Linearisation and potential symmetries of certain systems of diffusion equations

We consider systems of two pure one-dimensional diffusion equations that have considerable interest in Soil Science and Mathematical Biology. We construct non-local symmetries for these systems. These are determined by expressing the equations in a partially and wholly conserved form, and then by performing a potential symmetry analysis on those systems that can be linearised. We give several examples of such systems, and in a specific case we show how linearising and hodograph-type mappings can lead to new solutions of the diffusion system.     

Raman spectroscopy of acoustic phonons in periodic and Fibonacci superlattices

Results of Raman scattering experiments on (a) periodic superlattices made up of GaAs/In_xGa_1−xAs layers with high indium concentrations, (b) GaAs/Ga_1−xAl_xAs Fibonacci superlattices, are presented. We discuss the observed peak positions and intensities using the continuum theory of acoustic wave propagation in layered media and the photo-elastic coupling model.     

Properties of Josephson junctions in the inhomogeneous magnetic field of a system of ferromagnetic particles

The effect of an array of ferromagnetic nanoparticles on the field-dependent critical current of the short overlap Josephson junction is experimentally studied. Large reversible variations of the maximum critical current are observed depending on the magnetic state of the particles. The pronounced commensurability effects are detected which are proved by the additional peaks of magnetic field induced diffraction pattern.     

Magnetic field mapping in NMR imaging

The Hahn spin preparation sequence provides a practical means for rapid and sensitive mapping of magnetic field inhomogeneity in NMR imaging applications. Choice of the rf pulse delay times tau 1 and tau 2 as well as conditions and limitations on the proposed use of this sequence for chemical shift imaging are discussed.     

Elastic instability of the nano-structured state as an intrinsic probe to study the early formation stages of sol–gel derived (Pb<Subscript>1-x</Subscript>Ca<Subscript>x</Subscript>)TiO<Subscript>3</Subscript> thin films

A novel method to investigate the early formation stages of polycrystalline (Pb_1-xCa_x)TiO₃ (PCT) perovskite films by means of traditional Brillouin and micro-Brillouin spectroscopy (BS, mBS) is described in the present work. The films were prepared by chemical solution deposition (CSD) onto oxidized (100)Si substrates and treated at temperatures between 350–650 °C by rapid thermal processing (RTP). The elastic instability observed by Brillouin spectroscopy at the nano-structured state of the PCT films was used here to determine their crystallization temperatures. Coexistence of different nanocrystalline phases (e.g., pyrochlore, perovskite) in the films could also be detected by this technique. The reliability of these results is demonstrated by complementary information obtained by X-ray diffraction (XRD) and scanning force microscopy (SFM). The effects of the annealing temperature and of the Ca²⁺ content on the crystallization process of these films are also discussed. PACS 78.35.+c; 77.84.-s; 61.82.Rx     

Strong temperature effect on X-ray photo-etching of polytetrafluoroethylene using a 10 Hz laser-plasma radiation source based on a gas puff target

The first results of experiments on direct photo-etching of heated PTFE using a 10 Hz X-ray source based on a laser-irradiated gas puff target are presented. X-ray radiation in the wavelength range from 6 to 20 nm was produced as a result of irradiation of a double-stream gas puff target with Nd:YAG laser pulses of energy 0.8 J and time duration 3 ns. The resulting X-ray pulses with energy of about 100–200 mJ were used to irradiate samples of PTFE to create microstructures by direct photo-etching. Strong enhancement of the photo-etching process was observed for samples heated up to 300 °C. PACS 52.38.Ph; 81.65.Cf; 61.82.Pv     

Microdrilling for fabricating micrometer-scale holes in soft matter

Probing the response of soft materials at small scales requires examining fundamental behaviors that are often distinct from large-scale interactions. In the development of micrometer- and nanometer-sized holes in soft materials, understanding failure modes becomes essential. We observe fracture behavior in a soft material through a novel method, which leads to the fabrication of small-scale holes in polydimethylsiloxane. We utilize an ultra-sharp tungsten needle to drill this soft elastomeric polymer; this results in controlled hole size and exhibits fracture characteristics observed in brittle materials at larger length scales. We also examine the macroscopic characteristics known to contribute to brittleness and hardness for this material’s response with respect to curing times. This understanding will contribute to many applications including the development of porous materials and DNA sequencing efforts. PACS 81.05.Lg; 81.40.Np; 82.35.Lr