斜流通风机的准三元设计法

一、子午面流线的确定 由沿准正交线q(见图1)的平衡条件式 dC_m~2/dq+A(q)=B(q) (1)来计算子午面流线。 A(q)=2(1/(r_mcosε)+(sinφsinε)/r+(dφ)/(dq)tgε) (2)式中: B(q)=2[d/(dq)(P_0/ρ-(C_θ)/r (d(rC_θ)/dq] (3) P_0/ρ=(P_(01)/ρ)+(uC_θ-u_1C_(θ1))-ξ_PW_1~2/2 (4) 全压损失系数ξ_p和当量扩散系数D_(cq)分别表示     

《广义相对论入门讲座》连载④——度规张量

1度规张量的引入在三维平直空间中,在直角坐标系里,两点之间的距离dl可表示为dl2=dx2+dy2+dz2(1)变换到另一个直角坐标系,它变为dl2=dx′2+dy′2+dz′2(2)如果选用球坐标系,则为dl2=dr2+r2dθ2+r2sin2θd2(3)     

"小角度近似"方法及其在物理解题中的应用

1小角度近似公式 根据数学知识,三角函数sinθ,cosθ,tanθ的级数展开为 sinθ=θ-θ3/3+θ5/5+…+(-1)nθ2n+1/2n+1+…cosθ=1-θ2/2+θ4/4-θ6/6+…+(-1)nx2n/2n+…tanθ=θ+1/3θ3+2/15θ5+17/315θ7+…+22n(22n-1)Bn/2nθ2n-1+… 表1列出了1°～8°情况下,θ弧度值、sinθ、cosθ、tanθ、1-θ2/2的值.     

Ca+CH_3I→CaI+CH_3反应的矢量相关研究(英文)

本文采用准经典轨线方法,在LEPS势基础上计算了Ca+CH3I→CaI+CH3在不同碰撞能下的矢量相关计算了质心系中四个广义极化微分反应截面(2π/σ)(dσ00/dωt),(2π/σ)(dσ20/dωt),(2π/σ)(dσ22+/dωt),(2π/σ)(dσ21-/dωt),k-j′两矢量相关的P(θr)分布、k-k′-j′三矢量相关的极角分布P(φr)以及用θr和φr表示的产物转动角动量的空间分布P(θr,φr).     

全息透镜的特性及其应用(续)

<正> 七、离轴全息透镜的象差将各位相函数的1/d~3次项代入(21)式就得到离轴全息透镜的初级波象差W=-1/8ρ~4S+ρ~3/2(C_xcosθ+C_ysinθ) -ρ~2/2(A_xcos~2θ+A_ysin~2θ     

振动激发对H+CH反应矢量性质的影响

基于从头算势能面CH2(1A'),用准经典轨线(QCT)方法研究了不同振动激发(v=0-3)下反应H+CH→H2+C(1D)的动力学性质.在质心坐标系下计算了四个极化微分反应截面(PDDCDs),计算并讨论了描述k-j'矢量相关的P(θr)分布函数和描述k-k-'j'三矢量相关的二面角分布P(φr).研究结果表明势能面上的深势阱和不同的振动态对产物分子H2有重要影响.     

The collision energy effect on the stereodynamics of the Ca + HCl→CaCl + H reaction

The stereodynamics of the reaction of Ca + HCl are calculated at three different collision energies based on the potential energy surface [Verbockhaven G et al. 2005 J. Chem. Phys. 122 204307] using quasi-classical trajectory theory. The polarization-dependent differential cross sections (PDDCSs) (2π/σ )(dσ 00 /dω t ), (2π/σ )(dσ 20 /dωt ), (2π/σ )(dσ 22+ /dωt ), (2π/σ )(dσ 21 /dω t ) and the distributions of P(θ r ), P(φr ), and P(θr ,φr ) are calculated. The results indicate that the rotational polarization of the CaCl product presents different characteristics for the different collision energies, and the effects of the collision energy on the vector potential, including the alignment, orientation, and PDDCSs, are not obvious.     

Theoretical study of stereodynamics for the D'+ DS(v=0,j=0) → D'D + S abstraction reaction

Quasiclassical trajectory (QCT) calculations have been performed for the abstraction reaction, D'+ DS(v = 0, j = 0) → D'D + S on a new LZHH potential energy surface (PES) of the adiabatic 3 A electronic state [Lü et al. 2012 J. Chem. Phys. 136 094308]. The collision energy effect on the integral cross section and product polarization are studied over a wide collision energy range from 0.1 to 2.0 eV. The cross sections calculated by the QCT procedure are in good accordance with previous quantum wave packet results. The three angular distribution functions, P(θr), P(φr), and P(θr,φr), together with the four commonly used polarization-dependent differential cross sections ((2π/σ)(dσ00/dωt), (2π/σ)(dσ20/dωt), (2π/σ)(dσ22+/dωt), (2π/σ)(dσ21/dωt)) are obtained to gain insight into the chemical stereodynamics of the title reaction. Influences of the collision energy on the product polarization are exhibited and discussed.     

