Depletion potential in the infinite dilution limit

The depletion force and depletion potential between two in principle unequal "big" hard spheres embedded in a multicomponent mixture of "small" hard spheres are computed using the Rational Function Approximation method for the structural properties of hard-sphere mixtures [S. B. Yuste, A. Santos, and M. L\'opez de Haro, J. Chem. Phys. {\bf 108}, 3683 (1998)]. The cases of equal solute particles and of one big particle and a hard planar wall in a background monodisperse hard-sphere fluid are explicitly analyzed. An improvement over the performance of the Percus-Yevick theory and good agreement with available simulation results are foundComment: 10 pages, 5 figures; v2: few minor additions and reduction in the number of figures; v3: Fig. 2 corrected (see http://dx.doi.org/10.1063/1.4874639

Métodos matemáticos avanzados para científicos e ingenieros

El propósito de este libro es proporcionar una descripción sencilla y práctica de cierta clase de métodos matemáticos que son extraordinariamente útiles para científicos e ingenieros. Un modo muy efectivo de enseñar y aprender métodos matemáticos es mediante ejemplos en los que estos métodos se muestran en acción. Este procedimiento es usado en este manual, hay más de 100 ejemplos resueltos. También se incluyen más de 80 cuestiones y ejercicios sin resolver, como modo de reforzar la comprensión de lo expuesto y, en ocasiones, de provocar la reflexión del lector sobre las materias tratadas.The purpose of this book is to provide a simple description and practice of a certain class of mathematical methods that are extremely useful for scientists and engineers. A very effective way of teaching and learning mathematical methods is through examples in which these methods are shown in action. This procedure is used in this manual, there are more than 100 examples solved. Also included are more than 80 questions and exercises without resolve, as a means of strengthening the understanding of the foregoing and, sometimes, to cause the reflection of the reader on the subjects dealt with

Structural properties of fluids interacting via piece-wise constant potentials with a hard core

Publicado en: J. Chem. Phys. 139, 074505 (2013) DOI: 10.1063/1.4818601Se presentan las propiedades estructurales de fluidos cuyas moléculas interactúan a través de potenciales con un núcleo duro más dos secciones constantes de diferentes anchuras y alturas. Éstos se derivan de un desarrollo más general presentado previamente para potenciales con un núcleo duro además de ƞ constante [Condens. Matter Phys. 15, 23602 (2012)] en el que se hizo uso de un método analítico de aproximación racional-función y semi-analítico. Los resultados de casos ilustrativos que comprenden ocho diferentes combinaciones de pozos y barreras son comparadas con datos de simulación y con aquellos que se derivan de la solución numérica de las ecuaciones integrales de Percus–Yevick y cadenas superentrelazadas. Se encuentra que la aproximación racional-funcional generalmente predice una función de distribución radial más precisa que la teoría de Percus–Yevick y es comparable o incluso superior a la teoría de cadenas superentrelazadas. Esta superioridad sobre ambas teorías de la ecuación integral se pierde, sin embargo, en altas densidades, especialmente cuando aumenta la amplitud de los pozos y/o barreras.The structural properties of fluids whose molecules interact via potentials with a hard core plus two piece-wise constant sections of different widths and heights are presented. These follow from the more general development previously introduced for potentials with a hard core plus n piece-wise constant sections [Condens. Matter Phys. 15, 23602 (2012)] in which use was made of a semi-analytic rational-function approximation method. The results of illustrative cases comprising eight different combinations of wells and shoulders are compared both with simulation data and with those that follow from the numerical solution of the Percus–Yevick and hypernetted-chain integral equations. It is found that the rational-function approximation generally predicts a more accurate radial distribution function than the Percus–Yevick theory and is comparable or even superior to the hypernetted-chain theory. This superiority over both integral equation theories is lost, however, at high densities, especially as the widths of the wells and/or the barriers increase.Para Andrés Santos Reyes y Santos Bravo Yuste, este trabajo ha sido financiado por el Gobierno de España, a partir de la beca FIS2010-16587 y de la Junta de Extremadura (España) a partir de la beca GR10158. También han sido parcialmente financiados por fondos FEDER. Pedro Orea ha recibido ayuda del IMP, a partir del Molecular Engineering Progra

