A direct comparison of high-speed methods for the numerical Abel transform

The Abel transform is a mathematical operation that transforms a cylindrically symmetric three-dimensional (3D) object into its two-dimensional (2D) projection. The inverse Abel transform reconstructs the 3D object from the 2D projection. Abel transforms have wide application across numerous fields of science, especially chemical physics, astronomy, and the study of laser-plasma plumes. Consequently, many numerical methods for the Abel transform have been developed, which makes it challenging to select the ideal method for a specific application. In this work eight transform methods have been incorporated into a single, open-source Python software package (PyAbel) to provide a direct comparison of the capabilities, advantages, and relative computational efficiency of each transform method. Most of the tested methods provide similar, high-quality results. However, the computational efficiency varies across several orders of magnitude. By optimizing the algorithms, we find that some transform methods are sufficiently fast to transform 1-megapixel images at more than 100 frames per second on a desktop personal computer. In addition, we demonstrate the transform of gigapixel images.Comment: 9 pages, 5 figure

AUTODETACHMENT AND VIBRONIC COUPLED PHOTODETACHMENT TRANSITIONS OF C2H3O−

\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.7, clip]{C2H3O-PESvsMiller.eps} \end{wrapfigure} The photoelectron spectrum of the vinoxy anion C$_2$H$_3$O$^-$ is studied using velocity-imaging, with the angular distributions providing electronic-state and vibrational-mode specific characterization. A 355~nm photoelectron spectrum, together with anisotropy parameters determined for some of the stronger transitions is show in the figure. Photodetachment at longer wavelengths have also been measured. The spectroscopic analysis builds on a previous SEVI\footnote{Slow-Electron-Velocity-map-Imaging: Yacovitch \emph{et al.} J Chem Phys \textbf{130} 244309 (2009) doi:10.1063/1.3157208} study, and a CRDS\footnote{Cavity-Ring-Down-Spectroscopy: Thomas \emph{et al.} J Chem Phys \textbf{132} 114302 (2010) doi:10.1063/1.3352976} work. Forbidden asymmetric vibrational modes may gain intensity through vibronic coupling between the neutral ground state and an excited state, of the correct symmetry, and have an anomalous anisotropy parameter. The positive $\tilde{X}$ transition is $9^2_0 11^1_1$. In addition, the vinoxy anion has dipole-bound excited electronic states, that produce very narrow transitions. For C$_2$H$_3$O$^-$ there is evidence of autodetachment from dipole-bound states of the anion, and vibronic coupling of the neutral ground state. \makeatletter{\renewcommand*{\@makefnmark}{}\footnotetext{Research supported by the Australian Research Council Discovery Project Grant DP160102585.}\makeatother

Electron anisotropy as a signature of mode specific isomerization in vinylidene

[RESEARCH SUPPORTED BY THE AUSTRALIAN RESEARCH_X000D_ COUNCIL DISCOVERY PROJECT GRANT DP160102585] The nature of the isomerization process that turns vinylidene into acetylene has been awaiting advances in experimental methods, to better define fractionation widths beyond those available in the seminal 1989 photoelectron spectrum measurement.\footnote{K. M. Ervin, J. Ho, and W. C. Lineberger, \emph{J. Chem. Phys.} \textbf{91}, 5974 (1989). doi:10.1063/1.457415} This has proven a challenge. The technique of velocity-map imaging (VMI) is one avenue of approach. Images of electrons photodetached from vinylidene negative-ions, at various wavelengths, 1064~nm shown, provide more detail, including unassigned structure, but only an incremental improvement in the instrument line width. Intriguingly, the VMIs demonstrate a mode dependent variation in the electron anisotropy. Most notable in the figure, the inner-ring transition clusters are discontinuously, more isotropic. Electron anisotropy may provide an alternative key to examine the character of vinylidene transitions, mediating the necessity for an extreme resolution measurement. Vibrational dependent anisotropy has previously been observed in diatomic photoelectron spectra, associated with the coupling of electronic and nuclear motions.\footnote{M. van Duzor \emph{et al.} \emph{J. Chem. Phys.} \textbf{133}, 174311 (2010). doi:10.1063/1.3493349}Research supported by the Australian Research Council Discovery Project Grant dp160102585

Photodetachment of O− yielding o(1D2, 3P) atoms, viewed with velocity map imaging

