Haefliger’s codimension-one singular foliations, open books and twisted open books in dimension 3

We consider singular foliations of codimension one on 3-manifolds, in the sense defined by André Haefliger as being ??₁-structures. We prove that under the obvious linear embedding condition, they are ??₁-homotopic to a regular foliation carried by an open book or a twisted open book. The latter concept is introduced for this aim. Our result holds true in every regularity C ^r , r ?? 1. In particular, in dimension 3, this gives a very simple proof of Thurston??s 1976 regularization theorem without using Mather??s homology equivalence.     

A superdirective array of phase shift sources

A superdirective array of audio drivers is described, which is compact compared with the acoustic wavelength over some of its frequency range. In order to minimize the overall sound power output, and hence reduce the excitation of the reverberant field when used in an enclosed space, the individual drivers are made directional by using phase shift enclosures. The motivating application for the array is the enhancement of sound from a television, in a particular region of space, to aid hearing impaired listeners. The design is initially investigated, using free-field simulations, by comparing the performance of 8 monopoles, 8 phase shift loudspeakers, and a double array of 16 monopoles, with a contrast maximization formulation. The construction and testing of an array of 8 drivers is then discussed, together with its measured response in an anechoic environment. The result of using acoustic contrast maximization is then compared with a least squares formulation, which demonstrates that the performance of the least squares solution can be made similar to that given by acoustic contrast maximization in this application, with a suitable choice of the target field.     

An Update of DNA Hydrogel Application in Biosensing

DNA gel not only uses the skeleton function of hydrogel but also the biological function of DNA to realize the unified fusion of the structure and function of hydrogel material. By introducing specific small molecules into the DNA gel, it can respond to pH, temperature, ultraviolet, infrared, metal ions, and drug small molecules. To further realize the detection and loading of various small molecules in the biomedical field, the specific recognition and detection of heavy metal ions and toxins in the environment are done. In this paper, the preparation of pure DNA gel and hybrid DNA gel, their detection in the biomedical and environmental fields are reviewed, and their prospects and further development directions are discussed.     

Mechanical Enhancement of the Strain-Sensor Response in Dimers of Strongly Coupled Plasmonic Nanoparticles

Due to their particular optical and mechanical properties, plasmomechanical devices have become choice candidates in strain sensing applications. Using numerical simulation, a plasmomechanical system consisting of two gold nanoparticles with different shapes and separated by a small gap, deposited onto a deformable polydimethylsiloxane membrane, is investigated. With the aim of understanding the relationship between the plasmonic behavior of gold nanoparticles and induced mechanical deformations, mechanical extension ranging from 0% to 20% is applied to the polydimethylsiloxane membrane. In a first step, a mechanical calculation based on a hyperelastic model for polydimethylsiloxane shows that the interparticle spacing is enhanced nonlinearly by a percentage greater than the externally applied deformation, depending on the shape and size of the nanoparticles as well as the polydimethylsiloxane membrane thickness. Full optical simulation of the deformed nanosystems demonstrates that the plasmonic resonance wavelength is highly sensitive to the applied displacements and is enhanced compared to a basic approach where the gap deformation is taken as equal to the macroscopic applied deformation. The best figure of merit ($0.022{\%}^{-1}$) is obtained for the disk–rod dimer near the strong coupling regime, larger than the values reported in the literature for localized nanoparticle systems.