From one cell to the whole froth: a dynamical map

We investigate two and three-dimensional shell-structured-inflatable froths, which can be constructed by a recursion procedure adding successive layers of cells around a germ cell. We prove that any froth can be reduced into a system of concentric shells. There is only a restricted set of local configurations for which the recursive inflation transformation is not applicable. These configurations are inclusions between successive layers and can be treated as vertices and edges decorations of a shell-structure-inflatable skeleton. The recursion procedure is described by a logistic map, which provides a natural classification into Euclidean, hyperbolic and elliptic froths. Froths tiling manifolds with different curvature can be classified simply by distinguishing between those with a bounded or unbounded number of elements per shell, without any a-priori knowledge on their curvature. A new result, associated with maximal orientational entropy, is obtained on topological properties of natural cellular systems. The topological characteristics of all experimentally known tetrahedrally close-packed structures are retrieved.Comment: 20 Pages Tex, 11 Postscript figures, 1 Postscript tabl

Short Flip Sequences to Untangle Segments in the Plane

A (multi)set of segments in the plane may form a TSP tour, a matching, a tree, or any multigraph. If two segments cross, then we can reduce the total length with the following flip operation. We remove a pair of crossing segments, and insert a pair of non-crossing segments, while keeping the same vertex degrees. The goal of this paper is to devise efficient strategies to flip the segments in order to obtain crossing-free segments after a small number of flips. Linear and near-linear bounds on the number of flips were only known for segments with endpoints in convex position. We generalize these results, proving linear and near-linear bounds for cases with endpoints that are not in convex position. Our results are proved in a general setting that applies to multiple problems, using multigraphs and the distinction between removal and insertion choices when performing a flip.Comment: 19 pages, 10 figure

Topological correlations in soap froths

Correlation in two-dimensional soap froth is analysed with an effective potential for the first time. Cells with equal number of sides repel (with linear correlation) while cells with different number of sides attract (with NON-bilinear) for nearest neighbours, which cannot be explained by the maximum entropy argument. Also, the analysis indicates that froth is correlated up to the third shell neighbours at least, contradicting the conventional ideas that froth is not strongly correlated.Comment: 10 Pages LaTeX, 6 Postscript figure

Mediated water electrolysis in biphasic systems

peer-reviewedThe concept of efficient electrolysis by linking photoelectrochemical biphasic H2 evolution and water oxidation processes in the cathodic and anodic compartments of an H-cell, respectively, is introduced. Overpotentials at the cathode and anode are minimised by incorporating light-driven elements into both biphasic reactions. The concepts viability is demonstrated by electrochemical H2 production from water splitting utilising a polarised water-organic interface in the cathodic compartment of a prototype H-cell. At the cathode the reduction of decamethylferrocenium cations ([Cp2*Fe(III)]+) to neutral decamethylferrocene (Cp2*Fe(II)) in 1,2-dichloroethane (DCE) solvent takes place at the solid electrode/oil interface. This electron transfer process induces the ion transfer of a proton across the immiscible water/oil interface to maintain electroneutrality in the oil phase. The oil-solubilised proton immediately reacts with Cp2*Fe(II) to form the corresponding hydride species, [Cp2*Fe(IV)(H)]+. Subsequently, [Cp2*Fe(IV)(H)]+ spontaneously undergoes a chemical reaction in the oil phase to evolve hydrogen gas (H2) and regenerate [Cp2*Fe(III)]+, whereupon this catalytic Electrochemical, Chemical, Chemical (ECC’) cycle is repeated. During biphasic electrolysis, the stability and recyclability of the [Cp2*Fe(III)]+/Cp2*Fe(II) redox couple were confirmed by chronoamperometric measurements and, furthermore, the steady-state concentration of [Cp2*Fe(III)]+ monitored in situ by UV/vis spectroscopy. Post-biphasic electrolysis, the presence of H2 in the headspace of the cathodic compartment was established by sampling with gas chromatography. The rate of the biphasic hydrogen evolution reaction (HER) was enhanced by redox catalysis in the presence of floating catalytic molybdenum carbide (Mo2C) microparticles at the immiscible water/oil interface. The use of a superhydrophobic organic electrolyte salt was critical to ensure proton transfer from water to oil, and not anion transfer from oil to water, in order to maintain electroneutrality after electron transfer. The design, testing and successful optimisation of the operation of the biphasic electrolysis cell under dark conditions with Cp2*Fe(II) lays the foundation for the achievement of photo-induced biphasic water electrolysis at low overpotentials using another metallocene, decamethylrutheneocene (Cp2*Ru(II)). Critically, Cp2*Ru(II) may be recycled at a potential more positive than that of proton reduction in DCE

Analysis of signalling pathways using continuous time Markov chains

We describe a quantitative modelling and analysis approach for signal transduction networks. We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK+03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable

Statistical Mechanics of Two-dimensional Foams

The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics. The probability distribution of the number of sides for a cell of given area is derived. This expression allows to correlate the distribution of sides ("topological disorder") to the distribution of sizes ("geometrical disorder") in a foam. The model predictions agree well with available experimental data

DFR Perturbative Quantum Field theory on Quantum Space Time, and Wick Reduction

We discuss the perturbative approach a` la Dyson to a quantum field theory with nonlocal self-interaction :phi*...*phi:, according to Doplicher, Fredenhagen and Roberts (DFR). In particular, we show that the Wick reduction of non locally time--ordered products of Wick monomials can be performed as usual, and we discuss a very simple Dyson diagram.Comment: 15 pages, pdf has active hyperlinks. To appear in the proceedings of the conference on "Rigorous quantum Field Theory", held at Saclay on July 19-21, 2004, on the occasion of Jacques Bros' 70th birthda

On Random Bubble Lattices

We study random bubble lattices which can be produced by processes such as first order phase transitions, and derive characteristics that are important for understanding the percolation of distinct varieties of bubbles. The results are relevant to the formation of topological defects as they show that infinite domain walls and strings will be produced during appropriate first order transitions, and that the most suitable regular lattice to study defect formation in three dimensions is a face centered cubic lattice. Another application of our work is to the distribution of voids in the large-scale structure of the universe. We argue that the present universe is more akin to a system undergoing a first-order phase transition than to one that is crystallizing, as is implicit in the Voronoi foam description. Based on the picture of a bubbly universe, we predict a mean coordination number for the voids of 13.4. The mean coordination number may also be used as a tool to distinguish between different scenarios for structure formation.Comment: several modifications including new abstract, comparison with froth models, asymptotics of coordination number distribution, further discussion of biased defects, and relevance to large-scale structur

Description of Fischer Clusters Formation in Supercooled Liquids Within Framework of Continual Theory of Defects

Liquid is represented as complicated system of disclinations according to defect description of liquids and glasses. The expressions for the linear disclination field of an arbitrary form and energy of inter-disclination interaction are derived in the framework of gauge theory of defects. It allows us to describe liquid as a disordered system of topological moments and reduce this model to the Edwards--Anderson model with large-range interaction. Within the framework of this approach vitrifying is represented as a "hierarchical" phase transition. The suggested model allows us to explain the process of the Fischer clusters formation and the slow dynamics in supercooled liquids close to the liquid--glass transition point