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<jats:p>Caesium atomic fountain clock is a primary frequency standard, which realizes the duration of second. Its performance is mostly dominated by the frequency accuracy, and the C-field induced second-order Zeeman frequency shift is the major effect, which limits the accuracy improvement. By applying a high-precision current supply and high-performance magnetic shieldings, the C-field stability has been improved significantly. In order to achieve a uniform C-field, this paper proposes a doubly wound C-field solenoid, which compensates the radial magnetic field along the atomic flight region generated by the lead-out single wire and improves the accuracy evaluation of second-order Zeeman frequency shift. Based on the stable and uniform C-field, we launch the selected atoms to different heights and record the magnetically sensitive Ramsey transition |<jats:italic>F</jats:italic> = 3, <jats:italic>m<jats:sub>F</jats:sub> </jats:italic> = –1〉 → |<jats:italic>F</jats:italic> = 4, <jats:italic>m<jats:sub>F</jats:sub> </jats:italic> = –1〉 central frequency, obtaining this frequency shift as 131.03 × 10<jats:sup>−15</jats:sup> and constructing the C-field profile (<jats:italic>σ</jats:italic> = 0.15 nT). Meanwhile, during normal operation, we lock NTSC-F2 to the central frequency of the magnetically sensitive Ramsey transition |<jats:italic>F</jats:italic> = 3, <jats:italic>m<jats:sub>F</jats:sub> </jats:italic> = –1〉 → |<jats:italic>F</jats:italic> = 4, <jats:italic>m<jats:sub>F</jats:sub> </jats:italic> = –1〉 fringe for ten consecutive days and record this frequency fluctuation in time domain. The first evaluation of second-order Zeeman frequency shift uncertainty is 0.10 × 10<jats:sup>−15</jats:sup>. The total deviation of the frequency fluctuation on the clock transition induced by the C-field instability is less than 2.6 × 10<jats:sup>−17</jats:sup>. Compared with NTSC-F1, NTSC-F2, there appears a significant improvement.</jats:p>

<jats:p>In the real world, rule makers can only restrict, not completely control the behavior of the governed, while the governed can only choose their behavior patterns under these restrictions. In this paper, we design a new control protocol called free protocol to describe this situation. First, we calculate consensus probabilities based on the information of the interaction networks. Then, sufficient conditions are obtained for all agents converging to a same value with probability one. Finally, numerical simulation results are given to verify the above results.</jats:p>

<jats:p>This paper proposes a reasonable radiation-resistant composite channel structure for InP HEMTs. The simulation results show that the composite channel structure has excellent electrical properties due to increased modulation doping efficiency and carrier confinement. Moreover, the direct current (DC) and radio frequency (RF) characteristics and their reliability between the single channel structure and the composite channel structure after 75-keV proton irradiation are compared in detail. The results show that the composite channel structure has excellent radiation tolerance. Mechanism analysis demonstrates that the composite channel structure weakens the carrier removal effect. This phenomenon can account for the increase of native carrier and the decrease of defect capture rate.</jats:p>

<jats:p>Ni-rich layered lithium transition metal oxides LiNi<jats:sub> <jats:italic>x</jats:italic> </jats:sub>Mn<jats:sub> <jats:italic>y</jats:italic> </jats:sub>Co<jats:sub> <jats:italic>z</jats:italic> </jats:sub>O<jats:sub>2</jats:sub> (1 – <jats:italic>y</jats:italic> – <jats:italic>z</jats:italic> ≥ 0.6) are promising candidates for cathode materials, but their practical applications are hindered by high-voltage instability and fast capacity fading. Using density functional theory calculations, we demonstrate that Na-, F-doping, and Na/F-co-doping can stabilize the structure and result into a higher open circuit voltage than pristine LiNi<jats:sub>0.6</jats:sub>Mn<jats:sub>0.2</jats:sub>Co<jats:sub>0.2</jats:sub>O<jats:sub>2</jats:sub> (NMC622) during the charging process, which may attain greater discharge capacity. F doping may inhibit the diffusion of Li ions at the beginning and end of charging; Na doping may improve Li ion diffusion due to the increase in Li layer spacing, consistent with prior experiments. Na/F-co-doping into NMC622 promotes rate performance and reduces irreversible phase transitions for two reasons: (i) a synergistic effect between Na and F can effectively restrain the Ni/Li mixing and then enhances the mobility of Li ions and (ii) Ni/Li mixing hinders the Ni ions to migrate into Li layers and thus, stabilizes the structure. This study proposes that a layer cathode material with high electrochemical performance can be achieved via rational dopant modification, which is a promising strategy for designing efficient Li ion batteries.</jats:p>

