Finite-time blowup for a complex Ginzburg–Landau equation with linear driving

In this paper, we consider the complex Ginzburg–Landau equation ${u_t = e^{i\theta} [\Delta u + |u|^\alpha u] + \gamma u}$ on ${\mathbb{R}^N}$ , where ${\alpha > 0,\,\gamma \in \mathbb{R}}$ and ${-\pi /2 < \theta < \pi /2}$ . By convexity arguments, we prove that, under certain conditions on ${\alpha,\theta,\gamma}$ , a class of solutions with negative initial energy blows up in finite time.     

Metric complements of overt closed sets

We show that the set of points of an overt closed subspace of a metric completion of a Bishop‐locally compact metric space is located. Consequently, if the subspace is, moreover, compact, then its collection of points is Bishop‐compact. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Synthesis of thermosensitive guar‐based hydrogels with tunable physico‐chemical properties by click chemistry

Thermosensitive guar‐based hydrogels are obtained in water solutions by copper‐catalyzed 1,3‐dipolar cycloaddition between alkyne‐functionalized guars and α,ω‐diazido‐poly[(ethylene glycol)‐co‐(propylene glycol)]. Characterization by TGA, HR‐MAS ¹H NMR, and rheology have shown that hydrogels with tunable physico‐chemical properties, such as crosslinking density, viscoelasticity, swelling ratio, and so forth, could be obtained by varying the guar molar mass, the degree of alkyne functionality, the guar/crosslinker weight ratio, and the reaction temperature. Based on swelling measurements, it has been shown that the thermal sensitiveness of guar‐based hydrogels is fast, reversible, and intimately related to the weight fraction of the thermosensitive crosslinker in the network. Finally, the monitoring of doxorubicin hydrochloride release has demonstrated the potential of these hydrogels as temperature‐dependent drug release devices. The robust, efficient, and orthogonal approach described herein represents a general approach towards the development of well‐controlled guar‐based hydrogels using α,ω‐diazido crosslinkers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2733–2742, 2010     

Identification of Intermediates in Zeolite‐Catalyzed Reactions by In Situ UV/Vis Microspectroscopy and a Complementary Set of Molecular Simulations

The optical absorption properties of (poly)aromatic hydrocarbons occluded in a nanoporous environment were investigated by theoretical and experimental methods. The carbonaceous species are an essential part of a working catalyst for the methanol‐to‐olefins (MTO) process. In situ UV/Vis microscopy measurements on methanol conversion over the acidic solid catalysts H‐SAPO‐34 and H‐SSZ‐13 revealed the growth of various broad absorption bands around 400, 480, and 580 nm. The cationic nature of the involved species was determined by interaction of ammonia with the methanol‐treated samples. To determine which organic species contribute to the various bands, a systematic series of aromatics was analyzed by means of time‐dependent density functional theory (TDDFT) calculations. Static gas‐phase simulations revealed the influence of structurally different hydrocarbons on the absorption spectra, whereas the influence of the zeolitic framework was examined by using supramolecular models within a quantum mechanics/molecular mechanics framework. To fully understand the origin of the main absorption peaks, a molecular dynamics (MD) study on the organic species trapped in the inorganic host was essential. During such simulation the flexibility is fully taken into account and the effect on the UV/Vis spectra is determined by performing TDDFT calculations on various snapshots of the MD run. This procedure allows an energy absorption scale to be provided and the various absorption bands determined from in situ UV/Vis spectra to be assigned to structurally different species.     

Finite Volume schemes on unstructured grids for non-local models: Application to the simulation of heat transport in plasmas

In the so-called Spitzer–Härm regime, equations of plasma physics reduce to a nonlinear parabolic equation for the electronic temperature. Coming back to the derivation of this limiting equation through hydrodynamic regime arguments, one is led to construct a hierarchy of models where the heat fluxes are defined through a non-local relation which can be reinterpreted as well by introducing coupled diffusion equations. We address the question of designing numerical methods to simulate these equations. The basic requirement for the scheme is to be asymptotically consistent with the Spitzer–Härm regime. Furthermore, the constraints of physically realistic simulations make the use of unstructured meshes unavoidable. We develop a Finite Volume scheme, based on Vertex-Based discretization, which reaches these objectives. We discuss on numerical grounds the efficiency of the method, and the ability of the generalized models in capturing relevant phenomena missed by the asymptotic problem.     

Microwave-assisted synthesis of α-ethoxycarbamates

An efficient and reproducible synthesis of various α-ethoxycarbamates is described via a microwave heating mode. Compared to the thermal process, the microwave dielectric heating induces a dramatic reduction of the reaction time and the improvement of the yields. The reaction is general since applicable to aromatic and aliphatic aldehydes with various primary amines. Several examples involving chiral aldehydes have also been considered.     

Adsorption‐Induced Restructuring and Early Stages of Carbon‐Nanotube Growth on Ni Nanoparticles

Carbon adsorption on various Ni surfaces is investigated as a function of coverage via a combination of first‐principles simulations and field emission microscope experiments. It is found that carbon can be efficiently stored as subsurface carbides, but with different energetics on differently oriented surfaces depending on their compactness and density of adsorption sites. In the resulting morphological reshaping, {113} facets are predicted to grow at the expense of {111} and {100} facets, in excellent agreement with experimental observations. Moreover, at high coverage on the {113} surface the carbon adsorption energy passes through a maximum after which a structural crossover is realized such that carbon atoms tend to ascend to the surface to form one‐dimensional chains (which are the precursors of graphitic nanostructures). This rationalizes the experimental observation of an incubation time between carbon storage and the beginning of catalytic growth, and provides insight into the early stages (nucleation mechanism) of carbon nanotubes on Ni nanoparticles.