In the introduction a brief recollection is made of how one of us (RKC), accidentally, got into this field of linear and nonlinear spectroscopy of a dielectric micro-particle that can be treated as a micro-cavity or a micro-resonator. The basic principles of whispering gallery modes (WGMs) and their relationship with electromagnetic theory are presented. To simplify the mathematics, we only dis...

the nonlocal nonlinear buckling of a double layer graphene sheet (dlgs) covered by zinc oxide (zno) piezoelectric layers is investigated in this study. the surrounding circumstances of the system are considered as a pasternak foundation including spring constants and a shear layer. graphene sheets are subjected to longitudinal magnetic field and biaxial forces. on the other hand, the zno piezoe...

This paper establishes a novel control strategy for a nonlinear bilateral macro-micro teleoperation system with time delay. Besides position and velocity signals, force signals are additionally utilized in the control scheme. This modification significantly improves the poor transparency during contact with the environment. To eliminate external force measurement, a force estimation algorithm i...

Station-keeping and reorientation control of a cluster of fully-actuated low-thrust micro-satellites is considered in this paper. We propose a very general optimization based control methodology to solve constrained trajectory generation problems for stationkeeping and reorientation. By taking advantage of the fully-actuated structure of the micro-satellite, it is possible to compute the contro...

Inorganic insulating powder can potentially be used in nuclear power plant cables, fire-resistant and so on due to its high heat resistance radiation resistance. It is of great academic engineering value study the dielectric properties inorganic powder. In this paper, we aim nonlinear via measurement time-domain polarization current spectrum under application a DC electric field. Three kinds si...

in this study, nonlocal nonlinear instability and the vibration of a double carbon nanotube (cnt) system have been investigated. the visco-pasternak model is used to simulate the elastic medium between nanotubes, on which the effect of the spring, shear and damping of the elastic medium is considered. both of the cnts convey a viscose fluid and a uniform longitudinal magnetic field is applied t...

We prove global existence for a nonlinear Smoluchowski equation (a nonlinear FokkerPlanck equation) coupled with Navier-Stokes equations in 2d. The proof uses a deteriorating regularity estimate in the spirit of [5] (see also [1]) Key wordsNonlinear Fokker-Planck equations, Navier-Stokes equations, Smoluchowski equation, micro-macro interactions. AMS subject classification 35Q30, 82C31, 76A05.