Interfacial dynamics in transport-limited dissolution

Various model problems of ``transport-limited dissolution'' in two dimensions are analyzed using time-dependent conformal maps. For diffusion-limited dissolution (reverse Laplacian growth), several exact solutions are discussed for the smoothing of corrugated surfaces, including the continuous analogs of ``internal diffusion-limited aggregation'' and ``diffusion-limited erosion''. A class of non-Laplacian, transport-limited dissolution processes are also considered, which raise the general question of when and where a finite solid will disappear. In a case of dissolution by advection-diffusion, a tilted ellipse maintains its shape during collapse, as its center of mass drifts obliquely away from the background fluid flow, but other initial shapes have more complicated dynamics.Comment: 5 pages, 4 fig

Phase diagram of Pb(Zr,Ti)O3 solid solutions from first principles

A first-principles-derived scheme, that incorporates ferroelectric and antiferrodistortive degrees of freedom, is developed to study finite-temperature properties of PbZr1-xTixO3 solid solutions near its morphotropic phase boundary. The use of this numerical technique (i) resolves controversies about the monoclinic ground-state for some Ti compositions, (ii) leads to the discovery of an overlooked phase, and (iii) yields three multiphase points, that are each associated with four phases. Additional neutron diffraction measurements strongly support some of these predictions.Comment: 10 pages, 2 figure

Novel Regime of Operation for Superconducting Quantum Interference Filters

A new operating regime of the Superconducting Quantum Interference Filter (SQIF) is investigated. The voltage to magnetic field response function, V(H), is determined by a Fraunhofer dependence of the critical current and magnetic flux focusing effect in Josephson junctions (F-mode). For SQIF-arrays made of high-Tc superconducting bicrystal Josephson junctions the F-mode plays a predominant role in the voltage-field response V(H). The relatively large superconducting loops of the SQIF are used for inductive coupling to the external input circuit. It is shown that the output noise of a SQIF-array measured with a cooled amplifier in the 1-2 GHz range is determined by the slope of the V(H) characteristic. Power gain and saturation power were evaluated using low frequency SQIF parameters. Finally, we consider the influence of the spread in the parameters of Josephson junctions in the SQIF-array on the V(H) characteristic of the whole structure.Comment: 7 pages, 4 figure

Meniscus on a shaped fibre: Singularities and hodograph formulation

Using the method of matched asymptotic expansions, the problem of the capillary rise of a meniscus on the complex-shaped fibres was reduced to a nonlinear problem of determination of a minimal surface. This surface has to satisfy a special boundary condition at infinity. The proposed formulation allows one to interpret the meniscus problem as a problem of flow of a fictitious non-Newtonian fluid through a porous medium. As an example, the shape of a meniscus on a fibre of an oval cross section was analysed employing Chaplygin's hodograph transformation. It was discovered that the contact line may form singularities even if the fibre has a smooth profile: this statement was illustrated with an oval fibre profile having infinite curvature at two endpoints. © 2014 The Author(s) Published by the Royal Society. All rights reserved

On the effect of a filtration flow on an equilibrium shape of bodies formed under artificial freezing

Problem solution for determination of the maximum equilibrium shape of an ice body, formed around single freezing column, modeled by point cold source, is obtained, using apparatus of boundary problem theory for analytical functions. Influence of filtration flow velocity on the body shape is studied. Dependence of the ice body maximum dimensions on the Peclet number as well as its dependence on freezing temperature are presented. Calculation results are in fair agreement with experimental data

Singularities of meniscus at the V-shaped edge

© 2014 Elsevier Ltd. All rights reserved. An understanding of the capillary rise of the meniscus formed on the V-shaped fibers is crucial for many applications. We classified the cases when the meniscus cannot be smooth by analyzing the local behavior of the solutions to the Laplace equation of capillarity near the sharp edge. The V-angle and two contact angles that the meniscus forms on two chemically different sides of the fiber form a 3D phase space. Smooth menisci constitute a special domain in this 3D space. The constructed diagram allows one to separate the solutions with smooth and non-smooth menisci. The obtained criteria were illustrated using chemically inhomogeneous plates, blades, square corners, and Janus V-shaped edges

Piercing the water surface with a blade: Singularities of the contact line

© 2016 AIP Publishing LLC. An external meniscus on a narrow blade with a slit-like cross section is studied using the hodograph formulation of the Laplace nonlinear equation of capillarity. On narrow blades, the menisci are mostly shaped by the wetting and capillary forces; gravity plays a secondary role. To describe a meniscus in this asymptotic case, the model of Alimov and Kornev ["Meniscus on a shaped fibre: Singularities and hodograph formulation," Proc. R. Soc. A 470, 20140113 (2014)] has been employed. It is shown that at the sharp edges of the blade, the contact line makes a jump. In the wetting case, the contact line sitting at each side of the blade is lifted above the points where the meniscus first meets the blade edges. In the non-wetting case, the contact line is lowered below these points. The contours of the constant height emanating from the blade edges generate unusual singularities with infinite curvatures at some points at the blade edges. The meniscus forms a unique surface made of two mirror-symmetric sheets fused together. Each sheet is supported by the contact line sitting at each side of the blade

Dynamics of ice-rock barriers under conditions of freezing of filtering rocks

Nonstationary heat transport under conditions of freezing of filtering soils is studied using a mathematical model which takes into account an arbitrary distribution of sources of cold. © 1987 Plenum Publishing Corporation