INCOMMENSURATE AND COMMENSURATE PHASE TRANSITIONS IN Ti-Ni-Fe ALLOY

Measurements by using the ultrasonic technique together for electric resistance verified that the first sound velocity valley on cooling is mainly due to the soft-mode of driving the com- mensurate phase transition,and the second one due to the soft-mode of driving the martensitic transformation.The starting point,R_s,and finishing point,R_f,of the commensurate phase transition of the alloy have been determined.

The identification algorithm for commensurate order linear time-invariant fractional systems

An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at the same time. The basic idea is to change the system matrix into a diagonal one through basis transformation. This makes it possible to turn the system’s input-output relationships into the summation of several simple subsystems, and after the identification of these subsystems, the whole identification system is obtained which is algebraically equivalent to the former system. Finally an identification example verifies the effectiveness of the method previously mentioned.

Amplitude Oscillations of the Resonant Phenomena in a Frenkel-Kontorova Model with an Incommensurate Structure

Dynamical mode locking phenomena in incommensurate structures of the dc- and ac-driven overdamped FrenkelKontorova model are studied by molecular-dynamics simulations.It is found that the Shapiro steps exhibit significantly different amplitude and frequency dependences from the ones observed in the commensurate structures.The step widths still oscillate with the amplitude,but the form is no longer Bessel-like,i.e.,the anomaly appears in our simulations.The same type of anomalies is also exhibited by the critical depinning force.The oscillatory behavior and the anomalies are also revealed in the ((F),Fac) phase diagram where three phases are observed.These oscillations are directly correlated with the existence and the stability of interference phenomena in real systems.

Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model

Commensurate and incommensurate Haldane phases for a spin-1 bilinear-biquadratic model are investigated using an infinite matrix product state algorithm.The bipartite entanglement entropy can detect a transition point between the two phases.In both phases,the entanglement spectrum shows double degeneracy.We calculate the nonlocal order parameter of the bond-centered inversion in both phases,which rapidly approaches a saturation value of-1 as the segment length increases.The nonlocal order parameter of the bond-centered inversion with a saturation value-1 and the nonzero value string order indicate that the Haldane phase is a symmetry-protected topological phase.To distinguish the commensurate and incommensurate Haldane phases,the transversal spin correlation and corresponding momentum distribution of the structure factor are analyzed.As a result,the transversal spin correlations exhibit different decay forms in both phases.

Energy dissipation mechanism of commensurate graphene layers

The energy dissipation mechanism of graphene layers in commensurate contact is studied by molecular dynamics simulations.The commensurability between graphene layers is controlled by misfit angles between graphene layers or an in-plane strain applied to one of the graphene layers.We find that for small size graphene,the main energy dissipation is not caused by stick-slip.We propose two potential energy dissipation channels,the lattice distortion induced by the moirésuperlattice structure and variation of entropy of the contacting landscape.Our results provide an insight into the energy dissipation mechanism of commensurate contact graphene.

Commensurate stacking within confined ultramicropores boosting acetylene storage capacity and separation efficiency

Developing advanced porous materials possessing both a high storage capacity and selectivity for acetylene(C_(2)H_(2))remains challenging but a sought-after endeavor.Herein we show a strategy involving synergic combination of spatial confinement and commensurate stacking for enhanced C_(2)H_(2)storage and capture via maximizing the host–guest and guest–guest interactions.Two ultramicroporous metal-organic frameworks(MOFs),MIL-160 and MOF-303 are elaborately constructed to exhibit ultrahigh C_(2)H_(2)uptakes of 235 and 195 cm^(3)·g^(−1),respectively,due to the confinement effect of the suitable pore sizes and periodically dispersed molecular recognition sites.Specially,C_(2)H_(2)capacity of MIL-160 sets a new benchmark for C_(2)H_(2)storage.The exceptional separation performances of two materials for C_(2)H_(2)over both CO_(2)and ethylene(C_(2)H_(4)),which is rarely observed,outperform most of the benchmark materials for C_(2)H_(2)capture.We scrutinized the origins of ultrahigh C_(2)H_(2)loading in the confined channels via theoretical investigations.The superior separation efficiency for C_(2)H_(2)/CO_(2)and C_(2)H_(2)/C_(2)H_(4)mixtures with unprecedented C_(2)H_(2)trapping capacity(>200 L·kg^(−1))was further demonstrated by dynamic breakthrough experiments.

Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order systems

A Routh table test for stability of commensurate fractional degree polynomials and their commensurate fractional order systems is presented via an auxiliary integer degree polynomial. The presented Routh test is a classical Routh table test on the auxiliary integer degree polynomial derived from and for the commensurate fractional degree polynomial. The theoretical proof of this proposed approach is provided by utilizing Argument principle and Cauchy index. Illustrative examples show efficiency of the presented approach for stability test of commensurate fractional degree polynomials and commensurate fractional order systems. So far, only one Routh-type test approach [1] is available for the commensurate fractional degree polynomials in the literature. Thus, this classical Routh-type test approach and the one in [1] both can be applied to stability analysis and design for the fractional order systems, while the one presented in this paper is easy for peoples, who are familiar with the classical Routh table test, to use.

Direct fractional order MRAC adaptive control design for a class of fractional order commensurate linear systems

In this paper,we introduce a direct fractional order adaptive control design based on model reference adaptive control(MRAC)structure for a class of commensurate fractional order linear systems with an arbitrary relative degree,and whose parameters are unknown.By generalising the application of standard direct MRAC strategy to plants described by fractional order models,we develop a fractional adaptive control scheme(FOMRAC)based on the output feedback.We also define an adaptation control law ensuring the stability of the closed-loop system and the good tracking of the reference trajectory.The asymptotic stability of the fractional order control system is proven using an extension of the Lyapunov theorem.Simulation results show the effectiveness of the proposed control method even for plants with model parametric variations and additive noises.

On fractional discrete financial system:Bifurcation,chaos,and control

The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets.This paper introduces a new three-dimensional(3D)fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders.As such,we evaluate when the equilibrium points are stable or unstable at various fractional orders.We use many numerical methods,phase plots in 2D and 3D projections,bifurcation diagrams and the maximum Lyapunov exponent.These techniques reveal that financial maps exhibit chaotic attractor behavior.This study is grounded on the Caputo-like discrete operator,which is specifically influenced by the variance of the commensurate and incommensurate orders.Furthermore,we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy algorithm.Additionally,we offer nonlinear-type controllers to stabilize the fractional financial map.The numerical results of this study are obtained using MATLAB.

Prediction of the Hualian Earthquakes in Taiwan and an Extended Discussion on the Method of Commensurability

The method of commensurability was used by the authors to predict the great earthquake of magnitude 7.5 that occurred on March 31,2002 in Taiwan 70km away from Hualian. Analyzing the earthquakes of magnitude≥7.0 which occurred in the Hualian area of Taiwan within the 20th century, the authors discovered that the occurrences of the earthquakes are commensurable. The earthquakes of magnitude 7.6 which occurred in Hualian of Taiwan, on September 20th, 1999 and of magnitude 7.5 which occurred 70 km away from Hualian, on March 31th, 2002 appeared at the commensurable point of K=2 and the period times the golden section, respectively. An extended discussion is carried out on the method of commensurability and its implied physical significance, especially on the contribution of the commensurable periodic extension made by Prof. Weng Wenbo.

Multiscale mechanics of noncovalent interface in graphene oxide layered nanocomposites

Noncovalent interfaces play a vital role in inelastic deformation and toughening mechanisms in layered nanocomposites due to their dynamical recoverability. When interfacial engineering is applied to design layered nanocomposites, shear-lag analysis is usually implemented to evaluate the capability of interfacial loading transfer. Here, we introduce a multiscale shear-lag model that correlates macroscale mechanical properties with the molecular mechanisms to quantify the effects of interfacial configuration in graphene oxide(GO) layered nanocomposites. By investigating the mechanical responses of commensurate and incommensurate interfaces, we identify that the commensurate interface exhibits a pronounced size effect due to the nucleation and propagation of interfacial defects, whereas the incommensurate interface displays uniform deformation. Our predictions are further validated through large-scale molecular dynamics simulations for GO layered nanocomposites. This work demonstrates how size effects and interfacial configurations can be exploited to fabricate layered nanocomposites with superior mechanical properties despite relying on weak noncovalent interfaces.