\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.35]{O-fig.eps} \end{wrapfigure} Electron photodetachment of O$^-$($^{2}P_{3/2,1/2}$) is measured using velocity-map imaging at wavelengths near 350~nm, where detachment yields both O($^1\!D_2$) and O($^3P_{2,1,0}$) atoms, simultaneously, producing slow ($\sim 0.1$~eV) and fast electrons ($\sim 2$~eV). The photoelectron spectrum resolves the fine-structure transitions, which together with the well known atomic fine-structure splittings,\footnote{physics.nist.gov/cgi-bin/ASD/energy1.pl} and intensity ratios,\footnote{O. Scharf and M. R. Godefried, arXiv:0808.3529v1} provide an excellent test of the spectral quality of the velocity-map imaging technique. Although the photoelectron angular distribution for the two atomic limits have the same negative anisotropy sign, the energy dependence differs. The variation is qualitatively in accordance with $R$-matrix cross section calculations, that indicate a more gradual $d$-wave onset for the $^1\!D$ limit.\footnote{O. Zatsarinny and K. Bartschat, \emph{Phys. Rev. A}, \textbf{73}, 022714 (2006). doi:10.1103/PhysRevA.73.022714} However, more exact evaluation is only possible with information about the matrix element phases

Photodissociation of interstellar N2

Molecular nitrogen is one of the key species in the chemistry of interstellar clouds and protoplanetary disks and the partitioning of nitrogen between N and N2 controls the formation of more complex prebiotic nitrogen-containing species. The aim of this work is to gain a better understanding of the interstellar N2 photodissociation processes based on recent detailed theoretical and experimental work and to provide accurate rates for use in chemical models. We simulated the full high-resolution line-by-line absorption + dissociation spectrum of N2 over the relevant 912-1000 \AA\ wavelength range, by using a quantum-mechanical model which solves the coupled-channels Schr\"odinger equation. The simulated N2 spectra were compared with the absorption spectra of H2, H, CO, and dust to compute photodissociation rates in various radiation fields and shielding functions. The effects of the new rates in interstellar cloud models were illustrated for diffuse and translucent clouds, a dense photon dominated region and a protoplanetary disk.Comment: Online database: http://home.strw.leidenuniv.nl/~ewine/phot

DECOMPOSITION OF VIBRONIC AND RENNER-TELLER STRUCTURE IN C2H AND C2D FROM ANION HIGH-RESOLUTION PHOTOELECTRON IMAGING

\begin{wrapfigure}{r}{0pt} \includegraphics[scale=0.5,clip]{C2DvsC2H-PES.eps} \end{wrapfigure} The ethynyl radial, C$_2$H, has a complex spectral structure due to vibronic coupling between the ground \tilde{X}\,^2\Sigma^+ and low-lying \tilde{A}\,^2\Pi electronic states, and a Renner-Teller interaction within the $\Pi$ state. A good understanding of the low-lying rovibrational structure has come from measurements, including slow electron velocity-map imaging of anion photoelectron spectra\footnote{J. Zhou \emph{et al.} \emph{J. Chem. Phys.} \textbf{127}, 114313 (2007).}, and \emph{ab initio} calculations\footnote{R. Tarroni and S. Carter, \emph{J. Chem. Phys.} \textbf{119}, 12878 (2003).}, that give wavefunction character. In this work, high-resolution photoelectron velocity-map imaging of C$_2$H$^-$ and C$_2$D$^-$ photodetachment (the 355~nm wavelength illustrated), provide a quantitative comparison over an extended energy range, to reveal unassigned structure, anomalous intensities, and illustrate the dramatic difference between isotopologues in the region of the $A$-state. These measurements, together with the measured photoelectron angular distributions, provide new insight into the non-adiabatic couplings of ethynyl. \makeatletter{\renewcommand*{\@makefnmark}{}\footnotetext{Research supported by the Australian Research Council Discovery Project Grant DP160102585.}\makeatother

VIBRONIC COUPLING IN THE GROUND STATE OF VINYLIDENE X̃ 1A1 H2CC

begin{wrapfigure}{r}{0pt}_x000d_ includegraphics[scale=.8, clip]{../images/2758_image.eps}_x000d_ end{wrapfigure}_x000d_ The nature of the isomeration process that turns vinylidene H$_2$CC to_x000d_ acetylene HCCH, requiring a 1,2-hydrogen atom shift across the molecule,_x000d_ is a long standing puzzle that has its origin in a 1989 photoelectron_x000d_ measurement of vinylidide (H$_2$CC$^-$)footnote{K. M. Ervin emph{et al.} emph{J. Chem. Phys.}textbf{91} 5974 (1991).}._x000d_ In recent years the photoelectron spectrum of vinylidide has been_x000d_ revisited, using improved experimental techniques, including velocity-map imaging for the detection of photoelectrons, low-temperature near-threshold methods (cryo-SEVI)footnote{J. A. De~Vine emph{et al.} emph{J. Am. Chem. Soc.} textbf{138} 16417 (2016).}, and sophisticated emph{ab inito} calculationsfootnote{L.~Guo emph{et al.} emph{J. Phys. Chem.} textbf{119} 8488 (2015).}. The simple normal-mode structure, 1064~nm velocity-map image illustrated, is proving a challenge to decipher. However, the dramatic change in the photoelectron angular distribution of the inner-ring structure is characteristic of vibronic couplingfootnote{A. Weaver emph{et al.} emph{J. Chem. Phys.} textbf{94} 1740 (1991).}. The lowest electronic state with the correct symmetry, $tilde{B}; ^{1}!B_2$, is 4eV higher in energy.makeatletter{renewcommand*{@makefnmark}{}footnotetext{Research supported by the Australian Research Council Discovery Project Grant DP160102585.}makeatother

