Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Hydrogen spillover on carbon-supported metal catalysts studied by inelastic neutron scattering. Surface vibrational states and hydrogen riding modes

Hydrogen spillover on carbon-supported precious metal catalysts has been investigated with inelastic neutron scattering (INS) spectroscopy. The aim, which was fully realized, was to identify spillover hydrogen on the carbon support. The inelastic neutron scattering spectra of Pt/C, Ru/C, and PtRu/C fuel cell catalysts dosed with hydrogen were determined in two sets of experiments: with the catalyst in the neutron beam and, using an annular cell, with carbon in the beam and catalyst pellets at the edge of the cell excluded from the beam. The vibrational modes observed in the INS spectra were assigned with reference to the INS of a polycyclic aromatic hydrocarbon, coronene, taken as a molecular model of a graphite layer, and with the aid of computational modeling. Two forms of spillover hydrogen were identified: H at edge sites of a graphite layer (formed after ambient dissociative chemisorption of H-2), and a weakly bound layer of mobile H atoms (formed by surface diffusion of H atoms after dissociative chernisorption of H-2 at 500 K). The INS spectra exhibited characteristic riding modes of H on carbon and on Pt or Ru. In these riding modes H atoms move in phase with vibrations of the carbon and metal lattices. The lattice modes are amplified by neutron scattering from the H atoms attached to lattice atoms. Uptake of hydrogen, and spillover, was greater for the Ru containing catalysts than for the Pt/C catalyst. The INS experiments have thus directly demonstrated H spillover to the carbon support of these metal catalysts.

Conformational and hydration effects of site-selective sodium, calcium and strontium ion binding to the DNA Holliday junction structure d(TCGGTACCGA)(4)

The role of metal ions in determining the solution conformation of the Holliday junction is well established, but to date the picture of metal ion binding from structural studies of the four-way DNA junction is very incomplete. Here we present two refined structures of the Holliday junction formed by the sequence d(TCGGTACCGA) in the presence of Na+ and Ca2+, and separately with Sr2+ to resolutions of 1.85 Angstrom and 1.65 Angstrom, respectively. This sequence includes the ACC core found to promote spontaneous junction formation, but its structure has not previously been reported. Almost complete hydration spheres can be defined for each metal cation. The Na+ sites, the most convincing observation of such sites in junctions to date, are one on either face of the junction crossover region, and stabilise the ordered hydration inside the junction arms. The four Ca2+ sites in the same structure are at the CG/CG steps in the minor groove. The Sr2+ ions occupy the TC/AG, GG/CC, and TA/TA sites in the minor groove, giving ten positions forming two spines of ions, spiralling through the minor grooves within each arm of the stacked-X structure. The two structures were solved in the two different C2 lattices previously observed, with the Sr2+ derivative crystallising in the more highly symmetrical form with two-fold symmetry at its centre. Both structures show an opening of the minor groove face of the junction of 8.4degrees in the Ca2+ and Na+ containing structure, and 13.4degrees in the Sr2+ containing structure. The crossover angles at the junction are 39.3degrees and 43.3degrees, respectively. In addition to this, a relative shift in the base pair stack alignment of the arms of 2.3 Angstrom is observed for the Sr2+ containing structure only. Overall these results provide an insight into the so-far elusive stabilising ion structure for the DNA Holliday junction. (C) 2003 Elsevier Science Ltd. All rights reserved.

A policy model for secure information flow

When a computer program requires legitimate access to confidential data, the question arises whether such a program may illegally reveal sensitive information. This paper proposes a policy model to specify what information flow is permitted in a computational system. The security definition, which is based on a general notion of information lattices, allows various representations of information to be used in the enforcement of secure information flow in deterministic or nondeterministic systems. A flexible semantics-based analysis technique is presented, which uses the input-output relational model induced by an attacker's observational power, to compute the information released by the computational system. An illustrative attacker model demonstrates the use of the technique to develop a termination-sensitive analysis. The technique allows the development of various information flow analyses, parametrised by the attacker's observational power, which can be used to enforce what declassification policies.

