The Stefan problem with variable thermophysical properties and phase change temperature

In this paper we formulate a Stefan problem appropriate when the thermophysical properties are distinct in each phase and the phase-change temperature is size or velocity dependent. Thermophysical properties invariably take different values in different material phases but this is often ignored for mathematical simplicity. Size and velocity dependent phase change temperatures are often found at very short length scales, such as nanoparticle melting or dendrite formation; velocity dependence occurs in the solidification of supercooled melts. To illustrate the method we show how the governing equations may be applied to a standard one-dimensional problem and also the melting of a spherically symmetric nanoparticle. Errors which have propagated through the literature are highlighted. By writing the system in non-dimensional form we are able to study the large Stefan number formulation and an energy-conserving one-phase reduction. The results from the various simplifications and assumptions are compared with those from a finite difference numerical scheme. Finally, we briefly discuss the failure of Fourier's law at very small length and time-scales and provide an alternative formulation which takes into account the finite time of travel of heat carriers (phonons) and the mean free distance between collisions.Comment: 39 pages, 5 figure

The one-dimensional Stefan problem with non-Fourier heat conduction

We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time regimes we are able to reduce the problem to a system of two coupled ordinary differential equations describing the evolution of the solid-liquid interface and the heat flux. The reduced formulation is in good agreement with numerical simulations. In the case of silicon, differences between classical and non-classical solidification kinetics are relatively small, but larger deviations can be observed in the evolution in time of the heat flux through the growing solid. From this study we conclude that the heat flux provides more information about the presence of non-classical modes of heat transport during phase-change processes.Comment: 29 pages, 6 figures, 2 tables + Supplementary Materia

Regional Contagion and the Globalization of Securities Markets

This paper argues that the globalization of securities markets may promote contagion among investors by weakening incentives for gathering costly country-specific information and by strengthening incentives for imitating arbitrary market portfolios. In the presence of short-selling constraints, the utility gain of gathering information at a fixed cost converges to a constant level and may diminish as securities markets grow. Moreover, if a portfolio manager's marginal cost for yielding below-market returns exceeds the marginal gain for above-market returns, there is a range of optimal portfolios in which all investors imitate arbitrary market portfolios and this range widens as the market grows. Numerical simulations suggest that these frictions can have significant quantitative implications and they may induce large capital flows in emerging markets.

Composition-induced structural transitions in mixed rare-gas clusters

The low-energy structures of mixed Ar--Xe and Kr--Xe Lennard-Jones clusters are investigated using a newly developed parallel Monte Carlo minimization algorithm with specific exchange moves between particles or trajectories. Tests on the 13- and 19- atom clusters show a significant improvement over the conventional basin-hopping method, the average search length being reduced by more than one order of magnitude. The method is applied to the more difficult case of the 38-atom cluster, for which the homogeneous clusters have a truncated octahedral shape. It is found that alloys of dissimilar elements (Ar--Xe) favor polytetrahedral geometries over octahedra due to the reduced strain penalty. Conversely, octahedra are even more stable in Kr--Xe alloys than in Kr_38 or Xe_38, and they show a core-surface phase separation behavior. These trends are indeed also observed and further analysed on the 55-atom cluster. Finally, we correlate the relative stability of cubic structures in these clusters to the glassforming character of the bulk mixtures.Comment: 14 pages, 8 figures, 5 tables PRB vol 70, in pres

Enhancing single-parameter quantum charge pumping in carbon-based devices

We present a theoretical study of quantum charge pumping with a single ac gate applied to graphene nanoribbons and carbon nanotubes operating with low resistance contacts. By combining Floquet theory with Green's function formalism, we show that the pumped current can be tuned and enhanced by up to two orders of magnitude by an appropriate choice of device length, gate voltage intensity and driving frequency and amplitude. These results offer a promising alternative for enhancing the pumped currents in these carbon-based devices.Comment: 3.5 pages, 2 figure

Eye movements and processing stages in reading: Relative contribution of visual, lexical, and contextual factors.

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