Anomalies in stiffness and damping of a 2D discrete viscoelastic system due to negative stiffness components

The recent development of using negative stiffness inclusions to achieve extreme overall stiffness and mechanical damping of composite materials reveals a new avenue for constructing high performance materials. One of the negative stiffness sources can be obtained from phase transforming materials in the vicinity of their phase transition, as suggested by the Landau theory. To understand the underlying mechanism from a microscopic viewpoint, we theoretically analyze a 2D, nested triangular lattice cell with pre-chosen elements containing negative stiffness to demonstrate anomalies in overall stiffness and damping. Combining with current knowledge from continuum models, based on the composite theory, such as the Voigt, Reuss, and Hashin-Shtrikman model, we further explore the stability of the system with Lyapunov's indirect stability theorem. The evolution of the microstructure in terms of the discrete system is discussed. A potential application of the results presented here is to develop special thin films with unusual in-plane mechanical properties. © 2006 Elsevier B.V. All rights reserved.

Anisotropic model of kinetic roughening:he strong-coupling regime

We study the strong coupling (SC) limit of the anisotropic Kardar-Parisi-Zhang (KPZ) model. A systematic mapping of the continuum model to its lattice equivalent shows that in the SC limit, anisotropic perturbations destroy all spatial correlations but retain a temporal scaling which shows a remarkable crossover along one of the two spatial directions, the choice of direction depending on the relative strength of anisotropicity. The results agree with exact numerics and are expected to settle the long-standing SC problem of a KPZ model in the infinite range limit. © 2007 The American Physical Society.

Error-correcting codes on a Bethe-like lattice

We analyse Gallager codes by employing a simple mean-field approximation that distorts the model geometry and preserves important interactions between sites. The method naturally recovers the probability propagation decoding algorithm as a minimization of a proper free-energy. We find a thermodynamical phase transition that coincides with information theoretical upper-bounds and explain the practical code performance in terms of the free-energy landscape.

Lattice approach to the dynamics of phase-coded soliton trains

We address the collective dynamics of a soliton train propagating in a medium described by the nonlinear Schrödinger equation. Our approach uses the reduction of train dynamics to the discrete complex Toda chain (CTC) model for the evolution of parameters for each train constituent: such a simplification allows one to carry out an approximate analysis of the dynamics of positions and phases of individual interacting pulses. Here, we employ the CTC model to the problem which has relevance to the field of fibre optics communications where each binary digit of transmitted information is encoded via the phase difference between the two adjacent solitons. Our goal is to elucidate different scenarios of the train distortions and the subsequent information garbling caused solely by the intersoliton interactions. First, we examine how the structure of a given phase pattern affects the initial stage of the train dynamics and explain the general mechanisms for the appearance of unstable collective soliton modes. Then we further discuss the nonlinear regime concentrating on the dependence of the Lax scattering matrix on the input phase distribution; this allows one to classify typical features of the train evolution and determine the distance where the soliton escapes from its slot. In both cases, we demonstrate deep mathematical analogies with the classical theory of crystal lattice dynamics.

Optical frequency conversion, pulse compression and signal copying using triangular pulses

We propose techniques of optical frequency conversion, pulse compression and signal copying based on a combination of cross-phase modulation using triangular pump pulses and subsequent propagation in a dispersive medium.

Collective behaviour in a square lattice of driven Duffing resonators coupled to van der Pol oscillators

The global and local synchronisation of a square lattice composed of alternating Duffing resonators and van der Pol oscillators coupled through displacement is studied. The lattice acts as a sensing device in which the input signal is characterised by an external driving force that is injected into the system through a subset of the Duffing resonators. The parameters of the system are taken from MEMS devices. The effects of the system parameters, the lattice architecture and size are discussed.

Experimental optimization of triangular pulse generation in normal dispersion fiber for all optical processing applications

We experimentally investigate a multi-parameter optimization of conditions for generation of triangular pulses in normal dispersion fiber. We find that triangular pulses suitable for all optical processing applications can be generated for a wide range of input pulse chirps but that triangular pulse quality and stability is improved with increased input pulse chirp.

A preliminary study into emergent behaviours in a lattice of interacting nonlinear resonators and oscillators

Future sensor arrays will be composed of interacting nonlinear components with complex behaviours with no known analytic solutions. This paper provides a preliminary insight into the expected behaviour through numerical and analytical analysis. Specically, the complex behaviour of a periodically driven nonlinear Duffing resonator coupled elastically to a van der Pol oscillator is investigated as a building block in a 2D lattice of such units with local connectivity. An analytic treatment of the 2-device unit is provided through a two-time-scales approach and the stability of the complex dynamic motion is analysed. The pattern formation characteristics of a 2D lattice composed of these units coupled together through nearest neighbour interactions is analysed numerically for parameters appropriate to a physical realisation through MEMS devices. The emergent patterns of global and cluster synchronisation are investigated with respect to system parameters and lattice size.