Global and local expression of chirality in serine on the Cu{110} surface

Establishing a molecular-level understanding of enantioselectivity and chiral resolution at the organic−inorganic interfaces is a key challenge in the field of heterogeneous catalysis. As a model system, we investigate the adsorption geometry of serine on Cu{110} using a combination of low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. The chirality of enantiopure chemisorbed layers, where serine is in its deprotonated (anionic) state, is expressed at three levels: (i) the molecules form dimers whose orientation with respect to the substrate depends on the molecular chirality, (ii) dimers of l- and d-enantiomers aggregate into superstructures with chiral (−1 2; 4 0) lattices, respectively, which are mirror images of each other, and (iii) small islands have elongated shapes with the dominant direction depending on the chirality of the molecules. Dimer and superlattice formation can be explained in terms of intra- and interdimer bonds involving carboxylate, amino, and β−OH groups. The stability of the layers increases with the size of ordered islands. In racemic mixtures, we observe chiral resolution into small ordered enantiopure islands, which appears to be driven by the formation of homochiral dimer subunits and the directionality of interdimer hydrogen bonds. These islands show the same enantiospecific elongated shapes those as in low-coverage enantiopure layers.

Small-world effects in lattice stochastic diffusion search

Stochastic Diffusion Search is an efficient probabilistic bestfit search technique, capable of transformation invariant pattern matching. Although inherently parallel in operation it is difficult to implement efficiently in hardware as it requires full inter-agent connectivity. This paper describes a lattice implementation, which, while qualitatively retaining the properties of the original algorithm, restricts connectivity, enabling simpler implementation on parallel hardware. Diffusion times are examined for different network topologies, ranging from ordered lattices, over small-world networks to random graphs.

Real option pricing in mixed-use development projects

The application of real options theory to commercial real estate has developed rapidly during the last 15 Years. In particular, several pricing models have been applied to value real options embedded in development projects. In this study we use a case study of a mixed use development scheme and identify the major implied and explicit real options available to the developer. We offer the perspective of a real market application by exploring different binomial models and the associated methods of estimating the crucial parameter of volatility. We include simple binomial lattices, quadranomial lattices and demonstrate the sensitivity of the results to the choice of inputs and method.

The correlation structure of spatial autoregressions

This paper investigates how the correlations implied by a first-order simultaneous autoregressive (SAR(1)) process are affected by the weights matrix and the autocorrelation parameter. A graph theoretic representation of the covariances in terms of walks connecting the spatial units helps to clarify a number of correlation properties of the processes. In particular, we study some implications of row-standardizing the weights matrix, the dependence of the correlations on graph distance, and the behavior of the correlations at the extremes of the parameter space. Throughout the analysis differences between directed and undirected networks are emphasized. The graph theoretic representation also clarifies why it is difficult to relate properties ofW to correlation properties of SAR(1) models defined on irregular lattices.

Symmetry-break in Voronoi tessellations

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomaly in the scaling indicates that large cells preferentially feature large isoperimetric quotients. As the number of faces is strongly correlated with the sphericity (cells with more faces are bulkier), in 3D it is shown that the anomalous scaling is heavily reduced when we perform power law fits separately on cells with a specific number of faces.

