Intersystem crossing at singlet conical intersections

The energy of the lowest triplet state of organic molecules is intermediate between the ground state and the first excited singlet. At the S₁/S₀ conical intersection, the two singlet states are degenerate. It is shown that for some molecules (ethylene, benzene, toluene and pyrrole) the T₁ state is also degenerate with the two singlet states. Moreover, the spin orbit coupling matrix element at this structure is necessarily large, so that intersystem crossing can be quite efficient. If the lowest triplet state is repulsive (as in the studied molecules) it may significantly contribute to the dissociation yield under certain experimental conditions.     

The intersection seam between the 11A′ and 21A′ states of ozone

The intersection seam between the two lowest ¹A^′ states of ozone has been determined. The potential energy surfaces and the seam are calculated and discussed in perimetric coordinates which exhibit the full three-dimensional symmetry. The seam is shown to form a closed curve which crosses the C _{2 v} -restricted coordinate planes at six points. Three of these correspond to the previously determined intersection, the starting point of the present search. The other three correspond to highly repulsive regions on the potential energy surface where two atoms approach each other to within two-thirds of the O₂ bond length. At the former three points both states have ¹ A ₁ symmetry, but at the latter three points one state has ¹ A ₁ symmetry whereas the other has ¹ B ₂ symmetry. Consequently, there exist three additional branches of the intersection seam between these two states. Each of these branches lies entirely in one C _{2 v} -restricted coordinate plane and connects to the previously discussed C _s -seam at one point. The existence of a further intersection seam is established. A novel method for determining intersection points is described. Received: 10 January 1996 / Accepted: 2 January 1997     

Study on conical columns with different conical angles for semi-preparative liquid chromatography

The dynamic flow profiles and separation performances in conically shaped preparative liquid chromatographic columns (inlet i.d. larger than outlet i.d.) with three different angles (7, 10 and 15) were studied and compared with cylindrical column of the same length and internal volume. The shapes of dynamic flow profiles were studied by on-column visualization method. The transparent chromatographic columns made of polymethyl methacrylate (PMMA), packed with C18 bonded silica, were immerged into a cubic pool filled with glycerol to eliminate the cylindrical and conical lens effect. The flow profiles of colored iodine solution in the columns were observed clearly using cyclohexane as mobile phase since the refractive indices of C18, column wall and the mobile phase are very close. In the conical column of 15 degrees (20-7 mm i.d.) the mobile phase in the central region migrated slower than in wall region as it moved toward the column outlet, while in the conical column of 7 degrees (17-11 mm i.d.) the mobile phase in the central region migrated faster than in wall region just like in cylindrical column. We found that a plug-like flow profile was generated in the conical column of 10 degrees (18-9 mm i.d.) during the whole migration process. A carmine and brilliant blue mixture was used as a probe to test the separation ability of the columns. The resolutions of the two compounds on the conical column of 7, 10, 15 and on the cylindrical column were 0.6, 1.57, 1.29 and 0.8, respectively.     

利用多扇区介质透镜得到TM01模激励的圆锥喇叭笔形波束辐射

 给出了一种改善TM₀₁模辐射特性的方法,由不同厚度的扇区组成的介质透镜放置于圆锥喇叭口径处,适当地选择各个扇区的厚度,从而产生圆极化的轴向为极大值的远场方向图。推导出了该天线辐射场的解析公式,解析结果与数值模拟有较好的吻合。当工作频率为5 GHz时,天线的增益达19.6 dB,口径效率31.3%,具有15.8%的带宽(反射系数S11<0.2), 且适合于高功率辐射。     

Analyzing the longitudinal effect of hypersonic flow past a conical cone via the perturbation method