微波集成公度线FET放大器的简化实频技术设计法

将简化实频技术发展用于具有公度线匹配网络的微波集成FET多级放大器的设计。勿需FFT的数学模型,勿需设定匹配网络的拓扑,按照通带内的噪声系数与传输增益指标要求可直接求得最佳的网络散射矩阵,据此即可综合公度线匹配网络。设计的实践证明此方法是适用于工程实际的。

Gas Source Molecular Beam Epitaxy Growth of Si_(1-x)Ge_x/Si Alloys

Strained SiGe alloys are successfully grown on Si(100) substrate in gas source molecular beam epitaxy system using disilane (Si 2H 6) and germane (GeH 4). The surface reconstructions are monitored by in situ reflection high energy electron diffraction during epitaxy. At a fixed substrate temperature, the Ge composition in the alloys increase with GeH 4/(GeH 4+2Si 2H 6) gas flow rate ratio. Surface morphologies of the grown samples show a strong dependence on the Ge composition, substrate temperature and SiGe epilayer thickness. Results indicate that high substrate temperature and large Ge composition are favorable for the growth mode transition from two dimensional to three dimensional growth.

Symmetry and tendency judgment of Ms≥8. 0 strong earthquakes in Chile

The Ms ≥ 8.0 strong earthquakes occurring in Chile since 1800 were analyzed using the ternary, quaternary, and quinary commensurability methods and the butterfly structure diagram, and it was believed that the earthquake signal in Chile in 2014 is relatively strong, a large earthquake is likely to occur in Chile in 2014. An analysis of spatial epicenter migrations showed that the longitudinal and latitudinal epicenter migra- tions have symmetry and synchronism, and there were five obvious northward migrations and four southward migrations. The symmetry axis of the longitudinal migrations is at about 71.7°W and that of the latitudinal mi- grations is at about 30°S; these spatial symmetry axes are located at the subduction zone on the western margin of South America, where two major plates （the Nazca Plate and the South American Plate） converge.

On Fundamentals Predicting Floods-Landslides

Based on the floods landslides commensurability system, the paper presents and discusses the disasters/hazards with comprehensive interaction and erosional processes. However, people are not enough to get their possibility for the sustainability. They have had so many disasters to meet and to control continuously. Finally, the fundamentals should be built up with nonlinear solutions of landsliding problems; the events of geomagnetism anomaly should be considered.

Spatiotemporal characteristics and trend assessment of Ms≥5.6 earthquakes in the Tianshan area of China based on co-occurrence analysis and commensurability

Based on the complete seismic data of the Tianshan area in the past 118 years,the co-occurrence rate of earthquakes in different fault zones is calculated,the fault zone with the highest associative degree in the Tianshan area is determined as the research object,extracted the earthquake time series information of the strong associative fault zone and the commensurability method is used to obtain the commensurability expression,the year of strongest earthquake signal is calculated and predicted,then the butterfly structure diagram and commensurability structure system are drawn.Combined the butterfly structure diagram and commensurability structure system to analyze the seismic spatiotemporal structure characteristics of the Tianshan area,judge the trend of future earthquakes,and predict the time of future earthquakes.The results demonstrate that Ms≥5.6 earthquake signals are strong in 2020 and 2021.In order to determine the location of future earthquakes,the historical epicenter migration law of the strongly correlated fault zone in the Tianshan area is analyzed.It is revealed that the epicenter distribution is symmetric in both the longitude and latitude directions.Analyzing the spatial distribution of epicenters,the five successive earthquakes in the strong associative fault zone in the Tianshan area present a pentagonal symmetrical structure in space.It is judged that the next earthquake will migrate toward the northeast.Additionally,the sunspot has a strong seismic correlation with the strong associative fault zone in the Tianshan area.Specifi cally,on the 11-year cycle scale of sunspot activity,64.71% of earthquakes occurred in the fluctuation descending range;on the monthly scale of sunspot activity.Hence,it has been verified that the proposed disaster prediction method based on commensurability theory is scientifi c and has a broad application prospect.

