Critical Behaviors and Finite-Size Scaling of Principal Fluctuation Modes in Complex Systems

Complex systems consisting of N agents can be investigated from the aspect of principal fluctuation modes of agents. From the correlations between agents, an N×N correlation matrix C can be obtained. The principal fluctuation modes are defined by the eigenvectors of C. Near the critical point of a complex system, we anticipate that the principal fluctuation modes have the critical behaviors similar to that of the susceptibity. With the Ising model on a two-dimensional square lattice as an example, the critical behaviors of principal fluctuation modes have been studied. The eigenvalues of the first 9 principal fluctuation modes have been invesitigated. Our Monte Carlo data demonstrate that these eigenvalues of the system with size L and the reduced temperature t follow a finite-size scaling form λ_n(L, t)=L^γ/ν f_n(tL^1/ν), where γ is critical exponent of susceptibility and ν is the critical exponent of the correlation length. Using eigenvalues λ₁, λ₂ and λ₆, we get the finite-size scaling form of the second moment correlation length ξ(L, t)=Lξ(tL^1/ν). It is shown that the second moment correlation length in the two-dimensional square lattice is anisotropic.     

Multi-Type Directed Scale-Free Percolation

In this paper,we study a long-range percolation model on the lattice Z d with multi-type vertices and directed edges.Each vertex x ∈ Z d is independently assigned a non-negative weight Wx and a type ψx,where(Wx) x∈Z d are i.i.d.random variables,and(ψx) x∈Z d are also i.i.d.Conditionally on weights and types,and given λ,α 0,the edges are independent and the probability that there is a directed edge from x to y is given by pxy = 1 exp(λφψ x ψ y WxWy /| x-y | α),where φij 's are entries from a type matrix Φ.We show that,when the tail of the distribution of Wx is regularly varying with exponent τ-1,the tails of the out/in-degree distributions are both regularly varying with exponent γ = α(τ-1) /d.We formulate conditions under which there exist critical values λ WCC c ∈(0,∞) and λ SCC c ∈(0,∞) such that an infinite weak component and an infinite strong component emerge,respectively,when λ exceeds them.A phase transition is established for the shortest path lengths of directed and undirected edges in the infinite component at the point γ = 2,where the out/in-degrees switch from having finite to infinite variances.The random graph model studied here features some structures of multi-type vertices and directed edges which appear naturally in many real-world networks,such as the SNS networks and computer communication networks.     

锐钛矿金红石的高温原位X射线衍射研究

对TiO₂粉末进行了空气和真空条件下从室温到1200℃的加热原位X射线衍射实验, 得到了空气和真空条件下微米级锐钛矿颗粒转变为金红石的起始温度分别为850℃ 和855℃; 分别修正了空气条件下锐钛矿在(27–850℃)范围和金红石在(900–1200℃) 范围内的晶胞参数和真空条件下锐钛矿在(27–850℃)范围和金红石在(950–1200℃) 范围的晶胞参数, 从而得到了晶胞参数随温度变化的关系, 得到了锐钛矿和金红石在空气中和真空中的热膨胀系数, 并总结了热膨胀系数随温度变化的规律. 室温下锐钛矿在空气条件下的热膨胀系数为 α_a=4.55063×10^-6/℃, α_c=7.7543×10^-6/℃, β=16.85836×10^-6/℃; 真空下为 α_a=4.69429×10^-6/℃, α_c=9.02850×10^-6/℃, β=18.69688×10^-6/℃. 室温下, 金红石在空气条件下的热膨胀系数为 α_a=6.81243×10^-6/℃, α_c=8.71644×10^-6/℃, β=22.22178×10^-6/℃; 真空条件下为 α_a=6.05834×10^-6/℃, α_c= 8.39280×10^-6/℃, β=20.52362×10^-6/℃. 关键词： 2')" href="#">TiO₂ 原位X射线衍射 相转变 热膨胀     

The Universal Plateau Structure of Lyapunov Exponents for Period Doubling Cascade Attractors

Using algebraic. analysis method for periodic orbits of Hknon map, we derive the boundary equations of stable window and Lyapunov exponent plateau region on the space of nonintegrability parameter A and dissipation parameter J. Ekom the real root of these equations, we obtain the plateau width of Lyapunov exponent W_p = A_p,max - A_p,min and the stable tvindorv width W_s = A_p,max - A_p,min for high periodic orbits. The calculated result of plateau structure ratio α4 = W_p/W_S for period-4 orbit agrees with the conjectural analytical formula: α4 = 2J²/(1+J⁴). Hence our result presents further evidence of universal dependence of Lyapunov exponent plateau structure on the dissipation parameter for period doubling cascade attractors of nonlinear system in transition from order to chaos.     

