Study of synchronisation in chains of coupled non-linear oscillators and resonators

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Some aspects of the solution of non-linear differential equations

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A comparisation of methods for the optimisation of a non-linear function subject to non-linear constraints

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A non-linear encoder using a binary counterfor pulse-code modulation

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Challenges of developing non-linear devices to achieve the linear Shannon limit

To achieve the Shannon Capacity Limit, we need to develop practical, effective and deployable non-linear devices to invert the non-linear effects of the transmission line. In this work, we will summarise the progress we are making to realise these, specifically looking at optical phase conjugation and phase regenerators as methods to improve non-linear tolerances. © 2014 IEEE.

High spectral efficiency transmission emulation for non-linear transmission performance estimation for high order modulation formats

We demonstrate a simple method to experimentally evaluate nonlinear transmission performance of high order modulation formats using a low number of channels and channel-like ASE. We verify it's behaviour is consistent with the AWGN model of transmission.

Travelling-wave model of semiconductor optical amplifier based non-linear loop mirror

A travelling-wave model of a semiconductor optical amplifier based non-linear loop mirror is developed to investigate the importance of travelling-wave effects and gain/phase dynamics in predicting device behaviour. A constant effective carrier recovery lifetime approximation is found to be reasonably accurate (±10%) within a wide range of control pulse energies. Based on this approximation, a heuristic model is developed for maximum computational efficiency. The models are applied to a particular configuration involving feedback.

Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems

We present some results on the formation of singularities for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut + A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions (weaker than genuine non-linearity), we prove that the first order derivative of the solution blows-up in finite time.

Non-Linear Network-Flow Model of Lukasiewicz’s Multivalue Logic

The paper presents a new network-flow interpretation of Łukasiewicz’s logic based on models with an increased effectiveness. The obtained results show that the presented network-flow models principally may work for multivalue logics with more than three states of the variables i.e. with a finite set of states in the interval from 0 to 1. The described models give the opportunity to formulate various logical functions. If the results from a given model that are contained in the obtained values of the arc flow functions are used as input data for other models then it is possible in Łukasiewicz’s logic to interpret successfully other sophisticated logical structures. The obtained models allow a research of Łukasiewicz’s logic with specific effective methods of the network-flow programming. It is possible successfully to use the specific peculiarities and the results pertaining to the function ‘traffic capacity of the network arcs’. Based on the introduced network-flow approach it is possible to interpret other multivalue logics – of E.Post, of L.Brauer, of Kolmogorov, etc.

Approaching the non-linear Shannon limit

We review the recent progress of information theory in optical communications, and describe the current experimental results and associated advances in various individual technologies which increase the information capacity. We confirm the widely held belief that the reported capacities are approaching the fundamental limits imposed by signal-to-noise ratio and the distributed non-linearity of conventional optical fibres, resulting in the reduction in the growth rate of communication capacity. We also discuss the techniques which are promising to increase and/or approach the information capacity limit.

Non-linear temperature response of Bragg gratings in doped and un-doped holey polymer optical fibre

We present measurements on the non-linear temperature response of fibre Bragg gratings recorded in pure and trans-4-stilbenemethanol-doped polymethyl methacrylate (PMMA) holey fibres.

Caputo Derivatives in Viscoelasticity: A Non-Linear Finite-Deformation Theory for Tissue

Mathematics Subject Classification: 26A33, 74B20, 74D10, 74L15

Variational Markov chain Monte Carlo for Bayesian smoothing of non-linear diffusions

In this paper we develop set of novel Markov Chain Monte Carlo algorithms for Bayesian smoothing of partially observed non-linear diffusion processes. The sampling algorithms developed herein use a deterministic approximation to the posterior distribution over paths as the proposal distribution for a mixture of an independence and a random walk sampler. The approximating distribution is sampled by simulating an optimized time-dependent linear diffusion process derived from the recently developed variational Gaussian process approximation method. The novel diffusion bridge proposal derived from the variational approximation allows the use of a flexible blocking strategy that further improves mixing, and thus the efficiency, of the sampling algorithms. The algorithms are tested on two diffusion processes: one with double-well potential drift and another with SINE drift. The new algorithm's accuracy and efficiency is compared with state-of-the-art hybrid Monte Carlo based path sampling. It is shown that in practical, finite sample applications the algorithm is accurate except in the presence of large observation errors and low to a multi-modal structure in the posterior distribution over paths. More importantly, the variational approximation assisted sampling algorithm outperforms hybrid Monte Carlo in terms of computational efficiency, except when the diffusion process is densely observed with small errors in which case both algorithms are equally efficient. © 2011 Springer-Verlag.

Multi-threaded parallel simulation of non-local non-linear problems in ultrashort laser pulse propagation in the presence of plasma

We describe a parallel multi-threaded approach for high performance modelling of wide class of phenomena in ultrafast nonlinear optics. Specific implementation has been performed using the highly parallel capabilities of a programmable graphics processor. © 2011 SPIE.

The non-linear acousto-mechanical and thermodynamic response of spherical absorbers to laser pulses of various temporal profiles

This study is to theoretically investigate shockwave and microbubble formation due to laser absorption by microparticles and nanoparticles. The initial motivation for this research was to understand the underlying physical mechanisms responsible for laser damage to the retina, as well as the predict threshold levels for damage for laser pulses with of progressively shorter durations. The strongest absorbers in the retina are micron size melanosomes, and their absorption of laser light causes them to accrue very high energy density. I theoretically investigate how this absorbed energy is transferred to the surrounding medium. For a wide range of conditions I calculate shockwave generation and bubble growth as a function of the three parameters; fluence, pulse duration and pulse shape. In order to develop a rigorous physical treatment, the governing equations for the behavior of an absorber and for the surrounding medium are derived. Shockwave theory is investigated and the conclusion is that a shock pressure explanation is likely to be the underlying physical cause of retinal damage at threshold fluences for sub-nanosecond pulses. The same effects are also expected for non-biological micro and nano absorbers. ^