High winding number of topological phase in non-unitary periodic quantum walk

Topological phases and their associated multiple edge states are studied by constructing a one-dimensional non-unitary multi-period quantum walk with parity-time symmetry.It is shown that large topological numbers can be obtained when choosing an appropriate time frame.The maximum value of the winding number can reach the number of periods in the one-step evolution operator.The validity of the bulk-edge correspondence is confirmed,while for an odd-period quantum walk and an even-period quantum walk,they have different configurations of the 0-energy edge state andπ-energy edge state.On the boundary,two kinds of edge states always coexist in equal amount for the odd-period quantum walk,however three cases including equal amount,unequal amount or even only one type may occur for the even-period quantum walk.

Topological properties of tetratomic Su-Schrieffer-Heeger chains with hierarchical long-range hopping

We propose a new generalized Su–Schrieffer–Heeger model with hierarchical long-range hopping based on a onedimensional tetratomic chain. The properties of the topological states and phase transition, which depend on the cointeraction of the intracell and intercell hoppings, are investigated using the phase diagram of the winding number. It is shown that topological states with large positive/negative winding numbers can readily be generated in this system. The properties of the topological states can be verified by the ring-type structures in the trajectory diagram of the complex plane. The topological phase transition is strongly related to the opening(closure) of an energy bandgap at the center(boundaries) of the Brillouin zone. Finally, the non-zero-energy edge states at the ends of the finite system are revealed and matched with the bulk–boundary correspondence.

Mach Number Prediction for a Wind Tunnel Based on the CNN-LSTM-Attention Method

The test section’s Mach number in wind tunnel testing is a significant metric for evaluating system performance.The quality of the flow field in the wind tunnel is contingent upon the system's capacity to maintain stability across various working conditions.The process flow in wind tunnel testing is inherently complex,resulting in a system characterized by nonlinearity,time lag,and multiple working conditions.To implement the predictive control algorithm,a precise Mach number prediction model must be created.Therefore,this report studies the method for Mach number prediction modelling in wind tunnel flow fields with various working conditions.Firstly,this paper introduces a continuous transonic wind tunnel.The key physical quantities affecting the flow field of the wind tunnel are determined by analyzing its structure and blowing process.Secondly,considering the nonlinear and time-lag characteristics of the wind tunnel system,a CNN-LSTM model is employed to establish the Mach number prediction model by combining the 1D-CNN algorithm with the LSTM model,which has long and short-term memory functions.Then,the attention mechanism is incorporated into the CNN-LSTM prediction model to enable the model to focus more on data with greater information importance,thereby enhancing the model's training effectiveness.The application results ultimately demonstrate the efficacy of the proposed approach.

Determinant Theory in Banach Algebras

A determinant theory is developed for Banach algebras and a characterization of those traced unital Banach algebras admitting a determinant is given.

An experiment of dynamical behaviours in an erbium-doped fibre-ring laser with loss modulation

This paper reports a systematic experimental investigation on the dynamics in the low-frequency region in an erbium-doped fibre-ring laser with loss modulation. A rich variety of bifurcation is analyzed through the bifurcation diagram and structured with the concept of the winding numbers. The coexistence of multiple attractors and the crisis that appear in the saddle-node bifurcations, and an interesting structure of bifurcation which is similar to the bifurcations in high-frequency range, have been observed.

Topological Aspect and Bifurcation of Disclination Lines in Two—Dimensional Liquid Crystals

Using φ-mapping method and topological current theory, the topological structure and bifurcation ofdisclination lines in two-dimensional liquid crystals are studied. By introducing the strength density and the topologicalcurrent of many disclination lines, the total disclination strength is topologically quantized by the Hopf indices andBrouwer degrees at the singularities of the director field when the Jacobian determinant of director field does not vanish.When the Jacobian determinant vanishes, the origin, annihilation and bifurcation processes of disclination lines arestudied in the neighborhoods of the limit points and bifurcation points, respectively. The branch solutions at the limitpoint and the different directions of all branch curves at the bifurcation point are calculated with the conservation lawof the topological quantum numbers. It is pointed out that a disclination line with a higher strength is unstable and itwill evolve to the lower strength state through the bifurcation process.

Topological Structure of Disclination Lines in 2-Dimensional Liquid Crystals

Using mapping method and topological current theory, the topological structure of disclination lines in 2 dimensional liquid crystals is studied. By introducing the strength density and the topological current of many disclination lines, it is pointed out that the disclination lines are determined by the singulaities of the director field, and topologically quantized by the Hopf indices and Brouwer degrees. Due to the equivalence in physics of the director fields n (x) and n (x) , the Hopf indices can be integers or half integers, representing a generalization of our previous studies of integer Hopf indices.

Topological Defects in Liquid Crystal Films

A topological theory of liquid crystal films in the presence of defects is developed based on the Ф-mapping topological current theory. By generalizing the free-energy density in ＂one-constant＂ approximation, a covariant free- energy density is obtained, from which the U（1） gauge field and the unified topological current for monopoles and strings in liquid crystals are derived. The inner topological structure of these topological defects is characterized by the winding numbers of Ф-mapping.

Topological aspect of Chern-Simons p-branes

By generalizing the topological current of Abelian Chern Simons （CS） vortices, we present a topological tensor current of CS p-branes based on the φ-mapping topological current theory. It is revealed that CS p-branes are located at the isolated zeros of the vector field φ（x）, and the topological structure of CS p-branes is characterized by the winding number of the φ-mappings. Furthermore, the Nambu-Goto action and the equation of motion for multi CS p-branes are obtained.

