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.

Interplay between the charge transport phenomena and the charge-transfer phase transition in RbxMn[Fe(CN)6]y.zH2O

Charge transport and dielectric measurements were carried out on compacted powder and single-crystal samples of bistable RbxMn[Fe(CN)6]y·zH2O in the two valence-tautomeric forms (MnIIFeIII and MnIIIFeII) as a function of temperature (120-350 K) and frequency (10-2-106 Hz). The complex conductivity data reveal universal conductivity behavior and obey the Barton-Nakajima-Namikawa relationship. The charge transport is accompanied by dielectric relaxation that displays the same thermal activation energy as the conductivity. Surprisingly, the activation energy of the conductivity was found very similar in the two valence-tautomeric forms (0.55 eV), and the conductivity change between the two phases is governed mainly by the variation of the preexponential factor in each sample. The phase transition is accompanied by a large thermal hysteresis of the conductivity and the dielectric constant. In the hysteresis region, however, a crossover occurs in the charge transport mechanism at T < 220 K from an Arrhenius-type to a varying activation energy behavior, conferring an unusual “double-loop” shape to the hysteresis.

All-optical processing using cross-phase modulation

The following thesis presents results obtained from both numerical simulation and laboratory experimentation (both of which were carried out by the author). When data is propagated along an optical transmission line some timing irregularities can occur such as timing jitter and phase wander. Traditionally these timing problems would have been corrected by converting the optical signal into the electrical domain and then compensating for the timing irregularity before converting the signal back into the optical domain. However, this thesis posses a potential solution to the problem by remaining completely in the optical domain, eliminating the need for electronics. This is desirable as not only does optical processing reduce the latency effect that their electronic counterpart have, it also holds the possibility of an increase in overall speed. A scheme was proposed which utilises the principle of wavelength conversion to dynamically convert timing irregularities (timing jitter and phase wander) into a change in wavelength (this occurs on a bit-by-bit level and so timing jitter and phase wander can be compensated for simultaneously). This was achieved by optically sampling a linearly chirped, locally generated clock source (the sampling function was achieved using a nonlinear optical loop mirror). The data, now with each bit or code word having a unique wavelength, is then propagated through a dispersion compensation module. The dispersion compensation effectively re-aligns the data in time and so thus, the timing irregularities are removed. The principle of operation was tested using computer simulation before being re-tested in a laboratory environment. A second stage was added to the device to create 3R regeneration. The second stage is used to simply convert the timing suppressed data back into a single wavelength. By controlling the relative timing displacement between stage one and stage two, the wavelength that is finally produced can be controlled.

The chemistry of British bituminous coals : an assessment of phase transfer catalysed reactions in the determination of coal structure

Three British bituminous coals, (Gedling, Cresswell, and Cortonwood Silkstone) were selected for study. Procedures were developed, using phase transfer catalysts (PTC's), to degrade the solvent insoluble fractions of the coals. PTC's are of interest because they have the potential to bring about selective high conversion reactions, under mild conditions, (often in the past, severe reaction conditions have had to be used to degrade the coals, this in turn resulted in the loss of much of the structural information). We have applied a variety of physical and chemical techniques to maximise the amount of structural information, these include, elemental analysis, 1H-NMR, 13C-CPMAS-NMR, GPC, GC-MS, FTIR spectroscopy, DRIFT spectroscopy, and gas adsorption measurements. The main conclusions from the work are listed below:- ( 1 ) PTC O-methylation; This reaction removes hydrogen bonds within the coal matrix by 'capping' the phenolic groups. It was found that the polymer-like matrix could be made more flexible, but not significantly more soluble, by O-methylation. I.E. the trapped or 'mobile' phase of the coals could be removed at a faster rate after this reaction had been carried out. ( 2 ) PTC Reductive and Acidic Ether Cleavage; The three coals were found to contain insignificant amounts of dialkyl and alkyl aryl ethers. The number of diaryl ethers could not be estimated, by reductive ether cleavage, (even though a high proportion of all three coals was solublised). The majority of the ethers present in the coals were inert to both cleavage methods, and are therefore assumed to be heterocyclic ethers. ( 3 ) Trif!uoroperacetic Acid Oxidation; This oxidant was used to study the aliphatic portions of the polymer-like macromolecular matrix of the coals. Normally this reagent will only solublise low rank coals, we however have developed a method whereby trifluoroperacetic acid can be used to degrade high rank bituminous coals. ( 4 ) PTC/Permanganate Oxidation; This reagent has been found to be much more selective than the traditional alkaline permanganate oxidation, with a lot more structural information being retained within the various fractions. This degradative method therefore has the potential of yielding new information about the molecular structure of coals.

