Ising model for distribution networks

An elementary Ising spin model is proposed for demonstrating cascading failures (break-downs, blackouts, collapses, avalanches, ...) that can occur in realistic networks for distribution and delivery by suppliers to consumers. A ferromagnetic Hamiltonian with quenched random fields results from policies that maximize the gap between demand and delivery. Such policies can arise in a competitive market where firms artificially create new demand, or in a solidary environment where too high a demand cannot reasonably be met. Network failure in the context of a policy of solidarity is possible when an initially active state becomes metastable and decays to a stable inactive state. We explore the characteristics of the demand and delivery, as well as the topological properties, which make the distribution network susceptible of failure. An effective temperature is defined, which governs the strength of the activity fluctuations which can induce a collapse. Numerical results, obtained by Monte Carlo simulations of the model on (mainly) scale-free networks, are supplemented with analytic mean-field approximations to the geometrical random field fluctuations and the thermal spin fluctuations. The role of hubs versus poorly connected nodes in initiating the breakdown of network activity is illustrated and related to model parameters

Extraordinary wetting phase diagram for mixtures of Bose-Einstein condensates

The possibility of wetting phase transitions in Bose-Einstein condensed gases is predicted on the basis of Gross-Pitaevskii theory. The surface of a binary mixture of Bose-Einstein condensates can undergo a first-order wetting phase transition upon varying the interparticle interactions, using, e.g., Feshbach resonances. Interesting ultra-low-temperature effects shape the wetting phase diagram. The prewetting transition is, contrary to general expectations, not of first order but critical, and the prewetting line does not meet the bulk phase coexistence line tangentially. Experimental verification of these extraordinary results is called for, especially now that it has become possible, using optical methods, to realize a planar "hard wall" boundary for the condensates

Thermal fluctuation forces and wetting layers in colloid-polymer mixtures: derivation of an interface potential.

We discuss wetting layers in phase-separated colloid-polymer mixtures adsorbed at a vertical wall, observed in recent laser scanning confocal microscopy experiments. Matching of colloid and solvent dielectric properties renders van der Waals forces negligible and provides a system governed by short-range forces and thermal fluctuations on which the subtle predictions of renormalization group (RG) theory for wetting can be tested. The width w of the fluid-fluid ("liquid-gas") interface bounding the wetting layer scales with the square root of the wetting layer thickness l, in qualitative agreement with RG theory for short-range complete wetting in three dimensions. The measured wetting layer thickness l as a function of the height h above the horizontal plane of bulk phase separation is compared with two distinct theoretical predictions. A simple heuristic interface potential V(l), first proposed in a previous report, is now fully derived, and confronted here with the interface potential based on the linear RG theory. The heuristic approach does not capture fully the RG treatment. While fundamental differences exist between the two approaches, the resulting predictions for l(h) are almost identical. However, the theory does not follow the precise shape of the experimental curve of l(h)

Evidence for nonmonotonic magnetic field penetration in a type-I superconductor

The ability of the polarized neutron reflectivity (PNR) technique to reveal the non-local electrodynamics effect in the profile of magnetic field penetrated into a superconductor in the Meissner state is explored with an extreme low-¿ type-I superconductor. The sample is a thick film of pure indium deposited on a silicon oxide substrate having a neutron refraction index smaller than that for indium. It is shown that the PNR technique allows one to distinguish between exponential and non-exponential shape of the field profile. The data obtained are consistent with the magnetic field distribution following from the non-local theory