Nonlinear evolution of annular layers and liquid threads in electric fields

The nonlinear dynamics of viscous perfectly conducting liquid jets or threads under the action of a radial electric field are studied theoretically and numerically here. The field is generated by a potential difference between the jet surface and a concentrically placed electrode of given radius. A long-wave nonlinear model that is used to predict the dynamics of the system and in particular to address the effect of the radial electric field on jet breakup is developed, Two canonical regimes are identified that depend on the size of the gap between the outer electrode and the unperturbed jet surface. For relatively large gap sizes, long waves are stabilized for sufficiently strong electric fields but remain unstable as in the non-electrified case for electric field strengths below a critical value, For relatively small gaps, an electric field of any strength enhances the instability of long waves as compared to the non-electrified case. Accurate numerical simulations are carried out based on our nonlinear models to describe the nonlinear evolution and terminal states in these two regimes. It is found that jet pinching does not occur irrespective of the parameters, Regimes are identified where capillary instability leads to the formation of stable quasi-static microthreads (connected to large main drops) whose radius decreases with the strength of the electric field. The generic ultimate singular event described by our models is the attraction of the jet surface towards the enclosing electrode and its contact with the electrode in finite time. A self-similar closed form solution is found that describes this event with the interface near touchdown having locally a cusp geometry. The theory is compared with the time-dependent simulations with excellent agreement. In addition a core-annular flow problem is considered to include the external viscous fluid. A full problem simulation, based on a boundary integral technique is carried out to capture the full dynamics of the electrified viscous jet in the zero Reynolds number limit. Pinching solutions of either electrified or non-electrified viscous jets are obtained and the instantaneous velocity field and flow patterns are studied numerically near breakup, As the electric field strength increases, the size and shape of the drops are changed dramatically compared with the non-electrified problem. However, the local dynamics remain the same as shown in the non-electrified capillary breakup problem, since the main and satellite liquid masses joined by a collapsing neck have the same potential and would not feel the strong influence of the external field. The pinching is suppressed if the field strength is sufficiently large and another type of breakup behavior appears. Briefly speaking, the interface is attracted and touches the outer electrode in the radial direction in a similar phenomenon found for a single jet problem, This type of terminal state is also described by a lubrication model in the thin annulus limit. A comparison between the boundary-integral simulations and the asymptotic results is also carried out

A unified 3D phase diagram of growth induced surface instabilities

Biological world metabolizes itself with germination, growth, development, and aging every second. A variety of fascinating morphological patterns arise on surfaces of growing, developing or aging tissues, organs and micro--organism colonies. The basic mechanism has been long believed to be the mechanical mismatch due to -differential growth between layers with different biological compositions. These patterns have been observed in separate systems and topologically classified as crease, wrinkle-fold, period-double, ridge, delaminated-buckle, and coexistence states. However, a general and systematic understanding of their initiation and evolution remains largely elusive. We construct a unified 3D phase diagram that predicts initially flat tissue layers can transform to various instability patterns, systematically depending on three physical parameters: mismatch strain, modulus ratio between layers, and adhesion energy on the interface. Our phase diagram matches consistently with our mimic in vitro experiments and documented data in state-of-the-art literature

Solo: Data Discovery Using Natural Language Questions Via A Self-Supervised Approach

Most deployed data discovery systems, such as Google Datasets, and open data portals only support keyword search. Keyword search is geared towards general audiences but limits the types of queries the systems can answer. We propose a new system that lets users write natural language questions directly. A major barrier to using this learned data discovery system is it needs expensive-to-collect training data, thus limiting its utility. In this paper, we introduce a self-supervised approach to assemble training datasets and train learned discovery systems without human intervention. It requires addressing several challenges, including the design of self-supervised strategies for data discovery, table representation strategies to feed to the models, and relevance models that work well with the synthetically generated questions. We combine all the above contributions into a system, Solo, that solves the problem end to end. The evaluation results demonstrate the new techniques outperform state-of-the-art approaches on well-known benchmarks. All in all, the technique is a stepping stone towards building learned discovery systems. The code is open-sourced at https://github.com/TheDataStation/soloComment: To appear at Sigmod 202

Discrete self-similarity in the formation of satellites for viscous cavity break-up

The breakup of a jet of a viscous fluid with viscosity $\mu _{1}$ immersed into another viscous fluid with viscosity $\mu _{2}$ is considered in the limit when the viscosity ratio $\lambda =\mu _{1}/\mu _{2}$ is close to zero. We show that, in this limit, a transition from ordinary continuous selfsimilarity to discrete selfsimilarity takes place as $\lambda$decreases. The result being that instead of a single point breakup, the rupture of the inner jet occurs through the appearance of an infinite sequence of filaments of decreasing size that will eventually produce infinite sequences of bubbles of the inner fluid inside the outer fluid. The transition can be understood as the result of a Hopf bifurcation in the system of equations modelling the physical problem.Comment: 6 pages, 10 figure