Tentatively identified and predicted H- Fano resonances

Positions are calculated for the Fano resonances that are due to interactions of the discrete autoionized 1s3s, 1s3p, and 1s4p states of H^- with overlapping split-configuration continua. The two first-mentioned resonances are tentatively identified with the diffuse interstellar doublets at λλ6376,6379 and λλ5780, 5797 on the basis of the relative positions of the autoionized states and the relative intensities of the doublet components.The observed wave-numbers of the 1s2s, 1s3s, 1s2p, and 1s3p resonances seem to belong to two series that converge towards a common limit in a kind of reverse Rydberg-series fashion. The position of the limit is close to 9000 Å, in accordance with theory. An extrapolation leads to the identification of the 1s4p resonance with the diffuse λ 6614 line. A further extrapolation leads to the prediction of positions at about 7183 and 7583 Å for the 1s5p and 1s6p resonances.The half-widths calculated for the singlet components of the 1s3p and 1s4p resonances are of the order of magnetude of those observed for the diffuse lines, and of the observed distance between the probably partly mixed singlet and triplet 1s3p components. The profile of the λ 5780 resonance is calculated on the basis of an assumed helium-line value for the oscillator strength. Its shape indicates that the “λ 5778 band” may be just a misinterpretation of the asymmetric wings.Tables of Hartree functions for the 3s², 3p² and 4p² configurations of H^- are given in an appendix.     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).     

Simulation of the inherent turbulence and wake interaction inside an infinitely long row of wind turbines

The turbulence in the interior of a wind farm is simulated using large eddy simulation and the actuator line technique implemented in the Navier–Stokes equations. The simulations are carried out for an infinitely long row of turbines simulated by applying cyclic boundary conditions at the inlet and outlet. The simulations investigate the turbulence inherent to the wind turbines as no ambient turbulence or shear is added to this idealised case. The simulated data give insight into the performance of the wind turbines operating in the wake of others as well as details on key turbulent quantities. One of the key features of wakes behind wind turbines is the dynamic wake meandering, which is shown to be related to the wind turbine spacing and the vortex shedding from the turbine as a bluff body. The flow is analysed and reconstructed by applying proper orthogonal decomposition.     

Bier Spheres and Posets

In 1992 Thomas Bier presented a strikingly simple method to produce a huge number of simplicial (n – 2)-spheres on 2n vertices, as deleted joins of a simplicial complex on n vertices with its combinatorial Alexander dual. Here we interpret his construction as giving the poset of all the intervals in a boolean algebra that “cut across an ideal.” Thus we arrive at a substantial generalization of Bier’s construction: the Bier posets Bier(P, I) of an arbitrary bounded poset P of finite length. In the case of face posets of PL spheres this yields cellular “generalized Bier spheres.” In the case of Eulerian or Cohen–Macaulay posets P we show that the Bier posets Bier(P, I) inherit these properties. In the boolean case originally considered by Bier, we show that all the spheres produced by his construction are shellable, which yields “many shellable spheres,” most of which lack convex realization. Finally, we present simple explicit formulas for the g-vectors of these simplicial spheres and verify that they satisfy a strong form of the g-conjecture for spheres.     

Map dependence of the fractal dimension deduced from iterations of circle maps

Every orientation preserving circle mapg with inflection points, including the maps proposed to describe the transition to chaos in phase-locking systems, gives occasion for a canonical fractal dimensionD, namely that of the associated set of for whichf =+g has irrational rotation number. We discuss how this dimension depends on the orderr of the inflection points. In particular, in the smooth case we find numerically thatD(r)=D(r ^–1)=r ^–1/8.     

Convergence rate of numerical solutions to SFDEs with jumps

In this paper, we are interested in numerical solutions of stochastic functional differential equations with jumps. Under a global Lipschitz condition, we show that the pth-moment convergence of Euler-Maruyama numerical solutions to stochastic functional differential equations with jumps has order 1/p for any p≥2. This is significantly different from the case of stochastic functional differential equations without jumps, where the order is 1/2 for any p≥2. It is therefore best to use the mean-square convergence for stochastic functional differential equations with jumps. Moreover, under a local Lipschitz condition, we reveal that the order of mean-square convergence is close to 1/2, provided that local Lipschitz constants, valid on balls of radius j, do not grow faster than logj.     

Radiative capture of protons by the deformed nuclide232Th

The excitation function for the radiative capture²³²Th(p, γ)²³³Pa has been determined in the proton energy range 7 to 20 MeV by an activation method. The results are compared with a compound nucleus model prediction and earlier experimental data for another deformed nuclide¹⁷⁶Yb. As in previous cases an enhancement over the CN-model prediction is observed and the excitation of the giant dipole resonance via the direct-semidirect reaction process is a likely explanation. Supplementary measurements of the²³²Th (p, f) excitation function in the proton energy range 11–20 MeV have been performed.     

Three-Body Recombination with Two-Channel Contact Interactions

We use a two-channel contact interaction model to describe a system of three identical bosons. The two-channel model quantitatively describes the phenomena of Feshbach resonance in agreement with the phenomenological expression relating scattering length to magnetic detuning. The model also has a finite effective range. We investigate finite range effects in three-body recombination. The simpler one-channel contact interaction model predicts a characteristic geometric scaling of minima in the recombination coefficient as a function of scattering length with scaling parameter 22.7. We show that this factor is reduced when the effective range is included. We compare calculations to experiment.     

A Runge-Kutta method for index 1 stochastic differential-algebraic equations with scalar noise

The paper deals with the numerical treatment of stochastic differential-algebraic equations of index one with a scalar driving Wiener process. Therefore, a particularly customized stochastic Runge-Kutta method is introduced. Order conditions for convergence with order 1.0 in the mean-square sense are calculated and coefficients for some schemes are presented. The proposed schemes are stiffly accurate and applicable to nonlinear stochastic differential-algebraic equations. As an advantage they do not require the calculation of any pseudo-inverses or projectors. Further, the mean-square stability of the proposed schemes is analyzed and simulation results are presented bringing out their good performance.