Soliton structures in the (1+1)-dimensional Ginzburg–Landau equation with a parity-time-symmetric potential in ultrafast optics

In this paper, the （l＋l）-dimensional variable-coefficient complex Ginzburg-Landau （CGL） equation with a parity- time （PT） symmetric potential U（x） is investigated. Although the CGL equations with a PT-symmetric potential are less reported analytically, the analytic solutions for the CGL equation are obtained with the bilinear method in this paper. Via the derived solutions, some soliton structures are presented with corresponding parameters, and the influences of them are analyzed and studied. The single-soliton structure is numerically verified, and its stability is analyzed against additive and multiplicative noises. In particular, we study the soliton dynamics under the impact of the PT-symmetric potential. Results show that the PT-symmetric potential plays an important role for obtaining soliton structures in ultrafast optics, and we can design fiber lasers and all-optical switches depending on the different amplitudes of soliton-like structures.

Characteristic Functional Structure of Infinitesimal Symmetry Transformations for Nonholonomic System

It was proved that velocity-dependent infinitesima l symmetry transformations of nonholonomic systems have a characteristic functio nal structure, which could be formulated by means of an auxiliary symmetry tra nsformation function and is manifestly dependent upon constants of motion of th e system. An example was given to illustrate the applicability of the results.

Symmetric Structure of Induction Motor Systems

In this paper, symmetric structure of induction motor system in stationary αβ 0 coordinates is studied by the geometric approach. The results show that the system possesses symmetry ( G,θ,Φ ) and infinitesimal symmetry. Under certain conditions, the system can be transformed into a form possessing state space symmetry ( G,Φ ) and infinitesimal state space symmetry by means of state feedback and input coordinate base transform. The results can be extended to the fifth order induction motor system fed by hysteresis band current controlled PWM inverter.

THE PROLONGATION STRUCTURES AND NONLOCAL SYMMETRIES FOR MODIFIED BOUSSINESQ SYSTEM

The Wahlquist-Estabrook （WE） prolongation structures of modified Boussi-nesq （MB） system are studied from the coverings point of view. The realizations and classifications of one-dimensional coverings of this system are obtained completely. More-over the sufficient and necessary conditions for a vector field to be a nonlocal symmetry of this system are also demonstrated in the WE prolongation structures.

Electronic Structure and Magnetic Properties of Rh_(13) Cluster with Three Possible Symmetries

Electronic and magnetic properties of 13-atom Rh clusters with three possible high symmetry geometries have been studied by using the first-principles DV-LSD method. An anomalous symmetry dependence of the cluster magnetism was found that the total magnetic moment of the icosahedral Rh13 cluster is smaller than that of the other two lower-symmetry clusters in a wide range of interatomic spacings. An energy difference is identified to explain this anomalous relationship, which has been found to be also useful for judging whether the broadening technique is correctly used and whether multiple input potentials must be used to reach the actual ground state in the LSD calculations. The calculated results are compared and discussed with those of previous theory and recent experiment. The actual geometry of the Rh13 cluster is suggested to be a distorted icosahedron.

Disorder in parity-time symmetric quantum walks

We experimentally investigate the impact of static disorder and dynamic disorder on the non-unitary dynamics of parity-time(PT)-symmetric quantum walks.Via temporally alternating photon losses in an interferometric network,we realize the passive PT-symmetric quantum dynamics for single photons.Controllable coin operations allow us to simulate different environmental influences,which result in three different behaviors of quantum walkers:a standard ballistic spread,a diffusive behavior,and a localization,respectively,in a PT-symmetric quantum walk architecture.

Parity-time symmetric acoustic system constructed by piezoelectric composite plates with active external circuits

Researches on parity-time(PT)symmetry in acoustic field can provide an efficient platform for controlling the travelling acoustic waves with balanced loss and gain.Here,we report a feasible design of PT-symmetric system constructed by piezoelectric composite plates with two different active external circuits.By judiciously adjusting the resistances and inductances in the external circuits,we obtain the exceptional point due to the spontaneous breaking of PT symmetry at the desired frequencies and can observe the unidirectional invisibility.Moreover,the system can be at PT exact phase or broken phase at the same frequency in the same structure by merely adjusting the external circuits,which represents the active control that makes the acoustic manipulation more convenient.Our study may provide a feasible way for manipulating acoustic waves and inspire the application of piezoelectric composite materials in acoustic structures.

