Connections between Classical and Parametric Network Entropies

This paper explores relationships between classical and parametric measures of graph (or network) complexity. Classical measures are based on vertex decompositions induced by equivalence relations. Parametric measures, on the other hand, are constructed by using information functions to assign probabilities to the vertices. The inequalities established in this paper relating classical and parametric measures lay a foundation for systematic classification of entropy-based measures of graph complexity.

PHOTOPERTURBATION OF THE (1)A-][-(5)T SPIN EQUILIBRIUM IN AN IRON(II) COMPLEX IN SOLUTION VIA LIGAND-FIELD EXCITATION

Variable-temperature magnetic susceptibility measurements in the solid state of the bis complex of tris(1-pyrazolyl)-methane with Fe(II), [Fe(tpm)2](ClO4)2, suggest the existence of singlet-quintet spin crossover with the singlet isomer largely favored at room temperature. In acetonitrile solution, measurement of the absorption spectrum as a function of temperature reveals a spin equilibrium with the quintet population varying from ca. 6% at 233 K to ca. 30% at 295 K. When the complex in solution is irradiated with a laser pulse at wavelengths within the ligand field absorption band of the singlet isomer, ground-state depletion occurs within the pulse duration followed by fast recovery to the original absorbance level with a time constant of 25 +/- 5ns. The recovery time is virtually independent of temperature over the range +23 to -43-degrees-C, but the signal:noise ratio of the transient signals increases with decreasing temperature. The effect was observable at several monitoring wavelengths spanning the LF and MLCT absorption regions of the complex but only when the irradiation wavelength fell within the LF absorption region. Irradiation within the MLCT band produced no effect other than that of laser pulse scatter. The observations are interpreted in terms of photoperturbation of the singlet-quintet spin state equilibrium, which in this case occurs solely through excitation in the ligand field absorption region of the complex and is the first reported instance of this type for a spin-crossover complex in solution.

CONTRIBUTION OF RESONANCE RAMAN EXCITATION SPECTROSCOPY FOR PROBING ELECTRONICALLY EXCITED-STATES - NATURE OF A PORPHYRIN-DNA EXCIPLEX

The resonance Raman spectra of a water-soluble metalloporphyrin Cu(TMpy-P4), complexed with a synthetic nucleic acid, poly(dA-dT), were measured by using excitation wavelengths located within the B (Soret) transition of the porphyrin (417-470 nm), while its excited state was synchronously pumped with 545-nm pulsed excitation corresponding to the Q transition. In the presence of pump pulses, the aqueous solution of the Cu(TMpy-P4).poly(dA-dT) complex exhibits resonance Raman bands at 1558 and 1353 cm-1 that are not observed in the absence of pump pulses. These new features were previously assigned to electronically excited Cu(TMpy-P4), stabilized by forming an exciplex with the A-T sites of the nucleic acid. Here we present resonance Raman excitation profiles (RREP) of both the excited and ground states of the complex, and we experimentally confirm the very short lifetime of the exciplex. To our knowledge this is the first time that a RREP of a very short lived (ca. 20 ps) intermediate excited state has been obtained with a two-color experiment. We use this to help to characterize the nature of the porphyrin-AT specific complex formed in the porphyrin excited state.

Electron-impact excitation of CrII: A theoretical calculation of effective collision strengths for optically allowed transitions.

In this paper, we present electron-impact excitation collision strengths and Maxwellian averaged effective collision strengths for the complicated iron-peak ion Cr II. We consider specifically the allowed lines for transitions from the 3d(5) and 3d(4)4s even parity configuration states to the 3d(4)4p odd parity configuration levels. The parallel suite of R-Matrix packages, RMATRX II, which have recently been extended to allow for the inclusion of relativistic effects, were used to compute the collision cross sections. A total of 108 LS pi/280 J pi levels from the basis configurations 3d(5), 3d(4)4s, and 3d(4)4p were included in the wavefunction representation of the target including all doublet, quartet, and sextet terms. Configuration interaction and correlation effects were carefully considered by the inclusion of seven more configurations and a pseudo-corrector (4d) over bar type orbital. The 10 configurations incorporated into the Cr II model thus listed are 3d(5), 3d(4)4s, 3d(4)4p, 3d(3)4s(2), 3d(3)4p(2), 3d(3)4s4p, 3d(4)(4d) over bar, 3d(3)4s (4d) over bar, 3d(3)4p (4d) over bar, and 3d(3)(4d) over bar (2), constituting the largest Cr II target model considered to date in a scattering calculation. The Maxwellian averaged effective collision strengths are computed for a wide range of electron temperatures 2000-100,000 K which are astrophysically significant. Care has been taken to ensure that the partial wave contributions to the collision strengths for these allowed lines have converged with "top-up" from the Burgess-Tully sum rule incorporated. Comparisons are made with the results of Bautista et al. and significant differences are found for some of the optically allowed lines considered.

