Optical Force on a Metal Nanorod Exerted by a Photonic Jet

In this article, we study the optical force exerted on nanorods. In recent years, the capture of micro-nanoparticles has been a frontier topic in optics. A Photonic Jet (PJ) is an emerging subwavelength beam with excellent application prospects. This paper studies the optical force exerted by photonic jets generated by a plane wave illuminating a Generalized Luneburg Lens (GLLs) on nanorods. In the framework of the dipole approximation, the optical force on the nanorods is studied. The electric field of the photonic jet is calculated by the open-source software package DDSCAT developed based on the Discrete Dipole Approximation (DDA). In this paper, the effects of the nanorods’ orientation and dielectric constant on the transverse force Fx and longitudinal force Fy are analyzed. Numerical results show that the maximum value of the positive force and the negative force are equal and appear alternately at the position of the photonic jet. Therefore, to capture anisotropic nanoscale-geometries (nanorods), it is necessary to adjust the position of GLLs continuously. It is worth emphasizing that manipulations with nanorods will make it possible to create new materials at the nanoscale.

Inversion of the transverse force on a spinning sphere moving in a rarefied gas

The flow around a spinning sphere moving in a rarefied gas is considered in the following situation: (i) the translational velocity of the sphere is small (i.e. the Mach number is small); (ii) the Knudsen number, the ratio of the molecular mean free path to the sphere radius, is of the order of unity (the case with small Knudsen numbers is also discussed); and (iii) the ratio between the equatorial surface velocity and the translational velocity of the sphere is of the order of unity. The behaviour of the gas, particularly the transverse force acting on the sphere, is investigated through an asymptotic analysis of the Boltzmann equation for small Mach numbers. It is shown that the transverse force is expressed as $\boldsymbol{F}_L = {\rm \pi}\rho a^3 (\boldsymbol{\varOmega} \times \boldsymbol{v}) \bar{h}_L$ , where $\rho$ is the density of the surrounding gas, a is the radius of the sphere, $\boldsymbol {\varOmega }$ is its angular velocity, $\boldsymbol {v}$ is its velocity and $\bar {h}_L$ is a numerical factor that depends on the Knudsen number. Then, $\bar {h}_L$ is obtained numerically based on the Bhatnagar–Gross–Krook model of the Boltzmann equation for a wide range of Knudsen number. It is shown that $\bar {h}_L$ varies with the Knudsen number monotonically from 1 (the continuum limit) to $-\tfrac {2}{3}$ (the free molecular limit), vanishing at an intermediate Knudsen number. The present analysis is intended to clarify the transition of the transverse force, which is previously known to have different signs in the continuum and the free molecular limits.

Muscle volume imbalance may be associated with static posterior humeral head subluxation

Background The transverse force couple (TFC) of the rotator cuff (subscapularis vs. infraspinatus and teres minor muscle) is an important dynamic stabilizer of the shoulder joint in the anterior-posterior direction. In patients with posterior static subluxation of the humeral head (PSSH), decentration of the humeral head posteriorly occurs, which is associated with premature arthritis. We hypothesize that not only pathologic glenoid retroversion but also chronic muscle volume imbalance in the transverse force couple leads to PSSH. Methods A retrospective analysis of the TFC muscle volumes of 9 patients with symptomatic, atraumatic PSSH, within 8 were treated with glenoid correction osteotomy, was conducted. The imaging data (CT) of 9 patients/10 shoulders of the full scapula and shoulder were analyzed, and the muscle volumes of the subscapularis (SSC), infraspinatus (ISP) and teres minor muscles (TMM) were measured by manually marking the muscle contours on transverse slices and calculating the volume from software. Furthermore, the glenoid retroversion and glenohumeral distance were measured. Results The mean glenoid retroversion was − 16° (− 7° to − 31°). The observed mean glenohumeral distance was 4.0 mm (0 to 6.8 mm). Our study population showed a significant muscle volume imbalance between the subscapularis muscle and the infraspinatus and teres minor muscles (192 vs. 170 ml; p = 0.005). There was no significant correlation between the subscapularis muscle volume and the glenohumeral distance (r = 0.068), (p = 0.872). Conclusion The muscle volume of the SSC in patients with PSSH was significantly higher than the muscle volume of the posterior force couple (ISP and TMM). This novel finding, albeit in a small series of patients, may support the theory that transverse force couple imbalance is associated with PSSH. Level of evidence Level 4 – Case series with no comparison group.

Hydrodynamic Analysis of KVLCC2 Ship Sailing near Inclined Banks

The hydrodynamic forces of KVLCC2 ship sailing near inclined banks are calculated by using CFD based on RANS equation. Corresponding CFD uncertainty analysis is conducted according to the procedure recommended by ITTC. An unstructured grid, tetrahedral grid, is employed for discretization. To control the number of grids, global element scale factor is selected as the same as refinement ratio. In numerical simulation, straightforward and oblique navigation conditions are investigated. The variation of transverse force and yaw moment with the ship-shore distance, bank angle, water depth, and drift angle are analyzed. Both hull model and hull-propeller-rudder model are considered in numerical simulation. The simulation results show the hydrodynamic characteristics of ship sailing near inclined banks.

MODELING OF SPOKE STIFFNESS FOR EXTERNAL FIXATION DEVICES

A nonlinear calculation of the stiffness of the spokes of external fixation devices in traumatology is proposed. Taking into account the geometric nonlinearity of the spoke, the finite element method is used in the calculations of stiffness and stresses arising in the spoke fasteners. Under the action of the transverse force and its preliminary tension, deflections of the spoke and stresses in the attachment points are determined.