Electron-impact excitation of FeII - Collision strengths and effective collision strengths for low-lying fine-structure forbidden transitions

Context. Absorption or emission lines of Fe II are observed in many astrophysical spectra and accurate atomic data are required to interpret these lines. The calculation of electron-impact excitation rates for transitions among even the lowest lying levels of Fe II is a formidable task for theoreticians.

Aims. In this paper, we present collision strengths and effective collision strengths for electron-impact excitation of Fe II for low-lying forbidden transitions among the lowest 16 fine-structure levels arising from the four LS states 3d(6)4s D-6(e), 3d(7) F-4(e), 3d(6)4s D-4(e), and 3d(7) P-4(e). The effective collision strengths are calculated for a wide range of electron temperatures of astrophysical importance from 30-100 000 K.

Methods. The parallel suite of Breit-Pauli codes are utilised to compute the collision cross sections for electron-impact excitation of Fe II and relativistic terms are included explicitly in both the target and the scattering approximation. 100 LS or 262-jj levels formed from the basis configurations 3d(6)4s, 3d(7), and 3d(6)4p were included in the wavefunction representation of the target, including all doublet, quartet, and sextet terms. Collision strengths for a total of 34191 individual transitions were computed.

Results. A detailed comparison is made with previous theoretical works and significant differences were found to occur in the effective collision strengths, particularly at low temperatures.

Use of the child health utility and strengths and difficulties outcome measures in economic evaluations of school-based interventions: data from a cluster-randomised controlled trial in Northern Ireland

Background There is growing evidence linking early social and emotional wellbeing to later academic performance and various health outcomes including mental health. An economic evaluation was designed alongside the Roots of Empathy cluster-randomised trial evaluation, which is a school-based intervention for improving pupils’ social and emotional wellbeing. Exploration of the relevance of the Strengths and Diffi culties Questionnaire (SDQ) and Child Health Utility 9D (CHU9D) in school-based health economic evaluations is warranted. The SDQ is a behavioural screening questionnaire for 4–17-year-old children, consisting of a total diffi culties score, and also prosocial behaviour,
which aims to identify positive aspects of behaviour. The CHU9D is a generic preference-based health-related quality of life instrument for 7–17-year-old children.

Heat transport in harmonic oscillator systems with thermal baths: application to optomechanical arrays

We investigate the transport of phonons between N harmonic oscillators in contact with independent thermal baths and coupled to a common oscillator, and derive an expression for the steady state heat flow between the oscillators in the weak coupling limit. We apply these results to an optomechanical array consisting of a pair of mechanical resonators coupled to a single quantized electromagnetic field mode by radiation pressure as well as to thermal baths with different temperatures. In the weak coupling limit this system is shown to be equivalent to two mutually-coupled harmonic oscillators in contact with an effective common thermal bath in addition to their independent baths. The steady state occupation numbers and heat flows are derived and discussed in various regimes of interest.

Thermodynamics of trajectories of a quantum harmonic oscillator coupled to N baths

We undertake a thorough analysis of the thermodynamics of the trajectories followed by a quantum harmonic oscillator coupled to $N$ dissipative baths by using a new approach to large-deviation theory inspired by phase-space quantum optics. As an illustrative example, we study the archetypal case of a harmonic oscillator coupled to two thermal baths, allowing for a comparison with the analogous classical result. In the low-temperature limit, we find a significant quantum suppression in the rate of work exchanged between the system and each bath. We further show how the presented method is capable of giving analytical results even for the case of a driven harmonic oscillator. Based on that result, we analyse the laser cooling of the motion of a trapped ion or optomechanical system, illustrating how the emission statistics can be controllably altered by the driving force.

Factors influencing the compressive strengths of fly ash based geopolymers

Several factors affecting the reactivity of pulverised fuel ash (pfa) as a precursor for geopolymer concrete have been investigated. These include physical and chemical properties of various pfa sources, inclusion of ground granulated blast furnace slag (ggbs), chemical activator dosages and curing temperature. Alkali-activated pfa was found to require elevated curing temperatures and high alkali concentrations. A mixture of sodium hydroxide and sodium silicate was used and this was shown to result in high strengths, as high as 70 MPa at 28-days. The presence of silicates in solution was found to be a key factor. Detailed physical and chemical characterisation was carried out on thirteen pfa sources from the UK. The most important factor affecting the reactivity was found to be the particle size of pfa. The loss on ignition (LOI) and the amorphous content are also important parameters that need to be considered for the selection of pfa for use in geopolymer concrete. The partial replacement of pfa by ground granulated blast furnace slag (ggbs) was found to be beneficial in not only avoiding the need for elevated curing temperatures but also in improving compressive strengths. Microstructural characterisation with scanning electron microscope (SEM) coupled with energy dispersive X-ray spectroscopy (EDS) was performed on pfa/ggbs pastes. The reaction product of pfa and ggbs in these binary systems was calcium aluminium silicate hydrate gel (C-A-S-H) with inclusion of Na in the structure.

