Structural Stability of Discontinuous Galerkin Schemes

The goal of this work is to determine classes of traveling solitary wave solutions for a differential approximation of a discontinuous Galerkin finite difference scheme by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solutions of the original continuous equations. This paper extends our previous work about classical schemes to discontinuous Galerkin schemes (David and Sagaut in Chaos Solitons Fractals 41(4):2193?C2199, 2009; Chaos Solitons Fractals 41(2):655?C660, 2009).     

A finite‐volume scheme for the multidimensional quantum drift‐diffusion model for semiconductors

A finite‐volume scheme for the stationary unipolar quantum drift‐diffusion equations for semiconductors in several space dimensions is analyzed. The model consists of a fourth‐order elliptic equation for the electron density, coupled to the Poisson equation for the electrostatic potential, with mixed Dirichlet‐Neumann boundary conditions. The numerical scheme is based on a Scharfetter‐Gummel type reformulation of the equations. The existence of a sequence of solutions to the discrete problem and its numerical convergence to a solution to the continuous model are shown. Moreover, some numerical examples in two space dimensions are presented. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1483–1510, 2011     

Investigation of the interface in silica-encapsulated liposomes by combining solid state NMR and first principles calculations

In the context of nanomedicine, liposils (liposomes and silica) have a strong potential for drug storage and release schemes: such materials combine the intrinsic properties of liposome (encapsulation) and silica (increased rigidity, protective coating, pH degradability). In this work, an original approach combining solid state NMR, molecular dynamics, first principles geometry optimization, and NMR parameters calculation allows the building of a precise representation of the organic/inorganic interface in liposils. {(1)H-(29)Si}(1)H and {(1)H-(31)P}(1)H Double Cross-Polarization (CP) MAS NMR experiments were implemented in order to explore the proton chemical environments around the silica and the phospholipids, respectively. Using VASP (Vienna Ab Initio Simulation Package), DFT calculations including molecular dynamics, and geometry optimization lead to the determination of energetically favorable configurations of a DPPC (dipalmitoylphosphatidylcholine) headgroup adsorbed onto a hydroxylated silica surface that corresponds to a realistic model of an amorphous silica slab. These data combined with first principles NMR parameters calculations by GIPAW (Gauge Included Projected Augmented Wave) show that the phosphate moieties are not directly interacting with silanols. The stabilization of the interface is achieved through the presence of water molecules located in-between the head groups of the phospholipids and the silica surface forming an interfacial H-bonded water layer. A detailed study of the (31)P chemical shift anisotropy (CSA) parameters allows us to interpret the local dynamics of DPPC in liposils. Finally, the VASP/solid state NMR/GIPAW combined approach can be extended to a large variety of organic-inorganic hybrid interfaces.     

OH�� Radical Production Induces Direct Enhancement of the Amylo?d �� Protein/Chondroitin Sulfate Binding: Inhibition by Potentially Radical Scavengers, a Biochromatographic and Thermodynamic Model

??-Amyloid (A??) is a major component of the senile plaques characteristic of Alzheimer disease (AD). Chondroitin sulfate (CS) and glycoaminoglycan (GAG) are also localized throughout the senile plaques in AD. In previous studies, the interaction of the A?? protein with CS immobilized on a chromatographic support and the role of aluminum and copper cations was studied using a molecular chromatographic approach [1, 2]. Here, we demonstrated the direct implication of OH· radical formation on this binding via a novel analytical procedure. The binding of A?? amyloid on CS was accompanied by an OH· radical uptake. The A?¨CCS complex was stabilized by the OH· radical via the creation of about one to two hydrogen bonds. The addition in the medium of a radical scavenger allowed decreasing the A??/CS association and thus confirmed the positive role of these compounds in amyloidosis.     

New Triterpenoid and Ergostane Glycosides from the Leaves of Hydrocotyle umbellata L.

