Ground-state phase diagram,symmetries,excitation spectra and finite-frequency scaling of the two-mode quantum Rabi model

We investigate the two-mode quantum Rabi model(QRM)describing the interaction between a two-level atom and a two-mode cavity field.The quantum phase transitions are found when the ratioηof transition frequency of atom to frequency of cavity field approaches infinity.We apply the Schrieffer–Wolff(SW)transformation to derive the low-energy effective Hamiltonian of the two-mode QRM,thus yielding the critical point and rich phase diagram of quantum phase transitions.The phase diagram consists of four regions:a normal phase,an electric superradiant phase,a magnetic superradiant phase and an electromagnetic superradiant phase.The quantum phase transition between the normal phase and the electric(magnetic)superradiant phase is of second order and associates with the breaking of the discrete Z_(2) symmetry.On the other hand,the phase transition between the electric superradiant phase and the magnetic superradiant phase is of first order and relates to the breaking of the continuous U(1)symmetry.Several important physical quantities,for example the excitation energy and average photon number in the four phases,are derived.We find that the excitation spectra exhibit the Nambu–Goldstone mode.We calculate analytically the higher-order correction and finite-frequency exponents of relevant quantities.To confirm the validity of the low-energy effective Hamiltonians analytically derived by us,the finite-frequency scaling relation of the averaged photon numbers is calculated by numerically diagonalizing the two-mode quantum Rabi Hamiltonian.

The Theoretical Foundation and its Mode Transformation of Rural Public Goods Supply in the Perspective of Organizational Competition

Theoretical expositions of public goods supply by the liberalism,new institutionalism and the school of public choice are conducted in the perspective of organizational competition.And the theoretical foundation of rural public goods is put forward.Then,the changes of the supply mode of rural public goods are discussed before and after the tax reform,that is,the "Community Cooperation" supply mode of rural public goods before the tax reform and the "Organization Cooperation" supply mode of rural public goods after the tax reform.Finally,the diversification of rural public goods supply in China in future is forecasted.

Transformation of the Growth Mode:What Must Be Changed?

That the Chinese economy has been burgeoning for nearly 30 years is an irrefutable fact.However,this robust growth has been achieved amidst accusations of"extensive"development and"low-efficiency".Many scholars believe that low-priced labour is pivotal to China’s rapid growth.Even so,we find it hard to explain why China has been able to achieve sustained growth while so many countries with even lower labour costs remain trapped in poverty The following article offers a new perspective upon this paradox.

Transformation of alkali and alkaline-earth metals during coal oxy-fuel combustion in the presence of SO_2 and H_2O

The occurrence modes of alkali and alkaline-earth metals（AAEMs） in coal relate to their release behavior and ash formation during combustion. To better understand the transformation of AAEMs,the release behavior of water-soluble,HCl-soluble,HCl-insoluble AAEMs during Shenmu coal（SM coal） oxy-fuel combustion in the presence of SO2 and H2O in a drop-tube reactor was investigated through serial dissolution using H2O and HCl solutions. The results show that the release rates of AAEMs increase with an increase in temperature under the three atmospheres studied. The high release rates of Mg and Ca from SM coal are dependent on the high content of soluble Mg and Ca in SM coal. SO2 inhibits the release rates of AAEMs,while H2O promotes them. The effects of SO2 and H2O on the Na and K species are more evident than those on Mg and Ca species. All three types of AAEMs in coal can volatilize in the gas phase during coal combustion. The W-type AAEMs release excessively,whereas the release rates of I-type AAEMs are relatively lower. Different types of AAEM may interconvert through different pathways under certain conditions. Both SO2 and H2O promote the transformation reactions. The effect of SO2 was related to sulfate formation and the promotion by H2O occurs because of a decrease in the melting point of the solid as well as the reaction of H2O.

Mode Recognition of Lamb Wave Detecting Signals in Metal Plate Using the Hilbert-Huang Transform Method

The dispersion and multiple modes characteristics which exist in the propagation of Lamb waves (LW) in metal plates make it extremely hard to analyze and recognize the detection echo signals of defects. As a newly developed time-frequency analysis method in recent years, Hilbert-Huang transform (HHT) is one of the powerful tools to analyze non-stationary signals. The experimental LW detecting system for single aluminum plate is setup in this work, and the LW detecting signals are analyzed by HHT. The overlapped LW detecting signals of different modes are recognized by the means of extracting flight time of intrinsic mode functions (IMFs) after Hilbert transform (HT). The experiment results, agreeing well with the theoretical analysis, indicate that the HHT method can clearly recognize overlapped LW detecting signals of different modes in metal plates, but could hardly recognize that of the same mode. HHT can be an effective method to recognize LW detecting signals of different modes in metal plates.