Injection locked oscillator lock detector

A simple circuit that is able to indicate if an injection-locked oscillator is in the locked condition by providing a ‘high’ or ‘low’ output is presented. The detector is compatible with most injection-locked oscillators as all that is required is access to the low-frequency bias circuit, with no direct access needed to the RF/microwave signals. To prove the universal nature of the lock detector it is successfully demonstrated practically for two scenarios: (i) a 1 GHz injection-locked VCO and (ii) a 60 GHz SiGe VCO MMIC.

A comparison of theoretical Mg VI emission line strengths with active-region observations from SERTS

R-matrix calculations of electron impact excitation rates in N-like Mg VI are used to derive theoretical electron-density-sensitive emission line ratios involving 2s²2p³ - 2s2p⁴ transitions in the 269-403 Å wavelength range. A comparison of these with observations of a solar active region, obtained during the 1989 flight of the Solar EUV Rocket Telescope and Spectrograph (SERTS), reveals good agreement between theory and observation for the 2s²2p^{3 4}S - 2s2p ^{4 4}p transitions at 399.28, 400.67, and 403.30 Å, and the 2s²2p^{3 2}p - 2s2p^{4 2}D lines at 387.77 and 387.97 Å. However, intensities for the other lines attributed to Mg VI in this spectrum by various authors do not match the present theoretical predictions. We argue that these discrepancies are not due to errors in the adopted atomic data, as previously suggested, but rather to observational uncertainties or mis-identifications. Some of the features previously identified as Mg VI lines in the SERTS spectrum, such as 291.36 and 293.15 Å, are judged to be noise, while others (including 349.16 Å) appear to be blended.

Effective collision strengths for election impact excitation of Cl III

Effective collision strengths for electron-impact excitation of the phosphorus-like ion Cl III are presented for all fine-structure transitions among the levels arising from the lowest 23 LS states. The collisional cross sections are computed in the multichannel close-coupling R-matrix approximation, where sophisticated configuration-interaction wave functions are used to represent the target states. The 23 LS states are formed from the basis configurations 3s²3p³, 3s3p⁴, 3s²3p²3d, and 3s²3p²4s, and correspond to 49 fine-structure levels, leading to a total possible 1176 fine-structure transitions. The effective collision strengths, obtained by averaging the electron collision strengths over a Maxwellian distribution of electron velocities, are tabulated in this paper for all 1176 transitions and for electron temperatures in the ranges T(K)=7500-25,000 and log T(K)=4.4-5.4. The former range encompasses the temperatures of particular importance for application to gaseous nebulae, while the latter range is more applicable to the study of solar and laboratory-type plasmas. © 2001 Academic Press.

Effective collision strengths for forbidden transitions among the 3s23p3 fine-structure levels of Cl III

Effective collision strengths for the 10 astrophysically important fine-structure forbidden transitions among the ⁴S^o, ²D^o and ²P^o levels in the 3s²3p³ configuration of Cl III are presented. The calculation employs the multichannel R-matrix method to compute the electron-impact excitation collision strengths in a close-coupling expansion, which incorporates the lowest 23 LS target eigenstates of Cl III. These states are formed from the 3s²3p³, 3s3p⁴, 3s²3p²3d and 3s²3p²4s configurations. The Maxwellian-averaged effective collision strengths are presented graphically for all 10 fine-structure transitions over a wide range of electron temperatures appropriate for astrophysical applications [log T(K) = 3.3 - log T(K) = 5.9]. Comparisons are made with the earlier seven-state close-coupling calculation of Butler & Zeippen, and in general excellent agreement is found in the low-temperature region where a comparison is possible [log T(K) = 3.3 - log T(K) = 4.7]. However, discrepancies of up to 30 per cent are found to occur for the forbidden transitions which involve the ⁴S^o ground state level, particularly for the lowest temperatures considered. At the higher temperatures, the present data are the only reliable results currently available.

