Mesoscopic Modeling of Capillarity-Induced Two-Phase Transport in a Microfluidic Porous Structure

Mesoscopic modeling at the pore scale offers great promise in exploring the underlying structure transport performance of flow through porous media. The present work studies the fluid flow subjected to capillarity-induced resonance in porous media characterized by different porous structure and wettability. The effects of porosity and wettability on the displacement behavior of the fluid flow through porous media are discussed. The results are presented in the form of temporal evolution of percentage saturation and displacement of the fluid front through porous media. The present study reveals that the vibration in the form of acoustic excitation could be significant in the mobilization of fluid through the porous media. The dependence of displacement of the fluid on physicochemical parameters like wettability of the surface, frequency along with the porosity is analyzed. It was observed that the mean displacement of the fluid is more in the case of invading fluid with wetting phase where the driving force strength is not so dominant.     

Three-term polynomial progressions in subsets of finite fields

We prove that the group of diffeomorphisms of the interval [0, 1] contains surface groups whose action on (0, 1) has no global fix point and such that only countably many points of the interval (0, 1) have non-trivial stabiliser.     

Discrete-time models for releases of sterile mosquitoes with Beverton–Holt-type of survivability

In this paper, we formulate discrete-time mathematical models for the interactive wild and sterile mosquitoes. Instead of the Ricker-type of nonlinearity for the survival functions, we assume the Beverton–Holt-type in these models. We consider three different strategies for the releases of sterile mosquitoes and investigate the model dynamics. Threshold values for the releases of sterile mosquitoes are derived for all of the models that determine whether the wild mosquitoes are wiped out or coexist with the sterile mosquitoes. Numerical examples are given to demonstrate the dynamics of the models.     

Inference for a change-point problem under a generalised Ornstein–Uhlenbeck setting

Determining accurately when regime and structural changes occur in various time-series data is critical in many social and natural sciences. We develop and show further the equivalence of two consistent estimation techniques in locating the change point under the framework of a generalised version of the one-dimensional Ornstein–Uhlenbeck process. Our methods are based on the least sum of squared error and the maximum log-likelihood approaches. The case where both the existence and the location of the change point are unknown is investigated and an informational methodology is employed to address these issues. Numerical illustrations are presented to assess the methods’ performance.     

Metric Subregularity in Generalized Equations

In this article, we study the metric subregularity of generalized equations using a new tool of nonsmooth analysis. We obtain a sufficient condition for a generalized equation to be metrically subregular, which is not a necessary condition for metric regularity, using a subtle adjustment of the Mordukhovich coderivative. We apply these results to the study of the metric subregularity in a Cournot duopoly game.     

Integral Representations of the Large and Little Schröder Numbers

In the paper, the authors establish several integral representations for the generating functions of the large and little Schröder numbers and for the large and little Schröder numbers.     

Real-time phase measurement and correction of dynamic multimode beam using a single spatial light modulator

In this Letter,a novel system for adaptively correcting the phase of a dynamic multimode beam is proposed.While using merely one spatial light modulator,the phase measurement of the first-order diffraction pattern and the correction of the zeroth diffraction order are simultaneously realized.The real-time experimental result is obtained at a control rate of 10 Hz.The power-in-the-bucket value is improved from 38.5%to 61.8%,even with fundamental mode content that is consistently below 30%.To the best of our knowledge,this is the first implementation of real-time adaptive correction of the entire multimode beam.     

双稳态结构中的1/2次谐波共振及其对隔振特性的影响

以典型的双稳态系统——屈曲梁结构为例,基于等效模型,结合解析、数值和实验手段,研究了双稳态结构中的1/2次谐波共振特性、演化过程、参数调节规律及其对隔振特性的影响.研究发现,当非线性刚度系数或激励幅值增加到一定程度时,系统会在一定带宽下产生显著的1/2次谐波共振;随着激励幅值增加,阻尼系统的1/2次谐波遵循“产生-增强-衰退-消失”的过程,该过程对峰值频率和峰值传递率有重要影响;适当提高非线性强度能有效改善双稳态结构隔振特性.针对双稳态屈曲梁结构开展的实验验证了1/2次谐波特性和隔振特性变化规律.