Computer Assisted Proof of Transverse Saddle-to-Saddle Connecting Orbits for First Order Vector Fields

In this paper we introduce a computational method for proving the existence of generic saddle-to-saddle connections between equilibria of first order vector fields. The first step consists of rigorously computing high order parametrizations of the local stable and unstable manifolds. If the local manifolds intersect, the Newton–Kantorovich theorem is applied to validate the existence of a so-called short connecting orbit. If the local manifolds do not intersect, a boundary value problem with boundary values in the local manifolds is rigorously solved by a contraction mapping argument on a ball centered at the numerical solution, yielding the existence of a so-called long connecting orbit. In both cases our argument yields transversality of the corresponding intersection of the manifolds. The method is applied to the Lorenz equations, where a study of a pitchfork bifurcation with saddle-to-saddle stability is done and where several proofs of existence of short and long connections are obtained.     

Unraveling complex small-molecule binding mechanisms by using simple NMR spectroscopy

Heteronuclear NMR spectroscopy provides a unique way to obtain site-specific information about protein-ligand interactions. Usually, such studies rely on the availability of isotopically labeled proteins, thereby allowing both editing of the spectra and ligand signals to be filtered out. Herein, we report that the use of the methyl SOFAST correlation experiment enables the determination of site-specific equilibrium binding constants by using unlabeled proteins. By using the binding of L- and D-tryptophan to serum albumin as a test case, we determined very accurate dissociation constants for both the high- and low-affinity sites present at the protein surface. The values of site-specific dissociation constants were closer to those obtained by isothermal titration calorimetry than those obtained from ligand-observed methods, such as saturation transfer difference. The possibility of measuring ligand binding to serum albumin at physiological concentrations with unlabeled proteins may open up new perspectives in the field of drug discovery.     

Lewis base mediated autoionization of GeCl2 and SnCl2

Cationic and anionic species of heavier low-valent group 14 elements are intriguing targets in main group chemistry due to their synthetic potential and industrial applications. In the present study, we describe the synthesis of cationic (MCl(+)) and anionic (MCl(3)(-)) species of heavier low-valent group 14 elements of germanium(II) and tin(II) by using the substituted Schiff base 2,6-diacetylpyridinebis(2,6-diisopropylanil) as Lewis base (LB). Treatment of LB with 2 equiv of GeCl(2)·dioxane and SnCl(2) in toluene gives compounds [(LB)Ge(II)Cl](+)[Ge(II)Cl(3)](-) (1) and [(LB)Sn(II)Cl](+)[Sn(II)Cl(3)](-) (2), respectively, which possess each a low-valent cation and an anion. Compounds 1 and 2 are well characterized with various spectroscopic methods and single crystal X-ray structural analysis.     

Experimental observation of spatially localized dynamo magnetic fields

We report the first experimental observation of a spatially localized dynamo magnetic field, a common feature of astrophysical dynamos and convective dynamo simulations. When the two propellers of the von Kármán sodium experiment are driven at frequencies that differ by 15%, the mean magnetic field's energy measured close to the slower disk is nearly 10 times larger than the one close to the faster one. This strong localization of the magnetic field when a symmetry of the forcing is broken is in good agreement with a prediction based on the interaction between a dipolar and a quadrupolar magnetic mode.     

Homogenization of unbounded singular integrals in W 1,∞

We study homogenization by ??-convergence, with respect to the L ¹-strong convergence, of periodic multiple integrals in W ^1,?? when the integrand can take infinite values outside of a convex bounded open set of matrices.     

Fixed-bed column studies of pentachlorophenol removal by use of alginate-encapsulated pillared clay microbeads

The high rate of electron/hole pair recombination reduces the quantum yield of the processes with TiO(2) and represents its major drawback. Adding a co-adsorbent increases the photocatalytic efficiency of TiO(2). In order to hybridize the photocatalytic activity of TiO(2) with the adsorptivity of carbon nanotube, a composite of multi-walled carbon nanotubes and titanium dioxide (MWCNT/TiO(2)) has been synthesized. The composite was characterized by means of X-ray diffraction (XRD), field emission scanning electron microscopy (FESEM), Fourier transform infrared absorption spectroscopy (FTIR), and diffuse reflectance UV-vis spectroscopy. The catalytic activity of this composite material was investigated by application of the composite for the degradation of methyl orange. It was observed that the composite exhibits enhanced photocatalytic activity compared with TiO(2). The enhancement in photocatalytic performance of the MWCNT/TiO(2) composite is explained in terms of recombination of photogenerated electron-hole pairs. In addition, MWCNT acts as a dispersing agent preventing TiO(2) from agglomerating activity during the catalytic process, providing a high catalytically active surface area. This work adds to the global discussion of how CNTs can enhance the efficiency of catalysts.     

