We derive formulae for the coherent and incoherent tune shift due to the nonlinear resistive-wall wake field for a single beam travelling between two parallel plates. The theoretical predictions are compared with measurements performed on an LHC prototype collimator during the 2004 SPS run. We show that the tune shift derived from the nonlinear wake field yields a better agreement with the meas...

Nonlinear beam dynamics is an important issue in accelerator systems. The Poincar e section map plays a basic role in characterizing and analyzing such a nonlinear system. Although many kinds of nonlinear beam dynamics experiments have been conducted, no direct measurement of a nonlinear map has been reported for an accelerator in normal operation mode. In this paper, we will show that it appea...

This memo presents a simple analysis of small-scale self focusing or filamentation effects in strongly diverging or converging optical beams (“tapered beams”) propagating in nonlinear or saturable optical media. In contrast to the collimated beam case where the nonlinear perturbations can be modelled as uniformly spaced periodic ripples, the nonlinear phase and amplitude ripples in the tapered-...

This paper proposes a novel adaptive control law for nonlinear systems using Takagi-Sugeno fuzzy system. Takagi-Sugeno fuzzy system is used to identify nonlinear system components theta alpha and theta beta. Stable Indirect Adaptive control law is such that it has two control components one is certainty equivalence control and other is sliding mode control. Sliding mode controller is used to en...

We propose a novel all-optical, nonlinear mode-conversion scheme based on cascaded three-wave-mixing phase-matched interactions in quadratic nonlinear crystals. We demonstrate the method experimentally by performing all-optical mode conversion of an input 1636 nm Hermite-Gaussian mode from the zeroth order to the first order using two periodically poled LiNbO(3) crystals. Nonlinear mode convers...

Ultrafast laser processing applications need fast approaches to assess the nonlinear propagation of the laser beam in order to predict the optimal range of processing parameters in a wide variety of cases. We develop here a method based on the simple monitoring of the nonlinear beam shaping against numerical prediction. The numerical code solves the nonlinear Schrödinger equation with nonlinear...

This paper presents chaotic behavior of a nonlinear viscoelastic beam under a moving mass interaction. Considering the stretching effect which is modeled by the Lagrangian strain theory and using linear Kelvin-Voigt model to constitute viscoelastic behavior of the beam, the governing equations of transverse vibration is derived. Then Galerkin truncation is applied to find the ordinary different...

The aim of this study is the investigation of the large amplitude deflection of an Euler-Bernoulli beam subjected to an axial load on a viscoelastic foundation with the strong damping. In order to achieve this purpose, the beam nonlinear frequency has been calculated by homotopy perturbation method (HPM) and Hamilton Approach (HA) and it was compared by the exact solutions for the different bou...

in this paper a novel all-optical logic nand, nor and xor gate based on nonlinear directional coupler theory is demonstrated. we use the identical structure which contains three waveguides, for designing these gates; the only difference however, is the power of inputs light beam. in other words, while a beam with 4 w/μm in power considered as logical one, the output is nand gate and if a beam w...

Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framewo...