The Stokes-Einstein Relation at Moderate Schmidt Number

The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are expected. We study these corrections computationally using a recently-developed minimally-resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The numerical data is in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.Comment: Submitte

Comparative analysis of some modeal reconstruction methods of the cornea from corneal elevation data

Purpose. A comparative study of the ability of some modal schemes to reproduce corneal shapes of varying complexity is performed, using both standard radial polynomials and the radial basis functions (RBF). Our claim is that the correct approach in the case of highly irregular corneas should combine several bases. Methods. Standard approaches of reconstruction by Zernike and other types of radial polynomials are compared with the discrete least squares fit (LSF) by the RBF in three theoretical surfaces, synthetically generated by computer algorithms in the lack of measurement noise. For the reconstruction by polynomials the maximal radial order 6 was chosen, which corresponds to the first 28 Zernike polynomials or the first 49 Bhatia-Wolf polynomials. The fit with the RBF has been carried out using a regular grid of centers. Results. The quality of fit was assessed by computing for each surface the mean square errors (MSE) of the reconstruction by LSF, measured at the same nodes where the heights were collected. Another criterion of the fitting quality used was the accuracy in recovery of the Zernike coefficients, especially in the case of incomplete data. Conclusions. The Zernike (and especially, the Bhatia-Wolf) polynomials constitute a reliable reconstruction method of a non-severely aberrated surface with a small surface regularity index (SRI). However, they fail to capture small deformations of the anterior surface of a synthetic cornea. The most promising is a combined approach that balances the robustness of the Zernike fit with the localization of the RBF

Determinants and implications of the growing scale of livestock farms in four fast-growing developing countries:

"The rapid growth in consumer demand for livestock offers an opportunity to reduce poverty among smallholder livestock farmers in the developing world. These farmers' opportunity may be threatened, however, by competition from larger-scale farms. This report assesses the potential threat, examining various forms of livestock production in Brazil, India, the Philippines, and Thailand. Findings show that the competitiveness of smallholder farms depends on the opportunity cost of family labor and farmers' ability to overcome barriers to the acquisition of production- and market-related information and assets. Pro-poor livestock development depends, therefore, on the strengthening of institutions that will help smallholders overcome the disproportionately high transaction costs in securing quality inputs and obtaining market recognition for quality outputs. These and other findings make this report a useful guide for researchers and others concerned with the opportunities and risks of smallholder livestock farming." from Authors' SummaryDeveloping countries, Economic aspects, Industrialization, Profit efficiency, Environmental externalities, Smallholder competitiveness, Livestock productivity, Livestock Industrialization, Scaling up,

Tunnelling of plane waves through a square barrier

The time evolution of plane waves in the presence of a 1-dimensional square quantum barrier is considered. Comparison is made between the cases of an infinite and a cut-off (shutter) initial plane wave. The difference is relevant when the results are applied to the analysis of the tunnelling regime. This work is focused on the analytical calculation of the time-evolved solution and highlights the contribution of the resonant (Gamow) states. PACS numbers: 11.10.Ef, 11.10.Lm, 04.60Comment: 16 page

Phase diagram of the anti-ferromagnetic xxz model in the presence of an external magnetic field

The anisotropic s=1/2 anti-ferromagnetic Heisenberg chain in the presence of an external magnetic field is studied by using the standard quantum renormalization group. We obtain the critical line of the transition from partially magnetized (PM) phase to the saturated ferromagnetic (SFM) phase. The crossover exponent between the PM phase and anti-ferromagnetic Ising (AFI) phase is evaluated. Our results show that the anisotropy(\d) term is relevant and causes crossover. These results indicate that the standard RG approach yields fairly good values for the critical points and their exponents. The magnetization curve, correlation functions and the ground state energy per site are obtained and compared with the known exact results.Comment: A LaTex file(20 pages) and 9 PS figure