On a novel iterative method to compute polynomial approximations to Bessel functions of the first kind and its connection to the solution of fractional diffusion/diffusion-wave problems

We present an iterative method to obtain approximations to Bessel functions of the first kind $J_p(x)$ ($p>-1$) via the repeated application of an integral operator to an initial seed function $f_0(x)$. The class of seed functions $f_0(x)$ leading to sets of increasingly accurate approximations $f_n(x)$ is considerably large and includes any polynomial. When the operator is applied once to a polynomial of degree $s$, it yields a polynomial of degree $s+2$, and so the iteration of this operator generates sets of increasingly better polynomial approximations of increasing degree. We focus on the set of polynomial approximations generated from the seed function $f_0(x)=1$. This set of polynomials is not only useful for the computation of $J_p(x)$, but also from a physical point of view, as it describes the long-time decay modes of certain fractional diffusion and diffusion-wave problems.Comment: 14 pages, 4 figures. To be published in J. Phys. A: Math. Theo

Tocilizumab in refractory Caucasian Takayasu's arteritis: a multicenter study of 54 patients and literature review

Objective: To assess the efficacy and safety of tocilizumab (TCZ) in Caucasian patients with refractory Takayasu's arteritis (TAK) in clinical practice. Methods: A multicenter study of Caucasian patients with refractory TAK who received TCZ. The outcome variables were remission, glucocorticoid-sparing effect, improvement in imaging techniques, and adverse events. A comparative study between patients who received TCZ as monotherapy (TCZMONO) and combined with conventional disease modifying anti-rheumatic drugs (cDMARDs) (TCZCOMBO) was performed. Results: The study comprised 54 patients (46 women/8 men) with a median [interquartile range (IQR)] age of 42.0 (32.5-50.5) years. TCZ was started after a median (IQR) of 12.0 (3.0-31.5) months since TAK diagnosis. Remission was achieved in 12/54 (22.2%), 19/49 (38.8%), 23/44 (52.3%), and 27/36 (75%) patients at 1, 3, 6, and 12 months, respectively. The prednisone dose was reduced from 30.0 mg/day (12.5-50.0) to 5.0 (0.0-5.6) mg/day at 12 months. An improvement in imaging findings was reported in 28 (73.7%) patients after a median (IQR) of 9.0 (6.0-14.0) months. Twenty-three (42.6%) patients were on TCZMONO and 31 (57.4%) on TCZCOMBO: MTX (n = 28), cyclosporine A (n = 2), azathioprine (n = 1). Patients on TCZCOMBO were younger [38.0 (27.0-46.0) versus 45.0 (38.0-57.0)] years; difference (diff) [95% confidence interval (CI) = -7.0 (-17.9, -0.56] with a trend to longer TAK duration [21.0 (6.0-38.0) versus 6.0 (1.0-23.0)] months; diff 95% CI = 15 (-8.9, 35.5), and higher c-reactive protein [2.4 (0.7-5.6) versus 1.3 (0.3-3.3)] mg/dl; diff 95% CI = 1.1 (-0.26, 2.99). Despite these differences, similar outcomes were observed in both groups (log rank p = 0.862). Relevant adverse events were reported in six (11.1%) patients, but only three developed severe events that required TCZ withdrawal. Conclusion: TCZ in monotherapy, or combined with cDMARDs, is effective and safe in patients with refractory TAK of Caucasian origin.Funding: This work was partially supported by RETICS Programs, RD08/0075 (RIER), RD12/0009/0013 and RD16/0012 from “Instituto de Salud Carlos III” (ISCIII) (Spain)

Phase portrait and field directions of two-dimensional linear systems of ODEs

Educação Superior::Ciências Exatas e da Terra::MatemáticaThis Demonstration plots the phase portrait (or phase plane) and the vector field of directions around the fixed point (0,0) of the two-dimensional linear system of first-order ordinary differential equations x'=a1x+b1y y'=a2x+b2y. Drag the four locators to see the trajectories of four solutions of the system that go through them. The position of these points can be chosen by clicking on wherever you like inside the graphics. Thick orange lines parallel to the eigenvectors are shown if the eigenvalues of the system are rea