A unified analysis of a micro-beam,droplet and CNT ring adhered on a substrate:Calculation of variation with movable boundaries

In this study, we developed a general method to analytically tackle a kind of movable boundary problem from the viewpoint of energy variation. Having grouped the adhesion of a micro-beam, droplet and carbon nanotube （CNT） ring on a substrate into one framework, we used the developed line of reasoning to investigate the adhesion behaviors of these systems. Based upon the derived governing equations and transversality conditions, explicit solutions involving the critical parameters and morphologies for the three systems are successfully obtained, and then the parameter analogies and common characteristics of them are thor- oughly investigated. The presented method has been verified via the concept of energy release rate in fracture mechanics. Our analyses provide a new approach for exploring the mechanism of different systems with similarities as well as for understanding the unity of nature. The analysis results may be beneficial for the design of nano-structured materi- als, and hold potential for enhancing their mechanical, chemical, optical and electronic properties.

Fractional Pfaff-Birkhoff Principle and Birkhoff′s Equations in Terms of Riesz Fractional Derivatives

The dynamical and physical behavior of a complex system can be more accurately described by using the fractional model.With the successful use of fractional calculus in many areas of science and engineering,it is necessary to extend the classical theories and methods of analytical mechanics to the fractional dynamic system.Birkhoffian mechanics is a natural generalization of Hamiltonian mechanics,and its core is the Pfaff-Birkhoff principle and Birkhoff′s equations.The study on the Birkhoffian mechanics is an important developmental direction of modern analytical mechanics.Here,the fractional Pfaff-Birkhoff variational problem is presented and studied.The definitions of fractional derivatives,the formulae for integration by parts and some other preliminaries are firstly given.Secondly,the fractional Pfaff-Birkhoff principle and the fractional Birkhoff′s equations in terms of RieszRiemann-Liouville fractional derivatives and Riesz-Caputo fractional derivatives are presented respectively.Finally,an example is given to illustrate the application of the results.

Theoretical analysis on capillary adhesion of microsized plates with a substrate

The stiction of a thin plate induced by the capillary force has attracted much attention in the broad range of applications. A novel method is presented to calculate the capillary adhesion problem of the plate through analytical method. The expressions of the surface energy, the strain energy and the total potential energy of the plate-substrate system have been analyzed and delineated. By means of continuum mechanics and the principle of minimum potential energy, the governing equation of the plate with an arbitrary shape and the corresponding transversality boundary condition due to the moving bound have been derived. Then the critical adhesion radius of the circular plate has been solved according to the supplementary transversality condition. Thus the deflections of the plates are analytically calculated with different critical adhesion radii. The results may be beneficial to the engineering application and the micro/nanomeasurement.

Mathematical Analysis of Nipah Virus Infections Using Optimal Control Theory

The optimal use of intervention strategies to mitigate the spread of Nipah Virus (NiV) using optimal control technique is studied in this paper. First of all we formulate a dynamic model of NiV infections with variable size population and two control strategies where creating awareness and treatment are considered as controls. We intend to find the optimal combination of these two control strategies that will minimize the cost of the two control measures and as a result the number of infectious individuals will decrease. We establish the existence for the optimal controls and Pontryagin’s maximum principle is used to characterize the optimal controls. The numerical simulation suggests that optimal control technique is much more effective to minimize the infected individuals and the corresponding cost of the two controls. It is also monitored that in the case of high contact rate, controls have to work for longer period of time to get the desired result. Numerical simulation reveals that the spread of Nipah virus can be controlled effectively if we apply control strategy at early stage.

Fractional Noether's Theorems for El-Nabulsi's Fractional Birkhoffian Systems in Terms of Riemann-Liouville Derivatives

The fractional Pfaffian variational problem and Noether’s theorems were investigated in terms of Riemann-Liouville derivatives on the basis of El-Nabulsi fractional model.The problem of the calculus of variations with fractional derivatives is a hot topic recently.Firstly,within Riemann-Liouville derivatives,the ElNabulsi Pfaffian variational problem was presented,the fractional Pfaff-Birkhoff-d’Alembert principle was established,and the fractional Birkhoff equations and the corresponding transversality conditions were obtained.Then,the Noether’s theorems in terms of Riemann-Liouville derivatives for the Birkhoffian system on the basis of El-Nabulsi fractional model are investigated under the special and the general transformations respectively.Finally,an example is given to illustrate the methods and results appeared in this paper.

Optimal Control Analysis of Influenza Epidemic Model

The implementation of optimal control strategies involving preventive measures and antiviral treatment can significantly reduce the number of clinical cases of influenza. In this paper, a model for the transmission dynamics of influenza is formulated and two control strategies involving preventive measures (awareness campaign, washing hand, using hand sanitizer, wearing mask) and treatment are considered and used to minimize the total number of infected individuals and associated cost of using these two controls. The resulting optimality system is solved numerically. Hamiltonian is formulated to investigate the existence of the optimal control, in the optimal control model. Pontryagin’s Maximum Principle is applied to describe the control variables and the objective function is designed to reduce both the infection and the cost of interventions. From the numerical simulation, it is observed that in the case of high contact rate (β = 3), both the controls work for a longer period of time to reduce the disease burden. The optimal control analysis and numerical simulations reveal that the interventions reduce the number of exposed and infected individuals.

Peeling of Magneto-responsive Beams with Large Deformation Mediated by the Parallel Magnetic Field

Elasto-capillarity phenomena are prevalent in various industrial fields such as mechanical engineering,material science,aerospace,soft robotics,and biomedicine.In this study,two typical peeling processes of slender beams driven by the parallel magnetic field are investigated based on experimental and theoretical analysis.The first is the adhesion of two parallel beams,and the second is the self-folding of a long beam.In these two cases,the energy variation method on the elastica is used,and then,the governing equations and transversality boundary conditions are derived.It is shown that the analytical solutions are in excellent agreement with the experimental data.The effects of magnetic induction intensity,distance,and surface tension on the deflection curve and peeling length of the elastica are fully discussed.The results are instrumental in accurately regulating elasto-capillarity in structures and provide insights for the engineering design of programmable microstructures on surfaces,microsensors,and bionic robots.

Broadband transverse displacement sensing of silicon hollow nanodisk under focused radial polarization illumination in the near-infrared region

Broadband transverse displacement sensing by exploiting the interaction of a focused radially polarized beam with a silicon hollow nanodisk is proposed.The multipolar decomposition analysis indicates that the interference between a longitudinal total electric dipole(TED)moment and a lateral magnetic dipole(MD)moment is dominant in the far-field transverse scattering in the near-infrared region.Within a broadband wavelength range with the width of 155 nm,the longitudinal TED is almost in phase with the lateral MD,and then broadband position sensing based on the sensitivity of scattering directivity to transverse displacement can be achieved.