Noise-induced phase transition in the Vicsek model through eigen microstate methodology

This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of socialanimals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noiseremains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and nonequilibriumstates, the eigen microstate method is employed here for a quantitative examination of the phase transitions inthe Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phasetransitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for thesephase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions withescalation of population density.

A transition method based on Bezier curve for trajectory planning in cartesian space

In order to smooth the trajectory of a robot and reduce dwell time,a transition curve is introduced between two adjacent curves in three-dimensional space.G2 continuity is guaranteed to transit smoothly.To minimize the amount of calculation,cubic and quartic Bezier curves are both analyzed.Furthermore,the contour curve is characterized by a transition parameter which defines the distance to the corner of the deviation.How to define the transition points for different curves is presented.A general move command interface is defined for receiving the curve limitations and transition parameters.Then,how to calculate the control points of the cubic and quartic Bezier curves is analyzed and given.Different situations are discussed separately,including transition between two lines,transition between a line and a circle,and transition between two circles.Finally,the experiments are carried out on a six degree of freedom(DOF) industrial robot to validate the proposed method.Results of single transition and multiple transitions are presented.The trajectories in the joint space are also analyzed.The results indicate that the method achieves G2 continuity within the transition constraint and has good efficiency and adaptability.

Transition probabilities for NII 2p4f-2p3d and 2s2p^23d-2s2p^23p obtained by a semiclassical method

Based on NII spectra, some transition probabilities for 2p4f-2p3d and 2s2p23d-2s2p23p are obtained by a semi- classical method. The results are in good agreement with other measurements and the data reported by the National Institute of Standards and Technology. The transition probability for a line of 424.18nm is reported for the first time. Meanwhile, a feasible method of calculating transition parameters related to special excited configurations or highly excited states is provided.

A circular zone counting method of identifying a Duffing oscillator state transition and determining the critical value in weak signal detection

Identifying state transition and determining the critical value of the Duffing oscillator are crucial to indicating external signal existence and have a great influence on detection accuracy in weak signal detection. A circular zone counting （CZC） method is proposed in this paper, by combining the Duffing oscillator＇s phase trajectory feature and numerical calculation for quickly and accurately identifying state transition and determining the critical value, to realize a high- efficiency weak signal detection. Detailed model analysis and method construction of the CZC method are introduced. Numerical experiments into the reliability of the proposed CZC method compared with the maximum Lyapunov exponent （MLE） method are carried out. The CZC method is demonstrated to have better detecting ability than the MLE method, and furthermore it is simpler and clearer in calculation to extend to engineering application.

Size transition of spiral waves using the pulse array method

The domain size of spiral waves is an important issue in studies of two-dimensional （2D） spatiotemporal patterns. In this work, we use the 2D complex Ginzburg-Landau equation （CGLE） as our model and find that an initially big spiral can successfully transfer to several small spirals by applying a pulse array method. The impacts of several important factors, such as array density, controlling intensity and pulsing time, are investigated. This control approach may be useful for the control of 2D spatiotemporal patterns and has potential applications in the control of some realistic systems, such as meteorological and cardiac systems.

Solidification process and microstructure of transition layer of Cu-Al composite cast prepared by method of pouring molten aluminum

The Cu?Al composite casts were prepared by the method of pouring molten aluminum. The solidification process and themicrostructure of the transition layer were investigated during the recombination process of the liquid Al and the solid Cu. The results reveal that the microstructure of the transition layer in the Cu?Al composite cast consists of α(Al)+α(Al)?CuAl2 eutectic,α(Al)?CuAl2 eutectic, CuAl2+α(Al)?CuAl2 eutectic and Cu9Al4. Additionally, the pouring temperature, cooling mode of the Cu platesurface and start time of the forced cooling after pouring have no effect on the microstructure species. But the proportion of thevarious microstructures in the transition layer changes with the process parameters. The pure Al at the top of the transition layer startsto solidify first and then the α(Al) phase grows in a dendritic way, while the CuAl2 phase exhibits plane or cellular crystal growth from the two sides of the transition layer towards its interior. The stronger the cooling intensity of the Cu plate outer surface, the more developed the dendrite, and the easier it is for the CuAl2 phase to grow into a plane crystal.

Numerical Verification of Transition’s Energies of Excitons in Quantum Well of ZnO with the Finite Difference Method

This paper shows that the experimental results of quantum well energy transitions can be found numerically. The cases of several ZnO-ZnMgO wells are considered and their excitonic transition energies were calculated using the finite difference method. In that way, the one-dimensional Schrödinger equation has been solved by using the BLAS and LAPACK libraries. The numerical results are in good agreement with the experimental ones.

