最短轨道凝聚模型的相变

应用重整化群计算最短轨道模型的生长几率分布{P_α,i}及其构型权重C_α(2×2原胞和3×3原胞),从而得出多分形热力学的配分函数Z(q,L),自由能F(q,L),能量E(q,L),比热c(q,L)和广义维数D_q,结果表明该模型在q=q_c≈0处发生相变,即当q < q_c时,生长几率分布{P_α,i}不具有多分形性质。     

CeO2热力学性质的第一原理研究

使用第一性原理方法结合准谐德拜模型研究压力0~30 GPa,温度0~2 000 K,二氧化铈立方结构的热力学性质,包括常压下平衡体积V、体弹模量B₀、热容c_p和熵S随温度的变化以及不同压强下热容c_p、熵S、德拜温度Θ,体膨胀系数α与温度的关系.常压下计算的热容c_p和熵S随温度的变化与实验数据符合很好.     

微观相场法模拟Ni75Al5.3V19.7 中L12和D022结构反位缺陷的演化

运用微观相场法研究Ni₇₅Al_5.3V_19.7合金沉淀过程中L1₂结构和D0₂₂结构反位缺陷发现：在沉淀初期,L1₂结构反位缺陷Al_Ni,V_Ni,Ni_Al,D0₂₂结构反位缺陷V_Ni,Al_Ni关键词： 微观相场 反位缺陷 L1₂结构')" href="#">L1₂结构 D0₂₂结构')" href="#">D0₂₂结构     

在丙酮溶液中18-冠-6与CoCl2配位化合物的NMR研究

本文研究了丙酮溶液中配合物的平衡和结构。建立了一套计算机程序。通过化学位移数值的分析说明在溶液中主要存在两种平衡,并确定了平衡常数k₁₁=2.95×10²l/mol,k₁6.1l/mol以及冠醚络合物的极限化学位移D₁₁^(H)=350Hz,D₁₁^(C)=-290Hz,D₂^(H)=1300Hz,D^(C)=-1600Hz。确认位移机制是电子磁矩和共振核的核磁矩通过空间直接偶极-偶极相互作用。     

宽脉冲中子注入下中子裂变链统计涨落的数值计算

研究了裂变系统在宽脉冲外中子源注入驱动下裂变链统计涨落问题.提出了概率分布W_n方程的分解-合成数值模拟计算方法,使裂变系统注入中子源数值模拟计算扩展到一般广义条件(具有任意时间分布、注入时间零点t₀概率分布函数P(t₀)和数概率分布S(n)等).同时讨论了应用物理模型的等效条件.将基本前提等效条件从单介质区模型扩展到多介质区模型.为解概率分布W_n方程必备参数提供了计算平均公式.     

三角对称晶场下d8电子组态的EPR参量的普遍公式及其应用

本文考虑到d⁸电子组态中所有自旋三重态和自旋单态对基态的影响,用高阶微扰法导出了d⁸电子组态在三角对称晶场下光谱和基态EPR普遍公式。发现在三角对称晶场下,d⁸电子组态离子的g_⊥ > g_‖或g_⊥ < g_‖和D > 0或D < 0是以立方对称晶场为界,晶体中顺磁离子的配体沿C₃轴伸长或压缩所致。利用所得公式计算了NiCl₂和NiSiF₆·6H₂O晶体的EPR参量,其结果与实验吻合较好。     

Dynamic models of pest propagation and pest control

This paper proposes a pest propagation model to investigate the evolution behaviours of pest aggregates. A pest aggregate grows by self-monomer birth, and it may fragment into two smaller ones. The kinetic evolution behaviours of pest aggregates are investigated by the rate equation approach based on the mean-field theory. For a system with a self-birth rate kernel I(k)=Ik and a fragmentation rate kernel L(i,j)=L, we find that the total number M₀^A(t) and the total mass of the pest aggregates M₁^A(t) both increase exponentially with time if L ≠ 0. Furthermore, we introduce two catalysis-driven monomer death mechanisms for the former pest propagation model to study the evolution behaviours of pest aggregates under pesticide and natural enemy controlled pest propagation. In the pesticide controlled model with a catalyzed monomer death rate kernel J₁(k)=J₁k, it is found that only when I<J₁B₀ (B₀ is the concentration of catalyst aggregates) can the pests be killed off. Otherwise, the pest aggregates can survive. In the model of pest control with a natural enemy, a pest aggregate loses one of its individuals and the number of natural enemies increases by one. For this system, we find that no matter how many natural enemies there are at the beginning, pests will be eliminated by them eventually.     

