High-Temperature Interaction of Condensed Phosphates with Oxoacid Salts Oxides,Halogenides, Sulphides,Nitrides and Metals

Abstract

Melted condensed phosphates (CP) having high chemical activity, interact with oxoacid salts, halogenides, sulphides, oxides and nitrides as well as with metals, steels and alloys. Lithium and sodium sulphate destruct CP evolving O₂ and SO₂ into a gasous phase. In the reaction products di-, tri- and tetraphosphate solid and polymer anions have been revealed by paper-chromatography analysis. Increasing the temperature and the contact of sulphate, both the mean value of phosphate molecular mass and viscosity of metals decreased. Interacting with CP carbonates dissociated to form CO₂. Lithium nitrate dissociated at 443 K, sodium and potassium nitrates at 593 and 663 K respectively. Potassium sulphate decreases the mean molecular mass (KPO₃)_n less than twofold, potassium nitrate does it more than 10 times under similar conditions. In the series Li₆TeO₆-Li₂SO₄-Li₂CrO₄ potassium chromate reacted actively with (LiPO₃)_n to form chromium (III) monophosphate, a valuable binding material and catalyst. Interacting with Cr₂S₃MnS, NiS, Cu₂S₄FeS, melted condensed phosphates stimulated the formation on sulphur, SO₂ and P₄. In solid melts metal phosphides have been found as well a mono-, di- and tetrapolyphos-phates. Condensed phosphate reactions with Mg₃N₂, A1N and TiN resulted in evolving PN, N₂ and P₄ into gaseous phase.     

Perturbative-variational calculations of ground-state energies of lattice gauge theories

We apply the perturbative variational approximation scheme of Bessis and Villani to Z(2) gauge theory on a lattice in 2 + 1 and 3 + 1 dimensions and to a truncated version of SU(2) gauge theory in 3 + 1 dimensions. We find that the BV scheme tends to distinguish between first- and second-order transition already in the first approximant.     

Front tracking and two-dimensional Riemann problems

A substantial improvement in resolution has been achieved for the computation of jump discontinuities in gas dynamics using the method of front tracking. The essential feature of this method is that a lower dimensional grid is fitted to and follows the discontinuous waves. At the intersection points of these discontinuities, two-dimensional Riemann problems occur. In this paper we study such two-dimensional Riemann problems from both numerical and theoretical points of view. Specifically included is a numerical solution for the Mach reflection, a general classification scheme for two-dimensional elementary waves, and a discussion of problems and conjectures in this area.     

An NP-complete matching problem

We show that a restricted form of the perfect matching problem for bipartite graphs is NP-complete. The restriction involves partitions of the vertices of the graph. This problem is still NP-complete if the degrees of the vertices are restricted to be 3 or less. For degrees restricted to 2 or less, a polynomial time algorithm exists.     

Excitable elements controlled by noise and network structure

We study collective dynamics of complex networks of stochastic excitable elements, active rotators. In the thermodynamic limit of infinite number of elements, we apply a mean-field theory for the network and then use a Gaussian approximation to obtain a closed set of deterministic differential equations. These equations govern the order parameters of the network. We find that a uniform decrease in the number of connections per element in a homogeneous network merely shifts the bifurcation thresholds without producing qualitative changes in the network dynamics. In contrast, heterogeneity in the number of connections leads to bifurcations in the excitable regime. In particular we show that a critical value of noise intensity for the saddle-node bifurcation decreases with growing connectivity variance. The corresponding critical values for the onset of global oscillations (Hopf bifurcation) show a non-monotone dependency on the structural heterogeneity, displaying a minimum at moderate connectivity variances.     

Sequences of gluing bifurcations in an analog electronic circuit

We report on the experimental investigation of gluing bifurcations in the analog electronic circuit which models a dynamical system of the third order: Lorenz equations with an additional quadratic nonlinearity. Variation of one of the resistances in the circuit changes the coefficient at this nonlinearity and replaces the Lorenz route to chaos by a different scenario which leads, through the sequence of homoclinic bifurcations, from periodic oscillations of the voltage to the irregular ones. Every single bifurcation “glues” in the phase space two stable periodic orbits and creates a new one, with the doubled length: a sequence of such bifurcations results in the birth of the chaotic attractor.     

The Social Amplifier—Reaction of Human Communities to Emergencies

This paper develops a methodology to aggregate signals in a network regarding some hidden state of the world. We argue that focusing on edges around hubs will under certain circumstances amplify the faint signals disseminating in a network, allowing for more efficient detection of that hidden state. We apply this method to detecting emergencies in mobile phone data, demonstrating that under a broad range of cases and a constraint in how many edges can be observed at a time, focusing on the egocentric networks around key hubs will be more effective than sampling random edges. We support this conclusion analytically, through simulations, and with analysis of a dataset containing the call log data from a major mobile carrier in a European nation.     

Chiral analog gauge theories on the lattice

We discuss a class of lattice gauge theories with fermions that have properties in common with continuum chiral gauge theories. The symmetries we gauge have often been mistaken for chiral symmetries in the literature. We show that in the continuum limit they converge to ordinary vector-like symmetries, but that at strong coupling they behave like chiral symmetries. We find lattice analogs of the technicolor mechanism and of the generation of composite massless fermions in chiral gauge theories.