The logarithmic norm. History and modern theory

In his 1958 thesis Stability and Error Bounds, Germund Dahlquist introduced the logarithmic norm in order to derive error bounds in initial value problems, using differential inequalities that distinguished between forward and reverse time integration. Originally defined for matrices, the logarithmic norm can be extended to bounded linear operators, but the extensions to nonlinear maps and unbounded operators have required a functional analytic redefinition of the concept.This compact survey is intended as an elementary, but broad and largely self-contained, introduction to the versatile and powerful modern theory. Its wealth of applications range from the stability theory of IVPs and BVPs, to the solvability of algebraic, nonlinear, operator, and functional equations. In memory of Germund Dahlquist (1925–2005).AMS subject classification (2000) 65L05     

A procedure for measuring the flexibility of single wood-pulp fibres

A way of determining the flexibility of wood-pulp fibres is developed, which involves i) a precise measurement of the topology of single-fibres by using a confocal laser scanning microscope and ii) the measurement of the elastic modulus of the fibres by using a single-fibre fatigue cell. Reported in this paper are the initial results of tests carried out on black spruce fibres, which have been subjected to three different levels of mechanical refining energy, namely ∼1100, 2300, and 3500 kWh/t. It is found that the fibre flexibility rises significantly between the first and second energy levels, but it does not change to the same degree between the second and third ones. The described procedure of measuring the flexibility of fibres may be used to establish the appropriate refiner energy necessary for the production of a specific grade of paper. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 115–128, January–February, 2006.     

X-PEEM/NEXAFS and AFM of polypyrrole and copper micro-patterns on insulating fluoropolymer substrates

Micro-patterns (80 μm and 10 μm) of copper and semi-conducting polypyrrole on insulating fluorinated ethylene propylene substrates were characterized using synchrotron-based X-ray Photoemission Electron Microscopy (X-PEEM), Near Edge X-ray Absorption Fine Structure (NEXAFS), and Atomic Force Microscopy (AFM). Electronic states in the polypyrrole are verified using the NEXAFS data, and sample degradation upon irradiation is addressed. X-PEEM images show homogeneous distributions of the corresponding elements in the patterns. They do not exhibit dichroic effects and give information about the growth of copper and polypyrrole (i.e. nucleation of Cu, overgrowth of PPy, formation of PPy granules). AFM results are used to verify the topography of the patterns and support the findings on pattern growth.     

In situ preparation of Bi-Sr-Ca-Cu-O superconducting films by laser sputtering

Superconducting films of Bi-Sr-Ca-Cu-O on (100) MgO substrates have been fabricated by XeCl-excimer-laser sputtering from ceramic targets of Bi_2.5Sr₂Ca₂Cu₃O_y in O₂ atmosphere. The films were polycrystalline with the c-axis (30.80±0.02Å) preferably oriented normal to the substrate surface. Without post-annealing the films showed metallic resistance behavior with zero resistance temperatures of up to T_c(0) }- 79 K. The critical current density of the films had values of up to j_c(50K)}- 10⁴ A/cm².     

Multiferroic TbMnO3 nanoparticles

We report on the synthesis of TbMnO₃ nanoparticles by chemical co-precipitation route and their structural, chemical bonding, magnetic and dielectric properties. It is shown that the interesting multiferroic properties of this system as reflected by the concurrent occurrence of magnetic and dielectric transitions are retained in the nanoparticles (size∼40 nm). However, the nanoparticle constitution and properties are seen to depend significantly on the calcination temperature. While the nanoparticles obtained by calcination at 800 °C correspond very well with the reported properties of single phase TbMnO₃ (all the key magnetic and dielectric features near 7, 27 and 41 K, albeit with reduced dielectric constant) the nanoparticles obtained by calcination at 900 °C develop a Tb deficient skin which softens the transitions, reducing the dielectric constant further.     

Formation and magnetic properties of Co–Fe-based bulk metallic glasses with supercooled liquid region

A new Co–Fe-based ferromagnetic bulk metallic glass (BMG) was synthesized by copper mould casting method. The thermal stability and crystallization processes were investigated by differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The soft magnetic behavior was studied by DC magnetic measurements. The high glass formation ability was interpreted in terms of the effective suppression of nucleation and growth of the intermetallic compounds which appear in the multicomponent system during solidification. The high thermal stability indicates that the new Co–Fe-based BMG could be used as high-temperature magnetic material. The low coercivity which was as low as 8 A/m for the as-cast sample was found in the Co–Fe-based metallic glass cylinder with a diameter of 1.5 mm.     

Enhanced transmission of electromagnetic waves through metamaterials

This paper reviews our recent experimental and simulation results regarding the electromagnetic wave transmission through three configurations of sandwiching structures of metamaterials: a metallic mesh sandwiched between two identical layers composed of split rings, metallic fractals, and fractal slits, respectively. We observed the enhanced transmission of the waves through these three types of sandwiching composites with respect to the opaque metallic mesh. The locations of the transmission peaks in the spectrum are associated closely with the band characteristics of the sandwiching layer by appearing either on the left- or the right-hand side of its band. PACS 41.20.Jb; 42.70.Qs; 78.20.-e; 42.25.Bs; 47.53.+n