondestructive Evaluation, 2043–50. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4615-2848-7_262.

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Meulman, Jacqueline J., and Willem J. Heiser. "Nonlinear Biplots for Nonlinear Mappings." In Information and Classification, 201–13. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-50974-2_20.

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Adamy, Jürgen. "Nonlinear Control of Nonlinear Systems." In Nonlinear Systems and Controls, 343–501. Berlin, Heidelberg: Springer Berlin Heidelberg, 2022. http://dx.doi.org/10.1007/978-3-662-65633-4_5.

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Adamy, Jürgen. "Nonlinear Control of Nonlinear Systems." In Nonlinear Systems and Controls, 345–504. Berlin, Heidelberg: Springer Berlin Heidelberg, 2024. http://dx.doi.org/10.1007/978-3-662-68690-4_5.

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Gaeta, Giuseppe. "Geometric setting." In Nonlinear Symmetries and Nonlinear Equations, 1–22. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1018-1_1.

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Gaeta, Giuseppe. "Equations of Physics." In Nonlinear Symmetries and Nonlinear Equations, 205–22. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1018-1_10.

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Gaeta, Giuseppe. "Symmetries and their use." In Nonlinear Symmetries and Nonlinear Equations, 23–44. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1018-1_2.

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Gaeta, Giuseppe. "Examples." In Nonlinear Symmetries and Nonlinear Equations, 45–54. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1018-1_3.

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Gaeta, Giuseppe. "Evolution equations." In Nonlinear Symmetries and Nonlinear Equations, 55–82. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1018-1_4.

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Conference papers on the topic "Nonlinear"

1

Schawlow, Arthur L. "Nonlinear Spectroscopy." In Nonlinear Optics. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/nlo.1992.wc1.

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2

Mourou, Gérard. "Laser Ascent to Sub Atomic Physics and Applications." In Nonlinear Optics. Washington, D.C.: OSA, 2013. http://dx.doi.org/10.1364/nlo.2013.nm1a.1.

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3

Brevet, Pierre-François. "Second Harmonic Generation from Metallic Nanoparticles." In Nonlinear Optics. Washington, D.C.: OSA, 2013. http://dx.doi.org/10.1364/nlo.2013.nm2a.6.

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Fridman, Moti. "The Picoseconds Structure of Ultrafast Rogue Waves." In Nonlinear Photonics. Washington, D.C.: OSA, 2018. http://dx.doi.org/10.1364/np.2018.npth2c.7.

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Zheng, Jian, and Masayuki Katsuragawa. "Arbitrary dual-frequency generation in Raman-resonant four-wave-mixing process." In Nonlinear Optics. Washington, D.C.: OSA, 2017. http://dx.doi.org/10.1364/nlo.2017.nm3b.3.

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You, Jian Wei, and Nicolae C. Panoiu. "Simultaneous Tunable Enhancement of SHG and THG in Graphene Optical Gratings." In Nonlinear Optics. Washington, D.C.: OSA, 2017. http://dx.doi.org/10.1364/nlo.2017.nm3b.4.

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Poutrina, Ekaterina, and Augustine Urbas. "Nonreciprocal on the Nanoscale: Nonlinear Generation via Multipole Interference." In Nonlinear Optics. Washington, D.C.: OSA, 2017. http://dx.doi.org/10.1364/nlo.2017.nm3b.5.

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Obreshkov, Boyan, and Tzveta Apostolova. "Conversion efficiency of high harmonic generation in diamond for 800 nm wavelength." In Nonlinear Optics. Washington, D.C.: OSA, 2019. http://dx.doi.org/10.1364/nlo.2019.ntu4a.3.

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Devine, Ekaterina Ponizovskaya. "Second harmonics enhancement by nanostructures." In Nonlinear Optics. Washington, D.C.: OSA, 2019. http://dx.doi.org/10.1364/nlo.2019.ntu4a.31.

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Hartwig, H., and F. Mitschke. "Experimental Investigation of Slow Oscillations of Dispersion-Managed Solitons." In Nonlinear Photonics. Washington, D.C.: OSA, 2010. http://dx.doi.org/10.1364/np.2010.nmc5.

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Reports on the topic "Nonlinear"

1

Odom, Robert I. Nonlinear Inversion. Fort Belvoir, VA: Defense Technical Information Center, September 2009. http://dx.doi.org/10.21236/ada531411.

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Odom, Robert I. Nonlinear Inversion. Fort Belvoir, VA: Defense Technical Information Center, September 2010. http://dx.doi.org/10.21236/ada542163.

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Newhouse, Sheldon E. Nonlinear Dynamics. Fort Belvoir, VA: Defense Technical Information Center, July 1991. http://dx.doi.org/10.21236/ada251271.

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Kevorkian, J. Nonlinear resonance. Office of Scientific and Technical Information (OSTI), April 1990. http://dx.doi.org/10.2172/6996969.

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Odom, Robert I. Nonlinear Inversion from Nonlinear Filters for Ocean Acoustics. Fort Belvoir, VA: Defense Technical Information Center, September 2006. http://dx.doi.org/10.21236/ada612664.

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Odom, Robert I. Nonlinear Inversion from Nonlinear Filters for Ocean Acoustics. Fort Belvoir, VA: Defense Technical Information Center, September 2007. http://dx.doi.org/10.21236/ada573392.

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Beran, Philip S., Ned J. Lindsley, Jose Camberos, and Mohammad Kurdi. Stochastic Nonlinear Aeroelasticity. Fort Belvoir, VA: Defense Technical Information Center, January 2009. http://dx.doi.org/10.21236/ada494780.

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Ablowitz, Mark J. Nonlinear Wave Propagation. Fort Belvoir, VA: Defense Technical Information Center, February 2009. http://dx.doi.org/10.21236/ada495287.

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Dr. Katja Lindenberg. Noisy Nonlinear Systems. Office of Scientific and Technical Information (OSTI), November 2005. http://dx.doi.org/10.2172/881047.

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Dresner, L. Nonlinear differential equations. Office of Scientific and Technical Information (OSTI), January 1988. http://dx.doi.org/10.2172/5495671.

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