Drop size spectra in sprays from pressure-swirl atomizers

A study on the characterization of sprays from Newtonian liquids produced by pressure-swirl atomizers is presented. The global drop size spectra of the sprays are measured with phase-Doppler anemometry, and global mean drop sizes are derived as moments of the spectra for varying atomizer geometry, liquid flow rate, and physical properties of the liquids. Dimensional analysis provides a correlation for the non-dimensional global Sauter mean diameter. A relationship between the global Sauter mean drop size and the global drop size RMS is established. A method is developed for predicting the global drop size spectra in the sprays, using easily accessible experimental input parameters. The basis for the function defining the spectrum is a gamma distribution, which is known from the literature as physically relevant for ligament-mediated sprays.     

Structure of node polynomials for curves on surfaces

We provide a structural generalization of a theorem by Kleiman–Piene, concerning the enumerative geometry of nodal curves in a complete linear system on a smooth projective surface S. Provided that r, the number of nodes, is sufficiently small compared to the ampleness of the linear system, we show that, under certain assumptions, the number of r‐nodal curves passing through points in general position on S is given by a Bell polynomial in universally defined integers which we identify, using classical intersection theory, as linear, integral polynomials evaluated in four basic Chern numbers. Furthermore, we provide a decomposition of the as a sum of three terms with distinct geometric interpretations, and discuss the relationship between these polynomials and Kazarian's Thom polynomials for multisingularities of maps.     

Photoinduced Nonadiabatic Dynamics of 9H‐Guanine

Surface‐hopping simulations are used to study the nonradiative relaxation of 9H‐guanine. Two distinct S₁→S₀ (ππ*→gs) decay channels, both of which pass through a conical intersection (CI), are found to be responsible for the experimentally observed double‐decay behavior (see schematic diagram).

     

The effect of molecular distortions on spin–orbit coupling in simple hydrocarbons

Recent work [D.N.S. Parker et al., Chem. Phys. Lett. 469 (2009) 43–49] has found intersystem crossing (ISC) on an ultrafast timescale in electronically excited benzene, a surprise as hydrocarbons generally have small spin–orbit coupling. In this paper, the effect of molecular distortions on spin–orbit coupling (SOC) is calculated for cyclobutadiene and benzene. At equilibrium the SOC in both molecules is negligible, and therefore terms arising from molecular distortions must play a significant role in any fast ISC. We show that out-of-plane C–H bends, which leads to the hybridisation of σ and π orbitals, are responsible for the most significant effect. The S₁/S₀ conical intersection is an important feature for understanding the photochemistry of these molecules. We examine the SOC along the vector from the Franck–Condon point to the lowest energy point on the crossing seam and discuss the potential importance of the SOC to the ultrafast dynamics.     

The real interpolation method on couples of intersections

Suppose that (X ₀, X ₁) is a Banach couple, X ₀ ∩ X ₁ is dense in X ₀ and X ₁, (X₀,X₁)_θq (0 < θ < 1, 1 ≤ q < ∞) are the spaces of the real interpolation method, ψ ∈ (X ₀ ∩ X ₁), ψ ≠ 0, is a linear functional, N = Ker ψ, and N _i stands for N with the norm inherited from X _i (i = 0, 1). The following theorem is proved: the norms of the spaces (N₀,N₁)_θ,q and (X₀,X₁)_θ,q are equivalent on N if and only if θ ? (0, α) ∪ (β_∞, α₀ ∪ (β₀, α_∞) ∪ (β, 1), where α, β, α₀, β₀, α_∞, and β _∞ are the dilation indices of the function k(t)=K(t,ψ;X ₀ ^* ,X ₁ ^* ).     

The Jahn-Teller and pseudo-Jahn-Teller effects in the anion photoelectron spectroscopy of B3 cluster

The photodetachment spectroscopy of B3- anion is theoretically studied with the aid of a quantum dynamical approach. The theoretical results are compared with the available experimental photoelectron spectra of B3-. Both B3- and B3 possess D(3h) symmetry at the equilibrium configuration of their electronic ground state. Distortion of B3 along its degenerate vibrational mode nu2 splits the degeneracy of its excited C2E' electronic manifold and exhibits (E [symbol: see text] e)-Jahn-Teller (JT) activity. The components of the JT split potential energy surface form conical intersections, and they can also undergo pseudo-Jahn-Teller (PJT) crossings with the X2A1' electronic ground state of B3 via the degenerate nu2 vibrational mode. The impact of the JT and PJT interactions on the nuclear dynamics of B3 in its X2A1'-C2E' electronic states is examined here by establishing a diabatic model Hamiltonian. The parameters of the electronic part of this Hamiltonian are calculated by performing electronic structure calculations and the nuclear dynamics on it is simulated by solving quantum eigenvalue equation. The theoretical results are in good accord with the experimental data.     

A random construction for permutation codes and the covering radius

We analyse a probabilistic argument that gives a semi-random construction for a permutation code on n symbols with distance n − s and size Θ(s!(log n)^1/2), and a bound on the covering radius for sets of permutations in terms of a certain frequency parameter.      

Electronic structure of the photoactive yellow protein chromophore: Ab initio study of the low-lying excited singlet states

The excited electronic states of the p-coumaric acid thio-ester chromophore of the Photoactive Yellow Protein (PYP) are characterized in view of identifying the key factors determining the chromophore's isomerisation. These factors include the anionic nature of the chromophore, the presence of sulfur (rather than oxygen or nitrogen) in the ester moiety, and the presence of a hydrogen-bonding environment stabilizing the phenolate moiety. Two twisted stationary S₁ structures are identified, corresponding to a twist around the double bond conjugated with the aromatic ring, and the single bond adjacent to the ring, respectively. The latter structure is accessed directly by relaxation from the Franck–Condon (FC) geometry. These structures are shown to entail a substantial polarization effect (increasing charge separation when moving towards the twisted geometry). Further, an inversion of charge character is observed for the double-bond twisted minimum, which can be accounted for by the vicinity of an S₁–S₀ conical intersection. The S₁–S₀ gap at the minimum geometries depends in a sensitive fashion on the -carbonyl heteroatom. Based upon these observations for the intrinsic properties of the chromophore, we further address the effect of the Arg52 residue, which acts as a counter-ion in the native protein environment.     

Stable intersections of affine cantor sets

We construct open sets of pairs of affine Cantor sets (K, K′) with the simplest possible combinatorics (i. e., defined by two affine increasing maps) which have stable intersection, while the product of lateral thicknesses τ_R(K) • τ_L (K′) is smaller than one. Thus, in a strong form, the converse to the following classic result due to Newhouse is not true: if the product of the thicknesses of two Cantor sets is bigger than one then there are translations of them which have stable intersection. We also describe the topological structure of K—K′ for typical pairs (K, K′) in this open set.