Recent performance improvements to the DFT and TDDFT in GAMESS

The general atomic and molecular electronic structure system (GAMESS) is a quantum chemistry package used in the first-principles modeling of complex molecular systems using density functional theory (DFT) as well as a number of other post-Hartree-Fock methods. Both DFT and time-dependent DFT (TDDFT) are of particular interest to the materials modeling community. Millions of CPU hours per year are expended by GAMESS calculations on high-performance computing systems; any substantial reduction in the time-to-solution for these calculations represents a significant saving in CPU hours. As part of this work, three areas for improvement were identified: (1) the exchange-correlation (XC) integration grid, (2) profiling and optimization of the DFT code, and (3) TDDFT parallelization. We summarize the work performed in these task areas and present the resulting performance improvement. These software enhancements are available in 12JAN2009R3 or later versions of GAMESS.     

Design and FPGA-realization of a self-synchronizing chaotic decoder in the presence of noise

This paper describes requirement for wireless transmission of Chaotic Code Division Multiplexed Access (Chaotic CDMA) and it focuses on real-time synchronization algorithm embedded into electronic programmable device. CDMA with quasi-orthogonal codes is used to allow multi-users to transmit simultaneously in the same channel. Since the channel is shared between all users, the receiver system has to cope with channel noise and overall with interference from other users. As a result, one of the main problems of communication with quasi-orthogonal chaotic codes is to implement a real time decoder in presence of noise. Even if set-membership algorithm are efficient in real time synchronization of chaotic discrete generators in the presence of noise, these algorithms require a large memory resource. In this paper, we propose an evolution of set-membership algorithm toward genetic algorithm to be implemented into electronic programmable device. The advantage of genetic algorithm compared with set-membership algorithm is that they require a fixed size of memory.     

Hydration of calcium sulfate hemihydrate (CaSO4· H2O) into gypsum (CaSO4·2H2O). The influence of the sodium poly(acrylate)/surface interaction and molecular weight

The retarding influence of sodium poly(acrylate) (PANa) on the hydration of calcium sulfate hemihydrate (CaSO₄· H₂O) was investigated. This study reports the influence of sodium poly(acrylate) on hemihydrate dissolution, on homogenous and heterogeneous gypsum (CaSO₄·2H₂O) nucleation as well as on gypsum growth. It is shown that adsorption of PANa does not hinder the dissolution of hemihydrate in the present experimental conditions. The specific interaction of PANa with gypsum can explain the oriented growth of gypsum crystal. The gypsum growth is slowed down but cannot be blocked by the adsorption of PANa. On the other hand, PANa can block the heterogeneous and homogenous gypsum nucleation. As soon as a critical surface density of PANa onto the hemihydrate surface is reached, the heterogeneous gypsum nucleation is prevented and hemihydrate hydration is indefinitely blocked. The interaction between PANa and the hemihydrate surface is of prime importance to control hydration. Also, the influence of the molecular weight of PANa on homogenous nucleation has been investigated. The precipitation of calcium polyacrylate can explain the differences between the two molecular weights used (2100 and 20 000). This work leads to the conclusion that heterogeneous nucleation is the key process that controls hydration of a system in which hemihydrate dissolution, gypsum nucleation and growth are all occurring at the same time in a continuous manner.     

Palladium-catalyzed hydrosilylation of ynones to access silicon-stereogenic silylenones by stereospecific aromatic interaction-assisted Si–H activation

Hydrosilylation is one of the most important reactions in synthetic chemistry and ranks as a fundamental method to access organosilicon compounds in industrial and academic processes. However, the enantioselective construction of chiral-at-silicon compounds via catalytic asymmetric hydrosilylation remained limited and difficult. Here we report a highly enantioselective hydrosilylation of ynones, a type of carbonyl-activated alkynes, using a palladium catalyst with a chiral binaphthyl phosphoramidite ligand. The stereospecific hydrosilylation of ynones affords a series of silicon-stereogenic silylenones with up to 94% yield, 20:1 regioselectivity and 98:2 enantioselectivity. The density functional theory(DFT) calculations were conducted to elucidate the reaction mechanism and origin of high degree of stereoselectivity, in which the powerful potential of aromatic interaction in this reaction is highlighted by the multiple C–H-π interaction and aromatic cavity-oriented enantioselectivitydetermining step during desymmetric functionalization of Si–H bond.