单晶变角EPR谱的解释I.掺Cr3+铝铵矾单晶的EPR

对本征场的计算方法作了新的分析,提出了新的计算方案,根据这方案编写了程序,并应用这一程序对掺Cr³⁺铝铵矾单晶变角的EPR谱作了解析,得到了更加可靠更为准确的自旋-Hamilton参数;D=0.04845cm^-1,g_x=g_y=1.9761,g₂=1.9752.用上述参数,对各个离子不同角度下的广义本征场计算的共振磁场与实验数据拟合很好.充分说明采用此法处理EPR的优越性.     

关于Zn1-xBexO电子结构和光学性质的研究

采用基于密度泛函理论和平面波赝势技术的CASTEP程序对Zn_1-xBe_xO合金电子结构和光学性质进行了计算.当0≤x≤1,其带隙从0.963 eV变化到7.293 eV.分析了晶格畸变和能带间排斥效应对带隙的影响.当Be含量x=0.125,0.25,0.375,0.5,0.625,0.75时,a/b轴压应变控制着带隙变化;当x=0.875,1时,c轴压应变控制着带隙变化.能带间的p-d排斥影响价带顶变动,Γ_1v与Γ_1c之间排斥影响导带底变动.这些能带间的排斥效应被用来分析Zn_1-xBe_xO带隙变动.另外,也分析了Zn_1-xBe_xO介电函数虚部ε₂. 关键词： 带结构 光学性质 应变 排斥     

MPb10（M=Ti，V，Cr，Cu，Pd）几何结构和磁性的密度泛函计算研究

采用密度泛函理论（density functional theory,DFT）中的广义梯度近似（generalized gradient approximation,GGA）对MPb₁₀（M=Ti,V,Cr,Cu,Pd）四种同分异构体的几何结构和磁性进行了计算研究.发现在四种同分异构体中,D_4d结构的MPb₁₀（M=Ti,V,Cr,Cu,Pd）具有最大的结合 关键词： 几何结构 磁性 密度泛函     

Nanoparticle in a quantum crystal with a narrow vacancy band

Vacancy-assisted diffusion of a neutral probe nanoparticle with a radius R_p of a few lattice constants in a quantum crystal with a narrow vacancy band is considered. The diffusion coefficient of the probe D_p(T) in such a crystal should fall exponentially near T_melt, and it can go through a maximum at temperatures T_tr, where the transition from thermally activated hopping of localized vacancies to a proper band motion of delocalized vacancions takes place, under the condition that the mean free path of the vacancions l_v(T) at T_tr is less than R_p and increases with lowering the temperature quicker than the inverse value of the relative concentration of vacancies X_v(T). Below T_tr, where l_v is much longer than the probe diameter, the value of D_p should fall proportionally to X_v(T).     

Exactly solvable models of conformal-invariant quantum field theory in D-dimensional space

The method for exact solution of a certain class of models of conformal quantum field theory in D-dimensional Euclidean space is proposed. The method allows one to derive closed differential equations for all the Green functions and also algebraic equations to scale dimensions of all field. A scalar field P of a scale dimension d_p = D − 2 is needed for nontrivial solutions to exist. At D ≠ 2 this field is converted to a constant that coincides with the central charge of two-dimensional theories. A new class of D = 2 models has been obtained, where the infinite-parametric symmetry is not manifest. The two-dimensional Wess-Zumino model is used to illustrate the method of solution.     

Invariant tensors for simple groups

The forms of the invariant primitive tensors for the simple Lie algebras A_l, B_l, C_l, and D_l are investigated. A new family of symmetric invariant tensors is introduced using the non-trivial cocycles for the Lie algebra cohomology. For the A_l algebra it is explicitly shown that the generic forms of these tensors become zero except for the l primitive ones and that they give rise to the l primitive Casimir operators. Some recurrence and duality relations are given for the Lie algebra cocycles. Tables for the 3- and 5-cocycles for su(3) are su(4) are also provided. Finally, new relations involving the d and f su(n) tensors are given.     

