A nonlocal diffusion problem on manifolds

ABSTRACT

In this paper we study a nonlocal diffusion problem on a manifold. These kinds of equations can model diffusions when there are long range effects and have been widely studied in Euclidean space. We first prove existence and uniqueness of solutions and a comparison principle. Then, for a convenient rescaling we prove that the operator under consideration converges to a multiple of the usual Heat-Beltrami operator on the manifold. Next, we look at the long time behavior on compact manifolds by studying the spectral properties of the operator. Finally, for the model case of hyperbolic space we study the long time asymptotics and find a different and interesting behavior.     

13C solid-state NMR complemented by ATR-FTIR and micro-DSC to study modern collagen-based material and historical leather

Ancient vegetable tanned leathers and parchments are very complex materials in which both different manufacturing and deterioration processes make their study and chemical characterisation difficult. In this research, solid-state nuclear magnetic resonance (NMR) spectroscopy was applied to identify different tannin families (condensed and hydrolysable) in historical leather objects such as bookbindings, wall upholsters, footwear and accessories, and military apparel. Furthermore, leather deterioration with special focus on collagen gelatinisation was investigated. A comparison with Fourier transform infrared (FTIR) spectroscopy and micro-differential scanning calorimetry (micro-DSC) was also performed to support the ¹³C CP-MAS NMR findings and to point out the advantages and limitations of solid-state NMR in analysing historical and archaeological leathers. A wide database of NMR and FTIR spectra of commercial tannins compounds was also collected in order to characterise historical and archaeological leathers.     

Distinguishing Activities in the Photodynamic Arsenals of the Pigmented Ciliates Blepharisma sinuosum Sawaya, 1940 and Blepharisma japonicum Suzuki, 1954 (Ciliophora: Heterotrichea)

Blepharismins are photodynamic hypericin-like dianthrones produced as a variable pigment blend in Blepharisma ciliates and mostly studied in the Afro-Asiatic Blepharisma japonicum. The present work describes the bioactivity of pigments from the Brazilian Blepharisma sinuosum. Comparative analyses showed that the pigments from both species can trigger photo-induced modifications in phospholipids, but different redox properties and biological activities were assigned for each pigment blend. Stronger activities were detected for B. sinuosum pigments, with the lethal concentration LC₅₀ 10 × lower than B. japonicum pigments in light-irradiated tests against Bacillus cereus and less than half for treatments on the human HeLa tumor cells. HPLC showed B. sinuosum producing a simpler pigment blend, mostly with the blepharismin-C (~ 70%) and blepharismin-E (~ 30%) types. Each blepharismin engaged a specific dose–response profile on sensitive cells. The blepharismin-B and blepharismin-C were the most toxic pigments, showing LC₅₀ ~ 2.5–3.0 µm and ~ 100 µm on B. cereus and HeLa cells, respectively, after illumination. Similarity clustering analysis compiling the bioactivity data revealed two groups of blepharismins: the most active, B and C, and the less active, A, D and E. The B. sinuosum pigment blend includes one representative of each clade. Functional and medical implications are discussed.     

A rheological modelling and microscopic analysis of bigels

Bigels are two-phase systems in which each phase (organic or aqueous) is structured using a specific gelator. Currently, these systems are widely investigated, mainly as matrices for controlled drug delivery, because they possess the advantages of both organogels and hydrogels and are very stable owing to the structuration of the dispersing phase. A deeper knowledge of the relationship between macroscopic properties and microscopic parameters seems necessary to aim at designing materials with specific rheological properties and suitable for specific uses. From a rheological point of view, bigels can be considered as composite materials in which a structured system (organogel or hydrogel, according to the desired use) is dispersed in a gelled continuous phase. In the present paper, a number of rheological models, already proposed in literature for composite systems, were used to relate the bigel complex modulus to the rheological properties of dispersed and continuous phase and to their volumetric ratio. It was observed that these models are not able to describe properly bigel behaviour, probably owing to some theoretical assumptions such as the uniform distribution of spherical particles. An empirical modification of a literature model, proposed to take into account some peculiarities of bigels, yields an improvement of fitting even if further investigations are necessary to better understand the effects of particle size distribution and morphology on observed properties.     

