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

Calculation Method for Predicting AM0 Isc from High Altitude Aircraft Flight Data

High altitude aircraft have been used by the space photovoltaic (PV) community to determine the air mass Zero (AM0) performance of solar cells for over fifty years. Relative to in-space measurement opportunities, these methods are generally cheaper and more readily available. The data obtained, however, must be corrected for residual atmospheric effects. This paper details the correction method currently being used for the calculation of the estimated AM0 short-circuit current (Isc) for photovoltaic devices flown on the NASA ER-2 calibration platform. This method would also be applicable to other high altitude methods where Isc data is collected over a sufficiently large range of altitudes. An initial comparison with a four junction (4J) cell flown on the CASOLBA high altitude balloon platform showed an agreement to 0.2%

Calculation Method for Predicting AM0 Isc from High Altitude Aircraft Flight Data

High altitude aircraft have been used by by the space photovoltaic (PV) community to determine the Air Mass Zero (AM0) performance of solar cells for over fifty years. Relative to in-space measurement opportunities, these methods are generally cheaper and more readily available. The data obtained, however, must be corrected for residual atmospheric effects. This paper details the correction method currently being used for the calculation of the AM0 short-circuit current (Isc) for photovoltaic devices flown on the NASA ER-2 (Earth Resources-2) calibration platform. This method would also be applicable to any other high altitude method where Isc data is collected over a sufficiently large range of altitudes

Asymptotic reduction of a porous electrode model for lithium-ion batteries

We present a porous electrode model for lithium-ion batteries using Butler--Volmer reaction kinetics. We model lithium concentration in both the solid and fluid phase along with solid and liquid electric potential. Through asymptotic reduction, we show that the electric potentials are spatially homogeneous which decouples the problem into a series of time-dependent problems. These problems can be solved on three distinguished time scales, an early time scale where capacitance effects in the electrode dominate, a mid-range time scale where a spatial concentration gradient forms in the electrolyte, and a long-time scale where each of the electrodes saturate and deplete with lithium respectively. The solid-phase concentration profiles are linear functions of time and the electrolyte potential is everywhere zero, which allows the model to be reduced to a system of two uncoupled ordinary differential equations. Analytic and numerical results are compared with full numerical simulations and experimental discharge curves demonstrating excellent agreement.Comment: Accepted in SIAM Journal on Applied Mathematic

Effective thermal conductivity of rectangular nanowires based on phonon hydrodynamics

A mathematical model is presented for thermal transport in nanowires with rectangular cross sections. Expressions for the effective thermal conductivity of the nanowire across a range of temperatures and cross-sectional aspect ratios are obtained by solving the Guyer--Krumhansl hydrodynamic equation for the thermal flux with a slip boundary condition. Our results show that square nanowires transport thermal energy more efficiently than rectangular nanowires due to optimal separation between the boundaries. However, circular nanowires are found to be even more efficient than square nanowires due to the lack of corners in the cross section, which locally reduce the thermal flux and inhibit the conduction of heat. By using a temperature-dependent slip coefficient, we show that the model is able to accurately capture experimental data of the effective thermal conductivity obtained from Si nanowires, demonstrating that phonon hydrodynamics is a powerful framework that can be applied to nanosystems even at room temperature

Experimental simulation of closed timelike curves

Closed timelike curves are among the most controversial features of modern physics. As legitimate solutions to Einstein's field equations, they allow for time travel, which instinctively seems paradoxical. However, in the quantum regime these paradoxes can be resolved, leaving closed timelike curves consistent with relativity. The study of these systems therefore provides valuable insight into nonlinearities and the emergence of causal structures in quantum mechanics-essential for any formulation of a quantum theory of gravity. Here we experimentally simulate the nonlinear behaviour of a qubit interacting unitarily with an older version of itself, addressing some of the fascinating effects that arise in systems traversing a closed timelike curve. These include perfect discrimination of non-orthogonal states and, most intriguingly, the ability to distinguish nominally equivalent ways of preparing pure quantum states. Finally, we examine the dependence of these effects on the initial qubit state, the form of the unitary interaction and the influence of decoherence

GOLEM: an interactive graph-based gene-ontology navigation and analysis tool

BACKGROUND: The Gene Ontology has become an extremely useful tool for the analysis of genomic data and structuring of biological knowledge. Several excellent software tools for navigating the gene ontology have been developed. However, no existing system provides an interactively expandable graph-based view of the gene ontology hierarchy. Furthermore, most existing tools are web-based or require an Internet connection, will not load local annotations files, and provide either analysis or visualization functionality, but not both. RESULTS: To address the above limitations, we have developed GOLEM (Gene Ontology Local Exploration Map), a visualization and analysis tool for focused exploration of the gene ontology graph. GOLEM allows the user to dynamically expand and focus the local graph structure of the gene ontology hierarchy in the neighborhood of any chosen term. It also supports rapid analysis of an input list of genes to find enriched gene ontology terms. The GOLEM application permits the user either to utilize local gene ontology and annotations files in the absence of an Internet connection, or to access the most recent ontology and annotation information from the gene ontology webpage. GOLEM supports global and organism-specific searches by gene ontology term name, gene ontology id and gene name. CONCLUSION: GOLEM is a useful software tool for biologists interested in visualizing the local directed acyclic graph structure of the gene ontology hierarchy and searching for gene ontology terms enriched in genes of interest. It is freely available both as an application and as an applet at

Finding function: evaluation methods for functional genomic data

BACKGROUND: Accurate evaluation of the quality of genomic or proteomic data and computational methods is vital to our ability to use them for formulating novel biological hypotheses and directing further experiments. There is currently no standard approach to evaluation in functional genomics. Our analysis of existing approaches shows that they are inconsistent and contain substantial functional biases that render the resulting evaluations misleading both quantitatively and qualitatively. These problems make it essentially impossible to compare computational methods or large-scale experimental datasets and also result in conclusions that generalize poorly in most biological applications. RESULTS: We reveal issues with current evaluation methods here and suggest new approaches to evaluation that facilitate accurate and representative characterization of genomic methods and data. Specifically, we describe a functional genomics gold standard based on curation by expert biologists and demonstrate its use as an effective means of evaluation of genomic approaches. Our evaluation framework and gold standard are freely available to the community through our website. CONCLUSION: Proper methods for evaluating genomic data and computational approaches will determine how much we, as a community, are able to learn from the wealth of available data. We propose one possible solution to this problem here but emphasize that this topic warrants broader community discussion