Deposition pattern of drying droplets

The drying of liquid droplets is a common daily life phenomenon that has long held a special interest in scientific research. When the droplet includes nonvolatile solutes, the evaporation of the solvent induces rich deposition patterns of solutes on the substrate. Understanding the formation mechanism of these patterns has important ramifications for technical applications,ranging from coating to inkjet printing to disease detection. This topical review addresses the development of physical understanding of tailoring the specific ring-like deposition patterns of drying droplets. We start with a brief introduction of the experimental techniques that are developed to control these patterns of sessile droplets. We then summarize the development of the corresponding theory. Particular attention herein is focused on advances and issues related to applying the Onsager variational principle (OVP) theory to the study of the deposition patterns of drying droplets. The main obstacle to conventional theory is the requirement of complex numerical solutions, but fortunately there has been recent groundbreaking progress due to the OVP theory. The advantage of the OVP theory is that it can be used as an approximation tool to reduce the high-order conventional hydrodynamic equations to first-order evolution equations,facilitating the analysis of soft matter dynamic problems. As such, OVP theory is now well poised to become a theory of choice for predicting deposition patterns of drying droplets.     

SnSxSe2-x单晶纳米片的可控制备与表征

锡二硫族化合物可以通过改变硫和硒的含量来连续调控三元合金材料的带隙、载流子浓度等物理化学性质,在电子和光电子器件应用上具有巨大的潜力。本文采用化学气相沉积(CVD)技术可控地制备了不同元素组分的SnS_xSe_2-x(x=0,0.2,0.5,0.8,1.0,1.2,1.5,1.8,2.0)单晶纳米片。采用扫描电子显微镜(SEM)、原子力显微镜(AFM)、能量色散X射线光谱(EDS)、透射电子显微镜(TEM)以及拉曼光谱等手段对SnS_xSe_2-x纳米片进行了综合表征。结果表明本方法成功实现了元素百分比可调的SnS_xSe_2-x单晶纳米片的可控制备。重点研究了依赖于元素百分比的SnS_xSe_2-x的拉曼特征谱,实验结果与基于密度泛函理论(DFT)的第一性原理计算得到的SnS_xSe_2-x的拉曼仿真谱高度吻合,理论计算结果较好地诠释了实验拉曼光谱发生变化的原因。本研究提供了一种元素百分比可调的三元SnS_xSe_2-x单晶纳米片的可控制备方法,同时对锡二硫族化合物的明确、无损识别提供了方案。     

Study on the design of ZnO/PANI composites and the mechanism of enhanced humidity sensing properties

ZnO/PANI composite humidity sensor was prepared by hydrothermal method. The first principles of density functional theory study the sensing mechanism. The calculation shows that the oxygen vacancy on ZnO surface is beneficial to the adsorption of water molecules. The {0 0 0‾1} crystal plane with the largest lattice oxygen number in ZnO has a strong adsorption capacity for water molecules, which is also conducive to improving the humidity sensitivity. PANI is easy to be combined on {0 1‾1 0} plane of ZnO, and it indirectly promotes the growth of {0 0 0‾1} plane, increasing the adsorption of water molecules and the proportion of H⁺ and H₃O⁺ ions. In addition, the N–H group in ZnO/PANI enhances the H⁺ conduction, which further improves the performance of the sensor. The results concluded that the proportion of lattice oxygen in humidity sensor is an important factor of humidity sensor sensitive detection.     

Dynamic stability of a class of fractional-order nonlinear systems via fixed point theory

In this paper, the problem of the uniform stability for a class of fuzzy fractional-order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in $\left(\frac{1}{2},1\right)$. However, the case of the fractional-order belonging to $(0,\frac{1}{2})$ has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective.     

Measuring technical and environmental efficiency in a state-contingent technology

Most developed countries support farming activities through policies that are tailored to meet their specific social, economic and environmental objectives. Economic and environmental efficiency have recently become relevant targets of most of these policies, whose sound implementation can be enhanced by monitoring farm performance from a multidimensional perspective. This paper proposes farm-level technical and environmental efficiency measures that recognize the stochastic conditions in which production takes place. A state-contingent framework is used to model production uncertainty. An implementable representation of the technology is developed using data envelopment analysis. The application focuses on a sample of Catalan arable crop farms. Results suggest that technical efficiency is slightly lower in bad than in good growing conditions. Nitrogen pollution can decrease substantially more under good than bad growing conditions.     

A new distance measure including the weak preference relation: Application to the multiple criteria aggregation procedure for mixed evaluations

We introduce a new distance measure between two preorders that captures indifference, strict preference, weak preference and incomparability relations. This measure is the first to capture weak preference relations. We illustrate how this distance measure affords decision makers greater modeling power to capture their preferences, or uncertainty and ambiguity around them, by using our proposed distance measure in a multiple criteria aggregation procedure for mixed evaluations.     

Interval,ellipsoidal, and super-ellipsoidal calculi for experimental and theoretical treatment of uncertainty: Which one ought to be preferred?

In this study we compare three calculi listed in the title for analysis of structures involving uncertainty. The main idea is based on the consideration that the maximum structural response predicted by the preferred theory ought to be minimal, and the minimum structural response predicted by the preferred theory ought to be maximal, to constitute a lower overestimation. We present analytic results that allow one to calculate the structural response via the interval, ellipsoidal or super-ellipsoidal calculus. We provide several examples of truss structures and illustrate that in different situations, depending on the available data, one of these calculi ought to be preferred. Conclusion is made on the preferable approach to be the super-ellipsoidal calculus.     

Risk averse decision making under catastrophic risk

A nonstandard probabilistic setting for modeling of the risk of catastrophic events is presented. It allows random variables to take on infinitely large negative values with non-zero probability, which correspond to catastrophic consequences unmeasurable in monetary terms, e.g. loss of human lives. Thanks to this extension, the safety-first principle is proved to be consistent with traditional axioms on a preference relation, such as monotonicity, continuity, and risk aversion. Also, a robust preference relation is introduced, and an example of a monotone robust preference relation, sensitive to catastrophic events in the sense of Chichilnisky (2002), is provided. The suggested setting is demonstrated in evaluating nuclear power plant projects when the probability of a catastrophe is itself a random variable.     

An alternative proof of lower bounds for the first eigenvalue on manifolds

Recently, Andrews and Clutterbuck [1] gave a new proof of the optimal lower eigenvalue bound on manifolds via modulus of continuity for solutions of the heat equation. In this short note, we give an alternative proof of Theorem 2 in [1]. More precisely, following Ni's method (Section 6 of [5]), we give an elliptic proof of this theorem.     

Analysis of the mean squared derivative cost function

In this paper, we investigate the mean squared derivative cost functions that arise in various applications such as in motor control, biometrics and optimal transport theory. We provide qualitative properties, explicit analytical formulas and computational algorithms for the cost functions. We also perform numerical simulations to illustrate the analytical results. In addition, as a by‐product of our analysis, we obtain an explicit formula for the inverse of a Wronskian matrix that is of independent interest in linear algebra and differential equations theory. Copyright © 2017 John Wiley & Sons, Ltd.