Multidomain direct method and its applicability to the local time-step concept

A new multidomain direct (noniterative) method for solving boundary-value problems is presented. Using this method, the solution is expressed by a linear combination of auxiliary functions and unknowns which pertain to the boundaries of a subdomain. This approach enables us to solve problems independently and exactly, without any iterations between subdomains. As a consequence, different types of equations and coordinate systems may be considered in different subdomains. Moreover, different boundary conditions and variable (in space) time steps may be imposed on the subdomains as well. Applications are given for initial boundary-value problems with known analytical solutions, including a highly nonlinear porosity equation. © 1994 John Wiley & Sons, Inc.     

The convenient route to cd fragment for the synthesis of vitamin D3 relatives

The efficient degradation of $\text{1}$ to the α-methylene ketone $\text{4}$ is described. Compound $\text{4}$ was then converted to the allylic alcohol $\text{8a}$ - the precursor of vitamin D³ relatives.     

12H-naphtho[1′,2′:5,6]pyrano[2,3-d]pyrimidine derivatives

Reaction of 1-oxo-2-formyl-3-dimethylamino-1H-naphtho[2,1-b]pyran with amidines, guanidine, O-methylisourea, S-methylisothiourea afforded 9-substituted 12-oxo-12H-naphtho[1′,2′:5,6]pyrano[2,3-d]pyrimidines. When the reaction with O-methylisourea was carried out in anhydrous pyridine, 10,20-dioxo-10H,20H-dinaphtho[1,2-e:1′,2′-e′][1,5]diazocino[2,3-b:6,7-b′]dipyran was formed.     

Structural properties of transparent Ti-V oxide semiconductor thin films

Transparent oxide semiconducting thin films based on mixed Ti-V oxides were prepared using a modified reactive magnetron sputtering method. Based on structural investigations performed with the help of x-ray diffraction and transmission electron microscopy analysis, two distinct regions in the prepared thin film have been observed: a nanocrystalline TiO₂-V₂O₃-V₂O₅ mixed composition, and a thin layer consisting of amorphous phase and nanocystalline TiO₂ phase deposited directly at the substrate. Optical measurements show excellent transmission in the visible spectral range of 73%, on average. Resistivity of the thin film was found at the order of 10⁵ Ω cm at room temperature. The preparation of mixed Ti-V oxides provides a combination of high transparency and semiconducting properties.     

Controlling soliton refraction in optical lattices

We show in the framework of the 1D nonlinear Schr?dinger equation that the value of the refraction angle of a fundamental soliton beam passing through an optical lattice can be controlled by adjusting either the shape of an individual waveguide or the relative positions of the waveguides. In the case of the shallow refractive index modulation, we develop a general approach for the calculation of the refraction angle change. The shape of a single waveguide crucially affects the refraction direction due to the appearance of a structural form factor in the expression for the density of emitted waves. For a lattice of scatterers, wave-soliton interference inside the lattice leads to the appearance of an additional geometric form factor. As a result, the soliton refraction is more pronounced for the disordered lattices than for the periodic ones.     

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. I. Multiple-time-scale analysis and microscopic expression for the friction coefficient

The Fokker-Planck equation governing the evolution of the distribution function of a massive Brownian hard sphere suspended in a fluid of much lighter spheres is derived from the exact hierarchy of kinetic equations for the total system via a multiple-time-scale analysis akin to a uniform expansion in powers of the square root of the mass ratio. The derivation leads to an exact expression for the friction coefficient which naturally splits into an Enskog contribution and a dynamical correction. The latter, which accounts for correlated collisions events, reduces to the integral of a time-displaced correlation function of dynamical variables linked to the collisional transfer of momentum between the infinitively heavy (i.e., immobile) Brownian sphere and the fluid particles.     

Friction tensor for a pair of Brownian particles: Spurious finite-size effects and molecular dynamics estimates

In this work, we show thatin any finite system, the binary friction tensor for two Brownian particlescannot be directly estimated from an evaluation of the microscopic Green-Kubo formula, involving the time integral of force-force autocorrelation functions. This pitfall is associated with a subtle inversion of the thermodynamic and long-time limits and leads to spurious results for the estimates of the friction matrix based on molecular dynamics simulations. Starting from a careful analysis of the coupled Langevin equations for two interacting Brownian particles, we derive a method to circumvent these effects and extract the binary friction tensor from the correlation function matrix of the instantaneous forces exerted by the bath particles on the fixed Brownian particles, and from the relaxation of the total momentum of the bath in afinite system. The general methodology is applied to the case of two hard or soft Brownian spheres in a bath of light particles. Numerical estimates of the relevant correlation functions and of the resulting self and mutual components of the matrix of friction tensors are obtained by molecular dynamics simulations for various spacings between the Brownian particles. This paper is dedicated to B. Jancovici on the occassion of his 65th birthday.     

Mechanical properties of metallic ribbons investigated by depth sensing indentation technique

The paper presents mechanical properties of two kinds of Co-based and one Fe-based metallic ribbons by the depth sensing indentation (DSI) technique. Investigations were carried out on two kinds ternary alloy Co₇₇Si_11,5B_11,5 and Fe₇₈Si₁₃B₉ and multicomponent Co₆₈Fe₄Mo₁Si_13,5B_13,5, which are so-called “zero-magnetostriction” materials. Metallic ribbons were investigated in amorphous state and partially crystallized state after annealing in 400°C in argon atmosphere. Heating of ribbons obtained by melt spinning technique was performed to check its effect on changes of mechanical properties.     

Partitioning of atmospheric carbon dioxide over Central Europe: insights from combined measurements of CO 2 mixing ratios and their carbon isotope composition

Regular measurements of atmospheric CO ₂ mixing ratios and their carbon isotope composition (¹³C/¹²C and ¹⁴C/¹²C ratios) performed between 2005 and 2009 at two sites of contrasting characteristics (Krakow and the remote mountain site Kasprowy Wierch) located in southern Poland were used to derive fossil fuel-related and biogenic contributions to the total CO ₂ load measured at both sites. Carbon dioxide present in the atmosphere, not coming from fossil fuel and biogenic sources, was considered ‘background’ CO ₂. In Krakow, the average contribution of fossil fuel CO ₂ was approximately 3.4%. The biogenic component was of the same magnitude. Both components revealed a distinct seasonality, with the fossil fuel component reaching maximum values during winter months and the biogenic component shifted in phase by approximately 6 months. The partitioning of the local CO ₂ budget for the Kasprowy Wierch site revealed large differences in the derived components: the fossil fuel component was approximately five times lower than that derived for Krakow, whereas the biogenic component was negative in summer, pointing to the importance of photosynthetic sink associated with extensive forests in the neighbourhood of the station. While the presented study has demonstrated the strength of combined measurements of CO ₂ mixing ratios and their carbon isotope signature as efficient tools for elucidating the partitioning of local atmospheric CO ₂ loads, it also showed the important role of the land cover and the presence of the soil in the footprint of the measurement location, which control the net biogenic surface CO ₂ fluxes.     

Heat conduction in transversally graded laminates with non-uniform microstructure

Two-component laminates made of conductors distributed non-periodically as laminas along one direction are considered in this note. The macroscopic properties of these laminates are described by continuous slowly-varying functions across laminas. In order to analyse heat conduction, the approach, called the tolerance modelling, is used. The aim of this note is to use averaged equations of the tolerance model for transversally graded laminates to analyse stationary heat conduction across laminas. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)