A note on a solution of three body problem

Equilateral triangle solution of three-body problem for Apollo Earth-Moon libration point mission

Evolution of Surface Deformations of Weakly-Bound Nuclei in the Continuum

We study weakly-bound deformed nuclei based on the coordinate-space Skyrme Hartree-Fock-Bogoliubov approach, in which a large box is employed for treating the continuum and surface diffuseness. Approaching the limit of core-halo deformation decoupling, calculations found an exotic "egg"-like structure consisting of a spherical core plus a prolate halo in $^{38}$Ne, in which the resonant continuum plays an essential role. Generally the halo probability and the decoupling effect in heavy nuclei are reduced compared to light nuclei, due to denser level densities around Fermi surfaces. However, deformed halos in medium-mass nuclei are possible with sparse levels of negative parity, for example, in $^{110}$Ge. The surface deformations of pairing density distributions are also influenced by the decoupling effect and are sensitive to the effective pairing Hamiltonian.Comment: 5 pages and 5 figure

Aligning Manifolds of Double Pendulum Dynamics Under the Influence of Noise

This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised feature-level manifold alignment using global distance resulted in the most convincing visualisations. However, the semi-supervised feature-level local alignment methods resulted in smaller alignment errors. These local alignment methods were also more robust to noise and faster than the other methods.Comment: The final version will appear in ICONIP 2018. A DOI identifier to the final version will be added to the preprint, as soon as it is availabl

Small-scale CMB Temperature and Polarization Anisotropies due to Patchy Reionization

We study contributions from inhomogeneous (patchy) reionization to arcminute scale ($1000 < \ell < 10,000$) cosmic microwave background (CMB) anisotropies. We show that inhomogeneities in the ionization fraction, rather than in the mean density, dominate both the temperature and the polarization power spectra. Depending on the ionization history and the clustering bias of the ionizing sources, we find that rms temperature fluctuations range from 2 $\mu$K to 8 $\mu$K and the corresponding values for polarization are over two orders of magnitude smaller. Reionization can significantly bias cosmological parameter estimates and degrade gravitational lensing potential reconstruction from temperature maps but not from polarization maps. We demonstrate that a simple modeling of the reionization temperature power spectrum may be sufficient to remove the parameter bias. The high-$\ell$ temperature power spectrum will contain some limited information about the sources of reionization.Comment: 11 pages, 8 figures. Minor changes to match version accepted by Ap

Overall Evolution of Realistic Gamma-ray Burst Remnant and Its Afterglow

Conventional dynamic model of gamma-ray burst remnants is found to be incorrect for adiabatic blastwaves during the non-relativistic phase. A new model is derived, which is shown to be correct for both radiative and adiabatic blastwaves during both ultra-relativistic and non-relativistic phase. Our model also takes the evolution of the radiative efficiency into account. The importance of the transition from the ultra-relativistic phase to the non-relativistic phase is stressed.Comment: 9 pages, aasms4 style, 3 ps figures, minor changes, will be published in Chin. Phys. Let

Emergent Soft Monopole Modes in Weakly-Bound Deformed Nuclei

Based on the Hartree-Fock-Bogoliubov solutions in large deformed coordinate spaces, the finite amplitude method for quasiparticle random phase approximation (FAM-QRPA) has been implemented, providing a suitable approach to probe collective excitations of weakly-bound nuclei embedded in the continuum. The monopole excitation modes in Magnesium isotopes up to the neutron drip line have been studied with the FAM-QRPA framework on both the coordinate-space and harmonic oscillator basis methods. Enhanced soft monopole strengths and collectivity as a result of weak-binding effects have been unambiguously demonstrated.Comment: 5 pages, 4 figures, accepted for PRC (Rapid Comm.

A unified approach to combinatorial key predistribution schemes for sensor networks

There have been numerous recent proposals for key predistribution schemes for wireless sensor networks based on various types of combinatorial structures such as designs and codes. Many of these schemes have very similar properties and are analysed in a similar manner. We seek to provide a unified framework to study these kinds of schemes. To do so, we define a new, general class of designs, termed “partially balanced t-designs”, that is sufficiently general that it encompasses almost all of the designs that have been proposed for combinatorial key predistribution schemes. However, this new class of designs still has sufficient structure that we are able to derive general formulas for the metrics of the resulting key predistribution schemes. These metrics can be evaluated for a particular scheme simply by substituting appropriate parameters of the underlying combinatorial structure into our general formulas. We also compare various classes of schemes based on different designs, and point out that some existing proposed schemes are in fact identical, even though their descriptions may seem different. We believe that our general framework should facilitate the analysis of proposals for combinatorial key predistribution schemes and their comparison with existing schemes, and also allow researchers to easily evaluate which scheme or schemes present the best combination of performance metrics for a given application scenario

Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (COVID-19).

Background: Estimation of the fraction and contagiousness of undocumented novel coronavirus (COVID-19) infections is critical for understanding the overall prevalence and pandemic potential of this disease. Many mild infections are typically not reported and, depending on their contagiousness, may support stealth transmission and the spread of documented infection. Methods: Here we use observations of reported infection and spread within China in conjunction with mobility data, a networked dynamic metapopulation model and Bayesian inference, to infer critical epidemiological characteristics associated with the emerging coronavirus, including the fraction of undocumented infections and their contagiousness. Results: We estimate 86% of all infections were undocumented (95% CI: [82%-90%]) prior to the Wuhan travel shutdown (January 23, 2020). Per person, these undocumented infections were 52% as contagious as documented infections ([44%-69%]) and were the source of infection for two-thirds of documented cases. Our estimate of the reproductive number (2.23; [1.77-3.00]) aligns with earlier findings; however, after travel restrictions and control measures were imposed this number falls considerably. Conclusions: A majority of COVID-19 infections were undocumented prior to implementation of control measures on January 23, and these undocumented infections substantially contributed to virus transmission. These findings explain the rapid geographic spread of COVID-19 and indicate containment of this virus will be particularly challenging. Our findings also indicate that heightened awareness of the outbreak, increased use of personal protective measures, and travel restriction have been associated with reductions of the overall force of infection; however, it is unclear whether this reduction will be sufficient to stem the virus spread