We investigate the dynamics of an ion confined in a Paul-trap supplied by a fractional periodic impulsional potential. The Cantor-type cylindrical coordinate method is a powerful tool to convert differential equations on Cantor sets from cantorian-coordinate systems to Cantor-type cylindrical coordinate systems. By applying this method to the classical Laplace equation, a fractional Laplace equation in the Cantor-type cylindrical coordinate is obtained. The fractional Laplace equation is solved in the Cantor-type cylindrical coordinate, then the ions is modelled and studied for confined ions inside a Paul-trap characterized by a fractional potential. In addition, the effect of the fractional parameter on the stability regions, ion trajectories, phase space, maximum trapping voltage, spacing between two signals and fractional resolution is investigated and discussed.
In 2019, a new infectious disease called pandemic COVID-19 began to spread from Wuhan, China. In spite of the efforts to stop the disease, being out of the control of the governments it spread rapidly all over the world. From then on, much research has been done in the world with the aim of controlling this contagious disease. A mathematical model for modeling the spread of COVID-19 and also controlling the spread of the disease has been presented in this paper. We find the disease-free equilibrium points as trivial equilibrium (TE), virus absenteeism equilibrium (VAE) and virus incidence equilibrium (VIE) for the proposed model; and at the trivial equilibrium point for the presented dynamic system we obtain the Jacobian matrix so as to be used in finding the largest eigenvalue. Radius spectral method has been used for finding the reproductive number. In the following, by adding a controller to the model and also using the theory of optimal control, we can improve the performance of the model. We must have a correct understanding of the system i.e. how it works, the various variables affecting the system, and the interaction of the variables on each other. To search for the optimal values, we need to use an appropriate optimization method. Given the limitations and needs of the problem, the aim of the optimization is to find the best solutions, to find conditions that result in the maximum of susceptiblity, the minimum of infection, and optimal quarantination.
To understand the transmission dynamics of any infectious disease outbreak, identification of influential nodes plays a crucial role in a complex network. In most infectious disease outbreaks, activities of some key nodes can trigger rapid disease transmission in the population. Identification and immediate isolation of those influential nodes can impede the disease transmission effectively. In this paper, the technique for order of preference by similarity to ideal solution (TOPSIS) method with a novel formula has been proposed to detect the influential and top ranked nodes in a complex social network, which involves analyzing and studying of structural organization of a network. In the proposed TOPSIS method, several centrality measures have been used as multi-attributes of a complex social network. A new formula has been designed for calculating the transmission probability of an epidemic disease to identify the impact of isolating influential nodes. To verify the robustness of the proposed method, we present a comprehensive comparison with five node-ranking methods, which are being used currently for assessing the importance of nodes. The key nodes can be considered as a person, community, cluster or a particular area. The Susceptible-infected-recovered (SIR) epidemic model is exploited in two real networks to examine the spreading ability of the nodes, and the results illustrate the effectiveness of the proposed method. Our findings have unearthed that quarantine or isolation of influential nodes following proper health protocols can play a pivotal role in curbing the transmission rate of COVID-19.
The capabilities and performances of a quadrupole ion trap under damping force based on collisional cooling is of particular importance in high-resolution mass spectrometry and should be analyzed by Mathieu's differential solutions. These solutions describe the stability and instability of the ion's trajectories confined in quadrupole devices. One of the methods for solving Mathieu's differential equation is a two-point one block method. In this case, Mathieu's stability diagram, trapping parameters a(z) and q(z) and the secular frequency of the ion motion w(z), can be derived in a precise manner. The two-point one block method (TPOBM) of Adams Moulton type is presented to study these parameters with and without the effect of damping force and compared to the 5th-order Runge-Kutta method (RKM5). The simulated results show that the TPOBM is more accurate and 10 times faster than the RKM5. The physical properties of the confined ions in the r and z axes are illustrated and the fractional mass resolutions m/Δm of the confined ions in the first stability region were analyzed by the RKM5 and the TPOBM.