Dependence of Estimating Whitecap Coverage on Currents and Swells

The shipboard measurements of whitecap coverage(W)and the meteorological and oceanographic information from two cruises in the South China Sea and Western Pacific are explored for estimating W.This study aims at evaluating how to im-prove the parameterizations of W while considering the effects of currents and swells on wave breaking.Currents indeed affect W in a way that winds with following currents can decrease W,whereas winds with opposing currents can increase W.Then,10-m wind speed over sea surface(U_(10))is calibrated by subtracting the current velocity from U_(10) when the propagating directions of winds and currents are aligned.By contrast,when the direction is opposite,U_(10) is calibrated by adding the parallel velocity com-ponent of the opposing current to U_(10).The power fits of W dependence on the U_(10)-related parameters of U_(10),friction velocity,wind sea Reynolds number in terms of this calibrated-U_(10) obtain better results than those directly fitted to U_(10).Different from the effect of currents on W,wind blowing along the crest line of swells may contribute to the increase in W.The conclusions suggest that U_(10) should be calibrated first before parameterizing W in areas with a strong current or some swell-dominant areas.

Wind tunnel simulation of wind loading on a solid structure of revolution

The wind tunnel simulations of wind loading on a solid structure of revolution with one smooth and five rough surfaces were conducted using wind tunnel tests. Timemean and fluctuating pressure distributions on the surface were obtained, and the relationships between the roughness Reynolds number and pressure distributions were analyzed and discussed. The results show that increasing the surface roughness can significantly affect the pressure distribution, and the roughness Reynolds numbers play an important role in the change of flow patterns. The three flow patterns of subcritical, critical and supercritical flows can be classified based on the changing patterns of both the mean and the fluctuating pressure distributions. The present study suggests that the wind tunnel results obtained in the supercritical pattern reflect more closely those of full-scale solid structure of revolution at the designed wind speed.

Phase-field simulations of topological conservation in multi-vortex induced by surface charge in BiFeO_(3)thin films

The creations and manipulations of vortexes in ferroelectric materials with external stimuli are expected to be used in the design and fabrication of sensing materials and multifunctional electronic devices.In this work,we investigated the surface charge-induced multi-vortex evolution using the phase-field simulations in BiFeO_(3).A combination of domain morphology,polarization distribution and winding number calculation was considered.The results show that vortex and anti-vortex exist simultaneously in pairs,and the total value of winding numbers is always 0.In addition,the minimum distanceΔl between the surface charge regions is 9 nm when the vortex domains are independent of each other.This work provides a reference for the manipulation of ferroelectric vortex induced by surface charges,which lays a theoretical foundation for the design and fabrication of high-density vortex memories.

Realization of photonic p-orbital higher-order topological insulators

The orbital degrees of freedom play a pivotal role in understanding fundamental phenomena in solid-state materials as well as exotic quantum states of matter including orbital superfluidity and topological semimetals.Despite tremendous efforts in engineering synthetic cold-atom,as well as electronic and photonic lattices to explore orbital physics,thus far high orbitals in an important class of materials,namely,higher-order topological insulators(HOTIs),have not been realized.Here,we demonstrate p-orbital corner states in a photonic HOTI,unveiling their underlying topological invariant,symmetry protection,and nonlinearity-induced dynamical rotation.In a Kagome-type HOTI,we find that the topological protection of p-orbital corner states demands an orbital-hopping symmetry in addition to generalized chiral symmetry.Due to orbital hybridization,nontrivial topology of the p-orbital HOTI is“hidden”if bulk polarization is used as the topological invariant,but well manifested by the generalized winding number.Our work opens a pathway for the exploration of intriguing orbital phenomena mediated by higher-band topology applicable to a broad spectrum of systems.

Exact transformation optics by using electrostatics

We present a novel method for designing transformation optical devices based on electrostatics.An arbi-trary transformation of electrostatic field can lead to a new refractive index distribution,where wave-fronts and energy flux lines correspond to equipotential surfaces and electrostatic flux lines,respectively.Owing to scalar wave propagating exactly following an eikonal equation,wave optics and geometric optics share the same solutions in the devices.The method is utilized to design multipole lenses derived from multipoles in electrostatics.The source and drain in optics are considered as corre-sponding to positive charge and negative charge in the static field.By defining winding numbers in vir-tual and physical spaces,we explain the reason for some multipole lenses with illusion effects.Besides,we introduce an equipotential absorber to replace the drain to correspond to a negative charge with a grounded conductor.Therefore,it is a very general platform to design intriguing devices based on the combination of electrostatics and transformation optics.

Topological and dynamical phase transitions in the Su–Schrieffer–Heeger model with quasiperiodic and long-range hoppings

Disorders and long-range hoppings can induce exotic phenomena in condensed matter and artificial systems.We study the topological and dynamical properties of the quasiperiodic SuSchrier-Heeger model with long-range hoppings.It is found that the interplay of quasiperiodic disorder and long-range hopping can induce topological Anderson insulator phases with nonzero winding numbers ω=1,2,and the phase boundaries can be consistently revealed by the divergence of zero-energy mode localization length.We also investigate the nonequilibrium dynamics by ramping the long-range hopping along two different paths.The critical exponents extracted from the dynamical behavior agree with the Kibble-Zurek mechanic prediction for the path with W=0.90.In particular,the dynamical exponent of the path crossing the multicritical point is numerical obtained as 1/6~0.167,which agrees with the unconventional finding in the previously studied XY spin model.Besides,we discuss the anomalous and non-universal scaling of the defect density dynamics of topological edge states in this disordered system under open boundary condictions.