Dynamics of linear polymers in random media

We study phenomenological scaling theories of the polymer dynamics in random media, employing the existing scaling theories of polymer chains and the percolation statistics. We investigate both the Rouse and the Zimm model for Brownian dynamics and estimate the diffusion constant of the center-of-mass of the chain in such disordered media. For internal dynamics of the chain, we estimate the dynamic exponents. We propose similar scaling theory for the reptation dynamics of the chain in the framework of Flory theory for the disordered medium. The modifications in the case of correlated disorders are also discussed. .

Multi-threaded parallel numerical modelling of femtosecond pulse propagation in laser machining

Femtosecond laser microfabrication has emerged over the last decade as a 3D flexible technology in photonics. Numerical simulations provide an important insight into spatial and temporal beam and pulse shaping during the course of extremely intricate nonlinear propagation (see e.g. [1,2]). Electromagnetics of such propagation is typically described in the form of the generalized Non-Linear Schrdinger Equation (NLSE) coupled with Drude model for plasma [3]. In this paper we consider a multi-threaded parallel numerical solution for a specific model which describes femtosecond laser pulse propagation in transparent media [4, 5]. However our approach can be extended to similar models. The numerical code is implemented in NVIDIA Graphics Processing Unit (GPU) which provides an effitient hardware platform for multi-threded computing. We compare the performance of the described below parallel code implementated for GPU using CUDA programming interface [3] with a serial CPU version used in our previous papers [4,5]. © 2011 IEEE.

Proposal and design of airy-based rocket pulses for invariant propagation in lossy dispersive media

A novel kind of Airy-based pulse with an invariant propagation in lossy dispersive media is proposed. The basic principle is based on an optical energy trade-off between different parts of the pulse caused by the chromatic dispersion, which is used to compensate the attenuation losses of the propagation medium. Although the ideal concept of the proposed pulses implies infinite pulse energy, the numerical simulations show that practical finite energy pulses can be designed to obtain a partially invariant propagation over a finite distance of propagation.

Impact of signal-ASE four-wave mixing on the effectiveness of digital back-propagation in 112 Gb/s PM-QPSK systems

Limitations in the performance of coherent transmission systems employing digital back-propagation due to four-wave mixing impairments are reported for the first time. A significant performance constraint is identified, originating from four-wave mixing between signals and amplified spontaneous emission noise which induces a linear increase in the standard deviation of the received field with signal power, and linear dependence on transmission distance.

Proposal and design of airy-based rocket pulses for invariant propagation in lossy dispersive media

A novel kind of Airy-based pulse with an invariant propagation in lossy dispersive media is proposed. The basic principle is based on an optical energy trade-off between different parts of the pulse caused by the chromatic dispersion, which is used to compensate the attenuation losses of the propagation medium. Although the ideal concept of the proposed pulses implies infinite pulse energy, the numerical simulations show that practical finite energy pulses can be designed to obtain a partially invariant propagation over a finite distance of propagation.

Inference by belief propagation in composite systems

We devise a message passing algorithm for probabilistic inference in composite systems, consisting of a large number of variables, that exhibit weak random interactions among all variables and strong interactions with a small subset of randomly chosen variables; the relative strength of the two interactions is controlled by a free parameter. We examine the performance of the algorithm numerically on a number of systems of this type for varying mixing parameter values.

The effects of optical activity and absorption on two wave mixing in Bi12SiO20

We consider non-degenerate two-wave mixing in photorefractive Bi12SiO20. It is shown theoretically that the presence of absorption and optical activity in the photorefractive media may result in a number of maxima for the gain as the frequency detuning between the two beams is varied. Further, when the beam interaction is used for optical amplification, there may also exist an optimum crystal length beyond which there is a reduction in the useful gain obtainable. Experimental results are presented in confirmation of the theory.

The effects of optical activity and absorption on two wave mixing in Bi12SiO20

We consider non-degenerate two-wave mixing in photorefractive Bi12SiO20. It is shown theoretically that the presence of absorption and optical activity in the photorefractive media may result in a number of maxima for the gain as the frequency detuning between the two beams is varied. Further, when the beam interaction is used for optical amplification, there may also exist an optimum crystal length beyond which there is a reduction in the useful gain obtainable. Experimental results are presented in confirmation of the theory.

Power-controlled phase-matching and instability of CW propagation in multicore optical fibers with a central core

We present modulation instability analysis including azimuthal perturbations of steady-state continuous wave (CW) propagation in multicore-fiber configurations with a central core. In systems with a central core, a steady CW evolution regime requires power-controlled phase matching, which offers interesting spatial-division applications. Our results have general applicability and are relevant to a range of physical and engineering systems, including high-power fiber lasers, optical transmission in multicore fiber, and systems of coupled nonlinear waveguides. © 2013 Optical Society of America.