Application of Commensurability in Earthquake Prediction

This article introduces application of the expanding commensurability in earthquake prediction. The results show that most of the world’s major earthquake occurred at their commensurable points of time axis. An EQ 7.0 occurred in Lushan of China on 2013-04-20 and an EQ 8.2 occurred in Iquique of northern Chile on 2014-04-01 all occurred at their commensurable points of time axis. This once again proves that the commensurability provides an important scientific basis for the prediction of major earthquakes, which will occur in the area in future.

Generation and Propagation of Ultrasonic Waves in Piezoelectric Graphene Nanoribbon

Generation and propagation of ultrasonic waves in single layer Graphene Nanoribbon is studied using semi-classical approach. When piezoelectric Graphene Nanoribbon (GNR) is exposed to time varying light beam, ultrasonic waves are produced which propagate in the medium. At low frequencies, we observed oscillations of the ultrasonic observables, velocity change and attenuation which are characteristics of massless Dirac fermions in graphene. Exploiting this oscillatory behavior, we estimate graphene’s electronic mobility to be around . Propagating ultrasonic waves can be amplified, depending on the electric field amplitude. Specifically, amplification occurs when drift velocity exceeds sound velocity. This scheme can be employed for efficient ultrasonic amplifier device operation.

How to bridge China and Africa culturally?—New clues from the commensurability of Asiancentricity and Afrocentricity

With the frequent economic cooperation and the cultural communication from China to Africa focusing on foreign policies and economic efforts is insufficient.Because culture-oriented investigations make more contributions to the development of the pan-cultural exchange,and they complement general culture inquiries.Chinese philosophies are very representative for Asiancentricity.The reason why is that a common key of the Asian values,beliefs,and worldviews which exceed many philosophies and religions,like Confucianism,Buddhism,Taoism.Secondly,the aspects of ontology,epistemology and axiology of Asiancentricity and Afrocentricity are quite similar.This can also be understood as commensurability existing in Chinese and African philosophies in some ways.In Chinese philosophy,everything and everyone can become valuable in relationships with others,and the myriad becomes perceivable and meaningful.In the meantime,conforming to the fundamental principles of the Asiancentricity perspectives,all of the elements in the universe,including animals,human beings,natural phenomena and inanimate objects,are connected with each other.Both of two philosophies emphasise the importance of being communal and harmony,rather than emphasising the characteristics of ego and individualism.Although,Asiancentricity and Afrocentricity are not totally common and universal,they do have enumerable commensurable factors and are embedded in the communicative and cultural particularities.

Quantization of Particle Energy in the Analysis of the Boltzmann Distribution and Entropy

The Boltzmann equilibrium distribution is an important rigorous tool for determining entropy, since this function cannot be measured, but only calculated in accordance with Boltzmann＇s law. On the basis of the commensuration coefficient of discrete and continuous similarly-named distributions developed by the authors, the article analyses the statistical sum in the Boltzmann distribution to the commensuration with the improper integral of the similarly-named function in the full range of the term of series of the statistical sum at the different combination of the temperature and the step of variation （quantum） of the particle energy. The convergence of series based on the Cauchy, Maclaurin criteria and the equal commensuration of series and improper integral of the similarly-named function in each unit interval of variation of series and similarly-named function were estab- lished. The obtained formulas for the commensuration coefficient and statistical sum were analyzed, and a general expres- sion for the total and residual statistical sums, which can be calculated with any given accuracy, is found. Given a direct calculation formula for the Boltzmann distribution, taking into account the values of the improper integral and commensuration coefficient. To determine the entropy from the new expression for the Boltzmann distribution in the form of a series, the conver- gence of the similarly-named improper integral is established. However, the commensuration coefficient of integral and series in each unit interval turns out to be dependent on the number of the term of series and therefore cannot be used to determine the sum of series through the improper integral. In this case, the entropy can be calculated with a given accuracy with a corresponding quantity of the term of series n at a fixed value of the statistical sum. The given accuracy of the statistical sum turns out to be mathematically identical to the fraction of particles with an energy exceeding a given level of the energy barrier equal to the activation energy in the Arrhenius equation. The prospect of development of the proposed method for expressing the Boltzmann distribution and entropy is to establish the relationship between the magnitude of the energy quantum Ae and the properties of the system-forming particles.