To analyze the hypersonic flow past a conical cone, the variations of gasdynamic properties subjected to the longitudinal curvature effect by using the perturbation method. An outer perturbation expansion has been carried out by recent researchers, but a problem occurred, the outer expansion solutions are not uniformly valid in the shock layer, however, the outcome near the conical body surface called vortical layer remains deflective. This study intends to discover uniformly valid analytical solutions in the shock layer by applying the inner perturbation expansions matching with the out expansions to analyze the characteristics in the whole region including shock layer and vortical layer. Starting from the zero-order approximate solutions for hypersonic conical flow is then applied as the basic solutions for the outer perturbation expansions of a flow field. The governing equations and boundary conditions are also expanded via outer perturbations. Using an approximate analytical scheme in the derivation process, first-order perturbation equations can be simplified and the approximate closed-form solutions are obtained; furthermore, the various flow field quantities, including the normal force coefficient on the cone surface, have been calculated. According to the variations of gasdynamic properties, the longitudinal curvature effect for the hypersonic flow past a conical cone can be determined. Thicknesses of shock layer and vortical layer can be predicted as well. The physical phenomena inside both layers can be investigated carefully, the conditions for an elliptic cone with longitudinal curvature, m = 1 and n = 2 and other conditions of parameters; the perturbation parameter, ε_m2 = 0.1, semi-vertex angle of the unperturbed cone, δ = 10°, and hypersonic similarity parameter, K_δ = M_∞δ = 1.0, the thickness of vortical layer, η_VL, can be calculated at the position angle of conical cone body, ? = 30° was demonstrated here. Results show how very thin the vortical layer is approximately only 10% of the shock layer close to the body, the pressure in the whole shock layer is verified to be uniformly valid which agrees with previous studies. Large gradient changes in entropy and density are found when the flow approaches the cone surface, the most important is, this method provides a benchmark solution to the hypersonic flow past a conical cone and to assist the grids and numerics for numerical computation should be fashioned to accommodate the whole flow field region including the vortical layer of rapid adjustment, and let the analysis become more effective and low cost.     

Analysis of a conical horn fed by a slightly oversized waveguide

This paper discusses the case of a submillimetre conical feedhorn system which is overmoded due to an oversized waveguide, but is not in the geometric optics regime. The motivation for this system is to use the same feed as a multi-frequency receiver. Increased background loading is the greatest disadvantage in overmoded optics; and aperture efficiency also suffers due to non-optimum horn dimensions. The analysis is done using the Laguerre-Gauss beam expansion method.     

Heat flux measurement over a cone in a shock tube flow

This paper is the part 2 of our previous thin film heat transfer measurements. In the first report we measured time variations of heat flux over a cylinder placed in a shock tube flow and compared experimental results with CFD results, Saito et al. (Shock Waves 14:327–333, 2004). We report a result of heat transfer measurements over an 86° apex angle cone surface impinged by a Ms = 2.38 shock wave in air with distributed thin film transfer gauges along cone surface and its comparison with results of numerical simulations. We performed double exposure holographic interferometric observation, and also from the heat transfer measurement and numerical simulation, confirmed the presence of delayed transition from regular to Mach reflection over the cone. The numerical estimation of delayed transition distance from the apex agreed very well with experimental one.      

Explicit approximations of the indentation modulus of elastically orthotropic solids for conical indenters

The elastic problem of the contact between an axisymmetric indenter and a general anisotropic (21 independent elastic constants) half space has not been solved explicitly in closed form. Implicit methods to determine the indentation modulus originate from the work of Willis [J. Mech. Phys. Solids 14 (1966) 163]; and are now available for conical, parabolic and spherical indenters [Philos. Mag. A 81 (2001) 447; J. Mech. Phys. Solids 51 (2003) 1701]. The particular case of orthotropy has also been investigated [ASME J. Tribol. 115 (1193) 650, 125 (2003) 223]. This paper proposes an explicit solution for the indentation moduli of a transversely isotropic medium and a general orthotropic medium under rigid conical indentation in the three principal material symmetry directions. The half-space Green’s functions are interpolated from their exact extreme values, then integrated and finally simplified. The proposed closed form expressions are in very good agreement with the implicit solution schemes of [Philos. Mag. A 81 (2001) 447; J. Mech. Phys. Solids 51 (2003) 1701].     

晶体锥折射空心光束的位相差及偏振特性

根据双轴晶体内锥折射效应产生空心光环的基本原理,推导出空心光环上各点相对于光环最低点的位相差分布规律解析式.通过模拟得到了位相差分布规律,证明了光环上各点的偏振方向变化具有连续性.实验采用非偏振的He-Ne激光准直后经小孔光阑垂直照射KNbO3晶体获得了空心光束,对其偏振特性进行了测试,结果与理论分析相吻合,很好的验证了理论分析的正确性.