Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models

Let be a nonnegative, smooth function with , supported in , symmetric, , and strictly increasing in . We consider the Neumann boundary value problem for a nonlocal, nonlinear operator that is similar to the porous medium, and we study the equation

We prove existence and uniqueness of solutions and a comparison principle. We find the asymptotic behaviour of the solutions as : they converge to the mean value of the initial data. Next, we consider a discrete version of the above problem. Under suitable hypotheses we prove that the discrete model has properties analogous to the continuous one. Moreover, solutions of the discrete problem converge to the continuous ones when the mesh parameter goes to zero. Finally, we perform some numerical experiments.

     

Generic Fredholm alternative-type results for the one dimensional p-Laplacian

In this paper we give a generic necessary and sufficient condition for the solvability of? Received November 1999     

Nature of C60 and C70 fullerene encapsulation in a porphyrin- and metalloporphyrin-based cage: Insights from dispersion-corrected density functional theory calculations

The search for efficient synthetic hosts able to encapsulate fullerenes has attracted attention with regard to the purification and formation of ordered supramolecular architectures. This study of a porphyrin-based cage as an extension of the well-described ExCage⁶⁺ and BlueCage⁶⁺, involving viologen as sidearms, provides an interesting scenario where the oblate C₇₀ fullerene is preferred in comparison to the spherical C₆₀. Our results expose the nature of the fullerene-cage interaction involving ∼50% of dispersion-type interactions evidencing the strong π⋯π surface stacking, with a complementary contribution by the electrostatic and orbital polarization character produced by a charge reorganization with a charge accumulation facing the porphyrin macrocycles and a charge depletion along the equator formed by the viologens sidearms. Interestingly, the central N₄H₂ ring from each porphyrin contributes to the dispersion term via N-H⋯π interactions, which is decreased when the metallate N₄Zn is evaluated. Thus, the formation of stable and selective fullerene encapsulation can be achieved by taking into account two main driving forces, namely, (a) the extension of the π⋯π and X-H⋯π stacking surface and (b) charge reorganization over the fullerene surfaces, which can be used to control fine tuning of the encapsulation thanks to the introduction of more electron-deficient and electron-rich groups within the host cage.     

Synthesis and catalytic properties of nanoparticulate intermetallic Ga-Pd compounds

A two-step synthesis for the preparation of single-phase and nanoparticulate GaPd and GaPd(2) by coreduction of ionic metal-precursors with LiHBEt(3) in THF without additional stabilizers is described. The coreduction leads initially to the formation of Pd nanoparticles followed by a Pd-mediated reduction of Ga(3+) on their surfaces, requiring an additional annealing step. The majority of the intermetallic particles have diameters of 3 and 7 nm for GaPd and GaPd(2), respectively, and unexpected narrow size distributions as determined by disk centrifuge measurements. The nanoparticles have been characterized by XRD, TEM, and chemical analysis to ensure the formation of the intermetallic compounds. Unsupported nanoparticles possess high catalytic activity while maintaining the excellent selectivity of the ground bulk materials in the semihydrogenation of acetylene. The activity could be further increased by depositing the particles on α-Al(2)O(3).     

Propane dehydrogenation over extra-framework In(i) in chabazite zeolites

Indium on silica, alumina and zeolite chabazite (CHA), with a range of In/Al ratios and Si/Al ratios, have been investigated to understand the effect of the support on indium speciation and its corresponding influence on propane dehydrogenation (PDH). It is found that In₂O₃ is formed on the external surface of the zeolite crystal after the addition of In(NO₃)₃ to H-CHA by incipient wetness impregnation and calcination. Upon reduction in H₂ gas (550 °C), indium displaces the proton in Brønsted acid sites (BASs), forming extra-framework In⁺ species (In-CHA). A stoichiometric ratio of 1.5 of formed H₂O to consumed H₂ during H₂ pulsed reduction experiments confirms the indium oxidation state of +1. The reduced indium is different from the indium species observed on samples of 10In/SiO₂, 10In/Al₂O₃ (i.e., 10 wt% indium) and bulk In₂O₃, in which In₂O₃ was reduced to In(0), as determined from the X-ray diffraction patterns of the product, H₂ temperature-programmed reduction (H₂-TPR) profiles, pulse reactor investigations and in situ transmission FTIR spectroscopy. The BASs in H-CHA facilitate the formation and stabilization of In⁺ cations in extra-framework positions, and prevent the deep reduction of In₂O₃ to In(0). In⁺ cations in the CHA zeolite can be oxidized with O₂ to form indium oxide species and can be reduced again with H₂ quantitatively. At comparable conversion, In-CHA shows better stability and C₃H₆ selectivity (∼85%) than In₂O₃, 10In/SiO₂ and 10In/Al₂O₃, consistent with a low C₃H₈ dehydrogenation activation energy (94.3 kJ mol⁻¹) and high C₃H₈ cracking activation energy (206 kJ mol⁻¹) in the In-CHA catalyst. A high Si/Al ratio in CHA seems beneficial for PDH by decreasing the fraction of CHA cages containing multiple In⁺ cations. Other small-pore zeolite-stabilized metal cation sites could form highly stable and selective catalysts for this and facilitate other alkane dehydrogenation reactions.