Two new triterpenoid glycosides, together with two new ergostane glycosides, umbellatosides A–D ( 1 – 4 , resp.), have been isolated from the leaves of Hydrocotyle umbellata L. Their structures were established by 2D‐NMR spectroscopic techniques (¹H,¹H‐COSY, TOCSY, NOESY, HSQC, and HMBC) and mass spectrometry as 3β,22β‐dihydroxy‐3‐O‐[α‐L ‐rhamnopyranosyl‐(1→2)‐β‐D ‐glucuronopyranosyl]olean‐12‐en‐28‐oic acid 28‐O‐β‐D ‐glucopyranosyl ester ( 1 ), 3‐O‐[α‐L ‐rhamnopyranosyl‐(1→2)‐β‐D ‐glucuronopyranosyl]oleanolic acid 28‐O‐β‐D ‐glucopyranosyl ester ( 2 ), (3β,11α,26)‐ergosta‐5,24(28)‐diene‐3,11,26‐triol 3‐O‐(β‐D ‐glucopyranosyl)‐11‐O‐(α‐L ‐rhamnopyranosyl)‐26‐O‐β‐D ‐glucopyranoside ( 3 ), and (3β,11α,21,26)‐ergosta‐5,24(28)‐diene‐3,11,21,26‐tetrol 3‐O‐(β‐D ‐glucopyranosyl)‐11‐O‐(α‐L ‐rhamnopyranosyl)‐26‐O‐β‐D ‐glucopyranoside ( 4 ).     

Aerosol-assisted self-assembly of hybrid Layered Double Hydroxide particles into spherical architectures

Over the last decade, the use of nanocellulose in advanced technological applications has been promoted both due the excellent properties of this material in combination with its renewability. In this study, multilayered thin films composed of nanofibrillated cellulose (NFC), polyvinyl amine (PVAm) and silica nanoparticles were fabricated on polydimethylsiloxane (PDMS) using a layer-by-layer adsorption technique. The multilayer build-up was followed in situ by quartz crystal microbalance with dissipation, which indicated that the PVAm-SiO(2)-PVAm-NFC system adsorbs twice as much wet mass material compared to the PVAm-NFC system for the same number of bilayers. This is accompanied with a higher viscoelasticity for the PVAm-SiO(2)-PVAm-NFC system. Ellipsometry indicated a dry-state thickness of 2.2 and 3.4 nm per bilayer for the PVAm-NFC system and the PVAm-SiO(2)-PVAm-NFC system, respectively. Atomic force microscopy height images indicate that in both systems, a porous network structure is achieved. Young's modulus of these thin films was determined by the Strain-Induced Elastic Buckling Instability for Mechanical Measurements (SIEBIMM) technique. The Young's modulus of the PVAm/NFC films was doubled, from 1 to 2 GPa, upon incorporation of silica nanoparticles in the films. The introduction of the silica nanoparticles lowered the refractive index of the films, most probably due to an increased porosity of the films.     

The reduction of Ag+ in metallic silver on pseudomelanin films allows for antibacterial activity but does not imply unpaired electrons

Dopamine-melanin films produced through the oxidation of dopamine in the presence of oxygen as an oxidant allow to reduce silver ions onto silver particles as already described in the paper by Lee et al. (H. Lee, S.M. Dellatore, W.M. Miller, P.B. Messersmith, Science 318 (2007) 426.). This reduction process has to occur through the oxidation of moieties present in the melanin film. This investigation shows that the free radicals present in the pseudomelanin film, quantified by means of electron spin resonance spectroscopy (ESR) for the first time, are not used in the transformation of Ag(+) cations to deposit silver. The ESR signal is hardly affected by the deposition of silver particles. On the other hand, X-ray photoelectron spectroscopy shows a small increase in the density of quinone groups and a small decrease of catechol groups on the surface of the film during the deposition of silver. This suggests that the deposited pseudomelanin films contain a significant fraction of catechol groups able to trigger reduction processes of metallic cations. These silver nanoparticles remain adherent to the melanin films and allow for a quantitative killing of Escherichia coli over a broad range of bacterial dilutions. However, the presence of the bacteria induces a release of the nanoparticles. The pseudomelanin films cannot be reused again for a silver ion reduction step. Nevertheless, the easy preparation of the pseudomelanin-silver composite and its effective one shot bacterial killing activity renders the strategy presented in this paper attractive. Some fundamental questions about redox process allowed by the pseudomelanin films will also be asked.     

