On the Stability of Solitary Water Waves with a Point Vortex

This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude waves with small enough vortex strength are conditionally orbitally stable. In the process of obtaining this result, we develop a quite general stability/instability theory for bound state solutions of a large class of infinite-dimensional Hamiltonian systems in the presence of symmetry. This is in the spirit of the seminal work of Grillakis, Shatah, and Strauss (GSS) , but with hypotheses that are relaxed in a number of ways necessary for the point vortex system, and for other hydrodynamical applications more broadly. In particular, we are able to allow the Poisson map to have merely dense range, as opposed to being surjective, and to be state-dependent. As a second application of the general theory, we consider a family of nonlinear dispersive PDEs that includes the generalized Korteweg–de Vries (KdV) and Benjamin-Ono equations. The stability or instability of solitary waves for these systems has been studied extensively, notably by Bona, Souganidis, and Strauss , who used a modification of the GSS method. We provide a new, more direct proof of these results, as a straightforward consequence of our abstract theory. At the same time, we allow fractional dispersion and obtain a new instability result for fractional KdV. © 2020 Wiley Periodicals, Inc.     

Synthesis and characterization of ferrocene containing block copolymers

Narrowly dispersed diblock copolymers containing poly(methyl methacrylate) [PMMA] or poly(nonafluorohexyl methacrylate) [PF9MA] as the first block and poly(ferrocenylmethyl methacrylate) [PFMMA] as the second block, were prepared by anionic polymerization for the first time. Disordered bulk morphologies in the case of PMMA‐b‐PFMMA were observed and explained in terms of low Flory–Huggins interaction parameter (χ ≤ 0.04). In the case of PF9MA‐b‐PFMMA hexagonally packed cylinder morphology (HEX) was substantiated from TEM and SAXS observations. Furthermore, high incompatibility between PF9MA and PFMMA blocks allowed for the formation of well‐ordered ferrocene containing cylinders on silica substrate upon exposure of the thin films to a saturated solvent vapor. It was shown that the cylinder orientation, parallel or perpendicular to the surface, could easily be controlled by appropriate choice of the solvent and without the need for preliminary surface modification, for example by means of grafted brush layer. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 495–503     

Stress relaxation of bi-disperse polystyrene melts

We present start-up of uniaxial extension followed by stress relaxation experiments of a bi-disperse 50 % by weight blend of 95k and 545k molecular weight polystyrene. We also show, for comparison, stress relaxation measurements of the polystyrene melts with molecular weight 95k and 545k, which are the components of the bi-disperse melt. The measurements show three separated relaxation regimes: a fast regime, a transition regime, and a slow regime. In the fast regime, the orientation of the long chains is frozen and the stress relaxation is due to stretch relaxation of the short chains primarily. Conversely in the slow regime, the long chains have retracted and undergo relaxation of orientation in fully relaxed short chains.     

Diepoxide treatment of softwood kraft pulp: influence on absorption properties of fibre networks

Many different approaches to the introduction of intra-fibre cross-links in fibres for use in absorption products are described in the patent literature, but relatively little has been done in terms of academic research. In this study, the long fibre fraction of a Scandinavian softwood kraft pulp has been cross-linked with the diepoxide 1,4-butanediol diglycidyl ether (BDDE). The fibre properties and the performance of the pulp in low density fibre networks were analyzed. In experiments, the cross-linking agent (BDDE) was dissolved in acetone and then mixed with the pulp. It was shown that a prior wash with NaOH (0.1 M) activates the polysaccharides and increases the extent of cross-linking, detected as a decrease in the water retention value. Chemical analysis of modified fibres also gave a clear indication of that cross-linking reactions actually occurred. The pulp properties could furthermore be influenced by varying time, temperature and the amount of BDDE in the reaction. It was also shown that it is possible to use water as a solvent for the cross-linking agent, even though the reactivity of water towards diepoxide must be considered to be high. The cross-linked pulps showed wet bulk under load comparable to that of the mechanical pulps and enhanced properties than unmodified Scandinavian softwood kraft pulp. It was also observed that fibre network test pads of the cross-linked pulp fibres, after being tested in the wet state, regained a substantially large part of their low-density structure when air-dried.     

Tracing the Photoaddition of Pharmaceutical Psoralens to DNA

The psoralens 8-methoxypsoralen (8-MOP), 4,5′,8-trimethylpsoralen (TMP) and 5-methoxypsoralen (5-MOP) find clinical application in PUVA (psoralen + UVA) therapy. PUVA treats skin diseases like psoriasis and atopic eczema. Psoralens target the DNA of cells. Upon photo-excitation psoralens bind to the DNA base thymine. This photo-binding was studied using steady-state UV/Vis and IR spectroscopy as well as nanosecond transient UV/Vis absorption. The experiments show that the photo-addition of 8-MOP and TMP involve the psoralen triplet state and a biradical intermediate. 5-MOP forms a structurally different photo-product. Its formation could not be traced by the present spectroscopic technique.     

Assessing market uncertainty by means of a time-varying intermittency parameter for asset price fluctuations

Maximum likelihood estimation techniques for multifractal processes are applied to high-frequency data in order to quantify intermittency in the fluctuations of asset prices. From time records as short as one month these methods permit extraction of a meaningful intermittency parameter λ$\lambda$ characterising the degree of volatility clustering. We can therefore study the time evolution of volatility clustering and test the statistical significance of this variability. By analysing data from the Oslo Stock Exchange, and comparing the results with the investment grade spread, we find that the estimates of λ$\lambda$ are lower at times of high market uncertainty.     

Surface modification and oxidation kinetics of hot-pressed AlN–SiC–MoSi2 electroconductive ceramic composite

The effects of oxidation on the microstructural modification and on the electrical resistivity and mechanical strength of a hot-pressed AlN–SiC–MoSi₂ electroconductive ceramic composite were studied. The kinetic of the oxidation was also evaluated. After the oxidation at temperatures below 1000 °C samples do not gain weight, due to simultaneous formation of SiO₂ and evaporation of MoO₃ formed by the oxidation of MoSi₂. However, the AlN/SiC matrix disables the “pesting” phenomena and strength degradation, despite the fact that at these temperatures MoSi₂ oxidizes rapidly. At temperatures above 1000 °C, the composite gains weight due to protective mullite layer formation on the surface, that provides a good oxidation resistance for use at higher temperatures. The kinetics of the oxidation follows the parabolic law. The possible rate-controlling mechanism is the diffusion of oxygen through the mullite-rich surface oxide scale.     

Multimaterial hydrogel with widely tunable elasticity by selective photopolymerization of PEG diacrylate and epoxy monomers

We present a method to make continuous multi‐material structures from a monomer solution that becomes a soft hydrogel when exposed to blue light and a hard solid when exposed to UV light. We show that the material can be varied between a hard epoxy material to a several hundred times softer poly(ethylene glycol)‐diacrylate material. Moreover, the elastic properties of the material depend on both the wavelength of and exposure time of the light, which is used to produce a material with an elasticity gradient. We expect our material to find use in a range of fields, with immediate applications as 2D sheets with tunable mechanical properties for cell durotaxis studies, and 3D stereolithographically printed tissue mimicks, for example, for disease models and tissue engineering. Spatially resolved photo‐polymerization of a mixture of epoxy and acrylate monomers can be used to make multi‐material structure, with unique freedom to polymerize each monomer individually. The elastic compressive properties of the material are shown to be fully tunable from <100 kPa to >20 MPa depending on the light exposure time. This is used to make a functionally graded continuous material with a large variation in elastic properties. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1195–1201