Extraction of mode shapes of beam-like structures from the dynamic response of a moving mass

This paper proposes an approach to extract the mode shapes of beam-like structures from the dynamic response of a moving mass. When a mass passes through a beam containing several artificially installed humps, its vertical acceleration can be recorded. After applying fast Fourier transformation to the dynamic response, one can extract the mode shapes of the beam. The surface roughness was neglected compared to the humps and its adverse effect on the extraction was reduced. The passing mass performs as both “exciter” and “massage receiver”;therefore, this method requires only one single accelerometer, making it more convenient and time saving in practice. Moreover, to estimate the possible error in extracting mode shapes, a wavenumber domain filtering technique is used to reconstruct the general profiles of mode shapes. Experimental validation of this approach in laboratory scale was conducted. The experimental results show that the proposed method performs well in extracting lower order mode shapes. It should also be noted that the passing mass can not have a very high velocity (e.g. 80 mm/s), otherwise the mass may jump and separate from the beam, and the proposed method may fail to identify mode shapes.

Comprehensive Reliability Allocation Method for CNC Lathes Based on Cubic Transformed Functions of Failure Mode and Effects Analysis

Reliability allocation of computerized numerical controlled（CNC）lathes is very important in industry.Traditional allocation methods only focus on high-failure rate components rather than moderate failure rate components,which is not applicable in some conditions.Aiming at solving the problem of CNC lathes reliability allocating,a comprehensive reliability allocation method based on cubic transformed functions of failure modes and effects analysis（FMEA）is presented.Firstly,conventional reliability allocation methods are introduced.Then the limitations of direct combination of comprehensive allocation method with the exponential transformed FMEA method are investigated.Subsequently,a cubic transformed function is established in order to overcome these limitations.Properties of the new transformed functions are discussed by considering the failure severity and the failure occurrence.Designers can choose appropriate transform amplitudes according to their requirements.Finally,a CNC lathe and a spindle system are used as an example to verify the new allocation method.Seven criteria are considered to compare the results of the new method with traditional methods.The allocation results indicate that the new method is more flexible than traditional methods.By employing the new cubic transformed function,the method covers a wider range of problems in CNC reliability allocation without losing the advantages of traditional methods.

CONFORMAL TRANSFORMATION SOLUTION FOR THE ATTENUATION CONSTANT OF TEM TRANSMISSION LINES

The conformal transformation solution is presented for the attenuation constant ofTEM transmission lines which can be mapped into the coaxial or the parallel plate lines by certainconformal transformations including the numerical ones.The analytic and numerical results ofsome examples are also given.

The Theoretical Explanation of Non-ecological Economic Qualities of the Development Mode of Industrial Civilization:An Analysis Based on the Critical Perspective

The development mode of industrial civilization has created huge material wealth for human society,but at the same time the severe ecological problems that have arisen from it have made human civilization fall into the dispersion of unsustainable development.The industrialized development mode has obvious non-ecological economic qualities,which are specifically manifested in the destruction of the ecological economy relationship between nature and mankind,the emergence of cracks of metabolism between nature and mankind,the unbalanced development of the social productive forces and the natural productive forces,and the functioning of one-way linear non-circular economy.Under the trend of ecological evolution of human civilization,the industrial civilization will be replaced by the ecological civilization,and then the industrial economic development mode will be transformed into the ecological economic development mode.As a result,the predicament of once unsustainable development has been gradually dispersed and human civilization enters a beautiful new era of coordinated development of economic society and natural ecology.

THE GROWTH MODE OF ALTUN FAULT AND IT'S DYNAMICS

A set of ENE\|trending fault which locates in the rigid Tarim massif and flexible Qilian massif in the same dynamic system of the uplift of the Qinghai—Tibetan plateau is referred to as the Altun Fault (ALF). ALF displays a linear geometry or a geometry of overlapping of linear and arcuate segments and a growth and development process of the breakdown segment\|by\|segment, connection segment\|by\|segment and propagation gradually (northeastward migration of the northeast tip, southwestward growth of the southwest tip). The formation of the Altun fault began in the middle or upper Carboniferous. It was characteristic of the sinistral strike\|slip\|thrust before Eocene, of the thrust\|sinistral strike\|slip during Oligocene—Miocene, and of the normal slip, and thrust\|sinistral strike\|slip simultaneously since Miocene.

Analytical Approach for the Systematic Research of the Periodic Ferroresonant Solutions in the Power Networks

Ferroresonance is a complex and little known electrotechnical phenomenon. This lack of knowledge means that it is voluntarily considered responsible for a number of unexplained destructions or malfunctioning of equipment. The mathematical framework most suited to the general study of this phenomenon is the bifurcation theory, the main tool of which is the continuation method. Nevertheless, the use of a continuation process is not devoid of difficulties. In fact, to continue the solutions isolats which are closed curves, it is necessary to know a solution belonging to this isolated curve (isolat) to initialise the continuation method. The principal contribution of this article is to develop an analytical method allowing systematic calculation of this initial solution for various periodic ferroresonant modes (fundamental, harmonic and subharmonic) appearing on nonlinear electric system. The approach proposed uses a problem formulation in the frequency domain. This method enables to directly determine the solution in steady state without computing of the transient state. When we apply this method to the single-phase ferroresonant circuits (series and parallels configurations), we could easily calculate an initial solution for each ferroresonant mode that can be established. Knowing this first solution, we show how to use this analytical approach in a continuation technique to find the other solutions. The totality of the obtained solutions is represented in a plane where the abscissa is the amplitude of the supply voltage and the ordinate the amplitude of the system’s state variable (flux or voltage). The curve thus obtained is called “bifurcation diagram”. We will be able to then obtain a synthetic knowledge of the possible behaviors of the two circuits and particularly the limits of the dangerous zones of the various periodic ferroresonant modes that may appear. General results related to the series ferroresonance and parallel ferroresonance, obtained numerically starting from the theoretical and real cases, are illustrated and discussed.

