The role of alkali content in the devitrification mechanisms of SiO2–Fe2O3–Na2O–PbO SYSTEM

Three batch compositions of pure oxides (SiO₂, Fe₂O₃, PbO, Na₂O) with equivalent SiO₂, Fe₂O₃ and PbO contents and a gradually increased Na₂O content were vitrified through heating in a high temperature electric furnace and subsequent quenching. The resulting vitreous products were thermally treated in order to study the devitrification behaviour, under conditions designated from differential thermal analysis experiments. Depending on the Na₂O content, crystal phase separation gave rise to the growth of acmite and hematite or maghemite. A uniformly phase separated glass-ceramic material, with crystallites of similar size and population density, was produced from devitrification of the vitreous product with the higher Na₂O content.     

Microstructural assessment of InN-on-GaN films grown by plasma-assisted MBE

The structural properties of InN thin films, grown by rf plasma-assisted molecular beam epitaxy on Ga-face GaN/Al₂O₃(0001) substrates, were investigated by means of conventional and high resolution electron microscopy. Our observations showed that a uniform InN film of total thickness up to 1 μm could be readily grown on GaN without any indication of columnar growth. A clear epitaxial orientation relationship of , was determined. The quality of the InN film was rather good, having threading dislocations as the dominant structural defect with a density in the range of 10⁹–10¹⁰ cm⁻². The crystal lattice parameters of wurtzite InN were estimated by electron diffraction analysis to be a=0.354 nm and c=0.569 nm, using Al₂O₃ as the reference crystal. Heteroepitaxial growth of InN on GaN was accomplished by the introduction of a network of three regularly spaced misfit dislocation arrays at the atomically flat interface plane. The experimentally measured distance of misfit dislocations was 2.72 nm. This is in good agreement with the theoretical value derived from the in-plane lattice mismatch of InN and GaN, which indicated that nearly full relaxation of the interfacial strain between the two crystal lattices was achieved.     

Measurement of nonequilibrium entropy from space-time thermodynamic integration

The entropy of a system transiently driven out of equilibrium by a time-inhomogeneous stochastic dynamics is first expressed as a transient response function generalizing the nonlinear Kawasaki-Crooks response. This function is then reformulated into three statistical averages defined over ensembles of nonequilibrium trajectories. The first average corresponds to a space-time thermodynamic perturbation relation, while the two following ones correspond to space-time thermodynamic integration relations. Provided that trajectories are initiated starting from a distribution of states that is analytically known, the ensemble averages are computationally amenable to Markov chain Monte Carlo methods. The relevance of importance sampling in path ensembles is confirmed in practice by computing the nonequilibrium entropy of a driven toy system. We finally study a situation where the dynamics produces entropy. In this case, we observe that space-time thermodynamic integration still yields converged estimates, while space-time thermodynamic perturbation turns out to converge very slowly.     

The black hole and FRW geometries of non-relativistic gravity

We consider the recently proposed non-relativistic Ho?ava–Lifshitz four-dimensional theory of gravity. We study a particular limit of the theory which admits flat Minkowski vacuum and we discuss thoroughly the quadratic fluctuations around it. We find that there are two propagating polarizations of the metric. We then explicitly construct a spherically symmetric, asymptotically flat, black hole solution that represents the analog of the Schwarzschild solution of GR. We show that this theory has the same Newtonian and post-Newtonian limits as GR and thus, it passes the classical tests. We also consider homogeneous and isotropic cosmological solutions and we show that although the equations are identical with GR cosmology, the couplings are constrained by the observed primordial abundance of ⁴He.     

