Jorge Viñals · 2007
The objectives of our research are to improve our understanding of the mechanisms underlying the formation of complex spatio-temporal patterns in systems that are driven outside of thermodynamic equilibrium, to characterize the macroscopic properties of such states, and to apply the methodology to situations of interest in fluid physics and engineering. Current research focuses on pattern formation, secondary instabilities and the transition to spatio-temporal chaos in parametrically driven surface waves, and the development of hydrodynamic equations at the mesoscopic level to model short length scale phenomena that fall beyond a conventional hydrodynamic description. INTRODUCTION Fluid systems have provided a wealth of information on a variety of nonlinear phenomena that include bifurcation and instability, pattern formation, front propagation, localized and traveling states, intermittency, spatio-temporal chaos, and turbulence. Many fluid systems have become paradigms of one or more ...
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Ronald D. Henderson · 1997
Results are reported on direct numerical simulations of transition from two-dimensional to three-dimensional states due to secondary instability in the wake of a circular cylinder. These calculations quantify the nonlinear response of the system to three-dimensional perturbations near threshold for the two separate linear instabilities of the wake: mode A and mode B. The objectives are to classify the nonlinear form of the bifurcation to mode A and mode B and to identify the conditions under which the wake evolves to periodic, quasi-periodic, or chaotic states with respect to changes in spanwise dimension and Reynolds number. The onset of mode A is shown to occur through a subcritical bifurcation that causes a reduction in the primary oscillation frequency of the wake at saturation. In contrast, the onset of mode B occurs through a supercritical bifurcation with no frequency shift near threshold. Simulations of the three-dimensional wake for xed Reynolds number and increasing spanwise dimen-sion show that large systems evolve to a state of spatiotemporal chaos, and suggest that three-dimensionality in the wake leads to irregular states and fast transition to turbulence at Reynolds numbers just beyond the onset of the secondary instability. A key feature of these ‘turbulent ’ states is the competition between self-excited, three-dimensional instability modes (global modes) in the mode A wavenumber band. These instability modes produce irregular spatiotemporal patterns and large-scale ‘spot-like’ disturbances in the wake during the breakdown of the regular mode A pattern. Simu-lations at higher Reynolds number show that long-wavelength interactions modulate fluctuating forces and cause variations in phase along the span of the cylinder that reduce the fluctuating amplitude of lift and drag. Results of both two-dimensional and three-dimensional simulations are presented for a range of Reynolds number from about 10 up to 1000.
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Leonid Yaroslavsky · Nonlinear Biomedical Physics · 2007
Stochastic evolutionary growth and pattern formation models are treated in a unified way in terms of algorithmic models of nonlinear dynamic systems with feedback built of a standard set of signal processing units. A number of concrete models is described and illustrated by numerous examples of artificially generated patterns that closely imitate wide variety of patterns found in the nature.
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Eckehard Schöll · 2005
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F.‐J. Niedernostheide · Springer proceedings in physics · 1995
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Doelman, A., van Harten, A. · 1995
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Antonina N. Fedorova, Michael G. Zeitlin · 2003
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Ernesto M. Nicola · 2007
Abstract – We study the dynamics of fronts in parametrically forced oscillating lattices. Using as a prototypical example the discrete Ginzburg-Landau equation, we show that much information about front bifurcations can be extracted by projecting onto a cylindrical phase space. Starting from a normal form that describes the nonequilibrium Ising-Bloch bifurcation in the continuum and using symmetry arguments, we derive a simple dynamical system that captures the dynamics of fronts in the lattice. We can expect our approach to be extended to other pattern-forming problems on lattices. Copyright c © EPLA, 2008 Extended systems on lattices have played a major role in the development of nonlinear science. One may recall celebrated models as the discrete sine-Gordon equation or the Fermi-Pasta-Ulam experiment. Usually, the develop-ment of the field has been associated with conservative systems, but dissipative lattices have attracted growing attention in the last two decades (see [1] for a review).
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Peter G. Vekilov, S.‐T. Yau, Hsiu‐Mei Lin et al. · NASA Technical Reports Server (NASA) · 2002
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Robert C. Hilborn · 2001
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Alexander Nepomnyashchy, Anna Samoilova · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · 2023
Pattern formation is a widespread phenomenon observed in physical, chemical and biological systems. During the past decades, powerful experimental and theoretical tools for the investigation of that phenomenon have been developed. Also, the set of pattern forming system was diversified. The present issue presents a panorama of pattern formation and other nonlinear dynamical phenomena in different natural and engineering systems. Special attention is paid to nonlinear dynamics of fluids. Non-equilibrium phenomena in chemical and quantum systems are also considered. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.
