Sulfide determination in hydrothermal seawater samples using a vibrating gold micro-wire electrode in conjunction with stripping chronopotentiometry

A rapid electrochemical stripping chronopotentiometric procedure to determined sulfide in unaltered hydrothermal seawater samples is presented. Sulfide is deposited at −0.25 V (vs Ag/AgCl, KCl 3 M) at a vibrating gold microwire and then stripped through the application of a reductive constant current (typically −2 μA). The hydrodynamic conditions are modulated by vibration allowing a short deposition step, which is shown here to be necessary to minimize H₂S volatilization. The limit of detection (LOD) is 30 nM after a deposition step of 7 s. This LOD is in the same range as the most sensitive cathodic voltammetric technique using a mercury drop electrode and is well below those reported previously for other electrodes capable of being implemented in situ.     

The number of edges in a bipartite graph of given radius

Vizing established an upper bound on the size of a graph of given order and radius. We find a sharp upper bound on the size of a bipartite graph of given order and radius.     

Homoclinic Solutions for Swift-Hohenberg and Suspension Bridge Type Equations

We establish the existence of homoclinic solutions for a class of fourth-order equations which includes the Swift-Hohenberg model and the suspension bridge equation. In the first case, the nonlinearity has three zeros, corresponding to a double-well potential, while in the second case the nonlinearity is asymptotically constant on one side. The Swift-Hohenberg model is a higher-order extension of the classical Fisher-Kolmogorov model. Its more complicated dynamics give rise to further possibilities of pattern formation. The suspension bridge equation was studied by Chen and McKenna (J. Differential Equations136 (1997), 325-355); we give a positive answer to an open question raised by the authors.     

Correlated random networks

We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix c, and the relevant statistical ensembles are defined in terms of a partition function Z= summation operator exp([-betaH(c)]. The simplest cases are uncorrelated random networks such as the well-known Erd?s-Rényi graphs. Here we study more general interactions H(c) which lead to correlations, for example, between the connectivities of adjacent vertices. In particular, such correlations occur in optimized networks described by partition functions in the limit beta--> infinity. They are argued to be a crucial signature of evolutionary design in biological networks.     

Light filaments in air for ultraviolet and infrared wavelengths

The propagation of femtosecond UV laser pulses in air is numerically shown to form intense light filaments over several tenths of Rayleigh lengths. We compare UV filamentation with IR filamentation and show that the balance of the physical processes supporting the filaments is identical in both cases. For IR and UV wavelengths, it is shown that the intensity in the filament and the density of the electron plasma created by ionization of air molecules reach similar values as high as 10(14) W/cm(2) and 10(17) cm(-3). Spectral data exhibit a large broadening in the IR filament and a limited one for UV, which justifies the white-light generation associated with IR filamentation only.     

Monte Carlo simulations with Symanzik's improved actions in the lattice O(3) non-linear σ-model

The scaling properties of the lattice O(3) non-linear σ-model are studied. The mass-gap, energy momentum dispersion, correlation functions are measured by numerical Monte Carlo methods. Symanzik's tree-level and one loop improved actions are compared to the standard (nearest neighbour) action.     

The boson gas on a Cayley tree

We analyze the free boson gas on a Cayley tree using two alternative methods. The spectrum of the lattice Laplacian on a finite tree is obtained using a direct iterative method for solving the associated characteristic equation and also using a random walk representation for the corresponding fermion lattice gas. The existence of the thermodynamic limit for the pressure of the boson lattice gas is proven and it is shown that the model exhibits boson condensation into the ground state. The random walk representation is also used to derive an expression for the Bethe approximation to the infinite-volume spectrum. This spectrum turns out to be continuous instead of a dense point spectrum, but there is still boson condensation in this approximation.