Modelling interdiffusion in epitaxial multilayer structures using X-ray simulation techniques

The analysis of X-ray diffraction data forms an important non-destructive technique for the study of interdiffusion in multilayer structures. A frequently used approach is that of Fleming et al. in which the characteristic X-ray diffraction satellites from a superlattice structure are shown to be related to the corresponding Fourier components of the real space composition modulation. This relationship is derived assuming the strain to be small although the limitations on this parameter are unclear. To clarify this limitation the Fleming technique has been tested for a range of x values, and hence strain, using as examples a series of model multilayer CdTe:Cd_1-xMn_xTe structures. The approach has been to use a simulation technique based on the kinematical theory of X-ray diffraction to model the X-ray rocking curves from a series of structures in which the Mn diffusion profiles had been calculated using a particular value of the diffusion coefficient D. The values of the diffusion coefficient, derived from the diffraction data using the Fleming method, agree with the input D at low x values but differ for high x, high strain, structures and a criterion is suggested for the range of validity of the method.     

Released energy formula for proton radioactivity based on the liquid-drop model

In this work, based on the liquid-drop model and considering the shell correction, we propose a simple formula to calculate the released energy of proton radioactivity(Q_p). The parameters of this formula are obtained by fitting the experimental data of 29 nuclei with proton radioactivity from ground state. The standard deviation between the theoretical values and experimental ones is only 0.157 Me V. In addition, we extend this formula to calculate 51 proton radioactivity candidates in region 51≤Z≤83 taken from the latest evaluated atomic mass table AME2016 and compared with the Q_p calculated by WS4 and HFB-29. The calculated results indicate that the evaluation ability of this formula for Q_p is inferior to WS4 while better than HFB-29.     

Probing the isospin dependent in-medium nucleon–nucleon cross section by nucleon emissions

The effects of the symmetry potential and the isospin dependent in-medium nucleon–nucleon (NN) cross section on the number of proton(neutron) emissions N_p(N_n) are studied respectively within an isospin-dependent quantum molecular dynamics (IQMD) model. The isospin dependent in-medium NN cross section is found to have a strong influence on N_p(N_n) but N_p(N_n) is not sensitive to the symmetry potential for the neutron-deficient colliding system at relatively high energies. We propose to make use of the N_p(N_n) as a probe to extract information on the isospin dependent in-medium NN cross section.     

波动方程辛算法的迭代求解

对(∂²)/(∂x²)利用中心差商算子,对expt作对角Padé逼近,由波动偏微分方程可得到两类具有O(Δx²+Δt^2l)和O(Δx⁴+Δt^2l)精度的辛格式.对由此类辛格式产生的线性方程组构造了两种迭代解法,并对l=1,2,3,4给出了它们的收敛条件.并进行了数值实验.     

带源项的变系数非线性反应扩散方程的精确解

本文利用广义条件对称方法对带源项的变系数非线性反应扩散方程 f(x)u_t=(g(x)D(u)u_x)_x+h(x)P(u)u_x+q(x)Q(u)进行研究. 当扩散项D(u)取u^m (m≠-1,0,1)和e^u两种重要情形时, 对该方程进行对称约化,得到了具有广义泛函分离变量形式的精确解. 这些精确解包含了该方程对应常系数情况下的解. 关键词： 广义条件对称 精确解 非线性反应扩散方程     

Quantum bound states with zero binding energy

After reviewing the general properties of zero-energy quantum states, we give the explicit solutions of the Schrödinger equation with E = 0 for the class of potentials V = −|γ|/r^ν, where −∞ < ν < ∞. For ν > 2, these solutions are normalizable and correspond to bound states, if the angular momentum quantum number l > 0. (These states are normalizable, even for l = 0, if we increase the space dimension, D, beyond 4; i.e for D > 4.) For ν < −2 the above solutions, although unbound, are normalizable. This is true even though the corresponding potentials are repulsive for all r. We discuss the physics of these unusual effects.     

Scaling properties of resonant electron transfer in ion—metal-surface interactions

Scaling properties of resonant electron transfer in the interaction of atoms and positive ions with metal surfaces are revealed by examining the dependence of numerically calculated transition matrix elements and (first-order) transition rates upon the scaled ion-surface distance D = D/D_n, where D_n is the classical threshold distance for electron transfer involving ionic stat principal quantum number n. For zero orbital angular momentum and fixed energy of the ionic states, the n-dependence of the rates at D = 1 is found to approach, in the large-n limit, a simple power law. A scaling law is established that connects, in the range D 1, transition rates for arbitrary (large) principal quantum numbers.