Analysis of a chemo-repulsion model with nonlinear production: The continuous problem and unconditionally energy stable fully discrete schemes

We consider the following repulsive-productive chemotaxis model: Let $p\in (1,2)$, find $u \geq 0$, the cell density, and $v \geq 0$, the chemical concentration, satisfying \begin{equation}\label{C5:Am} \left\{ \begin{array} [c]{lll} \partial_t u - \Delta u - \nabla\cdot (u\nabla v)=0 \ \ \mbox{in}\ \Omega,\ t>0,\\ \partial_t v - \Delta v + v = u^p \ \ \mbox{in}\ \Omega,\ t>0, \end{array} \right. \end{equation} in a bounded domain $\Omega\subseteq \mathbb{R}^d$, $d=2,3$. By using a regularization technique, we prove the existence of solutions of this problem. Moreover, we propose three fully discrete Finite Element (FE) nonlinear approximations, where the first one is defined in the variables $(u,v)$, and the second and third ones by introducing ${\boldsymbol\sigma}=\nabla v$ as an auxiliary variable. We prove some unconditional properties such as mass-conservation, energy-stability and solvability of the schemes. Finally, we compare the behavior of the schemes throughout several numerical simulations and give some conclusions.Comment: arXiv admin note: substantial text overlap with arXiv:1807.0111

Chiral transition-metal complexes as Brønsted-acid catalysts for the asymmetric Friedel-Crafts hydroxyalkylation of indoles.

The Friedel-Crafts reaction between 3,3,3-trifluoropyruvates and indoles is efficiently catalysed by the iridium complex [(η5-C 5Me5)Ir{(R)-Prophos}(H2O)][SbF 6]2 (1) with up to 84% ee. Experimental data and theoretical calculations support a mechanism involving the Brønsted-acid activation of the pyruvate carbonyl by the protons of the coordinated water molecule in 1. Water is not dissociated during the process and, therefore, the catalytic reaction occurs with no direct interaction between the substrates and the metal. This journal is © the Partner Organisations 2014.The authors acknowledge the Ministerio de Economía y Competitividad (MINECO, Grants CTQ2006-03030/BQU, CTQ2009-10303/BQU, CTQ2011-27033 and Consolider Ingenio 2010 CSD2006-003), Gobierno de Aragón (Grupo Consolidado: Catálisis Homogénea Enantioselectiva), Generalitat de Catalunya (2009SGR0259) and the ICIQ foundation for financial support. A. S. and R. R. acknowledge MINECO for predoctoral fellowships. S. D.-G. acknowledges MINECO for a “Torres Quevedo” contract.Peer Reviewe

1/fα1/f^\alpha noise and integrable systems

An innovative test for detecting quantum chaos based on the analysis of the spectral fluctuations regarded as a time series has been recently proposed. According to this test, the fluctuations of a fully chaotic system should exhibit 1/f noise, whereas for an integrable system this noise should obey the 1/f^2 power law. In this letter, we show that there is a family of well-known integrable systems, namely spin chains of Haldane-Shastry type, whose spectral fluctuations decay instead as 1/f^4. We present a simple theoretical justification of this fact, and propose an alternative characterization of quantum chaos versus integrability formulated directly in terms of the power spectrum of the spacings of the unfolded spectrum.Comment: 5 pages, 3 figures, RevTe

Hexavalent Chromium Removal by a Paecilomyces sp. Fungal Strain Isolated from Environment

A resistant and capable fungal strain in removing hexavalent chromium was isolated from an environment near of Chemical Science Faculty, located in the city of San Luis Potosí, Mexico. The strain was identified as Paecilomyces sp., by macro- and microscopic characteristics. Strain resistance of the strain to high Cr (VI) concentrations and its ability to reduce chromium were studied. When it was incubated in minimal medium with glucose, another inexpensive commercial carbon source like unrefined and brown sugar or glycerol, in the presence of 50 mg/L of Cr (VI), the strain caused complete disappearance of Cr (VI), with the concomitant production of Cr (III) in the growth medium after 7 days of incubation, at 28°C, pH 4.0, 100 rpm, and an inoculum of 38 mg of dry weight. Decrease of Cr (VI) levels from industrial wastes was also induced by Paecilomyces biomass. These results indicate that reducing capacity of chromate resistant filamentous fungus Cr (VI) could be useful for the removal of Cr (VI) pollution