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

Entropy driven key-lock assembly

The effective interaction between a sphere with an open cavity (lock) and a spherical macroparticle (key), both immersed in a hard sphere fluid, is studied by means of Monte Carlo simulations. As a result, a 2d map of the key-lock effective interaction potential is constructed, which leads to the proposal of a self-assembling mechanism: there exists trajectories through which the key-lock pair could assemble avoiding trespassing potential barriers. Hence, solely the entropic contribution can induce their self-assembling even in the absence of attractive forces. This study points out the solvent contribution within the underlying mechanisms of substrate-protein assembly/disassembly processes, which are important steps of the enzyme catalysis and protein mediated transport

High resolution spectroscopy of the BCD galaxy Haro 15:I. Internal kinematics

Using echelle spectroscopy, obtained at Las Campanas Observatory, we present a detailed study of the internal kinematics of the nebular material in multiple knots of the blue compact dwarf galaxy Haro 15. A detailed analysis of the complex emission line profiles show the presence of an underlying broad component in almost all knots, and the brightest star-forming region shows unmistakable signs for the presence of two distinct narrow kinematical components. We also study the information that our analysis provides regarding the motion of the individual knots in the Haro 15 galaxy potential, confirming that they follow galactic rotation. Finally, we examine the relation between their velocity dispersion and luminosity, finding that almost all knots follow the relation for virialised systems. This holds for the strong narrow components identified in complex fits and for single profile fits, although the latter show a flatter slope. In agreement with previous findings, in this paper we show that the existence of multiple kinematical components among massive starbursts cannot be overlooked, as it has a noticeable effect on any subsequent analysis that relies on basic parameters.Comment: 12 pages, 21 figure

Rescue of endemic states in interconnected networks with adaptive coupling

We study the Susceptible-Infected-Susceptible model of epidemic spreading on two layers of networks interconnected by adaptive links, which are rewired at random to avoid contacts between infected and susceptible nodes at the interlayer. We find that the rewiring reduces the effective connectivity for the transmission of the disease between layers, and may even totally decouple the networks. Weak endemic states, in which the epidemics spreads when the two layers are interconnected but not in each layer separately, show a transition from the endemic to the healthy phase when the rewiring overcomes a threshold value that depends on the infection rate, the strength of the coupling and the mean connectivity of the networks. In the strong endemic scenario, in which the epidemics is able to spread on each separate network -and therefore on the interconnected system- the prevalence in each layer decreases when increasing the rewiring, arriving to single network values only in the limit of infinitely fast rewiring. We also find that rewiring amplifies finite-size effects, preventing the disease transmission between finite networks, as there is a non zero probability that the epidemics stays confined in only one network during its lifetime

Extraction of Aromatic Compounds from Their Mixtures with Alkanes: From Ternary to Quaternary (or Higher) Systems

Ionic liquids have been proposed as separation agents for liquid extraction of aromatic compounds from their mixtures with alkanes, with the aim of improving the separation process and replacing conventional organic solvents. A significant number of experimental liquid-liquid equilibrium data for ternary system alkane + aromatic compound + ionic liquid can be found in literature; however there are few data for quaternary or higher systems involving more than one aliphatic compound, several aromatic compounds or a mixture of ionic liquids as separation agent. These data are also necessary because molecular interactions between the compounds in the mixture can modify the affinity of the solvent for the aromatic compound of interest. In this chapter we review the published data involving more than three components, and we present new liquid-liquid equilibrium data for the quaternary systems heptane + cyclohexane + toluene +1-ethyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}imide and heptane + cyclohexane + toluene + 1-hexyl-3-methylimidazolium bis{(trifluoromethyl)sulfonyl}imide

Ion pairing in model electrolytes: A study via three particle correlation functions

A novel integral equations approach is applied for studying ion pairing in the restricted primitive model (RPM) electrolyte, i. e., the three point extension (TPE) to the Ornstein-Zernike integral equations. In the TPE approach, the three-particle correlation functions $g^{[3]}({\bf r}_{1},{\bf r}_{2},{\bf r}_{3})$ are obtained. The TPE results are compared to molecular dynamics (MD) simulations and other theories. Good agreement between TPE and MD is observed for a wide range of parameters, particularly where standard integral equations theories fail, i. e., low salt concentration and high ionic valence. Our results support the formation of ion pairs and aligned ion complexes.Comment: 43 pages (including 18 EPS figs) - RevTeX 4 - J. Chem. Phys. (in press

