Artificial Genetic Sets Composed of Size‐Expanded Base Pairs

We describe in this Minireview the synthesis, properties, and applications of artificial genetic sets built from base pairs that are larger than the natural Watson–Crick architecture. Such designed systems are being explored by several research groups to investigate basic chemical questions regarding the functions of the genetic information storage systems and thus of the origin and evolution of life. For example, is the terrestrial DNA structure the only viable one, or can other architectures function as well? Working outside the constraints of purine–pyrimidine geometry provides more chemical flexibility in design, and the added size confers useful properties such as high binding affinity and helix stability as well as fluorescence. These features are useful for the investigation of fundamental biochemical questions as well as in the development of new biotechnological, biomedical, and nanostructural tools and methods.     

Non‐contact evaluation of the electrical conductivity of thin metallic films by eddy current microscopy

An eddy current microscopy technique to evaluate the electrical conductivity of thin metallic films in a non‐contact manner is reported. A narrow track formed in an approximately 100 nm thick Au film was prepared, and a Co–Cr coated magnetic tip was driven to oscillate above the track both with and without current passing through the track. Despite the absence of current, the electromagnetic interaction between the tip and the stray magnetic field from the track gave rise to a phase delay in the probe. This was due to an eddy current being induced within part of the track. Moreover, measurements of the phase change in the probe oscillation for different metallic films with thicknesses of about 100 nm found this to be proportional to the electrical conductivity of the film. Finally, the electrical conductivity of an Al film was evaluated using the eddy current microscopy technique. Copyright © 2012 John Wiley & Sons, Ltd.     

On the usage of NURBS as interface representation in free‐surface flows

When simulating free‐surface flows using the finite element method, there are many cases where the governing equations require information which must be derived from the available discretized geometry. Examples are curvature or normal vectors. The accurate computation of this information directly from the finite element mesh often requires a high degree of refinement—which is not necessarily required to obtain an accurate flow solution. As a remedy and an option to be able to use coarser meshes, the representation of the free surface using non‐uniform rational B‐splines (NURBS) curves or surfaces is investigated in this work. The advantages of a NURBS parameterization in comparison with the standard approach are discussed. In addition, it is explored how the pressure jump resulting from surface tension effects can be handled using doubled interface nodes. Numerical examples include the computation of surface tension in a two‐phase flow as well as the computation of normal vectors as a basis for mesh deformation methods. For these examples, the improvement of the numerical solution compared with the standard approaches on identical meshes is shown. Copyright © 2011 John Wiley & Sons, Ltd.     

A class of finite difference schemes for interface problems with an HOC approach

In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.     

Split least‐squares finite element methods for non‐Fickian flow in porous media

In this article, we introduce two least‐squares finite element procedures for parabolic integro‐differential equations arising in the modeling of non‐Fickian flow in porous media. By selecting the least‐squares functional properly the presented procedure can be split into two independent subprocedures, one subprocedure is for the primitive unknown and the other is for the flux. The optimal order convergence analysis is established. Numerical examples are given to show the efficiency of the introduced schemes. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Ferroelasticity in non-group-subgroup transitions

Aizu's definition of ferroelasticity can be extended to transitions between two crystals whose point groups are not group-subgroup related. In general, two different variant structures then appear on both sides of the transition, each variant structure being determined by the operators “lost” at the transition. If a minimal common supergroup exists, then it is the prototype group. For each variant structure, a spontaneous strain tensor can be defined. Ferroelasticity occurs for both structures, and is termed “double ferroelasticity”, if none of the groups belong to the same symmetry system as the common minimal supergroup. Examples are discussed.