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.

Melting and solidification of Zinc-Aluminium alloys

Following a scene-setting introduction are detailed reviews of the relevant scientific principles, thermal analysis as a research tool and the development of the zinc-aluminium family of alloys. A recently introduced simultaneous thermal analyser, the STA 1500, its use for differential thermal analysis (DTA) being central to the investigation, is described, together with the sources of support information, chemical analysis, scanning electron microscopy, ingot cooling curves and fluidity spiral castings. The compositions of alloys tested were from the binary zinc-aluminium system, the ternary zinc-aluminium-silicon system at 30%, 50% and 70% aluminium levels, binary and ternary alloys with additions of copper and magnesium to simulate commercial alloys and five widely used commercial alloys. Each alloy was shotted to provide the smaller, 100mg, representative sample required for DTA. The STA 1500 was characterised and calibrated with commercially pure zinc, and an experimental procedure established for the determination of DTA heating curves at 10°C per minute and cooling curves at 2°C per minute. Phase change temperatures were taken from DTA traces, most importantly, liquidus from a cooling curve and solidus from both heating and cooling curves. The accepted zinc-aluminium binary phase diagram was endorsed with the added detail that the eutectic is at 5.2% aluminium rather than 5.0%. The ternary eutectic trough was found to run through the points, 70% Al, 7.1% Si, 545°C; 50% Al, 3.9% Si, 520°C; 30% Al, 1.4% Si, 482°C. The dendrite arm spacing in samples after DTA increased with increasing aluminium content from 130m at 30% to 220m at 70%. The smallest dendrite arm spacing of 60m was in the 30% aluminium 2% silicon alloy. A 1kg ingot of the 10% aluminium binary alloy, insulated with Kaowool, solidified at the same 2°C per minute rate as the DTA samples. A similar sized sand casting was solidified at 3°C per minute and a chill casting at 27°C per minute. During metallographic examination the following features were observed: heavily cored phase which decomposed into ' and '' on cooling; needles of the intermetallic phase FeAl4; copper containing ternary eutectic and copper rich T phase.

Design and application of nanoscale actuators using block-copolymers

Block copolymers are versatile designer macromolecules where a “bottom-up” approach can be used to create tailored materials with unique properties. These simple building blocks allow us to create actuators that convert energy from a variety of sources (such as chemical, electrical and heat) into mechanical energy. In this review we will discuss the advantages and potential pitfalls of using block copolymers to create actuators, putting emphasis on the ways in which these materials can be synthesised and processed. Particular attention will be given to the theoretical background of microphase separation and how the phase diagram can be used during the design process of actuators. Different types of actuation will be discussed throughout.

Solvable model for distribution networks on random graphs

We propose a simple model that captures the salient properties of distribution networks, and study the possible occurrence of blackouts, i.e., sudden failings of large portions of such networks. The model is defined on a random graph of finite connectivity. The nodes of the graph represent hubs of the network, while the edges of the graph represent the links of the distribution network. Both, the nodes and the edges carry dynamical two state variables representing the functioning or dysfunctional state of the node or link in question. We describe a dynamical process in which the breakdown of a link or node is triggered when the level of maintenance it receives falls below a given threshold. This form of dynamics can lead to situations of catastrophic breakdown, if levels of maintenance are themselves dependent on the functioning of the net, once maintenance levels locally fall below a critical threshold due to fluctuations. We formulate conditions under which such systems can be analyzed in terms of thermodynamic equilibrium techniques, and under these conditions derive a phase diagram characterizing the collective behavior of the system, given its model parameters. The phase diagram is confirmed qualitatively and quantitatively by simulations on explicit realizations of the graph, thus confirming the validity of our approach. © 2007 The American Physical Society.

Effect of electron-phonon coupling on transmission through Luttinger liquid hybridized with resonant level

We show that electron-phonon coupling strongly affects transport properties of the Luttinger liquid hybridized with a resonant level. Namely, this coupling significantly modifies the effective energy-dependent width of the resonant level in two different geometries, corresponding to the resonant or antiresonant transmission in the Fermi gas. This leads to a rich phase diagram for a metal-insulator transition induced by the hybridization with the resonant level.

Impurity scattering in a Luttinger liquid with electron-phonon coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations, which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in a rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.

Impurity scattering in Luttinger liquid with electron-phonon coupling

We study the influence of electron-phonon coupling on electron transport through a Luttinger liquid with an embedded weak scatterer or weak link. We derive the renormalization group (RG) equations which indicate that the directions of RG flows can change upon varying either the relative strength of the electron-electron and electron-phonon coupling or the ratio of Fermi to sound velocities. This results in the rich phase diagram with up to three fixed points: an unstable one with a finite value of conductance and two stable ones, corresponding to an ideal metal or insulator.

Duality of weak and strong scatterer in a Luttinger liquid coupled to massless bosons

We study electronic transport in a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are coupled to one-dimensional massless bosons (e.g., acoustic phonons). We find that the duality relation, ?WS?WL=1, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard Luttinger liquid, holds in the presence of the additional coupling for an arbitrary fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scattering from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering.

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.

Fast pyrolysis oil fuel blend for marine vessels

The main driver for the investigation of fast pyrolysis oil marine fuel blends is EU directive 2012/33/EU which aims to cut the sulphur content of marine fuel and thereby reduce air pollution caused by marine vessels. The aim of this study was to investigate the miscibility of 3- and 4- component blends containing pyrolysis oil, 1-butanol, biodiesel (RME) and/or marine gas oil (MGO). The ideal blend would be a stable homogenous product with a minimum amount of butanol, whilst maximising the amount of pyrolysis oil. A successful blend would have properties suitable for use in marine engines. In order to successfully utilise a marine fuel blend in commercial vessels it should meet minimum specification requirements such as a flash point ≥60°C. Blends of pyrolysis oil, RME, MGO and 1-butanol were evaluated and characterised. The mixed blends were inspected after 48 hours for homogeneity and the results plotted on a tri-plot phase diagram. Homogenous samples were tested for water content, pH, acid number, viscosity and flash point as these give indicate a blend’s suitability for engine testing. The work forms part of the ReShip Project which is funded by Norwegian industry partners and the Research Council of Norway (The ENERGIX programme).