Dynamic Stability Analysis of Size-Dependent Viscoelastic/Piezoelectric Nano-beam

This paper analyzes the dynamic stability of an isotropic viscoelastic Euler–Bernoulli nano-beam using piezoelectric materials. For this purpose, the size-dependent theory was used in the framework of the modified couple stress theory (MCST) for piezoelectric materials. In order to capture the geometrical nonlinearity, the von Karman strain displacement relation was applied. Hamilton’s principle was also employed to obtain the governing equations. Furthermore, the Galerkin method was used in order to convert the governing partial differential equations (PDEs) to a nonlinear second-order ordinary differential one. Dynamic stability analysis was performed and the effects of such parameters as viscoelastic coefficients, size effect, and piezoelectric coefficient were investigated. The results showed that in this system, saddle points, central points, Hopf bifurcation points, and fork bifurcation points could be created, and the phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, and homoclinic orbits.

Mathematical Approach to Investigate Stress due to Control Measures to Curb COVID-19

COVID-19 is a world pandemic that has affected and continues to affect the social lives of people. Due to its social and economic impact, different countries imposed preventive measures that are aimed at reducing the transmission of the disease. Such control measures include physical distancing, quarantine, hand-washing, travel and boarder restrictions, lockdown, and the use of hand sanitizers. Quarantine, out of the aforementioned control measures, is considered to be more stressful for people to manage. When people are stressed, their body immunity becomes weak, which leads to multiplying of coronavirus within the body. Therefore, a mathematical model consisting of six compartments, Susceptible-Exposed-Quarantine-Infectious-Hospitalized-Recovered (SEQIHR) was developed, aimed at showing the impact of stress on the transmission of COVID-19 disease. From the model formulated, the positivity, bounded region, existence, uniqueness of the solution, the model existence of free and endemic equilibrium points, and local and global stability were theoretically proved. The basic reproduction number ( R 0 ) was derived by using the next-generation matrix method, which shows that, when R 0 < 1 , the disease-free equilibrium is globally asymptotically stable whereas when R 0 > 1 the endemic equilibrium is globally asymptotically stable. Moreover, the Partial Rank Correlation Coefficient (PRCC) method was used to study the correlation between model parameters and R 0 . Numerically, the SEQIHR model was solved by using the Rung-Kutta fourth-order method, while the least square method was used for parameter identifiability. Furthermore, graphical presentation revealed that when the mental health of an individual is good, the body immunity becomes strong and hence minimizes the infection. Conclusively, the control parameters have a significant impact in reducing the transmission of COVID-19.

A New Chaotic System with Only Nonhyperbolic Equilibrium Points: Dynamics and Its Engineering Application

In this work, we introduce a new non-Shilnikov chaotic system with an infinite number of nonhyperbolic equilibrium points. The proposed system does not have any linear term, and it is worth noting that the new system has one equilibrium point with triple zero eigenvalues at the origin. Also, the novel system has an infinite number of equilibrium points with double zero eigenvalues that are located on the z -axis. Numerical analysis of the system reveals many strong dynamics. The new system exhibits multistability and antimonotonicity. Multistability implies the coexistence of many periodic, limit cycle, and chaotic attractors under different initial values. Also, bifurcation analysis of the system shows interesting phenomena such as periodic window, period-doubling route to chaos, and inverse period-doubling bifurcations. Moreover, the complexity of the system is analyzed by computing spectral entropy. The spectral entropy distribution under different initial values is very scattered and shows that the new system has numerous multiple attractors. Finally, chaos-based encoding/decoding algorithms for secure data transmission are developed by designing a state chain diagram, which indicates the applicability of the new chaotic system.

Public Health Events Emergency Management Supervision Strategy Considering New Media and Citizen Participation

Public health events endanger the citizen health, economic development, social stability and national security seriously. Emergency management requires the joint participation of multiple parties. Therefore, we construct an evolutionary game model involving government department, pharmaceutical enterprises, citizens and new media, analyze the evolutionary stability, solve the stable equilibrium points using the Lyapunov first method and conduct the simulation analysis with Matlab 2020b. The results show that, firstly, the greater the probability of citizens making true evaluation, the more inclined the government department is to strictly implement the emergency management system, and when true evaluation causes the government department to bear more punishment, the probability that the government department doesn't strictly implement is smaller; secondly, when the probability of citizens making true evaluation decreases, new media are more inclined to report after verification, and when new media lose more pageview value or should be punished more for reporting without verification, the probability that they report without verification is smaller; thirdly, the greater the probability of citizens making false evaluation, the less enthusiasm of pharmaceutical enterprises to participate in emergency management, which indicates that false evaluation is detrimental to prompt pharmaceutical enterprises to participate; what's more, the greater the probability of new media reporting after verification, the greater the probability of pharmaceutical enterprises actively participating, which shows that new media's verification to citizens' evaluation is beneficial to emergency management. So, this paper provides suggestions for the emergency management and supervision.

