Recurrence calculations of organic compound boiling temperatures from data on preceding homologues

A new approach to calculating the temperatures of boiling at atmospheric pressure (T _b) of organic compounds from arbitrary homologous series is suggested. The approach is based on the linear dependence of these values on T _b for the preceding homologues, T _b(n) = aT_b(n ? 1) + b. This dependence, revealed for the first time, was used to obtain a recurrence relation for calculating T _b of organic compounds within any series from the data on three simpler homologues of the same series. The mean a and b values can be used to estimate T _b of an arbitrary organic compound from T _b for one preceding homologue with an accuracy not inferior to that provided by the modern ACD software. Correlations of the general form P(n) = aP(n ? 1) + b are observed not only for the boiling points of organic compounds but also for their other properties P (refractive indexes, relative densities, and ionization energies). This opens up the possibility of creating unified algorithms for calculating various physicochemical constants of organic compounds instead of particular algorithms for every particular property known earlier.     

Intensities of inter-Stark transitions in activated crystals

A scheme of calculation of line strengths for indirect electric dipole transitions between Stark states of impurity ions in dielectric crystals is proposed. It is shown that knowledge of the three semiphenomenological Judd-Ofelt parameters of a crystalline system is sufficient for quantitative calculations. The formulas obtained were approved for YAG:Nd³⁺ crystals based on calculation of the spectroscopic characteristics of the lines of the inter-Stark transitions ⁴ F _3/2 → ⁴ I _9/2 and ⁴ F _3/2 → ⁴ I _11/2.     

Calculation of the dynamic temperature characteristics of a heated graphite tube used in electrothermal atomic absorption measurements

A method and computer program were developed for calculating the temperature of any part of a graphite furnace tube at any instant of time after onset of the heating cycle. Results for tubes of the Massman design show large differences in spatial temperature distributions during and at the end of the heating cycle when equilibrium is reached. When constant current is applied to contoured tubes, greater heating rates at the tube centres are obtained than with standard tubes.     

Adjoint equations and their applications

Proceedings of the Steklov Institute of Mathematics -     

High Curie temperature in B-site ordered Sr2CrWO6 epitaxial thin films

Epitaxial and c-axis oriented double perovskite Sr₂CrWO₆ thin films were prepared on SrTiO₃ (100) and LaAlO₃ (100) substrates by pulsed-laser deposition. Structural, magnetic and transport properties were found to be sensitive to the gas conditions employed during the deposition. A small amount of oxygen along with Ar during the deposition was found to be essential for B-site ordering; such films displayed lattice parameters close to the bulk value and display ferromagnetic metallic behavior. The Curie temperature observed above 500 K in these films is higher than bulk Sr₂CrWO₆ samples. Films grown without oxygen were observed to have long c-parameter and no B-site ordering; they were non-magnetic and semiconducting.     

High-energy gamma-rays accompanying the spontaneous fission of 252Cf

The γ-ray spectrum of ²⁵²Cf(sf) was measured in the Darmstadt-Heidelberg Crystal Ball spectrometer, with a double ionization chamber mounted inside to detect the fission fragments. The measurement was aimed at a better understanding of an unusual component found in the high-energy region between 3 and 8 MeV, with fragment mass splits near symmetry. This component was proved to be predominantly emitted by the heavier fragment, to reach its highest intensity at a fragment mass split of 132:120, and to have an almost isotropic angular distribution. Calculations with the statistical code CASCADE could reproduce the main features.     

Computational modelling of bubbles,droplets and particles in metals reduction and refining

A multi-phase framework is typically required for the CFD modelling of metals reduction processes. Such processes typically involve the interaction of liquid metals, a gas (often air) top space, liquid droplets in the top space and injection of both solid particles and gaseous bubbles into the bath. The exchange of mass, momentum and energy between the phases is fundamental to these processes. Multi-phase algorithms are complex and can be unreliable in terms of either or both convergence behaviour or in the extent to which the physics is captured. In this contribution, we discuss these multi-phase flow issues and describe an example of each of the main “single phase” approaches to modelling this class of problems (i.e., Eulerian–Lagrangian and Eulerian–Eulerian). Their utility is illustrated in the context of two problems – one involving the injection of sparging gases into a steel continuous slab caster and the other based on the development of a novel process for aluminium electrolysis. In the steel caster, the coupling of the Lagrangian tracking of the gas phase with the continuum enables the simulation of the transient motion of the metal–flux interface. The model of the electrolysis process employs a novel method for the calculation of slip velocities of oxygen bubbles, resulting from the dissolution of alumina, which allows the efficiency of the process to be predicted.     

New numerical methods and some applied aspects of the p-regularity theory

The theory of p-regularity is applied to optimization problems and to singular ordinary differential equations (ODE). The special variant of the method of the modified Lagrangian function proposed by Yu.G. Evtushenko for constrained optimization problems with inequality constraints is justified on the basis of the 2-factor transformation. An implicit function theorem is given for the singular case. This theorem is used to show the existence of solutions to a boundary value problem for a nonlinear differential equation in the resonance case. New numerical methods are proposed including the p-factor method for solving ODEs with a small parameter.