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Dissertations / Theses on the topic 'Nonlinear wave theories'

Author: Grafiati

Published: 28 June 2021

Last updated: 5 February 2022

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1

Girard, Réjean. "Relativistic nonlinear wave equations with groups of internal symmetry." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75688.

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A nonlinear wave equation invariant with respect to unitary representations of the Lorentz group is considered in an attempt to describe extended particles with spin and positive definite energy by means of a self-confined classical field. The wave function has an infinite number of components and, in the specific representations used, the corresponding internal degree of freedom is identified with the spin. A fractional power of the scalar bilinear invariant appears as an appropriate choice for the nonlinearity in order that all the stationary states be localized. Two approximation methods are proposed and both lead to results that bear a resemblance to the results of the MIT bag model.

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2

Hoseini, Sayed Mohammad. "Solitary wave interaction and evolution." Access electronically, 2007. http://www.library.uow.edu.au/adt-NWU/public/adt-NWU20080221.110619/index.html.

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3

Kim, Won-Gyu 1962. "A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean." Thesis, University of North Texas, 1996. https://digital.library.unt.edu/ark:/67531/metadc278092/.

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The Hamiltonian of a stably stratified incompressible fluid in an internal water wave in a deep ocean is constructed. Studying the ocean internal wave field with its full dynamics is formidable (or unsolvable) so we consider a test-wave Hamiltonian to study the dynamical and statistical properties of the internal water wave field in a deep ocean. Chaos is present in the internal test-wave dynamics using actual coupling coefficients. Moreover, there exists a certain separatrix net that fills the phase space and is covered by a thin stochastic layer for a two-triad pure resonant interaction. The stochastic web implies the existence of diffusion of the Arnold type for the minimum dimension of a non-integrable autonomous system. For non-resonant case, stochastic layer is formed where the separatrix from KAM theory is disrupted. However, the stochasticity does not increase monotonically with increasing energy. Also, the problem of relaxation process is studied via microscopic Hamiltonian model of the test-wave interacting nonlinearly with ambient waves. Using the Mori projection technique, the projected trajectory of the test-wave is transformed to a form which corresponds to a generalized Langevin equation. The mean action of the test-wave grows ballistically for a short time regime, and quenches back to the normal diffusion for a intermediate time regime and regresses linearly to a state of statistical equilibrium. Applying the Nakajima-Zwanzig technique on the test-wave system, we get the generalized master equation on the test-wave system which is non-Markovian in nature. From our numerical study, the distribution of the test-wave has non-Gaussian statistics.

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4

Narisetti, Raj K. "Wave propagation in nonlinear periodic structures." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/39643.

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A periodic structure consists of spatially repeating unit cells. From man-made multi-span bridges to naturally occurring atomic lattices, periodic structures are ubiquitous. The periodicity can be exploited to generate frequency bands within which elastic wave propagation is impeded. A limitation to the linear periodic structure is that the filtering properties depend only on the structural design and periodicity which implies that the dispersion characteristics are fixed unless the overall structure or the periodicity is altered. The current research focuses on wave propagation in nonlinear periodic structures to explore tunability in filtering properties such as bandgaps, cut-off frequencies and response directionality. The first part of the research documents amplitude-dependent dispersion properties of weakly nonlinear periodic media through a general perturbation approach. The perturbation approach allows closed-form estimation of the effects of weak nonlinearities on wave propagation. Variation in bandstructure and bandgaps lead to tunable filtering and directional behavior. The latter is due to anisotropy in nonlinear interaction that generates low response regions, or "dead zones," within the structure.The general perturbation approach developed has also been applied to evaluate dispersion in a complex nonlinear periodic structure which is discretized using Finite Elements. The second part of the research focuses on wave dispersion in strongly nonlinear periodic structures which includes pre-compressed granular media as an example. Plane wave dispersion is studied through the harmonic balance method and it is shown that the cut-off frequencies and bandgaps vary significantly with wave amplitude. Acoustic wave beaming phenomenon is also observed in pre-compressed two-dimensional hexagonally packed granular media. Numerical simulations of wave propagation in finite lattices also demonstrated amplitude-dependent bandstructures and directional behavior so far observed.

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5

Franz, David, and University of Lethbridge Faculty of Arts and Science. "Turing patterns in linear chemical reaction systems with nonlinear cross diffusion." Thesis, Lethbridge, Alta. : University of Lethbridge, Faculty of Arts and Science, 2007, 2007. http://hdl.handle.net/10133/659.

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Turing patterns have been studied for over 50 years as a pattern forming mechanism. To date the current focus has been on the reaction mechanism, with little to no emphasis on the diffusion terms. This work focuses on combining the simplest reaction mechanism possible and the use of nonlinear cross diffusion to form Turing patterns. We start by using two methods of bifurcation analysis to show that our model can form a Turing instability. A diffusion model (along with some variants) is then presented along with the results of numerical simulations. Various tests on both the numerical methods and the model are done to ensure the accuracy of the results. Finally an additional model that is closed to mass flow is introduced along with preliminary results.<br>vi, 55 leaves : ill. ; 29 cm.