Determining the parametric effectiveness of a CAD model

The motivation for this paper is to present an approach for rating the quality of the parameters in a computer-aided design model for use as optimization variables. Parametric Effectiveness is computed as the ratio of change in performance achieved by perturbing the parameters in the optimum way, to the change in performance that would be achieved by allowing the boundary of the model to move without the constraint on shape change enforced by the CAD parameterization. The approach is applied in this paper to optimization based on adjoint shape sensitivity analyses. The derivation of parametric effectiveness is presented for optimization both with and without the constraint of constant volume. In both cases, the movement of the boundary is normalized with respect to a small root mean squared movement of the boundary. The approach can be used to select an initial search direction in parameter space, or to select sets of model parameters which have the greatest ability to improve model performance. The approach is applied to a number of example 2D and 3D FEA and CFD problems.

Electron impact excitation of Kr XXVIII

Collision strengths (Ω ) are calculated for all 6328 transitions among the lowest 113 levels belonging to the 2s22p5,2s2p6,2s22p43ℓ,2s2p53ℓ, and 2p63ℓ configurations of fluorine-like krypton, Kr XXVIII, using the Dirac Atomic R -matrix Code. All partial waves with angular momentum J⩽40 are included, sufficient for the convergence of Ω for forbidden transitions. For allowed transitions a top-up is employed to obtain converged values of Ω up to an energy of 400 Ryd. Resonances in the thresholds region are resolved on a narrow energy mesh, and results for effective collision strengths (ϒ) are obtained after averaging the values of Ω over a Maxwellian distribution of electron velocities. Values of ϒ are reported over a wide temperature range below View the MathML source, and the accuracy of the results is assessed. In addition, effective collision strengths are listed for the temperature range View the MathML source, obtained from non-resonant collision strengths generated with the FAC code.

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Li II, Be III, B IV and C V

We report calculations for energy levels, radiative rates and electron impact excitation rates for transitions in He-like Li II, Be III, B IV and C V. grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates. For determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (darc) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 49 levels of each ion. Collision strengths have been averaged over a Maxwellian velocity distribution and the effective collision strengths so obtained are reported over a wide temperature range up to 10(6) K. Comparisons have been made with similar data obtained from the flexible atomic code (FAC) to highlight the importance of resonances, included in calculations from darc, in the determination of effective collision strengths. Discrepancies between the collision strengths from darc and fac, particularly for weak transitions and at low energies, have also been discussed. Additionally, lifetimes are also listed for all calculated levels of the above four ions.

Energy levels, radiative rates and electron impact excitation rates for transitions in Si XII, Si XIII and Si XIV

In this paper, we report calculations of energy levels, radiative rates and electron impact excitation rates for transitions in Li-like Si XII, He-like Si XIII and H-like Si XIV. The grasp (general-purpose relativistic atomic structure package) is adopted for calculating energy levels and radiative rates, while for determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (darc) is used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 24 levels of Si XII, 49 levels of Si XIII and 25 levels of Si XIV, belonging to the n≤5 configurations. Collision strengths have been averaged over a Maxwellian electron velocity distribution and the effective collision strengths so obtained are reported over a wide temperature range below 107 K. Comparisons have been made with similar data obtained from the flexible atomic code (fac) to highlight the importance of resonances, included in calculations from darc, in the determination of effective collision strengths. Discrepancies between the collision strengths from darc and fac, particularly for weak transitions and at low energies, are also discussed. Additionally, lifetimes are listed for all calculated levels of the above three ions, although no measurements are available with which to compare.