Phase equilibrium studies at normal pressures

A total pressure apparatus has been developed to measure vapour-liquid equilibrium data on binary mixtures at atmospheric and sub-atmospheric pressures. The method gives isothermal data which can be obtained rapidly. Only measurements of total pressure are made as a direct function of composition of synthetic liquid phase composition, the vapour phase composition being deduced through the Gibbs-Duhem relationship. The need to analyse either of the phases is eliminated. As such the errors introduced by sampling and analysis are removed. The essential requirements are that the pure components be degassed completely since any deficiency in degassing would introduce errors into the measured pressures. A similarly essential requirement was that the central apparatus would have to be absolutely leak-tight as any leakage of air either in or out of the apparatus would introduce erroneous pressure readings. The apparatus was commissioned by measuring the saturated vapour pressures of both degassed water and ethanol as a function of temperature. The pressure-temperature data on degassed water measured were directly compared with data in the literature, with good agreement. Similarly the pressure-temperature data were measured for ethanol, methanol and cyclohexane and where possible a direct comparison made with the literature data. Good agreement between the pure component data of this work and those available in the literature demonstrates firstly that a satisfactory degassing procedure has been achieved and that secondly the measurements of pressure-temperature are consistent for any one component; since this is true for a number of components, the measurements of both temperature and pressure are both self-consistent and of sufficient accuracy, with an observed compatibility between the precision/accuracy of the separate means of measuring pressure and temperature. The liquid mixtures studied were of ethanol-water, methanol-water and ethanol-cyclohexane. The total pressure was measured as the composition inside the equilibrium cell was varied at a set temperature. This gave P-T-x data sets for each mixture at a range of temperatures. A standard fitting-package from the literature was used to reduce the raw data to yield y-values to complete the x-y-P-T data sets. A consistency test could not be applied to the P-T-x data set as no y-values were obtained during the experimental measurements. In general satisfactory agreement was found between the data of this work and those available in the literature. For some runs discrepancies were observed, and further work recommended to eliminate the problems identified.

Phase equilibrium studies at moderate pressures

The theory of vapour-liquid equilibria is reviewed, as is the present status or prediction methods in this field. After discussion of the experimental methods available, development of a recirculating equilibrium still based on a previously successful design (the modified Raal, Code and Best still of O'Donnell and Jenkins) is described. This novel still is designed to work at pressures up to 35 bar and for the measurement of both isothermal and isobaric vapour-liquid equilibrium data. The equilibrium still was first commissioned by measuring the saturated vapour pressures of pure ethanol and cyclohexane in the temperature range 77-124°C and 80-142°C respectively. The data obtained were compared with available literature experimental values and with values derived from an extended form of the Antoine equation for which parameters were given in the literature. Commissioning continued with the study of the phase behaviour of mixtures of the two pure components as such mixtures are strongly non-ideal, showing azeotopic behaviour. Existing data did not exist above one atmosphere pressure. Isothermal measurements were made at 83.29°C and 106.54°C, whilst isobaric measurements were made at pressures of 1 bar, 3 bar and 5 bar respectively. The experimental vapour-liquid equilibrium data obtained are assessed by a standard literature method incorporating a themodynamic consistency test that minimises the errors in all the measured variables. This assessment showed that reasonable x-P-T data-sets had been measured, from which y-values could be deduced, but that the experimental y-values indicated the need for improvements in the design of the still. The final discussion sets out the improvements required and outlines how they might be attained.

Studies in three phase gas-liquid-solid fluidised systems

The work is a logical continuation of research started at Aston some years ago when studies were conducted on fermentations in bubble columns. The present work highlights typical design and operating problems that could arise in such systems as waste water, chemical, biochemical and petroleum operations involving three-phase, gas-liquid-solid fluidisation; such systems are in increasing use. It is believed that this is one of few studies concerned with `true' three-phase, gas-liquid-solid fluidised systems, and that this work will contribute significantly to closing some of the gaps in knowledge in this area. The research work was mainly experimentally based and involved studies of the hydrodynamic parameters, phase holdups (gas and solid), particle mixing and segregation, and phase flow dynamics (flow regime and circulation patterns). The studies have focused particularly on the solid behaviour and the influence of properties of solids present on the above parameters in three-phase, gas-liquid-solid fluidised systems containing single particle components and those containing binary and ternary mixtures of particles. All particles were near spherical in shape and two particle sizes and total concentration levels were used. Experiments were carried out in two- and three-dimensional bubble columns. Quantitative results are presented in graphical form and are supported by qualitative results from visual studies which are also shown as schematic diagrams and in photographic form. Gas and solid holdup results are compared for air-water containing single, binary and ternary component particle mixtures. It should be noted that the criteria for selection of the materials used are very important if true three-phase fluidisation is to be achieved: this is very evident when comparing the results with those in the literature. The fluid flow and circulation patterns observed were assessed for validation of the generally accepted patterns, and the author believes that the present work provides more accurate insight into the modelling of liquid circulation in bubble columns. The characteristic bubbly flow at low gas velocity in a two-phase system is suppressed in the three-phase system. The degree of mixing within the system is found to be dependent on flow regime, liquid circulation and the ratio of solid phase physical properties. Evidence of strong `trade-off' of properties is shown; the overall solid holdup is believed to be a major parameter influencing the gas holdup structure.

