RKKY interaction in helical higher-order topological insulators

We theoretically investigate the Ruderman–Kittel–Kasuya–Yosida(RKKY) interaction in helical higher-order topological insulators(HOTIs), revealing distinct behaviors mediated by hinge and Dirac-type bulk carriers. Our findings show that hinge-mediated interactions consist of Heisenberg, Ising, and Dzyaloshinskii–Moriya(DM) terms, exhibiting a decay with impurity spacing z and oscillations with Fermi energy εF. These interactions demonstrate ferromagnetic behaviors for the Heisenberg and Ising terms and alternating behavior for the DM term. In contrast, bulk-mediated interactions include Heisenberg, twisted Ising, and DM terms, with a conventional cubic oscillating decay. This study highlights the nuanced interplay between hinge and bulk RKKY interactions in HOTIs, offering insights into designs of next-generation quantum devices based on HOTIs.

Control system design for a pressure-tube-type supercritical water-cooled nuclear reactor via a higher order sliding mode method

Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.

Tunneling dynamics of Bose-Einstein condensates with higher-order interactions in optical lattice

The nonlinear Landau Zener tunneling and nonlinear Rabi oscillations of Bose-Einstein condensate （BEC） with higher-order atomic interaction between the Bloch bands in an accelerating optical lattice are discussed. Within the two-level model, the tunneling probability of BEC with higher-order atomic interaction between Bloch bands is obtained. We finds that the tunneling rate is closely related to the higher-order atomic interaction. Furthermore, the nonlinear Rabi oscillations of BEC with higher-order atomic interaction between the bands are discussed by imposing a periodic modulation on the level bias. Analytical expressions of the critical higher-order atomic interaction for suppressing/enhancing the Rabi oscillations are obtained. It is shown that the critical value strongly depends on the modulation parameters （i.e., the modulation amplitude and frequency） and the strength of periodic potential.

Record-Breaking Frequency of 44 GHz Based on the Higher Order Mode of Surface Acoustic Waves with LiNbO_(3)/SiO_(2)/SiC Heterostructures

Surface acoustic wave (SAW) technology has been extensively explored for wireless communication, sensors, microfluidics, photonics, and quantum information processing. However, due to fabrication issues, the frequencies of SAW devices are typically limited to within a few gigahertz, which severely restricts their applications in 5G communication, precision sensing, photonics, and quantum control. To solve this critical problem, we propose a hybrid strategy that integrates a nanomanufacturing process (i.e., nanolithography) with a LiNbO_(3)/SiO_(2)/SiC heterostructure and successfully achieve a record-breaking frequency of about 44 GHz for SAW devices, in addition to large electromechanical coupling coefficients of up to 15.7%. We perform a theoretical analysis and identify the guided higher order wave modes generated on these slow-on-fast SAW platforms. To demonstrate the superior sensing performance of the proposed ultra-high-frequency SAW platforms, we perform micro-mass sensing and obtain an extremely high sensitivity of approximately 33151.9 MHz·mm2·μg−1, which is about 1011 times higher than that of a conventional quartz crystal microbalance (QCM) and about 4000 times higher than that of a conventional SAW device with a frequency of 978 MHz.

A higher-order porous thermoelastic problem with microtemperatures

In this paper,we study a porous thermoelastic problem with microtemperatures assuming parabolic higher order in time derivatives for the thermal variables.The model is derived and written as a coupled linear system.Then,a uniqueness result is proved by using the logarithmic convexity method in the case that we do not assume that the mechanical energy is positive definite.Finally,the existence of the solution is obtained by introducing an energy function and applying the theory of linear semigroups.

Error Analysis of A New Higher Order Boundary Element Method for A Uniform Flow Passing Cylinders

A higher order boundary element method(HOBEM)is presented for inviscid flow passing cylinders in bounded or unbounded domain.The traditional boundary integral equation is established with respect to the velocity potential and its normal derivative.In present work,a new integral equation is derived for the tangential velocity.The boundary is discretized into higher order elements to ensure the continuity of slope at the element nodes.The velocity potential is also expanded with higher order shape functions,in which the unknown coefficients involve the tangential velocity.The expansion then ensures the continuities of the velocity and the slope of the boundary at element nodes.Through extensive comparison of the results for the analytical solution of cylinders,it is shown that the present HOBEM is much more accurate than the conventional BEM.

Identification of the Wave-Particles Interaction in Space Plasma Using Higher-Order Statistics

The interaction of wave-particles and wave-wave in the space plasmas are essentially non-linear or non-Gaussian processes. Using the higher-order statistical analyses methods (higher-order moments and bi-tri correlation or bi-tri spectrum), its physical properties can be described. The question addressed in this paper is that of the usefulness of higher-order statistical analysis for identification of the wave-particles interaction in space plasmas. The signals handled are from the ARCAD-3 ISOPROBE experiment on ELF frequency range, then strong electrostatic turbulence and electron density irregularities. Second and third order statistical analyses are applied: first, on time series associated with each type of measurement, then, on the two types. All results are presented for one typical case. Correlation functions estimated over the corresponding time intervals point out the existence of a, non-linear interaction between these fluctuations and electrostatic filed.

Galerkin-Bernstein Approximations for the System of Third-Order Nonlinear Boundary Value Problems

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical formulations in matrix form, in detail, by exploiting Bernstein polynomials as basis functions. A reasonable accuracy is found when the proposed method is used on few examples. At the end of the study, a comparison is made between the approximate and exact solutions, and also with the solutions of the existing methods. Our results converge monotonically to the exact solutions. In addition, we show that the derived formulations may be applicable by reducing higher order complicated BVP into a lower order system of BVPs, and the performance of the numerical solutions is satisfactory. .