Estudio petrológico de la "Unidad Salina" de la Cuenca del Tajo

Se presenta un esquema fotogeológico de los principales afloramien tos de Ja Unidad Salina y un mapa de distribución de las facies evaporíticas. Se estudia la petrografía de la Unidad Salina de la Cuenca del Tajo, que presenta una interesante paragénesis de sa les sódicas. Se describen estructu ras de deformación en facies anhidrítico - magnesíticas, diferentes formas de cristales de anhidrita (idiomorfos, manojos (asciculares, cristales en " lazo" ... ). texturas seudomórficas en yeso. texturas primarias y secundarias en glauberita y halita. Se analizan también las diferentes facies texturales polihalíticas, entre las que cabe destacar las esferulíticas y las "afieltradas", así como las facies thenardíticas. De todo ello se deduce una secuencia mineralógica

Kinematics of gas and stars in circumnuclear star-forming regions of early type spirals

(Abbr.) We present high resolution (R~20000) spectra in the blue and the far red of cicumnuclear star-forming regions (CNSFRs) in three early type spirals (NGC3351, NGC2903 and NGC3310) which have allowed the study of the kinematics of stars and ionized gas in these structures and, for the first time, the derivation of their dynamical masses for the first two. In some cases these regions, about 100 to 150 pc in size, are seen to be composed of several individual star clusters with sizes between 1.5 and 4.9 pc estimated from Hubble Space Telescope (HST) images. The stellar dispersions have been obtained from the Calcium triplet (CaT) lines at $\lambda\lambda$ 8494,8542,8662 \AA, while the gas velocity dispersions have been measured by Gaussian fits to the H$\beta$ and [OIII] $\lambda\lambda$ 5007 \AA lines on the high dispersion spectra. Values of the stellar velocity dispersions are between 30 and 68 km/s. We apply the virial theorem to estimate dynamical masses of the clusters, assuming that systems are gravitationally bounded and spherically symmetric, and using previously measured sizes. The measured values of the stellar velocity dispersions yield dynamical masses of the order of 10$^7$ to 10$^8$ solar masses for the whole CNSFRs. Stellar and gas velocity dispersions are found to differ by about 20 to 30 km/s with the H$\beta$ emission lines being narrower than both the stellar lines and the [OIII] $\lambda\lambda$ 5007 \AA lines. The twice ionized oxygen, on the other hand, shows velocity dispersions comparable to those shown by stars, in some cases, even larger. We have found indications of the presence of two different kinematical components in the ionized gas of the regions...Comment: 4 pages, proceeding of the meeting "Young massive star clusters - Initial conditions and environments", Granada, Spain, 200

Evolution of the spatio-temporal distribution of Xylotrechus arvicola (Olivier) (Coleoptera, Cerambycidae) in La Rioja vineyard (Spain)

Xylotrechus arvicola (Olivier) (Coleoptera, Cerambycidae) is a polyphagous species. Its larvae can be found feeding on different wooden cultivars and wild trees. Since 1990, this pest has become an important sanitary problem affecting vineyards in northern and central Spain (2000-2008). A study based on the distribution of the number of exit holes perforated by adults in the vinestocks was carried out for 9 years in a plot located in La Rioja wine producing region (Spain). The percentage of affected plants grew each year, from 51 % in 2004 to a level of 96 % in 2008. In 2005, dead vines began to appear with damage caused by the insect. In 2008 it increased to 17 % of the vines. This data indicated a very heavy attack of the insect which is becoming a very serious pest.The number of exit holes is directly related to the number of affected vinestocks and also dead plants. The spatial distribution of the holes of X. arvicola was studied using Taylor´s Potential Law and Iwao´s regression, as well as elaborating maps of population density. Statistical techniques indicated a uniform distribution of the pest in the sampling plot. During the cited period, several aggregation centers could be observed with a long term spatio-temporal stability using the Cramér-Von Mises test.