Bifurcated overtones of one-way localized Fabry-Pérot resonances in parity-time symmetric optical lattices

Since the first observation of parity-time（PT） symmetry in optics, varied interesting phenomena have been discovered in both theories and experiments, such as PT phase transition and unidirectional invisibility, which turns PT-symmetric optics into a hotspot in research. Here, we report on the one-way localized Fabry-Pérot（FP） resonance, where a welldesigned PT optical resonator may operate at exceptional points with bidirectional transparency but unidirectional field localization. Overtones of such one-way localized FP resonance can be classified into a blue shifted branch and a red shifted branch. Therefore, the fundamental resonant frequency is not the lowest one. We find that the spatial field distributions of the overtones at the same absolute order are almost the same, even though their frequencies are quite different.

The Second mKdV Equation and Its Hereditary Symmetry and Hamiltonian Structure

The isospectral problem of the second mKdV equation is found out firstly. It follows that the strong hereditary symmetry and the Hamiltonian structure of the second mKdV equation are presented.

An Analysis of Symmetry Effects on Structures of a 3-Boson System

A 3-boson system is examined,revealing that the quantum mechanical sym-metry plays a decisive role in determining the features of few-body systems.

Time Symmetry Analysis of Nonlinear Parity Based on S-P Compensation Network Structure

The wireless power transmission system based on nonlinear parity time symmetry is a robust sys-tem that can maintain high-efficiency transmission at a certain distance.Parity-Time Symmetry(PT symmetry)wireless power transfer system,due to its insensitivity to the position of the coupled resonant coil over a large range,can carry out constant power transfer to the load,and through coupled mode theory The PT symmetrical wireless power transmission circuit with S-P structure is analyzed,and the system has different transmission efficiencies in different coupling intervals,and the transmission effect of the structure at different distances is studied with the change of coupling coefficient.Then,the simulation is carried out by MATLAB and origin software.The final results show that the transmission efficiency does not change with the coupling coefficient in the strong coupling region and can maintain high-efficiency transmission.In the weak coupling region,the coupling coefficient has a great influence on the transmission efficiency of the system.

基于光学Parity-Time对称微腔结构的大范围电场传感器

为解决传统电场传感器测量范围受限的技术难题,设计了一种基于光学 Parity-Time(PT)对称掺杂电光介质的微腔结构,提出新的电场传感机制.利用传输矩阵方法计算结构的传输谱,发现独特的放大的缺陷模式.缺陷模式的峰值和波长位置均随外电场变化,由此可以利用缺陷模峰值变化和波长位置变化两种机制测量同一电场.测量范围仅受电光介质击穿电场的限制,可以为 0 0.06 V/nm,几乎涵盖了可能的电场环境.对峰值变化传感机制,灵敏度范围 38.042- 47.558 nm/V;对波长变化传感机制,灵敏度范围 18.357-18.642nm/V,在测量范围内平均分辨率为0.00925 V/nm.

Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomie mechanic systems with unilateral constraints axe established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups axe also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.

Exact Geometric Relationships, Symmetry Breaking and Structural Stability for Single-Walled Carbon Nanotubes

We pioneered a study about how the geometric relationship of single-walled carbon nanotubes(SWCNT) is influenced by curvature factor and non-planar geometry factor in cylindrical coordinate system based on the assumption of complete symmetry. The bond length and angle of every carbon-carbon bonds are determined by using the principle of the minimum energy. The results of the paper include(1) From the calculation result, the symmetry breaking appears for chiral carbon nanotubes, while the part symmetry appears for achiral carbon nanotubes with increasing curvature.(2) The synergistic effect of bond lengths and bond angles is first found.(3) We conclude that the influence of non-planar geometry factor can be completely ignored on bond lengths and bond angles when the curvature parameter has been included in the model.(4)The two fractal dimensions are given from the nanoscale to the macroscale for zigzag topology and armchair topology respectively. Fractal dimensions of SWCNT show special characteristics, varying with the length of SWCNT until the lengths approach infinity. The close and inevitable correlations among curvature, symmetry breaking and stability of SWCNTs can be summed up as: the increase of curvature causes symmetry breaking,and such symmetry breaking will further reduce the structural stability.