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6

Kuechler, Sebastian. "Wave Propagation in an Elastic Half-Space with Quadratic Nonlinearity." Thesis, Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19823.

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This study investigates wave propagation in an elastic half-space with quadratic nonlinearity due to a line load on the surface. The consideration of this problem is one of the well known Lamb problems. Even since Lamb's original solution, numerous investigators have obtained solutions to many different variants of the Lamb problem. However, most of the solutions existing in the current literature are limited to wave propagation in a linear elastic half-space. In this work, the Lamb problem in an elastic half-space with quadratic nonlinearity is considered. For this, the problem is first formulated as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. The accuracy of the numerical method is first studied by comparing the numerical solution with the analytical solution for a half-space with linear response (the original Lamb's problem). The numerical results for the half-space with quadratic nonlinearity are than studied using signal-processing tools such as the fast Fourier transform (FFT) in order to analyze and interpret any nonlinear effects. This in particular gives the possibility to evaluate the excitation of higher order harmonics whose amplitude is used to infer material properties. To quantify and compare the nonlinearity of different materials, two parameters are introduced; these parameters are similar to the acoustical nonlinearity parameter for plane waves.

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7

Kupčíková, Laura. "Částice plovoucí na volné hladině vln." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2021. http://www.nusl.cz/ntk/nusl-444637.

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This master’s thesis deals with analytical and numerical description of surface gravity waves. Wave theories and their influence on water particle movement is described in the theoretical part of the thesis. Water particle moves in the same direction as wave propagation and this phenomenon is called Stokes drift. It has a significant influence on sediment transport and floating particle movement at water free surface. The experimental part consists of wave profile monitoring and water particle tracking in a wave flume with wave generator and beach model. The experimental results are compared with numerical simulation performed in the ANSYS Fluent software. Finally, the wave profiles obtained from simulation are compared with experimental wave profiles extracted by digital image processing.

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8

Braun, Michael Rainer. "Characterization of nonlinearity parameters in an elastic material with quadratic nonlinearity with a complex wave field." Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26566.

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Thesis (M. S.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2009.<br>Committee Chair: Jacobs, Laurence; Committee Co-Chair: Qu, Jianmin; Committee Member: DesRoches, Reginald. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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9

Aceves, Alejandro Borbolla. "Snell's laws at the interface between nonlinear dielectrics." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184467.

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A theory is presented which describes the global reflection and transmission characteristics of a self-focused channel propagating at an oblique angle of incidence to an interface separating two or more self-focusing nonlinear dielectric media. A complete characterization of the different behavior of the channel is given in the proper parameter space. In the dominant region, the nonlinear wavepacket representing the self-focused channel is represented as an equivalent particle moving in an equivalent potential. The dynamics of the particle is described by Newton's equations of motion, with the asymptotic propagation paths of the channel being read off from the associated phase planes of the equivalent potential. This theory provides therefore, the nonlinear Snell's Laws of refleciton or transmission since the particle dynamics gives the critical angle of total reflection and in the case of transmission, the corresponding angle of transmission. This theory also gives the stability characteristics of nonlinear surface waves, which had only been partially established in the past through numerical simulations. Finally, some applications of the theory are presented such as the design of an all-optical power adjustable spatial scanning element and an all optical switch. Extensions of the theory to waveguides with multiple interfaces are also given and possible new directions are also suggested.

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10

Ohm, Won-suk. "Effects of dispersion on nonlinear surface acoustic waves in substrates laminated with films /." Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3038194.

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11

Vorpe, Katherine. "Understanding a Population Model for Mussel-Algae Interaction." Wittenberg University Honors Theses / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=wuhonors1617970789779916.

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12

"study of wave propagation in nonlinear dielectric multilayer system =: 電磁波於多層非線性電介質系統內傳播之硏究". 1999. http://library.cuhk.edu.hk/record=b5890076.