<jats:p>State-to-state time-dependent quantum dynamics calculations have been carried out to study H + DH’ → HH’ + D/HD + H’ reactions on BKMP2 surface. The total integral cross sections of both reactions are in good agreement with earlier theoretical and experimental results, moreover the rotational state-resolved reaction cross sections of H + DH’ → HH’ + D at collision energy <jats:italic>E</jats:italic> <jats:sub>C</jats:sub> = 0.5 eV are closer to the experimental values than the ones calculated by Chao <jats:italic>et al.</jats:italic> [<jats:italic>J. Chem. Phys.</jats:italic> <jats:bold>117</jats:bold> 8341 (2002)], which proves the higher precision of the quantum calculation in this work. In addition, the state-to-state dynamics of H + DH’ → HD’ + H reaction channel have been discussed in detail, and the differences of the micro-mechanism of the two reaction channels have been revealed and analyzed clearly.</jats:p>

<jats:p>Impurity agglomeration has a significant influence on shock response of metal materials. In this paper, the mechanism of Ti-clusters in metal Al under shock loading is investigated by non-equilibrium molecular dynamics simulations. Our results show that the Ti-cluster has obvious effects on the dislocation initiation and melting of bulk Al. First, the Ti clusters induces the strain concentrate and leads the dislocations to be initiated from the interface of Ti cluster. Second, dislocation distribution from the Ti-cluster model results in a formation of a grid-like structure, while the dislocation density is reduced compared with that from the perfect Al model. Third, the critical shock velocity of dislocation from the Ti-cluster model is lower than from perfect Al model. Furthermore, it is also found that the temperature near the interface of Ti-cluster is 100 K-150 K higher than in the other areas, which means that Ti-cluster interface melts earlier than the bulk area.</jats:p>

<jats:p>Electron–electron correlation plays an important role in the underlying dynamics in physics and chemistry. Helium is the simplest and most fundamental two-electron system. The dynamic process of helium in a strong laser field is still a challenging issue because of the large calculation cost. In this study, a graphic processing unit (GPU) openACC based <jats:italic>ab initio</jats:italic> numerical simulations package HeTDSE is developed to solve the full-dimensional time-dependent Schrödinger equation of helium subjected to a strong laser pulse. HeTDSE uses B-spline basis sets expansion method to construct the radial part of the wavefunction, and the spherical harmonic functions is used to express for the angular part. Adams algorithm is employed for the time propagation. Our example shows that HeTDSE running on an NVIDIA Kepler K20 GPU can outperform the one on an Intel E5-2640 single CPU core by a factor of 147. HeTDSE code package can be obtained from the author or from the author’s personal website (doi: 10.13140/RG.2.2.15334.45128) directly under the GPL license, so HeTDSE can be downloaded, used and modified freely.</jats:p>

<jats:p>We investigate the process of pulsed laser cooling using a self-constructed molecular dynamics simulation (MD-Simulation) program. We simulate the Doppler cooling process and pulsed laser Doppler cooling process of a single <jats:sup>40</jats:sup>Ca<jats:sup>+</jats:sup> ion, and the comparison with the experimental results shows that this self-constructed MD-Simulation program works well in the weak laser intensity situation. Furthermore, we analyze the pulsed laser Doppler cooling process of a single <jats:sup>27</jats:sup>Al<jats:sup>+</jats:sup> ion. This program can be used to analyze the molecular dynamic process of various situations of Doppler cooling in an ion trap, which could give predictions and experimental guidance.</jats:p>

