New exact solution structures and nonlinear dispersion in the coupled nonlinear wave systems

In this Letter, to further understand the role of nonlinear dispersion in coupled nonlinear wave systems in both real and complex fields, we study the coupled Klein–Gordon equations with nonlinear dispersion in real field (called CKG(m,n,k)$\mathrm{CKG}(m,n,k)$ equation) and (2+1)$(2+1)$-dimensional generalization of coupled nonlinear Schrödinger equation with nonlinear dispersion in complex field (called GCNLS(m,n,k)$\mathrm{GCNLS}(m,n,k)$ equation) via some transformations. As a consequence, some types of solutions are obtained, which contain compactons, solitary pattern solutions, envelope compacton solutions, envelope solitary pattern solutions, solitary wave solutions and rational solutions.     

Analytical theory for ion transfer–electron transfer coupled reactions at redox layer–modified/thick film–modified electrodes

Electrodes modified by liquid films or plasticized polymeric membranes containing a redox species offer valuable alternatives for the study of ion transfers and bimolecular electron transfers at liquid–liquid interfaces with conventional electrode arrangements and stable interfaces. The ion-to-electron (or electron-to-electron) transducer affects the electrochemical signal, complicating the accurate analysis of experimental data. This can be reduced through the use of an electrode surface-attached redox species of well-defined electrochemical behaviour. As will be demonstrated, the voltammetry of these systems show significant deviations with respect to individual charge transfers, which must be considered for appropriate diagnosis and quantitative analysis. For this, a simple analytical theory is presented here, deducing mathematical expressions for the current–potential response, as well as for the potential difference at the two polarized interfaces, the surface excess of the redox species and the ion interfacial concentrations.     

分布振子复合板的模态阻尼及多点激励下阻尼减振相关性

分布阻尼振子可拓宽结构减振频带,因此可将振子分布于板中以形成复合板（简称“分布振子复合板”）,进而实现较宽的减振频带．对于多点支撑处受到宽频非一致激励（例如在不同激励点处的激励频率、幅值与相位有差异）的分布振子复合板,目前还缺乏有效简便的优化控制指标．在作者之前的研究中,针对含分布振子的梁推导了基于模态应变能的模态阻尼计算理论,讨论了模态阻尼与单点激励下梁的减振效果的相关性,并应用于宽频减振设计优化．本文进一步将模态阻尼计算理论推广到分布振子复合板,并将研究从梁的单点激励扩展到板的多点非一致激励下的阻尼减振相关性．首先,在利用模态应变能法推导得到分布振子复合板的模态阻尼计算公式后,从理论上讨论了不同边界条件与模态阶次对计算结果的影响,以及计算理论的适用性．而后,进一步通过有限元参数分析了边界条件、频率比、模态阶次与质量比的影响．最后,通过算例分析了无振子板或分布振子复合板在四个激励点具有多种幅值与相位组合情况下的稳态响应．结果表明,推导的模态阻尼计算公式可正确预测不同边界条件下的模态阻尼,且理论预测的模态阻尼与基板的稳态平均加速度减小率、稳态峰值应变能减小率均有较高的相关性．     

Stability and bifurcation analysis in the delay-coupled van der Pol oscillators

In this paper, the dynamics of a system of two van der Pol equations with a finite delay are investigated. We show that there exist the stability switches and a sequence of Hopf bifurcations occur at the zero equilibrium when the delay varies. Using the theory of normal form and the center manifold theorem, the explicit expression for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived.     

Experimental PIV/V3V measurements of vortex-induced fluid–structure interaction in turbulent flow—A new benchmark FSI-PfS-2a

The investigation of the bidirectional coupling between a fluid flow and a structure motion is a growing branch of research in science and industry. Applications of the so-called fluid–structure interactions (FSI) are widespread. To improve coupled numerical FSI simulations, generic experimental benchmark studies of the fluid and the structure are necessary. In this work, the coupling of a vortex-induced periodic deformation of a flexible structure mounted behind a rigid cylinder and a fully turbulent water flow performed at a Reynolds number of Re=30 470 is experimentally investigated with a planar particle image velocimetry (PIV) and a volumetric three-component velocimetry (V3V) system. To determine the structure displacements a multiple-point laser triangulation sensor is used. The three-dimensional fluid velocity results show shedding vortices behind the structure, which reaches the second swiveling mode with a frequency of about 11.2 Hz corresponding to a Strouhal number of St=0.177. Providing phase-averaged flow and structure measurements precise experimental data for coupled computational fluid dynamics (CFD) and computational structure dynamics (CSD) validations are available for this new benchmark case denoted FSI-PfS-2a. The test case possesses four main advantages: (i) the geometry is rather simple; (ii) kinematically, the rotation of the front cylinder is avoided; (iii) the boundary conditions are well defined; (iv) nevertheless, the resulting flow features and structure displacements are challenging from the computational point of view. In addition to the flow field and displacement data a PIV-based force calculation method is used to estimate the lift and drag coefficients of the moving structure.     

Iterative solutions to coupled Sylvester-transpose matrix equations

This note studies the iterative solutions to the coupled Sylvester-transpose matrix equation with a unique solution. By using the hierarchical identification principle, an iterative algorithm is presented for solving this class of coupled matrix equations. It is proved that the iterative solution consistently converges to the exact solution for any initial values. Meanwhile, sufficient conditions are derived to guarantee that the iterative solutions given by the proposed algorithm converge to the exact solution for any initial matrices. Finally, a numerical example is given to illustrate the efficiency of the proposed approach.     

Transition to Amplitude Death in Coupled System with Small Number of Nonlinear Oscillators

In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either.     

An imaginary potential with universal normalization for dissipative processes in heavy-ion reactions

In this work we present new coupled channel calculations with the São Paulo potential (SPP) as the bare interaction, and an imaginary potential with system and energy independent normalization that has been developed to take into account dissipative processes in heavy-ion reactions. This imaginary potential is based on high-energy nucleon interaction in nuclear medium. Our theoretical predictions for energies up to ≈100 MeV/nucleon agree very well with the experimental data for the p,n+nucleus, ¹⁶O + ²⁷Al, ¹⁶O + ⁶⁰Ni, ⁵⁸Ni + ¹²⁴Sn, and weakly bound projectile ⁷Li + ¹²⁰Sn systems.     

Adaptive synchronization of weighted complex dynamical networks through pinning

This paper considers the problem of controlling weighted complex dynamical networks by applying adaptive control to a fraction of network nodes. We investigate the local and global synchronization of the controlled dynamical network through the construction of a master stability function and a Lyapunov function. Analytical results show that a certain number of nodes can be controlled by using adaptive pinning to ensure the synchronization of the entire network. We present numerical simulations to verify the effectiveness of the proposed scheme. In comparison with feedback pinning, the proposed pinning control scheme is robust when tested by noise, different weighting and coupling structures, and time delays.     

Resonance structure for 4s subshell in photoionization of Mn

It is shown that the 3d5(4X)4s(5X) of 4s satellites, except to the coupling between 3d54s(7,5S) and 3p→3d transition, plays a key role on the magnitude of photoionization of 4s cross section. The coupled equation method is improved to calculate this resonance by including these channels. The results of calculations are comp ared with the experimental data from 46 eV to 56 eV photon energies, which are in good agreement with the experiment.