On the Lamb vector and the hydrodynamic charge

This work is an attempt to test the concept of the hydrodynamic charge (analogous to the electric charge in electromagnetism) in the simple case of a coherent structure such as the Burgers vortex. We provide experimental measurements of both the so-called Lamb vector and its divergence (the charge) by two-dimensional particles images velocimetry. In addition, we perform a Helmholtz–Hodge decomposition of the Lamb vector in order to explore its topological features. We compare the charge with the well-known Q-criterion in order to assess its interest in detecting and characterizing coherent structure. Usefulness of this concept in studies of vortex dynamics is demonstrated.

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The synthesis and characterization of thiol-based aryl diazonium modified glassy carbon electrode for the voltammetric determination of low levels of Hg(II)

Electrochemical determination of Hg(II) in aquatic solutions on bare and modified glassy carbon electrode (GCE) is reported. Optimizing the parameters used for a bare GCE, such as the electrolyte solution, the potential and time of deposition, resulted in linear response over a large range of Hg(II) concentrations (4–160 ppb) using linear sweep anodic stripping voltammetry. Modification of the electrode with 4,4′-disulfanediyldibenzenediazonium (DSBD) yielded a lowest detection limit of 1 ppb. Two procedures for DSBD synthesis are described for the first time, and the product was characterized by microanalysis, FTIR and ¹H-NMR. The electrochemical attachment of DSBD to the electrode was studied and compared with the electrochemical behaviour of DSBD analogous molecules, i.e. 4-aminophenyl disulfide, p-aminothiophenol and phenyl disulfide.     

Dynamics of water and sodium in gels under salt‐induced phase transition

Synthetic and biological gels undergo a sharp volume phase transition when subjected to a variety of environmental changes. Water and ion dynamics within swollen and compact phases are critical for understanding fundamental concepts in cellular (specifically neuronal) biophysics, for models of bound, free, or ordered water in complex environments; and for practical applications such as the design of gels for drug release, biomimetics, sensors, or actuators. In this work, we find, for the first time, basic physical parameters that shed light on the interaction of gels with water and electrolytes, across a volume phase transition. Water within a gel can be separated into bound and free populations with high exchange rate. We show that free water dynamics in compact gels are the same as those in pure water. Bound water was found to comprise a single layer around the polymers in both phases, with a correlation time three orders of magnitude higher than that of free water. Most importantly, salt‐induced phase transition was found to be different from a standard coil‐globule transition (e.g., temperature‐induced), with no rejection of bound water as the gel compacts. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1620–1628     

NCIPLOT: a program for plotting non-covalent interaction regions

Non-covalent interactions hold the key to understanding many chemical, biological, and technological problems. Describing these non-covalent interactions accurately, including their positions in real space, constitutes a first step in the process of decoupling the complex balance of forces that define non-covalent interactions. Because of the size of macromolecules, the most common approach has been to assign van der Waals interactions (vdW), steric clashes (SC), and hydrogen bonds (HBs) based on pairwise distances between atoms according to their van der Waals radii. We recently developed an alternative perspective, derived from the electronic density: the Non-Covalent Interactions (NCI) index [J. Am. Chem. Soc. 2010, 132, 6498]. This index has the dual advantages of being generally transferable to diverse chemical applications and being very fast to compute, since it can be calculated from promolecular densities. Thus, NCI analysis is applicable to large systems, including proteins and DNA, where analysis of non-covalent interactions is of great potential value. Here, we describe the NCI computational algorithms and their implementation for the analysis and visualization of weak interactions, using both self-consistent fully quantum-mechanical, as well as promolecular, densities. A wide range of options for tuning the range of interactions to be plotted is also presented. To demonstrate the capabilities of our approach, several examples are given from organic, inorganic, solid state, and macromolecular chemistry, including cases where NCI analysis gives insight into unconventional chemical bonding. The NCI code and its manual are available for download at http://www.chem.duke.edu/~yang/software.htm.     

Prime and almost prime integral points on principal homogeneous spaces

We develop the affine sieve in the context of orbits of congruence subgroups of semisimple groups acting linearly on affine space. In particular, we give effective bounds for the saturation numbers for points on such orbits at which the value of a given polynomial has few prime factors. In many cases these bounds are of the same quality as what is known in the classical case of a polynomial in one variable where the orbit consists of the integers. When the orbit is the set of integral matrices of a fixed determinant, we obtain a sharp result for the saturation number, and thus establish the Zariski density of matrices all of whose entries are prime numbers. Among the key tools used are explicit approximations to the generalized Ramanujan conjectures for such groups, and sharp and uniform counting of points on such orbits when ordered by various norms.     

Lefschetz properties and basic constructions on simplicial spheres

The well known g-conjecture for homology spheres follows from the stronger conjecture that the face ring over the reals of a homology sphere, modulo a linear system of parameters, admits the strong-Lefschetz property. We prove that the strong-Lefschetz property is preserved under the following constructions on homology spheres: join, connected sum, and stellar subdivisions. The last construction is a step towards proving the g-conjecture for piecewise-linear spheres.     

Obtaining fast error rates in nonconvex situations

We show that under mild assumptions on the learning problem, one can obtain a fast error rate for every reasonable fixed target function even if the base class is not convex. To that end, we show that in such cases the excess loss class satisfies a Bernstein type condition.