Ternary erbium chromium sulfides : structural relationships and magnetic properties

Single crystals of four erbium-chromium sulfides have been grown by chemical vapor transport using iodine as the transporting agent. Single-crystal X-ray diffraction reveals that in Er(3)CrS(6) octahedral sites are occupied exclusively by Cr(3+) cations, leading to one-dimensional CrS(4)(5-) chains of edge-sharing octahedra, while in Er(2)CrS(4), Er(3+), and Cr(2+) cations occupy the available octahedral sites in an ordered manner. By contrast, in Er(6)Cr(2)S(11) and Er(4)CrS(7), Er(3+) and Cr(2+) ions are disordered over the octahedral sites. In Er(2)CrS(4), Er(6)Cr(2)S(11), and Er(4)CrS(7), the network of octahedra generates an anionic framework constructed from M(2)S(5) slabs of varying thickness, linked by one-dimensional octahedral chains. This suggests that these three phases belong to a series in which the anionic framework may be described by the general formula [M(2n+1)S(4n+3)](x-), with charge balancing provided by Er(3+) cations located in sites of high-coordination number within one-dimensional channels defined by the framework. Er(4)CrS(7), Er(6)Cr(2)S(11), and Er(2)CrS(4) may thus be considered as the n = 1, 2, and infinity members of this series. While Er(4)CrS(7) is paramagnetic, successive magnetic transitions associated with ordering of the chromium and erbium sub-lattices are observed on cooling Er(3)CrS(6) (T(C)(Cr) = 30 K; T(C)(Er) = 11 K) and Er(2)CrS(4) (T(N)(Cr) = 42 K, T(N)(Er) = 10 K) whereas Er(6)Cr(2)S(11) exhibits ordering of the chromium sub-lattice only (T(N) = 11.4 K).

Simulation of field-induced structural formation and transition in electromagnetorheological suspensions

A computer simulation method has been used to study the three-dimensional structural formation and transition of eleetromagnetorheological (EMR) suspensions under compatible electric and magnetic fields. When the fields are applied simultaneously and perpendicularly to each other, the particles rapidly arrange into single layer structures parallel to both fields. In each layer, there is a two-dimensional hexagonal lattice. The single layers then combine together to form thicker sheetlike structures. With the help of the thermal fluctuations, the thicker structures relax into three-dimensional close-packed structures, which may be face-centered cubic (fcc), hexagonal close-packed (hup) lattices, or, more probably, the mixture of them, depending on the initial configurations and the thermal fluctuations. On the other hand, if the electric field is applied first to induce the body-centered tetragonal (bct) columns in the system, and then the magnetic field is applied in the perpendicular direction, the bet to fee structure transition is observed in a very short time. Following that, the structure keeps on evolving due to the demagnetization effect and finally forms close-packed structures with fee and hcp lattice character. The simulation results are in agreement with the theoretical and experimental results.

Three-dimensional gallium sulphide open framework

The synthesis and crystal structure of four gallium sulphide open frameworks, built from supertetrahedral clusters, are described. The structures of [C4NH12]6[Ga10S18][C4NH12]6[Ga10S18](1) and [C4NH12]12[Ga20S35.5(S3)0.5O](2) contain supertetrahedral T3 clusters, while in the isostructural compounds [C4NH12]16[Ga10S18M4Ga16S33][C4NH12]16[Ga10S18M4Ga16S33] (M=CoM=Co(3), Zn (4)), T3 and T4 clusters alternate. These materials exhibit three-dimensional frameworks, with topologies consisting of two interpenetrating diamond lattices, and contain over 50% of solvent accessible void space. UV–Vis diffuse reflectance measurements indicate that these compounds are semiconducting, with band gaps over the range 3.4–4.1 eV.

Strangely dual orbifold equivalence I

In this brief note we prove orbifold equivalence between two potentials described by strangely dual exceptional unimodular singularities of type K14 and Q10 in two different ways. The matrix factorizations proving the orbifold equivalence give rise to equations whose solutions are permuted by Galois groups which differ for different expressions of the same singularity.

Realising the cup product of local Tate duality

We present an explicit description, in terms of central simple algebras, of a cup product map which occurs in the statement of local Tate duality for Galois modules of prime cardinality p. Given cocycles f and g, we construct a central simple algebra of dimension p^2 whose class in the Brauer group gives the cup product f\cup g. This algebra is as small as possible.