PHASE EXTENSION AND STRUCTURE ANALYSIS BY THE MAXIMUM ENTROPY METHOD

Excellent results are obtained in structure analysis with jew phases of structure factors by the maximum-entropy method (MEM) for CaGaN PbCO3 and ReBe22 single crystals. The computation time and memory space are minimized by symmetry operations so that structure analysis by the MEM can be carried out with a personal computer.

Shape-induced phase transition of vortex domain structures in ferroelectric nanodots and their controllability by electrical and mechanical loads

Shape-induced phase transition of vortex domain structures （VDSs） in BaTiO3 （BT） nanodots under open circuit boundary condition have been investigated using an effective Hamiltonian method. Our calculation indicates the tetragonal VDS missing in cubic BT nanodots can be induced by varying the shape of a nanodot from cube to platelet. Interestingly, a novel VDS is found in BT nanoplatelets in our simulations. Further investigation shows that it is a result of compromise between the ground state and the symmetry of the shape of the nanodot. Furthermore, based on the novel VDS, routes of controlling VDSs governed by homogeneous electric field and uniform stress are discussed. In particular, our results show the possibility of designing multi-states devices based on a single VDS. ~ 2017 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics.

Synthesis,Crystal and Electronic Structure of Ba_3ZnSb_2O_9 with the 6H-perovskite-type Structure

Crystals of Ba3ZnSb2O9 have been grown by a high-temperature solid-state reaction and characterized by single-crystal X-ray diffraction.Ba3ZnSb2O9 crystallizes in the hexagonal P63/mmc space group with a = 5.8663（4）,c = 14.478（2） ,V = 431.49（8） 3,Z = 2 and R（all data） = 0.0167.The structure of Ba3ZnSb2O9 consists of pairs of face-sharing Sb2O9 bi-octahedra connected via corners with two single layers of mutually isolated ZnO6 octahedra.Each Ba2＋ ion is bonded to 12 oxygen atoms.The UV-vis absorption spectrum of the compound has been investigated.Additionally,the calculations of band structure and density of states have also been performed with density functional theory method.The obtained results tend to support the experimental data of the absorption spectrum.

Layer Structure of Doped C_(60)

It is found in this letter that the doped C_(60) possesses layer-structure in both bond distortions and electronic states.There are eight layers of carbon atoms in the charged C_(60),and its symmetry is reduced from Ih to D_(5d).This layer-structure indicates that there exist four nonequivalent groups of carbon atoms in the doped C_(60).It contrasts with the pristine C_(60),in which all the sixty carbon atoms are equivalent.One observable consequence of such layer-structure is the split of its NMR spectrum with the ratio 1:1:2:2.

Covariant Prolongation Structure, Conservation Laws and Soliton Solutions of the Gross-Pitaevskii Equation in the Bose-Einstein Condensate

In this paper, we investigate the Gross-Pitaevskii (GP) equation which describes the propagation of an electron plasma wave packet with a large wavelength and small amplitude in a medium with a parabolic density and constant interactional damping by the Covariant Prolongation Structure Theory. As a result, we obtain general forms of Lax-Pair representations. In addition, some hidden structural symmetries that govern the dynamics of the GP equation such as SL(2,R), SL(2,C), Virasoro algebra, SU(1,1) and SU(2) are unearthed. Using the Riccati form of the linear eigenvalue problem, infinite number of conservation laws of the GP equation is explicitly constructed and the exact analytical soliton solutions are obtained by employing the simple and straightforward Hirota’s bilinear method.

Calculations of stability of alloyed cementite from valance electron structure

Based on the empirical electronic theory of solids and molecules （EET）, the actual model for unit cell of cementite （0-FeaC） was built and the valence electron structures （VES） of cementite with specified site and a number of Fe atoms substituted by alloying atoms of M （ M=Cr, V, W, Mo, Mn ） were computed by statistical method. By defining P as the stability factor, the stability of alloyed cementite with different numbers and sites of Fe atoms substituted by M was calculated. Calculation results show that the density of lattice electrons, the symmetry of distribution of covalent electron pairs and bond energy have huge influence on the stability of alloyed cementite. It is more stable as M substitutes for FeE than for Fe1. The alloyed cementite is the most stable when Cr, Mo, W and V substitute for 2 atoms of Fe2 at the sites of Nos. 2 and 3 （or No. 6 and No. 7）. The stability of alloyed cementite decreases gradually as being substitutional doped by W, Cr, V, Mo and Mn.