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“Once Nonlinear, Always Nonlinear”
AIP Conference Proceedings, 2006The phrase “Once nonlinear, always nonlinear” is attributed to David F. Pernet. In the 1970s he noticed that nonlinearly generated higher harmonic components (both tones and noise) don’t decay as small signals, no matter how far the wave propagates. Despite being out of step with the then widespread notion that small‐signal behavior is restored in “old
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Some diverse examples of exploiting the beneficial effects of geometric stiffness nonlinearity
Mechanical systems and signal processing, 2019The effects of nonlinearity, particularly stiffness nonlinearity, has been of concern to structural engineers for many years. The main reason for this is because this type of nonlinearity can cause unpredictable dynamics, and considerable effort is ...
G. Gatti, M. Brennan, B. Tang
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2018
The problem of non-linear data is one of the oldest in experimental science. The solution to this problem is very complex, since the exact mechanisms that describe a phenomenon and its nonlinearities, are often unknown. At the same time, environmental factors such as the finite precision of the processing machine, noise, and sensor limitations—among ...
Esposito, Anna +3 more
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The problem of non-linear data is one of the oldest in experimental science. The solution to this problem is very complex, since the exact mechanisms that describe a phenomenon and its nonlinearities, are often unknown. At the same time, environmental factors such as the finite precision of the processing machine, noise, and sensor limitations—among ...
Esposito, Anna +3 more
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Improved Surrogate Data for Nonlinearity Tests.
Physical Review Letters, 1996Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of the data.
T. Schreiber, A. Schmitz
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SIAM Journal on Matrix Analysis and Applications, 1999
The nonlinear eigenvalue problem \(A(\lambda)v=0\) with holomorphic matrix-valued function \(A(\lambda)\) defined on a domain \(\Omega\subset\mathbb{C}\) is considered. The author suggests a method for solving this problem connected with the calculation of the derivatives of the function \(x(\lambda)={A(\lambda)}^{-1}b,\) where \(b\) is a given vector.
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The nonlinear eigenvalue problem \(A(\lambda)v=0\) with holomorphic matrix-valued function \(A(\lambda)\) defined on a domain \(\Omega\subset\mathbb{C}\) is considered. The author suggests a method for solving this problem connected with the calculation of the derivatives of the function \(x(\lambda)={A(\lambda)}^{-1}b,\) where \(b\) is a given vector.
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Nonlinear photonic crystals: III. Cubic nonlinearity
Waves in Random Media, 2003Summary: Weakly nonlinear interactions between wavepackets in a lossless periodic dielectric medium are studied based on the classical Maxwell equations with a cubic nonlinearity. We consider nonlinear processes such that: (i) the amplitude of the wave component due to the nonlinearity does not exceed the amplitude of its linear component; (ii) the ...
Babin, Anatoli, Figotin, Alexander
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2014
The basics of nonlinear acoustics and its application to medical ultrasound imaging are introduced. First, a little historical introduction is given, and next, the coefficient of nonlinearity is introduced, together with a variety of equations, which step by step develop from simple to more sophisticated models.
Demi, Libertario, Martin D. Verweij
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The basics of nonlinear acoustics and its application to medical ultrasound imaging are introduced. First, a little historical introduction is given, and next, the coefficient of nonlinearity is introduced, together with a variety of equations, which step by step develop from simple to more sophisticated models.
Demi, Libertario, Martin D. Verweij
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Nonlinear Complex Programming with Nonlinear Constraints
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1977AbstractFollowing Mond [8, 9] a duality theory for nonlinear complex programming problems over polyhedral cones with nonlinear constraints is developed by making use of the linear duality theory.
Das, C., Swarup, K.
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Nonlinear controllers for nonlinear systems with input nonlinearities
Proceedings of the 36th IEEE Conference on Decision and Control, 1999The authors consider control systems of the type \[ \dot x= f(x,\sigma(u)),\quad x(0)= x_0,\quad t\geq 0, \] where \(\sigma\) denotes an input nonlinearity -- in many cases saturation -- and present a methodology for designing globally stabilizing nonlinear controllers.
Haddad, Wassim M. +2 more
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Nonlinear photonic crystals: I. Quadratic nonlinearity
Waves in Random Media, 2001Summary: We develop a consistent mathematical theory of weakly nonlinear periodic dielectric media for the dimensions one, two and three. The theory is based on the Maxwell equations with classical quadratic and cubic constitutive relations. In particular, we give a complete classification of different nonlinear interactions between Floquet-Bloch modes
Babin, A., Figotin, A.
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