Positive braids of maximal signature

We characterise positive braid links with positive Seifert form via a finite number of forbidden minors. From this we deduce a one-to-one correspondence between prime positive braid links with positive Seifert form and simply laced Dynkin diagrams, as well as a simple classification of alternating positive braid knots.

The D(D-3)-anyon chain: integrable boundary conditions and excitation spectra

Chains of interacting non-Abelian anyons with local interactions invariant under the action of the Drinfeld double of the dihedral group D-3 are constructed. Formulated as a spin chain the Hamiltonians are generated from commuting transfer matrices of an integrable vertex model for periodic and braided as well as open boundaries. A different anyonic model with the same local Hamiltonian is obtained within the fusion path formulation. This model is shown to be related to an integrable fusion interaction round the face model. Bulk and surface properties of the anyon chain are computed from the Bethe equations for the spin chain. The low-energy effective theories and operator content of the models (in both the spin chain and fusion path formulation) are identified from analytical and numerical studies of the finite-size spectra. For all boundary conditions considered the continuum theory is found to be a product of two conformal field theories. Depending on the coupling constants the factors can be a Z(4) parafermion or a M-(5,M-6) minimal model.

Machine recognition of hand-drawn circuit diagrams

An application of image processing techniques to recognition of hand-drawn circuit diagrams is presented. The scanned image of a diagram is pre-processed to remove noise and converted to bilevel. Morphological operations are applied to obtain a clean, connected representation using thinned lines. The diagram comprises of nodes, connections and components. Nodes and components are segmented using appropriate thresholds on a spatially varying object pixel density. Connection paths are traced using a pixel-stack. Nodes are classified using syntactic analysis. Components are classified using a combination of invariant moments, scalar pixel-distribution features, and vector relationships between straight lines in polygonal representations. A node recognition accuracy of 82% and a component recognition accuracy of 86% was achieved on a database comprising 107 nodes and 449 components. This recogniser can be used for layout “beautification” or to generate input code for circuit analysis and simulation packages

Functional and advanced functional and causal relationship diagrams for remote condition monitoring

Analysing the condition of an asset is a big challenge as there can be many aspects which can contribute to the overall functional reliability of the asset that have to be considered. In this paper we propose a two-step functional and causal relationship diagram (FCRD) to address this problem. In the first step, the FCRD is designed to facilitate the analysis of the condition of an asset by evaluating the interdependence (functional and causal) relationships between different components of the asset with the help of a relationship diagram. This is followed by the advanced FCRD (AFCRD) which refines the information from the FCRD into a comprehensive and manageable format. This new two-step methodology for asset condition monitoring is tested and validated for the case of a water treatment plant. © IMechE 2012.

Comments on the phase diagrams and crystallisation paths of Y-Ba-Cu-O materials

Our micro structural characterisation of Y-Ba-Cu-O quenched partial melts shows that the BaCuO2 (BC1) phase is crystalline at temperatures as high as 1100°C, and that the partial melt self-establishes a micro structural gradient from the surface towards the interior of the samples, which can be associated with a gradient in an equivalent partial pressure of O2 (pO2). The extension of the Y2BaCuO5-YBa2Cu3O7-x (Y211-Y123) tie-line intersects the primary crystallisation field of BC1 first. The actual peritectic reaction that takes place is Y2BaCuO5(s) + BaCuO2(s) + 2BaCu2O2(L) + 1/2O2 → 2YBa2Cu3O6(s). Two schematic representations which allow an analysis of the pO2 dependence are given. The gradient in micro structure self-established by the sample acts as a driving force for texturing. With this new perspective gained about the actual peritectic reaction and mechanisms of melt-texturing of Y123, it is possible to explain most of the aspects about partial melt-texturing. In addition, it seems possible to devise heat treatments that may allow for the production of well-oriented single domains with very large diameters. © 1999 Elsevier Science B.V.

The impact of incidents on macroscopic fundamental diagrams

The macroscopic fundamental diagram (MFD) traffic modelling method has been proved for large urban roads and freeway networks, but hysteresis and scatter have been found in both such networks. This paper investigates how incident variables affect the shape and scatter of the MFD using both simulated data and real data collected from the M3 Pacific motorway in Brisbane, Australia. Three key components of incidents are investigated based on the simulated data (i.e. incident location, incident duration and traffic demand). The results based on simulated data indicate that the diagram shape is a property not only of the network itself but also of the incident variables. Diagrams for three types of real incidents (crash, hazard and vehicle breakdown) are explored separately. The results based on the empirical data are consistent with the simulated results. The hysteresis phenomenon occurs both upstream and downstream of the incident location, but for opposite hysteresis loops. The gradient of the upstream diagram is greater than that downstream on the incident site, when traffic demand is for an off-peak period.

Note on stereo-diagrams of molecules

The paper elucidates a simple way ooJ'dcriving the coordinates for &awing sfereo-&gram of molecules. This method is an alternative, but not a substitute, to the 'ORTEP (suggested by C. K. Johnsori) which, is extensively used in the literature. Illustrations are given using a progrunz which was written based on the method mentioned here. The program is also given in an appendix for practical help.

Generalization of Dynkin's Identity and Some Applications

Let X(t) be a right continuous temporally homogeneous Markov pro- cess, Tt the corresponding semigroup and A the weak infinitesimal genera- tor. Let g(t) be absolutely continuous and r a stopping time satisfying E.( S f I g(t) I dt) < oo and E.( f " I g'(t) I dt) < oo Then for f e 9iJ(A) with f(X(t)) right continuous the identity Exg(r)f(X(z)) - g(O)f(x) = E( 5 " g'(s)f(X(s)) ds) + E.( 5 " g(s)Af(X(s)) ds) is a simple generalization of Dynkin's identity (g(t) 1). With further restrictions on f and r the following identity is obtained as a corollary: Ex(f(X(z))) = f(x) + k! Ex~rkAkf(X(z))) + n-1E + (n ) )!.E,(so un-1Anf(X(u)) du). These identities are applied to processes with stationary independent increments to obtain a number of new and known results relating the moments of stopping times to the moments of the stopped processes.

Monte Carlo simulation of low temperature phase diagrams of YBa2Cu3O6+x

We report the results of Monte Carlo simulation of oxygen ordering in the oxygen deficient portion (x<0.5) of YBa2Cu3O6+x at low temperatures. We find qualitative agreement among cluster - variation, Monte Carlo and transfer matrix methods. However, low temperature and ground state simulations clearly indicate the presence of a tetragonal phase. There is also evidence for two second order phase transition lines separating the tetragonal and the �double cell� ortho II phase. The effect of decreasing the inter-chain repulsion on oxygen ordering has also been investigated.

An asymmetric cascaded H-Bridge inverters for generating 12-sided polygonal space vector diagrams for Motor drives

A new topology of asymmetric cascaded H-Bridge inverter is presented in this paper It consists of two cascaded H-bridge cells per phase. They are fed from isolated dc sources having a dc bus ratio of 1:0.366. Out of many space vectors possible from this circuit, only those are chosen that lie on 12-sided polygons. Thus, the overall space vector diagram produced by this circuit consists of multiple numbers of 12-sided polygons. With a proper PWM timing calculations based on these selected space vectors, it is possible to eliminate all the 6n +/- 1, (n = odd) harmonics from the phase voltage under all operating conditions. The switching frequency of individual H-Bridge cells is also substantially low. Extensive experimental results have been presented in this paper to validate the proposed concept.