Limit Cycles in Discontinuous Planar Piecewise Linear Systems Separated by a Nonregular Line of Center–Center Type

Many natural phenomena can be modeled as discontinuous dynamical systems separated by a nonregular line. The number and distribution of limit cycles in discontinuous linear systems are important topics for research. In this paper, we focus on the limit cycles created by discontinuous planar piecewise linear systems separated by a nonregular line of center–center type, and prove that such systems have at most two limit cycles, which can be reached. Furthermore, the two limit cycles are nested and intersect the separation line at two points or four points, that is, either both intersect the separation line at two points or one intersects the separation line at two points and the other one at four points.

Rich dynamics of a Filippov avian-only influenza model with a nonsmooth separation line

Depopulation of birds has been authenticated to be an effective measure in controlling avian influenza transmission. In this work, we establish a Filippov avian-only model incorporating a threshold policy control. We choose the index—the maximum between the infected threshold level $I_{T}$ I T and the product of the number of susceptible birds S and a ratio threshold value ξ—to decide on whether to trigger the control measures or not, which then leads to a discontinuous separation line and two pieces of sliding-mode domains. Meanwhile, one more sliding-mode domain gives birth to more complex dynamics. We investigate the global dynamical behavior of the Filippov model, including the real and/or virtual equilibria and the two sliding modes and their dynamics. The solutions will eventually stabilize at the real endemic equilibrium of the subsystem or the pseudoequilibria on the two sliding modes due to different threshold values. Therefore an effective and efficient threshold policy is essential to control the influenza by driving the number of infected birds below a certain level or at a previously given level.

Characterization of Lung Tumors that the Pulmonologist can Biopsy from the Esophagus with Endosonography (EUS-B-FNA)

<b><i>Background:</i></b> According to guidelines, it is possible to biopsy lung tumors “immediately adjacent to the esophagus” with EUS-B-FNA. However, it is unknown what “immediately adjacent” exactly means. <b><i>Objective:</i></b> to investigate the possibility of achieving EUS-B-FNA biopsies from a lung tumor depending on the distance from the esophagus and to establish the maximal allowable distance between the tumor and the esophagus. <b><i>Methods:</i></b> In a prospective observational study, we included patients with a lung tumor located maximum 6 cm from the esophagus and indication of EUS-B-FNA from the tumor. The tumors were of different sizes. In a plot presenting the tumor size-distance relationship in cases with (biopsy) versus without (non-biopsy) successful EUS-B-FNA, a separation line representing the threshold between the groups were identified and a biopsy-index equation established. The maximal tumor-size corrected distance (TSCD) was calculated using the residuals to the separation line. <b><i>Results:</i></b> In total, 70 patients were included. EUS-B-FNA from the lung tumor was possible in 46 patients. All tumors with a distance from the esophagus below 19 mm could be biopsied. The maximal allowable esophagus-tumor distance depended on tumor size. From the separation line, a biopsy-index equation was established with the sensitivity of 93.5%, a specificity of 100%, and total accuracy of 95.7%. The TSCD was 31 mm (sensitivity: 95.7%, specificity 75.0%, and accuracy: 88.6%). <b><i>Conclusion:</i></b> We established a biopsy-index equation to predict the achievability of a lung tumor using EUS-B-FNA depending on distance to esophagus and tumor size. A general maximal TSCD was 31 mm.

Bifurcation of a Kind of Piecewise Smooth Generalized Abel Equation via First and Second Order Analyses

In this paper, we consider the problem of estimating the number of nontrivial limit cycles for a kind of piecewise trigonometrical smooth generalized Abel equation with the separation line [Formula: see text]. Under the first and second order analyses, we show that the first two order Melnikov functions of the equation share a same structure which can be studied by an ECT-system. Furthermore, let [Formula: see text] be the maximum number of nontrivial limit cycles of the equation bifurcating from the periodic annulus up to [Formula: see text]th order analysis. We prove that [Formula: see text] and [Formula: see text] (resp., [Formula: see text] and [Formula: see text]) when [Formula: see text] is even (resp., odd).

Vampire squids, ‘the broken internet’ and platform regulation

Google, Apple, Facebook, Amazon, Microsoft and Netflix have come under intense criticism for acquiring undue influence on the media, economy, society and democracy. Google and Facebook’s business models, especially, are cast as a form of ‘vampire economics’ responsible for the crisis of journalism and upending the media industries. Many media scholars argue that since the platforms increasingly function like media companies, media policy should be our North Star with respect to what new approaches to internet regulation should look like. This article agrees that a forceful response to the platforms is overdue but criticizes the case against them for too often resting on cherry-picked evidence and an exaggerated sense of their clout, while references to media policy obscure a better approach that draws on four principles from telecoms regulation to guide a new generation of internet regulation: structural separation, line of business restrictions (i.e., firewalls), public obligations and public alternatives.

