From low-rank approximation to an efficient rational Krylov subspace method for the Lyapunov equation

We propose a new method for the approximate solution of the Lyapunov equation with rank-$1$ right-hand side, which is based on extended rational Krylov subspace approximation with adaptively computed shifts. The shift selection is obtained from the connection between the Lyapunov equation, solution of systems of linear ODEs and alternating least squares method for low-rank approximation. The numerical experiments confirm the effectiveness of our approach.Comment: 17 pages, 1 figure

Interface states in junctions of two semiconductors with intersecting dispersion curves

A novel type of shallow interface state in junctions of two semiconductors without band inversion is identified within the envelope function approximation, using the two-band model. It occurs in abrupt junctions when the interband velocity matrix elements of the two semiconductors differ and the bulk dispersion curves intersect. The in-plane dispersion of the interface state is found to be confined to a finite range of momenta centered around the point of intersection. These states turn out to exist also in graded junctions, with essentially the same properties as in the abrupt case.Comment: 1 figur

The local phase transitions of the solvent in the neighborhood of a solvophobic polymer at high pressures

We investigate local phase transitions of the solvent in the neighborhood of a solvophobic polymer chain which is induced by a change of the polymer-solvent repulsion and the solvent pressure in the bulk solution. We describe the polymer in solution by the Edwards model, where the conditional partition function of the polymer chain at a fixed radius of gyration is described by a mean-field theory. The contributions of the polymer-solvent and the solvent-solvent interactions to the total free energy are described within the mean-field approximation. We obtain the total free energy of the solution as a function of the radius of gyration and the average solvent number density within the gyration volume. The resulting system of coupled equations is solved varying the polymer-solvent repulsion strength at high solvent pressure in the bulk. We show that the coil-globule (globule-coil) transition occurs accompanied by a local solvent evaporation (condensation) within the gyration volum

Revisión de la edad del Grupo de Asha en los Urales meridionales

The Asha Group of the South Urals, initially erected by Albert Olli as Palaeozoic sedimentary complex, more than half a century ago was considered as a key section for the Vendian (Ediacaran) of the western slope of the South Urals. However, the ca. 1700 m-thick terrigenous sedimentary sequence is characterised by unusual low biodiversity of Ediacaran macrofossils, which might be explained by relatively young age of the Asha Group and possible mass extinction event in the end of Ediacaran Period. The relatively young age was confirmed by the U-Pb zircon date of 547.6±3.8 Ma obtained from the tuff in the lower part of the Basa Formation as well as finding of ichnospecies Didymaulichnus tirasensis in the upper part of Zigan formation. However, in 2018 it has been documented there the mass appearing of D. tirasensis in the lowermost part of the Basa Formation. Therefore, the Vendian (Ediacaran) age of the Asha Group of the South Urals can be revisited in favour to terminal Ediacaran- Cambrian or even early Cambrian.El Grupo de Asha de los Urales meridionales, inicialmente definido por Albert Olli como complejo sedimentario paleozoico, hace más de medio siglo, fue considerado como una sección clave para el Véndico (Ediacárico) de la vertiente occidental de los Urales meridionales. Sin embargo, secuencia sedimentaria terrígena de unos 1.700 m de espesor se caracteriza por una biodiversidad inusualmente baja de macrofósiles ediacaranos, lo que podría explicarse por la edad relativamente temprana del grupo y el posible evento de extinción masiva que marca el final del período Ediacárico. La edad relativamente temprana fue confirmada por la datación de 547.6±3.8 Ma obtenida de una toba en la parte inferior de la Formación de Basa, así como por el hallazgo de la iconospecie Didymaulichnus tirasensis en la parte superior de la Formación de Zigan. Sin embargo, en 2018 se ha documentó la aparición masiva de D. tirasensis en la parte más baja de la Formación de Basa. Por lo tanto, la edad Véndico (Ediacárico) del Grupo de Asha de los Urales meridionales puede ser reconsiderada en favor del Ediacárico terminal-Cámbrico o incluso del Cambrian temprano