High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations

In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.

HIGHER ORDER SPECTRA AND ITS APPLICATION IN MACHINERY FAULT DIAGNOSIS

The application of higher order spectra to machinery faults diagnosis is studied in this paper.A brief review of bispectra is presented,and more emphasis is placed on the ability of higher order spectra to extract diagnostic information from fault signals.Furthermore,by use of the algorithm of higher order spectra,two kinds of typical mechanical faults are analyzed.Results show that the high order spectra analysis is a more efficient method in machinery diagnosis compared with the FFT based spectral analysis.

TheValueOrderof“Love”inTeacher-StudentInteraction：anExplorationintoTeachers’LoveGenerationMachanismBasedonHuoMaozhengandSiXia’SLovePractice

“师爱”是教育成功的前提，是优秀教师的核心价值品质；同时，“师爱”也是教育理论界研究的热点问题之一。但是理论界对“师爱”的认识比较模糊、研究缺乏深度，特别是对其发生机制的研究更少。著名的情感现象学家舍勒认为，在整个价值王国中，价值的相互关系具有一定的“级序”。根据这一理论，如果一个价值比另一个价值“更高”或“更低”，那么，就形成了价值秩序。价值秩序是支配一个人行为的价值品质秩序。爱作为师生交往的核心价值，教师爱的行为同样受爱的价值秩序的支配。从国内“师爱”名师霍懋征和斯霞的“师爱”实践来看，“师爱”的发生机制具有层次性或秩序性，它依次呈现为人性之爱、教育之爱，以及学生种种具体的爱，如公正、尊重等。

PARTIAL REGULARITY FOR MINIMIZERS OF HIGHER ORDER QUASICONVEX FUNCTIONALS

We consider the following quasiconvex functional I(u)=∫ Gf(x,δu,D mu) d x where u is a vector valued function in W m,p (G),m>1 and p>2. The partial C m,a —regularity is proved for minimizers of I(u) under weaker conditions.

Application of Scaffolding Theory to Higher Vocational Students Classroom Interaction in English Teaching

Scaffolding theory is one of the mature teaching methods of constructivism model . The effective interaction between teachers and students is one characteristic of scaffold teaching. This paper aims at combining scaffolding theory with classroom interaction in teaching higher vocational students English to help students arouse interest and enhance their comprehensive ability in English learning.

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Higher order aberration comparison between two aspherical intraocular lenses: MC6125AS and Akreos advanced optics

AIM: To compare higher order aberrations in two aspherical intraocular lenses(IOLs): Akreos advanced optics(AO) and Dr. Schmidt Microcrystalline 6125 aspheric anterior surface(MC6125AS) with each other. METHODS: Forty eyes of 39 patients underwent phacoemulsification and Akreos AO and MC6125 AS were implanted in their eyes in a random manner. Three months post-operatively, higher order aberrations including spherical aberration, coma aberration, and total aberrations were measured and compared.RESULTS: The total aberration was 0.24±0.17 in eyes with Dr. Schmidt and 0.20 ±0.01 in eyes with Akreos AO(P =0.361). The mean of coma aberration was 0.17 ±0.21 and 0.09 ±0.86 in Dr. Schmidt and Akreos lenses,respectively(P =0.825). Total spherical aberration was almost the same in both groups(mean: 0.05, P =0.933).Best corrected visual acuity in Akreos AO(0.10±0.68) and Dr. Schmidt(0.09±0.67) did not differ significantly(P =0.700). CONCLUSION: There is no statistically significant difference in the higher order aberrations between these two aspherical lenses.

HIGHER ORDER SPECTRAL ANALYSIS IN FAULT DIAGNOSIS OF ROTORS

The nonlinear properties of rotating machinery vibration signals are presented. The relationship between faults and quadratic phase coupling is discussed. The mechanism that gives rise to quadratic phase coupling is analyzed, and the coupling models are summarized. As a result, higher order spectra analysis is introduced into fault diagnosis of rotors. A brief review of the properties of higher order spectra is presented. Furthermore, the bicoherence spectrum is employed to extract the features that signify the machinery condition. Experiments show that bicoherence spectrum patterns of different faults are quite different, so it is proposed to identify the faults in rotors.

SINGULAR INTEGRAL EQUATIONS ALONG AN OPEN ARC WITH SOLUTIONS HAVING SINGULARITIES OF HIGHER ORDER

In this paper, the difficulties on calculation in solving singular integral equations are overcome when the restriction of curve of integration to be a closed contour is cancelled. When the curve is an open arc and the solutions for singular integral equations possess singularities of higher order, the solution and the solvable condition for characteristic equations as well as the generalized Noether theorem for complete equations are given.

Visual function and higher order aberration after implantation of aspheric and spherical multifocal intraocular lenses:a meta-analysis

AIMTo assess the visual outcomes of aspheric multifocal intraocular lenses (IOLs) compared with spherical multifocal IOL after cataract surgery.

Generalizations of Euler Numbers and Euler Numbers of Higher Order

The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended.

HIGHER ORDER SINGULAR INTEGRAL EQUATIONS ON COMPLEX HYPERSPHERE

A theory of a class of higher order singular integral under the operator （L f） （u） =[u1 σf/σu1（u） - u1σf/σu1（u） ＋ f（u）] is given. We transform the higher order singular integral to a usual Cauchy integral, extend the permutation formula of the higher order singular integral deduced by Qian and Zhong in [4] to a general case, and discuss the regularization problem of the higher order singular integral equations with Cauchy kernel and variable coefficients on complex hypersphere.