Numerical Computation of Figure-eight Solution for 3-body Problems

The main goal of this paper is to compute the Figure-eight solutions for the planar Newtonian 3-body problem with equal masses by finding the critical points of the functional associated with the motion equations of 3-body in plane R2. The algorithm adopted here is the steepest descent method, which is simple but very valid for our problem.

Selective construction of molecular Solomon links and figure-eight knots by fine-tuning unsymmetrical ligands

Using the strategy of ligand fine-tuning by steric hindrance, we successfully obtained Solomon links(4_(1)^(2)) and figure-eight knots(4_(1)) with half-sandwich organometallic unit and amino-acid embedded ligands. The two curved bidentate ligands exhibit subtle differences, whereas they result in totally distinct entanglement modes. An alcoholysis reaction with the ligands leads to the formation of a molecular tweezer. Notably, unsymmetrical ligands were utilized in the self-assembly process to explore the formation of directional molecules, and the reactions exhibited selectivity due to comprehensive π interactions and multiple hydrogen bonds. The topologies and behavior of the above structures were confirmed through single-crystal X-ray diffraction,nuclear magnetic resonance techniques and mass spectrometry.

All-polarization-maintaining figure-eight Er-fiber ultrafast laser with a bidirectional output coupler in the loss-imbalanced nonlinear optical loop mirror

In this Letter, we report on a novel architecture for a self-starting mode-locked figure-eight erbium-doped fiber laser using a loss-imbalanced nonlinear optical loop mirror(NOLM) with a bidirectional output coupler. An allpolarization-maintaining structure is adopted. A 2 × 2 optical coupler with a splitting ratio of 50:50 is used at the junction to form an NOLM. Another coupler with a splitting ratio of 10:90 is introduced at one end of the fiber loop. The 10:90 coupler plays two roles: power attenuator and bidirectional output coupler. This architecture can achieve both large modulation depth and good self-starting ability simultaneously. With this architecture,the self-starting mode-locking operation is achieved easily with pump power above the threshold. The clockwise and counter-clockwise mode-locked output powers are 10.1 and 10.3 mW, respectively, with the repetition rate of 3.63 MHz. The spectral bandwidths of the clockwise and counter-clockwise mode-locked output pulses are 7.4 and 2.9 nm, and the corresponding pulse widths of the direct outputs are 530.6 fs and 1.55 ps, respectively.

A Device that can Produce Net Impulse Using Rotating Masses

This paper describes a device capable of producing net impulse, through two synchronized masses, which move along a figure-eight-shaped orbit. In addition to the detailed description of the mechanical components of this device, particular attention is paid to the theoretical treatment of the innovative principle on which the device is based. In more details, the mechanical system consists of two independent but simultaneous rotations, the former being related to the formation of the figure-eight-shaped path and the latter to an additional spinning. Based on the parametric equations of motion of the lumped masses, and considering semi-static tensile deformation of the connecting rods carrying them, it was found that the resultant impulse towards the direction of the spin vector includes a non-vanishing term that is linearly proportional to the time. In addition, reduced but encouraging experimental results are reported. These findings sustain the capability of the proposed mechanism to achieve propulsion.