Harmonic Balance Methods:A Review and Recent Developments

The harmonic balance(HB)method is one of the most commonly used methods for solving periodic solutions of both weakly and strongly nonlinear dynamical systems.However,it is confined to low-order approximations due to complex symbolic operations.Many variants have been developed to improve the HB method,among which the time domain HB-like methods are regarded as crucial improvements because of their fast computation and simple derivation.So far,there are two problems remaining to be addressed.i)A dozen of different versions of HB-like methods,in frequency domain or time domain or in hybrid,have been developed;unfortunately,misclassification pervades among them due to the unclear borderlines of different methods.ii)The time domain HB-like methods suffer from non-physical solutions,which have been shown to be caused by aliasing(mixture of the high-order into the low-order harmonics).Although a series of dealiasing techniques have been developed over the past two decades,the mechanism of aliasing and the final solution to dealiasing are still not well known to the academic community.This paper aims to provide a comprehensive review of the development of HB-like methods and enunciate their principal differences.In particular,the time domain methods are emphasized with the famous aliasing phenomenon clearly addressed.

Formation of mono-dispersed droplets with electric periodic dripping regime in electrohydrodynamic(EHD) atomization

The formation of controllable size and dripping frequency in electrohydrodynamic(EHD)atomization with electric periodic dripping regime are of much interest and importance because of significant and wide applications,such as micro-encapsulation and ink-printing.In the present study,the experimental and theoretical works were carried out to explore droplet formation in periodic dripping regime in presence of an electric field.The dimensionless electric charge carried by each droplet produced is smaller than the 50%of critical value of the Rayleigh limit,where charge-to-mass ratio of droplets was obtained through the deflection distance in the presence of an electric field.The droplet in electric periodic dripping regime usually undergoes oscillating deformation,and finally forms a spherical droplet below the tip no more than ten times out diameter of tube.The droplet size tens of microns to one hundreds of microns decreases with an increase in applied potential.In the electric dripping mode,droplets size is independent of flow rate and affected by flow rate due to adsorption of surface active species in micro-dripping.The simplified model to predict droplets size was derived from the balance of electric,surface tension and gravity forces.The droplets size calculated in good agreement with the experiments.Meanwhile,the dripping frequency of droplets with rang of a few to several hundred hertz obtained from timeresolved images is highly dependent of liquid flow rate and electric potential.The largest dripping frequency was predicted and in reasonable agreement with the experimental results.In electric periodic dripping regime drop-on-demand droplets in size and dripping frequency further our understanding on the formation of identical droplets and are beneficial to many practical applications.

Unusual Band Splitting and Superconducting Gap Evolution with Sulfur Substitution in FeSe

High-resolution angle-resolved photoemission measurements were taken on FeSe;S;(x=0,0.04,and 0.08)superconductors.With an ultrahigh energy resolution of 0.4 meV,unusual two hole bands near the Brillouin-zone center,which was possibly a result of additional symmetry breaking,were identified in all the sulfur-substituted samples.In addition,in both of the hole bands highly anisotropic superconducting gaps with resolution limited nodes were evidenced.We find that the larger superconducting gap on the outer hole band is reduced linearly to the nematic transition temperature while the gap on the inner hole is nearly S-substitution independent.Our observations strongly suggest that the superconducting gap increases with enhanced nematicity although the superconducting transition temperature is not only governed by the pairing strength,demonstrating strong constraints on theories in the FeSe family.

三角格子伊辛磁体中量子效应的外场调控

文章结合中子散射和热力学测量研究了三角格子量子伊辛磁体TmMgGaO_(4)的磁关联行为在外加纵向磁场下的演变.实验发现,在中等强度的磁场下系统出现了一个量子涨落诱导的准平台相.该相的磁有序和自旋能隙表现出非单调的磁场和温度依赖关系,随着磁场的增大先变大后变小.在更高的外磁场下,量子涨落被大部分抑制后系统进入了一个无序相,自旋激发强度同时变弱.结合细致的半经典计算,该研究可以定量地理解量子涨落和阻挫伊辛相互作用之间的竞争作用所导致的上述新奇物理现象.