Boojum and stripe textures in long-range orientationally ordered monolayers on solid substrates

Long-range organization of molecular tilt azimuth is a striking feature in monolayers at the air-water interface. We show that the boojum and stripe textures of pentadecanoic acid (PDA) with the continuous variations of molecular tilt azimuth formed at the air-water interface at temperatures lower than room temperature can be preserved after being transferred to glass substrates at low dipping speeds. The long-range tilt order in the transferred boojums and stripes is resolved by frictional force microscopy at room temperature, suggesting that the tilt order is "frozen" through the interaction of PDA molecules with the glass surface. The transferred stripe structure can be used as a unique alignment layer to induce a continuously azimuthal orientation of nematic liquid crystals.     

Correction factors for boundary diffusion in reaction-diffusion master equations

The reaction-diffusion master equation (RDME) has been widely used to model stochastic chemical kinetics in space and time. In recent years, RDME-based trajectorial approaches have become increasingly popular. They have been shown to capture spatial detail at moderate computational costs, as compared to fully resolved particle-based methods. However, finding an appropriate choice for the discretization length scale is essential for building a reasonable RDME model. Moreover, it has been recently shown [R. Erban and S. J. Chapman, Phys. Biol. 4, 16 (2007); R. Erban and S. J. Chapman, Phys. Biol. 6, 46001 (2009); D. Fange, O. G. Berg, P. Sjo?berg, and J. Elf, Proc. Natl. Acad. Sci. U.S.A. 107, 46 (2010)] that the reaction rates commonly used in RDMEs have to be carefully reassessed when considering reactive boundary conditions or binary reactions, in order to avoid inaccurate--and possibly unphysical--results. In this paper, we present an alternative approach for deriving correction factors in RDME models with reactive or semi-permeable boundaries. Such a correction factor is obtained by solving a closed set of equations based on the moments at steady state, as opposed to modifying probabilities for absorption or reflection. Lastly, we briefly discuss existing correction mechanisms for bimolecular reaction rates both in the limit of fast and slow diffusion, and argue why our method could also be applied for such purpose.     

Multivariate Analysis of Electron Detachment Dissociation and Infrared Multiphoton Dissociation Mass Spectra of Heparan Sulfate Tetrasaccharides Differing Only in Hexuronic acid Stereochemistry

The structural characterization of glycosaminoglycan (GAG) carbohydrates by mass spectrometry has been a long-standing analytical challenge due to the inherent heterogeneity of these biomolecules, specifically polydispersity, variability in sulfation, and hexuronic acid stereochemistry. Recent advances in tandem mass spectrometry methods employing threshold and electron-based ion activation have resulted in the ability to determine the location of the labile sulfate modification as well as assign the stereochemistry of hexuronic acid residues. To facilitate the analysis of complex electron detachment dissociation (EDD) spectra, principal component analysis (PCA) is employed to differentiate the hexuronic acid stereochemistry of four synthetic GAG epimers whose EDD spectra are nearly identical upon visual inspection. For comparison, PCA is also applied to infrared multiphoton dissociation spectra (IRMPD) of the examined epimers. To assess the applicability of multivariate methods in GAG mixture analysis, PCA is utilized to identify the relative content of two epimers in a binary mixture.     

Geodesic restrictions for the Casimir operator

We consider the hyperbolic Casimir operator C defined on the tangent sphere bundle SY of a compact hyperbolic Riemann surface Y. We prove a non-trivial bound on the L²-norm of the restriction of eigenfunctions of C to certain natural hypersurfaces in SY. The result that we obtain goes beyond known (sharp) local bounds of L. Hörmander.     

Charge trapping and storage by composite P3HT/PC60BM nanoparticles investigated by fluorescence-voltage/single particle spectroscopy

Fluorescence-voltage/single particle spectroscopy (F-V/SPS) was employed to study exciton-hole polaron interactions and interfacial charge transfer processes for pure poly(3-hexylthiophene) (P3HT) nanoparticles (NPs) and composite P3HT/PC(60)BM NPs in functioning hole-injection devices. F-V/SPS data collected on a particle-by-particle basis reveal an apparent bistability in the fluorescence-voltage modulation curves for composite NPs of P3HT and [6,6]-phenyl-C(61)-butyric acid methyl ester (PC(60)BM) that is absent for pure P3HT NPs. A pronounced deep trapping of free electrons photogenerated from the composite P3HT/PC(60)BM NPs at the NP/dielectric interface and hole trapping by fullerene anions in composite P3HT/PC(60)BM NPs under photoexcitation lies at the basis of this finding. The deep electron trapping effect reported here for composite conjugated polymer/fullerene NPs presents an opportunity for future application of these NPs in nanoscale memory and imaging devices.     

Natural abundance solid-state 67Zn NMR characterization of microporous zinc phosphites and zinc phosphates at ultrahigh magnetic field

Zinc-phosphite and -phosphate based microporous materials are crystalline open framework materials with potential industrial applications. Although (31)P MAS NMR has been used for characterization of these materials, the local environments around zinc centres have never been directly probed by solid-state NMR due to the many unfavourable NMR characteristics of (67)Zn. In this work, we have characterized the local structure around the Zn centres in several representative microporous zinc phosphites and zinc phosphates by acquiring natural abundance (67)Zn solid-state NMR spectra at ultrahigh magnetic field of 21.1 T. The observed line-shapes are mainly determined by the second order quadrupolar interaction. The NMR tensor parameters were extracted from the spectra and are related to the local geometry around the Zn centre. Computational study of the electric field gradient (EFG) tensor at Zn was performed using hybrid density functional theory (DFT) calculations at B3LYP level of theory on model clusters. The calculations using Projector Augmented-Wave (PAW) method were also carried out with the CASTEP code wherever it was possible. The work has shown that it is possible to study Zn environments in porous materials which often have very low Zn concentration by natural abundance (67)Zn SSNMR at very high magnetic fields.     

Deformations of the hemisphere that increase scalar curvature

Consider a compact Riemannian manifold M of dimension n whose boundary ?M is totally geodesic and is isometric to the standard sphere S ^n?1. A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n?1), then M is isometric to the hemisphere $S_{+}^{n}$ equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. In this paper, we construct counterexamples to Min-Oo??s Conjecture in dimension n??3.     

Preconditioning trace coupled 3d‐1d systems using fractional Laplacian

Multiscale or multiphysics problems often involve coupling of partial differential equations posed on domains of different dimensionality. In this work, we consider a simplified model problem of a 3d‐1d coupling and the main objective is to construct algorithms that may utilize standard multilevel algorithms for the 3d domain, which has the dominating computational complexity. Preconditioning for a system of two elliptic problems posed, respectively, in a three‐dimensional domain and an embedded one dimensional curve and coupled by the trace constraint is discussed. Investigating numerically the properties of the well‐defined discrete trace operator, it is found that negative fractional Sobolev norms are suitable preconditioners for the Schur complement of the system. The norms are employed to construct a robust block diagonal preconditioner for the coupled problem.     

Correction of self-absorption spectral line and ratios of transition probabilities for homogeneous and LTE plasma

Expressions for fundamental spectral line parameters are reported for Gaussian and Lorentzian shape profiles for homogeneous plasma at equilibrium in presence of the self-absorption. These expressions for Lorentzian profiles are applied to the determination of the ratios of transition probabilities and the ratios of optical thicknesses by a new method that we propose in this article. The self-absorption is computed by spectral line profiles with a Simplex algorithm program fitting. Applications to some experimental lines illustrate the appropriate corrections.