Structure Evolution in the Even-Even 124-134Xe with IBM2

We have investigated the structure evolution of the ^124-134Xe isotopic chain in the framework of the proton-neutron interacting model IBM2. The positive parity spectra of the ground state, quasi-β and quasi-γ bands are reproduced well. The staggering in ^124-130Xe are almost completely removed and the γ band agree well with the experiment data, even for the high-spin quasi-γ states. The key quantities of the collective structure evolution, including level energies, the B(E2) transition branching ratios, and the M1 excitations to 1₁⁺ mixer-symmetry states are analyzed by comparing with the experimental data. The parameters for representation of the O_πν(6) and SU_πν^*(3) features in isotopes are examined. Both experimental data and theoretical results show that the shape phase transition of ^124-134Xe isotopic chain is from the SU_πν^*(3) (triaxial rotation) to the U_πν(5) (vibration motion) with a considerable constituent of the O_πν(6) symmetry (γ-unstable rotation), where the shape phase transition rapidly takes place between the neutron number N = 76 and N = 78.     

Third-Order Optical Nonlinearity in Two-Dimensional Transition Metal Dichalcogenides

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer twodimensional (2D) transition-metal dichalcogenides (TMDCs), having the formula MX₂ with M=Mo, W and X=S, Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semi-classical perturbation analysis of response functions. We numerically calculate the linear χ_μν⁽¹⁾ (-ω;ω) and nonlinear surface susceptibility tensors χ_μνζη⁽³⁾(-ω_Σ; ω_r; ω_s; ω_t) with ω_Σ=ω_r+ω_s+ω_t. Both non-degenerate and degenerate cases are studied for thirdharmonic generation and nonlinear refractive index, respectively. Computational results obtained with no external fitting parameters are discussed regarding two recent reported experiments on MoS₂, and thus we can confirm the extraordinarily strong optical nonlinearity of TMDCs. As a possible application, we demonstrate generation of a π/4-rotated squeezed state by means of nonlinear response of TMDCs, in a silica micro-disk resonator covered with the 2D material. Our proposed method will enable accurate calculations of nonlinear optical response, such as four-wave mixing and highharmonic generation in 2D materials and their heterostructures, thus enabling study of novel functionalities of 2D photonic integrated circuits.     

垂直载荷下颗粒物质的声波探测和非线性响应

对于玻璃珠组成的颗粒介质样品,本文测量了横波和纵波声速,同时分析了剪切模量(G)与体积模量(B)的比值(G/B)随压强的变化规律.结果表明,在低压强下,颗粒体系的纵波声速(C_L)明显大于横波声速(c_T),且体系的CL,CT及G/B均随压强p变化呈幂律标度,即CL∝p~(0.3817),CT∝p~(0.2809)G/B∝p~(-0.4539),幂指数与文献[1]中预言的-1/2非常接近,暗示在我们实验压强范围内的颗粒样品处于L玻璃状态.此外,本文还利用快速傅里叶变换法测量了玻璃珠样品中的声学衰减特性及二阶谐波随压强的变化,发现:纵波声衰减系数(α)、接收端二倍频振幅(μ_(2ω))与基频振幅(μ_(1ω))平方的比值(μ_(2ω)/μ_(1ω)~2)均随压强的增大而幂率减小,分别为α∝p~-(-0.1879),和μ_(2ω)/μ_(1ω)~2∝p~(-0.866).     

