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<jats:p>The Painlevé property for a (2+1)-dimensional Korteweg–de Vries (KdV) extension, the combined KP3 (Kadomtsev–Petviashvili) and KP4 (cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.</jats:p>

<jats:p>We study one- and two-soliton solutions for the Cahn–Allen (CA) equation and the Brethorton equation. The CA equation has broad spectrum of applications especially in anti-phase boundary motion and it is used in phase-field models. While the Brethorton equation is a model for dispersive wave systems, it is used to find the resonant nonlinear interaction among three linear modes. We use the Hirota bilinear method to obtain one- and two-soliton solutions to the CA equation and the Brethorton equation.</jats:p>

<jats:p>Using molecular dynamics simulations, we have revealed a novel wetting phenomenon with a droplet on composite structures formed by embedded water into (111) surface of <jats:italic>β</jats:italic>-cristobalite hydroxylated silica. This can be attributed to the formation of a composite structure composed of embedded water molecules and the surface hydroxyl (–OH) groups, which reduces the number of hydrogen bonds between the composite structure and the water droplet above the composite structure. Interestingly, a small uniform strain (±3%) applied to the crystal lattice of the hydroxylated silica surface can result in a notable change of the contact angles (&gt;40°) on the surface. The finding provides new insights into the correlation between the molecular-scale interfacial water structures and the macroscopic wettability of the hydroxylated silica surface.</jats:p>

<jats:p>Although many organic molecules found commonly in the atmosphere are known to be surface-active in aqueous solutions, their effects on the mechanisms underlying haze formation remain unclear. In this paper, based on a simple thermodynamic analysis, we report that the adsorption of amphiphilic organics alone not only lowers the surface tension, but also unexpectedly stabilizes nanodroplets of specific size under water vapor supersaturation. Then we determine how various factors, including relative humidity, water activity effect due to dissolution of inorganic components as well as surface tension effect due to surface adsorption of organic components, cooperatively induce the stability of nanodroplets. The nanodroplet stability behaviors not captured in the current theory would change the formation mechanism of haze droplets, from the hygroscopic growth pathway to a nonclassical two-step nucleation pathway.</jats:p>

<jats:p>In recent years, clapping synchronization between individuals has been widely studied as one of the typical synchronization phenomena. In this paper, we aim to reveal the synchronization mechanism of clapping interactions by observing two individuals’ clapping rhythms in a series of experiments. We find that the two synchronizing clapping rhythm series exhibit long-range cross-correlations (LRCCs); that is, the interaction of clapping rhythms can be seen as a strong-anticipation process. Previous studies have demonstrated that the interactions in local timescales or global matching in statistical structures of fluctuation in long timescales can be sources of the strong-anticipation process. However, the origin of the strong anticipation process often appears elusive in many complex systems. Here, we find that the clapping synchronization process may result from the local interaction between two clapping individuals and may result from the more global coordination between two clapping individuals. We introduce two stochastic models for mutually interacting clapping individuals that generate the LRCCs and prove theoretically that the generation of clapping synchronization process needs to consider both local interaction and global matching. This study provides a statistical framework for studying the internal synchronization mechanism of other complex systems. Our theoretical model can also be applied to study the dynamics of other complex systems with the LRCCs, including finance, transportation, and climate.</jats:p>

<jats:p>We present the photoelectron momentum distributions (PMDs) and the photoelectron angular distributions (PADs) of He<jats:sup>+</jats:sup> ions, aligned <jats:inline-formula> <jats:tex-math><?CDATA ${{\rm{H}}}_{2}^{+}$?></jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <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_30_1_013201_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula> molecules and N<jats:sub>2</jats:sub> molecules by intense orthogonally polarized laser pulses. Simulations are performed by numerically solving the corresponding two-dimensional time-dependent Schrödinger equations (TDSEs) within the single-electron approximation frame. Photoelectron momentum distributions and photoelectron angular distributions present different patterns with the time delays <jats:italic>T</jats:italic> <jats:sub>d</jats:sub>, illustrating the dependences of the PMDs and PADs on the time delays by orthogonally polarized laser pulses. The evolution of the electron wavepackets can be employed to describe the intensity of the PADs from the TDSE simulations for N<jats:sub>2</jats:sub> molecules.</jats:p>

<jats:p>The high-resolution three-dimensional photoelectron momentum distributions via above-threshold ionization (ATI) of Xe atoms are measured in an intense near circularly polarized laser field using velocity map imaging and tomography reconstruction. Compared to the linearly polarized laser field, the employed near circularly polarized laser field imposes a more strict selection rule for the transition via resonant excitation, and therefore we can selectively enhance the resonant ATI through certain atomic Rydberg states. Our results show the self-reference ionization delay, which is determined from the difference between the measured streaking angles for nonadiabatic ATI via the 4f and 5f Rydberg states, is 45.6 as. Our method provides an accessible route to highlight the role of resonant transition between selected states, which will pave the way for fully understanding the ionization dynamics toward manipulating electron motion as well as reaction in an ultrafast time scale.</jats:p>

<jats:p>The calculation results of the <jats:italic>R</jats:italic>-branch transition emission spectra of (0–0) band of the <jats:italic>A</jats:italic> <jats:sub>2</jats:sub> 1 → <jats:italic>X</jats:italic> <jats:sub>2</jats:sub> 1 transition system of SbNa molecule are presented in this paper. These <jats:italic>R</jats:italic>-branch high-lying transitional emission spectral lines are predicted by using the difference converging method (DCM). Our results show excellent agreement between DCM spectral lines and the experimental values, and the deviations are controlled within 0.0224 cm<jats:sup>−1</jats:sup>. What is more, based on the principle of over-determined linear equations, the prediction error is quantified in this work, which provides reliable theoretical support for our predicted DCM calculations. This work provides a lot of useful information for understanding the microstructure of SbNa molecule.</jats:p>

<jats:p>This review summarizes the recent advances on the application of <jats:sup>57</jats:sup>Fe Mössbauer spectrometry to study the magnetic and phase characteristics of Nd–Fe–B-based permanent magnets. First of all, the hyperfine structures of the Ce<jats:sub>2</jats:sub>Fe<jats:sub>14</jats:sub>B, (Ce, Nd)<jats:sub>2</jats:sub>Fe<jats:sub>14</jats:sub>B and MM<jats:sub>2</jats:sub>Fe<jats:sub>14</jats:sub>B phases are well-defined by using the model based on the Wigner-Seitz analysis of the crystal structure. The results show that the isomer shift <jats:italic>δ</jats:italic> and the quadrupole splitting Δ<jats:italic>E</jats:italic> <jats:sub>Q</jats:sub> of those 2:14:1 phases show minor changes with the Nd content, while the hyperfine field <jats:italic>B</jats:italic> <jats:sub>hf</jats:sub> increases monotonically with increasing Nd content and its value is influenced by the element segregation and phase separation in the 2:14:1 phase. Then, the hyperfine structures of the low fraction secondary phases are determined by the <jats:sup>57</jats:sup>Fe Mössbauer spectrometry due to its high sensitivity. On this basis, the content, magnetic behavior, and magnetization of the REFe<jats:sub>2</jats:sub> phase, the amorphous grain boundary (GB) phase, and the amorphous worm-like phase, as well as their effects on the magnetic properties, are systematically studied.</jats:p>