康普顿散射理论计算中的困惑

康普顿根据狭义相对论的质量与能量相关的能量与动量守恒条件 hv+m_0c~2=hv′+mc~2 (1) P=P′+mv (2) 求出康普顿散射波长移动公式 Δλ=h/mc(1-cosθ)=0.0485262sin~2(θ/2(?)) (3) 或写成能量损失公式 ΔE=E/(1+mc~2/E(1-cosθ)) (4) 由动量守恒条件(2)和公式(4),还求出电子反冲角Φ的余切公式 ctgΦ=(1+E/mc~2)tg(θ/2) (5) 近年来已发现康普顿理论与实验结果有一定的误差。而这种误差对于不同的散射材料有不同的数值,因而估计到这可能是来自于分子或原于中的电子本身的动量的影响,导致发现了康普顿散射缺陷。从而提出了修正的新理论,一种新的波长移动公式为 式中P_z为结晶学矢量。 对于康普顿缺陷,R.J.Weiss和M.J.Cooper作了深刻的研究,对于使用能量较低的X射线源(一般是Mo_(K_α)和Mo_(K_β)射线)测量到的康普顿缺陷值约10eV左右,但对于使用能量较高的γ射线,康普顿散     

Exact Solutions of Schr¨odinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and Coulomb Potential

We propose improved ring shaped like potential of the form,2V(r,θ)=V(r)+(2/2M r)[(βsin2θ+γcos2θ+2λ)/sinθcosθ]and its exact solutions are presented via the Nikiforov–Uvarov method.The angle dependent part V(θ)=(2/22M r)[(βsin22θ+γcos2θ+λ)/sinθcosθ],which is reported for the first time embodied the novel angle dependent(NAD)potential and harmonic novel angle dependent potential(HNAD)as special cases.We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.     

Influence of the reagent vibration on the stereo-dynamics of the reactions D^- ＋ H2 and H^- ＋ D2

Employing the quasi-classical trajectory method and the potential energy surface of Panda and Sathyamurhy [Panda A N and Sathyamurthy N 2004 J.Chem.Phys.121 9343],the effect of the reagent vibration on vector correlation of the ion-molecule reactions D～-+H₂ and H～-+D₂ is studied at a collision energy of 35.7 kcal/mol.Four generalized polarization-dependent differential cross sections （2π/σ）（dσ 00 /dωt）,（2π/σ）（dσ 20 /dωt）,（2π/σ）（dσ 22+ /dωt）,and （2π/σ）（dσ 21 /dωt） are presented in the centre-of-mass reference frame,separately.At the same time,the effects on the product angular distributions P （θr）,P （φr） and P （θr,φr） of the title reactions are also analysed.The calculated results show that the scattering tendencies of the product HD,the alignment and the orientation of j sensitively depend on reagent molecule vibration.     

《从零学相对论》连载(19)

正第8讲史瓦西时空§8.1史瓦西真空解史瓦西真空解是爱因斯坦方程的第一个精确解(§6.5),描述一个静态的、球对称的物质分布(通常是天体)在其外部(真空区域)造成的时空弯曲,这一弯曲线元可用史瓦西坐标系{t,r,θ,φ}表为     

Theoretical study of the stereodynamics of the He＋HD^＋ reaction

This paper investigates the stereodynamics of the reaction He+HD+ by the quasi-classical trajectory(QCT) method using the most accurate AQUILANTI surface [Aquilanti et al 2000 Mol.Phys.98 1835].The distribution P(φr) of dihedral angle and the distribution P(θr) of angle between k and j have been presented at three different collision energies.Four generalized polarization-dependent differential cross-sections(2π/σ)(dσ00/dωt),(2π/σ)(dσ20/dωt),(2π/σ)(dσ22+/dωt),(2π/σ)(dσ21 /dωt) are also calculated.Some interesting results are obtained from the comparison of the stereodynamics of the title reaction at different collision energies.     

采用准经典轨迹的方法研究碰撞能对C+CD→C2+D反应的影响

运用准经典轨线方法,基于¹A'势能面[Mol. Phys. 98, 1925(2000)],从理论上研究了碰撞能对C+CD→C₂+D反应的立体动力学性质的影响．计算并且详细讨论了与产物矢量相关的三个极化分布函数P(θr), P(φr)和P(θr,φr)．此外,在质心坐标系中,研究了碰撞能对两个极化微分反应截面的影响．结果表明,产物C₂的立体动力学性质对反应物分子的碰撞能非常敏感.     

双金属层状配位聚合物{[NO2 BzQl][MCr(ox)3]}∞的合成、光谱表征和磁性研究

合成了两种新的草酸根桥联的双金属层状配位聚合物 ,{ [NO2 BzQl][MCr(ox) 3 ]} ∞ ,其中 [NO2 BzQl]+为 1 (p nitrobenzyl) quinolinium ,ox2 -为Oxalate ,M为Ni2 + 或Cu2 + ,并经元素分析、红外光谱表征 .变温磁化率测定结果表明 ,在这两种层状配位聚合物中 ,相邻的金属离子之间存在反铁磁偶合作用 .应用Curie -Weiss公式拟合相应的变温磁化率数据为 :C =0 .6 6 2emuK/mol,θ =- 1.6 5 8K ,R =2 .0× 10 -5(Ni2 + ) ;C =0 .17emuK/mol,θ=- 0 .6 93K ,R =1.86× 10 -6(Cu2 + ) .     