Stable high-power TE01 gyro-TWT amplifiers

The stability of high power gyro-TWT amplifiers operating in the low-loss TE₀₁ mode of cylindrical waveguide has been studied, Linear theory has been used to determine the threshold start-oscillation beam current for absolute instability in the operating mode and the critical section lengths for the dominant gyro-BWO interactions occurring at various cyclotron harmonics in other waveguide modes. The performance of the amplifier was evaluated with a nonlinear, self-consistent slow-timescale simulation code. Utilizing interaction sections whose lengths are less than the threshold start-oscillation length and are separated by attenuating severs for isolation, two stable three-section devices have been designed which are predicted to yield: (1) a peak output power of 230 kW at 35 GHz with an efficiency of 23%, a saturated gain of 46 dB and a constant-drive bandwidth of 6% for a 100 kV, 10 A electron beam with an α=ν_⊥ /ν_z =1.0 and an axial velocity spread Δν_z/ν_z=5% and (2) 105 kW at 94 GHz with 21% efficiency, 45 dB saturated gain and 5% constant-drive bandwidth for a similar 5 A electron beam. In addition, the design of the 0 dB input/output couplers and the MIG electron gun are given. Due to the low loss of the TE₀₁ mode, both of these amplifiers can be operated continuously     

THE APPROXIMATE B-S WAVE FUNCTIOPiS FOR (XU) ATOM AND THE DECAY RATE FOR E°→(∑+μ-)+νμ

In this paper, the Bethe-Salpeter equation for a Coulombic bound system consisting of a fermion (mass m_l and spin 1/2) and an anti-fermion (mass m₂ and spin 1/2) is solved. The approximate B-S wave functions for (∑U) atom are given. Utilizing the perturbative expansion of the quantum field theory of composite particles, the decay rate and branching ratio for E°→(∑⁺μ^-)+ν_μ are calculated with accuracy up to order O(α).     

Lifshitz时空s波超导模型的关联长度和穿透深度

在D=d+2维各向异性的Lifshitz黑洞时空背景中, 在探子极限下, 用解析方法研究了临界温度附近引力系统的微扰, 计算出超导的关联长度ξα(1/T_c)(1-(T/T_c)^-1/2, 这与平均场论的结果一致. 进一步, 考虑在该系统中加一个均匀外磁场, 计算出穿透深度λα(T_c-T)^-1/2, 该结果与Ginzburg-Landau理论相符.     

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

We explore the tricritical points and the critical lines of both Blume-Emery-Griffiths and Ising model within long-range interactions in the microcanonical ensemble. For K=K_MTP, the tricritical exponents take the values β=1/4, 1=γ^-≠γ⁺=1/2 and 0=α^-≠α⁺=-1/2, which disagree with classical (mean field) values. When K>K_MTP, the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K_CTP), where the values of the critical expoents become β=1/2, 1=γ^-≠γ⁺=2 and 0=α⁺≠α⁺=1.     

Ge-As-S硫系玻璃的结构与性能调控

制备了系列具有不同化学配比特征的Ge-As-S硫系玻璃,并研究了玻璃的结构、折射率和光学带隙(Eg).Ge-As-S玻璃具有以[Ge S_4]四面体和[As S_3]三角锥为骨架结构单元相互交联形成的连续网络结构,当S过量时,结构中出现S链或S_8环;当S不足时,结构中形成As_4S_4/As_4S_3分子,甚至出现大量AsAs/Ge-Ge同极键.玻璃的组成元素在2—10μm波段的摩尔折射度分别为R_(Ge)=9.83—10.42 cm~3/mol,RAs=11.72—11.87 cm~3/mol和R_S=7.78—7.86 cm3/mol.Ge-As-S玻璃的折射率与密度和组成元素的摩尔折射度之间存在较好的定量关系,可根据该定量关系在1%偏差内对玻璃的折射率进行预测或调控.提出了采用玻璃粉末的漫反射光谱确定可靠Eg的方法,通过该方法可获得玻璃的强吸收数据用于确定Eg.Ge-As-S玻璃的Eg与玻璃的平均键能之间存在较好的关联,S含量较高的玻璃更倾向于具有较大的平均键能,因此具有较大的Eg.     