Vibronic coupling in the superoxide anion: The vibrational dependence of the photoelectron angular distribution

We present a comprehensive photoelectron imaging study of the O₂(X³Σg⁻,v′=0–6)←O₂⁻(X²Πg,v′′=0) and O₂(a¹Δg,v′=0–4)←O₂⁻(X²Πg,v′′=0)photodetachment bands at wavelengths between 900 and 455 nm, examining the effect of vibronic coupling on the photoelectron angular distribution (PAD). This work extends the v′=1–4 data for detachment into the ground electronic state, presented in a recent communication [R. Mabbs, F. Mbaiwa, J. Wei, M. Van Duzor, S. T. Gibson, S. J. Cavanagh, and B. R. Lewis, Phys. Rev. A82, 011401–R (2010)]. Measured vibronic intensities are compared to Franck–Condon predictions and used as supporting evidence of vibronic coupling. The results are analyzed within the context of the one-electron, zero core contribution (ZCC) model [R. M. Stehman and S. B. Woo, Phys. Rev. A23, 2866 (1981)]. For both bands, the photoelectron anisotropy parameter variation with electron kinetic energy,β(E), displays the characteristics of photodetachment from a d-like orbital, consistent with the π∗g 2p highest occupied molecular orbital of O₂⁻. However, differences exist between the β(E) trends for detachment into different vibrational levels of the X³Σg⁻ and a ¹Δg electronic states of O₂. The ZCC model invokes vibrational channel specific “detachment orbitals” and attributes this behavior to coupling of the electronic and nuclear motion in the parent anion. The spatial extent of the model detachment orbital is dependent on the final state of O₂: the higher the neutral vibrational excitation, the larger the electron binding energy. Although vibronic coupling is ignored in most theoretical treatments of PADs in the direct photodetachment of molecular anions, the present findings clearly show that it can be important. These results represent a benchmark data set for a relatively simple system, upon which to base rigorous tests of more sophisticated models.The authors gratefully acknowledge support by the National Science Foundation Grant No. CHE-0748738 and ANU ARC Discovery Projects under Grant Nos. DP0666267 and DP0880850

Source of Nitrogen Isotope Anomaly in HCN in the Atmosphere of Titan

The ^(14)N/^(15)N ratio for N_2 in the atmosphere of Titan was recently measured to be a factor of 2 higher than the corresponding ratio for HCN. Using a one-dimensional photochemical model with transport, we incorporate new isotopic photoabsorption and photodissociation cross sections of N_2, computed quantum-mechanically, and show that the difference in the ratio of ^(14)N/^(15)N between N_2 and HCN can be explained primarily by the photolytic fractionation of ^(14)N^(14)N and ^(14)N ^(15)N. The [HC^(14)N]/[HC^(15)N] ratio produced by N_2 photolysis alone is 23. This value, together with the observed ratio, constrains the flux of atomic nitrogen input from the top of the atmosphere to be in the range (1-2) × 10^9 atoms cm^(-2) s^(-1)

A Robust Solution Procedure for Hyperelastic Solids with Large Boundary Deformation

Compressible Mooney-Rivlin theory has been used to model hyperelastic solids, such as rubber and porous polymers, and more recently for the modeling of soft tissues for biomedical tissues, undergoing large elastic deformations. We propose a solution procedure for Lagrangian finite element discretization of a static nonlinear compressible Mooney-Rivlin hyperelastic solid. We consider the case in which the boundary condition is a large prescribed deformation, so that mesh tangling becomes an obstacle for straightforward algorithms. Our solution procedure involves a largely geometric procedure to untangle the mesh: solution of a sequence of linear systems to obtain initial guesses for interior nodal positions for which no element is inverted. After the mesh is untangled, we take Newton iterations to converge to a mechanical equilibrium. The Newton iterations are safeguarded by a line search similar to one used in optimization. Our computational results indicate that the algorithm is up to 70 times faster than a straightforward Newton continuation procedure and is also more robust (i.e., able to tolerate much larger deformations). For a few extremely large deformations, the deformed mesh could only be computed through the use of an expensive Newton continuation method while using a tight convergence tolerance and taking very small steps.Comment: Revision of earlier version of paper. Submitted for publication in Engineering with Computers on 9 September 2010. Accepted for publication on 20 May 2011. Published online 11 June 2011. The final publication is available at http://www.springerlink.co