No abstract

In this study, the properties of wave functions of the MHD oscillations for a single and a system of straight flux tubes are investigated. Magnetic flux tubes with a straight magnetic field and longitudinal density stratification were considered in zero‐β approximation. A single three‐dimensional wave equation (eigenvalue problem) is solved for longitudinal component of the perturbed magnetic field using the finite element method. Wave functions (eigenfunction of wave equation) of the MHD oscillations are categorized into sausage, kink, helical kink, and fluting modes. Exact recognition of the wave functions and the frequencies of oscillations can be used in coronal seismology and also helps to the future high‐resolution instruments that would be designed for studying the properties of the solar loop oscillations in details. The properties of collective oscillations of nonidentical and identical system of flux tubes and their interactions are studied. The ratios of frequencies, the oscillation frequencies of a system of flux tubes to their equivalent monolithic tube ( trueω~sys/trueω~mono), are obtained between 0.748 and 0.841 for a system of nonidentical tubes, whereas the related ratios of frequencies for a system of identical flux tubes are fluctuated around 0.761.

We study a nanoscale system composed of one corrugated cylinder (pinion) and one corrugated plate (rack). The pinion and rack have no mechanical contact, but are coupled via the lateral Casimir force. We consider the case where the rack position versus time is a periodic triangular signal. We find that the device can rectify the periodic but nonsinusoidal motion of the rack. Using the typical values of parameters, we find that the pinion rotates with an average angular velocity Ω=1∼100 Hz . Experimental observation of the pinion rotation will show that the quantum vacuum can intermesh the noncontact parts of nanomachines.

The lateral Casimir force is employed to propose a nanoscale mechanical device composed of one rack and N pinions. A coupling between the pinions via torsional springs is shown to coordinate their motion through a synchronization transition. The system can work against loads that are greater than the lateral Casimir force for each device. The existence of a stable synchronized state ensures that the system could operate in full coordination without the need of delicate fine tuning of all the characteristics such as the spring constants, the corrugation amplitudes, and the distances between the rack and the pinions.

We study a nanoscale system composed of one corrugated cylinder (pinion) placed between two corrugated plates (racks). The pinion and racks have no mechanical contact, but are coupled via the lateral Casimir force-one of the most spectacular consequences of quantum fluctuations of the electromagnetic field. The noncontact design of the device could help with the noteworthy wear problem in nanoscale mechanical systems. We consider the case where both racks undergo harmonic lateral motion. We assume that the amplitude, frequency, and phase of one of the racks are known. We show that probing the pinion motion, one can determine the vibration characteristics of the other rack.