低温燃烧合成法制备的氧化铝陶瓷粉体的发光特性

α-Al₂O₃∶C单晶具有优良的热释光特性,被用做热释光剂量计,但α-Al₂O₃∶C晶体剂量计的形状不易加工,生产成本高且碳在晶体中难以掺杂均匀。采用低温燃烧合成法以无水乙醇为溶剂,尿素为染料,硝酸铝为反应物制备少团簇、分散均匀的片状α-Al₂O₃∶C陶瓷粉体。探讨不同点火温度和不同退火温度对其光致发光特性的影响,不同退火温度对热释光特性的影响以及热释光与辐射剂量(90Sr β)的关系。通过分析α-Al₂O₃∶C陶瓷粉体的光致发光光谱得出：α-Al₂O₃∶C陶瓷粉体的发射波长在395 nm附近,点火温度T≤800℃时,点火温度为500 ℃制备的α-Al₂O₃∶C陶瓷粉体的光致发光强度最强;在相同点火温度T=500 ℃下,经不同温度退火制备α-Al₂O₃∶C陶瓷粉体,点火温度为500 ℃制备的α-Al₂O₃∶C陶瓷粉体经1 000 ℃退火后光致发光强度最强。通过分析α-Al₂O₃∶C陶瓷粉体的热释光曲线得出：退火后的α-Al₂O₃∶C陶瓷粉体在200 ℃左右的热释光峰值占主导,900 ℃退火的α-Al₂O₃∶C陶瓷粉体在200 ℃附近的热释光峰值最强;通过峰高法对900 ℃高温退火处理后的α-Al₂O₃∶C陶瓷粉体位于200 ℃左右的热释光峰做剂量响应曲线,可以看出,在1～50 Gy剂量范围内具有良好的热释光剂量线性响应关系,在50～200 Gy剂量范围内出现超线性响应关系。与α-Al₂O₃∶C晶体(1～10 Gy)和多孔Al₂O₃∶C薄膜(1～10 Gy)相比,α-Al₂O₃∶C陶瓷粉体的线性剂量响应范围明显扩大。此研究可为提高氧化铝陶瓷粉体的热释光性能提供思路。     

d-Dimensional Kinetic S4 Model

A single-spin transitional critical dynamics based on the Glauber theory is used to investigate the d-dimensional kinetic S⁴ model. We derive the fundamental dynamical equations by a cumulant expansion, and then, a one-dirnensional model is treated. We obtain approximately the local magnetization and equal-time spin-pair correlation function, in which the terms of k₃ and the higher orders are ignored (corresponding to high-temperature cutoff). These are finally extended to d-dimensional case. In addition, we obtain the critical point k_c of d-dimensional S⁴ model, and give a relation satisfied by the dynamic critical exponent Z and the correlation length critical exponent ν.     

Nonlinear analysis of high-harmonic slotted gyro-TWT amplifier

A nonlinear self-consistent simulation code is employed to investigate the behavior of the slotted gyrotron traveling-wave amplifier (gyro-TWT), in which an axis-encircling electron beam synchronously interacts with a high-order azimuthal mode in a magnetron-type waveguide. The efficiency of a fourth-harmonic device with an ideal 60 kV, 5 A beam is shown to reach 30% for α≡ν_⊥/ν_z=2. The growth rate for the π mode is roughly 25% larger than for the 2π mode. The efficiency increases for lower voltage and the device is found to be moderately sensitive to the radial spread of the beam's guiding center position and extremely sensitive to the axial velocity spread. For an ideal 60 kV, 5 A beam with α=1.5, the efficiency of a second-harmonic gyro-TWT is 42% and falls to 10% for an eighth-harmonic device. The design of a 35 GHz, 60 kV, 5A, α=1.5, eight-vane, fourth-harmonic gyro-TWT with 7% axial velocity spread is presented. It is predicted that this design will yield a peak output power of 90 kW, a peak efficiency of 30%, and 6.3% saturated bandwidth     