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.

Quasi-pilot aided phase noise estimation for coherent optical OFDM systems

In this letter, a novel phase noise estimation scheme has been proposed for coherent optical orthogonal frequency division multiplexing systems, the quasi-pilot-aided method. In this method, the phases of transmitted pilot subcarriers are deliberately correlated to the phases of data subcarriers. Accounting for this correlation in the receiver allows the required number of pilots needed for a sufficient estimation and compensation of phase noise to be reduced by a factor of 2 in comparison with the traditional pilot-aided phase noise estimation method. We carried out numerical simulation of a 40 Gb/s single polarization transmission system, and the outcome of the investigation indicates that by applying quasi-pilot-aided phase estimation, only four pilot subcarriers are needed for effective phase noise compensation. © 2014 IEEE.

A catalytic reactor for the trapping of free radicals from gas phase oxidation reactions

A catalytic reactor for the trapping of free radicals originating from gas phase catalytic reactions is described and discussed. Radical trapping and identification were initially carried out using a known radical generator such as dicumyl peroxide. The trapping of radicals was further demonstrated by investigating genuine radical oxidation processes, e.g., benzaldehyde oxidation over manganese and cobalt salts. The efficiency of the reactor was finally proven by the partial oxidation of cyclohexane over MoO3, Cr2O3, and WO3, which allowed the identification of all the radical intermediates responsible for the formation of the products cyclohexanol and cyclohexanone. Assignment of the trapped radicals was carried out using spin trapping technique and X -band electron paramagnetic resonance spectroscopy. © 2010 American Institute of Physics.

Single-phase active rectifier selection for fault tolerant machine

A fault tolerant, 5-phase PM generator has been developed for use on the low pressure (LP) shaft of an aircraft gas turbine engine. The machine operates at variable speed and therefore has a variable voltage, variable frequency electrical output (VVVF). The generator is to be used to provide a 350V DC bus for distribution throughout the aircraft, and a study has been carried out that identifies the most suitable AC-DC converter topology for this machine in terms of losses, electrical component ratings, filtering requirements and circuit complexity.

Side detection of strong radiation-mode out-coupling from blazed FBGs in single-mode and multimode fibers

We report on the effective side detection of radiation-mode out-coupling from blazed fiber Bragg gratings (BFBGs) fabricated in single-mode fiber (SMF) and multimode fiber (MMF). The far-field radiation power distribution from BFBGs have been measured achieving a high spatial-spectral resolution (0.17 mm/nm). We have also investigated comparatively the transmission-loss characteristics of BFBGs in both fiber types, fabricated using phase-mask and holographic inscription techniques. Our results reveal clearly that the radiation out-coupling from BFBGs is significantly stronger and spectrally more confined in MMF than in SMF.

Analytical BER performance in differential n-PSK coherent transmission system influenced by equalization enhanced phase noise

Long-haul high speed optical transmission systems are significantly distorted by the interplay between the electronic chromatic dispersion (CD) equalization and the local oscillator (LO) laser phase noise, which leads to an effect of equalization enhanced phase noise (EEPN). The EEPN degrades the performance of optical communication systems severely with the increment of fiber dispersion, LO laser linewidth, symbol rate, and modulation format. In this paper, we present an analytical model for evaluating the performance of bit-error-rate (BER) versus signal-to-noise ratio (SNR) in the n-level phase shift keying (n-PSK) coherent transmission system employing differential carrier phase estimation (CPE), where the influence of EEPN is considered. Theoretical results based on this model have been investigated for the differential quadrature phase shift keying (DQPSK), the differential 8-PSK (D8PSK), and the differential 16-PSK (D16PSK) coherent transmission systems. The influence of EEPN on the BER performance in term of the fiber dispersion, the LO phase noise, the symbol rate, and the modulation format are analyzed in detail. The BER behaviors based on this analytical model achieve a good agreement with previously reported BER floors influenced by EEPN. Further simulations have also been carried out in the differential CPE considering EEPN. The results indicate that this analytical model can give an accurate prediction for the DQPSK system, and a leading-order approximation for the D8PSK and the D16PSK systems.

Optimised phase disposition pulse-width modulation strategy for hybrid-clamped multilevel inverters using switching state sequences

This study describes an optimised modulation strategy based on switching state sequences for the hybrid-clamped multilevel converter. Two key control variables defined as 'phase shift angle' and 'switching state change' for a five-level hybrid-clamped inverter are proposed to improve all switches' operation, and by changing their values, different control methods can be obtained for modulation optimisation purposes. Two example methods can solve the voltage imbalance problem of the dc-link capacitors and furthermore avoid two switches' simultaneous switching transitions and improve the inverter's performance as compared with the traditional phase disposition pulse-width modulation strategy. A 6 kW prototype inverter is developed and a range of simulation and experiments are carried out for validation. It is found that simulation and experimental results are in a good agreement and the proposed modulation strategy is verified in terms of low-order harmonic reduction.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.