Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

Some effects of surface tension on fully nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are presented. Analytical expressions for new peaked traveling wave solutions are presented in the dispersionless case of critical surface tension. Numerical experiments are performed using a high-accurate finite element method based on smooth cubic splines and the four-stage, classical, explicit Runge–Kutta method of order 4.     

On the identification of a high-resolution multi-linear post-necking strain hardening model

The Finite Element Model Updating (FEMU) technique is an inverse method that enables to arrive at a complete solution to the problem of diffuse necking of a thick tensile specimen. Conventionally, FEMU relies on the identification of a phenomenological strain hardening law that inherently limits the accuracy of the method due to the predefined character of the adopted strain hardening law. A high-resolution multi-linear post-necking strain hardening model enables to describe more generically the actual strain hardening behaviour. A numerical concept study is used to scrutinise the identification of such a model using FEMU. It is shown that, unlike progressive identification strategies, a global identification strategy followed by a smoothing operation based on area conservation yields sufficiently accurate results. To study the experimental feasibility, the latter strategy is used to identify the post-necking strain hardening behaviour of a thick S690QL high-strength steel. To this purpose, a notched tensile specimen was loaded up to fracture, while the elongation was measured using Digital Image Correlation (DIC). It is shown that the global identification strategy suffers from experimental noise associated with DIC and the load signal.     

Environment‐Adopting Surfaces with Reversibly Switchable Morphology

Two‐component polymer brushes (polystyrene and poly(2‐vinylpyridine)) were synthesized by grafting from the surface of Si‐wafers. The brushes are sensitive to the surrounding medium, and their morphology and composition of the top of a brush can be switched upon exposure to different solvents. Thus surface energetic states and roughness of the film can be precisely tuned.     

Structural phase transitions and the equation of state of SnTe at high pressures up to 2 mbar

Synchrotron X-ray diffraction studies of the structure of SnTe have been performed at room temperature and high pressures under the conditions of quasihydrostatic compression up to 193.5 GPa created in diamond anvil cells. Two structural phase transitions have been detected at P ≈ 3 and 23 GPa. The first phase transition is accompanied by a stepwise decrease in the volume of the unit cell by 4% because of the orthorhombic distortion of the initial SnTe-B1 cubic structure of the NaCl type. It has been found that two intermediate rhombic phases of SnTe with the space groups Cmcm and Pnma coexist in the pressure range of 3–23 GPa. The second phase transition at 23 GPa occurs from the intermediate rhombic modification to the SnTe-B2 cubic phase with the CsCl structure type. This phase transition is accompanied by an abrupt decrease in the volume of the unit cell by 8%. The pressure dependence of the volumes per formula unit at room temperature has been determined.     

Lab-in-a-tube: ultracompact components for on-chip capture and detection of individual micro-/nanoorganisms

A review of present and future on-chip rolled-up devices, which can be used to develop lab-in-a-tube total analysis systems, is presented. Lab-in-a-tube is the integration of numerous rolled-up components into a single device constituting a microsystem of hundreds/thousands of independent units on a chip, each individually capable of sorting, detecting and analyzing singular organisms. Such a system allows for a scale-down of biosensing systems, while at the same time increasing the data collection through a large, smart array of individual biosensors. A close look at these ultracompact components which have been developed over the past decade is given. Methods for the capture of biomaterial are laid out and progress of cell culturing in three-dimensional scaffolding is detailed. Rolled-up optical sensors based on photoluminescence, optomechanics, optofluidics and metamaterials are presented. Magnetic sensors are introduced as well as electrical components including heating, energy storage and resistor devices.     

Spectral analysis of operators with the two-point Bohr spectrum

In this paper the representation theory of locally compact Abelian groups is used to introduce linear operators with the two-point Bohr spectrum and to study their spectral properties. In particular, the structure of the inverse operators is considered and the applications to the theory of difference operators are discussed.     

Krylov-Bogolyubov substitution in the perturbation theory of linear operators

Ukrainian Mathematical Journal -