Dynamical Aspects of Mean Field Plane Rotators and the Kuramoto Model

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc. We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N→∞ limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N→∞ limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K _c . We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K>K _c .     

Stability of W/O Emulsions Encapsulating Polysaccharides

In the frame of formulation of W/O emulsions entrapping polysaccharides devoted to agricultural applications, the aim of this work was to study the stability over time of these emulsions, stabilized with either soybean lecithin or polyglycerol polyricinoleate (PGPR) as emulsifiers. Emulsifiers were dissolved in oil phase, and polysaccharides (carboxymethycellulose (CMC), guar, xanthan) in ultrapure water. Emulsions stability was studied through natural aging tests and accelerated aging tests, using bottle tests, microscopy and calorimetry. Experiments showed that PGPR was more efficient than lecithin to stabilize emulsions containing the polysaccharides studied, and that emulsions prepared with CMC showed the best stability.     

Synthesis of New 1,3‐bis(Heteroaryl)‐4,5‐imidazolidinediones Through Reaction of N,N′‐bis(Heteroaryl)methanediamines with Oxalyl Chloride

Reaction of N,N′‐bis(2‐pyridinyl, 3‐pyridinyl, 4‐pyridinyl, 2‐thiazolyl, 4‐nitrophenyl, and 2‐benzothiazolyl)methanediamines 1a–f with oxalyl chloride in dry dichloroethane in the presence of pyridine affords the corresponding 1,3‐bis (heteroaryl)‐4,5‐imidazolidinediones 3a–f in good to excellent yields. The essential role of pyridine in the reaction mixture is described, and reaction details as well as product characterization is discussed.     

One-pot, three-component synthesis of novel δ-sultam scaffolds via N-sulfonylation—intramolecular Michael sequences

The synthesis of novel δ-sultam scaffolds utilizing one-pot, three-component reactions of 1,3-dicarbonyl compounds, primary aliphatic amines and substituted styrenesulfonyl chlorides is reported. A variety of six-membered sultams are obtained in moderate to good yields presumably via N-sulfonylation—intramolecular Michael addition sequences.     

Solvent-dependent reactions for the synthesis of β-keto-benzo-δ-sultone scaffolds via DBU-catalyzed O-sulfonylation/intramolecular Baylis-Hillman/1,3-H shift or dehydration tandem sequences

We have developed a solvent-dependent method for the synthesis of novel benzo-δ-sultone scaffolds. A variety of benzylbenzo[e][1,2]oxathiin-4(3H)-one-2,2-dioxides were obtained in high yields in DMF using a one-pot, DBU-catalyzed condensation of 2-hydroxybenzaldehydes with a number of (E)-2-phenylethenesulfonyl chlorides. On the other hand, the initially prepared 2-formylphenyl-(E)-2-phenylethenesulfonate derivatives underwent DBU-catalyzed reactions to a series of 3-[methoxy(phenyl)methyl]benzo[e][1,2]oxathiine-2,2-dioxides in moderate to good yields in MeOH. These reactions presumably proceed via DBU-catalyzed O-sulfonylation/intramolecular Baylis-Hillman/1,3-H shift or dehydration tandem sequences, respectively.     

Top-down approach to fiber-top cantilevers

Taking inspiration from conventional top-down micromachining techniques, we have fabricated a low mass gold fiber-top cantilever via align-and-shine photolithography. The cantilever is characterized by measuring its resonance frequency and mechanical quality factor. Our results show that the device grants mass sensitivity comparable to that reported for similar standard cantilevers. This proof-of-concept paves the way to series production of highly sensitive fiber-top devices for remote detection of biochemical substances.     

A magnetically recoverable copper–salen complex as a nano-catalytic system for amine protection via acetylation using thioacetic acid

Research on Chemical Intermediates - A novel copper(II)–salen complex was immobilized on the surface of magnetite nanoparticles using chitosan as a linker. This system exhibits superior...     

Antitumor evaluation and 3D-QSAR studies of a new series of the spiropyrroloquinoline isoindolinone/aza-isoindolinone derivatives by comparative molecular field analysis (CoMFA)

In current study, antitumor activity of two series of the newly synthesized spiropyrroloquinoline isoindolinone and spiropyrroloquinoline aza-isoindolinone scaffolds was evaluated against three human breast normal and cancer cell lines (MCF-10A, MCF-7 and SK-BR-3) and compared with cytotoxicity values of doxorubicin and colchicine as the standard drugs. It was found that several compounds were endowed with cytotoxicity in the low micromolar range. Among these two series, compounds 6i, 6j, 6k and 7l, 7m, 7n, 7o containing 3-ethyl-1H-indole moiety were found to be highly effective against both cancer cell lines ranging from \(0.080 \pm 0.001\) to \(11.91 \pm 1.39\,\upmu \hbox {M}\) in comparison with the corresponding analogs. Compared with human cancer cells, the most potent compounds did not show high cytotoxicity against human breast normal MCF-10A cells. Generally, most of the evaluated compounds 6a–l and 7a–o series showed more antitumor activity against SK-BR-3 than MCF-7 cells. Moreover, comparative molecular field analysis (CoMFA) as a popular tools of three-dimensional quantitative structure–activity relationship (3D-QSAR) studies was carried out on 27 spiropyrroloquinolineisoindolinone and spiropyrroloquinolineaza-isoindolinone derivatives with antitumor activity against on SK-BR-3 cells. The obtained CoMFA models showed statistically excellent performance, which also possessed good predictive ability for an external test set. The results confirm the important effect of molecular steric and electrostatic interactions of these compounds on in vitro cytotoxicity against SK-BR-3.     

Study of the numerical artifacts in differential analysis of highly conducting gratings

Li's Fourier factorization rule [J. Opt. Soc. Am. A13, 1870 (1996)] was recently shown to be problematic to apply to highly conducting metallic gratings. We provide further information about the applicability of different differential methods and are concerned with the relation of observed numerical artifacts, the total number of retained space harmonics, the presence of both positive and negative permittivity inside the groove region, and the validity of Li's inverse rule. Two different cases corresponding to lossless and low-loss binary metallic gratings are considered, and it is shown that an increase in the number of retained space harmonics can relieve the presence of numerical artifacts.     

Synthesis and Antibacterial Activity of Pyranopyrimidinedione Derivatives

Russian Journal of Organic Chemistry - Four pyranopyrimidinedione derivatives were prepared through a one-pot pseudo-three-component acetic acid-catalyzed reaction of 6-amino-1,3-dimethyluracil...