Search results for "Length"
showing 10 items of 2188 documents
A generalization of the inhomogeneity measure for point distributions to the case of finite size objects
2008
The statistical measure of spatial inhomogeneity for n points placed in chi cells each of size kxk is generalized to incorporate finite size objects like black pixels for binary patterns of size LxL. As a function of length scale k, the measure is modified in such a way that it relates to the smallest realizable value for each considered scale. To overcome the limitation of pattern partitions to scales with k being integer divisors of L we use a sliding cell-sampling approach. For given patterns, particularly in the case of clusters polydispersed in size, the comparison between the statistical measure and the entropic one reveals differences in detection of the first peak while at other sca…
Decomposable multiphase entropic descriptor
2013
To quantify degree of spatial inhomogeneity for multiphase materials we adapt the entropic descriptor (ED) of a pillar model developed to greyscale images. To uncover the contribution of each phase we introduce the suitable 'phase splitting' of the adapted descriptor. As a result, each of the phase descriptors (PDs) describes the spatial inhomogeneity attributed to each phase-component. Obviously, their sum equals to the value of the overall spatial inhomogeneity. We apply this approach to three-phase synthetic patterns. The black and grey components are aggregated or clustered while the white phase is the background one. The examples show how the valuable microstuctural information related…
Spatial decoherence in QED
2006
We consider the dynamics of a charged free particle, initially described by a coherent wave packet, interacting with an electromagnetic field characterized by the temperature T, considered as the environment. We have used dipole approximation neglecting the potential vector quadratic term in the minimal coupling Hamiltonian. This leads to the loss of coherence in the momentum representation, described by the decay of the off diagonal elements of the particle reduced density matrix, while the populations remain constant. Here we extend the analysis to the coordinate representation. We compute the particle reduced density matrix in this basis, analyzing in particular the mixing of various ef…
On multi-scale percolation behaviour of the effective conductivity for the lattice model with interacting particles
2015
Recently, the effective medium approach using 2x2 basic cluster of model lattice sites to predict the conductivity of interacting droplets has been presented by Hattori et al. To make a step aside from pure applications, we have studied earlier a multi-scale percolation, employing any kxk basic cluster for non-interacting particles. Here, with interactions included, we examine in what way they alter the percolation threshold for any cluster case. We found that at a fixed length scale k the interaction reduces the range of shifts of the percolation threshold. To determine the critical concentrations, the simplified model is used. It diminishes the number of local conductivities into two main…
Variable Length Memory Chains: Characterization of stationary probability measures
2021
Variable Length Memory Chains (VLMC), which are generalizations of finite order Markov chains, turn out to be an essential tool to modelize random sequences in many domains, as well as an interesting object in contemporary probability theory. The question of the existence of stationary probability measures leads us to introduce a key combinatorial structure for words produced by a VLMC: the Longest Internal Suffix. This notion allows us to state a necessary and sufficient condition for a general VLMC to admit a unique invariant probability measure. This condition turns out to get a much simpler form for a subclass of VLMC: the stable VLMC. This natural subclass, unlike the general case, enj…
The Second APOKASC Catalog: The Empirical Approach
2018
We present a catalog of stellar properties for a large sample of 6676 evolved stars with APOGEE spectroscopic parameters and \textit{Kepler} asteroseismic data analyzed using five independent techniques. Our data includes evolutionary state, surface gravity, mean density, mass, radius, age, and the spectroscopic and asteroseismic measurements used to derive them. We employ a new empirical approach for combining asteroseismic measurements from different methods, calibrating the inferred stellar parameters, and estimating uncertainties. With high statistical significance, we find that asteroseismic parameters inferred from the different pipelines have systematic offsets that are not removed b…
Intermetallic compounds of the heaviest elements: the electronic structure and bonding of dimers of element 112 and its homolog Hg
2002
Abstract Fully relativistic (four-component) density-functional calculations were performed for the element 112 dimers (112)X (X = Pd, Cu, Ag and Au) and those of its lighter homolog, Hg. A relatively small decrease of about 15–20 kJ/mol in bonding was found from the HgX to (112)X compounds. Respectively, the bond lengths were increased by 0.06 A on the average. The Mulliken population analysis has shown this effect to be a result of a decreasing contribution of the relativistically stabilized 7s-AO of element 112 to bonding. The following trend in the binding energies was predicted for (112)X as a function of X: Pd >Cu>Au>Ag, exactly as the trend obtained experimentally for adsorption of H…
Synthesis and crystal structure of {Rh2(O2CCH3)4·P(o-CH3OH6H4)Ph2}2. A novel dirhodium(II) monoadduct with intermolecular μ-oxo interactions
1997
Abstract We have investigated the reaction of dirhodium tetraacetate with the phosphine P( o -CH 3 OH 6 H 4 )Ph 2 (P) under different experimental conditions. From these reactions we have been able to isolate the dirhodium tetraacetate phosphine mono-adduct. The crystal structure shows that in the solid state this compound forms a centrosymmetric dimer of the dimer, {Rh 2 (O 2 CCH 3 ) 4 ·P(0-CH 3 OC 6 H 4 )Ph 2 } 2 , in which we oxygen atom from one acetate group in one Rh 2 (O 2 CCH 3 ) 4 ·P unit is axially coordinating one Rh atom on another Rh 2 (O 2 CCH 3 ) 4 · P unit (Rh⋯) 2.347(3) A intermolecular versus Rh⋯O 2.455(3) A intermolecular), and vice versa. The RhRh bond distance is 2.414…
3-formylphenylboronic acid.
2004
The molecule of the title compound, C(7)H(7)BO(3), is planar, and the bond lengths and angles are typical. The formyl group is essentially coplanar with the benzene ring but does not influence significantly the distortion of the ring, although the formyl group does have a strong influence on the crystal packing. The geometry of the boronic acid group is typical. In the crystal structure, the molecules are linked by O-H...O hydrogen bonds.
Selective ortho-metallation reaction of the phosphine P(o-ClC6H4)Ph2. Synthesis and crystal structure of [Rh2(μ-O2CCH3)3(μ-(ClC6H3)PPh2(OH2)2]·CHCl3
1993
Abstract From the reaction of [Rh2(O2CCH3)4(MeOH)2] in hot acetic acid with P(o-ClC6H4)Ph2, two monometallated compounds [Rh2(O2CCH3)3(C6H4)P(o-ClC6H4)Ph(HO2CCH3)2] (1), already described, and [Rh2(O2CCH3)3{(ClC6H3)PPh2}(OH2)2] have been isolated. The new compound has been characterized by an X-ray study. It crystallizes in the triclinic space group P1. It contains three acetate groups bridging a Rh24+ unit that has a Rh-Rh bond distance of 2.426(1) A; the fourth bridging ligand is derived from one P(o-ClC6H4)Ph2 metallated in the halogenated ring. The two water molecules occupy the axial coordination sites.