We present the results of the combined experimental and theoretical investigation of rope coiling arising from the buckling instability. The shape of the rope is perfectly circular in the coiling region and is straight in the region below the feeding point. In between these two distant regions, the rope assumes a catenary-like shape in the limit of slow feeding velocity and a helix-like shape in the limit of fast feeding velocity. When there is an increase in the feeding velocity, the transverse displacement of deformation persists over the long distance far beyond the coiling region. The catenary is associated with the purely imaginary wave number and the helix is associated with the real wave number. The catenary-to-helix shape transition is particularly evident when the rope is fed from a large height.

Solutions of the Schrödinger equation by spanning the wave function in a complete basis is a common practice in many-body interacting systems.We shall study the case of a two-dimensional quantum system composedof two interacting spin-less electrons and see that the correctness of the matrix approach depends inexplicably on the type of interaction existing between particles. Also, we shall extend the present study to other systems of specialinterest in order to illustrate the method.

The photodetachment of negative ions inside a two-dimensional microcavity has been studied by many researchers. As to the photodetachment of negative ions in the three-dimensional microcavity, the research is relatively little. In this paper, we study the photodetachment cross-section of $\rm{H}^{−}$ ion inside a three-dimensional cubical microcavity for the first time.We have observed the classical dynamics of the photodetached electron inside the cubical microcavity and found out its closed orbits. Then we calculate the photodetachment cross-section of this system. It is shown that owing to the interference effects of the electron wave travelling along various closed orbits, oscillatory structures appear in the photodetachment cross-section. And the oscillatory structures depend on the laser polarization sensitively. Compared to the photodetachment of $\rm{H}^{−}$ ion inside a square microcavity, in photodetachment of $\rm{H}^{−}$ ion in cubical cavity the number of the closed orbits is increased and the oscillatory structure in the photodetachment cross-section becomes much more complex. Through our study, researchers can gain a deep understanding on the correspondence of the classical dynamics and the quantum mechanics. Our study may guide future experimental research in the field of the photodetachment electron dynamics inside a three-dimensional microcavity.

A linearly implicit nonstandard finite difference method is presented for the numerical solution of modified Korteweg–de Vries equation. Local truncation error of the scheme is discussed. Numerical examples are presented to test the efficiency and accuracy of the scheme.

In this paper, the tristable stochastic resonance (SR) phenomenon induced by $\alpha$-stable noise is analysed. The mechanism for realizing resonance is explored based on research concerning the potential function and resonant output of a system. The rules for resonance system parameters $q$, $p$, skewness parameter $r$ and intensity amplification factor $mathcal{Q}$ of $\alpha$-stable noise to act on the resonant output are explored under different values of stability index $\alpha$ and asymmetric skewness $\beta$ of $\alpha$-stable noise. The results will contribute to a reasonable selection of parameter-induced tristable SR system parameters under $\alpha$-stable noise, and lay the foundation for a practical engineering application of weak signal detection based on the SR.

The symmetry energy of a nucleus is determined in a local density approximation and integrating over the entire density distribution of the nucleus, calculated utilizing the relativistic density-dependent Thomas-Fermiapproach. The symmetry energy is found to decrease with increasing neutron excess in the nucleus. The isovector coupling channel reduces the symmetry energy, and this effect increases with increased neutron excess. The isovector coupling channel increases the symmetry energy integral in $^{40}$Ca and reduces it in $^{48}$Ca, and the interplay between the isovector and the isoscalar channels of the nuclear force explains this isotope effect.

We show for the first time that the generalized seniority scheme explains reasonably well the $B(E3)$ systematics for the $(0^{+} → 3^{−}_{1})$ transitions in the Sn isotopes, which are odd-tensor $E3$ transitions connecting different seniority states $(\Delta\upsilon = 2)$. Additionally, we also present large scale shell model (LSSM) calculations to support our interpretation. The generalized seniority scheme points to the octupole character of these 3− states in Sn isotopes.

Intracavity propagation delay, a delay introduced by a semiconductor diode laser, is found to significantly influence synchronization of multiple semiconductor diode lasers, operated either in stable or in chaotic regime. Two diode lasers coupled in unidirectional scheme is considered in this numerical study. A diode laser subjected to an optical feedback, also called an external cavity diode laser, acts as the transmitter laser (TL). A solitary diode laser acts as the receiver laser (RL). The optical output of the TL is coupled to the RL and laser operating parameters are optimized to achieve synchronization in their output intensities. The time-of-flightbetween the TL and RL introduces an intercavity time delay in the dynamics of RL. In addition to this, an intracavity propagation delay arises as the TL’s field propagated within the RL. This intracavity propagation delay is evaluated by cross-correlation analysis between the output intensities of the lasers. The intracavity propagation delay is found to increase as the external cavity feedback rate of TL is increased, while an increment in the injection rate between the two lasers resulted in a reduction of intracavity propagation delay.

A periodic breather-wave solution is obtained using homoclinic test approach and Hirota’s bilinear method with a small perturbation parameter $u_0$ for the (2+1)-dimensional generalized Kadomtsev–Petviashvili equation. Based on the periodic breather-wave, a lump solution is emerged by limit behaviour. Finally, three different forms of the space–time structure of the lump solution are investigated and discussed using the extreme value theory.

Observer-based synchronization and parameter estimation of chaotic systems has been an interesting and important issue in theory and various fields of application. In this paper first we investigate the observer-based synchronization of a class of chaotic systems, and then discuss its parameter estimation via a single output. We assume that only the sum of the first and second state variables is available. By constructing a proper observer, some novel criteria for observer-based synchronization and parameter estimation are proposed via a scalar input. The Lü chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.

Energy levels, lifetimes and wave function compositions are computed for 127 fine structural levels in Ne-like ions (Z = 29−31). Configuration interaction has been included among 51 configurations (generating 1016levels) and multiconfigurational Dirac–Fock method is used to generate the wave functions. Similar calculations have also been performed using the fully relativistic flexible atomic code (FAC). Transition wavelength, oscillator strength, transition probabilities and line strength are reported for electric dipole (E1), electric quadrupole (E2), magnetic dipole (M1) and magnetic quadrupole (M2) transitions from the ground level. We compared our calculated results with the available data in the literature. The calculated results are found to be in close agreement with the previous results. Further, we predict some new atomic data which may be important for plasma diagnostics.