An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-space

We give an example of an infinitesimally nonrigid polyhedron in the Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron isn't stationary under the flex.Comment: 10 pages, 2 Postscript figure

Diamagnetism of real-space pairs above Tc in hole doped cuprates

The nonlinear normal state diamagnetism reported by Lu Li et al. [Phys. Rev. B 81, 054510 (2010)] is shown to be incompatible with an acclaimed Cooper pairing and vortex liquid above the resistive critical temperature. Instead it is perfectly compatible with the normal state Landau diamagnetism of real-space composed bosons, which describes the nonlinear magnetization curves in less anisotropic cuprates La-Sr-Cu-O (LSCO) and Y-Ba-Cu-O (YBCO) as well as in strongly anisotropic bismuth-based cuprates in the whole range of available magnetic fields.Comment: 4 pages, 4 figure

Parameter-free expression for superconducting Tc in cuprates

A parameter-free expression for the superconducting critical temperature of layered cuprates is derived which allows us to express Tc in terms of experimentally measured parameters. It yields Tc values observed in about 30 lanthanum, yttrium and mercury-based samples for different levels of doping. This remarkable agreement with the experiment as well as the unusual critical behaviour and the normal-state gap indicate that many cuprates are close to the Bose-Einstein condensation regime.Comment: 5 pages, 2 figures. Will be published in Physical Review

Polaron and bipolaron transport in a charge segregated state of doped strongly correlated 2D semiconductor

The 2D lattice gas model with competing short and long range interactions is appliedused for calculation of the incoherent charge transport in the classical strongly-correlated charge segregated polaronic state. We show, by means of Monte-Carlo simulations, that at high temperature the transport is dominated by hopping of the dissociated correlated polarons, where with thetheir mobility is inversely proportional to the temperature. At the temperatures below the clustering transition temperature the bipolaron transport becomes dominant. The energy barrier for the bipolaron hopping is determined by the Coulomb effects and is found to be lower than the barrier for the single-polaron hopping. This leads to drastically different temperature dependencies of mobilities for polarons and bipolarons at low temperatures

A complete analytical solution of the Fokker–Planck and balance equations for nucleation and growth of crystals

This article is concerned with a new analytical description of nucleation and growth of crystals in a metastable mushy layer (supercooled liquid or supersaturated solution) at the intermediate stage of phase transition. The model under consideration consisting of the non-stationary integro-differential system of governing equations for the distribution function and metastability level is analytically solved by means of the saddle-point technique for the Laplace-type integral in the case of arbitrary nucleation kinetics and time-dependent heat or mass sources in the balance equation. We demonstrate that the time-dependent distribution function approaches the stationary profile in course of time. This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’. © 2018 The Author(s) Published by the Royal Society. All rights reserved.Российский Фонд Фундаментальных Исследований (РФФИ), RFBR: 16-08-00932Data accessibility. This article has no additional data. Authors’ contributions. All authors contributed equally to this article. Competing interests. We declare we have no competing interests. Funding. This work was supported by the Russian Foundation for Basic Research (grant no. 16-08-00932)

On the theory of dendritic growth: Soret and temperature-dependent diffusion effects

An analytical solution is found for the problem of the growth of an isolated dendrite in a convective binary melt with allowance for the Soret and temperature-dependent diffusion effects. Nonlinear impurity transport is shown to radically change the impurity concentration in front of the growing crystal and, correspondingly, the concentration supercooling, which is responsible for the condition of choosing the dendrite tip growth rate. © 2013 Pleiades Publishing, Ltd

Selection of stable growth conditions for the parabolic dendrite tip in crystallization of multicomponent melts

Free growth of a dendrite crystal in a stationary multicomponent melt is investigated. A mathematical model of the process is developed and its analytic solution is constructed. A stability criterion is obtained for a 2D parabolic dendrite and the refined relation is derived for the growth rate of the dendrite tip taking into account the anisotropy of surface tension at the solid phase-melt interface. It is shown that the accumulation of impurity in the front of a dendrite makes it tip thinner and reduces its velocity. The theory contains limiting transitions to the familiar dendrite growth criteria for one-component and binary systems. © 2013 Pleiades Publishing, Ltd