Asymptotic expansions and fast computation of oscillatory Hilbert transforms

In this paper, we study the asymptotics and fast computation of the one-sided oscillatory Hilbert transforms of the form $$H^{+}(f(t)e^{i\omega t})(x)=-int_{0}^{\infty}e^{i\omega t}\frac{f(t)}{t-x}dt,\qquad \omega>0,\qquad x\geq 0,$$ where the bar indicates the Cauchy principal value and $f$ is a real-valued function with analytic continuation in the first quadrant, except possibly a branch point of algebraic type at the origin. When $x=0$, the integral is interpreted as a Hadamard finite-part integral, provided it is divergent. Asymptotic expansions in inverse powers of $\omega$ are derived for each fixed $x\geq 0$, which clarify the large $\omega$ behavior of this transform. We then present efficient and affordable approaches for numerical evaluation of such oscillatory transforms. Depending on the position of $x$, we classify our discussion into three regimes, namely, $x=\mathcal{O}(1)$ or $x\gg1$, $0<x\ll 1$ and $x=0$. Numerical experiments show that the convergence of the proposed methods greatly improve when the frequency $\omega$ increases. Some extensions to oscillatory Hilbert transforms with Bessel oscillators are briefly discussed as well.Comment: 32 pages, 6 figures, 4 table

Microscopic Marangoni Flows Cannot Be Predicted on the Basis of Pressure Gradients.

A concentration gradient along a fluid-fluid interface can cause flow. On a microscopic level, this so-called Marangoni effect can be viewed as being caused by a gradient in the pressures acting on the fluid elements or as the chemical-potential gradients acting on the excess densities of different species at the interface. If the interface thickness can be ignored, all approaches should result in the same flow profile away from the interface. However, on a more microscopic scale, the different expressions result in different flow profiles, only one of which can be correct. Here we compare the results of direct nonequilibrium molecular dynamics simulations with the flows that are generated by pressure and chemical-potential gradients. We find that the approach based on the chemical-potential gradients agrees with the direct simulations, whereas the calculations based on the pressure gradients do not

Pair interactions between complex mesoscopic particles from Widom's particle-insertion method

We demonstrate that Widom's particle insertion technique provides a convenient and efficient method to determine the effective pair interaction between complex, composite soft-matter particles in the zero-density limit. By means of three different test systems, i.e. amphiphilic dendrimers, electrostatic polymers and colloids coated with electrostatic polymers, we demonstrate the validity and the power of the presented method.Comment: 7 pages, 4 figures, to be published in Soft Matte

Draft Genome of Scalindua rubra, Obtained from the Interface Above the Discovery Deep Brine in the Red Sea, Sheds Light on Potential Salt Adaptation Strategies in Anammox Bacteria

Several recent studies have indicated that members of the phylum Planctomycetes are abundantly present at the brine-seawater interface (BSI) above multiple brine pools in the Red Sea. Planctomycetes include bacteria capable of anaerobic ammonium oxidation (anammox). Here, we investigated the possibility of anammox at BSI sites using metagenomic shotgun sequencing of DNA obtained from the BSI above the Discovery Deep brine pool. Analysis of sequencing reads matching the 16S rRNA and hzsA genes confirmed presence of anammox bacteria of the genus Scalindua. Phylogenetic analysis of the 16S rRNA gene indicated that this Scalindua sp. belongs to a distinct group, separate from the anammox bacteria in the seawater column, that contains mostly sequences retrieved from high-salt environments. Using coverage- and composition-based binning, we extracted and assembled the draft genome of the dominant anammox bacterium. Comparative genomic analysis indicated that this Scalindua species uses compatible solutes for osmoadaptation, in contrast to other marine anammox bacteria that likely use a salt-in strategy. We propose the name Candidatus Scalindua rubra for this novel species, alluding to its discovery in the Red Sea

Efficient Silicon Metasurfaces for Visible Light

Dielectric metasurfaces require high refractive index contrast materials for optimum performance. This requirement imposes a severe restraint; either devices have been demonstrated at wavelengths of 700 nm and above using high-index semiconductors such as silicon, or they use lower index dielectric materials such as TiO2 or Si3N4 and operate in the visible wavelength regime. Here, we show that the high refractive index of silicon can be exploited at wavelengths as short as 532 nm by demonstrating a crystalline silicon metasurface with a transmission efficiency of 71% at this wavelength and a diffraction efficiency of 95% into the desired diffraction order. The metasurfaces consist of a graded array of silicon posts arranged in a square lattice on a quartz substrate. We show full 2π phase control, and we experimentally demonstrate polarization-independent beam deflection at 532 nm wavelength. Our results open a new way for realizing efficient metasurfaces based on silicon for the technologically all-important display applications

Nucleocytoplasmic human O-GlcNAc transferase is sufficient for O-GlcNAcylation of mitochondrial proteins

O-linked N-acetylglucosamine modification (O-GlcNAcylation) is a nutrient-dependent protein post-translational modification (PTM), dynamically and reversibly driven by two enzymes: O-GlcNAc transferase (OGT) and O-GlcNAcase (OGA) that catalyse the addition and the removal of the O-GlcNAc moieties to/from serine and threonine residues of target proteins respectively. Increasing evidence suggests involvement of O-GlcNAcylation in many biological processes, including transcription, signalling, neuronal development and mitochondrial function. The presence of a mitochondrial O-GlcNAc proteome and a mitochondrial OGT (mOGT) isoform has been reported. We explored the presence of mOGT in human cell lines and mouse tissues. Surprisingly, analysis of genomic sequences indicates that this isoform cannot be expressed in most of the species analysed, except some primates. In addition, we were not able to detect endogenous mOGT in a range of human cell lines. Knockdown experiments and Western blot analysis of all the predicted OGT isoforms suggested the expression of only a single OGT isoform. In agreement with this, we demonstrate that overexpression of the nucleocytoplasmic OGT (ncOGT) isoform leads to increased O-GlcNAcylation of mitochondrial proteins, suggesting that ncOGT is necessary and sufficient for the generation of the O-GlcNAc mitochondrial proteome

The Lennard-Jones potential: when (not) to use it.

The Lennard-Jones 12-6 potential (LJ) is arguably the most widely used pair potential in molecular simulations. In fact, it is so popular that the question is rarely asked whether it is fit for purpose. In this paper, we argue that, whilst the LJ potential was designed for noble gases such as argon, it is often used for systems where it is not expected to be particularly realistic. Under those circumstances, the disadvantages of the LJ potential become relevant: most important among these is that in simulations the LJ potential is always modified such that it has a finite range. More seriously, there is by now a whole family of different potentials that are all called Lennard-Jones 12-6, and that are all different - and that may have very different macroscopic properties. In this paper, we consider alternatives to the LJ 12-6 potential that could be employed under conditions where the LJ potential is only used as a typical short-ranged potential with attraction. We construct a class of potentials that are, in many respects LJ-like but that are by construction finite ranged, vanishing quadratically at the cut-off distance, and that are designed to be computationally cheap. Below, we present this potential and report numerical data for its thermodynamic and transport properties, for the most important cases (cut-off distance rc = 2σ ("LJ-like") and rc = 1.2σ (a typical "colloidal" potential))