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<jats:p>In the measurement of the Newtonian gravitational constant <jats:italic>G</jats:italic> with the time-of-swing method, the influence of the Earth’s rotation has been roughly estimated before, which is far beyond the current experimental precision. Here, we present a more complete theoretical modeling and assessment process. To figure out this effect, we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum. With the correlation method and typical parameters, we estimate that the influence of the Earth’s rotation on <jats:italic>G</jats:italic> measurement is far less than 1 ppm, which may need to be considered in the future high-accuracy experiments of determining the gravitational constant <jats:italic>G</jats:italic>.</jats:p>

<jats:p>Chaotic motion and quasi-periodic motion are two common forms of instability in the giant magnetostrictive actuator (GMA). Therefore, in the present study we intend to investigate the influences of the system damping coefficient, system stiffness coefficient, disc spring cubic stiffness factor, and the excitation force and frequency on the output stability and the hysteresis vibration of the GMA. In this regard, the nonlinear piezomagnetic equation, Jiles–Atherton hysteresis model, quadratic domain rotation model, and the GMA structural dynamics are used to establish the mathematical model of the hysteresis vibration system of the GMA. Moreover, the multi-scale method and the singularity theory are used to determine the co-dimensional two-bifurcation characteristics of the system. Then, the output response of the system is simulated to determine the variation range of each parameter when chaos is imposed. Finally, the fourth-order Runge–Kutta method is used to obtain the time domain waveform, phase portrait and Poincaré mapping diagrams of the system. Subsequently, the obtained three graphs are analyzed. The obtained results show that when the system output is stable, the variation range of each parameter can be determined. Moreover, the stability interval of system damping coefficient, system stiffness coefficient, and the coefficient of the cubic stiffness term of the disc spring are obtained. Furthermore, the stability interval of the exciting force and the excitation frequency are determined.</jats:p>

<jats:p>Laser focused atomic deposition is a unique and effective way to fabricate highly accurate pitch standards in nanometrology. However, the stability and repeatability of the atom lithography fabrication process remains a challenging problem for massive production. Based on the atom–light interaction theory, channeling is utilized to improve the stability and repeatability. From the comparison of three kinds of atom–light interaction models, the optimal parameters for channeling are obtained based on simulation. According to the experimental observations, the peak to valley height of Cr nano-gratings keeps stable when the cutting proportion changes from 15% to 50%, which means that the channeling shows up under this condition. The channeling proves to be an effective method to optimize the stability and repeatability of laser focused Cr atomic deposition.</jats:p>

<jats:p>We present an intensive study of the coupling between different Feshbach states and the hyperfine levels of the excited states in the adiabatic creation of <jats:sup>23</jats:sup>Na<jats:sup>40</jats:sup>K ground-state molecules. We use coupled-channel method to calculate the wave function of the Feshbach molecules, and give the short-range wave function of triplet component. The energies of the hyperfine excited states and the coupling strength between the Feshbach states and the hyperfine excited states are calculated. Our results can be used to prepare a specific hyperfine level of the rovibrational ground state to study the ultracold collisions involving molecules.</jats:p>

<jats:p>To tailor properties of polymer composites are very important for their applications. Very small concentrations of nanoparticles can significantly alter their physical characteristics. In this work, molecular dynamics simulations are performed to study the thermodynamic and structural properties of polystyrene/C<jats:sub>60</jats:sub> (PS/C<jats:sub>60</jats:sub>) composites. The calculated densities, glass transition temperatures, and coefficient of thermal expansion of the bulk PS are in agreement with the experimental data available, implying that our calculations are reasonable. We find that the glass transition temperature <jats:italic>T</jats:italic> <jats:sub>g</jats:sub> increases accordingly with an added concentration of C<jats:sub>60</jats:sub> for PS/C<jats:sub>60</jats:sub> composites. However, the self-diffusion coefficient <jats:italic>D</jats:italic> decreases with increase of addition of C<jats:sub>60</jats:sub>. For the volumetric coefficients of thermal expansion (CTE) of bulk PS and PS/C<jats:sub>60</jats:sub> composites, it can be seen that the CTE increases with increasing content of C<jats:sub>60</jats:sub> above <jats:italic>T</jats:italic> <jats:sub>g</jats:sub> (rubbery region). However, the CTE decreases with increasing content of C<jats:sub>60</jats:sub> below <jats:italic>T</jats:italic> <jats:sub>g</jats:sub> (glassy region).</jats:p>