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by Leung, Kwok Kong.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 1999.<br>Includes bibliographical references (leaves 67).<br>Text in English; abstracts in English and Chinese.<br>by Leung, Kwok Kong.<br>Abstract --- p.ii<br>Acknowledgement --- p.iii<br>Contents --- p.iv<br>List of Figures --- p.vi<br>Chapter Chapter 1. --- Introduction --- p.1<br>Chapter Chapter 2. --- Transmittance in Metal-Dielectric Multilayers --- p.4<br>Chapter 2.1 --- Introduction --- p.4<br>Chapter 2.2 --- Transfer matrix approach --- p.5<br>Chapter 2.3 --- Transfer matrix simulation --- p.7<br>Chapter 2.4 --- Physical explanation --- p.14<br>Chapter Chapter 3. --- Optical Nonlinear Response of Composite Layer --- p.17<br>Chapter 3.1 --- Transfer matrix formalism for oblique incidence --- p.18<br>Chapter 3.1.1 --- Transfer matrix method in nonlinear region --- p.18<br>Chapter 3.1.2 --- S-polarization --- p.19<br>Chapter 3.1.3 --- P-polarization --- p.19<br>Chapter 3.1.4 --- Backward propagation technique --- p.22<br>Chapter 3.2 --- Nonlinear phase shift --- p.22<br>Chapter 3.3 --- Transfer matrix method approach --- p.24<br>Chapter 3.4 --- Analytic solution formalism --- p.26<br>Chapter Chapter 4. --- Study of Photonic Band Gap of Nonlinear Dielectrics --- p.33<br>Chapter 4.1 --- Introduction --- p.33<br>Chapter 4.2 --- Nonlinear response of single thin nonlinear layer --- p.34<br>Chapter 4.3 --- Nonlinear response of δ-function between two linear dielectric --- p.37<br>Chapter 4.4 --- Photonic band structure --- p.41<br>Chapter 4.4.1 --- Photonic band structure of linear thin films --- p.41<br>Chapter 4.4.2 --- Photonic band structure of linear layers --- p.42<br>Chapter 4.5 --- Photonic band gap of nonlinear dielectric multilayers --- p.46<br>Chapter Chapter 5. --- Optical Limiting of Composite Material --- p.49<br>Chapter 5.1 --- Transmittance of periodic multilayer structures --- p.50<br>Chapter 5.1.1 --- Transmittance properties at low intensity --- p.50<br>Chapter 5.1.2 --- Transmittance at high intensity: optical limiting effect --- p.52<br>Chapter 5.2 --- The effect of layer thickness on optical limiting --- p.53<br>Chapter 5.3 --- Optical limiting property of PBG materials --- p.55<br>Chapter Chapter 6. --- Conclusion --- p.63<br>Chapter Appendix A. --- Effective dielectric function --- p.64<br>Bibliography --- p.67

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13

Chang, Chia-Chin. "Nonlinear theories of forced surface waves in a circular basin." 1999. http://catalog.hathitrust.org/api/volumes/oclc/43274575.html.

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Thesis (Ph. D.)--University of Wisconsin--Madison, 1999.<br>Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 203-205).

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14

Sangeeta, K. "Numerical Simulation Of Converging Nonlinear Wavefronts." Thesis, 1996. http://etd.iisc.ernet.in/handle/2005/1901.

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15

"Nonlinear stability of viscous transonic flow through a nozzle." 2004. http://library.cuhk.edu.hk/record=b5892103.

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Xie Chunjing.<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2004.<br>Includes bibliographical references (leaves 65-71).<br>Abstracts in English and Chinese.<br>Acknowledgments --- p.i<br>Abstract --- p.ii<br>Introduction --- p.3<br>Chapter 1 --- Stability of Shock Waves in Viscous Conservation Laws --- p.10<br>Chapter 1.1 --- Cauchy Problem for Scalar Viscous Conservation Laws and Viscous Shock Profiles --- p.10<br>Chapter 1.2 --- Stability of Shock Waves by Energy Method --- p.15<br>Chapter 1.3 --- Nonlinear Stability of Shock Waves by Spectrum Anal- ysis --- p.20<br>Chapter 1.4 --- L1 Stability of Shock Waves in Scalar Viscous Con- servation Laws --- p.26<br>Chapter 2 --- Propagation of a Viscous Shock in Bounded Domain and Half Space --- p.35<br>Chapter 2.1 --- Slow Motion of a Viscous Shock in Bounded Domain --- p.36<br>Chapter 2.1.1 --- Steady Problem and Projection Method --- p.36<br>Chapter 2.1.2 --- Projection Method for Time-Dependent Prob- lem --- p.40<br>Chapter 2.1.3 --- Super-Sensitivity of Boundary Conditions --- p.43<br>Chapter 2.1.4 --- WKB Transformation Method --- p.45<br>Chapter 2.2 --- Propagation of a Stationary Shock in Half Space --- p.50<br>Chapter 2.2.1 --- Asymptotic Analysis --- p.50<br>Chapter 2.2.2 --- Pointwise Estimate --- p.51<br>Chapter 3 --- Nonlinear Stability of Viscous Transonic Flow Through a Nozzle --- p.58<br>Chapter 3.1 --- Matched Asymptotic Analysis --- p.58<br>Bibliography --- p.65

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16

Bruso, Keith Alvin. "Existence, uniqueness and blow-up results for non-linear wave equations." 1985. http://hdl.handle.net/2097/27403.

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