All-optical TDM to WDM signal conversion and partial regeneration using XPM with triangular pulses

We propose a new all-optical, all-fibre scheme for conversion of time-division multiplexed to wavelength-division multiplexed signals using cross-phase modulation with triangular pulses. Partial signal regeneration using this technique is also demonstrated.

Studies of the effects of molecular encounters on N.M.R. spin-lattice relaxation times

This thesis is concerned with investigations of the effects of molecular encounters on nuclear magnetic resonance spin-lattice relaxation times, with particular reference to mesitylene in mixtures with cyclohexane and TMS. The purpose of the work was to establish the best theoretical description of T1 and assess whether a recently identified mechanism (buffeting), that influences n.m.r. chemical shifts, governs Tl also. A set of experimental conditions are presented that allow reliable measurements of Tl and the N. O. E. for 1H and 13C using both C. W. and F.T. n.m.r. spectroscopy. Literature data for benzene, cyclohexane and chlorobenzene diluted by CC14 and CS2 are used to show that the Hill theory affords the best estimation of their correlation times but appears to be mass dependent. Evaluation of the T1 of the mesitylene protons indicates that a combined Hill-Bloembergen-Purcell-Pound model gives an accurate estimation of T1; subsequently this was shown to be due to cancellation of errors in the calculated intra and intemolecular components. Three experimental methods for the separation of the intra and intermolecular relaxation times are described. The relaxation times of the 13C proton satellite of neat bezene, 1,4 dioxane and mesitylene were measured. Theoretical analyses of the data allow the calculation of Tl intra. Studies of intermolecular NOE's were found to afford a general method of separating observed T1's into their intra and intermolecular components. The aryl 1H and corresponding 13C T1 values and the NOE for the ring carbon of mesitylene in CC14 and C6H12-TMS have been used in combination to determine T1intra and T1inter. The Hill and B.P.P. models are shown to predict similarly inaccurate values for T1linter. A buffeting contribution to T1inter is proposed which when applied to the BPP model and to the Gutowsky-Woessner expression for T1inter gives an inaccuracy of 12% and 6% respectively with respect to theexperimentally based T1inter.

Crystallographic studies of magnetite and titanomaghemite

The crystal structure of natural magnetite has been investigated on the basis of previously published X-ray intensity data and a newly acquired, more extensive data base. Both investigations show that the structure does not conform to the centrosymmetrical space group Fd3m, as is normally assumed, but the non-centrosymmetrical space group F43m. The structure refinement provides values for the atom positions, anisotropic thermal parameters and bond lengths. A study of Friedel related pairs of X-ray intensities shows that Friedel's law is violated in magnetite, further confirming that the space group is non-centrosymmetrical. It was found that the octahedral site cations in magnetite do not occupy special positions at the centres of the octahedral interstices as they should under the space group Fd3m, but are displaced along <111 > directions leading to F43m symmetry. A mechanism is known for the origin of these displacements and the likelihood of similar displacements occurring in other natural and synthetic spinels is discussed. The crystal structure of a natural titanomaghemite was determined by a combination of X-ray diffraction and Mõssbauer spectroscopy. This was confirmed as possessing a primitive cubic Bravais lattice with the space group P4332 and the structural formula: Fe3+.0.96 0 0.04 [Fe2+0.23 Fe3+0.99 Ti4+0.42 0 0.37 ] 042 - where 0 represents a cation vacancy. As the above formula shows, there are cation vacancies on both tetrahedral arrl octahedral sites, the majority being restricted to octahedral sltes. No tetrahedral site Fe2+ or Ti4+ was observed. Values for the atom positions, anisotropic thermal parameters and bond lengths have been determined for this particular specimen.

Generation of triangular-shaped optical pulses in normally dispersive fibre

We determine through numerical modelling the conditions for the generation of triangular-shaped optical pulses in a nonlinear, normally dispersive (ND) fibre and experimentally demonstrate triangular pulse formation in conventional ND fibre.

Generation of triangular pulses in normally dispersive fibre

In this scheme, nonlinearity and dispersion in the NDF lead to various reshaping processes of an initial, conventional pulse according to the chirping value and power level at the input of the fibre. In particular, we have observed that triangular-shaped pulses can be generated for sufficiently high energies and a positive initial chirp parameter. In our experiments, 2.8 ps-FWHM, transform-limited pulses generated from a mode-locked fibre laser source at a repetition rate of 1.25 GHz were pre-chirped by propagating the pulses through different lengths of standard mono-mode fibre. The chirped pulses were then amplified to different power levels before being launched into a 2.3 km section of True Wave fibre (TWF). The corresponding numerically calculated pulse temporal intensity profile and numerical and experimental second-harmonic generation frequency-resolved optical gating (SHG FROG) spectrograms were also derived. In conclusion, we have presented numerical modelling results which show the system design parameters required for the generation of triangular-shaped pulses in a nonlinear NDF, and experimentally demonstrated triangular pulse shaping in conventional NDF.