<jats:p>A two-ion pair in a linear Paul trap is extensively used in the research of the simplest quantum-logic system; however, there are few quantitative and comprehensive studies on the motional mode coupling of two-ion systems yet. This study proposes a method to investigate the motional mode coupling of sympathetically cooled two-ion crystals by quantifying three-dimensional (3D) secular spectra of trapped ions using molecular dynamics simulations. The 3D resonance peaks of the <jats:sup>40</jats:sup>Ca<jats:sup>+</jats:sup>–<jats:sup>27</jats:sup>Al<jats:sup>+</jats:sup> pair obtained by using this method were in good agreement with the 3D in- and out-of-phase modes predicted by the mode coupling theory for two ions in equilibrium and the frequency matching errors were lower than 2%. The obtained and predicted amplitudes of these modes were also qualitatively similar. It was observed that the strength of the sympathetic interaction of the <jats:sup>40</jats:sup>Ca<jats:sup>+</jats:sup>–<jats:sup>27</jats:sup>Al<jats:sup>+</jats:sup> pair was primarily determined by its axial in-phase coupling. In addition, the frequencies and amplitudes of the ion pair’s resonance modes (in all dimensions) were sensitive to the relative masses of the ion pair, and a decrease in the mass mismatch enhanced the sympathetic cooling rates. The sympathetic interactions of the <jats:sup>40</jats:sup>Ca<jats:sup>+</jats:sup>–<jats:sup>27</jats:sup>Al<jats:sup>+</jats:sup> pair were slightly weaker than those of the <jats:sup>24</jats:sup>Mg<jats:sup>+</jats:sup>–<jats:sup>27</jats:sup>Al<jats:sup>+</jats:sup> pair, but significantly stronger than those of <jats:sup>9</jats:sup>Be<jats:sup>+</jats:sup>–<jats:sup>27</jats:sup>Al<jats:sup>+</jats:sup>. However, the Doppler cooling limit temperature of <jats:sup>40</jats:sup>Ca<jats:sup>+</jats:sup> is comparable to that of <jats:sup>9</jats:sup>Be<jats:sup>+</jats:sup> but lower than approximately half of that of <jats:sup>24</jats:sup>Mg<jats:sup>+</jats:sup>. Furthermore, laser cooling systems for <jats:sup>40</jats:sup>Ca<jats:sup>+</jats:sup> are more reliable than those for <jats:sup>24</jats:sup>Mg<jats:sup>+</jats:sup> and <jats:sup>9</jats:sup>Be<jats:sup>+</jats:sup>. Therefore, <jats:sup>40</jats:sup>Ca<jats:sup>+</jats:sup> is probably the best laser-cooled ion for sympathetic cooling and quantum-logic operations of <jats:sup>27</jats:sup>Al<jats:sup>+</jats:sup> and has particularly more notable comprehensive advantages in the development of high reliability, compact, and transportable <jats:sup>27</jats:sup>Al<jats:sup>+</jats:sup> optical clocks. This methodology may be extended to multi-ion systems, and it will greatly aid efforts to control the dynamic behaviors of sympathetic cooling as well as the development of low-heating-rate quantum logic clocks.</jats:p>

<jats:p>Single pixel imaging is a novel imaging technique, and it becomes a focus of research in recent years due to its advantages such as high lateral resolution and high robustness to noise. Imaging speed is one of the critical shortcomings, which limits the further development and applications of this technique. In this paper, we focus on the issues of imaging efficiency of a single pixel imaging system. We propose semi-continuous wavelet transform (SCWT) protocol and introduce the protocol into the single pixel imaging system. The proposed protocol is something between continuous wavelet transform and discrete wavelet transform, which allows the usage of those smooth (usually non-orthogonal, and they have advantages in representing smooth signals compressively, which can improve the imaging speed of single pixel imaging) wavelets and with limited numbers of measurements. The proposed imaging scheme is studied, and verified by simulations and experiments. Furthermore, a comparison between our proposed scheme and existing imaging schemes are given. According to the results, the proposed SCWT scheme is proved to be effective in reconstructing a image compressively.</jats:p>