19,467 research outputs found
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
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