Nonmonotone travelling waves in a single species reaction-diffusion equation with delay

We prove the existence of a continuous family of positive and generally nonmonotone travelling fronts for delayed reaction-diffusion equations , when g∈C²(R₊,R₊) has exactly two fixed points: x₁=0 and x₂=K>0. Recently, nonmonotonic waves were observed in numerical simulations by various authors. Here, for a wide range of parameters, we explain why such waves appear naturally as the delay h increases. For the case of g with negative Schwarzian, our conditions are rather optimal; we observe that the well known Mackey-Glass-type equations with diffusion fall within this subclass of (∗). As an example, we consider the diffusive Nicholson's blowflies equation.     

Link Homologies and the Refined Topological Vertex

We establish a direct map between refined topological vertex and sl(N) homological invariants of the of Hopf link, which include Khovanov-Rozansky homology as a special case. This relation provides an exact answer for homological invariants of the Hopf link, whose components are colored by arbitrary representations of sl(N). At present, the mathematical formulation of such homological invariants is available only for the fundamental representation (the Khovanov-Rozansky theory) and the relation with the refined topological vertex should be useful for categorizing quantum group invariants associated with other representations (R ₁, R ₂). Our result is a first direct verification of a series of conjectures which identifies link homologies with the Hilbert space of BPS states in the presence of branes, where the physical interpretation of gradings is in terms of charges of the branes ending on Lagrangian branes.     

KAM theory and the 3D Euler equation

We prove that the dynamical system defined by the hydrodynamical Euler equation on any closed Riemannian 3-manifold M   is not mixing in the C^k$C^k$ topology (k>4$k>4$ and non-integer) for any prescribed value of helicity and sufficiently large values of energy. This can be regarded as a 3D version of Nadirashvili's and Shnirelman's theorems showing the existence of wandering solutions for the 2D Euler equation. Moreover, we obtain an obstruction for the mixing under the Euler flow of C^k$C^k$-neighborhoods of divergence-free vectorfields on M  . On the way we construct a family of functionals on the space of divergence-free C¹$C^1$ vectorfields on the manifold, which are integrals of motion of the 3D Euler equation. Given a vectorfield these functionals measure the part of the manifold foliated by ergodic invariant tori of fixed isotopy types. We use the KAM theory to establish some continuity properties of these functionals in the C^k$C^k$-topology. This allows one to get a lower bound for the C^k$C^k$-distance between a divergence-free vectorfield (in particular, a steady solution) and a trajectory of the Euler flow.     

Lost heat capacity and entropy in the helical magnet MnSi

The heat capacity of MnSi at B = 0 and B = 4 T was measured in the temperature range 2.5-100 K. To analyze the data, calculations of the phonon spectrum and phonon density of states in MnSi were performed. The calculated phonon frequencies were confirmed by means of inelastic neutron scattering. The analysis of the data suggests the existence of negative contributions to the heat capacity and entropy of MnSi at T > T(c) that may imply a specific ordering in the spin subsystem in the paramagnetic phase of MnSi.     

A model for the dissociative adsorption of N2O on Cu(1 0 0) using a continuous potential energy surface

For the first time, a continuous ab initio potential energy surface (PES) taking into account all molecular degrees of freedom is built and used to model the reaction of a polyatomic molecule with a surface. DFT slab calculations are used to sample the configuration space of the system N₂O/Cu(1 0 0), and the PES function is built with a method of Manzhos and Carrington [J. Chem. Phys. 127 (2007) 014103] using dimensionality reduction from only 4300 single-point energies. Molecular dynamics simulations are performed on the PES to calculate the probability of dissociative adsorption.     

Expansion of analytic functions in q-orthogonal polynomials

A classical result on the expansion of an analytic function in a series of Jacobi polynomials is extended to a class of q-orthogonal polynomials containing the fundamental Askey–Wilson polynomials and their special cases. The function to be expanded has to be analytic inside an ellipse in the complex plane with foci at ±1. Some examples of explicit expansions are discussed.      

Tailoring terahertz near-field enhancement via two-dimensional plasmons

We suggest a novel possibility for electrically tunable terahertz near-field enhancement in flatland electronic materials supporting two-dimensional plasmons, including recently discovered graphene. We employ electric-field effect modulation of electron density in such materials and induce a periodic plasmonic lattice with a defect cavity. We demonstrate that the plasmons resonantly excited in such a periodic plasmonic lattice by an incident terahertz radiation can strongly pump the cavity plasmon modes leading to a deep subwavelength concentration of terahertz energy, beyond λ/1000, with giant electric-field enhancement factors up to 10(4), which is 2 orders of magnitude higher than achieved previously in metal-based terahertz field concentrators.     

ATR-FTIR imaging for the analysis of organic materials in paint cross sections: case studies on paint samples from the National Gallery, London

The potential of attenuated total reflection Fourier transform infrared (ATR-FTIR) imaging for the characterisation of the chemical components of paint cross sections from old master paintings was investigated. Three cross sections were chosen to cover a variety of the analytical problems encountered in samples from paintings. The binding medium and degradation products in a green paint sample from a fifteenth-century Florentine painting were imaged, as well as a thin layer within a cross-section from a fifteenth-century German painting, and multiple thin surface coatings on a painting of the 1760s by Peter Romney. The application of chemometric methods for further analysis of the large data set generated for each sample was also explored. The study demonstrated the advantages of ATR-FTIR imaging, which allowed images to be obtained with high spatial resolution (ca. 3-4 microm) without the need to microtome the sample. The gain in sensitivity in detecting trace materials and the information derived from the location of these compounds in the sample was especially valuable, improving interpretation of the FTIR analysis and extending knowledge of the sample composition beyond that obtainable with other analytical techniques.     

High-throughput study of poly(ethylene glycol)/ibuprofen formulations under controlled environment using FTIR imaging

Simultaneous analysis of many samples under identical conditions improves the effectiveness of research and accelerates product design. A novel spectroscopic imaging approach using a multichannel detector has been developed for parallel analysis of pharmaceutical formulations under controlled environments. Samples of formulations of ibuprofen in poly(ethylene glycol) have been prepared with ibuprofen concentrations ranging from 0 to 100% using a microdroplet deposition approach. The concentration of ibuprofen in PEG at which dimerization of ibuprofen molecules can be avoided has been determined via simultaneous measurement of all samples using in situ FTIR spectroscopic imaging. FTIR spectra from all samples have been analyzed to assess the molecular state of the drug and the degree of polymer swelling as a function of drug concentration. The effect of elevated temperature on the stability of all formulations was also studied. This high-throughput approach identified the concentration range for stable formulations and provided evidence that hydrogen bonding between ibuprofen and the polymer is responsible for enhanced stability at higher temperatures. This high-throughput imaging approach, based on a miniature sampling system, significantly reduces the experimental time by allowing many (potentially a few thousand) experiments to be run in parallel and increases the accuracy by minimizing variations between experiments.