Numerical Analysis of Sweeping Jets for Active Flow Control Application

It has become apparent recently that the fluidic oscillators, also known as sweeping jets, can be used to create a combination of steady (streamwise vortices) and unsteady (spanwise vortices) forcing mechanisms which have the potential to fulfill many of the promises of active separation control. The fluidic oscillators contain no moving parts, but produce an unsteady component via a natural feedback loop inherent to their geometry. The oscillations are entirely self-induced and self-sustaining. Their simple and robust design and their effectiveness over a wide range of flow conditions make them more attractive than other flow control devices, such as synthetic jets and plasma actuators. Figure 1 shows the instantaneous jet generated in quiescent environment using the Improved Delayed Detached Eddy Simulation (IDDES) model, where the Large Eddy Simulation (LES) branch of the IDDES model is able to capture the turbulence structures properly. An instantaneous iso-surface of vorticity magnitude, colored by streamwise velocity for flow over a wall-mounted hump is depicted in Figure 2. As expected, a massive flow separation occurs behind the hump in the uncontrolled condition (Figure 2 (a)), with a nearly two-dimensional free shear layer at the edge of the separation line. Breakdown of the shear layer by an array of sweeping jets located slightly downstream of the separation line is seen in Figure 2 (b), which is followed by the elimination of the separation region behind hump. The three-dimensional structures generated by the sweeping jets are smaller and closer to the hump wall than those produced by the steady jets shown in Figure 2 (c). Presence of a large region of reversed flow near the hump wall in its aft section is also seen in the case of the steady jet. This study indicates a superior effectiveness of sweeping jets on separated flows.

Redefining Rational (Aqlī) and Revelation (Naqlī) into a Concept of Islamic Systemology

The way of thinking held by most Muslims has nowadays shifted away from Allah-centred to logical and empiricism. The separation line of Islam from ways of life can be seen clearly as the majority of Muslims hold secular thoughts. The paper aims to redefine ‘aqlī and naqlī way of thinking into the Islamic systemology concept. It is a concept that puts Allah as an agent of everything, with Him as the head of the system. Besides, the paper also discusses the process of the evolution of Greek philosophy deeply, how it became a phenomenon in the Muslim world. The application of rational and reasoning, which is championed by Aristotle, is slowly degrading Muslims’ faith, as Muslims start to verify everything based only on logical answers. The article is also strengthening the position of Abū Ḥāmid al-Ghazālī and supporting his arguments on the rejection of the Western philosophy by outlining the importance of yaqīn (strong inner faith) in taking action and making a better judgment. The Islamic systemology concepts are very important to make Muslims aware of the balancing between ‘aqlī and naqlī, as both of them are interconnected and complementary. Ignoring naqlī means Muslims put more emphasis on the world (dunyā) and put less belief in Allah. Hence they jeopardize the equilibrium of thinking.

Experimental and numerical investigation of an axisymmetric divergent dual throat nozzle

The dual throat nozzle achieves higher thrust vectoring efficiencies and lesser thrust loss than other fluidic thrust-vectoring nozzles. Separation always occurs at the bottom of the cavity with complex three-dimensional characteristics for the dual throat nozzle. In this paper, by comparing the flow structure, nozzle surface static pressure distributions and skin friction lines, which are obtained by numerical simulations and wind tunnel experiments, an axisymmetric divergent dual throat nozzle is investigated in detail. The main results show the following findings. (1) The experimental schlieren photographs confirm again that the divergent nozzle configuration has the starting problem from an intuitive perspective. Meanwhile, the flow structure and nozzle surface static pressure distributions obtained by numerical simulations are consistent with the experimental results, except for the low nozzle pressure ratios. (2) The circumferential pressure difference is negligible upstream of the separation line but obvious downstream of the separation line. The skin friction lines and nozzle surface static pressure distributions of different circumferential angles obtained by experiments both prove that the actual flow in the axisymmetric divergent dual throat nozzle indeed possesses three-dimensional characteristics. Therefore, it is necessary to utilize the full three-dimensional computational domain to study the complex three-dimensional characteristics of the flow for the axisymmetric divergent dual throat nozzle thoroughly.