KZnF3:Fe3+体系局域晶体结构的理论研究

本文采用对角化三角场中d5组态完全能量矩阵的方法,研究了KZnF3Fe3+体系的局域晶体结构和EPR参量之间的关系.在分析中我们引入了双层配位模型,即配位体包括Fe3+离子最近邻的6个F-离子和次近邻的8个K+离子.计算表明KZnF3Fe3+的局域结构畸变源于一个K+离子沿C3轴方向(即[111]方向)向Fe3+离子的移动,从而诱导F-离子的位移,使得Fe3+-F-键与C3轴夹角发生变化.通过计算EPR的低对称参量D和(a-F),我们分别得出室温(T=300K)时的畸变角为△θ1=2.58°,△θ2=-1.4°和低温(T7=77 K)时畸变角为△θ1=2.85°,△θ2=-1.40计算结果与实验观察值△θ1=2.8±0.3°,△θ2=-1.1±0.3°相符合.     

Effect of isotope on state-to-state dynamics for reactive collision reactions ■ and ■ in ground state 1~2 A’’ and first excited 1~2 A’ potential energy surfaces

We carry out quantum scattering dynamics and quasi-classical trajectory(QCT) calculations for the O+H_2~+ reactive collision in the ground(1~2 A").nd first excited(1~2 A') potential energy surface.We calculate the reaction probabilities of O+H_2~+(v=0,j=0)→OH~++H and O+H_2~+(v=0,j=0)→OH+H~+reaction for total angular momentum J=0.The results calculated by QCT are consistent with those from quantum mechanical wave packet.Using the QCT method,we generate in the center-of-mass frame the product state-resolved integral cross-sections(ICSs);two commonly used generalized polarization-dependent differential cross-sections(PDDCS s),(2π/σ)(dσ_(00)/dω_t),(2π/σ)(dσ_(20)/dω_t));and three angular distributions of the product rotational vectors,p(θ_r),P(φ_r),and p(θ_r,φ_r).We discuss the influence on the scalar and vector properties of the potential energy surface,the collision energy,and the isotope mass.Since there are deep potential wells in these two potential energy surfaces,their kinetic characteristics are similar to each other and the isotopic effect is not obvious.However,the well depths and configurations of the two potential energy surfaces are different,so the effects of isotopic substitution on the integral cross-section and the rotational polarization of product are different.     

氯与甲烷和重氢甲烷反应的矢量相关研究

在扩展的London-Eyring-Polanyi-Sato(LEPS)势能面基础上,利用准经典轨线法在碰撞能Ecol=3.67 kcal/mol下研究了Cl+CH4→HCl+CH3和Cl+CD4→DCl+CD3反应,在质心系计算得到四个广义极化微分反应截面((PDDCS)(2π/σ)(dσ00/dωt)、(2π/σ)(dσ20/dωt)、(2π/σ)(dσ22+/dωt)、(2π/σ)(dσ21-/dωt)和k-k′-j′三矢量相关的极角分布p(фr)、k-j′两矢量相关的p(θr)分布以及用θr和фr表示的产物转动角动量的空间分布.计算结果与有关实验及理论结果符合得很好,讨论了氯与甲烷和重氢甲烷反应的立体动力学同位素效应.     

类氢及碱金属原子激发态寿命的半经典计算公式

根据对应原理,得到了类氢原子能态平均寿命半经典的计算公式τ(n,l),然后利用相对论单通道量子数亏损理论进行推广,得到用来计算考虑总角动量J的激发态寿命公式τ(n,l,l+1/2)和τ(n,l,l-1/2),利用单通道量子数亏损理论得到了碱金属原子n、l远大于1时激发态寿命的半经典公式τ(n.l)=τ0(m+M/nm/v/+M)2v7l(l+1/2)/n4,其计算结果和实验数据符合的很好.     

边界形状的变化对偏微分方程本征值的影响

我们考虑下列方程和边界条件: 在区域V中:(~2十E)φ=0, (1) 在V的边界上: φ=0 (2)所定解的最低本征值E,简称为区域V的本征值。 例如V为半径为R的无穷长圆柱,则 E=a~2/R~2,φ=J_0(E~(1/2)r)=J_0((ar)/R)。 (3)此处a=2.405为Bessel函数J_0的最小根。设由于形状变化而使得V改为 r≤R(θ)=R[1+ sum form n=-∞ to ∞ s_ne~(inθ)) (4)其中 s_(-n)=s_n~* (n≠0),s_0=0. (5)我们用(4)的本征值 E=a~2/R~2f(s_n) (6)与等面积圆柱的本征值 a~2/R~2[1+ sum form n=-∞ to ∞ |s_n|~2]~(-1) 的比值 F(s_n)=[1+ sum form n=-∞ to ∞ |s_n|~2]f(s_n) (7)来表示边界形状的变化对柱的本征值的影响。 我们用边界微扰法计算(6)及(7)。为计算方便起见,我们选长度单位使得R=a;