Predicting evaporation rates of droplet arrays

The evaporation of multiple sessile droplets is both scientifically interesting and practically important, occurring in many natural and industrial applications. Although there are simple analytic expressions to predict evaporation rates of single droplets, there are no such frameworks for general configurations of droplets of arbitrary size, contact angle or spacing. However, a recent theoretical contribution by Masoud, Howell & Stone (J. Fluid Mech., vol. 927, 2021, R4) shows how considerable insight can be gained into the evaporation of arbitrary configurations of droplets without having either to obtain the solution for the concentration of vapour in the atmosphere or to perform direct numerical simulations of the full problem. The theoretical predictions show excellent agreement with simulations for all configurations, only deviating by 25 % for the most confined droplets.

Building 2D Model of Compound Eye Vision for Machine Learning

This paper presents a two-dimensional mathematical model of compound eye vision. Such a model is useful for solving navigation issues for autonomous mobile robots on the ground plane. The model is inspired by the insect compound eye that consists of ommatidia, which are tiny independent photoreception units, each of which combines a cornea, lens, and rhabdom. The model describes the planar binocular compound eye vision, focusing on measuring distance and azimuth to a circular feature with an arbitrary size. The model provides a necessary and sufficient condition for the visibility of a circular feature by each ommatidium. On this basis, an algorithm is built for generating a training data set to create two deep neural networks (DNN): the first detects the distance, and the second detects the azimuth to a circular feature. The hyperparameter tuning and the configurations of both networks are described. Experimental results showed that the proposed method could effectively and accurately detect the distance and azimuth to objects.

Wetting ridge assisted programmed magnetic actuation of droplets on ferrofluid-infused surface

Flexible actuation of droplets is crucial for biomedical and industrial applications. Hence, various approaches using optical, electrical, and magnetic forces have been exploited to actuate droplets. For broad applicability, an ideal approach should be programmable and be able to actuate droplets of arbitrary size and composition. Here we present an “additive-free” magnetic actuation method to programmably manipulate droplets of water, organic, and biological fluids of arbitrary composition, as well as solid samples, on a ferrofluid-infused porous surface. We specifically exploit the spontaneously formed ferrofluid wetting ridges to actuate droplets using spatially varying magnetic fields. We demonstrate programmed processing and analysis of biological samples in individual drops as well as the collective actuation of large ensembles of micrometer-sized droplets. Such model respiratory droplets can be accumulated for improved quantitative and sensitive bioanalysis - an otherwise prohibitively difficult task that may be useful in tracking coronavirus.

Building 2D Model of Compound Eye Vision for Machine Learning

This paper presents a two-dimensional mathematical model of compound eye vision. Such a model is useful for solving navigation issues for autonomous mobile robots on the ground plane. The model is inspired by the insect compound eye that consists of ommatidia, which are tiny independent photoreception units, each of which combines a cornea, lens, and rhabdom. The model describes the planar binocular compound eye vision, focusing on measuring distance and azimuth to a circular feature with an arbitrary size. The model provides a necessary and sufficient condition for the visibility of a circular feature by each ommatidium. On this basis, an algorithm is built for generating a training data set to create two deep neural networks (DNN): the first detects the distance, and the second detects the azimuth to a circular feature. The hyperparameter tuning and the configurations of both networks are described. Experimental results showed that the proposed method could effectively and accurately detect the distance and azimuth to objects.

Existence and Uniqueness of Isothermal, Slightly Compressible Stratified Flow

We show well-posedness for the equations describing a new model of slightly compressible fluids. This model was recently rigorously derived in Grandi and Passerini (Geophys Astrophys Fluid Dyn, 2020) from the full set of balance laws and falls in the category of anelastic Navier–Stokes fluids. In particular, we prove existence and uniqueness of global regular solutions in the two-dimensional case for initial data of arbitrary “size”, and for “small” data in three dimensions. We also show global stability of the rest state in the class of weak solutions.

Wallpaper group kirigami

Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms and simple planar tilings. Here, we complement these approaches by directly linking kirigami patterns to the symmetry associated with the set of 17 repeating patterns that fully characterize the space of periodic tilings of the plane. We start by showing how to construct deployable kirigami patterns using any of the wallpaper groups, and then design symmetry-preserving cut patterns to achieve arbitrary size changes via deployment. We further prove that different symmetry changes can be achieved by controlling the shape and connectivity of the tiles and connect these results to the underlying kirigami-based lattice structures. All together, our work provides a systematic approach for creating a broad range of kirigami-based deployable structures with any prescribed size and symmetry properties.

AdS3 gravity and RCFT ensembles with multiple invariants

We use the Poincaré series method to compute gravity partition functions associated to SU(N)1 WZW models with arbitrarily large numbers of modular invariants. The result is an average over these invariants, with the weights being given by inverting a matrix whose size is of order the number of invariants. For the chosen models, this matrix takes a special form that allows us to invert it for arbitrary size and thereby explicitly calculate the weights of this average. For the identity seed we find that the weights are positive for all N, consistent with each model being dual to an ensemble average over CFT’s.