Anomalous Dispersion of the S1 Lamb Mode

The S1 mode of the Lamb spectrum of an isotropic plate exhibits negative group velocity in a narrow frequency domain. This anomalous behavior is explained analytically by examining the slope of each mode first in its initial state and then near its turning points

Laser induced Zero-Group Velocity resonances in Transversely Isotropic cylinder

The transient response of an elastic cylinder to a laser impact is studied. When the laser source is a line perpendicular to the cylinder axis, modes guided along the cylinder are generated. For a millimetric steel cylinder up to ten narrow resonances can be locally detected by laser interferometry below 8 MHz. Most of these resonances correspond to Zero-Group Velocity guided modes while a few others can be ascribed to thickness modes. We observe that the theory describing the propagation of elastic waves in an isotropic cylinder is not sufficient to precisely predict the resonance spectrum. In fact, the texture of such elongated structure manifest as elastic anisotropy. Thus, a transverse isotropic (TI) model is used to calculate the dispersion curves and compare them with the measured one, obtained by moving the source along the cylinder. The five elastic constants of a TI cylinder are adjusted leading to a good agreement between measured and theoretical dispersion curves. Then, all the resonance frequencies are satisfactorily identified.Comment: 23 pages, 7 figures, submitted to the JAS

Lamb Modes for an Isotropic Incompressible Plate

Lamb modes for an incompressible isotropic plate behave in a manner different from those for a compressible plate. The plateau region disappears and anomalous behavior of modes does not exist

Charged particle dynamics in the surrounding of Schwarzschild anti-de Sitter black hole with topological defect immersed in an external magnetic field

In this paper, geodesic motion of the charged particles in the vicinity of event horizon of Schwarzschild anti-de-Sitter black hole (BH) with topological defects has been investigated. Weakly magnetized environment is considered in the surrounding of BH which only effects the motion of the particles and doesn’t effect the geometry of the BH. Hence, particles are under the influence of gravity and electromagnetic forces. We have explored the effect of magnetic field on the trajectories of the particles and more importantly on the position of the innermost stable circular orbit. It is observed that the trajectories of the particles in the surrounding of BH are chaotic. Escape conditions of the particles under the influence of gravitomagnetic force are also discussed. Moreover, the escape velocity of particles and its different features have been investigated in the presence and absence of magnetic field. Effect of dark energy on the size of event horizon, mass of the BH and stability of the orbits of the particles have also been explored in detail. These studies can be used to estimate the power of relativistic jets originated from the vicinity of BH

Stability analysis of pine wilt disease model by periodic use of insecticides

This work is related to qualitative behaviour of an epidemic model of pine wilt disease. More precisely, we proved that the reproductive number has sharp threshold properties. It has been shown that how vector population can be reduced by the periodic use of insecticides. Numerical simulations show that epidemic level of infected vectors becomes independent of saturation level by including the transmission through mating

Qualitative analysis and sensitivity based optimal control of pine wilt disease

Abstract We design a deterministic model of pine wilt affliction to analyze the transmission dynamics. We obtain the reproduction number in unequivocal form, and global dynamics of the ailment is totally controlled by this number. With a specific end goal to survey the adequacy of malady control measures, we give the affectability investigation of basic reproduction number R 0 $R_{0}$ and the endemic levels of diseased classes regarding epidemiological parameters. From the aftereffects of the sensitivity analysis, we adjust the model to evaluate the effect of three control measures: exploitation of the tainted pines, preventive control to limit vector host contacts, and bug spray control to the vectors. Optimal analysis and numerical simulations of the model show that limited and appropriate utilization of control measures may extensively diminish the number of infected pines in a viable way

A Mathematical and Statistical Estimation of Potential Transmission and Severity of COVID-19: A Combined Study of Romania and Pakistan

During the outbreak of an epidemic, it is of immense interest to monitor the effects of containment measures and forecast of outbreak including epidemic peak. To confront the epidemic, a simple SIR model is used to simulate the number of affected patients of coronavirus disease in Romania and Pakistan. The model captures the growth in case onsets, and the estimated results are almost compatible with the actual reported cases. Through the calibration of parameters, forecast for the appearance of new cases in Romania and Pakistan is reported till the end of this year by analysing the current situation. The constant level of number of patients and time to reach this level is also reported through the simulations. The drastic condition is also discussed which may occur if all the preventive restraints are removed

Transmission and epidemiological trends of pine wilt disease: Findings from sensitivity to optimality

In this work, a deterministic model is dedicatedly studied for the infection mechanism of pine wilt disease subject to varying sensitivity and optimality. We include time dependent controls into the pine wilt disease model and then analysed optimal conditions for the control of infection. Explicit form for the reproduction number has been obtained. Ultimate constant levels of infectious vectors and hosts have been discussed by employing the threshold condition. Two most effective techniques namely Lyapunov functional and graph theoretic have been used to find the final endemic level of population. The concept of full eradication of disease and reduction of constant level has been investigated through the utilization of two effective techniques. Using the concept of sensitivity analysis, control policies have been designed to control the disease. Additionally, the robustness of control plans has been shown graphically on the basis of data collected from open literature

Mathematical modelling approach to cholera transmission with vaccination strategy

In this work, we investigated the transmission of cholera infection through mathematical modelling. We calculated the contact number by applying the technique of next generation matrix method to find about infection dissemination as well as control in the population. Two types of constant solutions: infection free as well as infection present have been calculated. Stability of both constant solutions has been discussed. To control the dissemination of disease, we formulated an optimal control problem. Strategies, which are used to control this disease, have been composed on the consequences of sensitivity analysis. In order to gain better insight into the comparative results of analytical and numerical outcomes, the problem was revisited, and found that numerical results support our analytical findings. Our results conclude that pre-exposure vaccination can substantially reduce the risk of cholera