Adaptive back-propagation in on-line learning of multilayer networks

An adaptive back-propagation algorithm is studied and compared with gradient descent (standard back-propagation) for on-line learning in two-layer neural networks with an arbitrary number of hidden units. Within a statistical mechanics framework, both numerical studies and a rigorous analysis show that the adaptive back-propagation method results in faster training by breaking the symmetry between hidden units more efficiently and by providing faster convergence to optimal generalization than gradient descent.

On-line learning with adaptive back-propagation in two-layer networks

An adaptive back-propagation algorithm parameterized by an inverse temperature 1/T is studied and compared with gradient descent (standard back-propagation) for on-line learning in two-layer neural networks with an arbitrary number of hidden units. Within a statistical mechanics framework, we analyse these learning algorithms in both the symmetric and the convergence phase for finite learning rates in the case of uncorrelated teachers of similar but arbitrary length T. These analyses show that adaptive back-propagation results generally in faster training by breaking the symmetry between hidden units more efficiently and by providing faster convergence to optimal generalization than gradient descent.

Experimental observation of autosoliton propagation in a dispersion-managed system guided by nonlinear optical loop mirrors

Observation of autosoliton propagation in a dispersion-managed optical transmission system controlled by in-line nonlinear fiber loop switches is reported for what is believed to be the first time. The system is based on a strong dispersion map with large amplifier spacing. Operation at transmission rates of 10 and 40 Gbits/s is demonstrated. ©2004 Optical Society of America.

40Gbit/s single channel dispersion managed pulse propagation in standard fibre over 509km

Error free propagation of a single polarisation optical time division multiplexed 40Gbit/s dispersion managed pulse data stream over 509km has been achieved in standard (non-dispersion shifted) fibre. Dispersion compensating fibre was used after each amplifier to reduce the high local dispersion of the standard fibre. © IEE 1999.

The use of enzyme catalysts in organic media for the synthesis of biodegradable polyesters

The enzyme catalysed polytransesterification of diesters with diols was investigated under various conditions. The most consistent results were obtained using crude porcine pancreatic lipase (PPL) suspended in anhydrous diethyl ether. Addition of molecular sieve to the above system gave higher molecular weight products. The PPL catalysed reaction of bis(2,2,2-trichlorethyl) adipate and glutarate with butane-1,4-diol in anhydrous ether with and without molecular sieve was investigated over a range of times from 8 to 240 hours. The 72 hour adipate reaction with molecular sieve gave the highest molecular weight polymer (Mn 6,500 and Mw 9,400). The glutarate gave the maximum molecular weight polyester after 24 hours (Mn 5,700 and Mw 9,500). Occasionally the glutarate reaction produced very high molecular weight polyester-enzyme complexes. Toluene generally gave lower molecular weight products than diethyl ether. Dichloromethane and tetrahydrofuran gave mainly dimers and trimers. Alternative enzyme and diol systems were also investigated. These yielded no polymeric products. The molecular weights of the polyesters were determined by 1H NMR end-group analysis and by GPC. The molecular weights determined by NMR were on average about twice as great as those determined by GPC. The synthesis of the following diesters is described: i)Bis(2,2,2-trichloroethyl) succinate, glutarate, adipate, trans-3-hexenedioate, and trans-3,4-epoxyadipate. ii) Diphenyl glutarate and adipate.iii)Bis(2,2,2-fluoroethyl) glutarate and trans-3-hexendioate.iv) Divinyl glutarate. v) N,N'Glutaryl dicyclohexanone oxime.The polytransesterification of all the above esters with diols was investigated. The easily synthesised bis(2,2,2-trichloroethyl) glutarate and adipate gave the best results and the work was concentrated on these two esters.

Appearance of bound states in random potentials with applications to soliton theory

We analyze the stochastic creation of a single bound state (BS) in a random potential with a compact support. We study both the Hermitian Schrödinger equation and non-Hermitian Zakharov-Shabat systems. These problems are of special interest in the inverse scattering method for Korteveg–de-Vries and the nonlinear Schrödinger equations since soliton solutions of these two equations correspond to the BSs of the two aforementioned linear eigenvalue problems. Analytical expressions for the average width of the potential required for the creation of the first BS are given in the approximation of delta-correlated Gaussian potential and additionally different scenarios of eigenvalue creation are discussed for the non-Hermitian case.