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

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

Effect of filtration flow on the equilibrium shape of bodies formed by forced freezing

The effect of filtration flow on the shape of a body formed by freezing around an isolated freezing column is investigated on the basis of the mathematical model proposed in [1]. © 1992 Plenum Publishing Corporation

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

Hysteretic effects in the problems of artificial freezing

The technique of the Riemann problem with displacement is used to solve the steady two-dimensional problem of freezing of groundwater flow by two `freeze pipes'. A series of steady-state limiting configurations is analyzed, and it is shown that as the area of frozen soil around the pipes grows, the two frozen regions eventually `link' to form a single frozen zone. If the process is reversed (the united body is unfrozen in stages) the `division' (i.e., unlinking) follows a different path. Hence there is hysteresis in the linking and division of the frozen zone. Mathematically, it appears that within some range of input parameters the problem has several solutions. We obtain the `phase diagram' for frozen domains and show that the linking condition differs from the division condition by a perceptible amount. This allows the possibility of optimizing the technological regimes of freezing. Namely, once the overlapping of ice columns has occurred, the body could maintain this linked state even if the temperature of the freeze pipes was significantly reduced

Gravitational oscillations of a liquid column

We report gravity oscillations of a liquid column partially immersed in a bath of liquid. We stress in particular some peculiarities of this system, namely (i) the fact that the mass of this oscillator constantly changes with time; (ii) the singular character of the beginning of the rise, for which the mass of the oscillator is zero; (iii) the sources of dissipation in this system, which is found to be dominated at low viscosity by the entrance (or exit) effects, leading to a long-range damping of the oscillations. We conclude with some qualitative description of a second-order phenomenon, namely the eruption of a jet at the beginning of the rise.Comment: 22 pages, pdf. Submitted to Physics of Fluid

A combined theoretical and experimental study of the low temperature properties of BaZrO3

Low temperature properties of BaZrO3 are revealed by combining experimental techniques (X-ray diffraction, neutron scattering and dielectric measurements) with theoretical first-principles-based methods (total energy and linear response calculations within density functional theory, and effective Hamiltonian approaches incorporating/neglecting zero-point phonon vibrations). Unlike most of the perovskite systems, BaZrO3 does not undergo any (long-range-order) structural phase transition and thus remains cubic and paraelectric down to 2 K, even when neglecting zero-point phonon vibrations. On the other hand, these latter pure quantum effects lead to a negligible thermal dependency of the cubic lattice parameter below ~ 40 K. They also affect the dielectricity of BaZrO3 by inducing an overall saturation of the real part of the dielectric response, for temperatures below ~ 40 K. Two fine structures in the real part, as well as in the imaginary part, of dielectric response are further observed around 50-65 K and 15 K, respectively. Microscopic origins (e.g., unavoidable defects and oxygen octahedra rotation occurring at a local scale) of such anomalies are suggested. Finally, possible reasons for the facts that some of these dielectric anomalies have not been previously reported in the better studied KTaO3 and SrTiO3 incipient ferroelectrics are also discussed.Comment: 8 pages, 5 figures, submitted to Physical Review

Frequency and size dependence of ac Josephson effect in Nb/Au/YBCO heterojunctions

Abstract. High frequency dynamics of Nb/Au/YBaCuO heterojunctions on tilted NdGaO 3 substrates have been studied. The both integer and non-integer Shapiro steps have been observed at mm-wave frequencies. Unconventional dependence of the critical current and the amplitudes of Shapiro steps vs. applied microwave power have been registered. Observed behavior deviates from existing theories of Josephson effect for junctions made from conventional or d-wave superconductors. Although the maximal size of the heterojunctions was smaller than the Josephson penetration depth, calculated from an averaged value of the critical current density, the experimental magnetic field dependences I C (H) deviate from the Fraunhofer pattern, pointing on non-uniform distribution of superconducting current density. Experimental results could be speculatively explained by origination of self-induced fractional magnetic vortices, which may take place in a junction where the amplitude and the phase of superconducting current alternate significantly over the junction area. Introducing a new lengthscale, which is much smaller than the Josephson penetration depth, the fractional vortices are considered, modifying the high frequency dynamics, namely the ac Josephson effect. Experimental results have been analyzed taking into account the second harmonic of superconducting current-phase relation and the influence of heterojunction capacitance. Introduction It is known that in metal-oxide superconductors with high critical temperature, for example in YBCO, the d-wave symmetry of superconducting order parameter (D-superconductor) is predominant one in the basal (a-b) plan

Mobile π−\pi-kinks and half-integer zero-field-like steps in highly discrete alternating 0−π0-\pi Josephson junction arrays

The dynamics of a one-dimensional, highly discrete, linear array of alternating $0-$ and $\pi-$ Josephson junctions is studied numerically, under constant bias current at zero magnetic field. The calculated current - voltage characteristics exhibit half-integer and integer zero-field-like steps for even and odd total number of junctions, respectively. Inspection of the instantaneous phases reveals that, in the former case, single $\pi-$kink excitations (discrete semi-fluxons) are supported, whose propagation in the array gives rise to the $1/2-$step, while in the latter case, a pair of $\pi-$kink -- $\pi-$antikink appears, whose propagation gives rise to the $1-$step. When additional $2\pi-$kinks are inserted in the array, they are subjected to fractionalization, transforming themselves into two closely spaced $\pi-$kinks. As they propagate in the array along with the single $\pi-$kink or the $\pi-$kink - $\pi-$antikink pair, they give rise to higher half-integer or integer zero-field-like steps, respectively.Comment: 7 pages, 8 figures, submitted to Supercond. Sci. Techno

Conformal mapping methods for interfacial dynamics

The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the article begins with an overview of continuous conformal-map dynamics. This includes problems of interfacial motion driven by harmonic fields (such as viscous fingering and void electromigration), bi-harmonic fields (such as viscous sintering and elastic pore evolution), and non-harmonic, conformally invariant fields (such as growth by advection-diffusion and electro-deposition). The second part of the article is devoted to iterated conformal maps for analogous problems in stochastic interfacial dynamics (such as diffusion-limited aggregation, dielectric breakdown, brittle fracture, and advection-diffusion-limited aggregation). The third part notes that all of these models can be extended to curved surfaces by an auxilliary conformal mapping from the complex plane, such as stereographic projection to a sphere. The article concludes with an outlook for further research.Comment: 37 pages, 12 (mostly color) figure