Transitional methodologies of the second language grammar teaching in middle schools

Grammar teaching recently faces lots of problems not only in the teaching methods but also in its position it deserves. Through analyzing the importance and the confronting problems of grammar teaching in middle schools, the paper will do the further research on the methodologies in the transitional time and will surely conclude the theories that can direct teaching process.

High-Order Decoupled and Bound Preserving Local Discontinuous Galerkin Methods for a Class of Chemotaxis Models

In this paper,we explore bound preserving and high-order accurate local discontinuous Galerkin(LDG)schemes to solve a class of chemotaxis models,including the classical Keller-Segel(KS)model and two other density-dependent problems.We use the convex splitting method,the variant energy quadratization method,and the scalar auxiliary variable method coupled with the LDG method to construct first-order temporal accurate schemes based on the gradient flow structure of the models.These semi-implicit schemes are decoupled,energy stable,and can be extended to high accuracy schemes using the semi-implicit spectral deferred correction method.Many bound preserving DG discretizations are only worked on explicit time integration methods and are difficult to get high-order accuracy.To overcome these difficulties,we use the Lagrange multipliers to enforce the implicit or semi-implicit LDG schemes to satisfy the bound constraints at each time step.This bound preserving limiter results in the Karush-Kuhn-Tucker condition,which can be solved by an efficient active set semi-smooth Newton method.Various numerical experiments illustrate the high-order accuracy and the effect of bound preserving.

Calculation of Electronic Structure of Anatase TiO_2 Doped with Transition Metal V,Cr,Fe and Cu Atoms by the Linearized Augmented Plane Wave Method

The electronic density of states and band structures of doped and un-doped anatase TiO2 were studied by the Linearized Augmented Plane Wave method based on the density functional theory. The calculation shows that the band structures of TiO2 crystals doped with transition metal atoms become narrower. Interesting, an excursion towards high energy level with increasing atomic number in the same element period could be observed after doping with transition metal atoms.

Preliminary Estimation of Paleoproductivity via TOC and Habitat Types:Which Method Is More Reliable?—A Case Study on the Ordovician-Silurian Transitional Black Shales of the Upper Yangtze Platform, South China

New total organic carbon （TOC） data from the two Ordovician-Silurian transitional graptolite-bearing black shale intervals, the Wufeng （五峰） Formation and the Longmaxi （龙马溪） Formation in Central Guizhou （贵州） and West Hubei （湖北）, respectively, as well as previously reported TOC data from the same intervals in other places on the Yangtze platform of South China, have been used to produce an initial estimate of the primary paleoproductivity via a conventional inverse method （i.e., Rpp.inverse）. The values of the Rpp.inverse are estimated to be 32 （43-21） gC/（m^2·a）（Wufeng Formation） and 21 （27-16） gC/（m^2·a） （Longmaxi Formation）. Also, simultaneously, the habitat types （i.e., HT; cf., BA： benthic assemblage） and their temporal and spatial changes have been documented from the same succession, and an initial estimate of the primary paleoproductivity has been produced using a forward method （i.e., Rpp-forward） Beingbounded mainly by the peritidal to inner-shelf environment shelly-facies or mixed-facies successions with BA1 to BA3 faunas both at the top and the base, which indicates the habitat types from HT Ⅱ to HT Ⅲ2, the biohabitat type of the two graptolite-bearing black shale intervals can be limited to HT III to HT IV, corresponding to the inner shelf to the outer shelf, with depths from roughly 60 m to 200-300 m. Based on the current data from the South China Sea and the southern part of the East China Sea, values of Rpp-forward should be about 100 to 400 gC/（m^2·a）. The difference in the results via the two methods suggests that paleoproductivity estimates from the geological strata need to be made cautiously, with particular attention paid to the paleogeographic setting, oxic-anoxic conditions, as also the preservation factor of organic carbon.

Preparation of hydro-sodalite from fly ash using a hydrothermal method with a submolten salt system and study of the phase transition process

Hydro-sodalites are zeolitic materials with a wide variety of applications.Fly ash is an abundant industrial solid waste,rich in silicon and aluminum,from which hydro-sodalite can be synthesized.However,traditional hydrothermal synthesis methods are complex and cannot produce high-purity products.Therefore,there is a demand for processing routes to obtain high-purity hydro-sodalites.In the present study,high-purity hydro-sodalite(90.2 wt%)was prepared from fly ash by applying a hydrothermal method to a submolten salt system.Samples were characterized by powder X-ray diffraction(XRD),scanning electron microscopy(SEM),thermogravimetry and differential thermal analysis(TG–DTA),and Fourier transform infrared spectroscopy(FTIR)to confirm and quantify conversion of the raw material into the product phase.Purity of the samples prepared with an H2O/Na OH mass ratio of 1.5 and an H2O/fly ash mass ratio of 10 was calculated and the conversion process of the product phase was studied.Crystallinity of the product was influenced more by the Na OH concentration,less by the H2O/fly ash mass ratio.The main reaction process of the system is that the Si O ions produced by dissolution of the vitreous body in the fly ash and Na+ions in the solution reacted on the destroyed mullite skeleton to produce hydro-sodalite.This processing route could help mitigate processing difficulties,while producing high-purity hydro-sodalite from fly ash.

