Search results for "Nonlinear system"
showing 10 items of 1446 documents
Mixed predictability and cross-validation to assess non-linear Granger causality in short cardiovascular variability series
2006
A method to evaluate the direction and strength of causal interactions in bivariate cardiovascular and cardiorespiratory series is presented. The method is based on quantifying self and mixed predictability of the two series using nearest-neighbour local linear approximation. It returns two causal coupling indexes measuring the relative improvement in predictability along direct and reverse directions, and a directionality index indicating the preferential direction of interaction. The method was implemented through a cross-validation approach that allowed quantification of directionality without constraining the embedding of the series, and fully exploited the available data to maximise th…
Time-Varying Surrogate Data to Assess Nonlinearity in Nonstationary Time Series: Application to Heart Rate Variability
2009
We propose a method to extend to time-varying (TV) systems the procedure for generating typical surrogate time series, in order to test the presence of nonlinear dynamics in potentially nonstationary signals. The method is based on fitting a TV autoregressive (AR) model to the original series and then regressing the model coefficients with random replacements of the model residuals to generate TV AR surrogate series. The proposed surrogate series were used in combination with a TV sample entropy (SE) discriminating statistic to assess nonlinearity in both simulated and experimental time series, in comparison with traditional time-invariant (TIV) surrogates combined with the TIV SE discrimin…
Finite-element design sensitivity analysis for non-linear potential problems
1990
Design sensitivity analysis is performed for the finite-element system arising from the discretization of non-linear potential problems using isoparametric Lagrangian elements. The calculated sensitivity formulae are given in a simple matrix form. Applications to the design of electromagnets and airfoils are given.
Initial Data for Non-Linear Evolution Equations and Differentiable Vectors of Group Representations
1995
Regularity properties of non-linear Lie algebra representations are defined. These properties are satisfied in examples given by evolution equations. We prove that this regularity implies that the set of C ∞ vectors for the non-linear group representation obtained by integration of the Lie algebra representation coincide with the set of C ∞ vectors of the linear part (the order one term) of this group representation.
Optical Studies of Amphiphilic Molecules with Interesting Electro-Optical and Non-Linear Optical Properties
1990
Structural control is a major issue in both life science, investigating the function of the biological machinery, and in materials science, aiming at the design of novel devices. In part one, recent electro-optical investigations of the primary event of photosynthesis on purified protein preparations are described. Part two focuses on structural studies of monolayers at an air/water interface, and of Langmuir-Blodgett multilayers from a new molecule designed for nonlinear optical applications.
Beneficial impact of wave-breaking for coherent continuum formation in normally dispersive nonlinear fibers
2008
International audience; We study the evolution of a pulse propagating in a normally dispersive fiber in the presence of Kerr nonlinearity. We review the temporal and spectral impact of optical wave-breaking in the development of a continuum. The impact of linear losses or gain is also investigated.
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
2009
We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we…
Stress concentration for closely located inclusions in nonlinear perfect conductivity problems
2019
We study the stress concentration, which is the gradient of the solution, when two smooth inclusions are closely located in a possibly anisotropic medium. The governing equation may be degenerate of $p-$Laplace type, with $1<p \leq N$. We prove optimal $L^\infty$ estimates for the blow-up of the gradient of the solution as the distance between the inclusions tends to zero.
Oscillation criteria for even-order neutral differential equations
2016
Abstract We study oscillatory behavior of solutions to a class of even-order neutral differential equations relating oscillation of higher-order equations to that of a pair of associated first-order delay differential equations. As illustrated with two examples in the final part of the paper, our criteria improve a number of related results reported in the literature.
Nonradial normalized solutions for nonlinear scalar field equations
2018
We study the following nonlinear scalar field equation $$ -\Delta u=f(u)-\mu u, \quad u \in H^1(\mathbb{R}^N) \quad \text{with} \quad \|u\|^2_{L^2(\mathbb{R}^N)}=m. $$ Here $f\in C(\mathbb{R},\mathbb{R})$, $m>0$ is a given constant and $\mu\in\mathbb{R}$ is a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity $f$, we show the existence of one nonradial solution for any $N\geq4$, and obtain multiple (sometimes infinitely many) nonradial solutions when $N=4$ or $N\geq6$. In particular, all these solutions are sign-changing.