A modulation equations approach for numerically solving the moving soliton and radiation solutions of NLS

Based on our previous work for solving the nonlinear Schrodinger equation with multichannel dynamics that is given by a localized standing wave and radiation, in this work we deal with the multichannel solution which consists of a moving soliton and radiation. We apply the modulation theory to give a system of ODEs coupled to the radiation term for describing the solution, which is valid for all times. The modulation equations are solved accurately by the proposed numerical method. The soliton and radiation are captured separately in the computation, and they are solved on the translated domain that is moving with them. Thus for a fixed finite physical domain in the lab frame, the multichannel solution can pass through the boundary naturally, which can not be done by imposing any existing boundary conditions. We comment on the differences of this method from the collective coordinates.Comment: 19 pages, 7 figures. To appear on Phys. D. arXiv admin note: text overlap with arXiv:1404.115

Laser power stabilization for second-generation gravitational wave detectors

We present results on the power stabilization of a Nd:YAG laser in the frequency band from 1 Hz to 100 kHz. High-power, low-noise photodetectors are used in a dc-coupled control loop to achieve relative power fluctuations down to 5×10−9 Hz−1/2 at 10 Hz and 3.5×10−9 Hz−1/2 up to several kHz, which is very close to the shot-noise limit for 80 mA of detected photocurrent on each detector. We investigated and eliminated several noise sources such as ground loops and beam pointing. The achieved stability level is close to the requirements for the Advanced LIGO gravitational wave detector

Systems control theory applied to natural and synthetic musical sounds

Systems control theory is a far developped field which helps to study stability, estimation and control of dynamical systems. The physical behaviour of musical instruments, once described by dynamical systems, can then be controlled and numerically simulated for many purposes. The aim of this paper is twofold: first, to provide the theoretical background on linear system theory, both in continuous and discrete time, mainly in the case of a finite number of degrees of freedom ; second, to give illustrative examples on wind instruments, such as the vocal tract represented as a waveguide, and a sliding flute