Search results for "Nonlinear system"
showing 10 items of 1446 documents
Lagrangian dynamics and possible isochronous behavior in several classes of non-linear second order oscillators via the use of Jacobi last multiplier
2015
Abstract In this paper, we employ the technique of Jacobi Last Multiplier (JLM) to derive Lagrangians for several important and topical classes of non-linear second-order oscillators, including systems with variable and parametric dissipation, a generalized anharmonic oscillator, and a generalized Lane–Emden equation. For several of these systems, it is very difficult to obtain the Lagrangians directly, i.e., by solving the inverse problem of matching the Euler–Lagrange equations to the actual oscillator equation. In order to facilitate the derivation of exact solutions, and also investigate possible isochronous behavior in the analyzed systems, we next invoke some recent theoretical result…
Statistic moments of the total energy of potential systems and application to equivalent non-linearization
2000
In this paper some properties of the total energy moments of potential systems, subjected to external white noise processes, are shown. Potential systems with a polynomial form of energy-dependent damping have been considered. It is shown that the analytical relations between the statistical moments of the energy associated with such systems can be obtained with the aid of the standard Ito calculus. Furthermore, it is shown that, for the stationary case, these analytical relations are very useful for the application of the equivalent non-linearization technique.
�ber ein Verfahren der Ordnung $$1 + \sqrt 2 $$ zur Nullstellenbestimmung
1979
A new iterative method for solving nonlinear equations is presented which is shown to converge locally withR-order of convergence $$1 + \sqrt 2 $$ at least under suitable differentiability assumptions. The method needs as many function evaluations per step as the classical Newton method.
Some supplementary results on the 1+ $$\sqrt 2 $$ order method for the solution of nonlinear equations
1982
Recently an iterative method for the solution of systems of nonlinear equations having at leastR-order 1+ $$\sqrt 2 $$ for simple roots has been investigated by the author [7]; this method uses as many function evaluations per step as the classical Newton method. In the present note we deal with several properties of the method such as monotone convergence, asymptotic inclusion of the solution and convergence in the case of multiple roots.
Iterative closure method for non-linear systems driven by polynomials of Gaussian filtered processes
2008
This paper concerns the statistical characterization of the non-Gaussian response of non-linear systems excited by polynomial forms of filtered Gaussian processes. The non-Gaussianity requires the computation of moments of any order. The problem is solved profiting from both the stochastic equivalent linearization (EL), and the moment equation approach of Ito's stochastic differential calculus through a procedure divided into two parts. The first step requires the linearization of the system, while retaining the non-linear excitation; the response statistical moments are calculated exactly, and constitute a first estimate of the moments of the actual non-linear system. In the second step, t…
Noise stabilization effects in models of interdisciplinary physics
2009
Metastability is a generic feature of many nonlinear systems, and the problem of the lifetime of metastable states involves fundamental aspects of nonequilibrium statistical mechanics. The investigation of noise-induced phenomena in far from equilibrium systems is one of the approaches used to understand the behaviour of physical and biological complex systems. The enhancement of the lifetime of metastable states through the noise enhanced stability effect and the role played by the resonant activation phenomenon will be discussed in models of interdisciplinary physics: (i) polymer translocation dynamics; (ii) transient regime of FitzHugh-Nagumo model; (iii) market stability in a nonlinear …
Inducing Strong Non-Linearities in a Phonon Trapping Quartz Bulk Acoustic Wave Resonator Coupled to a Superconducting Quantum Interference Device
2018
International audience; A quartz Bulk Acoustic Wave resonator is designed to coherently trap phonons in such a way that they are well confined and immune to suspension losses so they exhibit extremely high acoustic Q-factors at low temperature, with Q × f products of order 10¹⁸ Hz. In this work we couple such a resonator to a Superconducting Quantum Interference Device (SQUID) amplifier and investigate effects in the strong signal regime. Both parallel and series connection topologies of the system are investigated. The study reveals significant non-Duffing response that is associated with the nonlinear characteristics of Josephson junctions. The nonlinearity provides quasi-periodic structu…
Incoherent solitons and condensation processes
2006
International audience; We study the nonlinear interaction of partially incoherent nonlinear optical waves. We show that, in spite of the incoherence of the waves, coherent phase effects may play a relevant role during the propagation, in contrast with the usual wave turbulence description of the interaction. These nonlinear phase effects may lead the system to unexpected processes of self-organization, such as condensation, or incoherent soliton generation in instantaneous response nonlinear media. Such self-organization processes may be characterized by a reduction of the non-equilibrium entropy, which violates the Boltzmann's H-theorem of entropy growth inherent to the wave turbulence th…
General approach to spatiotemporal modulational instability processes
2011
International audience; In this article, we derive the general exact solution of the modulation instability gain. The solution described here is valid for 1-D, 2-D, and 3-D cases considering any temporal response function of the medium and with possible higher order Kerr nonlinearities. In particular, we show that the gain induced by modulation instability is initial condition dependent, while the usual calculations do not lead to such a dependence. Applications for current and high-interest nonlinear propagation problems, such as 1-D optical fiber propagation with delayed Raman response and 2-D filamentation in gases, are investigated in detail. More specifically, we demonstrate that the 2-D …
Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution
1998
This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error term is written as a sum of firs…