A novel nonparametric computational strategy for identifying differential methylation regions

Background DNA methylation has long been known as an epigenetic gene silencing mechanism. For a motivating example, the methylomes of cancer and non-cancer cells show a number of methylation differences, indicating that certain features characteristics of cancer cells may be related to methylation characteristics. Robust methods for detecting differentially methylated regions (DMRs) could help scientists narrow down genome regions and even find biologically important regions. Although some statistical methods were developed for detecting DMR, there is no default or strongest method. Fisher’s exact test is direct, but not suitable for data with multiple replications, while regression-based methods usually come with a large number of assumptions. More complicated methods have been proposed, but those methods are often difficult to interpret. Results In this paper, we propose a three-step nonparametric kernel smoothing method that is both flexible and straightforward to implement and interpret. The proposed method relies on local quadratic fitting to find the set of equilibrium points (points at which the first derivative is 0) and the corresponding set of confidence windows. Potential regions are further refined using biological criteria, and finally selected based on a Bonferroni adjusted t-test cutoff. Using a comparison of three senescent and three proliferating cell lines to illustrate our method, we were able to identify a total of 1077 DMRs on chromosome 21. Conclusions We proposed a completely nonparametric, statistically straightforward, and interpretable method for detecting differentially methylated regions. Compared with existing methods, the non-reliance on model assumptions and the straightforward nature of our method makes it one competitive alternative to the existing statistical methods for defining DMRs.

Multistable autonomous motion of fruit on a smooth hotplate

Origin of scale coupling may be clarified by the understanding of multistability, or shifts between stable points via unstable equilibrium points due to a stimulus. When placed on a glasstop hotplate, cobs of corn underwent multistable autonomous oscillation, with unsteady viscous lubrication below and transitional plumes above, where the buoyancy to inertia force ratio is close to ≥ 1.0. Subsequently, viscous wall-frictional multistability occurred in six more types of smooth fruit with nominal symmetry. Autonomous motion observed are: cobs roll, pitch and yaw; but green chillies, blueberries, tropical berries, red grapes, oblong grapes and grape tomatoes roll and yaw. The cross products of the orthogonal angular momentum produce the observed motion. The prevalence of roll and yaw motion are the most common. Lubricant film thickness h$$\propto$$ ∝ U/(TF), for cob mass F, tangential velocity U and temperature T. In heavier cobs, the film thins, breaking frequently, changing stability. Lighter cobs have high h, favoring positive feedback and more spinning: more T rises, more viscosity of water drops, increasing U and h more, until cooling onsets. Infrequent popping of the tender corn kernel has the same mean sound pressure level as in hard popcorn. The plume vortex jets lock-in to the autonomous rolling cob oscillation. Away from any solid surface, the hot-cold side boundary produces plumes slanted at ± 45°. Surface fencing (13–26 μm high) appears to control motion drift.

Four-party evolutionary game analysis of supervision for vaccine quality in major epidemics

During major epidemics, monitoring vaccine quality can ensure the public health and social stability. Considering that social media has become an important way for the public to obtain external information during the epidemic. We developed a dual regulatory system of vaccine quality with the government in the leading role and the participation of We Media, and constructed a four-party evolutionary game model (government regulatory agency, We Media, vaccine industry groups, and the public) and analyzed the stability of each game player’s strategy choice. The system’s possible equilibrium points are identified using Lyapunov’s first law. Then the game trajectory between stakeholders is simulated by MATLAB, the effects of initial intention and parameters on the evolution process and results are analyzed. The results show that to ensure the quality and safety of vaccines and stabilize network public opinion during epidemics, the government should invest in an effective supervision mechanism. By strengthening responsibility, increasing penalties, and reducing supervision costs, the probability of vaccine industry groups providing high-quality vaccines is effectively enhanced. Restricting the behavior of We Media and supervising vaccine industry groups to reduce speculation reduces the cost of government supervision and improves its efficiency.

Partial state feedback sliding mode control for double-pendulum overhead cranes with unknown disturbances

In this paper, a novel sliding mode controller which requires partial state feedback is proposed for double-pendulum overhead cranes subject to unknown payload parameters and unknown external disturbances. Firstly, it is theoretically proved that the hook and payload tend to their respective equilibrium points concurrently. Secondly, a decoupling transformation is performed on the original nonlinear dynamics of double-pendulum overhead cranes. The novel sliding mode controller that does not require the prior information and motion signals of the payload is designed based on the decoupled nonlinear dynamics. Then, the asymptotic stability of the equilibrium point of double-pendulum overhead cranes is proved by rigorous analysis. Finally, several simulations are conducted to validate the effectiveness and robustness of the proposed controller.

A fuzzy fixed-point theorem and its applications to maximal elements and Nash equilibria in noncompact CAT(0) spaces

In this paper, based on the KKM method, we prove a new fuzzy fixed-point theorem in noncompact CAT(0) spaces. As applications of this fixed-point theorem, we obtain some existence theorems of fuzzy maximal element points. Finally, we utilize these fuzzy maximal element theorems to establish some new existence theorems of Nash equilibrium points for generalized fuzzy noncooperative games and fuzzy noncooperative qualitative games in noncompact CAT(0) spaces. The results obtained in this paper generalize and extend many known results in the existing literature.