Synthetic and structural studies of donor-functionalized alkoxy derivatives of gallium

The synthesis of a range of alkyl/chloro-gallium alkoxide and amido/alkoxide compounds was achieved via a series of protonolysis and alcoholysis steps. The initial reaction involved the synthesis of [Me(Cl)Ga{N(SiMe(3))(2)}](2) (1) via methyl group transfer from the reaction of GaCl(3) with two equivalents of LiN(SiMe(3))(2). Reaction of 1 with varying amounts of ROH resulted in the formation of [Me(Cl)Ga(OR)](2) (2, R = CH(2)CH(2)OMe; 3, CH(CH(3))CH(2)NMe(2)), [Me(Cl)Ga{N(SiMe(3))(2)}(μ(2)-OR)Ga(Cl)Me] (4, R = CH(2)CH(2)NMe(2)), or [MeGa(OR)(2)] (5, R = CH(CH(3))CH(2)NMe(2)). Compound 4 represents an intermediate in the formation of dimeric complexes, of the type [Me(Cl)Ga(OR)](2), when formed from compound [Me(Cl)Ga{N(SiMe(3))(2)}](2). A methylgallium amido/alkoxide complex [MeGa{N(SiMe(3))(2)}(OCH(2)CH(2)OMe)](2) (6) was isolated when 2 was further reacted with LiN(SiMe(3))(2). In addition, reaction of 2 with HO(t)Bu resulted in a simple alcohol/alkoxide exchange and formation of [Me(Cl)Ga(O(t)Bu)](2) (7). In contrast to the formation of 1, the in situ reaction of GaCl(3) with one equivalent of LiN(SiMe(3))(2) yielded [Cl(2)Ga{N(SiMe(3))(2)}](2) in low yield, where no methyl group transfer has occurred. Reaction of alcohol with [Cl(2)Ga{N(SiMe(3))(2)}](2) was then found to yield [Cl(2)Ga(OR)](2) (8, R = CH(2)CH(2)NMe(2)), and further reaction of 8 with LiN(SiMe(3))(2) yielded the gallium amido alkoxide complex, [ClGa{N(SiMe(3))(2)}(OR)](2) (9, R = CH(2)CH(2)NMe(2)), similar to 6. The structures of compounds 4, 5, 7, and 8 have been determined by single-crystal X-ray diffraction.     

Addition of N-heterocyclic carbenes to a ruthenium(VI) nitrido polyoxometalate: a new route to cyclic guanidines

The scope of N-atom transfer from the electrophilic ruthenium(VI) nitrido containing polyoxometalate [PW(11)O(39)Ru(VI)N](4-) has been extended to the N-heterocyclic carbene {CH(2)(Mes)N}(2)C and the coupling product {CH(2)(Mes)N}(2)CNH(2)(+) characterized by (1)H NMR and high-resolution mass spectrometry. Because guanidines display many fields of applications ranging from biology to supramolecular chemistry, this could afford an original route to the synthesis of cyclic guanidines. This also enlarges the potential of nitrido complexes in the synthesis of heterocycles, mainly illustrated in the literature through the formation of aziridines through N-atom transfer to alkenes. In the course of the reaction, the ruthenium(III)-containing polyoxometallic intermediate [PW(11)O(39)Ru(III){NC{N(Mes)CH(2)}(2)}](5-) has been thoroughly characterized by continuous-wave and pulsed electron paramagnetic resonance, which nicely confirms the presence of the organic moiety on the polyoxometallic framework, Ru K-edge X-ray absorption near-edge structure, and electrochemistry.     

Asymmetric synthesis of (+)-galbelgin, (-)-kadangustin J, (-)-cyclogalgravin and (-)-pycnanthulignenes A and B, three structurally distinct lignan classes, using a common chiral precursor

The enantioselective synthesis of three structurally distinct classes of lignan from a single, aza-Claisen-derived, chiral morpholine amide is reported. The class of lignan formed is dependent on the substitution pattern in the aryl rings and choice of protecting group on a key benzylic hydroxyl group. The methodology has been used to asymmetrically synthesize and determine the absolute stereochemistry of lignans (+)-cyclogalgravin 3, (-)-pycnanthulignene A 4, (-)-pycnanthulignene B 5, and (-)-kadangustin J 8.