The dynamics of second-order equations with delayed feedback and a large coefficient of delayed control

The dynamics of second-order equations with nonlinear delayed feedback and a large coefficient of a delayed equation is investigated using asymptotic methods. Based on special methods of quasi-normal forms, a new construction is elaborated for obtaining the main terms of asymptotic expansions of asymptotic residual solutions. It is shown that the dynamical properties of the above equations are determined mostly by the behavior of the solutions of some special families of parabolic boundary value problems. A comparative analysis of the dynamics of equations with the delayed feedback of three types is carried out.     

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system’s chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.     

HIGHER DIRAC COHOMOLOGY OF MODULES WITH GENERALIZED INFINITESIMAL CHARACTER

We modify the definition of Dirac cohomology in such a way that the standard properties of the usual Dirac cohomology, valid for modules with infinitesimal character, become valid also for modules with only generalized infinitesimal character.     

All-optical 2R-regeneration and continuous wave to pulsed signal wavelength conversion based on fiber nonlinearity

In this paper, we propose a novel all-optical 2R (re-amplification and re-shaping) regenerator based on inducing nonlinear chirp over a continuous wave probe. The regenerator also performs continuous wave to pulsed wavelength conversion. The chirp is induced in a highly nonlinear fiber by the data modulated pulsed signal that is to be regenerated. Offset filtering is employed at the output of the highly nonlinear fiber to extract the frequencies generated as a result of chirping. The regenerator performance has been evaluated with the help of bit-error-rate plots and eye diagrams at different values of optical signal to noise ratios. Apart from re-shaping and re-amplification, inclusion of the regenerator results in better resilience to amplified spontaneous emission noise.     

A note on general solution of Stokes equations

Li et al. (2015) claim that it is sufficient to use two harmonic functions to express the general solution of Stokes equations. In this paper, we demonstrate that this is not true in a general case and that we in fact need three scalar harmonic functions to represent the general solution of Stokes equations (Venkatalaxmi et al., 2004).     

Multi-frequency AOM for multi-beam laser scanning exposure system

Digital printing systems recorded on films or computer to plates (CTPs) have been required to improve their productivity and image quality. Under the circumstance, a printing technology of the multi-beam laser scanning for the drum capstan system, which is almost the same as optics configuration as the flat bed system, was developed using a newly developed multi-frequency acousto–optic modulator (AOM) as a key device instead of ultra-fast scanning devices toward a main scan direction. The multi-frequency AOM was developed with phased array-type transducers, achieving a wider bandwidth of over 160 MHz. The design consisted of a simultaneous three beams generation with interlace scan to avoid the beat effect by adjacent Doppler-shifted beams, which consequently attained the fastest recording speed of 5.0 mm/s compared with 2.0–3.0 mm/s of existing systems in those days. Furthermore, a couple of critical parameters of the multi-frequency AOM are studied, for example, a treatment of third-order intermodulation and also beat effect in connection with photosensitive media. As a result, the necessity of interlaces scanning to obtain good image quality without beat effect and also to allow a lower laser power to apply is proposed.     

Superintegrable cases of four-dimensional dynamical systems

Degenerate tri-Hamiltonian structures of the Shivamoggi and generalized Raychaudhuri equations are exhibited. For certain specific values of the parameters, it is shown that hyperchaotic Lü and Qi systems are superintegrable and admit tri-Hamiltonian structures.