Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

Analysis of common attacks in public-key cryptosystems based on low-density parity-check codes

The security and reliability of a class of public-key cryptosystems against attacks by unauthorized parties, who had acquired partial knowledge of one or more of the private key components and/or of the message, were discussed. The standard statistical mechanical methods of dealing with diluted spin systems with replica symmetric considerations were analyzed. The dynamical transition which defined decryption success in practical situation was studied. The phase diagrams which showed the dynamical threshold as a function of the partial acquired knowledge of the private key were also presented.

Synthetic analogues of protein-lipid complexes

Hypercoiling poly(styrene-alt-maleic anhydride) (PSMA) is known to undergo conformational transition in response to environmental stimuli. The association of PSMA with lipid 2-dilauryl-sn-glycero-3-phosphocholine (DLPC) produces polymer-lipid complex analogues to lipoprotein assemblies found in lung surfactant. These complexes represent a new bio-mimetic delivery vehicle with applications in the cosmetic and pharmaceutical industries. The primary aim of this study was to develop a better understanding of PSMA-DLPC association by using physical and spectroscopic techniques. Ternary phase diagrams were constructed to examine the effects of various factors, such as molecular weight, pH and temperature on PSMA-DLPC association. 31P-NMR spectroscopy was used to investigate the polymorphic changes of DLPC upon associating with PSMA. The Langmuir Trough technique and surface tension measurement were used to explore the association behaviour of PSMA both at the interface and in the bulk of solution, as well as its interaction with DLPC membranes. The ultimate aim of this study was to investigate the potential use of PSMA-DLPC complexes to improve the bioavailability and therapeutic efficacy of a range of drugs. Typical compounds of ophthalmic interest range from new drugs such as Pirenzepine, which has attracted clinical interest for the control of myopia progression, to the well-established family of non-steroid anti-inflammatory drugs. These drugs have widely differing structures, sizes, solubility profiles and pH-sensitivities. In order to understand the ways in which these characteristics influence incorporation and release behaviour, the marker molecules Rhodamine B and Oil Red O were chosen. PSMA-DLPC complexes, incorporated with marker molecules and Pirenzepine, were encapsulated in hydrogels of the types used for soft contact lenses. Release studies were conducted to examine if this smart drug delivery system can retain such compounds and deliver them at a slow rate over a prolonged period of time.

Statistical mechanics of distribution networks

This thesis presents an analysis of the stability of complex distribution networks. We present a stability analysis against cascading failures. We propose a spin [binary] model, based on concepts of statistical mechanics. We test macroscopic properties of distribution networks with respect to various topological structures and distributions of microparameters. The equilibrium properties of the systems are obtained in a statistical mechanics framework by application of the replica method. We demonstrate the validity of our approach by comparing it with Monte Carlo simulations. We analyse the network properties in terms of phase diagrams and found both qualitative and quantitative dependence of the network properties on the network structure and macroparameters. The structure of the phase diagrams points at the existence of phase transition and the presence of stable and metastable states in the system. We also present an analysis of robustness against overloading in the distribution networks. We propose a model that describes a distribution process in a network. The model incorporates the currents between any connected hubs in the network, local constraints in the form of Kirchoff's law and a global optimizational criterion. The flow of currents in the system is driven by the consumption. We study two principal types of model: infinite and finite link capacity. The key properties are the distributions of currents in the system. We again use a statistical mechanics framework to describe the currents in the system in terms of macroscopic parameters. In order to obtain observable properties we apply the replica method. We are able to assess the criticality of the level of demand with respect to the available resources and the architecture of the network. Furthermore, the parts of the system, where critical currents may emerge, can be identified. This, in turn, provides us with the characteristic description of the spread of the overloading in the systems.

