2,210 research outputs found

    Computational science and re-discovery: open-source implementations of ellipsoidal harmonics for problems in potential theory

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    We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this article, we suggest two possible reasons for the paucity relative to spherical harmonics. The first is essentially historical---ellipsoidal harmonics developed during the late 19th century and early 20th, when it was found that only the lowest-order harmonics are expressible in closed form. Each higher-order term requires the solution of an eigenvalue problem, and tedious manual computation seems to have discouraged applications and theoretical studies. The second explanation is practical: even with modern computers and accurate eigenvalue algorithms, expansions in ellipsoidal harmonics are significantly more challenging to compute than those in Cartesian or spherical coordinates. The present implementations reduce the "barrier to entry" by providing an easy and free way for the community to begin using ellipsoidal harmonics in actual research. We demonstrate our implementation using the specific and physiologically crucial problem of how charged proteins interact with their environment, and ask: what other analytical tools await re-discovery in an era of inexpensive computation?Comment: 25 pages, 3 figure

    Stationary Regime of Random Resistor Networks Under Biased Percolation

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    The state of a 2-D random resistor network, resulting from the simultaneous evolutions of two competing biased percolations, is studied in a wide range of bias values. Monte Carlo simulations show that when the external current II is below the threshold value for electrical breakdown, the network reaches a steady state with a nonlinear current-voltage characteristic. The properties of this nonlinear regime are investigated as a function of different model parameters. A scaling relation is found between /0/_0 and I/I0I/I_0, where is the average resistance, 0_0 the linear regime resistance and I0I_0 the threshold value for the onset of nonlinearity. The scaling exponent is found to be independent of the model parameters. A similar scaling behavior is also found for the relative variance of resistance fluctuations. These results compare well with resistance measurements in composite materials performed in the Joule regime up to breakdown.Comment: 9 pages, revtex, proceedings of the Merida Satellite Conference STATPHYS2

    An agent-based model to rural-urban migration analysis

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    In this paper we analyze the rural-urban migration phenomena as it is usually observed in economies which are in the early stages of industrialization. The analysis is conducted by means of a statistical mechanics approach which builds a computational agent-based model. Agents are placed on a lattice and the connections among them are described via an Ising like model. Simulations on this computational model show some emergent properties that are common in developing economies, such as a transitional dynamics characterized by continuous growth of urban population, followed by the equalization of expected wages between rural and urban sectors (Harris-Todaro equilibrium condition), urban concentration and increasing of per capita income.Comment: 16 pages, 9 figure

    The detection of patients at risk of gastrointestinal toxicity during pelvic radiotherapy by electronic nose and FAIMS : a pilot study

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    It is well known that the electronic nose can be used to identify differences between human health and disease for a range of disorders. We present a pilot study to investigate if the electronic nose and a newer technology, FAIMS (Field Asymmetric Ion Mobility Spectrometry), can be used to identify and help inform the treatment pathway for patients receiving pelvic radiotherapy, which frequently causes gastrointestinal side-effects, severe in some. From a larger group, 23 radiotherapy patients were selected where half had the highest levels of toxicity and the others the lowest. Stool samples were obtained before and four weeks after radiotherapy and the volatiles and gases emitted analysed by both methods; these chemicals are products of fermentation caused by gut microflora. Principal component analysis of the electronic nose data and wavelet transform followed by Fisher discriminant analysis of FAIMS data indicated that it was possible to separate patients after treatment by their toxicity levels. More interestingly, differences were also identified in their pre-treatment samples. We believe these patterns arise from differences in gut microflora where some combinations of bacteria result to give this olfactory signature. In the future our approach may result in a technique that will help identify patients at “high risk” even before radiation treatment is started

    Mathematical Analysis of the BIBEE Approximation for Molecular Solvation: Exact Results for Spherical Inclusions

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    We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to Generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBϵ\epsilon theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements.Comment: 33 pages, 5 figure

    Quantitative relations between corruption and economic factors

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    We report quantitative relations between corruption level and economic factors, such as country wealth and foreign investment per capita, which are characterized by a power law spanning multiple scales of wealth and investments per capita. These relations hold for diverse countries, and also remain stable over different time periods. We also observe a negative correlation between level of corruption and long-term economic growth. We find similar results for two independent indices of corruption, suggesting that the relation between corruption and wealth does not depend on the specific measure of corruption. The functional relations we report have implications when assessing the relative level of corruption for two countries with comparable wealth, and for quantifying the impact of corruption on economic growth and foreign investments.Comment: 10 pages, 9 figure
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