A brief review of the development and optimization of the three-dimensional magnetic configuration system in the J-TEXT tokamak

The three-dimensional(3D) magnetic configuration system in the J-TEXT tokamak has featured in many experimental studies.The system mainly consists of three subsystems:the static resonant magnetic perturbation(SRMP) system,the dynamic resonant magnetic perturbation(DRMP) system and the helical coil system.The SRMP coil system consist of two kinds of coils,i.e.three six-loop coils and two five-loop coils.It can suppress tearing modes with a moderate strength,and may also cause mode locking with larger amplitude.The DRMP coil system consists of 12 single-turn saddle coils(DRMP1) and 12 double-turn saddle coils(DRMP2).Its magnetic field can be rotated at a few kHz,leading to either acceleration or deceleration of the tearing mode velocity and the plasma rotation.The helical coil system consists of two closed coils,and is currently under construction to provide external rotational transform in J-TEXT.The 3D magnetic configuration system can suppress tearing modes,preventing and avoiding the occurrence of major disruption.

Determination of Instantaneous Frequencies of Low Plasma Waves in the Magnetosheath Using Empirical Mode Decomposition (EMD) and Hilbert Transform (HT)

The observations of in-situ spacecraft mission in the magnetosheath and a region of thermalized subsonic plasma behind the bow shock reveal a non-linear behaviour of plasma waves. The study of waves and optics in Physics has given the understanding of the effect of many waves coming together to form a wave field or wave packet. The common aspect of such study shows that two or more waves can superimpose constructively or destructively. The sudden high magnetic field data in the magnetosheath displays such possibility of superposition of waves. In this paper, we use the empirical mode decomposition (EMD) and Hilbert transform (HT) techniques to determine the instantaneous frequencies of low frequency plasma waves in the magnetosheath. Our analysis has shown that the turbulent behavior of magnetic field in the magnetosheath within the selected period is due to superposition of waves.

New 3-mode bosonic operator realization of SU(2) Lie algebra:From the point of view of squeezing

We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.

A passive source ranging method based on the frequency warping transform of the vertical intensity flux in shallow water

The phase of cross-correlation function of two different normal modes contains source range information, which can be extracted by warping transform due to the dispersive characteristics of the shallow water waveguide. The autocorrelation function of the received pressure or particle velocity contains both modal autocorrelation component(MAC) and modal cross-correlation component(MCC), with the former part usually treated as interference for source ranging. Because the real part of the vertical intensity flux(RPVIF) only contains MCC, a passive impulsive source ranging method based on the frequency warping transform of RPVIF with a single vector receiver in shallow water is presented. Using a waveguide-invariant-based frequency warping operator, the cross-correlation components of two different modes in the vertical intensity flux are warped into separable impulsive sequences, the time delays of which are subsequently used for source ranging. The advantages of source ranging based on warping the vertical intensity flux compared with warping the pressure autocorrelation function are pointed out, and the experiment results are also presented.

Wavelet analysis of acoustic emission signals from thermal barrier coatings

The wavelet transform is applied to the analysis of acoustic emission signals collected during tensile test of the ZrO2-8% Y2O3 (YSZ) thermal barrier coatings (TBCs). The acoustic emission signals are de-noised using the Daubechies discrete wavelets, and then decomposed into different wavelet levels using the programs developed by the authors. Each level is examined for its specific frequency range. The ratio of energy in different levels to the total energy gives information on the failure modes (coating micro-failures and substrate micro-failures) associated with TBCs system.

Effects of Residual Stress on the Hydro-Elastic Vibration of Circular Diaphragm

The effects of residual stress on the hydro-elastic vibration of circular diaphragm are theoretically investigated by using the added mass approach. The Kirchhoff theory of plates is used to model the elastic thin circular diaphragm on an aperture of an infinite rigid wall and in contact with a fluid on one side. The fluid is assumed to be incompressible and inviscid and the velocity potential is used to describe its irrotational motion. A non-dimensional tension parameter is defined, and the effects of the tension parameter on the frequency parameters and mode shapes of the diaphragm in the air are presented. The Hankel transform is applied to solve the fluid-diaphragm coupled system;boundary conditions are expressed by integral equations. Finally, the effects of residual stress on the non-dimensional added virtual mass incremental (NAVMI) factors of the diaphragm contact with a fluid on one side are investigated. It is found that the effects of the residual stress cannot be neglected when the edges of the circular diaphragm are clamped. The effects of residual stress for NAVMI factors can be increases 11% when the non-dimensional tension parameter is 1000.