Identification of optically clear regions of ternary polymer blends using a novel rapid screening method

The application of a rapid screening method for the construction of ternary phase diagrams is described for the first time, providing detailed visualization of phase boundaries in solvent-mediated blends. Our new approach rapidly identifies ternary blend compositions that afford optically clear materials, useful for applications where transparent films are necessary. The use of 96-well plates and a scanning plate reader has enabled rapid optical characterization to be carried out by transmission spectrophotometry (450 nm), whilst the nature and extent of crystallinity was examined subsequently by wide angle X-ray scattering (WAXS). The moderating effect of cellulose acetate butyrate can be visualized as driving the position of the phase boundaries in poly(l-lactic acid)/polycaprolactone (PLLA/PCL) blends. More surprisingly, the boundaries are critically dependent on the molecular weight of the crystallizable PLLA and PCL, with higher molecular weight polymers leading to blends with reduced phase separation. On the other hand, the propensity to crystallize was more evident in shorter chains. WAXS provides a convenient way of characterizing the contribution of the individual blend components to the crystalline regions across the range of blend compositions. © 2013 Society of Chemical Industry.

Duality in multi-channel Luttinger Liquid with local scatterer

We have devised a general scheme that reveals multiple duality relations valid for all multi-channel Luttinger Liquids. The relations are universal and should be used for establishing phase diagrams and searching for new non-trivial phases in low-dimensional strongly correlated systems. The technique developed provides universal correspondence between scaling dimensions of local perturbations in different phases. These multiple relations between scaling dimensions lead to a connection between different inter-phase boundaries on the phase diagram. The dualities, in particular, constrain phase diagram and allow predictions of emergence and observation of new phases without explicit model-dependent calculations. As an example, we demonstrate the impossibility of non-trivial phase existence for fermions coupled to phonons in one dimension. © 2013 EPLA.

Effects of solid poly (ethylene glycols) addition to the solutions of aniline or N,N-dimethylaniline with water:experimental measurements and modelling

In this work, the liquid-liquid and solid-liquid phase behaviour of ten aqueous pseudo-binary and three binary systems containing polyethylene glycol (PEG) 2050, polyethylene glycol 35000, aniline, N,N-dimethylaniline and water, in the temperature range 298.15-350.15 K and at ambient pressure of 0.1 MPa, was studied. The obtained temperature-composition phase diagrams showed that the only functional co-solvent was PEG2050 for aniline in water, while PEG35000 even showed a clear anti-solvent effect in the N,N-dimethylaniline aqueous system. The experimental solid-liquid equilibria (SLE) data have been correlated by the non-random two-liquid (NRTL) model, and the correlation results are in accordance with the experimental results.

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.

Novel real-time homodyne coherent receiver using a feed-forward based carrier extraction scheme for phase modulated signals

We report a novel real-time homodyne coherent receiver based on a DPSK optical-electrical-optical (OEO) regenerator used to extract a carrier from carrier-less phase modulated signals based on feed-forward based modulation stripping. The performance of this non-DSP based coherent receiver was evaluated for 10.66Gbit/s BPSK signals. Self-homodyne coherent detection and homodyne detection with an injection-locked local oscillator laser was demonstrated. The performance was evaluated by measuring the electrical signal-to-noise (SNR) and recording the eye diagrams. Using injection-locking for the LO improves the performance and enables homodyne detection with optical injection-locking to operate with carrier-less BPSK signals without the need for polarization multiplexed pilot-tones.

Evaluating the Capacity of Phase Modulator-Controlled Long-Haul Soliton Transmission

We review recent developments in the use of optical solitons for communication systems spanning transoceanic distances. The implementation of "soliton control" to alleviate the detrimental impact of effects such as amplifier noise is shown to be critical for obtaining advantages over competing technologies. The potential performance of two control strategies, namely straight line filtering and synchronous phase modulation, is examined in detail. Design diagrams are used to determine the maximum permissible amplifier spacing, which is a key determinant of system economics. To focus the enquiry, two example system spans are taken, representing transatlantic and transpacific distances. It is concluded that straight line filtering provides very little improvement over a basic design without control. However synchronous phase modulation, which may be implemented using a handful of actively driven components, provides very substantial benefits. These may be used either to extend the overall bit-rate-distance product of the system or to increase the amplifier spacing at more moderate capacities. © 1995 Academic Press. All rights reserved.