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Self-propelled droplet jumping during condensation has attractive prospects for energy harvesting, water collection and thermal management, but its real-life applications are greatly limited to the challenge of enabling a sustainable control on the entire droplet lifecycle. Herein, we propose a programmable jumping-droplet condensation that evolves along an artificially designed pathway without external stimulations, where the droplets can uniformly form at specific sites, spontaneously migrate and coalesce with their neighboring droplets, and jump off effectively to continuously refresh surface, significantly enhancing the heat transfer performance and durability of condensation. The programmable jumping-droplet condensation is achieved using a wedge-walled rhombus lattice structure surface inspired from the structures and functions of Namib desert beetle skin, shorebird beak and setaria viridis leaf vein. This surface integrates wetting contrast patterns with dual-gradient hierarchical structures, providing persistent and multidimensional droplet rectifications and thus realizing a sustainable control on the entire droplet lifecycle. Furthermore, we systematically investigate the morphology and behavior evolutions of droplets throughout their entire lifecycle, and fully elucidate the programmable control mechanisms of the lattice structure determined by its topology and wettability features. This work not only serves as theoretical foundations and reference framework to realize a durable jumping-droplet condensation and achieve its performance ceiling in a controlled manner, but also promotes the design and fabrication of functional structured surfaces for droplet manipulation and delivery, self-cleaning and anti-fogging/icing.

In this paper, a new bivariate random coefficient integer-valued autoregressive process based on modified negative binomial operator with dependent innovations is proposed. Basic probabilistic and statistical properties of this model are derived. To estimate unknown parameters, Yule-Walker, conditional least squares and conditional maximum likelihood methods are considered and evaluated by Monte Carlo simulations. Asymptotic properties of the estimators are derived. Moreover, coherent forecasting and possible extension of the proposed model is provided. Finally, the proposed model is applied to the monthly crime datasets and compared with other models.

In this paper, we propose a computationally valid and theoretically justified methods, the likelihood ratio scan method (LRSM), for estimating multiple change-points in a piecewise stationary generalized conditional integer-valued autoregressive process. LRSM with the usual window parameter $h$ is more satisfied to be used in long-time series with few and even change-points vs. LRSM with the multiple window parameter $h_{mix}$ performs well in short-time series with large and dense change-points. The computational complexity of LRSM can be efficiently performed with order $O((\log n)^3 n)$. Moreover, two bootstrap procedures, namely parametric and block bootstrap, are developed for constructing confidence intervals (CIs) for each of the change-points. Simulation experiments and real data analysis show that the LRSM and bootstrap procedures have excellent performance and are consistent with the theoretical analysis., Comment: 41 pages, 6 figures

In this paper, we introduce a new first-order mixture integer-valued threshold autoregressive process, based on the binomial and negative binomial thinning operators. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares (CLS) and conditional maximum likelihood (CML) estimators are derived and the asymptotic properties of the estimators are established. The inference for the threshold parameter is obtained based on the CLS and CML score functions. Moreover, the Wald test is applied to detect the existence of the piecewise structure. Simulation studies are considered, along with an application: the number of criminal mischief incidents in the Pittsburgh dataset., Comment: 34 pages;5 figures

This article considers the problem of modeling a class of nonstationary count time series using multiple change-points generalized integer-valued autoregressive (MCP-GINAR) processes. The minimum description length principle (MDL) is applied to study the statistical inference for the MCP-GINAR model, and the consistency results of the MDL model selection procedure are established respectively under the condition of known and unknown number of change-points. To find the ``best" combination of the number of change-points, the locations of change-points, the order of each segment and its parameters, a genetic algorithm with simulated annealing is implemented to solve this difficult optimization problem. In particular, the simulated annealing process makes up for the precocious problem of the traditional genetic algorithm. Numerical results from simulation experiments and three examples of real data analyses show that the procedure has excellent empirical properties., Comment: 32 pages, 6 figures

In the current study, a brand-new SINARS(1) model is proposed for stationary discrete time series defined on $\boldsymbol{Z}$, based on extended binomial distribution and the Pegram's operator. The model effectively characterizes the series of positive and negative integer values generated after differencing some non-stationary time series. The model's attributes are addressed. For the parameter estimation of the model, the conditional maximum likelihood method and Yule-Walker method are taken into consideration. And we prove the asymptotic normality of CML method. By using these two methods, we simulate our model comparing with some relevant ones proposed before. The model can deal with positive or negative autocorrelation data. The analysis of the number of differenced daily new cases in Barbados is done using the suggested model., Comment: 32 pages, 2 figures

The mobility of Leidenfrost drop has been exploited for the manipulation of drop motions. In the classical model, the Leidenfrost drop was levitated by a vapor cushion, in the absence of touch to the surface. Here we report a standing Leidenfrost state on a heated hydrophobic surface where drop stands on the surface with partial adhesion and further self-rotates like Sufi-whirling. To elucidate this new phenomenon, we imaged the evolution of the partial adhesion, the inner circulation, and the ellipsoidal rotation of the drop. The stable partial adhesion is accompanied by thermal and mechanical equilibrium, and further drives the development of the drop rotation., Comment: 16 pages, 4 figures

Directed, long-range and self-propelled transport of droplets on solid surfaces, especially on water repellent surfaces, is crucial for many applications from water harvesting to bio-analytical devices. One appealing strategy to achieve the preferential transport is to passively control the surface wetting gradients, topological or chemical, to break the asymmetric contact line and overcome the resistance force. Despite extensive progress, the directional droplet transport is limited to small transport velocity and short transport distance due to the fundamental trade-off: rapid transport of droplet demands a large wetting gradient, whereas long-range transport necessitates a relatively small wetting gradient. Here, we report a radically new strategy that resolves the bottleneck through the creation of an unexplored gradient in surface charge density (SCD). By leveraging on a facile droplet printing on superamphiphobic surfaces as well as the fundamental understanding of the mechanisms underpinning the creation of the preferential SCD, we demonstrate the self-propulsion of droplets with a record-high velocity over an ultra-long distance without the need for additional energy input. Such a Leidenfrost-like droplet transport, manifested at ambient condition, is also genetic, which can occur on a variety of substrates such as flexible and vertically placed surfaces. Moreover, distinct from conventional physical and chemical gradients, the new dimension of gradient in SCD can be programmed in a rewritable fashion. We envision that our work enriches and extends our capability in the manipulation of droplet transport and would find numerous potential applications otherwise impossible., Comment: 11 pages, 4 figures