There exist cislunar and trans-lunar libration points near the Moon, which are referred as the LL1 and LL2 points respectively and can generate the different types of low-energy trajectories transferring from Earth to Moon. The time-dependent analyti
c model including the gravitational forces from the Sun, Earth and Moon is employed to investigate the energy-minimal and practical transfer trajectories. However, different from the circular restricted three-body problem, the equivalent gravitational equilibria are defined according to the geometry of instantaneous Hills boundary due to the gravitational perturbation from the Sun. The relationship between the altitudes of periapsis and eccentricities is achieved from the Poincare mapping for all the lunar captured trajectories, which presents the statistical feature of the fuel cost and captured orbital elements rather than generating a specified Moon-captured segment. The minimum energy required by the captured trajectory on a lunar circular orbit is deduced in the spatial bi-circular model. It is presented that the asymptotical behaviors of invariant manifolds approaching to/from the libration points or halo orbits are destroyed by the solar perturbation. In fact, the energy-minimal cislunar transfer trajectory is acquired by transiting LL1 point, while the energy-minimal trans-lunar transfer trajectory is obtained by transiting LL2 point. Finally, the transfer opportunities for the practical trajectories escaped from the Earth and captured by the Moon are yielded by transiting halo orbits near LL1 and LL2 points, which can be used to generate the whole trajectories.
We present an event-driven molecular dynamics study for hard ellipses and assess the effects of aspect ratio and area fraction on their physical properties. For state points in the plane of aspect ratio (k=1-9) and area fraction (phi=0.01-0.8), we id
entify three different phases, including isotropic, plastic and nematic states. The equation of state (EOS) is shown for a wide range of aspect ratios and is compared with the scaled particle theory (SPT) for the isotropic states. We find that SPT provides a good description of the EOS for the isotropic phase of hard ellipses. At large fixed phi, the reduced pressure p increases with k in both the isotropic and the plastic phases, and interestingly, its dependence on k is rather weak in the nematic phase. We rationalize the thermodynamics of hard ellipses in terms of particle motions. The plastic crystal is shown to form for aspect ratios up to k=1.4, while appearance of the stable nematic phase starts approximately at k=3. We quantitatively determine the locations of the isotropic-plastic (I-P) transition and the isotropic-nematic (I-N) transition by analyzing the bond-orientation correlations and the angular correlations, respectively. As expected, the I-P transition point is found to increase with k, while a larger k leads to a smaller area fraction where the I-N transition takes place. Moreover, our simulations strongly support that the two-dimensional nematic phase in hard ellipses has only quasi-long-range orientational order. The self-diffusion of hard ellipses is further explored and connections are revealed between the structure and the self-diffusion. We discuss the relevance of our results to the glass transition in hard ellipses. Finally, the results of the isodiffusivity lines are evaluated for hard ellipses and we discuss the effect of spatial dimension on the diffusive dynamics of hard ellipsoidal particles.
We investigate theoretically the effects of interaction between an optical dipole (semiconductor quantum dot or molecule) and metal nanoparticles. The calculated absorption spectra of hybrid structures demonstrate strong effects of interference comin
g from the exciton-plasmon coupling. In particular, the absorption spectra acquire characteristic asymmetric lineshapes and strong anti-resonances. We present here an exact solution of the problem beyond the dipole approximation and find that the multipole treatment of the interaction is crucial for the understanding of strongly-interacting exciton-plasmon nano-systems. Interestingly, the visibility of the exciton resonance becomes greatly enhanced for small inter-particle distances due to the interference phenomenon, multipole effects, and electromagnetic enhancement. We find that the destructive interference is particularly strong. Using our exact theory, we show that the interference effects can be observed experimentally even in the exciting systems at room temperature.