A broadband self-powered UV photodetector of aβ-Ga2O3/γ-CuI p–n junction

The symmetric Ti/Au bi-layer point electrodes have been successfully patterned on theβ-Ga;O;films which are prepared by metal–organic chemical vapor deposition(MOCVD)and theγ-Cu I films which are prepared by spin-coating.The fabricated heterojunction has a large open circuit voltage(Voc)of 0.69 V,desired for achieving self-powered operation of a photodetector.Irradiated by 254-nm ultraviolet(UV)light,when the bias voltage is-5 V,the dark current(Idark)of the device is 0.47 p A,the photocurrent(Iphoto)is-50.93 n A,and the photo-to-dark current ratio(Iphoto/Idark)reaches about 1.08×10;.The device has a stable and fast response speed in different wavelengths,the rise time(τr)and decay time(τd)are 0.762 s and 1.741 s under 254-nm UV light illumination,respectively.While theτr andτd are 10.709 s and7.241 s under 365-nm UV light illumination,respectively.The time-dependent(I–t)response(photocurrent in the order of10-10 A)can be clearly distinguished at a small light intensity of 1μW·cm;.The internal physical mechanism affecting the device performances is discussed by the band diagram and charge carrier transfer theory.     

Critical Percolation Probabilities for the Next-Nearest-Neighbouring Site Problems on Sierpinski Carpets

In this paper, we compute the next-nearest-neighbouring site percolation (Connections exist not only between nearest-neighbouring sites, but also between next-nearest-neigh bouring sites.) probabilities PC on the two-dimensional Sierpinski carpets, using the translationaldilation method and Monte Carlo technique. We obtain a relation among PC, fractal dimensionality D and connectivity Q. For the family of carpets with central cutouts,(1 - P_c)/(1 - P_c^s) = (D - 1)^1.60, where P_c^s = 0.41, the critical percolation probability for the next-nearest-neighbouring site problem on square lattice. As D reaches 2, P_c = P_c^s = 0.41, which is in agreement with the critical percolation probability on 2-d square lattices with . next-nearest-neigh bouring interactions.     

Upper Bounds on Top Quark Mass,Z Boson Decay Widths and Mass Ratio MW/MZ

In this paper we made a comprehensive analysis of some latest esperimental data-the Z boson decay widths, the mass ratio M_W/M_Z and effective vector coupling constant g_v, within the framework of standard model. We considered the 0(α_s²), order QCD corrections in tlte calculation of T_h and T_z. The analysis shows that the mass ratio (M_W/M_Z)² is rather sensitive to the change of the strong coupling constant α_s(M_Z), and the smaller value α_s(M_Z)≤0.128 is preferred. The upper bounds on top quark Inass M_t are obtained from different analyses. The final averaged result is M_t= 102 37 GeV, or M_t< 186 GeV at 95% C.L. for Higgs boson mass M_H in the range of 50～1000 GeV.     

纳米SrHPO4：RE（RE=Eu3+或Tb3+）磷光体的水热合成与光谱特性

利用水热法合成了α-SrHPO₄：RE（RE=Eu³⁺,Tb³⁺）纳米磷光体,并研究了材料的形貌与光谱特性。α-SrHPO₄纳米粒子为长度90~200 nm的棒状结构,直径为24~36 nm。Eu³⁺和Tb³⁺的掺杂均会降低α-SrHPO₄的结晶度,并减小其长径比。α-Sr_0.97HPO₄：0.03Eu³⁺在395 nm近紫外光的激发下,存在分别由⁵D₀→⁷F₁和⁵D₀→⁷F₁₂跃迁引起的590 nm和614 nm发射峰,最终发射橙红光。α-Sr_0.97HPO₄：0.03Tb³⁺在217 nm近紫外光的激发下,存在由⁵D₄→⁷F₅跃迁引起的543 nm绿光发射。     

Initial Phase Dependence of the Soliton Decay Rate for the Nonlinear Schrodinger Equation with a Lossy Term

By using a recursion relation from the x-discrete nonlinear Schrödinger equation with a "lossy" term, we prove that the solitons propagate along the fiber in the decay rate exp -(I+ M₀)Γx if the "initial" input phase (at x = 0) is taken as the form M_oΓt²/2α_l. The same conclusions can also be obtained from the exact numerical calculations.