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2008
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Renji Han, Sanaa Moussa Salman · Physica D Nonlinear Phenomena · 2024
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Niedernostheide, Franz-Josef, International Conference on Nonlinear Dynamics and Pattern Formation in the Natural Environment 1994 Noordwijkerhout · 1995
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P. S. Vinayagam, Diya Krishnan, R. V. Kamaleshwaran et al. · Romanian Reports in Physics · 2025
We investigate the dynamics arising out of the propagation of light pulses with different polarizations through a condensate (referred to as a constant background field) with cross coupling described by a coupled nonlinear Schrodinger equation (NLSE) type equation. We then employ Gauge and Darboux transformation approach to bring out the rich dynamics arising out of the background field and cross coupling. The collisional dynamics of bright solitons is found to be inelastic. The constant background field is found to facilitate the periodic localization of light pulses during propagation. We have also unearthed breathers, bright-bright, bright-dark, and dark-bright solitons of the coupled NLSE. While the amplitude of breathers oscillate with time as predicted, their maximum (or minimum) amplitude is found to remain a constant and the addition of cross coupling only contributes to the rapid fluctuations in its amplitude over a period of time. In addition, the reinforcement of cross coupling in the presence of constant wave field facilitates the interference of light pulses leading to interesting pattern formation among bright-bright, bright-dark, and dark-bright solitons. The highlight of the results is that one obtains various localized excitations like breathers, bright, and dark solitons by simply manipulating the amplitude of the constant wave field.
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M. Daniel, K. M. Tamizhmani, R. Sahadevan · Medical Entomology and Zoology · 2000
Nonlinear Dynamics: General / Soliton Systems and Integrability / Discrete Nonlinear Systems: Integrability and Chaos / Classical and Quantum Chaos / Spatio-Temporal Chaos and Pattern Formation / Nonlinear Dynamics: Applications / List of Contributors
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R. G. Harrison, J. S. Uppal, P. Osborne · Medical Entomology and Zoology · 1993
Order Parameter of Oscillators: Introduction Linear and Nonlinear oscillators Spatially distributed oscillators Topological Defects in a CGL equation Defect-Dynamics in a CGL equation Conclusion (P Coullet et al). Pattern Formation and Pattern Recognition: Introduction Order parameters and the slaving principle Some examples of formation of spatial patterns Generalized Ginzburg-Landau Equations Some examples from fluid dynamics Pattern recognition (H Haken). Global Bifurcations in Finite Dimensional Flows: Introduction General principles of homoclinic bifurcations Examples Conclusion (C Sparrow). Pattern Formation and Space-Time Organization in Nonlinear Optics: Introduction Pattern formation and complexity phase singularities, topological defects and turbulence Pattern formation and pattern competition (F T Arecchi).Instabilities and Quantum Noise Reduction in Nonlinear optical Mixing: Introduction FWM in longitudinal modes FWM in transverse plane-wave modes FWM in Gauss-Laguerre transverse modes (M Brambilla). Complexity and Defects in Passive nonlinear Optical Systems: Introduction Pattern formation in an optical cavity Mirror Feedback Systems Counterpropagation instabilities in a Kerr medium Conclusion (W J Firth). Deterministic Chaos and Nonlinear Dynamics in Nonlinear Optics: Introduction Instabilities of counterpropagating laser beams Dynamics and instabilities in stimulated Brillouin scattering (R W Boyd). Spatio-Temporal Structures in Wide Aperture Lasers: Introduction Two level and Raman lasers: background theory Near and beyond threshold behavior: amplitude and phase equations Numerical simulations beyond threshold Conclusions (J V Moloney and A C Newell). Nonlinear Dynamics of Semiconductor Laser Arrays: Introduction Coupled-mode rate equations Stability boundaries for a two-emitter array Stability of three-emitter and larger arrays Phase-dynamical description of laser arrays (H Winful). Transverse Structure formation and Vortices in Lasers Introduction CGLE and vortex dynamics in class A lasers Beyond the CGLE Laser and hydrodynamics Vortices in class B lasers Conclusion (M F H Tarrojo et al). Amplification and Lasing without Inversion: Introduction Atomic interference The Maxwell-Bloch equations Linear analysis Nonlinear analysis The driven ^D*L and the ^Ih schemes The inversion problem Lasing without inversion Experimental results (P Mandel). Participant's addresses. Index.
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Miles Anderson, Yadong Wang, François Léo et al. · Physical Review X · 2017
Pattern formation in optical devices known as passive Kerr resonators has been studied for decades, but recent theoretical work has suggested the existence of entirely new dynamics when operated in the highly nonlinear regime. New experiments confirm these predictions, which could lead to innovative new sources of laser-like light and provide new insight into nonlinear dynamics and pattern formation.
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2005
PACS. 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems. PACS. 05.70.Ln – Nonequilibrium and irreversible thermodynamics. PACS. 81.10.Aj – Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation. PACS. 47.54.+r – Pattern selection; pattern formation. Abstract. – We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order parameter, or a concentration profile. We show that two types of dynamics occur around the transition: weakly nonlinear dynamics, or highly nonlinear dynamics. The conditions under which highly nonlinear evolution equations appear are determined, and their generic form is derived. Finally, examples are discussed. In the study of pattern formation, weakly nonlinear equations play a central role. By construction, these equations catch the main effects of nonlinearities via a limited number of nonlinear terms added to a linear equation. This approach has been used for a wide variety of physical systems such as crystal growth [1], reaction-diffusion systems [2], flame fronts [3], or
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Ulrich Brandt-Pollmann, Dirk Lebiedz, Moritz Diehl et al. · Chaos An Interdisciplinary Journal of Nonlinear Science · 2005
Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.
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