Energy levels, radiative rates and electron impact excitation rates for transitions in H-like N VII, O VIII, F IX, Ne X and Na XI

We report calculations of energy levels, radiative rates and electron impact excitation rates for transitions in H-like N VII, O VIII, F IX, Ne X and Na XI. The general-purpose relativistic atomic structure package (grasp) is adopted for calculating energy levels and radiative rates, while the Dirac atomic R-matrix code (DARC) and the flexible atomic code (FAC) are used for determining the collision strengths and subsequently the excitation rates. Oscillator strengths, radiative rates and line strengths are listed for all E1, E2, M1 and M2 transitions among the lowest 25 levels of the above five ions. Collision strengths have been averaged over a Maxwellian velocity distribution, and the effective collision strengths so obtained are reported over a wide temperature range below 10(7) K. Additionally, lifetimes are also given for all the calculated energy levels of the above five ions.

Energy levels, radiative rates and electron impact excitation rates for transitions in Li-like N V, F VII, Ne VIII and Na IX

In this paper, we report calculations of energy levels, radiative rates and electron impact excitation rates for transitions in Li-like N V, F VII, Ne VIII and Na IX. The general-purpose relativistic atomic structure package (GRASP) is adopted for calculating energy levels and radiative rates, while for determining the collision strengths and subsequently the excitation rates, the Dirac atomic R-matrix code (DARC) and the flexible atomic code (FAC) are used. Oscillator strengths, radiative rates and line strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 24 levels of N V, F VII, Ne VIII and Na IX. Collision strengths have been averaged over a Maxwellian velocity distribution and the effective collision strengths so obtained are reported over a wide temperature range below 10(6.6) K. Additionally, lifetimes are also reported for all calculated levels of the above four ions.

Radiative rates and electron impact excitation rates for transitions in Cr VIII

Aims. In this paper we report on calculations of energy levels, radiative rates, oscillator strengths, line strengths, and effective collision strengths for transitions among the lowest 362 levels of the (1s22s22p6) 3s23p5, 3s3p6, 3s23p43d, 3s3p53d, 3s23p33d2, 3s3p43d2, 3p63d, and 3s23p44 configurations of Cr viii. Methods. The general-purpose relativistic atomic structure package (grasp) and flexible atomic code (fac) are adopted for the calculations. Results. Radiative rates, oscillator strengths, and line strengths are reported for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transitions among the 362 levels. Comparisons are made with earlier available results and the accuracy of the data is assessed. Additionally, lifetimes for all 362 levels are listed, although comparisons with other theoretical results are limited to only a few levels. Our energy levels are estimated to be accurate to better than 3% (within 0.4 Ryd), whereas results for other parameters are probably accurate to better than 20%. Finally, electron impact collision strengths and excitation rates are computed for all transitions over a wide energy (temperature) range. For these calculations, FAC is adopted and results in the form of effective collision strengths are reported over a wide temperature range of 105.0−106.6 K.

Energy levels, radiative rates and electron impact excitation rates for transitions in He-like Cl XVI, K XVIII, Ca XIX and Sc XX.

We report calculations of energy levels, radiative rates and electron impact excitation cross
sections and rates for transitions in He-like Cl XVI, K XVIII, Ca XIX and Sc XX. The grasp
(general-purpose relativistic atomic structure package) is adopted for calculating energy levels
and radiative rates. To determine the collision strengths and subsequently the excitation rates,
the Dirac atomic R-matrix code (darc) is used. Oscillator strengths, radiative rates and line
strengths are reported for all E1, E2, M1 and M2 transitions among the lowest 49 levels of
each ion. Collision strengths are averaged over a Maxwellian velocity distribution and the
effective collision strengths obtained listed over a wide temperature range up to 107.4 K.
Comparisons are made with similar data obtained from the flexible atomic code (fac) to
highlight the importance of resonances, included in calculations with darc, in the
determination of effective collision strengths. Discrepancies between the collision strengths
from darc and fac, particularly for forbidden transitions, are also discussed. Additionally,
theoretical lifetimes are listed for all the 49 levels of the above four ions.