<jats:p>We carry out quantum scattering dynamics and quasi-classical trajectory (QCT) calculations for the <jats:inline-formula> <jats:tex-math><?CDATA ${\rm{O}}+{{\rm{H}}}_{2}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mi mathvariant="normal">H</mml:mi> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_29_2_023105_ieqn5.gif" xlink:type="simple" /> </jats:inline-formula> reactive collision in the ground (1<jats:sup>2</jats:sup>A″) and first excited (1<jats:sup>2</jats:sup>A′) potential energy surface. We calculate the reaction probabilities of <jats:inline-formula> <jats:tex-math><?CDATA ${\rm{O}}+{{\rm{H}}}_{2}^{+}(v=0,j=0)\to {{\rm{OH}}}^{+}+{\rm{H}}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mi mathvariant="normal">H</mml:mi> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>v</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>→</mml:mo> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">OH</mml:mi> </mml:mrow> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>+</mml:mo> <mml:mi mathvariant="normal">H</mml:mi> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_29_2_023105_ieqn6.gif" xlink:type="simple" /> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math><?CDATA ${\rm{O}}+{{\rm{H}}}_{2}^{+}(v=0,j=0)\to {\rm{OH}}+{{\rm{H}}}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> <mml:mo>+</mml:mo> <mml:msubsup> <mml:mi mathvariant="normal">H</mml:mi> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> </mml:msubsup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>v</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>j</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo stretchy="false">)</mml:mo> <mml:mo>→</mml:mo> <mml:mi mathvariant="normal">OH</mml:mi> <mml:mo>+</mml:mo> <mml:msup> <mml:mi mathvariant="normal">H</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_29_2_023105_ieqn7.gif" xlink:type="simple" /> </jats:inline-formula> reaction for total angular momentum <jats:italic>J</jats:italic> = 0. The results calculated by QCT are consistent with those from quantum mechanical wave packet. Using the QCT method, we generate in the center-of-mass frame the product state-resolved integral cross-sections (ICSs); two commonly used generalized polarization-dependent differential cross-sections (PDDCSs), (2<jats:italic>π</jats:italic>/<jats:italic>σ</jats:italic>)(d<jats:italic>σ</jats:italic> <jats:sub>00</jats:sub>/d<jats:italic>ω</jats:italic> <jats:sub>t</jats:sub>), (2<jats:italic>π</jats:italic>/<jats:italic>σ</jats:italic>)(d<jats:italic>σ</jats:italic> <jats:sub>20</jats:sub>/d<jats:italic>ω</jats:italic> <jats:sub>t</jats:sub>); and three angular distributions of the product rotational vectors, <jats:italic>P</jats:italic>(<jats:italic>θ</jats:italic> <jats:sub>r</jats:sub>), <jats:italic>P</jats:italic>(<jats:italic>ϕ</jats:italic> <jats:sub>r</jats:sub>), and <jats:italic>P</jats:italic>(<jats:italic>θ</jats:italic> <jats:sub>r</jats:sub>, <jats:italic>ϕ</jats:italic> <jats:sub>r</jats:sub>). We discuss the influence on the scalar and vector properties of the potential energy surface, the collision energy, and the isotope mass. Since there are deep potential wells in these two potential energy surfaces, their kinetic characteristics are similar to each other and the isotopic effect is not obvious. However, the well depths and configurations of the two potential energy surfaces are different, so the effects of isotopic substitution on the integral cross-section and the rotational polarization of product are different.</jats:p>

<jats:p>The time-dependent Schrödinger equation (TDSE) is usually treated in the real space in the textbook. However, it makes the numerical simulations of strong-field processes difficult due to the wide dispersion and fast oscillation of the electron wave packets under the interaction of intense laser fields. Here we demonstrate that the TDSE can be efficiently solved in the momentum space. The high-order harmonic generation and above-threshold ionization spectra obtained by numerical solutions of TDSE in momentum space agree well with previous studies in real space, but significantly reducing the computation cost.</jats:p>

