Periodic forcing in viscous fingering of a nematic liquid crystal

We study viscous fingering of an air-nematic interface in a radial Hele-Shaw cell when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its anisotropy (mainly enforced by a single groove in the cell). We observe undulations at the sides of the fingers which correlate with the switching frequency and with tip oscillations which give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise-induced) side branching. We conclude that the lateral undulations are generated by successive relaxations between two limiting finger widths. The change between these two selected pattern scales is mainly due to the change in the anisotropy. This scenario is confirmed by numerical simulations in the channel geometry, using a phase-field model for anisotropic viscous fingering.Comment: completely rewritten version, more clear exposition of results (14 pages in Revtex + 7 eps figures

Viscous fingering in liquid crystals: Anisotropy and morphological transitions

We show that a minimal model for viscous fingering with a nematic liquid crystal in which anisotropy is considered to enter through two different viscosities in two perpendicular directions can be mapped to a two-fold anisotropy in the surface tension. We numerically integrate the dynamics of the resulting problem with the phase-field approach to find and characterize a transition between tip-splitting and side-branching as a function of both anisotropy and dimensionless surface tension. This anisotropy dependence could explain the experimentally observed (reentrant) transition as temperature and applied pressure are varied. Our observations are also consistent with previous experimental evidence in viscous fingering within an etched cell and simulations of solidification.Comment: 12 pages, 3 figures. Submitted to PR

Phase-field model for Hele-Shaw flows with arbitrary viscosity contrast. II. Numerical study

We implement a phase-field simulation of the dynamics of two fluids with arbitrary viscosity contrast in a rectangular Hele-Shaw cell. We demonstrate the use of this technique in different situations including the linear regime, the stationary Saffman-Taylor fingers and the multifinger competition dynamics, for different viscosity contrasts. The method is quantitatively tested against analytical predictions and other numerical results. A detailed analysis of convergence to the sharp interface limit is performed for the linear dispersion results. We show that the method may be a useful alternative to more traditional methods.Comment: 13 pages in revtex, 5 PostScript figures. changes: 1 reference added, figs. 4 and 5 rearrange

Combining Multi-Fidelity Modelling and Asynchronous Batch Bayesian Optimization

Bayesian Optimization is a useful tool for experiment design. Unfortunately, the classical, sequential setting of Bayesian Optimization does not translate well into laboratory experiments, for instance battery design, where measurements may come from different sources and their evaluations may require significant waiting times. Multi-fidelity Bayesian Optimization addresses the setting with measurements from different sources. Asynchronous batch Bayesian Optimization provides a framework to select new experiments before the results of the prior experiments are revealed. This paper proposes an algorithm combining multi-fidelity and asynchronous batch methods. We empirically study the algorithm behavior, and show it can outperform single-fidelity batch methods and multi-fidelity sequential methods. As an application, we consider designing electrode materials for optimal performance in pouch cells using experiments with coin cells to approximate battery performance