Kinetic Enhancement of Direct Hydrogenation of MgB2 to Mg(BH4)2 upon Mechanical Milling with THF,MgH2, and/or Mg

Modification of magnesium diboride, MgB₂, by mechanical milling with THF, MgH₂, and/or Mg results in a lowering of the conditions required for its direct, bulk hydrogenation to magnesium borohydride, Mg(BH₄)₂, by 300 bar and 100 °C. Following mechanical milling with MgH₂ or THF and Mg, MgB₂ can be hydrogenated to Mg(BH₄)₂ at 300 °C under 700 bar of H₂ while achieving ∼54–71 % conversion to the borohydride. The discovery of a means of dramatically lowering the conditions required for the hydrogenation of MgB₂ is an important step towards the development of a practical onboard hydrogen storage system based on hydrogen cycling between Mg(BH₄)₂ and MgB₂. We suggest that mechano-milling with THF, Mg, and/or MgH₂ may possibly introduce defects in the MgB₂ structure which enhance hydrogenation. The ability to activate the MgB₂ through the introduction of structural defects transcends its relevance to hydrogen storage, as a method of overcoming its chemical inertness provides the key to harnessing other interesting properties of this material.     

S-(2-pyridinyl)-1,1,3,3-tetramethylthiouronium hexafluorophosphate. A new reagent for the synthesis of 2-pyridinethiol esters

[reaction: see text] A new thiouronium-based reagent for the synthesis of 2-pyridinethiol esters under non-nucleophilic conditions from the corresponding carboxylic acids was developed. The resulting procedure enables the preparation of previously unavailable alpha,beta-unsaturated 2-pyridinethiol esters as well as their aliphatic and aromatic counterparts.     

Palladium-mediated N-arylation of heterocyclic diamines: insights into the origin of an unusual chemoselectivity

The chemoselectivity of the palladium-mediated reaction of bromobenzene with various heterocyclic diamines was studied. Whatever the ligand used, 3-aminopyrrolidine underwent arylation of the secondary amine function (>82%), whereas the more flexible 3-aminoazepinine was arylated on its primary function (>70%). The ratio "arylation of primary amine versus arylation of secondary amine" of 3-aminopiperidine with bromobenzene varied from 90:10 (BINAP, electron-enriched and hindered biphenyls L2 or L3) to 32:68 with the Josiphos-type ligand L10. The same trend was observed when 4-aminopiperidine was used (82:18 with L2 and 17:83 with L10). This selectivity can be tuned by the choice of aryl halide partners having different steric and electronic properties. A cooperative effect of both nitrogens of diamines during the reaction was deduced from competitive experiments. Finally, 13C and 31P NMR experiments, carried out with 3-aminopyrrolidine at room temperature, support a fast coordination of the primary amine to the metal. Indeed, a palladium complex resulting from the unusual displacement of one phosphane group of the intermediate ArPdX(BINAP) by the primary amino group was characterized.     

Conformation dependence of the CalphaDalpha stretch mode in peptides. 1. Isolated alanine peptide structures

Ab initio normal mode calculations have been performed on isolated alanine di- through octa-(i.e., blocked) peptides in uniform alphaR, beta, and polyproline II conformations to determine how the CalphaDalpha stretch mode, which has been proposed as a possible determinant of the varphi,psi conformation at the Calpha atom (Mirkin, N. G.; Krimm, S. J. Phys. Chem. A 2004, 108, 10923), depends on conformation and sequence length. This set of frequencies, including results on some kinked structures, demonstrates that such a discrimination is likely to be possible through experimental observations of peptides synthesized with successive deuteration at the Halpha sites, on the basis of at least three properties: the values of the frequency at the first residue, the pattern of successive frequency differences, and the frequency differences between the first and last residues.     

Vestibular vocal fold behavior during phonation in unilateral vocal fold paralysis

Voice quality in patients with vocal fold paralysis can be affected by several factors, such as the position of the paralyzed vocal fold, its degree of atrophy, the configuration of its free edge, and the level differences between both vocal folds. Depending on the related vocal deficiency the patient will attempt to compensate using different maneuvers, such as increment of vocal tract and neck muscle contraction to improve glottal closure. This is probably one of the reasons why ventricular folds are frequently requested. The objective of this study is to analyze the behavior of the homolateral and contralateral vestibular folds to delineate patterns of vestibular motion during sustained phonation, in cases of unilateral vocal fold paralysis.