<jats:p>Using a real-space real-time implementation of time-dependent density functional theory coupled to molecular dynamics (TDDFT-MD) nonadiabatically, we theoretically study both static properties and collision process of cytosine by 150–1000 eV proton impact in the microscopic way. The calculated ground state of cytosine accords well with experiments. It is found that proton is scattered in any case in the present study. The bond break of cytosine occurs when the energy loss of proton is larger than 22 eV and the main dissociation pathway of cytosine is the breaks of C<jats:sub>1</jats:sub>N<jats:sub>2</jats:sub> and N<jats:sub>8</jats:sub>H<jats:sub>10</jats:sub>. In the range of 150 eV ≤ <jats:italic>E</jats:italic> <jats:sub>k</jats:sub> ≤ 360 eV, when the incident energy of proton increases, the excitation becomes more violent even though the interaction time is shortened. While in the range of 360 eV &lt; <jats:italic>E</jats:italic> <jats:sub>k</jats:sub> ≤ 1000 eV, the excitation becomes less violent as the incident energy of proton increases, indicating that the interaction time dominates mainly. We also show two typical collision reaction channels by analyzing the molecular ionization, the electronic density evolution, the energy loss of proton, the vibration frequency and the scattering pattern detailedly. The result shows that the loss of electrons can decrease the bond lengths of C<jats:sub>3</jats:sub>N<jats:sub>8</jats:sub> and C<jats:sub>5</jats:sub>N<jats:sub>6</jats:sub> while increase the bond lengths of C<jats:sub>4</jats:sub>H<jats:sub>11</jats:sub>, C<jats:sub>5</jats:sub>H<jats:sub>12</jats:sub> and C<jats:sub>4</jats:sub>C<jats:sub>5</jats:sub> after the collision. Furthermore, it is found that the peak of the scattering angle shows a little redshift when compared to that of the loss of kinetic energy of proton.</jats:p>

<jats:p>On the basis of second-order perturbation approximate and modal expansion approach, we investigate the enhancement effect of cumulative second-harmonic generation (SHG) of circumferential guided waves (CGWs) in a circular tube, which is inherently induced by the closed propagation feature of CGWs. An appropriate mode pair of primary- and double-frequency CGWs satisfying the phase velocity matching and nonzero energy flux is selected to ensure that the second harmonic generated by primary CGW propagation can accumulate along the circumference. Using a coherent superposition of multi-waves, a model of unidirectional CGW propagation is established for analyzing the enhancement effect of cumulative SHG of primary CGW mode selected. The theoretical analyses and numerical simulations performed directly demonstrate that the second harmonic generated does have a cumulative effect along the circumferential direction and the closed propagation feature of CGWs does enhance the magnitude of cumulative second harmonic generated. Potential applications of the enhancement effect of cumulative SHG of CGWs are considered and discussed. The theoretical analysis and numerical simulation perspective presented here yield an insight previously unavailable into the physical mechanism of the enhancement effect of cumulative SHG by closed propagation feature of CGWs in a circular tube.</jats:p>

<jats:p>The hierarchical structure of the composite cathodes brings in significant chemical complexity related to the interfaces, such as cathode electrolyte interphase. These interfaces account for only a small fraction of the volume and mass, they could, however, have profound impacts on the cell-level electrochemistry. As the investigation of these interfaces becomes a crucial topic in the battery research, there is a need to properly study the surface chemistry, particularly to eliminate the biased, incomplete characterization provided by techniques that assume the homogeneous surface chemistry. Herein, we utilize nano-resolution spatially-resolved x-ray spectroscopic tools to probe the heterogeneity of the surface chemistry on LiNi<jats:sub>0.8</jats:sub>Mn<jats:sub>0.1</jats:sub>Co<jats:sub>0.1</jats:sub>O<jats:sub>2</jats:sub> layered cathode secondary particles. Informed by the nano-resolution mapping of the Ni valance state, which serves as a measurement of the local surface chemistry, we construct a conceptual model to elucidate the electrochemical consequence of the inhomogeneous local impedance over the particle surface. Going beyond the implication in battery science, our work highlights a balance between the high-resolution probing the local chemistry and the statistical representativeness, which is particularly vital in the study of the highly complex material systems.</jats:p>