The attractive nonlinear delta-function potential

We solve the continuous one-dimensional Schr\"{o}dinger equation for the case of an inverted {\em nonlinear} delta-function potential located at the origin, obtaining the bound state in closed form as a function of the nonlinear exponent. The bound state probability profile decays exponentially away from the origin, with a profile width that increases monotonically with the nonlinear exponent, becoming an almost completely extended state when this approaches two. At an exponent value of two, the bound state suffers a discontinuous change to a delta-like profile. Further increase of the exponent increases again the width of the probability profile, although the bound state is proven to be stable only for exponents below two. The transmission of plane waves across the nonlinear delta potential increases monotonically with the nonlinearity exponent and is insensitive to the sign of its opacity.Comment: submitted to Am. J. of Phys., sixteen pages, three figure

From Disordered Crystal to Glass: Exact Theory

We calculate thermodynamic properties of a disordered model insulator, starting from the ideal simple-cubic lattice ($g = 0$) and increasing the disorder parameter $g$ to $\gg 1/2$. As in earlier Einstein- and Debye- approximations, there is a phase transition at $g_{c} = 1/2$. For $g<g_{c}$ the low-T heat-capacity $C \sim T^{3}$ whereas for $g>g_{c}$, $C \sim T$. The van Hove singularities disappear at {\em any finite $g$}. For $g>1/2$ we discover novel {\em fixed points} in the self-energy and spectral density of this model glass.Comment: Submitted to Phys. Rev. Lett., 8 pages, 4 figure

Dissipative vortex solitons in 2D-lattices

We report the existence of stable symmetric vortex-type solutions for two-dimensional nonlinear discrete dissipative systems governed by a cubic-quintic complex Ginzburg-Landau equation. We construct a whole family of vortex solitons with a topological charge S = 1. Surprisingly, the dynamical evolution of unstable solutions of this family does not alter significantly their profile, instead their phase distribution completely changes. They transform into two-charges swirl-vortex solitons. We dynamically excite this novel structure showing its experimental feasibility.Comment: 4 pages, 20 figure

A model of the geochemical and physical fluctuations of the lava lake at Erebus volcano, Antarctica

Erebus volcano, Antarctica, exhibits periodical surface fluctuations of both geochemical and physical nature. Modeling the physics driving the lake oscillation is a challenge, even with a relatively simple theoretical framework. We present a quantitative analysis that aims to reconcile both lake level and gas geochemical cycles. Our model is based on the assumption that the periodicity is caused by the regular release of magma batches and/or core annular flow that have a fixed volume of melt and ascend and degas in equilibrium. Results suggest that cycles are not caused by the mixing between magma residing in the lake and a deep magma but by two distinct deep sources that rise separately. These sources of bubbly magma come from at most 2–3 km depth and rise buoyantly. Individual batches detach from the rising magmas at depths of 20–250 m. The two batch types can coexist in a single conduit up to a depth of ~ 30 m, above which they rise alternately to release respectively 19 and 23 kg/s of gas at the lake surface every 10 min. The temperature of the descending flow is between 890 and 950 °C, which is roughly 100 °C colder than the ascending currents. Batch pairs have shapes likely constrained by the conduit width. Regardless of their shapes, the pairs reach very high porosities near the surface and have diameters of 4–14 m that are consistent with video observations showing spreading waves at the lake surface. The alternating arrival of these large batches suggests a lava lake mostly filled with gas-rich magma.This work is part of the first author's PhD thesis, which was funded by the 7th Framework Program of the EC (ERC grant 202844) and by Senescyt under the Prometeo Program (Ecuador). CO acknowledges support from the Isaac Newton Trust (project “Physical constraints for the interpretation of open-vent volcanism”) and the Natural Environment Research Council (National Centre for Earth Observation: COMET).This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.jvolgeores.2015.10.02

Thermal conductivity and thermodynamics of phonons for an exactly soluble model of disorder

Journal ArticleWe calculate the exact thermal conductivity and the heat capacity of an insulator for which the lattice dynamics are given by a phonon gas in the presence of frozen-in disorder, in the special case of the "backward-scattering'' model of impurity scattering

The thickness of a liquid layer on the free surface of ice as obtained from computer simulation

Molecular dynamic simulations were performed for ice Ih with a free surface by using four water models, SPC/E, TIP4P, TIP4P/Ice and TIP4P/2005. The behavior of the basal plane, the primary prismatic plane and of the secondary prismatic plane when exposed to vacuum was analyzed. We observe the formation of a thin liquid layer at the ice surface at temperatures below the melting point for all models and the three planes considered. For a given plane it was found that the thickness of a liquid layer was similar for different water models, when the comparison is made at the same undercooling with respect to the melting point of the model. The liquid layer thickness is found to increase with temperature. For a fixed temperature it was found that the thickness of the liquid layer decreases in the following order: the basal plane, the primary prismatic plane, and the secondary prismatic plane. For the TIP4P/Ice model, a model reproducing the experimental value of the melting temperature of ice, the first clear indication of the formation of a liquid layer appears at about -100 Celsius for the basal plane, at about -80 Celsius for the primary prismatic plane and at about -70 Celsius for the secondary prismatic plane.Comment: 41 pages and 13 figure