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We introduce a discrete numerical method based on the diffusion-limited aggregation (DLA) approach to simulate two-fluid Hele-Shaw flow subject to the Saffman-Taylor interfacial instability, in the case where the displaced fluid is non-Newtonian. Focusing on fluids for which the most relevant non-Newtonian aspect of the thin-gap flow is shear-thinning, we introduce a history-dependent aspect into the algorithm, modeling shear-rate-dependent fluid viscosity. The main finding is that the morphology of the emerging patterns, characterized by the fractal dimension, is modified in a nontrivial manner by the shear-thinning nature of the displaced fluid. In particular, we consistently find that shear-thinning leads to the formation of patterns characterized by a smaller fractal dimension, compared to the corresponding Newtonian fluid.

We present an experimental, theoretical, and computational study of the spreading of a millimetric silicon oil drop under the excitation of a surface acoustic wave (SAW), traveling in the underlying solid substrate. Our theoretical model, formulated within the long wave approach, dynamically captures the interplay between fluid dynamics and acoustic driving forces, emphasizing Eckart streaming as the dominant mechanism over Schlichting and Rayleigh streaming due to drop thickness. Following an initial deformation phase to accommodate acoustic stress, the drop accelerates to a sustained translation at nearly constant speed, leaving behind a thin wetting layer. This speed is sustained by the quasi-steady shape of the drop's main body, influenced by SAW attenuation. Notably, SAW attenuation becomes significant once the wave reaches the main body of the drop, with weaker effects observed under the air and the micron-thick liquid trail left behind the drop. The translating drop's speed is found to be dependent on the drop size, as well as on the SAW intensity. The drop's steady shape and speed are further informed by analytical consideration of a simplified traveling wave type model, that clarifies contributions from different physical effects. The theoretical results show qualitative and sometimes even quantitative agreement with the experiments, particularly regarding drop height and traveling speed.

Motivated by problems arising in tear film dynamics, we present a model for the extensional flow of thin sheets of nematic liquid crystal. The rod-like molecules of these substances impart an elastic contribution to its response. We rescale a weakly elastic model due to Cummings et al. [European Journal of Applied Mathematics 25 (2014): 397-423] to describe a case of moderate elasticity. The resulting system of two nonlinear partial differential equations for sheet thickness and axial velocity is nonlinear and fourth order in space, but still represents a significant reduction of the full system. We analyze solutions arising from several different boundary conditions, motivated by the underlying application, with particular focus on dynamics and underlying mechanisms under stretching. We solve the system numerically, via collocation with either finite difference or Chebyshev spectral discretization in space, together with implicit time stepping. At early times, depending on the initial film shape, pressure either aids or opposes extensional flow, which changes the shape of the sheet and may result in the loss of a minimum or maximum at the moving end. We contrast this finding with the cases of weak elasticity and Newtonian flow, where the sheet retains all extrema from the initial condition throughout time., Comment: Copyright (2023) M.J. Taranchuk, L.J. Cummings, T.A. Driscoll, and R.J. Braun. This article is distributed under a Creative Commons Attribution (CC BY) License. The following article has been submitted to Physics of Fluids. After it is published, it will be found at https://aip.scitation.org/journal/phf

Partially wetting nematic liquid crystal (NLC) films on substrates are unstable to dewetting-type instabilities due to destablizing solid/NLC interaction forces. These instabilities are modified by the nematic nature of the films, which influences the effective solid/NLC interaction. In this work, we focus on the influence of imposed substrate anchoring on the instability development. The analysis is carried out within a long-wave formulation based on the Leslie-Ericksen description of NLC films. Linear stability analysis of the resulting equations shows that some features of the instability, such as emerging wavelengths, may not be influenced by the imposed substrate anchoring. Going further into the nonlinear regime, considered via large-scale GPU-based simulations, shows however that nonlinear effects may play an important role, in particular in the case of strong substrate anchoring anisotropy. Our simulations show that instability of the film develops in two stages: the first stage involves formation of ridges that are perpendicular to the local anchoring direction; and the second involves breakup of these ridges and formation of drops, whose final distribution is influenced by the anisotropy imposed by the substrate. Finally, we show that imposing more complex substrate anisotropy patterns allows us to reach basic understanding of the influence of substrate-imposed defects in director orientation on the instability evolution.

We show that a new force, which appeared in a five-dimensional generalization of general relativity, implies precisely the flat circular velocity curves of luminous matter observed in the outer parts of spiral galaxies. A cosmological solution for the new force (not the galactic solution treated in this paper) might explain the cosmic negative, or repulsive, gravitation responsible for the accelerated expansion of the universe, attributed nowadays to ``dark energy'' and sometimes modelled by Einstein's cosmological constant.

Three systems of appraisal of employees are described with reference to major characteristics and the most appropriate application context. The first system, the developmental action program, is designed to be utilized on a job allowing the employee considerable discretion in reaching the job's objectives, and perhaps some autonomy in establishing goals. The maintenance action program is a system of appraisal applicable to the average acceptable performer with low potential for promotion because of limited ability or motivation. Finally, the remedial action program is intended for administrative use with those clearly below standard, whose performance has consistently been unacceptable. Also discussed is the nature, amount, and frequency of feedback given to performers in the different appraisal systems. The author concludes that variations in appraisal are necessary because of multiple performance problems, performance histories, and work situations. (MPJ)