Indium-containing chabazite zeolites show better stability and C₃H₆ selectivity for propane dehydrogenation than In₂O₃, In/SiO₂ and In/Al₂O₃. Extra-framework In⁺ is identified as the stable active site upon reduction of an impregnated sample.     

Direct Arylation in the Presence of Palladium Pincer Complexes

Direct arylation is an atom-economical alternative to more established procedures such as Stille, Suzuki or Negishi arylation reactions. In comparison with other palladium sources and ligands, the use of palladium pincer complexes as catalysts or pre-catalysts for direct arylation has resulted in improved efficiency, higher reaction yields, and advantageous reaction conditions. In addition to a revision of the literature concerning intra- and intermolecular direct arylation reactions performed in the presence of palladium pincer complexes, the role of these remarkably active catalysts will also be discussed.     

The effect of the pH on the interaction of L‐arginine with colloidal silver nanoparticles. A Raman and SERS study

Raman and surface enhanced Raman scattering (SERS) spectroscopies were used to study the pH effect (7 to 9) on the interaction of arginine (Arg) with colloidal Ag nanoparticles (AgNps). A new methodology was implemented in order to obtain reproducible SERS spectra in solution. The dependence of the Arg concentration on the stability of the AgNps is discussed. A pH increasing of the colloidal solution to the limits of the Arg pKa₂ value induces a preferential and stable Arg–metal interaction. ξ potential measurements of the Arg–AgNps system at different pH conditions studied provide information about the Arg–AgNps interaction; the pH increasing favors the interaction. SERS spectra at pH 7 indicate that the molecule interacts with the Ag surface only through the guanidinium fragment. By increasing the pH to 9, the molecule adopts a new conformation on the surface; the metal–analyte interaction is verified through the guanidinium, carboxylate and the aliphatic moieties. In addition, theoretical calculations performed by using the extended Hückel method for a model of Arg interacting with an Ag surface support the observed SERS results. Copyright © 2013 John Wiley & Sons, Ltd.     

Is it me or not me? Modulation of perceptual-motor awareness and visuomotor performance by mindfulness meditation

ABSTRACT: BACKGROUND: Attribution of agency involves the ability to distinguish our own actions and their sensory consequences which are self-generated from those generated by external agents. There are several pathological cases in which motor awareness is dramatically impaired. On the other hand, awareness-enhancement practices like tai-chi and yoga are shown to improve perceptual-motor awareness. Meditation is known to have positive impacts on perception, attention and consciousness itself, but it is still unclear how meditation changes sensorimotor integration processes and awareness of action. The aim of this study was to investigate how visuomotor performance and self-agency is modulated by mindfulness meditation. This was done by studying meditators' performance during a conflicting reaching task, where the congruency between actions and their consequences is gradually altered. This task was presented to novices in meditation before and after an intensive 8 weeks mindfulness meditation training (MBSR). The data of this sample was compared to a group of long-term meditators and a group of healthy non-meditators. RESULTS: Mindfulness resulted in a significant improvement in motor control during perceptual-motor conflict in both groups. Novices in mindfulness demonstrated a strongly increased sensitivity to detect external perturbation after the MBSR intervention. Both mindfulness groups demonstrated a speed/accuracy trade-off in comparison to their respective controls. This resulted in slower and more accurate movements. CONCLUSIONS: Our results suggest that mindfulness meditation practice is associated with slower body movements which in turn may lead to an increase in monitoring of body states and optimized re-adjustment of movement trajectory, and consequently to better motor performance. This extended conscious monitoring of perceptual and motor cues may explain how, while dealing with perceptual-motor conflict, improvement in motor control goes beyond the mere increase of movement time. The reduction of detection threshold in the MBSR group is also likely due to the enhanced monitoring of these processes. Our findings confirmed our assumptions about the positive effect of mindfulness on perceptual-motor integration processes.     

Adaptive numerical schemes for a parabolic problem with blow-up

In this paper we present adaptive procedures for the numericalstudy of positive solutions of the following problem: u_t = u_xx (x, t) (0, 1) x [0, T), u_x(0, t) = 0 t [0, T), u_x(1, t) = u^p(1, t) t [0, T), u(x, 0) = u₀(x) x (0, 1), with p > 1. We describe two methods. The first one refinesthe mesh in the region where the solution becomes bigger ina precise way that allows us to recover the blow-up rate andthe blow-up set of the continuous problem. The second one combinesthe ideas used in the first one with moving mesh methods andmoves the last points when necessary. This scheme also recoversthe blow-up rate and set. Finally, we present numerical experimentsto illustrate the behaviour of both methods.