Effective collision strengths for fine-structure forbidden transitions among the 2s22p3 levels of S x

Effective collision strengths for electron-impact excitation of the N-like ion S x are calculated in the close-coupling approximation using the multichannel R-matrix method. Specific attention is given to the 10 astrophysically important fine-structure forbidden transitions among the ⁴S^O, ²D^o and ²P^o levels in the 2s²2p³ ground configuration. The total (e^- + ion) wavefunction is expanded in terms of the 11 lowest LS eigenstates of S x, and each eigenstate is represented by extensive configuration-interaction wavefunctions. The collision strengths obtained are thermally averaged over a Maxwellian distribution of velocities, for all 10 fine-structure transitions, over the range of electron temperatures log T(K) = 4.6-6.7 (the range appropriate for astrophysical applications). The present effective collision strengths are the only results currently available for these fine-structure transition rates.

Effective collision strengths for fine-structure forbidden transitions among the 2s22p3 levels of Ne IV

Effective collision strengths for electron-impact excitation of the N-like ion NeIV are calculated in the close-coupling approximation using the multichannel R-matrix method. Specific attention is given to the 10 astrophysically important fine-structure forbidden transitions among the ⁴S^o, ²D^o and ²P^o levels in the 2s²2p³ ground-state configuration. The expansion of the total wavefunction incorporates the lowest 11 LS eigenstates of NeIV, consisting of eight n = 2 terms with configurations 2s²2p³, 2s2p⁴ and 2p⁵, together with three n = 3 states of configuration 2s²2p²3s. We present in graphical form the effective collision strengths obtained by thermally averaging the collision strengths over a Maxwellian distribution of velocities, for all 10 fine-structure transitions, over the range of electron temperatures log T(K) = 3.6 to log T(K) = 6.1 (the range appropriate for astrophysical applications). Comparisons are made with the earlier, less sophisticated close-coupling calculation of Giles, and excellent agreement is found in the limited temperature region where a comparison is possible [log T(K) = 3.7 to log 7(K) = 4.3]. At higher temperatures the present data are the only reliable results currently available.

Effective collision strengths for fine-structure forbidden transitions among the 3s 23p 3 levels of Ar IV

The multichannel R-matrix method is used to compute electron impact excitation collision strengths in Ar IV for all fine-structure transitions among the ⁴S°, ²D° and ²P° levels in the 3s ²3p ³ ground configuration. Included in the expansion of the total wavefunction are the lowest 13 LS target eigenstates of Ar iv formed from the 3s ²3p ³, 3s3p ⁴ and 3s ²3p ²3d configurations. The effective collision strengths, obtained by averaging the electron collision strengths over a Maxwellian distribution of electron velocities, are presented for all 10 fine-structure transitions over a wide range of electron temperatures of astrophysical interest (T _e = 2000-100 000 K). Comparisons are made with an earlier 7-state close-coupling calculation by Zeippen, Butler & Le Bourlot, and significant differences are found to occur for many of the forbidden transitions considered, in particular those involving the ⁴S° ground state, where discrepancies of up to a factor of 3 are found in the low-temperature region. © 1997 RAS.

Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

PLSR Models for Mechanical Strengths of Concrete Composite Materials Reinforced with Pultrusion Wastes

In this paper, we present two Partial Least Squares Regression (PLSR) models for compressive and flexural strength responses of a concrete composite material reinforced with pultrusion wastes. The main objective is to characterize this cost-effective waste management solution for glass fiber reinforced polymer (GFRP) pultrusion wastes and end-of-life products that will lead, thereby, to a more sustainable composite materials industry. The experiments took into account formulations with the incorporation of three different weight contents of GFRP waste materials into polyester based mortars, as sand aggregate and filler replacements, two waste particle size grades and the incorporation of silane adhesion promoter into the polyester resin matrix in order to improve binder aggregates interfaces. The regression models were achieved for these data and two latent variables were identified as suitable, with a 95% confidence level. This technological option, for improving the quality of GFRP filled polymer mortars, is viable thus opening a door to selective recycling of GFRP waste and its use in the production of concrete-polymer based products. However, further and complementary studies will be necessary to confirm the technical and economic viability of the process.