A new method for computing laminar-turbulent transition and turbulence in compressible boundary layers—PSE+DNS

A new method for computing laminar-turbulent transition and turbulence in compressible boundary layers is proposed. It is especially useful for computation of laminar-turbulent transition and turbulence starting from small-amplitude disturbances. The laminar stage, up to the beginning of the breakdown in laminar-turbulent transition, is computed by parabolized stability equations （PSE）. The direct numerical simulation （DNS） method is used to compute the transition process and turbulent flow, for which the inflow condition is provided by using the disturbances obtained by PSE method up to that stage. In the two test cases including a subsonic and a supersonic boundary layer, the transition locations and the turbulent flow obtained with this method agree well with those obtained by using only DNS method for the whole process. The computational cost of the proposed method is much less than using only DNS method.

An Improved Method for Estimating the Transition Probability Using Diameter Growth in Even-aged Forest Stands

The method of Zeng et al. (1991) employed diameter growth to estimate the transition probability of the matrix model in uneven-aged forest stands. In this paper the Weibull distribution for even-aged forest stands instead of uniform distribution chosen by Zeng is used. By comparing the results of the improved method with those of the original method of Zeng, it turns out that the improved method of Zeng given in this paper is more efficient.

Optimal precursors of double-gyre regime transitions with an adjoint-free method

In this paper, we find the optimal precursors which can cause double-gyre regime transitions based on conditional nonlinear optimal perturbation (CNOP) method with Regional Ocean Modeling System (ROMS). Firstly, we simulate the multiple-equilibria regimes of double-gyre circulation under different viscosity coefficient and obtain the bifurcation diagram, then choose two equilibrium states (called jet-up state and jet-down state) as reference states respectively, propose Principal Component Analysis-based Simulated Annealing (PCASA) algorithm to solve CNOP-type initial perturbations which can induce double-gyre regime transitions between jet-up state and jet-down state. PCASA algorithm is an adjoint-free method which searches optimal solution randomly in the whole solution space. In addition, we investigate CNOP-type initial perturbations how to evolve with time. The results show:(1) the CNOP-type perturbations present a two-cell structure, and gradually evolves into a three-cell structure at predictive time;(2) by superimposing CNOP-type perturbations on the jet-up state and integrating ROMS, double-gyre circulation transfers from jet-up state to jet-down state, and vice versa, and random initial perturbations don't cause the transitions, which means CNOP-type perturbations are the optimal precursors of double-gyre regime transitions;(3) by analyzing the transition process of double-gyre regime transitions, we find that CNOP-type initial perturbations obtain energy from the background state through both barotropic and baroclinic instabilities, and barotropic instability contributes more significantly to the fast-growth of the perturbations. The optimal precursors and the dynamic mechanism of double-gyre regime transitions revealed in this paper have an important significance to enhance the predictability of double-gyre circulation.

A gait generation and transition method for quadruped walking machine

In nature, quadrupeds as horses or cats change their gait to be suited to their motion speed. This fact is very important to realize smooth motion with different gaits. In this article a method of the gait transition for the quadruped walking machine is proposed. With analyzing the accustomed gaits of quadruped, some standard gaits and the relationships between duty factor and the phasic differences of the legs corresponding to the first leg could be concluded. With this, the gaits transferring could be continuous. Besides, celerity and on line method for generation and modifying gaits is studied, which can make the robot have a smooth motion to adapt the uncharted rough terrain.

Solving Energy Levels for SSH Hamiltonian Describing Peierls Phase Transition by Virtue of Invariant Eigen-operator Method

We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.

AN EMBEDDED BOUNDARY METHOD FOR ELLIPTIC AND PARABOLIC PROBLEMS WITH INTERFACES AND APPLICATION TO MULTI-MATERIAL SYSTEMS WITH PHASE TRANSITIONS

The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems.

Test for random in electrical signals time series of CO_2 short circuit transition welding process by the method of surrogate data

This paper introduced the basic theory and algorithm of the surrogate data method, which proposed a rigorous way to detect the random and seemingly stochastic characteristics in a system. The Gaussian data and the Rossler data were used to show the availability and effectivity of this method. According to the analysis by this method based on the short-circuiting current signals under the conditions of the same voltage and different wire feed speeds, it is demonstrated that the electrical signals time series exhibit apparently randomness when the welding parameters do not match. However, the electrical signals time series are deterministic when a match is found. The stability of short-circuiting transfer process could be judged exactly by the method of surrogate data.