L-fuzzy ⋎ and ⋏ hyperoperations and the associated l-fuzzy hyperalgebras

In this paper we study two fuzzy hyperoperations, denoted by ⋎ (which can be seen as a generalization of ∨) and ⋏ (which can be seen as a generalization of ∧). ⋎ is obtained from a family of crisp ∨; _p hyperoperations and ⋏ is obtained from a family of crisp ∧ _p hyperoperations. The hyperstructure (X, ⋎, ∧) resembles ahyperlattice and the hyperstructure (X, ∨, ⋏) resembles adual hyperlattice     

Low-Dimensional Architectures in Isomeric cis-PtCl2{Ph2PCH2N(Ar)CH2PPh2} Complexes Using Regioselective-N(Aryl)-Group Manipulation

The solid-state behaviour of two series of isomeric, phenol-substituted, aminomethylphosphines, as the free ligands and bound to Pt^II, have been extensively studied using single crystal X-ray crystallography. In the first library, isomeric diphosphines of the type Ph₂PCH₂N(Ar)CH₂PPh₂ [1a–e; Ar = C₆H₃(Me)(OH)] and, in the second library, amide-functionalised, isomeric ligands Ph₂PCH₂N{CH₂C(O)NH(Ar)}CH₂PPh₂ [2a–e; Ar = C₆H₃(Me)(OH)], were synthesised by reaction of Ph₂PCH₂OH and the appropriate amine in CH₃OH, and isolated as colourless solids or oils in good yield. The non-methyl, substituted diphosphines Ph₂PCH₂N{CH₂C(O)NH(Ar)}CH₂PPh₂ [2f, Ar = 3-C₆H₄(OH); 2g, Ar = 4-C₆H₄(OH)] and Ph₂PCH₂N(Ar)CH₂PPh₂ [3, Ar = 3-C₆H₄(OH)] were also prepared for comparative purposes. Reactions of 1a–e, 2a–g, or 3 with PtCl₂(η⁴-cod) afforded the corresponding square-planar complexes 4a–e, 5a–g, and 6 in good to high isolated yields. All new compounds were characterised using a range of spectroscopic (¹H, ³¹P{¹H}, FT–IR) and analytical techniques. Single crystal X-ray structures have been determined for 1a, 1b∙CH₃OH, 2f∙CH₃OH, 2g, 3, 4b∙(CH₃)₂SO, 4c∙CHCl₃, 4d∙½Et₂O, 4e∙½CHCl₃∙½CH₃OH, 5a∙½Et₂O, 5b, 5c∙¼H₂O, 5d∙Et₂O, and 6∙(CH₃)₂SO. The free phenolic group in 1b∙CH₃OH, 2f∙CH₃OH_, 2g, 4b∙(CH₃)₂SO, 5a∙½Et₂O, 5c∙¼H₂O, and 6∙(CH₃)₂SO exhibits various intra- or intermolecular O–H∙∙∙X (X = O, N, P, Cl) hydrogen contacts leading to different packing arrangements.     

Accessibility and Reliability for Connected Bipartite Graphs

In the recently published atlas of graphs [9] the general listing of graphs with diagrams went up to V=7 vertices but the special listing for connected bipartite graphs carried further up to V=8. In this paper we wish to study the random accessibility of these connected bipartite graphs by means of random walks on the graphs using the degree of the gratis starting point as a weighting factor. The accessibility is then related to the concept of reliability of the graphs with only edge failures. Exact expectation results for accessibility are given for any complete connected bipartite graph N₁ cbp N₂ (where cbp denotes connected bipartite) for several values of J (the number of new vertices searched for). The main conjecture in this paper is that for any complete connected bipartite graph N₁ cbp N₂: if |N₁–N₂| 1, then the graph is both uniformly optimal in reliability and optimal in random accessibility within its family. Numerical results are provided to support the conjecture.     

Simulating structural transitions by direct transition current sampling: the example of LJ38

Reaction paths and probabilities are inferred, in a usual Monte Carlo or molecular dynamic simulation, directly from the evolution of the positions of the particles. The process becomes time-consuming in many interesting cases in which the transition probabilities are small. A radically different approach consists of setting up a computation scheme where the object whose time evolution is simulated is the transition current itself. The relevant timescale for such a computation is the one needed for the transition probability rate to reach a stationary level, and this is usually substantially shorter than the passage time of an individual system. As an example, we show, in the context of the "benchmark" case of 38 particles interacting via the Lennard-Jones potential ("LJ(38)" cluster), how this method may be used to explore the reactions that take place between different phases, recovering efficiently known results, and uncovering new ones with small computational effort.