Search results for " Integra"

Application of the Pontryagin maximum principle to the time-optimal control in a chain of three spins with unequal couplings

2014

We solve a time-optimal control problem in a linear chain of three coupled spins 1/2 with unequal couplings. We apply the Pontryagin maximum principle and show that the associated Hamiltonian system is the one of a three-dimensional rigid body. We express the optimal control fields in terms of the components of the classical angular momentum of the rigid body. The optimal trajectories and the minimum control time are given in terms of elliptic functions and elliptic integrals.

Analytical Solutions for the Self- and Mutual Inductances of Concentric Coplanar Disk Coils

2013

In this paper, closed-form solutions are presented for the self- and mutual inductances of disk coils which lie concentrically in a plane. The solutions are given as generalized hypergeometric functions which are closely related to elliptic integrals. The method used is a Legendre polynomial expansion of the inductance integral, which renders all integrations straightforward. Excellent numerical agreement with previous studies is obtained. An asymptotic formula for the approach to the ring coil limit is also derived and numerically validated. The methods presented here can be applied to noncoaxial and noncoplanar cases.

Generation of High-Repetition-Rate Dark Soliton Trains and Frequency Conversion in Optical Fibers

1998

Induced modurational polarization instability in birefringent fibers leads to trains of dark soliton-like pulses. Optimal large-signal cw and soliton frequency conversion is also analysed.

Ultrasonic cavity solitons

2007

We report on a new type of localized structure, an ultrasonic cavity soliton, supported by large aspect-ratio acoustic resonators containing viscous media. These states of the acoustic and thermal fields are robust structures, existing whenever a spatially uniform solution and a periodic pattern coexist. Direct proof of their existence is given both through the numerical integration of the model and through the analysis and numerical integration of a generalized Swift-Hohenberg equation, derived from the microscopic equations under conditions close to nascent bistability. An analytical solution for the ultrasonic cavity soliton is given.

Hydrodynamics of periodic breathers

2014

We report the first experimental observation of periodic breathers in water waves. One of them is Kuznetsov–Ma soliton and another one is Akhmediev breather. Each of them is a localized solution of the nonlinear Schrödinger equation (NLS) on a constant background. The difference is in localization which is either in time or in space. The experiments conducted in a water wave flume show results that are in good agreement with the NLS theory. Basic features of the breathers that include the maximal amplitudes and spectra are consistent with the theoretical predictions.

Collision of Akhmediev Breathers in Nonlinear Fiber Optics

2013

We report here a novel fiber-based test bed using tailored spectral shaping of an optical-frequency comb to excite the formation of two Akhmediev breathers that collide during propagation. We have found specific initial conditions by controlling the phase and velocity differences between breathers that lead, with certainty, to their efficient collision and the appearance of a giant-amplitude wave. Temporal and spectral characteristics of the collision dynamics are in agreement with the corresponding analytical solution. We anticipate that experimental evidence of breather-collision dynamics is of fundamental importance in the understanding of extreme ocean waves and in other disciplines dri…

Inelastic scattering and interactions of three-wave parametric solitons.

2006

We study the interactions of velocity-locked three-wave parametric solitons in a medium with quadratic nonlinearity and dispersion. We reveal that the inelastic scattering between three-wave solitons and linear waves may be described in terms of analytical solutions with dynamically varying group velocity, or boomerons. Moreover, we demonstrate the elastic nature of three-wave soliton-soliton collisions and interactions.

Simple sampling Monte Carlo methods

2005

Dark-and-bright rogue waves in long wave-short wave resonance

2014

Nonlinear Photonics, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, in Proceedings Advanced Photonics, Part of Advanced Photonics, Barcelona, Spain, 28-31 July 2014

Orthorhombic Phase of Crystalline Polyethylene: A Constant Pressure Path Integral Monte Carlo Study

1998

In this paper we present a Path Integral Monte Carlo (PIMC) simulation of the orthorhombic phase of crystalline polyethylene, using an explicit atom force field with unconstrained bond lengths and angles. This work represents a quantum extension of our recent classical simulation (J. Chem. Phys. 106, 8918 (1997)). It is aimed both at exploring the applicability of the PIMC method on such polymer crystal systems, as well as on a detailed assessment of the importance of quantum effects on different quantities. We used the $NpT$ ensemble and simulated the system at zero pressure in the temperature range 25 - 300 K, using Trotter numbers between 12 and 144. In order to investigate finite-size e…