Search results for "Nonlinear"

Comment on "Dynamics and properties of waves in a modified Noguchi electrical transmission line"

2016

A recent paper [Phys. Rev. E 91, 022925 (2015)PRESCM1539-375510.1103/PhysRevE.91.022925] presents the derivation of the nonlinear equation modeling envelope waves in a specific case of band passed filter discrete nonlinear electrical transmission line (NLTL), called "A modified Noguchi electrical transmission line" according to the authors. Using the reductive perturbation approach in the semidiscrete approximation, they showed that the modulated waves propagating in this NLTL are described by the ordinary nonlinear Schrodinger (NLS) equation. On the basis of their results, the authors claimed that all previous works on the band passed filter NLTL, which considered the vanishing of the dc c…

Dissipative soliton interactions inside a fiber laser cavity

2005

We report our recent numerical and experimental observations of dissipative soliton interactions inside a fiber laser cavity. A bound state, formed from two pulses, may have a group velocity which differs from that of a single soliton. As a result, they can collide inside the cavity. This results in a variety of outcomes. Numerical simulations are based either on a continuous model or on a parameter-managed model of the cubic-quintic Ginzburg-Landau equation. Each of the models provides explanations for our experimental observations. © 2005 Elsevier Inc. All rights reserved.

Special Section on Fractional Operators in the Analysis of Mechanical Systems Under Stochastic Agencies

2017

Improved Neural Networks with Random Weights for Short-Term Load Forecasting.

2015

An effective forecasting model for short-term load plays a significant role in promoting the management efficiency of an electric power system. This paper proposes a new forecasting model based on the improved neural networks with random weights (INNRW). The key is to introduce a weighting technique to the inputs of the model and use a novel neural network to forecast the daily maximum load. Eight factors are selected as the inputs. A mutual information weighting algorithm is then used to allocate different weights to the inputs. The neural networks with random weights and kernels (KNNRW) is applied to approximate the nonlinear function between the selected inputs and the daily maximum load…

Universality of level spacing distributions in classical chaos

2007

Abstract We suggest that random matrix theory applied to a matrix of lengths of classical trajectories can be used in classical billiards to distinguish chaotic from non-chaotic behavior. We consider in 2D the integrable circular and rectangular billiard, the chaotic cardioid, Sinai and stadium billiard as well as mixed billiards from the Limacon/Robnik family. From the spectrum of the length matrix we compute the level spacing distribution, the spectral auto-correlation and spectral rigidity. We observe non-generic (Dirac comb) behavior in the integrable case and Wignerian behavior in the chaotic case. For the Robnik billiard close to the circle the distribution approaches a Poissonian dis…

Physical interpretation of laser phase dynamics

1990

The basic features characterizing the dynamical evolution of the phase of a detuned-laser field under an unstable regime are physically interpreted in terms of dispersive and dynamical effects. A general method for obtaining any attractor projection containing the phase information is established, which provides evidence for the heteroclinic character of the attractor in the presence of cavity detuning for any emission regime.

Wavelet-like orthonormal bases for the lowest Landau level

1994

As a first step in the description of a two-dimensional electron gas in a magnetic field, such as encountered in the fractional quantum Hall effect, we discuss a general procedure for constructing an orthonormal basis for the lowest Landau level, starting from an arbitrary orthonormal basis in L2(R). We discuss in detail two relevant examples coming from wavelet analysis, the Haar and the Littlewood-Paley bases.

Trivial S-Matrices, Wigner-Von Neumann Resonances and Positon Solutions of the Integrable Nonlinear Evolution Equations

1996

It is well known that the scattering matrix is different from the unit matrix in the case of 1-dimensional Schrodinger operator with smooth rapidly decreasing nonzero potential. This no more true in the case of the slowly decreasing and oscillating potentials for which the absence of scattering is accompanied by the occurrence of the Wigner-von Neumann resonances embedded in the positive absolutely continuous spectrum. Taken as initial conditions in the KdV like integrable partial differential equations these potentials generate interesting family of explicit solutions. Below we will call them positon or multipositon solutions. The interaction of an arbitrary finite number of positons and s…

Experimental and numerical investigations of a two-body floating-point absorber wave energy converter in regular waves

2019

Abstract This paper presents experimental and numerical studies on the hydrodynamics of a two-body floating-point absorber (FPA) wave energy converter (WEC) under both extreme and operational wave conditions. In this study, the responses of the WEC in heave, surge, and pitch were evaluated for various regular wave conditions. For extreme condition analysis, we assume the FPA system has a survival mode that locks the power-take-off (PTO) mechanism in extreme waves, and the WEC moves as a single body in this scenario. A series of Reynolds-averaged Navier–Stokes (RANS) simulations was performed for the survival condition analysis, and the results were validated with the measurements from exper…

Applications of wavelets to quantum mechanics: A pedagogical example

1995

We discuss in many details two quantum mechanical models of planar electrons which are very much related to the Fractional Quantum Hall Effect. In particular, we discuss the localization properties of the trial ground states of the models starting from considerations on the numerical results on the energy. We conclude that wavelet theory can be conveniently used in the description of the system. Finally we suggest applications of our results to the Fractional Quantum Hall Effect.